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newFactorizedWaveformPrec.c
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/**
* Writer: Xiaolin.liu
*
* This module contains basic functions for calculation.
* Functions list:
* Kernel:
* 20xx.xx.xx, LOC
**/
#include "newFactorizedWaveformPrec.h"
#include "myLog.h"
#include "pHamiltonian.h"
#include "pFactorizedWaveform.h"
#include <gsl/gsl_sf_gamma.h>
/**
* This function calculates coefficients for hlm mode factorized-resummed waveform.
* The coefficients are pre-computed and stored in the SpinEOBParams structure.
* Eq. 17 and the entire Appendix of PRD 86, 024011 (2012) + changes
* described in the section "Factorized waveforms" of https://dcc.ligo.org/T1400476
*/
int
EccPrec_CalcSpinPrecFacWaveformCoefficients(
FacWaveformCoeffs * const coeffs, /**< OUTPUT, pre-computed waveform coefficients */
const REAL8 m1, /**< mass 1 */
const REAL8 m2, /**< mass 2 */
const REAL8 eta, /**< symmetric mass ratio */
const REAL8 tmpa, /**< Kerr spin parameter for test-particle terms */
const REAL8 chiS,
const REAL8 chiA,
const REAL8 csx, /**< (chi1+chi2)/2 */
const REAL8 csy,
const REAL8 csz,
const REAL8 cax, /**< (chi1-chi2)/2 */
const REAL8 cay,
const REAL8 caz,
UINT SpinAlignedEOBversion /**< 1 for SEOBNRv1; 2 for SEOBNRv2; 4 for the coefficients
in the flux of v4P and v4Pwave for the coefficients in the waveform of v4P */
)
{
// int debugPK = 0;
// if (debugPK) {
// XLAL_PRINT_INFO("In XLALSimIMREOBCalcSpinPrecFacWaveformCoefficients: Renewing hlm coefficients.\n");
// XLAL_PRINT_INFO("PK:: chiS = %.12e, chiA = %.12e, a = %.12e (UNUSED), EOBVERSION = %d\n",
// chiS, chiA, tmpa, SpinAlignedEOBversion);
// }
REAL8 a = tmpa;
INT waveform = 0;
REAL8 eta2 = eta * eta;
REAL8 eta3 = eta2 * eta;
if (SpinAlignedEOBversion == 451) {
SpinAlignedEOBversion = 4;
waveform = 1;
}
//RC: Here I am taking care of the fact that the flux used to calibrate SEOBNRv4 is missing some terms
//in the 21 mode that I have added later in SEOBNRv4HM. For this reason when computing the Coefficients
//for the 21 mode one has to specify if they are needed for the flux or for the waveform.
REAL8 dM , dM2, chiA2, chiS2;
//dM3;
REAL8 aDelta , a2, a3;
/* Combination which appears a lot */
REAL8 m1Plus3eta, m1Plus3eta2;
REAL8 m1Plus3eta3;
dM2 = 1. - 4. * eta;
// REAL8 chiA = caz;
// REAL8 chiS = csz;
chiA2 = chiA*chiA;
chiS2 = chiS*chiS;
REAL8 chiS3 = chiS2*chiS;
REAL8 chiA3 = chiA2*chiA;
//XLAL_PRINT_INFO("****************************** a = %e *********************************\n", a);
/* Check that deltaM has a reasonable value */
if (dM2 < 0)
{
PRINT_LOG_INFO(LOG_CRITICAL, "eta seems to be > 0.25 - this isn't allowed!");
return CEV_FAILURE;
}
dM = sqrt(dM2);
if (m1 < m2)
{
dM = -dM;
}
//dM3 = dM2 * dM;
aDelta = 0.;
//a value in delta_lm is 0 in both SEOBNRv1 and SEOBNRv2
a2 = a * a;
a3 = a2 * a;
m1Plus3eta = -1. + 3. * eta;
m1Plus3eta2 = m1Plus3eta * m1Plus3eta;
m1Plus3eta3 = m1Plus3eta * m1Plus3eta2;
/* Initialize all coefficients to zero */
/* This is important, as we will not set some if dM is zero */
memset(coeffs, 0, sizeof(FacWaveformCoeffs));
/*
* l = 2, Eqs. A8a and A8b for rho, Eq. A15a for f, Eqs. 20 and 21 of
* DIN and Eqs. 27a and 27b of PBFRT for delta as well as eqns 28-29 of PBFRT
*/
coeffs->delta22vh3 = 7. / 3.;
coeffs->delta22vh6 = (-4. * aDelta) / 3. + (428. * CST_PI) / 105.;
if (SpinAlignedEOBversion == 4)
{
coeffs->delta22vh6 =
-4. / 3. * (dM * chiA + chiS * (1 - 2 * eta)) +
(428. * CST_PI) / 105.;
}
coeffs->delta22v8 = (20. * aDelta) / 63.;
coeffs->delta22vh9 = -2203. / 81. + (1712. * CST_PI * CST_PI) / 315.;
coeffs->delta22v5 = -24. * eta;
coeffs->delta22v6 = 0.0;
if (SpinAlignedEOBversion == 2 && chiS + chiA * dM / (1. - 2. * eta) > 0.) {
coeffs->delta22v6 = -540. * eta * (chiS + chiA * dM / (1. - 2. * eta));
// double chi = (chiS + chiA * dM / (1. - 2. * eta));
// coeffs->delta22v6 = eta*(1./4.*(1. - 1080.*chi - sqrt((1. - 1080.*chi)*(1. - 1080*chi) + 8.*(13.5 +270.*chi +13.5*chi*chi))));
}
if (SpinAlignedEOBversion == 3 /*&& chiS + chiA * dM / (1. - 2. * eta) > 0.*/) {
// coeffs->delta22v6 = -540. * eta * (chiS + chiA * dM / (1. - 2. * eta));
double chi = (chiS + chiA * dM / (1. - 2. * eta));
coeffs->delta22v6 = eta*(1./4.*(1. - 1080.*chi - sqrt((1. - 1080.*chi)*(1. - 1080*chi) + 8.*(13.5 +270.*chi +13.5*chi*chi))));
}
coeffs->rho22v2 = -43. / 42. + (55. * eta) / 84.;
coeffs->rho22v3 = (-2. * (chiS + chiA * dM - chiS * eta)) / 3.;
switch (SpinAlignedEOBversion) {
case 1:
coeffs->rho22v4 = -20555. / 10584. + 0.5 * a2
- (33025. * eta) / 21168. + (19583. * eta2) / 42336.;
break;
case 2:
coeffs->rho22v4 = -20555. / 10584. + 0.5 * (chiS + chiA * dM) * (chiS + chiA * dM)
- (33025. * eta) / 21168. + (19583. * eta2) / 42336.;
break;
case 3:
coeffs->rho22v4 = -20555. / 10584. + 0.5 * (chiS + chiA * dM) * (chiS + chiA * dM)
- (33025. * eta) / 21168. + (19583. * eta2) / 42336.;
break;
case 4:
coeffs->rho22v4 =
-20555. / 10584. + 0.5 * (chiS + chiA * dM) * (chiS + chiA * dM) -
(33025. * eta) / 21168. + (19583. * eta2) / 42336.;
break;
default:
PRINT_LOG_INFO(LOG_CRITICAL, "wrong SpinAlignedEOBversion value, must be 1, 2 or 3!");
return CEV_FAILURE;
break;
}
coeffs->rho22v5 = (-34. * a) / 21.;
if (SpinAlignedEOBversion == 4)
{
coeffs->rho22v5 =
(-34. / 21. + 49. * eta / 18. + 209. * eta2 / 126.) * chiS +
(-34. / 21. - 19. * eta / 42.) * dM * chiA;
}
coeffs->rho22v6 = 1556919113. / 122245200. + (89. * a2) / 252. - (48993925. * eta) / 9779616.
- (6292061. * eta2) / 3259872. + (10620745. * eta3) / 39118464.
+ (41. * eta * CST_PI * CST_PI) / 192.;
coeffs->rho22v6l = -428. / 105.;
coeffs->rho22v7 = (18733. * a) / 15876. + a * a2 / 3.;
if (SpinAlignedEOBversion == 4)
{
coeffs->rho22v7 =
a3 / 3. + chiA * dM * (18733. / 15876. + (50140. * eta) / 3969. +
(97865. * eta2) / 63504.) +
chiS * (18733. / 15876. + (74749. * eta) / 5292. -
(245717. * eta2) / 63504. + (50803. * eta3) / 63504.);
}
switch (SpinAlignedEOBversion) {
case 1:
coeffs->rho22v8 = eta * (-5.6 - 117.6 * eta) - 387216563023. / 160190110080. + (18353. * a2) / 21168. - a2 * a2 / 8.;
break;
case 2:
coeffs->rho22v8 = -387216563023. / 160190110080. + (18353. * a2) / 21168. - a2 * a2 / 8.;
break;
case 3:
coeffs->rho22v8 = -387216563023. / 160190110080. + (18353. * a2) / 21168. - a2 * a2 / 8.;
break;
case 4:
coeffs->rho22v8 =
-387216563023. / 160190110080. + (18353. * a2) / 21168. -
a2 * a2 / 8.;
break;
default:
PRINT_LOG_INFO(LOG_CRITICAL, "wrong SpinAlignedEOBversion value, must be 1, 2 or 3!");
return CEV_FAILURE;
break;
}
coeffs->rho22v8l = 9202. / 2205.;
coeffs->rho22v10 = -16094530514677. / 533967033600.;
coeffs->rho22v10l = 439877. / 55566.;
// if (debugPK) {
// XLAL_PRINT_INFO("\nPK:: dM, eta, chiS, chiA while renewing hlm coeffs: %e, %e, %e, %e\n",
// dM, eta, chiS, chiA);
// XLAL_PRINT_INFO("PK:: Renewed rho-lm coeffs: v2 = %.16e, v3 = %.16e, v4 = %.16e, v5 = %.16e\nv6 = %.16e, v6l = %.16e v7 = %.16e v8 = %.16e, v8l = %.16e v10 = %.16e v10l = %.16e\n",
// coeffs->rho22v2, coeffs->rho22v3, coeffs->rho22v4, coeffs->rho22v5,
// coeffs->rho22v6, coeffs->rho22v6l, coeffs->rho22v7, coeffs->rho22v8,
// coeffs->rho22v8l, coeffs->rho22v10, coeffs->rho22v10l);
// }
if(waveform == 1){
a = 0;
a2 = 0;
a3 = 0;
}
coeffs->delta21vh3 = 2. / 3.;
coeffs->delta21vh6 = (-17. * aDelta) / 35. + (107. * CST_PI) / 105.;
coeffs->delta21vh7 = (3. * aDelta * aDelta) / 140.;
coeffs->delta21vh9 = -272. / 81. + (214. * CST_PI * CST_PI) / 315.;
coeffs->delta21v5 = -493. * eta / 42.;
coeffs->delta21v7 = 0.0;
if (dM2) {
//coeffs->rho21v1 = (-3. * (chiS + chiA / dM)) / (4.);
coeffs->rho21v1 = 0.0;
//coeffs->rho21v2 = -59. / 56 - (9. * chiAPlusChiSdM * chiAPlusChiSdM) / (32. * dM2) + (23. * eta) / 84.;
switch (SpinAlignedEOBversion) {
case 1:
coeffs->rho21v2 = -59. / 56 + (23. * eta) / 84. - 9. / 32. * a2;
coeffs->rho21v3 = 1177. / 672. * a - 27. / 128. * a3;
break;
case 2:
coeffs->rho21v2 = -59. / 56 + (23. * eta) / 84.;
coeffs->rho21v3 = 0.0;
break;
case 3:
coeffs->rho21v2 = -59. / 56 + (23. * eta) / 84.;
coeffs->rho21v3 = 0.0;
break;
case 4:
coeffs->rho21v2 = -59. / 56 + (23. * eta) / 84.;
coeffs->rho21v3 = 0.0;
break;
default:
PRINT_LOG_INFO(LOG_CRITICAL, "wrong SpinAlignedEOBversion value, must be 1, 2 or 3!");
return CEV_FAILURE;
break;
}
/*
* coeffs->rho21v3 = (-567.*chiA*chiA*chiA -
* 1701.*chiA*chiA*chiS*dM + chiA*(-4708. + 1701.*chiS*chiS -
* 2648.*eta)*(-1. + 4.*eta) + chiS* dM3 *(4708. -
* 567.*chiS*chiS + 1816.*eta))/(2688.*dM3);
*/
coeffs->rho21v4 = -47009. / 56448. - (865. * a2) / 1792. - (405. * a2 * a2) / 2048. - (10993. * eta) / 14112.
+ (617. * eta2) / 4704.;
coeffs->rho21v5 = (-98635. * a) / 75264. + (2031. * a * a2) / 7168. - (1701. * a2 * a3) / 8192.;
coeffs->rho21v6 = 7613184941. / 2607897600. + (9032393. * a2) / 1806336. + (3897. * a2 * a2) / 16384.
- (15309. * a3 * a3) / 65536.;
coeffs->rho21v6l = -107. / 105.;
coeffs->rho21v7 = (-3859374457. * a) / 1159065600. - (55169. * a3) / 16384.
+ (18603. * a2 * a3) / 65536. - (72171. * a2 * a2 * a3) / 262144.;
coeffs->rho21v7l = 107. * a / 140.;
coeffs->rho21v8 = -1168617463883. / 911303737344.;
coeffs->rho21v8l = 6313. / 5880.;
coeffs->rho21v10 = -63735873771463. / 16569158860800.;
coeffs->rho21v10l = 5029963. / 5927040.;
coeffs->f21v1 = (-3. * (chiS + chiA / dM)) / (2.);
switch (SpinAlignedEOBversion) {
case 1:
coeffs->f21v3 = 0.0;
break;
case 2:
coeffs->f21v3 = (chiS * dM * (427. + 79. * eta) + chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84. / dM;
break;
case 3:
coeffs->f21v3 = (chiS * dM * (427. + 79. * eta) + chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84. / dM;
break;
case 4:
coeffs->f21v3 =
(chiS * dM * (427. + 79. * eta) +
chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84. / dM;
/*RC: New terms for SEOBNRv4HM, they are put to zero if use_hm == 0 */
if (waveform == 0)
{
coeffs->f21v4 = 0.0;
coeffs->f21v5 = 0.0;
coeffs->f21v6 = 0.0;
coeffs->f21v7c = 0;
}
else{
coeffs->f21v4 = (-3.-2.*eta)*chiA2 + (-3.+ eta/2.)*chiS2 + (-6.+21.*eta/2.)*chiS*chiA/dM;
coeffs->f21v5 = (3./4.-3.*eta)*chiA3/dM + (-81./16. +1709.*eta/1008. + 613.*eta2/1008.+(9./4.-3*eta)*chiA2)*chiS + 3./4.*chiS3
+ (-81./16. - 703.*eta2/112. + 8797.*eta/1008.+(9./4. - 6.*eta)*chiS2)*chiA/dM;
coeffs->f21v6 = (4163./252.-9287.*eta/1008. - 85.*eta2/112.)*chiA2 + (4163./252. - 2633.*eta/1008. + 461.*eta2/1008.)*chiS2 + (4163./126.-1636.*eta/21. + 1088.*eta2/63.)*chiS*chiA/dM;
}
/* End new terms for SEOBNRv4HM */
break;
default:
PRINT_LOG_INFO(LOG_CRITICAL, "wrong SpinAlignedEOBversion value, must be 1, 2 or 3!");
return CEV_FAILURE;
break;
}
} else {
coeffs->f21v1 = -3. * chiA / 2.; // Odd modes in dm->0 limit, note that there is a typo in Taracchini et.al. discussion after A7 (even->odd)
switch (SpinAlignedEOBversion) {
case 1:
coeffs->f21v3 = 0.0;
break;
case 2:
coeffs->f21v3 = (chiS * dM * (427. + 79. * eta) + chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84.;
break;
case 3:
coeffs->f21v3 = (chiS * dM * (427. + 79. * eta) + chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84.;
break;
case 4:
coeffs->f21v3 =
(chiS * dM * (427. + 79. * eta) +
chiA * (147. + 280. * dM * dM + 1251. * eta)) / 84.;
/* New terms for SEOBNRv4HM, they are put to zero if use_hm == 0 */
if (waveform == 0)
{
coeffs->f21v4 = 0.0;
coeffs->f21v5 = 0.0;
coeffs->f21v6 = 0.0;
}
else{
coeffs->f21v4 = (-6+21*eta/2.)*chiS*chiA;
coeffs->f21v5 = (3./4.-3.*eta)*chiA3 + (-81./16. - 703.*eta2/112. + 8797.*eta/1008. + (9./4. - 6.*eta)*chiS2)*chiA;
coeffs->f21v6 = (4163./126.-1636.*eta/21. + 1088.*eta2/63.)*chiS*chiA;
// printf("f21v1 = %.16f\n f21v3 = %.16f\n f21v4 = %.16f\n f21v5 = %.16f\n f21v6 = %.16f\n", coeffs->f21v1, coeffs->f21v3, coeffs->f21v4, coeffs->f21v5, coeffs->f21v6);
}
/* End new terms for SEOBNRv4HM */
break;
default:
PRINT_LOG_INFO(LOG_CRITICAL, "wrong SpinAlignedEOBversion value, must be 1, 2 or 3!");
return CEV_FAILURE;
break;
}
}
/*
* l = 3, Eqs. A9a - A9c for rho, Eqs. A15b and A15c for f, Eqs. 22 -
* 24 of DIN and Eqs. 27c - 27e of PBFRT for delta
*/
coeffs->delta33vh3 = 13. / 10.;
coeffs->delta33vh6 = (-81. * aDelta) / 20. + (39. * CST_PI) / 7.;
coeffs->delta33vh9 = -227827. / 3000. + (78. * CST_PI * CST_PI) / 7.;
coeffs->delta33v5 = -80897. * eta / 2430.;
if (dM2) {
coeffs->rho33v2 = -7. / 6. + (2. * eta) / 3.;
//coeffs->rho33v3 = (chiS * dM * (-4. + 5. * eta) + chiA * (-4. + 19. * eta)) / (6. * dM);
coeffs->rho33v3 = 0.0;
coeffs->rho33v4 = -6719. / 3960. + a2 / 2. - (1861. * eta) / 990. + (149. * eta2) / 330.;
coeffs->rho33v5 = (-4. * a) / 3.;
coeffs->rho33v6 = 3203101567. / 227026800. + (5. * a2) / 36.;
coeffs->rho33v6l = -26. / 7.;
coeffs->rho33v7 = (5297. * a) / 2970. + a * a2 / 3.;
coeffs->rho33v8 = -57566572157. / 8562153600.;
coeffs->rho33v8l = 13. / 3.;
if(waveform == 1){
//RC: This terms are in Eq.A6 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->rho33v6 = 3203101567. / 227026800. + (5. * a2) / 36. + (-129509./25740. + 41./192. * CST_PI*CST_PI)*eta - 274621./154440.*eta2+ 12011./46332.*eta3;
coeffs->rho33v10 = -903823148417327./30566888352000.;
coeffs->rho33v10l = 87347./13860.;
}
coeffs->f33v3 = (chiS * dM * (-4. + 5. * eta) + chiA * (-4. + 19. * eta)) / (2. * dM);
coeffs->f33v4 = 0;
coeffs->f33v5 = 0;
coeffs->f33v6 = 0;
coeffs->f33vh6 = 0;
if(waveform == 1){
//RC: This terms are in Eq.A10 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->f33v4 = (3./2. * chiS2 * dM + (3. - 12 * eta) * chiA * chiS + dM * (3./2. -6. * eta) * chiA2)/(dM);
coeffs->f33v5 = (dM * (241./30. * eta2 + 11./20. * eta + 2./3.) * chiS + (407./30. * eta2 - 593./60. * eta + 2./3.)* chiA)/(dM);
coeffs->f33v6 = (dM * (6. * eta2 -27. / 2. * eta - 7./ 4.) * chiS2 + (44. * eta2 - 1. * eta - 7./2.) * chiA * chiS + dM * (-12 * eta2 + 11./2. * eta - 7./4.) * chiA2)/dM;
coeffs->f33vh6 = (dM * (593. / 108. * eta - 81./20.) * chiS + (7339./540. * eta - 81./20.) * chiA)/(dM);
}
}
else {
coeffs->f33v3 = chiA * 3. / 8.;
if(waveform == 1){
//RC: This terms are in Eq.A10 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->f33v4 = ((3. - 12 * eta) * chiA * chiS);
coeffs->f33v5 = ((407./30. * eta2 - 593./60. * eta + 2./3.)* chiA);
coeffs->f33v6 = ((44. * eta2 - 1. * eta - 7./2.) * chiA * chiS);
coeffs->f33vh6 = ((7339./540. * eta - 81./20.) * chiA);
}
}
coeffs->delta32vh3 = (10. + 33. * eta) / (-15. * m1Plus3eta);
coeffs->delta32vh4 = 4. * aDelta;
coeffs->delta32vh6 = (-136. * aDelta) / 45. + (52. * CST_PI) / 21.;
coeffs->delta32vh9 = -9112. / 405. + (208. * CST_PI * CST_PI) / 63.;
coeffs->rho32v = (4. * chiS * eta) / (-3. * m1Plus3eta);
/** TODO The term proportional to eta^2 a^2 in coeffs->rho32v2 is wrong, but it was used in the calibration of SEOBNRv2 */
coeffs->rho32v2 = (-4. * a2 * eta2) / (9. * m1Plus3eta2) + (328. - 1115. * eta
+ 320. * eta2) / (270. * m1Plus3eta);
if (SpinAlignedEOBversion == 4) {
coeffs->rho32v2 = (328. - 1115. * eta +
320. * eta2) / (270. * m1Plus3eta);
}
//coeffs->rho32v3 = (2. * (45. * a * m1Plus3eta3
// - a * eta * (328. - 2099. * eta + 5. * (733. + 20. * a2) * eta2
// - 960. * eta3))) / (405. * m1Plus3eta3);
coeffs->rho32v3 = 2. / 9. * a;
coeffs->rho32v4 = a2 / 3. + (-1444528.
+ 8050045. * eta - 4725605. * eta2 - 20338960. * eta3
+ 3085640. * eta2 * eta2) / (1603800. * m1Plus3eta2);
coeffs->rho32v5 = (-2788. * a) / 1215.;
coeffs->rho32v6 = 5849948554. / 940355325. + (488. * a2) / 405.;
coeffs->rho32v6l = -104. / 63.;
coeffs->rho32v8 = -10607269449358. / 3072140846775.;
coeffs->rho32v8l = 17056. / 8505.;
if (dM2) {
coeffs->delta31vh3 = 13. / 30.;
coeffs->delta31vh6 = (61. * aDelta) / 20. + (13. * CST_PI) / 21.;
coeffs->delta31vh7 = (-24. * aDelta * aDelta) / 5.;
coeffs->delta31vh9 = -227827. / 81000. + (26. * CST_PI * CST_PI) / 63.;
coeffs->delta31v5 = -17. * eta / 10.;
coeffs->rho31v2 = -13. / 18. - (2. * eta) / 9.;
//coeffs->rho31v3 = (chiA * (-4. + 11. * eta) + chiS * dM * (-4. + 13. * eta)) / (6. * dM);
coeffs->rho31v3 = 0.0;
coeffs->rho31v4 = 101. / 7128.
- (5. * a2) / 6. - (1685. * eta) / 1782. - (829. * eta2) / 1782.;
coeffs->rho31v5 = (4. * a) / 9.;
coeffs->rho31v6 = 11706720301. / 6129723600. - (49. * a2) / 108.;
coeffs->rho31v6l = -26. / 63.;
coeffs->rho31v7 = (-2579. * a) / 5346. + a * a2 / 9.;
coeffs->rho31v8 = 2606097992581. / 4854741091200.;
coeffs->rho31v8l = 169. / 567.;
coeffs->f31v3 = (chiA * (-4. + 11. * eta) + chiS * dM * (-4. + 13. * eta)) / (2. * dM);
} else {
coeffs->f31v3 = -chiA * 5. / 8.;
}
/*
* l = 4, Eqs. A10a - A10d for rho, Eq. A15d for f Eqs. 25 - 28 of
* DIN and Eqs. 27f - 27i of PBFRT for delta
*/
coeffs->delta44vh3 = (112. + 219. * eta) / (-120. * m1Plus3eta);
coeffs->delta44vh6 = (-464. * aDelta) / 75. + (25136. * CST_PI) / 3465.;
coeffs->delta44vh9 = 0.;
if(waveform == 1){
//RC: This terms are in Eq.A15 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->delta44vh9 = -55144./375. + 201088.*CST_PI*CST_PI/10395.;
}
coeffs->rho44v2 = (1614. - 5870. * eta + 2625. * eta2) / (1320. * m1Plus3eta);
coeffs->rho44v3 = (chiA * (10. - 39. * eta) * dM + chiS * (10. - 41. * eta
+ 42. * eta2)) / (15. * m1Plus3eta);
coeffs->rho44v4 = a2 / 2. + (-511573572.
+ 2338945704. * eta - 313857376. * eta2 - 6733146000. * eta3
+ 1252563795. * eta2 * eta2) / (317116800. * m1Plus3eta2);
coeffs->rho44v5 = (-69. * a) / 55.;
coeffs->rho44v8 = 0.;
coeffs->rho44v8l = 0.;
coeffs->rho44v10 = 0.;
coeffs->rho44v10l = 0;
if(waveform == 1){
//RC: This terms are in Eq.A8 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->rho44v4 =
(-511573572. + 2338945704. * eta - 313857376. * eta2 -
6733146000. * eta3 +
1252563795. * eta2 * eta2) / (317116800. * m1Plus3eta2)
+ chiS2/2. + dM*chiS*chiA + dM2*chiA2/2.;
coeffs->rho44v5 = chiA*dM*(-8280. + 42716.*eta - 57990.*eta2 + 8955*eta3)/(6600.*m1Plus3eta2)
+ chiS*(-8280. + 66284.*eta-176418.*eta2+128085.*eta3 + 88650*eta2*eta2)/(6600.*m1Plus3eta2);
coeffs->rho44v8 = -172066910136202271./19426955708160000.;
coeffs->rho44v8l = 845198./190575.;
coeffs->rho44v10 = - 17154485653213713419357./568432724020761600000.;
coeffs->rho44v10l = 22324502267./3815311500;
}
coeffs->rho44v6 = 16600939332793. / 1098809712000. + (217. * a2) / 3960.;
coeffs->rho44v6l = -12568. / 3465.;
if (dM2) {
coeffs->delta43vh3 = (486. + 4961. * eta) / (810. * (1. - 2. * eta));
coeffs->delta43vh4 = (11. * aDelta) / 4.;
coeffs->delta43vh6 = 1571. * CST_PI / 385.;
//coeffs->rho43v = (5. * (chiA - chiS * dM) * eta) / (8. * dM * (-1. + 2. * eta));
coeffs->rho43v = 0.0;
coeffs->rho43v2 = (222. - 547. * eta + 160. * eta2) / (176. * (-1. + 2. * eta));
coeffs->rho43v4 = -6894273. / 7047040. + (3. * a2) / 8.;
coeffs->rho43v5 = (-12113. * a) / 6160.;
coeffs->rho43v6 = 1664224207351. / 195343948800.;
coeffs->rho43v6l = -1571. / 770.;
coeffs->f43v = (5. * (chiA - chiS * dM) * eta) / (2. * dM * (-1. + 2. * eta));
} else {
coeffs->f43v = -5. * chiA / 4.;
}
coeffs->delta42vh3 = (7. * (1. + 6. * eta)) / (-15. * m1Plus3eta);
coeffs->delta42vh6 = (212. * aDelta) / 75. + (6284. * CST_PI) / 3465.;
coeffs->rho42v2 = (1146. - 3530. * eta + 285. * eta2) / (1320. * m1Plus3eta);
coeffs->rho42v3 = (chiA * (10. - 21. * eta) * dM + chiS * (10. - 59. * eta
+ 78. * eta2)) / (15. * m1Plus3eta);
coeffs->rho42v4 = a2 / 2. + (-114859044. + 295834536. * eta + 1204388696. * eta2 - 3047981160. * eta3
- 379526805. * eta2 * eta2) / (317116800. * m1Plus3eta2);
coeffs->rho42v5 = (-7. * a) / 110.;
coeffs->rho42v6 = 848238724511. / 219761942400. + (2323. * a2) / 3960.;
coeffs->rho42v6l = -3142. / 3465.;
if (dM2) {
coeffs->delta41vh3 = (2. + 507. * eta) / (10. * (1. - 2. * eta));
coeffs->delta41vh4 = (11. * aDelta) / 12.;
coeffs->delta41vh6 = 1571. * CST_PI / 3465.;
//coeffs->rho41v = (5. * (chiA - chiS * dM) * eta) / (8. * dM * (-1. + 2. * eta));
coeffs->rho41v = 0.0;
coeffs->rho41v2 = (602. - 1385. * eta + 288. * eta2) / (528. * (-1. + 2. * eta));
coeffs->rho41v4 = -7775491. / 21141120. + (3. * a2) / 8.;
coeffs->rho41v5 = (-20033. * a) / 55440. - (5 * a * a2) / 6.;
coeffs->rho41v6 = 1227423222031. / 1758095539200.;
coeffs->rho41v6l = -1571. / 6930.;
coeffs->f41v = (5. * (chiA - chiS * dM) * eta) / (2. * dM * (-1. + 2. * eta));
} else {
coeffs->f41v = -5. * chiA / 4.;
}
/*
* l = 5, Eqs. A11a - A11e for rho, Eq. 29 of DIN and Eqs. E1a and
* E1b of PBFRT for delta
*/
coeffs->delta55vh3 =
(96875. + 857528. * eta) / (131250. * (1 - 2 * eta));
coeffs->delta55vh6 = 0;
coeffs->delta55vh9 = 0;
if(waveform == 1){
//RC: This terms are in Eq.A16 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->delta55vh6 = 3865./429.*CST_PI;
coeffs->delta55vh9 = (-7686949127. + 954500400.*CST_PI*CST_PI)/31783752.;
}
if (dM2) {
coeffs->rho55v2 = (487. - 1298. * eta + 512. * eta2) / (390. * (-1. + 2. * eta));
coeffs->rho55v3 = (-2. * a) / 3.;
coeffs->rho55v4 = -3353747. / 2129400. + a2 / 2.;
coeffs->rho55v5 = -241. * a / 195.;
coeffs->rho55v6 = 0.;
coeffs->rho55v6l = 0.;
coeffs->rho55v8 = 0.;
coeffs->rho55v8l = 0.;
coeffs->rho55v10 = 0.;
coeffs->rho55v10l = 0.;
coeffs->f55v3 = 0.;
coeffs->f55v4 = 0.;
coeffs->f55v5c = 0;
if(waveform == 1){
//RC: This terms are in Eq.A9 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->rho55v6 = 190606537999247./11957879934000.;
coeffs->rho55v6l = - 1546./429.;
coeffs->rho55v8 = - 1213641959949291437./118143853747920000.;
coeffs->rho55v8l = 376451./83655.;
coeffs->rho55v10 = -150082616449726042201261./4837990810977324000000.;
coeffs->rho55v10l = 2592446431./456756300.;
coeffs->f55v3 = chiA/dM *(10./(3.*(-1.+2.*eta)) - 70.*eta/(3.*(-1.+2.*eta)) + 110.*eta2/(3.*(-1.+2.*eta)) ) +
chiS*(10./(3.*(-1.+2.*eta)) -10.*eta/(-1.+2.*eta) + 10*eta2/(-1.+2.*eta));
coeffs->f55v4 = chiS2*(-5./(2.*(-1.+2.*eta)) + 5.*eta/(-1.+2.*eta)) +
chiA*chiS/dM *(-5./(-1.+2.*eta) + 30.*eta/(-1.+2.*eta) - 40.*eta2/(-1.+2.*eta)) +
chiA2*(-5./(2.*(-1.+2.*eta)) + 15.*eta/(-1.+2.*eta) - 20.*eta2/(-1.+2.*eta));
coeffs->f55v5c = 0; //RC: this is the calibration parameter which is initially set to 0.
}
}
else{
coeffs->f55v3 = 0;
coeffs->f55v4 = 0;
coeffs->f55v5c = 0;
if(waveform == 1){
//RC: This terms are in Eq.A12 in https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084028 [arXiv:1803.10701]
coeffs->f55v3 = chiA *(10./(3.*(-1.+2.*eta)) - 70.*eta/(3.*(-1.+2.*eta)) + 110.*eta2/(3.*(-1.+2.*eta)) );
coeffs->f55v4 = chiA*chiS *(-5./(-1.+2.*eta) + 30.*eta/(-1.+2.*eta) - 40.*eta2/(-1.+2.*eta));
coeffs->f55v5c = 0;
}
}
coeffs->delta54vh3 = 8. / 15.;
coeffs->delta54vh4 = 12. * aDelta / 5.;
coeffs->rho54v2 = (-17448. + 96019. * eta - 127610. * eta2
+ 33320. * eta3) / (13650. * (1. - 5. * eta + 5. * eta2));
coeffs->rho54v3 = (-2. * a) / 15.;
coeffs->rho54v4 = -16213384. / 15526875. + (2. * a2) / 5.;
if (dM2) {
coeffs->delta53vh3 = 31. / 70.;
coeffs->rho53v2 = (375. - 850. * eta + 176. * eta2) / (390. * (-1. + 2. * eta));
coeffs->rho53v3 = (-2. * a) / 3.;
coeffs->rho53v4 = -410833. / 709800. + a2 / 2.;
coeffs->rho53v5 = -103. * a / 325.;
}
coeffs->delta52vh3 = 4. / 15.;
coeffs->delta52vh4 = 6. * aDelta / 5.;
coeffs->rho52v2 = (-15828. + 84679. * eta - 104930. * eta2
+ 21980. * eta3) / (13650. * (1. - 5. * eta + 5. * eta2));
coeffs->rho52v3 = (-2. * a) / 15.;
coeffs->rho52v4 = -7187914. / 15526875. + (2. * a2) / 5.;
if (dM2) {
coeffs->delta51vh3 = 31. / 210.;
coeffs->rho51v2 = (319. - 626. * eta + 8. * eta2) / (390. * (-1. + 2. * eta));
coeffs->rho51v3 = (-2. * a) / 3.;
coeffs->rho51v4 = -31877. / 304200. + a2 / 2.;
coeffs->rho51v5 = 139. * a / 975.;
}
/*
* l = 6, Eqs. A12a - A12f for rho, Eqs. E1c and E1d of PBFRT for
* delta
*/
coeffs->delta66vh3 = 43. / 70.;
coeffs->rho66v2 = (-106. + 602. * eta - 861. * eta2
+ 273. * eta3) / (84. * (1. - 5. * eta + 5. * eta2));
coeffs->rho66v3 = (-2. * a) / 3.;
coeffs->rho66v4 = -1025435. / 659736. + a2 / 2.;
if (dM2) {
coeffs->delta65vh3 = 10. / 21.;
coeffs->rho65v2 = (-185. + 838. * eta - 910. * eta2
+ 220. * eta3) / (144. * (dM2 + 3. * eta2));
coeffs->rho65v3 = -2. * a / 9.;
}
coeffs->delta64vh3 = 43. / 105.;
coeffs->rho64v2 = (-86. + 462. * eta - 581. * eta2
+ 133. * eta3) / (84. * (1. - 5. * eta + 5. * eta2));
coeffs->rho64v3 = (-2. * a) / 3.;
coeffs->rho64v4 = -476887. / 659736. + a2 / 2.;
if (dM2) {
coeffs->delta63vh3 = 2. / 7.;
coeffs->rho63v2 = (-169. + 742. * eta - 750. * eta2
+ 156. * eta3) / (144. * (dM2 + 3. * eta2));
coeffs->rho63v3 = -2. * a / 9.;
}
coeffs->delta62vh3 = 43. / 210.;
coeffs->rho62v2 = (-74. + 378. * eta - 413. * eta2
+ 49. * eta3) / (84. * (1. - 5. * eta + 5. * eta2));
coeffs->rho62v3 = (-2. * a) / 3.;
coeffs->rho62v4 = -817991. / 3298680. + a2 / 2.;
if (dM2) {
coeffs->delta61vh3 = 2. / 21.;
coeffs->rho61v2 = (-161. + 694. * eta - 670. * eta2
+ 124. * eta3) / (144. * (dM2 + 3. * eta2));
coeffs->rho61v3 = -2. * a / 9.;
}
/*
* l = 7, Eqs. A13a - A13g for rho, Eqs. E1e and E1f of PBFRT for
* delta
*/
if (dM2) {
coeffs->delta77vh3 = 19. / 36.;
coeffs->rho77v2 = (-906. + 4246. * eta - 4963. * eta2
+ 1380. * eta3) / (714. * (dM2 + 3. * eta2));
coeffs->rho77v3 = -2. * a / 3.;
}
coeffs->rho76v2 = (2144. - 16185. * eta + 37828. * eta2 - 29351. * eta3
+ 6104. * eta2 * eta2) / (1666. * (-1 + 7 * eta - 14 * eta2
+ 7 * eta3));
if (dM2) {
coeffs->delta75vh3 = 95. / 252.;
coeffs->rho75v2 = (-762. + 3382. * eta - 3523. * eta2
+ 804. * eta3) / (714. * (dM2 + 3. * eta2));
coeffs->rho75v3 = -2. * a / 3.;
}
coeffs->rho74v2 = (17756. - 131805. * eta + 298872. * eta2 - 217959. * eta3
+ 41076. * eta2 * eta2) / (14994. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->delta73vh3 = 19. / 84.;
coeffs->rho73v2 = (-666. + 2806. * eta - 2563. * eta2
+ 420. * eta3) / (714. * (dM2 + 3. * eta2));
coeffs->rho73v3 = -2. * a / 3.;
}
coeffs->rho72v2 = (16832. - 123489. * eta + 273924. * eta2 - 190239. * eta3
+ 32760. * eta2 * eta2) / (14994. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->delta71vh3 = 19. / 252.;
coeffs->rho71v2 = (-618. + 2518. * eta - 2083. * eta2
+ 228. * eta3) / (714. * (dM2 + 3. * eta2));
coeffs->rho71v3 = -2. * a / 3.;
}
/* l = 8, Eqs. A14a - A14h */
coeffs->rho88v2 = (3482. - 26778. * eta + 64659. * eta2 - 53445. * eta3
+ 12243. * eta2 * eta2) / (2736. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->rho87v2 = (23478. - 154099. * eta + 309498. * eta2 - 207550. * eta3
+ 38920 * eta2 * eta2) / (18240. * (-1 + 6 * eta - 10 * eta2
+ 4 * eta3));
}
coeffs->rho86v2 = (1002. - 7498. * eta + 17269. * eta2 - 13055. * eta3
+ 2653. * eta2 * eta2) / (912. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->rho85v2 = (4350. - 28055. * eta + 54642. * eta2 - 34598. * eta3
+ 6056. * eta2 * eta2) / (3648. * (-1. + 6. * eta - 10. * eta2
+ 4. * eta3));
}
coeffs->rho84v2 = (2666. - 19434. * eta + 42627. * eta2 - 28965. * eta3
+ 4899. * eta2 * eta2) / (2736. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->rho83v2 = (20598. - 131059. * eta + 249018. * eta2 - 149950. * eta3
+ 24520. * eta2 * eta2) / (18240. * (-1. + 6. * eta - 10. * eta2
+ 4. * eta3));
}
coeffs->rho82v2 = (2462. - 17598. * eta + 37119. * eta2 - 22845. * eta3
+ 3063. * eta2 * eta2) / (2736. * (-1. + 7. * eta - 14. * eta2
+ 7. * eta3));
if (dM2) {
coeffs->rho81v2 = (20022. - 126451. * eta + 236922. * eta2 - 138430. * eta3
+ 21640. * eta2 * eta2) / (18240. * (-1. + 6. * eta - 10. * eta2
+ 4. * eta3));
}
/* New Factorized waveform coeffs */
coeffs->h22T0ff00 = 1./2.;
coeffs->h22T0ff02 = 1./2.;
coeffs->h22T0ff11 = 1;
coeffs->h22T0ff20 = -1./2.;
coeffs->h22T2ff40 = -1./14.-15.*eta/28.;
coeffs->h22T2ff31 = (1./7. + 15.*eta/14.);
coeffs->h22T2ff20 = -9./7. + 31.*eta/28.;
coeffs->h22T2ff13 = (1./7. + 15.*eta/14.);
coeffs->h22T2ff11 = (25./42. - 16.*eta/7.);
coeffs->h22T2ff04 = 1./14. + 15.*eta/28.;
coeffs->h22T2ff02 = -13./21. + 3.*eta/28.;
coeffs->h22T2ff00 = -3./2. + eta/2. + 0.5*I*(cax+cay + dM*(csx+csy));
coeffs->h22T3ff30 = -4.*dM*caz/3. - (4./3. - eta) * csz;
coeffs->h22T3ff21 = -8.*dM*caz/3. - (8./3. - 2.*eta) * csz;
coeffs->h22T3ff12 = 4.*dM*caz/3. + (4./3. - eta) * csz;
coeffs->h22T3ff10 = (1.*dM/3.)*caz + (1./3.+2.*eta/3.)*csz;
// coeffs->h22T3ff03 = (4.*dM/3.)*caz + (4./3.-eta)*csz;
coeffs->h22T3ff01 = -dM*caz + (-1. + 7.*eta/6.)*csz;
coeffs->h22T4ff60 = -1./42. - 179.*eta/336. - 25.*eta2/48.;
coeffs->h22T4ff51 = (1./21. + 179.*eta/168. + 25.*eta2/24.);
coeffs->h22T4ff42 = -1./42. - 179.*eta/336. -25.*eta2/48.;
coeffs->h22T4ff40 = -11./21. - 923.*eta/336. + 335.*eta2/336.;
coeffs->h22T4ff33 = (2./21. + 179.*eta/84. + 25.*eta2/12.);
coeffs->h22T4ff31 = (71./63. + 935.*eta/252. - 131.*eta2/63.);
coeffs->h22T4ff24 = 1./42. + 179.*eta/336. + 25.*eta2/48.;
coeffs->h22T4ff22 = 23./84. - 45.*eta/56. - 109.*eta2/168.;
coeffs->h22T4ff20 = -425./504. + 1355.*eta/252. - 20.*eta2/63.+ cax*I*(-3./2.-19.*eta/28.) + cay*(-3./2.-37.*eta/42.) + csx*dM*I*(-3./2.-9.*eta/28.) +
csy*dM*(-3./2.-11.*eta/14.) + 0.5*(pow(dM*cay+(1.-2.*eta)*csy, 2.) + pow(dM*caz+(1.-2.*eta)*csy, 2.));
coeffs->h22T4ff15 = (1./21. + 179.*eta/168. + 25.*eta2/24.);
coeffs->h22T4ff13 = (-1./168. + 29.*eta/12. - 58.*eta2/21.);
coeffs->h22T4ff11 = I*(-359./378. - 592.*eta/189. - 307.*eta2/378.) + cax*(-3./2.-51.*eta/28.) + cay*I*(5./2.-5.*eta/12.) + csx*dM*(-3./2.+125.*eta/84.) +
csy*I*dM*(5./2.+eta/12.) + (dM*cax + (1.-2.*eta)*csx)*(dM*cay + (1.-2.*eta)*csy);
coeffs->h22T4ff06 = 1./42. + 179.*eta/336. + 25.*eta2/48.;
coeffs->h22T4ff04 = 317./1008. - 1045.*eta/1008. - 101.*eta2/144.;
coeffs->h22T4ff02 = -10379./3024. - 635.*eta/189. + 26.*eta2/189. + cax*I*(9./4.-89.*eta/14.) + cay*(3./4.+71.*eta/84.) + csx*I*dM*(9./4.-55.*eta/42.) +
csy*dM*(3./4.+13.*eta/84.) - I*(dM*cax + (1.-2.*eta)*csx) * (dM*cay + (1.-2.*eta)*csy) + 0.5*(pow(dM*cay+(1.-2.*eta)*csy, 2.) + pow(dM*caz+(1.-2.*eta)*csy, 2.));
coeffs->h22T4ff00 = 65./252. - 31.*eta/36. + 205.*eta2/252. + cax*I*(-1.+19.*eta/14.) + cay*(-1./3.-19.*eta/21.) + csx*I*dM*(-1.+9.*eta/14.) +
csy*dM*(-1./3.+5.*eta/21.) -2.*I*(dM*cax+(1.+eta)*csx)*(dM*cay+(1.+eta)*csy) + 6.*I*csx*csy +
0.5*(pow(dM*cay+(1.+eta)*csy, 2.) + pow(dM*caz+(1.+eta)*csy, 2.) - 3.*eta2 * (csy*csy + csz*csz));
// h21
if (dM2)
{
coeffs->h21T0ff01 = 1.;
coeffs->h21T1ff00 = -3.*caz / 2. / dM - 3.*csz / 2.;
coeffs->h21T2ff21 = -20./7. - 11.*eta/14.;
coeffs->h21T2ff12 = 83./14. - 6.*eta/7.;
coeffs->h21T2ff03 = 5./28. - 5.*eta/14.;
coeffs->h21T2ff01 = -16./7. + 11.*eta/7. -6.*I*cax - I*(6.+eta) * csx / dM + 4.*eta * csy/dM;
coeffs->h21T2ff10 = -3.*cay + (-3. + 8.*eta) * csy/dM;
coeffs->h21T3ff20 = (9./2.+95.*eta/28.)*caz/dM + (9./2.+87.*eta/28.)*csz;
coeffs->h21T3ff11 = (-55./6.+44.*eta/21.)*caz/dM + (-55./6.-3.*eta/7.)*csz;
coeffs->h21T3ff02 = (-9./4.+327.*eta/28.)*caz/dM + (-9./4.+107.*eta/28.)*csz;
coeffs->h21T3ff00 = (6.-95.*eta/14.)*caz/dM + (6.-59.*eta/14.)*csz + I*(9.-36.*eta)*cax*caz/dM + 9.*I*(caz*csx+cax*csz) + 9.*I*csx*csz/dM;
}
else
{
coeffs->h21T1ff00 = -3.*caz/2.;
coeffs->h21T2ff10 = (-3. + 8.*eta) * csy;
coeffs->h21T2ff01 = -I*(6.+eta)*csx + 4.*eta*csy;
coeffs->h21T3ff20 = (9./2.+95.*eta/28.)*caz;
coeffs->h21T3ff11 = (-55./6.+44.*eta/21.)*caz;
coeffs->h21T3ff02 = (-9./4.+327.*eta/28.)*caz;
coeffs->h21T3ff00 = (6.-95.*eta/14.)*caz + I*(9.-36.*eta)*cax*caz + 9.*I*csx*csz;
}
// h33
if (dM2)
{
coeffs->h33T0ff30 = -2./9.;
coeffs->h33T0ff21 = -2./3.;
coeffs->h33T0ff12 = 2./3.;
coeffs->h33T0ff10 = 4./9.;
coeffs->h33T0ff03 = 2./9.;
coeffs->h33T0ff01 = 7./9.;
coeffs->h33T2ff50 = -2./27.-8.*eta/27.;
coeffs->h33T2ff41 = -2./9. - 8.*eta/9.;
coeffs->h33T2ff32 = 4./27. + 16.*eta/27.;
coeffs->h33T2ff30 = -28./27. + 20.*eta/27.;
coeffs->h33T2ff23 = -4./27. - 16.*eta/27.;
coeffs->h33T2ff21 = -20./9. + 19.*eta/9.;
coeffs->h33T2ff14 = 2./9. + 8.*eta/9.;
coeffs->h33T2ff12 = 2./3.-2.*eta;
coeffs->h33T2ff10 = -37./81.-4.*eta/81. + (-I)*(4.*eta/9.)*(csx-csy)/dM;
coeffs->h33T2ff05 = 2./27. + 8.*eta/27.;
coeffs->h33T2ff03 = -11./18.+2.*eta/3.;
coeffs->h33T2ff01 = -80./27 + 22.*eta/27. - (16.*eta*I/9.)*(csx+csy)/dM;
coeffs->h33T3ff40 = (8./9.-32.*eta/9.)*caz/dM + (8./9.-2.*eta/3.)*csz;
coeffs->h33T3ff31 = (-8./3.+32.*eta/3.)*caz/dM + (-8./3.+2.*eta)*csz;
coeffs->h33T3ff22 = (-8./3.+32.*eta/3.)*caz/dM + (-8./3.+2.*eta)*csz;
coeffs->h33T3ff13 = (8./9.-32.*eta/9.)*caz/dM + (8./9.-2.*eta/3.)*csz;
coeffs->h33T3ff20 = (-10./9. + 13.*eta/3.) * caz / dM + (-10./9. + eta/3.)*csz;
coeffs->h33T3ff11 = (10./9.-35.*eta/9.)*caz/dM + (-10./9. + 10.*eta/9.)*csz;
coeffs->h33T3ff02 = (-4./3. + 119.*eta/18.)*caz / dM + (-4./3. + 35.*eta/18.)*csz;
coeffs->h33T3ff00 = (-2./9. + 10.*eta/9.)*caz/dM + (-2./9.+eta/3.)*csz;
}
else
{
coeffs->h33T2ff10 = (-I)*(4.*eta/9.)*(csx-csy);
coeffs->h33T2ff01 = - (16.*eta*I/9.)*(csx+csy);
coeffs->h33T3ff40 = (8./9.-32.*eta/9.)*caz;
coeffs->h33T3ff31 = (-8./3.+32.*eta/3.)*caz;
coeffs->h33T3ff22 = (-8./3.+32.*eta/3.)*caz;
coeffs->h33T3ff13 = (8./9.-32.*eta/9.)*caz;
coeffs->h33T3ff20 = (-10./9. + 13.*eta/3.) * caz;
coeffs->h33T3ff11 = (10./9.-35.*eta/9.)*caz;
coeffs->h33T3ff02 = (-4./3. + 119.*eta/18.)*caz;
coeffs->h33T3ff00 = (-2./9. + 10.*eta/9.)*caz;
}
// h32
coeffs->h32T0ff11 = 1./4.;
coeffs->h32T0ff02 = 1.;
coeffs->h32T1ff10 = -eta*chiS / m1Plus3eta;
coeffs->h32T1ff01 = -4.*eta*chiS / m1Plus3eta;
coeffs->h32T2ff31 = (16. - eta*(47. + 10.*eta)) / (24.) / m1Plus3eta;
coeffs->h32T2ff22 = (28. - 5.*eta*(16.+5.*eta)) / 10. / m1Plus3eta;
coeffs->h32T2ff13 = (-31.+eta*(107.-26.*eta)) / 8. / m1Plus3eta;
coeffs->h32T2ff11 = (-73. + eta*(239.-26.*eta)) / 36. / m1Plus3eta;
coeffs->h32T2ff04 = (43. + 5.*eta*(-37.+eta)) / 60. / m1Plus3eta;
coeffs->h32T2ff02 = (527. + 5.*eta*(-347.+161.*eta)) / 180. / m1Plus3eta;
// h31
if (dM2)
{
coeffs->h31T0ff30 = -6.;
coeffs->h31T0ff21 = -6.;
coeffs->h31T0ff12 = -6.;
coeffs->h31T0ff10 = 12.;
coeffs->h31T0ff03 = -6.;
coeffs->h31T0ff01 = 7.;
coeffs->h31T2ff50 = -2.-8.*eta;
coeffs->h31T2ff41 = -2.-8.*eta;
coeffs->h31T2ff32 = -4.-16.*eta;
coeffs->h31T2ff30 = -28.+20.*eta;
coeffs->h31T2ff23 = -4.-16.*eta;
coeffs->h31T2ff21 = -20.+19.*eta;
coeffs->h31T2ff14 = -2.-8.*eta;
coeffs->h31T2ff12 = -6.+26.*eta;
coeffs->h31T2ff10 = -37./3. - 4.*eta/3.;
coeffs->h31T2ff05 = -2.-8.*eta;
coeffs->h31T2ff03 = 53./2.+6.*eta;
coeffs->h31T2ff01 = -80./3. + 22.*eta/3.;
coeffs->h31T3ff20 = (6.-25.*eta)*chiA / dM + (6.-9.*eta)*chiS;
coeffs->h31T3ff11 = (-6.+31.*eta)*chiA / dM - (6.+11.*eta)*chiS;
coeffs->h31T3ff02 = (-12.+87.*eta/2.)*chiA/dM + (-12.+19.*eta/2)*chiS;
coeffs->h31T3ff00 = (-2.+10.*eta)*chiA/dM + (-2.+3.*eta)*chiS;
}
else
{
coeffs->h31T3ff20 = (6.-25.*eta)*chiA;
coeffs->h31T3ff11 = (-6.+31.*eta)*chiA;
coeffs->h31T3ff02 = (-12.+87.*eta/2.)*chiA;
coeffs->h31T3ff00 = (-2.+10.*eta)*chiA;
}
// h44
coeffs->h44T0ff40 = (3./32.);
coeffs->h44T0ff31 = (-3./8.);
coeffs->h44T0ff22 = (-9./16.);
coeffs->h44T0ff20 = (-9./32.);
coeffs->h44T0ff13 = (3./8.);
coeffs->h44T0ff11 = (27./32.);
coeffs->h44T0ff04 = (3./32.);
coeffs->h44T0ff02 = (51./64.);
coeffs->h44T0ff00 = 7./64.;
REAL8 m2Plus35eta = -2. + 35.*eta;
coeffs->h44T2ff60 = 9.*(-4. + eta*m2Plus35eta)/704./m1Plus3eta;
coeffs->h44T2ff51 = -9.*(-4. + eta*m2Plus35eta)/176./m1Plus3eta;
coeffs->h44T2ff42 = 45. * (4. - eta*m2Plus35eta)/704./m1Plus3eta;
coeffs->h44T2ff40 = -9.*(46. + eta*(-186 + 109*eta))/704./m1Plus3eta;
coeffs->h44T2ff31 = 3. * (2348. + 25*eta*(-386+243*eta))/3520./m1Plus3eta;
coeffs->h44T2ff24 = 45. * ( 4. - eta * m2Plus35eta) / 704./m1Plus3eta;
coeffs->h44T2ff22 = 3.*(5426. + 5.*eta*(-4546. + 3237.*eta))/7040./m1Plus3eta;
coeffs->h44T2ff20 = (579. + eta*(-2290.+783.*eta) + 132*eta*(I*cax+cay-I*dM*(csx-I*csy)) )/1408./m1Plus3eta;
coeffs->h44T2ff15 = 9.*(-4.+eta*m2Plus35eta)/176./m1Plus3eta;
coeffs->h44T2ff13 = -3.*(577.+15.*eta*(-196+295*eta))/3520./m1Plus3eta;
coeffs->h44T2ff11 = (1416. - 5.*eta*(536.+465.*eta) - 825*eta*(I*cax+cay-dM*I*(csx-I*csy)) )/1760./m1Plus3eta;
coeffs->h44T2ff06 = 9.*(-4.+eta*m2Plus35eta)/704./m1Plus3eta;
coeffs->h44T2ff04 = 9. *(859.+10.*eta*(-512.+457.*eta))/14080./m1Plus3eta;
coeffs->h44T2ff02 = (53913. + 30.*eta*(-5746. + 1291.*eta) - 16180*eta*(I*cax+cay-dM*(I*csx+csy)))/14080./m1Plus3eta;
coeffs->h44T2ff00 = (397.+eta*(-1358.+621.*eta) - 132*eta*(I*cax+cay-dM*(I*csx+csy)) )/704./m1Plus3eta;
// h43
if (dM2)
{
coeffs->h43T0ff21 = -2./27.;
coeffs->h43T0ff12 = 10./27.;
coeffs->h43T0ff03 = 23. / 27;
coeffs->h43T0ff01 = 4./27.;
coeffs->h43T1ff20 = (chiA/dM - chiS) * 5. * eta / 27. / (1. - 2. * eta);
coeffs->h43T1ff11 = (-chiA/dM + chiS) * 25. * eta / 27. / (1. - 2. * eta);
coeffs->h43T1ff02 = (-chiA/dM + chiS) * 115. * eta / 54. / (1. - 2. * eta);
coeffs->h43T1ff00 = (-chiA/dM + chiS) * 10. * eta / 27. / (1. - 2. * eta);
}
else
{
coeffs->h43T1ff20 = 5.*chiA/54.;
coeffs->h43T1ff11 = -25.*chiA/54.;
coeffs->h43T1ff02 = -115.*chiA/108.;
coeffs->h43T1ff00 = -5.*chiA/27.;
}
// h42
coeffs->h42T0ff40 = 3./2.;
coeffs->h42T0ff31 = -3.;
coeffs->h42T0ff20 = -9./2.;
coeffs->h42T0ff13 = -3.;
coeffs->h42T0ff11 = 27./4.;
coeffs->h42T0ff04 = -3./2.;
coeffs->h42T0ff02 = 3./4.;
coeffs->h42T0ff00 = 7./4.;
coeffs->h42T2ff60 = 9.*(-4. + eta*m2Plus35eta) / 44. / m1Plus3eta;
coeffs->h42T2ff51 = 9.*(-4. + eta*m2Plus35eta) / (-22.) / m1Plus3eta;
coeffs->h42T2ff42 = coeffs->h42T2ff60;
coeffs->h42T2ff40 = -9.*(46.+eta*(-186+109*eta)) / 44. / m1Plus3eta;
coeffs->h42T2ff33 = 9.*(-4. + eta*m2Plus35eta) / (-11.) / m1Plus3eta;
coeffs->h42T2ff31 = 3.*(2348.+25.*eta*(-386.+243.*eta))/440./m1Plus3eta;
coeffs->h42T2ff24 = -coeffs->h42T2ff60;
coeffs->h42T2ff22 = (822.-15.*eta*(54.+199.*eta)) / 440. / m1Plus3eta;
coeffs->h42T2ff20 = (579.+eta*(-2290.+783.*eta)) / 88. / m1Plus3eta;
coeffs->h42T2ff15 = coeffs->h42T2ff51;
coeffs->h42T2ff13 = 3.*(523+5.*eta*(-952.+1535*eta)) / 440. / m1Plus3eta;
coeffs->h42T2ff11 = (1416. - 5.*eta*(536.+465.*eta)) / 220. / m1Plus3eta;
coeffs->h42T2ff06 = -coeffs->h42T2ff60;
coeffs->h42T2ff04 = (-8361.+30.*eta*(838.-35.*eta)) / 880. / m1Plus3eta;
coeffs->h42T2ff02 = 3.*(919.+10.*eta*(-344.+113.*eta)) / 880. / m1Plus3eta;
coeffs->h42T2ff00 = (397.+eta*(-1358.+621.*eta)) / 44. / m1Plus3eta;
// h41
if (dM2)
{
coeffs->h41T0ff21 = -6.;
coeffs->h41T0ff12 = 10.;
coeffs->h41T0ff03 = -11.;
coeffs->h41T0ff01 = 12.;
coeffs->h41T1ff20 = (chiA/dM - chiS) * 15. * eta / (1.-2.*eta);