Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hea-www.harvard.edu/~kim/pap/2009_XLF_apj.pdf Äàòà èçìåíåíèÿ: Mon Dec 6 20:20:19 2010 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:37:25 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: dust disk

The Astrophysical Journal, 703:829­844, 2009 September 20
C

doi:10.1088/0004-637X/703/1/829

2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

COMPARING GC AND FIELD LMXBs IN ELLIPTICAL GALAXIES WITH DEEP CHANDRA AND HUBBLE DATA
´ D.-W. Kim1 , G. Fabbiano1 , N. J. Brassington1 , T. Fragos2 , V. Kalogera2 , A. Zezas1 , A. Jordan1,3 , G. R. Sivakoff4 , A. Kundu5 , S. E. Zepf5 , L. Angelini6 , R. L. Davies7 , J. S. Gallagher8 ,A.M.Juett6 , A. R. King9 , S. Pellegrini10 , C. L. Sarazin4 , and G. Trinchieri11
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA; kim@cfa.harvard.edu, gfabbiano@cfa.harvard.edu, azezas@cfa.harvard.edu 2 Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA; vicky@northwestern.edu 3 Departamento de Astronom´ y Astrof´ ´ ia isica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile; ajordan@astro.puc.cl 4 Department of Astronomy, University of Virginia, VA 22904, USA; grs8g@virginia.edu, cls7i@virginia.edu 5 Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-2320, USA; zepf@pa.msu.edu Laboratory for High Energy Astrophysics, NASA Goddard Space Flight Center, Code 660, Greenbelt, MD 20771, USA; angelini@davide.gsfc.nasa.gov, Adrienne.M.Juett@nasa.gov 7 Denys Wilkinson Building, University of Oxford, Keble Road, Oxford, UK; rld@astro.ox.ac.uk 8 Astronomy Department, University of Wisconsin, 475 North Charter Street, Madison, WI 53706, USA; jsg@astro.wisc.edu 9 University of Leicester, Leicester, LE1 7RH, UK; ark@star.le.ac.uk 10 Dipartimento di Astronomia, Universita' di Bologna, Via Ranzani 1, 40127, Bologna, Italy; silvia.pellegrini@unibo.it 11 INAF-Osservatorio Astronomico di Brera, via Brera 28, 20121 Milano, Italy; ginevra.trinchieri@brera.inaf.it Received 2009 February 10; accepted 2009 July 23; published 2009 September 2
1

6

ABSTRACT We present a statistical study of the low-mass X-ray binary (LMXB) populations of three nearby, old elliptical galaxies: NGC 3379, NGC 4278, and NGC 4697. With a cumulative 1 Ms Chandra ACIS observing time, we detect 90­170 LMXBs within the D25 ellipse of each galaxy. Cross-correlating Chandra X-ray sources and HST optical sources, we identify 75 globular cluster (GC) LMXBs and 112 field LMXBs with LX > 1036 erg s-1 (detections of these populations are 90% complete down to luminosities in the range of 6 â 1036 to 1.5 â 1037 erg s-1 ). At the higher luminosities explored in previous studies, the statistics of this sample are consistent with the properties of GC-LMXBs reported in the literature. In the low-luminosity range allowed by our deeper data (LX < 5 â 1037 erg s-1 ), we find a significant relative lack of GC-LMXBs, when compared with field sources. Using the co-added sample from the three galaxies, we find that the incompleteness-corrected X-ray luminosity functions (XLFs) of GC and field LMXBs differ at 4 significance at LX < 5 â 1037 erg s-1 . As previously reported, these XLFs are consistent at higher luminosities. The presently available theoretical models for LMXB formation and evolution in clusters are not sophisticated enough to provide a definite explanation for the shape of the observed GC-LMXB XLF. Our observations may indicate a potential predominance of GC-LMXBs with donors evolved beyond the main sequence, when compared to current models, but their efficient formation requires relatively high initial binary fractions in clusters. The field LMXB XLF can be fitted with either a single power-law model plus a localized excess at a luminosity of (5­6) â 1037 erg s-1 , or a broken power law with a similar low-luminosity break. This XLF may be explained with NS-red-giant LMXBs, contributing to 15% of total LMXBs population at 5 â 1037 erg s-1 . The difference in the GC and field XLFs is consistent with different origins and/or evolutionary paths between the two LMXB populations, although a fraction of the field sources are likely to have originated in GCs. Key words: galaxies: elliptical and lenticular, cD ­ galaxies: individual (NGC 3379, NGC 4278, NGC 4697) ­ X-rays: binaries ­ X-rays: galaxies Online-only material: color figures

1. INTRODUCTION Low-mass X-ray binaries (LMXBs) are luminous X-ray binaries associated with old stellar populations; they are powered by the accretion of the atmosphere of a low-mass late-type star onto a compact stellar remnant, either a neutron star or a black hole (BH). Since their discovery in the Milky Way (see Giacconi 1974), the origin and evolution of LMXBs has been the subject of much discussion. Galactic LMXBs are found in both the stellar field and globular clusters (GCs; but their incidence per unit stellar mass is much higher in GCs, suggesting a dynamical formation mechanism for at least this sub-sample (Clark 1975;Katz 1975). The evolution of native binary systems is a viable, but still controversial, formation scenario for field LMXBs, which could also have been dynamically formed in GCs, and then 829

dispersed in the field (e.g., Grindlay 1984; see reviews in Verbunt & van den Heuvel 1995, Verbunt & Lewin 2006). Chandra observations have provided samples of LMXBs in many early-type galaxies, rekindling the discussion of their formation and evolution. Of order 20%­70% of these extraGalactic LMXBs are found in GCs (e.g., Kundu et al. 2002; Sarazin et al. 2003; Jordan et al. 2004; Kim et al. 2006b; Kundu et al. 2007, hereafter KMZ; Sivakoff et al. 2007; Humphrey & Buote 2008); as in the Milky Way, for a given stellar mass, LMXBs are more likely to be found in GCs than in the field. This result has again stimulated the hypothesis of exclusive formation in GCs for all LMXBs. However, there are also studies suggesting formation in situ for field LMXBs; in particular, this conclusion is supported by comparison of the LMXB population with the GC specific frequency (SN ) in several galaxies (e.g.,


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Table 1 Sample Galaxies Galaxy (1) NGC 3379 NGC 4278 NGC 4697 D (Mpc) (2) 10.57 16.07 11.75 R
25

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() (3)

P.A. (deg) (4) 67.5 27.5 67.5

B

T0

(mag) (5)

MB (mag) (6) -19.94 -20.06 -20.28

LB (L_Bo) (7) 1.46 â 1010 1.63 â 1010 2.00 â 1010

Age (Gyr) (8) 8.6­10 10.7­12 8.2­8.9

SN (9) 1.2 6.9 2.5

N(H) (1020 cm (10) 2.78 1.76 2.14

-2

)

2.69 â 2.39 2.04 â 1.90 3.62 â 2.34

10.18 10.97 10.07

Notes. Columns: (1) Galaxy name; (2) distance from Tonry et al. (2001); (3) semi-major and semi-minor axes determined at the 25th magnitude from RC3; (4) P.A. of the major axis from NED; (5) B_T_0 from RC3; (6) absolute blue magnitude; (7) blue luminosity calculated by adopting an absolute solar blue magnitude of 5.47 mag; (8) luminosity weighted average stellar age (Trager et al. 2000; Terlevich & Forbes 2002; Thomas et al. 2005); (9) GC specific frequency from Ashman & Zepf (1998); (10) H column density along the Galactic line of sight from Dickey & Lockman (1990).

Juett 2005; Irwin 2005; see Kim et al. 2006b for cautions and Fabbiano 2006 for review and earlier references). This work was all based on the observation of the most luminous LMXBs, with LX (0.3­8 keV) afew 1037 erg s-1 . Now, deep observations of three elliptical galaxies--NGC 3379 (Brassington et al. 2008, hereafter B08), NGC4278 (Brassington et al. 2009, hereafter B09), and NGC4697 (Sivakoff et al. 2008)--allow us to extend the comparison of field and GC-LMXBs to sources in the "normal" range of Galactic LMXB luminosity. The principal tool we use for this study is the X-ray luminosity function (XLF) of the LMXB populations (see, e.g., Kim & Fabbiano 2004, hereafter KF04; Gilfanov 2004; Fragos et al. 2008 for earlier studies of luminosity functions of X-ray sources in galaxies). The high-luminosity end (LX > several â 1037 erg s-1 ) of the XLF (GC+field co-added) is well constrained with a differential slope of 1.8 (e.g., KF04; Gilfanov 2004). The normalization (i.e., the total number of LMXBs in a given galaxy) is strongly related to the stellar mass of the galaxy, although a link to SN has also been reported (White et al. 2002; Kundu et al. 2002; KF04; Kim et al. 2006b). KF04 and Gilfanov (2004) independently found that the XLF is broken at LX 5 â 1038 erg s-1 , possibly reflecting the presence of both neutron star and black-hole LMXBs in the X-ray source populations, as suggested by Sarazin et al. (2001). This break is also predicted in the model of short-lived, high-birth-rate, ultra-compact (UC) binary evolution in GCs by Bildsten & Deloye (2004). Above the break (LX > 5 â 1038 erg s-1 ), the XLF slope becomes steep ( 2.8); very luminous X-ray sources (or ULX with LX > 2 â 1039 erg s-1 ) are extremely rare in typical old ellipticals (Irwin et al. 2004). The above considerations also apply to GC and field LMXB XLFs separately, since their XLFs are entirely consistent at high luminosity (Kim et al. 2006b). In the low LX range, the (GC+field) XLF is less well characterized, because of the lack of adequately deep Chandra observations. Voss & Gilfanov (2006, 2007a) found that the XLFs of the LMXB populations of the nearby galaxies NGC 5128 and M31 significantly flatten below LX 2 â 1037 erg s-1 . However, these galaxies also contain younger sources, and some contamination of the samples cannot be excluded. Instead, using early partial observations of the "old" elliptical galaxies NGC 3379 and NGC 4278 (110 and 140 ks, respectively), Kim et al. (2006a) found no evidence of this flattening (down to LX 1037 erg s-1 ), but suggested a possible local excess over a power law in the XLF of NGC 3379 at LX 4 â 1037 erg s-1 .It was also suggested, both in M31 and NGC 5128, that the XLF of GC-LMXBs may be flatter than that of field LMXBs (Voss & Gilfanov 2007a; Woodley et al. 2008). The present study seeks

to establish if there is a "universal" shape of the low-luminosity LMXB XLF in different galaxies, and if the difference suggested between field and GC XLFs is generally valid. This paper is organized as follows. In Section 2, we describe the target galaxies, and in Section 3 the Chandra observations and data reduction techniques. In Section 4, we cross-correlate the X-ray and optical sources to identify GC and field LMXBs and we describe the related uncertainties in terms of contamination by foreground and background objects and chance coincidence. In Section 5, we compare the fractions of LMXBs associated with GCs and the field in each galaxy, in different luminosity ranges. We also compare field and GC luminosity distributions, including upper limits for non-detections in GCs. In Section 6, we derive the XLF separately for GC and field samples and we present the fitting result. In Section 7, we discuss the implications of our results for the nature of LMXBs and their formation. Finally, we summarize our conclusions in Section 8. 2. THE TARGET GALAXIES We summarize the optical characteristics of the three target galaxies of this study in Table 1. Because these three elliptical galaxies are old (e.g., Trager et al. 2000; Terlevich & Forbes 2002), they provide a clean sample of LMXBs with no contamination by younger sources (high-mass X-ray binaries (HMXBs) and supernova remnants (SNRs)). These younger sources may contaminate LMXB populations extracted from observations of spiral galaxies (the Milky Way, M31) and of young or rejuvenated E and S0 galaxies resulting from recent mergers (e.g., NGC 5128). Moreover, all three galaxies harbor only small amounts of hot ISM (see Trinchieri et al. 2008, for a detailed study of NGC 3379), unlike typical X-ray bright ellipticals (e.g., M87, NGC 5128) where point sources may be confused with small-scale gas clumps, and the diffuse emission limits the detection of faint LMXBs. We adopt distances of 10.6 Mpc (NGC 3379), 16.1 Mpc (NGC 4278), and 11.8 Mpc (NGC 4697) throughout this paper, based on the surface brightness fluctuation analysis by Tonry et al. (2001). At these distances, 1 corresponds to 3.1 kpc, 4.7 kpc, and 3.4 kpc, respectively. 3. CHANDRA X-RAY OBSERVATIONS AND SOURCE DETECTION NGC 3379, NGC 4278 and NGC 4697 were observed with the S3 (back-illuminated) chip of Chandra Advanced CCD Imaging Spectrometer (ACIS; Garmire 1997) multiple times between 2001 and 2007, with individual exposures ranging from 30 to 110 ks. NGC3379 and NGC 4278 were observed as part of


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COMPARING GC AND FIELD LMXBs IN ELLIPTICAL GALAXIES
Table 2 Chandra Observations

831

Obsid N3379 1587 7073 7074 7075 7076 N4278 4741 7077 7078 7079 7080 7081 N4697 4727 4728 4729 4730

Observation Date

Exp (ks) (a) (b) 5 1 1 1 2 29.0 80.3 66.7 79.6 68.7 324.2 37.3 107.7 48.1 102.5 54.8 107.6 458.0 36.6 33.3 22.3 38.1 132.0 (c) 71 85 82 85 78 163 96 174 98 144 120 158 271 75 77 62 90 129

Nsrc (d) 44 57 54 57 49 93 58 116 63 93 74 104 168 68 64 54 71 102

2001 2006 2006 2006 2007 Merg 2005 2006 2006 2006 2007 2007 Merg 2003 2004 2004 2004 Merg

Feb 13 Jan 23 Apr 9 Jul 3 Jan 10 e

31. 84. 69. 83. 69.

Feb 3 Mar 16 Jul 25 Oct 24 Apr 20 Feb 20 e

37. 110. 51. 105. 5 5. 110.

5 3 4 1 8 7

Dec 26 Jan 6 Feb 12 Aug 18 e

39. 35. 38. 4 0.

9 7 1 0

Notes. Columns: (a) Live time from the CXC pipeline data; (b) effective exposure time after removing background flares; (c) the number of detected sources in the S3 chip; (d) the number of detected sources within the D25 ellipse.

a Chandra very large program (PI: G. Fabbiano); the archival data of NGC 4697 were obtained as part of a study by Sivakoff et al. (2008, and references therein). Observation dates and net exposure times are summarized in Table 2. In all the observations used in this study, the entire D25 ellipse of each galaxy falls within the S3 chip, and the ACIS temperature was -120 C. We did not use an older 36 ks observation of NGC 4697 taken on 2000 January 15, with a detector temperature of -110 C, because of the relatively large uncertainty in calibrating the detector characteristics (http://cxc.harvard.edu/cal/Acis/). The ACIS data were uniformly reduced in a similar manner as described in Kim & Fabbiano (2003) with a custom-made pipeline (XPIPE), specifically developed for the Chandra Multiwavelength Project (ChaMP; Kim et al. 2004a). Starting with the CXC pipeline level 2 products, we apply acis_process_event available in CIAO v3.4 with up-to-date calibration data, e.g., time-/position-dependent gain and QE variation. We note that the proper (serial) CTI (charge transfer inefficiency) correction for the S3 (BI) chip was only applied in the CXC pipeline processing after 2007 January (http://asc.harvard.edu/ caldb/downloads/Release_notes/CALDB_v3.3.0.html). After removing background flares, we re-project individual observations to a common tangent point and combine them by using merge_all available in the CIAO contributed package (http://cxc.harvard.edu/ciao/threads/combine/). The background flares are not very significant in most observations (the exposure time reduces by less than 8%), except for the third observation of NGC 4697 (obsid = 4729), where the exposure time is reduced by 40% (or 16 ks out of 38 ks). The total effective exposures of the merged observations are 324 ks, 458 ks, and 132 ks for NGC 3379, NGC 4278, and NGC 4697, respectively. The exposure time of NGC 4697 is not as long as for the first two galaxies, but given the distances, the detection limit is

comparable to that of NGC 4278. We show the merged images of the three galaxies in Figure 1, where the X-ray point sources and the optical size (D25 ) are marked. The X-ray point sources were detected using CIAO wavdetect. We set the significance threshold to be 10-6 , which corresponds approximately to one false source per chip and the exposure threshold to be 10% using an exposure map. The latter was applied to reduce the false detections often found at the chip edge. The performance and limitations of wavdetect are well understood and calibrated by extensive simulations (e.g., Kim & Fabbiano 2003; Kim et al. 2004a; Kim et al. 2007a). From the merged data, we detect 163, 271, and 129 point sources in the S3 CCD chip for NGC 3379, NGC 4278, and NGC 4697, respectively (Table 2). To measure the X-ray flux and luminosity (in 0.3­8 keV), we take into account the temporal and spatial QE variation (http://cxc.harvard.edu/cal/Acis/Cal_prods/qeDeg/) by calculating the energy conversion factor (ECF = ratio of flux to count rate) for each source in each observation. We assume a power-law spectral model with a photon index of = 1.7 (e.g., Irwin et al. 2003) and Galactic NH (see Table 1). To calculate the X-ray flux of sources detected in the merged data, we apply an exposure-weighted mean ECF. This will generate a flux as if the entire observations were done in one exposure, but with a variable detector QE as in the real observations. Among the five observations of NGC 3379, the ECF significantly differs only in the first observation (taken in 2001) by 12%, while it is almost identical for the other four observations. Among the six and four observations of NGC 4278 and NGC 4697, the ECF varies only by 2% and 1%, respectively. We note that the luminosity used in the XLF is an average value over the full observation interval. We exclude known transients (see Section 6 for the effect on the luminosity function.) We do not use X-ray sources, which are detected only in one or two individual observations, but not detected in the merged data. They may be transients and their luminosities (<1037 erg s-1 ) are below the LX range of the XLF (see Section 6). 4. SELECTION OF GC-LMXB AND FIELD LMXB SAMPLES We used the optical source lists from Kundu & Whitmore (2001) for NGC 3379 and NGC 4278 and from A. Jordan et al. (2009, in preparation) for NGC 4697. Both studies utilize Hubble Space Telescope (HST) images to identify optical GC candidates and background galaxies. The first two galaxies were observed with WFPC2 while the latter was observed with the Wide Field Channel of Advanced Camera for Surveys (ACS). We cross-correlated X-ray and optical sources to identify LMXBs in GCs and in the field, by applying strict matching criteria. We first determined the systematic positional offset between the samples of X-ray and optical sources, finding that the relative offset is <0. 8 for all three galaxies. After correcting for this offset, we assigned a match if the distance between X-ray and optical positions (dXO )iseither 1. dXO < 0. 5 or 2. 0. 5 dXO 1 and smaller than the X-ray positional uncertainty. While the quoted Chandra positional accuracy is 1 (Chandra Proposers' Observatory Guide; http://asc.harvard.edu/proposer), Chandra positions are often more accurate, particularly near


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Figure 1. Top panels: Chandra X-ray images of three target galaxies. The red circles indicate X-ray sources and the green ellipses indicate the optical sizes of the galaxies (D25 ). Bottom panels: HST optical images of the three galaxies. The blue crosses indicate globular clusters and the green ellipses indicate the optical sizes of the galaxies (D25 ). The HST WFPC2 fov is also marked for NGC 3379 and NGC 4278.

the aim point, as seen by comparing sources detected in multiple observations, (e.g., Chandra Deep Fields; see Kim et al. 2004a). However, the CCD pixel size (0. 492) and the mirror point spread function (PSF; 0. 3­0. 5 for a 50% encircled energy fraction) limit the practical minimum to be 0. 5. For faint and/or off-axis sources, the positional uncertainty of the X-ray source can be larger than 0. 5. The X-ray positional uncertainty is estimated with the empirical formula in Kim et al. (2007a). We take the uncertainty at a 95% confidence level. To include matches with a large positional uncertainty, we apply the second condition (B) listed above. The matching statistics are summarized in Table 3. The chance probability of random coincidence is very low, 0.5­1.5 in each galaxy (see below). We also consider possible matches sources that do not satisfy the conditions 1 or 2 above, but satisfy: 3. dXO < 2 . We applied the above criteria to matches with either GC or background galaxy (BG) obtaining four sub-samples: (1) Xray source (XRS)­GC matches, (2) XRS­GC possible matches, (3) XRS­BG matches, and (4) XRS­BG possible matches. The number of sources in each sub-sample is listed in Table 3. We take the first sub-sample, XRS­GC matches, as GC-LMXBs. And we take only non-matches which are within the HST field of view (fov), but do not belong to any of the above four subsamples as field LMXBs. We note that the chance probability of random coincidence among possible matches is appreciable and about half of them are real matches (see below). In Table 3, we list the number of sources within the D25 ellipse in the first three columns. For NGC 3379 and NGC 4278, the HST WFPC2 field of view (fov) covers only a part of the D25 ellipse (see Figure 1). For NGC 4697, the HST fov

covers the entire D25 ellipse. We do not use the sources located outside the D25 ellipse, because they have a higher probability to be associated with foreground/background objects. The X-ray luminosity of individual sources ranges from 1036 erg s-1 to 1039 erg s-1 in NGC 3379 and from several times 1036 erg s-1 to 1039 erg s-1 in NGC 4278 and NGC 4697. The completeness also varies from one galaxy to another (see Section 6). In the last three columns of Table 3, we further exclude sources inside the central region (r < 10 ). In the central region, both X-ray and optical data are rendered incomplete by the strong diffuse emission and also by nearby sources particularly for the X-ray sources. Because faint X-ray sources are difficult to detect near the center, the source detection is significantly incomplete and the incompleteness is hard to measure and correct. Even if relatively bright sources are detected, their photometric quantities (and possibly their positions) are uncertain. The HST optical sources are also affected by similar incompleteness, because of a high background level from the host galaxy (e.g., Tables 2 and 3 in Jordan et al. 2009). Moreover, both NGC 4278 and NGC 4697 are known to have central dust lanes, which make it even harder to detect GCs near the galaxy centers. Only a small number of very bright, compact GCs are found inside 10 ; this result may be at least in part because of detection incompleteness. As listed in Table 3 (row 3), only three GCs are found inside 10 of the center of NGC 3379 out of 70 GCs in the HST fov (eight out of 265 in NGC 4278; three out of 449 in NGC 4697). This is in contrast, for example, to 14 X-ray sources found inside 10 out of 59 X-ray sources in the HST fov in NGC 3379 (14 out of 113 in NGC 4278 and seven out of 102 in NGC 4697; row 2 in Table 3). Given that the X-ray source detection is also


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Table 3 Source and Match Results

833

S. No.

Number of Sources

N3379

N4278

N4697

N3379

N4278

N4697

(All sources in the D25 ellipse) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 XRS in D25 XRS in D25 & HST fov GC in D25 & HST fov BGC/RGC BG in D25 & HST fov XRS-GC matches XRS-BGC/RGC matches Possible GC matches XRS-BG matches Possible BG matches GC fraction with LMXBs BGC/RGC fraction with LMXBs Field LMXBs Fraction of GC-LMXBsa Fraction of faint field LMXBsb Fraction of faint GC-LMXBsb 93 59 70 30/40 346 9 4/5 5 3 6 168 112 265 144/121 73 37 12/25 14 5 8 102 102 449 195/254 1137 31 7/24 7 6 9

(Exclude sources within r < 10 ) 79 45 67 29/38 345 8 3/5 3 2 6 12% 10%/13% 26 0.24 81% 38% 154 98 257 140/117 66 37 12/25 11 3 5 14% 9%/21% 42 0.47 76% 43% 95 95 446 194/252 1134 30 7/23 7 6 8 7% 4%/9% 44 0.40 68% 50%

Notes. XRS: X-ray source; GC: Globular cluster; RGC: red GC (V-I > 1.05 for NGC 3379/N4278 and g-z > 1.1 for N4697); BGC: blue GC; BG is background galaxy, which is non-GC optical source. a N(GC-LMXBs)/N(all LMXBs). b N(faint LMXBs with L < 5 â 1037 erg s-1 )/N(all LMXBs). X

incomplete, the lack of GCs in the center is even more obvious. Although it is possible that a part of apparent field LMXBs might originate from the disrupted GCs, given that GCs could be disrupted more easily near the galaxy center, the incompleteness of GCs will cause more XRS identified as field LMXBs in the central region. If we had applied the same matching criteria, we would have one GC-LMXBs and 10 field LMXBs inside 10 of NGC 3379 (0 versus 6 in NGC 4278 and 1 versus 5 in NGC 4697). We note that this is not because of the different radial profiles of GC-LMXBs and field LMXBs. We will present a full description of the radial distribution in the forthcoming paper (D.-W. Kim et al. 2009, in preparation). We further divide GCs into two groups, blue and red GCs, separating them at V-I = 1.05 for NGC 3379 and N4278 and g-z = 1.1 for N4697, based on the C-M diagrams (row 4 in Table 3). We estimated the chance coincidence of the associations by re-matching X-ray and optical sources after shifting the X-ray sources randomly. Within the HST fov (excluding the central 10 region), we find the chance coincidence to be 1.5/1 for GC/BG matches in NGC 4278. The chance probabilities in the other two galaxies are lower than that of NGC 4278 which hosts the largest number of X-ray sources inside the smallest fov. Therefore, a false match in the GC-LMXB sample is extremely rare. Instead, in all three galaxies, about half of the "possible" matches may be chance associations. About 10% of the X-ray sources are found in non-GC optical sources (or background galaxies), if we count BG matches (row 9 in table 3) and one-half of the possible BG matches (row 10). The other half of the "possible BG matches" is likely to be due to chance coincidences, resulting from the crowded source fields (see above). Based on the ChaMP+CDF log(N)-log(S) (Kim et al. 2004b; Kim et al. 2007b), we estimate the number of cosmic background sources to be 21, 12, and 17 within the D25 ellipse of NGC 3379, NGC 4278, and NGC 4697, respectively. This is determined at the flux limit of 90% completeness (see Section 6). Cosmic background X-ray sources therefore account for 7%­23% of the X-ray sources within the D25 ellipse.

The number of background sources is further reduced, if we consider only the sources found inside the HST fov: five in NGC 3379, five in NGC 4278, and 17 in NGC 4697. These expected numbers are almost identical to those of sources matched with BG objects, except in NGC 4697 where seven background sources possibly remain undetected. Given that the LMXBs-GCs matches are highly significant (see above), the remaining background sources will primarily contaminate the field LMXB sample by 6% (seven out of a total 112 field LMXBs in the three galaxies). 5. STATISTICS OF LMXB SAMPLES In the GC-LMXB sample (row 7 of Table 3), LMXBs are preferentially matched (by a factor 2 or more, see row 12 of Table 3), with red, metal-rich rather than blue, metal-poor GCs, in agreement with previous reports (e.g., Kundu et al. 2002; Sarazin et al. 2003; Jordan et al. 2004; Kim et al. 2006b; Sivakoff et al. 2007). The cause of this trend is not fully understood yet, although there are a few suggested explanations (e.g., irradiation-induced stellar winds, Maccarone et al. 2004; metallicity-dependent convective zone, Ivanova 2005). Among the three galaxies, the number fraction of GC-LMXBs, FN,GCLMXB

=

NGC-LMXB NGC-LMXB +NField-

(1)
LMXB

ranges from 25% to 50% (row 14 in Table 3). This fraction increases with increasing GC specific frequency, SN (see Table 1), as previously suggested (e.g., Juett 2005). We further discuss the SN dependence in Section 6.1 At luminosities larger than 5 â 1037 erg s-1 , the fraction of GCs associated with a LMXB is 5% (Sarazin et al. 2003; see Fabbiano 2006). This fraction increases when the detection threshold moves to lower luminosities, as first suggested by Kundu et al. (2007). An increase would be expected, extrapolating to lower luminosities the high-luminosity XLF of Kim et al.


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Figure 2. Histograms of GC X-ray counts (lower panels) and background-subtracted net counts (upper panels) for the GCs included in the stacking. The vertical lines in the upper panels are the medians of the distributions. Table 4 GC Stacking Upper Limits and GC-field Comparison NGC 3379 No. GCs X-ray source counts (stacking) X-ray background counts (stacking) 68% net counts 28.8 68% LX (per GC in 1035 ) 99.7% net counts 99.7% LX (per GC in 1035 ) Pa (Peto-Prentice) NGC 56 1229 1239.3 463.3 1.1 101.1 5.44 0.005 4278 168 5864 5483.7 355.7 11.5 654.6 16.3 0.037 NGC 4697 433 4397 4109.1 7.0 507.4 10.0 0.030

Note. a Probability that two luminosity distributions of GC and field LMXBs come from the same parent population.

(2006a); how much this fraction increases depends on the lowluminosity slope of the XLF. Comparing the fraction of GCs associated with LMXBs in two increasingly deeper exposures of NGC 3379 (that used by KMZ and the full exposure of B08), Fabbiano (2008) noticed that this fraction does not increase, remaining at 12%­13% (for detection threshold going from 2 â 1037 erg s-1 to a few 1036 erg s-1 ). Instead, the number of detected LMXBs in the field increases by a factor of 2.4, so that the fraction of LMXBs associated with GCs decreases with deeper exposures. We now find a similar effect in NGC 4278 and NGC 4697. The fraction of faint (LX < 5 â 1037 erg s-1 ) LMXBs is given at the bottom of Table 3 for each galaxy for both GC and field samples. Comparing GC and field faint source fractions, we find that typically there is a dearth of lowluminosity GC cluster sources, in comparison with field sources. While the faint LMXB fraction is 70%­80% in the field sample (row 15 in Table 3), it is only 40%­50% in the GC sample (row 16 in Table 3). Applying a proportion test, available in the R package (http://www.r-project.org), we find that the statistical significance of this difference in the faint LXMB fraction is at the 3.8 level. The dearth of low-luminosity GC-LMXBs is confirmed by the results of a stacking experiment on the GCs with undetected X-ray counterparts. For this experiment, we included in the detections only sources with luminosities detected at 3 confidence. We created source regions, centered on the location of the GCs, excluding those with confirmed X-ray counterparts, or too close to multiple X-ray sources for reliable photometry. Then, we performed the same aperture photometry as applied for the real X-ray sources (see KF04 and Kim et al. 2004a for

photometry details). Table 4 summarizes the cumulative X-ray source and background counts (normalized to the source area) for each galaxy. Figure 2 shows the histograms of the source counts (lower panel) and background-subtracted net counts (upper panel) extracted from each stacking regions; the median value of the net count distributions are 0.80, 1.91, and 0.04 for NGC 3379, NGC 4278, and NGC 4697, respectively, showing that there are no biases in the determination of the background counts. Following the same Bayesian approach used in B08 and B09, which takes into account the Poisson nature of the probability distribution of the source and background counts, as well as the effective area at the position of the source (Park et al. 2006), we find upper b