Is the M81 Fast Radio Burst Host Globular Cluster Special?

The first two orbits of program 16,664 suffered a guide-star failure and guided on gyros only. As a result, only a subset of exposures from this visit was usable. We examined the calibrated, flat fielded charge-transfer efficiency corrected final data products files and retained only those images in which the FRB GC was detected. For F438W, these were iem701lxq and iem701lrq from Orbit 1, and iem751ibq and iem751i4q from Orbit 2 (2622 s total). For F606W, the usable images were iem701lvq from Orbit 1, iem751i9q from Orbit 2, and iem752u0q, iem752u1q, iem752u2q, and iem752u4q from Orbit 3 (4020 s total), and for F814W, iem701ltq in Orbit 1 and iem751i7q in Orbit 2 (1312 s total). The HST data can be found in MAST at doi:10.17909/vysd-m633.

We manually redrizzled the images using the DrizzlePac software (Hoffmann et al. 2021, stwcs Version 1.7.2, photutils Version 1.7.0), aligning the frames with tweakreg and verifying the shifts manually with IRAF (Tody 1986). In the F438W images, there were too few bright sources present in the field for the software to identify the offset, so we computed the shift manually with IRAF tasks and updated the headers. We drizzled the images with astrodrizzle, with the "minmed" combine type. A composite-color image of the HST data is presented in Figure 1.

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To determine the structural parameters of the cluster, we began by constructing an empirical point-spread function in F606W using three bright but unsaturated stars (confirmed as stars via Gaia Data Release 3, DR3). We then subsampled the point-spread function by a factor of 10. We carried out the King model fitting (King 1962) using this subsampled point-spread function and the ishape task in the baolab package 0.94.1 (Larsen 1999). We tried fitting radii of both 50 and 60 pixels, finding very similar results in each case. The specific results quoted below are for the 50 pixel case. We used the the WFC3 pixel scale of 00396 per pixel, ⁷ and the 3.6 Mpc distance to M81, resulting in a distance scale of 0.69 parsec per pixel.

When we fit for the cluster effective radius, we varied the value of the King model concentration parameter (defined as the ratio of the tidal radius to the core radius) using a finely spaced grid that ranged from c = 10 to 300 in steps of one. The best-fitting model has a concentration c = 53 and an effective radius r_h = 3.06 pc. As a King profile is completely specified by two parameters, such a fit implies a best-fitting projected core radius of r_c = 0.81 pc (Figure 2). All the models prefer slightly elliptical fits with a semiminor to semimajor axis ratio of about 0.92. The best-fitting model has a reduced χ² = 2.8, partially due to the presence of many resolved red giants and perhaps partially due to a minor background mismatch in the outer regions of the cluster, relevant given the large fitting radius of 50 pixels = 34.6 pc. Somewhat lower concentrations are possible, the model at c = 25 having a Δχ² ∼ 1, with a corresponding r_h = 2.84 pc and r_c = 1.08 pc.

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At the other end of the distribution, even very large concentrations of c = 300 or larger give formally reasonable fits with Δχ² < 1, but the best-fitting structural parameters for these models have large radii. For example, for c = 300, we find r_h = 5.30 pc, which would imply r_c = 0.62 pc and a tidal radius of 185 pc. Essentially, these fits place more light at large radii where it is poorly constrained by our observations. Solely considering these data, such models cannot be ruled out, but we also note that a similar combination of high concentration and large radius is essentially absent in the Galactic GC system (Djorgovski & Meylan 1994), while clusters with parameters close to our best-fit values are common.

Formally, we find an implied ${r}_{c}={0.81}_{-0.19}^{+0.27}$ pc. An r_h < 2.8 pc is ruled out even in low-concentration models, but as discussed above, models with high concentrations yield formally reasonable fits and have correspondingly larger values of r_h , in the range 5–6 pc. If the GCs around M81 are similar to those in the galaxy, these larger sizes are disfavored.

As many extragalactic studies assume a fixed concentration index of c = 30 (e.g., NH11), we also report parameters for this assumed value: r_h = 2.91 pc and the inferred r_c = 1.01 pc. Further comparisons in this paper to M81 GCs or Milky Way GCs also use this fixed c = 30 radius measurement.

2.1.1. FRB Offset from Cluster Center

We also measured the integrated magnitude of the candidate in the WFC3 F438W, F606W, and F814W images obtained by the HST 16,664 program following the photometric guidelines and calibrations recommended by the WFC3 data handbook (Sahu 2021). Formally the uncertainty in the photometry is as low as 0.001 mag in some filters. However, the FRB GC is resolved in the WFC3 images, with individual luminous stars associated with the cluster clearly distinguishable at some wavelengths. We measure the photometry at various radii out to 50 pixels in order to optimize the signal-to-noise ratio versus the flux, and estimate that the systematic uncertainty in the photometry is at least 0.02 mag. Using Vegamag zero points in order to be consistent with the ground based BVR observations we measure F438W = 20.75, F606W = 19.59, F814W =18.73 ± 0.02 mag, values generally consistent with those from previous works. The photometry of the FRB GC places the cluster securely within the expected magnitude and color range for a GC (e.g., Rhode & Zepf 2001). We do not expect that a stellar population analysis using this photometry would produce a meaningfully different inferred stellar mass or metallicity than previous work (e.g., Kirsten et al. 2022), though it could be illuminating to construct a color–magnitude diagram from the HST data in the future, an effort which is outside the scope of the present paper.

We compared the FRB GC optical absolute V magnitude (−8.19; this work), and half-light radius (2.91 pc for a King concentration of 30; this work) to a sample of 160 Galactic GCs from Baumgardt et al. (2020), and 210 M81 GCs from NH11. As shown in Figure 3, the FRB GC does not appear to be structurally exceptional.

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To estimate encounter rates for extragalactic GCs in M81, we use the proxy from Equation (5) of Sivakoff et al. (2007):

$$\begin{eqnarray}&&{{\rm{\Gamma }}}_{h}\equiv {\left(\displaystyle \frac{M}{2\pi {M}_{\odot }}\right)}^{\tfrac{3}{2}}{\left(\displaystyle \frac{{r}_{h}}{1{pc}}\right)}^{\tfrac{-5}{2}},\end{eqnarray} \tag{ 1 }$$

where M is the optical mass of the cluster, and r is the observed half-light radius.

Based on our updated measurements, and using the distance of 3.6 Mpc, the absolute V magnitude of the FRB GC is −8.19. We convert optical magnitude to cluster mass by adopting the median V magnitude GC mass-to-light-ratio of Galactic GCs (1.83; Baumgardt et al. 2020). Assuming a V magnitude of 4.81 for the Sun, we find the cluster mass of the FRB GC to be 2.9 ×10⁵ M_⊙. We perform the same conversion to the V magnitudes of the NH11 clusters.

We perform the same conversion to optical mass and encounter rate calculation using the Baumgardt et al. (2020) V magnitudes and half-light radii of Galactic GCs. We caution that this exercise is meant to demonstrate the encounter rates of Galactic GCs if they were observed in the M81 system. For ease of comparison, we normalize all estimated encounter rates to that of 47 Tuc, assuming Γ_47Tuc = 1000. As demonstrated in Figure 4, the FRB GC has an encounter rate that is ∼50% of that of 47 Tuc. This indicates that, in principle, a dynamical formation may be a plausible formation channel for the progenitor of FRB20200120E. However, we note that the comparison data that we are using—i.e., the measurements of Galactic GCs from a range of studies and data from extragalactic GCs that are derived from HST observations—have very different observational limits, selection biases, uncertainties, and contamination rates. Coupled with the differences in how cluster radii are estimated in these different data sets, comparisons of the absolute interaction rates of M81 and Milky Way GCs are subject to systematic uncertainties and should be considered indicative at best.

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Considering only the M81 GC candidates, we note that the effective radius of the FRB host is indistinguishable from the median of the sample, but the luminosity (mass) is ≈0.7 mag brighter than the peak of the GC luminosity function (Figure 3). It is this latter difference that manifests itself in Γ and suggests that the FRB resides in a GC that has a moderately higher interaction rate than the median (Figure 4). This is the consequence of an intriguing characteristic of GCs; the lack of a mass–radius relationship. This results in the stellar density and dynamical interaction rate in GCs to be strongly correlated to the mass of a cluster. A corollary to this feature is that the vast majority of dynamical interactions in GC systems occur in the most massive GCs. Therefore, the offset of the FRB GC from the median interaction rate hints at the possibility of the FRB being dynamically formed, but it is not conclusive.

We note that Kremer et al. (2021, 2023a) predict that white dwarf mergers should occur mainly in clusters undergoing core collapse or in the post-core-collapse phase. While our analysis does not allow us to determine whether the M81 FRB GC has reached core collapse, it is worth noting that the vast majority of post-core-collapse clusters in the Milky Way are located at small galactocentric distances (see, e.g., Chernoff & Djorgovski 1989; Djorgovski & Meylan 1994) and they are all closer to the Galactic center than the distance of the M81 FRB GC from the center of M81. Note that for the M81 FRB GC, 20.5 kpc is the projected galactocentric distance so the actual 3D distance is likely to be larger.

We also note that the FRB GC is located at a much larger galactocentric distance than the rest of the M81 sample and studies of the GC systems of the Milky Way and other Galaxies suggest a radial trend in GC sizes. A high-resolution survey of other clusters at the galactocentric distance of the FRB GC will help place the relative Γ of this GC and the importance of dynamical effects in better context.

While the FRB GC itself has been observed to show no evidence of X-ray emission (Pearlman et al. 2023), it is nevertheless worth comparing the cluster properties to those of other GCs in M81, which show X-ray emission, as bright X-ray activity from X-ray binaries can be transient. Several GCs in M81 are known to host X-ray binaries (Hunt et al. 2023). We crossmatched the NH11 GCs with the Chandra Source Catalog Version 2.1 (Evans et al. 2020), and found that 10 of the NH11 GCs have significant (at ≥3σ) X-ray counterparts detected by Chandra, with X-ray luminosities spanning from 2.0 × 10³⁷ erg s⁻¹ to 5.2 ×10³⁸ erg s⁻¹. We note that the majority (nine) of the X-ray hosting clusters are at projected distances within roughly 3 kpc of the galaxy center, and one is 11.1 kpc away.

The mean V magnitude for the entire NH11 sample is −7.0 mag, with a standard deviation of 1.4 mag. The mean half-light radius is 3.5 pc with a standard deviation of 2.5 pc. For the sample of NH11 GC candidates with X-ray counterparts, the mean V magnitude is −9.0 mag, with a 1.1 mag standard deviation. The mean half-light radius of the X-ray-detected NH11 GCs is 1.7 pc, with a standard deviation of 0.6 pc. While there is not a clear trend in absolute magnitude, beyond the FRB GC being on the faint end of the M81 X-ray binary hosting sample, it is clear that the X-ray detected GCs are on average more compact than the FRB GC.