Beyond the Impulsive Approximation: The Dynamics and Radio Emission of Tidal Disruption Jets

Abstract

Radio emission from relativistic tidal disruption events (TDEs) is commonly interpreted using the Blandford--McKee solution for an impulsive relativistic blast wave. Unlike gamma-ray bursts, however, TDE jets are powered by fallback accretion, injecting energy over weeks to months. We investigate how this sustained energy injection modifies the dynamics and radio emission of relativistic TDE jets using one- and two-dimensional relativistic hydrodynamic simulations coupled with synchrotron radiation calculations. For a fixed total energy, fallback-powered jets drive slower forward shocks, producing delayed and systematically fainter radio emission. We show that the impulsive approximation is valid only when the duration of energy injection is less than approximately ten percent of the deceleration time of an equivalent Blandford--McKee blast wave, a condition that is generally not satisfied for relativistic TDEs. As a result, continuously powered outflows are significantly less beamed than impulsive explosions, leading to a strong suppression of off-axis radio emission. These results demonstrate that the radio evolution of relativistic TDEs retains memory of the central engine and cannot, in general, be described by an impulsive solution. By substantially reducing the expected off-axis radio emission, sustained fallback-powered jets imply that relativistic jet production in tidal disruption events may be considerably more common than current radio observations suggest.