# A Heavily Scattered Fast Radio Burst Is Viewed Through Multiple Galaxy Halos

Jakob T. Faber Cahill Center for Astronomy and Astrophysics, MC 249-17
California Institute of Technology, Pasadena CA 91125, USA.  Vikram Ravi
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Stella Koch Ocker
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  The Observatories of the Carnegie
Institution for Science, Pasadena, CA 91101, USA.  Myles B. Sherman Cahill
Center for Astronomy and Astrophysics, MC 249-17 California Institute of
Technology, Pasadena CA 91125, USA.  Kritti Sharma Cahill Center for Astronomy
and Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA
91125, USA.  Liam Connor Cahill Center for Astronomy and Astrophysics, MC
249-17 California Institute of Technology, Pasadena CA 91125, USA.  Casey Law
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Nikita Kosogorov
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Gregg Hallinan Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Owens Valley Radio Observatory, California Institute
of Technology, Big Pine CA 93513, USA.  Charlie Harnach  Owens Valley Radio
Observatory, California Institute of Technology, Big Pine CA 93513, USA.  Greg
Hellbourg Cahill Center for Astronomy and Astrophysics, MC 249-17 California
Institute of Technology, Pasadena CA 91125, USA.  Owens Valley Radio
Observatory, California Institute of Technology, Big Pine CA 93513, USA.  Rick
Hobbs  Owens Valley Radio Observatory, California Institute of Technology, Big
Pine CA 93513, USA.  David Hodge  Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Mark Hodges  Owens Valley Radio Observatory, California Institute of
Technology, Big Pine CA 93513, USA.  James W. Lamb Owens Valley Radio
Observatory, California Institute of Technology, Big Pine CA 93513, USA.  Paul
Rasmussen  Owens Valley Radio Observatory, California Institute of Technology,
Big Pine CA 93513, USA.  Jean J. Somalwar Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Sander Weinreb Cahill Center for Astronomy and Astrophysics, MC 249-17
California Institute of Technology, Pasadena CA 91125, USA.  David P. Woody
Owens Valley Radio Observatory, California Institute of Technology, Big Pine
CA 93513, USA.

###### Abstract

We present a multi-wavelength study of the apparently non-repeating, heavily
scattered fast radio burst, FRB 20221219A, detected by the Deep Synoptic Array
110 (DSA-110). The burst exhibits a moderate dispersion measure (DM) of
$706.7^{+0.6}_{-0.6}$ $\mathrm{pc}~{}\mathrm{cm}^{-3}$ and an unusually high
scattering timescale of $\tau_{\mathrm{obs}}=19.2_{-2.7}^{+2.7}$ ms at 1.4
GHz. We associate the FRB with a Milky Way-like host galaxy at
$z_{\mathrm{host}}=0.554$ of stellar mass
$\mathrm{log}_{10}(M_{\star,\mathrm{host}})=10.20^{+0.04}_{-0.03}~{}M_{\odot}$.
We identify two intervening galaxy halos at redshifts
$z_{\mathrm{igh1}}=0.492$ and $z_{\mathrm{igh2}}=0.438$, with low impact
parameters, $b_{\mathrm{igh1}}=43.0_{-11.3}^{+11.3}$ kpc and
$b_{\mathrm{igh2}}=36.1_{-11.3}^{+11.3}$ kpc, and intermediate stellar masses,
$\mathrm{log}_{10}(M_{\star,\mathrm{igh1}})=10.01^{+0.02}_{-0.02}~{}M_{\odot}$
and
$\mathrm{log}_{10}(M_{\star,\mathrm{igh2}})=10.60^{+0.02}_{-0.02}~{}M_{\odot}$.
The presence of two such galaxies suggests that the sightline is significantly
overcrowded compared to the median sightline to this redshift, as inferred
from the halo mass function. We perform a detailed analysis of the sightline
toward FRB 20221219A, constructing both DM and scattering budgets. Our results
suggest that, unlike most well-localized sources, the host galaxy does not
dominate the observed scattering. Instead, we posit that an intersection with
a single partially ionized cloudlet in the circumgalactic medium of an
intervening galaxy could account for the substantial scattering in FRB
20221219A and remain in agreement with typical electron densities inferred for
extra-planar dense cloud-like structures in the Galactic and extragalactic
halos (e.g., high-velocity clouds).

Radio bursts (1339), Radio transient sources (2008), Interstellar medium
(847), Circumgalactic medium (1879), Intergalactic medium (813), Galaxy
stellar halos (598), Interstellar scattering (854)

††facilities: DSA-110, Keck-I/LRIS (Oke et al., 1995), Keck-II/DEIMOS (Faber
et al., 2003)††software: astropy (Price-Whelan et al., 2018); scipy (Virtanen
et al., 2020), numpy (Harris et al., 2020), hmf (Murray, 2014), matplotlib
(Hunter, 2007), LPipe (Perley, 2019), pPXF (Cappellari, 2017, 2022), PypeIt
(Prochaska et al., 2020), prospector (Johnson et al., 2021), astropath
(Aggarwal et al., 2021)

##  1 Introduction

Fast radio bursts (FRBs; Lorimer et al., 2007) are a class of highly luminous
extragalactic radio transients with durations ranging from nanoseconds to
seconds (Petroff et al., 2019; Cordes & Chatterjee, 2019; Majid et al., 2021;
Nimmo et al., 2022; CHIME/FRB Collaboration et al., 2022). Their dispersion
measures (DMs), which quantify the electron column density along the line of
sight (LoS), exceed the values expected from Milky Way electron density
models, suggesting extragalactic origins. This hypothesis has since been
confirmed by an increasing number of well-localized FRBs that reside in host
galaxies out to redshifts z $\sim$ 1 (Ryder et al., 2022; Law et al., 2023;
Gordon et al., 2023).

While the physical origins of FRBs remain unknown, many source models have
been proposed, ranging from isolated neutron stars to compact object mergers.
Recent observations have noted magnetars as viable sources, supported by
detections of millisecond radio bursts from the galactic magnetar SGR
1935$+$2154 by the STARE-2 and CHIME/FRB observatories, with measured
isotropic-equivalent energies of $2.2^{+0.4}_{-0.4}\times
10^{35}~{}\mathrm{erg}$ and $3_{-1.6}^{+3}\times 10^{35}~{}\mathrm{erg}$,
respectively, consistent with FRB source energetics (Bochenek et al., 2020;
CHIME/FRB Collaboration et al., 2020).

Despite their unknown formation channels, sources, and emission mechanisms, if
the source distance is known and intervening material is well-characterized,
FRB DMs serve as stringent probes of baryon densities within galaxy halos,
clusters, and filaments throughout the intergalactic medium (IGM; McQuinn,
2014; Macquart et al., 2020). FRB DMs can also facilitate the study of diffuse
ionized gas in the Milky Way and neighboring galaxies (Connor & Ravi, 2022;
Ravi et al., 2023a; Cook et al., 2023).

FRB observations are sensitive to inhomogeneities in intervening plasma
through the effects of multipath propagation, or scattering. This propagation
effect results in asymmetric, frequency-dependent pulse broadening and broadly
exponential scattering tails (assuming a Gaussian scattered image). In the
case of interstellar scattering, such tails are expected to follow a temporal
delay $\tau\propto\nu^{-\alpha}$, where $\alpha\gtrsim 4$ assuming an
infinitely wide, thin scattering screen described by Kolmogorov turbulence
($\alpha=4.4$ for scale-free power spectra, $\alpha=4$ in the case of a
diffractive scale below a finite inner scale, or where the density
fluctuations follow a Gaussian power spectrum; Rickett et al., 2009). These
assumptions are largely idealized, however, and may be challenged by flatter
values ($\alpha\lesssim 4$) inferred for Galactic pulsars (Löhmer et al.,
2001; Deneva et al., 2009; Dexter et al., 2017). The diffractive scintillation
bandwidth $\Delta\nu_{\mathrm{d}}\simeq(2\pi\tau)^{-1}$ yields more
information due to its preservation of phase information, though in practice,
most of the convincing measurements have been made for scintillation caused by
Galactic scattering (Masui et al., 2015; Gajjar et al., 2018; Hessels et al.,
2019; Marcote et al., 2020; Bhandari et al., 2020; Schoen et al., 2021; Ocker
et al., 2022a; Sammons et al., 2023), with the exception of FRB 150807 (Ravi
et al., 2016). While some FRBs at lower Galactic latitudes (e.g., FRB
20121102A, FRB 20180916B) are predominantly scattered by the Milky Way (MW)
(Ocker et al., 2021), the majority exhibit scattering timescales ($\tau(\nu)$)
that exceed those expected from purely Galactic contributions (Cordes & Lazio,
2002). The dominant scattering source for these FRBs is unconstrained in the
absence of both scintillation bandwidth and scattering timescales, which can
be used in tandem to constrain the presence of both Galactic and extragalactic
screens (Cordes et al., 2016).

To date, sightline-independent correlations between DM and $\tau$ have been
explored for the broader FRB population (Ravi, 2018; CHIME/FRB Collaboration
et al., 2019), and compared to the known $\tau$-DM correlation observed for MW
radio pulsars (Cordes et al., 2016, 2022). Such comparisons have been
difficult, however, as the canonical $\tau$-DM relation for pulsars relies on
Galactic DMs, while the DMs typically assumed for FRBs in comparison are
extragalactic (DMex; beyond the MW) and not specific to the host galaxy of the
source. The relatively small sample of well-localized FRBs available has
limited our ability to precisely constrain host DMs, and make what would be
more apt comparisons between $\tau$ and DMhost, rather than DMex. However, the
recent advent of precise FRB localizations has begun alleviating this dilemma,
which we discuss in §3.1.

Recent studies favor either the host galaxy or circumburst environment as the
dominant scattering medium (Simha et al., 2020; Chittidi et al., 2021; Ocker
et al., 2022c; Cordes et al., 2022), though it has been suggested that
intervening halos may contribute meaningfully to scattering in select cases as
well (Vedantham & Phinney, 2018; Connor et al., 2020; Chawla et al., 2022).
Determining whether scattering is, in certain instances, dominated by the
circumburst medium, host, or circumgalactic media (CGM) of intervening
galaxies could further constrain source models and offer insights into these
galactic halos, opening avenues for detailed studies of plasma turbulence in
both the host and intervening galaxies (Cordes et al., 2016; Simard & Ravi,
2021; Ocker et al., 2022c).

For scattering to dominate in the circumburst medium, high electron densities
$n_{e}\gg 10^{-2}$ cm-3 and high-amplitude density fluctuations (far exceeding
a MW-like ISM; Ocker et al., 2020) would be expected, as well as strong
magnetic fields $B\gtrsim 50~{}\mu\mathrm{G}$ (similar to the magnetized
filaments observed in the Crab nebula, for instance; Bietenholz & Kronberg,
1991) that induce extreme Faraday rotation. Highly magnetic environments do
not, however, guarantee strong scattering (e.g., in the case of the first
repeater FRB 20121102A; Michilli et al., 2018). To date, evidence for
circumburst scattering has only been found in FRB 20190520B, which exhibits
rapid variability in scattering between bursts (Ocker et al., 2022c).

Significant scattering in the interstellar medium (ISM) of FRB host galaxies
appears to be more common (Masui et al., 2015; Ocker et al., 2022a). Such
constraints require contemporaneous and discrepant scintillation and
scattering measurements, such that a two-screen scattering model can be
applied (Simard & Ravi, 2021). The two-screen model does, however, come with
certain assumptions: e.g., that there are only two dominant scattering
screens. Furthermore, placing constraints on the model necessitates measurable
scintillation in the scattering tail of the burst. Scattering in one or more
intervening galaxies, for instance, further complicates the two-screen model.

In this paper, we analyze the contributions to both DM and scattering in FRB
20221219A by intervening plasmas. In §2 we present the detection of the
heavily scattered burst, including its localization with the DSA-110 and
optical/IR follow-up observations of its host galaxy and two intervening
galaxies. In §3.1 we constrain contributions to the DM along the LoS (the so-
called “DM budget”) using HI-inferred HII column densities for intervening
galaxies based on results from the COS-Halos Survey (Werk et al., 2014), and
Illustris TNG simulation data (Zhang et al., 2021) for the intergalactic
medium (IGM). In §3.2 we present a detailed investigation aimed at identifying
the medium responsible for the uniquely high degree of scattering (the so-
called “scattering budget”), with a focus on the circumgalactic media (CGMs)
of two intervening galaxies. We conclude in §4. In this work, we adopt
standard cosmological parameters from Planck Collaboration et al. (2016) for
estimating DM contributions from the IGM (consistent with Illustris TNG;
Pillepich et al., 2017) and from Planck Collaboration et al. (2020) for all
other cosmological inferences.

##  2 DSA-110 Observation of FRB 20221219A

Table 1: Burst properties for FRB 20221219A (see Figure 1).

Parameter |  Value
---|---
$\mathrm{Localization~{}[R.A.~{}J2000,~{}Dec.~{}J2000]}$ |  $17^{h}10^{m}31.15^{s},+71^{\circ}37\arcmin 36.6\arcsec$
$\mathrm{Localization~{}Uncertainty~{}[1\sigma,arcsec]}$ |  1.5, 0.9
$\mathrm{Signal}\text{-}\mathrm{to}\text{-}\mathrm{Noise}$ |  $8.9^{+1}_{-1}$
$\mathrm{Dispersion~{}Measure~{}[pc~{}cm^{-3}]}$ |  $706.7^{+0.6}_{-0.6}$
$\mathrm{Intrinsic~{}FWHM~{}[ms]}$ |  $0.12_{-0.08}^{+0.65}$
$\mathrm{Scattering~{}Timescale~{}[ms]}$ |  $19.2_{-2.7}^{+2.7}$
$\mathrm{Linear~{}Polarization~{}Fraction~{}[L/I]}$ |  $0.502_{0.08}$

###  2.1 DSA-110 Discovery and Localization

As described in Ravi et al. (2023b), the DSA-110 is a radio interferometer
located at the Owens Valley Radio Observatory (OVRO) dedicated to the
discovery and arcsecond-scale localization of FRBs. FRB 20221219A was detected
during commissioning observations at a Modified Julian Date (MJD) of
59932.79297813 (arrival time at 1530 MHz at the observatory), with a real-time
detection signal-to-noise ratio111This was calculated using a weighted sum
matched filter. of 8.9. Antenna voltage measurements containing the burst were
recorded in two linear polarizations with a time resolution of 32.768 $\mu s$
across 6144 channels between 1311.25–1498.75 MHz. These data were used to
localize the burst to a sky location of (R.A. J2000, Dec. J2000) =
($+17^{h}10^{m}31.15^{s},+71^{\circ}37\arcmin 36.6\arcsec$) with $1\sigma$
uncertainties of 1.5″ in R.A. and 0.9″ in Dec. The data were also coherently
combined to measure the various burst properties given in Table 1, and a
dynamic spectrum of the burst is shown in Figure 1.

###  2.2 Inference of Burst Properties

We optimize the DM for temporal structure in the burst by searching for the DM
at which the forward-derivative of the dedispersed timeseries is maximized,
following methods outlined in Gajjar et al. (2018), Hessels et al. (2019), and
Josephy et al. (2019). We begin by calculating a 2D DM transform across the
burst in time for 0.075 $\mathrm{pc}~{}\mathrm{cm}^{-3}$ intervals, ranging
from $692~{}\text{-}~{}722$ $\mathrm{pc}~{}\mathrm{cm}^{-3}$. We then
calculate the forward-derivative and convolve with a $3\times
5\left(2.7~{}\mathrm{ms}\times 0.5~{}\mathrm{pc}~{}\mathrm{cm}^{-3}\right)$
smoothing kernel. Finally, we integrate the modulus of the forward-derivative
in time raised to $n\in(1,2,4)$. Gajjar et al. (2018) and Hessels et al.
(2019) elect to use $n=1$ and $n=2$, respectively. Josephy et al. (2019),
however, show that $n>2$ is optimal for identifying one uniquely bright peak
in the pulse-profile, while $n\lesssim 2$ typically prefer a series of lower-
amplitude peaks. For the curves corresponding to each value of $n$, we fit a
complex polynomial and take its peak as the structure-maximizing DM. To
estimate uncertainties, we fit a simple Gaussian function to the most
prominent peak in the polynomial fit and take the 1$\sigma$ offset. For both
$n=2$ and $n=4$, we find a structure-optimizing DM of
$706.7^{+0.6}_{-0.6}~{}\mathrm{pc~{}cm}^{-3}$, as both contain an unambiguous
peak.

Due to the low S/N of the burst, we confirm the presence of scattering by
dividing the observing band into three $\simeq 83$ MHz sub-bands and fit
exponentially-modified Gaussian functions $\mathbb{G}(t)$ to the timeseries of
each respective sub-band, defined as

$\displaystyle\mathbb{G}\left(t\mid\mathrm{A},\Delta
t,\sigma,\tau\right)=\mathrm{A}\times\left[\exp\left(-\frac{\left(t-\Delta
t\right)^{2}}{2\sigma^{2}}\right)\right]$ (1)
$\displaystyle\ast\left[\mathbb{H}\left(t-\Delta
t\right)\exp\left(-\frac{t-\Delta t}{\tau}\right)\right],$

where $t$ represents time, $\tau$ indicates the scattering timescale at the
central frequency of the band (in MHz), $\mathbb{H}(t)$ is the Heaviside unit
step function, $\Delta t$ is the time shift, $\sigma$ is Gaussian standard
deviation, and $\ast$ symbolizes a convolution. We find that the pulse
broadening timescale evolves in accordance with $\alpha=2.6\pm 1.8$,
consistent with $\alpha\gtrsim 4$ scatter-broadening to within uncertainties.
Fitting $\mathbb{G}(t)$ to the timeseries obtained by integrating across the
full observing band, we infer a scattering timescale $\tau=19.2_{-2.7}^{+2.7}$
ms. The uncertainties in $\tau$ are derived from the covariance matrix of the
least-squares fit, which is re-calculated for a set of pulse profiles within
the DM uncertainties to produce a total error that includes uncertainty in DM.
These fits are shown in Figure 1.

Figure 1: The dynamic (time-frequency) spectrum showing FRB 20221219A,
downsampled in time by a factor of 18 and in frequency by a factor of 96 to
for clarity. To better visualize the burst in the dynamic spectrum, we further
smoothed the data using a Savitzky-Golay smoothing filter with a window of 13
time bins and a polynomial order of 1. Above the dynamic spectrum, we show the
normalized, unsmoothed total-intensity ($I_{\rm norm}$) and linearly polarized
intensity ($L_{\rm norm}$) burst timeseries, as well as a non-linear least-
squares fit for $\mathbb{G}(t)$ (Eq. 1) to the pulse profile, which indicates
a $\tau=19.2_{-2.7}^{+2.7}$ ms. In the right-most panels, we fit timeseries to
three $\simeq 83$ MHz sub-bands, and the respective scattering timescales
measured for each sub-band with errors with a best-fit power-law of
$\tau\propto\nu^{-2.6\pm 1.8}$ power law. Uncertainties for all fits of
$\mathbb{G}(t)$ are shown as shaded regions surrounding the fitted profiles.

###  2.3 Optical/IR Follow-Up of Host & Intervening Galaxies

Using the 10th data release of the Legacy
Survey222https://www.legacysurvey.org/dr10/ (DR10 R-band image; Dey et al.,
2019) and the Pan-STARRS1 (PS1; Chambers et al., 2016) optical survey, we
identify a plausible host galaxy for FRB 20221219A (henceforth HG 20221219A)
consistent with the radio localization ellipse (see R-band field in Figure 3).
We also identify two closely neighboring galaxies (henceforth IGH1 and IGH2).

We use astropath (Aggarwal et al., 2021) for host galaxy validation, which
implements a Bayesian approach to estimate association probabilities for
neighboring galaxies with tunable priors based on the sky position of the FRB,
as well as their R-band magnitude, position, and R-band radius (see SED fit in
Figure 2; Sharma et al. (2023) and Law et al. (2023) provide details regarding
host association methods). We were able to successfully associate the host
galaxy to FRB 20221219A at a confidence level of $99.6\%$ using Legacy Survey
DR10 R-band imaging data from the Beijing-Arizona Sky Survey (BASS). We
discuss IGH1 and IGH2, also visible in the field (see Figure 3), in Sections
2.4, 3.2.4, and 3.2.5.

####  2.3.1 Optical/IR Photometry

We make photometric measurements using images from PS1 ($g,r,i,z,y$), DECam
($g,r,z$; Valdes et al., 2014), WISE ($w1,w2$; Wright et al., 2010), as well
as IR photometric data obtained with the Wide Field Infrared Camera (WIRC, Ks;
Wilson et al., 2003) on August 16, 2022. HG 20221219A, IGH1, and IGH2 are
characterized following the methods outlined in Sharma et al. (2023). We
measure isophotes for each using PS1 i-band images, setting a best-fit
coverage of $\gtrsim 95\%$. The isophote is then scaled in accordance with the
point spread functions of various photometric bands to execute aperture
photometry.

####  2.3.2 Optical/IR Spectroscopy

We observed HG 20221219A with the Deep Extragalactic Imaging Multi-Object
Spectrograph (Keck-II/DEIMOS; Faber et al., 2003) on April 20, 2023, and both
IGH1 and IGH2 with the Low-Resolution Imaging Spectrometer on the Keck I
telescope (Keck-I/LRIS; Oke et al., 1995) on June 14, 2023. We created a mask
of roughly 50 slits for our DEIMOS observation of the FRB 20221219A field.
Slits were placed on the positions of candidate foreground galaxies from the
Legacy Survey DR9 catalog, including on massive central members of the galaxy
cluster J171039.6+713427.

We reduce our spectra using PypeIt (Prochaska et al., 2020) and the standard
LPipe software (Perley, 2019) and calibrate using observations of the BD+28
4211 standard star. To account for slit losses, we scale the spectra to match
the PS1 photometry.

To measure the spectroscopic redshifts and line fluxes, we use the penalized
PiXel-Fitting software (pPXF; Cappellari, 2017, 2022). This jointly fits for
the stellar continuum and nebular emission lines based on the MILES stellar
library (Sanchez-Blazquez et al., 2006). This places the host galaxy at a
redshift of $z_{\mathrm{host}}=0.554$, and find the two neighboring galaxies
in the foreground at $z_{\mathrm{igh1}}=0.492$ and $z_{\mathrm{igh2}}=0.438$
(see Table 2).

####  2.3.3 SED Modeling

Using the spectral energy distribution (SED) fitting software Prospector
(Johnson et al., 2021), we perform a non-parametric fit for the stellar
properties of the HG 20221219A, IGH1 and IGH2. While we were unable to obtain
star formation rates for IGH1 and IGH2 due to low S/N in the FIR region of the
spectrum, we were able to identify HG 20221219A as a modestly star-forming
galaxy, $\dot{M}_{\star}=1.78_{-0.23}^{+0.24}~{}M_{\odot}\mathrm{yr}^{-1}$, of
stellar mass
$\mathrm{log}_{10}(M_{\star,\mathrm{host}})=10.20^{+0.03}_{-0.04}~{}M_{\odot}$
(see Figure 2), and IGH1, IGH2 as galaxies with stellar masses straddling that
of HG 20221219A,
$\mathrm{log}_{10}(M_{\star,\mathrm{igh1}})=10.60^{+0.02}_{-0.02}~{}M_{\odot}$,
$\mathrm{log}_{10}(M_{\star,\mathrm{igh2}})=10.01^{+0.02}_{-0.02}~{}M_{\odot}$
(see Table 2).

Figure 2: A non-parametric SED fit to observed spectroscopic and photometric
data (red) for the host galaxy (PSO J$257.6335+71.625$) of FRB 20221219A,
obtained with Keck-II/DEIMOS. The SED fit is performed using Prospector with
residuals for the best posterior sample (green).

###  2.4 Sightline Crowding

The extreme degree of scattering in FRB 20221219A and apparently unusual
presence of closely neighboring intervening galaxies suggests that the galaxy
population along the FRB 20221219A LoS may be overcrowded. To evaluate whether
this is true, we first calculate the number density of galaxies, $n_{50}(z)$,
along the full sightline within a 50 kpc comoving radius using data taken from
Legacy Survey DR10. A 50 kpc radius is chosen as the smallest radius that
fully encompasses the two interveners, accounting for uncertainty in the
localization, as shown in Figure 3; our conclusions are not sensitive to this
choice.

We then compare this count to the expected number densities using a Monte
Carlo-based approach. The predicted number density of galaxies, $n_{50}(z)$,
can be calculated using the halo mass function (HMF), which determines the
number density $n$ for a specific halo mass $M_{h}$ as

$\frac{dn}{d\ln(M_{h})}=f\left(\sigma_{m}\right)\frac{\rho_{m,0}}{M_{h}}\frac{d\ln\left(\sigma_{m}^{-1}\right)}{d\ln(M_{h})}$
(2)

where $\rho_{m,0}$ is the matter density at $z=0$, $\sigma_{m}$ is the root-
mean-square variance of the linear density field, which varies with the linear
matter power spectrum, and $f\left(\sigma_{m}\right)$ represents a function of
$\sigma_{m}$ that is redshift-independent. We utilize the Tinker et al. (2008)
HMF as implemented in the hmf Python package (Murray et al., 2013). The Tinker
HMF is precisely calibrated to redshifts $z\lesssim 2$ and evolves with
redshift in accordance with a predefined overdensity threshold.

To simulate expected values for $n_{50}(z)$ within the relevant spatial
domain, we set a target redshift to that of the host, $z=0.554$, and populate
the comoving volume with dark matter halos following a Poisson distribution,
based on the mean number of halos set by the HMF. Each halo is randomly
assigned a mass in accordance with the HMF distribution, bounded by a mass
range of $10^{11}~{}$-$~{}10^{15}M_{\odot}$. These limits are informed by the
halo mass estimates for each intervener,
$\log\left(M_{h,\mathrm{igh1}}\right)=11.96^{+0.02}_{-0.02}M_{\odot}$,
$\log\left(M_{h,\mathrm{igh2}}\right)=11.52^{+0.01}_{-0.01}M_{\odot}$, which
we obtain assuming the Moster et al. (2010) stellar-to-halo mass relation

$\frac{M_{\star}}{M_{h}}(z)=2A(z)\left[\left(\frac{M_{h}}{M_{A}(z)}\right)^{-\beta(z)}+\left(\frac{M_{h}}{M_{A}(z)}\right)^{\gamma(z)}\right]^{-1},$
(3)

parameterized by Girelli et al. (2020) using the $\Lambda$CDM DUSTGRAIN-
pathfinder simulation by $A=0.0429_{-0.0026}^{+0.0026},\
M_{A}=11.87_{-0.06}^{+0.06},\ \beta=0.99_{-0.07}^{+0.08},\
\gamma=0.669_{-0.015}^{+0.016}$ for a redshift range $0.2\leq z\leq 0.5$ (see
Table 2 in Girelli et al., 2020).

For each simulation, we randomly select a sightline and calculate the number
of halos within a 50 kpc comoving radius. Sightlines with a halo number
density equal to or greater than the observed number density of two
interveners are tallied, from which we construct a representative cumulative
distribution function (CDF), thereby assessing the rarity of the sightline
toward FRB 20221219A. We find that for FRB 20221219A
CDF$\left(n_{50}(z)=2\right)\sim 0.99$, indicating that the field is
significantly overcrowded. The number of intersected halos that would be
expected along this sightline amounts to only $N_{\mathrm{halos}}=0.18$.

Table 2: Summary of observed and derived parameters for the host galaxy HG 20221219A (see Figure 2), IGH1, and IGH2 (see Figure 3). We report spectroscopic redshifts ($z$), impact parameters ($b$), stellar masses ($\log_{10}(M_{\star})$), extinction-correct r-band magnitudes ($r$), and the star formation rate (SFR; $\dot{M}_{\star}$) of the host. The $\dot{M}_{\star}$ values of the interveners were not measured due to the low S/N of their respective SEDs. Object |  $z$ |  $b~{}\left[\mathrm{kpc}\right]$ |  $\log_{10}\left(M_{\star}\right)~{}\left[M_{\odot}\right]$ |  $r~{}\left[\mathrm{mag}\right]$ |  $\dot{M}_{\star}~{}\left[M_{\odot}~{}\mathrm{yr}^{-1}\right]$
---|---|---|---|---|---
HG 20221219A |  $0.554$ |  … |  $10.20_{-0.04}^{+0.03}$ |  $22.6_{-0.2}^{+0.2}$ |  $1.78_{-0.23}^{+0.24}$
IGH1 |  $0.492$ |  $43_{-11.3}^{+11.3}$ |  $10.60_{-0.02}^{+0.02}$ |  $21.6_{-0.2}^{+0.2}$ |  …
IGH2 |  $0.438$ |  $36.1_{-11.3}^{+11.3}$ |  $10.01_{-0.02}^{+0.02}$ |  $21.7_{-0.2}^{+0.2}$ |  …

Figure 3: Legacy Survey (BASS) R-band cutout of the field surrounding FRB
20221219A. The white dashed-line circle indicates a comoving radius of 50 kpc.
The host and intervening galaxies are outlined by white, purple, and magenta
dashed circles (labels consistent with Table 2). The virial radii
($\mathrm{R}_{200}$) are over-plotted as larger solid circles with consistent
coloring. The 3$\sigma$ radio localization ellipse is over-plotted in violet.
The upper panel shows the virial radius ($\mathrm{R}_{500}$) of the
intervening galaxy cluster J171039.6+713427 identified in the WISE survey (Wen
et al., 2017). Figure 4: A schematic showing the FRB 20221219A sightline,
including the two intervening galaxies (IGH1, IGH2), their respective impact
parameters ($b$), and virial radii ($\mathrm{R}_{200}$). We also show galaxy
cluster J171039.6+713427 identified in the WISE survey (Wen et al., 2017),
including its $\mathrm{R}_{500}$. The presence of this cluster is meaningful
when considering the DM contribution of the ICM, discussed in Section 3.1.

##  3 Analysis & Discussion

###  3.1 The Dispersion Measure Budget

The dispersion measure (DM) of the FRB is defined as the electron column
density along the LoS $\mathrm{DM}=\int n_{e}(z)dl$, where $n_{e}$ is the
electron density. The DM, expressed in standard units of $\mathrm{pc}\
\mathrm{cm}^{-3}$, is measured from the frequency-dependent delay in arrival
times present in radio signals passing through cold, sparse plasmas along the
LoS. As is typically done in the literature, we can express the measured DM
for a source at redshift $z_{\mathrm{host}}$ as the sum

$\displaystyle\mathrm{DM}_{\mathrm{obs}}$
$\displaystyle=\mathrm{DM}_{\mathrm{mw}}+\mathrm{DM}_{\mathrm{igm}}\left(z_{\mathrm{host}}\right)$
(4)
$\displaystyle+\frac{\mathrm{DM}_{\mathrm{icm}}}{1+z_{\mathrm{cluster}}}+\frac{\mathrm{DM}_{\mathrm{igh}}}{1+z_{\mathrm{igh}}}+\frac{\mathrm{DM}_{\mathrm{host}}}{1+z_{\mathrm{host}}}$

that includes components from the Milky Way (mw), intergalactic medium (igm),
intersecting intracluster medium (icm), intervening galaxy halos (igh), and
host galaxy (host). Due to cosmic variance, a statistical dependence of
$\mathrm{DM}_{\mathrm{igm}}$ on redshift, $z$, is needed. The
$\mathrm{DM}_{\mathrm{icm}}$, $\mathrm{DM}_{\mathrm{igh}}$, and
$\mathrm{DM}_{\mathrm{host}}$ terms require a further reduction of the rest-
frame dispersion measures by factors of $1/(1+z)$ for the respective redshifts
of each. For simplicity, the host galaxy disk and halo, as well as the
circumburst medium surrounding the FRB source, are treated as a single term.
In the following sections, we will evaluate the DM contributions we expect
from the Milky Way, IGM, ICM, and the intervening galaxies along the LoS. A
schematic of the full sightline is shown in Figure 4.

Due to the presence of a closely neighboring galaxy cluster and two
intervening galaxy halos, the DM budget is tight, leaving many of the
diagnostics for DM outside the MW biased towards underestimates, as we
describe later in §3.1.2 and §3.1.3. To alleviate this bias and remain
conservative in our DM attributions to local media, we omit the inclusion of a
DM contribution from the MW halo, as this is also a largely uncertain
quantity. The main purpose of this is to maximize the host galaxy DM
allotment, which, if determined to be smaller, would aid in our suggestion
that the observed scattering does not occur in the host. Upper limits on the
DM of the Milky Way halo have, however, been constrained to within
$\mathrm{DM}_{\mathrm{halo}}\lesssim 38$ pc cm-3 by Ravi et al. (2023a) using
the non-repeating FRB 20220319D, and $\mathrm{DM}_{\mathrm{halo}}\lesssim
52~{}\text{-}~{}111$ pc cm-3 by Cook et al. (2023) using the first FRB catalog
from CHIME/FRB (CHIME/FRB Collaboration et al., 2021).

####  3.1.1 Milky Way and Halo

The DM contribution from the MW is characterized by the Galactic electron
density model NE2001 (Cordes & Lazio, 2002), which estimates
$\mathrm{DM}_{\mathrm{mw}}\sim 44^{+4}_{-4}~{}\mathrm{pc}\ \mathrm{cm}^{-3}$
(assuming $\sim 10\%$ uncertainty, in accordance with Ocker et al., 2020)
along the LoS toward FRB 20221219A (positioned at $102.93^{\circ}$,
$33.53^{\circ}$), through the Galaxy.

####  3.1.2 Intergalactic Medium

While the IGM is a dominant contributor to the DM budgets of FRB signals
(Zhang et al., 2021; Walker et al., 2023), it does not appear to noticeably
scatter them. We assume this based on both modeling of gas densities in the
IGM (Macquart & Koay, 2013) and the absence of a universally applicable
correlation between observed scattering timescales and extragalactic DMs
(CHIME/FRB Collaboration et al., 2021; Chawla et al., 2022). The mean DM
contribution for a constant co-moving density in the IGM is given by (e.g.,
McQuinn, 2014)

$\langle\mathrm{DM}_{\mathrm{igm}}(z)\rangle=n_{e_{0}}D_{\mathrm{H}}\int_{0}^{z}dz^{\prime}\frac{\left(1+z^{\prime}\right)}{E\left(z^{\prime}\right)}$
(5)

where $n_{e_{0}}=2.2\times 10^{-7}\times f_{\mathrm{IGM}}$ is the IGM electron
density at $z=0$, $f_{\mathrm{IGM}}$ being the IGM baryon fraction based on
Planck 18 cosmology (Planck Collaboration et al., 2020),
$D_{\mathrm{H}}=c/H_{0}$ is the Hubble distance and $E(z)=$
$\left[\Omega_{\mathrm{m}}(1+z)^{3}+1-\Omega_{\mathrm{m}}\right]^{1/2}$ for a
flat $\Lambda$CDM universe with a matter density $\Omega_{\mathrm{m}}$. With
this, we generate and fit a DM distribution using the probability density
function (PDF) (Macquart et al., 2020; Zhang et al., 2021)

$p_{\mathrm{igm}}(\Delta)=A\Delta^{-b}\exp\left[-\frac{\left(\Delta^{-a}-C_{0}\right)^{2}}{2a^{2}\sigma_{\mathrm{DM}}^{2}}\right],\quad\Delta>0$
(6)

where
$\Delta=\mathrm{DM}_{\mathrm{igm}}/\left\langle\mathrm{DM}_{\mathrm{igm}}\right\rangle$,
$b$ depends on the halo gas density profile. We assume $a=b=3$ (Macquart et
al., 2020). The effective standard deviation is $\sigma_{\mathrm{DM}}$, and
$C_{0}$ impacts the transverse position, which is fitted for. We also assume
values for $A$, $\sigma_{\mathrm{DM}}$, and $C_{0}$, derived from Illustris
TNG simulation data by Zhang et al. (2021).

The IGM sightline for FRB 20221219A is, however, slightly complicated by the
presence of a proximate foreground galaxy cluster J171039.6+713427 cataloged
in the WISE survey and DR9 group catalog, positioned at a redshift of
$z_{\mathrm{cluster}}=0.16$ with mass $\log_{10}(M_{\mathrm{cluster}})\simeq
14.1^{+0.2}_{-0.2}M_{\odot}$ (the quoted 0.2 dex uncertainty for cluster
masses $\mathrm{log}_{10}\left(M_{\mathrm{cluster}}\right)\gtrsim
14M_{\odot}$) and a LoS offset of $\simeq 3.2^{\prime}$, corresponding impact
parameter $b\sim 553^{+11}_{-11}$ kpc (Wen et al., 2017). We evaluate the DM
contribution of the intracluster medium (ICM) surrounding the cluster at its
measured impacted parameter. The $n_{e,\mathrm{icm}}$ at $b$ is estimated
using a Navarro-Frenk-White profile as implemented by Vikhlinin et al. (2006)
and Prochaska et al. (2019), contributing
$\mathrm{DM}_{\mathrm{cluster}}\simeq 142^{+12}_{-12}$ pc cm-3. This
uncertainty does not, however, account for spatial asymmetry in the baryon
halos, which may be significant (Connor et al., 2023).

To estimate the collective PDF, Pigm+icm(DM), for the DM contributions from
the IGM and ICM, we assume a Gaussian PDF for $p_{\mathrm{icm}}(\Delta)$,
given by

$p_{\mathrm{icm}}(\Delta)=\frac{1}{\sqrt{2\pi\sigma_{\mathrm{DM}}^{2}}}\exp\left(-\frac{(\Delta-\mu)^{2}}{2\sigma_{\mathrm{DM}}^{2}}\right)$
(7)

where
$\Delta=\mathrm{DM}_{\mathrm{icm}}/\left\langle\mathrm{DM}_{\mathrm{icm}}\right\rangle$
and convolve with $p_{\mathrm{igm}}(\Delta)$ (see Eq. 6) to obtain
Pigm+icm(DM). Taking the 50th percentile of the convolution (uncertainties
given by the 15th and 85th percentiles), we estimate
$\mathrm{DM}_{\mathrm{igm+icm},50}=608_{-59}^{+60}\mathrm{pc~{}cm}^{-3}$ in
the host frame, as shown in Figure 5 and Table 3.

Figure 5: PDFs for DMigm (black), DMigm+cluster (magenta), DMHost (purple),
where P(DM $|~{}z=0.554$) is in units of [pc cm-3]-1. The 50th percentile
values of each PDF, as well as 15th and 85th percentile uncertainties are
indicated by black dotted lines and shaded regions, respectively. Due to the
narrowness of the Milky Way and intervening galaxy PDFs (see §3.1.1 and
§3.1.3), we omit them above for clarity.

####  3.1.3 Intervening Galaxies

We estimate DMigh for the CGM of both intervening galaxies based on HII column
densities (NHII) inferred from direct NHI measurements made for similar nearby
galaxies in the COS-Halos survey (for 44 gaseous halos with $T\sim 10^{4}$ K
photoionized CGMs at impact parameters of $b\lesssim 160$ kpc near $z\sim
0.2$; Werk et al., 2014). Inferences of NHII rely on photoionization modeling
relating NHI to NH, which shows that the CGMs are highly ionized, such that
$\mathrm{n}_{\mathrm{HII}}/\mathrm{n}_{\mathrm{H}}\gtrsim 99\%$. Interpolating
measurements from the COS-Halos survey across the full (NHII, $b$,
$M_{\star}$) parameter space, we converge on the regions applicable to $b$ and
$M_{\star}$ for both interveners and estimate
$\mathrm{log}_{10}(\mathrm{N}_{\mathrm{HII},\mathrm{igh1}})\simeq
19.5^{+0.1}_{-0.1}$ cm-2 and
$\mathrm{log}_{10}(\mathrm{N}_{\mathrm{HII},\mathrm{igh2}})\simeq
19.6^{+0.1}_{-0.1}$ cm-2, which correspond to
$\langle\mathrm{DM}_{\mathrm{igh1}}(z=0.492)\rangle\simeq
10^{+5}_{-5}\mathrm{pc}\mathrm{~{}cm}^{-3}$ and
$\langle\mathrm{DM}_{\mathrm{igh2}}(z=0.438)\rangle\simeq
14^{+5}_{-5}\mathrm{pc}\mathrm{~{}cm}^{-3}$. Similar to the ICM, we assume a
Gaussian PDF for $p_{\mathrm{igh}}(\Delta)$. In estimating DMHost, we
conservatively neglect the presence of any hot gas in the CGM of the
interveners, which is again challenging to include in the DM budget due to
tight constraints placed by the large contributions of the IGM and neighboring
galaxy cluster.

####  3.1.4 Host Galaxy

To estimate DMhost, we convolve $p_{\mathrm{igh+icm}}$ with $p_{\mathrm{MW}}$,
$p_{\mathrm{igh1}}$ and $p_{\mathrm{igh2}}$ to obtain
$\mathrm{P}_{\mathrm{host}}$(DM). We assume Gaussian PDFs (similar to Eq. 7)
for the MW and both interveners. Taking the 50th percentile of
$\mathrm{P}_{\mathrm{host}}$(DM), we estimate
$\mathrm{DM}_{\mathrm{host,50}}=62_{-43}^{+48}$ pc cm-3 in the host-galaxy
frame (see Figure 5 and Table 3). Given the large uncertainties in modeling
the DMs contributed by the intervening galaxy and cluster halos, we also
estimated $\mathrm{DM}_{\mathrm{host,50}}$ in the absence of their
contributions. In that case, we find
$\mathrm{DM}_{\mathrm{host,50}}=165_{-93}^{+81}$ pc cm-3.

Table 3: Estimated DM contributions (in pc cm-3) for each term in Eq. 4 derived from the PDFs in Figure 5, quoted as the 50th percentile with 15th and 85th percentile uncertainties. $\mathrm{P(DM)}$ |  $\mathrm{DM}_{50}$ $\left[\mathrm{pc~{}cm}^{-3}\right]$
---|---
$\mathrm{MW}$ |  $44^{+10}_{-10}$
$\mathrm{IGM+ICM}$ |  $608_{-59}^{+60}$
$\mathrm{IGH1}$ |  $10^{+5}_{-5}$
$\mathrm{IGH2}$ |  $14^{+5}_{-5}$
$\mathrm{HG\,20221219A}$ |  $62_{-43}^{+48}$

###  3.2 The Scattering Budget

We observe a high scattering timescale of
$\tau_{\mathrm{obs}}=19.2_{-2.7}^{+2.7}$ ms for FRB 20221219A at 1.4 GHz. The
pulse broadening, as measured for three individual sub-bands, is best
described by $\tau\propto\nu^{-\alpha}$, $\alpha=2.6\pm 1.8$. To assess the
origins of the scattering seen in FRB 20221219A, we can divide
$\tau_{\mathrm{obs}}$ for a source at redshift $z_{\mathrm{host}}$ into a sum
of terms corresponding to the various scattering media along the LoS as

$\begin{aligned}
\tau(\nu)_{\mathrm{obs}}=&\tau_{\mathrm{mw}}(\nu)+\tau_{\mathrm{igm}}(\nu,z)~{}+\\\
&\frac{\tau_{\mathrm{igh}}(\nu)}{\left(1+z_{\mathrm{igh}}\right)^{3}}+\frac{\tau_{\mathrm{host}}(\nu)}{\left(1+z_{\mathrm{host}}\right)^{3}}~{}+\frac{\tau_{\mathrm{cbm}}(\nu)}{\left(1+z_{\mathrm{host}}\right)^{3}}\end{aligned},$
(8)

that, similarly to the DM budget, includes lens rest-frame components from the
Milky Way (mw), the intergalactic medium (igm), intervening galaxies (igh),
the host galaxy (host), and now the circumburst medium (cbm). We adopt a
nominal power-law frequency scaling, $\tau(\nu)\propto\nu^{-4}$. The last
three terms of Eq. 8 scale with redshift to account for the fact that, for an
observation frequency $\nu$, scattering goes as $\nu^{\prime}=\nu(1+z)$ in the
galaxy’s rest frame and time dilation goes as $(1+z)$ (Macquart & Koay, 2013;
Cordes et al., 2016). In the following sections, we will consider each
scattering medium along the line of sight individually.

####  3.2.1 Electron Density Fluctuations

Density fluctuations are modeled within a volume of ionized cloudlets,
parameterized by the combined quantity $\widetilde{F}$, the density
fluctuation parameter, defined as

$\widetilde{F}=\frac{\zeta\varepsilon^{2}}{f_{\mathrm{v}}\left(l_{\mathrm{o}}^{2}l_{\mathrm{i}}\right)^{1/3}}~{}~{}~{}\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3},$
(9)

where $l_{\mathrm{o}}$ is the outer scale of the turbulence power spectrum (in
pc), $l_{\mathrm{i}}$ is the inner scale (in km), $f_{\mathrm{v}}$ is the
volume filling factor, $\epsilon^{2}$ is the intra-cloudlet variance in the
electron density fluctuations, and $\zeta$ is the inter-cloudlet variation
with respect to the mean electron density within the cloudlets. The
fluctuation parameter $\widetilde{F}$, in combination with the geometric
factor $G$, strongly affects $\tau$.

We assess the physical validity of two scattering scenarios: scattering by a
uniform, extended CGM (§3.2.4), and scattering by a single ionized cloudlet
(§3.2.5).

####  3.2.2 Line of Sight Geometry

In addition to the electron density fluctuations within intervening media, the
position of those media with respect to the source and observer serves as an
impactful factor in determining their scattering power. Treatments in Cordes
et al. (2016), Ocker et al. (2021), and Cordes et al. (2022) define a
dimensionless geometric factor $G$ to describe this. In Euclidean space, it is
defined as

$G=\frac{\int_{\mathrm{layer}}s(1-s/d)ds}{\int_{\mathrm{host}}s(1-s/d)ds},$
(10)

where $s$ represents a path element of the full path length $d$, and $G$ is of
order unity for a source contained within in the scattering medium (e.g., the
host galaxy), such that the distance to the source far exceeds the LoS extent
of the scattering medium. Typically, however, $G$ strongly depends on the
distribution of free electrons along the LoS and can increase by many orders
of magnitude for intervening galaxies. In the case of FRB 20221219A, the
intervening galaxies we consider are at non-negligible redshifts, so the
expression for $G$ can be rewritten (see Cordes et al. (2022) for the complete
derivation) as

$G\left(z_{\ell},z_{\mathrm{s}}\right)=\frac{2d_{\mathrm{sl}}d_{\mathrm{lo}}}{Ld_{\mathrm{so}}},$
(11)

where $d_{\mathrm{sl}}$, $d_{\mathrm{lo}}$, $d_{\mathrm{so}}$ are,
respectively, the source-to-intervener, intervener-to-observer, and source-to-
observer angular diameter distances (see schematic in Figure 4), and $L$ is
the thickness of the scattering layer.

Given this geometric factor, a source at redshift $z_{\mathrm{s}}$, and a
scattering region in an intervening galaxy at $z_{\ell}$, the scattering
timescale can be expressed as

$\displaystyle\tau\left(\mathrm{DM}_{\ell},\nu,z_{\ell},z_{\mathrm{s}}\right)$
(12) $\displaystyle\quad\simeq
0.48\mathrm{~{}ms}\times\frac{A_{\tau}\widetilde{F}G\left(z_{\ell},z_{\mathrm{s}}\right)\mathrm{DM}_{\ell,100}^{2}}{\nu^{4}\left(1+z_{\ell}\right)^{3}},$

where $\mathrm{DM}_{\ell}$ is in the rest frame of the intervening galaxy,
which contributes to the measured DM as
$\mathrm{DM}_{\ell}/\left(1+z_{\ell}\right)$, with $\nu$ in $\mathrm{GHz}$ and
$\mathrm{DM}_{\ell,100}\equiv\mathrm{DM}_{\ell}/\left(100~{}\mathrm{pc}~{}\mathrm{cm}^{-3}\right)$
(Cordes et al., 2022). The quantity $A_{\tau}$, in turn, accounts for the
shape of the pulse broadening function (typically falling between
$1/6~{}\text{-}~{}1$, though we henceforth assume $A_{\tau}=1$), and depends
on both the spectral index $\beta$ and inner scale $l_{\mathrm{i}}$ of the
scattering medium.

####  3.2.3 Host Galaxy & Circumburst Environment

It has been shown by Cordes et al. (2022) that the majority of FRBs detected
by CHIME/FRB (repeating and non-repeating), assuming host galaxy-dominated
scattering, emerge from an ISM with $\widetilde{F}\lesssim 1$
$\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$, with the exception of the
heavily scattered FRB 20191221A, which still suggests a host
$\widetilde{F}\lesssim 10$ $\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$
(see their Fig. 5; Cordes et al., 2022).

We find HG 20221219A to be MW-like in its star formation rate (SFR;
$\dot{M}_{\star}$). While the $M_{\star,\mathrm{host}}$ is a factor of $\sim
4$ smaller than that of the MW, and its SFR of
$\dot{M}_{\star}=1.78_{-0.23}^{+0.24}~{}M_{\odot}\mathrm{yr}^{-1}$, is
comparable to the MW’s
$\dot{M}_{\star}=1.65^{+0.19}_{-0.19}~{}M_{\odot}\mathrm{yr}^{-1}$ (Licquia &
Newman, 2015). Under the assumption that the two galaxies are comparable in
their properties, we can apply the established relation between $\tau$ and DM
values of Galactic pulsars (Cordes et al., 2016) to the host galaxy, and infer
its scattering contribution based on DMhost estimated in Section 3.1.4. First
discussed by Sutton (1971), Rickett (1977) and Cordes et al. (1991), and most
recently measured by Cordes et al. (2022), this relation was fitted against
scattering timescales and DMs for 568 Galactic pulsars. The canonical fitting
function used for the pulsar data is
$\widehat{\tau}(\mathrm{DM})=A\times\mathrm{DM}^{a}\left(1+B\times\mathrm{DM}^{b}\right)$
(Ramachandran et al., 1997), for which Cordes et al. (2016) found the
empirical $\tau$-DM relation

$\displaystyle\left[\widehat{\tau}\left(\mathrm{DM},\nu\right)\right]_{\mathrm{mw},\mathrm{psr}}=1.90\times
10^{-7}\mathrm{~{}ms}\times\nu^{-\alpha}\mathrm{DM}^{1.5}$ (13)
$\displaystyle\times\left(1+3.55\times 10^{-5}\mathrm{DM}^{3.0}\right),$

at frequencies $\nu$ in $\mathrm{GHz}$, with scatter $\sigma_{\log\tau}=0.76$
dex (Bhat et al., 2004; Cordes & Chatterjee, 2019).

Figure 6 shows the fitted $\tau$-DM relation from Cordes et al. (2016) for
Galactic pulsars. The steepening at large DMs occurs due to the cloudy nature
of the inner Galaxy, where high-DM pulsars are found, as opposed to those in
the outer regions of the galaxy or near the solar neighborhood (Cordes et al.,
1991; Cordes & Chatterjee, 2019). We over-plot a sample of well-localized FRBs
in comparison whose host DMs are inferred probabilistically using similar
methods as those outlined in §3.1. FRB 20221219A emerges from these
populations as a clearly over-scattered outlier333FRB scattering timescales
have scaled up by a factor 3, under the assumption that the scattered waves
are planar and not spherical (Cordes et al., 2016). (to
6.37$\sigma_{\mathrm{log}_{10}\tau}$ for
$[\widehat{\tau}(\mathrm{DM},\nu)]_{\mathrm{MW},\mathrm{psr}}$) given its
inferred DMhost, reflecting just how unique this event is in the context of
most FRBs that have been detected to date. We, therefore, tentatively suggest
that the host is unlikely to contribute significantly to the observed
scattering timescale. Still, there remains the possibility that a compact
scattering structure (e.g., a plasma lens) exists within HG 20221219A and
intersects the LoS. Such a structure could lead to strong deviations from the
$\tau$-DM relation and weaken the inference made on the scattering prospects
within HG 20221219A. As this scenario is difficult to constrain without
scintillation information, we do not expand on it in this work.

Figure 6: $\tau$-DM relation for Galactic pulsars. The fitted line (solid
black) and $\pm 1\sigma$ variations (dashed black) are based on measurements
and upper limits on $\tau$ for Galactic pulsars (568 in total; data provided
by courtesy of J. Cordes and also published in Cordes et al., 2016). The
scattering timescales and inferred host galaxy DMs for a subset of well-
localized FRBs are over-plotted as multi-colored diamonds (Cordes et al.,
2022). All scattering timescales have been scaled to their nominal values at 1
GHz. FRB 20221219A (denoted by a red diamond) dramatically exceeds the
expected scattering timescale from a Milky Way-like galaxy by
6.37$\sigma_{\mathrm{log}_{10}\tau}$ for its DMhost (see §3.1.4).

One possible indicator of a dynamic circumburst medium is a high Faraday
rotation measure (RM), defined as $\mathrm{RM}=0.81\int
B_{\|}(l)n_{\mathrm{e}}(l)\mathrm{d}l$, where $B_{\|}$ is the magnetic field
component along the LoS (in $\mu\mathrm{G}$), and $n_{\mathrm{e}}$ is the
electron number density. The low S/N of FRB 20221219A precludes any robust
constraints on the RM by RM synthesis or $QU$-fitting techniques. We were,
however, able to estimate a linear polarization fraction ($L/I$) in the non-
derotated spectrum, which we take to be the lower limit. With this, we set an
upper limit on its absolute $|\mathrm{RM}|$ via a Monte Carlo-based approach
to estimate the degree to which a 100% linearly polarized burst could be
Faraday depolarized.

We calculate the likelihood of a “true” (intrinsic) $L/I$ exceeding the
measured polarization fraction of FRB 20221219A ($L/I\sim 0.502$) by
simulating a linearly polarized signal completely in Stokes $Q$, a priori.
Using off-pulse noise statistics, we proceed to simulate $Q$ and $U$ for a
range of hypothetical RM values $|\mathrm{RM}|_{i}$ at the observing
wavelength $\lambda$ as

$\displaystyle Q$
$\displaystyle=\cos\left(|\mathrm{RM}|_{i}\times\lambda^{2}\right)$ (14)
$\displaystyle U$
$\displaystyle=-\sin\left(|\mathrm{RM}|_{i}\times\lambda^{2}\right),$

which we then sum in quadrature to obtain a linear polarization fraction
$L/I=\sqrt{\langle Q\rangle^{2}+\langle U\rangle^{2}}$, where $\langle
Q\rangle$ and $\langle U\rangle$ represent the mean of the simulated values
over the signal data. From this distribution of simulated polarization
fractions exceeding the measured value, we extract a lower limit $L/I\sim
0.42$ (estimated at $\sim$ 10%) for FRB 20221219A. Thus, we can set an upper
limit on $|\mathrm{RM}|$ of $\lesssim 345$ rad m-2, a relatively low value,
and conclude that the circumburst medium for FRB 20221219A is not highly
magnetic.

There is some evidence that a high RM is accompanied by strong local
scattering (such as in FRB 20190520B; Ocker et al., 2022c; Anna-Thomas et al.,
2023). Since RM is a tracer of both $B_{\|}$ and $n_{\mathrm{e}}$, it is
possible for a low RM to imply a less extreme local plasma environment and
thus a lack of scattering power, as further evidenced by the high RMs of
Galactic pulsars in the inner disk of the Milky Way, which exhibit high
degrees of scattering (Lazio & Cordes, 1998; Wharton et al., 2012; Eatough et
al., 2013; Cordes et al., 2022). We note, however, that there is not
necessarily correspondence between the $B_{\|}$ traced by RM and the possibly
turbulent electron density fluctuations that lead to scattering. FRB
20121102A, for instance, exhibits RM values $\gtrsim 10^{5}$ rad m-2,
indicating the presence of an extreme magneto-ionic local environment, but
exhibits no significant scattering in its host or circumburst environment
(Michilli et al., 2018).

To further assess the likelihood that scattering would originate from the
circumburst environment, we can take a more empirical approach using our
combined parameters outlined in §3.2.1 and §3.2.2 to compute the measurable
parameters, namely $G$, $\tau$, $\nu$, and $z_{\ell}$, and solve for
$\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}$ to better constrain the
electron column density and fluctuation statistics. If we consider the
scenario in which all the observed scattering originates from the circumburst
environment (where $G=1$), we find that
$\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}\simeq
580~{}\mathrm{pc}^{4/3}\mathrm{~{}km}^{-1/3}\mathrm{~{}cm}^{-1/3}$. If we
remain agnostic to the exact physics in the circumburst environment, and
simply consider the lower limit on $\widetilde{F}$ imposed by DMhost (see
Table 3), we find that $\widetilde{F}\gtrsim 1500$
$\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$. While the exact range of
$\widetilde{F}$ is poorly understood for local environments of FRB sources, we
see that the lower limit far exceeds the maximal expected $\widetilde{F}$ for
the thin disk ISM of a spiral galaxy by $\sim 10^{3}$ ($\sim 10^{4}$ for dwarf
galaxies, $\sim 10^{6}$ for elliptical galaxies; Ocker et al., 2022b). This
assumption is purely illustrative, however, as it of course ignores the
presence of an ISM in the host galaxy. Nonetheless, it highlights the
requirement that the local environment be extremely turbulent in order for it
to substantially contribute to $\tau_{\mathrm{obs}}$.

Next, we’ll evaluate the scattering contributions of each intervening galaxy,
again utilizing the scattering formalism developed by Cordes et al. (2016),
Ocker et al. (2021), and Cordes et al. (2022) to characterize the scattering
power of intervening plasma based on the LoS geometry (§3.2.2), and electron
density-fluctuation (i.e., turbulence) statistics (§3.2.1).

####  3.2.4 IGH Model A: Extended CGM

To evaluate the scattering power of a uniform, extended CGM, we assume DMigh
and a viral radius, $R_{200}$, based on the halo mass of each intervener. With
these assumptions, we take a similar approach to §3.2.3 and solve for
$\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}$. First, we take the path
length $L$ through the CGM (scattering layer) to be the geometric chord length
through a spherically symmetric dark matter halo of $R_{200}$, corresponding
to IGH1 or IGH2. With this, we calculate the geometrical factor $G$ using Eq.
11 for the angular diameter distances shown in Figure 4. Substituting the DM
values inferred for IGH1 and IGH2 in §3.1.3 based on the COS-Halos survey data
(Werk et al., 2014), we estimate the value of $\widetilde{F}$ that would be
required to reach $\tau_{\mathrm{obs}}$ using Eq. 12 (see Table 4). We find
the fluctuation parameters for each respective intervener,
$\widetilde{F}\sim\left[1100^{+3300}_{-610},410^{+580}_{-190}\right]$
$\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$, that would be required to
reach $\tau_{\mathrm{obs}}$ far exceed the physically valid range expected for
the CGM based on prior studies ($\tilde{F}\lesssim 10^{-3}$
$\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$; Ocker et al., 2021),
requiring values more appropriate for the Galactic thin disk
($\widetilde{F}\gtrsim 1$ $\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}$;
Ocker et al., 2021). The specific range of predicted $\widetilde{F}$ is
largely informed by the volume filling fraction of the gas, estimated to be
$f_{\mathrm{v}}\sim 10^{-4}$ (Vedantham & Phinney, 2018), inferred from areal
covering fractions measured using quasar (QSO) absorption spectroscopy and
photoionization modeling (Prochaska & Hennawi, 2008; Stocke et al., 2013;
Hennawi et al., 2015; Lau et al., 2016; McCourt et al., 2017). The volume
filling fraction relies on the assumption that the CGM can be described as a
two-phase medium: a warm $T\gtrsim 10^{6}$ K medium of tenuous coronal gas
that hosts within it a cooler $T\lesssim 10^{6}$ K medium, which becomes
unstable around $T\sim 10^{4}$ K and fragments or shatters into discrete
photoionized cloudlets that populate the tenuous gas with a high covering
fraction, but low filling factor (McCourt et al., 2017). We conclude that
scattering by an extended CGM is physically unreasonable.

This conclusion is, of course, highly sensitive to our estimate of $G$, and
therefore $L_{\mathrm{halo}}$. Minimizing $L_{\mathrm{halo}}$ to by a factor
of $\sim 10^{2}$ to of order $\sim 1~{}\mathrm{kpc}$, while keeping
$\mathrm{DM}_{\mathrm{halo}}$ fixed, while an unphysical assumption, would
better accommodate the scenario in which $\tau_{\mathrm{obs}}$ originates from
an extended CGM. This illustrates that in order for scattering to occur in an
IGH at all, it would need to originate from a highly confined scattering layer
in the halo. We consider this possibility as follows in §3.2.5.

Table 4: For each IGH, we estimate halo masses ($\log_{10}\left(M_{h}\right)$), virial radii ($R_{200}$), impact parameters ($b$), geometrical chord lengths through the spherical halos ($L_{\mathrm{halo}}$). We then calculate geometrical factors ($G$; Eq. 11) and solve for $\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}$ (with units $\mathrm{pc}^{4/3}\mathrm{~{}km}^{-1/3}\mathrm{~{}cm}^{-1/3}$, using Eq. 12). For IGH model A, we infer $\mathrm{DM}_{\mathrm{igh}}$ using the COS-Halos survey data (described in §3.1.3; Werk et al., 2014), and consequent values for $\widetilde{F}$. For IGH model B, we assume a cloudlet width ($L_{\mathrm{cloud}}$, which we take to be the outer scale $l_{o}$), electron density fluctuation statistics ($\zeta\varepsilon^{2}$), the Fresnel scale ($r_{F}$, which we take to be $10\times$ the inner scale $l_{i}$), and a volume-filling factor ($f_{v}$), to estimate the fluctuation parameter ($\widetilde{F}$), and infer a $\mathrm{DM}_{\mathrm{cloud}}$ required to achieve $\tau_{\mathrm{obs}}$. These assumptions are described and motivated in §3.2.5. All assumed or inferred parameters are indicated in bold font to distinguish them from data-driven measurements. Parameter |  IGH1 |  IGH2
---|---|---
$\log_{10}\left(M_{h}\right)\left[M_{\odot}\right]$ |  $11.52^{+0.05}_{-0.05}$ |  $11.96^{+0.01}_{-0.01}$
$\mathrm{R}_{200}$ [kpc] |  $122^{+5}_{-5}$ |  $174^{+2}_{-2}$
$b$ [kpc] |  $43^{+11}_{-11}$ |  $36^{+11}_{-11}$
IGH Model A: Extended CGM |  |
$L_{\mathrm{halo}}$ [kpc] |  $225^{+14}_{-14}$ |  $340^{+5}_{-5}$
$G$ |  $1100^{+70}_{-70}$ |  $1300^{+19}_{-19}$
$\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}$ |  $11^{+2}_{-2}$ |  $8^{+1}_{-1}$
$\mathrm{\textbf{DM}}_{\mathrm{\textbf{igh}}}\left[\mathrm{pc~{}cm}^{-3}\right]$ |  $10^{+5}_{-5}$ |  $14^{+5}_{-5}$
$\widetilde{\bm{F}}\left[\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}\right]$ |  $1100^{+3300}_{-610}$ |  $410^{+580}_{-190}$
IGH Model B: Partially Ionized CGM Cloudlet |  |
$\bm{L_{\mathrm{cloud}}}$ [$l_{o}$; pc] |  10 |  10
$\bm{G}$ |  $2.4\times 10^{7}$ |  $4.4\times 10^{7}$
$\widetilde{\bm{F}}\times\bm{\mathrm{DM}_{\ell,100}^{2}}$ |  $5^{+0.7}_{-0.7}\times 10^{-4}$ |  $2^{+0.3}_{-0.3}\times 10^{-4}$
$\bm{r_{\mathrm{F}}}$ [$10\times l_{i}$; km] |  $3.6\times 10^{8}$ |  $4.8\times 10^{8}$
$\bm{\zeta\varepsilon^{2}}$ |  1 |  1
$\bm{f_{\mathrm{v}}}$ |  $10^{-2}$ |  $10^{-2}$
$\widetilde{\bm{F}}\left[\left(\mathrm{pc}^{2}\mathrm{~{}km}\right)^{-1/3}\right]$ |  $0.07$ |  $0.06$
$\bm{\mathrm{DM}_{\mathrm{cloud}}}\left[\mathrm{pc~{}cm}^{-3}\right]$ |  $8.5^{+0.5}_{-0.5}$ |  $5.8^{+0.5}_{-0.5}$

####  3.2.5 IGH Model B: Partially Ionized CGM Cloudlet

The likelihood of intersecting a partially ionized cloudlet can be understood
based on the areal covering fraction of the cool ($T\sim 10^{4}$ K) gas.
Multiple studies investigating the prevalence of absorption features in QSO
spectra and lensing of those features (Churchill et al., 2003; Xavier
Prochaska et al., 2012; Lau et al., 2016), as well as fluorescent Ly-$\alpha$
emission in halos (Hennawi et al., 2015), support the conclusion that the
areal covering fraction exceeds unity. Hence, the scenario in which a single
sightline intersects a cool cloudlet is highly probable.

To evaluate the scattering power of a single, partially ionized cloudlet, we
again estimate $\widetilde{F}\times\mathrm{DM}_{\ell,100}^{2}$ (Eq. 9) based
on a fiducial width of the cloudlet residing in an intervening CGM. The width
is taken to be a typical upper limit on the size of a stable over-density of
ionized gas in a cool ($T\sim 10^{4}$ K), fragmented CGM,
$L_{\mathrm{cloud}}\sim 10$ pc (McCourt et al., 2017). We then estimate
$\widetilde{F}$, based on fiducial values for the metric that describes local
and ensemble electron density variations $\zeta\varepsilon^{2}$, the volume-
filling factor $f_{\mathrm{v}}$, as well as the inner ($l_{i}$) and outer
($l_{o}$) scales of the turbulence power spectrum within the cloudlet. Under
the well-justified assumption of homogeneous and isotropic turbulence, we take
$\zeta\varepsilon^{2}\sim 1$ (Spangler & Gwinn, 1990; Armstrong et al., 1995;
Rickett et al., 2009). We also assume $f_{\mathrm{v}}\sim 10^{-2}$ (typical
for $T\sim 10^{4}~{}\mathrm{K}$ gas; Ocker et al., 2021). It ought to be
noted, however, that this factor is largely uncertain for individual clouds
due to the inability to resolve and characterize this gas at sub-pc scales.

We set the inner scale $l_{i}$ to be a fraction444This is a somewhat arbitrary
choice and can be adjusted. We set this inner scale as $0.1\times
r_{\mathrm{F}}$ as it concretely satisfies the condition that, in order for
scattering to occur, the inner scale of the medium must lie below
$r_{\mathrm{F}}$. of the Fresnel scale $r_{\mathrm{F}}$, in this case
$l_{i}=0.1\times r_{\mathrm{F}}$, at the distance of the intervener, defined
as (Cordes et al., 2017)

$r_{\mathrm{F}}=\sqrt{\frac{\lambda d_{\mathrm{sl}}d_{\mathrm{lo}}}{2\pi
d_{\mathrm{so}}}}$ (15)

and an outer scale $l_{o}$ consistent with the width of the cloudlet (here
$L_{\mathrm{cloud}}\sim 10~{}\mathrm{pc}$. With these assumptions, we estimate
$\widetilde{F}$ using Eq. 9, and the DM required to produce
$\tau_{\mathrm{obs}}$ in Table 4. Under the assumptions outlined in Table 4,
we find that for IGH2, a DMcloud of only
$5.8^{+0.5}_{-0.5}~{}\mathrm{pc~{}cm}^{-3}$ is required to achieve
$\tau_{\mathrm{obs}}$.

While there are a variety of circumgalactic media that could provide this
electron column density, the most well-understood in the context of the Milky
Way are high-velocity clouds (HVCs). The Wisconsin H$\alpha$ Mapper (WHAM;
Tufte et al., 1998a, b) has observed HVCs at high galactic latitudes. As the
extinction at high latitudes is presumed to be minimal, the H$\alpha$
luminosity can be related directly to emission measure ($\mathrm{EM}=\int
n_{\mathrm{e}}^{2}dl$), for which WHAM report an
$\mathrm{EM}=0.18\mathrm{~{}cm}^{-6}\mathrm{pc}$. Assuming an HII temperature
of $T\sim 8000$ K and a small ionization fraction,
$\mathrm{N}_{\mathrm{HII}}/\mathrm{N}_{\mathrm{HI}}\sim 0.08$ (as HVCs are
known to be primarily neutral, ionized in part by external radiation), the
inferred HII column densities along an individual sightline reach an upper
limit of N${}_{\mathrm{HII}}\sim 2\times 10^{19}$ cm-2 (Tufte et al., 1998b).
This column density corresponds to a dispersion measure of
DM${}_{\mathrm{HVC}}\simeq 6.5~{}\mathrm{pc}~{}\mathrm{cm}^{-3}$, which
exceeds the DM${}_{\mathrm{cloud}}\simeq
5.8^{+0.5}_{-0.5}~{}\mathrm{pc}~{}\mathrm{cm}^{-3}$ sufficient to achieve
$\tau_{\mathrm{obs}}$.

While most Galactic HVCs lie at extra-planar distances $\lesssim 10$ kpc
(Wakker et al., 2008; Thom, 2006; Thom et al., 2008), there are notable
exceptions, such as those present in the Magellanic Stream (a stream of HVCs
traversing $\gtrsim 100^{\circ}$ over the Galactic South Pole), which can
extend out to $\sim 55~{}\text{-}~{}150$ kpc (Besla et al., 2010). Streams of
this kind are not necessarily unique to the Milky Way, as tidal interactions
between more massive galaxies and their neighboring dwarfs are not uncommon,
particularly at higher $z$. Hence, while the presence of HVCs extending to
extraplanar distances of order $b$ for IGH1 or IGH2 is challenging to
constrain and largely uncertain, it is certainly possible. Galactic and Local
Group HI surveys have also placed a subpopulation of so-called “compact” HVCs
out to distances of $\sim 40~{}\text{-}~{}80$ kpc from the Galactic disk, and
$\sim 50$ kpc around Andromeda (Putman et al., 2003; Pisano et al., 2007;
Westmeier, 2007). Similar, even smaller “ultra-compact” HVCs have been
observed within the Local Group, though their associations with individual
galaxies remain uncertain (Adams et al., 2013). Still, they remain interesting
candidate sources of FRB scattering.

Absorption line spectroscopy of QSOs has illuminated the intricate structures
and dynamic processes characterizing the CGMs of galaxies beyond the Milky Way
as well. High-velocity cloud-like structures, akin to those observed in the
Milky Way’s halo, have been detected in the CGMs of other galaxies, showcasing
a wide range of ionization states and physical scales. QSOs intersecting the
CGMs of intervening galaxies reveal the presence of ionized cloudlets through
the detection of species ranging from low ions like Si II and Mg II to highly
ionized ions such as O VI and Ne VIII (Fox et al., 2014; Prochaska et al.,
2017). These findings suggest that the CGM is a complex, multiphase medium
where different regions exhibit varying degrees of ionization (Werk et al.,
2013; Tumlinson et al., 2017). The column density distribution and the spatial
coherence of QSO absorption features suggest that these ionized clouds range
from tens to hundreds of parsecs across, similar to HVCs in the Milky Way
(Stocke et al., 2013; Prochaska et al., 2017).

The distributions of these ionized structures within the galactic halos are
substantial, extending from several tens to hundreds of kiloparsecs. This vast
reach underscores the CGM’s role as a reservoir of baryonic material that can
influence galaxy evolution (Werk et al., 2014; Burchett et al., 2016).
Ionization models employed to interpret the absorption spectra indicate that
some regions within these clouds are nearly fully ionized, revealing a complex
CGM phase structure (Oppenheimer & Schaye, 2013; Stocke et al., 2013). They
also indicate that these clouds occupy diverse thermal phases of the CGM, from
cool ($T\sim 10^{4}$ K), photoionized gas to hot ($T\gtrsim 10^{6}$ K),
collisionally ionized plasma (Werk et al., 2016; Tumlinson et al., 2017).

The evidence garnered from spectroscopic studies not only confirms the
presence of multiphase, dynamic HVC-like structures but also reveals their
substantial physical scales and diverse ionization fractions, making it all
the more reasonable that an intersection with a single, marginally ionized
cloudlet could occur for both IGH1 and IGH2, given their respective impact
parameters, and therefore dominate the scattering budget of FRB 20221219A.

##  4 Conclusions

By constructing detailed DM and scattering budgets for FRB 20221219A, we find
that the event is highly over-scattered in its host galaxy and lies along an
unusually rich sightline. We also find that the IGM and ICM likely dominate
the DM budget, leaving a modest allowance for DMhost.

We consider the possibility of scattering occurring in the CGMs of two closely
intervening galaxies, and find it plausible. Specifically, we note that a
fortuitous intersection with a single, partially ionized cloudlet in one of
the CGMs could produce $\tau_{\mathrm{obs}}$. The geometric leverage offered
by compact scattering structures at large distances from both the source and
observer, as well as the potential presence of partially ionized structures at
the impact parameters of both IGH1 and IGH2 along the LoS, make this scenario
likely. We further find that nothing about the host galaxy or local
environment is unusual with respect to other FRBs (and pulsars) with far lower
scattering, lending credence to this suggestion.

The fact that all FRBs are not scattered by the CGMs of intervening galaxies
can be explained by the far sparser distributions of such galaxies along most
sightlines, as well as the known bias against observing highly scattered FRBs.
We further note that scattering is highly stochastic for fixed DMs, as
evidenced by MW pulsars, inflating this bias even more.

In future case studies, it would be of great use, where possible, to measure
scintillation bandwidths in addition to pulse broadening to better understand
FRB scattering mechanisms and disentangle distinct LoS scattering media.
Comparisons between scintillation and pulse broadening of a single burst can
assist in constraining whether the scattering effects in FRBs are due to one
or multiple screens along the line of sight. Still, it is crucial to search
for repeat bursts from heavily scattered FRBs to characterize additional time-
variable effects.

##  5 Acknowledgements

The authors would like to thank Jim Cordes for insightful conversations, as
well as the staff members of the Owens Valley Radio Observatory and the
Caltech radio group whose efforts were vital to the success of the DSA-110,
including Kristen Bernasconi, Stephanie Cha-Ramos, Sarah Harnach, Tom
Klinefelter, Lori McGraw, Corey Posner, Andres Rizo, Michael Virgin, Scott
White, and Thomas Zentmyer. The DSA-110 is supported by the National Science
Foundation Mid-Scale Innovations Program in Astronomical Sciences (MSIP) under
grant AST-1836018.

This research is based in part on data gathered with the W.M. Keck
Observatory, which is operated, in scientific partnership, by the California
Institute of Technology, the University of California, and the National
Aeronautics and Space Administration. The Observatory was made possible by the
generous financial support of the W.M. Keck foundation.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; Proposal ID #2014B-0404; PIs: David
Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID
#2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy
Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS
together include data obtained, respectively, at the Blanco telescope, Cerro
Tololo Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward
Observatory, University of Arizona; and the Mayall telescope, Kitt Peak
National Observatory, NOIRLab. Pipeline processing and analyses of the data
were supported by NOIRLab and the Lawrence Berkeley National Laboratory
(LBNL). The Legacy Surveys project is honored to be permitted to conduct
astronomical research on Iolkam Du’ag (Kitt Peak), a mountain with particular
significance to the Tohono O’odham Nation.

NOIRLab is operated by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. LBNL is managed by the Regents of the University of California
under contract to the U.S. Department of Energy.

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho
de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de
Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia,
Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Energeticas, Medioambientales y Tecnologicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the Institut de
Fisica d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig
Maximilians Universitat Munchen and the associated Excellence Cluster
Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, and Texas A&M University.

BASS is a key project of the Telescope Access Program (TAP), which has been
funded by the National Astronomical Observatories of China, the Chinese
Academy of Sciences (the Strategic Priority Research Program “The Emergence of
Cosmological Structures” Grant #XDB09000000), and the Special Fund for
Astronomy from the Ministry of Finance. The BASS is also supported by the
External Cooperation Program of Chinese Academy of Sciences (Grant
#114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant
#12120101003, #11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director,
Office of Science, Office of High Energy Physics of the U.S. Department of
Energy under Contract No. DE-AC02-05CH1123, by the National Energy Research
Scientific Computing Center, a DOE Office of Science User Facility under the
same contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOAO.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

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