Multi-wavelength constraints on the outflow properties of the extremely bright millisecond radio bursts from the galactic magnetar SGR 1935 + 2154

Extremely bright coherent radio bursts with millisecond duration, reminiscent of cosmological fast radio bursts, were codetected with anomalously-hard X-ray bursts from a Galactic magnetar SGR 1935 + 2154. We investigate the possibility that the event was triggered by the magnetic energy injection inside the magnetosphere, thereby producing magnetically-trapped fireball (FB) and relativistic outflows simultaneously. The thermal component of the X-ray burst is consistent with a trapped FB with an average temperature of ∼200-300 keV and size of ∼105 cm. Meanwhile, the non-thermal component of the X-ray burst and the coherent radio burst may arise from relativistic outflows. We calculate the dynamical evolution of the outflow, launched with an energy budget of 1039-1040 erg comparable to that for the trapped FB, for different initial baryon load η and magnetization σ0. If hard X-ray and radio bursts are both produced by the energy dissipation of the outflow, the outflow properties are constrained by combining the conditions for photon escape and the intrinsic timing offset 10 ms among radio and X-ray burst spikes. We show that the hard X-ray burst must be generated at rX 108 cm from the magnetar, irrespective of the emission mechanism. Moreover, we find that the outflow quickly accelerates up to a Lorentz factor of 102 ≲ Γ ≲ 103 by the time it reaches the edge of the magnetosphere and the dissipation occurs at 1012 cm ≲ rradio, X ≲ 1014 cm. Our results imply either extremely-clean (η ≳ 104) or highly-magnetized (σ0 ≳ 103) outflows, which might be consistent with the rarity of the phenomenon.