def HS2011_Omega_SO_3p5PN_pt6(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-(8 / m1 + 9 * m2 / (2 * m1**2)) * dot(n12U, p1U) +
(59 / (4 * m1) + 27 / (2 * m2)) * dot(n12U, p2U)) *
cross(p1U, p2U)[i]) / r12**3
return Omega1
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_H_SS_2PN(m1,m2, S1U,S2U, nU, q):
S0U = ixp.zerorank1()
for i in range(3):
S0U[i] = (1 + m2/m1)*S1U[i] + (1 + m1/m2)*S2U[i]
global H_SS_2PN
mu = m1*m2 / (m1 + m2)
H_SS_2PN = mu/(m1 + m2) * (3*dot(S0U,nU)**2 - dot(S0U,S0U)) / (2*q**3)
def HS2011_Omega_SO_3p5PN_pt3(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-9*dot(n12U,p1U)*dot(p1U,p1U)/(16*m1**4)
+dot(p1U,p1U)*dot(n12U,p2U)/(m1**3*m2)
+27*dot(n12U,p1U)*dot(n12U,p2U)**2/(16*m1**2*m2**2)
-dot(n12U,p2U)*dot(p1U,p2U)/(8*m1**2*m2**2)
-5*dot(n12U,p1U)*dot(p2U,p2U)/(16*m1**2*m2**2))*cross(p1U,p2U)[i])/r12**2
return Omega1
def f_H_SO_1p5PN(m1,m2, n12U,n21U, S1U, S2U, p1U,p2U, r12):
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
global H_SO_1p5PN
Omega1 = f_Omega1(m1,m2, n12U, p1U,p2U, r12)
Omega2 = f_Omega1(m2,m1, n21U, p2U,p1U, r12)
H_SO_1p5PN = dot(Omega1,S1U) + dot(Omega2,S2U)
def HS2011_Omega_SO_3p5PN_pt4(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-3*m2*dot(n12U,p1U)**2/(2*m1**2)
+((-3*m2)/(2*m1**2) + 27*m2**2/(8*m1**3))*dot(p1U,p1U)
+(177/(16*m1) + 11/m2)*dot(n12U,p2U)**2
+(11/(2*m1) + 9*m2/(2*m1**2))*dot(n12U,p1U)*dot(n12U,p2U)
+(23/(4*m1) + 9*m2/(2*m1**2))*dot(p1U,p2U)
-(159/(16*m1) + 37/(8*m2))*dot(p2U,p2U))*cross(n12U,p1U)[i])/r12**3
return Omega1
def HS2011_Omega_SO_3p5PN_pt5(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(+4*dot(n12U,p1U)**2/m1
+13*dot(p1U,p1U)/(2*m1)
+5*dot(n12U,p2U)**2/m2
+53*dot(p2U,p2U)/(8*m2)
-(211/(8*m1) + 22/m2)*dot(n12U,p1U)*dot(n12U,p2U)
-(47/(8*m1) + 5/m2)*dot(p1U,p2U))*cross(n12U,p2U)[i])/r12**3
return Omega1
def f_H_SO_2p5PN(m1, m2, n12U, n21U, S1U, S2U, p1U, p2U, r12):
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
Omega1_2p5PNU = f_Omega_SO_2p5PN(m1, m2, n12U, p1U, p2U, r12)
Omega2_2p5PNU = f_Omega_SO_2p5PN(m2, m1, n21U, p2U, p1U, r12)
global H_SO_2p5PN
H_SO_2p5PN = dot(Omega1_2p5PNU, S1U) + dot(Omega2_2p5PNU, S2U)
def f_H_SO_3p5PN(m1,m2, n12U,n21U, S1U, S2U, p1U,p2U, r12):
Omega1_3p5PNU = ixp.zerorank1()
Omega2_3p5PNU = ixp.zerorank1()
for i in range(3):
Omega1_3p5PNU[i] = HS2011_Omega_SO_3p5PN_pt1(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt2(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt3(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt4(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt5(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt6(m1,m2, n12U, p1U,p2U, r12)[i]
Omega1_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt7(m1,m2, n12U, p1U,p2U, r12)[i]
Omega2_3p5PNU[i] = HS2011_Omega_SO_3p5PN_pt1(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt2(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt3(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt4(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt5(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt6(m2,m1, n21U, p2U,p1U, r12)[i]
Omega2_3p5PNU[i]+= HS2011_Omega_SO_3p5PN_pt7(m2,m1, n21U, p2U,p1U, r12)[i]
global H_SO_3p5PN
H_SO_3p5PN = dot(Omega1_3p5PNU,S1U) + dot(Omega2_3p5PNU,S2U)
def HS2011_Omega_SO_3p5PN_pt1(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (
(+7 * m2 * dot(p1U, p1U)**2 / (16 * m1**5) +
9 * dot(n12U, p1U) * dot(n12U, p2U) * dot(p1U, p1U) /
(16 * m1**4) + 3 * dot(p1U, p1U) * dot(n12U, p2U)**2 /
(4 * m1**3 * m2) + 45 * dot(n12U, p1U) * dot(n12U, p2U)**3 /
(16 * m1**2 * m2**2) + 9 * dot(p1U, p1U) * dot(p1U, p2U) /
(16 * m1**4) - 3 * dot(n12U, p2U)**2 * dot(p1U, p2U) /
(16 * m1**2 * m2**2) - 3 * dot(p1U, p1U) * dot(p2U, p2U) /
(16 * m1**3 * m2) -
15 * dot(n12U, p1U) * dot(n12U, p2U) * dot(p2U, p2U) /
(16 * m1**2 * m2**2) + 3 * dot(n12U, p2U)**2 * dot(p2U, p2U) /
(4 * m1 * m2**3) - 3 * dot(p1U, p2U) * dot(p2U, p2U) /
(16 * m1**2 * m2**2) - 3 * dot(p2U, p2U)**2 /
(16 * m1 * m2**3)) * cross(n12U, p1U)[i]) / r12**2
return Omega1
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 HS2011_Omega_SO_3p5PN_pt2(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (
+(-3 * dot(n12U, p1U) * dot(n12U, p2U) * dot(p1U, p1U) /
(2 * m1**3 * m2) - 15 * dot(n12U, p1U)**2 * dot(n12U, p2U)**2 /
(4 * m1**2 * m2**2) + 3 * dot(p1U, p1U) * dot(n12U, p2U)**2 /
(4 * m1**2 * m2**2) - dot(p1U, p1U) * dot(p1U, p2U) /
(2 * m1**3 * m2) + dot(p1U, p2U)**2 /
(2 * m1**2 * m2**2) + 3 * dot(n12U, p1U)**2 * dot(p2U, p2U) /
(4 * m1**2 * m2**2) - dot(p1U, p1U) * dot(p2U, p2U) /
(4 * m1**2 * m2**2) -
3 * dot(n12U, p1U) * dot(n12U, p2U) * dot(p2U, p2U) /
(2 * m1 * m2**3) - dot(p1U, p2U) * dot(p2U, p2U) /
(2 * m1 * m2**3)) * cross(n12U, 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_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_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)
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_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
