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

TL;DR

The paper addresses measuring the Hubble constant $H_0$ via bright sirens from QPEs expected to accompany EMRIs/IMRIs in the LISA band. It compares two secular-evolution models for QPEs—the stripping scenario and the orbiter-disk collision scenario—computing GW waveforms with FEW for EMRIs and IMRPhenomD for IMRIs, and uses Fisher analysis to forecast $d_L$ and $H_0$ uncertainties. The main results show no LISA-detectable sources in the stripping channel for known QPEs, but promising detectability in the orbiter-disk collision channel for eRO-QPE2 and eRO-QPE4, particularly with an iBH companion, yielding fractional $H_0$ uncertainties as low as a few percent. These findings highlight QPEs as potential bright sirens for precision cosmology in the 2030s, with improvements expected from longer mission durations and detector networks, while emphasizing the need to model environmental and warp effects for robust forecasts.

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.

Figures (3)

• Figure 1: The initial orbital decay $\dot P_\text{orb,init}$ with respect to $\mu_\text{WD}$ and $\beta_\text{init}$. With a larger $\beta_\text{init}$ and a larger $\mu_\text{WD}$, the $|\dot P_\text{orb,init}|$ increases. The observation indicates that $\dot P_\text{orb,init} \sim -10^{-5}$ for GSN 069. The gray block represents the parameter space that failed to match the observation. The constraint on $\dot P_\text{orb,init}$ leads high $\beta_\text{inital}$ and low $\mu_\text{WD}$.
• Figure 2: The dependence of orbital eccentricity $e$ and $\tau_\text{GW-d}$ with respect to $\mu_\text{WD}$ and $\beta_\text{init}$. With a larger $\beta_\text{init}$, the $\tau_\text{GW-d}$ increases and the $e$ decreases, while the situation is opposite with a larger $\mu_\text{WD}$. The gray dashed line in the top-right figure represents the $\tau_\text{GW-d}=3\text{ yr}$ of eRO-QPE2, indicated by the observation.
• Figure 3: The SNR vs the fractional $H_0$ uncertainty, $\Delta H_0/H_0$ for sources in our fiducial analysis with 4-yr LISA observation. Colors encode the elapsed secular orbital evolution (blue: 15 yr; orange: 25 yr; green: 35 yr). Symbols denote systems and scenarios: circles—eRO-QPE2 (sBH–disk); triangles—eRO-QPE2 (iBH–disk); squares—eRO-QPE4 (iBH–disk).. The dashed lines represent GSN 069 in the iBH-disk scenario. The gray shaded band marks the SNR threshold of $\leq 8$, i.e., below our detection threshold. As the evolution time increases, all sources move toward higher SNR and yield progressively tighter constraints on $H_0$. We plot the sources with SNRs over 1 in the figure.