No evidence for a supermassive black hole binary in GSN 069

Abstract

Quasi-periodic eruptions (QPEs) are recurrent soft X-ray flares from galactic nuclei and provide a new time-domain probe of stellar-mass objects (SMOs) orbiting supermassive black holes (SMBHs). In an extreme-mass-ratio inspiral (EMRI) system interacting with an accretion disk, QPEs are produced when the SMO repeatedly crosses an accretion disk, so that the eruption times trace the orbital motion of the EMRI. We investigate whether such timing information can be used to probe a more distant SMBH companion. We develop two complementary diagnostics: (1) the motion of the EMRI host SMBH around the SMBH-binary (SMBHB) center of mass induces a light-travel-time modulation in the observed QPE arrival times, specifically an \emph{in-phase} modulation in arrival times of even and odd eruptions; (2) if the QPE source contains a surviving stellar orbiter, the external SMBH must not drive the SMO into tidal disruption through eccentricity excitation by the von Zeipel--Lidov--Kozai (ZLK) mechanism. Using GSN 069 as an example, we find \emph{no} in-phase modulation in the QPE timing (i.e., no evidence for a SMBHB) and constrain the excluded parameter space of the companion SMBH. These results demonstrate that QPE timing and stellar survival offer complementary routes for constraining otherwise hidden SMBH companions in nearby galactic nuclei.