The X-ray Point Source Population Hosted by Globular Clusters in the Elliptical Galaxy NGC 4261

We analyze the Chandra data using version 4.13 of the ciao ¹¹1https://cxc.cfa.harvard.edu/ciao/ software package and caldb version 4.9.6, reprocessing both observations with chandra_repro. We generate a list of X-ray point sources using the wavdetect algorithm, filtering each X-ray image with an exposure map centered at an energy of 2.3 keV and wavelet scales of 1.0, 2.0, 4.0, 8.0 and 16.0. The enclosed fraction count (e.c.f.) parameter is set to 0.3 arcseconds. We set the significance threshold parameter at $10^{-6}$, corresponding to about one false detection per chip.

This produces a total of 63 X-ray point sources in ObsID 834, and 60 sources in ObsID 9569. We then implement srcflux using the source positions from wavdetect with background regions generated from the roi²²2https://cxc.cfa.harvard.edu/ciao/ahelp/roi.html tool to measure the fluxes from the detected sources, assuming an absorbed power-law with a photon index of $\Gamma$= 1.7 and hydrogen column density³³3https://cxc.harvard.edu/toolkit/colden.jsp, $N_{H}$=$1.58\times 10^{20}$ cm².

ObsID 9569 was taken eight years after ObsID 834, and both cover the same central field. Therefore we are able to probe the time domain aspect of the GC X-ray sources. We estimate the limiting X-ray sensitivities in the 0.5-8.0 keV band for both observations, using pimms ⁴⁴4https://cxc.harvard.edu/toolkit/pimms.jsp. ObsID 834 has a limiting sensitivity around $3\times 10^{37}$ erg s^-1 ( $2.5\times 10^{-5}$ cts/sec) and the corresponding limit for ObsID 9569 is $\sim 1\times 10^{37}$ erg s^-1 ( $6.9\times 10^{-6}$ cts/sec).

After ensuring that both the X-ray and optical data are aligned in the same astrometric frame, we use the globular cluster catalogue from Bonfini et al. (2012) to search for globular cluster counterparts to the detected X-ray sources in both ObsID 834 and ObsID 9569. We use Topcat⁵⁵5http://www.star.bris.ac.uk/~mbt/topcat/ to cross match between the X-ray point sources and optically selected GCs, with a matching radius of up to 1$"$. This results in a total of 20 X-ray sources that are co-spatial with a GC. Of these, we classify two as GCULXs, which are also identified by Giordano et al. (2005). While our X-ray analysis of ObsID 834 recovers the same X-ray sources as Giordano et al. (2005) in the central regions, we do not recover sources in the galaxy outskirts, as we only match to the HST globular cluster catalogue of Bonfini et al. (2012).

We recover two of the Giordano et al. (2005) GCULXs in NGC 4261 across two Chandra observations (Table 1). Hereafter, we refer to them as GCULX1 and GCULX2. GCULX1 is brighter than $2\times 10^{39}$ erg s^-1 at both epochs while GCULX2 has a peak luminosity of $0.75\times 10^{39}$ erg s^-1 in the 0.5-8.0 keV band in the second epoch. Conducting a band conversion for the 0.2-10.0 keV range with $\Gamma=1.7$ brings the luminosity of GCULX2 to $10^{39}$ erg s^-1. Given that GCULX2 fits the nominal definition of a ULX in the 0.2-10.0 keV band, we include the source in the further analysis as a GCULX. We also detect eighteen X-ray sources coincident with GCs that have X-ray luminosity values on the order of $10^{38}$ erg s^-1 which are then classified as GCLMXBs.

Given that both Chandra observations have similar limiting sensitivities and both cover the HST field of view, we are able to track variability in the X-ray sources down to $\sim$ $3\times 10^{37}$ erg s^-1 over the eight year time span. Both of the GCULXs appear in ObsID 834 and 9569. The X-ray luminosity of GCULX1 is self-consistent (within errors) across the two observations. By contrast, GCULX2 shows a factor of two increase in luminosity. Although our analysis would not have classified it as a ULX in ObsID 834, it became bright enough that that it exceeds the $10^{39}$ erg s^-1 Eddington limit in ObsID 9569.

X-ray variability is an important diagnostic of the accretion behaviour of the systems, and also has important implications for fast radio bursts originating in globular clusters: studies such as Sridhar et al. (2021) favour ULXs as originators of fast radio bursts, but Kirsten et al. (2022) note that X-ray limits rule out persistent X-ray sources for the globular cluster fast radio burst population. These studies do not, however, rule out X-ray sources that vary by an order of magnitude. Many GCULXs do show significant order of magnitude variability, in particular the source RZ2109 which shows an order of magnitude variability on the scale of hours, as well as over many years (e.g. Maccarone et al. 2007; Dage et al. 2018). Past studies of GCULXs have catalogued several different modes of unusual behaviour in GCULXs (Shih et al., 2010; Dage et al., 2019a; Dage et al., 2020; Dage et al., 2021) and identified nine sources with no short/long-term variability (within uncertainties), eight more which vary over the course of many years but have no discernible variation within an observation (and have a 3 $\sigma$ upper limit on RMS variability, Dage et al. 2020), and three which show intra-observational variability (defined as the flux changing by at least a factor of two within an observation). One of these is a transient ULX which was observed by ROSAT in the late 1990s, and by Chandra until 2003, but never detected in subsequent observations (Shih et al., 2010).

Based on our analysis, NGC 4261 GCULX1 does not appear to vary in the observations at hand, but GCULX2 shows long-term variability. We did not detect significant intra-observational variability in either source, and used lcstats to place 3 $\sigma$ RMS upper limits of $\sim 30\%$ for the two ULXs in ObsID 834 and $\sim 60\%$ in ObsID 9569. Although these sources are quite rare, the variability paradigms suggest different accretion physics and binary properties across the entire sample of GCULXs studied to date.

When we examine the rest of the GCLMXBs, we find two in ObsID 9569 that were not detected, although both observations covered the same field, and we find four GCLMXBs that “shut off” in ObsID 9569. The rest of the LXMBs do not differ significantly within their measurement uncertainties (Table 2).

GCULX variability has important implications in other fields: for instance, the X-ray binary population in globular clusters can be used to characterise the low mass X-ray binary population (Gilfanov, 2004; Lehmer et al., 2010, 2020), which in turn has implications for classifying populations of black holes and AGN (Lemons et al., 2015). GCULXs pin down the end points of these functions, and their variability may cause additional scatter in the scaling relations beyond normal statistics, as suggested by the histogram of the GCLMXB X-ray luminosities across observations (Figure 2). Indeed, in the first observation of NGC 4261, GCULX2 barely meets the threshold for a ULX, whereas eight years later, it reached a luminosity where it is securely classified as a ULX. This suggests that in addition to finding GCLMXB populations in many galaxies to improve statistics, we need to consider the time variability of these X-ray sources when trying to accurately determine the GCLMXB X-ray luminosity function.

We use the relations of Jester et al. (2005) and Peacock et al. (2010) to convert the V and I optical magnitudes in Bonfini et al. (2012) to $g$ and $z$ magnitudes⁶⁶6($g-z$) = 1.518$\times$(V-I)-0.443 and $g$ =V+0.39$\times$($g-z$)-0.08, since the majority of the previously studied GCULXs have colours presented in the $g-z$ system. The colour-magnitude diagram of the globular clusters in NGC 4261 is presented in Figure 3. The mean GCLMXB colour is 1.35 $\pm$ 0.05, and the mean GCULX host cluster colour is 1.61 $\pm 0.2$ (see Table 3). We note that most of the GCLMXB-hosting globular clusters in NGC 4261 (Table 4) have redder optical colours, which is similar to the trend identified by Kundu et al. (2003), who found a GCLMXB mean colour of $g-z$ = 1.22 ⁷⁷7 Kundu et al. (2003) reports ¡V-I¿=1.10., with a three to one preference for redder GCs to host GCLMXBs. Dage et al. (2021) found that the host clusters of previously identified GCULXs spanned a wide range of optical colours. The mean colours of the entire cluster sample are displayed in Table 3.

An Anderson-Darling test comparing the optical properties of the 20 clusters in NGC 4261 which host GCLMXBs to the rest of the GCs gives a statistic of 0.008 and a significance level of 0.25 for optical colour, and a statistic of 7.8 and significance level of 0.001 for magnitude. This further suggests that the clusters which host GCLMXBs are distinct populations in magnitude at high significance ($>3\sigma$).

While Figure 3 appears to suggest that$-$ unlike previous studies of GCULXs$-$ NGC 4261’s ULXs do not appear to be preferentially hosted by brighter clusters, but do have metal-rich hosts these correlations should be considered with an abundance of caution due to the pecularities of the Hubble Space Telescope data set used in the optical analysis of Bonfini et al. (2012). The analysis is based on relatively shallow 800s snapshot data of each field for this distant galaxy at 32 Mpc. Furthermore, the HST observations were obtained in late 2007 and early 2008 when the WFPC2 camera aboard the HST was near its end of life and suffered from significant charge transfer efficiency loss (Dolphin, 2009), which adds to the uncertainties in photometric parameters. Figure 4 shows the colour magnitude diagram of the NGC 4261 ULX hosts compared to the other GCULXs as well as the globular cluster populations in all of the six previously studied galaxies. This suggests that there is indeed a large variance in the small population of GCULXs and their host clusters.

We find that the GCULXs in NGC 4261 are located close to the host galaxy centre (Figure 5). Of the previously studied GCULXs, 17 are located within two effective radii of their respective host galaxy centres, and only three sources are more distant. We compare the optical colour of the host clusters to the distance from galaxy centre in units of the effective radius of the galaxy, (as measured by Cappellari et al. 2013), and show these results in Figure 6.

The clusters that host ULXs span a wide range of optical colours, from very blue (metal-poor) to extremely very red (metal-rich), and there does not appear to be a significant trend between optical colour and spatial distance. However, we note that the clusters that are the most distant from their galaxy centres are also very blue. This is broadly consistent with what is expected for globular cluster populations of giant galaxies; i.e, blue globular clusters tend to have more extended radial distributions compared to redder populations (Brodie & Strader, 2006).