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/*
Copyright 2018-2020 Frederic Vincent, Thibaut Paumard
This file is part of Gyoto.
Gyoto is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Gyoto is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Gyoto. If not, see <http://www.gnu.org/licenses/>.
*/
#include "GyotoKappaDistributionSynchrotronSpectrum.h"
#include "GyotoDefs.h"
#include <cmath>
#ifdef GYOTO_USE_XERCES
#include "GyotoFactory.h"
#include "GyotoFactoryMessenger.h"
#endif
using namespace Gyoto;
using namespace std;
#include "GyotoProperty.h"
GYOTO_PROPERTY_START(Spectrum::KappaDistributionSynchrotron,
"Kappa synchrotron emission")
GYOTO_PROPERTY_END(Spectrum::KappaDistributionSynchrotron, Generic::properties)
#define nstep_angint 100 // for angle-averaging integration
Spectrum::KappaDistributionSynchrotron::KappaDistributionSynchrotron()
: Spectrum::Generic("KappaDistributionSynchrotron"),
numberdensityCGS_(0.),
angle_B_pem_(0.), cyclotron_freq_(1.), thetae_(1.),
kappaindex_(0.), angle_averaged_(0), hypergeometric_(1)
{}
Spectrum::KappaDistributionSynchrotron::KappaDistributionSynchrotron(const KappaDistributionSynchrotron &o)
: Spectrum::Generic(o),
spectrumBB_(NULL),
numberdensityCGS_(o.numberdensityCGS_),
angle_B_pem_(o.angle_B_pem_),
cyclotron_freq_(o.cyclotron_freq_),
thetae_(o.thetae_),
kappaindex_(o.kappaindex_),
hypergeometric_(o.hypergeometric_),
angle_averaged_(o.angle_averaged_)
{
if (o.spectrumBB_()) spectrumBB_=o.spectrumBB_->clone();
}
double Spectrum::KappaDistributionSynchrotron::numberdensityCGS() const {
return numberdensityCGS_; }
void Spectrum::KappaDistributionSynchrotron::numberdensityCGS(double rho) {
numberdensityCGS_ = rho; }
double Spectrum::KappaDistributionSynchrotron::angle_B_pem() const {
return angle_B_pem_; }
void Spectrum::KappaDistributionSynchrotron::angle_B_pem(double angle) {
angle_B_pem_ = angle; }
double Spectrum::KappaDistributionSynchrotron::cyclotron_freq() const {
return cyclotron_freq_; }
void Spectrum::KappaDistributionSynchrotron::cyclotron_freq(double freq) {
cyclotron_freq_ = freq; }
double Spectrum::KappaDistributionSynchrotron::thetae() const {
return thetae_; }
void Spectrum::KappaDistributionSynchrotron::thetae(double th) {
thetae_ = th; }
double Spectrum::KappaDistributionSynchrotron::kappaindex() const {
return kappaindex_; }
void Spectrum::KappaDistributionSynchrotron::kappaindex(double ind) {
kappaindex_ = ind; }
double Spectrum::KappaDistributionSynchrotron::hypergeometric() const {
return hypergeometric_; }
void Spectrum::KappaDistributionSynchrotron::hypergeometric(double hh) {
hypergeometric_ = hh; }
bool Spectrum::KappaDistributionSynchrotron::angle_averaged() const {
return angle_averaged_; }
void Spectrum::KappaDistributionSynchrotron::angle_averaged(bool ang) {
angle_averaged_ = ang; }
Spectrum::KappaDistributionSynchrotron * Spectrum::KappaDistributionSynchrotron::clone() const
{ return new Spectrum::KappaDistributionSynchrotron(*this); }
double Spectrum::KappaDistributionSynchrotron::operator()(double nu) const {
GYOTO_ERROR("In PLSynch: "
"Synchrotron emission not defined for optically thick case");
return 0.;
}
double Spectrum::KappaDistributionSynchrotron::operator()(double nu,
double ,
double ds) const{
double dsCGS = ds*100.; // ds should be given in SI
// Returns intensity increment in SI:
return jnuCGS(nu)*dsCGS*exp(-alphanuCGS(nu)*dsCGS)*GYOTO_INU_CGS_TO_SI;
}
double Spectrum::KappaDistributionSynchrotron::jnuCGS(double nu) const{
// Pandya, Zhang, Chandra, Gammie, 2016
//cout << "in kappa jnu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
Js_low = pow(Xk,1./3.)*sinth*4.*M_PI*tgamma(kappaindex_-4./3.)/ \
(pow(3.,7./3.)*tgamma(kappaindex_-2.)),
Js_high = pow(Xk,-(kappaindex_-2.)/2.)*sinth*pow(3.,(kappaindex_-1.)/2.)* \
(kappaindex_-1.)*(kappaindex_-2.)/4.*tgamma(kappaindex_/4.-1./3.)* \
tgamma(kappaindex_/4.+4./3.),
expo = 3.*pow(kappaindex_,-3./2.),
Js = pow(pow(Js_low,-expo) + pow(Js_high,-expo),-1./expo);
double emis_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS*cyclotron_freq_/ \
GYOTO_C_CGS* \
Js;
//cout << "in kappa spec angleB jnu= " << angle_B_pem_ << " " << emis_synch << endl;
return emis_synch;
}
double Spectrum::KappaDistributionSynchrotron::jQnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
//cout << "in kappa jnu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
Js_low = 0.5*pow(Xk,1./3.)*sinth*4.*M_PI*tgamma(kappaindex_-4./3.)/ \
(pow(3.,7./3.)*tgamma(kappaindex_-2.)),
Js_high = (pow(4./5.,2.)+kappaindex_/50.)*pow(Xk,-(kappaindex_-2.)/2.)*sinth*pow(3.,(kappaindex_-1.)/2.)* \
(kappaindex_-1.)*(kappaindex_-2.)/4.*tgamma(kappaindex_/4.-1./3.)* \
tgamma(kappaindex_/4.+4./3.),
expo = 3.7*pow(kappaindex_,-8./5.),
Js = pow(pow(Js_low,-expo) + pow(Js_high,-expo),-1./expo);
double emis_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS*cyclotron_freq_/ \
GYOTO_C_CGS* \
Js;
//cout << "in kappa spec angleB jnu= " << angle_B_pem_ << " " << emis_synch << endl;
return emis_synch;
}
double Spectrum::KappaDistributionSynchrotron::jUnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
return 0.;
}
double Spectrum::KappaDistributionSynchrotron::jVnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
//cout << "in kappa jnu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
Js_low = pow(3./4.,2.)*pow(pow(sinth,-12./5.)-1.,12./25.)*pow(kappaindex_, -66./125.)/thetae_*\
pow(Xk,-7./20.)*pow(Xk,1./3.)*sinth*4.*M_PI*tgamma(kappaindex_-4./3.)/ \
(pow(3.,7./3.)*tgamma(kappaindex_-2.)),
Js_high = pow(7./8.,2.)*pow(pow(sinth,-5./2.)-1.,11./25.)*pow(kappaindex_, -11./25.)/thetae_*\
pow(Xk,-1./2.)*pow(Xk,-(kappaindex_-2.)/2.)*sinth*pow(3.,(kappaindex_-1.)/2.)* \
(kappaindex_-1.)*(kappaindex_-2.)/4.*tgamma(kappaindex_/4.-1./3.)* \
tgamma(kappaindex_/4.+4./3.),
expo = 3.*pow(kappaindex_,-3./2.),
Js = pow(pow(Js_low,-expo) + pow(Js_high,-expo),-1./expo)*cos(angle_B_pem_)/abs(cos(angle_B_pem_));
double emis_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS*cyclotron_freq_/ \
GYOTO_C_CGS* \
Js;
//cout << "in kappa spec angleB jnu= " << angle_B_pem_ << " " << emis_synch << endl;
return emis_synch;
}
double Spectrum::KappaDistributionSynchrotron::alphanuCGS(double nu) const{
// Pandya, Zhang, Chandra, Gammie, 2016
//cout << "in kappa anu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << " " << hypergeometric_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
As_low = pow(Xk,-2./3.)*pow(3.,1./6.)*10./41.* \
2.*M_PI/pow(thetae_*kappaindex_,10./3.-kappaindex_) * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/(3.*kappaindex_-1.) * \
tgamma(5./3.)*hypergeometric_,
As_high = pow(Xk,-(1.+kappaindex_)/2.)*pow(M_PI,3./2.)/3. * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/pow(thetae_*kappaindex_,3.)* \
(2.*tgamma(2.+kappaindex_/2.)/(2.+kappaindex_)-1.)* \
(pow(3./kappaindex_,19./4.)+3./5.),
expo = pow(-7./4.+8./5.*kappaindex_,-43./50.),
As = pow(pow(As_low,-expo) + pow(As_high,-expo),-1./expo);
double abs_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS/ \
(nu*GYOTO_ELECTRON_MASS_CGS*GYOTO_C_CGS)* \
As;
//cout << "in kappa spec angleB anu= " << angle_B_pem_ << " " << abs_synch << endl;
return abs_synch;
}
double Spectrum::KappaDistributionSynchrotron::alphaQnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
//cout << "in kappa anu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << " " << hypergeometric_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
As_low = 25./48.*pow(Xk,-2./3.)*pow(3.,1./6.)*10./41.* \
2.*M_PI/pow(thetae_*kappaindex_,10./3.-kappaindex_) * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/(3.*kappaindex_-1.) * \
tgamma(5./3.)*hypergeometric_,
As_high = pow(Xk,-(1.+kappaindex_)/2.)*pow(M_PI,3./2.)/3. * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/pow(thetae_*kappaindex_,3.)* \
(2.*tgamma(2.+kappaindex_/2.)/(2.+kappaindex_)-1.)* \
(pow(21.,2.)*pow(kappaindex_,-pow(12./5.,2.))+11./20.),
expo = 7./5.*pow(kappaindex_,-23./20.),
As = pow(pow(As_low,-expo) + pow(As_high,-expo),-1./expo);
double abs_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS/ \
(nu*GYOTO_ELECTRON_MASS_CGS*GYOTO_C_CGS)* \
As;
//cout << "in kappa spec angleB anu= " << angle_B_pem_ << " " << abs_synch << endl;
return abs_synch;
}
double Spectrum::KappaDistributionSynchrotron::alphaUnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
return 0.;
}
double Spectrum::KappaDistributionSynchrotron::alphaVnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
//cout << "in kappa anu stuff: " << cyclotron_freq_ << " " << thetae_ << " " << kappaindex_ << " " << hypergeometric_ << endl;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
As_low = 77./100./thetae_*pow(pow(sinth,-114./50.)-1.,223./500.)*pow(kappaindex_,-7./10.) *\
pow(Xk,-7./20.)*pow(Xk,-2./3.)*pow(3.,1./6.)*10./41.* \
2.*M_PI/pow(thetae_*kappaindex_,10./3.-kappaindex_) * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/(3.*kappaindex_-1.) * \
tgamma(5./3.)*hypergeometric_,
As_high = pow(Xk,-(1.+kappaindex_)/2.)*pow(M_PI,3./2.)/3. * \
(kappaindex_-1.)*(kappaindex_-2.)*kappaindex_/pow(thetae_*kappaindex_,3.)* \
(2.*tgamma(2.+kappaindex_/2.)/(2.+kappaindex_)-1.)* \
143./10.*pow(thetae_,-116./125.)*pow(pow(sinth,-41./20.)-1.,1./2.) *\
(pow(13.,2.)*pow(kappaindex_,-8.)+13./2500.*kappaindex_-263./5000.+47./200./kappaindex_)*pow(Xk,-0.5),
expo = 61./50.*pow(kappaindex_,-142./125.)+7./1000.,
As = pow(pow(As_low,-expo) + pow(As_high,-expo),-1./expo)*cos(angle_B_pem_)/abs(cos(angle_B_pem_));
double abs_synch = numberdensityCGS_* \
GYOTO_ELEMENTARY_CHARGE_CGS*GYOTO_ELEMENTARY_CHARGE_CGS/ \
(nu*GYOTO_ELECTRON_MASS_CGS*GYOTO_C_CGS)* \
As;
//cout << "in kappa spec angleB anu= " << angle_B_pem_ << " " << abs_synch << endl;
return abs_synch;
}
double Spectrum::KappaDistributionSynchrotron::rQnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
double rho_Q=0;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
rho_kappa=0;
if (Xk<0.1)
GYOTO_ERROR("Xk too low to compute rhoQ with these formula");
switch(int(kappaindex_*10))
{
case 35:
rho_kappa=17.*thetae_-3.*sqrt(thetae_)+7.*sqrt(thetae_)*exp(-5.*thetae_)*\
(1-exp(-pow(Xk,0.84)/30.)-sin(Xk/10.)*exp(-3./2.*pow(Xk,0.471)));
break;
case 40:
rho_kappa=46./3.*thetae_-5./3.*sqrt(thetae_)+17./3.*sqrt(thetae_)*exp(-5.*thetae_)*\
(1-exp(-pow(Xk,0.84)/18.)-sin(Xk/6.)*exp(-7./4.*pow(Xk,0.5)));
break;
case 45:
rho_kappa=14.*thetae_-13./8.*sqrt(thetae_)+9./2.*sqrt(thetae_)*exp(-5.*thetae_)*\
(1-exp(-pow(Xk,0.84)/12.)-sin(Xk/4.)*exp(-2.*pow(Xk,0.525)));
break;
case 50:
rho_kappa=25./2.*thetae_-sqrt(thetae_)+5.*sqrt(thetae_)*exp(-5.*thetae_)*\
(1-exp(-pow(Xk,0.84)/8.)-sin(3.*Xk/8.)*exp(-9./4.*pow(Xk,0.541)));
break;
default:
GYOTO_ERROR("Faraday coefficients not defined for values of kappa different of 3.5, 4., 4.5, 5.");
}
rho_Q=numberdensityCGS_*pow(GYOTO_ELEMENTARY_CHARGE_CGS*cyclotron_freq_*sinth,2.)/ \
(GYOTO_ELECTRON_MASS_CGS*GYOTO_C_CGS*pow(nu,3.))* \
rho_kappa;
return rho_Q;
}
double Spectrum::KappaDistributionSynchrotron::rUnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
return 0.;
}
double Spectrum::KappaDistributionSynchrotron::rVnuCGS(double nu) const{
// Marszewski, Prather, Joshi, Pandya, Gammie 2021
double rho_V=0;
double sinth = sin(angle_B_pem_),
nuk = cyclotron_freq_*pow(thetae_*kappaindex_,2.)*sinth,
Xk = nu/nuk,
rho_kappa=0;
if (Xk<0.1)
GYOTO_ERROR("Xk too low to compute rhoQ with these formula");
switch(int(kappaindex_*10))
{
case 35:
rho_kappa=(pow(thetae_,2.)+2.*thetae_+1.)/ \
(25./8.*pow(thetae_,2.)+4.*thetae_+1.)* \
(1-0.17*log(1.+0.447*pow(Xk,-0.5)));
break;
case 40:
rho_kappa=(pow(thetae_,2.)+54.*thetae_+50.)/ \
(30./11.*pow(thetae_,2.)+134.*thetae_+50.)* \
(1-0.17*log(1.+0.391*pow(Xk,-0.5)));
break;
case 45:
rho_kappa=(pow(thetae_,2.)+43.*thetae_+38.)/ \
(7./3.*pow(thetae_,2.)+185./2.*thetae_+38.)* \
(1-0.17*log(1.+0.348*pow(Xk,-0.5)));
break;
case 50:
rho_kappa=(thetae_+13./14.)/ \
(2.*thetae_+13./14.)* \
(1-0.17*log(1.+0.313*pow(Xk,-0.5)));
break;
default:
GYOTO_ERROR("Faraday coefficients not defined for values of kappa different of 3.5, 4., 4.5, 5.");
}
rho_V=2.*numberdensityCGS_*pow(GYOTO_ELEMENTARY_CHARGE_CGS,2.)*cyclotron_freq_*cos(angle_B_pem_)*bessk0(1./thetae_)/ \
(GYOTO_ELECTRON_MASS_CGS*GYOTO_C_CGS*pow(nu,2.)*bessk(2.,1./thetae_))* \
rho_kappa;
return rho_V;
}
void Spectrum::KappaDistributionSynchrotron::radiativeQ(double jnu[], // output
double alphanu[], // output
double const nu_ems[],
size_t nbnu
) {
for (size_t ii=0; ii< nbnu; ++ii){
double nu = nu_ems[ii];
double jnucur=0., anucur=0.;
if (!angle_averaged_){
jnucur = jnuCGS(nu);
anucur = alphanuCGS(nu);
}else{
double th0=0.01, thNm1=M_PI-0.01; // avoiding sinth=0.
double hh=(thNm1-th0)/double(nstep_angint);
double theta=th0;
angle_B_pem(theta);
double jnusinprev=jnuCGS(nu)*sin(theta), jnusinnext=jnusinprev;
double anusinprev=alphanuCGS(nu)*sin(theta), anusinnext=anusinprev;
for (int jj=1;jj<=nstep_angint;jj++){
theta=th0+double(jj)*hh;
angle_B_pem(theta);
jnusinnext=jnuCGS(nu)*sin(theta);
anusinnext=alphanuCGS(nu)*sin(theta);
jnucur+=0.5*0.5*hh*(jnusinprev+jnusinnext);
anucur+=0.5*0.5*hh*(anusinprev+anusinnext);
jnusinprev=jnusinnext;
anusinprev=anusinnext;
//NB: averaged jnu is: \int jnu dOmega = 1/2 * \int jnu*sinth dth
}
}
// OUTPUTS
jnu[ii]= jnucur * GYOTO_JNU_CGS_TO_SI;
alphanu[ii]= anucur * GYOTO_ANU_CGS_TO_SI;
}
}
void Spectrum::KappaDistributionSynchrotron::radiativeQ(double jInu[], double jQnu[], double jUnu[], double jVnu[], // Output
double aInu[], double aQnu[], double aUnu[], double aVnu[], // Output
double rQnu[], double rUnu[], double rVnu[], // Output
double const nu_ems[],
size_t nbnu ){
for (size_t ii=0; ii< nbnu; ++ii){
double nu = nu_ems[ii];
double jInucur=0., jQnucur=0.,jUnucur=0.,jVnucur=0.;
double aInucur=0., aQnucur=0., aUnucur=0., aVnucur=0.;
double rQnucur=0., rUnucur=0., rVnucur=0.;
if (!angle_averaged_){
jInucur = jnuCGS(nu);
jQnucur = jQnuCGS(nu);
jUnucur = jUnuCGS(nu);
jVnucur = jVnuCGS(nu);
aInucur = alphanuCGS(nu);
aQnucur = alphaQnuCGS(nu);
aUnucur = alphaUnuCGS(nu);
aVnucur = alphaVnuCGS(nu);
rQnucur = rQnuCGS(nu);
rUnucur = rUnuCGS(nu);
rVnucur = rVnuCGS(nu);
}else{
double th0=0.01, thNm1=M_PI-0.01; // sin(theta) must never be 0
double hh=(thNm1-th0)/double(nstep_angint);
double theta=th0;
angle_B_pem(theta);
double jInusinprev=jnuCGS(nu)*sin(theta), jInusinnext=jInusinprev;
double jQnusinprev=jQnuCGS(nu)*sin(theta), jQnusinnext=jQnusinprev;
double jUnusinprev=jUnuCGS(nu)*sin(theta), jUnusinnext=jUnusinprev;
double jVnusinprev=jVnuCGS(nu)*sin(theta), jVnusinnext=jVnusinprev;
double aInusinprev=alphanuCGS(nu)*sin(theta), aInusinnext=aInusinprev;
double aQnusinprev=alphaQnuCGS(nu)*sin(theta), aQnusinnext=aQnusinprev;
double aUnusinprev=alphaUnuCGS(nu)*sin(theta), aUnusinnext=aUnusinprev;
double aVnusinprev=alphaVnuCGS(nu)*sin(theta), aVnusinnext=aVnusinprev;
double rQnusinprev=rQnuCGS(nu)*sin(theta), rQnusinnext=rQnusinprev;
double rUnusinprev=rUnuCGS(nu)*sin(theta), rUnusinnext=rUnusinprev;
double rVnusinprev=rVnuCGS(nu)*sin(theta), rVnusinnext=rVnusinprev;
for (int jj=1;jj<=nstep_angint;jj++){
theta=th0+double(jj)*hh;
angle_B_pem(theta);
jInusinnext=jnuCGS(nu)*sin(theta);
jQnusinnext=jQnuCGS(nu)*sin(theta);
jUnusinnext=jUnuCGS(nu)*sin(theta);
jVnusinnext=jVnuCGS(nu)*sin(theta);
aInusinnext=alphanuCGS(nu)*sin(theta);
aQnusinnext=alphaQnuCGS(nu)*sin(theta);
aUnusinnext=alphaUnuCGS(nu)*sin(theta);
aVnusinnext=alphaVnuCGS(nu)*sin(theta);
rQnusinnext=rQnuCGS(nu)*sin(theta);
rUnusinnext=rUnuCGS(nu)*sin(theta);
rVnusinnext=rVnuCGS(nu)*sin(theta);
jInucur+=0.5*0.5*hh*(jInusinprev+jInusinnext);
jQnucur+=0.5*0.5*hh*(jQnusinprev+jQnusinnext);
jUnucur+=0.5*0.5*hh*(jUnusinprev+jUnusinnext);
jVnucur+=0.5*0.5*hh*(jVnusinprev+jVnusinnext);
aInucur+=0.5*0.5*hh*(aInusinprev+aInusinnext);
aQnucur+=0.5*0.5*hh*(aQnusinprev+aQnusinnext);
aUnucur+=0.5*0.5*hh*(aUnusinprev+aUnusinnext);
aVnucur+=0.5*0.5*hh*(aVnusinprev+aVnusinnext);
rQnucur+=0.5*0.5*hh*(rQnusinprev+rQnusinnext);
rUnucur+=0.5*0.5*hh*(rUnusinprev+rUnusinnext);
rVnucur+=0.5*0.5*hh*(rVnusinprev+rVnusinnext);
jInusinprev=jInusinnext;
jQnusinprev=jQnusinnext;
jUnusinprev=jUnusinnext;
jVnusinprev=jVnusinnext;
aInusinprev=aInusinnext;
aQnusinprev=aQnusinnext;
aUnusinprev=aUnusinnext;
aVnusinprev=aVnusinnext;
rQnusinprev=rQnusinnext;
rUnusinprev=rUnusinnext;
rVnusinprev=rVnusinnext;
//NB: averaged jnu is: 1/4pi * \int jnu dOmega = 1/2 * \int jnu*sinth dth
}
}
// OUTPUTS
jInu[ii]=jInucur * GYOTO_JNU_CGS_TO_SI;
jQnu[ii]=jQnucur * GYOTO_JNU_CGS_TO_SI;
jUnu[ii]=jUnucur * GYOTO_JNU_CGS_TO_SI;
jVnu[ii]=jVnucur * GYOTO_JNU_CGS_TO_SI;
aInu[ii]=aInucur * GYOTO_ANU_CGS_TO_SI;
aQnu[ii]=aQnucur * GYOTO_ANU_CGS_TO_SI;
aUnu[ii]=aUnucur * GYOTO_ANU_CGS_TO_SI;
aVnu[ii]=aVnucur * GYOTO_ANU_CGS_TO_SI;
rQnu[ii]=rQnucur * GYOTO_ANU_CGS_TO_SI;
rUnu[ii]=rUnucur * GYOTO_ANU_CGS_TO_SI;
rVnu[ii]=rVnucur * GYOTO_ANU_CGS_TO_SI;
}
}
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