Population synthesis of isolated NSs and tests of cooling curves

Sergei Popov

(Sternberg Astronomical Institute)Co-authors: D. Blaschke, H.Grigorian, B. Posselt, R. Turolla

JINR, Dubna, September 01, 2006

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Plan of the talk

Intro. Close-by NSs Population synthesis Solar vicinity. Stars Spatial distribution Mass spectrum Two tests of cooling Brightness constraint Sensitivity of two tests Mass constraint Application to hybrid stars Future plans Age-Distance diagram Final conclusions

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Isolated neutron stars population: in the Galaxy and at the backyard

INSs appear in many flavours Radio pulsars AXPs SGRs CCOs RINSs RRATs

Local population of young NSs is different (selection)

Radio pulsarsGeminga+RINSs

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Close-by radioquiet NSs

Discovery: Walter et al. (1996)

Proper motion and distance: Kaplan et al.

No pulsations Thermal spectrum Later on: six brothers

RX J1856.5-3754

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Magnificent Seven

Name Period, s

RX 1856 -

RX 0720 8.39

RBS 1223 10.31

RBS 1556 -

RX 0806 11.37

RX 0420 3.45

RBS 1774 9.44

Radioquiet (?)Close-byThermal emissionLong periods

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Population of close-by young NSs

Magnificent seven Geminga and 3EG J1853+5918 Four radio pulsars with thermal emission

(B0833-45; B0656+14; B1055-52; B1929+10) Seven older radio pulsars, without detected

thermal emission.

It is useful to study these stars using the population synthesis technique

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Population synthesis: ingredients

Birth rate of NSs Initial spatial distribution Spatial velocity (kick) Mass spectrum Thermal evolution Interstellar absorption Detector properties

A brief review on populationsynthesis in astrophysics canbe found in astro-ph/0411792

To build an artificial model

of a population of some astrophysical sources and

to compare the results ofcalculations with observations.

Task:

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Gould Belt : 20 NS Myr-1

Gal. Disk (3kpc) : 250 NS Myr-1

Arzoumanian et al. 2002

ROSAT

• Cooling curves by• Blaschke et al. • Mass spectrum

18°Gould BeltGould Belt

Population synthesis – I.

© Bettina Posselt

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Solar vicinity

Solar neighborhood is not a typical region of our Galaxy

Gould Belt R=300-500 pc Age: 30-50 Myrs 20-30 SN per Myr (Grenier 2000) The Local Bubble Up to six SN in a few Myrs

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The Gould Belt

Poppel (1997) R=300 – 500 pc Age 30-50 Myrs Center at 150 pc from

the Sun Inclined respect to the

galactic plane at 20 degrees

2/3 massive stars in 600 pc belong to the Belt

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Distribution of open clusters

(Piskunov et al. astro-ph/0508575)

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Surface density of open clusters

(Piskunov et al.)

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Spatial distribution of close-by open clusters in 3D

(Piskunov et al.)

Grey contours show projected densitydistribution of young(log T<7.9) clusters.

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Clusters and absorption

(Piskunov et al.)

Triangles – Gould Belt clusters.

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Initial spatial distribution

A very simple model for PS-I: The Gould Belt as a flat inclined disc pluscontribution from the galactic disc up to 3 kpc.

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Some results of PS-I.:Spatial distribution

(Popov et al. 2005 Ap&SS 299, 117)

More than ½ are in+/- 12 degrees from the galactic plane.

19% outside +/- 30o

12% outside +/- 40o

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Mass spectrum of NSs

Mass spectrum of local young NSs can be different from the general one (in the Galaxy)

Hipparcos data on near-by massive stars

Progenitor vs NS mass: Timmes et al. (1996); Woosley et al. (2002)

astro-ph/0305599(masses of secondary objects in NS+NS)

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Woosley et al. 2002

Progenitor mass vs. NS mass

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Woosley et al. 2002

Core mass vs. initial mass

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Two tests

Age – Temperature

&

Log N – Log S

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Standard test: temperature vs. age

Kaminker et al. (2001)

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Uncertainties in temperature

(Pons et al. astro-ph/0107404)

• Atmospheres (composition)• Magnetic field• Non-thermal contributions to the spectrum• Distance• Interstellar absorption• Temperature distribution

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Luminosity and age uncertainties

Page, Geppertastro-ph/0508056

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Log N – Log S

Log of flux (or number counts)

Lo

g o

f th

e n

um

ber

of

sou

rces

bri

gh

ter

than

th

e g

iven

flu

x

-3/2 sphere: number ~ r3

flux ~ r-2

-1 disc: number ~ r2

flux ~ r-2

calculations

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Log N – Log S as an additional test

Standard test: Age – Temperature Sensitive to ages <105 years Uncertain age and temperature Non-uniform sample

Log N – Log S Sensitive to ages >105 years (when applied to close-by NSs) Definite N (number) and S (flux) Uniform sample

Two test are perfect together!!!astro-ph/0411618

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List of models (Blaschke et al. 2004)

Model I. Yes C A Model II. No D B Model III. Yes C B Model IV. No C B Model V. Yes D B Model VI. No E B Model VII. Yes C B’ Model VIII.Yes C B’’ Model IX. No C A

Blaschke et al. used 16 sets of cooling curves.

They were different in three main respects:

1. Absence or presence of pion condensate

2. Different gaps for superfluid protons and neutrons

3. Different Ts-Tin

Pions Crust Gaps

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Model I

Pions. Gaps from Takatsuka & Tamagaki

(2004) Ts-Tin from Blaschke, Grigorian,

Voskresenky (2004)

Can reproduce observed Log N – Log S

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Model II

No Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1

Ts-Tin from Tsuruta (1979)

Cannot reproduce observed Log N – Log S

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Model III

Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1

Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)

Cannot reproduce observed Log N – Log S

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Model IV

No Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1

Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)

Cannot reproduce observed Log N – Log S

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Model V

Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1

Ts-Tin from Tsuruta (1979)

Cannot reproduce observed Log N – Log S

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Model VI

No Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1

Ts-Tin from Yakovlev et al. (2004)

Cannot reproduce observed Log N – Log S

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Model VII

Pions Gaps from Yakovlev et

al. (2004), 3P2 neutron gap suppressed by 0.1.

1P0 proton gap suppressed by 0.5

Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)

Cannot reproduce observed Log N – Log S

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Model VIII

Pions Gaps from Yakovlev et al.

(2004), 3P2 neutron gap suppressed by 0.1. 1P0

proton gap suppressed by 0.2 and 1P0 neutron gap suppressed by 0.5.

Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)

Can reproduce observed Log N – Log S

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Model IX

No Pions Gaps from Takatsuka &

Tamagaki (2004) Ts-Tin from Blaschke,

Grigorian, Voskresenky (2004)

Can reproduce observed Log N – Log S

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HOORAY!!!!

Log N – Log S can select models!!!!!Only three (or even one!) passed the second test!

…….still………… is it possible just to update the temperature-age test???

May be Log N – Log S is not necessary?Let’s try!!!!

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Brightness constraint

Effects of the crust (envelope)

Fitting the crust it is possible to fulfill the T-t test …

…but not the second test: Log N – Log S !!!

(H. Grigorian astro-ph/0507052)

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Sensitivity of Log N – Log S

Log N – Log S is very sensitive to gaps Log N – Log S is not sensitive to the crust if it is applied to

relatively old objects (>104-5 yrs) Log N – Log S is not very sensitive to presence or

absence of pions

We conclude that the two test complement each other

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Mass constraint

• Mass spectrum has to be taken into account when discussing data on cooling• Rare masses should not be used to explain the cooling data• Most of data points on T-t plot should be explained by masses <1.4 Msun

In particular:• Vela and Geminga should not be very massive

Phys. Rev .C (2006)nucl-th/0512098(published as a JINR preprint)

Cooling curves fromKaminker et al.

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Another attempt to test a set of models: hybrid stars

We studied several models for hybrid stars applying all possible tests: - T-t- Log N – Log S- Brightness constraint- Mass constraint

nucl-th/0512098

We also tried to present examples when a model successfully passesthe Log N – Log S test, but fails to pass the standard T-t test or fails tofulfill the mass constraint.

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Model I

Brightness - OKT-t - OKLog N – Log S - poorMass - NO

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Model II

Brightness - OK

T-t - No

Log N – Log S - OK

Mass - NO

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Model III

Brightness - OK

T-t - poor

Log N – Log S - OK

Mass - NO

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Model IV

Brightness - OK

T-t - OK

Log N – Log S - OK

Mass - OK

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Resume for HySs

One model among four was able to pass all tests.

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1. Spatial distribution of progenitor stars

a) Hipparcos stars up to 400 pc[Age: spectral type & cluster age (OB ass)]

b) Star associations: birth rate ~ Nstar

c) Field stars in the disc up to 3 kpc

Population sythesis – II.recent improvements

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3. Further improvements:

• Mass spectrum • fainter XMM EPIC PN count rates• cooling curves (Grigorian et al. 2005, Popov et al . 2006)

2. Spatial distribution of ISM (NH)

instead of : now :

+ new cross sections & abundances

1kpc

1kpc

Population synthesis – II.recent improvements

(by Bettina Posselt)

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b= +90°

b= -90°

First results First results The new initial distribution of progenitor stars:

For comparison: ROSAT, old ISM distribution, masses etc. as before

GB 500 pc

GB 300 pc

New

Popov et al. 2005

Outlook Outlook Different log N - log S curve for distinct sky regions

Population synthesis for fainter (XMM) sources

Count rate > 0.05 cts/s

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Age-distance diagram

(astro-ph/0407370)

Detectability of close-byyoung NSs stronglyDepends on their agesand distance from the Sun.

A toy-model: a localsphere (R=300 pc)and a flat disk.

Rate of NS formationin the sphere is235 Myr-1 kpc-3

(26-27 NS in Myr inthe whole sphere).

Rate in the disc is10 Myr-1 kpc-2

(280 NS in Myr up to3 kpc).

visibility

13 sources

1 source

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More realistic age-dist. diagram

Initial distributionfrom Popov et al. 2005.

Spatial evolution is notfollowed.

For the line of “visibility”(solid line in the middle)I assume the limitingflux 10-12 erg s-1 cm-2 and masses are <1.35(Yakovlev et al. curves).

In 4.3 Myr in 1 kpc around the Sun 200 NSsare expected to be born.

(astro-ph/0407370)

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Realistic age-distance diagram

Realistic initial distribution.

Spatial evolution is takeninto account.

The line of “visibility” isdrawn as the dotted line.

Five curves correspond to1, 4 , 13, 20 and 100 NSs.

At the moment in 1 kpconly about 10% of NSswith ages <4-5 Myrs areobserved.

(astro-ph/0407370)

visibility

100201 134

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Resume

We live in a very interesting region of the Milky Way! Log N – Log S test can include NSs with unknown ages, so additional sources (like the Magnificent Seven) can be used to test cooling curves. Two tests (LogN–LogS and Age-Temperature) are

perfect together. Additional considerations (brightness and mass constraints) have to be taken into account. More detailed PS models are welcomed. Age-distance diagram can be used as an additional tool.

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THAT’S ALL. THANK YOU!

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Radio detection

Malofeev et al. (2005) reported detection of 1RXS J1308.6+212708 (RBS 1223) in the low-frequency band (60-110 MHz) with the radio telescope in Pushchino.

In 2006 Malofeev et al. reported radio detectionof another one.

(back)

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NS+NS binaries

Pulsar Pulsar mass Companion mass

B1913+16 1.44 1.39B2127+11C 1.35 1.36B1534+12 1.33 1.35J0737-3039 1.34 1.25J1756-2251 1.40 1.18

(PSR+companion)/2

J1518+4904 1.35J1811-1736 1.30J1829+2456 1.25

(David Nice, talk at Vancouver 2005)

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