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The orbit of the star S2 around the Milky Way's central black hole, tracked to tens of microarcseconds, now serves as a dynamical census of the stellar-mass black holes that feed extreme-mass-ratio inspirals and bursts — and an upper limit

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2026-08-01 00:42 UTC pith:MQC67KQE

load-bearing objection Solid Milky Way upper limits from S2/GRAVITY, but the LISA-detectability headline leans on an upper-limit-cum-universal-cusp assumption that a factor-few lower cusp would overturn. the 2 major comments →

arxiv 2607.26127 v1 pith:MQC67KQE submitted 2026-07-28 astro-ph.GA astro-ph.COastro-ph.HEgr-qc

From S2 to LISA: Astrometric Bounds on Extreme-Mass-Ratio Inspirals and Bursts

Andrea Caputo , Valerie Domcke This is my paper
classification astro-ph.GA astro-ph.COastro-ph.HEgr-qc
keywords extreme-mass-ratio inspiralsextreme-mass-ratio burstsS2 stellar orbitastrometric constraintsstellar-mass black hole cuspGalactic CentreLISA gravitational-wave backgroundBahcall-Wolf profile
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.

This paper uses the measured orbit of the star S2 around the Milky Way's central black hole to count, from above, how many stellar-mass black holes can hide within about 0.02 pc of the Galactic Centre. Any such cusp leaves two marks on S2: a coherent extra precession proportional to the total enclosed mass, and a random-walk tilt of the orbital plane proportional to the square root of the number of individual perturbers. Requiring both effects to stay within the astrometric precision fixes the maximum allowed cusp normalisation, n0. Saturating that bound with a 10-solar-mass Bahcall–Wolf cusp gives a Milky Way EMRI rate below roughly 240 per Gyr and a detectable EMRI burst rate below about 0.2 per year — comfortably compatible with standard steady-state predictions, while excluding very dense cusps. Scaled self-similarly to other galactic nuclei, the same bound makes the extragalactic EMRI stochastic background detectable by LISA under the adopted black-hole mass functions.

Core claim

The central claim is that precision astrometry of a single stellar orbit can replace population-synthesis modelling as the empirical anchor for the compact-object density that feeds LISA's primary sources. Using an N-body integration of S2 under the central potential, 1PN precession, and a discrete population of stellar-mass black holes, the paper derives two constraints. The coherent apsidal precession, |delta-omega| = A N_p, bounds the smooth enclosed mass to about 1–2 × 10^3 solar masses within S2's orbit; the granular inclination random walk, delta-i = B sqrt(N_p), bounds the number of individual heavy perturbers. The tighter of the two yields n0 below about 1.2 × 10^-7 AU^-3 for the ben

What carries the argument

The load-bearing object is the phase-space distribution F(epsilon) proportional to epsilon^(gamma-3/2) of a power-law cusp n(a) proportional to a^(-gamma) around a massive black hole, obtained by Eddington inversion; it fixes both the burst kernel and the orbital sampling of the perturbers. Around it, two empirical scalings carry the argument: a coherent apsidal kick |delta-omega| = A N_p (sensitive to the smooth enclosed mass) and a random-walk inclination change delta-i = B sqrt(N_p) (sensitive to granularity), with A, B proportional to the perturber mass. The second half of the machinery is the empty-loss-cone flux, in which the boundary a_c between scattering-dominated and GW-dominated o

Load-bearing premise

For the extragalactic and LISA claims, the load-bearing assumption is that every galactic nucleus hosts the same kind of relaxed, mass-segregated, Bahcall–Wolf-like cusp of stellar-mass black holes as the Milky Way, with the same fraction of stellar mass ending up in black-hole remnants; if low-mass nuclei instead have unrelaxed or strongly segregated cusps, the normalisation could shift by an order of magnitude and the cosmological rates with it.

What would settle it

Directly measure the cusp normalisation: if continued astrometry of S2 through its 2026 apocentre passage, or of the tighter-orbit star S301, resolves the stochastic inclination jitter and gives an n0 an order of magnitude below the current upper bound, then the EMRI rate, scaling as n0^(6/5), falls below about 15 per Gyr and the cosmological EMRI background drops below the LISA power-law sensitivity. Such a measurement would falsify the paper's central detectability claim; a LISA non-detection of the EMRI background at the level shown in the paper would be a weaker but still informative falsi

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

If this is right

  • Standard steady-state EMRI predictions (roughly 1–10^2 per Gyr) are compatible with the current astrometric non-detection, while cusps dense enough to produce 10^4 per Gyr or more are excluded.
  • The Milky Way's detectable extreme-mass-ratio burst rate is at most about one per five years, so a LISA detection of a Galactic burst in the nominal 4-year mission is unlikely at the 1-sigma bound.
  • After self-similar extrapolation, the unresolved EMRI stochastic background exceeds the LISA power-law sensitivity for optimistic and fiducial MBH mass functions, and marginally for the pessimistic one, making the EMRI background a plausible LISA foreground.
  • The extragalactic EMRB background reaches LISA only under optimistic assumptions such as efficient mass segregation in low-mass nuclei; its spectrum is nearly flat in frequency, which would make it accessible to microhertz-band missions.
  • The scaling laws Gamma_EMRI proportional to n0^(6/5) and Gamma_EMRB proportional to n0^1.6, together with the fitted coefficients, allow any future improvement in astrometric precision to be translated directly into revised rate and background upper limits.

Where Pith is reading between the lines

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

  • If continued astrometry of S2 through its 2026 apocentre passage — or of the tighter-orbit star S301 — detects stochastic orbit jitter rather than just bounding it, the same pipeline turns an upper limit into a measurement of n0; a single measured normalisation would narrow the EMRI and EMRB rate predictions by roughly an order of magnitude.
  • Because the low-mass end of the black-hole mass function (below about 10^5 solar masses) dominates the extragalactic integrals, the paper's method effectively turns LISA into a probe of the black-hole occupation fraction in dwarf galactic nuclei — an inference the authors only hint at.
  • The flat, nearly frequency-independent EMRB background, if confirmed, would be a foreground that any search for primordial or cosmological millihertz backgrounds must subtract; this follows directly from the spectral shape the paper plots but is not one of its stated conclusions.
  • The same astrometric-calibration logic could be applied to other S-stars or to pulsar timing around the Galactic Centre, testing whether the cusp is truly Bahcall–Wolf or in a stronger mass-segregation regime — a check the current data cannot yet perform.

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

2 major / 5 minor

Summary. This paper uses GRAVITY astrometric monitoring of the S2 star around Sgr A* to derive upper limits on the normalization n0 of a stellar-mass black-hole (sBH) cusp on ~0.02 pc scales. The authors run N-body simulations of S2 under a Newtonian point-mass potential, 1PN Schwarzschild precession, and perturbations from a discrete population of sBHs drawn from a power-law cusp. They extract two complementary constraints: coherent apsidal precession (sensitive to the smooth enclosed mass) and a random-walk in orbital inclination (sensitive to the granularity of the perturber population). For a benchmark Bahcall-Wolf slope gamma=7/4 and 10 Msun perturbers they obtain n0_max ~ 1.2e-7 AU^-3, corresponding to a Milky Way EMRI rate upper limit of ~240 Gyr^-1 and an EMRB rate upper limit of ~0.2 yr^-1. They then extrapolate the Sgr A* calibration to other galactic nuclei using a self-similar scaling n0(M_bh) ∝ M_bh^{3/8}, convolve with an occupation-corrected local BH mass function, and compute cosmological EMRI and EMRB rates and stochastic gravitational-wave backgrounds. The paper concludes that the upper limit on the EMRI background lies above the LISA power-law sensitivity for all considered mass functions, while the EMRB background is detectable only under optimistic assumptions. The central scientific content is the astrometric calibration of the sBH cusp and its translation into local EMRI/EMRB rates; the cosmological extrapolation is explicitly model-dependent and presented as an

Significance. If the local calibration is sound—and it appears to be: the N-body integrator reproduces the known smooth-mass limit (~3.5e3 Msun) and Schwarzschild precession to better than 1%, and the two observational channels (precession and inclination) give consistent N_max values—this is a novel and valuable bridge between Galactic Center astrometry and LISA source predictions. The analytic scalings Γ_EMRI ∝ n0^{6/5} and Γ_EMRB ∝ n0^{1.6} are transparent, and the paper is the first to propagate the occupation-corrected MBH mass function of Burke et al. into EMRI/EMRB backgrounds. These strengths make the local upper limits on the sBH cusp and the Milky Way event rates a significant contribution even though the cosmological extrapolation rests on assumptions that are clearly acknowledged. The manuscript is generally careful to label results as upper limits, though some headline statements overstate what an upper limit can establish.

major comments (2)
  1. [Abstract and Sec. V, Fig. 9] The claim that 'the resulting EMRI background is detectable by LISA across all scenarios considered' is not supported by the analysis. The calculation sets n0 to the S2-derived upper limit n0_max (Eq. 3) in every nucleus, so the curves in Fig. 9 are upper limits on Ω_EMRI, not predictions. Since GRAVITY provides only a one-sided bound, any n0 < n0_max is equally consistent with data. Given Γ_EMRI ∝ n0^{6/5} (Eq. 37 and Sec. IV), a factor of ~3 reduction in n0 lowers Ω_EMRI by a factor of ~7, which can move the pessimistic-case curve below the LISA PLS. The wording should be changed to 'the upper limit on the EMRI background is above the LISA PLS for the scenarios considered,' and the figures should clearly show the saturation assumption. This is load-bearing for the central headline of the abstract.
  2. [Sec. III, Eq. (3)] The extrapolation n0(M_bh) = n0_max (M_bh/4e6 Msun)^{3/8} assumes that every galactic nucleus hosts a relaxed, mass-segregated, Bahcall-Wolf sBH cusp that saturates the Sgr A* upper limit. This is a strong assumption: the S2 data gives an upper limit, not a detection, and the low-M_bh end (M_bh ≲ 1e5 Msun) dominates all cosmological integrals (Figs. 2, 5, 7, 9). The paper brackets the high-density side with the phenomenological Eq. (4), but provides no lower bound on n0. A cusp with n0 a factor of a few below n0_max is fully consistent with GRAVITY and would suppress the cosmological background below the LISA PLS for several scenarios. The 'upper limits' in this work are therefore conditional on the saturation assumption; this should be stated explicitly wherever cosmological results are quoted, and ideally the dependence on a lower n0 (e.g., n0 = 0.1 n0_max) should be quantified.
minor comments (5)
  1. [Eq. (44)] The characteristic-strain conversion is dimensionally inconsistent and appears to contain a typo. The paper writes h_c = H0 / sqrt(2π f) * sqrt(3Ω); the correct relation is h_c = H0 / (π f) * sqrt(3Ω/2) (or equivalently H0 / (sqrt(2) π f) * sqrt(3Ω)). Please check and correct, since this formula is used to claim only marginal impact on transient measurements.
  2. [Sec. II / App. B, inclination threshold] The mapping from GRAVITY's 30 μas astrometric accuracy to the 40 arcsec inclination threshold is a simplified single-orbit proxy (footnote 2). The actual GRAVITY sensitivity is derived from a multi-epoch, multi-star fit that can probe correlated residuals. For the heaviest perturbers (m >~ 20-30 Msun), where the inclination channel is binding, the derived n0_max is approximate. This does not affect the main conclusions because the rates are nearly mass-independent, but the caveat should be stated.
  3. [Sec. III, paragraph after Eq. (3)] The phrase 'the value derived above, so that the simulations independently select the self-similar scaling of Eq. (2)' overstates the independence of the check. The matching to Hopman's Γ ∝ M_bh^{-1/4} uses the paper's own Γ ∝ n0^{6/5} M_bh^{-7/10} scaling, so it is a consistency check rather than an independent validation. The wording should be softened.
  4. [Sec. IV, paragraph after Eq. (33)] The sentence 'resulting in resulting in a stronger than linear' has a duplicated phrase. Also, 'the exponent varies a bit with density' is vague; a numerical range or a plot of the local exponent α(n0) would be more informative.
  5. [References [9] and [51]] References [9] and [51] are the same paper (Hopman, Freitag & Larson 2007, MNRAS 378, 129). Please merge or distinguish them; in the text at Fig. 4, Ref. [51] is cited as a separate follow-up, but it is the same work.

Circularity Check

0 steps flagged

No significant circularity: the S2/GRAVITY-derived n0 upper limits are propagated through standard rate/SGWB integrals; the self-referential passages are explicit caveats, not load-bearing predictions.

full rationale

The derivation chain is: external GRAVITY observables (f_SP and astrometric accuracy) to N-body scaling |Delta-omega|=A Np and Delta-i=B sqrt(Np), then to N_max, then to n0_max, then to per-galaxy EMRB/EMRI rates, then convolved with an external MBH mass function. None of the target quantities (Gamma_EMRI, Gamma_EMRB, Omega_GW) is fed back into the constraint, and no parameter is fitted to the predicted rates. The precession channel is explicitly acknowledged to use the same f_SP measurement as GRAVITY's smooth-mass limit: the paper states it 'does not add information independent of GRAVITY's mass limit but provides a consistency check, which our bound (built on the same f_SP measurement) passes by construction.' This is a calibration of the input rather than a circular prediction; the inclination channel, which carries the granular information, is independent. The self-similar exponent p=3/8 in Eq. (3) is derived from N_•(<rh) proportional to M_• and rh proportional to M_•^{1/2}; the later consistency check with Hopman's Gamma proportional to M_•^{-1/4} uses the paper's own scaling Gamma proportional to n0^{6/5} M_•^{-7/10}, but this check is not load-bearing because p=3/8 was already obtained without it. Eq. (4) is introduced explicitly as 'a purely phenomenological scaling' to bracket uncertainty, not as a derived prediction. The extragalactic and LISA-detectability statements are upper-limit propagations, and the paper repeatedly flags the dominant systematic uncertainties (low-MBH-mass mass-function extrapolation, sBH profile extrapolation). No self-citation is load-bearing, and no known empirical result is merely renamed.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

Everything in the rate predictions flows from the GRAVITY-derived n0 bound plus standard astrophysical formulas. The main free knobs are C_LC, e_min, k, m, and M_crit. The extrapolation scaling is an assumption, not a fitted entity; no new physical entities are introduced.

free parameters (6)
  • Loss-cone factor C_LC = 15
    Chosen fiducial value in Eq. (35); sets the overall EMRI rate amplitude and is not fitted to GRAVITY data.
  • EMRB eccentricity threshold e_min = 0.9
    Hand-chosen lower bound in Eq. (30) to keep the parabolic/harmonic-continuum approximation valid; directly increases or decreases the burst rate.
  • Capture boundary factor k = 1.36
    Order-unity coefficient from Ref. [18] used in Eq. (11) to define a_c; affects the EMRI integration domain.
  • Perturber benchmark mass m = 10 M_sun
    Fiducial single-mass population; results are shown for 5–30 M_sun. The final Milky Way rates are largely mass-insensitive by cancellation.
  • Maximal-normalisation transition mass M_crit = 2e5 M_sun
    Chosen in Eq. (4) as the MBH mass where the self-similar cusp would equal the MBH mass; used for the optimistic mass-segregation bracket.
  • Softening length eps = 0.007 AU
    Numerical softening in Eq. (A3) to avoid divergences; small compared with S2's pericenter but prevents exact Keplerian singularity.
axioms (7)
  • domain assumption The region probed is Keplerian-dominated by Sgr A*, with 1PN corrections; perturbers move on fixed Keplerian orbits with no perturber-perturber interactions.
    Used in the N-body integration, Eqs. (A1)–(A3); true over ~33 yr if two-body relaxation of the perturber population is negligible, but not proven.
  • domain assumption The sBH population follows a single-mass, isotropic, power-law cusp with a Bahcall-Wolf slope γ=7/4 as fiducial.
    Benchmark for all rate forecasts; Fig. 1 explores other γ, but the main LISA predictions adopt γ=7/4.
  • domain assumption The same sBH population acts as both EMRI source and relaxation scatterer (μ=m_sc=m), i.e. a self-consistent single-component cusp.
    Stated in Fig. 6 caption and used in Eq. (36); if scattering is dominated by lighter stars, the rates change.
  • domain assumption The local occupation-corrected MBH mass function of Burke et al. applies at z≤3 with no redshift evolution.
    Used in Eqs. (20)/(25); the authors limit z≤3 and call it plausible, but the low-mass end is an extrapolation.
  • standard math Standard Peters–Matthews and Newtonian inspiral waveforms describe the EMRB/EMRI spectra.
    Standard gravitational-wave formulas from Refs. [41, 61], used in Eqs. (39)–(43).
  • standard math Eddington inversion for a power-law Keplerian cusp yields F(ε)∝ε^{γ-3/2} and thermal eccentricity distribution p(e)=2e.
    Derived in App. C from standard isotropic phase-space theory; central for the burst kernel and for the S2 perturber sampling.
  • domain assumption LISA sensitivity is represented by the Robson et al. model with the Thrane–Romano power-law-integrated sensitivity curve.
    Used to define detectability; an external instrument model, not validated in this paper.

pith-pipeline@v1.3.0-alltime-deepseek · 29810 in / 21717 out tokens · 189497 ms · 2026-08-01T00:42:48.618470+00:00 · methodology

0 comments
read the original abstract

Stellar orbits around the massive black hole at the center of our galaxy provide a unique local probe of the compact-object population in the Galactic Centre and, consequently, of the sources of millihertz gravitational waves: periapse passages lead to extreme-mass-ratio bursts (EMRBs) while successful captures lead to extreme-mass ration inspirals (EMRIs). In this paper we use recent astrometric limits from the GRAVITY observatory on perturbations of the orbit of the star S2 to place upper limits on the normalisation of a stellar-mass black-hole cusp within ${\sim} \,0.02\,\mathrm{pc}$. For a benchmark $10\,M_\odot$ Bahcall--Wolf population anchored to this data, we obtain upper limits of ${\sim} \,2.4\times10^{2}\,\mathrm{Gyr}^{-1}$ on the EMRI rate and ${\sim} \, 0.2\,\mathrm{yr}^{-1}$ on the detectable EMRB rate in the Milky Way, which fall within the broad range of previous theoretical estimates. Assuming a self-similar scaling of the cusp normalisation with central black-hole mass, we extend this calibration to cosmological populations. The resulting EMRI background is detectable by LISA across all scenarios considered, whereas the flatter EMRB background can reach LISA sensitivity when mass segregation is efficient in low-mass galactic nuclei. Our results highlight the complementarity of precision stellar astrometry and millihertz gravitational-wave observations.

Figures

Figures reproduced from arXiv: 2607.26127 by Andrea Caputo, Valerie Domcke.

Figure 1
Figure 1. Figure 1: FIG. 1. Upper limits on the density normalisation [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Local, occupation-corrected central black-hole mass [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic phase-space structure in the ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Expected rate of detectable extreme-mass-ratio [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Stochastic gravitational wave background from the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. S2-derived upper limit on rate of EMRI detectable [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Upper limit on the extragalactic EMRI stochastic [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. S2 orbital perturbations from a stellar-mass black-hole population with individual mass [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

65 extracted references · 47 linked inside Pith

  1. [1]

    Astro- DarkLS

    We have verified this numerically over the full range of interest. V. Results EMRBs Event rate per galaxy .To estimate the rate of de- tectable EMRBs in our galaxy, we start from Eq. (29), with the upper integration boundaryr p,max set by the sensitivity of the observing instrument. For LISA, the signal-to-noise ratio (SNR) for these events can be esti- m...

    2012

  2. [2]

    J. R. Gair, S. Babak, A. Sesana, P. Amaro-Seoane, E. Barausse, C. P. L. Berry, E. Berti and C. Sopuerta, Prospects for observing extreme-mass-ratio inspirals with LISA,J. Phys. Conf. Ser.840(2017) 012021 [1704.00009]. [2]LISACollaboration, M. Colpi et al.,LISA Definition Study Report,2402.07571

    Pith/arXiv arXiv 2017

  3. [3]

    Babak, J

    S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau and A. Klein,Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals, Phys. Rev. D95(2017) 103012 [1703.09722]

    Pith/arXiv arXiv 2017

  4. [4]

    Amaro-Seoane, J

    P. Amaro-Seoane, J. R. Gair, M. Freitag, M. Coleman Miller, I. Mandel, C. J. Cutler and S. Babak,Astrophysics, detection and science applications of intermediate- and extreme mass-ratio inspirals,Class. Quant. Grav.24(2007) R113 [astro-ph/0703495]

    Pith/arXiv arXiv 2007

  5. [5]

    Bonetti and A

    M. Bonetti and A. Sesana,Gravitational wave background from extreme mass ratio inspirals,Phys. Rev. D102(2020) 103023 [2007.14403]

    Pith/arXiv arXiv 2020

  6. [6]

    C. P. L. Berry and J. R. Gair,Gravitational wave energy spectrum of a parabolic encounter,Phys. Rev. D 82(2010) 107501 [1010.3865]

    Pith/arXiv arXiv 2010

  7. [7]

    C. P. L. Berry and J. R. Gair,Observing the Galaxy’s massive black hole with gravitational wave bursts,Mon. Not. Roy. Astron. Soc.429(2013) 589 [1210.2778]

    Pith/arXiv arXiv 2013

  8. [8]

    L. J. Rubbo, K. Holley-Bockelmann and L. S. Finn, Event Rate for Extreme Mass Ratio Burst Signals in the Laser Interferometer Space Antenna Band, Astrophys.J.Lett.649(2006) L25

    2006

  9. [10]

    D. J. Oliver, A. D. Johnson, L. Janssen, J. Berrier, K. Glampedakis and D. Kennefick,Gravitational wave peep contributions to background signal confusion noise for LISA,Phys. Rev. D113(2026) 063001 [2507.19704]

    arXiv 2026

  10. [11]

    C. P. L. Berry and J. R. Gair, Extreme-mass-ratio-bursts from extragalactic sources, Mon. Not. Roy. Astron. Soc.433(2013) 3572 [1306.0774]

    Pith/arXiv arXiv 2013

  11. [12]

    C. P. L. Berry and J. R. Gair,Expectations for extreme-mass-ratio bursts from the Galactic Centre, Mon. Not. Roy. Astron. Soc.435(2013) 3521 [1307.7276]

    Pith/arXiv arXiv 2013

  12. [13]

    Hopman and T

    C. Hopman and T. Alexander,The Orbital statistics of stellar inspiral and relaxation near a massive black hole: Characterizing gravitational wave sources,Astrophys. J. 629(2005) 362 [astro-ph/0503672]

    Pith/arXiv arXiv 2005

  13. [14]

    Bar-Or and T

    B. Bar-Or and T. Alexander,Steady-state Relativistic Stellar Dynamics Around a Massive Black hole, Astrophys. J.820(2016) 129 [1508.01390]

    Pith/arXiv arXiv 2016

  14. [15]

    Amaro-Seoane,Relativistic dynamics and extreme mass ratio inspirals,Living Rev

    P. Amaro-Seoane,Relativistic dynamics and extreme mass ratio inspirals,Living Rev. Rel.21(2018) 4 [1205.5240]

    Pith/arXiv arXiv 2018

  15. [16]

    Pan and H

    Z. Pan and H. Yang,Formation Rate of Extreme Mass Ratio Inspirals in Active Galactic Nuclei,Phys. Rev. D 103(2021) 103018 [2101.09146]

    Pith/arXiv arXiv 2021

  16. [17]

    B. Rom, I. Linial, K. Kaur and R. Sari,Dynamics Around Supermassive Black Holes: Extreme-mass-ratio Inspirals as Gravitational-wave Sources,Astrophys. J. 977(2024) 7 [2406.19443]

    Pith/arXiv arXiv 2024

  17. [18]

    K. Kaur, B. Rom and R. Sari,Semianalytical Fokker–Planck Models for Nuclear Star Clusters, Astrophys. J.980(2025) 150 [2406.07627]

    Pith/arXiv arXiv 2025

  18. [19]

    Alexander and C

    T. Alexander and C. Hopman,Strong mass segregation around a massive black hole,Astrophys. J.697(2009) 1861 [0808.3150]

    Pith/arXiv arXiv 2009

  19. [20]

    J. N. Bahcall and R. A. Wolf,The star distribution around a massive black hole in a globular cluster. II. Unequal star masses.,Astrophys. J.216(1977) 883

    1977

  20. [21]

    J. E. Greene, J. Strader and L. C. Ho, Intermediate-mass black holes,Annual Review of Astronomy and Astrophysics58(2020) 257–312

    2020

  21. [22]

    C. J. Burke, P. Natarajan, V. F. Baldassare and M. Geha,Multiwavelength Constraints on the Local Black Hole Occupation Fraction,Astrophys. J.978 (2025) 77 [2410.11177]

    Pith/arXiv arXiv 2025

  22. [23]

    Schodel et al.,A Star in a 15.2 year orbit around the supermassive black hole at the center of the Milky Way, Nature419(2002) 694 [astro-ph/0210426]

    R. Schodel et al.,A Star in a 15.2 year orbit around the supermassive black hole at the center of the Milky Way, Nature419(2002) 694 [astro-ph/0210426]

    Pith/arXiv arXiv 2002

  23. [24]

    A. M. Ghez et al.,Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits,Astrophys. J.689(2008) 1044 [0808.2870]

    Pith/arXiv arXiv 2008

  24. [25]

    Gillessen, P

    S. Gillessen, P. M. Plewa, F. Eisenhauer, R. Sari, I. Waisberg, M. Habibi, O. Pfuhl, E. George, J. Dexter, S. v. Fellenberg, T. Ott and R. Genzel,An update on monitoring stellar orbits in the galactic center,The Astrophysical Journal837(2017) 30

    2017

  25. [26]

    Genzel, F

    R. Genzel, F. Eisenhauer and S. Gillessen,The Galactic Center massive black hole and nuclear star cluster, 21 Reviews of Modern Physics82(2010) 3121 [1006.0064]

    Pith/arXiv arXiv 2010

  26. [27]

    Abuter et al.,First light for GRA VITY: Phase referencing optical interferometry for the Very Large Telescope Interferometer,A&A602 (2017) A94 [1705.02345]

    GRA VITY Collaboration, R. Abuter et al.,First light for GRA VITY: Phase referencing optical interferometry for the Very Large Telescope Interferometer,A&A602 (2017) A94 [1705.02345]. [28]GRA VITYCollaboration, R. Abuter et al.,Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole,Astron. Astrophys...

    Pith/arXiv arXiv 2017

  27. [29]

    Abuter et al.,Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole,A&A636 (2020) L5 [2004.07187]

    GRA VITY Collaboration, R. Abuter et al.,Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole,A&A636 (2020) L5 [2004.07187]

    Pith/arXiv arXiv 2020

  28. [30]

    GRA VITY Collaboration et al.,Improving constraints on the extended mass distribution in the Galactic Center with stellar orbits,A&A692(2024) A242 [2409.12261]

    Pith/arXiv arXiv 2024

  29. [31]

    M. S. Bordoni et al.,Impact of a granular mass distribution on the orbit of S2 in the Galactic center, Astron. Astrophys.701(2025) A89 [2507.01510]

    Pith/arXiv arXiv 2025

  30. [32]

    Preto and P

    M. Preto and P. Amaro-Seoane,On strong mass segregation around a massive black hole: Implications for lower-frequency gravitational-wave astrophysics, Astrophys. J. Lett.708(2010) L42 [0910.3206]

    Pith/arXiv arXiv 2010

  31. [33]

    Tremaine et al.,The slope of the black hole mass versus velocity dispersion correlation,Astrophys

    S. Tremaine et al.,The slope of the black hole mass versus velocity dispersion correlation,Astrophys. J.574 (2002) 740 [astro-ph/0203468]

    Pith/arXiv arXiv 2002

  32. [34]

    Kroupa,On the variation of the initial mass function,MNRAS322(2001) 231 [astro-ph/0009005]

    P. Kroupa,On the variation of the initial mass function,MNRAS322(2001) 231 [astro-ph/0009005]

    Pith/arXiv arXiv 2001

  33. [35]

    Hopman and T

    C. Hopman and T. Alexander,Resonant relaxation near a massive black hole: The stellar distribution and gravitational wave sources,The Astrophysical Journal 645(2006) 1152–1163

    2006

  34. [36]

    Miralda-Escud´ e and A

    J. Miralda-Escud´ e and A. Gould,A Cluster of Black Holes at the Galactic Center,Astrophys. J.545(2000) 847 [astro-ph/0003269]

    Pith/arXiv arXiv 2000

  35. [37]

    Freitag, P

    M. Freitag, P. Amaro-Seoane and V. Kalogera,Stellar Remnants in Galactic Nuclei: Mass Segregation, Astrophys. J.649(2006) 91 [astro-ph/0603280]

    Pith/arXiv arXiv 2006

  36. [38]

    Hopman,Extreme mass ratio inspiral rates: dependence on the massive black hole mass,Astrophys

    C. Hopman,Extreme mass ratio inspiral rates: dependence on the massive black hole mass,Astrophys. J.700(2009) 1933 [0901.1667]

    Pith/arXiv arXiv 2009

  37. [39]

    Barausse,The evolution of massive black holes and their spins in their galactic hosts,Mon

    E. Barausse,The evolution of massive black holes and their spins in their galactic hosts,Mon. Not. Roy. Astron. Soc.423(2012) 2533 [1201.5888]

    Pith/arXiv arXiv 2012

  38. [40]

    Pozzoli, S

    F. Pozzoli, S. Babak, A. Sesana, M. Bonetti and N. Karnesis,Computation of stochastic background from extreme-mass-ratio inspiral populations for LISA,Phys. Rev. D108(2023) 103039 [2302.07043]. [Erratum: Phys.Rev.D 110, 049903 (2024)]

    Pith/arXiv arXiv 2023

  39. [41]

    P. C. Peters and J. Mathews,Gravitational radiation from point masses in a Keplerian orbit,Phys. Rev.131 (1963) 435

    1963

  40. [42]

    Spitzer,Dynamical evolution of globular clusters

    L. Spitzer,Dynamical evolution of globular clusters. 1987

    1987

  41. [43]

    Binney and S

    J. Binney and S. Tremaine,Galactic Dynamics. Princeton Series in Astrophysics, 1987

    1987

  42. [44]

    Qunbar and N

    I. Qunbar and N. C. Stone,Enhanced Extreme Mass Ratio Inspiral Rates and Intermediate Mass Black Holes,Phys. Rev. Lett.133(2024) 141401 [2304.13062]

    Pith/arXiv arXiv 2024

  43. [45]

    Mancieri, L

    D. Mancieri, L. Broggi, M. Bonetti and A. Sesana, Hanging on the cliff: Extreme mass ratio inspiral formation with local two-body relaxation and post-Newtonian dynamics,Astron. Astrophys.694 (2025) A272 [2409.09122]

    Pith/arXiv arXiv 2025

  44. [46]

    E. S. Phinney,A Practical theorem on gravitational wave backgrounds,astro-ph/0108028

    Pith/arXiv arXiv

  45. [47]

    Toonen, C

    S. Toonen, C. Hopman and M. Freitag,The gravitational wave background from star-massive black hole fly-bys,Mon. Not. Roy. Astron. Soc.398(2009) 1228 [0902.3253]

    Pith/arXiv arXiv 2009

  46. [48]

    D. J. Oliver, A. D. Johnson, J. Berrier, K. Glampedakis and D. Kennefick,Gravitational wave peeps from EMRIs and their implication for LISA signal confusion noise, Class. Quant. Grav.41(2024) 115004 [2305.05793]

    Pith/arXiv arXiv 2024

  47. [49]

    A. P. Lightman and S. L. Shapiro,The distribution and consumption rate of stars around a massive, collapsed object.,Astrophys. J.211(1977) 244

    1977

  48. [50]

    Cohn and R

    H. Cohn and R. M. Kulsrud,The stellar distribution around a black hole: numerical integration of the Fokker-Planck equation.,Astrophys. J.226(1978) 1087

    1978

  49. [51]

    Hopman, M

    C. Hopman, M. Freitag and S. L. Larson,Gravitational wave bursts from the Galactic massive black hole,Mon. Not. Roy. Astron. Soc.378(2007) 129 [astro-ph/0612337]

    Pith/arXiv arXiv 2007

  50. [52]

    Thrane and J

    E. Thrane and J. D. Romano,Sensitivity curves for searches for gravitational-wave backgrounds,Phys. Rev. D88(2013) 124032 [1310.5300]

    Pith/arXiv arXiv 2013

  51. [53]

    Robson, N

    T. Robson, N. J. Cornish and C. Liu,The construction and use of LISA sensitivity curves,Class. Quantum Grav.36(2019) 105011 [1803.01944]

    Pith/arXiv arXiv 2019

  52. [54]

    M. C. Aller and D. Richstone,The Cosmic density of massive black holes from galaxy velocity dispersions, Astron. J.124(2002) 3035 [astro-ph/0210573]

    Pith/arXiv arXiv 2002

  53. [55]

    R. M. O’Leary, B. Kocsis and A. Loeb,Gravitational waves from scattering of stellar-mass black holes in galactic nuclei,Mon. Not. Roy. Astron. Soc.395(2009) 2127 [0807.2638]

    Pith/arXiv arXiv 2009

  54. [56]

    Sesana et al.,Unveiling the gravitational universe at µ-Hz frequencies,Exper

    A. Sesana et al.,Unveiling the gravitational universe at µ-Hz frequencies,Exper. Astron.51(2021) 1333 [1908.11391]

    Pith/arXiv arXiv 2021

  55. [57]

    Ni,ASTROD-GW: Overview and Progress,Int

    W.-T. Ni,ASTROD-GW: Overview and Progress,Int. J. Mod. Phys. D22(2013) 1341004 [1212.2816]

    Pith/arXiv arXiv 2013

  56. [58]

    Amaro-Seoane and M

    P. Amaro-Seoane and M. Preto,The impact of realistic models of mass segregation on the event rate of extreme-mass ratio inspirals and cusp re-growth,Class. Quant. Grav.28(2011) 094017 [1010.5781]

    Pith/arXiv arXiv 2011

  57. [59]

    Emami and A

    R. Emami and A. Loeb,Detectability of gravitational waves from a population of inspiralling black holes in Milky Way-mass galaxies,Mon. Not. Roy. Astron. Soc. 502(2021) 3932 [1903.02579]

    arXiv 2021

  58. [60]

    Emami and A

    R. Emami and A. Loeb,Observational signatures of the black hole mass distribution in the galactic center, JCAP02(2020) 021 [1903.02578]

    arXiv 2020

  59. [61]

    Maggiore,Gravitational Waves

    M. Maggiore,Gravitational Waves. Vol. 1: Theory and Experiments. Oxford University Press, 2007, 10.1093/acprof:oso/9780198570745.001.0001

    arXiv 2007

  60. [62]

    Barack and C

    L. Barack and C. Cutler,Confusion noise from LISA capture sources,Phys. Rev. D70(2004) 122002 [gr-qc/0409010]

    Pith/arXiv arXiv 2004

  61. [63]

    K. A. E. Dayem et al.,Discovery of a star sensitive to the spin of Sgr A*,2607.12664. [64]EPTA, InPTACollaboration, J. Antoniadis et al.,The second data release from the European Pulsar Timing Array - IV. Implications for massive black holes, dark matter, and the early Universe,Astron. Astrophys.685 (2024) A94 [2306.16227]. [65]NANOGravCollaboration, G. A...

    Pith/arXiv arXiv 2024

  62. [66]

    Sato-Polito, M

    G. Sato-Polito, M. Zaldarriaga and E. Quataert,Where are the supermassive black holes measured by PTAs?, Phys. Rev. D110(2024) 063020 [2312.06756]

    Pith/arXiv arXiv 2024

  63. [67]

    Goncharov et al.,Reading signatures of supermassive binary black holes in pulsar timing array observations, Nature Commun.16(2025) 9692 [2409.03627]

    B. Goncharov et al.,Reading signatures of supermassive binary black holes in pulsar timing array observations, Nature Commun.16(2025) 9692 [2409.03627]

    arXiv 2025

  64. [68]

    Sesana and D

    A. Sesana and D. G. Figueroa,Nanohertz Gravitational Waves,2512.18822

    arXiv

  65. [69]

    Linial and R

    I. Linial and R. Sari,Stellar distributions around a supermassive black hole: Strong-segregation regime revisited,The Astrophysical Journal940(2022) 101

    2022