Refractive lensing of scintillating FRBs by subparsec cloudlets in the multiphase CGM

Abstract

We consider the refractive lensing effects of ionized cool ([Formula: see text]) gas cloudlets in the circumgalactic medium (CGM) of galaxies. In particular, we discuss the combined effects of lensing from these cloudlets and scintillation from plasma screens in the Milky Way interstellar medium (ISM). We show that, if the CGM comprises a mist of subparsec cloudlets with column densities of order [Formula: see text] (as predicted by [M. McCourt, S. P. Oh, R. O'Leary, A. M. Madigan, MNRAS 473, 5407-5431 (2018)]), then fast radio bursts (FRBs) whose sightlines pass within a virial radius of a CGM halo will may be lensed into tens of refractive images with a ∼10 ms scattering timescale. When these images are formed, they will be resolved by scintillating screens in the Milky Way ISM and will suppress the observed scintillation. We illustrate this effect in refractive lensing and argue that positive detections of FRB scintillation may constrain the properties of these cool-gas cloudlets, with current scintillation observation weakly disfavoring the cloudlet model. We propose that sheet-like geometries for the cool gas in the CGM can reconcile quasar absorption measurements (from which we infer the presence of the cool gas with structure on subparsec scales) and the unexpected lack of lensing signals from this gas thus far observed.

Keywords: circumgalactic medium; fast radio bursts; plasma lensing; scintillation.

Fig. 1.

Diagram of the two-screen lensing. (A) When only the scintillation screen is present, the multipath propagation of light leads to intensity modulations as a function of frequency, $I(f)$. The black intensity curves show the intrinsic intensity modulation, whereas the blue curve shows the observed intensity modulation taking into account finite frequency resolution (the observed intensity is the intrinsic intensity smoothed over the frequency resolution). If the characteristic scale of these modulations (the “scintillation bandwidth”) is smaller than the frequency resolution, then the observed intensity is effectively the same as the intrinsic intensity. (B) In the presence of a background resolving lens, an additional timescale is present, due to the multipath propagation through the lens, as well as the scintillation screen. This leads to intensity modulations on a smaller frequency scale, which, if below the frequency resolution, results in the observed intensity modulations being suppressed relative to the case where the background lens is absent.

Fig. 2.

Lensing by the double lens with a sinusoidal phase screen and rational lens with ${\kappa }_1=200$, ${\kappa }_2=-10$, γ = 1, $z_3=0.1$, $d_{03}/d_{02}=2$, ${\tau }_s=10\mathrm{\mu }\mathrm{s}$, and fixed source position $y=\beta /{\theta }_l=5.7$. Columns show the results for different values of $\rho =0.01,1,10$, which corresponds to varying the distance to the sinusoidal screen, d₀₁. The Top row shows the lens map from the background lens plane to the source plane, ${\theta }_2\to \beta$. The gray vertical line corresponds to the source position. The second row shows the magnification and time delay of the images formed by this lens model. The blue dots show the images formed by the background lens and scintillation screen together, whereas the black dots show the images formed by the scintillation screen on its own. The third row shows the intensity modulation as a function of frequency, $I(f)$. Again the blue curves show the full lens model, whereas the black curves show the intensity modulation induced by the scintillation screen on its own. The green curve in the leftmost column shows the result of the blue curve smoothed over some finite frequency resolution, $\delta f=0.1\mathrm{MHz}$. The Bottom row shows the autocorrelation function of these curves, $⟨\delta T(f)\delta T(f+\mathrm{\Delta }f)⟩$, where $\delta T\equiv (I-\overline{I})/\overline{I}$. The zero-lag of this autocorrelation function is the modulation index, m.

Fig. 3.

Average scattering time (Top) and number of refractive images (Bottom) formed by an ensemble of cool gas cloudlets as a function of the average number of cloudlets intersected by a given sightline (Eq. 25). We take the cloudlets to have uniform size, $r_c=0.1\mathrm{pc}$, with a uniform maximum column density, $N_e^c={10}^{17}{\mathrm{cm}}^{-2}$, and a symmetric Gaussian density profile. We take the galaxy to have a virial radius of $r_{200}=100\mathrm{kpc}$ and the clouds to have a power-law volume filling factor given by Eq. 22, with β = 0.2. We vary the number of intersected cloudlets by varying the overall amplitude of the volume filling factor, $f_V^{200}$. We choose a distance parameter of $d_{02}{d}_{23}/d_{03}=1\mathrm{Gpc}$ for the lensing geometry, an observing frequency of $1\mathrm{GHz}$, and an impact parameter of $b=r_{200}$.

Fig. 4.

Conditions under which FRB scintillation is expected to be suppressed for an FRB at a given source redshift, z_s, with a sightline passing within the virial radius of galactic halo. We assume the galactic halo comprises an ensemble of cool-gas cloudlets of uniform radius r_c and electron column density N_e, with a volume filling factor of $f_V^{200}={10}^{-4}$ at the virial radius. Scintillation is suppressed when the cloudlets produce many refractive images, $N_{\mathrm{im}}>1$, which produce frequency modulations on a scale finer than the frequency resolution of the observation, which we take to be $\mathrm{\Delta }{f}_{\mathrm{res}.}=0.1\mathrm{MHz}$. This latter condition corresponds to a scattering timescale of ${\tau }_d>10\mathrm{\mu }\mathrm{s}$. Inverting Eqs. 26 and 27, we compute the values of N_e for which scintillation is suppressed as a function of source redshift for fixed $r_c=0.1\mathrm{pc}$ (Top panel), as well as the values of r_c for which scintillation is suppressed for fixed $N_e={10}^{17}{\mathrm{cm}}^{-2}$. The shaded regions show the excluded values of these parameters given a positive detection of scintillation. The green curves show the condition that CGM lens resolves the scintillation screen; however, note that whenever $N_{\mathrm{im}}>1$, this condition is always satisfied. The horizontal dashed line shows the fiducial values of the parameters r_c and N_e as predicted by the shattering picture proposed by ref. . The vertical gray line shows the inferred redshift of FRB 110523, which was the first FRB to be confirmed to scintillate due to multipath propagation in the Milky Way ISM, with a modulation index of m = 0.27.