mcfacts.physics.lum

Module for calculating bolometric luminosities from a merger remnant interacting with gas via shocks or jets.

mcfacts.physics.lum.jet_luminosity(mass_final, bin_orb_a, disk_density, spin_final, v_kick, disk_sound_speed)

Estimate the jet luminosity produced by Bondi-Hoyle-Lyttleton (BHL) accretion.

Based on Graham et al. (2020), the luminosity goes as:

L_BHL ≈ 2.5e45 erg s -1 * (eta / 0.1) * (M / 100 M_sun)**2 * (v_kick / 200 km/s)-3 * (rho / 1e-9 g/cm^3)

where eta is the radiation efficiency, which is well modeled as eta ~ a**2, where a is the spin of the remnant BH (Tagawa et al. (2023)), M is the mass of the remnant black hole, v_kick is the kick velocity imparted to the remannt upon merger, and rho is the local gas density of the AGN accretion disk.

Parameters:

mass_finalnumpy.ndarray

mass of remnant post-merger (mass loss accounted for via Tichy & Maronetti 08)

bin_orb_anumpy.ndarray

Distance between the SMBH and the binary at the time of merger (in gravitational radii).

disk_densitycallable

Function that returns the gas density at a given radius (in [kg m**-3]).

spin_finalnumpy.ndarray

Spin of the remnant black hole. Unitless.

v_kicknumpy.ndarray

Kick velocity imparted to the remnant (in [km s**-1]).

disk_sound_speedcallable

Function that returns the disk sound speed at a given radius (in [m s**-1]).

Returns:

LBHLnumpy.ndarray

Estimated jet luminosity (in [erg s**-1]).

mcfacts.physics.lum.shock_luminosity(smbh_mass, mass_final, bin_orb_a, disk_aspect_ratio, disk_density, v_kick)

Estimate the shock luminosity from the interaction between a merger remnant and gas within its Hill sphere.

Based on McKernan et al. (2019) (arXiv:1907.03746v2), this function computes: - The Hill radius of the remnant system. - The local height of the disk. - The gas volume inside the Hill sphere. - The mass of gas inside the remnant’s Hill sphere. - The energy and timescale over which energy is dissipated into the disk.

The shock luminosity is given by:

L_shock ≈ E / t,

where

E = 1e47 erg * (M_gas / M_sun) * (v_kick / 200 km/s)^2 t ~ R_Hill / v_kick

Parameters:

smbh_massfloat

Mass of the supermassive black hole (in solar masses).

mass_finalnumpy.ndarray

Final mass of the binary black hole remnant (in solar masses).

bin_orb_anumpy.ndarray

Distance between the SMBH and the binary at the time of merger (in gravitational radii).

disk_aspect_ratiocallable

Function that returns the aspect ratio (height/radius) of the disk at a given radius.

disk_densitycallable

Function that returns the gas density at a given radius (in [kg m**-3]).

v_kicknumpy.ndarray

Kick velocity imparted to the remnant (in [km s**-1]).

Returns:

L_shockfloat

Shock luminosity (in [erg s**-1]).