Numerical Studies on the Radio Afterglows in TDE (I): Forward Shock

TL;DR

This study investigates radio afterglows from tidal disruption events under the forward-shock paradigm by coupling two-fluid hydrodynamics (shock-accelerated relativistic electrons treated as a separate fluid) with radiative-transfer calculations to produce spatially resolved synchrotron spectra. It explores CNM density profiles and outflow energetics, finding that a moderate outflow in a Galactic Center–like CNM can yield GHz self-absorption and mJy-level emission at 100 Mpc, with spectra that are anisotropic and sensitive to the outflow opening angle. A key result is that standard equipartition analyses substantially underestimate shock radii and energies compared to the full simulations, underscoring the need to incorporate spatial CR electron evolution and radiative transfer when interpreting observations. The work provides diagnostic signatures for FS-dominated TDE radio afterglows and highlights the importance of multiepoch, multiangle data to distinguish FS from other scenarios such as bow shocks or jet-driven emission.

Abstract

Recent long-term radio monitoring of tidal disruption events (TDEs) suggests that radio afterglows are common. Most studies argue that these afterglows may arise from forward shocks (FS) produced by the interaction between the TDE outflow and the hot, diffuse circumnuclear medium (CNM). Current theoretical models do not model the evolution of relativistic electrons in space, which introduces uncertainties. Here we conducted hydrodynamic simulations to study the hydrodynamic evolution of relativistic electrons, and calculated the synchrotron spectra via radiative transfer. We focus on the FS scenario with non-relativistic outflows, and various parameters of the outflow and CNM are explored. A moderate outflow with kinetic energy of several $10^{50}$ erg in a Galactic center - like CNM can produce mJy-level radio afterglows at a distance of 100 Mpc. The self-absorption frequency exhibits a slow decline at early times and a rapid decrease at late times. We derived the temporal evolution of the high-frequency radio flux, revealing its characteristic rise and decline pattern. We also find that: (1) the radio spectra for narrow outflows are clearly anisotropic along different sight lines; (2) the FS parameters inferred from radio spectra using conventional analytical formulas deviate significantly from those in simulations, in which the inferred shock radii are half of those from simulations, and the inferred energies are an order of magnitude lower.

Figures (11)

• Figure 1: Schematic diagram of the CRe injection method. The energy density distributions ($e_1$ and $e_2$) refer to those in the nine meshes intersected by the blue line segment in the upper right panel. The simulation code uses 4 grid levels to capture the shock, which stabilizes at the 4th mesh (see the orange line). The CRe component is injected at the 4th mesh. Due to numerical diffusion, the values of $e_2$ in the 1st -- 3rd mesh subsequently become nonzero, but this has a negligible effect on the results.
• Figure 2: Schematic diagram of data processing and spectral calculation. First, the 2.5-dimensional spherical coordinates are re-gridded into a 3D coordinate system, and the CRe energy density distribution in the new coordinates is obtained via interpolation. Next, quadrant reconstruction is carried out to recover the full 3D physical scenario. Finally, synchrotron radiation transfer is performed along the polar and equatorial directions to compute the emitting spectra in both directions.
• Figure 3: Snapshots of run A (fiducial run) at $t=2$ yr (left), 5 yr (middle) and 10 yr (right). In each panel, the left half window shows the density distribution, and the right half window shows the energy density of CRe.
• Figure 4: The left panel shows the synthetic radio spectra along the equatorial direction (Eqt) and polar direction (Pol). Note that we have considered the light-travel time difference in the polar direction. The middle panel presents the time evolution of the self-absorption frequency $\nu_p$. The right panel presents the light curves of $F_{\nu}$ for three frequencies.
• Figure 5: The emitting radio spectra for different outflow opening angles $\theta_0$. The left panel shows the spectra at different epochs for run Fo10 ($\theta_0=10^{\circ}$), and the right panel is for run Go60 ($\theta_0=60^{\circ}$). Obviously when the outflow's opening angle is smaller, the anisotropy of the spectra is more significant.