Hubble constant measurement from QPEs as electromagnetic counterparts to extreme mass ratio inspirals

Abstract

Gravitational waves (GWs) accompanied by electromagnetic (EM) counterparts provide a novel methodology to measure the Hubble constant ($H_0$), known as bright sirens. However, the rarity of such multi-messenger events limits the precision of the $H_0$ constraint. Recently, the newly-discovered nuclear transient, quasi-periodic eruptions (QPEs) show intriguing evidence of a stellar-mass companion captured by a supermassive black hole (SMBH) in an extreme/intermediate mass-ratio inspiral (EMRI/IMRI), which is the most promising sources of the space-based GW detectors, such as LISA. Here, we model the secular orbital evolution of known QPE systems using two frameworks: a stripping scenario in which periodic mass transfer at periapsis drives the evolution; and an orbiter-disk collision scenario in which the companion interacts with a misaligned accretion disk, modulated by coupled orbiter-disk precession. For each framework, we assess detectability by LISA, together with the resulting constraints on $H_0$. Our principal findings are: (i) in the stripping scenario, no currently known QPE reaches detectability within a four-year LISA mission. (ii) in the orbiter-disk scenario, two sources-eRO-QPE2 and eRO-QPE4-are detectable with signal-to-noise ratios $\simeq 8.5-28.8$ and constrain $H_0$ with fractional uncertainty of 6.7-14.9\%. QPE systems remain uncertain on the decade-long secular evolution. Therefore, they motivate continued time-domain monitoring of QPE candidates.