x-ray binary evolution across cosmic time · 9 iesl, foundation for research and technology, 71110...

The Astrophysical Journal, 764:41 (13pp), 2013 February 10 doi:10.1088/0004-637X/764/1/41C© 2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

X-RAY BINARY EVOLUTION ACROSS COSMIC TIME

T. Fragos1, B. Lehmer2,3, M. Tremmel4, P. Tzanavaris2,3, A. Basu-Zych3, K. Belczynski5,6,A. Hornschemeier3, L. Jenkins3, V. Kalogera7, A. Ptak3, and A. Zezas1,8,9

1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA; [email protected] Department of Physics and Astronomy, The Johns Hopkins University, Homewood Campus, Baltimore, MD 21218, USA

3 NASA Goddard Space Flight Centre, Code 662, Greenbelt, MD 20771, USA4 Department of Astronomy, University of Washington, Box 351580, U.W., Seattle, WA 98195-1580, USA

5 Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw, Poland6 Center for Gravitational Wave Astronomy, University of Texas at Brownsville, Brownsville, TX 78520, USA

7 Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA8 Department of Physics, University of Crete, P.O. Box 2208, 71003 Heraklion, Crete, Greece

9 IESL, Foundation for Research and Technology, 71110 Heraklion, Crete, GreeceReceived 2012 June 10; accepted 2012 November 20; published 2013 January 24

ABSTRACT

High-redshift galaxies permit the study of the formation and evolution of X-ray binary (XRB) populations oncosmological timescales, probing a wide range of metallicities and star formation rates (SFRs). In this paper, wepresent results from a large-scale population synthesis study that models the XRB populations from the first galaxiesof the universe until today. We use as input to our modeling the Millennium II cosmological simulation and theupdated semi-analytic galaxy catalog by Guo et al. to self-consistently account for the star formation history andmetallicity evolution of the universe. Our modeling, which is constrained by the observed X-ray properties of localgalaxies, gives predictions about the global scaling of emission from XRB populations with properties such as SFRand stellar mass, and the evolution of these relations with redshift. Our simulations show that the X-ray luminositydensity (X-ray luminosity per unit volume) from XRBs in our universe today is dominated by low-mass XRBs, andit is only at z � 2.5 that high-mass XRBs become dominant. We also find that there is a delay of ∼1.1 Gyr betweenthe peak of X-ray emissivity from low-mass XRBs (at z ∼ 2.1) and the peak of SFR density (at z ∼ 3.1). The peakof the X-ray luminosity from high-mass XRBs (at z ∼ 3.9) happens ∼0.8 Gyr before the peak of the SFR density,which is due to the metallicity evolution of the universe.

Key words: binaries: close – galaxies: stellar content – stars: evolution – X-rays: binaries – X-rays:diffuse background – X-rays: galaxies

Online-only material: color figures, machine-readable table

1. INTRODUCTION

X-ray observations of galaxies are a key component tounraveling the physics of compact object formation. Stellarremnants and the distribution of the hot interstellar medium arebest studied via their X-ray emission. With Chandra severalglobal galaxy X-ray correlations have been established andappear to hold to at least z = 1 (e.g., Bauer et al. 2002; Lehmeret al. 2008, 2012; Vattakunnel et al. 2012; Symeonidis et al.2011), implying a large-scale regularity to the production ofX-ray binaries (XRBs) and hot gas, the primary sources ofhigh energy emission in “normal” (non-active galactic nucleus)galaxies. These include a very strong correlation betweentotal X-ray emission from high-mass XRBs (HMXBs) andthe galaxy-wide star formation rate (SFR; e.g., Ranalli et al.2003; Gilfanov et al. 2004; Hornschemeier et al. 2005; Lehmeret al. 2010; Mineo et al. 2012a), as well as a scaling betweentotal X-ray emission from low-mass XRBs (LMXBs) and stellarmass (M∗; Gilfanov 2004; Lehmer et al. 2010; Boroson et al.2011; Zhang et al. 2012). These correlations present excitingchallenges for models of accreting binary evolution (e.g., Fragoset al. 2008, 2009; Belczynski et al. 2008) that predict significantvariability in these relations based on, e.g., star formation historyand metallicity.

Recent ultradeep Chandra and multiwavelength surveys (e.g.,Xue et al. 2011) have permitted robust observational tests ofthese correlations in distant galaxies (see also the review ofBrandt & Hasinger 2005). In a broad sense, curiously, the

X-ray emission per unit SFR seems to evolve little with red-shift, despite the evolution in gas metallicity, for example, overthe same epochs (e.g., Lehmer et al. 2008). Ptak et al. (2007)and Tzanavaris & Georgantopoulos (2008) used rich multiwave-length data sets to construct X-ray luminosity functions (XLFs)of normal galaxies in different redshift bins, and found that theXLF shows a statistically significant evolution with redshift andthat it is the late-type galaxies that are driving this evolution.

Despite the significant investment of observing time in X-raystudies of distant normal galaxies, and the recent theoreticaladvances in modeling the X-ray source populations in nearbygalaxies, our understanding of the cosmological evolution ofpopulations of compact objects is still in its infancy. The firststeps in this direction have been made by means of semi-analytic, empirical models (White & Ghosh 1998; Ghosh &White 2001). Considering a time-dependent SFR, these modelspredicted that the time required for binaries to reach theX-ray phase (due to the donor’s nuclear evolution and angularmomentum losses) leads to a significant time delay between astar formation episode and the production of X-ray emissionfrom XRBs from these populations.

State-of-the-art binary population models (e.g., Belczynskiet al. 2008) provide us with a more physical picture of XRBpopulations as a function of galaxy properties. This type of de-tailed modeling has been applied to both starburst and ellipticalnearby galaxies, where large populations of individual XRBsare resolved, and detailed ages, star formation histories, andmetallicities are measured. Belczynski et al. (2004) constructed

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http://dx.doi.org/10.1088/0004-637X/764/1/41mailto:[email protected]

The Astrophysical Journal, 764:41 (13pp), 2013 February 10 Fragos et al.

the first synthetic XRB populations for direct comparison withthe Chandra observed XLFs of NGC 1569, a star-forming dwarfirregular galaxy. Linden et al. (2009, 2010) developed modelsfor the HMXB and Be XRBs of Small Magellanic Cloud, study-ing the XLF and the spatial distribution of this population, andinvestigating the effect of electron-capture supernovae of mas-sive ONeMg stellar cores. Fragos et al. (2008, 2009) performedextensive population synthesis (PS) simulations, modeling thetwo old elliptical galaxies NGC 3379 and NGC 4278, con-straining the relative contribution to the observed XLF fromsub-populations of LMXBs with different donor and accretortypes, and the effects of the transient behavior of LMXBs. Morerecently, Zuo & Li (2011) studied the evolution of XRB pop-ulations in late-type galaxies, using a modified version of theBSE PS code (Hurley et al. 2002). Considering different starformation history scenarios, they were able to derive the X-rayemissivity as well as XLFs of the XRB populations. However,their model predictions are not in good agreement with obser-vations for most of the universe lifetime: from 4.5 to 13.7 Gyr(z = 0–1.4).

The next step in this long-term effort is to apply thesemodels in a cosmological context, in order to understand thenature of the accreting populations in high-redshift normalgalaxies. In this paper, we study the global scaling relationof emission from XRB populations with properties such asSFR and stellar mass, and the evolution of these relationswith redshift. More specifically, we developed a large gridof XRB PS models for which the information about thestar formation history and metallicity evolution were derivedfrom cosmological simulations. Our models, which we havealready constrained with observations of XRB populations ofthe local universe, give predictions for the evolution of theaforementioned global scaling relations back to the formationof the very first galaxies at redshift z � 15.

The plan of this paper is as follows. In Section 2 wedescribe our simulation tools, the StarTrack PS code andMillennium II simulation, and the methodology we follow indeveloping models for the evolution of XRBs on cosmolog-ical timescales. Section 3 discusses the necessary bolometriccorrections we employ in order to directly compare our modelresults with observations. In Section 4, we present the obser-vational data we use to constrain our models and the statisticalanalysis we follow. We present the predictions of our maximumlikelihood models for the evolution of XRB population in thehigh-redshift universe in Section 5. Finally, in Section 6 wesummarize the main findings and conclusions of our work.

2. POPULATION SYNTHESIS MODELING

2.1. Population Synthesis Code: StarTrack

The main tool we use to perform the PS simulations isStarTrack (Belczynski et al. 2002, 2008), a state-of-the-artcode with special emphasis on processes leading to the forma-tion and further evolution of compact objects. Both single andbinary star populations are considered. The code incorporatescalculations of all mass-transfer phases, a full implementationof orbital evolution due to tides, as well as estimates of magneticbraking. StarTrack has been extensively tested and calibratedusing detailed mass-transferring binary star calculations and ob-servations of binary populations. For a comprehensive summaryof StarTrack and its model parameters, see Belczynski et al.(2008).

Recently, the StarTrack code has undergone three majorrevisions. The first one allows for the updated stellar windsand their re-calibrated dependence on metallicity (Belczynskiet al. 2010). This revision is fully incorporated into our results.The second update, based on the fully consistent supernovasimulations, resulted in the revised neutron star (NS) and blackhole (BH) mass spectrum (Belczynski et al. 2012; Fryer et al.2012). Finally, the most recent upgrade involves a more physicaltreatment of donor stars in common envelope (CE) events viausage of actual value of λ parameter for which usually a constantvalue is assumed (Dominik et al. 2012). The last two coderevisions are not employed in our simulations as these wereperformed well before the revisions became available.

Several XRB PS studies that used StarTrack (Belczynskiet al. 2004; Belczynski & Taam 2004; Fragos et al. 2008, 2009,2010; Linden et al. 2009, 2010) have been pivotal in interpretingobservations of nearby galaxies and showed that despite thesignificant number of free parameters (∼10) and the complexityof the physical processes involved, PS models can provide robustresults that can be used to understand the properties of moredistant galaxies.

We should stress here that our PS code only models XRBsformed via the evolution of primordial isolated binaries, i.e.,the field XRB population. A dynamically formed populationof LMXBs can have a significant contribution to the integratedX-ray luminosity of some globular-cluster rich elliptical galax-ies, where in certain cases more than half of the bright LMXBsreside in globular clusters (e.g., Humphrey & Buote 2008). Thedetailed modeling of the dynamically formed LMXBs, althoughpossibly important for this subset of elliptical galaxies, is out-side the scope of this paper, and in fact it is not feasible giventhe tools that exist to date for simulations of such scale. Theonly PS studies to date of dynamically formed LMXBs havebeen done for a few specific Galactic globular clusters and onlyin order to identify the various formation channels and theirrelative importance (Ivanova et al. 2006, 2008, 2010).

In the work presented here we consider the global XRB pop-ulation, i.e., XRBs in a general galaxy population of both early-and late-type galaxies, where the contribution of dynamicallyformed LMXBs is much smaller. In the low-redshift universe,approximately half of the stellar mass is in early-type galax-ies (Bell et al. 2003). Furthermore, approximately half of theearly-type galaxies are old, globular-cluster-rich ellipticals, andfinally in these globular-cluster-rich ellipticals approximatelyhalf of the bright LMXBs are located in globular clusters. Thiseffectively translates to a possible error of 10%–25% in thedetermination of the integrated X-ray luminosity coming fromthe LMXB population when neglecting the dynamically formedpopulation. This contribution of the dynamically formed pop-ulation is decreasing further as we move to higher redshifts.However, comparing the X-ray luminosity per unit stellar masscoming from LMXBs in star-forming galaxies (Lehmer et al.2010), where the dynamically formed LMXB population is neg-ligible, and in elliptical galaxies (Boroson et al. 2011), showsthat any correction that one should make due to the contributionof dynamically formed LMXBs is smaller than the observationaluncertainties.

2.2. The Millennium II Simulation

The Millennium II simulation (Boylan-Kolchin et al. 2009)is a very large N-body simulation of dark matter evolution inthe concordance ΛCDM cosmology. The simulation uses ∼1010particles in a 100 Mpc h−1 box, resulting in a spatial resolution

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of 1 kpc h−1 and a mass resolution of 6.89 × 106 M� h−1.Sixty-seven full snapshots of the simulation were stored,with time intervals between them varying from ∼30 Myr to∼300 Myr, which were then used to derive merger trees of thedark-matter halos.

Using the stored halo/subhalo merger trees of theMillennium II simulation, Guo et al. (2011) recently released anupdated semi-analytic galaxy catalog. Guo et al. (2011) revisedthe modeling of several physical processes involved in galaxyformation, such as gas stripping and supernova feedback. Thisnewly released catalog yields an excellent fit to the galaxy massand luminosity function of low-redshift galaxies over five ordersof magnitude in stellar mass and nine magnitudes in luminosity.The Guo et al. (2011) catalog provides a wealth of informa-tion for each galaxy in the cosmological simulation, includinggalaxy type, SFR, metallicity, hot and cold gas content, cen-tral BH mass, and rest-frame absolute magnitudes in the SloanDigital Sky Survey filters, as a function of time.

As already mentioned, the Millennium II simulation is a dark-matter-only simulation, and the baryonic matter is modeled as anadd-on, using semi-analytic prescriptions. Despite the high com-plexity of the galaxy formation modeling by Guo et al. (2011),which takes into account most physical processes involved, itremains an approximate model. In that sense, the detailed evo-lution of a specific galaxy formed in the simulation may notbe fully consistent with more advanced galaxy formation sim-ulations (Scannapieco et al. 2012). However, the semi-analyticprescriptions used by Guo et al. (2011) have been calibratedso that the statistical properties (e.g., mass function, global starformation history, stellar metallicity distribution) as a functionof redshift of the modeled galaxy population are consistent withavailable observational data. Figure 1 shows the predictions ofthe Millennium II simulation and the Guo et al. (2011) mod-eling for the SFR density (top panel), the stellar mass density(middle panel), and the metallicity of the newly formed starsas a function of redshift. For comparison, observed data for theSFR density and stellar mass density are also plotted (upperand middle panels, respectively), showing a good agreementbetween model and observations.

2.3. The Millennium II Simulation as Initial Conditionsof Populations Synthesis Models

The first step of our analysis is to derive for each combinationof PS model parameters, and each value of metallicity, theevolution of the specific X-ray luminosity (X-ray luminosityper unit stellar mass) of a coeval population of XRBs as afunction of its age. Assuming a single instantaneous starburst,we follow the evolution of the XRB population, keeping trackof the total (cumulative) X-ray luminosity of the whole XRBpopulation, and the contribution of the different sub-populations(e.g., XRBs with different types of accretors) as a function ofthe age of the population. We note that in this work we define asan LMXB, an XRB with donor star whose current mass is lessthan 3 M�, while an HMXB is any XRB with a donor star moremassive than 3 M�.

In the top panel of Figure 2, we show the specific X-rayluminosity of XRBs, X-ray luminosity per unit stellar mass(LX/M∗), versus age for a single coeval population of binariesat solar metallicity. These curves were generated using our“reference” model (Model 245; see also Sections 2.4 and 4.2).In the bottom panel of Figure 2, we show how these curvesvary if instead initial metallicities of ∼0.1 Z� (green dashed)and ∼1.5 Z� (magenta dot-dashed) are chosen. As seen in the

Figure 1. Top panel shows the SFR density evolution with redshift, as predictedby the Guo et al. (2011) modeling (solid line). Observational determinations ofthe SFR density at different redshifts (gray squares) are shown for comparison(Schiminovich et al. 2005; Bouwens et al. 2007; Reddy & Steidel 2009). Thestellar mass density as a function of redshift, as predicted by the Guo et al. (2011)modeling, is shown in the middle panel (solid line), as well as a compilationof observed data (gray squares) by Marchesini et al. (2009). The bottom panelshows the mass-weighted mean metallicity of the newly formed stellar massas a function of redshift. The dark gray area shows the metallicity range withwhich 68.2% of the new stars form, as a function of redshift, while the lightgray area corresponds to the 95.4% of the newly formed stars.

top panel of Figure 2 over the lifetime of the stars produced ina given star formation event, there is an initial ramp-up in theformation of HMXBs over the first ∼5 Myr as the first compactobjects form, followed by a period of HMXB dominance thatlasts for ∼100–300 Myr. At this point, the LMXB populationemerges, peaks, and then slowly declines by ∼1–2 orders ofmagnitude out to ∼14 Gyr timescales. In the lower panel ofFigure 2, we show the XRB luminosity evolution with respectto solar for low- and high-metallicity cases. We note that theX-ray luminosity is expected to be significantly higher forlow-metallicity regions, due to the fact that the young massiveO/B stars, which are the precursors to compact object accretorsin XRBs, will lose less stellar mass from line-driven windsover their lifetimes for lower metallicities. This results in morenumerous and more massive BH populations, and subsequentlymore luminous XRB populations (see also Section 5.1 for a

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Figure 2. Evolution of an XRB population formed from a single-burstpopulation of stars. Top panel: specific bolometric X-ray luminosity, i.e.,luminosity per unit stellar mass, of a coeval stellar population as a function of thepopulation’s age for our “reference” model (Model 245; see also Sections 2.4and 4.2) and for solar metallicity, broken down into HMXB (blue dotted)and LMXB (red long-dashed) contributions. After an initial ∼5 Myr ramp-up, HMXBs dominate the X-ray power output for ∼100–300 Myr. Followingthis, LMXBs take over, peak in formation at ∼0.5–1 Gyr, and then passivelyfade with increasing age. The bumps and wiggles present at �4 Gyr are dueto statistical fluctuations as bright sources turn on and off. Bottom panel: XRBevolution for the cases of metallicities Z = 0.1 Z� (green short-dashed) andZ = 1.5 Z� (magenta dot-dashed) compared to solar (i.e., LX[Z]/LX[Z�]).(A color version of this figure is available in the online journal.)

detailed discussion). Some evidence has already indicated thatthe X-ray luminosity from XRBs per unit of SFR (LX/SFR) forlow-metallicity dwarf galaxies may be enhanced compared tomore typical galaxies (Kaaret et al. 2011).

The Millennium II simulation and the Guo et al. (2011)semi-analytic galaxy catalog provide us information about theevolution of the properties of each galaxy in the simulation.In this first study, we consider only the global characteristicsand scaling relations of the XRB evolution across cosmic time.Having this in mind, we consider the whole simulation box of theMillennium II simulation as representative of the universe, andwe keep track of the total new stellar mass that is formed betweeneach snapshot of the simulation. In addition, we keep track ofthe metallicity of the new stellar mass formed. In practice, weconsider nine metallicity bins, centered at the values reported inTable 1, and calculate how much new stellar mass was formedat each snapshot and at each metallicity bin. Finally, we assumethat the new stellar mass is formed with a constant SFR betweeneach snapshot. This results in a self-consistent prescription of thestar formation history and metallicity evolution of the universe.

We now have all the necessary information in hand toconstruct models for the evolution of XRBs across cosmictime. We convolve the relations we derived in the first step,with the star formation history for different metallicity ranges.The result is a mixed XRB population, with a broad range ofages and metallicities, representative of the XRB population ofthe universe, at each redshift. From this convolution we derivemodel predictions such as the X-ray luminosity from XRBs perunit volume, stellar mass, or SFR, as a function of redshift.

2.4. Parameter Study

StarTrack PS models have a significant number of freeparameters that can be categorized into two groups. In thefirst group there are parameters that usually correspond to thedistributions of the initial properties of the binary population,such as the initial mass function (IMF), the initial binary massratio (q), and the distribution of initial orbital separations.For these parameters, we primarily use fixed values derived fromthe most updated observational surveys. Only in the case wherethere is an ongoing debate regarding a parameter we actuallytreat it as a free parameter. In the same group one should addparameters such as the stellar wind prescriptions and the natalkick distribution of NSs, as these parameters are also derivedfrom observational data. The second group is that of the few“true” free parameters that correspond to poorly understoodphysical processes which we are not able to model in detail. Inthis second group belong parameters such as those involved inthe CE phase modeling.

We created the largest ever grid of 288 PS models. Eachof these 288 models was run at nine different values ofmetallicity (Z = 10−4–0.03), where we followed the evolutionof ∼45 million binaries per model. The whole set of simulationsrequired ∼2 million CPU hours of computational time. In thisgrid, we varied six parameters (in addition to the metallicity)known from previous studies (Belczynski et al. 2007, 2010;Fragos et al. 2008, 2010; Linden et al. 2009) to affect theevolution of XRBs and the formation of compact objects ingeneral. Namely, we varied the CE efficiency (αCE × λ =0.1–0.5), the IMF (Kroupa 2001 or Kroupa & Weidner 2003),the initial mass ratio (q) distribution (flat with q = 0–1,twin with q = 0.9–1.0, or a mixture of 50% flat and 50%twin), the stellar wind strength (ηwind = 0.25, 1.0, or 2.0;parameter with which we multiply the stellar wind prescriptiondescribed in Belczynski et al. 2010), and the distribution ofnatal kicks for BHs formed though direct core collapse (zerokicks, or 10% of the standard kicks for NS). Finally, we allowfor various outcomes of CE phase, in particular taking intoaccount the possible CE inspirals with Hertzsprung gap donorsthat terminate binary evolution barring the subsequent XRBformation (Belczynski et al. 2007). The grid of 288 models wecreated includes all the possible combinations of the parameterswe varied. The various parameter values used are shown inTable 1.

We note that in our calculations we combine αCE andλ into one CE parameter, where λ is a measure of the centralconcentration of the donor and the envelope binding energy. Inthe rest of the text, whenever we mention the CE efficiency αCE,we refer in practice to the product αCE ×λ (see Belczynski et al.2008 for details).

3. BOLOMETRIC CORRECTIONS TO THECHANDRA X-RAY BANDS

StarTrack, our PS synthesis code, keeps track of the mass-transfer rate as a function of time for every modeled XRB. Fromthis mass-transfer rate, we derive the bolometric luminositybased on the prescriptions presented by Fragos et al. (2008,2009), which also take into account the transient behaviorof XRBs. However, in order to compare our models withobservational data, we need to estimate the X-ray luminosityin the specific energy band where the data were taken.

McClintock & Remillard (2006) and Wu et al. (2010) com-piled two samples of RXTE observations of Galactic NS and

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Table 1Model Parameters

Parameter Notation Value Reference

Initial orbital period distribution F (P ) Flat in log P Abt (1983)Initial eccentricity distribution F (e) Thermal F (e) ∼ e Heggie (1975)Binary fraction fbin 50%Magnetic braking Ivanova & Taam (2003)Metallicity Z 0.0001, 0.0002, 0.005, 0.001,

0.002, 0.005, 0.01, 0.02, 0.03IMF (slope) −2.35 or −2.7 Kroupa (2001); Kroupa & Weidner (2003)Initial mass ratio distribution F (q) Flat, twin, or 50% flat + 50% twin Kobulnicky & Fryer (2007); Pinsonneault & Stanek (2006)CE efficiency αCE 0.1, 0.2, 0.3, or 0.5 Podsiadlowski et al. (2003)Stellar wind strength ηwind 0.25, 1.0, or 2.0 Belczynski et al. (2010)CE during HG Yes or No Belczynski et al. (2007)SN kick for ECS/AICa NS 20% of the normal NS kicks Linden et al. (2009)SN kick for direct collapse BH Yes or No Fragos et al. (2010)

Note. a Electron capture supernova/accretion induced collapse.

BH XRBs at different spectral states, for which they also calcu-lated the best-fit parameters of simple spectral models. Out ofthe two lists (which in some cases contained multiple observa-tions of the same object at different spectral states) we chose allXRBs for which there was a distance measurement and a BHmass determination for BH XRBs. For the case of NS XRBs,we assumed a nominal mass of 1.4 M�. Using the appropri-ate XSPEC models, we calculated bolometric correction factorsbetween the bolometric X-ray luminosity (0.03–100 keV) in-ferred by the best-fitting model for each observation, and theX-ray luminosity in a specific energy band. We should notehere that the fraction of the energy emitted by XRBs outsidethe 0.03–100 keV range is negligible, and hence the terms bolo-metric luminosity and X-ray bolometric luminosity can be usedinterchangeably. For each system, we calculate these bolomet-ric correction factors with and without absorption corrections.These factors would correspond to the observed and intrinsicX-ray luminosity at a specific energy band, respectively.

According to McClintock & Remillard (2006) and Wu et al.(2010), the XRBs in their compilations are in either a low-hardspectral state, where the spectrum is dominated by a power-law component, or in a high-soft state, where the spectrum isdominated by the thermal emission of the disk. McClintock& Remillard (2006) also use a third category of a “steeppower-law” state for BH XRBs with accretion rates close tothe Eddington limit. These systems do show a soft spectrum,which, however, can be fit better with an absorbed steep powerlaw than with a thermal disk model. For our purposes, we donot treat separately systems in the high-soft and steep power-lawstates, as they turn out to have very similar bolometric correctionfactors.

In our calculations we treat separately NS and BH XRBs.The transition between low-hard and high-soft states in bothcases happens at a luminosity of ∼5% LEdd (McClintock &Remillard 2006). Figure 3 shows the correction factor (ηBol)between the bolometric X-ray luminosity and the intrinsic (aftercorrecting for absorption) luminosity in the 0.3–8 keV band (i.e.,ηBolLBol = L0.3–8 keV), as a function of the Eddington ratio ofthe source. For each energy band, we calculate the mean andthe variance of the bolometric correction for the high-soft andlow-hard states, and BH and NS XRBs separately. Furthermore,we perform our calculations with and without correcting forabsorption due to circumstellar or interstellar gas, correspondingto the observed and the intrinsic luminosity accordingly. The fulllist of the calculated bolometric corrections for different bands

Figure 3. Bolometric correction factors for the 0.3–8 keV band for each of theobservations from the McClintock & Remillard (2006) and Wu et al. (2010)samples. The star symbols denote systems in the low-hard state, while the opensquares denote systems in the high-soft state. The blue color corresponds to NSXRBs and red to BH XRBs. The dashed vertical line shows the approximateEddington ratio at which the state transition happens. The horizontal lines denotethe mean bolometric correction of NS or BH XRBs at the low-hard or high-softstate, respectively.

(A color version of this figure is available in the online journal.)

can be found in Table 2. The mean values of the calculatedbolometric corrections for the different energy bands are used inEquations (1)–(6) of Fragos et al. (2008) in order to compare ourPS models with observational data. The variances we calculatecan enter in the estimation of the uncertainties of our models.In the rest of the paper, we use the absorption uncorrectedvalues in our comparison, as these may be most easily comparedwith observed X-ray luminosities of galaxies. This is effectivelyequivalent with the assumption that all galaxies in the universehave similar intrinsic absorption as the Milky Way.

Although these bolometric corrections are based on spectralfits of RXTE data that have a low-energy limit of ∼2.5 keV,the RXTE band covers most of the Wien tail of the diskblackbody component, allowing a reliable measurement of thedisk temperature (e.g., Figures 4.8 and 4.9 in McClintock &Remillard 2006). A comparison between the disk temperaturebased on RXTE measurements, with similar measurements forthe same objects in similar states derived from spectra extendingto lower energies (using data obtained with XMM-Newton,Suzaku, BeppoSAX, or ASCA; e.g., Kotani et al. 2000; Kubota

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Table 2Mean Value and Standard Deviation of the Bolometric Correction (ηbol) Factor at Different Energy Bands

Absorption Corrected Absorption Uncorrected

High-Soft State Low-Hard State High-Soft State Low-Hard State

Energy Band NS BH NS BH NS BH NS BH

0.3–2 keV 0.06 ± 0.09 0.28 ± 0.20 0.08 ± 0.06 0.13 ± 0.11 0.05 ± 0.08 0.09 ± 0.10 0.05 ± 0.03 0.08 ± 0.060.3–7 keV 0.61 ± 0.09 0.75 ± 0.18 0.29 ± 0.12 0.36 ± 0.13 0.57 ± 0.09 0.48 ± 0.14 0.25 ± 0.08 0.30 ± 0.080.3–8 keV 0.67 ± 0.09 0.78 ± 0.16 0.31 ± 0.12 0.39 ± 0.13 0.63 ± 0.09 0.51 ± 0.13 0.27 ± 0.09 0.33 ± 0.100.3–10 keV 0.77 ± 0.08 0.82 ± 0.13 0.36 ± 0.13 0.43 ± 0.13 0.73 ± 0.08 0.55 ± 0.12 0.32 ± 0.10 0.38 ± 0.100.5–2 keV 0.06 ± 0.09 0.26 ± 0.19 0.08 ± 0.06 0.12 ± 0.09 0.05 ± 0.08 0.09 ± 0.10 0.05 ± 0.03 0.07 ± 0.050.5–10 keV 0.77 ± 0.08 0.80 ± 0.11 0.36 ± 0.13 0.42 ± 0.13 0.73 ± 0.07 0.55 ± 0.12 0.32 ± 0.10 0.37 ± 0.102–10 keV 0.71 ± 0.08 0.54 ± 0.12 0.28 ± 0.09 0.30 ± 0.11 0.68 ± 0.07 0.46 ± 0.09 0.27 ± 0.08 0.30 ± 0.11

et al. 2005; Gou et al. 2009; Caballero-Garcı́a et al. 2009;Tamura et al. 2012), shows very good agreement, indicating thatindeed the relatively restricted soft X-ray coverage of RXTE doesnot significantly bias the temperature of the thermal componentof sources in the high state.

4. OBSERVATIONAL CONSTRAINTS AND STATISTICALMODEL COMPARISON

4.1. Available Observational Constraints

To constrain our model parameters, we compare our mod-els to observations of the X-ray properties of local galaxies.There have been several recent studies where high-quality mul-tiwavelength data are used to derive scaling relations betweentotal X-ray emission from HMXBs and the galaxy-wide SFRas well as a scaling between total X-ray emission from LMXBsand stellar mass, in the local universe. Boroson et al. (2011)selected a sample of 30 normal early-type galaxies, for allof which optical spectroscopy and Chandra data were avail-able. From the optical data they estimated the stellar mass,while from spectral fitting of the X-ray data they estimated thecontribution of unresolved LMXBs to the diffuse X-ray emis-sion. We averaged the measurements for the Boroson et al.(2011) sample to calculate the X-ray emission from LMXBsper unit stellar mass, finding log(LX,LMXBs [0.5–8 keV]/M∗) =29.18 ± 0.17 erg s−1 M−1� . Lehmer et al. (2010) usedChandra observations of star-forming galaxies to study thegalaxy-wide XRB emission and its correlation with SFR andstellar mass. They assumed that X-ray emission in the hardX-ray band (2–10 keV) of these galaxies can be decomposedinto two components. The first component is related to HMXBsand should be proportional to the SFR of the galaxy, while thesecond component is related to LMXBs and should be propor-tional to the stellar mass of the galaxy. This simple model, whichis described by the equation LX [2–10 keV] = αM∗ + β × SFR,was fitted to their data, and the best-fitting values werefound to be log α ≡ log(LX,LMXBs [2–10 keV]/M∗) = 28.96 ±0.34 erg s−1 M−1� and log β ≡ log(LX,HMXBs [2–10 keV]/SFR) =29.21±0.34 erg s−1 M−1� yr. Most recently, Mineo et al. (2012a),based on a homogeneous set of X-ray, infrared, and ultravio-let observations from the Chandra, Spitzer, GALEX, and TwoMicron All Sky Survey archives, studied populations of HMXBsin a sample of 29 nearby star-forming galaxies and their re-lation to the SFR. In agreement with previous results, theyfound that HMXBs are a good tracer of the recent star for-mation activity in the host galaxy and their collective lumi-nosity scales with the SFR as log(LX,HMXBs [0.3–8 keV]/SFR) =29.47 ± 0.4 erg s−1 M−1� yr.

Tzanavaris & Georgantopoulos (2008) used multiwavelengthdata sets of the CDFS, E-CDFS, CDFN, and XBootes fields toconstruct XLFs of normal galaxies in different redshift bins. Theintegral of these XLFs gives us the total X-ray luminosity perunit volume of normal galaxies in three redshift bins. Tzanavaris& Georgantopoulos (2008) used the soft, 0.5–2 keV, Chandraenergy band, as Chandra is most sensitive in this band. However,this band likely also contains significant emission from hotdiffuse gas. Hence we can only use these observed values asupper limits when comparing them to our simulations whichdo not include any emission from hot gas. We should notehere that in the last few years there have been several X-raystacking studies, especially in the Chandra deep fields (e.g.,Lehmer et al. 2007, 2008; Symeonidis et al. 2011), wherethe X-ray luminosity per unit stellar mass or unit SFR, forearly- and late-type galaxies, respectively, has been measured atz ≈ 0–1.4. However, a proper comparison of our models withthese observational surveys would require a careful matching ofthe sample selection of these studies, which is outside the scopeof this paper.

4.2. Model Likelihood Calculation

We compare the results by Boroson et al. (2011) and Lehmeret al. (2010) to the prediction of our models for LX, LMXBs/M∗at z = 0 and in two different energy bands, and the results byMineo et al. (2012a) and Lehmer et al. (2010) to our models’predicted LX,HMXBs/SFR, again in two different energy bands.Furthermore, we compare our model predictions for the X-rayluminosity per unit volume with values reported by Tzanavaris& Georgantopoulos (2008), which we use as upper limits. Thequantitative comparison is done by calculating the likelihoodof the observations given a model, for each model, and thencomparing the likelihood values.

Assuming that the reported errors for all observed quantitiesare Gaussian in the log space, then the likelihood of the datagiven a model becomes

Li(D|M,fj ) =∏

j=1,7G(Mi,j ; fjμj , σj )P (fj ), (1)

where G is the Gaussian function, μj and σj forj = 1, 4 are the observed values and the associ-ated errors at z = 0 for log(LX,LMXBs [0.5–8 keV]/M∗)(Boroson et al. 2011), log(LX,LMXBs [2–10 keV]/M∗) (Lehmer et al.2010), log(LX,HMXBs [2–10 keV]/SFR) (Lehmer et al. 2010), andlog(LX,HMXBs [0.3–8 keV]/SFR) (Mineo et al. 2012a), μj and σjfor j = 5, 7 are the observed values and the associated errorsat z ∼ 0.13, ∼0.38, and ∼0.78 for log(LX [0.5–2 keV]/Volume)(Tzanavaris & Georgantopoulos 2008). Mi,j are the predictions

6


Table 3List of Selected PS Models that Appear in the Text and Figures of This Paper

Model αCEa IMF Exponentb ηwindc CE-HGd q Distributione κDC BHf Rankg log(Likelihood Ratio)h

245 0.1 −2.7 1.0 No 50–50 0.1 1 0.0000000229 0.1 −2.7 2.0 Yes 50–50 0.0 2 −0.035048515269 0.1 −2.7 1.0 Yes 50–50 0.1 3 −0.11226917205 0.1 −2.7 2.0 No 50–50 0.0 4 −0.13235138249 0.1 −2.35 2.0 No 50–50 0.1 5 −0.28666705273 0.1 −2.35 2.0 Yes 50–50 0.1 6 −0.2892639353 0.1 −2.7 1.0 No flat 0.1 20 −1.3945094246 0.2 −2.7 1.0 No 50–50 0.1 25 −2.0332112241 0.1 −2.35 1.0 No 50–50 0.1 31 −2.3582808253 0.1 −2.7 2.0 No 50–50 0.1 14 −0.90617906261 0.1 −2.7 0.25 No 50–50 0.1 43 −3.4548391197 0.1 −2.7 1.0 No 50–50 0.0 13 −0.80759106

Notes.a CE efficiency parameter.b Exponent of the high-mass power-law component of the IMF: Kroupa (2001, −2.35) or Kroupa & Weidner (2003, −2.7).c Stellar wind strength parameter with which the “standard” (Belczynski et al. 2010) stellar wind prescription is multiplied.d Yes: all possible outcomes of a CE event with an HG donor are allowed; No: a CE with an HG donor star will always result to a merger.e Binary mass ratio distribution. “50–50” indicates half of the binaries originate from a “twin binary” distribution and half from flat massratio distribution.f Parameter with which the “standard” Hobbs et al. (2005) kick distribution is multiplied for BHs formed though an SN explosion withnegligible ejected mass.g Ranking of the model in our statistical comparison.h Ratio of the likelihood of the observations given a model to our maximum likelihood model (log L(O|Mi ) − log L(O|Mref )).(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regardingits form and content.)

of the ith model for each of these quantities and fj is the frac-tion of the luminosity density μj assumed to be due to XRBs.P (fj ) is the prior probability for a given value of fj. Since weare not attempting to constrain the X-ray binary fraction f wemarginalize over f, i.e.,

Li,j (Mi,j |D) =∫

Li(D|Mi,j , fj )P (fj )dfj . (2)

For the z = 0 points we assume that the luminosity densitiesare purely due to XRBs and therefore f = 1. In this caseP (fj=1,4) = δ(fj = 1). We assume a flat prior for the XRBfraction for the z > 0 luminosity densities, i.e., P (fj ) = Cj ,where the constants Cj are chosen so that the likelihood functionremains normalized to unity. Noting that∫ 1

0G(Mi,j ; fjμj , σj )Cjdfj =

∫ μj0

G(Mi,j ;μ′j , σj )Cjdμ′j

=∣∣∣∣∣erf

[(μj − Mi,j)2

2σ 2j

]− erf

[M2i,j2σ 2j

]∣∣∣∣∣ ,(3)

the marginalized likelihood is then

Li,j (Mi,j |D) =∏

j=1,4G(Mi,j ;μj , σj )

×∏

j=5,7

∣∣∣∣∣erf[

(μj − Mi,j)22σ 2j

]− erf

[M2i,j2σ 2j

]∣∣∣∣∣.(4)

Figure 4 shows the likelihood ratio of each of our 288 modelsto the maximum likelihood model (L(D|Mref.)). This effectively

Figure 4. Ratio of the likelihood of the observations given a model to ourmaximum likelihood model.

means that we renormalized the likelihood of the observationsgiven a model, so that our maximum likelihood model has alikelihood value of 1. A list of the likelihood values of eachmodel can be found in Table 3. One should note that the scale ofthe Y-axis in Figure 4 is logarithmic, and only a small fractionof all the 288 models we considered have a likelihood close tothe our reference, maximum likelihood model (Models 245).Namely, only 14 out of 288 models have likelihood valueswithin a factor of 10 from the maximum likelihood model,and only 24 within a factor of 100, respectively, which isencouraging evidence that our calculated likelihood is a gooddiscriminator between the different models. One other apparentfeature of Figure 4 is that Models 100–199 have systematicallylower likelihood values than the rest. In all these models theinitial binary mass ratio is assumed to be “twin,” i.e., a flatdistribution between 0.9 and 1.0, which always results in anLMXB population inconsistent with observations (see alsoSection 5.1 for further discussion).

Figure 5 shows the X-ray luminosity in the 2–10 keV range,from the LMXB population, per unit stellar mass (top left panel)

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Figure 5. X-ray luminosity in the 2–10 keV range, from the LMXB population, per unit stellar mass (top left panel) and X-ray luminosity in the same range, fromthe HMXB population, per unit SFR (top right panel), as a function of redshift, for the six models that satisfy within 1σ all the observational constraints. The greensquares show the observed values for LX,LMXBs[2–10 keV]/M∗ (top left panel) and LX,HMXBs[0.5–8 keV]/SFR (top right panel) as derived by Lehmer et al. (2010). The redsquares show the observed constraints for LX,LMXBs[0.3–8 keV]/M∗ by Boroson et al. (2011), and for LX,HMXBs[0.5–8 keV]/SFR by Mineo et al. (2012a) after convertedfor demonstration purposes to the 2–10 keV energy band, in the left and right panels, respectively. The bottom panel shows the X-ray luminosity density coming fromthe whole XRB population as a function of redshift. The green squares show the observed values as reported by Tzanavaris & Georgantopoulos (2008), which we usedas upper limits in our statistical analysis. The parameters of the different models are shown in Table 3.


and X-ray luminosity in the same range, from the HMXBpopulation, per unit SFR (top right panel) as a function ofredshift. The six models shown in this figure are the ones thatsatisfy within 1σ all the observational constraints, which are alsothe six models with the highest likelihood values. The observedvalues of these two quantities for z = 0 by Lehmer et al. (2010),and by Boroson et al. (2011) and Mineo et al. (2012a) afterconverting them to the 2–10 keV range, are also shown forcomparison. The bottom panel of Figure 5 shows the X-rayluminosity density coming from the whole XRB population asa function of redshift. The observational constraints derived byTzanavaris & Georgantopoulos (2008), shown as green squaresin the figure, are used as upper limits in our statistical analysis.Figure 5 demonstrates the robustness of our model predictions.All six maximum likelihood models exhibit a very similarbehavior for the whole range of redshifts, and the differencesbetween the different models at higher redshifts are equivalentto the uncertainties of the observed values in the local universe.

4.3. The Specific X-Ray Luminosity of Local Elliptical Galaxies

Kim & Fabbiano (2010), using a sample of local ellipticalgalaxies with measured stellar ages, found that the fractionof bright LMXBs in “young” elliptical galaxies is highercompared to “old” ellipticals. More recently, Zhang et al.(2012), using a similar sample of nearby ellipticals, reporteda positive correlation between the normalization of the XLFs ofthese galaxies, and the luminosity average age of their stellarpopulation, as estimated by single stellar population spectralenergy distribution fitting results. The specific X-ray luminosity

in these galaxies (LX/M∗), which depends both on the shape andthe normalization of the XLF, shows little to no evolution withthe estimated stellar age of the galaxies (see also Boroson et al.2011), which at face value seems to be inconsistent with ourprediction for the evolution of LX/M∗ with redshift. However,the galaxy sample in both of these studies also shows a strongcorrelation of the estimated stellar age with the globular clusterspecific frequency (SN), as typical nearby old giant ellipticalstend to have a high SN . At the same time, a strong correlationbetween LX/M∗ and SN has been observed in these galaxies(Boroson et al. 2011). In addition, the age estimates of theobserved galaxies are derived under the assumption of a singleage stellar population, and assigning single ages to “young”ellipticals will suffer from large uncertainties in the stellarages due to very young populations mixing with old stellarpopulations (see, e.g., Idiart et al. 2007). Hence, it is hard todisentangle whether the observed correlation reported by Zhanget al. (2012) means that the specific X-ray luminosity of theLMXB population in these galaxies indeed does not evolvewith stellar population age, or it is an effect of the underlyingcorrelations in the properties of the galaxy sample they used,and uncertainties in the age estimates. In either case, we shouldstress again here that our models consider only field XRBsand a general galaxy population, where the dynamically formedXRBs are expected to have minimal contribution. In contrast, theobserved correlations discussed above are driven by globular-cluster rich old elliptical galaxies whose LMXB population isprobably dominated by dynamically formed LMXBs (e.g., Irwin2005).

8


Figure 6. Specific X-ray luminosity in the 0.3–8 keV energy range, i.e.,luminosity per unit stellar mass, of a coeval stellar population as a function of thepopulation’s age for our “reference” model (Model 245; see also Sections 2.4and 4.2) and for solar metallicity. In the same figure, overplotted are the specificX-ray luminosities, in the same energy band, of nearby elliptical galaxies forwhich estimates of their stellar population age are available in the literature.These data points are derived from the galaxy sample presented in Borosonet al. (2011).


Figure 6 shows the evolution of the specific X-ray luminosityfrom a coeval stellar population (similar to Figure 2, but in the0.3–8 keV energy range) as a function of the stellar populationage for our “reference” model (Model 245; see also Sections 2.4and 4.2) and for solar metallicity. In the same figure, we haveoverplotted the LX/M∗ in the same energy range for ellipticalgalaxies with stellar age estimates from the Boroson et al.(2011) sample. The galaxy sample in Boroson et al. (2011)is very similar to the sample by Zhang et al. (2012). Wewant to stress here that a direct comparison of the modelcurve to the observed data points is not appropriate for twomain reasons: the model curve neglects the dynamically formedLMXB population which can be significant for some of thesegalaxies, and the age estimates of the observed galaxies arederived under the assumption of a single age stellar population.However, assigning single ages to young ellipticals will sufferfrom large uncertainties in the stellar ages due to very “young”populations mixing with old stellar populations. Keeping inmind these two important caveats, we can make a few instructiveobservations. (1) Comparing the model curve to the observedLX/M∗ of the “old” (∼9–12 Gyr) ellipticals, we find that ourmodels underpredict the LMXB specific luminosity. This isto be expected, as in these galaxies the dynamically formedLMXB population is significant, and our models consider onlythe field LMXB population. (2) Comparing the model curveto the ellipticals with ages ∼4–5 Gyr (which also tend to havelower specific globular cluster frequencies), we find that ourmodels predict the same LX/M∗ as the observations. This canalso be seen in the top left panel of Figure 5. The average mass-weighted age of the stellar population at z = 0 based on theMillennium II simulation is ∼4.7 Gyr, and that predicted fromour models LX/M∗ (coming from LMXBs) is in very goodagreement with the LX/M∗ as reported by Boroson et al.(2011). (3) Our model curve is in disagreement with theobservationally determined LX/M∗ of the “young” ellipticals(ages of ∼1–2 Gyr). However, these are the galaxies for whichthe single age stellar population assumption most likely breaksdown. This makes the ages highly uncertain, as a small fractionof young stars (


Figure 7. Bolometric X-ray luminosity of the LMXB population per unit stellar mass (left panel) and X-ray luminosity of the HMXB population per unit SFR (rightpanel), as a function of redshift, for eight selected models that show the dependence of the models’ predictions to the different model parameters. Our maximumlikelihood model (Model 245) is shown with the bold solid (black) line. The parameters of the different models are shown in Table 3.


bound envelopes. This in fact seems to be true for massive starsbased on the actual estimates of envelope binding energies (seeFigures 1–4 of Dominik et al. 2012).

Changing the initial binary mass ratio distribution between aflat distribution and 50% flat–50% twin distribution affects theXRB population in a similar way (compare Model 53 and Model245 in Figure 7). The progenitor of an LMXB is a binary withhigh-mass ratio. By forcing half of the systems to have an initialmass ratio close to 1, the formation rate of LMXBs is decreasedby a factor of two. On the other hand, the HMXB populationis largely unaffected. This suggests that in a binary populationwith a flat initial mass ratio distribution, approximately 10%of the HMXBs have as progenitors primordial binaries witha mass ratio between 0.9 and 1. The statistical comparisonof our models with observations favors a mixed initial massratio distribution of 50% flat–50% twin distribution, which isconsistent with observational surveys of young binaries (e.g.,Pinsonneault & Stanek 2006), although some recent studieshint toward a single flat distribution (Sana & Evans 2011).A pure twin mass ratio distribution, although it is includedin our parameter study (Models 100–199), results in modelsthat are inconsistent with observations, as it will completelyprevent the formation of LMXBs. Figure 4 shows that modelswith a pure twin mass ratio distribution (Models 100–199) havesystematically lower likelihood values than the rest.

Stellar winds also play an important role in the formationand evolution of XRBs, and they do so primarily in two ways.A stronger stellar wind will increase the accretion rate on thecompact object of a wind-fed HMXB, making it more luminous.In contrast, a weaker stellar wind will result in smaller overallmass loss of the primary star that will form the compact object,and hence in the formation of more numerous and more massiveBHs. BH-XRBs tend to be more luminous than XRBs with NSaccretors, as on the one hand they can form stable Roche lobeoverflow (RLO) XRB systems with massive companion stars,and on the other hand they can drive in general higher accretionrates (compared again to NS accretors), both in RLO and wind-fed systems, because of the higher mass of the BH accretor.Furthermore, a reduced stellar wind would result in less orbitalexpansion due to angular momentum loss from the wind, and inoverall more systems that will encounter Roche lobe overflowmass transfer. It turns out that the latter two effects are thedominant ones. Comparing Model 253 (ηWind = 2.0) and Model261 (ηWind = 0.25) to our maximum likelihood model (Model

245, ηWind = 1.0), one can see the large effect of stellar winds:for stronger winds (model 253) the emission of both LMXBsand HMXB is suppressed while for weaker winds (model 261)the emission of both is boosted. Our statistical analysis showedthat the “standard” wind prescription (ηWind = 1.0), compiledand calibrated by Belczynski et al. (2010), is favored, but modelswith stellar winds increased by a factor of two are also consistentwith observations. If this result is taken at face value (i.e., ifpotential degeneracies with other free parameters are neglected),it indicates that there is not much more unaccounted clumpingin winds of massive stars that in the past led to overestimates ofmass-loss rates.

The power-law slope at the high-mass end of the IMF affectsthe population of XRBs in a way equivalent to stellar winds, inthe sense that a flatter IMF will produce relatively more BHscompared to a steeper one. Hence, a flatter IMF will resultin more luminous populations of both LMXBs and HMXBs(compare Model 241 to Model 245). In our standard treatmentof supernova events, the most massive BHs receive no kickduring their formation. Allowing for a small kick (10% ofthe standard kicks that NSs receive) in these systems doesnot significantly affect the LMXB population, but results in anoverall less luminous HMXB population (compare Model 245to Model 197). HMXBs originate from more massive binarieson average, where the formation of a BH through direct corecollapse is more likely. Thus, allowing for small kicks in thesesupernova events leads to the disruption of binaries that wouldotherwise form an HMXB.

Finally, we found that whether or not allowing for all possibleoutcomes in CE phases with donor stars in the Hertzsprung gap,although it affects the shape of the XLF for a given galaxy(Luo et al. 2012), has a negligible effect on the integrated X-rayluminosity of an LMXB population and slightly increases theluminosity of an HMXB population (compare Model 245 toModel 269). This comes from the fact that LMXB progenitorsare on average less massive than stars producing HMXBs. Theprobability of a CE phase happening while the donor star is onthe Hertzsprung gap is very low, since only very massive starsexperience significant expansion during Hertzsprung gap. Incontrast, for massive binaries the Hertzsprung gap CE happensfrequently and if the survival is allowed some systems surviveand form extra population of HMXBs. These additional sourceslead to a factor of ∼1.5 increase in the integrated HMXBX-ray luminosity throughout the cosmic time. This is a very

10


Figure 8. Bolometric X-ray luminosity per unit volume (top panel), unit ofstellar mass (middle panel), and unit of SFR (bottom panel), as a function ofredshift, for our maximum likelihood model (Model 245). The solid (black) linescorrespond to the whole XRB population, while the dotted (blue) lines show thecontribution of the HMXBs, and the dashed (red) lines show the contributionof the LMXBs. For comparison, the SFR density is shown in the top panel witha gray dash-dotted line. The vertical solid (black), dotted (blue), dashed (red),and dash-dotted (gray) lines denote the redshifts at which the peaks of the X-rayluminosity density from the whole XRB population, the HMXBs, the LMXBs,and the SFR density occur.


similar effect as noted for double compact object populations,for which massive BH–BH progenitors are greatly affected byHertzsprung gap CE while lighter NS–NS progenitors are not(Belczynski et al. 2007).

5.2. Evolution of Global Scaling Relations with Redshift

Figure 8 shows the bolometric X-ray luminosity per unitvolume, unit of stellar mass, and unit of SFR, as a functionof redshift, for our maximum likelihood model (Model 245).The relative contribution in these quantities of the LMXB andHMXB populations is also shown. Comparing in the top panelof Figure 8 the redshift evolution of the SFR density to theevolution of the X-ray luminosity density coming from LMXBs,one notices an evident time difference between the peaks of the

two quantities. The peak of the SFR density occurs at z ∼ 3.1,while the peak of the X-ray luminosity density coming fromthe LMXB populations happens at z ∼ 2.1. This delay betweenthe two peaks translates into a typical delay time of ∼1.1 Gyrbetween the formation of a progenitor binary star and time thatthe systems reaches the LMXB phase. In earlier work by White& Ghosh (1998) and Ghosh & White (2001), this timescale wasa free parameter in their models which they were not able toconstrain. We should note here that the value of timescale isdependent on the exact definition of what one calls an LMXB.As mentioned earlier, in this work we define as LMXB anyRLO XRB with a donor star less massive than 3 M�. Shiftingthis mass boundary to lower masses will lengthen the delay.

Comparing now the SFR density peak to the peak of theX-ray luminosity density coming from HMXBs, one wouldexpect that two peaks occur simultaneously. However, thepeak X-ray luminosity density coming from HMXBs occurs atz ∼ 3.9, ∼0.5 Gyr before the peak of the star formation. As wecan see from the bottom panel of Figure 8, the X-ray luminositycoming from HMXBs, per unit SFR, is not constant with time,but instead it is increasing with redshift. This is a result of themetallicity evolution. The mean metallicity of the newly formedstars is decreasing with redshift (see Figure 1, lower panel). Alower metallicity translates into weaker stellar winds, which inturn results in more numerous and more massive BHs. SinceBH-HMXBs tend to be more luminous than NS-HMXBs, theX-ray luminosity coming from HMXBs per unit SFR is higherfor lower metallicity stellar populations, and hence at higherredshifts. Coming back to the time difference between the peakof the SFR and the peak of the X-ray luminosity density fromHMXBs, it is now evident that it is because of the dependenceof the HMXB population to the metallicity and the evolution ofthe metallicity with redshift.

One additional point that is demonstrated in Figure 8 isthat LMXBs dominate the X-ray emission from XRBs in ouruniverse today by a factor of ∼2.5. The transition between anHMXB and an LMXB-dominated XRB population happens atz ∼ 2.5. This finding implies that the X-ray luminosity of anXRB population in a “typical” galaxy, with a star formationhistory similar to the global star formation history of theuniverse, is dominated by the X-ray emission of LMXBs. Thisis not an unexpected result, given that in the Milky Way, whichis a typical spiral galaxy, there are only a few HMXBs withluminosity above 1037 erg s−1 (Grimm et al. 2002; Voss & Ajello2010). However, our finding should serve as an extra caution toa usual misconception that the XRB population of galaxies thatcurrently show some star formation have a negligible LMXBpopulation. Lehmer et al. (2010) showed observational evidencethat the X-ray luminosity from galaxies with SFR as high as∼2 M� yr−1 has a non-negligible contribution from LMXBs.

Our modeling predicts that the X-ray luminosity coming fromHMXBs, per unit SFR is increasing with redshift, and that this isa result of the metallicity evolution of the universe. The evolutionof the X-ray luminosity from HMXBs per unit SFR predicted byour models (by a factor of ∼10 out to z ∼ 15) is consistent withthe constraint set by the observed cosmic X-ray background(Dijkstra et al. 2012). Although the X-ray luminosity comingfrom HMXBs, per unit SFR, changes by a factor of five betweenz = 0 and z ∼ 10, the observed signature of this effect wouldbe masked by the contamination of LMXBs. The bottom panelof Figure 8 shows that the contamination of LMXBs operatesin such a way that the X-ray luminosity from the whole XRBpopulation, per unit SFR, remains approximately constant with

11


time. These results are in agreement with the findings by Lehmeret al. (2008) and Mineo et al. (2012b) for the late-type galaxypopulation. Hence, our modeling suggests that the effect ofthe metallicity evolution to the HMXB population can only beobserved with a carefully selected galaxy sample, where allgalaxies have high enough SFR to stellar mass ratios, ensuringthat their XRB populations are dominated by HMXBs.

The middle panel of Figure 7 shows that the X-ray luminosityof the whole XRB population, per unit stellar mass, evolves withredshift following approximately a single power law from z = 0back to z ∼ 15. This relation probes two distinct phases of thecosmic evolution of the XRB population. At z � 2.5, where theemission from LMXBs dominates the total X-ray luminosity,the evolution of the X-ray luminosity per unit stellar mass isrelated to the average age of the LMXB population. The fact thatrelatively younger stellar populations are associated with moreluminous populations of LMXBs has already been observed inX-ray stacking studies of distant galaxies (Lehmer et al. 2007).Lehmer et al. (2007) investigated the average X-ray propertiesof early-type galaxies within the Extended Chandra Deep Field-South, and found a slight increase of LX/LB,�, where LB,�is the optical luminosity in the B band, with redshift, over theredshift range z = 0–0.7, in excellent agreement with our modelpredictions. At z � 2.5, it is the emission from HMXBs thatdominates the X-ray luminosity of the XRB population. Thetotal X-ray luminosity coming from HMXBs is to the first order,neglecting the metallicity evolution effects, proportional to theSFR. Hence, the evolution of X-ray luminosity per unit stellarmass at z � 2.5 can be a probe of the evolution of the specificSFR (SFR per unit stellar mass) with redshift.

In the interpretation of our simulation results, and the com-parison with the observational data, one should keep in mindthat all the quantities calculated in this paper correspond to theaverage of all galaxies in the universe. A more detailed compar-ison of our models with galaxy surveys of early- and late-typegalaxies separately, where all the sample selection effects aretaken into account, is discussed in other works (Tremmel et al.2012; Basu-Zych et al. 2012; A. Hornschemeier et al. 2013, inpreparation).

6. SUMMARY AND CONCLUSIONS

We present here the first PS study of XRBs in a cosmo-logical context. We created the largest grid of 288 PS modelsover nine metallicities, where we varied all the major modelparameters that are known to affect the evolution of XRBs. Weconvolved these models with information about the star forma-tion history and metallicity evolution of the universe from theMillennium II simulation and the Guo et al. (2011) semi-analyticgalaxy catalog. The combination of our PS models with a cosmo-logical simulation allowed us to derive global scaling relationsof the XRB population with properties such as SFR and stellarmass, and the evolution of these relations with redshift. Thesepredictions were compared statistically with observations fromthe local universe in order to constrain our models and makerobust predictions about the high-redshift universe. The mainconclusions of this work can be summarized as follows.

1. The statistical comparison of our model predictions re-vealed several models that are in excellent agreement withobservations of the local universe. Furthermore, we foundthat all models that are consistent with observational datain the local universe exhibit very similar behavior at higher

redshifts, indicating that our predictions for the redshiftevolution of XRB populations are robust.

2. Although the main goal of this paper is not to constrain theparameters of our PS models but instead to study the redshiftevolution of XRB populations, our parameter study allowsfor some general conclusions on the possible values of thePS parameters we varied. The statistical analysis showedthat a CE efficiency λ × αCE � 0.1, where λ is a measureof the central concentration of the donor star, and possiblya mixed initial mass ratio distribution (i.e., 50% of thebinaries are drawn from a flat initial mass ratio distributionand 50% from a “twin” distribution) is necessary in order toproduce an LMXB population consistent with observations.These two parameters show some degeneracy, and a slightlylower CE efficiency would possibly favor a flat initial massratio distribution. On the other hand, model parameters thatregulate the formation rate of BH-XRBs, such as the IMFand the stellar wind strength, appear to be important for boththe LMXB and HMXB populations. This is not surprisingas XRBs with BH accretors can be very luminous, andeven a relatively small number of them can dominate theintegrated X-ray luminosity of a population. Again, theseparameters show a degeneracy as they affect the populationin a similar way, and only their combined effect can beconstrained from observations.

3. The X-ray luminosity of XRBs per unit stellar mass orunit SFR is significantly higher for low-metallicity stellarpopulations, due to the fact that the young massive O/Bstars, which are the precursors to compact object accretorsin XRBs, will lose less stellar mass from line-driven windsover their lifetimes for lower metallicities. This results inmore numerous and more massive BHs, and subsequentlymore luminous XRB populations.

4. The X-ray emission from XRBs in the local universe isdominated by LMXBs, and it is only at z � 2.5 thatHMXBs start to dominate the X-ray emission. The redshiftthat this transition happens is lower than that of the peakof star formation (z ∼ 3), which shows that there is adelay between the formation of primordial binaries andthe time at which these binaries become LMXBs. Theformation timescale of LMXBs is estimated to be ∼1.1 Gyr.This finding also implies that the X-ray luminosity of anXRB population in a “typical” galaxy, with a star formationhistory similar to the global star formation history of theuniverse, is dominated by the X-ray emission of LMXBs.

5. The formation rate of HMXBs follows closely the SFR.However, the X-ray luminosity from HMXBs per unit SFR(LX, HMXBs/SFR) depends also on metallicity. Taking intoaccount the metallicity evolution of the universe, we findthat the peak of the X-ray luminosity from HMXBs per unitvolume occurs ∼0.5 Gyr before the peak of the SFR density.Although the X-ray luminosity coming from HMXBs, perunit SFR, changes by half an order of magnitude over theevolution of the universe, the observed signature of thiseffect is masked by the contamination of LMXBs, makingthe X-ray luminosity from the whole XRB population perunit SFR approximately constant with redshift.

6. Finally, we found that at z � 2.5, where the emission fromLMXBs dominates the total X-ray luminosity, the evolutionof the X-ray luminosity per unit stellar mass is related to theaverage age of the LMXB population, while at z � 2.5 theevolution of X-ray luminosity per unit stellar mass can bea probe of the evolution of the specific SFR with redshift.

12


This first PS study of the evolution of XRB populationsacross comic time highlights the importance of the study ofX-ray luminous normal galaxies at high redshift. Furthermore,it lays the ground for future work that will study the role playedby XRBs in the formation and evolution of galaxies throughfeedback processes (e.g., Mirabel et al. 2011; Haiman 2011;Justham & Schawinski 2012).

The authors thank the anonymous referee whose careful re-port has helped to improve this paper. T.F. acknowledges supportfrom the CfA and the ITC prize fellowship programs. This workwas partially supported from NASA ADAP grant 09-ADP09-0071 (PI: A.H.). B.L. thanks the Einstein Fellowship Program.P.T. acknowledges support through a NASA Postdoctoral Pro-gram Fellowship at Goddard Space Flight Center, administeredby Oak Ridge Associated Universities through a contract withNASA. K.B. acknowledges support from MSHE grant N203404939. Computational resources supporting this work wereprovided by Northwestern University Quest HPC cluster andthe NASA High-End Computing (HEC) Program through theNASA Center for Climate Simulation (NCCS) at Goddard SpaceFlight Center.

REFERENCES

Abt, H. A. 1983, ARA&A, 21, 343Basu-Zych, A. R., Lehmer, B. D., Hornschemeier, A. E., et al. 2013, ApJ, 762,

45Bauer, F. E., Alexander, D. M., Brandt, W. N., et al. 2002, AJ, 123, 1163Belczynski, K., Bulik, T., Fryer, C. L., et al. 2010, ApJ, 714, 1217Belczynski, K., Kalogera, V., & Bulik, T. 2002, ApJ, 572, 407Belczynski, K., Kalogera, V., Rasio, F. A., et al. 2008, ApJS, 174, 223Belczynski, K., Kalogera, V., Zezas, A., & Fabbiano, G. 2004, ApJL, 601, 147Belczynski, K., & Taam, R. E. 2004, ApJ, 616, 1159Belczynski, K., Taam, R. E., Kalogera, V., Rasio, F. A., & Bulik, T. 2007, ApJ,

662, 504Belczynski, K., Wiktorowicz, G., Fryer, C. L., Holz, D. E., & Kalogera, V.

2012, ApJ, 757, 91Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003, ApJS, 149, 289Boroson, B., Kim, D.-W., & Fabbiano, G. 2011, ApJ, 729, 12Bouwens, R. J., Illingworth, G. D., Franx, M., & Ford, H. 2007, ApJ, 670, 928Boylan-Kolchin, M., Springel, V., White, S. D. M., Jenkins, A., & Lemson, G.

2009, MNRAS, 398, 1150Brandt, W. N., & Hasinger, G. 2005, ARA&A, 43, 827Caballero-Garcı́a, M. D., Miller, J. M., Trigo, M. D., et al. 2009, ApJ,

692, 1339Dijkstra, M., Gilfanov, M., Loeb, A., & Sunyaev, R. 2012, MNRAS, 421, 213Dominik, M., Belczynski, K., Fryer, C., et al. 2012, ApJ, 759, 52Fragos, T., Kalogera, V., Belczynski, K., et al. 2008, ApJ, 683, 346Fragos, T., Kalogera, V., Willems, B., et al. 2009, ApJL, 702, 143Fragos, T., Tremmel, M., Rantsiou, E., & Belczynski, K. 2010, ApJL, 719, 79Fryer, C. L., Belczynski, K., Wiktorowicz, G., et al. 2012, ApJ, 749, 91Ghosh, P., & White, N. E. 2001, ApJL, 559, 97Gilfanov, M. 2004, MNRAS, 349, 146Gilfanov, M., Grimm, H.-J., & Sunyaev, R. 2004, MNRAS, 347, L57Gou, L., McClintock, J. E., Liu, J., et al. 2009, ApJ, 701, 1076Grimm, H.-J., Gilfanov, M., & Sunyaev, R. 2002, A&A, 391, 923

Guo, Q., White, S., Boylan-Kolchin, M., et al. 2011, MNRAS, 413, 101Haiman, Z. 2011, Natur, 472, 47Heggie, D. C. 1975, MNRAS, 173, 729Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS,

360, 974Hornschemeier, A. E., Heckman, T. M., Ptak, A. F., Tremonti, C. A., & Colbert,

E. J. M. 2005, AJ, 129, 86Humphrey, P. J., & Buote, D. A. 2008, ApJ, 689, 983Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897Idiart, T. P., Silk, J., & de Freitas Pacheco, J. A. 2007, MNRAS, 381, 1711Irwin, J. A. 2005, ApJ, 631, 511Ivanova, N., Chaichenets, S., Fregeau, J., et al. 2010, ApJ, 717, 948Ivanova, N., Heinke, C. O., Rasio, F. A., Belczynski, K., & Fregeau, J. M.

2008, MNRAS, 386, 553Ivanova, N., Heinke, C. O., Rasio, F. A., et al. 2006, MNRAS, 372, 1043Ivanova, N., & Taam, R. E. 2003, ApJ, 599, 516Justham, S., & Schawinski, K. 2012, MNRAS, 423, 1641Kaaret, P., Schmitt, J., & Gorski, M. 2011, ApJ, 741, 10Kim, D.-W., & Fabbiano, G. 2010, ApJ, 721, 1523Kobulnicky, H. A., & Fryer, C. L. 2007, ApJ, 670, 747Kotani, T., Kawai, N., Nagase, F., et al. 2000, ApJL, 543, 133Kroupa, P. 2001, MNRAS, 322, 231Kroupa, P., & Weidner, C. 2003, ApJ, 598, 1076Kubota, A., Ebisawa, K., Makishima, K., & Nakazawa, K. 2005, ApJ, 631, 1062Lehmer, B. D., Alexander, D. M., Bauer, F. E., et al. 2010, ApJ, 724, 559Lehmer, B. D., Brandt, W. N., Alexander, D. M., et al. 2007, ApJ, 657, 681Lehmer, B. D., Brandt, W. N., Alexander, D. M., et al. 2008, ApJ, 681, 1163Lehmer, B. D., Xue, Y. Q., Brandt, W. N., et al. 2012, ApJ, 752, 46Linden, T., Kalogera, V., Sepinsky, J. F., et al. 2010, ApJ, 725, 1984Linden, T., Sepinsky, J. F., Kalogera, V., & Belczynski, K. 2009, ApJ, 699, 1573Luo, B., Fabbiano, G., Fragos, T., et al. 2012, ApJ, 749, 130Marchesini, D., van Dokkum, P. G., Förster Schreiber, N. M., et al. 2009, ApJ,

701, 1765McClintock, J. E., & Remillard, R. A. 2006, in Cambridge Astrophysics Series

39, Compact Stellar X-Ray Sources, ed. W. Lewin & M. van der Klis(Cambridge: Cambridge Univ. Press), 157

Mineo, S., Gilfanov, M., & Sunyaev, R. 2012a, MNRAS, 419, 2095Mineo, S., Gilfanov, M., & Sunyaev, R. 2012b, arXiv:1207.2157Mirabel, I. F., Dijkstra, M., Laurent, P., Loeb, A., & Pritchard, J. R. 2011, A&A,

528, A149Pinsonneault, M. H., & Stanek, K. Z. 2006, ApJL, 639, 67Podsiadlowski, P., Rappaport, S., & Han, Z. 2003, MNRAS, 341, 385Ptak, A., Mobasher, B., Hornschemeier, A., Bauer, F., & Norman, C. 2007, ApJ,

667, 826Ranalli, P., Comastri, A., & Setti, G. 2003, A&A, 399, 39Reddy, N. A., & Steidel, C. C. 2009, ApJ, 692, 778Sana, H., & Evans, C. J. 2011, in IAU Symp. 272, Active OB Stars: Structure,

Evolution, Mass Loss, and Critical Limits (Cambridge: Cambridge Univ.Press), 474

Scannapieco, C., Wadepuhl, M., Parry, O. H., et al. 2012, MNRAS, 423, 1726Schiminovich, D., Ilbert, O., Arnouts, S., et al. 2005, ApJL, 619, 47Symeonidis, M., Georgakakis, A., Seymour, N., et al. 2011, MNRAS, 417, 2239Tamura, M., Kubota, A., Yamada, S., et al. 2012, ApJ, 753, 65Tremmel, M., Fragos, T., Lehmer, B. D., et al. 2012, arXiv:1210.7185Tzanavaris, P., & Georgantopoulos, I. 2008, A&A, 480, 663Valsecchi, F., Glebbeek, E., Farr, W. M., et al. 2010, Natur, 468, 77Vattakunnel, S., Tozzi, P., Matteucci, F., et al. 2012, MNRAS, 420, 2190Voss, R., & Ajello, M. 2010, ApJ, 721, 1843White, N. E., & Ghosh, P. 1998, ApJL, 504, 31Wu, Y. X., Yu, W., Li, T. P., Maccarone, T. J., & Li, X. D. 2010, ApJ, 718, 620Xue, Y. Q., Luo, B., Brandt, W. N., et al. 2011, ApJS, 195, 10Zhang, Z., Gilfanov, M., & Bogdán, Á. 2012, A&A, 546, 36Zuo, Z.-Y., & Li, X.-D. 2011, ApJ, 733, 5

13

http://dx.doi.org/10.1146/annurev.aa.21.090183.002015http://adsabs.harvard.edu/abs/1983ARA&A..21..343Ahttp://adsabs.harvard.edu/abs/1983ARA&A..21..343Ahttp://dx.doi.org/10.1088/0004-637X/762/1/45http://adsabs.harvard.edu/abs/2013ApJ...762...45Bhttp://adsabs.harvard.edu/abs/2013ApJ...762...45Bhttp://dx.doi.org/10.1086/338903http://adsabs.harvard.edu/abs/2002AJ....123.1163Bhttp://adsabs.harvard.edu/abs/2002AJ....123.1163Bhttp://dx.doi.org/10.1088/0004-637X/714/2/1217http://adsabs.harvard.edu/abs/2010ApJ...714.1217Bhttp://adsabs.harvard.edu/abs/2010ApJ...714.1217Bhttp://dx.doi.org/10.1086/340304http://adsabs.harvard.edu/abs/2002ApJ...572..407Bhttp://adsabs.harvard.edu/abs/2002ApJ...572..407Bhttp://dx.doi.org/10.1086/521026http://adsabs.harvard.edu/abs/2008ApJS..174..223Bhttp://adsabs.harvard.edu/abs/2008ApJS..174..223Bhttp://dx.doi.org/10.1086/382131http://adsabs.harvard.edu/abs/2004ApJ...601L.147Bhttp://adsabs.harvard.edu/abs/2004ApJ...601L.147Bhttp://dx.doi.org/10.1086/424916http://adsabs.harvard.edu/abs/2004ApJ...616.1159Bhttp://adsabs.harvard.edu/abs/2004ApJ...616.1159Bhttp://dx.doi.org/10.1086/513562http://adsabs.harvard.edu/abs/2007ApJ...662..504Bhttp://adsabs.harvard.edu/abs/2007ApJ...662..504Bhttp://dx.doi.org/10.1088/0004-637X/757/1/91http://adsabs.harvard.edu/abs/2012ApJ...757...91Bhttp://adsabs.harvard.edu/abs/2012ApJ...757...91Bhttp://dx.doi.org/10.1086/378847http://adsabs.harvard.edu/abs/2003ApJS..149..289Bhttp://adsabs.harvard.edu/abs/2003ApJS..149..289Bhttp://dx.doi.org/10.1088/0004-637X/729/1/12http://adsabs.harvard.edu/abs/2011ApJ...729...12Bhttp://adsabs.harvard.edu/abs/2011ApJ...729...12Bhttp://dx.doi.org/10.1086/521811http://adsabs.harvard.edu/abs/2007ApJ...670..928Bhttp://adsabs.harvard.edu/abs/2007ApJ...670..928Bhttp://dx.doi.org/10.1111/j.1365-2966.2009.15191.xhttp://adsabs.harvard.edu/abs/2009MNRAS.398.1150Bhttp://adsabs.harvard.edu/abs/2009MNRAS.398.1150Bhttp://dx.doi.org/10.1146/annurev.astro.43.051804.102213http://adsabs.harvard.edu/abs/2005ARA&A..43..827Bhttp://adsabs.harvard.edu/abs/2005ARA&A..43..827Bhttp://dx.doi.org/10.1088/0004-637X/692/2/1339http://adsabs.harvard.edu/abs/2009ApJ...692.1339Chttp://adsabs.harvard.edu/abs/2009ApJ...692.1339Chttp://dx.doi.org/10.1111/j.1365-2966.2011.20292.xhttp://adsabs.harvard.edu/abs/2012MNRAS.421..213Dhttp://adsabs.harvard.edu/abs/2012MNRAS.421..213Dhttp://dx.doi.org/10.1088/0004-637X/759/1/52http://adsabs.harvard.edu/abs/2012ApJ...759...52Dhttp://adsabs.harvard.edu/abs/2012ApJ...759...52Dhttp://dx.doi.org/10.1086/588456http://adsabs.harvard.edu/abs/2008ApJ...683..346Fhttp://adsabs.harvard.edu/abs/2008ApJ...683..346Fhttp://dx.doi.org/10.1088/0004-637X/702/2/L143http://adsabs.harvard.edu/abs/2009ApJ...702L.143Fhttp://adsabs.harvard.edu/abs/2009ApJ...702L.143Fhttp://dx.doi.org/10.1088/2041-8205/719/1/L79http://adsabs.harvard.edu/abs/2010ApJ...719L..79Fhttp://adsabs.harvard.edu/abs/2010ApJ...719L..79Fhttp://dx.doi.org/10.1088/0004-637X/749/1/91http://adsabs.harvard.edu/abs/2012ApJ...749...91Fhttp://adsabs.harvard.edu/abs/2012ApJ...749...91Fhttp://dx.doi.org/10.1086/323641http://adsabs.harvard.edu/abs/2001ApJ...559L..97Ghttp://adsabs.harvard.edu/abs/2001ApJ...559L..97Ghttp://dx.doi.org/10.1111/j.1365-2966.2004.07473.xhttp://adsabs.harvard.edu/abs/2004MNRAS.349..146Ghttp://adsabs.harvard.edu/abs/2004MNRAS.349..146Ghttp://dx.doi.org/10.1111/j.1365-2966.2004.07450.xhttp://adsabs.harvard.edu/abs/2004MNRAS.347L..57Ghttp://adsabs.harvard.edu/abs/2004MNRAS.347L..57Ghttp://dx.doi.org/10.1088/0004-637X/701/2/1076http://adsabs.harvard.edu/abs/2009ApJ...701.1076Ghttp://adsabs.harvard.edu/abs/2009ApJ...701.1076Ghttp://dx.doi.org/10.1051/0004-6361:20020826http://adsabs.harvard.edu/abs/2002A&A...391..923Ghttp://adsabs.harvard.edu/abs/2002A&A...391..923Ghttp://dx.doi.org/10.1111/j.1365-2966.2010.18114.xhttp://adsabs.harvard.edu/abs/2011MNRAS.413..101Ghttp://adsabs.harvard.edu/abs/2011MNRAS.413..101Ghttp://dx.doi.org/10.1038/472047ahttp://adsabs.harvard.edu/abs/2011Natur.472...47Hhttp://adsabs.harvard.edu/abs/2011Natur.472...47Hhttp://adsabs.harvard.edu/abs/1975MNRAS.173..729Hhttp://adsabs.harvard.edu/abs/1975MNRAS.173..729Hhttp://dx.doi.org/10.1111/j.1365-2966.2005.09087.xhttp://adsabs.harvard.edu/abs/2005MNRAS.360..974Hhttp://adsabs.harvard.edu/abs/2005MNRAS.360..974Hhttp://dx.doi.org/10.1086/426371http://adsabs.harvard.edu/abs/2005AJ....129...86Hhttp://adsabs.harvard.edu/abs/2005AJ....129...86Hhttp://dx.doi.org/10.1086/592590http://adsabs.harvard.edu/abs/2008ApJ...689..983Hhttp://adsabs.harvard.edu/abs/2008ApJ...689..983Hhttp://dx.doi.org/10.1046/j.1365-8711.2002.05038.xhttp://adsabs.harvard.edu/abs/2002MNRAS.329..897Hhttp://adsabs.harvard.edu/abs/2002MNRAS.329..897Hhttp://dx.doi.org/10.1111/j.1365-2966.2007.12355.xhttp://adsabs.harvard.edu/abs/2007MNRAS.381.1711Ihttp://adsabs.harvard.edu/abs/2007MNRAS.381.1711Ihttp://dx.doi.org/10.1086/432611http://adsabs.harvard.edu/abs/2005ApJ...631..511Ihttp://adsabs.harvard.edu/abs/2005ApJ...631..511Ihttp://dx.doi.org/10.1088/0004-637X/717/2/948http://adsabs.harvard.edu/abs/2010ApJ...717..948Ihttp://adsabs.harvard.edu/abs/2010ApJ...717..948Ihttp://dx.doi.org/10.1111/j.1365-2966.2008.13064.xhttp://adsabs.harvard.edu/abs/2008MNRAS.386..553Ihttp://adsabs.harvard.edu/abs/2008MNRAS.386..553Ihttp://dx.doi.org/10.1111/j.1365-2966.2006.10876.xhttp://adsabs.harvard.edu/abs/2006MNRAS.372.1043Ihttp://adsabs.harvard.edu/abs/2006MNRAS.372.1043Ihttp://dx.doi.org/10.1086/379192http://adsabs.harvard.edu/abs/2003ApJ...599..516Ihttp://adsabs.harvard.edu/abs/2003ApJ...599..516Ihttp://dx.doi.org/10.1111/j.1365-2966.2012.20985.xhttp://adsabs.harvard.edu/abs/2012MNRAS.423.1641Jhttp://adsabs.harvard.edu/abs/2012MNRAS.423.1641Jhttp://dx.doi.org/10.1088/0004-637X/741/1/10http://adsabs.harvard.edu/abs/2011ApJ...741...10Khttp://adsabs.harvard.edu/abs/2011ApJ...741...10Khttp://dx.doi.org/10.1088/0004-637X/721/2/1523http://adsabs.harvard.edu/abs/2010ApJ...721.1523Khttp://adsabs.harvard.edu/abs/2010ApJ...721.1523Khttp://dx.doi.org/10.1086/522073http://adsabs.harvard.edu/abs/2007ApJ...670..747Khttp://adsabs.harvard.edu/abs/2007ApJ...670..747Khttp://dx.doi.org/10.1086/317276http://adsabs.harvard.edu/abs/2000ApJ...543L.133Khttp://adsabs.harvard.edu/abs/2000ApJ...543L.133Khttp://dx.doi.org/10.1046/j.1365-8711.2001.04022.xhttp://adsabs.harvard.edu/abs/2001MNRAS.322..231Khttp://adsabs.harvard.edu/abs/2001MNRAS.322..231Khttp://dx.doi.org/10.1086/379105http://adsabs.harvard.edu/abs/2003ApJ...598.1076Khttp://adsabs.harvard.edu/abs/2003ApJ...598.1076Khttp://dx.doi.org/10.1086/432900http://adsabs.harvard.edu/abs/2005ApJ...631.1062Khttp://adsabs.harvard.edu/abs/2005ApJ...631.1062Khttp://dx.doi.org/10.1088/0004-637X/724/1/559http://adsabs.harvard.edu/abs/2010ApJ...724..559Lhttp://adsabs.harvard.edu/abs/2010ApJ...724..559Lhttp://dx.doi.org/10.1086/511297http://adsabs.harvard.edu/abs/2007ApJ...657..681Lhttp://adsabs.harvard.edu/abs/2007ApJ...657..681Lhttp://dx.doi.org/10.1086/588459http://adsabs.harvard.edu/abs/2008ApJ...681.1163Lhttp://adsabs.harvard.edu/abs/2008ApJ...681.1163Lhttp://dx.doi.org/10.1088/0004-637X/752/1/46http://adsabs.harvard.edu/abs/2012ApJ...752...46Lhttp://adsabs.harvard.edu/abs/2012ApJ...752...46Lhttp://dx.doi.org/10.1088/0004-637X/725/2/1984http://adsabs.harvard.edu/abs/2010ApJ...725.1984Lhttp://adsabs.harvard.edu/abs/2010ApJ...725.1984Lhttp://dx.doi.org/10.1088/0004-637X/699/2/1573http://adsabs.harvard.edu/abs/2009ApJ...699.1573Lhttp://adsabs.harvard.edu/abs/2009ApJ...699.1573Lhttp://dx.doi.org/10.1088/0004-637X/749/2/130http://adsabs.harvard.edu/abs/2012ApJ...749..130Lhttp://adsabs.harvard.edu/abs/2012ApJ...749..130Lhttp://dx.doi.org/10.1088/0004-637X/701/2/1765http://adsabs.harvard.edu/abs/2009ApJ...701.1765Mhttp://adsabs.harvard.edu/abs/2009ApJ...701.1765Mhttp://adsabs.harvard.edu/abs/2006csxs.book..157Mhttp://dx.doi.org/10.1111/j.1365-2966.2011.19862.xhttp://adsabs.harvard.edu/abs/2012MNRAS.419.2095Mhttp://adsabs.harvard.edu/abs/2012MNRAS.419.2095Mhttp://www.arxiv.org/abs/1207.2157http://dx.doi.org/10.1051/0004-6361/201016357http://adsabs.harvard.edu/abs/2011A&A...528A.149Mhttp://adsabs.harvard.edu/abs/2011A&A...528A.149Mhttp://dx.doi.org/10.1086/502799http://adsabs.harvard.edu/abs/2006ApJ...639L..67Phttp://adsabs.harvard.edu/abs/2006ApJ...639L..67Phttp://dx.doi.org/10.1046/j.1365-8711.2003.06464.xhttp://adsabs.harvard.edu/abs/2003MNRAS.341..385Phttp://adsabs.harvard.edu/abs/2003MNRAS.341..385Phttp://dx.doi.org/10.1086/520824http://adsabs.harvard.edu/abs/2007ApJ...667..826Phttp://adsabs.harvard.edu/abs/2007ApJ...667..826Phttp://dx.doi.org/10.1051/0004-6361:20021600http://adsabs.harvard.edu/abs/2003A&A...399...39Rhttp://adsabs.harvard.edu/abs/2003A&A...399...39Rhttp://dx.doi.org/10.1088/0004-637X/692/1/778http://adsabs.harvard.edu/abs/2009ApJ...692..778Rhttp://adsabs.harvard.edu/abs/2009ApJ...692..778Rhttp://adsabs.harvard.edu/abs/2011IAUS..272..474Shttp://dx.doi.org/10.1111/j.1365-2966.2012.20993.xhttp://adsabs.harvard.edu/abs/2012MNRAS.423.1726Shttp://adsabs.harvard.edu/abs/2012MNRAS.423.1726Shttp://dx.doi.org/10.1086/427077http://adsabs.harvard.edu/abs/2005ApJ...619L..47Shttp://adsabs.harvard.edu/abs/2005ApJ...619L..47Shttp://dx.doi.org/10.1111/j.1365-2966.2011.19405.xhttp://adsabs.harvard.edu/abs/2011MNRAS.417.2239Shttp://adsabs.harvard.edu/abs/2011MNRAS.417.2239Shttp://dx.doi.org/10.1088/0004-637X/753/1/65http://adsabs.harvard.edu/abs/2012ApJ...753...65Thttp://adsabs.harvard.edu/abs/2012ApJ...753...65Thttp://www.arxiv.org/abs/1210.7185http://dx.doi.org/10.1051/0004-6361:20078193http://adsabs.harvard.edu/abs/2008A&A...480..663Thttp://adsabs.harvard.edu/abs/2008A&A...480..663Thttp://dx.doi.org/10.1038/nature09463http://adsabs.harvard.edu/abs/2010Natur.468...77Vhttp://adsabs.harvard.edu/abs/2010Natur.468...77Vhttp://dx.doi.org/10.1111/j.1365-2966.2011.20185.xhttp://adsabs.harvard.edu/abs/2012MNRAS.420.2190Vhttp://adsabs.harvard.edu/abs/2012MNRAS.420.2190Vhttp://dx.doi.org/10.1088/0004-637X/721/2/1843http://adsabs.harvard.edu/abs/2010ApJ...721.1843Vhttp://adsabs.harvard.edu/abs/2010ApJ...721.1843Vhttp://dx.doi.org/10.1086/311568http://adsabs.harvard.edu/abs/1998ApJ...504L..31Whttp://adsabs.harvard.edu/abs/1998ApJ...504L..31Whttp://dx.doi.org/10.1088/0004-637X/718/2/620http://adsabs.harvard.edu/abs/2010ApJ...718..620Whttp://adsabs.harvard.edu/abs/2010ApJ...718..620Whttp://dx.doi.org/10.1088/0067-0049/195/1/10http://adsabs.harvard.edu/abs/2011ApJS..195...10Xhttp://adsabs.harvard.edu/abs/2011ApJS..195...10Xhttp://dx.doi.org/10.1051/0004-6361/201219015http://adsabs.harvard.edu/abs/2012A&A...546A..36Zhttp://adsabs.harvard.edu/abs/2012A&A...546A..36Zhttp://dx.doi.org/10.1088/0004-637X/733/1/5http://adsabs.harvard.edu/abs/2011ApJ...733....5Zhttp://adsabs.harvard.edu/abs/2011ApJ...733....5Z

1. INTRODUCTION2. POPULATION SYNTHESIS MODELING2.1. Population Synthesis Code: StarTrack2.2. The Millennium II Simulation2.3. The Millennium II Simulation as Initial Conditions of Populations Synthesis Models2.4. Parameter Study

3. BOLOMETRIC CORRECTIONS TO THE CHANDRA X-RAY BANDS4. OBSERVATIONAL CONSTRAINTS AND STATISTICAL MODEL COMPARISON4.1. Available Observational Constraints4.2. Model Likelihood Calculation4.3. The Specific X-Ray Luminosity of Local Elliptical Galaxies

5. RESULTS5.1. Effects of the Different Model Parameters on the X-Ray Binary Population5.2. Evolution of Global Scaling Relations with Redshift

6. SUMMARY AND CONCLUSIONSREFERENCES

x-ray binary evolution across cosmic time · 9 iesl, foundation for research and technology, 71110...

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