New Radiation of Neutron Stars - Key for their Equation of State · 2009. 7. 15. · Radiation of Neutron Stars - Key for their Equation of State V. Suleimanov1,3 in collaboration

Radiation of Neutron Stars -Key for their

Equation of State

V. Suleimanov1,3 in collaboration with K. Werner1, T. Rauch1, and J. Poutanen2

1- Kepler Center for Astro and Particle Physics, IAAT, Tübingen, Germany2 -University of Oulu, Finland3 - Kazan State University, Russia

Kepler Kolloquium 9 May 2008

Neutron stars – main properties and short history

M ≈ 1.4 MSun R ≈ 10 km Eg ≈ GM2 / R ~ 5 1053 erg ρ ≈ 7 1014 g/ccPressure of degenerate neutrons

Crab nebula (Chandra)

First idea – L. Landau (1932)

Neutron stars arise due toSupernova outburstsW. Baade, F. Zwicky (1934)

Discovery of Pulsars - A. Hewish, Jocelyn Bell (1968)

ESN ~ 1053 erg ~ Eg (NS)

Supernova (type II) – finale of a massive star life

Massive stars evolve along supergiant branch up to SNII explosion

Effective temperature

Lum

inos

ity

Hertzsprung – Russel Diagram

Supernova (type II) – finale of a massive star life

Massive star structure before explosion SNII explosion calculations (T. Janka, MPA)

Reason – gravitational collapse of Fe core due toPhotodisintegration Neutronizationand

nFe 41356 +=+ αγ enep ν+→+−

White

dwarf

s

Neu

tron

star

s

Brown dwarfs,Giant planets

Maximum-massneutronstar

Minimum-massneutron star

Maximum-masswhite dwarf

km 250~ 1.0~ Sun

RMM

km 129~ )5.25.1(~ Sun

−−

RMM

Stellar remnants – White Dwarfs and Neutron Stars

Neutron star structure

Main problem – inner core Equation of State (EoS)

Prohibited byGeneralRelativity

Universal low-masscurveSpecial family of

low-mass strange stars

Zoo of NS inner core EoS

Solution – M and R from observations!

Many faces of NS

Radio Pulsars

NSs in X-ray Binaries

Isolated NSs

How can we find the EOS in NSs ?

1. Find the most massive NSs

Mass of NSs – from binaries



2. Find the limits on the M/R relation

Influence of GR effects on the NS observed properties

Gravitational redshift 2/12/1 )/1(,)/1(11 RRTT

RRz Seffobs

S−=

−=+

22/122/1 2,

)/1(,)/1(

cGMR

RRRGM

gRRLL SS

Sobs =−=−=

Light bending

2/1)/1( RRRR

Sobs −

=



2. Find the limits on the M/R relationGravitational redshift 1)/1(

12/1 −−

=∆

=RR

zSλ

λ

8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

z = const

causali

ty

M /

M

R (km)




12/1 −−

=RR

zS

Observed color temperature of objects close to the Eddington limit

Eddington limitc

TXRRR

GMgg EddS

radgrav

4

2/12 )1(2.0)/1(σ+=

−⇒=

Problems: chemical composition (X– mass fraction of hydrogen)- hardness factor9.15.1, ÷≈= cEddcc fTfT

8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

Tobs = const ( L=LEdd )

z = const

causali

ty

M /

M

R (km)




12/1 −−

=RR

zS


Eddington limitc

TXRRR

GMgg EddS

radgrav

4

2/12 )1(2.0)/1(σ+=

−⇒=

Problems: chemical composition (X– mass fraction of hydrogen)- hardness factor9.15.1, ÷≈= cEddcc fTfT

Observed size of isolated NSs2

24

dRTF obsobsobs σ=

Problems: distance dTeff from observed spectrum (chemical composition etc.)

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

Robs = const


z = const

causali

ty

M /

M

R (km)

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

Robs = const


z = const

causali

ty

M /

M

R (km)

In any case it is necessary to model emergent radiation spectra(spectral energy distribution)

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

Pmin

Robs = const


z = const

causali

ty

M /

M

R (km)

M /

M

R (km)

Other possibilities:minimum NS spin period (Kepler with GR corr.)

23

1092.0 −⎟

⎠⎞

⎜⎝⎛≥ ms

sunP

kmR

MM

From Lattimer & Prakash (2007)

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

10 150.0

0.5

1.0

1.5

2.0

2.5

3.0

Pmin

Robs = const


z = const

causali

ty

M /

M

R (km)

M /

M

R (km)

Other possibilities: NS oscillations during SGR bursts

From Lattimer & Prakash (2007)

METHOD - Stellar atmosphere modeling

Hydrostatic equilibrium

Radiation transfer

Energy conservation

Equation of state

Conservation of charges, number of particles

νσπρ νν

dkHc

gdz

dPe

gas )(41 ++−= ∫

ννν

ντ

ϑ SII −=∂∂cos

Parameters: ,)/1(

, 2/12 RRRGMgT

Seff −

= chemical composition

0)( =−∫ νννν dBJk

kTNP totgas =

It is necessary to model emergent radiation spectra (spectral energy distributions)

METHOD - Stellar atmosphere modelingIt is necessary to take into account ~ 25 most abundant chemical elements

and ~ 104 – 108 spectral lines → ~ 30 000 frequencies

Large computer codesMain results – a model atmosphere and a spectral energy distribution

Flux

erg

cm-2

s-1

Hz-

1 (Å

-1, k

eV-1

)

Frequency (wavelength, photon energy)Hz ( Å, keV )

X-ray Binaries

High Mass Low Mass

M2 >> MSunYoung systems (Pop. I)Accretion from wind

X-ray Pulsars

M2 < MSunOld systems (Pop. II)

Secondary overfilled of the Roche lobeAtoll- and Z-sources, Bursters,

Millisecond X-ray Pulsars

X-ray bursting neutron stars• X-ray bursting NSs – LMXBs with thermonuclear

explosions at the neutron star surface• Close to Eddington limit during the burst• Burst duration ~10 sec, time between bursts ~1 day

Figure from Pavlinsky et al (2001)

Absorption lines in the spectra of EXO 0748-676 during outburst ?Cottam et al. 2002, Cottam et. al 2008

Cottam et al. 2002

Tobs≈ 1.8 keV

Tobs ≤ 1.5 keV

Gravitational redshift

Grids of non-LTE NS model atmospheres (Teff from 1 to 20 MK, log g = 14.39) with various Fe abundances

(solar, 30%, 99% mass fractions) have been calculated.

10 20 30Wavelength, A

F λer

g cm

-2 s

ec-1

cm-1

Importance of Compton scattering

10 MK

1520

Identification of lines

Cottam et al. (2002)suggested that theyobserved this line

Why FeXXV lines so weak?

FeXXV FeXXIV

Line intensity depends on low energy level number density

~ 6.

7 ke

V

NFeXXV exp(-6.7 keV/1 keV)

Comparison with observations.

1. The lines have been wrongly identified. The Fe XXV lines are too weak to be observed. They have to be Fe XXIV lines. In this case z=0.24 instead of z = 0.35.

2. Predicted relative depth of the absorption lines (FeXXIV) are too small to be observed.

3. At the moment our knowledge about gravitationalredshift is ambiguous.

Conclusions for gravitational redshift

Absorption lines in the spectra of EXO 0748-676 during outburst ?Cottam et al. 2002, Cottam et. al 2008

Cottam et al. 2008 NO LINES !!!!

By the way ….

Bursters – luminosity near the Eddington limit(see Lewin et al. 1993, Galloway et al. 2007, …)

Problems – hardness factor fc, chemical composition…

Our Attempt

Boundary Layers between accretion disc and NS inLow Mass X-ray Binaries

(Suleimanov & Poutanen 2006)


Boundary layer (BL)• Region between an accretion disk and a neutron star• In BL fast rotating (with the Keplerian velocity) accretion disk matter

is decelerated to the neutron star rotation velocity.• Luminosity of the BL comparable to the accretion disk luminosity

ADNS

NSKBL LR

GMMVML ~21

2~

.2.=

Size of BL is smaller than the accretion disk size. Therefore, effective temperature of BL is larger than the effective temperature of accretiondisk.

Hard black body component in the soft state of LMXB –a boundary layer spectrum ?

Figures taken from Gilfanov, Revnivtsev and Molkov (2003). They have shown that the shape of boundary layer spectra is independent of luminosity.

BL spectra are close to Planck spectrum with a color temperature 2.4 ± 0.1 keV

Spectra of Boundary Layers

BL as a spreading layer (SL)Picture suggested byInogamov & Sunyaev (1999), below IS99

Matter has a significant latitudevelocity component, spreading abovethe neutron star surface and deceleratingdue to friction at the neutron star surface(wind above the sea).

Figures from Inogamov and Sunyaev (1999)

Theory of Boundary Layers

Numerical simulations confirm this picture

Kley, 1989 Fisker et al. 2005

Scheme of the spreading layer spectrum calculation1. For each ring the model along height and emergent spectrum2. SL are divided into N rings

are calculated3. Spectra of all rings are summed with all relativistic corrections

ji

iiijiijEijj

NSE IRL ϕθθαθαδηπ ∆∆= ∑∑ coscos),(cos4 ''332 '

Diluted blackbody spectrum

)(14 effcc

TfBf

F νν =

Bν – Planck functionfc – color correction (hardness factor)Tc= fcTeff - color temperaturefc ~(1.3 – 1.9) mainly depends on L / LEdd

If Compton scattering is taken into account, hard photons heat electrons atthe surface up to T>Teff. This results in an emergent spectrum close to that of a diluted black body.

Compton scattering is very important!

Spectra of local spreading layer models from previous figure

Comparison of the observed spectra of the BLs and the model spectra ofthe SL. Black circles – GX 340+0 in the normal branch, green circles – 5 Zand atoll sources in horizontal branch (Suleimanov & Poutanen 2006).

Allowed areas (shaded) for the NS masses and radii, which can have SLs with color temperatures 2.4 +/- 0.1 keV. Various theoretical mass-radius relations forneutron and strange stars are shown for comparison. Red dashed curve corresponds to the NS with apparent radius 16.5 km (Suleimanov & Poutanen 2006).

• Integral spectra of the high luminosity spreading layers (LSL > 0.2 LEdd ) are close to diluted Planck spectra.

• Radiation spectra of the spreading layers on the surface of the neutron stars with stiff equations of state are compatible with the observed spectra of boundary layers in LMXBs.

Conclusions for Observed color temperature of Boundary Layers

Observed size of isolated NSs

2

24

dRTF obsobsobs σ= 2

2)()(

dRFF obstheorobs νν =or

Problems: I – distance da) X-ray transients during quiescence in globular clusters

with known distancesb) nearby isolated NSs - distances from astrometry (parallax)

II – theoretical spectra

model atmospheres (!)

)(νtheorF

Example

X7 (NS in 47 Tuc, Heinke et al 2006)

RNS ≈ 14.5 ± 1.7 kmat M = 1.4 MSun

They used pure hydrogen model atmospheres.

RNS ≈ 14.9 ± 1.5 kmat M = 1.4 MSun(Suleimanov & Poutanen 2006)

Isolated NSs have a strong (B ≥ 1012 G) magnetic field ?

• Soft Gamma Repeaters (SGR) • Compact objects in supernova

remnants (CCO) • Dim isolated neutron stars (DINS) • Anomalous X-ray Pulsars (AXP)

Why strong magnetic field ?

Coherent pulsation of the radiation

Change of period in accordance with magneto-dipole radiation (for isolated NS)

Proton cyclotron line in spectra ( ECp= 0.63 (B/1014 G) keV )

⋅P

Observational properties of dim isolated neutron stars(«Magnificent seven» = DINSs)

X-ray and optical flux not explained by a single blackbody spectrum

RX J1856.5-3754

D = 140 +/- 20 pcRobs> 17 km (Trümper et al. 2005)

Excellently fitted by blackbody in X-ray!

Two blackbody models -nonuniform temperature distribution ?

Thin plasma layer abovesolid surface?Hard radiation is very close to blackbody

Observational properties of dim isolated neutron stars

Absorption features in the spectra – proton cyclotron lines ?

1Е 1210-5226 (CCO in the supernova remnant) 0.7 and 1.4 keV

Proton cyclotron line and harmonic ?B from line doesn’t agree to B from Pdot

Blends of the spectral lines of the highly charged ions in the strongmagnetic field?

Problem:Modeling the magnetizedneutron star atmospheres

Opacity:( ) eOCe

eX EEE σσσσ ∝−

∝ ,22

Strong angular dependence

Radiation transfer in a plasma with a strong magnetic field

θ

X - modeO - mode

k

X - mode

O - mode

k

B

n,z

xy

0 20 40 60 8010-7

10-3

101

105

10-6

10-4

10-2

100

102

E ~ ECp

ES

FF

Opa

city

(cm

2 /g)

θ (degree)

E=1 keV

electron scattering (ES)

free-free absorption (FF)

X - mode

O - mode

Opa

city

(cm

2 /g)

Plasma in a strong magnetic field actslike quartz crystal: birefringence!

It is necessary to consider

TWO modes of radiation

Radiation transfer in a plasma with a strong magnetic field

( ) ( ) CeCpCeXffEE

EEEEk

Models of magnetized NS atmospheres

Magnetized model atmospheres:

• have two photospheres correspondingto fluxes in two modes

• radiation is formed in deeper layers in comparison with atmosphere without magnetic field

• flux in the X-mode is dominating

• radiation is strongly polarized

0.1 1 10

1019

1020

1021

10-4 10-2 100 102 104 10602468

10121416

10-4 10-2 100 102 104 10602468

10121416

HE (

erg

/ cm

2 / s

/ ke

V )

X - mode O - mode

B = 0 G

B = 5 1014 G

BB

Energy (keV)

Teff = 5 106 К

log g = 14.3pure H

column density (g/cm2 )

Т (1

06 К

)


Vacuum polarization suppresses the proton cyclotron line, if the resonance layers are close to X-mode photosphere ( B > 1014 G )

0.1 1 10

1019

1020

1021

vacuum polarization

Energy (keV)

H E

(erg

cm

-2 s

-1 k

eV-1 )

B = 0 G

no vacuum polarization

BB


Thin atmosphere above solid surface

From Ho et al. 2007

Used to explain the relation between optical and X-ray fluxes

10-6 10-4 10-2 100 102 104 106

0

2

4

0.01 0.1 11013101410151016101710181019

0.01 0.1 11013101410151016101710181019

10-6 10-4 10-2 100 102 104 106

0

2

4

T (1

06 K

)


infinite atmosphere

Energy (keV)

H E

(erg

cm

-2 s

-1 k

eV-1 )

Σ = 1 g cm -2

Energy (keV)

H E

(erg

cm

-2 s

-1 k

eV-1 )

T (1

06 K

)

Teff = 4.3 105 К

log g = 14.1B = 4 1012 Gpure H


Models of magnetized NS atmospheresThin atmosphere above solid surface

0.1 1

1017

1018

1019

0.1 1

1017

1018

1019

0.1 1

1017

1018

1019

blackbodyslab 1 g cm-2slab 100 g cm-2semi-infinity

Teff = 106 K

B = 1014 G

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Proton cyclotron line can be depressed if the atmosphere is thin

Models of magnetized NS atmospheresThin atmosphere above solid surface

Hydrogen slab above helium slab can explain two absorption features

0.1 1

1017

1018

1019

0.1 1

1017

1018

1019

blackbody

slab 100 g cm-2

He - 0.75, H - 0.25

slab 100 g cm-2, pure H

Teff = 106 K

B = 1014 G

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Unresolved problems

Partially ionized atmospheres (especially with heavy elements)

0.1 1

1017

1018

1019

0.1 1

1017

1018

1019

0.1 1

1017

1018

1019

blackbody

part. ion. Hwith vacuum polar.

part. ion. Hfully ion. H

Teff = 106 K

B = 1013 G

Flux

, erg

cm

-2 s

-1 k

eV-1

Photon energy, keV

Problem resolved for partially ionized hydrogen atmosphere only

Conclusion for observed size of isolated NSs

Necessary to perform a lot of theoreticalwork with magnetized NS atmospheresbefore the confidence results will be obtained

Common Conclusion

It seems that NS inner core has a stiff EoS

R ap = 17 k m 1.6 m s

3 R S

Contours at 68% (dotted curves), 90% (dashed curves), and 99% (long-dashed curves) confidence in the mass-radius plane derived for X7 (NS in 47 Tuc) by spectral fitting (Heinke et al. 06). Allowed area from our model and limitations fromthe apparent radius of RX J1856 and from the rotation period of B1937 are added.

X7

R=14.5 +/-1.7 km

(1.4 M_sun)

OurResult

R=14.9 +/-1.5 km

(1.4 M_sun)

Absorption in spectral lines

kline~ NLow gfline , NLow ≈ NIon exp(-ELow /kT)

NFeXXV > NFeXXIV BUT:for FeXXV 10.5 A ELow~ 7 keV

for FeXXIV 10.6-11.2 A ELow~ 0 keV

kT ~ 1 keV NLow(FeXXV)

Documents

New Radiation of Neutron Stars - Key for their Equation of State · 2009. 7. 15. · Radiation of Neutron Stars - Key for their Equation of State V. Suleimanov1,3 in collaboration