Master's Thesis Abbas Askar

University of Padova

Department of Physics and Astronomy

Optical Counterparts of UltraluminousX-ray Sources

Abbas Askar

Supervisor: Dr. Luca Zampieri

Local Coordinator: Prof. Luigi Secco

Master Thesis for Erasmus Mundus Joint Master Course in

Astronomy and Astrophysics

24th September 2012

University of Padova

Department of Physics and Astronomy

Optical Counterparts of UltraluminousX-ray Sources

Abbas Askar

Supervisor: Dr. Luca Zampieri

Local Coordinator: Prof. Luigi Secco

Master Thesis for Erasmus Mundus Joint Master Course in

Astronomy and Astrophysics

24th September 2012

“There is nothing deep down inside us except what we have put there ourselves.”-Richard Rorty

To my parents and my younger brother

Abstract

An interesting discovery in the field of X-ray astronomy was the existence of Ul-traluminous X-ray Sources (ULXs). The majority of these sources are posited to benon-nuclear accreting black hole binaries with luminosities exceeding the Eddingtonluminosity for a stellar mass black hole (∼ 10M�). These sources are extragalacticand have typical luminosities greater than 1039 erg s−1. A key unresolved physical issuein the understanding of ULX phenomenology is whether they are powered by normalstellar mass black holes or massive stellar black holes or Intermediate mass black holes(IMBH). In this thesis, the emission properties of Ultraluminous X-ray sources (ULXs)are modelled and their optical luminosity (including effects of X-ray irradiation) iscomputed. The evolutionary tracks for ULX binary systems with high-mass compan-ion stars and stellar through massive black holes (20 M� and 100M�) are plotted on acolour-magnitude diagram. These plots are then compared with the positions of opticalcounterparts for 13 ULXs recently studied using the HST by Tao et al. (2011). Weconstrain the mass of the black hole and companion by comparing the stellar evolution-ary tracks of ULXs with the photometric properties of their optical counterparts on thecolour-magnitude diagram for the 13 ULXs with accurate photometric data. Further-more, in this thesis, a general discussion of ULXs is provided, the details of modellingtheir optical luminosity is also given along with the results of the study.

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Acknowledgements

I would like to thank my family for all their love and support. I am particularlyindebted to my thesis supervisor, Dr. Luca Zampieri for introducing me to the topicof ULXs, and for his advice and support in preparing and carrying out this study.I would also like to thank Prof. Luigi Secco for all his support and help with theadministrative issues at the University of Padova. I am also grateful to organizers ofthe Astromundus Masters program and all the instructors and local coordinators atthe partner universities of Innsbruck, Belgrade and Padova. I am grateful for all thesupport provided by Ammar Askar in helping me with the coding and LaTeX outputof the thesis. Lastly, I am also very thankful for all the support given to me by myfriends and colleagues.

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Table of Contents

Abstract i

Acknowledgements iii

1. Introduction 11.1 Brief Introduction to ULXs . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Motivation to study ULXs . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Background & Aims of this Thesis . . . . . . . . . . . . . . . . . . . . . 51.4 Contents of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.0 ULX Phenomenology 72.1 X-ray Emission from ULXs . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Models of ULXs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Emission Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Ordinary Stellar Mass Black Holes . . . . . . . . . . . . . . . . . 142.2.3 Massive Stellar Black Holes . . . . . . . . . . . . . . . . . . . . . 152.2.4 Intermediate Mass Black Holes . . . . . . . . . . . . . . . . . . . 16

2.3 X-ray Spectra and Variability of ULXs . . . . . . . . . . . . . . . . . . . 182.4 ULX Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Optical Counterparts of ULXs . . . . . . . . . . . . . . . . . . . . . . . . 23

3.0 Modelling the Optical Emission from ULXs 263.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Computing the Optical Luminosity . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Initial Data Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 X-ray Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.3 Computing Total Luminosity . . . . . . . . . . . . . . . . . . . . 31

3.3 Binary Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.0 Observational Data for Optical Counterparts 354.1 Counterparts of 13 ULXs . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.1 Holmberg II X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.2 Holmberg IX X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.3 IC 342 X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.1.4 M81 ULS1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.1.5 M81 X-6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.1.6 M83 IXO 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.7 M101 ULX-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.1.8 NGC 1313 X-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1.9 NGC 4559 X-7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1.10 NGC 5204 X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.1.11 NGC 5408 X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1.12 NGC 6946 ULX-1 . . . . . . . . . . . . . . . . . . . . . . . . . . 524.1.13 NGC 2403 X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2 Table of Photometric Data . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.0 Results 585.1 Sources with Nebular Extinction . . . . . . . . . . . . . . . . . . . . . . 59

5.1.1 Results for a 20M� Black Hole . . . . . . . . . . . . . . . . . . . 595.1.2 Results for a 100M� Black Hole . . . . . . . . . . . . . . . . . . . 61

5.2 Sources with Galactic Extinction . . . . . . . . . . . . . . . . . . . . . . 635.2.1 Results for a 20M� Black Hole . . . . . . . . . . . . . . . . . . . 635.2.2 Results for a 100M� Black Hole . . . . . . . . . . . . . . . . . . . 65

5.3 Modified Albedo Parameter . . . . . . . . . . . . . . . . . . . . . . . . . 675.3.1 Results for M101 ULX-1 . . . . . . . . . . . . . . . . . . . . . . . 675.3.2 Results for M83 IXO 82 . . . . . . . . . . . . . . . . . . . . . . . 69

6.0 Discussion of the Results 71

7.0 Conclusions 81

Bibliography 83

1. Introduction

In this section, a brief history of X-ray astronomy is discussed and the topic of ultralu-minous X-ray sources (ULXs) is introduced. The section also provides the motivationfor the thesis and explains its’ structure and contents.

Due to advancements in observations in X-ray astronomy and astrophysics duringthe past fifty years, many interesting objects which are sources of X-rays have beendiscovered. Observations of these X-ray sources has elucidated the nature of diverseastrophysical objects that include stars, supernova remnants, compact objects, binarysystems, active galactic nuclei and galaxy clusters. Furthermore, X-ray astronomyhas been essential in our understanding of high-energy astrophysical phenomena whichoccurs under extreme physical conditions. X-rays are high energy electromagnetic ra-diation and the energies of photons in this band are between 102 eV and 105 eV. Theseenergies correspond to wavelengths between 10-0.01 nm. X-rays of energies between∼100 eV to 10 keV are categorized as soft X-rays whereas energies between ∼10 keVto 100 keV are referred to as hard X-rays.

The potential and scope of X-ray astronomy was realized in the early 1970s with thelaunch of the UHURU satellite. This was the first dedicated X-ray observatory thatmapped the X-ray sky (Giacconi et al. 1972). Since UHURU, many advanced X-rayspace telescopes with better angular and energy resolution have been launched. Promi-nent active X-ray observatory satellites are XMM-Newton observatory, Chandra X-rayObservatory (Brickhouse 2000) and Swift X-ray Telescope (XRT). X-ray observatorieshave to be space based as the atmosphere of the Earth is opaque to X-rays due tophotoelectric absorption by atoms that make up the gas in the atmosphere. Observa-tions have shown that the X-ray sky is dominated by point sources of strongly varyingbrightness on short scales (Longair 2011). X-ray continuum radiation can be producedby various radiative processes like bremsstrahlung, synchrotron radiation and inverseCompton scattering. The emission from X-ray sources can be classified into thermaland non-thermal emission. Non-thermal X-ray emission is prevalent in more unusualobjects like supernovas, accretion disk powered systems and compact objects. In thisthesis, the main objects of study are Ultraluminous X-ray sources (ULXs). As thename suggests, these are incredibly bright X-ray emitting objects. A brief introductionto ULXs is provided in the next section.

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1.1 Brief Introduction to ULXs


The high energy radiation from relativistic accreting systems heavily populates the X-ray Universe. An interesting discovery in the field of X-ray astronomy was the existenceof extragalactic point-like sources which emit at luminosities higher than 1039 erg s−1.These sources are known as Ultraluminous X-ray sources (ULXs) and the majorityof them are posited to be accreting binary systems in which the compact object is ablack hole. Theoretically, the maximum luminosity of an accreting compact object isaround the Eddington luminosity. This is the luminosity at which the outward-directedradiation force is balanced by the inward-directed gravitational force. The Eddingtonluminosity for a pure Hydrogen gas is given in equation 1

LEdd =4πcGMmp

σT≈ 1.38× 1038(

M

M�)erg s−1 (1)

where σT is the Thomson scattering cross section, M is the black hole mass and mp

is the proton mass.

The luminosities of ULXs indicate that the mass of the accreting object has to behigher than a ten solar mass black hole. Typically, ULXs have bolometric luminositiesabove the Eddington limit for a 20M� black hole which is considered to be a mass limitfor a stellar mass black hole considering standard stellar evolution. The true nature ofULXs is still unclear and it is likely that they are a composite class of several differenttypes of objects (Kolb 2010; Feng & Soria 2011).

Few ULXs (with apparent luminosities in excess of 1039 erg s−1) were first observedduring the 1980s by the Einstein satellite in nearby star forming galaxies (Long & vanSpeybroeck 1983; Feng & Soria 2011). Due to the relatively low spatial resolution of theEinstein satellite, it was hard to distinguish these sources from Galactic stellar massblack hole candidates. Furthermore, long-term monitoring of these sources was notpossible which made it difficult to differentiate between persistently luminous sourcesand transient events like young supernovae (Feng & Soria 2011). With the launch ofX-ray satellites like ROSAT and ASCA in the following decade, ULXs became moredistinguishable sources. Better resolution and spectral coverage of these X-ray satellitesshowed that some of these sources were non-nuclear and could not be supernova events.

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Furthermore, it also became clear that the apparent luminosities of these sources weremuch higher than the Eddington limit for known stellar mass black holes. Observationsfrom ROSAT also showed that the ULXs are prevalent extragalactic objects and arepresent in galaxies with different types of morphologies. The ASCA satellite had awider spectral coverage and sensitivity and the data pointed towards these sources be-ing accretion powered systems with very high temperatures (Feng & Soria 2011). Thenumber of known ULXs increased considerably with data from ASCA and ROSAT andthe first surveys of these sources were made possible. The improved data also allowedfor reliable spectral analysis of these sources and different models have been proposedand tested to explain their high luminosities.

More than two decades after the launch of Einstein, significant progress has beenmade by the latest X-ray observatories XMM-Newton and Chandra. These X-ray ob-servatories have a much higher spectral and angular resolution than any of their pre-decessors. Figure 1, shows a composite X-ray image of the spiral galaxy M74 with aULX highlighted. This image was produced from the data provided by Chandra X-rayObservatory.

Figure 1: This is a composite X-ray (red)/optical (blue & white) image of the spiral galaxy M74 madeusing data from the Chandra X-ray Observatory. An ultraluminous X-ray source (ULX) in this galaxyis shown in the box (NASA Chandra X-Ray Observatory 2005)

With the high angular resolution of current X-ray missions like Chandra, many X-ray point sources have been resolved for the first time. These studies have allowed forbetter cataloguing and testing of various models that explain the high luminosities ofULXs. It is now possible to study multiwavelegnth counterparts of ULXs. Moreover,data from new missions has also been useful in allowing intensive modelling of X-rayspectral and timing properties of ULXs. In Section 2 of the thesis, the phenomenology

3

1.2 Motivation to study ULXs

of ULXs is discussed in more detail.

1.2 Motivation to study ULXs

The main motivation to study ULXs is to explain the possible mechanism that couldresult in such high apparently isotropic luminosities. ULXs are posited to be accretingsystems and if their luminosities are higher than the Eddington limit for accretingstellar mass black holes then an alternative model is required to explain the nature ofthese sources. Considering all the observational data and theoretical possibilities, thereare three posited models for ULXs.

1. They could be an ultra-powerful X-ray binary with a stellar-mass black hole ac-creting at highly super-Eddington rates (King et al. 2001; Begelman 2002).

2. The compact object in the binary system is an intermediate mass black hole(IMBH) with a mass higher than 100M� (Colbert & Mushotzky 1999).

3. The compact object in ULXs are massive stellar black holes(∼ 30 − 80M�) thatwere formed from the evolution of massive stars in low metallicity environments(Mapelli et al. 2009; Zampieri & Roberts 2009; Belczynski et al. 2010).

It is also possible that the most luminous ULXs may be explained by a combinationof all three predominant models that account for such high luminosities (Feng & Soria2011). The details of these models are discussed in the second section of the thesis.Regardless of their exact nature, ULXs are of great interest in astrophysics because ifthe accreting black holes in some of these sources do have a mass between 102− 103M�then ULXs could be a new class of astrophysical objects, possibly unconnected with theevolution of the normal stellar population of a galaxy. ULXs could represent a new typeof black hole population which bridges the gap between stellar mass black holes andsupermassive black holes found at the centre of galaxies. The very high luminosity ofsome ULXs (∼ 1041 erg s−1) along with their cool disks point towards the IMBH model(Feng & Soria 2011). The main problem of this model is the formation mechanism ofsuch an extreme object. It has been hypothesized that these black holes could be theremnants of collapsed primordial stars in the early universe or they could have formedin the core collapse of young dense stellar clusters. Even though our understanding ofULXs has been greatly advanced by new X-ray telescopes, the current observationalX-ray data alone does not allow us to clearly distinguish whether ULXs are powered

4

1.3 Background & Aims of this Thesis

by IMBH or normal stellar mass black holes. Attempts to directly measure the mass ofa ULX compact object by studying the motion of a companion star have been unsuc-cessful. This makes it important to carry out multi-wavelength studies of ULXs to findindirect clues regarding the properties of ULX systems. It is important to be able toconstrain and determine the mass of the black hole being hosted by ULXs in order toconclusively determine whether they are being powered by an intermediate mass blackhole. This thesis aims at using available photometric data for optical counterparts ofULXs in order to constrain the mass of the black hole in ULXs. An introduction to themethod that will be employed in order to do this is given in the next subsection.

1.3 Background & Aims of this Thesis

In the previous section it was discussed that ULXs are binary systems in which thereis a donor star accreting onto a black hole. It was also established that the mainmotivation of this project is to be able to constrain the mass of the black hole usingavailable photometric data for the optical counterparts of ULXs. In two studies byPatruno & Zampieri entitled, ‘Optical emission from massive donors in ultraluminousX-ray source binary systems’ (2008) and ‘The black hole in NGC 1313 X-2: constraintson the mass from optical observations’ (2010) the mass of the black hole and donor inthe ULX was constrained by computing stellar evolutionary tracks of ULX counterpartson the colour-magnitude diagram and then comparing them to available photometricdata. This thesis uses the same method to constrain black hole masses and uses newphotometric data available for optical counterparts obtained using HST data by Taoet al. (2011).

More specifically, the aims of this project are to model the emission properties ofULXs and compute their optical luminosity (including effects of X-ray irradiation) (Pa-truno & Zampieri 2008). We then try to constrain the mass of the black hole in theULX by comparing the computed stellar evolutionary tracks of ULXs with the photo-metric properties of their optical counterparts on the colour-magnitude diagram for 13known ULXs with accurate photometric data (Tao et al. 2011). Optical counterpartrefers to the point-like optical source that is spatially associated with the ULX. Theoptical emission from the counterpart arises from the donor star or outer accretion disk,or both. This optical emission gives interesting information about the nature of thedonor star, binary evolution history, disk geometry, mode of mass transfer and can help

5

1.4 Contents of the Thesis

to constrain the black hole mass. The evolutionary tracks of binary systems with highmass companion stars and stellar to IMBH are computed using a modified version ofEggleton code for stellar evolution (Patruno & Zampieri 2008; 2010).

1.4 Contents of the Thesis

The first chapter of this thesis aims at briefly introducing the topic of UltraluminousX-ray sources and puts forth the background, motivation and the aims of this thesis.The second chapter on ULX Phenomenology goes into the theoretical details of ULXsand discusses the X-ray emission from ULXs, various models and factors that couldexplain their high luminosities, observations of ULX counterparts and the environmentaround ULXs. The third chapter entitled ‘Modelling the Emission Properties of ULXBinary Systems provides a detailed account of the method that was employed in order tomodel and compute the optical luminosities from ULX sources. It discusses the variousconditions and assumptions for our ULX model and describes how the modified Eggle-ton code is used to produce stellar evolutionary tracks. The fourth chapter summarizesthe details of the available photometric data of 13 known ULXs that were studied byTao et al. In the fifth chapter, the computational results explained in chapter 3 andthe observational data from chapter 4 are combined in order to constrain the black holemass for the 13 ULXs. These results are summarized and discussed in chapter 6. Asummary and conclusions of the project are given in the final chapter of the thesis.

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2.0 ULX PHENOMENOLOGY

2.0 ULX Phenomenology

In chapter 1, the topic of ultraluminous X-ray sources (ULXs) was briefly introduced.In this chapter the details of the X-ray emission from ULXs will be discussed and theirmain properties will be described. The models that are used to account for the high X-ray luminosities of these sources are also explained. The X-ray spectra and variabilityof ULXs are also discussed along with information related to the optical counterpartsand environments of these sources.

2.1 X-ray Emission from ULXs

In the first chapter, ULXs were introduced as being very bright X-ray sources thathave apparent bolometric luminosities higher than the Eddington limit for stellar massblack holes. The Eddington limit can be applied to any accreting system to limit themaximum theoretical luminosity that it could have. The Eddington limit is calculatedby setting the gravitational force equal to the radiative force acting on an atom. Inequation 1, the Eddington luminosity for fully ionized hydrogen was defined. If themass of the black hole in the accreting system is 10M� then the Eddington luminosityof the system is 1.38× 1039ergs−1.

Generally, ULXs are defined as non-nuclear, point like objects which have at leastonce been observed at an apparent isotropic luminosity which is higher than Lx > 1039

erg s−1 (maximum luminosity of a stellar mass Galactic black hole) in the 0.3-10 KeVband (Feng & Soria 2011). Some authors define the luminosity for ULXs to be higherthan 3 × 1039 erg s−1, which is the Eddington limit of the most massive stellar blackholes (20M�) with standard metallicity (Belczynski et al. 2010; Feng & Soria 2011;Kaaret 2008). This definition excludes a large number of ULXs that have faint lu-minosities (less than 3 × 1039 erg s−1) by designating them to be normal black holebinaries. However, as Feng & Soria (2011) point out, an empirical definition for ULXs

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2.1 X-ray Emission from ULXs 2.0 ULX PHENOMENOLOGY

is ambiguous as it may include objects such as X-ray pulsars, supernovae and supernovaremnants. In order to avoid this ambiguity, ULXs can more specifically be defined as“non-nuclear accreting black holes with peak luminosities inferred assuming isotropicemission above the Eddington limit of a normal stellar mass black hole” (Feng & So-ria 2011). Using this definition, ULXs are limited to being binary systems in whicha compact object is accreting from a companion star. For the purpose of this study,we use a definition of ULX given by Patruno & Zampieri (2008). ULX is defined byPatruno & Zampieri (2008) as a source which has a bolometric luminosity greater thanthe Eddington limit for a stellar mass black hole of 20M� and is less luminous than1041ergs−1. This definition rules out Galactic X-ray binaries radiating isotropically asULXs. The upper luminosity limit for observed ULX is 1042 erg s−1 (correspondingto the lower luminosities observed for active galactic nuclei which are powered by asuper massive black hole). The brightest ULXs typically have a luminosity of 1041 ergs−1 (Sutton et al. 2012). One source can reach a maximum luminosity of 1042 erg s−1

and is the best IMBH candidate to date (Farrell et al. 2009). A composite X-ray andoptical image (from Chandra and HST ) of the ULX in M83 is shown in the right panelof Figure 2. The light curve of M101 ULX-1 on 2 different dates in separate energybands is shown in Figure 3 (Mukai et al. 2005).

Figure 2: On the left panel is an optical image of M83 (or NGC 5236) from the Very Large Telescope(VLT ) in Chile. On the right panel is a composite image (showing X-ray data from Chandra in pinkand optical data from the HST in blue and yellow) of a zoomed portion of this barred spiral galaxy.The prominent X-ray source in the marked box near the bottom of the composite image is a highlyvariable ULX (NASA Chandra X-Ray Observatory 2012).

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2.1 X-ray Emission from ULXs 2.0 ULX PHENOMENOLOGY

Figure 3: Chandra ACIS-S light curve of M101 ULX-1 on 2004 December 30 (in 648 s bins) and on2005 January 1 (256 s bins), in two energy bins (taken from Mukai et al. 2005).

Observations of ULXs reveal that they are very diverse sources, few ULXs exhibitstrong X-ray variability over time scales of a few minutes. While many other ULXs showrandom variations over time scales which range from weeks, days to years (Zampieriet al. 2004; Kaaret & Feng 2009; Kong et al. 2010; Grise et al. 2010). The observedvariability of ULXs confirms their compact nature. Moreover, variability informationis required to define a ULX, as objects which are not black hole binaries may appear tobe ULXs if timing and multiwavelength properties of those sources are not available.Young supernovae events can have X-ray luminosities in the order of 1040 erg s−1 (Feng& Soria 2011). Mostly, distinguishing between such events and ULXs requires one toknow the variability of such sources (Kaaret 2008). However, in certain cases this isnot enough and a detailed study of the X-ray spectra is required to elucidate the truenature of these sources.ULXs exhibit a composite X-ray spectrum which is similar butnot equal to that of Galactic X-ray binaries (XRBs) (Foschini et al. 2002a; Zampieri& Roberts 2009). The X-ray spectum of a bright ULXs shows a typical rollover above3-5 keV and is described in terms of a two component model, a low temperature diskand an optically thick corona at high energies (Gladstone et al. 2009).

Another problem with observing ULXs is that background active galactic nuclei(AGN) that are located behind a galaxy could be misidentified as ULXs in that galaxy(Feng & Soria 2011). The cosmological location of such souces may be verified by

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2.2 Models of ULXs 2.0 ULX PHENOMENOLOGY

measuring the redshift from optical lines (Clark et al. 2005), this can allow one todetermine whether the source is in the galaxy being studied or in the background. Thenumber of background objects that contaminate ULX sources are higher in massiveelliptical galaxies (Feng & Soria 2011). Many ULXs in spiral or starburst galaxies arespatially associated with young star clusters, emission nebulae and star forming regions(Zampieri et al. 2004; Grise et al. 2008, 2011). Such sources are most likely to belocated within the galaxy being studied rather than the background or the foreground(Feng & Soria 2011). The environments of ULXs are discussed in a separate sectionin this chapter. Few models and scenarios have been developed to explain the highluminosities of ULXs. These emission models and more details of the X-ray emissionfrom ULXs are discussed in the next subsection of this chapter.

2.2 Models of ULXs

It has been discussed that ULXs have luminosities higher than the Eddington lu-minosity for typical stellar mass black holes. This implies that they are sources whichare different from typical Galactic X-ray binaries. In this section, the different emissionscenarios for ULXs are discussed. In the first subsection of this section, the general emis-sion scenarios that could possibly explain the high luminosities of ULXs are discussed.In the subsequent subsections, different types of the black hole masses that could powerthem will be discussed individually. These black hole types are distinguished by theirmass ranges and they are

1. Ordinary Stellar Mass Black Hole (M . 20M�)

2. Massive Stellar Black Hole (20M� . M . 100M�)

3. Intermediate Mass Black Holes (M ∼ 102 − 104M�)

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2.2.1 Emission Scenarios

Fundamentally, there are three possible ways that could explain the apparent ac-cretion luminosities being higher than 1039ergs−1 for non-nuclear sources like ULXs.Using standard accretion physics propounded by the Shakura & Sunyaev model (1973),the most straightforward way to increase the luminosity of an accreting system is toincrease the black hole mass (the Eddington luminosity is directly proportional to themass of the black hole). This would mean that the black hole within a ULX could bemore massive than an ordinary stellar mass black hole. The second possibility whichcould account for the high luminosities of ULXs is that such sources have beamed emis-sion. This beamed emission could either be a geometric or relativistic phenomenonwhich could reproduce the observed ULX luminosities. The third possibility whichcould explain such high X-ray luminosities is that the mass accretion rate onto theblack hole is so high that the accretion disk does not have a standard structure and theemission from the binary system is able to exceed the Eddington luminosity (Feng &Soria 2011). As it has been pointed out earlier, it is possible that the brightest ULXsare powered by a combination of the three possibilities.

Assuming standard accretion physics and solar abundances for donor stars, the ap-parent luminosity of an accreting black hole is given by

L ≈ 1.3× 1038

bm(

MBH

M�) erg s−1 m . 1 (2)

L ≈ 1.3× 1038

b(1 +

3

5ln m)(

MBH

M�) erg s−1 1 . m . 100 (3)

(Shakura & Sunyaev 1973; Poutanen et al. 2007; Feng & Soria 2011) “where b is thebeaming factor (has values between 0 and 1), and m is the dimensionless mass accre-tion rate from the donor star at large radii, normalized to the Eddington accretion rate

(m ≡ 0.1 MMEdd

)” (Feng & Soria 2011)

Using equations 2 and 3, we can now discuss the the details of the different possibleemission scenarios involving beaming, super-Eddington accretion or a combination ofboth these scenarios. These different emission scenarios have been discussed in detail

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by Feng & Soria (2011).

Strong Beaming

It can be seen from equations 2 and 3 that the luminosity is inversely proportional tothe beaming factor ‘b’. If 1

b� 1, then the value of luminosity will increase significantly

and this will result in the strong beaming scenario. There are many known extragalac-tic accreting black hole systems that exhibit strong beamed emission (Feng & Soria2011). Examples of these sources are blazars and BL Lac objects (Urry & Shafer 1984).There is also one source known as ‘SS 433’, which is a Galactic binary that is knownto have beamed anisotropic emission and semi-relativistic jets (Feng & Soria 2011). Itwas initially postulated that a sample of ULXs catalogued using ROSAT were actuallyblazars or BL Lac objects or objects similar to ’SS 433’ that were being observed faceon (Fabrika & Mescheryakov 2001, Kording et al. 2002, Begelman et al. 2006; Feng& Soria 2011). The main issue with the relativistic beaming scenario is that there isa lack of observation of a large number of lower-luminosity beamed sources which thisemission scenario predicts (the model predicts ≈ 30 sources with apparent luminosity∼ 1039ergs−1 for every ULX at L = 1× 1040ergs−1) (Davis & Mushotzky 2004; Feng &Soria 2011). However, much fewer sources with luminosities higher than ∼ 1039ergs−1)are observed (≈ 5 − 10 sources for every ULX at L = 1040ergs−1 (Feng & Soria 2011;Swartz et al. 2004; Grimm et al. 2003). These observations are consistent with thehigher end of the luminosity function for high mass X-ray binaries (HMXBs) (Feng &Soria 2011). The presence of photoionized bubbles around many ULXs like ‘HolmbergII X-1’ (Pakull & Mirioni 2002; Kaaret et al. 2004) and NGC5408 X-1 (Kaaret & Cor-bel 2009) require at least quasi-isotropic X-ray emission of luminosities ≈ 1040ergs−1.Moreover, the vast majority of ULXs do not exhibit fast X-ray variability and haveno radio counterparts that would be expected for strong relativistic beaming effects(Feng & Soria 2011). It is because of these reasons that the strong relativistic beamingemission scenario is not regarded as a plausible general model which could explain thehigh luminosities of ULXs.

Mild Beaming with Super-Eddington Accretion

Another possible emission scenario involves a combination of a very high accretionrate and mild beaming. In this scenario the value of 1

bis . 10 in equation 3 and the

value of the dimensionless accretion m is� 1. If super-Eddington accretion does occurthan radiative outflows are driven out from the inner part of the accretion disk (in thepart where the disk becomes geometrically thick) (Shakura & Sunyaev 1973; Poutanenet al. 2007; King 2009; Feng & Soria 2011). In an emission scenario suggested in Kinget al. (2001) and King (2009), the radiative wind produced as a result of the highaccretion could produce a funnel wall which would scatter and beam the emission in

12


a direction perpendicular to the the axis of the disk plane (Feng & Soria 2011). Thisemission scenario combines both beaming and high mass accretion rates (m ≈ 10− 30)for almost all ULXs up to luminosities ≈ 1041ergs−1 with ordinary stellar mass blackholes (M . 20M�).

Results from recent numerical “radiation-magneto-hydrodynamical simulations (Ohsugaet al. 2009; Takeuchi et al. 2010; Mineshige & Ohsuga 2011) show that even a moder-ately super-critical mass supply can produce total luminosities [in excess of ≈ 1.7LEddand] apparent luminosities of ≈ 22LEdd for face on observers [due to mild beamingeffects] (Mineshige & Ohsuga 2011)” (Feng & Soria 2011).

In an alternative emission scenario, there is a possibility that only super-Eddingtonaccretion (without mild beaming) could result in the high apparent luminosities ob-served from ULXs. Due to the development of photon bubble instabilities in radiationpressure dominated accretion discs, strong density inhomogeneities arise (Begelman2002). The radiation coming from these disk regions would escape at a much fasterrate (≈ 10 times above the typical Eddington limit for stellar mass black holes) (Feng& Soria 2011).

Quasi-isotropic Eddington Luminosity

Some emission models and simulations propose that the classical Eddington limit isnot a constraint on the luminosity of a ULX. However, the Eddington limit has empiri-cally worked to constrain the luminosities of many compact objects like Galactic blackholes and neutron stars. Feng & Soria (2011) point out that the luminosities of over60,000 quasars (at redshift 0.2 < z < 4) in the Sloan Digitized Sky Survey (SDSS) arestrongly limited by the Eddington luminosity for all types of black hole masses. Only avery small fraction of these quasars have luminosities between 1 to 3 Ledd (Steinhardt& Elvis 2010). In a quasi-isotropic emission model, the luminosities of the ULXs areassumed not to exceed the Eddington luminosity (LEdd ≈ 1). The radiative anisotropyof a ULX would only be a factor of & 1 (Feng & Soria 2011). In the absence of anycollimation, the beaming factor for a standard accretion disk will be 1

b= 2) (Feng &

Soria 2011). Now, in order for such a model to produce luminosities in the same ordersof magnitude as ULXs, the mass of the accreting black hole will have to increase. For aULX with a luminosity of 1040ergs−1, the accreting black hole in the system must havea mass of M� . 100 (Feng & Soria 2011). This mass is the theoretical upper limit forthe single core collapse of the most massive stars in our universe. This number is alsothe lower limit for the population of black holes proposed to be intermediate mass blackholes (IMBHs). In such an emission scenario, ULXs more luminous than 1040ergs−1

must be powered by an IMBH. For instance, the ULX catalogued as ‘HLX-1’ has apeak bolometric luminosity of ≈ 1042ergs−1 (Farrell et al. 2009; Davis et al. 2011). Ifthe luminosity of this source is Eddington limited and quasi-isotropic, then the inferred

13


mass of the black hole is at least 104M� (Feng & Soria 2011).

Quasi-isotropic sub-Eddington Luminosity

As the previously described emission model, it could also be true that the ULX sys-tem is actually emitting at sub-Eddington luminosities. The emission could be nearlyisotropic or disk beamed. In this straightforward emission scenario, the mass of theblack hole powering the ULX would simply have to be an IMBH, approximately in themass range of ∼ 102 − 104M�. In such an emission scenario, similar X-ray spectralproperties and state transitions will be seen from both ULXs and Galactic black holebinaries ((Feng & Soria 2011).

The emission scenarios described above require three different mass ranges of blackholes that were mentioned in the beginning of section 2.2. In the next subsections, eachof these mass ranges for black holes and the emission scenario they could support willbe discussed.

2.2.2 Ordinary Stellar Mass Black Holes

Black holes are defined to be regions of space-time from which even light cannotescape. Our understanding of black holes arise from Einstein’s general theory of rela-tivity. The main formation mechanism for black holes is provided by our understandingof stellar evolution. Gravitational core collapse of aging stars results in the formation ofcompact objects. This occurs when the stars burn out and have no radiation pressurethat could balance the gravitational force pulling the star inwards. Ordinary stellarmass black holes (M . 20M�) are formed as a result of the gravitational collapse ofheavy stars. In the context of ULXs, ordinary stellar mass black holes would requirea strong beaming or some super-Eddington accretion emission scenario to be able topower ULXs. There is direct observational evidence for stellar mass black holes in ourlocal universe and more than 20 black holes with M ≈ 5− 10M� have been identifiedin high mass X-ray binary systems (McClintock & Remillard 2006; Feng & Soria 2011).The largest observed Galactic stellar mass black holes have masses around 14.0±4.4M�(in GRS 1915+105 (Harlaftis & Greiner 2004)) and 14.8± 1M� (in Cygnus X-1 (Oroszet al. 2011)). Similar stellar mass black holes have been observed in HMXBs in othergalaxies. The X-ray binary in M33-X 7 hosts a stellar mass black hole estimated to be≈ 15.7M� (Orosz et al. 2007). As a constrain for this mass class of black holes, anupper limit of ≈ 20M� is used. An accreting binary system in which a black hole has

14


been observed in the starburst galaxy IC 10 could have a mass ≈ 20−40M� (Prestwichet al. 2007; Silverman & Filippenko 2008). This high uncertainty in mass calculationis due to the unknown mass of the companian star and inclination angle of the binaryplane (Feng & Soria 2011).

For ordinary stellar mass black holes, the formation mechanism is explained by stellarevolution model and their existence and formation are fairly well understood. However,as it was discussed in the previous section, in order for a ULX to be powered by ablack hole of mass ≈ 20Modot then the emission scenarios are fairly constrained. Thestrong beaming emission scenario was discussed and shown to be a very unlikely emis-sion scenario that could explain ULXs. Furthermore, the presence of super-Eddingtonaccretion would have to be shown in ordinary stellar mass black hole binaries for themto be a plausible model that could explain the high ULX luminosities.

2.2.3 Massive Stellar Black Holes

Massive stellar black holes have a mass range between ≈ 20M�to100M�. It wasbriefly discussed that the formation of a stellar mass black hole requires a massive starto go through its’ evolution and if the resulting compact remnant has a mass exceed-ing the ‘Tolman-OppenheimerVolkoff limit’ (≈ 2− 3M�) then an ordinary stellar massblack hole can form. The mass of this compact remnant depends on the initial masswhich the progenitor of the black hole has, and is also affected by the amount of massthat is lost by the star through stellar winds during its’ life (Feng & Soria 2011). Theamount of radiatively driven stellar winds from massive stars depend significantly ontheir metallicity (Vink et al. 2011). The maximum mass of a stellar black hole is thusdependent on the metallicity of the progenitor star (the mass of the remnant core ishigher if the metallicity of the star is lower). Belczynski et al. (2010) determined themass limits for the formation of black holes at different metallicities. They posit thatthe collapse of a single star with solar metallicity can form a black hole of ≈ 15M�,≈ 30M� for a star with 0.3 times the metallicity of the sun (Feng & Soria 2011). Astellar black hole could possibly have a mass of ≈ 80M� if metallicity is as low as 0.01times the metallicity of the sun (Belczynski et al. 2010; Feng & Soria 2011). Otherstudies which constrain black hole mass from metallicity also give a similar mass limit of≈ 70M� for low metallicity stars (Feng & Soria 2011). This relationship between stellarblack holes and metallicity is consistent with the results of dynamical mass estimates ofblack holes in Galactic X-ray binaries and estimated metallicities of their progenitors.Present stellar evolutionary model give a black hole remnant distribution that peaks at

15


≈ 10M�, but theoretically the black hole could have a mass as high as ≈ 100M� (Feng& Soria 2011). The scenario for the formation of ULXs in low metallicity environmentshas been explored quantitatively in detail by Mapelli et al. (2009, 2010) and Zampieri& Roberts (2009).

The distinction between ordinary stellar mass black holes and massive stellar blackholes is made here because the formation mechanism for the latter is much more uniqueand requires extreme formation conditions. Furthermore, another difference in the for-mation mechanism of ordinary stellar mass black holes and massive stellar black holesis that the former are formed through a supernova explosion followed by rapid fallbackof the remnant core. Whereas massive stellar black holes are posited to form throughdirect core collapse without an explosion (Fryer 1999). The reason for this formationmechanism for massive stellar black holes is attributed to the lower gravitational energyreleased during core collapse for massive objects. This low gravitational energy is notstrong enough to expel the stellar envelope outwards and cause a supernova explosion(Feng & Soria 2011). This is believed to be true for massive low metallicity stars. Thethreshold mass for direct collapse without a supernova type even for low metallicitystars is estimated to be 40M� (Fryer 1999; Heger et al. 2003). For massive stellarblack holes the emission scenarios that could account for ULXs with luminosities lowerthan 1040 ergs s−1 is quasi-isotropic Eddington luminosity. Mild beaming and super-Eddington accretion scenario could also be attributed to ULXs with higher luminositiesand a massive stellar black hole.

2.2.4 Intermediate Mass Black Holes

In the known universe, observational evidence has proven the existence of both stel-lar mass black holes and supermassive black holes (which are believed to be located atthe center of most galaxies. These supermassive black holes have masses in the order of105 − 109M�. No conclusive evidence has been found for black holes that have a massin the range of 102−104M�. This mass range for black hole classifies what are believedto be intermediate mass black holes (IMBHs). There are no certain explanations forthe formation of IMBHs. It is very unlikely that they arise from the core collapse ofvery massive population I or II stars. Even though there are observed stars with mass≈ 200M�, the formation of an IMBH would be very difficult from the collapse of thesestars as Helium cores more massive than ≈ 70M� undergo a pair instability explosionwhich destroys the entire star without the formation of any black hole(Bond et al. 1984;Heger & Woosley 2002). There is a possibility of a black hole forming in the case that

16


the remnant Helium core has a mass of ≈ 130M�, this would require an initial stellarmass of at least 260M� and zero metallicity (Heger & Woosley 2002; Feng & Soria 2011).

There are three plausible formation mechanisms for IMBHs. The first formationmechanism posits that the progenitors of IMBHs are metal-free population III starsthat formed in the early universe. These stars are thought to be very massive starsthat could reach masses of up to a few hundred solar masses (above the pair instabilitylimit). These population III stars could have collapsed to form IMBH which couldpower ULXs (Madau & Rees 2001). It is also possible that IMBH are formed throughcollisions and mergers of massiver stars in dense young star clusters. Dynamical frictioncould lead to mergers of stars on times scales of less than a million years which couldresult in the formation of a very massive star which could then go on to collapse into anIMBH (Portegies Zwart & McMillan 2002; Gurkan et al. 2004; Portegies Zwart et al.2004; Vanbeveren et al. 2009). It has been postulated using dynamical mass estimatesthat few global clusters could contain an IMBH (M ≈ 104M�)(Gebhardt et al. 2005).It has also been suggested that stellar mass black holes within globular clusters couldgrow 100 times their mass through accretion of gases lost by the stars that reach the redgiant phase in these clusters (Anderson & van der Marel 2010; Vesperini et al. 2010).For some extreme ULXs, it has been hypothesized that it could be possible for IMBH todrift in to the Halo of major galaxies following tidal stripping of merging dwarf satellitethat contain a nuclear black hole (King & Dehnen 2005; Bellovary et al. 2010). Thehigher the mass of the black hole powering the ULX will be, the more the luminositywill be (as the Eddington limit would be higher for such an accreting source).Feng & Soria 2011 summarize these three classifications of non-nuclear black holes thatcould power ULXs in a table which has been reproduced below.

Table 1: Table reproduced from Feng & Soria (2011) showing the different mass classifications forblack holes that could power ULXs, their progenitors and possible emission scenarios

Type of Black Hole Mass Progenitor Emission Scenario

Ordinary Stellar Mass BH . 20M� Regular starsBeaming and/orsuper-Eddingtonaccretion

Ordinary Stellar Mass BH ∼ 20M�-100M� Low metallicity starsQuasi-isotropicemission atEddington luminosities

Intermediate Mass BH ∼ 102 − 104M�

pop III starsCluster coreStripped core

Quasi-isotropicemission atsub-Eddington luminosities

17

2.3 X-ray Spectra and Variability of ULXs 2.0 ULX PHENOMENOLOGY

2.3 X-ray spectra and Variability of ULXs

ULX Spectra

X-ray spectral and variability properties of accreting black holes have been studiedin quite a detail. This subsection aims at briefly highlighting only the essential featuresof the X-ray spectra and variability of ULXs. Observations have shown that one of themain features of the spectra of an accreting black hole is a power law. In a power-lawspectral energy distribution the energy flux emitted by the source per unit area and perunit time is F (E) ∝ E−Γ−1, where Γ is referred to as the photon index and Gamma-1as the spectral index (α). This power law feature of the spectra is primarily attributedto the radiative processes such as synchrotron emission from a jet or inverse Comptonscattering of photons from the inner accretion disk. In the first scenario, synchrotronemission is caused by relativistic electrons spiralling in a magnetic field. In the inverseCompton scattering scenario, the power law continuum is produced in the hot coronalgas of the accretion disk. The photons from the accretion disk are scattered to higherenergies after interactions with energetic relativistic electrons in the surrounding corona.

The spectra of an accreting black hole is not limited to the power law feature. X-rayspectra may exhibit other features (like soft excess, emission lines, reflection compo-nent, absorption lines ). The X-ray spectral and timing properties of ULXs (in the0.3-10 keV band) have been widely studied and modelled as a result of the data madeavailable by XMM-Newton and Chandra telescopes (Feng & Soria 2011). In the caseof ULXs, good quality energy spectra are split into two types. The first type of spectraare consistent with a simple power law while the second type of spectra exhibit morecomplex features. In the second type of spectra, “mainly a mild broad curvature overthe whole band [is seen], with a break or steepening above ∼ 2 keV, or soft excessbelow ∼ 2 keV” (Feng & Soria 2011). Low counting statistics spectra of many ULXscan reasonably well be fitted with a broad power-low model, in which the photon indexΓ has an average value of ≈ 1.8 − 2 (Swartz et al. 2004; Winter et al. 2006; Bergheaet al. 2008). The value of the photon index varies depending on whether the sourceis hard or soft. Some sources with a hard spectrum (lower values of photon index)also show strong flux variability. This behavior is also observed in hard state GalacticX-ray binaries (Feng & Soria 2011). Presence of compact continuous radio jets are alsoexpected from hard state sources. For soft sources (with higher values of Γ) the ULX

18


spectra can be classified as being like the steep power law state of Galactic black holebinaries emitting near Eddington luminosities (Feng & Kaaret 2005; Winter et al. 2006;Soria 2007). An example of the X-ray spectrum of the ULX source NGC 1313 X-1 isshown in Figure 4.

Figure 4: The left panel shows an XMM EPIC-pn spectrum of NGC 1313 X-1 in which absorbed MCD(multicolour disk model -dotted line)+power law (dashed line) model with three gaussian components(thin solid lines) at energies 0.59, 1.8 and 4.7 keV (from Turolla et al. 2006). The right panel shows theunfolded MOS-1 and MOS-2 spectra of NGC 1313 X-2. The total spectrum, cool (kT ' 160 eV) diskcomponent, and power-law components are shown in black, blue, and red, respectively (from Miller etal. 2003).

As mentioned above, a characteristic feature of high counting statistics spectra ofseveral ULXs is the presence of a soft excess. The excess residuals at lower energies(< 2 keV) are observed when power law fits are made for higher energies (Feng & So-ria 2011). To model these fits, an additional disk component (e.g. the diskbb model;Mitsuda et al. 1984) is needed which corresponds to disk temperatures between 0.1-0.4keV (Feng & Soria 2011). This additional component is cooler and more luminous forULXs than it is for Galactic black hole binaries. It has been suggested that the lowtemperature and high luminosity of the disk can be explained by accretion onto anIMBH. However, there are alternative explanations which suggest that the soft excesscould arise from massive outflows as a result of supercritical accretion or that the ex-cess may originate from the outer accretion disk, as the inner part may be obscuredby outflows or a scattering corona (Feng & Soria 2011). An image of a typical ULXspectra taken from Feng & Soria (2011) showing the features of soft excess and hardcurvature is reproduced in Figure 5.

19


Figure 5: The typical ULX spectra shape is given in the figure above in the colour grey. The soft excessfeature can be seen between 0.1 and 2 keV and the hard component is seen from 2 keV to 10 keV.In the left part of the figure, the soft excess is shown to be modelled by a cool diskbb (cool thermalcomponent), over the power-law extension of the hard component. The hard curvature is adequatelyfit using a slim disk model (p-free) or a warm, thick Comptonization model (comptt) (taken from Feng& Soria 2011).

Another feature of high quality ULX spectra is the high energy steepening. This cur-vature effect can generally be fitted by a Comptonization model (as comptt; Titarchuck1994) with low energy electrons and high optical depth (Feng & Soria 2011). The reasonfor this feature varies from source to source and has been attributed to hot standarddisk, thermal slim disk and p-free model, warm disk corona, bulk motion Comptoniza-ton. Details of these various varieties of scenarios that can explain ULX spectra can beread in Feng & Soria (2011).

X-ray Variability

The power spectrum of Galactic black hole binaries have been split into broad andnarrow components (such as quasi-periodic oscillations, QPOs) based on their promi-nent observational features. The study of these temporary features of power spectrum

20


have been useful in determining various accretion states and properties of the blackhole (Feng & Soria 2011). Observations of ULXs that have similar luminosities andenergy spectra can be split into two groups based on their X-ray variability (Heil etal. 2009). One group of these sources exhibit very strong variability while the secondgroup shows weak variability. For Galactic black hole binaries, low variability is positedto be caused by thermal emission with no jets while high variability is associated withthe corona and steady jets (Belloni 2010; Feng & Soria 2011 ).

One way to find the mass of the black hole in a ULX is by studying its variability.Correlations which are believed to scale with the mass of the black hole have been madebetween spectral parameters and frequency. (Feng & Soria 2011). Correlations havebeen made between the frequency of QPOs in the power density spectrum and the diskflux in Galactic black hole binaries. However, there is still difficulty in knowing how theblack hole mass scales with regards to QPOs (Feng & Soria 2011). Broad continuumfeatures in the power density spectrum are thought to provide a better determinationof the black hole mass in ULXs. The correlation between broad continuum and blackhole mass has been well studied for a wide range of black hole masses and frequencies.The results of most of these scaling relationships between characteristic frequenciesand black hole masses indicate that ULXs could host black holes with masses between102−104M� (Feng & Soria 2011). However, there are many issues with regards to thesescaling relations as we do not know whether variability features of ULXs are exactlythe same as Galactic black hole binaries. Moreover, the scaling relationship used forAGNs and Galactic black hole binaries do not consider high accretion rates close toEddington luminosity. Furthermore, the low signal to noise ratio makes it difficult todetect QPOs with high frequencies which could provide direct scaling with black holemass (Feng & Soria 2011).

21

2.4 ULX Environments 2.0 ULX PHENOMENOLOGY

2.4 ULX Environments

In this subsection the galactic and immediate environments of ULXs are briefly dis-cussed. In the context of the study carried out in this project, ULXs are consideredto be binary systems in which a black hole is accreting directly from donor stars witha mass of at least 8 M�. Indeed the properties of the majority of the ULX opticalcounterparts are consistent with massive donors (e.g. Liu et al. 2007; Mucciarelli etal. 2007; Grise et al. 2008, 2011). This makes ULXs comparable to HMXB(high massX-ray binaries) which are predominantly located in spiral and irregular galaxies (Feng& Soria 2011). ULX populations are found in both spiral/irregular galaxies and ellip-tical galaxies. However, very few genuine ULXs are believed to be found in ellipticalgalaxies. The vast majority has rather low luminosity(apparent Lx . 2 × 1039ergs−1

(Swartz et al. 2004; Feng & Soria 2011) and most are thought to be background orforeground noise. More luminous ULXs are located in spiral and irregular galaxies andparticularly in star-forming galaxies. Both early and late type spirals (on the Hubblescale)host ULXs. However, it is difficult to assume what sort of donor star could be ina ULX simply by knowing in what type of galaxy the ULX is being hosted (for a spiralgalaxy, the donor is not necessarily an OB star)(Feng & Soria 2011). Moreover, thecharacteristic age of the neighbouring stellar populations of some ULXs were found tobe greater than 10 million years (e.g. Grise et al. 2008, 2011)).

Studies trying to determine whether ULXs are hosted within stellar clusters havenot been able to find a significant spatial association between ULXs and stellar clusters(Feng & Soria 2011). ULXs are generally found close to star forming regions and toyoung star clusters, but often displaced from them, by a distance ≈ 0.11 kpc (e.g. Zezaset al. 2002; Swartz, Tennant & Soria 2009; Berghea 2009). This undermines the ULXformation scenario involving direct core collapse in stellar clusters. A large number ofULXs have been shown to be surrounded by optical emission nebulae. The nebulaeappear to be young and are most likely to have been ionized by the X-ray emissionfrom ULXs or through shock ionization. This distinction between these two regimes ofionization is difficult to make and requires detailed spectral analysis. In figure 6, anexample of the optical images of the nebulae surrounding two ULX are shown. Theenvironment of ULXs can play a crucial role in avoiding the contamination problem ofULX observations that was briefly mentioned earlier. ULX environments are furtherdiscussed in the next subsection.

22

2.5 Optical Counterparts of ULXs 2.0 ULX PHENOMENOLOGY

Figure 6: The image on the left shows the continuum subtracted Hα image of the nebula LH9/10around the ULX M81 X-9 (Holmberg IX X-1) and the image on the right is a 600 pc diameter Hαbubble around the ULX NGC 1313 X-2. This is a shock excited nebula which is expanding at 80 kms−1 (taken from Pakull & Mirioni 2003).

2.5 Optical Counterparts of ULXs

Optical counterparts of ULXs refer to the optical sources that are spatially asso-ciated with a ULX. It is expected that the optical emission from a ULX counterpartcould come from the donor star, the outer accretion disk or could be combined emis-sion from both (Feng & Soria 2011). Observations of optical counterparts have beenuseful in some cases for resolving the contamination problem from background AGNs.The study of optical counterparts with regards to ULXs is important in the context ofthis work. Studying counterparts can give information regarding the binary evolution,nature of the donor star and mode of mass transfer. In this study, photometric data ofthe optical counterparts is used to constrain the black hole mass. The identification ofoptical counterparts has been made possible by the positional accuracy of the Chandratelescope and the Hubble Space Telescope (HST ). Spatial resolution is very importantwhen determining optical counterparts for ULXs as they are extragalactic sources andit would be difficult to pinpoint the counterparts as there maybe many stars associatedwith the ULX due to errors in the resolution.

Studies have been able to model the optical emission properties of ULXs. By cal-culating and modelling the X-ray irradiaton expected from the disk (Copperwheat et

23


al. 2005, 2007) one can account for both the contribution of the donor star and theouter accretion disk. However, identification of a unique optical counterpart among adensely populated star forming region is the main challenge. In this study, photometricdata for optical counterparts of 13 ULXs is taken from a study by Tao et al. (2011).Identification of these counterparts is made by aligning Chandra and HST images (thishelps to reduce the error in the source position from Chandra (Tao et al 2011). Anexample of an HST image for the ULX NGC 5408 X-1 is given in figure 7.

Figure 7: This is a HST/WFC3 composite image (blue - F225W, green -F502N, red - F845M) of thefield surrounding ULX NGC 5408 X-1. The yellow circle represents the overplotted radio position fromthe VLA and the red dotted circle are the ATCA positions. Inside the whitebox are the nearby stellarassociations (Grise et al. 2012).

In figure 8, the HST images around 3 ULXs that were studied by Tao et al. (2011)are shown.

Figure 8: HST images around 3 ULXs: NGC 4559 X-7, M83 IXO 82 and NGC 2403 X-1 . The originalX-ray position of the ULX is indicated by the solid circle (with a radius of 0.6” corresponding to theabsolute error of Chandra). The arrow points towards north and has a length of 1”. The dashedcircle represents the X-ray position corrected after alignment. For NGC 2403 X-1, there are 2 Chandraobservations and the dashed circle is the mean position of those observations (taken from Tao et al.2011).

24


In chapter 4, the data of optical counterparts for ULXs taken from Tao et al. (2011)will be discussed in detail. Optical counterparts are central to this study becauseby computing stellar evolutionary tracks for different donor masses it is possible toconstrain the properties of the donor star and the black hole in the ULX. In the nextchapter, a detailed account is given as to how the optical luminosity of a ULX binarysystem is modelled in this study.

25

3.0 MODELLING THE OPTICAL EMISSION FROM ULXS

3.0 Modelling the Optical Emission from

ULXs

The main aim of this research thesis is to be able to compute stellar evolutionary tracksfor massive stars (8M� up to 50M�) in a binary system with an accreting black hole(with mass of 20M� and 100M�. These stellar evolutionary tracks involve computingthe optical luminosity that will be emitted by the donor star and accretion disk asthe star evolves. In this chapter, a detailed account is provided of the model that isassumed for the binary system and the parameters that are needed to be taken intoaccount are discussed. Moreover, the computation of the optical luminosity and thecode which was used to compute this and the evolutionary track for massive donor starsare also explained.

3.1 The Model

For the purpose of our study, we consider a binary system with a black hole of 20M�or 100M�. In this ULX model, it is assumed that the companion star of this black holeis a massive companion (M≥ 8M�). This companion star orbiting around the blackhole is assumed to eventually transfer matter onto the black hole. The evolution of thebinary system is computed in the same way as it has been done by Patruno & Zampieri(2008; 2010) using a modified version of the updated Eggleton code (Eggleton 1971;Pols et al. 1995). The different parameters obtained from this code will be discussedlater in this chapter.

There are many factors that had to be taken into account by Patruno & Zampieri(2008; 2010) in order to model the evolution of such systems properly. The donor starsin this case are assumed to be massive (Zampieri & Roberts 2009). The modified Eggle-ton code then allows for non conservative stellar evolution while taking into account theamount of mass lost by massive stars due to stellar wind (de Jager et al. 1988). The

26

3.1 The Model 3.0 MODELLING THE OPTICAL EMISSION FROM ULXS

adopted mixing length parameters and overshooting constants were fixed to α = 2.0and δoν = 1.2 respectively (Pols et al. 1998, Patruno & Zampieri 2008). The amountof anuglar momentum lost through the emission of gravitational waves (Landau & Lif-shitz 1975) and particles in winds (Soberman, Phinney & van den Heuvel 1997) wasalso accounted for in the evolution of this system (Patruno & Zampieri 2008).

The accretion mechanism for the system also needs to be taken into account whilethe evolved stellar parameters are computed for every time step. An accretion disk willform if accretion occurs through Roche-Lobe overflow (RLOF), Patruno & Zampieriuse an efficiency value of η = 0.1(10%) for the conversion of gravitational potentialenergy into radiation in a disk. The bolometric luminosity of the ULX is computedusing L = ηMc2 where M denotes the mass transfer rate from the donor star and iscomputed by the numerical code for the evolution. For other accretion mechanisms likewind-fed accretion, the mass of the black hole in the binary system plays an importantrole. A more massive black hole will have a stronger gravitational potential and as aresult the stronger gravitational pull will cause more loss through stellar wind to fallonto the black hole. The creation of an accretion disk through wind-fed accretion is alikely phenomena if the mass of the black hole is above 100M�, in the range of IMBHs,but will not be considered in the present investigation. The other parameters whichneed to be taken into account when considering the evolution of a binary ULX systemare initial orbital separation and stability of the accretion disk.

In our model of the ULX, the evolutionary tracks are considered for the time duringwhich accretion due to Roche-Lobe overflow occurs (the tracks are computed until theend of the H-shell burning). It is assumed that a geometrically thin and optically thickaccretion disk forms around the black hole and the accretion rate is taken to be equalto the mass-transfer rate from the companion. If the accretion rate M exceeds theEddington rate MEdd then the accretion rate is set to the Eddington accretion rateassuming that the excess mass transferred is expelled from the system (Patruno &Zampieri 2010). In order for accretion to occur through RLOF, the radius of the starhas to exceed its’ Roche Lobe radius. If a donor star’s radius exceeds its’ Roch Loberadius during main sequence then it is likely that there is a second phase of mass transferafter the terminal age main sequence (TAMS) (Patruno & Zampieri 2010). This maybeafter the H-shell burning has begun. These are some of the fundamental assumptionsregarding the ULX model that is used for the computation of stellar evolution tracksfor the time the Roche-Lobe overflow (RLOF) occurs. In the next section, details aregiven regarding the emission component from X-ray irradiation and the implementationof the code in order to model the total luminosity of the source.

27

3.2 Computing the Optical Luminosity 3.0 MODELLING THE OPTICAL EMISSION FROM ULXS

3.2 Computing the Optical Luminosity

In order to compute the optical luminosity from a ULX binary system, variouscalculations have to be performed on the model discussed in the previous section foreach time step. For our study, data was available from Zampieri & Patruno (2008;2010) with regards to the evolution of the parameters of different donor star accretingon to 20M� and 100M� black holes. Data was available for donor stars with initialmasses of 8M�, 10M�, 12M�, 15M�, 20M� and 25M�. In the subsequent subsections,the working of the code that was used to model the optical luminosities of ULXs isexplained.

3.2.1 Initial Data Files

The initial data files contained parameters of the donor stars in the ULX model foreach time step. There was a separate data file for each donor star mass accreting onto both a 20M� and 100M� black hole. So the data files with evolutionary parameterswere available for the following cases

1. 8M� donor star accreting onto a 20M� black hole









28





Additional data files were also available for the following cases:





In the first 12 data files, the parameters of the donor stars evolution were availablefor the time periods when the radius of the star was greater than its’ Roche Lobe radius.While for the remaining 4 files, the output file was filtered in order to remove all linesin which the radius of the star was less than the Roche-Lobe radius. The header ofeach of these data files contained the following parameters:

1. Mass of the donor star in units of M�

2. Mass of the black hole in units of M�

3. Time in years

4. The orbital period in days

5. The effective temperature of the unirradiated star in Kelvins

6. The radius of the star in cm

7. Logarithm value of the luminosity of the star (in solar units)

8. Ratio between the logarithm value of the radius of the star and the logarithm valueof the Roche Lobe radius (lg( Rs

RL)

These were the parameters that were input into the code. Before going on to explain,how the code works, it is important to discuss X-ray irradiation and how it has beenmodelled to calculate the optical luminosity of the ULX by Zampieri & Partruno (2008;2010). The next subsection discusses the modelling of the X-ray irradiation.

29


3.2.2 X-ray Irradiation

A very important effect which needs to be considered when modelling the emissionproperties of ULXs is the optical emission from the accretion disk and in the case ofisotropic emission, the reprocessed X-ray emission (Zampieri & Partruno 2008). Themain areas in which X-ray irradiation is dominant are the outer parts of the accretiondisk and the surface of the donor star. There is a significant contribution from the accre-tion disk in the UV and B photometric bands when accretion occurs due to Roche-lobeoverflow. The total UV/optical luminosity of the ULX system has to be computed bysumming over the contribution by the donor, the accretion disk and the reprocessedX-ray radiation. The Copperwheat et al. (2005) model for irradiation assumes isotropicX-ray emission from the ULX. The model considers the effects of radiative transportand radiative equilibrium in the irradiated surfaces of the star and the accretion disk(Copperwheat et al. 2007). The model also assumes a geometrically thin disk and takesinto account the effects of radiation pressure, gravity and limb darkening (Copperwheatet al. 2007). The Copperwheat et al. (2005; 2007) model works well for the geomet-ric constraints imposed by the Roche-Lobe overflow on the accretion and a simplifiedversion of this model is adopted by Patruno & Zampieri (2008, 2010). The code usedin this study and by Patruno & Zampieri (2008, 2010) simplifies the irradiation modelfurther by assuming that the the companion star remains spherical and at uniform tem-perature (this assumption allows one to neglect the changes in the geometry of the starcaused by Roche-Lobe geometry or radiation pressure). Moreover, the effects of gravityand limb darkening are not included. Another important consideration when modellingthe optical emission is the hardness parameter of the X-rays. The Copperwheat et al.(2005) model showed that the results of the irradiative calculations are sensitive to thehardness parameter ξ. This parameter is defined as the flux ratio between the hard(> 1.5 keV) and the soft (< 1.5 keV) component of the incident X-ray flux. In the codeused for modelling the emission properties of ULXs, the hardness parameter was takento be 0.1 (a locally soft irradiating spectrum is expected (Copperwheat et al. 2007)).

30


3.2.3 Computing Total Luminosity

In this study, the code used by Patruno & Zampieri (2010) was again used to computethe total optical luminosity of the ULX model for the different cases that were statedin section 3.2.1. These output values were highly dependent on various parameters andconstants that were fixed for this study (some of the results with modified parame-ters are reported in Chapter 5). This code was written in the programming language‘python’ and was modified for this thesis. The output of the code is dependent on threemain parameters that the code obtains using the data files. These are the mass of thedonor star, the mass of the black hole and the binary period (from which the orbitalseparation is calculated) and the effective temperature of the unirradiated donor star).

The parameters that have been fixed in the code are the inclination angle (ι) and theorbital phase (φ). The inclination angle was fixed such that the disk is face-on (cosι=1)and the value of the orbital phase was taken to be φ=0 (for a non zero inclination, thedonor is on the opposite side of the BH with respect to the observer). The albedo forthe irradiated surface layer of the disk was fixed to be fa = 0.9. The distance to thesource was fixed at 10pc so that the obtained total magnitudes are absolute (makingit simpler to compare them with the optical counterparts). The absorption parameters(ratio of the opacity to the electron scattering opacity) for hard and soft componentswere fixed to be kh = 0.01 and ks = 2.5. For this study, the code was modified so thatit only outputs the absolute magnitude in the V band and the B-V colour. This wasbecause the data for the counterparts with which the evolutionary tracks are going tobe compared is available in this band.

Now that the fundamental parameters have been defined, we briefly describe themain parts of the algorithm implemented in the code to compute the optical magni-tudes and colours.

1. An iterative loop starts off by reading the first line of the input data file and theparameters for donor star mass, black hole mass, time, period, temperature, radiusetc are stored as variables.

2. Various calculations are made by the code to calculate parameters such as innerdisk radius, outer disk radius, X-ray luminosity intercepted by the star and thatintercepted by the disk.

3. The total luminosity of the irradiated disk is found by integrating over its’ spec-trum. The spectrum is integrated over the optical band using values of the filterwidth and flux calibration for the UBVRI Johnson system (Cox, Allen’s Astro-

31


physical Quantities, 1999, chap. 15). In the modified version of the code this wasonly done for the B and V filters.

4. The effective temperature of the irradiated and unirradiated donor surfaces arecomputed and their magnitudes are calculated using analytic fitting functions ofcalibration tables of MK spectral type stars (taken from Cox, Allen’s Astrophys-ical Quantities, 1999, chap. 15). From the magnitudes, the flux and the opticalluminosity of the donor are calculated.

5. Once the the irradiated optical luminosities for both the disk and the donor surfaceare obtained, the total luminosity and magnitude of the ULX is computed.

6. An output file is written in which the time, B-V colour, and the V band absolutemagnitude are printed. (the output file was modified so that the output file iswritten after every iteration).

7. The code reiterates for the next line in the data file and outputs the results in anew line on the output file.

32

3.3 Binary Evolution 3.0 MODELLING THE OPTICAL EMISSION FROM ULXS

3.3 Binary Evolution

Once the code has run, it becomes possible to plot the output track on a colour-magnitude diagram. In order to do this a script was written in ‘gnuplot’. For thepurpose of this study, the colour-magnitude diagrams were made for each differentdonor mass star in section 3.2.1. As an example of the output produced from the code,figure 4 and figure 5 showing the evolutionary track for 8M�, 10M�, 12M�, 15M�,20M� and 25M� donors are plotted for accretion on to a 20M� and 100M� black hole.

Figure 9: This is a colour-magnitude diagram generated using the data output by the code, it showsthe evolutionary tracks during RLOF for a ULX binary system in which the donor stars have masses8M�, 10M�, 12M�, 15M�, 20M� and 25M� and the black hole has a mass of 20M�. The y axisrepresents the absolute V band magnitude and the x-axis gives the B-V colour of the donor star. Theoptical contribution from X-ray irradiation has been taken into account for each evolutionary track.This figure is plotted as an example of the output of the code. Six different data files were used to plotthe tracks for each donor mass. The data files were filtered to ensure that the plots were only madewhen the radius of the star was greater than its Roche-Lobe radius (to ensure RLOF).

33

3.3 Binary Evolution 3.0 MODELLING THE OPTICAL EMISSION FROM ULXS

Figure 10: This is a colour-magnitude diagram generated using the data output by the code, it showsthe evolutionary tracks during RLOF for a ULX binary system in which the donor stars have masses8M�, 10M�, 12M�, 15M�, 20M� and 25M� and the black hole has a mass of 100M�. The y axisrepresents the absolute V band magnitude and the x-axis gives the B-V colour of the donor star. Theoptical contribution from X-ray irradiation has been taken into account for each track. This figure isplotted as an example of the output of the code. Six different data files were used to plot the tracksfor each donor mass. The data files were filtered to ensure that the plots were only made when theradius of the star was greater than its Roche-Lobe radius (to ensure RLOF)

The stellar evolutionary tracks have been modelled and obtained, it is now possibleto compare them with the photometric data for optical counterparts obtained by Taoet al. (2011). In the next section, the observational data available for 13 ULXs ispresented.

34

4.0 OBSERVATIONAL DATA FOR OPTICAL COUNTERPARTS

4.0 Observational Data for Optical

Counterparts

In this section, details of the ULXs for which the data for optical counterparts (Taoet al 2011) is available, are presented. Their photometric properties are also discussed.These will be the ULXs for which optical counterparts will be compared to the modelledoptical evolutionary tracks.

4.1 Counterparts of 13 ULXs

In a paper entitled, “Compact optical counter of ultraluminous X-ray sources” by Taoet al (2011), the multiband photometric properties of 13 ULXs which have a uniquecompact counterpart were reported. The study by Tao et al. (2011) was made usingarchival data from the Hubble Space Telescope (HST ). Before the beginning of the workby Tao et al. (2011), there were 10 ULXs with identified optical counterparts. However,due to the error boxes in optical data and X-ray data it was difficult to pinpoint theexact counterpart and in some cases there were more than one candidate for the opticalcounterpart of the source. In the study by Tao et al. (2011), the ULX catalogues weresurveyed in order to improve the relative astrometry between the data from the HSTand the Chandra telescope. Relative astrometric corrections are made by aligning ob-jects shown on both telescopes. The details of how these astrometrical corrections aredone is described by Feng & Kaaret (2008).

The photometry of the 13 ULXs in the sample of Tao et al. (2011) was made usingarchival data from either the Advanced Camera for Surveys (ACS ) or the Wide-FieldPlanetary Camera 2 (WFPC2 ) instruments on the HST (Tao et al. 2011). From theseinstruments optical data for the counterparts is obtained in different filter bands. Animportant consideration in the results of this thesis is the total extinction in the lineof sight to the counterpart. For certain ULX sources which are associated with opticalnebulae, it is possible to have a more accurate value for the extinction. The extinctionvalue of these sources are measured from emission lines from the optical spectra of the

35

4.1 Counterparts of 13 ULXs 4.0 OBSERVATIONAL DATA FOR OPTICAL COUNTERPARTS

nebulae with which they are associated. If there is no optical nebular association forthe source then the Galactic extinction is adopted (Tao et al. 2011). An accuratevalue for the extinction measurement is important as it affects the colour of the source.The results of this study are separated for sources which have nebular extinction andthose that have Galactic extinction. For 9 out the 13 ULXs sampled by Tao et al.2011, there is nebular association. However, the values of nebular extinction are onlyavailable for 7 of these sources. The extinction can also be estimated from the neutralhydrogen column density, which is derived via X-ray spectral fitting. According to Taoet al. (2011), the latter often overestimates the total extinction. In addition, the X-raycolumn density usually varies dramatically, causing additional difficulty in deriving theextinction. Therefore, Tao et al. (2011) adopted Galactic extinction when the nebularextinction was unavailable. Clearly, this should be treated as a lower limit. The detailsof the photometry and how photometric data was obtained for ULXs can be found inTao et al. (2011).

Concerning the error estimates on the magnitude and colours, for the absolute Vband magnitude, the value of the uncertainty was taken from the V-band error of theHST band given in Table 3 of Tao et al. (2011). For the uncertainty in colour, thesquare root of the sum of the squared values of the error in B and V band was calculated.

In the next subsections, the individual sources sampled by Tao et al. (2011) thatwill be used for comparison with the evolutionary tracks for ULXs are discussed. Table2 lists these 13 sources along with their Chandra coordinates and adopted distances totheir host galaxies.

36


Table 2: List of the 13 ULXs that are studied in this thesis. The adopted distance to the host galaxyis given in Mpc. The Chandra J2000.0 coordinates (right ascension (R.A.) and declination (Decl.) arealso listed for each source.

ULX Distance (Mpc) R.A. (J2000.0) Decl. (J2000.0)

Holmberg II X-1 3.05 08 19 28.980 +70 42 19.30

Holmberg IX X-1 3.6 09 57 53.32 +69 03 48.10

IC 342 X-1 3.3 03 45 55.61 +68 04 55.30

M81 ULS1 3.63 09 55 42.20 +69 03 36.50

M81 X-6 3.63 09 55 32.95 +69 00 33.36

M83 IXO 82 4.7 13 37 19.799 −29 53 48.43

M101 ULX-1 7.2 14 03 32.37 +54 21 02.75

NGC 1313 X-2 3.7 03 18 22.18 −66 36 03.3

NGC 2403 X-1 3.2 07 36 25.563 +65 35 39.93

NGC 4559 X-7 10 12 35 51.725 +27 56 04.41

NGC 5204 X-1 4.3 13 29 38.62 +58 25 05.60

NGC 5408 X-1 4.8 14 03 19.62 −41 22 58.54

NGC 6946 ULX-1 5.1 20 35 00.752 +60 11 30.55

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4.1.1 Holmberg II X-1

The X-ray source Holmberg II X-1 was catalogued by ROSAT (Kerp et al. 2002).It is a well studied source for which many multiband properties are known. The en-vironment of the source is also well known (Kaaret et al. 2004). Holmberg II is adwarf irregular star-forming galaxy located in the M81 group of galaxies. The sourceis known to be in an ionized nebula (Pakull & Mirioni 2002). In the Tao et al (2011)sample, the information for the nebular extinction is available for this source. A studyregarding the nature of the UV/Optical emission from Holmberg II X-1 was recentlycarried out by Tao et al. (2012). The evolution of X-ray spectral properties (includingthe high energy curvature) of the ULX in Holmberg II X-1 has also been studied indetail (Kajava et al. (2012) and references therein).

Figure 11: False colour images of the continuum subtracted line emissiom from the nebula associatedwith the ULX in Holmberg II. The first 3 images are for the emission lines HeII λ4686, Hβ λ4861 and[OI] λ6300. The fourth image is of the V-band continuum. In each image, the arrow points Northwardand has a length of 1” (15 pc).The green cross marks the position of the bright star within the nebula,and the green curves are contours of HeII emission. The cyan circle and X in the narrow-V imagedenote the best Chandra position for the ULX and the relative Chandra/HST error circle (taken fromKaaret et al. 2004).

38


Figure 12: Unabsorbed spectrum of Holmberg II X-1 from the X-rays to the UV/optical band withthe best-fitting diskir model (taken from Tao et al. 2012).

Tao et al. (2011) list data for 3 different observations of the optical counterpartfor Holmberg II X-1. The proposed spectral types of the counterpart vary for eachobservation and are given to be B6-B7 Ib-Iab, B0-B1 Ib, B1-B2 Ib and O9-B0 Ib.

The observations with quasi-simultaneous (within ∼ 1 hour) measurements of theV band magnitude and B-V colour of the optical counterpart of Holmberg II X-1 arereported in Table 3.

Table 3: Data for the counterpart of the source Holmberg II X-1

ULX Date B-V Mv

Holmberg II X-1 10/3/2007 −0.24 ± 0.02 −5.93 ± 0.0110/5/2007 −0.18 ± 0.02 −5.94 ± 0.0110/9/2007 −0.27 ± 0.02 −5.94 ± 0.01

More details of this source are discussed in the results and discussion section of thethesis.

39


4.1.2 Holmberg IX X-1

The source Holmberg IX X-1 (Grise et al. 2011) is also known as M81 X-9 and itis embedded in an ionized nebula inside the dwarf irregular companion galaxy of M-81known as Holmberg IX (Pakull & Mirioni 2002, Patruno & Zampieri 2008). HolmbergIX is considered to be one of the youngest nearby galaxies (≈ 200 Myr old) based on theobserved age distribution of the stars that it contains (Sabbi et al. 2008). The spectralcurvature for Holmberg IX X-1 is in the high energy part of the X-ray spectrum above 2keV (Dewangan et al. 2006). The optical properties of Holmberg IX X-1 and its stellarenvironments are discussed in detail by Grise et al. (2011). The nebular extinction forthis source is known. However, the extinction varies from 0.09 to 0.26 mag within thenebula. (Tao et al. 2011). The value of extinction taken for this source by Tao et al.(2011) is 0.26±0.04. The size of the nebula is roughly measured to be 3× 1012 cm (Taoet al. 2011).

Figure 13: Identification of the optical counterpart for Holmberg IX X-1 on an HST/ACS image inthe F435W filter (left) and in the F330W filter (right). The counterpart is designated by a blue cross(left). Slits from the SUBARU (position angle of 180◦) and GEMINI observations (position angleof 90◦) are overlaid on the right image. The Chandra green circle) and XMM-Newton (red circle)positions are also overlaid (taken from Grise et al. 2011).

For this source, one multicolour quasi-simultaneous observation of the optical coun-terpart is available. The possible spectral types of this counterpart could be O5V, O6III(Tao et al. 2011). The B-V colour index for Holmberg IX X-1 given by Tao et al. (2011)has a significantly different value (B − V = −0.42) from the value (B − V = −0.25)

40


reported by Grise et al. (2011). The colour index and absolute value of the V bandmagnitude obtained by Grise et al. (2011) in their study of the optical counterpart ofHolmberg IX X-1 have also been included in this study. The date of the observationwith quasi-simultaneous (within ∼ 1 hour) measurements of the B-V colour and V bandmagnitude is reported in the table below.

Table 4: Data for the counterpart of the source Holmberg IX X-1. The * indicates that the photometricdata was taken from Grise et al. (2011).

ULX Date B-V Mv

Holmberg IX X-1 2/7/2004 −0.42± 0.04 −5.88± 0.032/7/2004* −0.25±0.05 −6.00±0.02

4.1.3 IC 342 X-1

The source IC 342 X-1 is located in the intermediate spiral galaxy known as IC 342(also referred to as Caldwell 5) in the constellation Camelopardalis. It is part of the IC342/Maffei Group of galaxies which is located just outside the Local Group of galaxies.IC 342 X-1 is also among the sample of ULXs for which a unique optical counterparthas been identified (Feng & Kaaret 2008). The ULX is observed inside an ionized neb-ula (Roberts et al. 2003; Grise et al 2006) and the nebular extinction for this source isknown (Tao et al. 2011). Recently, an unresolved radio source coincident with the ULXIC 342 X-1 was discovered (Kaaret et al. 2011). Radio emission at the position of theULX IC 342 X-1 suggests that there could be the presence of an outflow in this object(Grise 2010). There has also been the discovery of a radio nebula associated with theULX IC 342 X-1 using the Very Large Array (VLA) (Cseh et al. 2012).

41


Figure 14: HST F625W band image of the region around IC 342 X-1. The dashed circle indicates thedirectly measured Chandra position of IC 342 X-1 with an uncertainty of 0.6”, the solid circle indicatesthe corrected position (obtained by adding the known position coordinates with the correspondingoffset) of the source and stars A and B are two possible optical counterparts (taken from Feng &Kaaret 2008). Tao et al. (2011) improved the position of the counterpart by using a smaller apertureand added the aperture correction into their results.

There is data for two observations of the optical counterpart of IC 342 X-1. Theproposed spectral types of donor stars corresponding to these two observations are F5Ib-Iab and F5 Ib-Iab. The dates of the observations with quasi-simultaneous measure-ments of the B-V colour and V band magnitude are given in the table below.

Table 5: Data for the counterpart of the source IC 342 X-1

ULX Date B-V Mv

IC 342 X-1 9/2/2005 0.37±0.15 −5.94±0.1012/18/2005 0.3±0.13 −5.95±0.09

4.1.4 M81 ULS1

The source M81 ULS1 (Liu et al. 2008) is an ultraluminous supersoft source locatedin the spiral galaxy M81 (also known as NGC 3031 or Bode’s Galaxy). Supersoft X-raysources emit very low energy X-rays and the typical temperature of the soft componentobtained from the X-ray spectral fits is ∼ 0.02 − 0.1 keV (Kahabka 2006). For anultraluminous supersoft source, the compact object in the binary system could possibly

42


be a massive white dwarf or a black hole. Optical and infrared studies along with thedetailed study of the spectrum of M81 ULS1 point towards the compact object beinga black hole instead of a white dwarf (Liu 2008). Tao et al. (2011) provide the opticalHST data for the counterpart of M81 ULS1. There is no known nebular association forthis source and only Galactic extinction is available.

Figure 15: HST images of the optical counterpart for M81 ULS1 in F547M (1996), F656N (1996),F658N (2003), F814W (2004), F435W (2006) and F606W (2006). The WFPC2 F547M/F656N andACS/WFC F435W images are plagued with cosmic rays. All images are aligned with the counterpartat the image centres. The red circle indicates the counterpart (taken from Liu et al. 2008).

There is data for 2 observations of the counterpart for M81 ULS1. Tao et al. (2011)give possible spectral types of A5-A7 Iab and F2 Ib-Iab for these observations. Thedates of the observations with quasi-simultaneous measurements of the B-V colour andV band magnitude are given in the table below.

Table 6: Data for the counterpart of the source M81 ULS1

ULX Date B-V Mv

M81 ULS1 3/21/2006 0.11±0.04 −6.26±0.043/27/2006 0.22±0.04 −5.99±0.04

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4.1.5 M81 X-6

The source M81 X-6 is also referred to in the literature as ULX NGC 3031 X-11(Liu et al. 2002). M81 X-6 is a ULX which is located in the spiral galaxy M81. Thesource M81 X-6 is thought to be surrounded by a highly ionized nebula (Moon et al.2011). Tao et al. (2011) acknowledge the nebular association of this source, however,they do not have a known value for the nebular extinction of this source and rely onthe Galactic extinction instead. Spectral Variability of M81 X-6 has also been studiedusing X-ray data taken from ASCA (Mizuno et al. 2001).

Figure 16: The WFPC2 HST image of the optical counterpart of M81 X-6 and its environments. Thecounterpart,indicated by a cross, is a point source (taken from Liu et al. 2002).

There is data for 2 observations of the counterpart for M81 X-6. The proposedspectral types corresponding to these observations are B5-A3 II and B7-B8 II. Thedates of the observations with quasi-simultaneous measurements of the B-V colour andV band magnitude are given in the table below.

44


Table 7: Data for the counterpart of the source M81 X-6

ULX Date B-V Mv

M81 X-6 1/31/1995 0.06±0.18 −3.91±0.066/4/2001 −0.13±0.07 −4.01±0.06

4.1.6 M83 IXO 82

The source M83 IXO 82 (Stobbart et al. 2006) is a ULX located in the barred spiralgalaxy M83 (also known as NGC 5236 or the Southern Pinwheel Galaxy). It is a veryinteresting source. Its optical spectrum could be consistent with the spectral index(α = 1/3) expected for intrinsic emission of a standard multicolour disk if the assumedreddening (B − V = 0.066) is incorrect (Tao et al. 2011). As there is no nebular ex-tinction available for the source, the reddening was calculated using Galactic extinction(Tao et al. 2011). M83 IXO 82 is a good candidate for a source in which the opticalemission is dominated by intrinsic emission from an accretion disk (Tao et al. 2011).This source is among the sample of ULXs for which observations of the counterpartwere made by Tao et al. (2011). Figure 8 shows the HST image around M83 IXO 82.

There is data for 2 observations of the counterpart for M83 IXO 82 with possiblespectral type of A2-F2 II or B1 V. The date of the observation with quasi-simultaneousmeasurements of the B-V colour and V band magnitude is given in the table below.

Table 8: Data for the counterpart of the source M83 IXO 82

ULX Date B-V Mv

M83 IXO 82 2/25/2006 0.26±0.13 −3.11±0.09

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4.1.7 M101 ULX-1

The source M101 ULX-1 (Kuntz et al. 2005) is a ULX located in the M101 galaxy(also known as NGC 5457 or Pinwheel Galaxy) which is a face-on spiral galaxy. TheX-ray properties including variability of M101 ULX-1 are presented in detail by Mukaiet al. (2005). The mass of the accretor in M101 ULX-1 was inferred to be between20 and 40M� on the basis of X-ray spectral fits (Mukai et al. 2005). Outbursts fromM101 ULX-1 have also been studied in detail. Chandra and XMM-Newton results ofan outburst from M101 ULX-1 in December 2004 give a peak bolometric luminosity ofabout 3 × 1040ergs−1 (Kong & Di Stefano 2005). Kong & Di Stefano (2005) suggestthat M101 ULX-1 could harbour an intermediate-mass black hole. M101 ULX-1 isassociated with an optical nebula and the extinction value for the nebula is given byTao et al. (2011).

Figure 17: HST ACS F435W image of M101 ULX-1. The circle marks a 0.3” radius error box aroundthe X-ray position (taken from Kuntz et al. 2005).

There is data for many observations of the counterpart for M101 ULX-1 with possible

46


spectral types of B5 Iab or A3 Iab, O5 III or O8 II and O5 III or O8-O9 II or B7 Ib.The dates of the observations with quasi-simultaneous measurements of the B-V colourand V band magnitude are given in the table below.

Table 9: Data for the counterpart of the source M101 ULX-1

ULX Date B-V Mv

M101 ULX-1 3/22/1994 −0.11±0.08 −6.39±0.034/8/1994 −0.28±0.08 −6.15±0.03

11/15/2002 −0.31±0.04 −6.00±0.03

4.1.8 NGC 1313 X-2

The source NGC 1313 X-2 (Ramsey et al. 2006; Pakull et al. 2006; Liu et al.2007) is among the sample of ULXs for which counterparts were determined by Taoet al (2011). The source has been extensively studied in the X-ray and optical bands(e.g. Zampieri et al. 2004; Mucciarelli et al. 2007; Grise et al. 2008) and Patruno &Zampieri (2011) have been able to constrain the parameters of this ULX employing thesame methodology as the one used in this thesis. The ULX NGC 1313 X-2 is locatedinside the barred spiral galaxy NGC 1313 (also known as Topsy Turvy Galaxy). NGC1313 X-2 is so far the only ULX with available Hubble Space Telescope light curvesand a claim of detection of an optical periodicity at a low significance level (Liu et al.2009, 2012; Zampieri et al. 2012). The binned light curve for NGC 1313 X-2 in theB band (Zampieri et al. 2012) is shown in Figure 20. Many studies have been doneto constrain the mass of the black hole in ULX NGC 1313 X-2 (Liu et al. 2012). Theenvironment of the ULX is also very well studied (Zampieri et al. 2004; Grise et al.2008) and NGC 1313 X-2 does have an optical nebular association and the value of thenebular extinction is known (Tao et al. 2011).

47


Figure 18: “True colour HST image for a 50” × 50” region centred at the counterpart for NGC 1313X-2. The image was composed with F435W,F555W,F814W images from a 2003 observation. Thestellar field is dominated by red stars with scattered blue stars” (taken from Liu et al. 2007)

Figure 19: Binned light curve (6 bins) of the B band VLT+HST dataset of NGC 1313 X-2, foldedover the best estimate of the period (6 days). The phase was measured from MJD=54390. (takenfrom Zampieri et al. 2012)

Multiple quasi-simultaneous observations were available for NGC 1313 X-2. Thisallowed Tao et al. (2011) to study the long-term variability of the source. For NGC1313 X-2 (as previously shown by Impiombato et al. (2011)), the variability is higher inthe B-band than in the V-band (Tao et al. 2011). The spectral type of the counterpart

48


for NGC 1313 X-2 is posited to be O9V or B0-B1 III (Tao et al. 2011). The average valuefor the B-V colour index of the source taking into account 20 observations performedin 2008 (Table 3.0 from Tao et al. (2011) obtained after converting the F435W bandmagnitude to the B band Johnson system (Sirianni et al. 2005)) was found to be -0.20.The average value for the absolute V band magnitude (MV ) from the 20 observationswas found to be -4.59. These average values of the quasi-simultaneous observations ofthe counterpart of NGC 1313 X-2 were used for the purpose of this study. The datesof these observations and the average value for the the B-V colour index and V bandmagnitude are given in the table below.

Table 10: Data for the counterpart of the source NGC 1313 X-2

ULX Date B-V Mv

NGC 1313 X-2From 05/21/2008 to06/09/2008

−0.20±0.02 −4.59±0.01

4.1.9 NGC 4559 X-7

The source NGC 4559 X-7 (Stobbart et al. 2006) is a ULX located in the spiralgalaxy NGC 4559 (also known as Caldwell 36). This is also a well studied source.Copperwheat et al. (2006) modelled its optical emission(in terms of an irradiated com-panion star and disk). The X-ray variability of NGC 4559 X-7 have also been studiedin detail and reported by Cropper et al. (2004) and Barnard et al. (2007). An opticalstudy of the star-forming environment around this source has been done by Soria et al.(2005). They found that the ULX is located near a small group of OB stars, but is notassociated with any massive young clusters nor with any extraordinary massive stars.

This source is among the sample of ULXs for which observations of the counterpartwere made by Tao et al. (2011). Figure 8 shows the HST image around NGC 4559 X-7.There is data for 2 observations of the counterpart for NGC 4559 X-7 with possiblespectral types of B2-B5 Ia and B3-B5 Ia. The dates of the observations with quasi-simultaneous measurements of the B-V colour and V band magnitude are given in thetable below.

49



ULX Date B-V Mv

NGC 4559 X-7 5/25/2001 −0.17±0.03 −6.98±0.023/8/2005 −0.12±0.04 −7.10±0.03

4.1.10 NGC 5204 X-1

The source NGC 5204 X-1 (Liu et al. 2004) is a ULX located in the spiral galaxyNGC 5204 which is part of the M101 group of galaxies. The X-ray variability ofNGC 5204 X-1 was monitored for over 2 months using the Chandra X-ray Observatory(Roberts et al. 2006). Inconsistent extinction was found for NGC 5204 X-1 and its sur-rounding nebula by Tao et al. (2011) suggesting that they may be unrelated. Detailedstudy of the spectral states and evolution of the ULX have also been made and it hasbeen suggested that the emission in the ULX arises from the accretion disk (Feng &Kaaret 2009). The nebular association of the ULX NGC 5204 X-1 is questionable andTao et al. (2011) use Galactic extinction for this source.

Figure 20: The optical counterpart of the ULX in NGC 5204 X-1 in an HST -ACS (Hubble SpaceTelescope, Advanced Camera for Surveys) image. The small error ellipses are derived from Chandradata. The slit position for the STIS MAMA/FUV observation is also shown on the figure. The nominalerror circle includes HST-3 (which is designated as U1), while HST-1 and HST-2 (which breaks downto a chain of separate sources) are outside of this error circle. (taken from Liu et al. 2004).

50


There is data available for 3 observations of the counterpart for NGC 5204 X-1with possible spectral types of O5V or O8III, B2 II-Ib and B3 II-Ib. The dates ofthe observations with quasi-simultaneous measurements of the B-V colour and V bandmagnitude are given in the table below.


ULX Date B-V Mv

NGC 5204 X-1 8/8/2008 −0.35±0.03 −5.57±0.028/10/2008 −0.23±0.03 −5.62±0.028/13/2008 −0.20±0.03 −5.69±0.02

4.1.11 NGC 5408 X-1

The source NGC 5408 X-1 (Lang et al. 2007) is a ULX located in the dwarf irregu-lar galaxy NGC 5408 in the constellation Centaurus. NGC 5408 X-1 is a well studiedsource. Evidence of a rather long, regular modulation in the X-ray flux has been gath-ered for this source using data from the Swift telescope (∼115 days; Strohmayer 2009).It was interpreted as an orbital period or a super-orbital precession phenomenon (Fos-ter et al. 2010). The optical spectra and the photoionized nebula surrounding NGC5408 X-1 have also been well studied (Kaaret & Corbel 2009). The continuum com-ponent in the optical spectrum of NGC 5408 X-1 is found to be consistent with thespectrum from a standard accretion disk with irradiation (Kaaret & Corbel 2009). Aradio nebula has also been observed in the surroundings of NGC 5408 X-1 (Corbel et al.2009). The value of the nebular extinction is known for this source (Tao et al. 2011).The HST/WFC3 composite image of the field surrounding NGC 5408 X-1 is shown inFigure 7.

There is data for 1 observation of the counterpart for NGC 5408 X-1 with possiblespectral type of O9 Ib. Both quasi-simultaneous V and B band measurement wereperformed. They are reported in the table below.


ULX Date B-V Mv

NGC 5408 X-1 4/4/2009 −0.28±0.04 −6.27±0.02

51


4.1.12 NGC 6946 ULX-1

The source NGC 6946 ULX-1 (Kaaret et al. 2010) is a ULX located in the interme-diate spiral galaxy NGC 6946 (also known as Fireworks Galaxy, Caldwell 12 and Arp29). The spectral variability of the ULX NGC 6946 ULX-1 has been studied by Kajavaet al. (2009). The optical nebula associated with the NGC 6946 ULX-1 is known asMF16 and has also been thoroughly investigated (Abolmasov et al. 2007). Data for theoptical spectroscopy of this nebula is also available (Abolmasov et al. 2008). This is oneof the sources for which nebular extinction was known in the study by Tao et al. (2011).

Figure 21: The HST image of the counterpart to the X-ray source NGC 6946 ULX-1. The panels showA: FUV (F140LP lter), B: B-band (F450W lter), C: V-band (F555W lter), and D: I-band (F814Wlter). The small circles mark the counterparts to the X-ray source and have radii of 0.15”. The ellipsesmark the extent of the nebula. The length of arrow pointing North in panel A is 1” (taken from Kaaretet al. 2011).

There is data available for 2 observations of the counterpart for NGC 6946 ULX-1. Tao et al. (2011) give possible spectral types of B6-B7 Ia and B2 Ia for theseobservations. The date of the observations with quasi-simultaneous measurements ofthe B-V colour and V band magnitude is given in the table below.

52


Table 14: Data for the counterpart of the source NGC 6946 ULX-1

ULX Date B-V Mv

NGC 6946 ULX-1 01/27/1996 0.07±0.23 7.26±0.1606/08/2001 0.42±0.18 7.27±0.12

4.1.13 NGC 2403 X-1

The source NGC 2403 X-1 (Feng & Kaaret 2005) is located in NGC 2403, which isan intermediate spiral galaxy in the constellation Camelopardalis. It is part of the M81Group of galaxies. NGC 2403 X-1 is a sparsely studied source. Weng et al. (2008) usedthe p-free model to fit the spectra of NGC 2403 X-1. It is possible that the observedemission from NGC 2403 X-1 is the intrinsic emission of a standard multicolour disk(similar to the source M83 IXO 82) (Tao et al. 2011). This source is among the sampleof ULXs for which observations of the counterpart were made by Tao et al. (2011).Figure 8 shows the HST image around NGC 2403 X-1. There is no known nebularassociation for NGC 2403 X-1 and the Galactic extinction value is taken for the sourceby Tao et al. (2011).

There is data for 1 observation of the counterpart for NGC 2403 X-1 with possiblespectral type of B0-B2V. Both quasi-simultaneous V and B band measurement wereperformed. They are reported in the table below.


ULX Date B-V Mv

NGC 2403 X-1 10/17/2005 0.07±0.08 −2.90±0.06

53

4.2 Table of Photometric Data 4.0 OBSERVATIONAL DATA FOR OPTICAL COUNTERPARTS

4.2 Table of Photometric Data

A table summarizing the photometric data for the optical counterparts analyzed by Taoet al. (2011) and considered in the present investigation is reported on the next page.

54


Table 16: Table giving the data for the optical counterparts of the ULXs considered in this study(taken from Tao et al. 2011). The table gives the date (dd/mm/yy) of the observation, absolute Vband magnitude, colour (corrected for extinction) of the counterparts. Whether nebular extinction forthe source is available or not is also indicated and the adopted extinction value is given in the lastcolumn. * indicates that the photometric data for the date was taken from Grise et al. (2011).

ULX Date B-V Mv Nebular Extinction Extinction Value

Holmberg II X-1 03/10/2007 −0.24 ± 0.02 −5.93 ± 0.01 Y 0.0705/10/2007 −0.18 ± 0.02 −5.94 ± 0.0109/10/2007 −0.27 ± 0.02 −5.94 ± 0.01

Holmberg IX X-1 07/02/2004 −0.42± 0.04 −5.88± 0.03 Y 0.26±0.04

07/02/2004* −0.25±0.05 −6.00±0.02 Y 0.26±0.04

IC 342 X-1 02/09/2005 0.37±0.15 −5.94±0.10 Y 0.8218/12/2005 0.3±0.13 −5.95±0.09

M81 ULS1 21/03/2006 0.11±0.04 −6.26±0.04 N 0.0827/03/2006 0.22±0.04 −5.99±0.04

M81 X-6 31/01/1995 0.06±0.18 −3.91±0.06 N 0.0804/06/2001 −0.13±0.07 −4.01±0.06

M83 IXO 82 25/02/2006 0.26±0.13 −3.11±0.09 N 0.066

M101 ULX-1 22/03/1994 −0.11±0.08 −6.39±0.03 Y 0.1308/04/1994 −0.28±0.08 −6.15±0.0315/11/2002 −0.31±0.04 −6.00±0.03

NGC 1313 X-221/05/2008 to09/06/2008

−0.20±0.02 −4.59±0.01 Y 0.13±0.03

NGC 2403 X-1 17/10/2005 0.07±0.08 −2.90±0.06 N 0.04

NGC 4559 X-7 25/05/2001 −0.17±0.03 −6.98±0.02 N 0.01808/03/2005 −0.12±0.04 −7.10±0.03

NGC 5204 X-1 08/08/2008 −0.35±0.03 −5.57±0.02 N 0.01310/08/2008 −0.23±0.03 −5.62±0.0213/08/2008 −0.20±0.03 −5.69±0.02

NGC 5408 X-1 04/04/2009 −0.28±0.04 −6.27±0.02 Y 0.08±0.03

NGC 6946 ULX-1 27/01/1996 0.07±0.22 7.26±0.16 Y 0.5+0.08−0.07

08/06/2001 0.42±0.18 7.27±0.12

55


Distribution of the Magnitudes of the Counterparts

The figure below shows the distribution of the absolute magnitudes of the differentobservations of the counterparts for the 13 sources.

Figure 22: Distribution of the absolute V band magnitude of the different observations of the opticalcounterparts for the 13 sources listed by Tao. et al. (2011). It can be seen from the distribution thatmost of the counterparts have an absolute V band magnitude between -5.5 and -6.5.

56


Distribution of the B-V Colour Index of the Counterparts

The figure below shows the distribution of the absolute magnitudes of the differentobservations of the counterparts for the 13 sources.

Figure 23: Distribution of the B-V colour of the different observations of the optical counterpartsfor the 13 sources listed by Tao. et al. (2011) and reported in Table 16. It can be seen from thedistribution that most of the counterparts have a B-V value between -0.30 and -0.10. The very brightand blue counterparts are likely to be either massive stars and/or strongly irradiated.

57

5.0 RESULTS

5.0 Results

In this section, the results of the study carried out are presented in the form of colour-magnitude diagrams showing stellar evolutionary tracks for ULXs (section 3) and theobservational data for the optical counterparts discussed in the previous section. Theresults are split into two categories of sources. Firstly, the results from sources withknown values for nebular extinction are given and then the result for the sources withGalactic extinction are presented. The results are further split into two subsections foreach type of extinction. In one subsection the black hole mass is taken to be 20M� andin the other the mass of the black hole is 100M�. In the third section of this chapter,the results with the modified albedo parameters for particular tracks and sources areprovided.

It can be seen from Table 16, many ULXs show a certain degree of intrinsic opticalvariability that is expected in an accreting binary and may be due to varying physi-cal conditions (e.g. instantaneous accretion rate) in the accretion disk. This clearlyintroduces some uncertainty (in addition to that induced by the photometric error) onthe donor and black hole mass estimates. An example of how the colour of a source isaffected by intrinsic optical variability is shown in the Figure 24.

Figure 24: Colour variation as a result of intrinsic optical variability of NGC 1313 X-2 (representedby plus) and a comparison object (diamond) (taken from Tao et al. 2011).

58

5.1 Sources with Nebular Extinction 5.0 RESULTS

5.1 Sources with Nebular Extinction

5.1.1 Results for a 20M� Black Hole

Figure 25: Colour-magnitude diagram showing the evolutionary tracks for a ULX binary system witha black hole of 20M� and the position of the counterparts of Holmberg II X-1, Holmberg IX X-1, IC342 X-1, M101 ULX-1, NGC 1313 X-2, NGC 5408 X-1 and NGC 6946 ULX-1. These were the sourcesfor which the value of nebular extinction was available. The tracks are plotted for 8M�, 10M�, 12M�,15M�, 20M� and 25M� donor stars. The tracks for donor stars of mass 30M� and 50M� in a binarysystem with a 10M� black hole have also been added to this figure. The effects of X-ray irradiationare taken into account for each track. For the position of the counterparts the error in the values ofthe absolute V band magnitude and colour (B-V) is represented by the error bars.

59


From Figure 25, it is now possible to see which of the tracks intersect with the posi-tion of the optical counterparts of the ULXs for which the value of nebular extinction isknown. For the source Holmberg II X-1 (shown in yellow) there were 3 observations ofthe counterpart with colour values (B-V) between -0.16 to -0.29 (shown with the orangecolour in the figure). It can be seen that only one of these observations intersects withthe track for a 25M� donor in a binary system with a 20M� black hole. The inter-section is in the post main sequence (MS) phase of the star. Another observation ofthe counterpart also intersects with the track for a 50M� donor star (post MS) in a bi-nary system with a 10M� black hole. The third observation is in between the other twoand appears to be fully consistent with a donor mass in the interval 30-50M� (post-MS).

For the source Holmberg IX X-1 there are 2 (shown in green colour with an inversetriangle) observations of the counterpart. One was taken from Tao et al. (2011) andthe other was taken from Grise et al. (2011). The photometric data of the counterparttaken from Tao et al. (2011) is too blue and does not intersect with any of the tracks.The photometric data taken from Grise et al. (2011) intersects with the tracks for30-50M� donor stars. The 2 observations of the counterpart for the source IC 342 X-1(shown in purple) do not intersect with any other tracks either.

2 observations of the optical counterpart of the source M101 ULX-1 (light blue withan empty circle) are consistent with the evolutionary track for a 50M� post-MS donorstar in a binary system with a 10M� black hole. The other observed value of thecounterpart of M101 ULX-1 does not intersect with any of the tracks. The counterpartobservations for the source NGC 6946 ULX-1 (shown in pink colour) also do not inter-sect with any of the tracks.

The only 1 observation of the optical counterpart of the source NGC 5408 X-1 (darkgreen) is consistent with the evolutionary track for a 50M� post-MS donor star in abinary system with a 10M� black hole. The average value of the B-V colour index andV band magnitude for the observations of the counterpart of NGC 1313 X-2 (shown inmaroon) is consistent with the track of a 20M� (post-MS) donor star. A summary ofthese results is presented in chapter 6.

60



Figure 26: Colour-magnitude diagram showing the evolutionary tracks for a ULX binary system witha black hole of 100M� and the position of the counterparts of Holmberg II X-1, Holmberg IX X-1,IC 342 X-1, M101 ULX-1, NGC 1313 X-2, NGC 5408 X-1 and NGC 6946 ULX-1. These were thesources for which the value of nebular extinction was available. The tracks are plotted for 8M�, 10M�,12M�, 15M�, 20M�, 25M�, 30M� and 50M�. The effects of X-ray irradiation are taken into accountfor each track. For the position of the counterparts the error in the values of the absolute V bandmagnitude and colour (B-V) is represented by the error bars.

61


In Figure 26, it is now possible to see which of the tracks intersect with the positionof the optical counterparts of ULX binary systems with a black hole of 100M� for whichthe value of nebular extinction is known.

For the source Holmberg II X-1 there were 3 observations of the counterpart withcolour values (B-V) between -0.16 to -0.29 (shown with the orange colour in the figure).It can be seen that one of the observations of the counterpart is consistent with theevolution track for 30M� donor stars (post-MS). While the other two observations ofthe counterpart are consistent with the evolutionary track of a 50M� MS donor star.For the source Holmberg IX X-I, the photometric data of the counterpart taken fromTao et al. (2011) does not intersect with any of the tracks. The photometric data takenfrom Grise et al. (2011) intersects with the tracks for a 50M� donor star.

The 2 observations of the counterpart for the source IC 342 X-1 (shown in purple)are consistent with the evolutionary track for a 8M� or 10M� (post-MS) donor star.

One observation of the optical counterpart of the source M101 ULX-1 is consistentand another almost consistent with the evolutionary track of a 50M� MS donor star.The third observation of the counterpart (B-V=-0.11) is consistent with the evolution-ary track for a 20-30M� post-MS donor star. The counterpart observations for thesource NGC 5408 X-1 is close to intersecting the track for a 50M� MS donor star.One of the observations for the counterpart of NGC 6946 ULX-1 (shown in pink) isconsistent with a 50M� post-MS donor star. The other observation for the counterpartis too blue to intersect with any of the evolutionary tracks but may be consistent witha donor slightly more massive than 50M�.

The average value for the photometric data of the observations of the optical counter-part of the source NGC 1313 X2 (shown in maroon) is consistent with the evolutionarytrack for a 20M� donor star which is either in MS or in the terminal-age MS phase. Asummary of these results is presented in chapter 6.

62

5.2 Sources with Galactic Extinction 5.0 RESULTS

5.2 Sources with Galactic Extinction


Figure 27: Colour-magnitude diagram showing the evolutionary tracks for a ULX binary system witha black hole of 20M� and the position of the counterparts of M81 ULS1, M81 X-6, M83 IXO 82, NGC2403 X-1, NGC 4559 X-7 and NGC 5204 X-1. These were the sources for which the value of Galacticextinction was available. The tracks are plotted for 8M�, 10M�, 12M�, 15M�, 20M� and 25M�donor stars. The tracks for donor stars of mass 30M� and 50M� in a binary system with a 10M�black hole have also been added to this figure. The effects of X-ray irradiation are taken into accountfor each track. For the position of the counterparts the error in the values of the absolute V bandmagnitude and colour (B-V) is represented by the error bars.

63


From the colour-magnitude diagram in Figure 27, it is possible to see which sourceswith available data for the Galactic extinction are consistent with the the plotted evo-lutionary tracks for the donor masses. For the 2 observations of the counterpart forthe source M81 ULS1 (shown in orange), it can be seen that none of the evolutionarytracks intersect them. The tracks for 8M� to 15M� MS or post-MS donor stars in abinary system with a 20M� black hole are consistent with the 2 observations of theoptical counterpart of the source M81 X-6 (shown in green).

The observation of the optical counterpart for the source M83 IXO 82 (shown inpurple) does not intersect with any of the evolutionary tracks. The optical counterpartfor the source NGC 2403 X-1 (shown in blue) also does not intersect any of the evolu-tionary tracks. However, the track for 8M� donor star in a binary system with a 20M�does come very close to intersecting the counterpart. The observations of the opticalcounterpart for NGC 4559 X-7 do not intersect any of the evolutionary tracks either.

One of the observations of the optical counterparts for the source NGC 5204 X-1(B-V = -0.20) (shown in light green) is consistent with both the evolutionary track fora 25M� post-MS donor star in a binary system with a 20M� black hole and 30M�post-MS donor star in a binary system with a 10M� black hole. Another observation ofthe counterpart (B-V = -0.23) is also consistent with the evolutionary track for 30M�post-MS donor star in a binary system with a 10M� black hole. A third observation isalmost consistent with the track of a 10 Msun black hole accreting from a 50M� MSdonor. These results are summarized and discussed in chapter 6.

64



Figure 28: Colour-magnitude diagram showing the evolutionary tracks for a ULX binary system witha black hole of 100M� and the position of the counterparts of M81 ULS1, M81 X-6, M83 IXO 82, NGC2403 X-1, NGC 4559 X-7 and NGC 5204 X-1. These were the sources for which the value of Galacticextinction was available. The tracks are plotted for 8M�, 10M�, 12M�, 15M�, 20M�, 25M�, 30M�and 50M� donor stars. The effects of X-ray irradiation are taken into account for each track. Forthe position of the counterparts the error in the values of the absolute V band magnitude and colour(B-V) is represented by the error bars.

65


From the colour-magnitude diagram in Figure 28, it is possible to see which sourceswith available data for the Galactic extinction are consistent with the the plotted evo-lutionary tracks for various donor masses in a ULX binary sytem with a 100M� blackhole. The 2 observations of the counterpart for the source M81 ULS1 (shown in orange)are consistent with the evolutionary tracks for 8-10M� and 12M� post-MS donor stars.The observations of the optical counterpart of the source M81 X-6 (shown in green) areconsistent with the evolutionary tracks for 8M� to 15M� donor stars (both in MS andpost-MS phase).

The observation of the optical counterpart for the source M83 IXO 82 (shown inpurple) does not intersect with any of the evolutionary tracks. The optical counterpartfor the source NGC 2403 X-1 also does not intersect any of the evolutionary tracks.However, the track for 8M� donor star does come very close to intersecting the coun-terpart.

The two observations of the optical counterpart for NGC 4559 X-7 (shown in maroon)are consistent with the evolutionary tracks for a 30M� and 50M� post-MS donor star.

One of the observations of the optical counterparts for the source NGC 5204 X-1 (B-V = -0.20) (shown in light green) comes close to being consistent with the evolutionarytrack for a 50M� MS donor star . The other 2 observations of the counterpart areconsistent with the evolutionary track for 30M� MS phase donor star. These resultsare summarized and discussed in chapter 6.

66

5.3 Modified Albedo Parameter 5.0 RESULTS

5.3 Modified Albedo Parameter

5.3.1 Results for M101 ULX-1

Figure 29: Colour-magnitude diagram showing the evolutionary track for a ULX binary system (witha donor star mass of 20M� and a black hole of 20M�) and the positions of the observations of thecounterpart of M101 ULX-1. In the calculation of this track, the albedo parameter for the computationof the track was changed from 0.9 to 0.7. The effects of X-ray irradiation are taken into account. Forthe position of the counterparts the error in the values of the absolute V band magnitude and colour(B-V) is represented by the error bars.

67


In the plot in Figure 30, the CMD with the evolutionary track of a 20M� donorstar in a binary system with a black hole of 20M� is given along with the position ofthe observations of the optical counterpart for the source M101 ULX-1. This track wascomputed with the modified albedo parameter (fa = 0.7). The evolutionary track forthe 20M� donor star (post-MS phase) does come very close to the observation of theoptical counterpart (at B-V=-0.11).

These models were run to show the uncertainties related to the actual choice of thealbedo. From the work of van Paradijs and collaborators (e.g. de Jong, van Paradijs &Augusteijn 1996), for a disk irradiated from grazing incident X-rays values of fa in therange 0.85-0.95 are reasonable.

68


5.3.2 Results for M83 IXO 82

Figure 30: Colour-magnitude diagram showing two evolutionary tracks(one for a ULX binary systemwith a donor star mass of 8M� and a black hole of 20M� and the other for a donor star mass of 8M�and a black hole of 100M�) and the position of the counterpart of M83 IXO 82. In the calculationof this track, the albedo parameter for the computation of the track was changed from 0.9 to 1 whichcorresponds to complete reflection (no absorbtion) of the incident X-rays. For the position of thecounterparts the error in the values of the absolute V band magnitude and colour (B-V) is representedby the error bars.

69


In the plot in Figure 30, the CMD with the evolutionary tracks for a 8M� donorstar in a binary system with a black hole of 20M� and 100M� are given. The positionof the observation of the optical counterpart for the source M83 IXO 82 is also shown.It was previously observed in Figures 27 and 28 that the evolutionary tracks for 8M�did not intersect the position of the optical counterpart of M83 IXO 82, although itwas not far from it. In this plot, the tracks were computed with the modified albedoparameter (fa = 1). This value of the albedo parameter corresponds to complete re-flection (no absorbtion) of the incident X-rays. The modified tracks are even closer tothe counterpart. However, a clear intersection is still not observed.

The tracks for these models were computed to show the strength of X-ray irradiation.They may be relevant in a scenario in which X-ray emission is beamed and does nothit the accretion disk and donor surfaces.

70

6.0 DISCUSSION OF THE RESULTS

6.0 Discussion of the Results

In the previous section, the colour-magnitude diagrams with the optical photometryof the ULX counterparts were plotted with the evolutionary tracks for a system withdonor stars of varying masses accreting onto both a stellar mass black hole of 10-20M�and massive stellar black hole of 100M�. The sources were split into two groups de-pending on whether nebular extinction data was available for them or not and it canbe seen from Table 16 that the B-V colour index has a much higher value for sourcesin which nebular extinction was not available. The results for each of the sources arediscussed in this section.

The constraints on the donor mass for sources with nebular extinction in a binarysystem with a 20M� black hole (tracks for donor stars with 30M� and 50M� arecomputed for a 10M� black hole and are indicated by an *) are summarized in Table17.

71


Table 17: The possible mass constraints on the donor star for each observation of the ULX counterpartsfor sources with nebular extinction is given in this table. The mass of the black hole is taken to be20M� (10M� for values with *). MS and post-MS indicate whether the donor star is in the mainsequence phase or post-main sequence phase. TAMS indicates that the star is in the terminal-ageMS phase. No intersection means that no constraints can be placed on the observation based on thecomputed data.

ULX Date B-V Mv Constraints

Holmberg II X-1 03/10/2007 −0.24 ± 0.02 −5.93 ± 0.01 30-50M� donor star (post-MS)*05/10/2007 −0.18 ± 0.02 −5.94 ± 0.01 25M� donor star (post-MS)09/10/2007 −0.27 ± 0.02 −5.94 ± 0.01 50M� donor star (post-MS)*

Holmberg IX X-1 07/02/2004 −0.42± 0.04 −5.88± 0.03 No Intersections07/02/2004 −0.25±0.05 −6.00±0.02 30−50M� donor star (post-MS)

IC 342 X-1 02/09/2005 0.37±0.15 −5.94±0.10 No Intersections18/12/2005 0.3±0.13 −5.95±0.09 No Intersections

M101 ULX-1 22/03/1994 −0.11±0.08 −6.39±0.03 No Intersections08/04/1994 −0.28±0.08 −6.15±0.03 50M� donor star (post-MS)*15/11/2002 −0.31±0.04 −6.00±0.03 50M� donor star (post-MS)*

NGC 1313 X-221/05/2008 to09/06/2008

−0.20±0.02 −4.59±0.01 20M� donor star (post-MS)

NGC 5408 X-1 04/04/2009 −0.28±0.04 −6.27±0.02 50M� donor star (post-MS)*

NGC 6946 ULX-1 27/01/1996 0.07±0.23 7.26±0.12 30M� donor star (post-MS)*08/06/2001 0.42±0.18 7.27±0.12 No Intersections

The constraints on the donor mass for sources with nebular extinction in a binarysystem with a 100M� black hole are summarized in Table 18.

72


Table 18: The possible mass constraints on the donor star for each observation of the ULX counterpartsfor sources with nebular extinction is given in this table. The mass of the black hole is taken to be100M�. MS and post-MS indicate whether the donor star is in the main sequence phase or post-mainsequence phase. TAMS indicates that the star is in the terminal-age MS phase. No intersection meansthat no constraints can be placed on the observation based on the computed data. No Intersections*indicates that while no intersection was seen on the figure, the counterpart could be consistent withthe track of a donor star slightly more massive than 50M�.


Holmberg II X-1 03/10/2007 −0.24 ± 0.02 −5.93 ± 0.01 50M� donor star (MS)05/10/2007 −0.18 ± 0.02 −5.94 ± 0.01 30M� donor star (post-MS)09/10/2007 −0.27 ± 0.02 −5.94 ± 0.01 50M� donor star (MS)

Holmberg IX X-1 07/02/2004 −0.42± 0.04 −5.88± 0.03 No Intersections07/02/2004 −0.25±0.05 −6.00±0.02 50M� donor star (MS)

IC 342 X-1 02/09/2005 0.37±0.15 −5.94±0.10 8-10M� donor star (post-MS)18/12/2005 0.3±0.13 −5.95±0.09 8-10M� donor star (post-MS)

M101 ULX-1 22/03/1994 −0.11±0.08 −6.39±0.03 30M� donor star (post-MS)08/04/1994 −0.28±0.08 −6.15±0.03 50M� donor star (MS)15/11/2002 −0.31±0.04 −6.00±0.03 ∼50M� donor star (MS)

NGC 1313 X-221/05/2008 to09/06/2008

−0.20±0.02 −4.59±0.01 20M� donor star (MS or TAMS)

NGC 5408 X-1 04/04/2009 −0.28±0.04 −6.27±0.02 ∼50M� donor star (MS)

NGC 6946 ULX-1 27/01/1996 0.07±0.23 7.26±0.12 30M� or 50M� donor star(post-MS)

08/06/2001 0.42±0.18 7.27±0.12 No Intersections*

The constraints on the donor mass for sources with Galactic extinction in a binarysystem with a 20M� black hole (tracks for donor stars of 30M� and 50M� are computedfor a 10M� black hole and are indicated by an *) are summarized in Table 19.

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Table 19: The possible mass constraints on the donor star for each observation of the ULX counterpartsfor sources with Galactic extinction is given in this table. The mass of the black hole is taken to be20M� (10M� for values with *). MS and post-MS indicate whether the donor star is in the mainsequence phase or post-main sequence phase. No intersection means that no constraints can be placedon the observation based on the computed data.


M81 ULS1 21/03/2006 0.11±0.04 −6.26±0.04 No Intersections27/03/2006 0.22±0.04 −5.99±0.04 No Intersections

M81 X-6 31/01/1995 0.06±0.18 −3.91±0.06 8-12M� donor star (MS or post-MS)04/06/2001 −0.13±0.07 −4.01±0.06 10-15M� donor star (MS or post-MS)

M83 IXO 82 25/02/2006 0.26±0.13 −3.11±0.09 No Intersections

NGC 2403 X-1 17/10/2005 0.07±0.08 −2.90±0.06 ∼8M� donor star (MS)

NGC 4559 X-7 25/05/2001 −0.17±0.03 −6.98±0.02 No Intersections08/03/2005 −0.12±0.04 −7.10±0.03 No Intersections

NGC 5204 X-1 08/08/2008 −0.35±0.03 −5.57±0.02 ∼50M� donor star (MS)10/08/2008 −0.23±0.03 −5.62±0.02 30M�* donor star (post-MS)13/08/2008 −0.20±0.03 −5.69±0.02 25M�-30M�* donor star (post-MS)

The constraints on the donor mass for sources with Galactic extinction in a binarysystem with a 100M� black hole are summarized in Table 20.

74


Table 20: The possible mass constraints on the donor star for each observation of the ULX counterpartsfor sources with Galactic extinction is given in this table. The mass of the black hole is taken to be100M�. MS and post-MS indicate whether the donor star is in the main sequence phase or post-mainsequence phase. No intersection means that no constraints can be placed on the observation based onthe computed data.


M81 ULS1 21/03/2006 0.11±0.04 −6.26±0.04 8-10M� donor star (post-MS)27/03/2006 0.22±0.04 −5.99±0.04 12M� donor star (post-MS)

M81 X-6 31/01/1995 0.06±0.18 −3.91±0.06 8-12M� donor star (MS or post-MS)04/06/2001 −0.13±0.07 −4.01±0.06 10-15M� donor star (MS or post-MS)

M83 IXO 82 25/02/2006 0.26±0.13 −3.11±0.09 No Intersections

NGC 2403 X-1 17/10/2005 0.07±0.08 −2.90±0.06 ∼8M� donor star (MS)

NGC 4559 X-7 25/05/2001 −0.17±0.03 −6.98±0.02 50M� donor star (post-MS)08/03/2005 −0.12±0.04 −7.10±0.03 30M� donor star (post-MS)

NGC 5204 X-1 08/08/2008 −0.35±0.03 −5.57±0.02 ∼50M� donor star (MS)10/08/2008 −0.23±0.03 −5.62±0.02 30M� donor star (MS)13/08/2008 −0.20±0.03 −5.69±0.02 30M� donor star (MS)

Holmberg II X-1

For the source Holmberg II X-1 it can be stated that if the black hole mass in theULX system was around 20M� then a companion donor star would have to be in apost-main sequence phase and have a mass between 25M� to 50M� (assuming a 10M�black hole) to account for the position of the optical counterpart. In the case of ac-cretion onto a 100M� black hole, a 30M� (post-MS) or 50M� (MS) star would beneeded in order for the evolutionary tracks to pass through the available counterpartdata. Thanks to the more revised and more accurate photometry reported by Tao etal. (2011), we can improve upon the estimates reported by Patruno & Zampieri (2008).They found that if the accretor in Holmberg II X-1 is a stellar mass black hole then thedonor star has to be a post-MS star between 15-30M� or a MS of ≈ 50M�. For a largeaccretor of 100M�, Patruno & Zampieri (2008) write that even a 10M� in post-MSphase could account for the observed counterparts. In this study, we have shown thatif the black hole in the ULX is 20M� then the mass for a donor in the post-MS phaseis between 25M� to ∼ 50M�. If the black hole in the ULX is 100M� then still a highmass companion star (at least 30M� to 50M�) is needed to account for the observedphotometric properties of the counterpart.

75


Holmberg IX X-1

For the photometric data of the optical counterpart of Holmberg IX X-1 reported byTao et al. (2011), it can be stated that if the black hole mass in the ULX system wasaround 20M� then even a very massive companion could not account for the positionof the counterpart. Even in the case of accretion onto a 100M� black hole there isno evolutionary track which passes through the source. The colour of the star is tooblue for any of the tracks to account for its photometric properties. However, for thephotometric values of the counterpart obtained by Grise et al. (2011), the position ofthe star on the CM diagram is consistent with the tracks for a 30-50M� (post-MS)donor star accreting onto a 10M�. Interestingly, the counterpart is also consistent witha 50M� MS donor star accreting onto a 100M� black hole. These results indicate thatHolmberg IX X-1 harbours a very massive donor star.

IC 342 X-1

For the source IC 342 X-1 it can be seen that if the black hole mass in the ULX sys-tem was around 20M� then none of the tracks intersect with the available photometricdata of the counterpart. In the case of accretion onto a 100M� black hole, an 8M� to10M� donor star (in the post-MS phase) would be required in order to account for theavailable counterpart data. This source requires that the mass of the black hole in theULX be at least around 100M�. In a recent study by Cseh et al.(2012), an upper limitto the mass of the black hole in this ULX has been estimated (by doing a multibandstudy of the nebula around it) to be ≈ 1000M�.

M101 ULX-1

For the source M101 ULX-1, the photometric data of the counterpart can be ac-counted for if the black hole mass in the ULX is a stellar mass black hole of 10M� andthe donor star has a mass between 20M� (with smaller X-ray albedo) and 50M� (inthe post-MS phase). Also, in the case of accretion onto a 100M� black hole, a 30M�(post-MS phase) or 50M� (MS phase) donor star would be required in order to accountfor the high magnitude of the counterpart data. Kuntz et al. (2005) have suggestedthat M101 ULX-1 is a high mass X-ray binary. The results of this study for this sourcealso point towards a high mass companion star (regardless of whether the black hole is10M� or 100M�, a 20M� to 50 M� donor star is required to explain the photometricdata of the counterpart).

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NGC 1313 X-2

If the average values of the colour index and magnitude are taken for all the availablequasi-simultaneous observations then an intersection is found with the track of a 20M�donor star accreting on to a 20M� or 100M� black hole. The constrained value of thedonor mass for this source is almost consistent with the value obtained by Patruno &Zampieri (2010). Their constrained value for the donor mass is between 12 to 15M�. Inthis study we rule out the possibility of a 12M� donor star. The discrepancy betweenthe two results is explained by the revised colour values for the optical counterpart thatwere used in this study (we took the average colour of the 2008 HST observations, whilePatruno & Zampieri (2010) used photometric data from the 2003 HST observation).

As it was discussed in subsection 4.1.8, the estimated period of the source is 6 days(Liu et al. 2009, 2012; Zampieri et al. 2012). The orbital period corresponding tothe points of intersection can be found by checking the data files generated by thestellar evolution code. For a 20M� donor star accreting onto a 20M� black hole, thepoint of intersection of the average value (for the colour index and absolute magnitude)corresponds to an orbital period of ∼ 6.7 days. Assuming that the estimated 6 dayperiod is correct, this value indicates that a 20M� donor star in a binary system witha 20M� black hole is a likely scenario. A scenario involving a 20M� (MS) donor staraccreting onto a 100M� black hole can be ruled out as the points of intersection ofthe track and the average value corresponds to an orbital period of ∼ 1.8 days . Thescenario involving a 20M� (TAMS) donor star accreting onto a 100M� black is verylikely as the points of intersections correspond to a orbital periods of ∼ 5.85 days and∼5.86-6.3 days respectively. The counterparts intersect with the track just when thedonor star is entering the post-MS phase. This result is consistent with the estimatedoptical periodicity (Liu et al. 2009, 2012; Zampieri et al. 2012).

NGC 5408 X-1

For the source NGC 5408 X-1, the photometric data for the counterpart can beaccounted for by a binary system in which the donor mass is ∼ 50M� (post-MS fora 10 M� black hole, MS for a black hole of 100M�). This source is one of the fewULXs to show strong variability on short timescales (Strohmayer et al. 2007). Thevariability along with the spectral properties has been used to estimate the black holemass. Values in excess of 100M�) (e.g. Casella et al. 2008, Zhou et al. 2010) andsmaller than this value (Middleton et al. 2011) have been suggested.

77


NGC 6946 ULX-1

For the source NGC 6946 ULX-1, the 2 observations of the optical counterpart havesignificantly different values for the colour. One observation gives the value of B-Vto be -0.07 and the other is -0.42. For the observation with B-V=-0.42 there are nointersections with the evolution tracks (despite large error bars in the colour). However,considering the large uncertainty in the colour, the position of the counterpart may beconsistent with the track of a donor slightly more massive than 50M�, if the BH massis 100M� (for 10M� the counterpart is too far from the nearest computed track to drawany conclusion). The results also indicate that a high donor mass is needed in order toaccount for the photometric data of the optical counterpart.

Now the results for the sources for which only the Galactic extinction value wasavailable will be discussed.

M81 ULS1

The photometric data for the 2 observations of the optical counterparts for the M81ULS1 do not intersect with any of the evolutionary tracks for a 10-20M� black hole.They have significantly different values for the colour. However, the photometric datacan be accounted for by the evolutionary tracks of 8 through 12M� (post-MS) donorstars in a binary system with a 100M� black hole. This source requires a large valuefor the mass of the black hole in order to explain the photometric data. As this is anultraluminous supersoft source, this study also disfavours the interpretation that thecompact object in this system could be a white dwarf.

M81 X-6

For the source M81 X-6, the two observations of the optical counterpart intersectwith the evolutionary tracks for 8 through 15M� (MS or post-MS) donor stars in abinary system with a 20M� or a 100M� black hole. The consistency of the results forM81 X-6 for both black hole masses makes it difficult to put definitive constraints onthe mass of the system. A better result could be obtained for the source if the value ofthe nebular extinction was known.

78


M83 IXO 82

The photometric data of the optical counterpart for M83 IXO 82 did not intersectwith any of the evolutionary tracks for the various donor masses in binary system witha 20M� or 100M� black hole. For this source, the albedo parameter was modifiedfrom 0.9 to 1, to see if the photometric data of the counterpart could be accountedfor. The tracks in Figure 30 show the result of this modified parameter. The trackfor a 8M� donor star (in post-MS phase) with a 20M� black hole came very close tointersecting the position of the counterpart. An albedo equal to unit corresponds tocomplete reflection (no absorption) of the incident X-rays. This suggests that switch-ing off X-ray irradiation is favoured for M83 IXO 82. This is possible in a scenario inwhich X-ray emission is beamed and does not hit the accretion disk and donor surfaces.This result appears then to favour some degree of beaming in the emission of this source.

NGC 2403 X-1

For the source NGC 2403 X-1, the observation of the optical counterpart did notintersect any of the tracks for the various donor star masses for either a 20M� or 100M�black hole. However, in both cases the position of the counterpart is very close to thetrack of a 8M� donor in MS.

NGC 4559 X-7

The 2 observations of the optical counterpart for NGC 4559 X-7 had no intersectionswith the evolutionary tracks for various donor masses for a 20M� black hole. However,the photometric data of the counterpart could be accounted for by evolutionary tracksof 30M� and 50M� (post MS phase) donor stars in a binary system with a 100M�.The photometric data of the counterpart of NGC 4559 X-7 rule out the possibility ofhaving a low mass donor star. Partuno & Zampieri (2008) had shown that the thenavailable photometric data for the same counterpart of NGC 4559-7 considered here(object 1 in their paper) could be explained by a ∼50M� donor star accreting onto a100M� black hole. Our results are fully consistent with their findings.

NGC 5204 X-1

There is photometric data available for 3 observations of the optical counterpart ofNGC 5204 X-1. None of the evolutionary tracks for the various donor masses intersectwith the counterpart observation for which the colour index B-V=-0.35. However, suchobservation falls very close to the track of a 50M� donor in MS for both a 10 and100M� black hole. The position of the 2 other observations of the counterpart can

79


be accounted for by a 25M� donor star (post-MS phase) and a 20M� black hole. Thepositions can also be accounted for by a 30 M� donor star (post-MS phase) and a 10M�black hole. For a black hole of a 100M�, the photometric data for the two observationsis accounted for by a 30M� donor star (post-MS phase). These results point towardsa massive donor star in the ULX NGC 5204 X-1. Feng & Kaaret (2009) have pointedout that the luminosity, disk size, and temperature of NGC 5204 X-1 suggest that itharbours a compact object more massive than a stellar mass black hole. The results ofthis study are consistent with this finding as the observations are consistent also withthe tracks of a 100M� black hole.

80

7.0 CONCLUSIONS

7.0 Conclusions

ULXs are posited to be accreting binary systems with a donor star and a black hole. Inthis study, we tried to determine constraints for the mass of the black hole for 13 differentsources (Tao et al. 2011) by modelling their optical emission for various scenariosinvolving the donor star mass being between 8M� to 50M� and taking stellar throughmassive black holes (20M� and 100M�). The modelled emission properties were thenplotted onto a colour-magnitude diagram with the observed optical counterpart datafor each source. The position of the counterpart on the colour-magnitude diagram wasthen compared with the evolution track for the ULX. If the evolutionary track for aULX passes through available data for the counterpart then it becomes possible toconstrain the mass of the black hole and the donor in the ULX. The main conclusionsfrom the results of this study are:

• A consistent group of sources has blue colours (Holmberg II X-1, M 101 ULX-1, NGC 5408 X-1, NGC 6946 ULX-1, NGC 4559 X-7, NGC 5204 X-1) and isconsistent with a massive black hole (100M�) and donors of ∼ 25 − 50M�, inagreement with previous findings. The majority of these sources (exceptions areNGC 4559 X-7 and NGC 6946 X-1) are also consistent with the tracks of donorsin the same mass range accreting onto a stellar mass black hole(10-20M�). InNGC 5408 X-1 and NGC 6946 ULX-1 the donor may be slightly more massivethan 50M�.

• A smaller group of sources has redder colours (IC 342 X-1, M 81 ULS1, M81X-6, NGC 2403 X-1) and is consistent with a massive black hole and donors of∼ 8− 15M�. M 81 X-6 and NGC 2403 X-1 are also consistent with the tracks ofdonors in the same mass range accreting onto a stellar-mass black hole.

• When the agreement is with a post-MS phase, if there is a nebula around theULX, the source probably underwent case AB mass transfer with a first episodeoccurring during MS (see Patruno & Zampieri 2008, 2010). The first contact phaseduring MS is sufficiently long to inject the required energy in the bubble nebula.

• Using the photometry of Tao et al. (2011), Holmberg IX X-1 appears to be tooblue to be consistent with any of the computed tracks. We suggest that, becauseof the significant variability of the nebular extinction, the latter may have beenslightly overestimated by Tao et al. (2011). On the other hand, photometry byGrise et al. (2011) indicates that Holmberg IX X-1 is consistent with a ∼ 30-50M�donor star.

81

7.0 CONCLUSIONS

• In M83 IXO 82, either there is no irradiation with beamed emission and accretiononto a stellar mass black hole or the donor is less massive than 8M�.

• NGC 1313 X-2 is consistent with the evolutionary track for a 20M� donor starin a binary system with either a stellar-mass black hole or a massive black hole.Furthermore, the value of the orbital period obtained from these results (in thecase of accretion onto a 100M� black hole) was between ∼ 5.85 to 6.3 days. Thisvalue is in agreement with the ∼ 6 days orbital period estimated from the opticallight curve of NGC 1313 X-2 (Zampieri et al. 2012).

The sample of observations for ULX counterparts taken in this study showed thatthe majority of sources had B-V colour index value between -0.30 and -0.10. This showsthat there were more blue (hot) counterparts than red (cool) counterparts. The resultsshow that most of the blue counterparts are very massive MS stars. On the otherhand, red counterparts are less massive and are usually in the post-MS phase. All thecounterparts can essentially be accounted for by evolutionary tracks with a massiveblack hole. The results also show that the tracks with a stellar mass black hole cannotaccount for all the ULXs studied in this thesis. However, results for the source M83IXO 82 suggest that there could be some degree of beaming. In such a scenario, astellar-mass black hole could account for the high X-ray luminosities of this ULX.

82

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