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)