The Properties and Redshift Evolution of Intermediate-Luminosity Off-Nuclear X-ray Sources in the Chandra Deep Fields B. D. Lehmer,1 W. N. Brandt,1 A. E. Hornschemeier,2 D. M. Alexander,3 F. E. Bauer,4 A. M. Koekemoer,5 D. P. Schneider,1 & A. T. Steffen1 6 0 0 ABSTRACT 2 n a We analyze a population of intermediate-redshift (z ≈ 0.05−0.3), off-nuclear J 1 X-ray sources located within optically-bright galaxies in the Great Observato- 3 ries Origins Deep Survey (GOODS) and Galaxy Evolution from Morphology and 1 SEDs (GEMS) fields. A total of 24 off-nuclear source candidates are classified v 1 using deep Chandra exposures from the Chandra Deep Field-North, Chandra 0 Deep Field-South, and Extended Chandra Deep Field-South; 15 of these are 0 2 newly identified. These sources have average X-ray spectral shapes and optical 0 environments similar to those observed for off-nuclear intermediate-luminosity 6 0 (L ≥ 1039 erg s−1 in the 0.5–2.0 keV band) X-ray objects (IXOs; sometimes re- X / h ferred to as ultraluminous X-ray sources [ULXs]) in the local universe. This sam- p ple improves the available source statistics for intermediate-redshift, off-nuclear - o r sources with LX ∼> 1039.5 erg s−1, and it places significant new constraints on the t s redshift evolution of the off-nuclear source frequency in field galaxies. The frac- a : tion of intermediate-redshift field galaxies containing an off-nuclear source with v Xi LX ∼> 1039 erg s−1 is suggestively elevated (≈80% confidence level) with respect to that observed for IXOs in the local universe; we calculate this elevation to be r a a factor of ≈1.9+1.4. A rise in this fraction is plausibly expected as a consequence −1.3 of the observed increase in global star-formation density with redshift, and our results are consistent with the expected magnitude of the rise in this fraction. 1 Department of Astronomy & Astrophysics, 525 Davey Lab, The Pennsylvania State University, Univer- sity Park, PA 16802,USA 2Laboratory for X-ray Astrophysics, NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771,USA 3Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, United Kingdom 4Columbia Astrophysics Laboratory, Columbia University, Pupin Labortories, 550 W. 120th St., Rm 1418, New York, NY 10027,USA 5 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,USA – 2 – Subject headings: cosmology: observations — diffuse radiation — surveys — X-rays: galaxies — X-rays: general 1. Introduction Intermediate-luminosity X-ray objects (IXOs) in the local universe are off-nuclear X-ray sources having 0.5–8.0 keV luminosities exceeding ∼1039 erg s−1 (e.g., Colbert & Ptak 2002). X-ray sources making up the high-luminosity end (i.e., ∼> 2 × 1039 erg s−1) of the IXO pop- ulation are commonly referred to as ultraluminous X-ray sources (ULXs); they are referred to as “ultraluminous” because their inferred isotropic luminosities exceed that expected for an≈10 M black holeaccreting atthe Eddington limit. Investigations of this enigmatic pop- ⊙ ulation suggest that many IXOs may be intermediate-mass black holes (IMBHs) with masses exceeding ≈10 M (e.g., Colbert & Miller 2004; Miller et al. 2004) and/or normal high mass ⊙ X-ray binaries (HMXBs) anisotropically beaming X-rays into our line-of-sight (e.g., King et al. 2001). Recent observations indicate IXOs may be a natural high-luminosity extension of the HMXB X-ray luminosity function, suggesting that these sources trace relatively young stellar populations (e.g., Gilfanov et al. 2004). Indeed, analyses of the physical and environ- mental properties of IXOs have shown that the number and cumulative X-ray luminosities of IXOs are correlated with star-formation rate (e.g., Kilgard et al. 2002; Swartz et al. 2004). As a consequence of this, IXOs are more commonly observed in late-type spiral and irregular galaxies than in early-type ellipticals. Furthermore, investigations of X-ray populations in early-type galaxies find that luminous (LX ∼> 2×1039 erg s−1) IXOs (i.e., ULXs) are gener- ally absent (e.g., Irwin et al. 2003); however, exceptions have been noted (e.g., Loewenstein et al. 2005). Recently, the fraction of galaxies in the local universe containing IXOs (as a function of X-ray luminosity) has been constrained statistically using ROSAT observations of a sample of 766 relatively nearby (D < 66.7 Mpc) galaxies (Ptak & Colbert 2004; hereafter PC04) from the Third Reference Catalog of Bright Galaxies (RC3; de Vaucouleurs et al. 1991). PC04 report that, after correcting for expected background sources, ≈12% and ≈1% of all local RC3 spiral and irregular galaxies have one or more IXOs with 2–10 keV luminosities L > 1039 erg s−1 and L > 1040 erg s−1, respectively. Here, 2–10 keV luminosities were X X estimatedfromthe0.2–2.4 keVfluxwithanassumedIXOpower-lawphotonindexofΓ = 1.7. Atincreasing redshifts, itisplausiblyexpected thatthefractionofgalaxieshostingIXOs will increase as a result of the observed rise in global star-formation density with redshift (e.g., Madau et al. 1998; Ghosh & White 2001). Evidence for the global evolution of star- formationactivity hasalso beenobserved asanincrease inthe average X-rayluminosity from – 3 – normalgalaxies out toz ≈ 1 (e.g., Hornschemeier et al. 2002); IXOs likely play animportant role in this evolution. Thus far, low X-ray flux levels and limited angular resolution have restricted the study of relatively distant (z ∼> 0.05; D ∼> 200 Mpc) IXOs. However, deep multiwavelength extragalactic surveys that combine the optical imaging capabilities of the Hubble Space Telescope (HST) and the sub-arcsecond X-ray imaging of the Chandra X-ray Observatory (Chandra) have made the detection and classification of intermediate-redshift (z ≈ 0.05−0.3; lookback times of≈ 0.7–3.4Gyr) off-nuclear sources possible. Hornschemeier et al. (2004; hereafter H04) isolated and characterized ten off-nuclear source candidates in optically-bright field galaxies with redshifts in the range z = 0.04 − 0.23 (z ≈ 0.1). median This investigation utilized HST observations with Advanced Camera for Surveys (ACS) filters B , V , i , and z from the Great Observatories Origins Deep Survey (GOODS; 435 606 775 850 Giavalisco et al. 2004) and deep Chandra observations coincident with these fields through the ≈2 Ms Chandra Deep Field-North (CDF-N; Alexander et al. 2003) and ≈1 Ms Chandra Deep Field-South(CDF-S; Giacconiet al. 2002)surveys. H04found that the fractionof field galaxies with detectable off-nuclear X-ray sources (L0.5−2.0 keV ∼> 1038.9 erg s−1) at z ≈ 0.1 is 36+24%, suggestively larger than that observed for galaxies in the local universe. Moreover, −15 due to an angular-resolution bias, this “observed” fraction was only considered to be a lower limit to the true fraction, which would include off-nuclear sources with offsets smaller than the Chandra positional error circles. Unfortunately, a study of the dependence of this fraction upon off-nuclear source X-ray luminosity fraction was not possible due to limited source statistics, most notably for sources with 0.5–2.0 keV luminosities LX ∼> 1039.5 erg s−1. In this investigation, we estimate the true fraction of intermediate-redshift field galaxies hosting off-nuclear X-raysources asa function of0.5–2.0 keV luminosity andcompare it with that observed for local galaxies (from PC04). We improve the source statistics available for intermediate-redshift, off-nuclear sources by combining the multiwavelength data within the ≈2 Ms CDF-N and ≈1 Ms CDF-S with new HST and Chandra observations of the Extended Chandra Deep Field-South (E-CDF-S; Lehmer et al. 2005a). The E-CDF-S is composed of four contiguous ≈250 ks Chandra fields covering an ≈0.3 deg2 region, which flanks the ≈1 Ms CDF-S. A large fraction of the E-CDF-S (≈80%) has been observed with HST in two ACS filters, V and z , through the Galaxy Evolution from Morphology and SEDs 606 850 (GEMS; Rix et al. 2004) survey. The E-CDF-S Chandra observations can detect z = 0.1 off-nuclear sources with projected physical offsets of ∼> 2 kpc and 0.5–2.0 keV luminosities of ∼> 3×1039 erg s−1 in the most sensitive regions. Furthermore, z = 0.1 sources with physical offsets of ∼> 3 kpc and 0.5–2.0 keV luminosities ∼> 3×1040 erg s−1 can be detected over the entire ≈0.3 deg2 E-CDF-S field. The Galactic column densities are ≈1.3 × 1020 cm−2 for the CDF-N (Lockman 2003) and ≈8.8 × 1019 cm−2 for the CDF-S and E-CDF-S (Stark et al. 1992). All of the X-ray – 4 – fluxes and luminosities quoted throughout this paper have been corrected for Galactic ab- sorption using these column densities. Often we quote Poisson errors with values indicating 1σ significance levels; these are computed following Gehrels (1986). H = 70 km s−1 Mpc−1, 0 Ω = 0.3, and Ω = 0.7 are adopted throughout this paper (Spergel et al. 2003), and the m Λ coordinates are J2000.0. 2. Off-Nuclear Source Sample Construction 2.1. Sample Selection As discussed above, the combination of the high spatial resolution of HST imaging and sensitive X-ray observations with Chandra is effective in detecting and classifying off- nuclear X-ray sources out to z ≈ 0.3. The ≈2 Ms CDF-N, ≈1 Ms CDF-S, and ≈250 ks E-CDF-S (hereafter CDFs) are currently the deepest extragalactic X-ray surveys conducted with Chandra (see, e.g., Brandt & Hasinger 2005 for a review), and all of these surveys have good HST coverage. These observations reach 0.5–2.0 keV sensitivity limits ranging from 1.8 ×10−17 erg cm−2 s−1 in the CDF-N to 1.1 ×10−16 erg cm−2 s−1 in the E-CDF-S. However, as demonstrated in § 3.4.2 of Alexander et al. (2003) and § 3.3.2 of Lehmer et al. (2005a), legitimate lower-significance X-ray sources below these quoted sensitivity limits can be identified by matching such sources to associated optically bright galaxies. We therefore searched for off-nuclear sources using both the published main Chandra catalogs of Alexander et al. (2003; CDF-N and CDF-S) and Lehmer et al. (2005a; E-CDF-S) as well as additional lower-significance X-ray sources detected in these fields by running the CIAO source-searching algorithm wavdetect (Freeman et al. 2002) at a false-positive probability threshold of 1×10−5. A total of 933, 689, and 1085 X-ray sources in the CDF-N, CDF-S, and E-CDF-S, respectively, were thus used in our searching; these numbers do not take into account the overlapping regions of the CDF-S and E-CDF-S. We searched for and classified off-nuclear X-ray source candidates in the CDFs using the following criteria: 1. An X-ray source is considered to be an off-nuclear candidate if its position is offset from the optical nucleus of an optically-bright galaxy (ACS magnitudes of V < 21; 606 see below for a description of how this limit was selected) by ≥1.5 × the radius of the Chandra positional error circle (see equations (2) and (3) of Alexander et al. (2003) and Lehmer et al. (2005a), respectively) but is still observed to lie within the optical extent of the candidate host galaxy. The radius of the positional error circle (80–90% confidence) for Chandra sources detected in the CDFs ranges from ≈0′.′3–1′.′5 and is de- – 5 – pendent on the Chandra point-spread function (PSF) size and the number of observed counts. Our required minimum offset of 1.5 × the radius of the Chandra positional error circle was chosen empirically based on histograms showing the number of sources with X-ray-to-optical flux ratios similar to those of active galactic nuclei (AGNs) (i.e., sources with log[f /f ] > −0.5) versus their X-ray-to-optical positional offsets; we X V found that ≈98% of AGN-like sources with V < 24 were matched to within 1.5 × 606 the radius of the Chandra positional error circle. For illustrative purposes, we provide Figure 1, which shows the logarithm of the X-ray-to-optical flux ratio (log[f /f ]) ver- X V sus positional offset in units of the Chandra positional error for 0.5–2.0 keV detected sources with optical counterparts having V < 24. On the basis of our analysis, the 606 number of V < 21 nuclear sources in our sample expected to have offsets larger than 606 1.5 × the radius of the Chandra positional error circle is calculated to be ≈0.91+2.11. −0.75 2. We required that candidate host galaxies have redshifts in the range of 0 < z ≤ 0.3. We used spectroscopic redshifts for ≈98% of the field galaxies in the CDF-N (e.g., Barger et al. 2003; Wirth et al. 2004) and ≈6% of the field galaxies in the CDF-S and E-CDF-S (e.g., Szokoly et al. 2004). For the remaining field galaxies in the CDF-N (≈2%) and CDF-S and E-CDF-S (≈94%), we used high-quality photometric redshifts from GOODS (Mobasher et al. 2004) and COMBO-17 (Wolf et al. 2004), respectively. We note that in the CDF-Sand E-CDF-S, where the majority of the field galaxies have only photometric redshifts via the 17-filter photometry from COMBO-17, the redshift uncertainties are small (i.e., δ /(1+z) ≈ 0.01). The selected redshift range was chosen z empirically by considering the observed number of off-nuclear sources detected as a function of redshift. Furthermore, for redshifts larger than 0.3, the projected linear distance corresponding to the typical Chandra positional error ( ∼> 7 kpc) becomes unreasonably large for detecting many off-nuclear sources. 3. In aneffort to minimize confusion with unrelated background X-ray sources, we further required that each off-nuclear source candidate is detected in either the 0.5–2.0 keV or 0.5–8.0 keV bands and has a 0.5–2.0 keV luminosity ≤1041 erg s−1. These restrictions are based on the observed spectral and luminosity properties of local IXOs. X-ray luminosities were computed using the equation L = 4πd2 f (1+z)Γ−2 (1) X L X where d is the luminosity distance, f is the X-ray flux of each source, and Γ is the L X X-ray photon index assuming a power-law Spectral Energy Distribution (SED). We adopt a photon index of Γ = 1.8 throughout this paper (see § 2.2 for justification). – 6 – The sky density of optically-bright galaxies is relatively low, and thus the probability of finding an unrelated background X-ray source within the optical extent of these galaxies is also low. In order to estimate the total number of background sources that may be con- taminating our sample and to determine the optimal optical-magnitude limit down to which we search for off-nuclear sources, we followed a similar methodology to that outlined in § 2 of PC04. We first chose a tentative optical magnitude limit down to which we search for off-nuclear sources. For each candidate host galaxy, we then visually estimated the galactic area within which we would consider an X-ray source to be off-nuclear. This area was ap- proximated by defining an ellipse with a semimajor and semiminor axis and position angle for each galaxy with a circle of radius 1.5 × the radius of the Chandra positional error circle removed. Next, we calculated the average 0.5–2.0 keV sensitivity limit over the relevant area of each galaxy using empirically calculated sensitivity maps that were calibrated ap- propriately for sources detected by wavdetect using a false-positive probability threshold of 1×10−5. We chose to use the 0.5–2.0 keV band because of its low background and cor- respondingly high sensitivity. The number of expected background 0.5–2.0 keV sources per galaxy was estimated using the galactic area, galaxy sensitivity limit, and best-fit number- counts relation presented in § 4 of Bauer et al. (2004). Finally, the total number of expected contaminating background sources was computed by summing the contributions from each galaxy. We found that when restricting our search to galaxies with V < 21, the number of 606 expected contaminating background sources in the entire survey is reasonably low (≈2.22), so we chose V = 21 as our optical magnitude limit. For galaxies brighter than this limit, 606 the median (mean) number of expected background X-ray sources was ≈0.0029 (0.0064) galaxy−1. We appropriately correct for contaminating background sources in our analyses below. 2.2. X-ray and Optical Properties of Off-Nuclear Sources and Host Galaxies Using the criteria presented above, we identified a total of 24 off-nuclear source can- didates (see Figure 2); nine of these were previously detected by H04. The additional source presented in H04 that is not included here (CXOCDFS J033220.35−274555.3) was within 1.5 × the Chandra positional error and was only detected in the 0.5–1.0 keV band. All of the off-nuclear source candidates are coincident with late-type galaxies (i.e., spirals and irregulars); this is generally consistent with studies of IXOs in the local universe (see § 1). We also note that two of the off-nuclear sources (CXOHDFN J123701.99+621122.1 and CXOHDFDN J123706.12+621711.9) are located in galaxies having discernable bars of optical emission. The X-ray properties of the off-nuclear sources are summarized in Ta- ble 1 and additional properties, including those of the host-galaxies, are summarized in – 7 – Table 2; median properties of are listed in the last rows of these Tables. The median off- nuclear source is offset by ≈2.1 × the Chandra positional error, and only two sources (CX- OCDFS J033230.01−274404.0and CXOECDFS J033322.97−273430.7)have offsets near our required minimum offset of 1.5 × the Chandra positional error (see Figure 1). CXOCDFS J033230.01−274404.0was detected and classified as being off-nuclear in both the CDF-S and E-CDF-S data sets independently, lending additional support to its off-nuclear classification. The off-nuclear X-ray sources span a 0.5–2.0 keV luminosity range of 8×1038 erg s−1 to 6×1040 erg s−1 and have a median luminosity of ≈8×1039 erg s−1. The host galaxies have a medianredshift ofz ≈ 0.14, which corresponds toalookbacktime of≈1.8Gyr, andamedian V magnitude of 19.1. In Figure 3a, we show the X-ray luminosities of these 24 off-nuclear 606 sources as a function of redshift. The fifteen new objects (filled symbols) presented here significantly improve the source statistics at L0.5−2.0 keV ∼> 1039.5 erg s−1 and z = 0.15−0.3; many of these sources are from the relatively wide solid-angle E-CDF-S survey. All sources with 0.5–2.0 keV upper limits are detected in the 0.5–8.0 keV band. We constrained the average X-ray spectral shape of our off-nuclear sources by stacking the 0.5–2.0 keV and 2–8 keV source counts and exposures. We then computed a vignetting- corrected band ratio by taking the ratio Φ /Φ , where Φ is defined to be the 2−8 keV 0.5−2.0 keV X-ray count rate in units of counts s−1. The band ratio was converted into a mean effective photon index Γ using the Chandra X-ray Center’s Portable, Interactive, Multi-Mission eff Simulator (PIMMS). For the 24 off-nuclear X-ray sources, the mean effective photon index is Γ = 1.83+0.21, a value consistent with that for IXOs observed in the local universe (e.g., eff −0.17 Liu & Mirabel 2005 and references therein). We therefore adopted Γ = 1.8 when computing X-ray luminosities for our off-nuclear sources using equation (1). Since all of our off-nuclear sources are coincident with late-type galaxies (see Figure 2), we chose to restrict further comparative analyses to galaxies with late-type morphologies. We selected galaxies in the ACS-covered regions of the CDFs and required V < 21 in the 606 redshift range 0 < z ≤ 0.3. At the quoted optical-magnitude limit, roughly half of the ob- jects detected are Galactic stars; these were characterized visually as point-like sources with diffraction spikes and removed from our list of candidate field galaxies. In total, 385 objects were selected as being non-stellar extragalactic sources with V < 21 and 0 < z ≤ 0.3. We 606 visually classified each galaxy as being either anelliptical (48 galaxies) or a spiral or irregular (337 galaxies). Figure 3b shows the estimated rest-frame 6000 ˚A luminosities (νL [6000 ˚A]) ν for all of the 337 spiral and irregular galaxies in our sample (small filled circles). Galaxies hosting off-nuclear sources are plotted with larger open and filled symbols (for H04 and new sources, respectively); most of these occupy the high-luminosity end of the distribution. Optical luminosities were estimated using the V magnitude and applying a K-correction 606 – 8 – assuming an Scd spiral-galaxy optical SED (Coleman et al. 1980); this SED was chosen since it is commonly observed for star-forming galaxies. We chose to use the V band 606 to compute the 6000 ˚A luminosities because (1) it is availabile over all of the CDFs and (2) the 6000 ˚A continuum traces the emission from relatively old stellar populations. The K-corrections for the galaxies are small ( ∼< 0.4 mag) and have little dependence on galaxy SED choice. The median 6000 ˚A luminosities (6000 ˚A absolute magnitudes, M ) of the 606 intermediate-redshift field galaxies and the host galaxies of off-nuclear X-ray sources are νL (6000 ˚A) ≈ 1.9 ×1043 erg s−1 (−19.8) and ≈2.7 ×1043 erg s−1 (−20.2), respectively. ν Ten of our 24 (41+18%) off-nuclear X-ray sources appear to be coincident with optical −13 knots of emission (see column 8 of Table 2 and the images in Figure 2). In the local universe, IXOs often appear to be located within or near star-forming regions, ranging from small (< 100 pc diameter) diffuse Hα emission complexes to giant ( ∼> 500 pc diameter) H II regions (e.g., Pakull & Mirioni 2002; Liu & Bregman 2005; Ramsey et al. 2006). The optical knots in our sample have apparent diameters of ≈500–1000 pc and optical luminosities of νL (6000 ˚A) ≈ 1040−41 erg s−1. These optical properties are broadly consistent with those ν of giant H II regions in the local universe (e.g., Kennicutt 1984), suggesting these off-nuclear sources trace distant star-formation regions. In the GOODS fields, high-resolution ACS imaging is available over four optical bands (B , V , i , and z ); for the eight off- 435 606 775 850 nuclear sources with optical knots located in these ACS regions, we analyzed the colors in the immediate vicinity of the knots. Figure 4 shows the relative color difference between the optical knots and their host galaxies. These relative colors are defined as follows: ∆(B −V ) ≡ (B −V ) −(B −V ) 435 606 435 606 knot 435 606 galaxy ∆(V −i ) ≡ (V −i ) −(V −i ) . (2) 606 775 606 775 knot 606 775 galaxy We find that the optical knots are relatively blue compared to their host galaxies (i.e., mean values of ∆(B −V ) = −0.22±0.14 and ∆(V −i ) = −0.13±0.18 are observed). We 435 606 606 775 stacked the 0.5–2.0 keV and 2–8 keV counts from our off-nuclear sources with and without optical knots to see if we could distinguish between the mean effective photon indices (Γ ; eff see text above) of these two populations. We found that the average spectral shapes of these two populations are statistically consistent (i.e., Γ = 1.90+0.26 and 1.70+0.41, for sources eff −0.21 −0.28 with and without optical knots, respectively). Wealsoinvestigatedtheopticalcolorsofthehostgalaxiestoseeiftheoff-nuclearsources are found in more actively star-forming galaxies. We utilized B- and V-band magnitudes from ground-based observations of the CDF-N with the Subaru 8.2 m telescope (Capak et al. 2004), and of the CDF-S and E-CDF-S with the Wide Field Imager of the MPG/ESO – 9 – telescope at La Silla (see § 2 of Giavalisco et al. 2004); small corrections for the differing bandpasses were applied to the CDF-S and E-CDF-S magnitudes to match those in the CDF-N. Optical emission lines produced by star-forming galaxies can influence the observed broad-band fluxes. At the median redshift of our off-nuclear source sample (z = 0.14), the strong nebular emission line due to [O II] λ3727 is located in the B-band and the redder emission lines from the [O III] λλ4959, 5007 doublet and Hβ λ4861 are located in the V-band. In Figure 5, we show the B −V colors vs. V -band magnitudes for our 337 606 spiral and irregular galaxies in the CDFs. Field galaxies hosting off-nuclear sources have been outlined with open squares and circles, which distinguish between sources with and without optical knots, respectively. The mean B − V optical colors have been plotted for the galaxies (solid line), galaxies hosting off-nuclear sources (dot-dashed line), and galaxies hosting off-nuclear sources with (dashed line) and without (dotted line) optical knots. The typical galaxy hosting an off-nuclear X-ray source shows somewhat bluer optical colors than typical galaxies in the field. We utilized the two-sample Kolmogorov-Smirnov (K-S) test on the unbinned B −V samples of field galaxies and galaxies hosting off-nuclear sources, and repeated the test to compare the B − V sample of field galaxies with off-nuclear sources with and without optical-knot counterparts. We found that, at the ≈89% confidence level (i.e., K-S probability ≈ 0.11), the B − V colors of galaxies hosting off-nuclear sources are statistically different from typical field galaxies in the CDFs. Furthermore, the colors of galaxies hosting off-nuclear sources with optical knots are statistically different from those of typical field galaxies at the ≈96% confidence level, but galaxies hosting off-nuclear sources without optical knots have colors statistically consistent with those of typical field galaxies. These tests suggest that off-nuclear sources are indeed preferentially located in galaxies undergoing intense star formation; the optical knots directly trace star-forming complexes in such galaxies. For comparison, we plotted the distribution of Johnson U −B colors versus V-band magnitude for RC3 galaxies (inset to Figure 5) and highlighted six local galaxies (NGC 1566, NGC 1672, NGC 3623, NGC 4088, NGC 4303, and NGC 4490) observed to host IXOs coincident with distinct, luminous optical knots from Liu & Bregman (2005). These galaxies appear to be notably bluer than typical RC3 galaxies, and using the K-S test, we find that the colors of these galaxy samples are statistically different at the ≈96% confidence level. Locally, the U- and B-band magnitudes sample the strong emission features expected in the B- and V-bands, respectively, at z = 0.14. 3. Analysis and Results A primary goal of this investigation is to determine whether the “true” luminosity- dependent fraction of galaxies containing off-nuclear X-ray sources (f ) evolves with cos- T – 10 – mic time (see § 1). Below, we describe our procedure for computing this fraction for our intermediate-redshift galaxy sample and a matched comparison sample of local galaxies from PC04. We assess observational constraints on the X-ray luminosity detection limit and an- gular resolution for both our sample and that of PC04. To this end, we first describe the computation of the luminosity-dependent “observed” fraction of galaxies hosting off-nuclear sources (f ); this takes into account the spatially varying sensitivity of the Chandra observa- O tions. We then estimate the true fraction (f ) by calculating correction factors to f , which T O account for (1) the number of off-nuclear sources we expect to miss due to angular-resolution limitations (i.e., the number of off-nuclear sources with offsets smaller than the resolution limit) and(2)the multiplicity ofthese sources within hostgalaxies (i.e., theexpected number of off-nuclear sources within a galaxy having at least one off-nuclear source). 3.1. The Observed Fraction (f ) O To compute the observed fraction of intermediate-redshift galaxies hosting off-nuclear X-raysources, wefollowedaproceduresimilartothatoutlinedin§2ofPC04. Foreachofour 337 spiral and irregular galaxies, we used the 0.5–2.0 keV sensitivity maps described in § 2.1 and corresponding redshift information to compute an X-ray luminosity limit above which we could detect an off-nuclear source. All luminosities were calculated using equation (1), adoptingΓ = 1.8. InFigure6a, weshowthenumber ofgalaxieswithX-raycoveragesensitive enough to detect an off-nuclear source of a given 0.5–2.0 keV luminosity, L . For example, X there are 20 galaxies with X-ray coverage sensitive enough to detect an off-nuclear source with L ≈ 1038.9 erg s−1 (i.e., the leftmost bin of Figure 6a), and there are 337 galaxies X with coverage sensitive enough to detect an off-nuclear source with L ≈ 1041 erg s−1 (i.e., X the rightmost bin of Figure 6a). Figure 6b shows the number of galaxies in each L bin of X Figure6aobserved tohost anoff-nuclearsource ofL orgreater. InFigure6b, thenumber of X galaxies included in a given L bin versus its neighboring lower-luminosity L bin is affected X X by both the addition of galaxies hosting off-nuclear sources with less sensitive X-ray coverage and the subtraction of galaxies hosting off-nuclear sources that fall below L . In order to X aid in the understanding of this progression, we have created Figures 6c and 6d, which show the number of added and subtracted galaxies (in ascending order from L ≈ 1038.9 erg s−1 X to L ≈ 1041 erg s−1), respectively. For example, six galaxies in the first L bin of Figure 6a X X that host off-nuclear sources with LX ∼> 1038.9 erg s−1 are added to the first LX ≈ 1038.9 erg s−1 bin of Figure 6b. In the next higher L bin (i.e., L ≈ 1039.3 erg s−1), two new X X galaxies hosting off-nuclear sources with LX ∼> 1039.3 erg s−1 are added to the appropriate L bin of Figure 6b, and two galaxies with off-nuclear source luminosities < 1039.3 erg s−1 X are subtracted from the same bin. Thus the total number of galaxies with off-nuclear sources