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A&A
Volume 513, April 2010
Article Number A16
Number of page(s) 11
Section Galactic structure, stellar clusters, and populations
DOI https://doi.org/10.1051/0004-6361/200811245
Published online 15 April 2010
A&A 513, A16 (2010)

Study of Hubble Space Telescope counterparts to Chandra X-ray sources in the globular cluster M 71

R. H. H. Huang1 - W. Becker1 - P. D. Edmonds2 - R. F. Elsner3 - C. O. Heinke4 - B. C. Hsieh5

1 - Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
2 - Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
3 - NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
4 - Department of Physics, University of Alberta, Edmonton, Alberta, Canada
5 - Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan

Received 28 October 2008 / Accepted 2 December 2009

Abstract
Aims. We report on archival Hubble Space Telescope (HST) observations of the globular cluster M 71 (NGC 6838).
Methods. These observations, covering the core of the globular cluster, were performed by the Advanced Camera for Surveys (ACS) and the Wide Field Planetary Camera 2 (WFPC2). Inside the half-mass radius ( $r_{\rm h} = 1\hbox{$.\mkern-4mu^\prime$ }65$) of M 71, we find 33 candidate optical counterparts to 25 out of 29 Chandra X-ray sources, while 6 possible optical counterparts to 4 X-ray sources are found outside the half-mass radius.
Results. Based on the X-ray and optical properties of the identifications, we find 1 certain and 7 candidate cataclysmic variables (CVs). We also classify 2 X-ray sources as certain and 12 as potential chromospherically active binaries (ABs), respectively. The only star in the error circle of the known millisecond pulsar (MSP) is inconsistent with being the optical counterpart.
Conclusions. The number of X-ray faint sources with $L_{\rm X}>4\times10^{30}$ erg s-1 (0.5-6.0 keV) found in M 71 is higher than extrapolations from other clusters on the basis of either collision frequency or mass. Since the core density of M 71 is relatively low, we suggest that those CVs and ABs are primordial in origin.

Key words: globular clusters: individual: M 71 globular clusters: individual: NGC 6838

1 Introduction

There are 158 Galactic globular clusters (GGCs) found in the halo of our galaxy, and they typically contain 104-107 stars. They are very old and dense star systems that are tightly bound by gravity, which gives them their spherical shapes and relatively high stellar density toward the center. The dense stellar environment in globular clusters triggers various dynamical interactions, i.e., exchanges in encounters with binaries, direct collisions, destruction of binaries, and tidal capture. These dynamical interactions not only can change the evolution of individual stars, but can also produce tight binary systems (see, e.g., Ashman & Zepf 1998; Verbunt & Lewin 2004, for review).

One of the most powerful ways to probe the binary content of globular clusters is by studying the X-ray source population. In the early 1970 s, X-ray sources with luminosity greater than $10^{36}~{\rm erg~s^{-1}}$were first detected by using the Uhuru and OSO-7 Observatories. Following the Einstein and ROSAT era, the number of faint X-ray sources ( $L_{\rm X} < 10^{34.5}~{\rm erg~s^{-1}}$) was dramatically increased. Those bright X-ray sources have been identified with low-mass X-ray binaries (LMXBs; Grindlay et al. 1984), while the identification of the weaker sources remained limited by low photon statistics and insufficient spatial resolution. The launch of the Chandra X-ray Observatory ushered in a new age of studying the crowded centers of Galactic globular clusters with far greater sensitivity and resolving power than ever before (e.g., Grindlay et al. 2001a,b). With the aid of the Hubble Space Telescope (HST), many of these faint X-ray sources were identified as quiescent low-mass X-ray binaries (qLMXBs; in which a neutron star accretes matter from its companion at a low rate), cataclysmic variables (CVs; in which a white dwarf accretes from its low-mass companion), and millisecond pulsars (MSPs), as well as chromospherically active binaries (ABs; e.g., RS CVn and BY Dra systems) (e.g., Heinke et al. 2005; Bassa et al. 2004; Edmonds et al. 2003b; Kong et al. 2006; Pooley et al. 2002; Edmonds et al. 2003a; Bassa et al. 2008; Lugger et al. 2007; Grindlay et al. 2001b).

The globular cluster M 71 (NGC 6838) lies close to the Galactic plane with Galactic longitude $l=56\hbox{$.\!\!^\circ$ }74$ and latitude $b = - 4\hbox{$.\!\!^\circ$ }56$. Similarly to 47 Tuc, it is a fairly metal-rich globular cluster with metallicity of [Fe/H] = - 0.73. Its relatively small distance ($d \sim 4$ kpc) to Earth and low central luminosity density ( $\rho_{\rm c} = 10^{3.05}~{L_{\odot}/\rm pc^{3}}$) makes M 71 a good target for both optical and X-ray observations. The core, half-mass, and tidal radii are $r_{\rm c}$ = 0 $\hbox{$.\mkern-4mu^\prime$ }$63, $r_{\rm h}$ = 1 $\hbox{$.\mkern-4mu^\prime$ }$65, and $r_{\rm t}$ = 8 $\hbox{$.\mkern-4mu^\prime$ }$96, respectively. M 71 shows no evidence of core collapse. Its moderate optical reddening EB-V = 0.25 may be converted into a nominal X-ray absorption column of $N_{\rm H} = 1.39 \times 10^{21} ~{\rm cm^{-2}}$ (Predehl & Schmitt 1995). The aforementioned parameters related to M 71 were obtained from Harris (1996, updated 2003[*]).

Table 1:   Spectral fits of the X-ray sources with source counts $C_{\rm {0.3{-}8.0~keV}} \geq 50$.

In this work we report on archival Chandra and HST observations of the globular cluster M 71. We obtained a 52.4-kilosecond Chandra observation of M 71 taken with the Advanced CCD Imaging Spectrometer (ACIS), reaching the limiting X-ray luminosities of $1.5\times10^{30}~{\rm erg~s^{-1}}$ and $7.9\times10^{29}~{\rm erg~s^{-1}}$ in the energy ranges of 0.3-8.0 and 0.5-2.5 keV, respectively. In Elsner et al. (2008), we reported the identification of 29 X-ray sources within the cluster half-mass radius, including the known millisecond pulsar PSR J1953+1846A (M 71A), and their X-ray properties, and found that $18\pm6$ of these 29 sources are likely to be associated with M 71 from a radial distribution analysis. The present paper extends our study of the X-ray sources in M 71 by using archival HST data to identify optical counterparts to the majority of M 71's X-ray sources, improving our understanding of their nature.

In Sect. 2 we discuss the Chandra X-ray observations and spectral analysis. HST observations, data reduction, and analysis are described in Sect. 3. In Sect. 4 we present the source identification. A discussion and comparison with other globular clusters is given in Sect. 5.

\begin{figure} \par\includegraphics[width=12.5cm,clip]{11245fg1.eps} \vspace*{2mm} \end{figure} Figure 1:

Chandra ACIS-S3 image of the globular cluster M 71 within the energy range of 0.3-8.0 keV. The large circles are centered on the nominal center of the cluster and have radii $r_{\rm c}$ (inner circle), $r_{\rm h}$ (middle circle), and 2$r_{\rm h}$ (outer circles). The small circles show the positions of the 63 X-ray sources within $r_{\rm M~71} \leq 2r_{\rm h}$ (Elsner et al. 2008). Straight lines mark the nominal boundaries of the ACIS-S3 and ACIS-S2 CCDs, with most of the figure falling on S3 and the lower left-hand portion on S2. The field of view of the HST ACS (GO10775) marked by the black square covers the entire half-mass radius. The green (dashed) and red (solid) polygons are the field of view of the HST WFPC2 for GO10524 and GO8118, respectively.

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2 X-ray observations

Elsner et al. (2008) described the Chandra X-ray observations of M 71. We note here some relevant information for our analysis and extend the spectral fitting in this paper to test alternative models besides the power laws considered by Elsner et al. (2008). Only seven of the 29 detected X-ray sources have enough counts (six sources with at least 50 source counts and one known MSP with 37.5 source counts[*]) to warrant a detailed spectral analysis. We used the CIAO tool dmextract to extract spectra of the brighter sources and the source-free background regions near to those sources. Response files were constructed by using the CIAO tool mkacisrmf and mkarf. The extracted spectra were binned with at least 5 source counts per bin. Background-subtracted spectral modeling was performed with XSPEC using data in the energy band 0.3-8.0 keV. To characterize the spectra of these sources, we fitted each of the 7 brightest X-ray sources with several different models (i.e., power law (PL), thermal bremsstrahlung (TB), and blackbody (BB)) by using Cash (1979) statistics. Assuming all the X-ray sources within the half-mass radius are associated with the globular cluster M 71, we fixed the hydrogen column density to the value of $N_{\rm H} = 1.39 \times 10^{21} ~{\rm cm^{-2}}$ from optical extinction to attempt spectral fitting.

In Table 1, Col. 1 shows the Chandra source name given in Elsner et al. (2008), and Col. 2 lists the spectral model we used. (We omitted the models that could not provide any physically acceptable description of the observed spectra.) Column 3 gives the minimum number of counts used to group the spectral data for fitting, column 4 shows the best-fit photon index ($\Gamma $) or the temperature (keV), Cols. 5, 6 gives the C-statistic and the number of PHA[*] bins, and the last column lists the unabsorbed X-ray flux in units of $10^{-14}~{\rm erg~s^{-1}~cm^{-2}}$ in the energy bands 0.3-8.0 and 0.5-2.5 keV.

The X-ray spectra discussed here can help us classify the faint X-ray sources. The brightest X-ray sources with $L_{\rm X} \geq 10^{32}~{\rm erg~s^{-1}}$ in the energy band 0.5-2.5 keV and soft spectra ( $f_{\rm0.5-2.0~keV}/f_{\rm 2.0{-}6.0~keV} \geq 1$) are mostly quiescent low-mass X-ray binaries (qLMXBs; Verbunt et al. 2008). None of the X-ray sources in our sample shows this characteristic, and we conclude that M 71 does not contain this kind of binary system. Cataclysmic variables (CVs) usually have hard spectra (power-law photon indices $\Gamma<2$) and their X-ray luminosities are typically between a few 1030 and a few $10^{32}~{\rm erg~s^{-1}}$. Most faint ( $L_{\rm X} < 3\times10^{31}~{\rm erg~s^{-1}}$) sources with soft spectra belong to chromospherically active binaries (ABs; Verbunt et al. 2008). Looking at the brightest seven X-ray sources within the half-mass radius, we see that three have soft spectra ($\Gamma>2$), three have hard spectra ($\Gamma<2$), and one (s20) is borderline with $\Gamma\sim2$. These spectra suggest that s05, s08, and s29 might be CVs, AGN, or MSPs, while the softer spectra of s02, s15, s19 and s20 may indicate that these are ABs. Definitive classifications require optical identification, which we turn to now.

3 Optical observations

Two fields located inside the half-mass radius of the globular cluster M 71 were observed with the Wide Field and Planetary Camera 2 (WFPC2) onboard the Hubble Space Telescope (HST) in 2000 and 2006. An image of the observations is shown in Fig. 1. For these observations, the PC camera was centered on the cluster center and the F336W (similar to U, hence $U_{\rm 336}$ hereafter), F439W ( $B_{\rm 439}$), and F555W ( $V_{\rm 555}$) filters were used. Exposure times were 800 s in F336W (GO10524) and 240 s in F439W (GO8118). The two exposure times corresponding to the F555W filter are 80 s and 63 s for GO10524 and GO8118, respectively. GO10524 also contains F255W images, which did not go deep enough to identify our targets. To estimate whether the nondetections may be meaningful, we used Ferraro et al. (2000) to estimate that CVs may be up to 3 mag brighter (absolute magnitude) in F255W than V. Using Seaton (1979), we estimate the extinction $A_{\rm 255}=7.0$ for M 71, and thus any CVs would be observed to be at least 3.2 mag fainter in F255W than V. Using the WFPC2 exposure time calculator (ETC), we estimate that the brightest CV candidate in our WFPC2 field, s29, could attain a signal-to-noise ratio (S/N) of 1.4 in the F255W data if it showed the maximum F255W/V excess, which many of Ferraro et al.'s UV-selected objects do not. Therefore we do not discuss the F255W data further in this paper. The 5-$\sigma$ limiting magnitudes of $U_{\rm 336}$, $B_{\rm 439}$, and $V_{\rm 555}$ for point sources are 21.09, 20.87, and 21.87, respectively. M 71 was also observed with the HST Advanced Camera for Surveys (ACS). The observations (GO10775) consist of F606W ( $V_{\rm 606}$) and F814W ( $I_{\rm 814}$) images covering the entire half-mass radius of the cluster (see Fig. 1). The exposure times for the F606W and F814W filters were 304 and 324 s with 5-$\sigma$ limiting magnitudes of $V_{\rm 606}=25.17$ and $I_{\rm 814}=23.91$ for point sources. The median value of the point sources with the $S/N \sim 5$ is used to define the 5-sigma limiting magnitude.

This section outlines the data reduction, photometry, and astrometry of the HST/WFPC2 and ACS images.

3.1 Data reduction and photometry

The HST/WFPC2 data obtained from the ESO archive were processed through the WFPC2 Associations Science Products Pipeline[*]. For each filter, single exposures were calibrated, including full bias subtraction and flat-fielding, and combined to remove the cosmic-ray events and correct the geometrical distortions[*]. We also downloaded the archival HST/ACS drizzled images. Those images were combined from two Wide Field Channel (WFC) images and calibrated with MultiDrizzle package (Koekemoer et al. 2002), which corrected for geometric distortion and performed cosmic ray rejection.

Although M 71 is a globular cluster, its stellar surface density is not as dense as that of a typical globular cluster. Even in the central region of M 71, the average distance between stars is around  $2\hbox{$^{\prime\prime}$ }$, which is about 10 times more than the typical FWHMs of WFPC2 and ACS cameras. Therefore, a simple aperture photometry method with the aperture correction is applicable to our data. We tested the flux measurement using several different psf-fitting photometry methods and the simple aperture photometry. We found that aperture photometry method had a better S/N and less magnitude error. Therefore, we decided to use aperture photometry to measure the fluxes of our data.

For the data taken with WFPC2, we basically followed the instruction of aperture photometry described in Holtzman et al. (1995). To deal with the PSF variances within each chip and between chips, we separated the images further into 4 and 9 equal-size regions for the PC and WF chips, respectively, and performed the aperture photometry with aperture correction for each separated regions individually. We used an aperture with the size of $0\hbox{$.\!\!^{\prime\prime}$ }5$ in radius to measure fluxes, for all the objects with 3$\sigma$ detection found using the IRAF daofind task. There is only less than 1% objects in each chip with a separation of $\leq $$0\hbox{$.\!\!^{\prime\prime}$ }5$ to their neighbors, so that using an aperture with the size of $0\hbox{$.\!\!^{\prime\prime}$ }5$ does not suffer from the PSF overlapping problem. The local sky values were measured using an inner sky annulus of 4 arcsecs with a width of 2 arcsecs, and the aperture correction value was calculated using the averages of the differences between the magnitudes measured using apertures with sizes of $0\hbox{$.\!\!^{\prime\prime}$ }5$ and $4\hbox{$^{\prime\prime}$ }$ in radius for 4 to 5 isolated stars in each separated region. The aperture correction value is 0.11 $\pm$ 0.02 mag, which is consistent with the value shown in Holtzman et al. (1995). The final output magnitudes in the VEGAMAG system were corrected for the appropriate zeropoints based upon the sensitivity information in each header and the charge transfer efficiency effect (Dolphin 2000).

For the data taken with ACS, we performed the aperture photometry based on the method described in Sirianni et al. (2005). The method is very similar to what we did for WFPC2. We also separated the ACS drizzled images into 9 equal-size regions to deal with the PSF variances. We used an aperture size of $0\hbox{$.\!\!^{\prime\prime}$ }5$ in radius to measure the fluxes with sky annulus from 4 arcsecs to 6 arcsecs. The aperture correction value is 0.08 $\pm$ 0.01, which agrees with the values shown in Sirianni et al. (2005). However, several optical counterparts, e.g., s08, s19, suffer from the PSF overlapping problem since the distances between them and their neighbors are $\la$ $ 1\hbox{$.\!\!^{\prime\prime}$ }0$. To measure accurate fluxes for these counterparts, we first subtracted their neighbors by using the PSF generated from isolated stars that are close to the counterparts, and then performed the aperture photometry on these sources. By doing this, we can minimize the photometric effect from the PSF wings of neighbors.

A comparison with the photometry of M 71 kindly provided by Anderson et al. (2008) for the ACS images and reported by Piotto et al. (2002) for the WFPC2 B-band and V-band images shows that their results are consistent with what we have obtained by using aperture photometry, but have the main sequence and the giant branch with less noise. We therefore used their photometry in our study. In addition, for those possible optical counterparts undetected in their photometry, we used our own results for the magnitudes, which have been corrected for the appropriate zeropoint.

The most informative of these diagrams are shown in Fig. 2, on which all stars located within the 95$\%$ confidence error circles (see Sect. 2 and Table 1 of Elsner et al. 2008) of the Chandra source positions are indicated. Numbers have been assigned to all candidate counterparts corresponding to the `s' designation given in Elsner et al. (2008), with ``a'', ``b'', or ``c'' appended if multiple potential optical counterparts exist.

\begin{figure} \par\hspace{-8mm} \hbox {\psfig{figure=11245f21.eps,width=6.3cm}\... ...th=6.3cm}\psfig{figure=11245f23.eps,width=6.3cm} } \vspace*{-3mm} \end{figure} Figure 2:

Color magnitude diagrams (CMDs) for all the sources detected in the WFPC2 and ACS field of view. The HST candidate counterparts matched to the X-ray sources are indicated by red squares. We note here s14b in the (V, V-I) CMD is plotted as a leftward-pointing arrow since its $I_{\rm 814}$-band magnitude is far below the 5-sigma limiting magnitude and with a large magnitude error.

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3.2 Astrometry

To identify optical counterparts to the Chandra X-ray sources, we aim to place both the X-ray and the optical frames onto the International Celestial Reference System (ICRS). We use this approach to improve the astrometry of Chandra and HST images.

For the X-ray sources, the positions listed in Elsner et al. (2008) are already on the ICRS. In this paper, we aim to tie the HST pointing to the ICRS by finding matches between stars appearing on HST images and stars with accurate positions in the Two Micron All Sky Survey (2MASS) Point Source Catalog (Skrutskie et al. 2006). On the basis of the HST pointing information contained in each image header, we used the WCSTools/imwcs[*] task on each corrected image to do the cross-correlation. The resulting positions were matched to those stars from the 2MASS catalog. There are hundreds of 2MASS stars within each HST image. By using those 2MASS stars as reference, the astrometric solution yielded root-mean-square residuals of $0\hbox{$.\!\!^{\prime\prime}$ }057$ in right ascension (RA) and $0\hbox{$.\!\!^{\prime\prime}$ }065$ in declination (Dec) relative to the 2MASS astrometry for the ACS images. The resulting solution gave the residual errors of $0\hbox{$.\!\!^{\prime\prime}$ }068$ and $0\hbox{$.\!\!^{\prime\prime}$ }148$ in RA and $0\hbox{$.\!\!^{\prime\prime}$ }066$ and $0\hbox{$.\!\!^{\prime\prime}$ }149$ in Dec relative to the 2MASS astrometry for the PC and WF images, respectively. The final uncertainties of the optical source position in RA and Dec are the root of the square sum of the uncertainty of the astrometry in 2MASS and HST image alignment and the general uncertainties of 2MASS point source astrometry of typically $\sim $ $0\hbox{$.\!\!^{\prime\prime}$ }1$relative to the ICRS (Skrutskie et al. 2006).

4 Source identification and classification

To obtain optical identifications for the X-ray sources, we used the precise astrometry described in Sect. 3. We searched for optical counterparts within the 95% Chandra error circle of the source positions (see Table 1 of Elsner et al. 2008), which includes the positional uncertainty of X-ray sources reported by the wavelet source detection algorithm, the uncertainty in the X-ray boresight correction, and the uncertainty in the optical astrometry. Within the half-mass radius of M 71, there were 29 sources detected by Chandra and we suggest optical counterparts based on positional coincidence alone to 25 of them. In the case of multiple sources inside the X-ray error circle, we included all the candidates. The results of each candidate optical counterpart are summarized in Table 2, and finding charts are shown in Figs. 3 and 4.

\begin{figure} \par\includegraphics[width=18cm,clip]{11245fg3.eps} \end{figure} Figure 3:

$5\hbox {$^{\prime \prime }$ }\times 5\hbox {$^{\prime \prime }$ }$finding charts for candidate optical counterparts within the half-mass radius of M 71. The finding charts were obtained from the HST/ACS $V_{\rm 606}$ images. The 95% confidence uncertainties on the Chandra positions are overlaid on these charts, while the candidate counterparts are indicated with an arrow. The finding charts are set with their dynamic range. The grayscale of these images was chosen to enhance the visibility of the candidate counterparts. All images have north to the top and east to the left.

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\begin{figure} \par\includegraphics[width=18cm,clip]{11245fg4.eps} \end{figure} Figure 4:

$5\hbox {$^{\prime \prime }$ }\times 5\hbox {$^{\prime \prime }$ }$finding charts for candidate optical counterparts outside the half-mass radius of M 71. The finding charts were obtained from the HST/ACS $V_{\rm 606}$ images. The 95% confidence uncertainties on the Chandra positions are overlaid on these charts, while the candidate counterparts are indicated with an arrow. The finding charts are set with their dynamic range. The grayscale of these images is chosen to enhance the visibility of the candidate counterparts. All images have north to the top and east to the left.

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\begin{figure} \par\includegraphics[width=9cm,clip]{11245fg5.eps} \vspace*{4mm} \end{figure} Figure 5:

X-ray luminosity as a function of absolute magnitude, for low-luminosity X-ray sources in globular clusters. Five types of X-ray sources are shown, qLMXBs (diamonds), MSPs (crosses), CVs (triangles), ABs (stars), and unclassified sources (squares). The larger and numbered symbols in this figure correspond to the optically identified X-ray sources in the field of view of the Chandra observation of M 71, where we compute absolute magnitude and X-ray luminosity under the assumption that the sources are associated with M 71. The smaller symbols in this figure indicate objects found in other clusters, i.e. 47 Tuc, NGC 6397, NGC 6752, M 4, NGC 288, M 55, and NGC 6366. Ambiguous sources coming from other clusters were discarded in this figure. The dashed line of constant X-ray to optical flux ratio given by log $L_{\rm X,0.5{-}2.5~keV} {\rm (erg~s^{-1}}) = 34.0$ - 0.4 $M_{\rm V}$ (after Bassa et al. 2004) roughly separates CVs from ABs.

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Table 2:   Optical counterparts to Chandra X-ray sources within the HST/ACS field of view.

The first step in classifying faint ( $L_{\rm X} \leq 10^{34.5}~{\rm erg~s^{-1}}$) X-ray sources is to study their X-ray properties, e.g. their X-ray luminosity and spectral behavior (see Sect. 2). The second step in the identification process can be made when the sources have other information coming from different wavelengths. The coincidence between accurate radio-timing positions of millisecond pulsars and the positions of X-ray sources can provide reliable identification. In the optical band, the color-magnitude diagrams (CMDs) of globular clusters have been studied for a long time because they reflect the fundamental properties of these stars and the evolutionary stage of the globular clusters. We extract further information from the locations of the optical stars in the CMDs of Fig. 2. CVs usually lie much bluer than the main sequence stars in the (V, U-V) and (V, B-V) CMDs, while the X-ray ABs may be located on or slightly above the main sequence or on the giant branch. Stars on the main sequence in the V vs. V-I CMD cannot be clearly classified: they could either be CVs or ABs since their optical flux is dominated by the donor stars or brighter stars of the binary systems.

The ratio of X-ray to optical flux is also useful to distinguish CVs from X-ray ABs (see Bassa et al. 2004). In Fig. 5 we show the X-ray luminosity as a function of the absolute magnitude for low-luminosity X-ray sources from 47 Tuc, NGC 6397, NGC 6752, M 4, NGC 288, M 55, NGC 6366 (data from Bassa et al. 2004; Grindlay et al. 2001a; Pooley et al. 2002; Kong et al. 2006; Edmonds et al. 2003a; Taylor et al. 2001; Cool et al. 1998; Bassa et al. 2008; Grindlay et al. 2001b), and M 71. The large symbols in this figure indicate the X-ray sources with possible optical counterparts in the field of view of the Chandra observation of M 71, while the smaller symbols show classified objects found in other clusters. The absolute magnitudes and X-ray luminosities for the sources in the observations were computed under the assumption that they are cluster members. As discussed in Elsner et al. (2008), we caution that $\sim $40% of the 29 X-ray sources within the half-mass radius are background or foreground objects.

Now we turn to those stars unrelated to the globular clusters. Foreground stars are likely to have counterparts that are not on the main sequence, that have soft spectra, and that have low $f_{\rm X}/f_{\rm O}$ ratios (Krautter et al. 1999). For background active galactic nuclei (AGN), they will also have counterparts not on the main sequence, but with hard spectra. Their $f_{\rm X}/f_{\rm O}$ ratios can be high (Krautter et al. 1999). However, the AGN will not necessarily be detected at all; in some cases, the only object in an error circle may be a cluster main-sequence star that is not related to the X-ray source.

We first consider those X-ray sources with only one suggested counterpart in the Chandra error circle. S08 is a known millisecond pulsar, PSR J1953+1846A = M 71A, with a spin period of 4.89 ms. It is in a 4.24 h eclipsing binary system with a low-mass ($\geq$0.032 $M_{\odot}$) companion. It was discovered with Arecibo (Hessels et al. 2007; Ransom et al. 2005,2003), and its radio emission is partially eclipsed in the orbital phase interval 0.18-0.36 for approximately 20% of each orbit (Hessels et al. 2007). The X-ray counterpart was detected by Elsner et al. (2008). Within the Chandra error circle we find a possible optical counterpart of this pulsar in the $V_{\rm 606}$ and $I_{\rm 814}$ band. The candidate optical counterpart to s08 lies on the main sequence in our V-I CMD with an absolute magnitude $M_{\rm V} \sim 8.5$, which implies that it has a mass of about 0.5 $M_{\odot}$. The radio timing indicates a minimum mass of 0.03 $M_{\odot}$ (Hessels et al. 2007) for the companion star. In order to allow for such a massive companion (i.e. $\sim $0.5 $M_{\odot}$), conceivably the orbit could be seen nearly face-on (within 4 degrees). However, in that (extremely unlikely) case we do not expect regular radio eclipses, which are observed. M 71A's radio properties are very similar to those of other very low-mass binary pulsars such as PSR J1701-3006E (M 62E, Freire 2005), and therefore we conclude that M 71A's companion is not this star. Although this star's position agrees within $0\hbox{$.\!\!^{\prime\prime}$ }1$ with M 71A's position from radio timing (I. Stairs 2009, private comm.), transferred with $0\hbox{$.\!\!^{\prime\prime}$ }1$ accuracy (1$\sigma$) onto the 2MASS frame (Skrutskie et al. 2006), this could be coincidence due to the crowding in this field (Fig. 3); alternatively, M 71A could be a hierarchical triple system. Future radio timing may determine this.

The star in the error circle of s02 is nearly located on the main-sequence turn-off point (MSTO) in the (V, V-I) CMD of Fig. 2 and slightly below the subgiant branch, which is similar to the ``red straggler'' active binaries seen as X-ray sources in other clusters (Albrow et al. 2001; Edmonds et al. 2003a; Bassa et al. 2008; Edmonds et al. 2003b). Its ratio of the X-ray to optical flux locates in the region of ABs in Fig. 5. Since s02 has a soft spectrum and shows significant time variability in the X-ray band (Elsner et al. 2008) we suggest that s02 is a chromospherically AB, and its temporal variation can be explained as flaring on the coronally active star. S04 and s18 are also believed to be in the same group as ABs since both of them are located slightly above the main-sequence turn-off point, have soft X-ray spectra, and have lower X-ray to optical flux ratios.

S05 is the brightest X-ray source within the half-mass radius of M 71. It is worth noting that s05 is the only X-ray source detected with ROSAT (Elsner et al. 2008; Panzera et al. 2003) inside the half-mass radius. Its optical counterpart is bluer than the main sequence, and it has a relatively high X-ray luminosity ( $L_{\rm X} \sim 4 \times 10^{31}~{\rm erg~s^{-1}}$). It is unlikely to be an AB. Its X-ray spectrum is too hard to consider it as a quiescent low-mass X-ray binary (qLMXB). S05 gives a bremsstrahlung temperature consistent with $\sim $10 keV, as appropriate for luminous magnetic CVs (Mukai 2003; Eracleous et al. 1991). During the 52.4 ks observation time, it is not consistent with being steady at 99.9% confidence. We suggest that a CV interpretation is plausible. In addition, s05 has a high value of ${\rm log}(f_{\rm X}/f_{\rm O}) \sim 0.37$ and the blue color, which implies this source could be a background AGN. However, the power-law fit of its X-ray spectrum, with photon index $\Gamma = 1.55 \pm 0.1$, might be considered as arising from the intra-binary shock formed due to interaction between the relativistic pulsar wind and material from its companion star. An irradiated main-sequence companion could be this blue; e.g. 47 Tuc W (Bogdanov et al. 2005). MSPs with main-sequence companions of the mass of $\sim $ $ 0.5~ M_{\odot}$have not yet been detected, but may well be hidden from radio detection by clouds of ionized gas from the companion (e.g. Freire et al. 2004). Therefore, we cannot rule out the interpretation that it is a binary MSP system though this unusual scenario must be judged unlikely.

The candidate cluster counterpart to s29 has ultraviolet excess with respect to the main sequence (Fig. 2) and has a high X-ray-to-optical flux ratio. The source can be well-fitted with a power law model with a photon index of $\Gamma = 1.29 \pm 0.4$, and its X-ray luminosity is $L_{\rm X,0.3-8.0~keV} \sim 2.1 \times10^{31}~{\rm erg~s^{-1}}$. Its U-V color is far too blue to be an AB, while the optical color is redder, almost on the main sequence. That indicates s29 is a CV with two spectral components, a blue disk and a red companion star.

Source s15 is a good AB candidate since there is no evidence of any blue color in the VI CMD and it has a soft X-ray spectrum ( $f_{\rm0.5-2.0~keV}/f_{\rm 2.0{-}6.0~keV} \geq 1$). On the other hand, without the information from the U-V or B-V color, a CV interpretation is still plausible. Its relatively high value of log  $(f_{\rm X}/f_{\rm O}) \sim -0.79$suggests that s15 could be a CV, although it does not rule out an AB.

The star in the error circle of s20 lies on the giant branch and has a soft X-ray spectrum, which gives strong evidence that it is a chromospherically active binary containing a giant star (i.e., a RS CVn system). Its temporal variation in the X-ray band (Elsner et al. 2008) can be explained by magnetic activity. Since s07 and s12 are located on the giant branch and have relatively low X-ray-to-optical flux ratios, we believe that they are likely RS CVn systems as well.

The optical counterparts associated with those X-ray sources having lower photon statistics, s01, s06, and s23, are located on the main sequence and have lower X-ray-to-optical flux ratios. We then consider that all of them may be X-ray ABs. S22 exhibits rather interesting colors. In the V-I CMD it is on the main sequence, but as we shift to progressively bluer colors, its color gets redder and redder while in the U-V CMD it is way off the main sequence. Thus we suggest that it is either a foreground or background source, not associated with M 71.

We turn now to the sources with more than one possible counterpart in the error circle. We find two or three possible optical counterparts within each of the Chandra error circles for s03, s14, s19, s27, and s28.

S03a and s03b both fall on the main-sequence in the (V, U-V), (V, B-V), and (V, V-I) CMDs. Their colors and low X-ray-to-optical flux ratios suggest that either s03a or s03b is a chromospherically AB. However, the blue color and the relatively high X-ray-to-optical flux ratio of s03c indicates that it is a CV or a background AGN. S14a and s28a are located far from the main sequence, suggesting that they do not belong to M 71, while s28b located on the main sequence could be an active binary system since it has the relatively low X-ray to optical flux ratio. In Fig. 3, we find two additional possible optical counterparts, s14b and s14c, within the Chandra error circle of s14, which are fainter than the 5-$\sigma$ limiting magnitudes of $V_{\rm 606}$ and $I_{\rm 814}$. Based on the blue color and the high value of $f_{\rm X}/f_{\rm O}$, s14b could be either a CV or a background AGN. The optical-faint source s14c is located near the downward-extended part of the main sequence, suggesting that it could be a main-sequence star. However, it is located in the $L_{\rm X}$ vs. $M_{\rm V}$ diagram in a region where no authentic cluster members have been found if we compute its X-ray luminosity and absolute magnitude under the assumption that it belongs to M 71. We then rule out the AB interpretation. Therefore, due to its high X-ray-to-optical flux ratio of this source, s14c is considered as either a good candidate for background AGN with a optically faint object inside the error circle not related to the X-ray source or a CV candidate with a secondary star that dominates the optical flux in the (V, V-I) CMD. There are three optical counterparts within the Chandra error circle of s19. The position of s19a is near the MSTO point and slightly below the subgiant branch, which is similar to the case of s02, while s19b is located on the main sequence. Both of their X-ray-to-optical flux ratios are located in the region that is primarily populated by ABs (Fig. 5). For the third optical counterpart, s19c, its location in the VI CMD and soft X-ray spectrum indicate that s19c is an active binary as well. However, without the information from the UV color, we cannot eliminate the CV interpretation because of its relatively high X-ray-to-optical flux ratio, which is similar to the case of s15. We suggest that s19a is the most likely counterpart, as red stragglers are very often associated with X-ray sources (e.g. Heinke et al. 2005). According to the positions of two possible optical counterparts to s27 in the CMDs and in the absolute magnitude vs. X-ray luminosity diagram, we believe that either s27a or s27b is likely to be an active binary.

The optical counterparts of s16, s24, and s26 are located farther above or to the right of the main sequence than the binary sequence. We therefore believe that they are foreground objects and unrelated to M 71. The positions of two faint optical counterparts to s10 and s25 in the (V, V-I) CMD and their relatively high X-ray-to-optical flux ratios are very similar to the case of s14c so that s10 and s25 could be either CVs or background AGN. The highest X-ray-to-optical flux ratio among 39 possible counterparts and blue color suggests that s21 is the most likely background AGN, although we cannot eliminate the interpretation of a CV. Furthermore, the regions of the X-ray sources, s09, s11, s13, and s17, were also observed with the HST/WFPC2 and ACS, but we do not find any optical counterparts inside their Chandra error circles. If we set the 5-$\sigma$ limiting magnitude of $V_{\rm 606}=25.17$ as the upper limit for these sources, their X-ray-to-optical flux ratios fall on a range of $\sim $0.2-0.6, which are higher than the highest ${\rm log}(f_{\rm X}/f_{\rm O})$ value known for an AB in a cluster, e.g. W64 in 47 Tuc (Edmonds et al. 2003a). Therefore, an AB interpretation can be rejected. If we take their X-ray colors into account, s11 and s17 are located near the bottom-right corner and close to the position of s40 in the X-ray color-color diagram shown in Fig. 4 of Elsner et al. (2008), which implies they have very hard spectra with over half of their counts above 2 keV. This infers a high intrinsic $N_{\rm H}$, which strongly suggests that these are background AGN. For the other three sources with medium X-ray colors, we then tentatively classify them all as CVs, MSPs, or background AGN, though AGN are probably the most likely category.

Outside the half-mass radius of M 71, we find 6 optical counterparts to X-ray sources, s41, s42, s49, and s54 in the ACS field-of-view. The candidate counterpart to s42, located on the edge of the ACS, is saturated in the optical band, which prevents us from obtaining a reliable magnitude of this optical source or searching for any other faint optical sources inside the Chandra error circle. There are 2 possible optical counterparts to s49. Both of them are located far from the main sequence, so we suggest that they are not associated with M 71. Inside the error circle of s54, the brighter object s54a is on the giant branch, while the fainter one, s54b, is located blueward of the main sequence in the CMD and has a relatively high X-ray-to-optical flux ratio, suggesting that s54b might be a CV. However, s54b lies on the spikes produced by s54a, which prevents us from obtaining an accurate magnitude for s54b. S41's color is bluer than the main sequence, and its X-ray-to-optical flux ratio is higher than that of an AB. We then suggest that s41 is a CV candidate. Furthermore, a background AGN scenario is also plausible for s41 and s54b due to their blue colors, high ${\rm log}(f_{\rm X}/f_{\rm O})$ values, and their locations outside the half-mass radius of M 71, where they are more likely to be background sources.

5 Summary and discussion

In summary, we find one certain CV (s29), seven possible candidate CVs (s05, s10, s14, s21, s25, s41, and s54), and two certain ABs (s02 and s20) and 12 good candidate ABs (s01, s03, s04, s06, s07, s12, s15, s18, s19, s23, s27, and s28) in the globular cluster M 71. Some of our candidate CVs (and/or candidate ABs) might be MSPs in binary systems or AGN, which often (but not always) show blue colors.

To interpret our results, understanding how many of our objects are likely false matches will be critical. We calculated the expected number of false matches in several ways. First, we shifted all our X-ray source positions by 9 $\hbox{$^{\prime\prime}$ }$and 18 $\hbox{$^{\prime\prime}$ }$(somewhat arbitrary, but chosen to be larger than the largest uncertainties) in four directions, and searched for matches against the $V_{\rm 606}$frame. From this exercise, we expect 11+4-8 false matches among our 39 possible matches, indicating that $\gtrsim$70% of the 34 total X-ray sources in our field of view have a true match. By chance, then, 70% of our false matches should occur with sources that have a true match-suggesting that $\sim $7.7 sources should have two possible optical counterparts. We see seven sources that have two or more possible $V_{\rm 606}$ counterparts, which is nicely consistent.

To know which sources are more likely to have false matches, we calculated the probability of a chance coincidence in % shown in Col. 10 of Table 2 by using Eq. (3) from Elsner et al. (2008) (see also Verbunt et al. 2008). Within the half-mass radius, there are 6 sources with a false alarm probability lower than 1%, which indicates that those associations between X-ray sources and optical counterparts have a >99% confidence level. Adding up the false alarm probabilities gives a total expected number of false matches of $\sim $5, which is consistent with the expectation of 11+4-8 false matches above. Among the 10 X-ray sources with optical counterparts and $L_{\rm X,0.5{-}6.0~keV} > 4 \times 10^{30} ~{\rm erg~s^{-1}}$, adding the false alarm probabilities indicates that roughly one of them is expected to be a false match. (We believe s08 to be a false match, but to be a true cluster member; and that s19 has three potential counterparts.)

Inside the half-mass radius of M 71, we find 14 X-ray sources with $L_{\rm X,0.5{-}6.0~keV} > 4 \times 10^{30} ~{\rm erg~s^{-1}}$, of which 10 have optical counterparts. Assuming that all X-ray sources outside the half-mass radius are fore- or background sources, we can estimate that $\sim $ 3.7+3.1-1.8 X-ray sources among 14 are unrelated to M 71. The error quote here is from the Poisson statistic (Gehrels 1986). This is consistent with our estimate above that we have identified true optical counterparts for $\sim $9 X-ray sources.

Pooley et al. (2003) have shown that for 12 globular clusters observed by Chandra, the number of globular cluster X-ray sources that are above the lower limit of $4 \times 10^{30} ~{\rm erg~s^{-1}}$ (0.5-6 keV) can be approximately linearly fitted with the predicted stellar encounter rate $\Gamma' \propto {\rho_o}^{1.5}{r_c}^2 \equiv \Gamma$, where $\Gamma $ is referred to as the collision number (Verbunt 2003). Here, $\rho_o $ is the central density of the cluster, and $r_{\rm c}$ is the core radius. To examine if M 71 fits this relation, we compared its number of X-ray sources and its collision number $\Gamma $ with those of some other clusters, NGC 6266, 47 Tuc, M 28, M 4, NGC 6366, M 55, and NGC 288 (see Fig. 6), using the parameters listed in Table 3. The core-collapsed globular clusters are not considered in our study since their core parameters are generally uncertain, introducing strong uncertainties into interaction rates derived from those parameters. The encounter number for M 71 is $\sim $230 and $\sim $10 times less than those of 47 Tuc and M 4, respectively. Pooley et al. (2003) reports 41 $\pm$ 2 sources above the lower luminosity limit in 47 Tuc, which are revised by Heinke et al. (2005) to $63\pm4$ (for a distance of 4.5 kpc), with the uncertainty due to the estimated number of background sources. Thus, if the number of sources scales with the encounter rate, the presence of $\sim $$10\pm3$ sources with $L_{\rm X,0.5{-}6.0~keV} > 4 \times 10^{30} ~{\rm erg~s^{-1}}$ in M 71 is a very significant overabundance, even if we take the errors due to Poissonian fluctuations into account. The same conclusion is reached on the basis of comparison with any other globular clusters listed in Table 3 except for M 55 and NGC 288, in which the number of the X-ray sources is also in excess of the predicted value. This indicates that most of the sources in M 71, M 55, and NGC 288 are not formed via stellar encounters.

Table 3:   Scaling parameters of NGC 6266, 47 Tuc, M 28, M 4, M 71, NGC 6366, M 55, and NGC 288.

\begin{figure} \par\hspace{-0.3cm} \includegraphics[angle=-90,width=9.0 cm]{11245fg6.ps} \vspace{8mm} \end{figure} Figure 6:

Number of globular cluster X-ray sources (N) with $L_{\rm X, 0.5{-}6.0~keV} \geq 4 \times 10^{30} ~{\rm erg~s^{-1}}$ inside the half-mass radius vs. the normalized collision number $\Gamma $ of the cluster. The dashed line indicates the best power-law fit of the data points from 47 Tuc, NGC 6266, M 28, M 4, and NGC 6366 (cf. Table 3). The relation between N and $\Gamma $, i.e. ${N} \propto \Gamma ^{0.74\pm 0.03}$, is consistent with the result derived from Pooley et al. (2003).

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As suggested by Verbunt (2002), ABs are most likely primordial binaries, so that to first order their numbers should scale with mass. Following Kong et al. (2006), we calculated the half masses with 10-0.4 MV, assuming the visual mass-to-light ratio is the same for all clusters listed in Table 3. M 71 has the lowest half mass, containing only $\sim $30% of the mass within the half-mass radius of M 4. Scaled by mass, the predicted number of ABs with $L_{\rm X,0.5-6~keV}> 4 \times10^{30}$ erg s-1 in M 71 should be similar to that of NGC 6366 and smaller than those in any other cluster shown in Table 3, but this contradicts our results.

The scaling of source number with the collision number for the sources with $L_{\rm X,0.5-6~keV}> 4 \times10^{30}$ erg s-1 suggests that CVs are mostly made via stellar encounters (Pooley et al. 2003). If we assumed that all of the CVs in M 71 were formed dynamically, we would not expect to find more than one CV by scaling with the encounter numbers from any other cluster listed in Table 3. However, most of the globular clusters studied by Pooley et al. (2003) have high $\Gamma $ numbers and many dynamically produced CVs. It is reasonable to suspect that primordial CVs may dominate in the low-density clusters. According to the computations by Davies (1997), a cluster core with a star density of 1000 pc-3 allows most of the CV progenitors to evolve into a CV. This could explain the existence of at least one (and several candidate) CV within the half-mass radius of M 71.

It is interesting that in M 71 $\sim $ 7 optical counterparts to Chandra X-ray sources are classified as potential RS CVn systems, in which X-ray emission is produced primarily in (sub)giant flare outbursts. A couple of possible RS CVn X-ray sources have been identified in 47 Tuc (Heinke et al. 2005) and $\omega$ Centauri (Cool et al. 2002), but, besides M 71, only the low-density clusters M 55 and NGC 6366 (Bassa et al. 2008) have significant fractions of X-ray sources identified as possible RS CVns. Considering the even lower density case, the total X-ray luminosity of the old open cluster M 67 is dominated by binaries with giants (van den Berg et al. 2004). From the ROSAT census, the X-ray emission of most globular clusters per unit mass is lower than that of the old open cluster M 67 (Verbunt 2001,2002). There are three possible explanations for this:
a) M 67 is a very sparse cluster, which is evaporating its lowest-mass stars (Hurley et al. 2005). Open clusters do not survive very long. As a cluster evaporates its lowest-mass stars, it tends to retain its heaviest systems - binaries - which are more likely to be X-ray sources.
b) M 67 is a rather young cluster. Younger stars may produce more X-rays (Randich 1997), since they tend to be rotating faster than older stars.
c) A large fraction of binary systems are destroyed in globular clusters (see Ivanova et al. 2005), in particular those with longer orbits. RS CVn systems involve giants that are spun up by stellar companions. These systems must be relatively wide binaries, in order to avoid the giant swallowing its companion as it evolves, but such wide binaries are destroyed in globular clusters. Thus there are fewer RS CVn binaries in globulars. Since RS CVn binaries tend to be brighter than BY Dra binaries (main-sequence ABs), low-density clusters can have startlingly high X-ray luminosities per unit mass.

To summarize the results of this paper, the number of X-ray faint sources with $L_{\rm X,0.5-6~keV}> 4 \times10^{30}$ erg s-1 found in M 71 is higher than the predicted value on the basis of either the collision frequency or the half mass. We suggest that those CVs and ABs in M 71 are primordial in origin. The last interpretation above may explain the X-ray overabundance of low-density clusters like M 71, where fewer primordial binaries may have been destroyed through binary interactions. Study of other low-density globular clusters will help us better understand their evolution and dynamics.

Acknowledgements
This work made use of the Chandra and HST data archives. We acknowledge that Stairs et al. kindly provided the information of M 71A in advance of publication. We also thank Anderson et al. for the photometry. The first author thanks Albert K.H. Kong for some helpful suggestions and acknowledges the receipt of funding provided by the Max-Planck Society in the frame of the International Max-Planck Research School (IMPRS). COH acknowledges support from NASA Chandra grants, and funding from NSERC and the University of Alberta.



References

Footnotes

... 2003[*]
http://physwww.mcmaster.ca/ harris/Databases.html
... counts[*]
The number of source counts is a result of modeling the background and the PSF, and represents a background subtracted expectation value for the source counts within the detect cell.
... PHA[*]
PHA: pulse height analysis.
... Pipeline[*]
See http://archive.eso.org/archive/hst/wfpc2_asn/
... distortions[*]
See http://archive.stsci.edu/hst/wfpc2/pipeline.html
... WCSTools/imwcs[*]
See http://tdc-www.harvard.edu/software/wcstools/index.html

All Tables

Table 1:   Spectral fits of the X-ray sources with source counts $C_{\rm {0.3{-}8.0~keV}} \geq 50$.

Table 2:   Optical counterparts to Chandra X-ray sources within the HST/ACS field of view.

Table 3:   Scaling parameters of NGC 6266, 47 Tuc, M 28, M 4, M 71, NGC 6366, M 55, and NGC 288.

All Figures

  \begin{figure} \par\includegraphics[width=12.5cm,clip]{11245fg1.eps} \vspace*{2mm} \end{figure} Figure 1:

Chandra ACIS-S3 image of the globular cluster M 71 within the energy range of 0.3-8.0 keV. The large circles are centered on the nominal center of the cluster and have radii $r_{\rm c}$ (inner circle), $r_{\rm h}$ (middle circle), and 2$r_{\rm h}$ (outer circles). The small circles show the positions of the 63 X-ray sources within $r_{\rm M~71} \leq 2r_{\rm h}$ (Elsner et al. 2008). Straight lines mark the nominal boundaries of the ACIS-S3 and ACIS-S2 CCDs, with most of the figure falling on S3 and the lower left-hand portion on S2. The field of view of the HST ACS (GO10775) marked by the black square covers the entire half-mass radius. The green (dashed) and red (solid) polygons are the field of view of the HST WFPC2 for GO10524 and GO8118, respectively.

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In the text

  \begin{figure} \par\hspace{-8mm} \hbox {\psfig{figure=11245f21.eps,width=6.3cm}\... ...th=6.3cm}\psfig{figure=11245f23.eps,width=6.3cm} } \vspace*{-3mm} \end{figure} Figure 2:

Color magnitude diagrams (CMDs) for all the sources detected in the WFPC2 and ACS field of view. The HST candidate counterparts matched to the X-ray sources are indicated by red squares. We note here s14b in the (V, V-I) CMD is plotted as a leftward-pointing arrow since its $I_{\rm 814}$-band magnitude is far below the 5-sigma limiting magnitude and with a large magnitude error.

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In the text

  \begin{figure} \par\includegraphics[width=18cm,clip]{11245fg3.eps} \end{figure} Figure 3:

$5\hbox {$^{\prime \prime }$ }\times 5\hbox {$^{\prime \prime }$ }$finding charts for candidate optical counterparts within the half-mass radius of M 71. The finding charts were obtained from the HST/ACS $V_{\rm 606}$ images. The 95% confidence uncertainties on the Chandra positions are overlaid on these charts, while the candidate counterparts are indicated with an arrow. The finding charts are set with their dynamic range. The grayscale of these images was chosen to enhance the visibility of the candidate counterparts. All images have north to the top and east to the left.

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In the text

  \begin{figure} \par\includegraphics[width=18cm,clip]{11245fg4.eps} \end{figure} Figure 4:

$5\hbox {$^{\prime \prime }$ }\times 5\hbox {$^{\prime \prime }$ }$finding charts for candidate optical counterparts outside the half-mass radius of M 71. The finding charts were obtained from the HST/ACS $V_{\rm 606}$ images. The 95% confidence uncertainties on the Chandra positions are overlaid on these charts, while the candidate counterparts are indicated with an arrow. The finding charts are set with their dynamic range. The grayscale of these images is chosen to enhance the visibility of the candidate counterparts. All images have north to the top and east to the left.

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In the text

  \begin{figure} \par\includegraphics[width=9cm,clip]{11245fg5.eps} \vspace*{4mm} \end{figure} Figure 5:

X-ray luminosity as a function of absolute magnitude, for low-luminosity X-ray sources in globular clusters. Five types of X-ray sources are shown, qLMXBs (diamonds), MSPs (crosses), CVs (triangles), ABs (stars), and unclassified sources (squares). The larger and numbered symbols in this figure correspond to the optically identified X-ray sources in the field of view of the Chandra observation of M 71, where we compute absolute magnitude and X-ray luminosity under the assumption that the sources are associated with M 71. The smaller symbols in this figure indicate objects found in other clusters, i.e. 47 Tuc, NGC 6397, NGC 6752, M 4, NGC 288, M 55, and NGC 6366. Ambiguous sources coming from other clusters were discarded in this figure. The dashed line of constant X-ray to optical flux ratio given by log $L_{\rm X,0.5{-}2.5~keV} {\rm (erg~s^{-1}}) = 34.0$ - 0.4 $M_{\rm V}$ (after Bassa et al. 2004) roughly separates CVs from ABs.

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In the text

  \begin{figure} \par\hspace{-0.3cm} \includegraphics[angle=-90,width=9.0 cm]{11245fg6.ps} \vspace{8mm} \end{figure} Figure 6:

Number of globular cluster X-ray sources (N) with $L_{\rm X, 0.5{-}6.0~keV} \geq 4 \times 10^{30} ~{\rm erg~s^{-1}}$ inside the half-mass radius vs. the normalized collision number $\Gamma $ of the cluster. The dashed line indicates the best power-law fit of the data points from 47 Tuc, NGC 6266, M 28, M 4, and NGC 6366 (cf. Table 3). The relation between N and $\Gamma $, i.e. ${N} \propto \Gamma ^{0.74\pm 0.03}$, is consistent with the result derived from Pooley et al. (2003).

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In the text

Copyright ESO 2010

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