def f_H_SS_S1S2_3PN(m1, m2, n12U, S1U, S2U, p1U, p2U, r12):
global H_SS_S1S2_3PN
H_SS_S1S2_3PN = (
+div(3, 2) *
(dot(cross(p1U, S1U), n12U) * dot(cross(p2U, S2U), n12U)) + 6 *
(dot(cross(p2U, S1U), n12U) * dot(cross(p1U, S2U), n12U)) -
15 * dot(S1U, n12U) * dot(S2U, n12U) * dot(p1U, n12U) * dot(p2U, n12U)
- 3 * dot(S1U, n12U) * dot(S2U, n12U) * dot(p1U, p2U) +
3 * dot(S1U, p2U) * dot(S2U, n12U) * dot(p1U, n12U) +
3 * dot(S2U, p1U) * dot(S1U, n12U) * dot(p2U, n12U) +
3 * dot(S1U, p1U) * dot(S2U, n12U) * dot(p2U, n12U) +
3 * dot(S2U, p2U) * dot(S1U, n12U) * dot(p1U, n12U) - div(1, 2) *
dot(S1U, p2U) * dot(S2U, p1U) + dot(S1U, p1U) * dot(S2U, p2U) -
3 * dot(S1U, S2U) * dot(p1U, n12U) * dot(p2U, n12U) +
div(1, 2) * dot(S1U, S2U) * dot(p1U, p2U)) / (2 * m1 * m2 * r12**3)
H_SS_S1S2_3PN += (-dot(cross(p1U, S1U), n12U) * dot(cross(p1U, S2U), n12U)
+ dot(S1U, S2U) * dot(p1U, n12U)**2 -
dot(S1U, n12U) * dot(S2U, p1U) * dot(p1U, n12U)) * 3 / (
2 * m1**2 * r12**3)
H_SS_S1S2_3PN += (-dot(cross(p2U, S2U), n12U) * dot(cross(p2U, S1U), n12U)
+ dot(S1U, S2U) * dot(p2U, n12U)**2 -
dot(S2U, n12U) * dot(S1U, p1U) * dot(p2U, n12U)) * 3 / (
2 * m2**2 * r12**3)
H_SS_S1S2_3PN += (+dot(S1U, S2U) - 2 * dot(S1U, n12U) *
dot(S2U, n12U)) * 6 * (m1 + m2) / r12**4
def dE_GW_dt_OBKPSS2015_consts(m1, m2, _n12U, S1U, S2U): # _n12U unused.
# define scalars:
m = (m1 + m2)
nu = m1 * m2 / m**2
delta = (m1 - m2) / m
# define vectors:
Stot = ixp.zerorank1()
Sigma = ixp.zerorank1()
l = ixp.zerorank1()
l[2] = sp.sympify(1)
chi1U = ixp.zerorank1()
chi2U = ixp.zerorank1()
chi_s = ixp.zerorank1()
chi_a = ixp.zerorank1()
for i in range(3):
Stot[i] = S1U[i] + S2U[i]
Sigma[i] = (m1 + m2) / m2 * S2U[i] - (m1 + m2) / m1 * S1U[i]
chi1U[i] = S1U[i] / m1**2
chi2U[i] = S2U[i] / m2**2
chi_s[i] = div(1, 2) * (chi1U[i] + chi2U[i])
chi_a[i] = div(1, 2) * (chi1U[i] - chi2U[i])
# define scalars that depend on vectors
s_l = dot(Stot, l) / m**2
# s_n = dot(Stot,n12U)/m**2
sigma_l = dot(Sigma, l) / m**2
# sigma_n = dot(Sigma,n12U)/m**2
return nu, delta, l, chi_a, chi_s, s_l, sigma_l
def f_MOmega(m1,m2, chi1U,chi2U, r):
a = ixp.zerorank1(DIM=10)
MOmega__a_2_thru_a_4(m1,m2, chi1U[0],chi1U[1],chi1U[2], chi2U[0],chi2U[1],chi2U[2])
a[2] = a_2
a[3] = a_3
a[4] = a_4
MOmega__a_5_thru_a_6(m1,m2, chi1U[0],chi1U[1],chi1U[2], chi2U[0],chi2U[1],chi2U[2])
a[5] = a_5
a[6] = a_6
MOmega__a_7( m1,m2, chi1U[0],chi1U[1],chi1U[2], chi2U[0],chi2U[1],chi2U[2])
a[7] = a_7
global MOmega
MOmega = 1 # Term prior to the sum in parentheses
for k in range(8):
MOmega += a[k]/r**div(k,2)
MOmega *= 1/r**div(3,2)
def f_p_r(m1, m2, n12U, n21U, chi1U, chi2U, S1U, S2U, p1U, p2U, r):
q = m2 / m1 # It is assumed that q >= 1, so m2 >= m1.
f_Htot_xyplane_binary(m1, m2, n12U, n21U, S1U, S2U, p1U, p2U, r)
f_dr_dt(Htot_xyplane_binary, m1, m2, n12U, chi1U, chi2U, S1U, S2U, r)
chi1x = chi1U[0]
chi1y = chi1U[1]
chi1z = chi1U[2]
chi2x = chi2U[0]
chi2y = chi2U[1]
chi2z = chi2U[2]
p_r_num = (-dr_dt +
(-(6 * q + 13) * q**2 * chi1x * chi2y / (4 * (q + 1)**4) -
(6 * q + 1) * q**2 * chi2x * chi2y / (4 * (q + 1)**4) + chi1y *
(-q * (q + 6) * chi1x / (4 * (q + 1)**4) - q *
(13 * q + 6) * chi2x / (4 * (q + 1)**4))) / r**div(7, 2) +
(+chi1z *
(+3 * q * (5 * q + 2) * chi1x * chi2y /
(2 * (q + 1)**4) - 3 * q**2 * (2 * q + 5) * chi2x * chi2y /
(2 * (q + 1)**4)) + chi1y * chi2z *
(+3 * q**2 * (2 * q + 5) * chi2x / (2 * (q + 1)**4) - 3 * q *
(5 * q + 2) * chi1x / (2 * (q + 1)**4))) / r**4)
p_r_den = (
-(q + 1)**2 / q - (-7 * q**2 - 15 * q - 7) / (2 * q * r) -
(47 * q**4 + 229 * q**3 + 363 * q**2 + 229 * q + 47) /
(8 * q * (q + 1)**2 * r**2) -
(+(4 * q**2 + 11 * q + 12) * chi1z / (4 * q * (q + 1)) +
(12 * q**2 + 11 * q + 4) * chi2z / (4 * (q + 1))) / r**div(5, 2) -
(+(-53 * q**5 - 357 * q**4 - 1097 * q**3 - 1486 * q**2 - 842 * q - 144)
* chi1z / (16 * q * (q + 1)**4) +
(-144 * q**5 - 842 * q**4 - 1486 * q**3 - 1097 * q**2 - 357 * q - 53)
* chi2z / (16 * (q + 1)**4)) / r**div(7, 2) -
(+(q**2 + 9 * q + 9) * chi1x**2 / (2 * q * (q + 1)**2) +
(3 * q**2 + 5 * q + 3) * chi2x * chi1x / ((q + 1)**2) +
(3 * q**2 + 8 * q + 3) * chi1y * chi2y /
(2 * (q + 1)**2) - 9 * q**2 * chi2y**2 / (4 * (q + 1)) +
(3 * q**2 + 8 * q + 3) * chi1z * chi2z /
(2 * (q + 1)**2) - 9 * q**2 * chi2z**2 / (4 * (q + 1)) +
(9 * q**3 + 9 * q**2 + q) * chi2x**2 / (2 * (q + 1)**2) +
(-363 * q**6 - 2608 * q**5 - 7324 * q**4 - 10161 * q**3 -
7324 * q**2 - 2608 * q - 363) / (48 * q *
(q + 1)**4) - 9 * chi1y**2 /
(4 * q * (q + 1)) - 9 * chi1z**2 / (4 * q *
(q + 1)) - sp.pi**2 / 16) / r**3)
global p_r
p_r = p_r_num / p_r_den
def f_H_SS_particle(m1,m2, n12U, S1U,_S2U, p1U,p2U, r12): # _S2U unused.
H_SS_S1sq_S2sq_3PN_particle = (
+ m2/(4*m1**3)*dot(p1U,S1U)**2
+3*m2/(8*m1**3)*dot(p1U,n12U)**2*dot(S1U,S1U)
-3*m2/(8*m1**3)*dot(p1U,p1U)*dot(S1U,n12U)**2
-3*m2/(4*m1**3)*dot(p1U,n12U)*dot(S1U,n12U)*dot(p1U,S1U)
-3/(4*m1*m2)*dot(p2U,p2U)*dot(S1U,S1U)
+9/(4*m1*m2)*dot(p2U,p2U)*dot(S1U,n12U)**2
+3/(4*m1**2)*dot(p1U,p2U)*dot(S1U,S1U)
-9/(4*m1**2)*dot(p1U,p2U)*dot(S1U,n12U)**2
-3/(2*m1**2)*dot(p1U,n12U)*dot(p2U,S1U)*dot(S1U,n12U)
+3/(m1**2) *dot(p2U,n12U)*dot(p1U,S1U)*dot(S1U,n12U)
+3/(4*m1**2)*dot(p1U,n12U)*dot(p2U,n12U)*dot(S1U,S1U)
-15/(4*m1**2)*dot(p1U,n12U)*dot(p2U,n12U)*dot(S1U,n12U)**2)/r12**3
H_SS_S1sq_S2sq_3PN_particle+= -(+div(9,2)*dot(S1U,n12U)**2
-div(5,2)*dot(S1U,S1U)
+7*m2/m1*dot(S1U,n12U)**2
-3*m2/m1*dot(S1U,S1U))*m2/r12**4
return H_SS_S1sq_S2sq_3PN_particle
def f_p_t(m1, m2, chi1U, chi2U, r):
q = m2 / m1 # It is assumed that q >= 1, so m2 >= m1.
a = ixp.zerorank1(DIM=10)
p_t__a_2_thru_a_4(m1, m2, chi1U[0], chi1U[1], chi1U[2], chi2U[0], chi2U[1],
chi2U[2])
a[2] = a_2
a[3] = a_3
a[4] = a_4
p_t__a_5_thru_a_6(m1, m2, chi1U[0], chi1U[1], chi1U[2], chi2U[0], chi2U[1],
chi2U[2])
a[5] = a_5
a[6] = a_6
p_t__a_7(m1, m2, chi1U[0], chi1U[1], chi1U[2], chi2U[0], chi2U[1],
chi2U[2])
a[7] = a_7
global p_t
p_t = 1 # Term prior to the sum in parentheses
for k in range(8):
p_t += a[k] / r**div(k, 2)
p_t *= q / (1 + q)**2 * 1 / r**div(1, 2)
def f_Omega_SO_2p5PN(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(+(-div(11, 2) * m2 - 5 * m2 ** 2 / m1) * cross(n12U, p1U)[i]
+ (6 * m1 + div(15, 2) * m2) * cross(n12U, p2U)[i]) / r12 ** 3
+ (+(-div(5, 8) * m2 * dot(p1U, p1U) / m1 ** 3
- div(3, 4) * dot(p1U, p2U) / m1 ** 2
+ div(3, 4) * dot(p2U, p2U) / (m1 * m2)
- div(3, 4) * dot(n12U, p1U) * dot(n12U, p2U) / m1 ** 2
- div(3, 2) * dot(n12U, p2U) ** 2 / (m1 * m2)) * cross(n12U, p1U)[i]
+ (dot(p1U, p2U) / (m1 * m2) + 3 * dot(n12U, p1U) * dot(n12U, p2U) / (m1 * m2)) *
cross(n12U, p2U)[i]
+ (div(3, 4) * dot(n12U, p1U) / m1 ** 2 - 2 * dot(n12U, p2U) / (m1 * m2)) * cross(p1U, p2U)[
i]) / r12 ** 2)
return Omega1
def f_H_SSS_3PN_pt(m1,m2, nU, S1U,S2U, p1U,p2U, r):
p2_minus_m2_over_4m1_p1 = ixp.zerorank1()
for i in range(3):
p2_minus_m2_over_4m1_p1[i] = p2U[i] - m2/(4*m1)*p1U[i]
H_SSS_3PN_pt = (+div(3,2)*(+dot(S1U,S1U)*dot(S2U,cross(nU,p1U))
+dot(S1U,nU)*dot(S2U,cross(S1U,p1U))
-5*dot(S1U,nU)**2*dot(S2U,cross(nU,p1U))
+dot(nU,cross(S1U,S2U))*(+dot(S1U,p1U)
-5*dot(S1U,nU)*dot(p1U,nU)))
-3*m1/(2*m2)*( +dot(S1U,S1U) *dot(S2U,cross(nU,p2U))
+2*dot(S1U,nU) *dot(S2U,cross(S1U,p2U))
-5*dot(S1U,nU)**2*dot(S2U,cross(nU,p2U)))
-dot(cross(S1U,nU),p2_minus_m2_over_4m1_p1)*(dot(S1U,S1U) - 5*dot(S1U,nU)**2))/(m1**2*r**4)
return H_SSS_3PN_pt
def f_H_Newt__H_NS_1PN__H_NS_2PN(m1,m2, PU, nU, q):
mu = m1*m2 / (m1+m2)
eta = m1*m2 / (m1+m2)**2
pU = ixp.zerorank1()
for i in range(3):
pU[i] = PU[i]/mu
global H_Newt, H_NS_1PN, H_NS_2PN
H_Newt = mu*(+div(1,2)*dot(pU,pU) - 1/q)
H_NS_1PN = mu*(+div(1,8)*(3*eta-1)*dot(pU,pU)**2
-div(1,2)*((3+eta)*dot(pU,pU) + eta*dot(nU,pU)**2)/q
+div(1,2)/q**2)
H_NS_2PN = mu*(+div(1,16)*(1 - 5*eta + 5*eta**2)*dot(pU,pU)**3
+div(1,8)*(+(5 - 20*eta - 3*eta**2)*dot(pU,pU)**2
-2*eta**2*dot(nU,pU)**2*dot(pU,pU)
-3*eta**2*dot(nU,pU)**4)/q
+div(1,2)*((5+8*eta)*dot(pU,pU) + 3*eta*dot(nU,pU)**2)/q**2
-div(1,4)*(1+3*eta)/q**3)
def f_compute_quantities(mOmega, m1, m2, n12U, S1U, S2U, which_quantity):
if not which_quantity in ('dM_dt', 'dE_GW_dt', 'dE_GW_dt_plus_dM_dt'):
print("which_quantity == " + str(which_quantity) +
" not supported!")
sys.exit(1)
nu, delta, l, chi_a, chi_s, s_l, sigma_l = dE_GW_dt_OBKPSS2015_consts(
m1, m2, n12U, S1U, S2U)
x = (mOmega)**div(2, 3)
# Compute b_5_Mdot:
b_5_Mdot = (-div(1, 4) *
(+(1 - 3 * nu) * dot(chi_s, l) *
(1 + 3 * dot(chi_s, l)**2 + 9 * dot(chi_a, l)**2) +
(1 - nu) * delta * dot(chi_a, l) *
(1 + 3 * dot(chi_a, l)**2 + 9 * dot(chi_s, l)**2)))
if which_quantity == "dM_dt":
return div(32, 5) * nu**2 * x**5 * b_5_Mdot * x**div(5, 2)
b = ixp.zerorank1(DIM=10)
b[2] = -div(1247, 336) - div(35, 12) * nu
b[3] = +4 * sp.pi - 4 * s_l - div(5, 4) * delta * sigma_l
b[4] = (-div(44711, 9072) + div(9271, 504) * nu + div(65, 18) * nu**2 +
(+div(287, 96) + div(1, 24) * nu) * dot(chi_s, l)**2 -
(+div(89, 96) + div(7, 24) * nu) * dot(chi_s, chi_s) +
(+div(287, 96) - 12 * nu) * dot(chi_a, l)**2 +
(-div(89, 96) + 4 * nu) * dot(chi_a, chi_a) +
div(287, 48) * delta * dot(chi_s, l) * dot(chi_a, l) -
div(89, 48) * delta * dot(chi_s, chi_a))
b[5] = (-div(8191, 672) * sp.pi - div(9, 2) * s_l -
div(13, 16) * delta * sigma_l + nu *
(-div(583, 24) * sp.pi + div(272, 9) * s_l +
div(43, 4) * delta * sigma_l))
if which_quantity == "dE_GW_dt_plus_dM_dt":
b[5] += b_5_Mdot
b[6] = (+div(6643739519, 69854400) + div(16, 3) * sp.pi**2 -
div(1712, 105) * gamma_EulerMascheroni -
div(856, 105) * sp.log(16 * x) +
(-div(134543, 7776) + div(41, 48) * sp.pi**2) * nu -
div(94403, 3024) * nu**2 - div(775, 324) * nu**3 -
16 * sp.pi * s_l - div(31, 6) * sp.pi * delta * sigma_l)
b[7] = (
+(+div(476645, 6804) + div(6172, 189) * nu - div(2810, 27) * nu**2)
* s_l +
(+div(9535, 336) + div(1849, 126) * nu - div(1501, 36) * nu**2) *
delta * sigma_l + (-div(16285, 504) + div(214745, 1728) * nu +
div(193385, 3024) * nu**2) * sp.pi)
b[8] = (+(-div(3485, 96) * sp.pi + div(13879, 72) * sp.pi * nu) * s_l +
(-div(7163, 672) * sp.pi + div(130583, 2016) * sp.pi * nu) *
delta * sigma_l)
b_sum = sp.sympify(1)
for k in range(9):
b_sum += b[k] * x**div(k, 2)
return div(32, 5) * nu**2 * x**5 * b_sum
def f_Omega1(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (div(3, 2) * m2 / m1 * cross(n12U, p1U)[i] -
2 * cross(n12U, p2U)[i]) / r12**2
return Omega1
def f_H_NS_3PN(m1,m2, PU, nU, q):
mu = m1*m2 / (m1+m2)
eta = m1*m2 / (m1+m2)**2
pU = ixp.zerorank1()
for i in range(3):
pU[i] = PU[i]/mu
global H_NS_3PN
H_NS_3PN = mu*(+div(1,128)*(-5 + 35*eta - 70*eta**2 + 35*eta**3)*dot(pU,pU)**4
+div(1, 16)*(+(-7 + 42*eta - 53*eta**2 - 5*eta**3)*dot(pU,pU)**3
+(2-3*eta)*eta**2*dot(nU,pU)**2*dot(pU,pU)**2
+3*(1-eta)*eta**2*dot(nU,pU)**4*dot(pU,pU) - 5*eta**3*dot(nU,pU)**6)/q
+(+div(1,16)*(-27 + 136*eta + 109*eta**2)*dot(pU,pU)**2
+div(1,16)*(+17 + 30*eta)*eta*dot(nU,pU)**2*dot(pU,pU)
+div(1,12)*(+ 5 + 43*eta)*eta*dot(nU,pU)**4)/q**2
+(+(-div(25, 8) + (div(1,64)*sp.pi**2 - div(335,48))*eta - div(23,8)*eta**2)*dot(pU,pU)
+(-div(85,16) - div(3,64)*sp.pi**2 - div(7,4)*eta)*eta*dot(nU,pU)**2)/q**3
+(+div(1,8)+(div(109,12) - div(21,32)*sp.pi**2)*eta)/q**4)
