Faint Chandra Sources in M3

Identifications of Faint Chandra Sources in the Globular Cluster M3

Yue Zhao, Craig O. Heinke, Haldan N. Cohn, Phyillis M. Lugger, Adrienne M. Cool
Department of Physics, University of Alberta, CCIS 4-183, Edmonton, AB T6G 2E1, Canada
Department of Astronomy, Indiana University, 727 E. Third St., Bloomington, IN 47405, USA;
Department of Physics and Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA
E-mail: zhao13@ualberta.ca
Accepted XXX. Received YYY; in original form ZZZ

We report a Chandra ACIS-S survey of the globular cluster M3. Sixteen X-ray sources were detected within the half-light radius () with . We used Hubble Space Telescope WFC3/UVIS and ACS/WFC images to find 10 plausible optical/UV counterparts.We fit the spectral energy distribution of the known cataclysmic variable 1E1339.8+2837 with a blue (, 90% conf.) spectral component from an accretion disc, plus a red component () potentially from a subgiant donor. The second brightest source (CX2) has a soft blackbody-like spectrum suggesting a quiescent low-mass X-ray binary (qLMXB) containing a neutron star. Six new counterparts have obvious UV and/or blue excesses, suggesting a cataclysmic variable (CV) or background active galactic nucleus (AGN) nature. Two (CX6 and CX8) have proper motions indicating cluster membership, suggesting a CV nature. CX6 is blue in UV filters but red in V-I, which is difficult to interpret. Two CV candidates, CX7 and CX13, show blue excesses in B-V colour but were not detected in the UV. The other two CV candidates were only detected in the two UV bands ( and ), so do not have proper motion measurements, and may well be AGNs. One Chandra source can be confidently identified with a red straggler (a star redward of the giant branch). The observed X-ray source population of M3 appears consistent with its predicted stellar interaction rate.

globular clusters: individual (M3) – X-ray: binaries – novae, cataclysmic variables – stars: neutron
pagerange: Identifications of Faint Chandra Sources in the Globular Cluster M3Apubyear: 2018

1 Introduction

Galactic globular clusters (GCs) are gravitationally-bound dense and old stellar populations harbouring stars. The high stellar density in the core region leads to many stellar encounters, and therefore creates a favourable environment to form a variety of close binary systems through dynamical processes (e.g. Fabian et al., 1975; Hills, 1976; Camilo & Rasio, 2005; Ivanova et al., 2006). Bright X-ray binaries () in globular clusters are transient or persistent low-mass X-ray binaries (LMXBs) typically harbouring accreting neutron stars (NSs) with low-mass optical companions (Lewin & Joss, 1983; Grindlay et al., 1984). These LMXBs are clearly produced dynamically, based on their association with the densest globular clusters in our Galaxy (Clark, 1975; Verbunt & Hut, 1987; Verbunt, 2003) and in other galaxies (Jordán et al., 2004; Sivakoff et al., 2007; Jordán et al., 2007; Peacock et al., 2009). High angular resolution X-ray observations with Chandra have revealed large numbers of faint () X-ray sources in globular clusters (Verbunt & Lewin, 2006; Heinke et al., 2010). The faint X-ray population is composed of multiple source classes, including: quiescent low-mass X-ray binaries (qLMXBs) in which accretion onto the NS is thought to be stopped or at least largely suppressed (Campana et al., 1998; Rutledge et al., 2002; Heinke et al., 2003; Chakrabarty et al., 2014) with luminosities typically times fainter than during outbursts; cataclysmic variables (CVs) where white dwarfs accrete from low-mass companions (Hertz & Grindlay, 1983; Cool et al., 1995; Pooley et al., 2002; Cohn et al., 2010; Rivera Sandoval et al., 2018); millisecond pulsars (MSPs), thought to be radio pulsars that have been spun up by accretion (Bhattacharya & van den Heuvel, 1991), which are observed in both X-ray (Saito et al., 1997; Bogdanov et al., 2006) and radio (Ransom et al., 2005; Freire et al., 2017); and chromospherically active binaries (ABs) composed of two tidally-locked non-degenerate stars, wherein fast rotation induces active coronal regions that emit (relatively faint, ) X-rays (Bailyn et al., 1990; Dempsey et al., 1993; Grindlay et al., 2001; Heinke et al., 2005b). The qLMXBs and CVs appear to be correlated with encounter rate (Pooley et al., 2003; Heinke et al., 2003; Pooley & Hut, 2006; Bahramian et al., 2013), while the ABs are expected to be primordial in origin (Bassa et al., 2004; Verbunt et al., 2008; Bassa et al., 2008; Lu et al., 2009; Huang et al., 2010).

The globular cluster M3 (or NGC 5272) is a good target to study for several reasons. First, M3 is massive, but has a relatively low core density (central luminosity according to Harris 1996, 2010 version), which suggests a relative predominance of primordially, over dynamically, formed X-ray binaries (XRBs). Moreover, a less dense core facilitates the optical identification of counterparts to X-ray sources, which is difficult in denser clusters due to crowding. The X-ray sources in M3 also show a relatively dispersed distribution, which allows easier identifications and also makes them good targets for future X-ray observations with instruments that have larger collecting area but relatively larger PSFs (e.g. XMM-Newton, and the future telescope Athena). Secondly, M3’s position far from the Galactic Plane means it suffers relatively little reddening, making photometric studies easier and more precise. This will, in turn, support the identification of possible counterparts.

Previous X-ray studies of M3 have focused on the brightest X-ray source, 1E1339.8+2837 (1E1339 hereafter). 1E1339 was first discovered as a faint X-ray source () by the Einstein Observatory (Hertz & Grindlay, 1983). It underwent a bright outburst observed by ROSAT in 1991-1992, during which it showed a very soft spectrum (, , Hertz et al. 1993; Verbunt et al. 1995). The source returned back to quiescence with a much harder X-ray spectrum, observed by ASCA (Dotani et al., 1999) and Chandra (; see Stacey et al. 2011, which used the same Chandra observations presented here). The optical counterpart of 1E1339 was identified by Edmonds et al. (2004) as a star with a very blue colour, showing marked variability on timescales of hours.

1E1339 is the only supersoft X-ray source (SSS) identified in a Galactic GC, though three transient SSSs have been identified in M31 GCs (Henze et al., 2009, 2013), two of them clearly identified with nova explosions, which are the most frequent class of transient SSSs in M31 (e.g. Henze et al., 2011). The bright outburst and the supersoft spectrum suggest a physical connection to other galactic supersoft X-ray sources (SSSs). However, 1E1339’s peak observed X-ray luminosity was times fainter than that of standard SSSs, suggesting a much smaller burning area.

The present work focuses on a systematic multiwavelength study of the faint X-ray sources in M3. The paper is organized as follows: in section 2, we report the Chandra and HST data we used in our studies. In section 3, we describe our analyses including data reduction, source detection, and the relevant techniques and methodologies used in astrometry, photometry, and counterpart identifications. In section 4, we discuss the possible nature of each X-ray source based on its photometric and spectroscopic properties. Finally, in section 5, we summarise our results.

2 Observations

2.1 Chandra Observations

The globular cluster M3 was observed by the Advanced CCD Imaging Spectrometer (ACIS-S) on board the Chandra X-ray Observatory, using the very faint mode. Three observations, at roughly 6-month intervals, were taken, focused on monitoring 1E1339. A 1/2 subarray was used to reduce the frametime, and thus pileup from this relatively bright source, but the field of view still covers the whole half-light region of the cluster. Observation details are listed in Tab. 1.

ObsID Time of observation Exposure time Chip
2003-11-11 16:33:18 ACIS-S
2004-05-09 17:26:32 ACIS-S
2005-01-10 08:54:31 ACIS-S
Table 1: Chandra Observations
Figure 1: Merged Chandra exposure-corrected ACIS-S X-ray image of the central region of M3. The dashed blue circle shows the core region; the solid blue circle shows the half-light radius (Harris, 1996, 2010 edition). Sources detected by wavdetect are marked with solid black circles. The size of each pixel is .

2.2 Hst Observations

We used HST WFC3/UVIS (GO12605, PI: Piotto), ACS/WFC (GO10775, PI: Sarajedini) and ACS/HRC and ACS/WFC (GO10008, PI; Grindlay) imaging data to search for possible optical counterparts. The WFC3 2012 data contained observations in the F275W (), F336W (), and F438W () filters, while the 2006 ACS data used the F606W () and F814W () filters. The ACS/HRC and ACS/WFC 2004 data were taken over a broad range of UV and optical bands, in conjunction with the second Chandra observation. This enables us to construct a simultaneous spectral energy distribution (SED) for the supersoft X-ray source 1E1339. Details of these observations are listed in Tab. 2.

GO Time of observation Exposure time Camera/Channel Filter
10008 2004-05-09 17:51:18 ACS/HRC F220W
2004-05-09 17:41:19 ACS/HRC F250W
2004-05-09 17:17:33 ACS/HRC F330W
2004-05-09 19:05:02 ACS/WFC F435W
2004-05-09 19:22:02 ACS/WFC F555W
2004-05-09 18:52:26 ACS/WFC F814W
10775 2006-02-20 11:16:31 ACS/WFC F606W ()
2006-02-20 12:55:54 ACS/WFC F814W ()
2012-05-15 01:39:53 WFC3/UVIS F275W ()
12605 2012-05-15 01:49:19 WFC3/UVIS F336W ()
2012-05-15 01:36:38 WFC3/UVIS F438W ()
Table 2: HST Observations

3 Analyses

3.1 Merging Chandra Observations

The Chandra data were reduced using the Chandra Interactive Analysis of Observations software (CIAO) version 4.10111http://cxc.harvard.edu/ciao/ and CALDB version 4.7.8. We first reprocessed the data using the CIAO chandra_repro script to update the calibration, generating new level-2 event files. We then add the three observations to get a deeper view of the cluster. We first adjust aspect solutions between observations by using the brightest source 1E1339. The new aspect solutions were applied to the event files by using the CIAO wcs_update tool. Finally, the combined exposure map and the corresponding exposure-corrected image were generated by using the CIAO merge_obs tool. The resulting merged broad-band exposure-corrected () X-ray image is shown in Fig. 1.

3.2 Source Detection

We generated an X-ray source list by running the CIAO wavdetect222http://cxc.harvard.edu/ciao/threads/wavdetect/ tool on the combined broad-band X-ray image. The wavdetect algorithm correlates possible source pixels with a “Mexican Hat” function with different scale sizes and identifies pixels with sufficiently large positive correlation values to further calculate source positions, error circles and other information about the sources. We chose to cover the possible sizes of point sources at different off-axis angles, and used (the reciprocal of the area of the region) to limit the expected number of false detections to . The detected sources are listed in Tab. 3. The right ascensions and declinations are the coordinates as calculated by wavdetect. is the error circle following the empirical formula from Hong et al. (2005).

Positions Net Counts (absorbed)
Name (J2000) (J2000) Dist. Notes
CX1 13:42:09.771 +28:22:47.618 25.8 0.295 1038.1 (32.3) 738.6(27.2) 299.5 (17.4) SSS (1E1339)
CX2 13:42:15.364 +28:22:41.458 49.5 0.321 138.4 (11.8) 137.5 (11.7) 1.0 (1.0) qLMXB
CX3 13:42:08:218 +28:23:28.528 67.5 0.362 41.8 (6.5) 23.9 (4.9) 17.8 (4.2) -
CX4 13:42:10.105 +28:24:03:498 87.6 0.410 19.8 (4.4) 10.0 (3.2) 9.8 (3.2) -
CX5 13:42:14.511 +28:23:31.053 64.4 0.382 18.6 (4.5) 13.8 (3.7) 4.8 (2.2) -
CX6 13:42:13.899 +28:23:04.927 40.2 0.403 16.0 (4.0) 3.0 (1.7) 13.0 (3.6) CV
CX7 13:42:13.411 +28:24:41.737 125.8 0.519 8.8 (3.0) 5.0 (2.2) 3.9 (2.0) CV/AGN
CX8 13:42:14.664 +28:23:44.921 78.7 0.482 7.9 (2.5) 4.9 (2.2) 2.9 (1.7) CV?
CX9 13:42:11.730 +28:22:34.608 3.9 0.490 7.8 (2.8) 5.0 (2.2) 3.0 (1.7) RS/AB
CX10 13:42:15.322 +28:21:59.867 62.1 0.539 7.0 (2.8) 3.0 (1.7) 4.0 (2.0) -
CX11 13:42:14.023 +28:21:24.128 80.6 0.620 6.0 (2.6) 5.0 (2.2) 1.0 (1.0) -
CX12 13:42:13.901 +28:23:08.819 42.9 0.498 5.8 (2.5) 6.0 (2.4) 0.0 (0.0) CV/AGN
CX13 13:42:13.678 +28:22:44.243 27.8 0.453 5.8 (2.4) 4.9 (2.2) 1.0 (1.0) CV/AGN
CX14 13:42:13.903 +28:22:20.201 35.1 0.543 4.9 (2.2) 3.9 (2.0) 1.0 (1.0) AB?
CX15 13:42:05.389 +28:23:06.513 87.0 0.784 4.0 (2.0) 2.0 (1.4) 2.0 (1.4) -
CX16 13:42:12.668 +28:23:36.034 59.4 0.534 3.9 (2.0) 3.0 (1.7) 1.0 (1.0) CV/AGN
Coordinates from wavdetect
Offsets from the center of the core in arcsec
95% error circles as calculated by Hong et al. (2005)
errors generated by CIAO srcflux tool
Table 3: A catalogue of X-ray sources in M3.

3.3 Source counts

We used the CIAO srcflux333http://cxc.harvard.edu/ciao/threads/fluxes/ script to calculate the source counts in 3 energy bands: broad (), soft (), and hard (). The effective energy of each band was calculated as the flux-weighted average using the best-fit models of 1E1339 in Stacey et al. (2011). To calculate the combined counts, we first apply the script to each individual observation, and then add up the counts. For all sources except CX6 and CX12, the extraction region is defined by a circle that encloses of the PSF at , and the background region is an annulus with inner radius the same as that of the extraction region and outer radius times the radius of the source region. Because CX6 and CX12 are close to one another, their background regions were defined separately as annuli excluding the other source. In Tab. 3, we ordered the sources in descending order of their observed counts in the broad band.

3.4 Optical Photometry

We used the wide-field observations from three epochs (2004, 2006, and 2012) to systematically study the photometry of this GC.

The 2012 WFC3/UVIS photometry has been analysed as part of the Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters (Piotto et al., 2015, GO-13297), and the reduced data and data products, including magnitudes of detected point sources, are now available to the public (Soto et al., 2017). However, we found that some stars detected on our images, which coincide with X-ray error circles, are not included in the Padova catalogue, though evidence for their presence is visible to the eye. Therefore, we also generated our own photometric catalogue by performing PSF-fitting photometry on the three WFC3/UVIS filters for counterpart searching. We used HST data products that are pipeline-processed, flat-fielded, and with charge transfer efficiency (CTE) trails removed (i.e., FLC images) to get the stacked images for photometry, absolute astrometry, and counterpart searches. We used the HST Drizzlepac software version 2.0444http://www.stsci.edu/hst/HST_overview/drizzlepac for image alignment and combination. For each filter, all FLC frames are first aligned to a reference frame (one of the FLC images) with the Drizzlepac Tweakreg tool. The aligned images were then combined using the Drizzlepac AstroDrizzle tool with pixfrac=1.0. In order to get higher resolution, the drizzle-combined images were oversampled by a factor of two so that their pixel size is half of the original ( for WFC3/UVIS, and for ACS/WFC). The drizzle-combined images of ACS/WFC were used for visual inspection of candidates and for making finding charts.

We then performed aperture and PSF-fitting photometry on the drizzle-combined WFC3 images (2012 observation) using the PyRAF555http://www.stsci.edu/institute/software_hardware/pyraf DAOPHOT (Stetson, 1987) package. A star list was first generated for each filter by the daofind task with detection threshold. We then chose relatively bright and isolated stars to model the PSFs. In order to account for possible spatial variability, at least PSF candidate stars were selected across each image and the PSF model was set to be a second-order function of and (). The best-fit PSF model was then applied to all stars in the field by using allstar.

The following three steps were taken to calibrate the DAOPHOT/allstar photometry. First, magnitudes corresponding to a finite aperture were calibrated to those corresponding to an infinite aperture using the "curve of growth" method applied to a subset of reasonably isolated bright stars. Second, instrumental magnitudes of infinite aperture were shifted to the VEGAMAG system by using the WFC3 zeropoints from the STScI web page666http://www.stsci.edu/hst/wfc3/phot_zp_lbn. Finally, PSF-fitting photometry only gives relative magnitudes, so we cross-identified stars between aperture photometry and PSF-fitting photometry, and applied the average offsets to convert magnitudes in PSF photometry to instrumental magnitudes.

The photometry of the 2006 ACS/WFC observations (GO-10775, PI: Sarajedini) has been produced as part of the ACS Globular Cluster Treasury Program (Sarajedini et al., 2007; Anderson et al., 2008, GO-10775) which provides and magnitudes (available at the Mikulski Archive for Space Telescopes (MAST) website777https://archive.stsci.edu/prepds/acsggct/).

We obtained photometry for the 2004 F435W (B) and F555W (V) images (GO-10008, PI: Grindlay) using software based on the program developed for the ACS Globular Cluster Treasury Program, described in Anderson et al. (2008) and known as Ksync. We performed photometric calibration to the VEGAMAG system by doing aperture photometry on moderately bright, isolated stars within a 0.15 arcsec radius aperture, finding the aperture correction to an infinite radius aperture from Sirianni et al. (2005), calculating the median offset between the Ksync photometry and the aperture photometry, and applying the calibrations from the HST calibration website.888https://acszeropoints.stsci.edu/.

With the obtained magnitudes for different filters, we constructed colour-magnitude diagrams (CMDs) by cross-matching catalogues in different filters. In Fig. 2 we show the resulting , the , and the CMDs; in Fig. 3, we show the CMD.

Figure 2: Left: CMD generated by stars within a region of centered on the cluster core. Middle: CMD generated by stars within the same region. Both left and middle panels were generated using DAOPHOT results. Right: CMD from the catalogue of the ACS Globular Cluster Treasury Program. Optical counterparts are shown with red circles and annotated with their CX IDs (two potential counterparts are shown for CX9, though we find the brighter, redder one more likely). The error bars of CX8 and CX13 were indicated to show the uncertainty of their blue excesses.
Figure 3: CMD from the 2004 ACS/WFC observation. Optical counterparts are annotated by red circles. The large photometric errors of CX16 are indicated with error bars.

3.5 Astrometry

The accuracy of HST astrometry is limited by at least two error sources. The first type of error comes from the fact that positions of guide stars used to derive the astrometric information are known with some uncertainties ( for WFC3; for ACS. See ACS and WFC3 Handbooks; Lucas 2016, Deustua 2016). Secondly, errors are also introduced when the instrument aperture is mapped to the guide stars. The Chandra images are not astrometrized at the sub-arcsecond level, and therefore also require astrometric calibrations.

Our process of calibrating for astrometry includes two steps: 1. Calibrate one of the optical images to a known catalogue that has superior astrometry, and use this image as the reference frame; 2. Align other optical images to the reference frame, and align the Chandra catalogue to the reference frame for boresight correction–such that CX1 centres on its known counterpart (Edmonds et al., 2004). To fulfill this, we cross-matched source positions in one of our daofind catalogues with those from the Gaia Catalogue (Data Release 2; see Gaia Collaboration et al. 2016, 2018a). We chose the image as the reference image because it has a sufficiently long exposure, yet not so long to render bright sources saturated. We used a total of 895 Gaia sources that have relatively accurate positions (with errors in RA and DEC both ) found within a search radius centred on the cluster core. Cross-matching resolved a total of 868 matches. We calculated the average offsets () in RA and DEC, finding an average and an average ( errors). For boresight correction, we found the offsets of CX1 to be and .

3.6 Counterpart search

The principle of hunting for optical counterparts to XRBs more or less depends on the source class. For example, CVs typically have a strong UV excess that originates from the shock-heated region on the WD surface and/or the accretion disc, so they usually appear as blue outliers on or CMDs. ABs are either K/M type main sequence stars (BY Draconis, or BY Dra) or F/K type subgiants (RS Canum Venaticorum or RS CVn). Examples of works using these classifications include Cohn et al. (2010) and Cool et al. (2013). Using these criteria, we searched possible counterparts primarily in the 95% error circles. If no interesting object was found within the 95% error circle, we also applied a somewhat larger searching region (), recognising that this procedure incurs a higher risk of spurious coincidences.

We also have to consider possible confusion from foreground stars and background AGNs. Foreground stars usually appear redder, while background AGNs appear bluer, than cluster members. To exclude non-members, we check the proper motion (PM) of each counterpart candidate and compare that with the PM of the GC. The cluster membership can be confirmed if the star moves in accordance with the cluster’s systematic PM, and in disagreement with the PM of other possibilities. The enhanced angular resolution of HST cameras (e.g. ACS and WFC3) has made proper motion measurement possible over a relatively short span of time. Therefore, as part of the Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters, Piotto et al. (2015) includes a PM study of M3 by cross-matching the WFC3 source list with the ACS source list obtained 6.2 years earlier. Using the ACS(2006) and WFC3(2012) and positions from the Padova catalogue, we first calculated the displacements in and for each counterpart. The displacement can then be converted to proper motions with (see Soto et al. 2017), where is the time interval between the ACS and the WFC3 observations. As another check on cluster membership, we incorporated the membership probability () from the 2018 release of the public catalogue (see Nardiello et al. 2018).

We used stars that have at least one good photometric measurement in all three UV filters from the Padova catalogue as the sample for our PM check. We first computed PMs for each candidate counterpart and then compare them with the PM rms of the sample. A star is accepted as a cluster member if both its and are smaller than times the PM rms (). Fig. 5 shows the PM distribution of the selected sample plotted in 4 separate magnitude bins, with candidate counterparts marked with red circles. The 3-rms limit of each bin is indicated with a dashed circle. Because the first bin is made of bright stars that are close to saturation, it has a relatively large rms. To exclude background AGN, we used the proper motion measurement of the cluster from GAIA DR2 (Gaia Collaboration et al., 2018b, see Table C.1.), from which we found and for background AGN (marked with a red cross in Fig. 5).

Relying purely on photometric properties, we found potential counterparts to 10 of 16 Chandra sources. 8 of these are located within the corresponding 95% error circles, all except for the possible counterparts to CX7 and CX16. Fig. 4 shows a histogram of offsets for 10 identified counterparts in unit of their 95% error radii. PMs for our proposed counterparts to CX2, CX7, CX12, CX13 and CX16 are not available due to their nondetections in either 2006 or 2012, or both (see Tab. 4). However, the counterparts to CX1, CX6, CX8, CX9 and CX14 all have PMs less than 3 rms different from M3 (both in the and directions), and are inconsistent with the expected location of AGN, outside the expected PM radius expected for background sources. The cluster memberships of the counterparts to CX1, CX6, CX9 and CX14 are confirmed by the calculated membership probability (). The counterpart to CX8 was detected as a very faint extension to a relatively bright star in the 2006 ACS/WFC observations (see Fig. 6), which might cause ambiguity in measuring the positions, so the PM information should be taken with care. Fig. 6 shows a mosaic of finding charts, wherein the most likely counterpart to each Chandra source is annotated with a red arrow. The corresponding optical colours and magnitudes of these stars are marked with red circles in Fig. 2. The magnitudes used for identification are summarised in Tab. 4.

Figure 4: A histogram showing the distribution of offsets for the 10 identified couterparts. Each offset was normalised to the corresponding 95% error radius (). The dashed line marks edges of the error circles.

3.7 Cluster Subpopulations and Chance Coincidences

In crowded regions (e.g. the cluster core), the chance of a potential counterpart being a coincidence is significant, so it is important to estimate the number of chance coincidences for different cluster subpopulations. To get a census of cluster members, we used the PM information in the Padova catalogue to remove the non-members. We found cluster members detected in the WFC3 FOV. We applied polygonal selection areas on the CMD to divide members into different subpopulations (see Fig. 8). We found evolved stars, including subgiants, and red giants. 108 stars were identified as (moderately) blue stars. Finally, we found a population of 169 blue stragglers and a population of only 9 red stragglers. The predicted number of chance coincidences per error circle was estimated by multiplying the number of stars in each subpopulation by the ratio of the average area of the error circles () to the WFC3 FOV. We found that the average error circle contains normal cluster stars, though this varies somewhat by location in the cluster (see Fig. 6). Among evolved members, an average error circle contains red giants and subgiants, so there is a substantial chance of finding a giant and/or subgiant star within an error circle. However, the probability of finding a blue star in an error circle is quite small (), as is the probability of a red straggler star () or a blue straggler star (). Thus, the probability of finding a blue star in any of the 16 error circles by chance is only 5%, and that of finding a red straggler is only 0.4%. The probability of finding a blue straggler by chance coincidence is comparable to that of finding a blue star ().

Figure 5: Proper motion distribution of stars with at least one good photometric measurement in each filter from the Padova Catalogue plotted in 4 magnitude bins. The cluster’s average proper motion corresponds to the zero point. The proper motion of background galaxies, obtained from GAIA DR2’s estimate of the cluster motion, is marked with a red cross. Counterparts are shown with red points. The orange dashed circle in each panel shows the rms radius within which stars are considered as likely cluster members. The red dotted-dashed circle in each panel shows the corresponding composite error radius of the AGN proper motion.
Figure 6: Finding charts for 7 identified optical counterparts in 5 different bands (UV bands are from the 2012 WFC3/UVIS observations; and bands are from the 2006 ACS/WFC observations) made from drizzle-combined images. North is up and east is to the left. The green solid circles represent the 95% Chandra error circles as calculated in Hong et al. (2005). Identified counterparts are annotated with red arrows. Note that the counterparts to CX12 was only found in the two UV filters (, ); similarly, the counterparts to CX2 and CX13 were only detected in the two ACS/WFC bands, so the red arrows on the other finding charts only point to their nominal positions. The counterpart to CX8 appears to be a faint extension in and . Also, notice that a cosmic ray on the finding chart of CX8 has been excluded to avoid confusion. The red straggler (RS) and subgiant (SG) potential counterparts to CX9 are annotated with arrows and texts.
Figure 7: continued

CX7 was only covered by the 2004 ACS/WFC observations. Plausible counterparts for CX7 and CX16 lie somewhat outside the 95% Chandra error circle.

Figure 8: Proper motion cleaned CMD overplotted with different subpopulations.
CX Magnitudes Notes
2012 2006 2004
Blue in UV,
moderate red excess in V-I
2 - - - -
Faint MS star,
small red excess
Blue in UV,
large red excess in V-I
7 - - - - - -
Faint blue star
outside the error circle
8 - - - -
Faint blue star
Red straggler
12 - - - - - -
Faint blue star,
only detected in UV
13 - - - -
Moderately blue star
14 - -
Red giant
16 - - - -
Faint blue star
outside the error circle,
only detected in UV
Magnitudes are calibrated to VEGAMAG system
Probability of being a member of the cluster, from Nardiello et al. (2018)
superscript indicates that the magnitude has a very large uncertainty and should be taken with care
superscript indicates that the optical counterpart is outside the 95% it Chandra error circle
Table 4: Magnitudes and colours of identified optical counterparts.

3.8 Optical Variability

Signs of optical/UV variability can be helpful to further confirm the nature of the source, especially for CV identifications, since most CVs appear as blue variable stars (see e.g. Cool et al. 1998; Edmonds et al. 2003b; Dieball et al. 2017; Rivera Sandoval et al. 2018).

For the new counterparts that were detected in multiple exposures, we constructed HST light curves in the 2012 WFC3/UVIS and the 2006 ACS/WFC bands by doing DAOPHOT photometry (aperture photometry if the surrounding field of the counterpart is relatively uncrowded, e.g. CX16. Otherwise, PSF-fitting photometry was applied, e.g. CX9) on individual CR-removed, distortion-corrected FLC frames. The resulting light curves are shown in Fig. 9. We then used least-square fitting to fit each light curve to a constant and used the resulting reduced (on Fig. 9) as a measure of variability. The resulting are summarised in Tab. 5.

CX Filters
2012 2006
12 - - -
14 - -
16 - - -
Table 5: Summary on resulting from fitting counstants to light curves in different filters.
Figure 9: Optical/UV light curves of the identified counterparts that have detections in multiple exposures in the WFC3/UVIS observations (2012) and/or the ACS/WFC observations (2006). Photometric errors are from DAOPHOT software. The best fit constants are indicated with a solid green line.

3.9 SED-Modelling of 1E1339

As mentioned above, the 2004 ACS data for 1E1339 (see Tab. 2) were taken over a broad range of filters, which yielded a dataset that can be used to construct and analyse the spectral energy distribution (SED). The target is well resolved and isolated in the three HRC filters, so that we can obtain photometric results with relatively high accuracy. However, the source is affected by saturation blemish from a nearby bright star on the , and images. We, therefore, performed photometry with relatively small apertures (radius of or 1 ACS/WFC pixel) for these three filters. To calculate fluxes, we first calculated count rates from instrumental magnitudes. These count rates were then calibrated to infinite apertures by dividing the corresponding encircled energy (EE) fractions from Sirianni et al. (2005). Finally, count rates were converted to specific fluxes () by multiplying the corresponding inverse sensitivities (PHOTFLAM999http://www.stsci.edu/hst/acs/analysis/), i.e.


The specific fluxes in different filters are summarised in Tab. 6. The calibrated and magnitudes are also summarised in Tab. 4.

Filters F220W F250W F330W F435W F555W F814W
Flux ()
Table 6: Calibrated specific fluxes () of CX1 in different filters from the 2004 ACS observation.

We used tabulated stellar SED models from the Pickles library, an atlas of 131 stellar spectral models, (Pickles, 1998) to model the SED. Spectra were convolved with the filter bandpasses and corrected for the expected extinction using PySynphot package101010http://pysynphot.readthedocs.io/en/latest/. The model spectra were then renormalised with a minimization process (see Appendix). We first tried fits with one-component models. The minimum of was obtained with a type B5I spectrum, but still a bad fit (). This was mainly caused by an obvious excess in the data (vs. the models) in the band (, corresponding to a difference in magnitude of ), requiring a second cooler component to compensate for the excess. We, therefore, tried with two-component composite models. This is done by looping over all possible combinations of two components drawn from the Pickles library and picking out the combination with the smallest . The best fit was obtained with a B2 + M0 model, which is a greatly improved fit (). The M0 component now accounts for the V and I excesses relative to the B2 component. To constrain the spectral types of each component, we stepped one component at a time through different spectral types, allowing the other fit parameters to vary. We found a 90% confidence interval of K3-M2 or for the redder component. For the bluer component, we found O8-B5 or . The data overplotted with the best fit models are shown in Fig. 10.

Care should be taken, however, that the above spectral types do not necessarily reflect the actual traits of the accretor or the donor. Typically in CVs, the O or B type spectral components are ascribed to the combined light from the accretion disc and/or the WD surface, while the M type component might be caused by binary interactions. We will further discuss this in Sec. 4.1

Figure 10: Best fit SED models and data from the 2004 observations. Left panel shows the best fit single-component model (solid black) overplotted with the data (red). Right panel shows the same data (red) and the best fit two-component model (solid black), composed of a renormalised B2 component (blue dashed-dotted) and an renormalised M0 component (orange dashed).

3.10 X-ray spectral analysis

We performed detailed X-ray spectral analysis for sources with 100 counts that have not previously been published; only one source in our Chandra catalogue fits this description, CX2. For other sources with 10 counts, we perform simplified spectral analyses. We used the CIAO specextract111111http://cxc.cfa.harvard.edu/ciao/threads/pointlike/ script to extract spectra of these sources from each of the 3 observations. Because these observations do not span a very long time, to get better statistics, we combined the 3 spectra and their responses using FTOOLS/ADDSPEC121212https://heasarc.gsfc.nasa.gov/ftools/caldb/help/addspec.txt before doing the analysis. The combined spectra were then re-binned using the CIAO dmgroup131313http://cxc.harvard.edu/ciao/ahelp/dmgroup.html tool to at least 1 count per bin. Spectral analysis was then performed on the combined spectra with HEASoft/Xspec version 12.9.1 using C-statistics (Cash, 1979). Because the accuracy of the Chandra response matrix file falls off at low energies, we ignored energy channels below during the fits. (These channels are included in the plots just to demonstrate the obvious excess at low energies.) We fixed the absorption hydrogen column density at the cluster value , which is derived by applying the conversion factor () from Bahramian et al. (2015) and using from Harris (1996, 2010 edition).

We tried fits to CX2 with multiple models including an empirical power law (POWERLAW), a blackbody (BBODYRAD), a neutron star atmosphere (NSATMOS), and a hot plasma model (VMEKAL). For sources with more than counts but fainter than CX2, we fit an individual power law to each source. We combined the spectra of sources with less than counts (CX7-CX16) and fit a power law to the combined spectrum to get an average photon index. We obtained an average index of , which was then applied to the spectra of CX7-CX16 to calculate fluxes (fluxes of sources fainter than CX9 were calculated with srcflux, so no C-statistic or goodness calculation is available). All fitting results are summarised in Tab. 7.

Source Model or Cstat/dof Goodness
10 - -
11 - -
12 - -
13 - -
14 - -
15 - -
16 - -
Values in the parentheses indicates that the parameter is fixed during the fit
is the radius of the emission region for BBODYRAD model, or the neutron star radius for the NSATMOS model, both in km
indicates that the error extends beyond the hard limit
Table 7: Summary of X-ray spectral analyses.

4 Individual Sources & Discussions

4.1 Cx1/1e1339

The optical counterpart of 1E1339 was first identified by Edmonds et al. (2004), using WFPC2 data, to be a star with a very blue colour (but lying on the subgiant branch in a CMD), showing marked variability on timescales of hours. Our photometry confirms its blue excess. Though 1E1339 lies on the blue straggler region in UV-NUV and CMDs, it does not lie in the blue straggler region in other CMDs (see Figures 2, 3). This illustrates that multiple emission components are required, as expected in cataclysmic variables; examples of real blue straggler counterparts, and another CV that only appears to lie on the blue straggler sequence in some CMDs, can be found in Edmonds et al. (2003a). The ACS photometry from the ACS Globular Cluster Treasury Program revealed a red excess in colour ( with respect to the red giant branch), suggesting a red straggler (RS) secondary (Mathieu et al., 2003; Geller et al., 2017). Unusually red secondaries in XRBs have been observed in some CVs in 47 Tuc (Edmonds et al., 2003a), M30 (Lugger et al., 2007), and NGC 6752 (Thomson et al., 2012). Such bloating may be due to irradiation, or more likely due to continued mass loss from the donor, as expected under standard CV evolutionary theory (Knigge et al., 2011). Using the correspondences between and colours from Cox (2000), we found that the envelope of 1E1339’s companion should have expanded by roughly in order to have the observed red excess. Leiner et al. (2017) and Ivanova et al. (2017) show evolutionary models for binary mass-transfering systems that indeed demonstrate optical colours like these. This star also varies by s in the UV and filters on timescales of hours. Fitting its lightcurves to a constant gives a poor reduced (e.g. reduced for the filter, see Fig. 9).

Our SED fitting result corroborates this observed red excess ( as mentioned in Sec. 3.9), since a second, cooler component is required to get a satisfactory fit. The red excess might be partly due to variability, either long term or short term, of CX1. However, the presence of this red excess in two independent HST epochs (2004 and 2006 CMDs) indicates its extreme colour is likely real. The 0.92-mag difference between the observed and expected magnitudes is larger than can reasonably be explained by the observed short-term variability, of typically 0.2 magnitudes (Edmonds et al., 2004).

The cooler spectral component suggests an M0-type subgiant, while the bluer component has a spectral type for a B2-type giant, which is likely to represent the combined light from the WD and the accretion disc. We note that the extreme UV brightness indicates a high rate of mass transfer through the accretion disc. Should the accretor be a neutron star or black hole, a very high X-ray luminosity ( erg/s) would be expected; the lack of such bright X-rays indicates that the accretor is almost certainly a white dwarf.

4.2 CX2— a quiescent low-mass X-ray binary (qLMXB)?

To model CX2’s X-ray spectrum, we first tried a simple absorbed power-law model (TBabs*POWERLAW) and found a rather soft photon index (). The soft nature of this source was further confirmed by the low () from a blackbody fit (TBabs*BBODYRAD). We then tried fits with more physically motivated models. A thermal plasma fit (TBabs*VMEKAL) yielded a slightly worse fit () with a . A neutron star atmosphere model (TBabs*NSATMOS, Heinke et al. 2006) consistently yielded a low (typical for a quiescent low-mass X-ray binary (qLMXB)) with an NS radius (), or when was frozen to (). The models and best fit parameters are summarised in Tab. 7. Fig. 11 shows the spectrum overplotted with the best fit models (see Tab. 7). Below 0.5 keV, the data are poor fits, but we attribute this to the difficulty of calibrating this portion of the X-ray spectrum.

We identify a potential optical counterpart to this source, a star that lies on the red side of the main sequence in the CMD (Fig. 3). This star shows a relatively large photometric error in the band (see Tab. 4), which makes its CMD position uncertain. However, as this counterpart is not clearly off the main sequence, Sec. 3.6 suggests that this star may well be a chance coincidence.

We consider several possible natures for CX2; quiescent LMXB, MSP, CV, or AB in the cluster, or a background or foreground source. The NS atmosphere fit is consistent with a qLMXB nature, with a radius consistent with emission from a full NS surface. However, it is inconsistent with the expectation of emission from NS polar caps as seen in typical MSPs (Zavlin et al., 2002; Bogdanov et al., 2006). Although the VMEKAL fit is statistically reasonable, the implied temperature is low. If CX2 is a member of M3, its X-ray luminosity of erg/s is at the very high end of X-ray luminosities for globular cluster CVs, and all known CVs in globular clusters with erg/s have much harder X-ray spectra (e.g. Heinke et al., 2005b; Pooley & Hut, 2006), so a CV nature can be ruled out empirically. Verbunt et al. (2008) showed that nearby chromospherically active stars are limited in their X-ray luminosity, with log, while active binaries in globular clusters are limited by log (Bassa et al., 2004). CX2’s suggested counterpart has (Tab. 4) and erg/s (Tab. 7), so CX2 lies well above both limits (see Fig. 12), strongly suggesting that it is not an AB. If CX2 were instead a foreground AB, the optical counterpart to CX2 should be brighter than ; however, no bright cluster non-members were found within the error circle of CX2, arguing against a foreground system. A bright cluster MS star () is located NW of the error circle (Fig.6), but is still too faint (by 0.6 mags, ; see Fig. 12). Furthermore, X-ray bright cluster ABs generally have harder X-ray spectra than fainter ones (e.g. Heinke et al. 2005b), which contradicts the soft nature of the source. We therefore conclude that CX2 is most likely to be a qLMXB.

Figure 11: Chandra spectra of CX2. The top panel shows the rebinned (only for plotting purpose) data (black) with the best fit POWERLAW model and BBODYRAD model overplotted with a solid red line and a solid blue line, respectively. The bottom panel shows the same data, but overplotted with the best fit VMEKAL model (blue) and NSATMOS model (red). The yellow dashed line indicates the energy limit at , below which channels were ignored during the fits. Ratio = data/model.
Figure 12: keV vs. absolute V band magnitudes (using for CX7 and CX16, and for others). of CX1 is from Stacey et al. (2011). The dashed line corresponds to the separatrix from Bassa et al. (2004), dividing cluster CVs and ABs. The dotted-dashed line corresponds to the separatrix from Verbunt et al. (2008), marking the upper limit of for nearby ABs. CV candidates with confirmed cluster memberships are marked with filled blue squares. Possible CV/AGN candidates are marked with filled blue diamonds. The red filled circle marks the location of CX2 if we were to adopt the suggested counterpart. For comparison, the red open circle indicates the location of CX2 on the plot if we adopt the bright MS star mentioned in Sec. 4.2 as the counterpart.

Considering the relatively low central density and large mass of M3, it is interesting to consider whether this quiescent LMXB is more likely to be generated from a primordial binary (that is, via a similar evolutionary path as similar objects outside clusters), or via dynamical encounters (as the majority of quiescent LMXBs and millisecond pulsars in GCs are thought to be produced). To calculate the probability of this quiescent LMXB being a primordial binary, we use estimates of the total number of quiescent neutron star LMXBs in the Milky Way, which center around to systems (Pfahl et al., 2003; Kiel & Hurley, 2006; Jonker et al., 2011; Britt et al., 2014, Heinke et al. 2018, in prep.). We use the Milky Way’s stellar mass of (Cox, 2000), and an estimate of M3’s stellar mass of (adjusting the calculations of Gnedin et al. 2002141414http://www-personal.umich.edu/ ognedin/gc/vesc.dat to use the average mass-to-light ratio of 1.86 from Watkins et al. 2015), to predict 0.01 to 0.1 quiescent LMXBs in M3. Some population syntheses (e.g. Pfahl et al., 2003) do generate up to LMXBs in the current Milky Way, which would predict of order 1 quiescent LMXB in M3. However, such a large number of quiescent LMXBs, in a Galaxy with of order 100 persistently bright LMXBs, is strongly empirically disfavored by the observed ratio of 10-20 quiescent LMXBs per persistently bright LMXB in globular clusters (Heinke et al., 2003; Heinke et al., 2005a), and by the other empirical estimates cited above. From the dynamical side, 5 quiescent LMXBs are observed in 47 Tuc (Heinke et al., 2005a), and M3 has a stellar interaction rate 19% that of 47 Tuc (Bahramian et al., 2013), so 0.97 dynamically-formed quiescent LMXBs are predicted in M3. Thus, we find it 10-100 times more likely that this quiescent LMXB was formed dynamically, rather than primordially.

As a point of interest, performing the same calculation for the quiescent LMXB in Centauri (Rutledge et al., 2002) indicates a prediction of 0.04-0.4 primordial systems, vs. 0.45 dynamically formed systems, suggesting that the Centauri quiescent LMXB has a decent chance to be a primordial system.

4.3 Cx6

A power-law fit to CX6’s X-ray spectrum produces a negative photon index () if we freeze the at the cluster value. However, becomes more physically reasonable when is allowed to float to a higher value. For example, at , .

The optical counterpart to this source is very blue in UV colours (), but the colour indicates a very large red excess in visible light, , compared to the main sequence. This red excess was confirmed in the 2004 ACS/WFC CMD (see Fig. 13) with with respect to the MS; however, using the and magnitudes from the same epoch, the star shows moderate blue excess relative to the MS (see Fig. 3). Assuming the same V magnitude as CX6, the colour on the main sequence () corresponds to an F9V-G0V dwarf with , whereas CX6 corresponds to a K3V-K3.5V dwarf with (spectral types and ’s are from Pecaut & Mamajek 2013). Again, if we apply the “bloated envelope" scenario as for CX1, the change in requires that the companion to be bloated by a factor of , which does not seem physically reasonable. Although high measured ’s are common among AGNs, both CX6’s PM and the associated strongly support its cluster membership. In Sec. 3.6, we estimated the number of chance coincidences of blue stars to be minuscule (), so the suggested counterpart is very unlikely to be spurious. Therefore, the high might imply a CV seen edge-on, such as the CVs W8, W15, and AKO9 in 47 Tuc (Heinke et al., 2005b), but the red excess remains unexplained. Optical/UV variability analyses indicate strong UV and B variabilities to this star, suggestive of a CV nature, which might also be the cause of the observed simultaneous blue and red excess. Future spectroscopic study (e.g. with integral field units, such as MUSE) of this object could determine its nature.

Figure 13: CMD from the 2004 ACS/WFC observations. The red circle marks the location of the CX6 counterpart.
Figure 14: Number of non-AGN X-ray sources () in multiple GCs v.s. renormalised stellar encounter rates () from Bahramian et al. (2013). s have been renormalised such that NGC 6266 has a of 100. The lower limit inferred from our results of M3 is indicated with an orange square. The dashed line indicates the linear regression fit from Lugger et al. (2017).

4.4 CX8, CX12 and CX16

Similar to CX1 and CX6, the counterparts to these sources also show obvious UV excesses. Considering the calculations of Sec. 3.7, none of these counterparts are likely to be chance coincidences, so they should be CVs or background AGNs. The 2012 WFC3 observations only detected these three counterparts in the two UV bands ( and ). However, the 2004 ACS observations detected the counterpart to CX16, which shows a blue excess in the CMD with a relatively larger error bar (see Fig. 3). Although CX8 is apparently detected in the ACS GC survey catalogue (and therefore has a measured PM), this detection appears as a faint extension to a nearby bright star, which results in a larger photometric error and makes the blue excess more uncertain. Identifications of the faint optical counterparts to CX12 and CX16 are even more difficult, due to the lack of both accurate colours, and proper motions.

Another potential issue with these faint sources is that they have poorer localizations than bright sources. The potential counterpart to CX16 is a faint UV source northeast of its error circle with a distance of (or ) from the nominal Chandra position, which suggests that it may be a chance coincidence. However, the HST lightcurve for CX16 reveals variability on hours timescales (reduced ), suggesting a faint CV nature, since AGN tend to show less short-term variability. New HST imaging could reveal their PMs, testing an AGN hypothesis.

4.5 CX7 and CX13

Our suggested counterparts to CX7 and CX13 show moderately blue colors in (2004) and/or (2006) CMDs (see Fig. 3 and Tab. 4). The counterpart to CX13 (within the error circle) was too faint to be detected in the 2012 WFC3 observations, so no proper motion is available for it. The counterpart to CX7 is outside the 95% error circle (, or , from the nominal Chandra position). Because it was only covered by the 2004 ACS/WFC observations, only limited information can be drawn from the photometry. Considering the lack of PM measurements for these sources, we conclude that they could either be CVs or AGNs.

4.6 CX9 and CX14

We found evolved stars that coincide with the error circles of CX9 and CX14. A red straggler (lying to the red of the giant branch; see Geller et al. 2017 for the definitions of red stragglers and sub-subgiants) and a subgiant are located in CX9’s error circle, while a red giant is in CX14’s error circle. The red straggler to CX9 was also detected in the Ksync photometry (2004 ACS/WFC observations; see Fig. 3) to have an obvious red excess. CX9 and CX14 may be RS Canum Venaticorum (RS CVn) variables, which are systems with an evolved primary (e.g. F/K type subgiant or K type giant) in a close binary, where the primary has active chromospheric regions that induce large stellar spots. The observed X-ray emissions in RS CVn stars are thought to originate from active coronal regions on the primary and/or the secondary star.

However, it is also possible that the evolved stars in these error circles are simply chance coincidences, or that the evolved stars have unseen compact companions. Considering the very low number of expected chance coincidences () for a red straggler to reside within the Chandra error circle, vs. a subgiant (with the number of chance coincidence ), we regard the red straggler as a highly likely optical counterpart of CX9. Red stragglers are rare, may be the product of mass transfer in a binary system, and have often been identified as X-ray sources (Belloni et al., 1998; Mathieu et al., 2003; Leiner et al., 2017). CX9 is a very interesting target for future observations, and fortunately, it is not affected by serious crowding in the core, which makes it resolvable with instruments that have even larger PSFs.

4.7 Estimate of XRBs and AGNs

The number of AGN expected within the half-light radius can be estimated using the empirical model with three power-law components from Mateos et al. (2008). Applying a soft () flux limit of , the model predicts that ( confidence limits are from Gehrels 1986) within the half-light radius. Thus, we expect that 14 of our detected sources are likely members of M3, with CX12, and CX16 being plausible AGN (with no PM or available). CX8 does have a PM suggestive of a cluster member; however, further information is required for more secure identification. There are probably other AGNs among our X-ray sources without optical counterparts, which lie below our optical/UV detection limits.

Three confirmed MSPs (and one candidate) are known in M3, two with timing solutions and thus known positions (Hessels et al., 2007). The two known MSP positions do not correspond to any detected X-ray sources in our data. This is not surprising, since most MSPs observed in globular clusters have (0.3-8 keV) between ergs s (e.g. only 1 of 23 MSPs with known positions in 47 Tuc has erg s; Bogdanov et al. 2006; Ridolfi et al. 2016; Bhattacharya et al. 2017). Due to the larger distance to M3 (10.2 kpc; Harris 1996, 2010 version) and the relatively short exposures here, we do not have X-ray detections below . However, it is still possible that one of our X-ray sources might be an MSP with an unusually high X-ray luminosity.

We compared the number of X-ray sources we found in M3 with those from other GCs, and with the expected numbers of dynamically formed X-ray binaries. We used stellar encounter rates () from Bahramian et al. (2013), and numbers of non-AGN X-ray sources () in multiple GCs from Pooley et al. (2003) and Lugger et al. (2007). Since our luminosity limit () is higher than Pooley’s (), the in M3 () reported here should be regarded as a lower limit. We compare our results of M3 with other GCs in Fig. 14 (where we have renormalised all s so that for NGC 6266 is 100), together with a linear regression fit ( ) from Lugger et al. (2017). Deeper Chandra and HST observations would be helpful to verify the X-ray source content, and source classification, of M3. M3 will be a particularly helpful cluster, along with M13, M5, and Cen, in studying how lower-density clusters produce X-ray sources, as these clusters are likely to contain both primordial and dynamically-formed X-ray binaries.

5 Conclusions

Using of Chandra observations, we detected 16 X-ray point sources within the half-light radius of the globular cluster M3. The X-ray sources include the transient supersoft source and CV 1E1339, and a likely quiescent LMXB with a neutron star companion. Our optical/UV identification campaign has identified plausible optical and/or UV counterparts to 10 of 16 sources, including the previously identified 1E1339, a red straggler, a likely CV with unusually red optical colours, a faint red MS star to the qLMXB candidate, a possible giant (perhaps an RS CVn chromospherically active star), and five objects with UV and/or blue excesses, which may be CVs or AGNs.


We thank J. Anderson for making his KSYNC code available for our use, and for discussions. CH is supported by an NSERC Discovery Grant and a Discovery Accelerator Supplement. Our X-ray analyses are based on data obtained from the Chandra Data Archive, observations made by the Chandra X-ray Observatory and published previously in cited articles. Optical analyses are based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has also made use of the NASA Astrophysics Data System (ADS) and software provided by the Chandra X-ray Center (CXC) in the application package CIAO.


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Appendix A Renormalization of SED models with Minimization method

For a single component model, the is defined as


where and are the model value and the data value at , respectively, and is a normalization factor. We want to find such that


Plugging eq.(2), one can solve for and find that


For the case of an composite model with two additive components, i.e.


one can use similar method to find that

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