Supermassive black holes swallow stellar objects at high rates: the data and code

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.