Connecting the metallicity dependence and redshift evolution of high-mass X-ray binaries
aa r X i v : . [ a s t r o - ph . H E ] A p r MNRAS , 1–14 (2019) Preprint 29 April 2020 Compiled using MNRAS L A TEX style file v3.0
Connecting the metallicity dependence and redshiftevolution of high-mass X-ray binaries
Francesca M. Fornasini, ⋆ Francesca Civano, and Hyewon Suh Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA Subaru Telescope, National Astronomical Observatory of Japan (NAOJ), 650 North A’ohoku place, Hilo, HI 96720, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The integrated X-ray luminosity ( L X ) of high-mass X-ray binaries (HMXBs) in agalaxy is correlated with its star formation rate (SFR), and the normalization ofthis correlation increases with redshift. Population synthesis models suggest that theredshift evolution of L X /SFR is driven by the metallicity ( Z ) dependence of HMXBs,and the first direct evidence of this connection was recently presented using galaxies at z ∼ . To confirm this result with more robust measurements and better constrain the L X -SFR- Z relation, we have studied the Z dependence of L X /SFR at lower redshifts.Using samples of star-forming galaxies at z = . − . with optical spectra from thehCOSMOS and zCOSMOS surveys, we stacked Chandra data from the COSMOSLegacy survey to measure the average L X /SFR as a function of Z in three redshiftranges: z = . − . , . − . , and . − . . We find no significant variation ofthe L X -SFR- Z relation with redshift. Our results provide further evidence that the Z dependence of HMXBs is responsible for the redshift evolution of L X /SFR. Combiningall available z > measurements together, we derive a best-fitting L X -SFR- Z relationand assess how different population synthesis models describe the data. These resultsprovide the strongest constraints to date on the L X -SFR- Z relation in the range of . < < . . Key words:
X-rays: binaries – X-rays: galaxies – galaxies: abundances
High-mass X-ray binaries (HMXBs), which consist of aneutron star or black hole accreting material from astellar companion with M ∗ > M ⊙ , are young stellarsystems with ages of ∼ − Myr (Iben et al. 1995;Bodaghee et al. 2012; Antoniou & Zezas 2016). As a con-sequence, the number of HMXBs in a galaxy and their in-tegrated X-ray luminosity ( L X ) is correlated with a galaxy’sstar formation rate (SFR; Ranalli et al. 2003; Grimm et al.2003; Persic et al. 2004; Gilfanov 2004; Lehmer et al. 2010;Mineo et al. 2012a hereafter M12; Lehmer et al. 2019 here-after L19). This correlation exhibits large scatter of ≈ . dex (Mineo et al. 2012a) and its normalization increaseswith redshift (Basu-Zych et al. 2013a; Lehmer et al. 2016;Aird et al. 2017).Binary population synthesis models have suggested thatthe redshift evolution and part of the scatter of the L HMXBX -SFR relation may be driven by the metallicity ( Z ) de-pendence of HMXB evolution (Dray 2006; Linden et al. ⋆ E-mail: [email protected] Z -dependenceof HMXBs arises from the fact that higher- Z stars have morepowerful radiatively-driven winds. As a result, high- Z starslose more mass prior to exploding as supernovae and high- Z binaries lose more angular momentum compared to theirlow- Z counterparts. Thus, these studies predict that lower- Z HMXB populations should host more massive compactobjects and more Roche-lobe overflow systems, resulting inhigher accretion rates and higher L X on average.In general agreement with these predictions, it hasbeen observed that local low- Z dwarf galaxies do host alarger number of luminous HMXBs at fixed SFR comparedto high- Z galaxies (Mapelli et al. 2011; Kaaret et al. 2011;Prestwich et al. 2013; Basu-Zych et al. 2013b; Brorby et al.2014; Douna et al. 2015; Basu-Zych et al. 2016; L19;Ponnada et al. 2020). Expanding on work by Douna et al.(2015), Brorby et al. (2016) (hereafter B16) used a sampleof 49 nearby galaxies to measure the anti-correlation be-tween L X /SFR and Z , and found decent agreement with thetheoretical expectations of Fragos et al. (2013b). It is un-clear whether the excess number of bright HMXBs in low- Z © F. M. Fornasini et al. galaxies can be explained by an increase in the normalizationof the HMXB luminosity function from higher- Z galaxies(Brorby et al. 2014; Ponnada et al. 2020), whether a shal-lower bright end slope to the HMXB luminosity function isalso required (Basu-Zych et al. 2016), or whether the HMXBluminosity function varies with Z in more complicated ways(L19). While it has been shown that significant scatter in the L X -SFR relation can be introduced at low SFR as a resultof incomplete Poissonian sampling of the HMXB luminosityfunction (Gilfanov et al. 2004; Justham & Schawinski 2012;L19), the results of the aforementioned studies clearly in-dicate that Z variations in galaxy samples can introducescatter as well.Recently, Fornasini et al. (2019) (hereafter F19) pre-sented the first direct evidence that the redshift evo-lution of HMXBs can be attributed to the Z depen-dence of L HMXBX /SFR, as hypothesized by previous studies(Basu-Zych et al. 2013a; Fragos et al. 2013a; Lehmer et al.2016). By stacking the X-ray data of z ∼ galaxies groupedinto Z bins, F19 found that L X /SFR is anti-correlated with Z at z ∼ , and that, for a given Z , the L X /SFR valuesof HMXB-dominated galaxies at this redshift are consistentwith the local L X -SFR- Z relation measured by B16. Thus,on average, z ∼ galaxies have higher L X /SFR values than z = galaxies of similar stellar mass ( M ∗ ) because the aver-age Z is lower at z ∼ .However, the observed L X /SFR- Z anti-correlation at z ∼ is significant only at 97% confidence (F19). Further-more, it is possible that measurements of the local L X -SFR- Z relation may be biased due to selection effects (Douna et al.2015; B16), and therefore may not provide a representativebenchmark for z = HMXBs. Thus, in order to make a morerobust conclusion about the extent to which the Z depen-dence of HMXBs drives the redshift evolution of L X /SFR,it is important to study the Z dependence of HMXBs overa broad redshift range.We present a study of the Z dependence of HMXBs inthree redshift intervals: z = . − . , . − . , and . − . .The goal of this study is to measure the L X -SFR- Z relationat these redshifts, compare it to previous measurements at z = and z = , and if the relation appears to be redshift-independent, use all the currently available data to betterconstrain the Z dependence of HMXBs. In §
2, we describethe hCOSMOS and zCOSMOS spectroscopic surveys fromwhich we selected our galaxy sample and the X-ray datafrom the
Chandra
COSMOS Legacy survey we used in ouranalysis. § §
4, we presentour results on the L X -SFR- Z relation across redshift. Wesummarize our findings in § Ω m = . , Ω Λ = . , and h = . and adopt the solar abundances fromAsplund et al. (2009) ( Z ⊙ = . , 12+log(O/H) ⊙ = . ). Studying the relationship between L HMXBX , SFR, and Z re-quires a large sample of star-forming galaxies with: 1) rest-frame optical spectra from which oxygen abundance can be measured, 2) sensitive X-ray data ( L X , lim . erg s − )to screen out X-ray active galactic nuclei (AGN) and de-tect HMXB-dominated galaxies via X-ray stacking, and 3)sufficient photometric coverage to estimate SFRs throughSED-fitting or spectroscopic coverage of emission line SFRindicators such as H α . The multi-wavelength coverage of theCOSMOS field (Scoville et al. 2007) offers suitable datasetsfor such studies. We use two spectroscopic surveys (hCOS-MOS and zCOSMOS), the Chandra
COSMOS Legacy sur-vey, and the multiwavelength photometry available in theCOSMOS field (Laigle et al. 2016) to perform this study.Here we briefly describe these data sets.
One of our galaxy samples is taken from the hCOSMOSsurvey, which was performed using the Hectospec mul-tifiber spectrograph on the 6.5m MMT (Fabricant et al.1998; Fabricant et al. 2005). Hectospec covers the wave-length range − ˚A at a resolution of R ∼ . ThehCOSMOS survey targeted galaxies in the COSMOS fieldwith r < . , and obtained 4362 reliable spectroscopic red-shifts, including 1701 new redshifts (Damjanov et al. 2018).Hectospec data were reduced with HSRED v2.0, developedby the SAO Telescope Data Center. Redshifts were measuredby cross-correlating the observed spectra against a library oftemplate spectra (Kurtz & Mink 1998). The majority of thegalaxies observed by Hectospec are at . < z < . . The de-tails of Hectospec spectral calibration and spectroscopic red-shift determination are provided in Damjanov et al. (2018). Our second galaxy sample is selected from the zCOSMOS-bright survey, which obtained spectra of 20,000 galaxies with i < . and . < z < . (Lilly et al. 2007). The zCOS-MOS survey was performed with the VIMOS spectrograph(Le F`evre et al. 2003) on the 8m ESO VLT. The VIMOSMR grism provides R ∼ resolution over the spectralrange − ˚A. The calibration of zCOSMOS spectraand measurement of spectroscopic redshifts is described indetail in (Lilly et al. 2007). In this study, we use the sub-sample of 939 zCOSMOS galaxies at . < z < . for whichMaier et al. (2015) measured metallicities. Metallicity mea-surements are also available for 164 zCOSMOS galaxies at z < . (Cresci et al. 2012). However, we did not use thesegalaxies in our analysis because, due to significant overlapbetween the zCOSMOS and hCOSMOS samples, includingthe unique zCOSMOS z < . galaxies would only increasethe sample size by 6% while introducing heterogeneity in themeasurement of galaxy properties. Both of our spectroscopic galaxy samples reside in the COS-MOS field, which covers roughly 2 deg and was observed bythe Chandra X-ray Observatory to a fairly uniform depth ofapproximately 160 ks. The
Chandra
COSMOS Legacy sur-vey detected 4016 X-ray sources, reaching limiting fluxes of . × − , . × − , and . × − erg s − cm − in the . − , − , and . − keV bands (Civano et al. 2016). MNRAS000
COSMOS Legacy sur-vey detected 4016 X-ray sources, reaching limiting fluxes of . × − , . × − , and . × − erg s − cm − in the . − , − , and . − keV bands (Civano et al. 2016). MNRAS000 , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution For an absorbed power-law spectrum with a photon index of Γ = . (the photon index of the cosmic X-ray background)and Galactic obscuration of N H = . × cm − , these sen-sitivity limits correspond to rest-frame − keV limitingluminosities of L X ∼ − for z = . − . . Thus, thissurvey is sufficiently deep as to be able to detect all moder-ate and bright luminosity X-ray AGN over the redshift rangespanned by our galaxy samples, which is important for ouranalysis (see § To derive the M ∗ and SFR of each galaxy, we make useof the most recent COSMOS photometric catalog from(Laigle et al. 2016). This catalog includes the near-UV bandfrom GALEX , the u ∗ band from the Canada-France-HawaiiTelescope (CFHT/MegaCam), five Subaru Suprime-Cambands( B , V , r , i , z + ), four UltraVista bands( Y , H , J , Ks ),and four Spitzer /IRAC bands (3.6, 4.5, 5.8, and 8.0 µ m).To constrain the MIR and FIR emission as much as pos-sible, we also use the 24 µ m and 70 µ m Multiband Imag-ing Photometer for Spitzer (MIPS) bands (Sanders et al.2007; Le Floc’h et al. 2009), as well as the
Herschel SpaceObservatory
PACS (100 µ m, 160 µ m) and SPIRE (250 µ m,350 µ m, 500 µ m) bands (Griffin et al. 2010; Pilbratt et al.2010; Poglitsch et al. 2010). In §
4, we use measurements of L X /SFR from additional sam-ples of star-forming galaxies at different redshifts to investi-gate the connection between L X /SFR, Z , and redshift. F19studied the Z dependence of HMXBs in z ∼ galaxies,and we use the L X /SFR values they measure as a func-tion of O/H for high sSFR (sSFR > − . yr − ) galaxies.F19 measure SFRs from the H α luminosity and apply a Z -dependent conversion factor, assuming the Hao et al. (2011)conversion factor appropriate for Z = . for galaxies with12+log(O/H) > . and adjusted for Z = . using theconversion factor from Reddy et al. (2018) for galaxies with12+log(O/H) < . . Their L X /SFR results derived using H α SFRs are consistent within 0.15 dex with results based onSED-derived SFRs assuming Z = . BC03 stellar modelsand the Calzetti et al. (2000) extinction curve.We also include results from four different studies of z = galaxies as points of comparison. All four of these stud-ies are based on individually X-ray detected nearby galaxiesand use UV+IR SFRs. One of these studies is B16, whichcombined new and archival samples of nearby galaxies withO/H measurements to measure the local L X -SFR- Z rela-tion. Two of the studies, L10 and M12, did not include Z information in measuring the scaling relation between L X and SFR. However, F19 calculated the average O/H of thegalaxies used in these studies by combining O/H measure-ments available in the literature and O/H estimates basedon the M ∗ - Z relation from Kewley & Ellison (2008). Thefourth study, L19, performed subgalactic modeling of theHMXB and LMXB scaling relations in order to better dis-entangle their contributions compared to previous works.This study provides an estimate of L HMXBX /SFR for theircomplete sample of 38 nearby galaxies as well as an esti- mate based on a “cleaned” subsample. This subsample ex-cludes galaxies with lower Z or a higher frequency of globularclusters compared to the bulk of the sample, because suchgalaxies are found to be significant outliers to the scalingrelations. We use this “cleaned” scaling relation as a point ofcomparison for our results. We calculated the mean O/H ofthis sample using the O/H values based on strong line indi-cators compiled in L19 and O/H estimates based on the M ∗ - Z relation from Kewley & Ellison (2008) for galaxies lack-ing strong line measurements; these choices were made forconsistency with the other mean O/H estimates calculatedby F19 for the other z = samples. We ensured that allO/H values were properly converted to the Pettini & Pagel(2004) O3N2 metallicity scale using the prescriptions fromKewley & Ellison (2008).We made some corrections to the L X /SFR measure-ments from z = studies to allow a more direct comparisonto our results. The SFR values from the local studies wereconverted to be consistent with a Chabrier IMF. In addition,the M12, B16, and L19 L X values were converted from the . − to − keV band. To calculate the L X conversion fac-tors, we assumed an absorbed power-law spectrum and theaverage Γ and N H parameters used in these respective stud-ies, which span the ranges of Γ = . − . and N H ≤ × cm − . M ∗ and SFR We derived M ∗ and SFR for all the galaxies in the hCOS-MOS and zCOSMOS samples in a consistent way by fittingtheir SEDs following the procedure described in Suh et al.(2017), which is briefly summarized here. Each near-UV tofar-IR SED was decomposed into a galactic stellar popu-lation and a starburst component representing the infraredemission from dust heated by the UV light from young stars;unlike Suh et al. (2017), we did not include an AGN com-ponent because we removed any confirmed AGN from oursample (as described in § Z = . , the Calzetti et al. (2000) dustextinction law, and considered both exponentially decay-ing and constant star formation histories (SFHs). To rep-resent the cold dust emission, we used starburst templatesfrom Chary & Elbaz (2001) and Dale & Helou (2002). Foreach galaxy, the spectroscopic redshift from hCOSMOS orzCOSMOS was adopted as a fixed input to the SED-fitting.The best-fit template combination was determined using χ minimization, while the most representative value for eachphysical parameter and corresponding uncertainties were de-termined via Bayesian estimation.The M ∗ of each galaxy is calculated by integrating theSFH of the best-fitting template. In order to account forboth obscured and unobscured star formation, we do notsimply use the SFRs derived from the SFHs, but combinethe contributions from the UV and IR luminosities, usingthe following relation from Arnouts et al. (2013), which is MNRAS , 1–14 (2019)
F. M. Fornasini et al. adjusted for a Chabrier (2003) IMF:
SFR total ( M ⊙ yr − ) = . × − × ( L IR / L ⊙ + . × ν L ) (1)where L IR is the rest-frame − µ m star-forming IR lu-minosity integrated from the starburst template, and L represents the rest-frame absorption-corrected near-UV lu-minosity at 2300 ˚A in units of L ⊙ . For galaxies which are un-detected at MIR and FIR wavelengths, we calculate a lowerbound to the SFR based on the UV luminosity alone, andan upper bound by combining the UV contribution with theupper limits in the MIR-FIR bands. For these galaxies, wealso adopt a best estimate SFR value derived by multiplyingtheir UV luminosity by the median ratio of the total SFRto the UV-only SFR as a function of E(B-V) for the MIR-FIR detected galaxies, where E(B-V) is determined from theSED-fitting. This median ratio varies from . − . . Ourresults are not significantly changed if we ignore the varia-tion of SFR total /SFR UV with E(B-V) and instead adopt thesame median ratio for all galaxies that are not detected atMIR-FIR wavelengths. If this SFR estimate exceeds the up-per bound set by the Spitzer
MIPS and
Herschel limits, thenwe adopt that upper bound as the best estimate SFR. In § M ∗ measurements fornon-AGN galaxies from the hCOSMOS and zCOSMOS sam-ples. Galaxies that are detected at MIR-FIR wavelengthsare shown by circles, while those that are undetected atMIR-FIR wavelengths are shown by squares. We find thatour M ∗ and SFR values are in good agreement with mea-surements from other studies that use different SED fittingcodes (Cresci et al. 2012; Laigle et al. 2016; Damjanov et al.2018). As done in previous studies of the Z dependence of HMXBs(e.g. B16; F19), we use the oxygen abundance (O/H) of star-forming H II regions as a proxy for the Z of HMXBs, whichare young stellar systems. For both the hCOSMOS and thezCOSMOS samples, O/H measurements are derived usingthe R line ratio, which is defined as: R = [ OII ] λ + [ OIII ] λ , β (2)For the hCOSMOS galaxies, we fit the continuumaround each of the emission lines required for the R in-dicator using a linear polynomial. We then normalize thespectral region containing the emission line to the fitted con-tinuum, fit the line with a Gaussian profile, and measure theequivalent width (EW) of the line. To calculate the R lineratio, we use the EWs rather than fluxes of the lines becausethis method has been found to be reliable and less sensi-tive to interstellar reddening (Kobulnicky & Phillips 2003).To ensure the O/H measurements are robust, we requireS/N > in the [OII] λ and H β emission lines. We correctfor Balmer absorption by fitting stellar population synthesismodels following Zahid et al. (2013).To convert the R ratio to an O/H measurement, weuse the calibration of Kobulnicky & Kewley (2004). Metal-licity is not a monotonic function of R , and the degener-acy between the upper and lower value solutions is usually logM * (M Sun ) l og S F R ( M S un y r − ) −0.50.00.51.01.52.02.5 hCOSMOS z=0.1−0.49.0 9.5 10.0 10.5 11.0−0.50.00.51.01.52.02.5 zCOSMOS z=0.5−0.9 Figure 1.
Best estimates of SFR versus M ∗ for our galaxy sam-ples taken from the hCOSMOS and zCOSMOS surveys are shownin the top and bottom panels, respectively. Each galaxy is coloredaccording to its metallicity. Galaxies that are detected at MIR-FIR wavelengths are shown by circles, with their median sta-tistical M ∗ and SFR errors represented by the black circle witherror bars. Galaxies that are undetected at MIR-FIR wavelengthsare shown by squares, with their median M ∗ statistical error andthe median difference between their upper and lower SFR boundsshown by the black square with error bars. The dashed lines showthe sSFR selection cuts we make as described in § broken by using another line ratio, typically [NII]/H α . How-ever, since these lines are affected by red light leak or areredshifted out of the Hectospec spectral window for the bulkof the hCOSMOS sample, we assume the galaxies lie on the R upper branch, which is likely a robust assumption on av-erage for these low redshifts ( z = . − . ) and M ∗ & M ⊙ (Zahid et al. 2011). We are able to estimate O/H for 1257hCOSMOS galaxies. Our O/H measurements reproduce the M ∗ − Z relation measured by Zahid et al. (2013) at z ∼ . .For the subsample of 83 galaxies that are in common be-tween the hCOSMOS and zCOSMOS surveys, our O/Hvalues are consistent with measurements from Cresci et al.(2012) within the expected ± . − . dex uncertainties. Onlythree of these galaxies exhibit O/H measurement differencessignificantly in excess of what would be expected due tostatistical uncertainty; in all three cases, our O/H measure-ments are higher than those of Cresci et al. (2012) by > . dex. Since Cresci et al. (2012) base their O/H measurementson the [NII]/H α indicator, which does exhibit the same de-generacy as R , it is possible that these three galaxies shouldlie on the lower R branch. Given that this subsample isfairly representative of the full hCOSMOS sample in termsof M ∗ which correlates with Z , the fact that only 4% of MNRAS000
Best estimates of SFR versus M ∗ for our galaxy sam-ples taken from the hCOSMOS and zCOSMOS surveys are shownin the top and bottom panels, respectively. Each galaxy is coloredaccording to its metallicity. Galaxies that are detected at MIR-FIR wavelengths are shown by circles, with their median sta-tistical M ∗ and SFR errors represented by the black circle witherror bars. Galaxies that are undetected at MIR-FIR wavelengthsare shown by squares, with their median M ∗ statistical error andthe median difference between their upper and lower SFR boundsshown by the black square with error bars. The dashed lines showthe sSFR selection cuts we make as described in § broken by using another line ratio, typically [NII]/H α . How-ever, since these lines are affected by red light leak or areredshifted out of the Hectospec spectral window for the bulkof the hCOSMOS sample, we assume the galaxies lie on the R upper branch, which is likely a robust assumption on av-erage for these low redshifts ( z = . − . ) and M ∗ & M ⊙ (Zahid et al. 2011). We are able to estimate O/H for 1257hCOSMOS galaxies. Our O/H measurements reproduce the M ∗ − Z relation measured by Zahid et al. (2013) at z ∼ . .For the subsample of 83 galaxies that are in common be-tween the hCOSMOS and zCOSMOS surveys, our O/Hvalues are consistent with measurements from Cresci et al.(2012) within the expected ± . − . dex uncertainties. Onlythree of these galaxies exhibit O/H measurement differencessignificantly in excess of what would be expected due tostatistical uncertainty; in all three cases, our O/H measure-ments are higher than those of Cresci et al. (2012) by > . dex. Since Cresci et al. (2012) base their O/H measurementson the [NII]/H α indicator, which does exhibit the same de-generacy as R , it is possible that these three galaxies shouldlie on the lower R branch. Given that this subsample isfairly representative of the full hCOSMOS sample in termsof M ∗ which correlates with Z , the fact that only 4% of MNRAS000 , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution the galaxies in this subsample show significant discrepancieswith the Cresci et al. (2012) measurements suggests that ourassumption that all galaxies lie on the upper R branch doesnot introduce significant bias.For the zCOSMOS galaxies, we use the O/H measure-ments from Maier et al. (2015). These O/H measurementsare also based on the R line ratio, but Maier et al. (2015)use the Kewley & Dopita (2002) calibration. For 39 of theirgalaxies, Maier et al. (2015) obtain near-IR spectra to breakthe degeneracy between O/H and R using [NII]/H α ; basedon this subsample of 39 galaxies, they find a trend betweenthe Dn4000 index, [OIII] λ β , and whether galaxies lieon the upper/lower R branch which is then used to breakthe R degeneracy for the remaining 900 galaxies in theirsample. About 20% of the zCOSMOS galaxies in Maier et al.(2015) are found to lie on the lower R branch based onthese observed trends. Since these trends are likely to varywith redshift (Maier et al. 2015), we cannot apply the samecriteria to our hCOSMOS sample at z = . − . . Nonethe-less, we note that, considering the redshift evolution of the M ∗ − Z relation (Zahid et al. 2013), it is likely that the frac-tion of hCOSMOS galaxies falling on the lower R branchis lower than for the zCOSMOS sample.In order to compare the results based on the hCOS-MOS and zCOSMOS samples to one another and to previ-ous studies of the L X -SFR- Z relation, we convert all O/Hmeasurements to the Pettini & Pagel (2004) calibration forthe O3N2 indicator using the conversions established byKewley & Ellison (2008). In order to study the X-ray emission from HMXBs, it isimportant to remove contamination from AGN as much aspossible. Therefore, we identified AGN candidates throughmultiwavelength diagnostics and removed them from ourgalaxy samples. We identified any individually detected X-ray sources with L X > erg s − from Civano et al. (2016)as X-ray AGN. We further excluded any X-ray sources withoptical counterparts that were identified as optical AGNbased on the photometric or spectroscopic classification ofMarchesi et al. (2016). IR AGN were identified based on thecriteria of Donley et al. (2012) and removed from the sam-ple. Finally, we also excluded optical AGN identified via op-tical line ratio diagnostic diagrams. In the case of hCOSMOSsources, we identified optical AGN as sources lying abovethe Kauffmann et al. (2003) line in the [OIII]/H β versus[NII]/H α diagram. In the case of zCOSMOS, we excludedoptical AGN using the blue diagnostic diagram based on[OII], H β , and [OIII] (Lamareille 2010; P´erez-Montero et al.2013) as done by Maier et al. (2015).In addition to removing contamination from AGN, it isalso important to limit contamination from low-mass X-raybinaries (LMXBs). Whereas L HMXBX is proportional to SFR, L LMXBX is proportional to M ∗ (Gilfanov 2004; Lehmer et al.2010). Thus, the relative contribution of HMXBs andLMXBs to the integrated L X of a galaxy depends on thespecific SFR (sSFR=SFR/ M ∗ ). The sSFR value at whichgalaxies transition from being LMXB to HXMB dominatedis found to increase with redshift (Lehmer et al. 2016). Thus,to limit the contribution of LMXBs, it is important to se- lect galaxies above the transition sSFR value appropriatefor a given redshift. Therefore, we used a lower thresh-old of log(sSFR) = − . for the hCOSMOS sample andlog(sSFR) = − . for the zCOSMOS sample. Above thisthreshold value, the total L X /SFR of galaxies as a func-tion of increasing sSFR is expected to gradually asymp-tote to the value appropriate for a pure HMXB popula-tion; L X /SFR drops by about 0.3 dex as sSFR increasesby a factor of 10 from the threshold value (Lehmer et al.2010). Therefore, to minimize variations in the sSFR distri-butions of galaxies in different Z bins, we also set an upperthreshold of log(sSFR) = − . for the hCOSMOS sample andlog(sSFR) = − . for the zCOSMOS sample.Finally, we limited the hCOSMOS sample tolog ( M ∗ / M ⊙ ) > . , for which O/H values are reliablyfound to correspond to the upper branch of the R ratio,as discussed in § ( M ∗ / M ⊙ ) > . because the M ∗ distribution of galaxieswith Z measurements from Maier et al. (2015) drops offsteeply below this value. After applying these selectioncriteria, our hCOSMOS sample consists of 858 galaxies,319 of which are at z = . − . and 539 of which are at z = . − . , and the zCOSMOS sample consists of 786galaxies at z = . − . . The vast majority of the galaxies in our samples are toofaint to be individually detected by
Chandra . Therefore, todetermine the mean X-ray luminosity for each set of galaxiesgrouped by z , O/H, or other physical properties, we firststack all the undetected galaxies and calculate their h L X i .Then, we compute a weighted average of the stacked h L X i and the L X measurements of individually detected galaxiesas detailed below.To perform our X-ray stacking analysis, weuse the Chandra stacking tool CSTACK v4.32( http://cstack.ucsd.edu/cstack/ ). For each galaxyposition, CSTACK provides the net (background sub-tracted) count rate in the . − and − keV bands.CSTACK defines the aperture region for each object as acircle with radius equal to the 90% encircled counts fraction(ECF) radius ( r ). The background region is defined as a ′′ × ′′ area centered on each object; this region excludesa ′′ -radius circle around the object as well as circularregions around any detected X-ray sources with radii whichdepend on the net X-ray source counts. For each object,CSTACK only uses the Chandra observations in whichthe object is located within 8 ′ of the aim point, such that r < ′′ . The reliability of the CSTACK code has beencarefully vetted by previous studies (Mezcua et al. 2016;Fornasini et al. 2018).As reported in Fornasini et al. (2018) (hereafter F18),the CSTACK source apertures are typically larger than twicethe effective radii of star-forming galaxies with M ∗ > M ⊙ and z > . . Thus, the X-ray photometric information de-rived is representative of the galaxies as a whole rather thanjust the nuclear component. We find that < % of the galax-ies in our sample have a neighboring galaxy of similar orlower magnitude within r . We expect that these neighbor-ing galaxies will only impact the stacked L X by < . dexbased on the estimates presented in F18. MNRAS , 1–14 (2019)
F. M. Fornasini et al.
For each stack of individually X-ray undetected galax-ies, we calculate the probability that the source could begenerated by a noise fluctuation of the local background,and convert this to a Gaussian-equivalent detection signif-icance. The robustness of this stacking method was thor-oughly investigated by F18. For each stack, we also com-pute the exposure-weighted average net count rates, andconvert the . − keV count rate to a mean X-ray lu-minosity based on the X-ray spectrum described in § k -correction. We also calculate the exposure-weighted meansof galaxy properties (i.e. M ∗ , SFR, sSFR, O/H, z ). Full de-tails of all these calculations are provided in F18. The mean L X /SFR for each stack of X-ray undetected galaxies is calcu-lated as h L X i/h SFR i . F19 estimate that h L X i/h SFR i shouldapproximate h L X /SFR i with 0.05 dex accuracy based on the0.3-0.4 dex of scatter observed in the local L X -SFR relations(Mineo et al. 2012a; Brorby et al. 2016). The 1 σ statisticaluncertainties on the stacked count rate are calculated us-ing a bootstrapping technique; the galaxies in each stackare resampled 1,000 times while the number of galaxies isconserved, and the stacking analysis is repeated in order toobtain the statistical distribution of the mean net count rate.The errors associated with mean galaxy properties are alsocalculated using the bootstrapping technique described inLehmer et al. (2016).Having measured the mean L X and galaxy properties ofstacks of X-ray undetected galaxies, we combine this infor-mation with the L X and galaxy property measurements ofindividually X-ray detected galaxies. To calculate the mean L X and galaxy properties of both the X-ray detected andundetected galaxies in a stack, we perform a weighted av-erage in which the weights are the number of galaxies rep-resented by a given measurement. In estimating h L X /SFR i for a stack, we use h L X i/h SFR i for the individually X-rayundetected galaxies and the L X /SFR measurements of indi-vidually X-ray detected galaxies. The galaxy properties andX-ray properties of each stack are provided in Table 1 and2, respectively. Converting the . − keV net count rates to − keVrest-frame luminosities requires a spectral model. Since ourstacks do not possess sufficient X-ray counts for meaningfulspectral analysis, we use hardness ratios to roughly constrainthe average X-ray spectrum of our galaxies. For each stack ofX-ray undetected galaxies, we use the Bayesian estimationcode BEHR (Park et al. 2006) to estimate the hardness ratiodefined as HR = ( H − S )/( H + S ) , where H and S represent thenet count rates in the − and . − keV bands, respectively.The HRs of stacks N H ) and photon index ( Γ ). The HRs of stacks N H . cm − ) and Γ ≈ . − . ,a typical range of photon indices for HMXBs. The HRs ofstacks N H = cm − and Γ = , which is the same model assumed by previ- HR = ( H − S ) / ( H + S ) Γ = 1.42.0N H = 10 cm −2 Figure 2.
Hardness ratios versus redshift for stacks
H R = ( H − S )/( H + S ) where H and S represent the net count rates inthe − and . − keV bands, respectively. Error bars repre-sent 1 σ uncertainties. Blue lines display the expected hardnessratios for sources with different absorbed power-law spectra; theline style represents different column densities ( N H ) while the linecolor represents different Γ . Our stacks are consistent with rela-tively unobscured ( N H < cm − ) spectra with Γ = . − . . ous studies of the HMXB Z -dependence (B16; F19). Varying N H and Γ within the ranges consistent with the data resultsin differences of ± . dex in L X . Following F18, if we considera more complex spectral model which includes a thermal apec component representing the hot gas in a galaxy and as-sume that the L X contribution of this gas obeys the scalingrelation with SFR parameterized by Mineo et al. (2012b),the absorbed power-law model representing the HMXB pop-ulation would be consistent with higher N H ≈ × cm − and Γ ≈ . Adopting this more complex spectral model doesnot significantly change our estimate of the rest-frame − keV luminosities. L X /SFR as a function of redshift We first checked whether our galaxies exhibit similar L X /SFR as a function of redshift as found by previousstudies. We divided our galaxies into three redshift bins( z = . − . , . − . , . − . ), and stacked the X-ray data. The properties of these stacks are listed in rows − in Tables 1 and 2, and their L X /SFR values versusredshift are shown in Figure 3 with circles.The L X /SFR of the z ∼ sample from F19 is signifi-cantly enhanced relative to our stacks at z = . − . . Since Z information is available for both these samples, togetherthey can be used to test the connection between the redshiftevolution and Z dependence of HMXBs, which is discussedin § L X /SFR valuesexpected based on the redshift evolution relations of L16and A17 shown by lines in Figure 3, which are derived usinggalaxies at z = . − . The stack luminosities fall below theupper limit on XRB emission estimated using the redshift-dependent parametrization of F18. We note that the hard-ness ratios of our stacks are lower than those of most of thestacks of star-forming galaxies from F18 at similar redshift;as a key difference between our sample selection and that MNRAS000
H R = ( H − S )/( H + S ) where H and S represent the net count rates inthe − and . − keV bands, respectively. Error bars repre-sent 1 σ uncertainties. Blue lines display the expected hardnessratios for sources with different absorbed power-law spectra; theline style represents different column densities ( N H ) while the linecolor represents different Γ . Our stacks are consistent with rela-tively unobscured ( N H < cm − ) spectra with Γ = . − . . ous studies of the HMXB Z -dependence (B16; F19). Varying N H and Γ within the ranges consistent with the data resultsin differences of ± . dex in L X . Following F18, if we considera more complex spectral model which includes a thermal apec component representing the hot gas in a galaxy and as-sume that the L X contribution of this gas obeys the scalingrelation with SFR parameterized by Mineo et al. (2012b),the absorbed power-law model representing the HMXB pop-ulation would be consistent with higher N H ≈ × cm − and Γ ≈ . Adopting this more complex spectral model doesnot significantly change our estimate of the rest-frame − keV luminosities. L X /SFR as a function of redshift We first checked whether our galaxies exhibit similar L X /SFR as a function of redshift as found by previousstudies. We divided our galaxies into three redshift bins( z = . − . , . − . , . − . ), and stacked the X-ray data. The properties of these stacks are listed in rows − in Tables 1 and 2, and their L X /SFR values versusredshift are shown in Figure 3 with circles.The L X /SFR of the z ∼ sample from F19 is signifi-cantly enhanced relative to our stacks at z = . − . . Since Z information is available for both these samples, togetherthey can be used to test the connection between the redshiftevolution and Z dependence of HMXBs, which is discussedin § L X /SFR valuesexpected based on the redshift evolution relations of L16and A17 shown by lines in Figure 3, which are derived usinggalaxies at z = . − . The stack luminosities fall below theupper limit on XRB emission estimated using the redshift-dependent parametrization of F18. We note that the hard-ness ratios of our stacks are lower than those of most of thestacks of star-forming galaxies from F18 at similar redshift;as a key difference between our sample selection and that MNRAS000 , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution Table 1.
Mean Galaxy Properties of StacksStack ID z range h z i log h M ∗ i h SFR i log h sSFR i Detected Stack ( M ⊙ ) ( M ⊙ yr − ) (yr − )(a) (b) (c) (d) (e) (f) (g) (h) (i) Redshift binning . − . . + . − . . + . − . . + . − . − . + . − . . − . . + . − . . + . − . . + . − . − . + . − . . − . . + . − . . + . − . . + . − . − . + . − . Metallicity binning . − . . + . − . . ± .
001 0 . + . − . − . + . − . . − . . + . − . . ± .
002 1 . + . − . − . + . − . . − . . + . − . . + . − . . + . − . − . + . − . . − . . + . − . . + . − . . + . − . − . + . − . . − . . + . − . . ± .
001 3 . + . − . − . + . − . . − . . + . − . . + . − . . ± . − . + . − .
10 0 143 . − . . + . − . . + . − . . + . − . − . + . − .
11 2 200 . − . . + . − . . ± .
002 8 . + . − . − . + . − .
12 0 480 . − . . + . − . . + . − . . + . − . − . + . − .
13 0 306 . − . . + . − . . ± .
001 12 . + . − . − . + . − . Notes:(g) Mean O/H based on R indicator converted to Pettini & Pagel (2004) calibration.(h) SED SFR listed assumes Z = . and Calzetti extinction curve. Table 2.
Stacked X-ray PropertiesStack ID Stack exposure Stack Stack h L X i log h L X SFR i (Ms) Significance Net counts ( erg s − )(a) (b) (c) (d) (e) (f) Redshift binning ±
27 0 . + . − . . ± . ±
33 1 . + . − . . ± . ±
34 2 . + . − . . ± . Metallicity binning ±
12 0 . + . − . . ± . ±
15 0 . + . − . . ± . ±
13 0 . + . − . . ± . ±
14 0 . + . − . . ± . + − . + . − . . ± . ±
16 1 . + . − . . ± .
10 16.5 6.2 ±
17 1 . ± .
38 39 . ± .
11 23.6 7.7 ±
21 2 . + . − . . ± .
12 51.0 3.1 ±
27 2 . + . − . . ± .
13 31.8 3.0 ±
21 2 . + . − . . ± . Notes:(c) Detection significance expressed in Gaussian σ based on the probability that thesource could be generated by a noise fluctuation of the local background.(d) Net counts of stacked, individually undetected galaxies in the . − keV band. Errorsare based on Poisson statistics.(e) Mean − keV X-ray luminosity, including both individually detected and unde-tected sources. Errors are based on bootstrapping.(f) Mean − keV L X /SFR, including individually detected and undetected sources.MNRAS , 1–14 (2019) F. M. Fornasini et al. l og ( L X / S F R ) [ e r g s − / ( M S un y r − ) ] Aird et al. (2017)Lehmer et al. (2016)Lehmer et al. (2010)Mineo et al. (2012)Lehmer et al. (2019)Fornasini et al. (2019)This work
Figure 3.
Stacked − keV L X /SFR values versus redshift ofthe hCOSMOS and zCOSMOS samples are shown by circles.The hCOSMOS sample has been split into two redshift bins: z = . − . and z = . − . . Stars represent the stacked L X /SFRof high sSFR galaxies from F19. The diamond and triangles rep-resent local ( z = ) measurements of the L X -SFR relation. Thesymbol colors represent the mean O/H of the galaxy samples.The long and short dashed lines display the redshift evolutionof L X /SFR for HMXBs measured by Lehmer et al. (2016) andAird et al. (2017), respectively; since the A17 HMXB-only evo-lution is parametrized as a non-linear relation between L X andSFR, this curve has been normalized for SFR = M ⊙ yr − , themean SFR of our hCOSMOS and zCOSMOS galaxy samples. of F18 is our rejection of sources with AGN signatures, it ispossible that the higher hardness ratios of the F18 sampleare due to the presence of obscured AGN. If the obscura-tion of the F18 stacks is associated with AGN and not theHMXB populations, then the HMXB redshift evolution of L X /SFR measured by F18 would be consistent with L16 andA17. However, since there are additional differences betweenthe F18 sample and ours (including our S/N requirementsfor emission lines which could bias us against galaxies withmore obscured star-forming regions), we cannot definitivelyassess that the difference in the hardness ratios of the sam-ples is due to the presence or absence of obscured AGN.It is worth noting that our stacks and previous measure-ments from L16 and A17 at similar redshift lie in betweenthe local ( z = ) measurements of h L X / SFR i . The fact thatthese z ∼ . − . measurements lie below some z = mea-surements does not necessarily rule out redshift evolutionof L X /SFR. The differences of . − . dex between the z = measurements and our stacks could be accounted forby systematic effects, which are discussed in § § Z dependence of L X /SFR at differentredshifts In order to study the relationship between L X /SFR and Z in more detail, we divide the galaxies in each of our threeredshift intervals by Z . The properties of the resulting X-ray stacks are reported in rows L X /SFR versus Z of these stacks, along withlocal measurements from M12, L10, and L19 and stackedmeasurements of z ∼ galaxies from F19; the different colorsand symbol shapes represent the different redshift intervalsof the galaxy samples.Overall, these data from z = . − combined togethershow that a clear anti-correlation between L X /SFR and Z exists and this relationship appears to be very similaracross redshift. The probability that L X /SFR and Z areanti-correlated for the z > samples combined togetheris > . % using both the Pearson correlation and Spear-man rank correlation tests. The strong agreement between L X /SFR values at similar O/H in galaxy samples spanning z ≈ . − provides the strongest evidence to date that theredshift evolution of L X /SFR can be attributed to the Z dependence of HMXB populations.However, some > σ differences can be observed be-tween some of the L X /SFR measurements at similar Z .Therefore, it is important to test whether the relationshipbetween L X /SFR and Z exhibits any significant variationwith redshift.One potentially significant disagreement between thedifferent redshift samples visible in Figure 4 is that the z ≈ . stacks exhibit a steeper anti-correlation between L X /SFR and Z than the z ≈ . stacks. There are sufficientstacks that we can independently fit the L X -SFR- Z relationat these redshifts. We find the best-fitting relation for thesetwo sets of stacks using χ minimization and adopting asimple power-law relation of the form: L X SFR = α (cid:18) ( O / H )( O / H ) ⊙ (cid:19) β (3)For z ≈ . , the best-fit values are log( α ) = . ± . and β = − . ± . , while for z ≈ . , they are log( α ) = . ± . and β = − . ± . . Thus, the z ≈ . stacks dofavor a steeper L X -SFR- Z relation, albeit weakly. As shownin Figure 5, the 1 σ confidence contours of the fit parametersfor the two samples overlap slightly, their 2 σ confidence con-tours overlap substantially, but the best-fit values are onlyconsistent at − % confidence. Fitting both sets of stackstogether results in a good fit with a reduced χ of 0.64 andbest-fitting values of log( α ) = . ± . and β = − . ± . .Thus, while the z ≈ . stacks favor a steeper relation thanthe z ≈ . stacks, this result is not very statistically signifi-cant.Even though the evidence for a steeper L X -SFR- Z re-lation at z ≈ . compared to z ≈ . is weak, it is worthconsidering whether a flattening of this relation with red-shift could be explained by observational biases or is likely tobe intrinsic. As discussed in § L X /SFR is known to varywith sSFR because the relative contributions of HMXBs andLMXBs change with sSFR. Therefore, if the way in whichthe sSFR distributions vary with Z differs at different red-shifts, the L X -SFR- Z relation could appear flatter or steeper.However, we found that the difference in the L X /SFR- Z slope for galaxy stacks below and above z = . persistedregardless of whether we selected low sSFR or high sSFRgalaxies or if we narrowed the sSFR range of our sample.F19 found that another factor which can affect the steepnessof the L X -SFR- Z relation is AGN contamination. Like F19,we find that including known AGN in our stacks can change MNRAS000
Stacked − keV L X /SFR values versus redshift ofthe hCOSMOS and zCOSMOS samples are shown by circles.The hCOSMOS sample has been split into two redshift bins: z = . − . and z = . − . . Stars represent the stacked L X /SFRof high sSFR galaxies from F19. The diamond and triangles rep-resent local ( z = ) measurements of the L X -SFR relation. Thesymbol colors represent the mean O/H of the galaxy samples.The long and short dashed lines display the redshift evolutionof L X /SFR for HMXBs measured by Lehmer et al. (2016) andAird et al. (2017), respectively; since the A17 HMXB-only evo-lution is parametrized as a non-linear relation between L X andSFR, this curve has been normalized for SFR = M ⊙ yr − , themean SFR of our hCOSMOS and zCOSMOS galaxy samples. of F18 is our rejection of sources with AGN signatures, it ispossible that the higher hardness ratios of the F18 sampleare due to the presence of obscured AGN. If the obscura-tion of the F18 stacks is associated with AGN and not theHMXB populations, then the HMXB redshift evolution of L X /SFR measured by F18 would be consistent with L16 andA17. However, since there are additional differences betweenthe F18 sample and ours (including our S/N requirementsfor emission lines which could bias us against galaxies withmore obscured star-forming regions), we cannot definitivelyassess that the difference in the hardness ratios of the sam-ples is due to the presence or absence of obscured AGN.It is worth noting that our stacks and previous measure-ments from L16 and A17 at similar redshift lie in betweenthe local ( z = ) measurements of h L X / SFR i . The fact thatthese z ∼ . − . measurements lie below some z = mea-surements does not necessarily rule out redshift evolutionof L X /SFR. The differences of . − . dex between the z = measurements and our stacks could be accounted forby systematic effects, which are discussed in § § Z dependence of L X /SFR at differentredshifts In order to study the relationship between L X /SFR and Z in more detail, we divide the galaxies in each of our threeredshift intervals by Z . The properties of the resulting X-ray stacks are reported in rows L X /SFR versus Z of these stacks, along withlocal measurements from M12, L10, and L19 and stackedmeasurements of z ∼ galaxies from F19; the different colorsand symbol shapes represent the different redshift intervalsof the galaxy samples.Overall, these data from z = . − combined togethershow that a clear anti-correlation between L X /SFR and Z exists and this relationship appears to be very similaracross redshift. The probability that L X /SFR and Z areanti-correlated for the z > samples combined togetheris > . % using both the Pearson correlation and Spear-man rank correlation tests. The strong agreement between L X /SFR values at similar O/H in galaxy samples spanning z ≈ . − provides the strongest evidence to date that theredshift evolution of L X /SFR can be attributed to the Z dependence of HMXB populations.However, some > σ differences can be observed be-tween some of the L X /SFR measurements at similar Z .Therefore, it is important to test whether the relationshipbetween L X /SFR and Z exhibits any significant variationwith redshift.One potentially significant disagreement between thedifferent redshift samples visible in Figure 4 is that the z ≈ . stacks exhibit a steeper anti-correlation between L X /SFR and Z than the z ≈ . stacks. There are sufficientstacks that we can independently fit the L X -SFR- Z relationat these redshifts. We find the best-fitting relation for thesetwo sets of stacks using χ minimization and adopting asimple power-law relation of the form: L X SFR = α (cid:18) ( O / H )( O / H ) ⊙ (cid:19) β (3)For z ≈ . , the best-fit values are log( α ) = . ± . and β = − . ± . , while for z ≈ . , they are log( α ) = . ± . and β = − . ± . . Thus, the z ≈ . stacks dofavor a steeper L X -SFR- Z relation, albeit weakly. As shownin Figure 5, the 1 σ confidence contours of the fit parametersfor the two samples overlap slightly, their 2 σ confidence con-tours overlap substantially, but the best-fit values are onlyconsistent at − % confidence. Fitting both sets of stackstogether results in a good fit with a reduced χ of 0.64 andbest-fitting values of log( α ) = . ± . and β = − . ± . .Thus, while the z ≈ . stacks favor a steeper relation thanthe z ≈ . stacks, this result is not very statistically signifi-cant.Even though the evidence for a steeper L X -SFR- Z re-lation at z ≈ . compared to z ≈ . is weak, it is worthconsidering whether a flattening of this relation with red-shift could be explained by observational biases or is likely tobe intrinsic. As discussed in § L X /SFR is known to varywith sSFR because the relative contributions of HMXBs andLMXBs change with sSFR. Therefore, if the way in whichthe sSFR distributions vary with Z differs at different red-shifts, the L X -SFR- Z relation could appear flatter or steeper.However, we found that the difference in the L X /SFR- Z slope for galaxy stacks below and above z = . persistedregardless of whether we selected low sSFR or high sSFRgalaxies or if we narrowed the sSFR range of our sample.F19 found that another factor which can affect the steepnessof the L X -SFR- Z relation is AGN contamination. Like F19,we find that including known AGN in our stacks can change MNRAS000 , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution l og ( L X / S F R ) [ e r g s − / ( M S un y r − ) ] Fragos et al. (2013) modelMadau & Fragos (2017) modelBrorby et al. (2016) z=0 relationz=1.3−2.7: Fornasini et al. (2019)z=0.5−0.9: zCOSMOS (this work)z=0.25−0.4: hCOSMOS (this work)z=0.1−0.25: hCOSMOS (this work)z=0: Lehmer et al. (2019)z=0: Mineo et al. (2012)z=0: Lehmer et al. (2010)
Figure 4.
Average − keV L X /SFR versus O/H for galaxy samples in different redshift ranges are shown by different symbols/colors.For the z = data points, since many of the O/H estimates are based on the M ∗ − Z relation (see 2.5), the horizontal error bars representthe scatter of M ∗ − Z relation from Kewley & Ellison (2008).The local L X -SFR- Z relation from B16 is shown by the dotted line with corresponding error shown by the light gray shaded region. Thedash-dotted line represents the mean of the six highest likelihood models from F13, with the parameter space covered by these sixmodels shown by the dark gray shaded region. The dashed line shows the best-fit model from M17, which has been converted from theKobulnicky & Kewley (2004) R scale to the O3N2 scale from Pettini & Pagel (2004) using the prescription of Kewley & Ellison(2008). the stacked L X /SFR by ± . − . dex and overall flatten theanti-correlation between L X /SFR and Z . At lower redshift,we can identify lower-luminosity AGN because most of thesurvey data we use for AGN identification are flux-limited.Therefore, it would be natural to expect more AGN con-tamination in our higher redshift stacks, and this increasein AGN contamination at higher redshift could help explainthe flatter L X /SFR- Z slope observed at z ≈ . compared to z ≈ . .Comparing the z > results to z = measurements,we find general agreement with the L X -SFR- Z relation fromB16, with 10 of the 12 stacked values being within 1 σ of thisrelation. However, all our stacks with 12+log(O/H) ≥ . fallbelow the B16 relation, and we calculate that the probabil-ity that the z > stacks are drawn from the B16 relation is2.2% assuming χ statistics. The M12 z = L X /SFR mea-surement is in good agreement with our stacks with similarmean O/H. At high O/H, there is some disagreement be-tween different z = measurements of L X /SFR, and our z > stacks fall in between these measurements. The L10value is consistent with the z ≈ . and z ≈ . stacks, whilethe L19 value is higher than all our stacked values by > %confidence. The discrepancy among these z = measure-ments and between them and the z > stacks at high O/H could result from several causes including: (i) the high ob-scuration of the LIRGs and ULIRGs in the L10 sample, (ii)the average O/H of the z = samples not being properlyestimated since for many of the galaxies in these samples werely on the M ∗ − Z relation and not on actual O/H measure-ments, (iii) the uncertainties on the average X-ray spectrumof our stacks and the z = galaxy samples, (iv) the hetero-geneity of SFR calibrations used in different studies, and (v)selection effects that result in local samples being incompleteor unrepresentative. These discrepancies highlight the needfor further studies of the HMXB scaling relation at z = asa function of Z with more complete samples. Nonetheless,given all the sources of uncertainty listed above, we do notfind any compelling evidence of variation of the L X -SFR- Z relation between z = and the higher redshift samples.In summary, we find no strong evidence that the L X -SFR- Z relation varies with redshift, and the weak trend thatis seen between z ≈ . and z ≈ . could be explained byAGN contamination rather than being of intrinsic origin.Thus, these combined data sets provide strong direct ev-idence that the observed redshift evolution of L X /SFR isdriven by the Z dependence of HMXBs. MNRAS , 1–14 (2019) F. M. Fornasini et al. −2.0 −1.5 −1.0 −0.5 0.0 0.539.139.239.339.439.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5Power−law index β N o r m a li z a t i on α z~0.3z~0.268%90%95%99% 68% 90% 95% 99% Figure 5.
Parameter confidence contours for the normalization(y-axis) and power-law index (x-axis) of the L X -SFR- Z relationfrom Equation 3 fit to the z ∼ . and z ∼ . stacks are shown inblue and green, respectively. The best-fit values are indicated bycross symbols, and the contours shown represent 68%, 90%, 95%,and 99% confidence levels. L X -SFR- Z relation Having found no definitive evidence of redshift variation ofthe L X -SFR- Z relation between z ≈ . and z ≈ , we pro-ceed to jointly fit the galaxy samples across redshift to bestconstrain this relationship. Using χ minimization, we firstfind the best relation for all z > stacks using the followingfunctional form used by B16: L X = α (cid:18) ( O / H )( O / H ) ⊙ (cid:19) β (cid:18) SFR M ⊙ yr − (cid:19) δ (4)The z = measurements are not included in this fit because:(i) the average O/H of the local galaxy samples are based ona mixture of actual O/H measurements and O/H estimatesderived from the M ∗ - Z relation and thus are more uncer-tain, and (ii) the local samples are subject to more compli-cated selection effects than our z > stacks. The best-fitparameters are log( α ) = . ± . , β = − . ± . , and δ = . ± . , resulting in a reduced χ = . . Since δ isconsistent with a linear dependence of L X on SFR, we fix it to1 and fit the stacks using the functional form in Equation 3.In this case, the best-fit parameters are log( α ) = . ± . , β = − . ± . , and the reduced χ = . . This best-fitrelation is shown in Figure 6.The L X /SFR- Z slope ( β ) for the z > stacks is steeperthan the slope found at z = by B16 ( β = − . ± . ) butconsistent with the slope measured by Douna et al. (2015)( β = − . ) using a smaller sample of z = galaxies. Onthe other hand, the normalization ( α ) for the z > stacksis consistent with that of the B16 z = sample but higherthan that found by Douna et al. (2015). Thus, the best-fitrelation for the z > stacks at least falls within the range of z = measurements, although a more quantitative compari-son of the agreement will require better understanding andcontrolling for the selection effects affecting local samples.While a power-law relation between L X /SFR and Z provides a good fit to the z > stacks, such a model isunphysical and likely would not extend to lower Z than isprobed by our stacks (12+log(O/H) < . ). Population syn-thesis models predict that the dependence of L X /SFR on Z should flatten at low Z because the wind mass loss ratesbecome so low that the effects of Z on stellar evolutionsaturate (Madau & Fragos 2017). Basu-Zych et al. (2016)showed how variation of the normalization or slope of theHMXB luminosity function with Z could reproduce the Z -dependence of L X /SFR predicted by theoretical models.In order to provide more realistic constraints on the L X -SFR- Z relation, we assess to what extent these theoret-ical models are consistent with our data. We calculate theprobability that the z > stacks are consistent with a givenmodel assuming χ statistics. The highest likelihood modelfrom M17 and the mean of the six highest likelihood mod-els from F13 are inconsistent with our stacks with > . %probability. However, we find that the lower bound of pa-rameter space occupied by the F13 models, which is about0.15 dex lower in L X /SFR than the mean F13 model, is ingood agreement with the z > stacks. The null hypothe-sis that the z > stacked data is consistent with this lowerF13 model is rejected only with 56% probability, which isnot significant. This model is shown by a dash-dotted linein Figure 6.An important consequence of a redshift-independent L X -SFR- Z relation is that the redshift evolution of L X /SFRmeasured by a given study will depend on the Z distributionof the galaxy sample used, which is correlated with the M ∗ and SFR distribution of the sample (e.g. Mannucci et al.2010; Maier et al. 2014; Maier et al. 2015; Sanders et al.2015). Thus, some of the differences between previous mea-surements of the redshift evolution of L X /SFR (shown inFigure 3) may be due to selection effects impacting the Z distribution of the galaxy samples. In comparing the data to population synthesis models, it isimportant to acknowledge the possible impact of systematiceffects. As discussed in § L X -SFR- Z relation,as was found by F19 for their z ∼ sample. It is there-fore possible that the intrinsic relation is steeper than weobserve.It is also important to consider the impact of uncertain-ties associated with SFR indicators on the observed slopeand normalization of the L X -SFR- Z relation. One source ofuncertainty is the fact that the total SED-derived SFRs ofgalaxies that are not detected at MIR-FIR wavelengths arenot well constrained. Strong constraints on the dust emissionassociated with obscured star formation requires detectionsat wavelengths ≥ µ m, although data at 24 µ m and 70 µ mprovides some constraining power on this emission. In ourhCOSMOS and zCOSMOS samples, 66% of the galaxies aredetected in at least one band ≥ µ m, while only 32% aredetected at ≥ µ m. To assess the impact of uncertaintiesof the total SED-derived SFR on our results, we calculateupper and lower bounds on the average L X /SFR of eachstack accounting for uncertainties in the SFR measurementsof galaxies that are not detected at MIR-FIR wavelengths.We perform these calculations for two scenarios: a more lib-eral case in which we consider having at least one detectionat ≥ µ m as sufficient for constraining the IR dust emis-sion, and a more conservative case in which we require atleast one detection at ≥ µ m to consider a galaxy’s IR MNRAS , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution l og ( L X / S F R ) [ e r g s − / ( M S un y r − ) ] Fragos et al. (2013) model (low normalization)Best power−law fit (this work)z=1.3−2.7: Fornasini et al. (2019)z=0.5−0.9: zCOSMOS (this work)z=0.25−0.4: hCOSMOS (this work)z=0.1−0.25: hCOSMOS (this work)
Figure 6.
Average − keV L X /SFR versus O/H for galaxy samples in different redshift ranges are shown by different symbols/colors.Our best-fit power-law L X -SFR- Z relation for the z > stacks is shown by the solid line, with corresponding error shown by the grayshaded region. The lower bound of the F13 models (which is 0.15 dex lower than the mean of their best-fitting models) also provides agood fit to the z > stacks and is shown by a dash-dotted line. dust emission as well-constrained. In calculating these up-per and lower bounds on L X /SFR, we use the best estimateSFR values for galaxies considered to have well-constrainedIR dust emission, and the lower/upper bounds on SFR de-scribed in § L X /SFR as a functionof Z for both scenarios outlined above are shown in Figure7. The horizontal bar symbols show the upper and lowerbounds on L X /SFR for the stacks when using the lower orupper bounds on SFR, respectively, for galaxies which arenot detected at wavelengths ≥ µ m. The open symbols inthe figure show the results for the more conservative casein which we adopt the lower and upper bounds on SFR forgalaxies which are not detected at wavelengths ≥ µ m. Ascan be seen in Figure 7, even if we consider these extremebounds on the L X /SFR values, the z ≈ . and z ≈ . stacksfavor an anti-correlation between L X /SFR and Z . The L X -SFR- Z relation at z ≈ . remains steeper than at z ≈ . ,but at a given O/H, the L X /SFR of stacks from z = . − mostly remain consistent within the statistical errors (shownin Figure 6). The most significant caveat introduced by theuncertainties in the SED-derived SFRs illustrated in Figure7 is that, if the true SFRs are closer to the lower SFR boundsthan our best estimates, the L X -SFR- Z relation would bemore consistent with the normalizations of the preferred F13and M17 models.The Z dependence of SFR indicators may also impact the observed slope of the L X -SFR- Z relation. We have usedsolar metallicity stellar population models and the Calzettiextinction curve in deriving our SFR estimates, but theseassumptions may not be appropriate for some of our low- Z galaxy stacks. F19 explored in detail the impact of usingdifferent SFR indicators on the L X /SFR values measuredfor the stacks of z ∼ MOSDEF galaxies included in Fig-ures 3-6. Using Z = . BC03 stellar population modelsand adopting the SMC extinction curve (Gordon et al. 2003)can result in SFRs that are 0.3 dex lower than those derivedusing Z = . and the Calzetti curve. However, F19 alsofound that the latter were in better agreement with H α de-rived SFRs. If the SFRs of our low- Z stacks have been over-estimated, that would imply that the L X -SFR- Z relation issteeper, with a slope that could more closely resemble theM17 model. As our understanding of SFR indicators at low- Z and high redshift improves, it will be important to updatethese constraints on the L X -SFR- Z relation.Finally, the assumed X-ray spectrum also affects thederived L X . Changing the spectral parameters within therange consistent with the hardness ratios of the stacks canchange the measured L X by + /− L X -SFR- Z re-lation, but not its slope. If the true spectrum of the sourcesis harder than the Γ = power-law we have assumed, thenour stacks would be more consistent with the mean of thehighest likelihood F13 models shown in Figure 4. MNRAS , 1–14 (2019) F. M. Fornasini et al. l og ( L X / S F R ) [ e r g s − / ( M S un y r − ) ] Fragos et al. (2013) modelMadau & Fragos (2017) modelBrorby et al. (2016) z=0 relationBest power−law fit (this work)z=0.5−0.9: zCOSMOS (this work)z=0.25−0.4: hCOSMOS (this work)z=0.1−0.25: hCOSMOS (this work)
Figure 7.
Average − keV L X /SFR upper/lower limits versus O/H for galaxy stacks from the hCOSMOS and zCOSMOS surveys indifferent redshift ranges are shown by different symbols/colors. For each galaxy stack, the horizontal bar symbols show the upper/lowerlimits on L X /SFR based on adopting the UV-only lower bound on SFR or the Herschel -limit upper bound on SFR, respectively, forgalaxies which have no detections at wavelengths ≥ µ m. The open symbols show the upper/lower limits on L X /SFR based on adoptingthe lower/upper bounds on SFR for all galaxies which are undetected at wavelengths ≥ µ m. The lines are as described in Figures 4and 6. While systematic effects may therefore impact the over-all slope and normalization of the L X -SFR- Z relation, it isimportant to note that these effects do not impact the pri-mary conclusion that the Z dependence of HMXBs is con-sistent across redshift and drives the observed redshift evo-lution of L X /SFR of star-forming galaxies. We have used samples of star-forming galaxies at z = . − . with optical spectra from the hCOSMOS and zCOSMOSsurveys and deep Chandra data to expand upon a previousinvestigation of the connection between the redshift evolu-tion and the Z dependence of HMXBs. Using a sample of z ∼ galaxies, F19 found the first direct evidence that theredshift evolution of L X /SFR is driven by the Z dependenceof HMXBs. Their conclusion relied on comparing the L X -SFR- Z relation at z ∼ with local measurements, whichmay be biased due to sample selections effects. Thus, thegoal of this work was to measure the L X -SFR- Z relation atmultiple redshifts, compare these results to the z ∼ mea-surements, and provide stronger constraints for populationsynthesis models.Dividing our sample of z = . − . galaxies by red-shift and O/H, we stacked the X-ray data from the Chandra
COSMOS Legacy Survey at the galaxy locations to measure the average L X /SFR of each stack. We find that L X /SFRand Z are anti-correlated at all redshifts ( z = . − . , . − . , . − . ). At z ≈ . and z ≈ . , there are sufficientstacked detections that we can determine the best-fit of the L X -SFR- Z relation independently. A steeper anti-correlationis favored at z ≈ . compared to z ≈ . , but this differenceis not statistically significant.When we split our sample by redshift alone, we findthe mean L X /SFR values of the z ≈ . , 0.3, and 0.7 sam-ples are significantly lower than the mean L X /SFR of the z ∼ sample from F19. This result is consistent with previ-ous measurements of the redshift evolution of HMXB emis-sion. Comparing the L X -SFR- Z values of the z ∼ stackswith our lower redshift stacks at similar O/H, we find verygood agreement. These results provide the strongest, directevidence that the observed redshift evolution of L X /SFR isdriven by the Z dependence of HMXBs.Combining all the z > stacks together, we find thatthe anti-correlation between L X /SFR and Z is significant at > . % confidence. Parametrizing the L X -SFR- Z relationas a power-law, we find that the best-fitting parameters arewithin the range measured for galaxies at z = . Comparingthe z > stacked measurements with population synthesismodels, we find they are in good agreement with the lowerbound of the F13 models, which is 0.15 dex lower than themean of their six highest likelihood models. However, sys- MNRAS000
COSMOS Legacy Survey at the galaxy locations to measure the average L X /SFR of each stack. We find that L X /SFRand Z are anti-correlated at all redshifts ( z = . − . , . − . , . − . ). At z ≈ . and z ≈ . , there are sufficientstacked detections that we can determine the best-fit of the L X -SFR- Z relation independently. A steeper anti-correlationis favored at z ≈ . compared to z ≈ . , but this differenceis not statistically significant.When we split our sample by redshift alone, we findthe mean L X /SFR values of the z ≈ . , 0.3, and 0.7 sam-ples are significantly lower than the mean L X /SFR of the z ∼ sample from F19. This result is consistent with previ-ous measurements of the redshift evolution of HMXB emis-sion. Comparing the L X -SFR- Z values of the z ∼ stackswith our lower redshift stacks at similar O/H, we find verygood agreement. These results provide the strongest, directevidence that the observed redshift evolution of L X /SFR isdriven by the Z dependence of HMXBs.Combining all the z > stacks together, we find thatthe anti-correlation between L X /SFR and Z is significant at > . % confidence. Parametrizing the L X -SFR- Z relationas a power-law, we find that the best-fitting parameters arewithin the range measured for galaxies at z = . Comparingthe z > stacked measurements with population synthesismodels, we find they are in good agreement with the lowerbound of the F13 models, which is 0.15 dex lower than themean of their six highest likelihood models. However, sys- MNRAS000 , 1–14 (2019) onnecting HMXB Z -dependence and z -evolution tematic uncertainties associated with the X-ray spectrumand poor constraints in the MIR-FIR bands for a significantfraction of the galaxy sample could bring our results in bet-ter agreement with the preferred F13 and M17 models. Wealso note that the intrinsic L X -SFR- Z may be steeper thanthat observed due to systematic effects arising from AGNcontamination and uncertainties in the variation of SFR in-dicators with Z . However, these systematic effects do notimpact our conclusion that the Z dependence of HMXBsdrives the redshift evolution of L X /SFR.Over the next two decades, order of magnitude improve-ments in studies of the L X -SFR- Z relation will be enabledby the larger samples of galaxies with Z and H α SFR mea-surements provided by 30-meter class optical/infrared tele-scopes, improved measurements of the IR SFRs of galaxiesusing
JWST and future FIR telescopes, and the larger anddeeper X-ray surveys that will be performed by the nextgeneration of X-ray telescopes.
ATHENA will be capableof individually detecting XRB-dominated galaxies out to z ∼ (Nandra et al. 2013), and the Lynx X-ray Observa-tory would push this limit to z ∼ (Vikhlinin 2019). TheseX-ray telescopes would also allow more complete surveys ofHMXB populations in nearby galaxies and improved char-acterization of the X-ray spectrum of HMXBs as a functionof Z (Basu-Zych et al. 2019; Zezas et al. 2019). Better con-straints on the L X -SFR- Z will inform models of stellar evo-lution, including the progenitor pathways of gravitationalwave sources, and improve estimates of the impact of X-raybinaries to the heating of the intergalactic medium duringreionization. ACKNOWLEDGEMENTS
We thank J. H. Zahid, C. Maier, and G. Cresci for provid-ing O/H measurements for galaxies from the hCOSMOS andzCOSMOS surveys. We are grateful to B. Lehmer for provid-ing helpful feedback that improved the quality and clarity ofthis paper during peer review. We also thank I. Damjanovfor helpful conversations about the hCOSMOS survey andusing hCOSMOS data. F. M. F. acknowledges support fromthe National Aeronautics and Space Administration throughChandra Award Number AR7-18009X and AR8-19010X is-sued by the Chandra X-ray Center, which is operated by theSmithsonian Astrophysical Observatory for and on behalf ofthe National Aeronautics Space Administration under con-tract NAS8-03060. The development of CSTACK, which wasused in this work, is supported by UNAM-DGAPA PAPIITIN104216 and CONACyT 252531. The scientific results re-ported in this article are based on observations made by the
Chandra X-ray Observatory , GALEX , the
Herschel SpaceObservatory , and the
Spitzer Space Observatory . This studyalso made use of data obtained at the MMT Observatory, ajoint venture of the Smithsonian Institution and the Uni-versity of Arizona, the Subaru Telescope, which is oper-ated by the National Astronomical Observatory of Japan,the Canada-France-Hawaii Telescope (CFHT), which is op-erated by the National Research Council (NRC) of Canada,the Institut National des Science de l’Univers of the CentreNational de la Recherche Scientifique (CNRS) of France, andthe University of Hawaii, and ESO Telescopes at the La SillaParanal Observatory under ESO programme ID 179.A-2005. We extend special thanks to those of Hawaiian ancestry, onwhose sacred mountain we are privileged to be guests.
Software : CIAO (Fruscione et al. 2006), BEHR(Park et al. 2006), CSTACK (Miyaji et al. 2008)
Facilities : Chandra X-ray Observatory, GALEX, Her-schel Space Observatory, Spitzer Space Telescope, MMT Ob-servatory, Subaru Telescope
REFERENCES
Aird J., Coil A. L., Georgakakis A., 2017, MNRAS, 465, 3390Antoniou V., Zezas A., 2016, MNRAS, 459, 528Arnouts S., et al., 2013, Astronomy and Astrophysics, 558, A67Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A,47, 481Basu-Zych A. R., et al., 2013a, ApJ, 762, 45Basu-Zych A. R., et al., 2013b, ApJ, 774, 152Basu-Zych A. R., Lehmer B., Fragos T., Hornschemeier A., YukitaM., Zezas A., Ptak A., 2016, ApJ, 818, 140Basu-Zych A., et al., 2019, BAAS, 51, 70Bodaghee A., Tomsick J. A., Rodriguez J., James J. B., 2012,ApJ, 744, 108Brorby M., Kaaret P., Prestwich A., 2014, MNRAS, 441, 2346Brorby M., Kaaret P., Prestwich A., Mirabel I. F., 2016, MNRAS,457, 4081Bruzual G., Charlot S., 2003, MNRAS, 344, 1000Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J.,Storchi-Bergmann T., 2000, ApJ, 533, 682Chabrier G., 2003, PASP, 115, 763Chary R., Elbaz D., 2001, The Astrophysical Journal, 556, 562Civano F., et al., 2016, The Astrophysical Journal, 819, 62Cresci G., Mannucci F., Sommariva V.,Maiolino R., Marconi A., Brusa M., 2012,Monthly Notices of the Royal Astronomical Society,421, 262Dale D. A., Helou G., 2002, The Astrophysical Journal, 576, 159Damjanov I., Zahid H. J., Geller M. J., Fabricant D. G., HwangH. S., 2018, The Astrophysical Journal Supplement Series,234, 21Donley J. L., et al., 2012, ApJ, 748, 142Douna V. M., Pellizza L. J., Mirabel I. F., Pedrosa S. E., 2015,A&A, 579, A44Dray L. M., 2006, MNRAS, 370, 2079Fabricant D. G., Hertz E. N., Szentgyorgyi A. H., Fata R. G.,Roll J. B., Zajac J. M., 1998, in D’Odorico S., ed., Society ofPhoto-Optical Instrumentation Engineers (SPIE) ConferenceSeries Vol. 3355, Optical Astronomical Instrumentation. pp285–296, doi:10.1117/12.316814Fabricant D., et al., 2005, Publications of the Astronomical Society of the Pacific,117, 1411Fornasini F. M., Civano F., Fabbiano G., Elvis M., Marchesi S.,Miyaji T., Zezas A., 2018, ApJ, 865, 43Fornasini F. M., et al., 2019, arXiv e-prints, p. arXiv:1909.08635Fragos T., et al., 2013a, ApJ, 764, 41Fragos T., Lehmer B. D., Naoz S., Zezas A., Basu-Zych A., 2013b,ApJ, 776, L31Fruscione A., et al., 2006, CIAO: Chandra’s data analysis system.p. 62701V, doi:10.1117/12.671760Gilfanov M., 2004, MNRAS, 349, 146Gilfanov M., Grimm H.-J., Sunyaev R., 2004, MNRAS, 347, L57Gordon K. D., Clayton G. C., Misselt K. A., Landolt A. U., WolffM. J., 2003, ApJ, 594, 279Griffin M. J., et al., 2010, Astronomy and Astrophysics, 518, L3Grimm H.-J., Gilfanov M., Sunyaev R., 2003, MNRAS, 339, 793Hao C.-N., Kennicutt R. C., Johnson B. D., Calzetti D., DaleD. A., Moustakas J., 2011, ApJ, 741, 124MNRAS , 1–14 (2019) F. M. Fornasini et al.
Iben Jr. I., Tutukov A. V., Yungelson L. R., 1995, ApJS, 100, 217Justham S., Schawinski K., 2012, MNRAS, 423, 1641Kaaret P., Schmitt J., Gorski M., 2011, ApJ, 741, 10Kauffmann G., et al., 2003, MNRAS, 346, 1055Kewley L. J., Dopita M. A., 2002,The Astrophysical Journal Supplement Series, 142, 35Kewley L. J., Ellison S. L., 2008, ApJ, 681, 1183Kobulnicky H. A., Kewley L. J., 2004, ApJ, 617, 240Kobulnicky H. A., Phillips A. C., 2003,The Astrophysical Journal, 599, 1031Kurtz M. J., Mink D. J., 1998,Publications of the Astronomical Society of the Pacific,110, 934Laigle C., et al., 2016, ApJS, 224, 24Lamareille F., 2010, Astronomy and Astrophysics, 509, A53Le F`evre O., et al., 2003, in Iye M., Moorwood A. F. M., eds, Soci-ety of Photo-Optical Instrumentation Engineers (SPIE) Con-ference Series Vol. 4841, Instrument Design and Performancefor Optical/Infrared Ground-based Telescopes. pp 1670–1681,doi:10.1117/12.460959Le Floc’h E., et al., 2009, The Astrophysical Journal, 703, 222Lehmer B. D., Alexander D. M., Bauer F. E., Brandt W. N.,Goulding A. D., Jenkins L. P., Ptak A., Roberts T. P., 2010,ApJ, 724, 559Lehmer B. D., et al., 2016, ApJ, 825, 7Lehmer B. D., et al., 2019, ApJS, 243, 3Lilly S. J., et al., 2007, The Astrophysical Journal Supplement Series,172, 70Linden T., Kalogera V., Sepinsky J. F., Prestwich A., Zezas A.,Gallagher J. S., 2010, ApJ, 725, 1984Madau P., Fragos T., 2017, ApJ, 840, 39Maier C., Lilly S. J., Ziegler B. L., Contini T., P´erez Montero E.,Peng Y., Balestra I., 2014, ApJ, 792, 3Maier C., Ziegler B. L., Lilly S. J., Contini T., P´erez-MonteroE., Lamareille F., Bolzonella M., Le Floc’h E., 2015,Astronomy and Astrophysics, 577, A14Mannucci F., Cresci G., Maiolino R., Marconi A., Gnerucci A.,2010, MNRAS, 408, 2115Mapelli M., Ripamonti E., Zampieri L., Colpi M., 2011,Astronomische Nachrichten, 332, 414Marchesi S., et al., 2016, The Astrophysical Journal, 817, 34Mezcua M., Civano F., Fabbiano G., Miyaji T., Marchesi S., 2016,ApJ, 817, 20Mineo S., Gilfanov M., Sunyaev R., 2012a, MNRAS, 419, 2095Mineo S., Gilfanov M., Sunyaev R., 2012b, MNRAS, 426, 1870Miyaji T., Griffiths R. E., C-COSMOS Team 2008, in AAS/HighEnergy Astrophysics Division A TEX file prepared bythe author. MNRAS000