The FRB 20190520B Sight Line Intersects Foreground Galaxy Clusters

In Simha et al. (2023), we adopted dynamical halo masses estimated using the virial theorem applied to the projected size and velocity dispersion of the galaxy groups. For the foreground sample of FRB 20190520B, however, the observations were much shallower, and the spectroscopic success rate was considerably lower than the equivalent data sets in Simha et al. (2023). For example, Simha et al. (2023) had 1493 galaxy redshifts for the FRB 20190714A field, which is at z_frb = 0.2365, whereas for FRB 20190520B at a similar redshift of z_frb = 0.241, we only have 701 successful galaxy redshifts. We therefore consider the FRB 20190520B sample too sparse for reliable application of the virial theorem for group/cluster mass estimation.

Instead, we use the group richness, N_rich, combined with a forward-modeling approach based on semianalytic models of galaxy formation. Specifically, we use the Henriques et al. (2015) light-cone catalogs that were generated by applying the "Munich" semianalytic galaxy formation model (Guo et al. 2011) to the L = 500 h⁻¹ Mpc Millennium N-body simulation (Springel 2005). In particular, we use the "all-sky" catalogs that are designed to simulate footprints covering 4π sr in order to maximize the number of simulated groups and clusters. We queried the simulation SQL database ¹⁵ to download z < 0.25 cluster catalogs with ${\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })\geqslant 14.2$ from over the full sky, whereas for the halo mass range $13.0\,\leqslant {\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })\lt 14.2$, a subsample over a footprint of 400 deg² was deemed to provide a sufficient sample size to probe the diversity of the groups without having to download an excessively large file. This simulated group catalog includes effects such as k-corrected photometry based on the realistic galaxy spectral energy distributions (including the effect of dust), redshift space distortions, and the distance modulus (i.e., increasingly faint magnitudes as a function of redshift).

Using these mock catalogs, we build forward models matched to the observed redshift, z_grp, of each detected group in our sample. First, we selected groups/clusters from the mock catalog within z_grp ± 0.005 and applied the same magnitude cut as that corresponding to our field center, r ≤ 18.42 (with a small distance modulus correction to account for the finite width of the Δz = 0.005 redshift selection bin). This step yields ${N}_{\mathrm{rich}}^{\mathrm{true}}$ group members that would be observed within our observing setup if we had achieved 100% spectroscopic completeness. We then downsample each group to our actual observed completeness by drawing a random Poisson variate with a mean of $\mu ={f}_{\mathrm{obs}}\,{N}_{\mathrm{rich}}^{\mathrm{true}}$, where f_obs = 56.6% is the completeness of our FRB 20190520B spectroscopy. The selected group galaxies are used to compute the observed mock richness, ${N}_{\mathrm{rich}}^{\mathrm{mock}}=\mu \,{N}_{\mathrm{rich}}^{\mathrm{true}}$, for that simulated group. In Figure 3, the gray lines show ${N}_{\mathrm{rich}}^{\mathrm{mock}}$ computed as a function of ${\mathrm{log}}_{10}({M}_{\mathrm{halo}})$ for an ensemble of simulated groups selected to be at the same redshift as one of our observed groups. The scatter originates from both the intrinsic diversity of group properties at fixed halo mass and the stochasticity induced by the Poisson sampling at our low spectroscopic completeness. We then fit a spline function to obtain ${N}_{\mathrm{rich}}^{\mathrm{mock}}$ as a function of ${\mathrm{log}}_{10}({M}_{\mathrm{halo}})$. While there are gaps in the sample of mock groups at certain masses, especially at the massive end, the spline fit appears to be a reasonable model for ${N}_{\mathrm{rich}}^{\mathrm{mock}}$ as a function of ${\mathrm{log}}_{10}({M}_{\mathrm{halo}})$.

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To estimate the halo masses, we then use the standard χ² minimization methodology,

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \frac{{\left({N}_{\mathrm{rich}}-{N}_{\mathrm{rich}}^{\mathrm{mock}}\right)}^{2}}{{\sigma }_{N}^{2}},\end{eqnarray} \tag{ 2 }$$

where ${\sigma }_{N}=\sqrt{{N}_{\mathrm{rich}}}$ is the observational error on N_rich, which we estimate to be simply the Poisson uncertainty. We evaluate this on a grid of halo masses in the range $13.0\lt {\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })\lt 14.9$ using the spline-fit model for ${N}_{\mathrm{rich}}^{\mathrm{mock}}$ described above obtained for each redshift. The best-fit halo mass is given by the minimum χ², while we also estimate the 68th percentile uncertainties by evaluating the halo masses at Δχ² = 1. The estimated halo masses are listed in Table 1, along with the corresponding r₂₀₀, the characteristic halo radius within which the halo matter density is 200× the mean density of the Universe at that redshift.

Notably, we find several foreground galaxy clusters with halo masses of ${\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })\gt 14$. Two of these clusters are intersected by the FRB sight line within their characteristic cluster radius: (1) at z_grp = 0.1867, a galaxy cluster with ${\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })={14.34}_{-0.28}^{+0.18}$ lies a mere 279 or b_⊥ = 542 pkpc from the FRB sight line, which corresponds to 0.388 × r₂₀₀, and (2) another, separate, cluster is at z = 0.2170 with an estimated halo mass of ${\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })={14.44}_{-0.40}^{+0.20}$, intersecting the sight line at 0.765 × r₂₀₀.

At first glance, it might appear that there are preferentially more low-mass groups at the low-redshift end of our spectroscopic data, while the more massive clusters lie preferentially toward the higher redshifts. However, this is a selection effect in that only more massive groups or clusters are detectable as multiple galaxy members with our relatively shallow magnitude threshold and low completeness. This is shown in Figure 4, in which we use the light-cone galaxy catalogs of Henriques et al. (2015) to derive the expected completeness of N_rich ≥ 4 groups and clusters as a function of halo mass and redshift. This takes into account the estimated observational depth and incompleteness, as well as the intrinsic variance in the number of member galaxies for each halo mass. The masses that can be selected do indeed increase as a function of redshift, consistent with what we see in our data. While we are confident that we have ruled out massive clusters at z < 0.15 in our field, we suspect that more complete spectroscopic observations would reveal multiple lower-mass groups associated with the clusters detected at z > 0.17. Indeed, our detected clusters are not isolated, with multiple entities detected at similar redshifts—indicative of true overdensities and related structures in the cosmic web.

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We have now established that the FRB 20190520B sight line directly intersects within <1 r₂₀₀ of at least two galaxy clusters in the foreground. In order to calculate the DM_halos contribution, we need to make assumptions about the distribution of free electrons in the circumhalo medium of these halos.

With the assumption that the free electrons trace the fully ionized circumgalactic halo gas, we use the same halo gas density profile previously adopted in Simha et al. (2020, 2021, 2023), in which the radial profile of the halo baryonic gas density is

$$\begin{eqnarray}&&{\rho }_{b}(y)={f}_{\mathrm{hot}}\left(\displaystyle \frac{{{\rm{\Omega }}}_{b}}{{{\rm{\Omega }}}_{m}}\right)\left[\displaystyle \frac{{\rho }_{0}({M}_{\mathrm{halo}})}{{y}^{1-\alpha }{\left({y}_{0}+y\right)}^{2+\alpha }}\right].\end{eqnarray} \tag{ 4 }$$

The expression in brackets is a modified Navarro–Frenk–White (NFW; Navarro et al. 1997) radial halo profile for the matter density, as modified by Prochaska & Zheng (2019) in order to approximate the properties of a multiphase circumgalactic medium (CGM; Maller & Bullock 2004). With the central density of ρ₀ set by the halo mass M_halo, it is a function of y, the scaled radius parameter (see Mathews & Prochaska 2017), while we adopt α = 2 and y₀ = 2 in this analysis. The ratio Ω_b /Ω_m = 0.157 is the baryon fraction relative to the overall matter density, while f_hot determines the number of baryons that are present in the hot gas of the halo. The truncation radius of the gaseous halo, ${r}_{\max }$, is another free parameter of this model.

In our model, the DM_halo contributed by a halo intersected at a fixed impact parameter is therefore a function of $\{{M}_{\mathrm{halo}},{r}_{\max },{f}_{\mathrm{hot}}\}$. The uncertainties in M_halo have been explicitly estimated in Section 3.1 and will be directly taken into account in the subsequent analysis. To incorporate some of the uncertainties in ${r}_{\max }$ and f_hot, however, we adopt two different models for the foreground halo contributions that we believe bracket their plausible range.

• 1.  
  We truncate the gas halos at ${r}_{\max }={r}_{200}$. For cluster-sized halos (M_halo > 10¹⁴ M_⊙), we adopt a halo gas fraction of f_hot = 0.90. This is driven by X-ray constraints on the baryonic gas fractions in intracluster media that suggest that clusters retain essentially all of their baryonic content thanks to their deep gravitational potentials (e.g., Gonzalez et al. 2013; Chiu et al. 2018). The value of f_hot = 0.90 assumes that the stars and interstellar medium (ISM) within member galaxies comprise f_⋆ ≈ 0.1 of the cluster baryons, with the rest residing in the intracluster medium gas. For lower-mass halos with M_halo < 10¹⁴ M_⊙, we use the same value of f_hot = 0.75 that was adopted by Prochaska & Zheng (2019) and Simha et al. (2020), which allows for some of the halo gas to have been expelled from within the characteristic halo radius.
• 2.  
  The truncation radius of the gas halos is now increased to ${r}_{\max }=2\,{r}_{200}$. For cluster halos with M_halo > 10¹⁴ M_⊙, we again assume f_hot = 0.90. For the lower-mass halos, however, we introduce a baryonic "cavity" to the central parts of the halos, such that we have f_hot = 0.3 at r < r₂₀₀ and a "pileup" of evacuated baryons of f_hot = 2 at r₂₀₀ < r < 2 r₂₀₀. This is inspired by recent results from hydrodynamical simulations (e.g., Ayromlou et al. 2023; Sorini et al. 2022) that suggest that galaxy or AGN feedback processes can eject baryons from the central regions of galactic halos into the surrounding environment, leaving a reduced baryon fraction in the halo CGM compared with the primordial value.

For brevity, we will refer to the above models as the ${r}_{\max }={r}_{200}$ and ${r}_{\max }=2\,{r}_{200}$ models, respectively. While it is, in principle, possible for ${r}_{\max }$ to be larger, the modified NFW declines radially, so the DM_halo contribution converges with increasing ${r}_{\max }$. For example, for a halo intersected at b_⊥ = 0.5 r₂₀₀, the DM_halo increases by 24% when ${r}_{\max }$ is increased from ${r}_{\max }={r}_{200}$ to $2\,{r}_{200}$, but the corresponding increase is only about 5% going from ${r}_{\max }=2\,{r}_{200}$ to $3\,{r}_{200}$.

To compute DM_halos, we first generate a group halo catalog of the FLIMFLAM spectroscopic data, in which the groups and clusters detected in Section 3 are each treated as individual halos, with the masses estimated from Section 3.1. We then remove the member galaxies of these groups from the overall spectroscopic catalog and treat the remaining field galaxies as individual lower-mass halos.

To assign a halo mass to the field galaxies, we first estimated the stellar masses, M_⋆, by running the galaxy population synthesis code CIGALE (Boquien et al. 2019) on the griz photometry, with the redshifts fixed by our spectroscopy. The stellar masses were then converted into halo masses using the stellar mass–halo mass relationship (SHMR) of Moster et al. (2013).

The halo lists from the field galaxies and the identified groups were collated for the DM_halo calculation, which integrates the line-of-sight segment through the gas halo profile of Equation (4) assuming the corresponding halo masses, impact parameters from the FRB sight line, and maximum extent of the halo profiles (${r}_{\max }$). We did this as a Monte Carlo calculation in order to take into account the uncertainties in the halo masses. For field galaxies, we drew random realizations corresponding to the mean halo mass, as well as a standard deviation of 0.3 dex, the latter of which is a typical halo mass error taking into account uncertainties in the stellar mass estimation, as well as the intrinsic scatter in the SHMR. For the groups and clusters, we sample over the halo mass uncertainties listed in Table 1. However, the χ² distributions are asymmetric about the minima; therefore, we approximate this by sampling from an asymmetric Gaussian distribution based on the 16th and 84th percentile errors on either side of the best-fit value. In other words, we first draw the Gaussian random deviate with unit standard deviation and then scale them by the upper or lower error bars depending on whether the draw is positive or negative. We repeat this exercise for ∼100 iterations and keep track of the resulting individual DM_halo contributions from every iteration.

In Table 2, we list the foreground halos that provide nonzero contributions to DM_halos. The z_grp = 0.1867 cluster, which is intersected well within its virial radius (b_⊥ ∼ 0.4 r₂₀₀), provides the largest contribution, with DM_halo ≈ 300 and 350 pc cm⁻³ assuming the ${r}_{\max }={r}_{200}$ and $2\,{r}_{200}$ models, respectively. There is also a large contribution from the z_grp = 0.2170 cluster, which has a slightly larger mass but is intersected through its outskirts (b_⊥ ∼ 0.8 r₂₀₀). Because of this, the two different truncation radii provide a relatively greater difference for this cluster, changing from DM_halo ≈ 110 to 180 pc cm⁻³ with the increased gas halo radius. The z_grp = 0.1867 cluster, on the other hand, exhibits a smaller fractional change in DM_halo with respect to ${r}_{\max }$, since the sight line passes through the central region of the halo that gives large contributions with less sensitivity to ${r}_{\max }$.

Table 2. Foreground DM_halo Contributors

ID	z	R.A. a	Decl. a	${\mathrm{log}}_{10}({M}_{\mathrm{halo}}/{M}_{\odot })$	b⊥		DMhalo (pc cm−3) b
		(deg)	(deg)		(kpc)	(r200)	${r}_{\max }={r}_{200}$	${r}_{\max }=2\,{r}_{200}$
2403390701118753	0.0536	240.3391	−11.1875	${12.87}_{-0.90}^{+0.21}$	789	1.58	${0}_{-0}^{+20}$	${20}_{-12}^{+65}$
2405167901131499	0.1862	240.5168	−11.3150	${11.78}_{-0.30}^{+0.30}$	313	1.57	${0}_{-0}^{+0}$	${10}_{-10}^{+17}$
2405265701133378	0.1867	240.5266	−11.3338	${14.34}_{-0.28}^{+0.18}$	542	0.38	${300}_{-81}^{+130}$	${350}_{-87}^{+140}$
2406051301130845	0.2170	240.6051	−11.3085	${14.44}_{-0.40}^{+0.20}$	1156	0.76	${110}_{-50}^{+150}$	${180}_{-52}^{+160}$

Notes.

^a R.A. and decl. in equatorial J2000 coordinates. ^b Contribution to the FRB 20190520B DM assuming two different CGM models with ${r}_{\max }={r}_{200}$ and $2\,{r}_{200}$. We retain only two significant figures of these results.

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There is also a possible contribution from the lower-redshift galaxy group at z_grp = 0.0536, which has a halo mass of M_halo ≈ 9 × 10¹³ M_⊙ but is intersected at b_⊥ ≈ 1.6 r₂₀₀, nominally outside the characteristic halo radius. For the ${r}_{\max }={r}_{200}$ model, this clearly cannot contribute to DM_halos but does provide a contribution of DM_halo ≈ 20 pc cm⁻³ for the ${r}_{\max }=2\,{r}_{200}$ model. In this extended model, another small contribution (DM_halo ≈ 10 pc cm⁻³) is provided by an individual galaxy at z = 0.1862 with a halo mass of M_halo ≈ 6 × 10¹¹ M_⊙ also intersected at b_⊥ ≈ 1.6 r₂₀₀. While it is debatable whether individual group/cluster members should have their subhalos modeled separately from the main halo, in our case, the difference is negligible.

The FLIMFLAM survey was designed to observe numbers of foreground galaxies to act as tracers for density reconstructions of the large-scale density field in order to enable precise constraints on the DM_IGM contribution (e.g., Simha et al. 2020; Lee et al. 2022). However, in the case of FRB 20190520B, the observations were shallower and more incomplete for its FRB redshift due to the significant dust extinction within the field. The FRB 20190520B data were therefore deemed insufficient for density reconstructions using, e.g., methods from Ata et al. (2015), Kitaura et al. (2021), or Horowitz et al. (2019). Therefore, instead of a bespoke calculation of DM_IGM based directly on the observed foreground field, in principle, we have to settle for a global estimate of 〈DM_IGM〉(z_frb).

However, we do have a catalog of foreground groups and clusters, which we will take into account when trying to estimate 〈DM_IGM〉. Again, we use the "all-sky" Henriques et al. (2015) light-cone catalogs and associated density fields from the Millennium simulation (Springel 2005), largely following the methodology described in Section 3.1 of Lee et al. (2022). In order to avoid double-counting of the group/cluster contributions in both 〈DM_IGM〉 and DM_halos, we "clip" the simulation density field within two grid cells of the groups and clusters within the light cone, with the cell values clipped to δ ≡ ρ/〈ρ〉 − 1 = 3. Whether or not a group/cluster is clipped from the density field depends on its selection probability as shown in Figure 4, which we implement as a linearly increasing probability with p = 0 probability below the minimum detectable halo mass at each redshift to p = 1 at masses above the 100% completeness threshold. In other words, for example, at low redshifts (z < 0.1), even relatively low-mass groups with M_halo ∼ 10¹³ M_⊙ would not be counted in DM_IGM, since they can, in principle, be detected in our spectroscopy, and their DM_halo contribution is already taken into account. At higher redshifts, such low-mass groups are undetected, and their influence would need to be considered as part of 〈DM_IGM〉. The effect of this halo clipping is to reduce both the mean 〈DM_IGM〉 and its variance.

On the other hand, the FRB 20190520B sight line intersects two separate galaxy clusters, which means that it must be crossing through overdense regions of the Universe even if we have already removed the direct influence of the clusters themselves within ∼1–2 Mpc. For the 〈DM_IGM〉 calculation, we therefore selected mock sight lines at z_frb = 0.241 ± 0.001 that intersect within r₂₀₀ of two clusters with M_halo > 10¹⁴ M_⊙. Compared with randomly selected sight lines at this redshift selected to originate within galaxies with an observed magnitude of r < 20 (see, e.g., Pol et al. 2019), we find that 0.07% of the sight lines intersect two separate foreground cluster halos, i.e., ∼1 in 1400.

We integrate the selected sight lines through Millennium density fields that have already been clipped of "observed" clusters and compute DM_IGM assuming f_igm = 0.85, which is the typical fraction of cosmic baryons expected to reside in the diffuse IGM as found in cosmological hydrodynamical simulations (e.g., Jaroszynski 2019; Batten et al. 2021; Takahashi et al. 2021; Zhang et al. 2021; Zhu & Feng 2021). The resulting DM_IGM distribution is shown in Figure 5 with a median $\langle {\mathrm{DM}}_{\mathrm{IGM}}\rangle (z=0.241)={204}_{-39}^{+62}\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$, where the errors are quoted at the 16th and 84th percentiles. In comparison, for random sight lines at the same redshift through the normal "unclipped" density field, we find $\langle {\mathrm{DM}}_{\mathrm{IGM}}\rangle \,={191}_{-39}^{+64}\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$, while for random sight lines through the clipped density fields, we get $\langle {\mathrm{DM}}_{\mathrm{IGM}}\rangle ={179}_{-33}^{+51}$. The effects of clipping the influence of group/cluster halos and selecting sight lines that go through two clusters thus appear to largely cancel each other out, although the median DM_IGM for our double-cluster sight lines is indeed slightly higher than the usual mean.

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With the estimates of the foreground contributions in hand, we now subtract these from the total DM of FRB 20190520B in order to constrain the host contribution. Since the distributions for DM_IGM and DM_halos are significantly non-Gaussian, instead of propagating errors, we take the direct route of calculating the distribution of DM_host based on the Monte Carlo realizations we have calculated for DM_IGM and DM_halos.

In other words, we compute multiple iterations of

$$\begin{eqnarray}&&{\mathrm{DM}}_{\mathrm{host},i}={\mathrm{DM}}_{\mathrm{FRB},i}-{\mathrm{DM}}_{\mathrm{MW},i}-{\mathrm{DM}}_{\mathrm{IGM},i}-{\mathrm{DM}}_{\mathrm{halos},i},\end{eqnarray} \tag{ 5 }$$

where DM_halos,i and DM_IGM,i were drawn from the Monte Carlo realizations computed in Sections 4.1 and 4.2, respectively. For DM_FRB,i and DM_MW,i , we draw Gaussian random deviates for each iteration based on the values reported by Niu et al. (2022), DM_FRB = (1205 ± 4) and DM_MW = (113 ± 17) pc cm⁻³, where the uncertainties are adopted as the Gaussian standard deviations. We enforce the prior that DM_host ≥ 0 pc cm⁻³.

After computing Equation (5) over N = 2000 iterations, we compute the median and 16th/84th percentiles of the resulting DM_host,i distribution. These quantities, as well as the individual DM components, are listed in Table 3; note that since the medians are listed for each component, they do not necessarily obey Equation (3) precisely.

Table 3. FRB 20190520B DM Components

Component a	${r}_{\max }={r}_{200}$	${r}_{\max }=2\,{r}_{200}$
DMFRB	${1205}_{-4}^{+4}$
DMMW	${113}_{-13}^{+13}$
DMIGM	${204}_{-39}^{+62}$
DMhalos	${450}_{-130}^{+240}$	${640}_{-150}^{+260}$
DMhost b	${430}_{-220}^{+140}$	${280}_{-170}^{+140}$

Notes.

^a All DM values are in units of pc cm⁻³. ^b In the observed frame.

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We separately calculated the DM_host for the two different assumptions of ${r}_{\max }$ for the foreground halo contributions. Assuming ${r}_{\max }={r}_{200}$ (see Section 4.1), we find ${\mathrm{DM}}_{\mathrm{host}}\,={430}_{-220}^{+140}\,\mathrm{pc}\,{\mathrm{cm}}^{-3};$ on the other hand, for the ${r}_{\max }=2\,{r}_{200}$ model, the resulting host contribution is ${\mathrm{DM}}_{\mathrm{host}}\,={280}_{-170}^{+140}\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ (both in the observed frame; the corresponding rest-frame values are ${{\rm{D}}{\rm{M}}}_{{\rm{h}}{\rm{o}}{\rm{s}}{\rm{t}}}={540}_{-270}^{+170}$ and ${350}_{-210}^{+180}\,{\rm{p}}{\rm{c}}\,{{\rm{c}}{\rm{m}}}^{-3}$, respectively). These estimates are much lower than the value of ${\mathrm{DM}}_{\mathrm{host}}={903}_{-111}^{+72}\,\mathrm{pc}\,{\mathrm{cm}}^{-3}$ originally reported by Niu et al. (2022). The 68th percentile errors we derive are significantly larger than the Niu et al. (2022) estimate, since they are driven by the uncertainties in the foreground cluster masses. Adopting the upper 68th percentile errors of our DM_host values as a σ, the original estimate for DM_host is 3.4σ and 4.3σ away from our ${r}_{\max }={r}_{200}$ and $2\,{r}_{200}$ model estimates, respectively.

Given the association of FRB 20190520B with the z = 0.241 host galaxy HG 20190520B by Niu et al. (2022), we can start by estimating the contribution from the CGM of the host halo. For the reported stellar mass of M_⋆ ≈ 6 × 10⁸ M_⊙ (Niu et al. 2022), we use the dwarf galaxy SHMR of Read et al. (2017) to estimate a halo mass of M_halo = 9 × 10¹⁰ M_⊙. Allowing for the fact that the FRB originates 5 kpc (Niu et al. 2022) from the galaxy center, and adopting the models described in Section 4.1, we estimate rest-frame CGM contributions of ${{\rm{D}}{\rm{M}}}_{{\rm{h}}{\rm{o}}{\rm{s}}{\rm{t}}}^{{\rm{c}}{\rm{g}}{\rm{m}}}=18$ and $12\,{\rm{p}}{\rm{c}}\,{{\rm{c}}{\rm{m}}}^{-3}$ assuming the ${r}_{\max }={r}_{200}$ and $2\,{r}_{200}$ models, respectively. In other words, the CGM of HG 20190520B provides only a small contribution to the DM_host of FRB 20190520B. This allows us to estimate the rest-frame values of the inner host contribution to be ${\mathrm{DM}}_{\mathrm{host}}^{\mathrm{in}}\approx {520}_{-270}^{+170}$ and ${330}_{-210}^{+180}$, where we have neglected the error on ${\mathrm{DM}}_{\mathrm{host}}^{\mathrm{cgm}}$ due to the small central value.

In their analysis of FRB 20190520B, Niu et al. (2022) and Ocker et al. (2022) evaluated the emission measure (EM) from the observed optical Hα lines in HG 20190520B, which can be converted into an equivalent DM (Tendulkar et al. 2017). This was found to yield an observed-frame value in the range DM_host ≈ 230–650 pc cm⁻³, which was in tension with the original estimate of DM_host = 903 pc cm⁻³. In comparison, our new estimate for the inner host contribution spans a 68th percentile confidence region of approximately DM_host ∼ 110–690 pc cm⁻³ (after combining results from both models in Section 4.1). The EM estimation is thus now in agreement with DM_host without having to invoke unusually high gas temperatures (T ≫ 10⁴ K) in the Hα-emitting medium, as suggested by Ocker et al. (2022). Given the broad agreement between the EM and DM estimates, the Hα emitting gas—presumably in the galaxy disk—also now appears to make up the bulk of the ionized medium responsible for the dispersion seen in HG 20190520B.

Across a large number of repeating signals, FRB 20190520B has also been measured by Ocker et al. (2022) to have a mean scattering time delay of τ = 10.9 ± 1.5 ms (measured at 1.41 GHz) that can be attributed to the host. This DM of the scattering screen can be estimated from the scattering timescale using the expression from Cordes et al. (2022),

$$\begin{eqnarray}&&\tau (\mathrm{DM},\nu ,z)\approx 48.03\,\mu s\,\times \,\displaystyle \frac{{A}_{\tau }\widetilde{F}G{\mathrm{DM}}^{2}}{{\left(1+{z}_{\mathrm{frb}}\right)}^{3}\,{\nu }^{4}},\end{eqnarray} \tag{ 7 }$$

where ν is the measured frequency in gigahertz. The A_τ is a dimensionless quantity relating the mean scattering delay to the 1/e time, which we assume to be A_τ ≈ 1 following Ocker et al. (2022). The combined factor $\widetilde{F}G$ describes the combined amplification from turbulent density fluctuations and the geometry of the scattering screen, respectively, which Ocker et al. (2022) estimated to be $\widetilde{F}G={1.5}_{-0.3}^{+0.8}{({\mathrm{pc}}^{2}\,\mathrm{km})}^{-1/3}$ using the old value of DM_host = 903 pc cm⁻³.

With our updated rest-frame ${\mathrm{DM}}_{\mathrm{host}}^{\mathrm{in}}$ values for FRB 20190520B (Section 5.1), we recalculate $\widetilde{F}G\propto 1/{\mathrm{DM}}^{2}$ to find $\widetilde{F}G\approx 4.5\mbox{--}11\,{({\mathrm{pc}}^{2}\,\mathrm{km})}^{-1/3}$, with the range allowing for our model uncertainty in subtracting off the foreground galaxy clusters. This contrasts with the value originally estimated by Ocker et al. (2022), which is close to unity. This larger value implies that either $\widetilde{F}\gt 1$, G > 1, or both. If $\widetilde{F}\gt 1$, it would imply that the scattering screen is highly turbulent. Meanwhile, G ≈ 1 is expected if the turbulent scattering screen is close to the source, but it could be greater than unity if the screen is somewhere along the intervening path yet still farther away from the Milky Way, e.g., if they were associated with the foreground clusters. However, Connor et al. (2023) recently studied two FRBs that were localized to host galaxies embedded within galaxy clusters and did not see significant scattering in those FRB signals. We therefore consider it unlikely that foreground clusters are the source of the scattering; it is more likely that the large $\widetilde{F}G$ value is due to a highly turbulent scattering screen associated with the host and perhaps even close to the FRB engine itself. This conclusion is corroborated by the recent Ocker et al. (2023) paper, which reports significant scattering variations in the repeated FRB 20190520B signals, as well as the sign changes observed in their Faraday rotation (Anna-Thomas et al. 2023).

When FRB 20190520B was discovered, its DM_host estimate and those of nearly all other localized FRBs were done through guesstimated DM_host values after subtracting the mean 〈DM_IGM〉(z). At the time of writing, approximately a half-dozen localized FRBs now have credible foreground analyses that enable more confidence in their estimated DM_host.

Arguably the first reliable estimate was done by Simha et al. (2020), who analyzed the foreground of FRB 20190608 based on Sloan Digital Sky Survey and Keck data using an analogous technique to ours. They estimated DM_host ≈ 80–200 pc cm⁻³ (observed frame), which is in fact consistent with an independent analysis of the host galaxy (Chittidi et al. 2021).

More recently, Simha et al. (2023) analyzed four FRB sight lines known to exhibit DMs significantly higher than the cosmic mean using FLIMFLAM spectroscopic data of the foreground fields.

Like FRB 20190520B, FRB 20210117A was suspected to be a high-DM_host source given its clear excess DM_FRB = 731 pc cm⁻³ and localized redshift of z_frb = 0.2145. However, unlike FRB 20190520B, no significant excess was found from DM_halos based on the foreground data, so it is confirmed to be a high-DM_host source, with DM_host ≈ 665 pc cm⁻³ in the rest frame. This is in fact higher than the revised rest-frame values of DM_host ∼ 350–540 pc cm⁻³ we now find for FRB 20190520B, which now makes FRB 20210117A in principle the FRB with the highest known DM_host, although the uncertainties are large enough for either to be the true record holder. Also, FRB 20200906A was shown to not have significant foreground contributions despite a high DM_FRB, yielding an estimate of DM_host ≈ 420 pc cm⁻³. Both FRB 20190714A and FRB 20200430A are shown to have significant foreground contributions; thus, they do not have large DM_host. We note that this subsample is explicitly biased toward excess DM sources; thus, it is possible that the DM_host from this sample might be biased high as well, even though some of the FRBs are shown to be from overdense foregrounds.

James et al. (2022) and, subsequently, Baptista et al. (2023) performed population modeling of a sample of ≈70 FRBs, including 21 with redshifts from host associations. Their forward model includes two parameters to describe a lognormal distribution for DM_host. Taking their preferred values of σ = 0.5 and μ = 2.43, we find that 40% of the FRB hosts are expected to have DM_host > 500 pc cm⁻³. We conclude, therefore, that our inferred value for FRB 20190520B is consistent with the full population.