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arxiv: 2606.25020 · v1 · pith:VHGWLCSXnew · submitted 2026-06-23 · 🌌 astro-ph.HE · astro-ph.CO· astro-ph.GA

Multi-messenger and Multi-band Studies of Massive Black Holes: the Synergies Between LISA and SKAO

Pedro R. Capelo , Alberto Mangiagli , Lorenz Zwick , Lucio Mayer , Marta Volonteri This is my paper

Pith reviewed 2026-06-25 22:32 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.COastro-ph.GA
keywords massive black hole binariesgravitational wavesLISASKAOmulti-messengerpulsar timing arraysradio counterpartshydrodynamical torques
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The pith

LISA sources have radio counterparts whose numbers stay steady across jet models and SKA configurations.

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

The paper uses the same simulated populations of massive black hole binaries to forecast how many will produce both millihertz gravitational waves visible to LISA and radio emission visible to SKAO. It finds that the count of these joint detections changes little when different models for jets and flares are substituted or when the SKA-Mid AA* versus AA4 sensitivity is assumed. The same populations also show that binaries in gas discs experience hydrodynamical torques that add small higher-frequency gravitational wave harmonics. These harmonics would register as a stochastic signal in LISA while the main lower-frequency waves appear as a deterministic signal in SKAO-era pulsar timing arrays, opening the first multi-band gravitational wave detections of individual objects.

Core claim

By employing identical underlying black hole binary populations from numerical simulations and mock catalogues, the analysis demonstrates that the number of radio counterparts of LISA sources is relatively insensitive to the jet or flare model employed and to whether SKA-Mid AA* or AA4 is assumed. Supermassive black hole binaries embedded in gas discs undergo hydrodynamical torques that generate additional small-amplitude higher-frequency gravitational waves; the primary carrier waves may be identified as deterministic signals by SKAO-era pulsar timing arrays while the harmonics appear as stochastic signals in LISA, so that correlating the two bands supplies constraints on the environments o

What carries the argument

The common black hole binary populations drawn from numerical simulations and mock catalogues, which serve as the shared foundation for both gravitational-wave and electromagnetic predictions.

If this is right

  • Coincident millihertz gravitational-wave and radio detections of the same massive black hole binaries become feasible.
  • The first low-frequency multi-band gravitational-wave detection of an individual object is possible when SKAO contributes to a pulsar timing array.
  • Correlating the multi-band gravitational-wave signals yields constraints on the gas environments around the most massive black holes.
  • Hydrodynamical torques in gas discs produce identifiable additional higher-frequency gravitational-wave components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Joint detections could link electromagnetic signatures directly to the gravitational-wave inspiral phase, helping trace how gas influences binary evolution.
  • The robustness to emission models reduces the modeling burden before SKAO can be used to follow up LISA localizations.
  • Multi-band gravitational-wave observations may distinguish between different torque mechanisms that single-band data cannot separate.

Load-bearing premise

The black hole binary populations taken from numerical simulations and mock catalogues accurately represent the real systems that exist in the universe.

What would settle it

If the predicted number of radio counterparts changes by a large factor when a different jet or flare model is substituted, or if no higher-frequency gravitational wave harmonics correlated with pulsar-timing-array signals appear in LISA data, the central claims would be falsified.

Figures

Figures reproduced from arXiv: 2606.25020 by Alberto Mangiagli, Lorenz Zwick, Lucio Mayer, Marta Volonteri, Pedro R. Capelo.

Figure 1
Figure 1. Figure 1: Distribution of jet radio spectral flux densities according to two of the models discussed in the text. Left-hand panel: Jet-M01/M22 – Meier (2001) model for the total jet emission with the parameters from M22. Right-hand panel: Jet-M01/D23 – Meier (2001) model for the total jet emission with the (corrected; see Footnote 3) parameters from D23. Different colours and linestyles correspond to three different… view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of flare radio spectral flux densities according to the two models discussed in the text. Left-hand panel: Flare-M22 – adopted by M22. Right-hand panel: Flare-D23 – adopted by D23. Different colours and linestyles correspond to three different population of MBHBs as reported in the legend. The vertical line shows the assumed spectral flux density limit of SKA-Mid (AA4) at 2 𝜇Jy. In [PITH_FULL… view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of radio spectral flux densities according to the models discussed in the main text. Left-upper panel: Jet-M01/M22 + Flare-M22. Right-upper panel: Core-FP/G19 + Flare-M22. Left-lower panel: Jet-M01/M22 + Flare-D23. Right-lower panel: Core-FP/G19 + Flare-D23. Different colours and linestyles correspond to three different population of MBHBs as reported in the legend. The vertical line shows the… view at source ↗
Figure 4
Figure 4. Figure 4: Spectral flux density distributions for the EM counterparts we can detect with SKA-Mid for the four different scenarios discussed in the text. The vertical line shows the assumed spectral flux density limit of SKA-Mid (AA4) at 2 𝜇Jy [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The number of expected single-source detections with SNR > 3 for a PTA sensitivity curve with a given peak sensitivity, for a 15 yr dataset or a 20 yr dataset. Reference values are the current NANOGrav 15 yr reported sensitivity (in red, see Agazie et al. 2023c) and the projected SKAO-era sensitivity (in dark blue, for the projected 20-yr AA4 case with 174 pulsars, and in light blue, for a case wherein 100… view at source ↗
Figure 7
Figure 7. Figure 7: Left-hand panel: we show the characteristic strain evolution of a gas-embedded 109 M⊙ equal-mass MBHB at 𝑧 = 0.2. The dashed black line traces the binary’s inspiral, with markers at 𝑓GW = 10−9 , 10−8 , and 10−7 Hz. The dashed coloured curves show additional GW harmonics induced by stochastic torques from a circumbinary disc accreting at 𝑓Edd = 1. Right-hand panel: LISA 4-yr sensitivity to DWs, shown in bla… view at source ↗
read the original abstract

Depending on its mass, the same gas-embedded massive black hole (BH) binary can emit gravitational waves (GWs) in one or more bands (nHz and mHz) concurrently, along with electromagnetic (EM) waves over the entire spectrum. The Square Kilometre Array Observatory (SKAO), thanks to its unparalleled sensitivity, will be pivotal in achieving coincident GW-EM (mHz-radio) and GW-GW (nHz-mHz) detections. We review the state-of-the-art predictions - achieved by means of numerical simulations and mock catalogues - of the numbers of detectable coincident GW-EM signals when employing the Laser Interferometer Space Antenna (LISA) and SKA-Mid. By exploiting the same underlying BH binary populations, to allow for a fairer comparison, we then assess the importance of a variety of EM models for the radio flares and jets, finding that the number of radio counterparts of LISA sources is relatively insensitive to the jet/flare model employed and to whether SKA-Mid AA* or AA4 is assumed. Additionally, we describe how SKAO - as part of a pulsar timing array (PTA) - and LISA will provide the opportunity to detect the first low-frequency, multi-band (nHz-mHz) GW detection of the same object. Supermassive BH binaries embedded in gas discs are subjected to hydrodynamical torques, causing perturbations that produce additional small-amplitude, higher-frequency GWs. The main carrier GWs may thus be identifiable as a deterministic signal by SKAO-era PTAs, while the higher-frequency harmonics would shine in LISA as stochastic signals. Correlating these multi-band GWs would provide unprecedented constraints on the environment of the most massive BHs.

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.

Referee Report

2 major / 2 minor

Summary. The paper reviews predictions from numerical simulations and mock catalogues for coincident mHz GW (LISA) and radio (SKAO) detections of gas-embedded massive BH binaries, as well as nHz-mHz multi-band GW detections. Using the same underlying BH binary populations, it reports that the number of detectable radio counterparts is relatively insensitive to the choice of jet/flare EM models and to SKA-Mid AA* versus AA4 configurations. It further argues that hydrodynamical torques in gas discs generate higher-frequency GW harmonics that appear as stochastic signals in LISA while the main signal is detectable by SKAO-era PTAs, enabling the first multi-band GW detections of the same object.

Significance. If the simulation-based populations prove representative, the reported insensitivity to EM modeling choices would be a practical result for observation planning, and the multi-band GW synergy would offer a novel route to constrain the environments of the most massive BHs. The work usefully synthesizes LISA-SKAO synergies but does not introduce new derivations or falsifiable predictions beyond the reviewed simulation outputs.

major comments (2)
  1. [Abstract and population modeling sections] The central claims of model insensitivity for radio counterpart counts and the multi-band GW detection forecast both rest on the fidelity of the BH binary populations drawn from the cited numerical simulations and mock catalogues. No sensitivity analysis to variations in mass/redshift distributions, formation channels, or gas-disc physics is presented, so quantitative results may shift if those populations are revised.
  2. [Multi-band GW discussion] The description of hydrodynamical torques producing identifiable higher-frequency GW harmonics as stochastic LISA signals lacks quantitative details on amplitude thresholds, harmonic orders, or how the stochastic background is distinguished from other LISA noise sources; this is load-bearing for the multi-band claim.
minor comments (2)
  1. [Introduction] Notation for SKA-Mid configurations (AA* vs. AA4) should be defined at first use with a brief reference to the relevant SKAO technical document.
  2. [Results on radio counterparts] The manuscript would benefit from a table summarizing the different jet/flare models tested and the resulting counterpart counts for each SKA configuration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our review of LISA-SKAO synergies. We address each major comment below, clarifying the scope of the work as a synthesis of existing simulation results rather than new modeling.

read point-by-point responses

  1. Referee: [Abstract and population modeling sections] The central claims of model insensitivity for radio counterpart counts and the multi-band GW detection forecast both rest on the fidelity of the BH binary populations drawn from the cited numerical simulations and mock catalogues. No sensitivity analysis to variations in mass/redshift distributions, formation channels, or gas-disc physics is presented, so quantitative results may shift if those populations are revised.

    Authors: We agree that all quantitative forecasts inherit uncertainties from the underlying BH binary populations. The manuscript is explicitly a review that compiles and compares predictions from multiple published numerical simulations and mock catalogues, using the same populations to enable direct comparison of EM models. No new populations or sensitivity analyses were generated, as that lies outside the review's scope. In the revised version we will add an explicit caveats subsection in the population modeling section that summarizes how variations in mass functions, formation channels, and gas-disc physics (as explored in the cited works) could affect the reported numbers, while retaining the finding that radio counterpart counts remain relatively insensitive within the range of models already published. revision: partial

  2. Referee: [Multi-band GW discussion] The description of hydrodynamical torques producing identifiable higher-frequency GW harmonics as stochastic LISA signals lacks quantitative details on amplitude thresholds, harmonic orders, or how the stochastic background is distinguished from other LISA noise sources; this is load-bearing for the multi-band claim.

    Authors: The multi-band GW paragraph is a concise qualitative outline of a mechanism already discussed in the hydrodynamics and PTA literature. We acknowledge that the current text does not include explicit amplitude thresholds or harmonic-order calculations. In revision we will expand the section with references to the specific torque-induced harmonic amplitudes and frequency ranges reported in the cited hydrodynamical studies, and we will briefly note how the higher-frequency stochastic component can be separated from LISA's instrumental noise and the galactic binary foreground using standard LISA data-analysis techniques already validated in the literature. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on external simulations and mock catalogues

full rationale

The paper reviews predictions from numerical simulations and mock catalogues for BH binary populations, then varies EM models (jets/flares) on the same fixed populations for comparison. The insensitivity finding and multi-band GW discussion follow directly from those external inputs without self-definition, fitted parameters renamed as predictions, or load-bearing self-citations that collapse the chain. No equations or steps reduce by construction to the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the accuracy of prior numerical simulations of BH binary populations and standard assumptions about radio emission from jets/flares and hydrodynamical torques in gas discs; no new free parameters or invented entities introduced in the abstract.

axioms (2)
  • domain assumption Numerical simulations and mock catalogues provide representative BH binary populations for detection rate predictions.
    Invoked to enable fair comparison of EM models and multi-band signals.
  • domain assumption Hydrodynamical torques in gas discs produce additional small-amplitude higher-frequency GWs identifiable as stochastic signals in LISA.
    Central to the multi-band GW detection opportunity described.

pith-pipeline@v0.9.1-grok · 5878 in / 1408 out tokens · 22767 ms · 2026-06-25T22:32:30.740001+00:00 · methodology

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