Ram-pressure Stripping of a Kicked Hill Sphere: Prompt Electromagnetic Emission from the Merger of Stellar Mass Black Holes in an AGN Accretion Disk

Accretion disks around supermassive black holes (SMBHs) are promising sites for stellar mass black hole (BH) mergers due to mass segregation and merger acceleration by disk gas torques. Here we show that a gravitational-wave (GW) kick at BH merger causes ram-pressure stripping of gas within the BH Hill sphere. If R_H ≥ H, the disk height, an off-center UV flare at a_(BH) ~ 10³ r_g, emerges within t_(UV) ~ O(2 days)(a_(BH)/10³ r_g)(M_(SMBH)/10⁸ M_⊙)(v_(kick)/10² km s⁻¹) postmerger and lasts O(R_H/v_(kick)) ~ O(5t_(UV)). The flare emerges with luminosity O(10⁴² erg s⁻¹(t_(UV)/2 days)⁻¹(M_(Hill)/1M_⊙)(v_(kick)/10² km s⁻¹)². Active galactic nucleus optical/UV photometry is altered and asymmetric broad emission line profiles can develop after weeks. If R_H < H, detectability depends on disk optical depth. Follow-up by large optical sky surveys is optimized for small GW error volumes and for Laser Interferometer Gravitational-Wave Observatory/Virgo triggers >50M_⊙.