DOI: 10.5281/zenodo.17882704
title: Eccentricity distribution of extreme mass ratio inspirals

description: This dataset provides eccentricity distributions for extreme mass ratio inspirals around non-spinning massive black holes. It includes distributions both at decoupling from the host nuclear star cluster and at the final plunge, evaluated for five different central black hole masses.

Contents

The zip file contains a folder with five CSV files within, each corresponding to a different central massive black hole (MBH) mass (in solar masses). The secondary mass is fixed at 10 M_sun. All files share the following columns:



p0 [Rg]  — semi-latus rectum (in units of the MBH gravitational radius) at decoupling from the nuclear star cluster

e0          — eccentricity at decoupling

ppl [Rg] — semi-latus rectum at plunge (where FEW stops)

epl         — eccentricity at plunge (where FEW stops)

weight   — astrophysical weight of each run (weights in each file sum to 1)


Methods Overview

This is a short overview of the methods used to generate these data. Further details are provided in the companion papers (Mancieri+25b [arXiv:2509.02394] and Mancieri+25a [A&A 694, A272; arXiv:2409.09122])

The initial EMRI population is taken from the Monte Carlo simulations of Mancieri et al. 2025a (A&A 694, A272; arXiv:2409.09122). In those simulations, EMRIs are followed until they reach the point where they are decoupled from the nuclear star cluster and gravitational wave (GW) emission only determines their evolution. This is defined by the condition on the GW emission timescale

    t_GW = 10^-3 * t_rlx ,

where t_rlx is the angular-momentum relaxation time due to two-body interactions in the nuclear star cluster. Parameters (p0, e0) in the dataset generally represent the EMRIs at the moment of decoupling. However, a subset of EMRIs, primarily in the high MBH mass models, had to be terminated before this condition was reached for computational cost reasons (see Sect. 3.4 of Mancieri+25a). When the condition t_GW = 10^-3 * t_rlx could not be satisfied, the parameters (p0, e0) were recorded at a stage where 10^-3 < t_GW / t_rlx < 1. In this interval, relaxation is already subdominant, although its residual influence may slightly perturb the parameters at full decoupling relative to those that would be obtained in an integration neglecting relaxation entirely.

From these initial conditions, each EMRI is evolved to plunge (ppl, epl) using the FastEMRIWaveforms (FEW) package (v2.0.0). The evolution is performed in two stages:



PN5 module for the early inspiral, used until the orbit reaches e = 0.8–0.9 (the limiting value depends on p).

KerrEccEqFlux module from that point down to plunge. At the time these data were produced, this module is only valid below e = 0.8–0.9.


The integration stops when the Schwarzschild separatrix is reached,

    p_sep = 6 + 2*e ,

but FEW returns the last point slightly before the separatrix, such that

    ppl - (6 + 2*epl) = 2*10^-3 .

A small fraction (the tail at e > 0.82 in Fig. 5 of Mancieri+25b) of EMRIs plunge before entering the domain of validity of the KerrEccEqFlux module; in that case, the final point satisfies

    ppl - (6 + 2*epl) = 10^-1 .

Astrophysical Weights

Each EMRI carries a weight representing its expected contribution to the astrophysical EMRI population. The weight depends on the initial semi-major axis a_i used in the Monte Carlo simulations of Mancieri et al. 2025a (A&A 694, A272; arXiv:2409.09122).

Two competing effects shape the EMRI formation rate as a function of a_i:



relaxation more efficiently scatters compact objects close to the MBH at large semi-major axes,

but objects on wide, very eccentric orbits tend to directly plunge rather than form long-lived EMRIs.


Together, these effects produce a peak EMRI formation rate around a_i = 10^-2 R_inf (where R_inf is the MBH influence radius). Because a different number of simulations n_i were performed at each a_i, the final weight for each run is

    w_i = (1 / n_i) * <dot{N}_i> / ( sum_j <dot{N}_j> ) ,

where <dot{N}_i> is the time-averaged EMRI production rate at that a_i.

References

Please cite the companion papers and the dataset itself if you use it

Title: Eccentricity distribution of extreme mass ratio inspirals  Authors: Davide Mancieri, Luca Broggi, Morgan Vinciguerra, Alberto Sesana, Matteo Bonetti  DOI: https://doi.org/10.48550/arXiv.2509.02394

Title: Hanging on the cliff: Extreme mass ratio inspiral formation with local two-body relaxation and post-Newtonian dynamics  Authors: Davide Mancieri, Luca Broggi, Matteo Bonetti, Alberto Sesana  DOI: https://doi.org/10.1051/0004-6361/202452306

 

Contact: d.mancieri@campus.unimib.it