FRB scattering statistics through the CGM are sensitive to morphology and intermittency

Abstract

The small-scale properties of circumgalactic gas in ordinary galaxies drive its bulk properties: the mass loading of cold neutral gas in galactic outflows affects their bulk momentum; gas cooling processes on small scales affect the spatial distribution of gas in the cool (T~$10^4$K) circumgalactic medium (CGM). However, hydrodynamical simulations have yet to resolve the CGM on such small scales. Spectroscopy remains our primary probe of the small-scale CGM, with which sub-parsec scales are challenging to resolve. Fast radio bursts (FRBs)--microsecond to millisecond duration radio pulses--are temporally broadened ("scattered") by gradients in the electron density transverse to the line of sight, often generated by fluctuations on the smallest spatial scales. This makes FRB scattering a powerful, complementary, and scalable probe of the small-scale CGM. We show that the distribution of scattering timescales introduced by density fluctuations within a single, foreground halo--the tau distribution function, or TDF--is sensitive to the small-scale spatial morphology of the gas. The TDF is readily measurable and is analogous to areal covering factors reported in quasar absorption statistics. We compute the TDF in two regimes: scattering from a turbulent, volume-filling medium ("volumetric scattering") distributed along the line of sight; and scattering from discrete structures localized along the line of sight ("intermittent scattering"). Within these regimes, the TDF is sensitive to whether the cool gas comprises primarily spherical, filamentary (1D), or sheet-like (2D) structures. This work sets the stage for upcoming observations which will use hundreds of sight-lines through nearby halos to probe the small-scale CGM, and points out a novel science case for FRB detectors like MeerKAT, Parkes, FAST, and the DSA-2000, which are exquisitely sensitive over a narrow field of view.

Figures (8)

• Figure 1: Predictions of the distribution of scattering timescale distribution function (the "TDF"; equivalently the covering factor at a certain scattering timescale) for four different scattering scenarios. (Solid blue) Volumetric scattering due to a complex of size $R$ comprising spherical cool gas cloudlets of uniform radius, $r_c$, with volume filling factor $f_V$, such that $f_V R = 0.2\,{\rm kpc}$. The different opacity curves are computed for differing cloudlet optical depths, $N_c = 20, 80$ and $320$, which correspond to cloudlets of size $r_c = 10, 2.5$, and $0.625\,{\rm pc}$, respectively. We assume a mean-square-bending-angle-per-unit-length of $311\,{\rm \mu as^2 / pc}$ (see Section \ref{['sec:volumetric_scattering']}). We place the scattering surface at a distance of $d_{\rm eff} = 0.8\,{\rm Mpc}$, corresponding to the distance to M31, and set the source wavelength to $\lambda = 75\,{\rm cm}$, corresponding to the low-end of the CHIME band. (Dotted purple / dot-dash green) An identical set-up to the blue curve with $N_c = 20$, except the cloudlets are given a filamentary / sheet-like geometry with an aspect ratio of $A = 500$, keeping the volume of the cloudlets fixed in all cases. (Dashed red) Intermittent refractive scattering from corrugated sheets where the sheets have a density of $n_e = 10^{-2}\,{\rm cm}^{-3}$ and the individual corrugations have an aspect ratio of $A = 10^4$. The distance to the scatterer and wavelength are the same as in the previous cases, as well as $f_V R = 0.2\,{\rm kpc}$. The opacity refers to the same values of $N_c$ as before, which correspond to sheet thicknesses of $\delta = 0.16, 0.04$ and $0.01\,{\rm pc}$.
• Figure 2: (Top) Distribution of intersection lengths for a complex of spherical cloudlets with radius $r_c = 10\,{\rm pc}$ and different clouldets optical depths, $N_c = f_V R /r_c$. The distributions become narrower as $N_c$ increases. (Bottom) The solid lines show the cumulative distribution functions for the scattering timescale (assuming $\eta = 311\,{\rm \mu as^2}/{\rm pc}$ and $d_{\rm eff} = 0.8\,{\rm Mpc}$) for the above intersection length distributions. The upper $x$-axis on the right panel shows the intersection length converted to a scattering time for $d_{\rm eff} = 0.8\,{\rm Mpc}$ and $\eta = 311\,{\rm \mu as}^2/{\rm pc}$. The dashed lines show the analytic approximation derived assuming that the above distributions follow $\delta L \sim \mathcal{N}(0,N_c^{-1})$.
• Figure 3: A simulation of intersection lengths through a complex of spherical cloudlets with a power-law distribution of radii ($\alpha = 2$, $r_{\rm c, min} = 0.1\,{\rm pc}$, $r_{\rm c, max} = 10\,{\rm pc}$). The left panel shows the mist of cloudlets, randomly distributed in a box of dimensions $10 r_{\rm c, max} \times 10 r_{\rm c, max} \times R$, with $R = 1\,{\rm kpc}$. The co-ordinate axes are in units of $r_{\rm c, max}$. The middle panel shows the intersection length contrast, $\delta L = (L - \overline{L}) / \overline{L}$, for a grid of vertical sight-lines through the box, and the right shows the cumulative distribution function of these intersection lengths in blue. The dashed line shows the analytic curve for a Gaussian distribution (Eq. \ref{['eq:ftau_sphere_analytic']}).
• Figure 4: Diagram showing the geometric parameters used in Eqs. \ref{['eq:Lc_sphere']}, \ref{['eq:Lc_filament']}, and \ref{['eq:Lc_sheet']} to define the intersection length through a spherical, filamentary, or sheet-like cloudlet, for a line of sight with impact parameter ${\bf b}$ from the centre of the cloudlet.
• Figure 5: (Top row) The intersection lengths of a mist of spherical (left), filamentary (middle), and sheet-like (right) cloudlets through a box of dimension $0.2 \,{\rm kpc} \times 0.2 \,{\rm kpc} \times 1\,{\rm kpc}$. The spheres have uniform radius $r_c = 10\,{\rm pc}$. The filaments have dimension $\delta \times \delta \times \Lambda$ and the sheets have dimension $\delta \times \Lambda \times \Lambda$, where in both cases we choose $\Lambda / \delta = 500$. The smaller dimension is chosen so that the volume of each object is equal to the $\frac{4}{3}\pi r_c^3$. Each box is randomly populated with cloudlets to have a volume filling factor of $f_V = 0.2$. The colour map shows the intersection length contrast $\delta L = (L -\overline{L}) / \overline{L}$ where $\overline{L} = f_V R$. (Bottom row) The distribution of the intersection length contrast values in the top row.