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Stellar bars systematically slow the orbital decay of massive black hole pairs, and a machine-learning emulator trained on 100,000 orbital integrations transfers that effect to cosmological galaxy populations.

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2026-08-01 00:43 UTC pith:YTUCJBUU

load-bearing objection A credible NF emulator with a solid held-out validation, but the bar effect it reports is inherited from training data whose dynamical friction uses one fixed rotation curve; stress-test that before believing the TNG50 conclusions. the 4 major comments →

arxiv 2607.26125 v1 pith:YTUCJBUU submitted 2026-07-28 astro-ph.GA astro-ph.COastro-ph.HE

Emulating the complex galactic-scale orbital dynamics of LISA massive black hole pairs with normalizing flows

Pedro R. Capelo , Carlos Moreno Martinez , Nodens Koren , Tommaso Zana , Elisa Bortolas , Matteo Bonetti , Janis Fluri , Thomas Hofmann
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Lucio Mayer
This is my paper
classification astro-ph.GA astro-ph.COastro-ph.HE
keywords massive black holesdynamical frictionstellar barsnormalizing flowssemi-analytical modelsgravitational wavesLISAgalaxy mergers
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that stellar bars demote the formation of massive black hole binaries: in its semi-analytical model, 53.3 percent of secondaries without a bar decay to 10 pc within a Hubble time versus 45.2 percent with a bar, and heavier or shorter bars hinder decay further. To make this claim usable at population scale, it builds a conditional normalizing flow that learns the full stochastic distribution of decay times from about 10^5 orbital integrations, then applies the emulator to galaxies from the TNG50 cosmological simulation. The emulator reproduces the simulation's decay-time distributions and is well calibrated, and applying it with bar information versus treating all galaxies as unbarred changes the cumulative binary-formation fraction by up to about five percent. If correct, this means that ignoring bars, as previous population studies have done, overestimates how many massive black hole pairs will coalesce in time to be seen by LISA.

Core claim

Bars demote binary formation. In the semi-analytical model, the fraction of secondary massive black holes that reach 10 pc from the galactic centre within a Hubble time is 53.3 percent in non-barred galaxies and 45.2 percent in barred galaxies; among barred galaxies the fraction decreases with increasing bar mass and decreasing bar length. The conditional normalizing flow trained on these runs reproduces the decay-time distributions across mass, radius, and orbital-circularity selections, with probability-probability coverage close to the diagonal. When the emulator is applied to TNG50 galaxies, treating barred galaxies as barred rather than as non-barred reduces the cumulative fraction of b

What carries the argument

Conditional normalizing flow: a neural spline flow that maps a one-dimensional standard normal distribution to the target distribution of binary-formation times via an invertible transformation conditioned on nine physical features (black hole mass, initial position and velocity, bar mass fraction, bar length, and a barred/non-barred flag). The flow is trained by maximum likelihood on about 1.1 x 10^5 semi-analytical orbital integrations of a secondary massive black hole in a multi-component galactic remnant with a rotating bar; once trained, it samples decay-time distributions orders of magnitude faster than the simulations, capturing the stochasticity of the dynamics rather than a single p

Load-bearing premise

Every dynamical-friction force in all 10^5 semi-analytical runs is computed from one fixed galactic rotation curve—taken from a single barred galaxy with a particular bar mass, pattern speed, and scale lengths—regardless of the bar mass, length, and pattern speed of the run itself.

What would settle it

Take a subsample of the SAM initial conditions, recompute the galactic rotation curve for each run from its own bar mass, length, and pattern speed, and re-integrate the orbits; if the resulting decay-time distributions and the sign or magnitude of the bar dependence change significantly, then the emulator's bar effect is an artifact of the fixed curve.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If bars demote decay as claimed, population forecasts for LISA and other mHz gravitational-wave detectors will need to include galaxy morphology, not just dynamical friction in symmetric potentials.
  • Treating all galaxies as non-barred—as past SAM-based population studies have done—overestimates the number of massive black hole binaries that form by up to about five percent cumulatively, and by more for barred-only subsamples.
  • The emulator's speed (about 10^7 samples in seconds) makes it feasible to propagate full orbital-decay distributions through large cosmological volumes, which was previously intractable with direct integration.
  • The methodology transfers to other stochastic sub-grid astrophysical processes where per-system integration is well understood but population-scale sampling is too expensive.
  • The learned dependence on bar mass, length, and pattern speed is a testable prediction that full N-body simulations of merger remnants can check directly.

Where Pith is reading between the lines

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

  • If the fixed-rotation-curve assumption biases the drag in the training data, then the emulator's learned bar dependence—and the five-percent cumulative effect—could be partly an artifact of that choice; re-running a subset of SAM runs with per-run rotation curves would settle this.
  • The claim implies that galaxy populations with higher bar fractions at a given redshift should show relatively fewer massive black hole binaries; comparing different cosmological simulations with different bar fractions could test this statistically.
  • The emulator is conditioned on bar mass fraction and length but not on bar pattern speed or shape; extending the conditioning vector to include those parameters might reveal additional bar effects, including resonances that the current fixed-curve model cannot capture.
  • A stronger, direct test would be to run a few live, self-consistent N-body simulations of barred merger remnants and compare their decay-time distributions with the emulator's predictions for the same initial conditions.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. The paper presents a conditional normalizing-flow emulator for the decay time τ_d of a secondary massive black hole inspiralling in a merger remnant with a rotating stellar bar. The training set consists of 10^5 new semi-analytical integrations plus 10,075 non-barred runs from B22, with bar mass, length, and pattern speed varied at fixed total stellar mass. The emulator is validated on a held-out 20% of the SAM data (Fig. 3, P-P plot in Fig. 4) and then applied to TNG50 galaxies by replacing the SAM bar features with mordor-measured bar fractions and lengths, plus a host-mass rescaling of τ_d. The central astrophysical claim is that stellar bars slightly demote MBH binary formation: barred SAM runs have a 45.2% decay fraction within a Hubble time versus 53.3% for non-barred runs, and the TNG50 bar-aware versus bar-agnostic comparison shows up to ~5% fewer cumulative events (Figs. 7–8).

Significance. If the emulator is a faithful surrogate, the paper offers a genuinely useful tool: conditional normalizing flows are a natural way to preserve the stochasticity of DF-driven orbital decay, the held-out validation is a proper non-circular test, and the computational speedup (10^7 samples in ~15 s) makes population-scale application feasible. The use of Sobol sampling, the explicit calibration check, and the public TNG50+mordor data are strengths. The TNG50 analysis is best read as a proof-of-concept propagation of the SAM's learned bar dependence rather than an independent discovery; the authors themselves call it a proof of concept in Section 4. The main risk to the headline claim is the fixed rotation curve used in all DF calculations and the ambiguity in the bar-agnostic counterfactual, both of which bear directly on the magnitude and even the sign of the reported bar effect.

major comments (4)
  1. [§2.1.1, footnote 2] All 10^5 SAM runs compute dynamical friction from a single rotation curve, that of a B22 barred galaxy with M_bar=3×10^9 M⊙, ω_bar=40 km/s/kpc, and scale lengths (5,2,0.3) kpc, while M_bar is varied over a factor of 10, a_bar over 1–9 kpc, and ω_bar over 23–122 km/s/kpc via Eq. (6). The cited B22 result concerns barred vs non-barred at fixed total stellar mass, not the range explored here. Since the Chandrasekhar drag depends on the local velocity distribution (not just the potential), the learned f_bar/a_bar dependence — and hence the TNG50 bar effect in Figs. 7–8 — could be artificially created, suppressed, or reversed. Please rerun a subset of the SAM (or at least a few representative M_bar, a_bar, ω_bar combinations) with self-consistent rotation curves and quantify the change in the τ_d distributions and in the decay fraction as a function of bar properties.
  2. [§2.4, Figs. 7–8] The 'bar-agnostic' evaluation is described as 'setting x_bar = 0 for all galaxies,' but the conditioning vector also contains f_bar and a_bar. Please specify explicitly what values f_bar and a_bar take when x_bar is set to 0. If they remain at the TNG-measured barred values, the model receives a feature combination never seen in training (non-barred with non-zero bar mass/length), which would invalidate the comparison. If they are set to 0 (or to the B22 nominal a_bar=5 kpc), then the counterfactual is not the same TNG galaxy without its bar but the SAM's idealized non-barred model with rescaled disc/bulge masses; this should be stated and its effect on the magnitude of the 5% difference discussed.
  3. [§3.3, Figs. 7–8] The headline quantitative statement is that bars reduce the cumulative binary fraction by 'up to five per cent,' but no uncertainty is reported on these cumulative fractions. The P-P plot in Fig. 4 shows good calibration of the marginal predictive distribution, but that does not directly give error bars on the redshift-binned fractions or on the difference between the solid and dashed curves in Fig. 7. Please provide confidence intervals (e.g., by bootstrapping over TNG galaxies and/or over multiple NF training seeds) so the reader can assess whether the 5% effect is significant relative to emulator and sampling noise.
  4. [§2.2] The treatment of non-decaying systems (τ_d = ∞) is described only as 'resampled by extrapolating the finite-τ_d distribution tail into larger times than allowed,' with no specification of the extrapolation method. This is not a purely cosmetic detail: roughly half of the training systems do not decay within t_H, and the 'inclusive' calibration in Fig. 4 includes these extrapolated values, which can make the model look better calibrated than it is in the physically relevant range. Please specify the extrapolation procedure, justify that it does not bias the CDF for τ_d < t_H, and show the P-P plot restricted to τ_d < t_H as the primary calibration diagnostic.
minor comments (7)
  1. [§3.2, Fig. 3] The agreement between SAM and emulator histograms is shown by overplotting without a quantitative divergence metric. Please add a two-sample test (KS or AD) or a proper scoring rule (e.g., CRPS) for the overall and conditional distributions.
  2. [Abstract / §4] The abstract's 'Our results show that stellar bars can alter the distribution...' could be read as an independent cosmological finding; since the bar dependence originates in the SAM training data and the TNG analysis propagates it, I suggest phrasing such as 'our emulator, trained on barred/non-barred SAM simulations, predicts...' to avoid overclaiming.
  3. [§2.1.1, Eq. (6)] The pattern-speed relation is a polynomial fitted to a single galaxy's rotation curve; if the fixed-curve assumption is revisited, Eq. (6) and the ω_bar range should be re-derived consistently.
  4. [§2.1.1, footnote 4] The B22 non-barred runs stopped at t_H rather than 2t_H, while the new barred runs stop at 2t_H. Please state explicitly how this inconsistency is handled in the tail-extrapolation step for the mixed training set.
  5. [§2.4] The post-processing mass rescaling τ_d ∝ M_host^{1/2} is acknowledged as approximate, but the paper does not report the range of M⋆,tng50/M⋆ factors actually present after the lower-mass cut; a sentence with the median and 5–95% range would help the reader judge the extrapolation depth.
  6. [§2.3 / Table B1] The TNG50 barred-galaxy sample is restricted to f_bar and a_bar within SAM ranges, while the non-barred sample is not restricted by any analogous structural constraint. Please state whether this asymmetry could bias the bar-aware versus bar-agnostic comparison.
  7. [Data Availability] The data availability statement says data will be shared 'on reasonable request.' For a machine-learning-based method, releasing the trained model and the training/validation splits (or a public code repository) would considerably strengthen reproducibility.

Circularity Check

0 steps flagged

No significant circularity: the NF emulator is validated on held-out SAM data, and the TNG50 application is a conditional evaluation on external TNG50 morphology inputs; the fixed B22 rotation curve is a modeling caveat, not a circular reduction.

full rationale

The derivation chain is compositional rather than circular. The SAM generates decay times from dynamical integrations over varied bar and MBH parameters; the conditional normalizing flow is trained on an 80/20 split and evaluated on the held-out validation set (Fig. 3 and the PP plot in Fig. 4), including conditional checks on MBH mass, radius, and circularity. This is a genuine out-of-sample test, not a restatement of the training data. The TNG50 application is a forward pass of the trained conditional distribution using externally measured TNG50 bar fractions, bar lengths, and bar flags; Section 2.4 replaces only fbar and abar with TNG50 values and samples the rest of the conditioning vector from SAM validation runs. That is a Monte Carlo evaluation of p(tau_d | c), not a fit to TNG50 outcomes, so the resulting bar-aware versus bar-agnostic comparison is a counterfactual on the learned conditional model. The conclusion that bars demote binary formation is inherited from the SAM physics, but inheritance from training data is the intended role of an emulator, not circularity by construction. The main caveat, footnote 2 in Section 2.1.1, is that all DF computations use one B22 rotation curve regardless of the run's own bar mass, length, and pattern speed. This is a potentially important approximation that could bias the learned bar dependence, and B22 is prior work with overlapping authors, but the bar dependence in the SAM arises from integrating the bar potential, and the cited B22 similarity result is an external falsifiable claim rather than a self-imported uniqueness theorem. No equation in the paper makes the predicted quantity equal to a fitted input by definition, and no fitted parameter is relabeled as a prediction. Therefore no circular step is exhibited; the low score reflects only a minor self-citation/assumption, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

No new physical entities are introduced; the conditional NF is a statistical surrogate, not a new dynamical agent. The ledger's free parameters are mostly fitting/choice points inside the SAM and the rate estimate; the axioms show the central claim rests on the SAM's dynamical-friction description, the fixed-structure host, and the two-feature TNG50 mapping.

free parameters (5)
  • Bar pattern-speed polynomial coefficients (Eq. 6) = ω_bar = (0.21 a³ − 5.56 a² + 47.13 a + 80.15)/a_bar, a ∈ [1,9] kpc
    Polynomial fitted to the galactic rotation curve to set the bar pattern speed under the corotation-resonance assumption; the bar frequency controls resonance trapping, so the fitted coefficients enter the dynamics directly.
  • Fixed dynamical-friction rotation curve = B22 barred-galaxy curve (M_bar=3×10^9 M⊙, ω=40 km/s/kpc, scales 5/2/0.3 kpc) used for all runs
    Footnote 2: one rotation curve powers the DF computation in all 10^5 models regardless of bar mass/length; a modeling choice that freezes the bar's influence on the drag force.
  • Bar/disc/bulge mass-compensation slope = 0.1 factor in Eqs 7-8 (abulge/abar terms)
    Hand-chosen split of how M_bar changes are compensated by disc versus bulge mass to keep M⋆ fixed; it sets the density environment the MBH sinks through.
  • Tail extrapolation of non-decaying systems = τ_d = ∞ values resampled from extrapolated finite-τ_d tail
    Section 2.2: the 45-55% of runs that do not decay within t_H/2t_H are reassigned decay times by extrapolating the finite distribution; a procedure that shapes the learned distribution's tail.
  • Occupation fraction f_occ = 0.1 (constant)
    Section 3.4: toy-model injection rate for the binary-formation-rate estimate; the paper notes f_occ is likely mass- and redshift-dependent.
axioms (7)
  • domain assumption Chandrasekhar dynamical friction with the fixed B22 rotation curve and a constant Coulomb logarithm describes the secondary MBH's orbital decay above 10 pc
    Section 2.1 and footnote 2; the entire training set and all population inferences inherit this drag model.
  • domain assumption Galactic components (halo, bulge, disc) and the bar's mass, length, and pattern speed are constant over the multi-Gyr integration
    Section 4 caveats; bars can weaken, strengthen, or disappear, and a fixed potential neglects co-evolution during inspiral.
  • domain assumption Binary formation is defined by the secondary reaching 10 pc from the primary; no gas dynamics, MBH feedback, or mass growth at these scales
    Section 2.1: integration stops at 10 pc and the perturber mass is fixed; neglects accretion/feedback regimes that alter the late inspiral.
  • domain assumption TNG50 galaxies are represented by the four SAM features via cross joint sampling: only f_bar and a_bar are replaced, plus a global τ_DF ∝ M_host^{1/2} rescaling
    Section 2.4: all other host structure (disc/bulge scalelengths, halo concentration) is held at the single fixed SAM galaxy; the M^{1/2} scaling is an isothermal-sphere result applied to every TNG50 prediction.
  • domain assumption The isotropic/uniform SAM sampling of MBH initial conditions represents the distribution of secondary MBHs in TNG50 merger remnants
    Sections 2.1.2 and 3.4: seeding is quasi-random, not tied to TNG50 merger histories; the paper states merger tracking is beyond scope.
  • domain assumption TNG50's volume is representative of the Universe for the rate estimates
    Section 3.4: V_sim is used as the comoving volume; the disc-like fraction ~80% below z~2 is cited as justification for the redshift range.
  • standard math Normalizing-flow density estimation via the change-of-variables formula is valid for this conditional target
    Appendix A1-A2: the emulator's likelihood and sampling rest on the standard bijective-transformation formalism.

pith-pipeline@v1.3.0-alltime-deepseek · 31502 in / 20718 out tokens · 179175 ms · 2026-08-01T00:43:05.076932+00:00 · methodology

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read the original abstract

Massive black hole (MBH) pairs, formed in galaxy mergers, may coalesce in a burst of gravitational waves. Estimating the coalescence time-scales and rates is a long-standing astrophysical problem, essential to inform predictions for future gravitational-wave detectors such as the Laser Interferometer Space Antenna, but remains challenging: MBH orbital decay in realistic galactic environments is complex and stochastic, and non-axisymmetric structures such as stellar bars can perturb MBH pair dynamics, delaying or accelerating binary formation and undermining the assumption that dynamical friction alone sets the inspiral duration. Capturing this evolution requires simulations too expensive to run at population scale. Here we present an artificial-intelligence framework that emulates the galactic-scale orbital decay of an inspiralling MBH using conditional normalizing flows trained on a large suite of semi-analytical orbital integrations. Our model captures the evolution of secondary MBHs orbiting within multi-component galactic merger remnants featuring rotating stellar discs and bars, across a broad range of MBH masses, orbital configurations, and bar properties. The trained emulator reproduces the simulations' decay-time distributions while reducing computational cost by orders of magnitude. For the first time, we apply this model to galaxy populations drawn from a cosmological simulation, exploiting morphological information on barred and non-barred galaxies to infer MBH binary formation time-scales across cosmic time. Our results show that stellar bars can alter the distribution of MBH binary formation times. More broadly, this demonstrates how simulation-based, surrogate machine-learning emulators can unlock a class of astrophysical problems where the physics is well understood system-by-system but intractable at scale.

Figures

Figures reproduced from arXiv: 2607.26125 by Carlos Moreno Martinez, Elisa Bortolas, Janis Fluri, Lucio Mayer, Matteo Bonetti, Nodens Koren, Pedro R. Capelo, Thomas Hofmann, Tommaso Zana.

Figure 1
Figure 1. Figure 1: Initial distribution of the eight free parameters of our SAM, considering all NSAM simulations (gray), shown together with the distribution of the same quantities, but considering only the 45239 simulations yielding τd < tH (blue). All distributions use 40 equally spaced bins and are normalized to the initial number of generated simulations. Orbital decay is promoted when MBHs are initially relatively mass… view at source ↗
Figure 2
Figure 2. Figure 2: Initial distribution of the six free parameters used in B22 for NSAM,B22 non-barred (top panels; part of our training set) and barred (bottom panels; shown here simply for comparison with [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Decay time distribution comparison between the SAM simulations (solid lines) and the emulation with the conditional-NF model (dots). The first panel shows the distribution comparison for the SAM validation set [∼0.2(NSAM + NSAM,B22)]. The other panels show the same comparison in different selections of the mass, the initial position, and the initial velocity of the MBHs, respectively. All distributions use… view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of decay times for four select tng50 snap￾shots (S34, S50, S67, and S91; see Table B1), including all galaxies contemplated in this work (i.e. non-barred galaxies and barred galaxies with a bar stellar mass fraction and a bar length within the SAM ranges, all with a central stellar mass above 3×109 M⊙), normalized by the number of galaxies considered in each snapshot. The vertical lines denote… view at source ↗
Figure 6
Figure 6. Figure 6: Fraction of secondary MBHs for all considered tng50 galaxies at z = 1 (snapshot S50) that form an MBH binary with the primary MBH by z = 0, as a function of all six MBH model quantities. These fractions are consistent with Figures 1 and 2. We do not show the fraction as a function of the bar model quantities, because of low-number statistics in the tng50 simulation. of the binary formation time τd on the p… view at source ↗
Figure 7
Figure 7. Figure 7: Fraction of binary formation events occurred between the time of the considered snapshot and z = 0, for each of the 18 tng50 snapshots we considered, treating the galaxies according to their own morphology (solid line) and treating all galaxies as non￾barred (dashed line). Taking into account the stellar bars tends to produce fewer events, with discrepancies of up to five per cent. This is the approach tak… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of decay times for two tng50 snapshots (S34 and S50, at z = 1.9 and 1, respectively), using two differ￾ent methods. Top panel: comparison between treating galaxies ac￾cording to their bar morphology (solid lines) and assuming that all galaxies are non-barred (dashed lines). Treating all galaxies as non-barred yields a slightly larger fraction of MBH binaries, more prominent at lower redshift, … view at source ↗
Figure 10
Figure 10. Figure 10: Estimated contribution from disc-like galaxies to the global binary formation rates, assuming focc = 0.1 and without tracking galaxy mergers. are smoothed out in the zinj dimension by means of quan￾tile interpolation amongst the distributions obtained for the available tng50 snapshots. This conditional probability ker￾nel is obtained assuming that the properties of the injected MBH are quasi-random variab… view at source ↗

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Reference graph

Works this paper leans on

123 extracted references · 18 canonical work pages · 1 internal anchor

  1. [1]

    Agazie G., et al., 2023a, @doi [ ] 10.3847/2041-8213/acdac6 , https://ui.adsabs.harvard.edu/abs/2023ApJ...951L...8A 951, L8

    doi:10.3847/2041-8213/acdac6 2041

  2. [2]

    Agazie G., et al., 2023b, @doi [ ] 10.3847/2041-8213/ace18b , https://ui.adsabs.harvard.edu/abs/2023ApJ...952L..37A 952, L37

    doi:10.3847/2041-8213/ace18b 2041

  3. [3]

    Amaro-Seoane P., et al., 2023, @doi [Living Reviews in Relativity] 10.1007/s41114-022-00041-y , https://ui.adsabs.harvard.edu/abs/2023LRR....26....2A 26, 2

    doi:10.1007/s41114-022-00041-y 2023

  4. [4]

    Bairagi A., Wandelt B., Villaescusa-Navarro F., 2025, @doi [ ] 10.1051/0004-6361/202554602 , https://ui.adsabs.harvard.edu/abs/2025A&A...703A.301B 703, A301

    doi:10.1051/0004-6361/202554602 2025

  5. [5]

    Battistini L., et al., 2026, @doi [ ] 10.1051/0004-6361/202659543 , https://ui.adsabs.harvard.edu/abs/2026A&A...710A.232B 710, A232

    work page doi:10.1051/0004-6361/202659543 2026

  6. [6]

    C., Blandford R

    Begelman M. C., Blandford R. D., Rees M. J., 1980, @doi [ ] 10.1038/287307a0 , https://ui.adsabs.harvard.edu/abs/1980Natur.287..307B 287, 307

    doi:10.1038/287307a0 1980

  7. [7]

    Princeton University Press, Princeton

    Binney J., Tremaine S., 2008, Galactic Dynamics: Second Edition . Princeton University Press, Princeton

    2008

  8. [8]

    Bird S., Ni Y., Di Matteo T., Croft R., Feng Y., Chen N., 2022, @doi [ ] 10.1093/mnras/stac648 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.512.3703B 512, 3703

    doi:10.1093/mnras/stac648 2022

  9. [9]

    A., Barnes J

    Blumenthal K. A., Barnes J. E., 2018, @doi [ ] 10.1093/mnras/sty1605 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.3952B 479, 3952

    doi:10.1093/mnras/sty1605 2018

  10. [10]

    R., Faber S

    Blumenthal G. R., Faber S. M., Primack J. R., Rees M. J., 1984, @doi [ ] 10.1038/311517a0 , https://ui.adsabs.harvard.edu/abs/1984Natur.311..517B 311, 517

    doi:10.1038/311517a0 1984

  11. [11]

    C., Blecha L., 2022, @doi [Living Reviews in Relativity] 10.1007/s41114-022-00037-8 , https://ui.adsabs.harvard.edu/abs/2022LRR....25....3B 25, 3

    Bogdanovi \'c T., Miller M. C., Blecha L., 2022, @doi [Living Reviews in Relativity] 10.1007/s41114-022-00037-8 , https://ui.adsabs.harvard.edu/abs/2022LRR....25....3B 25, 3

    doi:10.1007/s41114-022-00037-8 2022

  12. [12]

    Bondi H., 1952, @doi [ ] 10.1093/mnras/112.2.195 , https://ui.adsabs.harvard.edu/abs/1952MNRAS.112..195B 112, 195

    doi:10.1093/mnras/112.2.195 1952

  13. [13]

    Bondi H., Hoyle F., 1944, @doi [ ] 10.1093/mnras/104.5.273 , https://ui.adsabs.harvard.edu/abs/1944MNRAS.104..273B 104, 273

    doi:10.1093/mnras/104.5.273 1944

  14. [14]

    I., 2020, @doi [ ] 10.1093/mnras/staa964 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.3053B 494, 3053

    Bonetti M., Bortolas E., Lupi A., Dotti M., Raimundo S. I., 2020, @doi [ ] 10.1093/mnras/staa964 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.3053B 494, 3053

    work page doi:10.1093/mnras/staa964 2020

  15. [15]

    Bonetti M., Bortolas E., Lupi A., Dotti M., 2021, @doi [ ] 10.1093/mnras/stab222 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.3554B 502, 3554

    doi:10.1093/mnras/stab222 2021

  16. [16]

    R., Zana T., Mayer L., Bonetti M., Dotti M., Davies M

    Bortolas E., Capelo P. R., Zana T., Mayer L., Bonetti M., Dotti M., Davies M. B., Madau P., 2020, @doi [ ] 10.1093/mnras/staa2628 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.3601B 498, 3601

    doi:10.1093/mnras/staa2628 2020

  17. [17]

    R., Mayer L., Sesana A., 2022, @doi [ ] 10.1093/mnras/stac645 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.512.3365B 512, 3365

    Bortolas E., Bonetti M., Dotti M., Lupi A., Capelo P. R., Mayer L., Sesana A., 2022, @doi [ ] 10.1093/mnras/stac645 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.512.3365B 512, 3365

    work page doi:10.1093/mnras/stac645 2022

  18. [18]

    Princeton University Press, Princeton

    Bovy J., 2026, Dynamics and Astrophysics of Galaxies . Princeton University Press, Princeton

    2026

  19. [19]

    J., Bourne M

    Buttigieg S., Sijacki D., Moore C. J., Bourne M. A., 2025, @doi [ ] 10.1093/mnras/staf1336 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.542.2019B 542, 2019

    doi:10.1093/mnras/staf1336 2025

  20. [20]

    R., Dotti M., 2017, @doi [ ] 10.1093/mnras/stw2872 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.465.2643C 465, 2643

    Capelo P. R., Dotti M., 2017, @doi [ ] 10.1093/mnras/stw2872 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.465.2643C 465, 2643

    doi:10.1093/mnras/stw2872 2017

  21. [21]

    R., Volonteri M., Dotti M., Bellovary J

    Capelo P. R., Volonteri M., Dotti M., Bellovary J. M., Mayer L., Governato F., 2015, @doi [ ] 10.1093/mnras/stu2500 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.447.2123C 447, 2123

    doi:10.1093/mnras/stu2500 2015

  22. [22]

    R., Dotti M., Volonteri M., Mayer L., Bellovary J

    Capelo P. R., Dotti M., Volonteri M., Mayer L., Bellovary J. M., Shen S., 2017, @doi [ ] 10.1093/mnras/stx1067 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.469.4437C 469, 4437

    doi:10.1093/mnras/stx1067 2017

  23. [23]

    R., Feruglio C., Hickox R

    Capelo P. R., Feruglio C., Hickox R. C., Tombesi F., 2023, in , Handbook of X-ray and Gamma-ray Astrophysics. Springer Nature Singapore, p. 126, @doi 10.1007/978-981-16-4544-0_115-1

    doi:10.1007/978-981-16-4544-0_115-1 2023

  24. [24]

    R., Mangiagli A., Zwick L., Mayer L., Volonteri M., 2026, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2026arXiv260625020C p

    Capelo P. R., Mangiagli A., Zwick L., Mayer L., Volonteri M., 2026, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2026arXiv260625020C p. arXiv:2606.25020

    Pith/arXiv arXiv 2026

  25. [25]

    K., Bekki K., Groves B

    Cavanagh M. K., Bekki K., Groves B. A., Pfeffer J., 2022, @doi [ ] 10.1093/mnras/stab3786 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.5164C 510, 5164

    work page doi:10.1093/mnras/stab3786 2022

  26. [26]

    Chakraborty S., Gallerani S., Di Mascia F., Zana T., Valentini M., Carniani S., Vito F., Bhatt M., 2025, @doi [ ] 10.1051/0004-6361/202452926 , https://ui.adsabs.harvard.edu/abs/2025A&A...698A.268C 698, A268

    work page doi:10.1051/0004-6361/202452926 2025

  27. [27]

    Chandrasekhar S., 1943, @doi [ ] 10.1086/144517 , https://ui.adsabs.harvard.edu/abs/1943ApJ....97..255C 97, 255

    doi:10.1086/144517 1943

  28. [28]

    D., 2018, @doi [ ] 10.1103/PhysRevD.97.083004 , https://ui.adsabs.harvard.edu/abs/2018PhRvD..97h3004C 97, 083004

    Charnock T., Lavaux G., Wandelt B. D., 2018, @doi [ ] 10.1103/PhysRevD.97.083004 , https://ui.adsabs.harvard.edu/abs/2018PhRvD..97h3004C 97, 083004

    doi:10.1103/physrevd.97.083004 2018

  29. [29]

    Chen N., Ni Y., Tremmel M., Di Matteo T., Bird S., DeGraf C., Feng Y., 2022, @doi [ ] 10.1093/mnras/stab3411 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510..531C 510, 531

    doi:10.1093/mnras/stab3411 2022

  30. [30]

    arXiv:2402.07571

    Colpi M., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2402.07571 , https://ui.adsabs.harvard.edu/abs/2024arXiv240207571C p. arXiv:2402.07571

    Pith/arXiv arXiv doi:10.48550/arxiv.2402.07571 2024

  31. [31]

    F., Kalmbach J

    Crenshaw J. F., Kalmbach J. B., Gagliano A., Yan Z., Connolly A. J., Malz A. I., Schmidt S. J., The LSST Dark Energy Science Collaboration 2024, @doi [ ] 10.3847/1538-3881/ad54bf , https://ui.adsabs.harvard.edu/abs/2024AJ....168...80C 168, 80

    doi:10.3847/1538-3881/ad54bf 2024

  32. [32]

    Damiano A., Valentini M., Borgani S., Tornatore L., Murante G., Ragagnin A., Ragone-Figueroa C., Dolag K., 2024, @doi [ ] 10.1051/0004-6361/202450021 , https://ui.adsabs.harvard.edu/abs/2024A&A...692A..81D 692, A81

    doi:10.1051/0004-6361/202450021 2024

  33. [33]

    C., Banik U., Weinberg M., Natarajan P., Li Z., Dekel A., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2511.11804 , https://ui.adsabs.harvard.edu/abs/2025arXiv251111804D p

    Dattathri S., van den Bosch F. C., Banik U., Weinberg M., Natarajan P., Li Z., Dekel A., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2511.11804 , https://ui.adsabs.harvard.edu/abs/2025arXiv251111804D p. arXiv:2511.11804

    doi:10.48550/arxiv.2511.11804 2025

  34. [34]

    R., Gair J., Macke J

    Dax M., Green S. R., Gair J., Macke J. H., Buonanno A., Sch \"o lkopf B., 2021, @doi [ ] 10.1103/PhysRevLett.127.241103 , https://ui.adsabs.harvard.edu/abs/2021PhRvL.127x1103D 127, 241103

    doi:10.1103/physrevlett.127.241103 2021

  35. [35]

    De Rosa A., et al., 2019, @doi [ ] 10.1016/j.newar.2020.101525 , https://ui.adsabs.harvard.edu/abs/2019NewAR..8601525D 86, 101525

    arXiv 2019

  36. [36]

    DeGraf C., Sijacki D., 2020, @doi [ ] 10.1093/mnras/stz3309 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.4973D 491, 4973

    doi:10.1093/mnras/stz3309 2020

  37. [38]

    Dehnen W., 1993, @doi [ ] 10.1093/mnras/265.1.250 , https://ui.adsabs.harvard.edu/abs/1993MNRAS.265..250D 265, 250

    doi:10.1093/mnras/265.1.250 1993

  38. [39]

    arXiv:1906.04032

    Durkan C., Bekasov A., Murray I., Papamakarios G., 2019, @doi [arXiv e-prints] 10.48550/arXiv.1906.04032 , https://ui.adsabs.harvard.edu/abs/2019arXiv190604032D p. arXiv:1906.04032

    Pith/arXiv arXiv doi:10.48550/arxiv.1906.04032 2019

  39. [40]

    S., 1916, @doi [ ] 10.1093/mnras/77.1.16 , https://ui.adsabs.harvard.edu/abs/1916MNRAS..77...16E 77, 16

    Eddington A. S., 1916, @doi [ ] 10.1093/mnras/77.1.16 , https://ui.adsabs.harvard.edu/abs/1916MNRAS..77...16E 77, 16

    doi:10.1093/mnras/77.1.16 1916

  40. [41]

    Einstein A., 1916, Sitzungsberichte der K \"o niglich Preussischen Akademie der Wissenschaften, https://ui.adsabs.harvard.edu/abs/1916SPAW.......688E pp 688--696

    1916

  41. [42]

    Haidar H., et al., 2022, @doi [ ] 10.1093/mnras/stac1659 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.514.4912H 514, 4912

    doi:10.1093/mnras/stac1659 2022

  42. [43]

    Hernquist L., 1990, @doi [ ] 10.1086/168845 , https://ui.adsabs.harvard.edu/abs/1990ApJ...356..359H 356, 359

    doi:10.1086/168845 1990

  43. [44]

    F., Quataert E., 2010, @doi [ ] 10.1111/j.1365-2966.2010.17064.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.407.1529H 407, 1529

    Hopkins P. F., Quataert E., 2010, @doi [ ] 10.1111/j.1365-2966.2010.17064.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.407.1529H 407, 1529

    arXiv 2010

  44. [45]

    A., 1939, @doi [Proceedings of the Cambridge Philosophical Society] 10.1017/S0305004100021150 , https://ui.adsabs.harvard.edu/abs/1939PCPS...35..405H 35, 405

    Hoyle F., Lyttleton R. A., 1939, @doi [Proceedings of the Cambridge Philosophical Society] 10.1017/S0305004100021150 , https://ui.adsabs.harvard.edu/abs/1939PCPS...35..405H 35, 405

    doi:10.1017/s0305004100021150 1939

  45. [46]

    arXiv:2605.00092

    Izquierdo-Villalba D., et al., 2026, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2026arXiv260500092I p. arXiv:2605.00092

    Pith/arXiv arXiv 2026

  46. [47]

    arXiv:1505.05770

    Jimenez Rezende D., Mohamed S., 2015, @doi [arXiv e-prints] 10.48550/arXiv.1505.05770 , https://ui.adsabs.harvard.edu/abs/2015arXiv150505770J p. arXiv:1505.05770

    Pith/arXiv arXiv doi:10.48550/arxiv.1505.05770 2015

  47. [48]

    Kacprzak T., Fluri J., Schneider A., Refregier A., Stadel J., 2023, @doi [ ] 10.1088/1475-7516/2023/02/050 , https://ui.adsabs.harvard.edu/abs/2023JCAP...02..050K 2023, 050

    doi:10.1088/1475-7516/2023/02/050 2023

  48. [49]

    L., Kelley L

    Katz M. L., Kelley L. Z., Dosopoulou F., Berry S., Blecha L., Larson S. L., 2020, @doi [ ] 10.1093/mnras/stz3102 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2301K 491, 2301

    doi:10.1093/mnras/stz3102 2020

  49. [50]

    Kim J.-h., et al., 2016, @doi [ ] 10.3847/1538-4357/833/2/202 , https://ui.adsabs.harvard.edu/abs/2016ApJ...833..202K 833, 202

    doi:10.3847/1538-4357/833/2/202 2016

  50. [51]

    P., Ba J., 2015, in Proceedings of the 3rd International Conference on Learning Representations

    Kingma D. P., Ba J., 2015, in Proceedings of the 3rd International Conference on Learning Representations. ( @eprint arXiv 1412.6980 )

    Pith/arXiv arXiv 2015

  51. [52]

    C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    Kormendy J., Ho L. C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    doi:10.1146/annurev-astro-082708-101811 2013

  52. [53]

    Koss M., Mushotzky R., Treister E., Veilleux S., Vasudevan R., Trippe M., 2012, @doi [ ] 10.1088/2041-8205/746/2/L22 , https://ui.adsabs.harvard.edu/abs/2012ApJ...746L..22K 746, L22

    doi:10.1088/2041-8205/746/2/l22 2012

  53. [54]

    Krause M. G. H., et al., 2025, @doi [ ] 10.1017/pasa.2025.10120 , https://ui.adsabs.harvard.edu/abs/2025PASA...42..162K 42, e162

    arXiv 2025

  54. [55]

    A., et al., 2024, @doi [ ] 10.1093/mnras/stae921 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.530.1984L 530, 1984

    Le Conte Z. A., et al., 2024, @doi [ ] 10.1093/mnras/stae921 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.530.1984L 530, 1984

    doi:10.1093/mnras/stae921 2024

  55. [56]

    A., et al., 2026, @doi [ ] 10.1093/mnras/staf2010 , https://ui.adsabs.harvard.edu/abs/2026MNRAS.545f2010L 545, staf2010

    Le Conte Z. A., et al., 2026, @doi [ ] 10.1093/mnras/staf2010 , https://ui.adsabs.harvard.edu/abs/2026MNRAS.545f2010L 545, staf2010

    doi:10.1093/mnras/staf2010 2026

  56. [57]

    R., 2020a, @doi [ ] 10.3847/1538-4357/ab93c6 , https://ui.adsabs.harvard.edu/abs/2020ApJ...896..113L 896, 113

    Li K., Bogdanovi \'c T., Ballantyne D. R., 2020a, @doi [ ] 10.3847/1538-4357/ab93c6 , https://ui.adsabs.harvard.edu/abs/2020ApJ...896..113L 896, 113

    doi:10.3847/1538-4357/ab93c6

  57. [58]

    R., 2020b, @doi [ ] 10.3847/1538-4357/abc555 , https://ui.adsabs.harvard.edu/abs/2020ApJ...905..123L 905, 123

    Li K., Bogdanovi \'c T., Ballantyne D. R., 2020b, @doi [ ] 10.3847/1538-4357/abc555 , https://ui.adsabs.harvard.edu/abs/2020ApJ...905..123L 905, 123

    work page doi:10.3847/1538-4357/abc555

  58. [59]

    R., Bonetti M., 2022, @doi [ ] 10.3847/1538-4357/ac74b5 , https://ui.adsabs.harvard.edu/abs/2022ApJ...933..104L 933, 104

    Li K., Bogdanovi \'c T., Ballantyne D. R., Bonetti M., 2022, @doi [ ] 10.3847/1538-4357/ac74b5 , https://ui.adsabs.harvard.edu/abs/2022ApJ...933..104L 933, 104

    doi:10.3847/1538-4357/ac74b5 2022

  59. [60]

    Li E.-K., et al., 2025, @doi [Reports on Progress in Physics] 10.1088/1361-6633/adc9be , https://ui.adsabs.harvard.edu/abs/2025RPPh...88e6901L 88, 056901

    doi:10.1088/1361-6633/adc9be 2025

  60. [61]

    Long K., Murali C., 1992, @doi [ ] 10.1086/171764 , https://ui.adsabs.harvard.edu/abs/1992ApJ...397...44L 397, 44

    doi:10.1086/171764 1992

  61. [62]

    Luo J., et al., 2016, @doi [Classical and Quantum Gravity] 10.1088/0264-9381/33/3/035010 , https://ui.adsabs.harvard.edu/abs/2016CQGra..33c5010L 33, 035010

    doi:10.1088/0264-9381/33/3/035010 2016

  62. [63]

    Luo Z., Wang Y., Wu Y., Hu W., Jin G., 2021, @doi [Progress of Theoretical and Experimental Physics] 10.1093/ptep/ptaa083 , https://ui.adsabs.harvard.edu/abs/2021PTEP.2021eA108L 2021, 05A108

    doi:10.1093/ptep/ptaa083 2021

  63. [64]

    Marinacci F., et al., 2018, @doi [ ] 10.1093/mnras/sty2206 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.5113M 480, 5113

    doi:10.1093/mnras/sty2206 2018

  64. [65]

    Princeton University Press, Princeton

    Merritt D., 2013, Dynamics and Evolution of Galactic Nuclei . Princeton University Press, Princeton

    2013

  65. [66]

    Merritt D., Vasiliev E., 2011, @doi [ ] 10.1088/0004-637X/726/2/61 , https://ui.adsabs.harvard.edu/abs/2011ApJ...726...61M 726, 61

    work page doi:10.1088/0004-637x/726/2/61 2011

  66. [67]

    Milosavljevi \'c M., Merritt D., 2001, @doi [ ] 10.1086/323830 , https://ui.adsabs.harvard.edu/abs/2001ApJ...563...34M 563, 34

    doi:10.1086/323830 2001

  67. [68]

    P., et al., 2018, @doi [ ] 10.1093/mnras/sty618 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.1206N 477, 1206

    Naiman J. P., et al., 2018, @doi [ ] 10.1093/mnras/sty618 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.1206N 477, 1206

    doi:10.1093/mnras/sty618 2018

  68. [69]

    F., Frenk C

    Navarro J. F., Frenk C. S., White S. D. M., 1996, @doi [ ] 10.1086/177173 , https://ui.adsabs.harvard.edu/abs/1996ApJ...462..563N 462, 563

    doi:10.1086/177173 1996

  69. [70]

    Nelson D., et al., 2018, @doi [ ] 10.1093/mnras/stx3040 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.475..624N 475, 624

    doi:10.1093/mnras/stx3040 2018

  70. [71]

    Nelson D., et al., 2019, @doi [ ] 10.1093/mnras/stz2306 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.490.3234N 490, 3234

    doi:10.1093/mnras/stz2306 2019

  71. [72]

    Ntampaka M., et al., 2019, @doi [ ] 10.3847/1538-4357/ab14eb , https://ui.adsabs.harvard.edu/abs/2019ApJ...876...82N 876, 82

    doi:10.3847/1538-4357/ab14eb 2019

  72. [73]

    C., 1999, @doi [ ] 10.1086/306858 , https://ui.adsabs.harvard.edu/abs/1999ApJ...513..252O 513, 252

    Ostriker E. C., 1999, @doi [ ] 10.1086/306858 , https://ui.adsabs.harvard.edu/abs/1999ApJ...513..252O 513, 252

    doi:10.1086/306858 1999

  73. [74]

    Papamakarios G., Nalisnick E., Jimenez Rezende D., Mohamed S., Lakshminarayanan B., 2021, @doi [The Journal of Machine Learning Research] 10.48550/arXiv.1912.02762 , https://ui.adsabs.harvard.edu/abs/2019arXiv191202762P 22, 2617

    Pith/arXiv arXiv doi:10.48550/arxiv.1912.02762 2021

  74. [75]

    Park K., Bogdanovi \'c T., 2017, @doi [ ] 10.3847/1538-4357/aa65ce , https://ui.adsabs.harvard.edu/abs/2017ApJ...838..103P 838, 103

    doi:10.3847/1538-4357/aa65ce 2017

  75. [76]

    Park K., Bogdanovi \'c T., 2019, @doi [ ] 10.3847/1538-4357/ab3f30 , https://ui.adsabs.harvard.edu/abs/2019ApJ...883..209P 883, 209

    work page doi:10.3847/1538-4357/ab3f30 2019

  76. [77]

    L., 2019, @doi [ ] 10.1093/mnras/sty3277 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483.2721P 483, 2721

    Peschken N., okas E. L., 2019, @doi [ ] 10.1093/mnras/sty3277 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483.2721P 483, 2721

    doi:10.1093/mnras/sty3277 2019

  77. [78]

    W., Weaver K

    Pfeifle R. W., Weaver K. A., Secrest N. J., Rothberg B., Patton D. R., 2025, @doi [ ] 10.3847/1538-4365/adf845 , https://ui.adsabs.harvard.edu/abs/2025ApJS..281...25P 281, 25

    doi:10.3847/1538-4365/adf845 2025

  78. [79]

    R., Volonteri M., Bellovary J

    Pfister H., Lupi A., Capelo P. R., Volonteri M., Bellovary J. M., Dotti M., 2017, @doi [ ] 10.1093/mnras/stx1853 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.471.3646P 471, 3646

    work page doi:10.1093/mnras/stx1853 2017

  79. [80]

    Pfister H., Volonteri M., Dubois Y., Dotti M., Colpi M., 2019, @doi [ ] 10.1093/mnras/stz822 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.486..101P 486, 101

    doi:10.1093/mnras/stz822 2019

  80. [81]

    Pillepich A., et al., 2018a, @doi [ ] 10.1093/mnras/stx2656 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.473.4077P 473, 4077

    doi:10.1093/mnras/stx2656

Showing first 80 references.