Hubble Constant Measurement from Quasiperiodic Eruptions as Electromagnetic Counterparts to Extreme Mass Ratio Inspirals

Gravitational waves (GWs) accompanied by electromagnetic counterparts, known as bright sirens, provide a novel methodology to measure the Hubble constant ( H _0 ). However, the rarity of such multimessenger events limits the precision of the H _0 constraint. Recently, the newly discovered class of nuclear transient, quasiperiodic eruptions (QPEs), shows intriguing evidence of a stellar-mass companion captured by a supermassive black hole in an extreme/intermediate mass ratio inspiral, which is the most promising source of 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 ≃8.5–28.8 and constrain H _0 with a 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.