CHANDRA OBSERVATIONS OF THE X-RAY POINT SOURCE POPULATION IN NGC 4636

The distribution of the X-ray point sources as a function of distance from the center of NGC 4636 is shown in Figure 3. The radial profiles of sources in the ACIS-S and ACIS-I observations are shown separately, and are seen to have the same shape, with the deeper ACIS-I observations having a larger number of sources with greater than 10 net counts.

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From point source statistics in the Chandra Deep Fields (Bauer et al. 2004), we estimate a background AGN density of ∼0.3 arcmin⁻² at our limiting flux of ∼4 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the 0.5–2 keV band (shown as a horizontal line in Figure 3). Based on this estimate, our field becomes AGN-dominated beyond ∼6' of the galaxy center. Between 15 and 6', we estimate that 25% of our sources are background sources (AGN) and 75% are LMXBs within the galaxy.

Traditionally, X-ray colors for sources are calculated as ratios of counts in different energy bands (e.g., Swartz et al. 2004; Prestwich et al. 2003). However, since we want to directly compare sources observed by X-ray detectors with different responses (i.e., the ACIS-S and ACIS-I) and on different parts of the detectors, we convert source counts to fluxes before computing X-ray colors. We define three bands: soft (S = 0.5–1 keV), medium (M = 1–2 keV), and hard (H = 2–8 keV), and calculate two colors as C₁ = (M − S)/(S + M + H) and C₂ = (H − M)/(S + M + H), as defined in Swartz et al. (2004). The resulting color–color diagram is shown in Figure 4. The plotting symbol size is proportional to the 0.5–2 keV band luminosity. We identify two distinct populations: a large cluster of harder, less luminous sources with power-law indices between 1 and 2, and a smaller group of softer, more luminous sources (L_X ≈ 10³⁸ erg s⁻¹) with steeper power-law indices. Points in black lie less than 6' from the center of the galaxy and are most likely members, while points in red lie further than 6' from the center. The source represented by a purple × is located at the galactic nucleus, and the two sources with steep spectra represented by the purple asterisk and plus sign lie within 5'' of the nucleus. These may be signatures of black holes (see Sections 3.6.1 and 3.6.2). The large red circle near these points is a bursting X-ray source, which we discuss further in Section 3.6.4. Due to its distance from the galactic center (>11') it is most likely not a member of NGC 4636.

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To make this flux based color–color diagram, we performed an iterative flux calculation as follows. Beginning with source counts in each band for both the ACIS-I and ACIS-S detectors, we convert to source and model flux, assuming a power-law model with slope Γ = 1.5 and column density n_H = 1.81 × 10²⁰ cm⁻² and computing response matrices at each location on the appropriate ACIS chip (as described in Section 2). We convert the model curves from counts to flux assuming the same power-law model and using response matrices calculated at the aim-point location of each observation. Since in earlier works the color–color diagram has been based on counts, we show in Figure 5 the counts-based diagram (with model curves for the ACIS-I). We show in Figure 6 the color–color diagram from this first flux iteration. Next, we use model grids and source colors from this first iteration to determine the values of Γ and n_H closest to each source in color–color space. We then use these individual values of Γ and n_H to calculate a more accurate counts-to-flux conversion factor for the given source (again computing response matrices at each location on the appropriate ACIS chip). Note that the model grid shown in Figure 6 is a subset of the much finer grid that we use to pick the individual Γ = 1.5 and n_H for each source. For example, our grid has Γ ranging from 1 to 4 in steps of 0.1, but for clarity on the plot, we only show integer values of Γ.

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After performing this iterative flux conversion for the sources, we again calculate the colors, now comparing them to grids directly calculated from model flux values. This is shown in Figure 4. We note that this figure has much less scatter than the color–color plot based on counts for the same set of sources (Figure 5), making it easier to identify populations and trends.

We present a comparison of source fluxes between the 2000 January ACIS-S observation and co-added 2003 February ACIS-I observations in Figure 7. To search for long-term variable sources, we determine a significance threshold as

$$\begin{equation} S = \frac{\left| f_{S} - f_{I}\right|}{\sqrt{\sigma _{I}^{2} + \sigma _{S}^{2}}} > 3, \end{equation} \tag{ 1 }$$

where f is the 0.5–2 keV band flux and σ is the flux uncertainty (dominated by the Poisson error on the number of counts—the error on the counts-to-flux conversion factor is minimal and we do not include it here). For the 228 sources in the common FOV detected with ⩾10 net counts in at least one of the observations, we find 54 (∼24%) are long-term variable sources. These are marked with a "V" in the last column of Table 2. Of these 54 sources, 17 have ⩾10 net counts in both observations. These are shown in red in Figure 7. The remaining 37 variable sources are "transient"—that is, they have ⩾10 net counts in only one observation, and are not "reliably" detected in the other observation. Of these 37 transient sources, 31 have ⩾20 net counts in one observation and <10 net counts in the other observation.

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To measure variability on shorter timescales, we compare source fluxes between the two 2003 February ACIS-I observations (see Figure 8). These observations were done successively, each lasting for ∼75 ks (∼21 hr). Of 188 sources detected in the common FOV with at least 10 net counts in one observation or the other, nine (5%) vary significantly (S> 3) between the two observations. These sources are marked "MV" in the last column of Table 2. Figure 8 shows a subset of these sources: those detected with at least 10 net counts in both observations.

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For yet another look at short-term variability, we use the IDL PINTofALE program timevarvk (Kashyap & Drake 2000), to search for sources which vary within the course of an observation. The timevarvk routine uses a one sample Kolmogorov–Smirnov (K–S) test to compare the source light curve to a flat model, then calibrates the observed deviation with Monte Carlo simulations. Good time intervals are accounted for and gaps are removed. In addition, the deviations between the source light curve and the model are averaged over a given number of photons to suppress random Poisson deviations. We ran 1000 Monte Carlo simulations per source, and averaged over two photons. Of 132 sources detected in the ACIS-S observation with at least 10 net counts, 17 (13%) are variable at a 3σ level (p⩽ 0.0027). Of 233 sources detected in the summed ACIS-I observation with at least 10 net counts, 19 (8%) are variable at a 3σ level. These sources are marked with "SV-I" and/or "SV-S" in the last column of Table 2.

An example of a variable light curve is shown in Figure 9. This source shows short-term variability during both the ACIS-I and ACIS-S observations, and also shows variability between the two observations. Note the flare in the ACIS-S observation (top panel). We estimate its duration to be approximately 600 s. We discuss this bursting X-ray source further in Section 3.6.4.

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Comparing our short- and long-term variability results to X-ray point-source surveys of other galaxies is challenging due to the different methods and criteria used to determine and quantify variability in each case. To minimize the effects of these differences, we attempt to compare results for a subset of the brightest sources in each galaxy. For example, Kraft et al. (2001) find 35 out of 246 (14%) of X-ray point sources in Cen A to be variable with a ⩾3σ significance over a five month period separating the two observations. Computing the χ² statistic for individual light curves (bin size ∼ 3600 s), they find only two sources with short-term (within an observation, each about 36 ks) variability. Of the 17 sources with luminosity greater than 10³⁸ erg s⁻¹, 8 (47%) show significant long-term variability. Jordán et al. (2004) search for long-term variability among a subset of sources detected in two M87 observations spanning two years. Of the 23 sources with luminosity greater than 10³⁸ erg s⁻¹, 7 (30%) vary significantly. In NGC 4636, we find that of the 52 sources with luminosity greater than 10³⁸ erg s⁻¹, 21 (42%) show some type of variability: 13 (24%) long term and 12 (23%) short term. (Four of these very luminous sources show both long- and short-term variability.)

Loewenstein et al. (2005) find five transient sources out of 39 (13%) and an additional six (15%) highly variable sources in two observations of NGC 1399 spanning three years. Three of these six sources have luminosities greater than 10³⁹ erg s⁻¹, although since luminosities are not given for the whole source list, we have no basis for comparison with our results.

Of 126 sources with luminosity greater than 1.4 ×10³⁷ erg s⁻¹ in NGC 4697, Sivakoff et al. (2008) find that five sources (4%) display short-term variability and 16% display long-term variability. Restricting our NGC 4636 population to the 157 sources lying less than 6' from the galactic center with luminosity greater than 1.4 ×10³⁷ erg s⁻¹, we find 16 (10%) that display short-term variability and 29 (18%) that show long-term variability.

Figure 10 shows the LF in the 0.5–2 keV band for X-ray point sources lying between 15 and 6' from the center of NGC 4636. We plot here only the sources that have 10 net counts, after subtraction of the local background, in each observation. Our requirement of having at least 10 net counts per source, leads to a different minimum luminosity for the two sets of observations (1.2 × 10³⁷ erg s⁻¹ and 1.8 × 10³⁷ erg s⁻¹ for ACIS-I and ACIS-S, respectively). At the bright end, consistent with Irwin et al. (2004) and Raychaudhury et al. (2008), we do not find any ULXs (L_X> 1×10³⁹ erg s⁻¹).

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We model the LF of these sources as a single power law, since we see no evidence for a break in the LF. Jordán et al. (2004) demonstrate that there is no compelling evidence for a break in the LFs of the Virgo cluster galaxies M87, M49, and NGC 4697. We adopt a robust method of measuring the slope of the LF, which is usually expressed in the cumulative form

$$\begin{equation} \log N(>S) = -\alpha \log S + \kappa. \end{equation} \tag{ 2 }$$

Each of our n point sources has a measured luminosity F_i, given the adopted distance to the galaxy, and an estimated error σ_i. The probability of a point source to have a luminosity S is

$$\begin{equation} P(S) \,dS = A S^{-\beta }\, dS. \end{equation} \tag{ 3 }$$

On comparison with Equation (2), β = 1 + α. We maximize the log likelihood function

$$\begin{equation} \mathcal {L}= \sum ^n_{i=1} \ln P(F_i,\sigma _i), \end{equation} \tag{ 4 }$$

where the distribution of our measured values of flux and error (F_i, σ_i) is given by

$$\begin{equation} P(F_i,\sigma _i) = \frac{\int _0^\infty P(F_i,\sigma _i | S)\: P(S) \,dS}{\int _{F_{\rm min}}^\infty \int _0^\infty P(F_i,\sigma _i | S)\: P(S) \,dS\,dF}. \end{equation} \tag{ 5 }$$

A more detailed account of this method, and its variants, can be found in Temple et al. (2005).

Assuming the errors in measuring flux and luminosity are distributed as a Gaussian, and that the minimum measured flux F_min is the flux of the faintest source (as quoted above) in each observation, we numerically find the value of β (thus α) for which $\mathcal {L}$ in Equation (4) is maximum, individually for both observations.

The ACIS-I data (the red histogram in Figure 10) give the slope of the cumulative LF α = 1.14 ± 0.03, and the ACIS-S data (blue histogram) yields α = 1.19 ± 0.03, which are consistent with each other within errors. From samples of four and 14 early-type galaxies Gilfanov (2004) and Kim & Fabbiano (2004), respectively, found point-source LF slopes in the range α= 0.6–1.2; our values for NGC 4636 are at the higher end of this range.

It is well known that a significant fraction of LMXBs in the Milky Way and elsewhere is associated with globular clusters. In the Milky Way, ∼10% of all bright (>10³⁶ erg s⁻¹) LMXBs are found in globular clusters (GCs), even though GCs account for <10⁻³ of the stellar mass of the galaxy (e.g., Katz 1975; Clark 1975; Grindlay 1993). This has led to the suggestion that LMXBs are very close binary systems formed as a result of dissipative two-body or three-body encounters. This could be in the form of encounters between neutron stars and ordinary stars, which are more likely in the dense cluster cores (Fabian et al. 1975; Hut et al. 1992), or the exchange of a companion, where a compact object replaces a member of a binary in a three-body interaction (Clark 1975; Hills 1976). Indeed, it has been suggested that LMXBs are formed primarily in the cores of globular clusters, and some of the resulting binaries are later ejected from their host clusters (White et al. 2002). If so, one expects the LMXB population in a galaxy to be a good tracer of globular clusters. Alternatively, a significant fraction of the LMXBs could have formed in the field, possibly as part of the last major star formation episode of the galaxy (Irwin 2005, Juett 2005), in which case the populations of GCs and LMXBs need not be strongly correlated.

In early-type galaxies, Chandra observations show that there is an association of LMXBs with globular clusters. The fraction of LMXBs identified with known GCs varies from at least 20% in the Virgo elliptical NGC 4697 (Sarazin et al. 2001) to up to 70% in NGC 1399, the central galaxy of the Fornax cluster (Angelini et al. 2001). Furthermore, it is observed that the LMXBs in early-type galaxies are greater than three times more likely to be in the redder globular clusters, for galaxies which exhibit bimodality in color of the GCs, e.g., M87, Jordán et al. (2004); NGC 4472, Kundu et al. (2002); more recently in 10 others; Kundu et al. (2007); Sivakoff et al. (2007); Cen A (NGC 5128), Minniti et al. (2004); Jordán et al. (2007); Woodley et al. (2008); NGC 3379, Brassington et al. (2008). Since the redder GCs are relatively more metal-rich (e.g., Kundu & Zepf 2007), this can be a diagnostic of the characteristics of the compact object's companion star in the LMXB, and its history of formation (Maccarone et al. 2004; Ivanova 2006). However, this could also result from systematic variation in the initial mass function (IMF) of the GCs (Grindlay 1987), a possibility that has not been observationally explored, but could give rise to the same effect, independent of the nature of the companions.

We matched our list of X-ray point sources with the list of globular cluster candidates, from the study of Dirsch et al. (2005), which uses a deep mosaic CCD observation using the CTIO Blanco telescope. The photometry is available in the Washington C and Kron-Cousins R system. Of the optical point sources listed in this work which extend over an area of 0.25 deg² around the galaxy, we chose the sources with magnitude R < 23.5 and color 0 < C − R < 2.5 as globular cluster candidates. These are not spectroscopically confirmed to be globular clusters belonging to the galaxy. Figure 11 shows the distribution of both X-ray and optical point sources, together with other background sources that are known in the field. In a more recent paper, the group responsible for the original list has published spectral observations of a small subset of 200 of the original list of GC candidates (Schuberth et al. 2006). Of the sources with magnitude R < 23.5 and color 0 < C − R < 2.5, greater than 80% of the candidates were found to be globular clusters from measured redshift and the rest foreground stars.

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The positions of both X-ray and optical sources are known to an accuracy of better than an arcsecond. We matched the two lists by taking each X-ray point source, and finding its offset from the nearest GC candidate. We checked for systematic translation and rotation between the two lists by seeking to maximize the matches for small values of rotation and translation of all sources, but could not improve upon the matching done above. Based on the distribution of offsets, we chose to limit the search radius to 15. If two GC candidates fell within this radius, we assigned the X-ray source to the nearer one in angular distance. Of the 318 sources in our list, 77 were matched to globular cluster candidates. These sources are marked "GC" in the last column of Table 2 and are listed separately in Table 3. Of these 77 matched point sources, 48 lie within 15 < r < 60 of the center of NGC 4636 and have more than 10 net counts in either of the ACIS-S or combined ACIS-I observations. Based on the number of X-ray sources and GC candidates in this annulus, we expect only three chance coincidences. No other known background sources from NED were matched with X-ray sources within 10' of the center of the galaxy.

A C − R color histogram of globular cluster candidates is shown in the top panel of Figure 12 (dashed histogram). As in many other early-type galaxies, the distribution of the colors of candidate globular clusters here is bimodel. Dirsch et al. (2005) fit a two-Gaussian model to their color distribution, and find that the two peaks are at C − R = 1.28 and 1.77, with the intervening minimum occurring at C − R = 1.5. We adopt these values, and here refer to those with C − R>1.5 as the "redder" GCs, and the rest, the "bluer" ones. Of the 48 matched GCs between 15–60 of the galactic center, 13 have colors between 0.85 ⩽ C − R < 1.5, and 30 have colors C − R ⩾ 1.5, so 70% of the matched GCs in Figure 12 with colors between 0.8 and 2.5 are in the redder category.

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The difference in color between the two populations is predominantly due to a difference in metal abundance, since for stellar populations that are more than a few Gyr old, the optical colors would be more sensitive to the [Fe/H] index than to age (e.g., Worthey 1994; Bruzual & Charlot 1993). In NGC 4636, even though bluer GCs are more abundant, a majority of the X-ray point sources (LMXBs) are associated with the redder GCs (those of near-solar abundance), as is shown by the solid histogram in the left panel of Figure 12, which represents the color distribution of the GCs matched with X-ray point sources. A similar association has been reported for other nearby early-type galaxies (Kundu et al. 2002; Jordán et al. 2004; Kim et al. 2006; Kundu et al. 2007; Sivakoff et al. 2007). This is also consistent with the observation that most LMXBs associated with GCs in the Galaxy and M31 lie in those systems with a near-solar abundance (Grindlay 1993; Bellazzini et al. 1995; Bregman et al. 2006).

Other studies have found that X-ray point sources are preferentially found in optically more luminous globular clusters (Angelini et al. 2001; Sarazin et al. 2003; Kundu et al. 2002; Jordán et al. 2004; Kim et al. 2006; Xu et al. 2005). GCs containing LMXBs also have been noted to be significantly denser in the Galaxy and in M31 (e.g., Bellazzini et al. 1995). Since the mean size of a GC does not significantly vary with luminosity (McLaughlin 2000), more luminous GCs can be expected to be denser, and such a correlation can result from the higher density of potential companion stars in such systems. In the lower panel of Figure 12, we show the distribution of all GC candidates 1.5' < r < 6' from the center of NGC 4636 (dashed histogram), plotted along with those that match with X-ray point sources (solid histogram). The dotted line shows the ratio of matched to total GC candidates as a function of R magnitude. This ratio declines toward fainter GCs, indicating that the probability of a GC containing an LMXB is proportional to its luminosity, consistent with other studies (e.g., Sarazin et al. 2003; Jordán et al. 2004; Sivakoff et al. 2007; Woodley et al. 2008).

In Figure 13, we plot the apparent magnitude and color of the host globular clusters against the X-ray luminosity of the matched X-ray point sources. These plots indicate that the X-ray luminosity of the matched point sources does not depend on the color or absolute luminosity of the host GCs, which agrees with earlier work noted above. Together with the previous observation, this should be a useful constraint on the formation process of LMXBs in globular clusters.

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Finally, we compare the LF of the X-ray point sources matched with globular cluster candidates to the LF of those that are not matched with any optical source. Here, we study only the point sources within 15 < r < 60 of the center of NGC 4636, where the X-ray sources are not seriously contaminated by background AGNs (see Figure 3). In Figure 14, we plot the LFs of GC-matched and non-GC-matched X-ray point sources. The two plots represent X-ray luminosities obtained from two different epochs of observations, to account for the possible change in LF due to long-term variability in these sources. The solid histogram shows the LF of the matched point sources, and the dashed histogram is the LF of all X-ray point sources that did not match a GC candidate. Note that the brightest X-ray sources are not matched with any GC candidate. In both cases, the slopes of the LFs of the GC sources and non-GC sources in the range 1.8 × 10³⁷ erg s⁻¹ ⩽ L_x ⩽ 1 × 10³⁸ erg s⁻¹ match within 2σ. For the ACIS-S observation, from a K–S test, the probability that the two samples are drawn from the same population is 78%, whereas for the ACIS-I samples, the corresponding value is 50%, with the maximum deviation occurring at the faint end in both cases. We note that the K–S test underestimates this probability for discrete distributions (see, for example, Sheskin 2003). At the faint end of the LF, there is emerging evidence, from nearby galaxies like Cen A (NGC 5128) where more complete samples of fainter sources can be studied, that there are fewer X-ray faint sources found in GCs than X-ray bright ones (e.g., Woodley et al. 2008). We see perhaps some evidence for a dearth of GC matches at lower luminosities in the ACIS-I LFs (Figure 14, bottom panel).

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3.6.1. Galactic Nucleus

3.6.2. Additional Black Hole Candidates

3.6.3. SN 1939A

3.6.4. Bursting X-Ray Source

A light curve for the bursting X-ray source, detected at α(J2000) = 1908825, δ(J2000) = 26190, is shown in Figure 9. The matching source (08 away) in the 2MASS All-Sky Catalog of Point Sources, 2MASS J12433175+0237080 (α(J2000) = 190882303, δ(J2000) = 2618898) has J, H, and K-band magnitudes of 10.139 ± 0.032, 9.485 ± 0.03, and 9.293 ± 0.028, respectively (Skrutskie et al. 2006). From the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we get g and r-band magnitudes of 13.92 ± 0.01 and 14.83 ± 0.01, respectively, for matching source SDSS J124331.75+023708.0 (α(J2000) = 1908823016, δ(J2000) = 261889293, separation = 08) (Adelman-McCarthy et al. 2008). Based on the source's optical and infrared brightness and its large distance from the center of the galaxy (113), it is most likely not a member of NGC 4636, but is probably a relatively nearby flare star in our Galaxy.

Figure 15 shows hard and soft band light curves for this source from the ACIS-S observation. No hard (2–6 keV) counts are detected above the background prior to the burst.

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