DOI: 10.5281/zenodo.18471816
title: Supermassive black holes swallow stellar objects at high rates: the data and code

description: The data files and code in this repository are associated with the work at https://arxiv.org/abs/2602.15929, a work completed in collaboration with Joseph Silk.

 

Abbreviations:



BH: black hole

SMBH: supermassive black hole

NSC: nuclear star cluster

TDE: tidal disruption event

MS: main sequence

WD: white dwarf

NS: neutron star

GW: gravitational wave

SNR: signal-to-noise ratio

SAMS: zero-age main-sequence


 

Data Files:



cluster_M*_t*_g1.5_G2.0_a0.5_R0_r0_N0_l0.08_u150.0_V265_Z0.002_s1.npz: snapshot of the NSC for central SMBH mass $M=10^5, 10^6, 10^7\,M_\odot$ at time $t=10^0, 10^1, 10^2, 10^3, 10^4\,\rm Myr$. Keys:



type: stellar type (integer value; see below)

m_star: stellar object mass (solar masses)

r_star: stellar object radius (solar radii)

L_star: stellar object luminosity (solar luminosities)

T_eff: effective surface stellar temperature (Kelvin)

M_core: stellar core mass (Msun)

M_env: stellar envelope mass (Msun)

S: stellar global spin

r: stellar radius from the center of the NSC (pc)

E: energy

L: angular momentum

a: semimajor axis (pc)

e: eccentricity

P: period (Myr)

t_R: relaxation time (Myr)

r_t: tidal radius (pc)

r_brem: gravitational bremsstrahlung radius (pc)

r_mb: marginally bound radius (gravitational radii of SMBH)

r_lc: loss-cone radius (pc)

phi: orbital inclination relative to SMBH's spin orientation

theta_lc: loss-cone angle (radians)

thetaD_plunge: diffusion angle for plunge/capture (radians)

thetaD_inspiral: diffusion angle for inspiral (radians)

beta: encounter strength parameter

r_p: orbital pericenter with SMBH (pc)

r_a: orbital apocenter with SMBH (pc)

v_p: pericentric velocity (km/s)

t_p: pericenter timescale (Myr)

t_I: stellar internal timescale (Myr)

v_star: stellar current velocity magnitude (km/s)

R_elc: empty-loss-cone rates (/Myr)

Rflc_plunge: full-loss-cone capture rates (/Myr)

Rflc_inspiral: fill-loss-cone inspiral rates (/Myr)

Rlc_plunge: loss-cone capture rates (/Myr)

Rlc_inspiral: loss-cone inspiral rates (/Myr)

t_gw: gravitational-wave inspiral timescale (Myr)

t_AP: general-relativistic apsidal-precession timescale (Myr)

t_MP: mass-precession timescale (Myr)

t_coh: coherence timescale (Myr)

t_RR: resonant-relaxation timescale (Myr)

t_NRR: non-resonant-relaxation timescale (Myr)

t_fb: fallback timescale of each possible TDE (Myr)

eta_R: TDE radiative efficiency

t: current time (Myr)

M_BH: SMBH mass (Msun)

a_BH: SMBH dimensional spin parameter

gamma_light: light component cusp power law

gamma_heavy: heavy compotent cusp power law

m_lower: lower ZAMS mass (Msun)

m_upper: heavier ZAMS mass (Msun)

Z: absolute metallicity

seed: seed integer number

r_min_light: minimum radius of light component (pc)

r_min_heavy: minimum radius of heavy component (pc)

r_infl: radius of influence (pc)

N_star: number of stars

N_star_original:

N_NS: number of neutron stars

N_BH: number of stellar-mass black holes

velo_disp: velocity dispersion (km/s)

v_esc: escape velocity (km/s)

psi: multimass relaxation factor

m_avg: average stellar mass (Msun)

lnL: Coulomb logarithm of the system

MS: main sequence mask

giant: giant mask

core: core mask

WD: WD mask

NS: NS mask

BH: BH mask

t12MS_subset: half-life decay timescale (days) of TDE flare for a subset of 10^4 MS stars

LpkMS_subset: peak luminosity (erg/s) of TDE flare for the subset of 10^4 MS stars

mS_subset: masses (Msun) in the subset of the 10^4 MS stars

rS_subset: radii (Rsun) in the subset of the 10^4 MS stars

Rlc_plunge_MS: number loss-cone capture rate per unit star for MSs

Rlc_plunge_giant: number loss-cone capture rate per unit star for giants

Rlc_plunge_core: number loss-cone capture rate per unit star for cores

Rlc_plunge_WD: number loss-cone capture rate per unit star for WDs

Rlc_plunge_NS: number loss-cone capture rate per unit star for NSs

Rlc_plunge_BH: number loss-cone capture rate per unit star for BHs

Rlc_inspiral_MS:  number loss-cone inspiral rate per unit star for MSs

Rlc_inspiral_giant: number loss-cone inspiral rate per unit star for giants

Rlc_inspiral_core: number loss-cone inspiral rate per unit star for cores

Rlc_inspiral_WD: number loss-cone inspiral rate per unit star for WDs

Rlc_inspiral_NS: number loss-cone inspiral rate per unit star for NSs

Rlc_inspiral_BH: number loss-cone inspiral rate per unit star for BHs

Mlc_plunge_MS: mass loss-cone capture rate per unit star for MSs

Mlc_plunge_giant: mass loss-cone capture rate per unit star for giants

Mlc_plunge_core: mass loss-cone capture rate per unit star for cores

Mlc_plunge_WD: mass loss-cone capture rate per unit star for WDs

Mlc_plunge_NS: mass loss-cone capture rate per unit star for NSs

Mlc_plunge_BH: mass loss-cone capture rate per unit star for BHs

Mlc_inspiral_MS: mass loss-cone inspiral rate per unit star for MSs

Mlc_inspiral_giant: mass loss-cone inspiral rate per unit star for giants

Mlc_inspiral_core: mass loss-cone inspiral rate per unit star for cores

Mlc_inspiral_WD: mass loss-cone inspiral rate per unit star for WDs

Mlc_inspiral_NS: mass loss-cone inspiral rate per unit star for NSs

Mlc_inspiral_BH: mass loss-cone inspiral rate per unit star for BHs

Dlc_plunge_MS: capture duty cycle per unit star for MSs

Dlc_plunge_giant: capture duty cycle per unit star for giants

Dlc_plunge_core: capture duty cycle per unit star for cores

Dlc_plunge_WD: capture duty cycle per unit star for WDs

Dlc_plunge_NS: capture duty cycle per unit star for NSs

Dlc_plunge_BH: capture duty cycle per unit star for BHs

Dlc_inspiral_MS: inspiral duty cycle per unit star for MSs

Dlc_inspiral_giant: inspiral duty cycle per unit star for giants

Dlc_inspiral_core: inspiral duty cycle per unit star for cores

Dlc_inspiral_WD: inspiral duty cycle per unit star for WDs

Dlc_inspiral_NS: inspiral duty cycle per unit star for NSs

Dlc_inspiral_BH: inspiral duty cycle per unit star for BHs



Lpkt12MSsubset_M*_t*_g1.5_G2.0_a0.5_R0_r0_N0_l0.08_u150.0_V265_Z0.002_s1.npz: Keys:



Lpk: Peak luminosities in erg/s

t12: half-life of flare emission in days

mS: MS star mass in solar masses

rS: MS star radius in solar radii



RMDlc_M*_g1.5_G2.0_a0.5_R0_r0_N0_l0.08_u150.0_V265_Z0.002.npz: Keys:



Rlc_plunge_MS: mean plunge number rate of MS stars

dRlc_plunge_MS: standard deviation of the plunge number rate of MS stars

Rlc_inspiral_MS: mean inspiral number rate of MS stars

dRlc_inspiral_MS: standard deviation of the inspiral number rate of MS stars

Rlc_plunge_giant: mean plunge number rate of giant stars

dRlc_plunge_giant: standard deviation of the plunge number rate of giant stars

Rlc_inspiral_giant: mean inspiral number rate of giant stars

dRlc_inspiral_giant: standard deviation of the inspiral number rate of giant stars

Rlc_plunge_WD: mean plunge number rate of WD stars

dRlc_plunge_WD: standard deviation of the plunge number rate of WD stars

Rlc_inspiral_WD: mean inspiral number rate of WD stars

dRlc_inspiral_WD: standard deviation of the inspiral number rate of WD stars

Rlc_plunge_NS: mean plunge number rate of NSs

dRlc_plunge_NS: standard deviation of the plunge number rate of NSs

Rlc_inspiral_NS: mean inspiral number rate of NSs

dRlc_inspiral_NS: standard deviation of the inspiral number rate of NSs

Rlc_plunge_BH: mean plunge number rate of BHs

dRlc_plunge_BH: standard deviation of the plunge number rate of BHs

Rlc_inspiral_BH: mean inspiral number rate of BHs

dRlc_inspiral_BH: standard deviation of the inspiral number rate of BHs

Mlc_plunge_MS: mean plunge-mass accretion rate of MS stars

dMlc_plunge_MS: standard deviation of the plunge-mass accretion rate of MS stars

Mlc_inspiral_MS: mean inspiral-mass accretion rate of MS stars

dMlc_inspiral_MS: standard deviation of the inspiral-mass accretion rate of MS stars

Mlc_plunge_giant: mean plunge-mass accretion rate of giant stars

dMlc_plunge_giant: standard deviation of the plunge-mass accretion rate of giant stars

Mlc_inspiral_giant: mean inspiral-mass accretion rate of giant stars

dMlc_inspiral_giant: standard deviation of the inspiral-mass accretion rate of giant stars

Mlc_plunge_WD: mean plunge-mass accretion rate of WD stars

dMlc_plunge_WD: standard deviation of the plunge-mass accretion rate of WD stars

Mlc_inspiral_WD: mean inspiral-mass accretion rate of WD stars

dMlc_inspiral_WD: standard deviation of the inspiral-mass accretion rate of WD stars

Mlc_plunge_NS: mean plunge-mass accretion rate of NSs

dMlc_plunge_NS: standard deviation of the plunge-mass accretion rate of NSs

Mlc_inspiral_NS: mean inspiral-mass accretion rate of NSs

dMlc_inspiral_NS: standard deviation of the inspiral-mass accretion rate of NSs

Mlc_plunge_BH: mean plunge-mass accretion rate of BHs

dMlc_plunge_BH: standard deviation of the plunge-mass accretion rate of BHs

Mlc_inspiral_BH: mean inspiral-mass accretion rate of BHs

dMlc_inspiral_BH: standard deviation of the inspiral-mass accretion rate of BHs

Dlc_plunge_MS: mean plunge duty cycle of MS stars

dDlc_plunge_MS: standard deviation of the plunge duty cycle of MS stars

Dlc_inspiral_MS: mean inspiral duty cycle of MS stars

dDlc_inspiral_MS: standard deviation of the inspiral duty cycle of MS stars

Dlc_plunge_giant: mean plunge duty cycle of giant stars

dDlc_plunge_giant: standard deviation of the plunge duty cycle of giant stars

Dlc_inspiral_giant: mean inspiral duty cycle of giant stars

dDlc_inspiral_giant: standard deviation of the inspiral duty cycle of giant stars

Dlc_plunge_WD: mean plunge duty cycle of WD stars

dDlc_plunge_WD: standard deviation of the plunge duty cycle of WD stars

Dlc_inspiral_WD: mean inspiral duty cycle of WD stars

dDlc_inspiral_WD: standard deviation of the inspiral duty cycle of WD stars

Dlc_plunge_NS: mean plunge duty cycle of NSs

dDlc_plunge_NS: standard deviation of the plunge duty cycle of NSs

Dlc_inspiral_NS: mean inspiral duty cycle of NSs

dDlc_inspiral_NS: standard deviation of the inspiral duty cycle of NSs

Dlc_plunge_BH: mean plunge duty cycle of BHs

dDlc_plunge_BH: standard deviation of the plunge duty cycle of BHs

Dlc_inspiral_BH: mean inspiral duty cycle of BHs

dDlc_inspiral_BH: standard deviation of the inspiral duty cycle of BHs



GW-*_M*_*_g1.5_G2.0_a0.5_R0_r0_N0_l0.08_u150.0_V265_Z0.002_s1.npz: Keys:



f_0: initial GW frequency of each bound captured pair

e_0: initial eccentricity of each bound captured pair

f_EMRI: initial frequency of each inspiral

e_EMRI: initial eccentricity of each inspiral

m: secondary's mass (solar masses)

R: secondary's radius (pc)

v: secondary's velocity at infinity (km/s)

prograde: it is True if orbital angular momentum points in the direction of SMBH's spin, else it is False

x: maximum between the radius of the compact object and the marginally-bound radius of the SMBH, normalized to the gravitational radius of the system

z: redshift of the event

f: observer-frame GW frequency bins (Hz)

h_plunge: characteristic GW strain for all captures in a subset over the frequency bins f, including 100 harmonics

h_inspiral: characteristic GW strain for all EMRIs in a subset over the frequency bins f, including 100 harmonics

t_plunge: time for merger in a captured pair

Rlc_plunge: loss-cone rate for captures

Rlc_inspiral: loss-cone rate for EMRIs

M_BH: mass of the SMBH

N_true: true number of compact objects

N_used: subset of at most 1000 randomly-sampled compact objects

V: effective comoving volume accounting for time delays (Mpc^3)

n: number density of SMBHs (Mpc^-3)

N_plunge_Tobs: intrinsic number of captures in observation time Tobs

N_inspiral_Tobs: intrinsic number of EMRIs in observation time Tobs

h_plunge_z10: characteristic GW strain for all captures in a subset over the frequency bins f, including 100 harmonics, at redshift z=10

h_inspiral_z10: characteristic GW strain for all EMRIs in a subset over the frequency bins f, including 100 harmonics, at redshift z=10

SNR_plunge_LISA: SNR of each capture in LISA

SNR_inspiral_LISA: SNR of each inspiral in LISA

SNR_plunge_LGWA: SNR of each capture in LGWA

SNR_inspiral_LGWA: SNR of each inpsiral in LGWA

fdet_plunge_LISA_SNR10: fraction of captures with a LISA-SNR>10

fdet_inspiral_LISA_SNR10: fraction of inspirals with a LISA-SNR>10

fdet_plunge_LGWA_SNR10: fraction of captures with a LGWA-SNR>10

fdet_inspiral_LGWA_SNR10: fraction of inspirals with a LGWA-SNR>10




 

Code Files:



module.py: contains all imports, constants, and functions used to create the NSC snapshot.

main.py: accepts user inputs, calls routines from the module, and exports the NSC snapshot in the cluster*.npz file.

postanalysis.py: calculates mean rates and standard deviations over different realizations, the properties of MS TDEs, and exports the Lpkt*.npz and RMDlc*.npz files.

gravitational_waves.py: computes the GW strain for plunges and inspirals of all compact objects as well as the SNRs for LISA, and exports the GW*.npz files.


 

Important Note:

Some snapshot files were used in the post-analysis but were not uploaded to this dataset due to storage limitations. Please contact Konstantinos Kritos, the creator and owner of this repository, to get access to all data files.