Prompt shocks in the gas disk around a recoiling supermassive black hole binary

Supermassive black hole binaries (BHBs) produced in galaxy mergers recoil at the time of their coalescence due to the emission of gravitational waves (GWs). We simulate the response of a thin, 2D disk of collisionless particles, initially on circular orbits around a 10^6 M_sun BHB, to kicks that are either parallel or perpendicular to the initial orbital plane. Typical kick velocities (v_k) can exceed the sound speed in a circumbinary gas disk. While the inner disk is strongly bound to the recoiling binary, the outer disk is only weakly bound or unbound. This leads to differential motions in the disturbed disk that increase with radius and can become supersonic at ~700 Schwarzschild radii for v_k ~500 km/s, implying that shocks form beyond this radius. We indeed find that kicks in the disk plane lead to immediate strong density enhancements (within weeks) in a tightly wound spiral caustic, propagating outward at the speed v_k. Concentric density enhancements are also observed for kicks perpendicular to the disk, but are weaker and develop into caustics only after a long delay (>1 year). Unless both BH spins are low or precisely aligned with the orbital angular momentum, a significant fraction (> several %) of kicks are sufficiently large and well aligned with the orbital plane for strong shocks to be produced. The shocks could result in an afterglow whose characteristic photon energy increases with time, from the UV (~10eV) to the soft X-ray (~100eV) range, between one month and one year after the merger. This could help identify EM counterparts to GW sources discovered by LISA.