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!