  The tidal disruption of a star by a supermassive black hole can result in
transient radio emission. The electrons producing these synchrotron radio
flares could either be accelerated inside a relativistic jet or externally by
shocks resulting from an outflow interacting with the circumnuclear medium.
Until now, evidence for the internal emission mechanism has been lacking;
nearly all tidal disruption flare studies have adopted the external shock model
to explain the observed properties of radio flares. Here we report a result
that presents a challenge to external emission models: we discovered a
cross-correlation between the soft X-ray (0.3-1 keV) and 16 GHz radio flux of
the tidal disruption flare ASASSN-14li. Variability features in the X-ray light
curve appear again in the radio light curve, but after a time lag of about 13
days. This demonstrates that soft X-ray emitting accretion disk regulates the
radio emission. This coupling appears to be inconsistent with all previous
external emission models for this source but is naturally explained if the
radio emission originates from a freely expanding jet. We show that emission
internal to an adiabatically expanding jet can also reproduce the observed
evolution of the radio spectral energy distribution. Furthermore, both the
correlation between X-ray and radio luminosity as well as our radio spectral
modeling imply an approximately linear coupling between the accretion rate and
jet power.
