double xe_PostSahaH(double nH, double H, double T, HRATEEFF *rate_table, TWO_PHOTON_PARAMS *twog,
double zstart, double dlna, double **logfminus_hist, double *logfminus_Ly_hist[],
unsigned iz, double z, double *Dxe, int model, double energy_rate){
double s, xeSaha, dxeSaha_dlna, Ddxedlna_Dxe;
s = 3.016103031869581e21 *T*sqrt(T) *exp(-EI/T)/nH; /* xe^2/(1-xe) in Saha eq.*/
xeSaha = 2./(1.+sqrt(1.+4./s)); /* Saha equilibrium */
dxeSaha_dlna = -(EI/T - 1.5)/(2.*xeSaha + s)*xeSaha*xeSaha; /* Analytic derivative of above expression */
if (model == 0) { /* Peebles model */
Ddxedlna_Dxe = (rec_HPeebles_dxedlna(xeSaha+0.01*(1.-xeSaha), nH, H, T, T, energy_rate)
- rec_HPeebles_dxedlna(xeSaha-0.01*(1.-xeSaha), nH, H, T, T, energy_rate))/0.02/(1.-xeSaha);
}
else if (model == 1) { /* "Recfast" model */
Ddxedlna_Dxe = (rec_HRecFast_dxedlna(xeSaha+0.01*(1.-xeSaha), nH, H, T, T, energy_rate)
- rec_HRecFast_dxedlna(xeSaha-0.01*(1.-xeSaha), nH, H, T, T, energy_rate))/0.02/(1.-xeSaha);
}
else if (model == 2) { /* EMLA model with 2s and 2p decays only, no radiative transfer */
Ddxedlna_Dxe = (rec_HMLA_dxedlna(xeSaha+0.01*(1.-xeSaha), nH, H, T, T, energy_rate, rate_table)
- rec_HMLA_dxedlna(xeSaha-0.01*(1.-xeSaha), nH, H, T, T, energy_rate, rate_table))/0.02/(1.-xeSaha);
}
else { /* Default mode, with radiative transfer */
Ddxedlna_Dxe = (rec_HMLA_2photon_dxedlna(xeSaha+0.01*(1.-xeSaha),nH, H, T, T,
rate_table, twog, zstart, dlna, logfminus_hist, logfminus_Ly_hist, iz, z, energy_rate)
- rec_HMLA_2photon_dxedlna(xeSaha-0.01*(1.-xeSaha), nH, H, T, T,
rate_table, twog, zstart, dlna, logfminus_hist, logfminus_Ly_hist, iz, z, energy_rate))/0.02/(1.-xeSaha);
}
*Dxe = dxeSaha_dlna/Ddxedlna_Dxe;
/* Compute derivative again just so the fminuses are properly updated */
//dxedlna = rec_HMLA_2photon_dxedlna(xeSaha + *Dxe, nH, H, T, T,rate_table, twog, zstart, dlna, logfminus_hist, logfminus_Ly_hist, iz, z, energy_rate);
return xeSaha + *Dxe;
}
void rec_get_xe_next2(REC_COSMOPARAMS *param, double z1, double xe_in, double Tm_in, double *xe_out, double *Tm_out,
HRATEEFF *rate_table, int func_select, unsigned iz, TWO_PHOTON_PARAMS *twog_params,
double **logfminus_hist, double *logfminus_Ly_hist[],
double *z_prev, double *dxedlna_prev, double *dTmdlna_prev,
double *z_prev2, double *dxedlna_prev2, double *dTmdlna_prev2) {
double dxedlna, dTmdlna, Tr, nH, ainv, H;
Tr = param->T0 * (ainv=1.+z1);
nH = param->nH0 * ainv*ainv*ainv;
H = rec_HubbleConstant(param, z1);
#if (MODEL == PEEBLES)
dxedlna = func_select==FUNC_HEI ? rec_helium_dxedt(xe_in, param->nH0, param->T0, param->fHe, H, z1)/H:
rec_HPeebles_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, energy_injection_rate(param,z1));
#elif (MODEL == RECFAST)
dxedlna = func_select==FUNC_HEI ? rec_helium_dxedt(xe_in, param->nH0, param->T0, param->fHe, H, z1)/H:
rec_HRecFast_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, energy_injection_rate(param,z1));
#elif (MODEL == EMLA2s2p)
dxedlna = func_select==FUNC_HEI ? rec_helium_dxedt(xe_in, param->nH0, param->T0, param->fHe, H, z1)/H:
rec_HMLA_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, energy_injection_rate(param,z1), rate_table);
#else
dxedlna = func_select==FUNC_HEI ? rec_helium_dxedt(xe_in, param->nH0, param->T0, param->fHe, H, z1)/H:
func_select==FUNC_H2G ? rec_HMLA_2photon_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, rate_table, twog_params,
param->zstart, param->dlna, logfminus_hist, logfminus_Ly_hist, iz, z1,
energy_injection_rate(param,z1)):
func_select==FUNC_HMLA ? rec_HMLA_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, energy_injection_rate(param,z1), rate_table)
:rec_HPeebles_dxedlna(xe_in, nH*1e-6, H, Tm_in*kBoltz, Tr*kBoltz, energy_injection_rate(param,z1)); /* used for z < 20 only */
#endif
dTmdlna = rec_dTmdlna(xe_in, Tm_in, Tr, H, param->fHe, nH*1e-6, energy_injection_rate(param,z1));
*xe_out = xe_in + param->dlna * (1.25 * dxedlna - 0.25 * (*dxedlna_prev2));
*Tm_out = Tm_in + param->dlna * (1.25 * dTmdlna - 0.25 * (*dTmdlna_prev2));
*z_prev2 = *z_prev;
*dxedlna_prev2 = *dxedlna_prev;
*dTmdlna_prev2 = *dTmdlna_prev;
*z_prev = z1;
*dxedlna_prev = dxedlna;
*dTmdlna_prev = dTmdlna;
}