Host Galaxy Properties and Offset Distributions of Fast Radio Bursts: Implications for Their Progenitors

An FRB signal alone cannot directly establish the redshift of the source, and one relies on an association with a host galaxy for a precise measurement. To date and in this work, the association of the FRB with a host galaxy is primarily based on probabilistic arguments given their position relative to coincident or nearby galaxies. Following standard practice for other transients (e.g., Bloom et al. 2002; Blanchard et al. 2016, for GRBs), one may estimate the probability of a chance coincidence (P_chance) based on the angular offset, θ, of the FRB position from the galaxy centroid, the uncertainty of the FRB localization, and the galaxy's apparent magnitude. Further work may adopt additional properties and priors for establishing associations.

The derivation of P_chance is based on galaxy number counts and captures the fact that apparently faint galaxies are more common on the sky. We adopt the formalism developed by Bloom et al. (2002), derived from optical galaxy number counts (Hogg et al. 1997), which gives the number density of galaxies brighter than apparent r-band magnitude m_r (not taking into account clustering of galaxies), as

$$\begin{eqnarray}\begin{array}{rcl}{\rm{\Sigma }}(\leqslant {m}_{r}) & = & \displaystyle \frac{1}{{3600}^{2}\times 0.334\,{\mathrm{log}}_{e}(10)}\\ & & \times \ {10}^{0.334({m}_{r}-22.963)+4.320}\,{\mathrm{arcsec}}^{-2}.\end{array}\end{eqnarray} \tag{ 1 }$$

We then calculate the probability of chance coincidence, given by

$$\begin{eqnarray}&&{P}_{\mathrm{chance}}=1-\exp (-\eta ),\end{eqnarray} \tag{ 2 }$$

where η ≡ πθ²Σ(≤m_r). We report the estimated chance probabilities of each of the FRB-host galaxies in Table 1. Here, we also provide the association radius δx, representing the offset from a given galaxy with r-band magnitude m_r within which the FRB can be securely associated with the galaxy (Tunnicliffe et al. 2014).

Table 1.  Overview of the Main Sample of FRBs and Their Putative Hosts

FRB	R.A.FRB	Decl.FRB	σR	Repeating	R.A.host	Decl.host	θ	δ x	r1/2	ri	m	Filter	${P}_{\mathrm{chance}}$	Sample
	(deg)	(deg)	('')		(deg)	(deg)	('')	('')	('')	('')	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
121102	82.9946	33.1479	0.100	y	82.9946	33.1480	0.17	1.2	0.2	0.44	23.73	GMOS_N_r	0.0023	A
180916	29.5031	65.7168	0.002	y	29.5012	65.7147	7.87	44.8	5.1	12.95	16.17	SDSS_r	0.0059	A
180924	326.1052	−40.9000	0.102	n	326.1052	−40.9002	0.71	4.7	0.6	1.35	20.50	DES_r	0.0018	A
181112	327.3485	−52.9709	1.626	n	327.3486	−52.9709	0.28	2.7	1.2	3.25	21.68	DES_r	0.0257	C
190102	322.4157	−79.4757	0.502	n	322.4150	−79.4757	0.45	4.1	1.0	2.02	20.77	VLT_FORS2_I	0.0050	A
190523	207.0650	72.4697	2.449	n	207.0643	72.4708	3.79	2.4	0.5	4.90	22.01	Pan-STARRS_r	0.0733	C
190608	334.0199	−7.8982	0.258	n	334.0204	−7.8989	3.00	20.5	1.3	3.96	17.55	SDSS_r	0.0016	A
190611	320.7455	−79.3976	0.671	n	320.7428	−79.3972	2.13	2.3	0.4	2.27	22.07	GMOS_S_r	0.0169	A
190614	65.0755	73.7067	0.566	n	65.0738	73.7064	2.22	1.4	1.0	2.99	23.25	GMOS_S_r	0.0708	D
190711	329.4195	−80.3580	0.350	y	329.4192	−80.3581	0.49	1.3	0.5	1.04	23.49	GMOS_S_r	0.0106	A
190714	183.9797	−13.0210	0.283	n	183.9796	−13.0211	0.49	4.3	1.0	2.09	20.69	Pan-STARRS_r	0.0050	A
191001	323.3516	−54.7477	0.149	n	323.3519	−54.7485	2.86	13.5	1.4	4.07	18.34	DES_r	0.0031	A
200430	229.7064	12.3769	0.546	n	229.7063	12.3766	1.04	3.0	0.6	1.55	21.51	Pan-STARRS_r	0.0051	A

Note. Column 1: FRB source. Columns 2 and 3: R.A. and decl. of the FRB (J2000). Column 4: Approximate FRB localization uncertainty (geometric mean of R.A. and decl. axes). Column 5: FRB classification. Repeating = yes(y)/no(n). Columns 6 and 7: R.A. and decl. of the associated host galaxy (J2000). Column 8: Projected angular offset of the FRB to the host-galaxy center. Column 9: Association radius δx (Tunnicliffe et al. 2014). Column 10: Angular effective radius of the host measured from a Sérsic model using GALFIT (Peng et al. 2010) on the i-band images (or equivalent). Column 11: Effective search radius (Bloom et al. 2002). Column 12: Measured apparent magnitude of the host. Column 13: Filter used for the magnitude measurement. Column 14: Probability of chance coincidence using the Bloom et al. (2002) formalism. Column 15: Sample designations following the criteria outlined in Section 2.1.

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In previous works, we estimated the probability of chance coincidence with an empirical approach (Bannister et al. 2019) and reported ${P}_{\mathrm{chance}}\lt {10}^{-3}$ for the first well-localized ASKAP-detected FRBs (e.g., Bannister et al. 2019; Prochaska et al. 2019a). The formalism described above yields consistent results. We note that Eftekhari & Berger (2017) have developed a similar framework to quantify the robustness of the FRB-host galaxy associations with a more recent number count estimation. This generally provides lower chance probabilities; here, we use the formalism described above to be more conservative. In this work, we also estimate the uncertainty on the offsets from the FRB to the host galaxy center by integrating over the FRB localization ellipse.

Our approach is designed to (i) minimize the deleterious effect of false positives on this somewhat small sample of events and (ii) define a high-confidence sample that can be used in future analyses to generate priors for a full Bayesian analysis. To do this, we define four subsamples based solely on ${P}_{\mathrm{chance}}$ and the quality of the galaxy redshift estimation. These are:

• 1.  
  Sample A: The host-galaxy association is considered highly probable (${P}_{\mathrm{chance}}\lt 0.05$) based on the FRB localization and galaxy photometry. The galaxy has a spectroscopically confirmed redshift ${z}_{\mathrm{spec}}$.
• 2.  
  Sample B: Same as Sample A, except that only a photometric redshift ${z}_{\mathrm{phot}}$ has been estimated.
• 3.  
  Sample C: The host-galaxy association is less secure due to a poor FRB localization, multiple host candidates, and/or because additional priors were adopted in the association (e.g., the Macquart DM–z relation; Macquart et al. 2020). A spectroscopic redshift ${z}_{\mathrm{spec}}$ has been measured.
• 4.  
  Sample D: Same as Sample C, except that only a photometric redshift ${z}_{\mathrm{phot}}$ has been measured.

We consider all the FRB hosts compiled in this work throughout the paper but caution about the potential pitfalls of the uncertain host-galaxy identifications where relevant. For the statistical analyses we only consider the FRBs in Sample A. In the following section we introduce all of the candidate FRB-host galaxies and enumerate the number in each sample type.

In continuation of the first four FRBs detected and accurately localized by ASKAP/CRAFT (presented in Bhandari et al. 2020b), we here report the observations and basic properties of five more recent FRB-host galaxies: those of FRBs 190611, 190711, 190714, 191001, and 200430.

2.2.1. FRB 190611

On UT 2019 June 11 at 05:45:43.3, the ASKAP telescope recorded FRB 190611 as reported by Macquart et al. (2020), who also briefly described its host-galaxy candidates. The FRB position is at R.A., decl. (α, δ) = 21^h22^m5891, −79^d23^m513 (J2000), with an uncertainty of σ_α,δ = 07, 07.

We obtained deep Gemini-S/GMOS images in the r and i bands (the latter shown in Figure 1) revealing a bright source (r = 22.65 mag) approximately 2'' to the northwest at α, δ = 21^h22^m5828, −79^d23^m501 (J2000), identified as the host galaxy by Macquart et al. (2020). We do not detect any significant structure (e.g., spiral arms) and measure an effective half-light radius of R_eff = 040. We also tentatively detect a considerably fainter source coincident within the FRB error ellipse (r ≈ 26 mag; at 21^h22^m5897, −79^d23^m517) at a smaller offset of 043 from the FRB position. We estimate chance probabilities for the two galaxies to be unrelated to the FRB host of ${P}_{\mathrm{chance}}=0.017\,\mathrm{and}\,0.10$ for the bright and faint galaxy, respectively. Given the only tentative detection of the faint source and that the bright source has ${P}_{\mathrm{chance}}\approx 2 \%$, we consider the more clearly offset, bright galaxy to be the host of FRB 190611 and place it in our primary Sample A.

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Spectroscopy of this host-galaxy candidate with the FORS2 instrument on the ESO Very Large Telescope (VLT) was reduced using the PypeIt reduction package (Prochaska et al. 2020), which optimally extracts a 1D spectrum from the flat-fielded and sky-subtracted 2D spectral image. We additionally performed a 2D coaddition of the spectra presented in Macquart et al. (2020). This yields a spectroscopic redshift of ${z}_{\mathrm{spec}}=0.3778$ based on the Hα, Hβ, and [O iii] line features. At this redshift, the physical projected offset of the FRB from the bright galaxy centroid is ≈11 kpc.

2.2.2. FRB 190711

2.2.3. FRB 190714

2.2.4. FRB 191001

2.2.5. FRB 200430

In addition to the five new FRB hosts presented here, we include all other (currently) known FRB-host galaxies in our analysis. These include FRBs 121102 (Bassa et al. 2017; Chatterjee et al. 2017; Tendulkar et al. 2017), 180916 (Marcote et al. 2020), 180924 (Bannister et al. 2019; Bhandari et al. 2020b), 181112 (Prochaska et al. 2019a), 190102 (Bhandari et al. 2020b; Macquart et al. 2020), 190523 (Ravi et al. 2019), 190608 (Bhandari et al. 2020b; Chittidi et al. 2020; Macquart et al. 2020), and 20190614D (hereafter referred to as FRB 190614; Law et al. 2020).

In Appendix A we briefly describe these additional galaxies associated with well-localized FRBs and any new observations obtained after the primary publications. We separate them primarily by FRB survey. For the hosts previously reported by Bhandari et al. (2020b), we simply include their reported measurements here. For the host galaxy of FRB 180916 (Marcote et al. 2020), we extract the photometry from the SDSS and Wide-field Infrared Survey Explorer (WISE) catalogs to obtain a more precise estimate of the stellar mass. We find the best-fit value to be approximately a factor of five lower than the stellar mass reported by Marcote et al. (2020). We also obtained independent spectra of the putative host galaxy of FRB 190523 (Prochaska et al. 2019b; Ravi et al. 2019), allowing us to derive an upper limit on the line flux of Hβ, which we use to place a stronger limit on the star-formation rate (SFR) of <0.09 M_⊙ yr⁻¹. Finally, we used the photometry reported by Bassa et al. (2017) for the host galaxy of FRB 121102 to model our own spectral energy distribution (SED; see Section 3.1) for consistency with the rest of the sample.

Our overall parent sample consists of 13 FRB-host galaxies as presented in Table 1. Out of these 13 hosts, 10 satisfy the Sample A criteria. These include all the 5 new host galaxies characterized in detailed here (FRBs 190611, 190711, 190714, 191001, and 200430) and the hosts of FRBs 121102, 180916, 180924, 190102, and 190608 (i.e., all the hosts of the repeating FRBs are also in Sample A). We have placed the host of FRB 190523 discovered by Ravi et al. (2019) into Sample C because the poor FRB localization makes the host-galaxy association less secure. The host galaxy of FRB 181112 identified by Prochaska et al. (2019a) is also placed in Sample C because the proposed foreground galaxy has a similarly low (${P}_{\mathrm{chance}}\lt 0.05$) chance association probability. The observed dispersion measure of ${\mathrm{DM}}_{\mathrm{FRB}}=589\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ for this event, however, supports the association that the background galaxy is the host of FRB 181112. To be conservative and consistent with the other sample classifications, we rely only on the statistical properties of the FRB-host associations here to avoid biasing the host identifications. For FRB 190614, Law et al. (2020) identified two potential host-galaxy candidates, for which only photometric redshifts have been obtained, placing it in Sample D.

This more than doubles the number of ASKAP-detected FRB hosts studied in our previous work (Bhandari et al. 2020b). The FRBs are distributed throughout the celestial sphere, and our full sample spans redshifts of z_FRB = 0.03–0.66. We wish to caution, however, that because the number of FRB-host identifications is still small, we consider all known FRB hosts here regardless of their initial selection. A more careful homogeneous selection is required when a larger number of FRBs with subarcsecond localizations and their associated host galaxies have been properly identified.

Throughout the paper, we distinguish the hosts of the three FRBs that are currently known to repeat (FRBs 121102, 180916, and 190711) from the hosts of the other apparently nonrepeating one-off FRBs. Repeating FRBs by definition cannot be cataclysmic events, whereas apparently nonrepeating FRBs might be. In principle, all FRBs could be found to repeat if observed on long enough timescales and with an appropriate cadence, but it appears unlikely that they do (at least similarly to FRB 121102; James et al. 2020). The apparently longer intrinsic temporal pulse width for repeating FRBs compared as an ensemble to as yet nonrepeating FRBs (CHIME/FRB Collaboration et al. 2019; Fonseca et al. 2020) also suggests that repeating sources show different pulse morphologies than nonrepeating sources, including wider burst envelopes and distinct time-frequency drifting. This could imply a different emission mechanism for repeating and one-off sources. We caution that it is possible that FRBs that are currently classified as nonrepeating may exhibit repeat pulses in the future, which would change their classification here. As noted by Day et al. (2020) and others, signposts of probable repetition can be discerned from high time and frequency resolution analyses of FRB detections, although it appears to reflect a continuum of spectro-temporal polarimetric properties of FRBs more. Here, we reserve the repeater label for events with multiple confirmed bursts.

Even with a sample of three known repeating FRBs, it is possible to examine the physical properties of their host galaxies compared to the sample of hosts of apparently nonrepeating FRBs. This may provide additional clues on whether two populations of FRBs exist.

Following our previous studies of FRB-host galaxies (Bannister et al. 2019; Prochaska et al. 2019a; Bhandari et al. 2020b; Chittidi et al. 2020), we have analyzed the existing photometry and spectroscopy of all hosts with the pPXF (Cappellari 2017) and CIGALE (Noll et al. 2009) software packages. Each package fits a set of stellar population models and a star formation history (SFH) to the spectra (pPXF) or photometry (CIGALE) and generates best estimates for quantities such as stellar mass M_⋆, internal extinction E(B − V), and age of the main stellar population.

We adopt the following assumptions in these analyses:

• 1.  
  A delayed-exponential SFH model with no late-burst population ($\mathrm{SFR}(t)\propto t/{\tau }^{2}\times \exp (-t/\tau )$). Here t is the age, with t = 0 the onset of star formation, and τ is the e-folding time of the decaying part of the SFH.
• 2.  
  The Bruzual & Charlot (2003) simple stellar population with the initial mass function (IMF) from Chabrier (2003) and a metallicity allowed to vary from 0.005Z_⊙ to 2.55Z_⊙.
• 3.  
  The Calzetti et al. (2000) dust extinction model, modified following Lo Faro et al. (2017).
• 4.  
  The Dale et al. (2014) dust emission model with an AGN fraction f_AGN ≤ 0.2 and a power-law exponent of 2.

We determine the internal host-galaxy extinction E(B − V)_host from the SED modeling without adopting the visual extinction derived from the Balmer decrement as input, but note that the two independent estimates are generally consistent. In all cases, we have input observations corrected for Galactic extinction using the E(B − V)_Gal values derived from Schlafly & Finkbeiner (2011) and the Fitzpatrick & Massa (2007) extinction law with R_V = 3.1 implemented in the extinction²¹ software package. The derived photometry for all FRB hosts considered here is provided in Appendix B, in Tables 6–8. The precise input parameter file for CIGALE is available in the cigale.py module of the FRB repository on GitHub.

The best-fit models for the host galaxies described in Section 2.2 are presented in Figures 2 and 3. These include fluxes for common emission lines derived from the pPXF analysis (provided in Table 2), which corrects for Balmer absorption. For uniformity, we also performed the same analysis on FRB hosts drawn from the literature, especially for all galaxies in Sample A. This includes reanalyses of hosts from our own previous publications (e.g., Bhandari et al. 2020b). Any substantial differences from previously reported estimates are described in Appendix A. The results are summarized in Table 3.

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Table 3.  Host-galaxy Properties

FRB host	zhost	Mr	Mu − Mr	M⋆	SFR	Age	Z	Offset	Reff
		(mag)	(mag)	(109 M⊙)	(M⊙ yr−1)	(Gyr)	$12+\mathrm{log}$(O/H)	(kpc)	(kpc)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
121102	0.1927	−16.20 ± 0.08	1.49 ± 0.18	0.14 ± 0.07	0.15 ± 0.04	0.26	<8.08	0.6 ± 0.3	0.7 ± 0.1
180916	0.0337	−19.46 ± 0.05	1.53 ± 0.06	2.15 ± 0.33	0.06 ± 0.02	0.15	⋯	5.5 ± 0.1	3.6 ± 0.4
180924	0.3212	−20.81 ± 0.05	1.78 ± 0.15	13.2 ± 5.1	0.88 ± 0.26	0.38	${8.93}_{-0.02}^{+0.02}$	3.4 ± 0.5	2.7 ± 0.1
181112	0.4755	−20.40 ± 0.07	1.12 ± 0.15	3.98 ± 2.02	0.37 ± 0.11	0.57	${8.86}_{-0.13}^{+0.10}$	1.7 ± 19.2	7.2 ± 1.7
190102	0.2912	−19.85 ± 0.06	1.40 ± 0.12	3.39 ± 1.02	0.86 ± 0.26	0.06	${8.70}_{-0.08}^{+0.07}$	2.0 ± 2.2	4.4 ± 0.5
190523	0.6600	−22.06 ± 0.12	1.92 ± 0.19	61.2 ± 40.1	<0.09a	0.69	⋯	27 ± 23	3.3 ± 0.2
190608	0.1178	−21.22 ± 0.05	1.40 ± 0.09	11.6 ± 2.8	0.69 ± 0.21	0.38	${8.85}_{-0.02}^{+0.02}$	6.6 ± 0.6	2.8 ± 0.2
190611	0.3778	⋯	⋯	∼0.8	0.27 ± 0.08	⋯	${8.71}_{-0.28}^{+0.17}$	11 ± 4	2.1 ± 0.1
190711	0.5220	−19.01 ± 0.08	0.95 ± 0.16	0.81 ± 0.29	0.42 ± 0.12a	0.61	⋯	3.2 ± 2.1	2.9 ± 0.2
190714	0.2365	−19.92 ± 0.05	1.19 ± 0.17	14.9 ± 7.1	0.65 ± 0.20	1.59	${9.03}_{-0.04}^{+0.04}$	1.9 ± 1.1	3.9 ± 0.1
191001	0.2340	−22.13 ± 0.05	1.67 ± 0.19	46.4 ± 18.8	8.06 ± 2.42	0.64	${8.94}_{-0.05}^{+0.05}$	11 ± 1	5.5 ± 0.1
200430	0.1600	−18.05 ± 0.05	1.78 ± 0.31	1.30 ± 0.60	∼0.2b	0.69	⋯	3.0 ± 2.4	1.6 ± 0.5

Notes. Column 1: FRB source. Column 2: Host redshift. Spectroscopic redshifts are reported to four significant digits (typical uncertainty), and photometric redshifts to two significant digits. Column 3: Absolute r-band magnitude. Column 4: Rest-frame M_u − M_r colors. Column 5: Stellar mass from SED modeling. Column 6: Star-formation rate derived from the line luminosity of Hα, assuming a Chabrier (2003) IMF. Column 7: Estimate of the mass-weighted stellar population age from SED modeling. Column 8: Oxygen abundance derived using the O3N2 calibration from Hirschauer et al. (2018). Column 9: Projected physical offset of the FRB from the galaxy center. Column 10: Effective radius of the host galaxy measured in the i band (or equivalent).

^aThe SFR is derived from Hβ assuming a nominal scaling with Hα (i.e., no internal host extinction). ^bThe SFR is derived from the best-fit photometric SED model.

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We derive the SFR for each FRB host by first computing the dust-corrected Hα line fluxes using the A_V derived from the Balmer decrement to obtain the intrinsic Hα line luminosities as L_Hα (erg s⁻¹) = F_Hα(erg s⁻¹ cm⁻²) × 10^A(λ)/2.5 × (4 π d_L²), with d_L the luminosity distance.

This we translate into an SFR via the conversion factor

$$\begin{eqnarray}&&\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})=4.98\times {10}^{-42}\,{L}_{{\rm{H}}\alpha }(\mathrm{erg}\,{{\rm{s}}}^{-1})\end{eqnarray} \tag{ 3 }$$

following Kennicutt (1998), but adopting the IMF from Chabrier (2003).²² We report the uncertainties on the SFR estimates including the scatter in the SFR-L_Hα relation (≈30%). For the three FRB hosts where the Hα line flux has not been measured, we derive the SFR from Hβ assuming the nominal relative strength compared to Hα (FRB190523 in Sample C and FRB190711 in Sample A) or from the best-fit SED model from CIGALE (for FRB 200430, Sample A). We find that the overall sample of FRB hosts are characterized by a large range in SFR, spanning 0.05–10 M_⊙ yr⁻¹. For the host of FRB 190614, no constraints could be placed on the SFR because the nature of the host galaxy and redshift are uncertain (Sample D; Law et al. 2020).

To infer the gas-phase metallicities of the FRB hosts, we rely on commonly used diagnostic ratios of strong nebular emission lines (see Maiolino & Mannucci 2019, for a recent review). These allow us to compute the oxygen abundances $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ for each host galaxy. The strong-line diagnostics are calibrated to more direct methods, relying on measurements of the electron temperature T_e or derived from photoionization models. In the following, we adopt the O3N2 calibration from Hirschauer et al. (2018), which parameterizes the oxygen abundance as

$$\begin{eqnarray}&&\begin{array}{l}12+\mathrm{log}({\rm{O}}/{\rm{H}})=8.987-0.297\times {\rm{O}}3{\rm{N}}2\\ \quad \ -\ 0.0592\times {\rm{O}}3{\rm{N}}{2}^{2}-0.0090\times {\rm{O}}3{\rm{N}}{2}^{3},\end{array}\end{eqnarray} \tag{ 4 }$$

where O3N2 = log[([O iii]λ 5007/Hβ)/([N ii]λ 6584/Hα)]. This calibration has been shown to be consistent with more direct T_e-based methods, and has an rms uncertainty of 0.111 dex. The majority of the FRB hosts are relatively metal rich, with oxygen abundances distributed between $12+\mathrm{log}({\rm{O}}/{\rm{H}})=8.7\mbox{--}9.0$. For the host of FRB 121102, we could only place an upper limit on the oxygen abundance of $12+\mathrm{log}$(O/H) < 8.08 because of the non-detection of [N ii]λ 6584. For the hosts of FRBs 190523, 190614, 190711, and 200430, too few nebular lines have been detected to determine their metallicity.

We caution that because the oxygen abundances derived using the O3N2 calibration are specifically calibrated to SF galaxies, the actual metallicities might be slightly different if the emission-line ratios do not represent typical SF galaxies (as reported for FRB hosts by Bhandari et al. 2020b, see also Section 4.2). However, because the adopted calibration takes both the [N ii]/Hα and the [O iii]/Hβ ratios into account, the line flux excess of the two ratios should effectively cancel out.

To place the FRB hosts in the context of galaxies at similar redshifts, we present the apparent r-band magnitudes m_r of the FRB hosts as a function of redshift in Figure 4. We compare the values of m_r to the characteristic luminosity L* across redshift, using available galaxy luminosity functions (Brown et al. 2001; Wolf et al. 2003; Willmer et al. 2006; Reddy & Steidel 2009; Finkelstein et al. 2015). For each redshift, we adopt the value of L* in the rest-frame band that corresponds to the observed r band. Interpolation across redshift results in smooth contours corresponding to the luminosity tracks of field-selected galaxies at L = 0.01L*, 0.1L*, and L*. We find that the majority of the FRB hosts are in the intermediate region between L ∼ 0.1L* − L* compared to the underlying galaxy population at 0.0 < z < 0.7. The only exception is the host galaxy of FRB 121102 (Tendulkar et al. 2017), which has a luminosity of L ∼ 0.01L*.

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We then consider the color–magnitude properties of the FRB hosts, which is a useful indicator of the overall stellar population in these galaxies. In Figure 5 we compare the absolute r-band magnitudes M_r and the rest-frame M_u − M_r colors of the FRB hosts to the galaxies from the PRIMUS survey (Moustakas et al. 2013), here representing the general population of z < 0.5 galaxies. We find that the majority of FRB-host galaxies sample the brighter region of the magnitude distribution, consistent with the initial sample studied in Bhandari et al. (2020b). This suggests that FRB hosts typically trace more massive galaxies than the underlying galaxy population (see also Section 4.3). Moreover, we note that the host galaxies of the three repeating FRBs are fainter than nearly all of the hosts of the apparently nonrepeating FRBs.

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Approximately half of the FRB-host galaxies have colors consistent with the SF so-called "blue cloud," similar to most late-type galaxies (Strateva et al. 2001). The remainder (FRBs 180916, 180924, 190523, 191001, and 200430) are located in the so-called "green valley," the intermediate region between the two main populations. These galaxies may be transitioning from SF to the quiescent galaxies of the "red sequence" (Martin et al. 2007).

Figure 5 further reveals that the FRB hosts do not populate either of the main loci of the blue or red sequences. To quantify this impression, we perform 2D Kolmogorov–Smirnov (KS) tests on the color–magnitude distribution of FRB-host galaxies (considering one-off, repeaters, and the full population) compared to the distribution of early- and late-type galaxies. The results are summarized in Table 4. The hypothesis that the full FRB population is drawn from the same underlying distribution as the full galaxy population is rejected with a KS probability ${P}_{\mathrm{KS}}=0.007$. Other scenarios are rejected at higher significance levels (${P}_{\mathrm{KS}}\lt 0.002$). Considering only the repeating FRBs, we find ${P}_{\mathrm{KS}}$ values consistent with those drawn from the late-type population.

In Figure 6 we show the [O iii]/Hβ and [N ii]/Hα nebular emission-line ratios of the FRB hosts in a Baldwin-Phillips-Terlevich (BPT) diagram (Baldwin et al. 1981). This allows us to assess the dominant source of ionization and distinguish between typical SF galaxies, low-ionization nuclear emission-line region (LINER) galaxies, and AGNs (see Kewley et al. 2019, for a recent review).

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We have measured emission-line fluxes for the majority of the hosts in Sample A, most of which were previously reported in Bhandari et al. (2020b). For comparison, we show the distribution of ∼75,000 nearby (0.02 < z < 0.4) emission-line galaxies from the Sloan Digital Sky Survey (SDSS), with each emission line required to be detected at S/N > 5. We also include the standard demarcation lines between SF, AGN, and LINER galaxies (Kauffmann et al. 2003; Cid Fernandes et al. 2010).

Examining Figure 6, we find that the FRB hosts occupy a distinct region of the BPT diagram from the dominant locus of SF galaxies: the majority of FRB hosts show an excess in the [N ii]/Hα ratio compared to the ridge line tracing the highest density of local SF galaxies (Brinchmann et al. 2008), with many located in the LINER region. The only exception is the host galaxy of the repeater FRB 121102, which is located in the tail of the SF galaxy population.

We use 2D KS tests to compare the FRB-host galaxy population (both with and without the repeater FRB 121102) to each galaxy class. Galaxy classes are assigned according to the BPT diagram (Figure 6), and the results are summarized in Table 5. The FRB-host galaxy population is statistically inconsistent with the distribution of SF galaxies (${P}_{\mathrm{KS}}=0.015$) and may favor the AGN+LINER populations.

The excess of emission-line ratios from the locus of regular SF galaxies in the BPT diagram is generally attributed to a hard stellar ionizing radiation field or elevated ionization parameters of the interstellar medium (ISM; Brinchmann et al. 2008; Steidel et al. 2014). The underlying emission mechanism is not completely clear, however. Thomas et al. (2018) argue that the excess in line flux ratios can be described by an increased "mixing" of AGN emission with the H ii region emission. Alternatively, the same ionization effect can be produced by a dominating population of post-asymptotic giant branch (post-AGB) stars (Yan & Blanton 2012; Singh et al. 2013). The latter scenario aligns with the typical old stellar populations of the FRB hosts inferred from the SED modeling (see Section 3.1 and Table 3). We do note, however, that the host galaxy of FRB 190608 is found to contain a Type I AGN based on the detection of broad Hα emission (Stern & Laor 2012; Chittidi et al. 2020). We do not detect similar broad Hα emission lines in the other FRB-host spectra. Ultimately, integral field unit (IFU) observations at high spatial resolution of the host galaxies are needed to distinguish whether the central AGN or the overall LINER emission are the most common emission mechanisms producing the elevated ionization observed in FRB hosts.

We show the SFR–M_⋆ distribution of the FRB hosts in Figure 7. For the control sample, we again show the galaxies from the PRIMUS survey (Moustakas et al. 2013). We caution that due to the LINER-like emission observed for most of the FRB-host galaxies, the SFR could in some cases only represent an upper limit on the actual rate because the total line emission might not solely reflect the star formation activity.

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Similar to the color–magnitude distribution (Figure 5; Section 4.1), we find that the FRB-host galaxies avoid the main sequence of SF galaxies (i.e., the main locus of the control sample). Moreover, a 2D KS test yields a low probability that the two distributions were drawn from the same parent population (${P}_{\mathrm{KS}}\lt 0.001$). Intriguingly, the host galaxies of the known repeating FRBs show more diverse behavior than those hosting nonrepeating bursts, ranging from faint starburst (FRB 121102), to regularly SF (FRB 190711), and finally to quiescent (FRB 180916) galaxies. The hosts of the repeating FRBs are all relatively low-mass galaxies (M_⋆ < 2 × 10⁹ M_⊙) compared to the overall FRB-host population (as described before in Section 4.1).

We now consider the hypothesis that FRBs track stellar mass. Specifically, we compare the observed distribution f_FRB (M_⋆) with the stellar mass function of low-z galaxies ϕ(M_⋆) weighted by stellar mass, i.e., f_FRB (M_⋆) ∝ M_⋆ ϕ(M_⋆). For this analysis we assume the parameterization of ϕ(M_⋆) derived by Davidzon et al. (2017) for galaxies at 0.2 < z < 0.5 in the COSMOS field.

In Figure 8 we plot the cumulative stellar mass distribution of the FRB hosts in Sample A. We first consider all the hosts (top panel) and then only the hosts of the one-off FRBs (bottom panel). The uncertainty regions on the cumulative distribution functions (CDFs) are estimated by combining the two sources of uncertainty: the errors on the individual data points, and the error from the sample size. We calculate the former using Monte Carlo error propagation, assuming that the probability density function (PDF) of each data point is described by a Gaussian profile, with the standard deviation given by the error on the measurement (similar to the procedure described in Palmerio et al. 2019). We then estimate the median and 1σ confidence bounds on the CDF from 10,000 realizations of the data sampling. The error from the sample size is then computed via bootstrapping and added to show the combined uncertainty region.

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A comparison of the CDF of all the FRB hosts to the mass-weighted stellar mass distribution of field galaxies f_FRB (M_⋆) yields a probability of P_KS < 0.001 from a one-sided KS test for the two distributions to be drawn from the same underlying mass distribution. Therefore these results rule out the null hypothesis that FRBs directly track stellar mass. When we limit this to one-off FRBs (Figure 8, lower panel) the offset is reduced, but the probability remains low.

In addition to the stellar mass and SFR, the gas-phase metallicity is a strong indicator of the present stellar populations and can thus also provide constraints on the most likely progenitor channels. Indeed, the typical low-metallicity environments of LGRB host galaxies were vital in the conception of the "collapsar" progenitor model for LGRBs (e.g., Yoon et al. 2006). A more direct, quantitative comparison between FRB and LGRB hosts (in addition to the hosts of other types of transients) is provided in Section 5.1.

In Figure 9 we show the metallicities of the FRB-host galaxies in terms of their oxygen abundances $12+\mathrm{log}$(O/H) as a function of stellar mass (i.e., the mass–metallicity relation). For the control sample, we show the SF galaxies from the SDSS emission-line sample, with metallicities calibrated using the same strong-line diagnostics as for the FRB hosts (see Section 3.3). For comparison, we overplot the mass–metallicity relations at z ∼ 0.07 and z ∼ 0.7 by Maiolino et al. (2008). We find that the majority of FRB hosts is consistent with the z ∼ 0.07–0.7 mass–metallicity relations and the underlying field galaxy population.

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Last we consider the projected physical offsets (ρ) of the expanded sample of FRBs, in addition to the projected offsets normalized by the half-light radii of the hosts (ρ/R_eff). When operating in the ICS mode, ASKAP/CRAFT can now deliver subarcsecond localizations of FRBs upon detection, without requiring the use of follow-up facilities on repeat bursts. Both approaches allow us to accurately determine the FRB emission sites with respect to their host-galaxy centers ("offsets"), which provide additional clues to the progenitors of FRBs. Indeed, the offset distributions of other transients have provided a key diagnostic for understanding their origins (discussed further in Section 5).

For each FRB in Sample A, we measure the angular offset between the FRB location and its host-galaxy center, taking into account positional and astrometric uncertainties for each measurement and use the redshift of the host galaxy to convert to physical offsets in kpc. We determine a broad range of projected physical offsets for the FRBs in Sample A, spanning from 0.6 kpc (FRB 121102) to ≈11 kpc (FRBs 190611 and 191001); they are listed in Table 3. Overall, we find that FRBs have significant offsets relative to the centers of their host galaxies, with median and mean values of 3.3 and 4.8 kpc, respectively. We caution that the observed FRB population presented here could be biased against small offsets due to an increasing effect of DM scattering or "smearing" caused by the dense ISM, thus decreasing the FRB detection probability closer to their host-galaxy centers. However, we expect this effect to be minor. Using the derived host-galaxy sizes (R_eff), we also measure the host-normalized offsets for Sample A. We caution that most of the ${R}_{\mathrm{eff}}$ values were derived from seeing-limited observations and are therefore subject to significant uncertainty for the smaller galaxies (${R}_{\mathrm{eff}}\lesssim 1^{\prime\prime}$). Nevertheless, we find a range of values, ρ = 0.4–5.3 R_eff with median and mean values of 1.4 R_eff and 1.7 R_eff, respectively. We note that this is larger than the median expected offset if FRBs traced the locations of stars in their disks (e.g., $1\,{R}_{\mathrm{eff}}$).

The host galaxies of other known transients such as LGRBs, SGRBs, CC, and SNe Ia provide a natural baseline for comparison to the FRB-host population because these have been intensively studied, and have known or likely known progenitors. Investigating the connection between their hosts and galaxies hosting FRBs can therefore provide important (though indirect) clues to the most likely FRB progenitor channels. Based on the first small samples of FRB-associated hosts (Bhandari et al. 2020b; Li & Zhang 2020), it was already evident that the majority had generally high masses and low SFRs (excluding FRB 121102). Our work has further cemented this picture based on a sample of 10 secure host galaxies.

5.1.1. Luminosity, SFR, and Stellar Mass

Here, we further discuss the connection between FRB hosts and those of other astronomical transients and compare them quantitatively. The typically high luminosities and stellar masses but modest SFRs observed in this work are generally consistent with the galaxy populations hosting CC-SNe and SGRBs, which are found to predominantly occur in luminous, massive galaxies (Prieto et al. 2008; Berger 2009; Kelly & Kirshner 2012; Taggart & Perley 2019). These physical properties are in stark contrast to the typically elevated specific SFRs (sSFR = SFR/M_⋆) observed for the hosts of LGRBs. Moreover, the host galaxies of LGRBs at z ≲ 1 are typically at the faint, low-mass end of the SF galaxy population (Savaglio et al. 2009; Schulze et al. 2015; Vergani et al. 2015; Perley et al. 2016), in contrast to what we have observed for the majority of FRB hosts.

In Figure 10 we compare the stellar mass distribution of the FRB hosts to the host galaxies of these other transients, namely SGRBs (Nugent et al. 2020), LGRBs (Vergani et al. 2015), and CC-SNe (Schulze et al. 2020). To mitigate the effects of the cosmological evolution of galaxies and ensure a fair comparison, we require z < 1 for the host galaxies for all of the comparison samples. The ${M}_{\star }$ CDF for FRBs is intermediate between the lower mass hosts of LGRBs and the higher mass hosts of SGRBs, and most closely following those of CC-SNe. Neither of the SGRB or CC-SNe host populations, however, has statistically inconsistent CDFs. When the comparison is restricted to the one-off FRBs, the correspondence to the host galaxies of LGRBs is further disfavored with ${P}_{\mathrm{KS}}\lt 0.05$.

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5.1.2. No Evidence for Metal Aversion in FRB Hosts

5.1.3. Physical and Host-normalized Offsets

We then compare the physical and host-normalized offset distributions of FRBs to that of the SGRB (Fong & Berger 2013, W. Fong et al. 2020, in preparation), LGRB (Blanchard et al. 2016), and CC/SNe Ia (Prieto et al. 2008; Kelly & Kirshner 2012) populations in Figure 11. For context, the locations of LGRBs match expectations for the H ii regions of massive stars in an exponential disk, commensurate with their massive star progenitors (Bloom et al. 2002; Blanchard et al. 2016; Lyman et al. 2017). For SGRBs, which originate from older stellar populations, the broad range of projected offsets of SGRBs extending to tens of kiloparsec are believed to result from neutron star kicks and delay times, providing a strong link to their neutron star merger progenitors (Fong & Berger 2013).

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In comparison, it is already evident that most FRBs are not coincident with the nucleus of their hosts, disfavoring models involving AGN or supermassive black holes in general (see Figure 1; and also Bhandari et al. 2020b). The offset distribution of the full sample of FRBs is found to closely follow the observed distribution of CC and SNe Ia, with one-sided KS tests yielding P_KS = 0.96 and P_KS = 0.95, respectively. The FRB and SGRB offset distributions are also consistent, but a larger fraction of SGRBs are observed to occur at even greater distances from their host-galaxy centers (Fong & Berger 2013), which is more consistent with theoretical expectations of binary neutron star mergers (Fryer & Kalogera 1997; Bloom et al. 1999; Belczynski et al. 2006). We find similar results when we restrict our analysis to the hosts of one-off FRBs. On the other hand, LGRBs are observed to be one of the most centrally concentrated populations, which is inconsistent with that of FRBs (with P_KS = 0.008).

When the offsets are normalized by the effective radii of the host galaxies (Figure 11, right), the results are qualitatively similar, although the LGRB distribution is no longer inconsistent at high confidence.

5.1.4. Implications for FRB Progenitor Channels

An intriguing new clue to the origin of FRBs came from the discovery of a brief radio burst from the Galactic magnetar/soft gamma repeater SGR 1935+2154 (Bochenek et al. 2020a; Scholz & Chime/Frb Collaboration 2020). The released radio energy in this event is approximately two orders of magnitude lower than that observed for the weakest of the cosmological FRBs (Bochenek et al. 2020b; The CHIME/FRB Collaboration et al. 2020), and approximately five orders of magnitude fainter than typical one-off bursts (such as FRBs 180924 and 181112). This is not unexpected, however, because such weak bursts would be difficult to detect at z ≳ 0.1, and this Galactic "FRB" might therefore represent the faint end of the observed extragalactic FRB distribution.

To further examine this possibility, we can now pose the question whether the Milky Way is a typical FRB-host galaxy. Based on the inferred properties of M_⋆,MW = (6.08 ± 1.14) × 10¹⁰ M_⊙ and SFR_MW = 1.65 ± 0.19 M_⊙ yr⁻¹ (Licquia & Newman 2015), we find that the Milky Way is indeed consistent with being a typical FRB-host galaxy. Its SFR–M_⋆ relation places it in the transition region between SF and quiescent galaxies, intermediate to what has been observed for the most massive (M_⋆ > 10¹⁰ M_⊙) FRB hosts. The same is true for the mass–metallicity relation of the Milky Way. Our Galaxy is thus a typical FRB-host galaxy. In addition, SGR 1935+2154 is located approximately 9 kpc from the Galactic center (Kothes et al. 2018; Bochenek et al. 2020b), which is in the high end of the physical offset distribution of the burst sites observed here. All these considerations further support the connection between the radio emission from SGR 1935+2154 and low-luminosity FRBs.

FRB 180924, FRB 181112, FRB 190102, FRB 190608, and FRB 191001. All of these FRBs and their host galaxies were presented in previous CRAFT publications (Bannister et al. 2019; Prochaska et al. 2019a; Bhandari et al. 2020a, 2020b; Chittidi et al. 2020; Macquart et al. 2020). Several of the FRB coordinates have been improved from refined analysis of the saved baseband data, enabling more precise positions for the FRBs and/or a better estimate of the astrometric registration of the FRB image (Day et al. 2020). For FRB 190102 we also include the HST/F160W band photometry measured by A. Mannings et al. (2020, in preparation) of m_F160W = 20.45 ± 0.01 mag in the SED fit of the host galaxy to improve the estimates of the stellar population parameters. We note that for FRB191001, the R.A. uncertainty reported in Bhandari et al. (2020a) of 0.006s was incorrectly calculated, and should have been 0.02s (the latter adopted in this work). All of these except for FRB 181112 are included in Sample A. While we still maintain the association of FRB 181112 to DES J214923.66−525815.28 to be highly secure, the foreground galaxy studied in Prochaska et al. (2019a) is sufficiently bright to also give ${P}_{\mathrm{chance}}\lt 0.05$. Therefore this association places it within Sample C. A future Bayesian framework for FRB-host associations will enable a direct comparison of the probabilities of the two sources, and we expect that DES J214923.66−525815.28 will by highly favored.

FRB 190714 and FRB 200430. The final positions and uncertainties for these FRBs were determined following the method used for all previous ASKAP/CRAFT FRBs (for detailed descriptions of this method, see Bannister et al. 2019; Prochaska et al. 2019a; Day et al. 2020; Macquart et al. 2020). Briefly, the statistical position and uncertainty in R.A. and decl. are derived by fitting a 2D Gaussian to a region containing the FRB in a Stokes I frequency-averaged image. Any errors in the phase-calibration solutions (due to the spatial and temporal differences in the FRB and calibrator observations) are corrected for by comparing the positions of continuum field sources detected in an image made with the 3.1 s of voltage data containing the FRB to positions from reference catalogs, thereby aligning the ASKAP reference frame with the International Celestial Reference Frame (ICRF3). The systematic uncertainties and any offsets are then determined following the method described in Macquart et al. (2020). The statistical FRB position is then corrected for any offset, with the final uncertainty being the quadrature sum of the statistical and systematic uncertainties.

For FRB 190714, two quick-look images from the Karl G. Jansky Very Large Array Sky Survey (VLASS, Lacy et al. 2020) were used for comparison with the ASKAP field sources, with offsets and systematic uncertainties in R.A. and decl. determined to be 071 ± 032 and −145 ± 023, respectively. For comparison with the FRB 200430 field sources, catalog positions from the Faint Images of the Radio Sky at Twenty centimetres (FIRST, Becker et al. 1995) survey were used and offsets and uncertainties determined as above. Unusually, FRB 200340 exhibits a dependence of position in decl. on frequency (yielding an offset in decl. ≈7'' across the frequency band). This indicates a frequency-dependent phase error, potentially due to the ionosphere. Because the FRB and field sources have different spectral indices, their frequency-averaged centroids will likewise differ. In order to account for the bias introduced in correcting the FRB position with the field sources, a coarse spectral index of the FRB was determined by performing a linear fit to the log of the flux densities (extracted from a 56 MHz resolution image cube of the FRB) versus frequency, yielding spectral index α = −5.46, and compared to a typical spectral index of the field sources (α = −0.7). This was then used to derive the expected deviation in decl. given the offset in the flux-weighted centroid frequencies (49 MHz) by evaluating a weighted linear fit of the decl. offsets in the FRB image cube versus frequency at both central frequencies. An offset of 093 was derived, which we also conservatively take to be the typical uncertainty expected due to this bias. Combining this with the offsets and systematic uncertainties derived via the standard field-source comparison method, we obtain a total systematic offset and uncertainty in R.A. and decl. of −003 ± 025 and 412 ± 104, respectively.

CIGALE. As noted in Section 3, we have reanalyzed the SED models of all the previously published hosts from ASKAP/CRAFT using the same set of model inputs applied to the new hosts. Because of the sensitivity of ${M}_{\star }$ and SFR to assumptions on the SFH and dust, the new values are quantitatively different. This is reflected by their large uncertainties, but we caution that the results are further subject to systematic errors related to model assumptions. In one case (FRB 190608), we also identified an error in our database that led to the misreporting of results in Bhandari et al. (2020b).

FRB 180916. Marcote et al. (2020) reported the first FRB discovered by the CHIME experiment (CHIME/FRB Collaboration et al. 2018) to be localized to high-precision, FRB 180916.J0158+65 (hereafter FRB 180916 for convenience). It is coincident with the spiral arm of the previously cataloged galaxy SDSS J015800.28+654253.0. As detailed by these authors, the probability of a chance association is very low, and our own estimate is ${P}_{\mathrm{chance}}=0.0059$. We therefore include it in Sample A.

We also performed SED modeling of the host with CIGALE, using archival SDSS optical and mid-infrared WISE photometric data. We compute a stellar mass of M_⋆ = (2.15 ± 0.33) × 10⁹ M_⊙, which is approximately a factor of five lower than the estimate by Marcote et al. (2020). We caution that both of these estimates suffer from large systematic uncertainties due to the substantial corrections for Galactic extinction.

FRB 190523. Ravi et al. (2019) reported the detection of FRB 190523 with the Owens Valley DSA observatory. The 3'' × 8'' 95% error ellipses is nearly coincident with the centers of two sources labeled S1 and S2 by these authors (at J134815.44+722814.72 and J134815.74+722805.9, respectively). Ravi et al. (2019) favor associating S1 with the FRB owing to its somewhat closer angular offset (θ_S1 = 38 versus θ_S2 ≈ 51) and because its spectroscopic redshift ${z}_{\mathrm{spec}}=0.660$ agrees well with the Macquart DM–z relation (Macquart et al. 2020). Based on the formalism for associations adopted here (Section 2.1), we find ${P}_{\mathrm{chance}}({\rm{S}}1)=0.07$ and ${P}_{\mathrm{chance}}({\rm{S}}2)=0.10$.

Subsequent to the Ravi et al. (2019) publication, we observed S1 and S2 with the DEIMOS spectrograph on the Keck II telescope (Prochaska et al. 2019b). The instrument was configured with the 600ZD grating tilted to cover λ ≈ 5000–9500 Å and the 1'' longslit yields a resolution R ≈ 2500. These data were reduced using the PypeIt software package in the same manner as described above. These data confirm the redshift of S1 reported by Ravi et al. (2019) and yield a spectroscopic redshift for S2 of ${z}_{\mathrm{spec}}=0.363$ based on Hα and [N ii] nebular emission.

We here revisit the effective prior adopted by Ravi et al. (2019) by adopting the DM–z relation. These authors report ${\mathrm{DM}}_{\mathrm{FRB}}=760.8\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$, and the Galactic ISM contribution along this sightline is ${\mathrm{DM}}_{\mathrm{MW},\mathrm{ISM}}=37\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$. Assuming a Galactic halo contribution of ${\mathrm{DM}}_{\mathrm{MW},\mathrm{halo}}=50\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ (Prochaska & Zheng 2019; Platts et al. 2020, but see Keating & Pen 2020) and a host contribution of $80\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ in the host rest-frame, we have an estimated cosmic dispersion measure of ${\mathrm{DM}}_{\mathrm{cosmic}}({\rm{S}}1)=625\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ and ${\mathrm{DM}}_{\mathrm{cosmic}}({\rm{S}}2)=616\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ for each source. These are to be compared against the average cosmic dispersion measure to the redshift of each galaxy, $\langle {\mathrm{DM}}_{\mathrm{cosmic}}\rangle ({\rm{S}}1)=607\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ and $\langle {\mathrm{DM}}_{\mathrm{cosmic}}\rangle ({\rm{S}}2)=319\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ for each source. Even allowing for many tens of $\mathrm{pc}\,{\mathrm{cm}}^{-3}$ uncertainty in the ${\mathrm{DM}}_{\mathrm{MW},\mathrm{halo}}$ and ${\mathrm{DM}}_{\mathrm{host}}$ terms that contribute to the ${\mathrm{DM}}_{\mathrm{cosmic}}$ estimate, the observations favor S1. In any event, neither candidate satisfies ${P}_{\mathrm{chance}}\lt 0.05$, and we place this association in Sample C and associate S1 with the FRB.

FRB 190614. Law et al. (2020) report the first putative detection of an FRB from the realfast collaboration (Law et al. 2018), FRB 20190614D (here referred to as FRB 190614). They further report the galaxy pair J042017.71+734222.9 and J042017.87+734224.4 at separations ≈15 from the FRB centroid and estimate chance probabilities for both galaxies of ${P}_{\mathrm{chance}}({\rm{A}},{\rm{B}})=0.07$. Despite follow-up spectroscopy with the Keck I telescope, neither has a secure spectroscopic redshift. Photometric analysis yields ${z}_{\mathrm{phot}}=0.6$ for each galaxy with uncertainties of 0.15, 0.2 for A and B respectively. These are roughly consistent with the large dispersion measure reported for FRB 190614. In our analysis, we have adopted J042017.87+734224.4 as the host, but we include this system in Sample D.

FRB 121102. The host galaxy of FRB 121102 (also known as "the Repeater") was studied in detail by Tendulkar et al. (2017). We adopt the majority of their measurements here, but use the updated coordinates for the host galaxy centroid in addition to the estimate of the galaxy's effective half-light radius R_eff from Bassa et al. (2017). The probability of a chance coincidence with the host is ${P}_{\mathrm{chance}}=0.002$, and we include this system in Sample A.