1. A Simple Discussion on X-ray Luminosity Function Analysis

2. 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

3. 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):

4. 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.

5. 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

6. If the break is real (?)higher luminosity for an Eddington break of normal neutron star binaries. 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 & Irwin 2003) He-enriched neutron star binaries (1.9 ± 0.6 Msun; see Ivanova & Kalogera 2005) Whatever the cause, the shape of the XLF points to a dearth of very luminous sources in E and S0 galaxies.

7. 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.

8. 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

10. 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.

11. 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.

12. Model Luminosity Distribution The time evolution of n is : lifetime of an X-ray binary:

13. Impulsive Event (1) Impulsive Event (i.e. no subsequent X-ray binary formation) Differential luminosity distribution: Cumulative Number:

14. (2) Steady-state star formation event Lifetime of longest lived X-ray point-source < star formation interval  equilibrium  birth rate ==death rate Cumulative Number: steeper This luminosity distribution is steeper than that of the impulsive case with an exponent that differs by one

15. (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:

16. 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

17. 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.

18. My Recent Work

19. Luminosity Calculation: (Belczynski 2003) for persistent sources: Lx=min(Lx,10L_edd)

20. Critical luminosity: For kw2=0-9 : For kw2=10-12(WD) ： Magnetic Braking:

21. 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

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

23. αce ＝ 1.0 αce ＝ 1.0&10L_edd

27. αce ＝ 0.5&10L_eddαce ＝ 1.0&10L_edd

28. αce ＝ 0.3&10L_eddαce ＝ 0.1&10L_edd

29. αce ＝ 0.3&10L_eddαce ＝ 0.1&10L_edd

30. αce ＝ 0.3&10L_edd αce ＝ 0.1&10L_edd

31. αce ＝ 0.3&10L_edd αce ＝ 0.1&10L_edd

32. αce ＝ 0.3&10L_edd αce ＝ 0.1&10L_edd

33. Calculated by Liuxw NS transient sources dominate by short period systems

34. Lx revised by critical periods removed αce ＝ 0.3&10L_edd αce ＝ 0.1&10L_edd

35. Thanks!