Radio constraint on outflows from tidal disruption events

Radio flares from tidal disruption events (TDEs) are generally interpreted as synchrotron emission arising from the interaction of an outflow with the surrounding circumnuclear medium (CNM). We generalize the common equipartition analysis to be applicable in cases lacking a clear spectral peak or even with just an upper limit. We show that, for detected events, there is a lower limit on the combination of the outflow's velocity v and solid angle Omega, similar or equal to v Omega(a) (with a similar or equal to 0.5). Considering several possible outflow components accompanying TDEs, we find that: isotropic outflows such as disc winds with v similar to 10(4) km s(-1) and Omega = 4 pi can easily produce the observed flares; the bow shock of the unbound debris has a wedge-like geometry and it must be geometrically thick with Omega greater than or similar to 1. A fraction of its mass (greater than or similar to 0.01 M-circle dot) has to move at v greater than or similar to 2 x 10(4) km s(-1); Conical Newtonian outflows such as jets can also be a radio source but both their velocity and the CNM density should be larger than those of isotropic winds by a factor of similar to(Omega/4 pi)(-0.5). Our limits on the CNM densities are typically 30-100 times larger than those found by previous analysis that ignored non-relativistic electrons. We also find that late (a few years after the TDE) radio upper limits rule out energetic, similar to 10(51-52) erg, relativistic jets like the one observed in TDE Sw J1644+57, implying that such jets are rare.