A Simple Discussion on X-ray A Simple Discussion on X-ray Luminosity Function AnalysisLuminosity Function Analysis

The Astrophysical Journal, 611:846–857, 2004 August 20

X-RAY LUMINOSITY FUNCTION AND TOTAL LUMINOSITY OF LOW-MASS X-RAY BINARIES

IN EARLY-TYPE GALAXIES

Dong-Woo Kim and Giuseppina Fabbiano

The apparent strong XLF breaks near LX,Edd visible in Figure 1a mostly disappear after the corrections are applied.

‘‘backward’’ method

a single, unbroken power law(differential):

a steepening of the XLF at higher luminosities

note that the high-luminosity slope is more uncertain, given the small number of very bright sources.

compare well with our cumulative XLF

absence of the luminous sources (LX > 2*10^38 ergs s1) for M.W.&M31

a low-luminosity break in the XLFs of E and S0

If the break is real• (?)higher luminosity for an Eddington break of normal neutron star bi

naries.

• the most massive neutron stars (3.2 ± 1 Msun; see Ivanova & Kalogera 2005)

• low-mass black hole binaries(3.5 Msun)• Both neutron star and black hole binaries (e.g. Sivakoff, Sarazin & Ir

win 2003)• He-enriched neutron star binaries (1.9 ± 0.6 Msun; see Ivanova & K

alogera 2005)

Whatever the cause, the shape of the XLF points to a dearth of very luminous sources in E and S0 galaxies.

Conclusion

• After correcting for incompleteness, the individual XLFs are statistically consistent with a single power law of a (differential) slope β＝ 1.8- 2.2

• Although the combined XLF is marginally consistent with a single power law, a broken power law gives an improved fit.

• If the change in slope is real, the high-luminosity portion of the XLF could reflect the mass function of black holes in these galaxies.

• The proximity of the Milky Way and M31 sources allows a measurement of their XLFs down to significantly lower luminosities, demonstrating that the single power law (withβ=2.2) continues down to Lx=10^37 erg/s.

The Astrophysical Journal, 573:138–143, 2002 July 1

A MINISURVEY OF X-RAY POINT SOURCES IN STARBURST AND NONSTARBURST GALAXIES

R. E. Kilgard, P. Kaaret, M. I. Krauss, A. H. Prestwich, M. T. Raley, and A. Zezas

LF slope range is 1.5- 2.1, steeper than the spirals and starbursts

the trend of steeper slopes correlating with less star formation extends to early-type spirals and ellipticals.

Model Luminosity Distribution

• single population

• constant luminosity through its lifetime

• power-law form for the birth rate distribution

• binaries turn on in X-rays instantaneously after they are formed.

Model Luminosity DistributionThe time evolution of n is :

lifetime of an X-ray binary:

(1) Impulsive EventImpulsive Event (i.e. no subsequent X-ray binary formation)

Differential luminosity distribution:

Cumulative Number:

(2) Steady-state star formation event

Lifetime of longest lived X-ray point-source < star formation intervalequilibriumbirth rate ==death rate

Cumulative Number:

This luminosity distribution is steepersteeper than that of the impulsive case with an exponent that differs by one

(3) sufficiently low luminosities

broken power-law form

Differential distribution Below the break : same slope as that of the birth distribution Above the break : slope will be steeper by one

Cumulative Number:

• older systems have a steep slope in the high-luminosity range

• younger systems have a flatter slope over the same luminosity range

• younger systems extend to higher luminosities

• X-ray sources in starbursts are likely to be HMXBs

• old systems is likely to be dominated by LMXBs

10Myr

20Myr

1Gyr

2Gyr

Conclusions

• the luminosity distribution of the starburst galaxies directly reflects the birth luminosity distribution

• other galaxies have a similar birth luminosity distribution and an observed luminosity distribution modified by the effects of an aging X-ray binary population.

• X-ray point-source luminosity distributions should prove to be a powerful tool in understanding the evolutionary history of massive star populations in external galaxies.

My Recent Work

• Luminosity Calculation: 2cMLX

(Belczynski 2003)

for persistent sources: Lx=min(Lx,10L_edd)

Critical luminosity:• For kw2=0-9 :

• For kw2=10-12(WD) ：

BH

NS

hrP

hrP

L

L

sun

critX

)/lg(07.122.2

)/lg(07.162.1)log( ,

Magnetic Braking:

Donor Type• 0 = MS star M <0.7 deeply or fully convective• 1 = MS star M >0.7

• 2 = Hertzsprung Gap (HG)• 3 = First Giant Branch (GB)• 4 = Core Helium Burning (CHeB)• 5 = Early Asymptotic Giant Branch (EAGB)• 6 = Thermally Pulsing AGB (TPAGB)

• 7 = Naked Helium Star MS (HeMS)• 8 = Naked Helium Star Hertzsprung Gap (HeHG)• 9 = Naked Helium Star Giant Branch (HeGB)

• 10 = Helium White Dwarf (HeWD)• 11 = Carbon/Oxygen White Dwarf (COWD)• 12 = Oxygen/Neon White Dwarf (ONeWD)

• 13 = Neutron Star (NS)• 14 = Black Hole (BH)• 15 = massless remnant

high luminosity cut-off of the LMXB XLF and power-law distribution of the HMXB XLF

αce＝ 1.0αce＝ 1.0&10L_edd

αce＝ 1.0&10L_edd

αce＝ 1.0&10L_edd

αce＝ 1.0&10L_eddαce＝ 1.0&10L_edd

αce＝ 0.5&10L_eddαce＝ 1.0&10L_edd

αce＝ 0.3&10L_edd αce＝ 0.1&10L_edd

αce＝ 0.3&10L_edd αce＝ 0.1&10L_edd

αce＝ 0.3&10L_edd αce＝ 0.1&10L_edd

αce＝ 0.3&10L_edd αce＝ 0.1&10L_edd

αce＝ 0.3&10L_eddαce＝ 0.1&10L_edd

Calculated by Liuxw

out38

, M103.11.0 NSNSXL

NS transient sources dominate by short period systems

Lx revised by critical periods removed

αce＝ 0.3&10L_edd αce＝ 0.1&10L_edd

Thanks!