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.
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