Probing the Cosmic Web with Fast Radio Bursts. I. Scattering

Abstract

We study the formation of multiphase gas in the post-accretion-shock regions of cosmic sheets, filaments, and the circumgalactic medium (CGM) of haloes, i.e., cosmic web objects (CWOs). Local instabilities in the hot medium result in fragmentation and cooling, eventually forming small-scale overdensities with temperatures of $\sim 10^{4}{\,\rm K}$ in pressure equilibrium with the hot environment. Such dense, ionised inhomogeneities can affect the propagation of radio waves from fast radio bursts (FRBs), thereby offering us a way to probe their presence and properties in CWOs through scattering signatures in the observed FRB flux. We find that high-$z$ filaments \& sheets have a negligible contribution to the total observed scattering. The high rates of FRBs expected even at high redshifts may still allow detection from high-temperature filaments along rare sightlines, and we suggest other methods for such systems in a companion paper. Our model further predicts that if turbulent cloudlets exist in the CGM of intervening massive haloes with a volume-filling fraction of $f_{\rm v}\gtrsim 10^{-3}$, they are expected to cause considerable cumulative scattering along an average sightline, resulting in a significant correlation between the total scattering time and source redshifts. The lack of such a correlation in current observations may imply that the cool gas in the CGM has substantial non-thermal pressure, reducing its density, or significant damping of small-scale density fluctuations. Forthcoming localised FRB samples can map these constraints into bounds on volume-filling fractions, densities, cloud sizes, and the strength of turbulence.

Figures (14)

• Figure 1: Example of the cooling length as a function of temperature calculated using lcool, assuming isobaric cooling. This is shown for typical filament pressure and metallicity at $z=4$m21.
• Figure 2: Properties of shattered cloudlets as a function of thermal pressure (y-axis), redshift (x-axis), and metallicity - $Z/\zsol=10^{-4}$ (left column), $10^{-2}$ (middle column), and $1.0$ (right column), crudely representing CW sheets, filaments, and halo CGM, respectively. From top to bottom, we show the cloud size (the minimal cooling length, $\lc=\lcmin$), the cloud temperature ($\Tmin$), the cloud electron density ($\n$), and the electron column density over a cloud diameter ($\N$). These are calculated assuming isobaric cooling at the given pressure, and account for a redshift-dependent haardt_madau96 UV background with self-shielding of dense gas rahmati13. At a fixed pressure and redshift, metallicity is not important below $10^{-2}\zsol$. The dashed lines in each panel indicate the pressure near the outskirts of a CWO with virial (post-shock) temperature of $\Tv=10^{5}$, $10^{5.5}$, $10^{6}$, $10^{6.5}$, and $10^7\Kel$ from bottom to top, according to our model presented in P. The black lines indicate the contours of the quantity shown in colour, and are labelled in log scale. At a fixed virial temperature, sheets have the lowest pressures, largest cloud sizes, and smallest densities, while the CGM is at the opposite extreme with filaments in between. The orange dot-dashed lines in the right column represent halos with a fixed mass of $\Mh=10^{12}$, $10^{13}$, and $10^{14}\msun$ from bottom to top.
• Figure 3: Similar to clump_prop, but showing the diffractive scale ($\lpi$, top), and the temporal broadening ($\taus$, bottom) for CW screens as a function of thermal pressure and redshift, assuming an observed frequency of $\nuo=1\ghz$, $\fa=1$ clump per los across the CWO, and Kolmogorov turbulence with $\alpha=1/3$ in the clump. The redshift along the bottom $x$-axis indicates the CW screen redshift. For the temporal broadening, the source is assumed to be at redshift $\zs=6$ and $\Deff(z,\zs=6)$ is marked on the top $x$-axis. For filaments with $\Tv\sim (10^{5.5}-10^{6})\Kel$ we estimate a temporal broadening of $\taus\sim(10^{-4}-10^{-3})\ms$, while for sheets $\taus$ is two orders of magnitude lower. For the CGM, our model predicts a temporal broadening of $\taus\gsim0.1\ms$ for $10^{14}\msun$ halos at $z>0.5$, or $10^{13}\msun$ halos at $z>4$, scaling approximately as halo mass at a fixed redshift.
• Figure 4: The average number per unit redshift of CW sheets (left) and filaments (middle) with virial temperature above a given threshold, and halos with virial mass above a given threshold (right), intercepted by a random los as a function of the CWO redshift, $z$. For filaments and sheets, the solid lines correspond to the median mass using the conditional mass distribution function, and the shaded regions indicate the scatter (see text).
• Figure 5: The ratio of cooling time to ten times the free-fall time for virialized gas in CW sheets (left), filaments (middle), and halos (right), with different virial temperatures or masses as indicated in the legend. According to our simple model, CWOs are unstable to thermal condensation and fragmentation if this ratio is $\lsim 1$. This is always the case for low and intermediate mass halos and filaments, though the most massive halos are stable at $z\lsim4$, and the most massive filaments are stable at $z\lsim 1$. Low and intermediate mass sheets are stable at $z\lsim 1$ while high mass sheets are stable at $z\lsim 2$.