🔭 astrophysics

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

This paper models the secular orbital evolution of quasi-periodic eruption (QPE) systems under stripping and orbiter-disk collision scenarios to evaluate their potential as bright sirens for measuring the Hubble constant, finding that while current stripping models yield no detectable LISA signals, the orbiter-disk scenario identifies two promising candidates (eRO-QPE2 and eRO-QPE4) capable of constraining $H_0$ with 6.7–14.9% uncertainty, thereby motivating continued time-domain monitoring of these candidates.

Original authors: Yejing Zhan, Di Wang, Shuang-Xi Yi, Fa-Yin Wang

Published 2026-01-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yejing Zhan, Di Wang, Shuang-Xi Yi, Fa-Yin Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Measuring the Universe's Speedometer

Imagine the universe is a giant race track, and we are trying to measure exactly how fast the track is stretching (expanding). This speed is called the Hubble Constant. Currently, scientists have two different ways of measuring this speed, and they disagree with each other. It's like having two different GPS apps that give you two different arrival times for the same destination.

To fix this, we need a new, super-accurate ruler. In physics, this ruler is called a "Bright Siren."

How it works: When two massive objects (like black holes) crash together, they create ripples in space-time called Gravitational Waves. These waves tell us exactly how far away the crash happened. If we can also see the crash with a telescope (an Electromagnetic counterpart), we know exactly how fast that galaxy is moving away from us.
The Problem: So far, we haven't found enough of these "crashes" to get a precise measurement. The ones we have found are rare and hard to locate.

The New Suspects: Quasi-Periodic Eruptions (QPEs)

The authors of this paper are looking at a new type of cosmic event called Quasi-Periodic Eruptions (QPEs).

The Analogy: Imagine a supermassive black hole (a giant vacuum cleaner) sitting in the center of a galaxy. Every few hours, a smaller object (like a star or a smaller black hole) swings by, gets a little bit of a "belch" of energy, and then swings back out. This happens over and over, like a clockwork mechanism.
The Mystery: These eruptions are getting faster and faster. The time between the "belches" is shrinking. This means the small object is spiraling inward, getting closer to the giant black hole every time it swings by.

The Two Theories: How the Spiral Works

The paper tests two different stories to explain why these objects are spiraling in:

1. The "Peeling" Scenario (Stripping)

The Story: The small object is a white dwarf star (a dead, dense star). As it swings close to the giant black hole, the black hole's gravity peels off layers of the star like an onion.
The Result: The paper calculates that for the known QPEs, this "peeling" happens too slowly to be seen by our future space detectors. By the time the signal gets strong enough, the star might have already been eaten or the signal is too weak. Verdict: No detection expected.

2. The "Collision" Scenario (Orbiter-Disk)

The Story: The small object isn't peeling; it's crashing. Imagine the giant black hole has a flat, spinning disk of gas around it (like Saturn's rings, but made of hot gas). The small object swings in a tilted orbit, crashing into this gas disk twice every time it goes around.
The Result: Every time it hits the gas, it loses energy and slows down, causing it to spiral inward faster.
The Discovery: The authors found that two specific QPEs (eRO-QPE2 and eRO-QPE4) fit this story perfectly. If the small object is a medium-sized black hole (about 1,000 times the mass of our Sun), these systems will become loud enough to be heard by the LISA detector (a future space-based gravitational wave observatory) in the 2030s.

The Payoff: Solving the Hubble Constant Puzzle

If LISA can "hear" these two specific QPEs, it will be a game-changer.

The "Bright Siren" Success: Because we can see the QPE with telescopes, we know exactly which galaxy it is in. Because LISA hears the gravitational waves, it knows exactly how far away that galaxy is.
The Precision: By combining these two pieces of information, the paper predicts we could measure the expansion rate of the universe with a precision of about 6.7% to 14.9%.
The Metaphor: Think of it like this: If you are trying to guess how fast a car is driving, you usually have to guess the distance. But if you have a GPS that tells you the exact distance, you can calculate the speed perfectly. These QPEs provide that perfect GPS.

The Catch: We Have to Wait

The paper emphasizes that we cannot see these signals right now. The objects are still too far away in their orbits. They need to spiral in a bit more over the next 15 to 35 years to get close enough to the "sweet spot" where LISA can hear them.

Summary of Findings

Peeling Stars (Stripping): None of the known QPEs will be detectable by LISA in this scenario. The signal is too faint.
Crashing into Gas (Collision): Two specific QPEs (eRO-QPE2 and eRO-QPE4) are promising candidates.
- If the crashing object is a small black hole, we can detect it, but the measurement won't be super precise.
- If the crashing object is a medium-sized black hole, we can detect it very clearly, and it will give us one of the best measurements of the universe's expansion rate we've ever had.
The Future: We need to keep watching these objects with telescopes to confirm their behavior. If they keep spiraling in as predicted, they will be the "Bright Sirens" that help us solve the mystery of the universe's speed.

In short: The paper suggests that by watching specific cosmic "clocks" (QPEs) that are crashing into gas disks, we might finally get a clear, accurate reading on how fast the universe is expanding, provided we wait until the 2030s for our space detectors to be ready.

Technical Summary: Hubble Constant Measurement from QPEs as Electromagnetic Counterparts to Extreme Mass Ratio Inspirals

Problem Statement
The precise measurement of the Hubble constant ( $H_0$ ) remains a critical challenge in cosmology due to the tension between early-universe (CMB) and late-universe (distance ladder) measurements. The "bright siren" method, utilizing gravitational waves (GWs) with electromagnetic (EM) counterparts, offers a model-independent solution. However, current ground-based detectors (LIGO-Virgo-Kagra) face significant limitations: the event rate of neutron star mergers is low, sky localization is poor, and the fraction of mergers with detectable EM counterparts (kilonovae, GRBs) is small. Consequently, there is an urgent need to identify novel classes of bright sirens.

Quasi-periodic eruptions (QPEs) are a class of X-ray transients originating from galactic centers, hypothesized to be the EM counterparts of extreme/intermediate mass-ratio inspirals (EMRIs/IMRIs). While current QPE recurrence times ( $P \sim$ hours) correspond to GW frequencies ( $\sim 10^{-5}$ Hz) below the sensitivity band of space-based detectors like LISA ( $\sim 10^{-3}$ Hz), observations indicate that some QPEs exhibit rapid secular orbital decay ( $\dot{P}_{orb}$ ). This paper investigates whether known QPE systems will evolve into the LISA detection band by the 2030s and, if so, whether they can serve as bright sirens to constrain $H_0$ .

Methodology
The authors model the secular orbital evolution of nine known QPE sources under two distinct physical frameworks:

Stripping Scenario: A white dwarf (WD) on a highly eccentric orbit ( $e \gtrsim 0.9$ ) undergoes periodic mass transfer (MT) at periapsis. The evolution is driven by both gravitational wave (GW) emission and MT. The authors calculate the duration of the GW-dominated phase ( $\tau_{GW-d}$ ) before MT takes over, which would increase the orbital period and reduce GW amplitude.
Orbiter–Disk Collision Scenario: A compact companion (stellar-mass black hole, sBH, or intermediate-mass black hole, iBH) on a circular orbit intersects a misaligned accretion disk. The orbital decay is driven by energy loss from hydrodynamic and gravitational drag during disk crossings. The evolution of the decay rate is modulated by the coupled Lense-Thirring (LT) precession of the orbiter and the disk, which changes the misalignment angle over time.

GW Waveform and Detectability Analysis:

Waveform Models: For the stripping scenario (EMRI), the authors use the FastEmriWaveform (FEW) framework. For the collision scenario (IMRI), they utilize the IMRPhenomD model for sBHs and FEW for iBHs with small mass ratios.
Evolution Projection: The authors project a 15-year secular evolution for each source (assuming a 2035 LISA launch) to determine the final orbital period and signal-to-noise ratio (SNR) over a 4-year observation window.
Parameter Estimation: Using the Fisher Information Matrix (FIM), they estimate the uncertainty in luminosity distance ( $d_L$ ). Combined with the redshift ( $z$ ) derived from the host galaxy (identified via the QPE), they calculate the fractional uncertainty on $H_0$ ( $\Delta H_0/H_0$ ), accounting for peculiar velocity uncertainties.

Key Results
The study yields distinct outcomes for the two scenarios:

Stripping Scenario (WD companion):
- GSN 069: Observational constraints on $\dot{P}_{orb}$ imply the system enters the MT-dominated phase within $\sim 15$ years. By the time of LISA observation, GW emission is too weak for detection (SNR $\ll 1$ ).
- eRO-QPE2: The GW-dominated phase lasts only $\sim 3$ years. The system is MT-dominated during the LISA era, rendering it undetectable.
- eRO-QPE3 & eRO-QPE4: While eRO-QPE3 remains in the GW-dominated phase for 15 years, its predicted SNR is $\sim 0.06$ , far below the detection threshold.
- Conclusion: No currently known QPE is detectable by LISA in the 2030s under the stripping scenario.
Orbiter–Disk Collision Scenario (BH companion):
- sBH-disk ( $\mu = 100 M_\odot$ ):
  - eRO-QPE2: Predicted to reach an SNR of $\sim 8.5$ after 15 years of evolution, crossing the detection threshold. This yields a constraint on $H_0$ with a fractional uncertainty of 14.9%.
  - eRO-QPE4: Remains undetectable (SNR $< 1$ ).
- iBH-disk ( $\mu = 10^3 M_\odot$ ):
  - eRO-QPE2: SNR increases to $\sim 28.8$ , constraining $H_0$ to 10.4%.
  - eRO-QPE4: Becomes detectable with an SNR of $\sim 21.8$ . Despite a lower SNR than eRO-QPE2, its larger luminosity distance suppresses the impact of peculiar velocity uncertainties, resulting in the tightest constraint of 6.7%.
- Other Sources: GSN 069 and eRO-QPE3 remain undetectable in this scenario even with iBH companions.

Significance and Claims
The paper claims that QPE systems, specifically those evolving under the orbiter–disk collision scenario with an intermediate-mass black hole companion, represent a promising new class of bright sirens for precision cosmology in the 2030s.

Novelty: The work identifies eRO-QPE2 and eRO-QPE4 as the first known QPE candidates capable of providing a model-independent $H_0$ measurement with LISA, potentially achieving precision comparable to other major cosmological probes.
Caveats: The authors emphasize that these results rely on the assumption of regular secular evolution and specific physical models (e.g., disk alignment timescales, drag forces). They note that environmental effects (gas drag, tidal heating) and uncertainties in the central black hole mass could alter detectability.
Future Outlook: The study motivates continued time-domain monitoring of QPE candidates to refine orbital decay rates and identify new, regular sources with compact orbits that may enter the LISA band. It also suggests that a network of space-based detectors (LISA, Taiji, Tianqin) could further enhance SNR and $H_0$ constraints.

The authors conclude that while the stripping scenario fails to produce detectable bright sirens from current QPEs, the collision scenario offers a viable pathway to measuring the Hubble constant, provided the physical parameters (companion mass, disk properties) align with the fiducial models presented.