Dynamical Formation Channels for Fast Radio Bursts in Globular Clusters

Fast radio bursts (FRBs) are bright flares of coherent radio emission with millisecond durations and large dispersion measures (DMs) that imply extragalactic origin (e.g., Lorimer et al. 2007; Keane et al. 2012; Thornton et al. 2013; Cordes & Chatterjee 2019). A fraction of FRBs have been observed to repeat (e.g., Spitler et al. 2016; CHIME/FRB Collaboration et al. 2019), indicating that cataclysmic models can be ruled out for at least a subset of FRBs. Perhaps the most popular model for repeating FRBs is bursts generated by young flaring magnetars (e.g., Popov & Postnov 2013; Kulkarni et al. 2014; Lu & Kumar 2016; Metzger et al. 2017). The recent detection of an FRB-like burst coincident with the Galactic magnetar SGR 1935+2154 (Bochenek et al. 2020; CHIME/FRB Collaboration et al. 2020) provides clear evidence that at least some FRBs are magnetar-powered. Magnetars are traditionally expected to form in association with massive stellar evolution, for instance in connection with standard core-collapse supernovae (SNe), superluminous SNe, and/or long gamma-ray bursts (e.g., Nicholl et al. 2017), in part due to the association of a number of Galactic magnetars with SN remnants (e.g., Kaspi & Beloborodov 2017).

The recently discovered repeating FRB 20200120E (Bhardwaj et al. 2021) was localized to an old (t ∼ 10 Gyr) globular cluster (GC) in M81 (Kirsten et al. 2021). In a present-day GC, neutron stars (NSs)/magnetars formed in association with massive star evolution have been inactive for billions of years. Thus, standard magnetized NS progenitor models cannot explain this source.

Due to their high stellar densities, GCs are efficient factories of various high-energy sources including X-ray binaries (e.g., Clark 1975; Katz 1975), millisecond pulsars (MSPs; e.g., Ransom 2008), cataclysmic variables (e.g., Grindlay et al. 1995), and gravitational wave (GW) sources (e.g., Rodriguez et al. 2016). Recent work shows the central regions of core-collapsed GCs are dominated by dynamically active massive white dwarfs (WDs) and NSs (e.g., Ye et al. 2019; Kremer et al. 2020, 2021; Vitral & Mamon 2021; Rui et al. 2021b). In addition to the well-observed MSP population in GCs, four young pulsars (with estimated ages ≲ 100 Myr) are observed in Galactic GCs, suggesting that young NSs are formed at late times in GCs through some mechanism (e.g., Tauris et al. 2013; Boyles et al. 2011). Binary WD mergers (e.g., King et al. 2001; Schwab et al. 2016; Kremer et al. 2021), accretion-induced collapse (AIC) of WDs in binaries (e.g., Nomoto & Kondo 1991; Tauris et al. 2013), binary NS mergers (e.g., Rosswog et al. 2003; Giacomazzo & Perna 2013), and/or NS–WD mergers (e.g., Liu 2018; Zhong & Dai 2020) may all lead to young NS formation in clusters. Thus, a number of scenarios may operate in GCs that could produce a progenitor of the M81 FRB.

In this Letter, we explore channels through which FRB-emitting objects may form in GCs. In Section 2, we describe the N-body simulations used for this study. In Section 3, we calculate the rate of young NS formation through various mechanisms in old GCs using a suite of N-body cluster models and compare to the inferred rate from the M81 FRB. In Section 4, we discuss energetics and explore whether the properties of the M81 FRB can be reasonably reproduced by these young NSs. In Section 5, we discuss the specific case of millisecond pulsars and X-ray binaries. We summarize our results and conclude in Section 6.

To model GCs, we use the N-body simulations from Kremer et al. (2021) computed with the cluster dynamics code CMC (Kremer et al. 2020; Rodriguez et al. 2021). CMC is a star-by-star Hénon-type (Hénon 1971) Monte Carlo integrator that includes all relevant physics for modeling the formation/evolution of compact objects in dense stellar clusters including two-body relaxation, direct integration of 3/4 body resonant encounters, and cluster evolution within a galactic tidal field. CMC uses the COSMIC population synthesis code (Breivik et al. 2020) to model stellar and binary evolution, which includes prescriptions for formation of MSPs (Ye et al. 2019).

The cluster models of Kremer et al. (2021; 18 models total) are tuned specifically to core-collapsed GCs. As shown in Ye et al. (2019, 2020) and Kremer et al. (2020, 2021), core-collapsed clusters are ideal environments for dynamical interactions of WDs and NSs at late times. The most obvious reason is that core-collapsed clusters generally have the highest central densities (e.g., Harris 1996). Also, because the process of cluster core collapse is connected to the dynamical depletion of stellar-mass black holes (BHs; e.g., Kremer et al. 2018), massive WDs and NSs are expected to be the most massive objects in core-collapsed clusters, enabling WDs/NSs to efficiently mass-segregate to the cluster center (e.g., Kremer et al. 2020). Observational evidence suggests that core-collapsed clusters host dense subsystems of massive WDs and NSs in their central regions (Kremer et al. 2021; Vitral & Mamon 2021; Rui et al. 2021b). In Table 1, we list basic properties of various stellar populations in our cluster models.

To estimate the rate of a given event in old GCs, we use the following procedure. First, we count the total number of occurrences of the given event in our models at late times (t > 9 Gyr) representative of the ages of the GCs in the Milky Way (e.g., Harris 1996) and also consistent with the age estimates for the M81 FRB's host cluster (Kirsten et al. 2021). The total rate per core-collapsed cluster can then be estimated simply as the total number of events divided by Δt = 5 Gyr (and divided by the total number of models). Because these models are roughly half the mass of typical GCs in the Milky Way, we multiply by an additional factor of two (Kremer et al. 2021). To estimate the local universe volumetric rate, we use an average volumetric number density of clusters of 3 Mpc⁻³ (e.g., Portegies Zwart & Mcmillan 2000; Rodriguez et al. 2015) and assume that roughly 20% of GCs have undergone core collapse, which is consistent with the fraction in the Milky Way (e.g., Harris 1996). Note these last two factors are uncertain (although not likely by more than a small factor). Thus, our model-inferred rates can be viewed with a factor of a few uncertainty.

M81 is expected to host roughly 200–500 GCs (Perelmuter & Racine 1995; Chandar et al. 2004; a factor of a few more than the Milky Way) with mean metallicity [Fe/H] = − 1.48 ± 0.19 (Perelmuter et al. 1995; comparable to the Galactic GCs). Thus, the Kremer et al. (2021) models reasonably capture the properties of the M81 GCs.

The single repeating FRB in M81 detected at a distance of 3.6 Mpc implies a volumetric density of at least n_FRB ≈ 5 × 10⁶ Gpc⁻³. The formation rate for the source of the M81 FRB can then be inferred as

$$\begin{eqnarray}\,\begin{array}{rcl}{{ \mathcal R }}_{\mathrm{src}} & \approx & 50\left(\displaystyle \frac{{n}_{\mathrm{FRB}}}{5\times {10}^{6}\,{\mathrm{Gpc}}^{-3}}\right)\\ & & \times \,{\left(\displaystyle \frac{\tau }{{10}^{5}\,\mathrm{yr}}\right)}^{-1}\left(\displaystyle \frac{1}{{f}_{v}\zeta }\right){\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1},\end{array}\,\end{eqnarray} \tag{ 1 }$$

where τ is the lifetime of the FRB source, f_v is the visibility fraction (the chance of seeing a burst from the source, which is related to the beaming factor, luminosity function, etc.), and ζ is the duty cycle (the fraction of time a source is actively producing bursts similar to the M81 FRB during its lifetime). Any viable formation channel for producing the M81 FRB must create FRB sources at a rate comparable to ${{ \mathcal R }}_{\mathrm{src}}$.

In the following subsections, we summarize each of the FRB progenitor channels that we consider in this work. As a reference, their rates that we calculate using N-body simulations are summarized in Table 2. Dividing the volumetric rate by n_FRB, we derive the active FRB lifetime required for each channel to reproduce the M81 FRB (summarized in the last column of Table 2). This timescale is an important constraint on the properties of the NSs produced from any of these channels.

Table 2. Formation Rates for Several Proposed FRB Progenitors in GCs

Event Type	Total # in Models	Rate per CC GC	Volumetric Rate	Active Lifetime Required (τ)
		(yr−1)	(Gpc−3yr−1)	($\times {({f}_{v}\zeta )}^{-1}$)
Super-Chandrasekhar WD+WD mergers	283	6 × 10−9	4	106 yr
(estimate including tidal capture)	⋯	7 × 10−8	45	105 yr
WD+NS mergers	59	10−9	0.8	6 × 106 yr
(estimate including tidal capture)	⋯	10−8	6	8 × 105 yr
NS+NS mergers	6	10−10	0.08	6 × 107 yr
AIC from binary RLO	21	5 × 10−10	0.3	2 × 107 yr
WD+MS collisions (MWD > 1.2 M⊙)	1098	2 × 10−8	15	3 × 105 yr
NS+MS collisions	301	7 × 10−9	4	106 yr
Inferred rate for M81 FRB	⋯	⋯	≈ 5 × 106/τ	⋯

Note. Rates for a number of events occurring in dense star clusters that may produce objects that could power FRBs. We show the rate per core-collapsed GC and the inferred volumetric rate in the local universe (assuming a GC number density of 3 Mpc⁻³ and assuming that 20% of GCs have undergone core collapse, consistent with core-collapsed fraction in the Milky Way). These rates may be viewed as upper limits, as the exact fraction of these events leading to NS formation is uncertain. In the final column, we show the active lifetime required in order to reproduce the inferred rate of the M81 burst (scaled by the duty cycle ζ and visibility fraction f_v ).

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3.1. White Dwarf Mergers

3.2. White Dwarf–Neutron Star Mergers

3.3. Neutron Star Mergers

3.4. AIC from Binary Mass Transfer

3.5. Alternative Formation Channels

By adding the total burst fluence of 6.6 Jy ms for the M81 FRB (Table 1 of Bhardwaj et al. 2021) over CHIME's total on-source time of ≈ 100 hr, we estimate a time-averaged isotropic equivalent luminosity of $\langle \dot{E}\rangle \approx {10}^{29}{f}_{{\rm{r}}}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. ⁴ Here f_r is the highly uncertain efficiency factor for creating coherent radio emission. The total energy required to supply the bursting activity for time τ ≈ 10⁵ yr is then ${E}_{\mathrm{FRB},\mathrm{tot}}\approx 5\times {10}^{41}{f}_{{\rm{r}}}^{-1}\,\mathrm{erg}$. Energy emission from NSs can be broadly divided into two categories: magnetically powered and rotation powered. We consider each in turn next.

In the magnetically powered scenario, the intrinsic energy budget is estimated as ${E}_{\mathrm{mag}}\approx ({B}_{\mathrm{NS}}^{2}{R}_{\mathrm{NS}}^{3}$)/6. As in Beloborodov & Li (2016) and Margalit et al. (2019), we estimate the magnetic activity timescale in the modified Urca case as

$$\begin{eqnarray}&&{\tau }_{\mathrm{mag}}\approx 2\times {10}^{5}{\left(\displaystyle \frac{{B}_{\mathrm{NS}}}{{10}^{14}\,{\rm{G}}}\right)}^{-1.2}{\left(\displaystyle \frac{L}{{10}^{5}\,\mathrm{cm}}\right)}^{1.6}\mathrm{yr},\end{eqnarray} \tag{ 2 }$$

assuming δ B ∼ B/2 as the amplitude of magnetic field fluctuations over an (uncertain) length-scale L within the NS core. In this case, the characteristic luminosity from magnetic activity is

$$\begin{eqnarray}&&\langle {\dot{E}}_{\mathrm{mag}}\rangle \approx {E}_{\mathrm{mag}}/{\tau }_{\mathrm{mag}}\approx 3\times {10}^{32}{\left(\displaystyle \frac{{B}_{\mathrm{NS}}}{{10}^{14}\,{\rm{G}}}\right)}^{3.2}\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 3 }$$

By combining Equations (2) and (3) with the inferred time-averaged luminosity, we find radio emission efficiencies of f_r ≳ 10⁻⁴ (and field strengths of roughly 2 × 10¹⁴ G) are required to produce active lifetimes, τ_mag ≈ 10⁵ yr, necessary to explain the FRB event rate for the young NS formation scenarios discussed in Section 3. Although highly uncertain, radio emission efficiencies this high have been demonstrated by some FRB models (e.g., Plotnikov & Sironi 2019; Lu et al. 2020).

In the rotation-power scenario, the intrinsic energy budget is simply the rotational energy of the NS: ${E}_{\mathrm{rot}}\approx 2{\pi }^{2}{{IP}}_{\mathrm{NS}}^{-2}$ where I ≈ (2/5)MR² is the moment of inertia of the NS and P_NS is the NS spin period. The characteristic spin-down timescale of a magnetic dipole is

$$\begin{eqnarray}&&{\tau }_{\mathrm{sd}}\approx \displaystyle \frac{P}{2\dot{P}}\approx 5\times {10}^{5}\,\mathrm{yr}{\left(\displaystyle \frac{{\text{}}{P}_{\mathrm{NS}}}{10\,\mathrm{ms}}\right)}^{2}{\left(\displaystyle \frac{{\text{}}{B}_{\mathrm{NS}}}{{10}^{11}\,{\rm{G}}}\right)}^{-2},\end{eqnarray} \tag{ 4 }$$

which yields a characteristic spin-down luminosity of

$$\begin{eqnarray}&&{\dot{E}}_{\mathrm{rot}}\approx {10}^{37}{\left(\displaystyle \frac{{\text{}}{B}_{\mathrm{NS}}}{{10}^{11}\,{\rm{G}}}\right)}^{2}{\left(\displaystyle \frac{{\text{}}{P}_{\mathrm{NS}}}{10\,\mathrm{ms}}\right)}^{-4}\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 5 }$$

For f_r ≳ 10⁻⁸, the spin-down luminosity is sufficient to supply the energy required to power the FRB for a τ_sd ≳ 10⁵ yr lifetime.

In Figure 1, we use a $P\dot{P}$ diagram to explore the range of NS properties required to produce the rates and energetics inferred for the M81 FRB. Using colored lines, we show the minimum active lifetime τ required for a young NS formed through the various channels discussed in Section 3 to produce the volumetric density of n_FRB = 5 × 10⁶ Gpc⁻³ inferred from the M81 FRB (assuming a duty cycle and f_v of order unity). The thick blue and green bands denote the range in timescales inferred for WD–WD and WD–NS mergers, respectively, reflecting the uncertainty in the contribution of tidal capture to the merger rate (as discussed in Section 3). Dark cyan and red curves show the inferred rates for AIC in binary systems and NS–NS mergers, respectively. As dashed black curves, we show the time-averaged isotropic equivalent luminosity for three different radio emission efficiency factors that bracket the large uncertainty in this parameter: f_r = 1 (as an unrealistic upper limit), f_r = 10⁻⁶ (representative of the efficiency inferred for the Galactic magnetar; CHIME/FRB Collaboration et al. 2020), and f_r = 10⁻⁸ (representative of highly inefficient radio emission as adopted in some previous studies; e.g., Lyubarsky 2014; Metzger et al. 2017). For reference, we also show using blue markers Galactic magnetars (blue stars), X-ray/γ-ray emitters (triangles), and standard radio pulsars (blue points; open circles indicate pulsars found in binary systems). See Manchester et al. (2005) and Olausen & Kaspi (2014) for further detail.

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Using a hatched gray band we show the range in magnetic field values required for a magnetically powered energy source for radio efficiencies ranging from f_r ≈ 10⁻⁴ (minimum required value corresponding to B ≈ 2 × 10¹⁴ G and τ_mag ≈ 10⁵ yr) to f_r ≈ 10⁻³ (corresponding to B ≈ 7 × 10¹³ G and τ_mag ≈ 3 × 10⁵ yr). As shown, a magnetically powered scenario would require a magnetic activity timescale in excess of the spin-down timescale (with the exception of objects with P_NS ≳ 10 s, which are disfavored by theoretical models; see Section 3). Furthermore, such magnetically powered sources must be physically distinct from the Galactic magnetars (Duncan & Thompson 1992), which have empirically constrained lifetimes ≲10⁴yr (Kaspi & Beloborodov 2017); these are too small to explain the inferred rate of the M81 FRB for any of the young NS formation channels described here (see Table 2).

The intersection between the bold dashed lines and colored lines indicate regions of parameter space that reproduce the rate and energetics of the M81 FRB for a spin-down powered source. Therefore, these regions also imply allowable magnetic field ($B\propto \sqrt{P\dot{P}}$) for the M81 progenitor. This shows that highly magnetized NSs (B ≳ 5 × 10¹⁴ G) with spin-down timescales ≲10⁴yr, can likely be ruled out based on rate arguments alone, as the active lifetimes of these objects are too small. Additionally, unless NS–NS mergers produce NS remnants with lifetimes ≳10⁸yr (high unlikely; e.g., Piro et al. 2017), the binary NS merger scenario can likely also be ruled out by the rate alone.

For radio emission efficiencies f_r ≲ 10⁻⁶, WD–WD mergers, WD–NS mergers and AIC in a binary system all appear viable for the rotation-powered scenario, provided these channels can produce NSs with magnetic fields strengths in the range ≈ 10¹¹–10¹² G and spin periods in the range ≈10–100 ms. Intriguingly, these properties are comparable to those predicted for NS remnants formed through WD mergers (see Section 3.1). In principle, the WD–MS and NS–MS collision scenarios are plausible based on the rates and energetics; however, more detailed simulations are required to test whether or not these events may lead to magnetized/spinning NS remnants.

The region of the $P\dot{P}$ diagram occupied by young NSs with required properties for the M81 FRB is near the region occupied by Galactic pulsars (particularly for f_r ≳ 10⁻⁶), most of which are associated with SN remnants and therefore likely formed through core collapse. The core-collapse SN rate (roughly 10⁵ Gpc⁻³ yr⁻¹; e.g., Taylor et al. 2014) is substantially higher than the NS formation rate in old GCs. In this case, a factor of ≳1000 more FRBs similar to the M81 burst would be produced by the spin-down luminosity powered pulsar population in the galactic field. Unless there is a yet-understood mechanism that may prevent NSs in the field from emitting FRBs but that does not operate in GCs, this implies a spin-down-powered model with radio efficiency factor ≲10⁻⁷ may be necessary. In this case, the NS properties required to explain the rate and energetics occupy a region of parameter space comfortably unique from any of the known Galactic radio sources.

We have assumed in Figure 1 that the duty cycle ζ to flare as a repeating FRB similar to the M81 source is of order unity. Although the exact duty cycle is highly uncertain, this is likely an optimistic assumption. As shown in Equation (1), lower duty cycles would require larger active lifetimes. We have also assumed f_v of order unity, also an optimistic choice. For instance, some studies argue a beaming factor f_v ≈ 0.1 (consistent with the value expected for pulsars; Tauris & Manchester 1998) may be more appropriate. If for instance we adopt f_v ≈ 0.1 and ζ ≈ 0.1 (as in, e.g., Nicholl et al. 2017), the binary AIC channel and WD–NS merger scenarios may be ruled out, as NSs with lifetimes in excess of roughly 10⁸ yr would be required to reproduce the inferred rate, in tension with values predicted from simulations. In this case, WD–WD mergers (especially invoking the tidal capture scenario discussed in Section 3.1) may be the only viable young NS scenario, assuming NSs with active lifetimes ≳10⁶ yr can be produced.

We use time-average luminosity in this Letter, as it gives a lower limit on the energy reservoir required to supply the bursting activity over the source lifetime. Note that the peak luminosity of some of the bright bursts from this source (${\dot{E}}_{\mathrm{peak}}\approx {10}^{39}{f}_{{\rm{r}}}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1};$ Majid et al. 2021) may be larger than the expected spin-down luminosities invoked to power the source (∼10³⁷ erg s⁻¹). However, this can be reconciled with a Doppler beaming, where the luminosity per solid angle is boosted by the Lorentz factor γ⁴ in the observed frame relative to the inertial frame. This process requires that the emission region be smaller than the relativistic beaming angle, similar to what has been invoked to explain observations of the Crab pulsar (Bij et al. 2021). With γ ≳ 10 (minimum requirement for FRBs from curvature radiation models; e.g., Kumar et al. 2017; Katz 2020), the rest-frame peak luminosity will be below the spin-down luminosity. The time-average luminosity would average over instances when the relativistic beaming is pointed away from us.

GCs are well known to efficiently create MSPs (e.g., Ransom 2008). MSPs are expected to form in GCs when NS binaries (either primordial binaries or binaries assembled dynamically through exchange encounters) are driven to mass transfer through a combination of stellar evolution of the companion and hardening by repeated fly-by encounters in the cluster (e.g., Pooley et al. 2003; Ivanova et al. 2008; Ye et al. 2019). To date, roughly 200 MSPs have been observed in 36 Galactic GCs ⁵ . In our cluster models, we identify 105 total MSPs (defined as spin periods less than 30 ms and formed through binary mass transfer channels similar to those described in Ye et al. 2019), or roughly six MSPs per cluster, which is consistent with the 200/36 ≈ five MSPs per cluster one can infer from the observed population.

Given the well-observed abundance of MSPs in GCs, one may ask if these objects may plausibly explain the M81 FRB. Unlike the scenarios discussed in Section 3, the formation rates and spin-down timescales of MSPs in clusters are relatively well understood from the actual observed populations. Thus for the MSP scenario, we can constrain empirically the radio efficiency and duty cycle required to explain the observed FRB.

The relatively low magnetic fields and high spin periods imply low spin-down rates for MSPs and long lifetimes τ_sd ≈ 10¹⁰ yr. The spin-down luminosity of a typical MSP (assuming P = 3 ms and B = 5 × 10⁸ G) is roughly 4 × 10³⁴ erg s⁻¹ (Equation (5)). Thus, the roughly ${10}^{29}{f}_{{\rm{r}}}^{-1}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ time-averaged luminosity inferred for the M81 FRB can be reproduced for radio emission efficiencies f_r ≳ 10⁻⁶. From a rates perspective, assuming roughly 5–10 MSPs per cluster, we can estimate an MSP volumetric density of roughly 10¹⁰ Gpc⁻³ in GCs in the local universe. Thus, MSPs could explain the density of repeating FRBs inferred from the M81 burst ( ≈ 5 × 10⁶ Gpc⁻³) if the duty cycle for MSPs to produce repeating FRBs similar to the observed burst is roughly 10⁻⁴. Thus (pending the uncertain details of radio efficiency and duty cycle which future studies may elucidate), we conclude a MSP could reasonably explain the M81 FRB.

Recent studies have suggested that accretion-powered stellar-mass compact objects could also be viable (repeating) FRB sources, for instance as generated by plasmoids ejected from the accretion funnel (Sridhar et al. 2021; Lu et al. 2021). In particular, NS X-ray binaries (the expected progenitors of MSPs; e.g., Alpar et al. 1982) may be relevant in the GC context, as these systems are observed in abundance in GCs (e.g., Clark 1975; Heinke 2010). ⁶ Theory and observations (e.g., Heinke et al. 2003; Ivanova et al. 2008) suggest an average of ∼1–10 NS X-ray binaries per typical GC (in our models, we find roughly one accreting NS binary per model at late times), implying a volumetric density ≳10⁹ Gpc⁻³ in clusters. Thus, similar to the MSP scenario, X-ray binaries are likely only viable progenitors if their duty cycles for bursts similar to the M81 FRB are small.

In old GCs, various dynamical scenarios create NSs that may plausibly power FRBs similar to the repeating FRB observed in M81. Using a suite of N-body cluster models, we have shown that WD–WD mergers, WD–NS mergers, and AIC of WDs in binary systems are all plausible candidates, assuming visibility fraction and duty cycles for repeating FRB emission of order unity. For less optimistic choices of visibility fraction and duty cycle, WD–WD mergers are likely the only scenario that may yield a sufficiently high rate.

We consider two energy emission mechanisms. We show a magnetically powered source (e.g., a magnetar) may be viable for f_r ≳ 10⁻⁴. These objects would have to be distinct from the magnetars observed in the Milky Way, which have empirically constrained lifetimes ≲10⁴ yr, too short to explain the inferred event rate of the M81 FRB. Additionally, the magnetic activity lifetimes of these magnetically powered objects would need to exceed their spin-down lifetimes. Alternatively, if magnetic fields strengths of ≈10¹¹ G and spin periods of ≈10 ms can be produced (consistent with those predicted from WD merger models; e.g., Schwab 2021), rotation-powered NS remnants formed through these scenarios can plausibly explain both the rate and burst energetics inferred from the M81 FRB. WD–MS collisions and NS–MS collisions occur at a high enough rates to also be viable progenitors, although whether or not a rapidly spinning and/or highly magnetized NS may be produced in these scenarios is less certain. The relatively low event rate of NS–NS mergers implies this channel is a less likely scenario. In addition to the young NS scenario, we also showed that recycled MSPs with spin-down times of ≳10¹⁰ yr as well as X-ray binaries may be viable channels from a rates and energetics perspective.

If indeed MSPs and/or young NSs formed through the AIC/MIC of WDs provide a channel for FRBs in GCs, this FRB channel should operate similarly for analogous sources in the galactic field. The rate of AIC in the galactic field (through either stable accretion from a companion star or through the merger of a super-Chandrasekhar WD binary) is highly uncertain, with previous studies predicting rates in the range 0.1–10² Gpc⁻³ yr⁻¹ (e.g., Yungelson & Livio 1998; Fryer et al.1999; Tauris et al. 2013; Kwiatkowski 2015).

Additionally, the number of X-ray binaries per unit stellar mass is roughly a factor of 100–1000 times higher in GCs compared to the galactic field (e.g., Clark 1975). In the Milky Way, GCs constitute roughly 0.1% of the total Galactic stellar mass. This implies roughly a factor of 10 more MSPs/X-ray binaries (and therefore potential FRBs) in the field compared to clusters. The M81 FRB has the lowest extragalactic DM in the CHIME/FRB Collaboration catalog (Bhardwaj et al. 2021; The CHIME/FRB Collaboration et al. 2021). The low DM is critical to constraining the source distance and host association. Being offset from their host galaxies, GCs contribute relatively little host DM compared to galactic field environments. Therefore, roughly 10 more FRBs from galactic field environments at similar distances to M81 may simply have not yet been localized because of the relatively large host DM contribution. As more FRBs are localized to the fields and clusters of galaxies in the future, it will provide a better test of the progenitor scenario.

We have focused specifically on the possibility that the M81 FRB occurred in a core-collapsed GC. In non-core-collapsed clusters, the rates of the various formation scenarios summarized in Table 2, are roughly 10–100 times smaller (see, e.g., Kremer et al. 2020), due to the relatively low central densities facilitated by the presence of large numbers of stellar-mass BHs. Current observations place rough constraints on the total mass and metallicity of the host cluster for the M81 FRB (both consistent with the models adopted in this study); however, detailed features of the host (such as the density profile, core radius, etc.) are not constrained. Future observations may further constrain the FRB's host cluster, including whether or not the cluster is core collapsed.

We thank Sterl Phinney for discussions during the early stages of this work, Josiah Schwab for helpful feedback on the fate of white dwarf mergers and comments on the manuscript, Wenbin Lu, Ben Margalit, and Bing Zhang for useful discussions, and the anonymous referee for constructive comments and suggestion. K.K. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2001751.