Disentangling the Cosmic Web Towards FRB 190608

Galaxies are the result of gravitational accretion of baryons onto dark matter halos, i.e. the dense gas that has cooled and condensed to form dust, stars, and planets. The dark matter halos, according to simulations, are embedded in the cosmic web, a filamentous structure of matter (e.g. Springel et al., 2005). The accretion process of galaxies is further predicted, at least for halo masses $M_{\rm halo}\gtrsim 10^{12}~{}{\rm M}_{\odot}$, to generate a halo of baryons, most likely dominated by gas shock-heated to the virial temperature of the potential well (White & Rees, 1978; White & Frenk, 1991; Kauffmann et al., 1993; Somerville & Primack, 1999; Cole et al., 2000). At $T\gtrsim$ $10^{6}$ K and $n_{e}\sim 10^{-4}\,{\rm cm^{-3}}$, however, this halo gas is very difficult to detect in emission (Kuntz & Snowden, 2000; Yoshino et al., 2009; Henley & Shelton, 2013) and similarly challenging to observe in absorption (e.g. Burchett et al., 2019). And while experiments leveraging the Sunyaev-Zeldovich effect are promising (Planck Collaboration et al., 2016a), these are currently limited to massive halos and are subject to significant systematic effects (Lim et al., 2020).

Therefore, there has been a wide range of predictions for the mass fraction of baryons in massive halos that range from $\approx 10\%$ to nearly the full complement relative to the cosmic mean $\Omega_{b}/\Omega_{m}$ (Pillepich et al., 2018). Here, $\Omega_{b}$ and $\Omega_{m}$ are the average cosmic densities of baryons and matter respectively. Underlying this order-of-magnitude spread in predictions are uncertain physical processes that eject gas from galaxies and can greatly shape them and their environments (e.g. Suresh et al., 2015).

Fast radio bursts (FRBs) are dispersed by intervening ionized matter such that the pulse arrival delay, with respect to a reference frequency, scales as the inverse square of frequency times the DM. The DM is the path integral of the electron density, $n_{e}$, weighted by the scale factor $(1+z)^{-1}$, i.e. ${\rm DM}\equiv\int n_{e}\,ds/(1+z)$. These FRB measurements are sensitive to all of the ionized gas along the sightline. Therefore, they have the potential to trace the otherwise invisible plasma surrounding and in-between galaxy halos (Macquart et al., 2020). The Fast and Fortunate for FRB Follow-up (F⁴) team¹¹1http://www.ucolick.org/f-4 has initiated a program to disentangle the cosmic web by correlating the dispersion measure (DM) of fast radio bursts (FRBs) with the distributions of foreground galaxy halos (McQuinn, 2014; Prochaska & Zheng, 2019). This manuscript marks our first effort.

Since the DM is an additive quantity, it may be split into individual contributions of intervening, ionized gas reservoirs:

Here, $\rm DM_{\rm MW}$ refers to the contribution from the Milky Way which is further split into its ISM and halo gas contributions (${\rm DM}_{\rm MW,ISM}$ and ${\rm DM}_{\rm MW,halo}$ respectively). Additionally, ${\rm DM}_{\rm host}$ is the net contribution from the host galaxy and its halo, including any contribution from the immediate environment of the FRB progenitor. Meanwhile, ${\rm DM}_{\rm cosmic}$ is the sum of contributions from gas in the circumgalactic medium (CGM) of intervening halos (${\rm DM}_{\rm halos}$) and the intergalactic medium (IGM; ${\rm DM}_{\rm IGM}$). Here, CGM refers to the gas found within dark matter halos including the intracluster medium of galaxy clusters, and the IGM refers to gas between galaxy halos.

Macquart et al. (2020) have demonstrated that the FRB population defines a cosmic DM-$z$ relation that closely tracks the prediction of modern cosmology (Inoue, 2004; Prochaska & Zheng, 2019; Deng & Zhang, 2014), i.e., the average cosmic DM is

with $\bar{n}_{e}=f_{d}(z)\rho_{b}(z)/m_{p}(1-Y_{\rm He}/2)$, which is the mean density of electrons at redshift $z$. Here, $m_{p}$ is the proton mass, $Y_{\rm He}=0.25$ is the mass fraction of Helium (assumed doubly ionized in this gas), $f_{d}(z)$ is the fraction of cosmic baryons in diffuse ionized gas, i.e. excluding dense baryonic phases such as stars and neutral gas (see Macquart et al., 2020, and Appendix A). $\rho_{b}(z)=\Omega_{b,0}\rho_{c,0}(1+z)^{3}$, $\rho_{c,0}$ is the critical density at $z=0$, and $\Omega_{b,0}$ is the baryon energy density today relative to $\rho_{c,0}$. $c$ is the speed of light in vacuum and $H(z)$ is the Hubble parameter. Immediately relevant to the study at hand, for FRB 190608, $\langle{\rm DM}_{\rm cosmic}\rangle\approx 100$ ${\rm pc\,cm^{-3}}$ at $z_{\rm host}$= 0.11778.

Of the five FRBs in the Macquart et al. (2020) ‘gold’ sample, FRB 190608 exhibits a ${\rm DM}_{\rm cosmic}$ value well in excess of the average estimate for its redshift: ${\rm DM_{\rm cosmic}}/\langle{\rm DM}_{\rm cosmic}\rangle\approx 2$ based on the estimated contributions of ${\rm DM}_{\rm MW,halo}$ and ${\rm DM}_{\rm host}$. This is illustrated in Fig. 1, which compares the measured ${\rm DM}_{\rm FRB}=339.8\,{\rm pc\,cm^{-3}}$ (Day et al., 2020) with the cumulative contributions from the Galactic ISM (taken as ${\rm DM}_{\rm MW,ISM}$= 38 ${\rm pc\,cm^{-3}}$; Cordes & Lazio, 2003), the Galactic halo (taken as ${\rm DM}_{\rm MW,halo}$= 40 ${\rm pc\,cm^{-3}}$; Prochaska & Zheng, 2019), and the average cosmic web (Equation 2). These fall $\approx 160\,{\rm pc\,cm^{-3}}$ short of the observed value. Chittidi et al. (2020) estimate the host galaxy ISM contributes $\rm DM_{host,ISM}=82\pm 35~{}{\rm pc\,cm^{-3}}$ based on the observed H$\beta$ emission measure and $\rm DM_{host,halo}=28\pm 13\,{\rm pc\,cm^{-3}}$ for the host galaxy’s halo, thus nearly accounting for the deficit. The net ${\rm DM}_{\rm host}$ is therefore taken here to be $110\pm 37~{}{\rm pc\,cm^{-3}}$.

While these estimates almost fully account for the large ${\rm DM}_{\rm FRB}$, several of them bear significant uncertainties (e.g., ${\rm DM}_{\rm MW,halo}$  and ${\rm DM}_{\rm host}$). Furthermore, we have assumed the average ${\rm DM}_{\rm cosmic}$ value, a quantity predicted to exhibit significant variance from sightline to sightline (McQuinn, 2014; Prochaska & Zheng, 2019; Macquart et al., 2020). Therefore, in this work we examine the galaxies and large-scale structure foreground to FRB 190608 to analyze whether ${\rm DM}_{\rm cosmic}\approx\langle{\rm DM}_{\rm cosmic}\rangle$ or whether there is significant deviation from the cosmic average. These analyses constrain several theoretical expectations related to $\langle{\rm DM}_{\rm cosmic}\rangle$ (e.g. McQuinn, 2014; Prochaska & Zheng, 2019). In addition, FRB 190608 exhibits a relatively large rotation measure ($\rm RM=353~{}\rm rad~{}m^{-2}$) and a large, frequency dependent exponential tail ($\tau_{1.4{\rm Ghz}}=2.9$ ms) in its temporal pulse profile that corresponds to scatter-broadening (Day et al., 2020). We explore the possibility that these arise from foreground matter overdensities and/or galactic halos (similar to the analysis by Prochaska et al., 2019).

This paper is organized as follows. In Section 2, we present our data on the host and foreground galaxies and our spectral energy distribution (SED) fitting method for determining galaxy properties. In Section 3, we describe our methods and models in estimating the separate ${\rm DM}_{\rm cosmic}$  contributions from intervening halos and the diffuse IGM. Section 4 explores the possibility of a foreground structure accounting for the FRB rotation measure and pulse width. Finally, in Section 5, we summarise and discuss our results. Throughout our analysis, we use cosmological parameters derived from the results of Planck Collaboration et al. (2016b).

This section estimates ${\rm DM}_{\rm halos}$, and ${\rm DM}_{\rm IGM}$. For the sake of clarity, we make a distinction in the terminology we use to refer to the cosmic contribution to the dispersion measure estimated in two different ways. First, we name the difference between ${\rm DM}_{\rm FRB}$ and the estimated host and Milky Way contributions ${\rm DM}_{\rm FRB,C}$ i.e. ${\rm DM}_{\rm FRB,C}={\rm DM}_{\rm FRB}-\rm DM_{MW}-{\rm DM}_{\rm host}\approx 152\,{\rm pc\,cm^{-3}}$. Second, we shall henceforth use the term ${\rm DM}_{\rm cosmic}$  to refer to the sum of ${\rm DM}_{\rm halos}$ and ${\rm DM}_{\rm IGM}$ semi-empirically estimated from the foreground galaxies.

We briefly consider the potential contributions of foreground galaxies to FRB 190608’s observed temporal broadening and rotation measure. As evident in Table 1, there is only a single halo within 200 kpc of the sightline with $z\leq z_{\rm host}$. It has redshift $z=0.09122$ and an estimated halo mass $M_{\rm halo}=10^{12}{\rm M}_{\odot}$.

FRB 190608 exhibits a large, frequency-dependent pulse width $\tau=3.3\,\rm~{}ms$ at 1.28 GHz (Day et al., 2020), which exceeds the majority of previously reported pulse widths (Petroff et al., 2016). Pulses are broadened when interacting with turbulent media. While we expect a scattering pulse width much smaller than a few milliseconds from the diffuse IGM alone (Macquart & Koay, 2013), we consider the possibility that the denser halo gas at $z=0.09122$ contributes significantly to FRB 190608’s intrinsic pulse profile. Here, we estimate the extent of such an effect, emphasizing that the geometric dependence of scattering greatly favors gas in intervening halos as opposed to the host galaxy.

Assuming the density profile as described in Section 3.1 (extending to $r_{\rm max}$=1), the maximum electron density ascribed to the halo is at its impact parameter $b=158$ kpc: $n_{e}\sim 10^{-4}\,\rm cm^{-3}$. Note that $b$ is much greater than the impact parameter of the foreground galaxy of FRB 181112 (29 kpc, Prochaska et al., 2019) and indeed that of the host or the Milky Way with FRB 190608’s sightline. The entire intervening halo can be thought of effectively as a “screen” whose thickness is the length the FRB sightline intersects with the halo, $\Delta L=265~{}\rm kpc$. We assume the turbulence is described by a Kolmogorov distribution of density fluctuations with an outer scale $L_{0}=1\rm~{}pc$. This choice of $L_{0}$ arises from assuming stellar activity is the primary driving mechanism. To get an upper bound on the pulse width produced, we also assume the electron density is equal to $10^{-4}\rm~{}cm^{-3}$ for the entire length of the intersected sightline. Following the scaling relation in equation 1 from Prochaska et al. 2019, we obtain:

Here, $\alpha$ is a dimensionless number that encapsulates the root mean-squared amplitude of the density fluctuations and the volume-filling fraction of the turbulence. It is typically of order unity. We note that our chosen value of $L_{0}$ presents an upper limit on the scattering timescale. Were $L_{0}\gg 1~{}\rm pc$ (e.g. if driven by AGN jets), $\tau\ll 0.03~{}\rm ms$. The observed scattering timescale exceeds our conservative upper bound by two orders of magnitude. One would require $n_{e}>6\times 10^{-4}~{}\rm cm^{-3}$ to produce the observed pulse width. This exceeds the maximum density estimation through the halo, even for the relatively flat and high $f_{\rm hot}$ assumed. We thus conclude that the pulse broadening for FRB 190608 is not dominated by intervening halo gas.

FRB 190608 also has a large estimated ${\rm RM}_{\rm FRB}=353\pm 2$ $\rm rad~{}m^{-2}$ (Day et al., 2020). We may estimate the RM contributed by the intervening halo, under the assumption that its magnetic field is characterized by the equipartition strength magnetic fields in galaxies ($\sim 10~{}\mu G$) (Basu & Roy, 2013). We note that this exceeds the upper limit imposed on gas in the halo intervening FRB 181112 (Prochaska et al., 2019).

We estimate:

and conclude that it is highly unlikely that the RM contribution from intervening halos dominates the observed quantity.

To summarize, we have created a semi-empirical model of the matter distribution in the foreground universe of FRB 190608 using spectroscopic and photometric data from the SDSS database and our own KCWI observations. We modeled the virialized gas in intervening halos using a modified NFW profile and used the MCPM approach to estimate the ionized gas density in the IGM. Table 3 summarizes the estimated DM contributions from each of the individual foreground components. Adding $\langle{\rm DM}_{\rm halos}\rangle$ and ${\rm DM}_{\rm IGM}$ for this sightline, we infer ${\rm DM}_{\rm cosmic}=98-154{\rm pc\,cm^{-3}}$, which is comparable to $\langle{\rm DM}_{\rm cosmic}\rangle$= 100 ${\rm pc\,cm^{-3}}$. The majority of ${\rm DM}_{\rm cosmic}$ is accounted for by the diffuse IGM, implying that most of the ionized matter along this sightline is not in virialized halos. We found only 4 galactic halos within 550 kpc of the FRB sightline and only 1 halo within 200 kpc. We found no foreground object in emission from our $\sim 1$ sq. arcmin KCWI coverage and no galaxy group or cluster having an impact parameter of less than its virial radius with our FRB sightline.

We also find it implausible that the foreground structures are dense enough to account for either the pulse broadening or the large rotation measure of the FRB. We expect the progenitor environment and the host galaxy together are the likely origins of both Faraday rotation and turbulent scattering of the pulse (discussed in further detail by Chittidi et al., 2020).

The results presented here are not the first attempt to measure ${\rm DM}_{\rm cosmic}$ along FRB sightlines by accounting for density structures. Li et al. (2019) estimated ${\rm DM}_{\rm cosmic}$ (termed ${\rm DM}_{\rm IGM}$ in their paper) for five FRB sightlines, making use of the 2MASS Redshift Survey group catalog (Lim et al., 2017) to infer the matter density field along their lines of sight. They assumed NFW profiles around each identified group. This enabled them to estimate the DM contribution from intervening matter for low DM (${\rm DM}_{\rm cosmic}+{\rm DM}_{\rm host}<100~{}{\rm pc\,cm^{-3}}$) FRBs. Our approach differs in the methods used to estimate ${\rm DM}_{\rm cosmic}$. The precise localization of FRB 190608 allows us to estimate ${\rm DM}_{\rm halos}$ and ${\rm DM}_{\rm IGM}$ separately. Li et al. (2019) were limited by the large uncertainties ($\sim 10^{\prime}$) in the FRB position and therefore their estimates of $\langle{\rm DM}_{\rm cosmic}\rangle$ depended on the assumed host galaxy within the localization regions. Furthermore, the MCPM model estimates the cosmic density field, and thus the ionized gas density of the IGM, due to filamentary large-scale structure. We note that our estimates of $n_{e}$ from the MCPM model in overdense regions is similar to their reported values ($10^{-6}-10^{-5}$  cm^-3). This naturally implies our ${\rm DM}_{\rm cosmic}$ estimates are of the same order of magnitude around $z=0.1$ as their estimate. Together with the results presented by Chittidi et al. (2020), our study represents a first of its kind: an observationally driven, detailed DM budgeting along a well-localized FRB sightline. We have presented a framework for using FRBs as quantitative probes of foreground ionized matter. Although aspects of this framework carry large uncertainties at this juncture, the methodology should become increasingly precise as this nascent field of study matures. For instance, our analysis required spectroscopic data across a wide area (i.e. a few square degrees) around the FRB, which enabled us to constrain the individual contributions of halos and also to model the cosmic structure of the foreground IGM. An increase in sky coverage and depth of spectroscopic surveys would enable the use of cosmic web mapping tools like the MCPM estimator with higher precision and on more FRB sightlines. Upcoming spectroscopic instruments such as DESI and 4MOST will map out cosmic structure in greater detail and will, no doubt, aid in the use of FRBs as cosmological probes of matter.

We expect FRBs to be localized more frequently in the future, thanks to thanks to continued improvements in high-time resolution backends and real-time detection systems for radio interferometers. One can turn the analysis around and use the larger set of localized FRBs to constrain models of the cosmic web in a region and possibly perform tomographic reconstructions of filamentary structure. Alternatively, by accounting for the DM contributions of galactic halos and diffuse gas, one may constrain the density and ionization state of matter present in intervening galactic clusters or groups. Understanding the cosmic contribution to the FRB dispersion measures can also help constrain progenitor theories by setting upper limits on the amount of dispersion measure arising from the region within a few parsecs of the FRB. We are at the brink of a new era of cosmology with new discoveries and constraints coming from FRBs.

Acknowledgments: Authors S.S., J.X.P., N.T., J.S.C. and R.A.J., as members of the Fast and Fortunate for FRB Follow-up team, acknowledge support from NSF grants AST-1911140 and AST-1910471. J.N.B. is supported by NASA through grant number HST-AR15009 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. This work is supported by the Nantucket Maria Mitchell Association. R.A.J. and J.S.C. gratefully acknowledge the support of the Theodore Dunham, Jr. Grant of the Fund for Astrophysical Research. K.W.B., J.P.M, and R.M.S. acknowledge Australian Research Council (ARC) grant DP180100857. A.T.D. is the recipient of an ARC Future Fellowship (FT150100415). R.M.S. is the recipient of an ARC Future Fellowship (FT190100155) N.T. acknowledges support by FONDECYT grant 11191217. The Australian Square Kilometre Array Pathfinder is part of the Australia Telescope National Facility which is managed by CSIRO. Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Centre. Establishment of ASKAP, the Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund. We acknowledge the Wajarri Yamatji as the traditional owners of the Murchison Radio-astronomy Observatory site. Spectra were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among Caltech, the University of California, and the National Aeronautics and Space Administration (NASA). The Keck Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.