def hfpc(f,
Mc,
eta,
chi1z,
chi2z,
DL,
tc,
phic,
iota,
lam_t,
delta_lam_t,
is_lam12=0):
'''
Mc ... in solar mass
DL ... in mega parsec
'''
# convert to sec
Mc = Mc * time_fac
DL = DL * time_fac / strain_fac
# get sym and asym chi combinations
chi_s = brs.chi_s(chi1z, chi2z)
chi_a = brs.chi_a(chi1z, chi2z)
if is_lam12:
# in this case: lam_t = lam1, delta_lam_t = lam2
lam1 = lam_t
lam2 = delta_lam_t
delta = sqrt(1 - 4 * eta)
lam_t = 8. / 13. * ((1. + 7. * eta - 31. * eta**2) *
(lam1 + lam2) + delta *
(1. + 9. * eta - 11. * eta**2) * (lam1 - lam2))
delta_lam_t = 0.5 * (
delta * (1319. - 13272. * eta + 8944. * eta**2) / 1319. *
(lam1 + lam2) +
(1319. - 15910. * eta + 32850. * eta**2 + 3380. * eta**3) / 1319. *
(lam1 - lam2))
'''
Mc is in sec, e.g., Mc = 10*MTSUN_SI (for 10 solar mass)
DL is in sec, e.g., DL = 100*1e6*PC_SI/C_SI (for 100 Mpc)
'''
M = Mc / eta**(3. / 5.)
delta = (1. - 4. * eta)**0.5
v = (PI * M * f)**(1. / 3.)
flso = brs.f_isco(M)
vlso = (PI * M * flso)**(1. / 3.)
A = ((5. / 24.)**0.5 / PI**(2. / 3.)) * (Mc**(5. / 6.) / DL)
# 3.5PN phasing (point particle limit)
p0 = 1.
p1 = 0
p2 = (3715. / 756. + (55. * eta) / 9.)
p3 = (-16. * PI + (113. * delta * chi_a) / 3. + (113. / 3. -
(76. * eta) / 3.) * chi_s)
p4 = (15293365. / 508032. + (27145. * eta) / 504. +
(3085. * eta**2) / 72. + (-405. / 8. + 200. * eta) * chi_a**2 -
(405. * delta * chi_a * chi_s) / 4. + (-405. / 8. +
(5. * eta) / 2.) * chi_s**2)
gamma = (732985. / 2268. - 24260. * eta / 81. - 340. * eta**2 /
9.) * chi_s + (732985. / 2268. + 140. * eta / 9.) * delta * chi_a
p5 = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma)
p5L = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma) * 3 * log(
v / vlso)
p6 = (11583231236531./4694215680. - 640./3.*PI**2 - 6848./21.*GammaE + eta*(-15737765635./3048192. + 2255./12.*PI**2) + eta*eta*76055./1728. - eta*eta*eta*127825./1296. \
- (6848./21.)*log(4.) + PI*(2270.*delta*chi_a/3. + (2270./3. - 520.*eta)*chi_s) + (75515./144. - 8225.*eta/18.)*delta*chi_a*chi_s \
+ (75515./288. - 263245.*eta/252. - 480.*eta**2)*chi_a**2 + (75515./288. - 232415.*eta/504. + 1255.*eta**2/9.)*chi_s**2)
p6L = -(6848. / 21.) * log(v)
p7 = (((77096675. * PI) / 254016. + (378515. * PI * eta) / 1512. -
(74045. * PI * eta**2) / 756. +
(-25150083775. / 3048192. + (10566655595. * eta) / 762048. -
(1042165. * eta**2) / 3024. + (5345. * eta**3) / 36. +
(14585. / 8. - 7270. * eta + 80. * eta**2) * chi_a**2) * chi_s +
(14585. / 24. - (475. * eta) / 6. +
(100. * eta**2) / 3.) * chi_s**3 + delta *
((-25150083775. / 3048192. + (26804935. * eta) / 6048. -
(1985. * eta**2) / 48.) * chi_a +
(14585. / 24. - 2380. * eta) * chi_a**3 +
(14585. / 8. - (215. * eta) / 2.) * chi_a * chi_s**2)))
phase = 2 * f * PI * tc - phic - PI / 4. + (3. / (128. * v**5 * eta)) * (
p0 + v * p1 + v**2 * p2 + v**3 * p3 + v**4 * p4 + v**5 *
(p5 + p5L) + v**6 * (p6 + p6L) + v**7 * p7)
# From Lesli Wade's paper ... adding the tidal deformability phase
pT = (3. / 128. / eta /
v**5.) * (-39. * lam_t * v**10 / 2. +
(-3115. * lam_t / 64. + 6595. *
(1 - 4 * eta)**0.5 * delta_lam_t / 364.) * v**12)
phase += pT
hp = 0.5 * (1 + (cos(iota))**2) * A * f**(-7. / 6.) * (cos(phase) -
1j * sin(phase))
hc = -1j * cos(iota) * A * f**(-7. / 6.) * (cos(phase) - 1j * sin(phase))
return hp, hc
def hfpc(f, Mc, eta, chi1z, chi2z, DL, tc, phic, iota, Heff5, Heff8, e0):
'''
Mc ... in solar mass
DL ... in mega parsec
'''
# convert to sec
Mc = Mc * time_fac
DL = DL * time_fac / strain_fac
# get sym and asym chi combinations
chi_s = brs.chi_s(chi1z, chi2z)
chi_a = brs.chi_a(chi1z, chi2z)
'''
Mc is in sec, e.g., Mc = 10*MTSUN_SI (for 10 solar mass)
DL is in sec, e.g., DL = 100*1e6*PC_SI/C_SI (for 100 Mpc)
'''
M = Mc / eta**(3. / 5.)
delta = (1. - 4. * eta)**0.5
v = (PI * M * f)**(1. / 3.)
flso = brs.f_isco(M)
vlso = (PI * M * flso)**(1. / 3.)
f0 = 10.
fbyf0 = f / f0
A = ((5. / 24.)**0.5 / PI**(2. / 3.)) * (Mc**(5. / 6.) / DL)
# 3.5PN phasing (point particle limit)
p0 = 1. - (2355. / 1462.) * e0**2. * fbyf0**(-19. / 9.)
p1 = 0
p2 = (3715. / 756. + (55. * eta) / 9.)
p3 = (-16. * PI + (113. * delta * chi_a) / 3. + (113. / 3. -
(76. * eta) / 3.) * chi_s)
p4 = (15293365. / 508032. + (27145. * eta) / 504. +
(3085. * eta**2) / 72. + (-405. / 8. + 200. * eta) * chi_a**2 -
(405. * delta * chi_a * chi_s) / 4. + (-405. / 8. +
(5. * eta) / 2.) * chi_s**2)
gamma = (732985. / 2268. - 24260. * eta / 81. - 340. * eta**2 /
9.) * chi_s + (732985. / 2268. + 140. * eta / 9.) * delta * chi_a
p5 = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma)
p5L = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma) * 3 * log(
v / vlso)
p6 = (11583231236531./4694215680. - 640./3.*PI**2 - 6848./21.*GammaE + eta*(-15737765635./3048192. + 2255./12.*PI**2) + eta*eta*76055./1728. - eta*eta*eta*127825./1296. \
- (6848./21.)*log(4.) + PI*(2270.*delta*chi_a/3. + (2270./3. - 520.*eta)*chi_s) + (75515./144. - 8225.*eta/18.)*delta*chi_a*chi_s \
+ (75515./288. - 263245.*eta/252. - 480.*eta**2)*chi_a**2 + (75515./288. - 232415.*eta/504. + 1255.*eta**2/9.)*chi_s**2)
p6L = -(6848. / 21.) * log(v)
p7 = (((77096675. * PI) / 254016. + (378515. * PI * eta) / 1512. -
(74045. * PI * eta**2) / 756. +
(-25150083775. / 3048192. + (10566655595. * eta) / 762048. -
(1042165. * eta**2) / 3024. + (5345. * eta**3) / 36. +
(14585. / 8. - 7270. * eta + 80. * eta**2) * chi_a**2) * chi_s +
(14585. / 24. - (475. * eta) / 6. +
(100. * eta**2) / 3.) * chi_s**3 + delta *
((-25150083775. / 3048192. + (26804935. * eta) / 6048. -
(1985. * eta**2) / 48.) * chi_a +
(14585. / 24. - 2380. * eta) * chi_a**3 +
(14585. / 8. - (215. * eta) / 2.) * chi_a * chi_s**2)))
phase = 2 * f * PI * tc - phic - PI / 4. + (3. / (128. * v**5 * eta)) * (
p0 + v * p1 + v**2 * p2 + v**3 * p3 + v**4 * p4 + v**5 *
(p5 + p5L) + v**6 * (p6 + p6L) + v**7 * p7)
#phase due to tidal heating
#--------------------------------------------------------------------------------
psi_so1 = (1 / 6.) * (-56 * eta - 73 * np.sqrt(1 - 4 * eta) + 73) * chi1z
psi_so2 = (1 / 6.) * (-56 * eta - 73 * np.sqrt(1 - 4 * eta) + 73) * chi2z
psi_so = psi_so1 + psi_so2
con = (3. / 128. * eta) / v**5
term1 = -(10 / 9.) * (v**5) * Heff5 * (3 * np.log(v) + 1)
term2 = -(5 / 168.) * (v**7) * Heff5 * (952 * eta + 995)
term3 = (5 / 9.) * (v**8) * (3 * np.log(v) - 1) * (-4 * Heff8 +
Heff5 * psi_so)
heated_phase = con * (term1 + term2 + term3)
phase += heated_phase
hp = 0.5 * (1 + (cos(iota))**2) * A * f**(-7. / 6.) * (cos(phase) -
1j * sin(phase))
hc = -1j * cos(iota) * A * f**(-7. / 6.) * (cos(phase) - 1j * sin(phase))
return hp, hc