def calc_polar_roots(aa, slr, ecc, x, digits):
"""
Compute polar roots.
Parameters:
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
zp (mpf): polar root
zm (mpf): polar root
"""
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
zp, zm = polar_roots(En, Lz, aa, slr, x)
return zp, zm
finally:
mp.prec = prec
def calc_radial_roots(aa, slr, ecc, x, digits):
"""
Compute radial roots.
Parameters:
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
r1 (mpf): apastron
r2 (mpf): periastron
r3 (mpf): radial root 3
r4 (mpf): radial root 4
"""
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
r1, r2, r3, r4 = radial_roots(En, Q, aa, slr, ecc)
return r1, r2, r3, r4
finally:
mp.prec = prec
def calc_consts(aa, slr, ecc, x, digits):
"""
Compute adiabatic constants.
Parameters:
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
En (mpf): energy
Lz (mpf): angular momentum
Q (mpf): Carter constant
"""
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
return En, Lz, Q
finally:
mp.prec = prec
def calc_mino_freqs(aa, slr, ecc, x, digits, M=1):
"""
Compute Mino frequencies.
Parameters:
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
ups_r (mpf): radial Mino frequency
ups_theta (mpf): polar Mino frequency
ups_phi (mpf): azimuthal Mino frequency
gamma (mpf): temporal Mino frequency
"""
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
r1, r2, r3, r4 = radial_roots(En, Q, aa, slr, ecc, M)
ups_r, ups_theta, ups_phi, gamma = mino_freqs(
r1, r2, r3, r4, En, Lz, Q, aa, slr, ecc, x
)
return ups_r, ups_theta, ups_phi, gamma
finally:
mp.prec = prec
def mino_coords(mino_t, aa, slr, ecc, x, digits):
"""
Compute coordinates of the orbit given two angles psi and chi.
Parameters:
mino_t (float): mino time coordinate lambda
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
t (mpf): time coordinate
r (mpf): radial coordinate
theta (mpf): theta coordinate
phi (mpf): phi coordinate
"""
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
mino_t = mpf(str(mino_t))
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
r1, r2, r3, r4 = radial_roots(En, Q, aa, slr, ecc, M=1)
zp, zm = polar_roots(En, Lz, aa, slr, x)
ups_r, ups_theta, ups_phi, gamma = mino_freqs(
r1, r2, r3, r4, En, Lz, Q, aa, slr, ecc, x
)
t, r, theta, phi = calc_gen_coords_mino(
mino_t,
ups_r,
ups_theta,
ups_phi,
gamma,
r1,
r2,
r3,
r4,
zp,
zm,
En,
Lz,
Q,
aa,
)
return t, r, theta, phi
finally:
mp.prec = prec
def coordinates(psi, aa, slr, ecc, x, digits):
"""
Compute coordinates of the orbit given two angles psi and chi.
Parameters:
psi (float): radial angle
chi (float): polar angle
aa (float): SMBH spin
slr (float): semi-latus rectum
ecc (float): eccentricity
x (float): cos of the inclination
digits (int): number of digits of accuracy requested
Returns:
t (mpf): time coordinate
r (mpf): radial coordinate
theta (mpf): theta coordinate
phi (mpf): phi coordinate
"""
if x ** 2 == 1:
chi = 0 # equatorial orbits don't need chi
try:
mp.dps = digits
prec = mp.prec
mp.prec += 30
psi = mpf(str(psi))
# chi = mpf(str(chi))
aa = mpf(str(aa))
slr = mpf(str(slr))
ecc = mpf(str(ecc))
x = mpf(str(x))
En, Lz, Q = calc_constants(aa, slr, ecc, x)
r1, r2, r3, r4 = radial_roots(En, Q, aa, slr, ecc, M=1)
zp, zm = polar_roots(En, Lz, aa, slr, x)
ups_r, ups_theta, ups_phi, gamma = mino_freqs(
r1, r2, r3, r4, En, Lz, Q, aa, slr, ecc, x
)
print(psi)
# print(chi)
t, r, theta, phi = calc_coords(
psi,
# chi,
ups_r,
ups_theta,
ups_phi,
gamma,
r1,
r2,
r3,
r4,
zp,
zm,
En,
Lz,
Q,
aa,
slr,
ecc,
x,
)
return t, r, theta, phi
finally:
mp.prec = prec