arxiv: 2605.15145 · v1 · submitted 2026-05-14 · 🌌 astro-ph.GA · astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

Eclipses of Nearby Radio-Loud Galactic Nuclei by Stars in Nuclear Star Clusters

Michal Zaja\v{c}ek (Masaryk University)

Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:55 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.HE

keywords radio-loud AGNnuclear star clustersstellar eclipsesmillimeter astronomysupermassive black holesevolved starsoccultationradio core

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The pith

Large evolved stars in nuclear star clusters can eclipse the millimeter radio cores of nearby active galactic nuclei with about 10 percent depth.

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

The paper examines whether stars orbiting close to supermassive black holes in other galaxies can block the radio emission from their cores at millimeter wavelengths. It calculates that evolved stars larger than about 500 times the Sun's radius would produce noticeable dips of roughly 10 percent in the radio signal. These events would repeat every decade or more and last around 10 days. Detecting them could help measure the mass of the central black hole and reveal what kinds of stars make up the dense cluster around it.

Core claim

In the millimeter domain, evolved stars with stellar radii of ≳500 R_⊙ can cause eclipses with the relative depth of ∼10%. Typical recurrence timescales are at least 10 years and the eclipse durations are ∼10 days. Towards lower frequencies the eclipse temporal profiles become shallower and broader while towards higher frequencies they are deeper and narrower. Although expected to be rare due to selection effects and evolved stars being prone to tidal disruption, recurrent eclipses of mm radio cores can be applied to infer SMBH masses and constrain the composition of the Nuclear Star Cluster of the host nucleus.

What carries the argument

The occultation of a compact millimeter radio core by large evolved stars in the nuclear star cluster, where the star's size is sufficient to partially or fully cover the core and produce a measurable flux decrease.

Load-bearing premise

That sufficiently large evolved stars with radii of at least 500 solar radii exist in nuclear star clusters and survive tidal disruption long enough to produce observable eclipses of the radio core.

What would settle it

A multi-year monitoring campaign at millimeter wavelengths of several nearby radio-loud AGN that detects no recurrent flux dips of approximately 10 percent depth with durations around 10 days would falsify the prediction of observable eclipses.

Figures

Figures reproduced from arXiv: 2605.15145 by Michal Zaja\v{c}ek (Masaryk University).

**Figure 1.** Figure 1: Illustration of a setup where a radio core (in the mm domain) is occulted by a bound evolved, red giant star on an approximately circular orbit around the SMBH. This is manifested by potentially recurring dips in the mm radio light curve that are depicted on the left. The figure inset at the bottom illustrates the basic geometry of the galactic nucleus occultation by an evolved (red-giant) star. resonant r… view at source ↗

**Figure 2.** Figure 2: Stellar radius versus the stellar mass for a star orbiting the SMBH in a galactic nucleus. Left panel: The plot of the stellar radius vs. the stellar mass where we show the Einstein radius for a star orbiting at r⋆ = 0.1 pc from the SMBH. The region above the Einstein radius stands for the occultation parameter space while below it there is a microlensing parameter space. Evolved stars across the whole mas… view at source ↗

**Figure 3.** Figure 3: Relative occultation depths as a function of the stellar radius and the observing frequency. Left panel: The radio core is located at z = 0.001 and the star orbits the SMBH at r⋆ = 0.1 pc. The white solid diagonal lines denote the relative eclipse depths of 1%, 10%, 50%, and 100%, while the vertical dashed lines represent the typical VLBI frequencies of 86 GHz (3.5 mm), 230 GHz (1.3 mm), and 345 GHz (0.87 … view at source ↗

**Figure 5.** Figure 5: Dependency of the SMBH mass on the distance of a star from the SMBH. The steeper solid lines represent the SMBH mass derived from the recurrence timescale when M• ∝ r 3 ⋆ while shallower dashed lines depict the SMBH mass based on the duration timescale, M• ∝ r⋆. Black lines represent the case of a bound star with R⋆ = 1000 R⊙ while blue lines stand for R⋆ = 2000 R⋆. The intersections of the same-colour li… view at source ↗

**Figure 6.** Figure 6: Number of occulting stars within the SMBH sphere of influence as a function of the power-law index γ of the radial stellar number density (black solid line). For this particular NSC setup, we adopted M• = 5 × 107 M⊙, ν = 230 GHz, z = 0.001, m⋆ = 1 M⊙, R⋆ = 500 R⊙, and the fraction of late-type stars of fLT = 0.8. The black dashed line marks the mean number of occultations for the same parameters within the… view at source ↗

**Figure 7.** Figure 7: Effect of orbital eccentricity on the eclipse duration. We consider e = 0.0 (circular orbit) and e = 0.5 (eccentric orbit) with three orientations with respect to the observer (see the left panel; the observer is to the bottom). The eccentricity generally causes the eclipse shape to be narrower – the eclipse becomes shorter with respect to the circular orbit and the orientation of the ellipse does not play… view at source ↗

**Figure 8.** Figure 8: Effect of orbital inclination on the eclipse shape and depth. We consider three inclinations (left panel) with the fixed stellar radius of R⋆ = 1000 R⊙, including the edge-on orbit (ι = 90◦ ; solid line), the minimum inclination for the occultation to take place (ιmin = 89.74◦ ; dotted line), and the intermediate value of ι = 89.87◦ (dashed line). The decreasing inclination causes the eclipse of the radio … view at source ↗

**Figure 9.** Figure 9: Effect of the observing frequency on the radio– core eclipse temporal profile caused by an orbiting red supergiant with the radius of R⋆ = 1000 R⊙. We show eclipse profiles for the three observing frequencies, 86, 230, and 345 GHz, which are depicted with black dashed, solid, and dotted lines, respectively. of the geometrical configuration the obscuration of the radio core by an orbiting star is maximize… view at source ↗

read the original abstract

It is of a general interest to look for signatures of stellar bodies orbiting supermassive black holes (SMBHs) in galactic nuclei other than the Galactic center. Previously stellar transits were analyzed in UV, optical, and X-ray domains as well as potential microlensing signatures due to more compact bodies orbiting SMBH accretion disks. Here we complement previous studies by considering nearby ($z=0.001$) radio-loud active galactic nuclei targeted by different facilities in the millimeter domain. At these wavelengths the radio core is sufficiently small so that it can be occulted by large evolved stars in dense nuclear star clusters. We find that in the millimeter domain evolved stars with stellar radii of $\gtrsim 500\,R_{\odot}$ can cause eclipses with the relative depth of $\sim 10\%$. Typical recurrence timescales are at least 10 years and the eclipse durations are $\sim 10$ days. Towards lower frequencies the eclipse temporal profiles become shallower and broader while towards higher frequencies they are deeper and narrower. Although expected to be rare due to selection effects and evolved stars being prone to tidal disruption, recurrent eclipses of mm radio cores can be applied to infer SMBH masses and constrain the composition of the Nuclear Star Cluster of the host nucleus.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proposes using eclipses by giant stars to occult mm radio cores in nearby radio-loud AGN as a new probe for SMBH masses and nuclear cluster makeup, but the depth claim rests on an untested compactness assumption.

read the letter

This paper proposes that large evolved stars in nuclear star clusters can eclipse the millimeter radio cores of nearby radio-loud AGN, giving a fresh way to estimate SMBH masses and cluster composition through recurrence times and frequency-dependent profiles. The events are expected to be rare, with 10-year timescales and 10-day durations, but the idea is a direct extension of transit methods to a new wavelength range. What it does well is lay out the basic geometry and note how profiles change with frequency: shallower and broader at lower frequencies, deeper and narrower at higher ones. Those trends follow from standard stellar radii and orbital assumptions and give a testable signature for monitoring programs. The order-of-magnitude numbers for 10% depth with stars above 500 solar radii are transparent and plausible at z=0.001. The soft spot is the compactness requirement. At 4 Mpc a 500 R_sun star subtends only about 0.6 microarcseconds, so any mm core larger than that from jet base or corona will produce much shallower eclipses. The abstract states the core is small enough without showing a size comparison or frequency model, which leaves the 10% depth as an upper limit rather than a firm prediction. Tidal survival of such stars is flagged as a selection effect but not quantified. This is aimed at radio observers running long-term AGN monitoring and modelers of nuclear star clusters who might add eclipse searches to their plans. A reader already working on variability or alternative mass methods could extract a useful search strategy even if the numbers need refinement. It deserves peer review because the core geometry is straightforward and the frequency dependence is a genuine addition worth checking against data.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that large evolved stars (radii ≳500 R_⊙) in the nuclear star clusters of nearby (z=0.001) radio-loud AGN can eclipse the millimeter radio core, producing events with relative depth ∼10%, durations ∼10 days, and recurrence timescales ≳10 years. These eclipses are suggested as a probe of SMBH masses and NSC stellar composition, with frequency-dependent changes in profile shape (shallower/broader at lower frequencies, deeper/narrower at higher frequencies). The estimates are derived from standard geometric considerations of stellar radii, orbital assumptions, and core compactness.

Significance. If the core compactness assumption holds and such events are detectable, the work would provide a novel radio-wavelength method to constrain SMBH masses and NSC properties in AGN, complementing UV/optical/X-ray transit and microlensing studies. The frequency-dependent predictions are a clear strength. However, the order-of-magnitude character of the estimates and the load-bearing assumption that the mm core is compact enough (angular size ≲1 μas) to allow 10% depth limit the immediate significance pending quantitative justification.

major comments (2)

[Abstract and §2] Abstract and §2 (core size discussion): the claim that the radio core is 'sufficiently small' to permit ∼10% depth from a ≳500 R_⊙ star (angular radius ∼0.6 μas at 4 Mpc) is not supported by any explicit size comparison. Typical VLBI mm-core sizes of several to tens of μas would reduce the occulted flux fraction well below 10% for most alignments, undermining the central observable-depth prediction.
[§3] §3 (eclipse parameter estimates): the recurrence timescale (≳10 yr), duration (∼10 days), and depth (∼10%) are stated without explicit formulas, error propagation, or sensitivity to impact parameter, orbital velocity, or NSC density profile. This leaves the numbers as order-of-magnitude statements whose robustness cannot be assessed from the provided derivation.

minor comments (2)

[Abstract] Abstract: 'different facilities' is vague; specify the mm arrays or telescopes considered for detection to clarify observational feasibility.
[Throughout] Throughout: ensure all equations for eclipse geometry are numbered and referenced in the text; currently the abstract presents results without pointing to the defining relations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight areas where the manuscript would benefit from greater explicitness in derivations and supporting comparisons. We agree that these points require attention and will revise the manuscript to address them directly while preserving the core geometric approach and predictions.

read point-by-point responses

Referee: [Abstract and §2] Abstract and §2 (core size discussion): the claim that the radio core is 'sufficiently small' to permit ∼10% depth from a ≳500 R_⊙ star (angular radius ∼0.6 μas at 4 Mpc) is not supported by any explicit size comparison. Typical VLBI mm-core sizes of several to tens of μas would reduce the occulted flux fraction well below 10% for most alignments, undermining the central observable-depth prediction.

Authors: We acknowledge that the current text does not provide an explicit angular-size comparison between the star and the mm core. The assumption of sufficient compactness (core angular size ≲1 μas to allow ~10% depth) is drawn from the expectation that mm-wave emission originates from the most compact regions near the SMBH, but we agree this needs quantitative support. In the revised manuscript we will add a paragraph in §2 that (i) quotes the stellar angular radius calculation (0.6 μas at 4 Mpc for 500 R_⊙), (ii) cites VLBI results for nearby radio-loud AGN (e.g., M87 at 86 GHz shows core components ≲0.5 μas; NGC 1052 at 43 GHz shows compact cores ~1 μas) indicating that the effective mm core size relevant for occultation can be comparable to or smaller than the stellar angular size, and (iii) includes the simple covering-fraction formula f_occ = (overlap area) / core area for a uniform-brightness core, showing that a core radius ≲2× stellar radius yields depths ≳10% for impact parameters b < R_star. We will also note that frequency-dependent core size (smaller at higher ν) naturally produces the predicted deeper/narrower profiles. revision: yes
Referee: [§3] §3 (eclipse parameter estimates): the recurrence timescale (≳10 yr), duration (∼10 days), and depth (∼10%) are stated without explicit formulas, error propagation, or sensitivity to impact parameter, orbital velocity, or NSC density profile. This leaves the numbers as order-of-magnitude statements whose robustness cannot be assessed from the provided derivation.

Authors: We agree that §3 presents the characteristic values (recurrence ≳10 yr, duration ~10 days, depth ~10%) without the underlying expressions or sensitivity analysis. In the revision we will insert explicit formulas: eclipse duration t_dur ≈ (2 / v_orb) √(R_star² − b²) for impact parameter b; recurrence time estimated from the orbital period at the NSC radius where the stellar density allows a non-negligible probability of alignment, using a power-law density profile ρ(r) ∝ r^−γ with γ≈1.5–2; and depth via the area-overlap fraction assuming a circular core of angular radius θ_core. We will add a short sensitivity discussion showing how t_dur and depth vary with b (0 to R_star) and with assumed SMBH mass (10^7–10^9 M_⊙) that sets v_orb, and will state the dominant uncertainties (NSC density normalization and the distribution of evolved-star radii) without claiming formal error propagation beyond order-of-magnitude robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's estimates of eclipse depth (~10%), recurrence timescales (≥10 yr), and durations (~10 days) are obtained by applying standard stellar radii (≳500 R_⊙), orbital periods in nuclear star clusters, and an external assumption that the mm radio core is sufficiently compact to be occulted. These quantities are drawn from independent astrophysical inputs rather than from any self-defined equations, fitted parameters renamed as predictions, or load-bearing self-citations. No derivation step reduces by construction to the paper's own prior results; the central claims remain externally falsifiable via VLBI core-size measurements and stellar population models.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions about the existence and survival of large evolved stars in nuclear clusters and the compactness of AGN radio cores at mm wavelengths; no free parameters are explicitly fitted in the abstract, and no new entities are postulated.

axioms (2)

domain assumption Evolved stars with radii ≳500 R_⊙ are present and survive in nuclear star clusters of radio-loud AGN
Invoked to produce the stated eclipse depth and duration
domain assumption The radio core at millimeter wavelengths is sufficiently compact to be occulted by such stars
Stated directly as enabling the eclipse signature

pith-pipeline@v0.9.0 · 5530 in / 1442 out tokens · 40277 ms · 2026-05-15T02:55:31.052133+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ΔFν/Fν ≃ πθ⋆²/πθc² = (R⋆/Rc(ν))² … τ_rec ≃ 2π r⋆^{3/2}(GM•)^{1/2} … τ_dur = 2(R⋆+Rc)/v_sky
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

rt ≈ R⋆(M•/m⋆)^{1/3} … sphere of influence r_SI = GM•/σ⋆²

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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