Angular sizes

bh_angular_sizes.py

#!/usr/bin/env python

import numpy as np
from astropy import units as u
from astropy import constants as const

@u.quantity_input # input validation decorator

def photon_ring_angular_size(mass: u.Msun, dist: u.pc):

    r_g = const.G * mass / const.c**2 #  event horizon radius for a Schwarzschild (i.e., a=0) black hole
    
    # For Kerr BH, photon ring has diameter (approx): 
    l = 10.4 * r_g # Johannsen & Psaltis 2010, basically independent of spin/inclination
    
    # small angle approx, so it's just theta_ring = l / dist 
    angular_size = (l / dist).to(u.microarcsecond,equivalencies=u.dimensionless_angles())
    
    return np.round(angular_size,2)

sgrA_bh_dist = 8178 * u.pc # GRAVITY collab 2019 distance to Sgr A* is 8178 \pm 13(stat.) \pm 22(sys.) pc
sgrA_bh_mass = 4.154 * 1e6 * u.Msun # GRAVITY collab 2019 down-sampled mass is (4.154\pm0.014) x 10^6 Msol

m87_bh_dist = 16.8 * 1e6 * u.pc # EHT2019 adopted M87* dist is 16.8 \pm 0.8 Mpc
m87_bh_mass = 6.5 * 1e9 * u.Msun # EHT2019 adopted M87* mass is (6.5\pm0.7) x 10^9 Msol

print(f'Sgr A* Photon Ring angular size is {photon_ring_angular_size(sgrA_bh_mass, sgrA_bh_dist)}')
print(f'M87* Photon Ring angular size is {photon_ring_angular_size(m87_bh_mass, m87_bh_dist)}')
print(f"In other words, while Sgr A* is {np.round(m87_bh_dist / sgrA_bh_dist, 2)} times closer to Earth than the black hole in M87, its event horizon is {np.round(m87_bh_mass / sgrA_bh_mass)} times smaller, and so the two black holes subtend almost the same angular size on the sky. ")