Millihertz Oscillations Near the Innermost Orbit of a Supermassive Black Hole

Adam Ingram; Andrew C. Fabian; Benny Trakhtenbrot; Christos Panagiotou; Ciro Pinto; Claudio Ricci; Dev R. Sadaula; Eileen T. Meyer; Erin Kara; Giovanni Miniutti

REVIEW 3 major objections 4 minor 2 cited by

Millihertz Oscillations Near the Innermost Orbit of a Supermassive Black Hole

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read 1ES 1927+654 shows a highly significant X-ray QPO whose frequency rises from 0.93 to 2.34 mHz between 2022 and 2024, placing the oscillation within roughly 10 gravitational radii of the supermassive black hole.

desk verdict A robust, genuinely new mHz QPO with a decelerating chirp in 1ES 1927+654; the detection is solid, but the 'within 10 Rg' location claim is model-dependent and the deceleration is not yet fit. read the letter →

arxiv 2501.01581 v1 pith:GFOYWI73 submitted 2025-01-03 astro-ph.HE

Megan Masterson , Erin Kara , Christos Panagiotou , William N. Alston , Joheen Chakraborty , Kevin Burdge , Claudio Ricci , Sibasish Laha

show 17 more authors

Iair Arcavi Riccardo Arcodia S. Bradley Cenko Andrew C. Fabian Javier A. García Margherita Giustini Adam Ingram Peter Kosec Michael Loewenstein Eileen T. Meyer Giovanni Miniutti Ciro Pinto Ronald A. Remillard Dev R. Sadaula Onic I. Shuvo Benny Trakhtenbrot Jingyi Wang

This is my paper · ORCID

classification astro-ph.HE

keywords quasi-periodicoscillationsupermassiveblackhole1ES1927+654X-raytimingaccretiondiskextrememassratioinspiralLISAmHzgravitationalwaves

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports the discovery of a coherent, highly significant millihertz X-ray quasi-periodic oscillation (QPO) in the active supermassive black hole 1ES 1927+654. The oscillation was first seen in July 2022 at about 0.93 mHz, an 18-minute period, and by March 2024 had risen to 2.34 mHz, a 7.1-minute period, with the frequency increase itself decelerating over time. If the frequency tracks orbital motion, the signal originates within about 10 gravitational radii of the black hole, far closer in than the quasi-periodic eruptions seen in other galaxies. The paper argues that pure gravitational-wave inspiral cannot reproduce the observed evolution, so any stellar-mass companion must be gaining angular momentum through stable mass transfer or losing it through gas drag, while instability and coronal-oscillation models face their own difficulties. A companion origin would make this source a promising low-frequency gravitational-wave target for LISA.

What carries the argument

The load-bearing tool is the mapping from a measured QPO frequency to a radius in the Kerr spacetime, $f_\phi = c^3/(2\pi G M)(r^{-3/2}+a)^{-1}$ for orbital frequency, which converts the highest observed frequency into the claim of less than 10 gravitational radii and yields the mass and spin limits. The second essential element is the comparison of the observed $\dot{f}>0$, $\ddot{f}<0$ evolution with the leading-order gravitational-wave chirp $\dot{f} \propto f^{11/3}$, which shows that ordinary inspiral alone fails, and a series of alternative model equations including the mass-transfer angular-momentum balance and the coronal oscillation frequency $f\approx 2\pi c_s/r_c$.

What would settle it

A future X-ray campaign that resolves the QPO at a frequency which stops rising, reverses, or jumps discontinuously while the X-ray flux continues its current trend would falsify the claimed decelerating period evolution and, with it, the mass-transfer and coronal-contraction models, while a non-detection of the predicted roughly 2.34 mHz gravitational-wave signal by LISA in the 2030s would rule out the $0.1\,M_\odot$ white-dwarf companion interpretation.

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Extended reading notes

Core claim

The central claim is that 1ES 1927+654, a roughly $1.38\times10^6\,M_\odot$ black hole that underwent a major changing-look outburst in 2018, now hosts a persistent mHz QPO whose frequency rises monotonically from $0.93\pm0.06$ mHz to $2.34\pm0.05$ mHz between July 2022 and March 2024, with $\dot{f}>0$ and $\ddot{f}<0$, equivalently $\ddot{P}>0$. The QPO is detected at roughly $5\sigma$ to $7\sigma$ in individual 2023 and 2024 XMM-Newton epochs, has a quality factor $Q\approx8$ to $10$, strengthens with photon energy from fractional RMS below about 7 percent in soft X-rays to 15 to 20 percent in the 2 to 10 keV band, and its frequency correlates with the X-ray flux and spectral index. Associating the frequency with orbital motion at the innermost stable circular orbit gives a black hole mass upper limit of about $5.8\times10^6\,M_\odot$ and, for the preferred mass of $1.38\times10^6\,M_\odot$, a spin lower limit of $a\gtrsim0.43$. The paper concludes that pure gravitational-wave inspiral of a compact companion cannot explain the decelerating frequency rise, and it presents a roughly $0.1\,M_\odot$ white dwarf undergoing mass transfer, disk-tearing instabilities, and magnetoacoustic coronal oscillations as the leading candidate mechanisms, each with unresolved tensions.

Load-bearing premise

The arguments that the signal comes from within 10 gravitational radii, that the black hole mass is below about $5.8\times10^6\,M_\odot$, and that the spin exceeds 0.43 all assume the QPO frequency is tied to an orbital or epicyclic timescale in the Kerr spacetime, an assumption the paper itself notes would not hold if the oscillation arises in the corona or jet instead.

Editorial extensions

If this is right

The QPO provides a timing-based probe of the innermost accretion flow of a supermassive black hole: if orbital in origin, the emitting region lies below 10 gravitational radii, closer in than quasi-periodic eruptions, and the black hole must be spinning with $a\gtrsim0.43$ for the preferred mass.
A roughly $0.1\,M_\odot$ white dwarf companion on the inferred orbit should produce a detectable LISA signal, with an estimated signal-to-noise ratio near 10 over four years at a distance of 84 Mpc, making 1ES 1927+654 a potential multi-messenger source.
The observed decelerating period evolution rules out pure gravitational-wave inspiral as the driver, so if the QPO is an extreme-mass-ratio orbiter, stable mass transfer and likely gas drag must supply angular momentum; this model predicts a long-lived QPO at a similar frequency for roughly ten years or more.
If the QPO is instead a coronal oscillation, the rising frequency accompanied by spectral softening implies the corona contracts from roughly 5 to 2 gravitational radii, a prediction tied to the observed correlation between QPO frequency and X-ray flux.
Continued X-ray monitoring can discriminate between the models: the companion model predicts persistence at a similar frequency, whereas instability and oscillation models predict continued correlated changes between the QPO frequency and the X-ray flux and spectral shape.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the QPO originates in the corona or jet rather than in orbital motion, the radius, mass, and spin claims do not follow; the detection itself would stand, but the near-ISCO interpretation would require a different clock.
The strong correlation between QPO frequency and X-ray flux suggests a sharp testable prediction: if the frequency tracks the accretion rate continuously rather than only across the two-year trend, then a future state change in the source should shift or extinguish the QPO within roughly one viscous timescale.
The proposed connection to quasi-periodic eruptions implies that some QPEs and mHz QPOs may be different manifestations of the same companion-disk physics, distinguished by orbital radius and by whether the interaction shocks the disk or transfers mass; a deliberate search for mHz QPOs in known QPE hosts could find additional examples.
If LISA detects the predicted signal, the measured frequency evolution could become a direct probe of angular-momentum exchange between an embedded companion and an AGN disk, constraining gas-drag and migration-trap prescriptions well beyond this single source.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: the detection is real and the paper is worth taking seriously. The QPO in 1ES 1927+654—mHz, coherent, energy-dependent, evolving from ~0.93 to 2.34 mHz—is exactly the kind of thing that changes how we think about SMBH timing. The analysis is careful. They use two independent significance tests (light-curve simulations and AIC), the feature is resolved in multiple frequency channels, Q~8–10 in later epochs, RMS rises with energy, and they check the broadband noise models. Code and data are public. That's a solid observational result.

The GW chirp comparison is an actual falsification test: they match one epoch, integrate the Peters equation, and show a pure-GR inspiral cannot reproduce the frequency evolution. That's a clean argument. The alternative models—mass-transferring WD, disk tearing, coronal oscillations—are laid out with their problems stated. They even flag in Sec 3 that the ISCO radius/spin limits don't hold if the QPO is coronal or jet. That honesty is real credit.

Now the soft spots. The abstract says 'coherent motion on scales of less than 10 gravitational radii' before the origin is established. That is an interpretation, not a measurement. The frequency-to-radius mapping assumes the QPO is orbital or epicyclic; the coronal oscillation model makes the same frequency with a different radius. So 'near the innermost orbit' in the title is conditional. I'd like to see the paper separate 'detection + frequency evolution' from 'location.' Second, the claim of decelerating evolution (\ddot{P} > 0, or negative \ddot{f}) is stated qualitatively; there is no fit to the four frequency points, so the significance of the curvature is not quantified. That weakens the 'never seen before' framing and the model-discrimination argument. It's fixable—fit a few curves to four points—but as written it's an eyeball claim. The 2022 epoch is marginal on its own, though the fact that it lands where the trend predicts helps.

Who's this for? X-ray timing people, QPE/EMRI modelers, LISA forecasters. It deserves a serious referee; I'd send it out. My recommendation: ask for a fit to the frequency evolution and a rewrite of the abstract/title that separates the robust measurement from the interpretation. Then it's a strong paper.

Referee Report

3 major / 4 minor

Summary. The paper reports the discovery of a mHz quasi-periodic oscillation (QPO) in the changing-look AGN 1ES 1927+654 using XMM-Newton observations from July 2022 to March 2024. The QPO is detected in the 2-10 keV power spectral densities at approximately 0.93, 1.67, 2.21, and 2.34 mHz, with significance assessed both by simulated light curves and by AIC model comparison. The authors report that the frequency increases while its rate of increase decreases, and they argue that pure gravitational-wave inspiral of a stellar-mass companion cannot reproduce the observed frequency evolution. They discuss three classes of models (a mass-transferring white dwarf companion, disk-tearing and Lense-Thirring precession, and coronal magnetoacoustic oscillations) and predict a LISA-detectable signal if the 0.1 solar mass companion interpretation is correct.

Significance. The detection itself appears robust: the QPO is resolved in multiple frequency channels, has Q ~ 8-10 in the 2023-2024 epochs, is strongest in hard X-rays, and is supported by two independent significance tests. If confirmed, the secular frequency increase across four epochs would make this the first strongly evolving mHz QPO in a supermassive black hole and a promising electromagnetic counterpart to a future mHz gravitational-wave source. The paper also makes testable predictions, including continued QPO behavior for the companion model and a LISA SNR near 10. The release of code and data is a strength. The main caveat is that the headline claim of motion on scales below 10 gravitational radii, and the associated mass and spin constraints, depend on identifying the QPO with an orbital or epicyclic frequency; the authors themselves state in Section 3 that these limits may not hold in other QPO models, and Section 6.3 presents a viable coronal-oscillation model with a different frequency-to-radius mapping.

major comments (3)

[Section 3; Section 6.2; abstract] The claims that the QPO corresponds to 'coherent motion on scales of less than 10 gravitational radii' and that the black hole has spin a > 0.43 are conditional on identifying the QPO frequency with an orbital or epicyclic frequency in the Kerr spacetime. The paper itself acknowledges in Section 3 that 'these limits may not hold in other QPO models (e.g. if the QPO is produced in the corona or jet and not constrained by the orbital timescale at the ISCO).' Section 6.3 then presents a coronal-oscillation model in which the frequency is set by the coronal sound speed and radial extent rather than by an ISCO radius. As written, the title and abstract present the radius claim as a measurement rather than as a model-dependent inference. The radius, mass, and spin statements should be explicitly framed as conditional, for example 'if the QPO is produced by orbital motion near the ISCO, the implied radius is less than 10 gravitational radii.' Without this change, the headline overstates what the data alone establish.
[Figure 3; Section 6.1; abstract] The 'decelerating period evolution' (Pddot > 0, equivalently fddot < 0) is asserted from four frequency measurements without a quantitative fit. I request a fit of a simple parametric model (e.g. a quadratic or power law in time) to f(t), with posterior distributions for fdot and fddot, and a robustness test that excludes the broad 2022 epoch. In addition, the rejection of the pure gravitational-wave model uses a visual comparison anchored at February 2023; because Equation (6) predicts a frequency drift of only about 0.01 mHz over 1.6 years for the masses considered, the model is rejected only if the frequency measurements are all taken at face value. The rejection significance should be computed, for example by evaluating a chi-square or likelihood ratio for Equation (6) against the observed points. This matters because the novelty claim that 'this evolution has never been seen' rests on the deceleration being real and statistically significant.
[Methods 2.2; Equations (2)-(3)] The quantity pAIC = exp(-Delta AIC / 2) is a relative likelihood, not a frequentist p-value, and the conversion to a Gaussian-equivalent sigma (for example 'approximately 6.5 sigma' or 'around 4 sigma' for the 2022 data) is not justified. This is particularly important for the 2022 epoch, where the AIC method is the only claimed significant detection and the SSE test gives p ~ 0.5. The significance of the first detection needs a calibrated null-hypothesis test, for example by extending the light-curve simulations to include a Lorentzian with free frequency and width fit jointly to the four observations. The SSE simulations for the 2023-2024 epochs are convincing, but the reporting of sigma values derived from pAIC should be revised or replaced with calibrated simulation-based significances.

minor comments (4)

[Methods 2.2] The sentence 'we except the SSE estimator to provide a lower bound' contains a typo; 'except' should be 'expect.'
[Figure 3] The color-bar label 'Mcompanion [M]' is missing the solar-mass symbol; it should read 'Mcompanion [M_sun]' or equivalent.
[Methods 2.2] The description of the simulation procedure states that for each of the 10^5 simulated light curves the authors computed the PSD and 'proceeded with the same analysis that we performed on the observed data (i.e. fitting with maximum likelihood and then running an MCMC).' If the MCMC is run only on the observed data, please clarify; as written, this implies 10^5 MCMC runs, which is not described in detail and may be impractical.
[Abstract] The phrase 'over two years' for the period decrease from 18 minutes to 7.1 minutes spans July 2022 to March 2024, which is about 1.6 years; please adjust the wording to 'over the two-year monitoring campaign' or 'over roughly 1.6 years.'

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: the mHz QPO detection and the GR-chirp falsification are self-contained; the only mild circular step is the coronal-contraction model, which reparametrizes observed frequencies into inferred corona sizes.

other [Section 6.3 (Coronal Oscillations)]
"The oscillation frequency is set by the size and temperature of the corona, and thus, the increase in QPO frequency in 1ES 1927+654 can naturally be explained by a decrease in the size of the corona... Assuming a constant temperature, the corona would need to shrink in radial extent from roughly 5 Rg (July-August 2022, f = 0.93 mHz) to roughly 2 Rg (March 2024, f = 2.34 mHz)."

The coronal radius is not independently measured; it is computed from the observed QPO frequency through the assumed relation f ≈ 2πcs/rc. Using the first observed frequency to set rc ≈ 5 Rg and then 'explaining' the later observed frequencies by a contraction to rc ≈ 2 Rg is an inversion of the same relation, so the inferred contraction contains no information beyond the frequency evolution itself. This is a mild, non-central circularity: it is a reparametrization of the data rather than an independent test. The QPO detection and the GR-chirp comparison do not depend on this step.

full rationale

The central claim—detection of a highly significant, evolving mHz QPO—is a direct measurement. Its significance is established through Monte Carlo simulations of 10^5 light curves and AIC differences, neither of which imports the physical model being tested. The frequency evolution is measured directly from the data. The paper's falsification of pure GW inspiral is a genuine test: GR evolutionary tracks are computed from Peters' formula with a fixed initial condition at February 2023 and then compared with subsequent observed frequencies. The mass/spin/radius constraints are conditional on equating the QPO frequency with Kerr orbital or epicyclic frequencies; the paper explicitly flags this in Section 3 ('these limits may not hold in other QPO models'), so conditional model dependence is acknowledged rather than disguised as a derivation. Self-citations, e.g. Masterson et al. 2022 and Ricci et al. 2020/2021, are used for historical context and prior monitoring, not to justify the QPO detection. The one mild circular element is the coronal oscillation model, which infers corona radius from the observed frequency via f ≈ 2πcs/rc and then 'explains' the frequency evolution by a contraction; this is a reparametrization, but it is not the basis of the detection and is presented as one of several candidate models. The qualitative 'decelerating' claim (f-dot-dot < 0) is not fit-quantified, which is an evidentiary weakness but not a circularity. Overall, the core result is self-contained against external benchmarks, so the circularity score is low.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The paper's central claim rests on standard Fourier statistics, on the assumption that the QPO frequency maps to a radius in the Kerr spacetime, and on the host-galaxy mass estimate. The model sections introduce tuned parameters (WD mass, mass-transfer rate, corona temperature and size) that are reasonable but not independently measured. No new physics entities are required beyond a candidate white dwarf companion, which has a falsifiable LISA prediction.

free parameters (5)

SMBH mass = 1.38e6 Msun (ref 8)
Used for spin lower limit, ISCO radius mapping, and LISA SNR; carries large systematic uncertainty from host galaxy scaling relations.
White dwarf companion mass = 0.1 Msun
Chosen in Sec 6.1 as the minimum mass that fills its Roche lobe at 7.1 min period; central to the EMRI model and LISA prediction.
Mass transfer rate for turnaround = 3e-4 Msun/yr (no gas drag); 1e-2 Msun/yr (with gas drag)
Required in Sec 6.1 to stall the orbital decay at f=2.34 mHz; higher than observed accreting WDs but near theoretical expectation.
Corona temperature and initial radius = T=2e8 K; r_c=5 Rg
Inputs to the coronal oscillation model in Sec 6.3, used to match the first QPO frequency; the radius at later epochs is inferred from the observed frequencies.
Black hole spin for mass upper limit = a=0.998 (assumed maximum)
Used in Sec 3 to derive M <= 5.8e6 Msun; a is not known independently and is chosen to maximize the orbital frequency.

assumptions (5)

standard math The unbinned periodogram follows a chi-squared distribution with 2 degrees of freedom.
Used in Eq (1) for the PSD likelihood; standard result in Fourier analysis of light curves.
domain assumption The QPO frequency corresponds to an orbital or epicyclic frequency in the Kerr spacetime near the ISCO.
Used in Sec 3 and the 'less than 10 Rg' claim; the paper itself notes this may not hold for coronal or jet models.
domain assumption The host galaxy scaling relations (MBH-sigma*, MBH-Mbulge, MBH-M*) give the correct SMBH mass.
Used to normalize spin and LISA calculations; the mass has 1-sigma uncertainty from 0.72 to 2.63e6 Msun.
domain assumption The leading-order Peters (1964) gravitational wave chirp applies to a circular EMRI embedded in a gaseous disk with efficient eccentricity and inclination damping.
Used in Eq (6) and Figure 3 to rule out pure GW-driven inspiral.
domain assumption The narrowband QPO is not an artifact of red noise leakage and the two tested broadband noise models (power-law or zero-centered Lorentzian) are adequate descriptions.
Assumed in the significance testing; the authors test both models and account for parameter uncertainty via MCMC draws.

invented entities (1)

0.1 M_sun white dwarf companion independent evidence
purpose: Proposed in Sec 6.1 to explain the QPO frequency and its decelerating evolution through stable mass transfer.
The model predicts a mHz gravitational wave signal detectable by LISA at 84 Mpc (SNR ~10 over 4 years), which is a falsifiable prediction outside this paper. No direct electromagnetic detection of the companion is reported.

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Cite this review

Pith. "Pith review of Millihertz Oscillations Near the Innermost Orbit of a Supermassive Black Hole." pith.science (2026). https://pith.science/paper/GFOYWI73

@misc{pith2026250101581,
  author       = {Pith},
  title        = {Pith review of: Millihertz Oscillations Near the Innermost Orbit of a Supermassive Black Hole},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GFOYWI73}},
  note         = {Machine review of arXiv:2501.01581}
}

abstract

Recent discoveries from time-domain surveys are defying our expectations for how matter accretes onto supermassive black holes (SMBHs). The increased rate of short-timescale, repetitive events around SMBHs, including the newly-discovered quasi-periodic eruptions (QPEs), are garnering further interest in stellar-mass companions around SMBHs and the progenitors to mHz frequency gravitational wave events. Here we report the discovery of a highly significant mHz Quasi-Periodic Oscillation (QPO) in an actively accreting SMBH, 1ES 1927+654, which underwent a major optical, UV, and X-ray outburst beginning in 2018. The QPO was first detected in 2022 with a roughly 18-minute period, corresponding to coherent motion on scales of less than 10 gravitational radii, much closer to the SMBH than typical QPEs. The period decreased to 7.1 minutes over two years with a decelerating period evolution ($\ddot{P} > 0$). This evolution has never been seen in SMBH QPOs or high-frequency QPOs in stellar mass black holes. Models invoking orbital decay of a stellar-mass companion struggle to explain the period evolution without stable mass transfer to offset angular momentum losses, while the lack of a direct analog to stellar mass black hole QPOs means that many instability models cannot explain all of the observed properties of the QPO in 1ES 1927+654. Future X-ray monitoring will test these models, and if it is a stellar-mass orbiter, the Laser Interferometer Space Antenna (LISA) should detect its low-frequency gravitational wave emission.

Figures

Figures reproduced from arXiv: 2501.01581 by the authors.

**Figure 1.** X-ray spectral-timing overview of 1ES 1927+654. a, Long-term X-ray light curve (0.3-10 keV) beginning 2 months after the optical outburst. NICER (XMM-Newton) data is shown with blue circles (diamonds, colored by time). The observed flux and luminosity have been scaled from count rates assuming a Γ = 3 power-law spectrum. The horizontal black dashed line shows the Eddington limit for a 106 M⊙, and the grey dot-dashed… view at source ↗

**Figure 2.** XMM-Newton light curves (left) and PSDs (right) in the 2-10 keV band for the [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Evolution of the QPO frequency over time. The black points show the observed QPO [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The emergence of X-ray emission lines during relativistic radio-jet formation in the changing-look active galactic nucleus 1ES 1927+654
astro-ph.HE 2026-07 conditional novelty 6.0 of 10

X-ray emission lines and a broad iron feature emerged in changing-look AGN 1ES 1927+654 concurrently with radio-jet formation and declining ionized outflows from 2022 to 2025.
Multidisciplinary Science in the Multimessenger Era
astro-ph.HE 2025-02 unverdicted novelty 3.0 of 10

A community white paper recommending an NNSA-style end-to-end integration of astrophysics, nuclear, plasma, atomic, and computational sciences to maximize return from time-domain and multimessenger facilities.

Reference graph

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This simplified picture has only included the effects of mass transfer, gas drag, and GW emission, neglecting potential additional sources of angular momentum

This brings into question whether the orbiter could survive for an extended period of time, but the orbiter is likely embedded in the disk and therefore continuously fed with material. This simplified picture has only included the effects of mass transfer, gas drag, and GW emi...

1927

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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