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cooling.c
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#include "mode.h"
#ifdef GASOLINE
#ifndef NOCOOLING
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
/* General accuracy target */
#define EPS 1e-5
#define MAXABUNDITERATIONS 20
/* Accuracy for Temperature estimation for E,rho assuming eqm abundances */
#define EPSTEMP 1e-5
#define ETAMINTIMESTEP 1e-4
#include "stiff.h"
/* Integrator constants */
/* When to use to just do a first order step and quit */
/* Good value to use I think */
#define ECHANGEFRACSMALL 1e-4
/* Accuracy target for intergrators */
#define EPSINTEG 1e-5
#define MAXINTEGITS 20000
#if defined(COOLDEBUG) || defined(STARFORM)
#include "pkd.h"
#else
#include "cooling.h"
#endif
#define NDOT_MIN 1e-60
#define CL_eHI (13.60*CL_eV_erg)
#define CL_eHeI (24.59*CL_eV_erg)
#define CL_eHeII (54.42*CL_eV_erg)
#define CL_E2HeII (3.0*13.6*CL_eV_erg)
#define EMUL (1.01)
CL *clInit( )
{
CL *cl;
cl = (CL *) malloc(sizeof(CL));
assert(cl!=NULL);
cl->nUV = 0;
cl->UV = NULL;
cl->nTable = 0;
cl->RT = NULL;
cl->DerivsData = malloc(sizeof(clDerivsData));
assert(cl->DerivsData != NULL);
((clDerivsData *) (cl->DerivsData))->IntegratorContext =
StiffInit( EPSINTEG, 1, cl->DerivsData, clDerivs, clJacobn );
return cl;
}
void clFinalize(CL *cl )
{
StiffFinalize( ((clDerivsData *) (cl->DerivsData))->IntegratorContext );
free(cl->DerivsData);
if (cl->UV != NULL) free(cl->UV);
if (cl->RT != NULL) free(cl->RT);
free(cl);
}
void clInitConstants( CL *cl, double dGmPerCcUnit, double dComovingGmPerCcUnit,
double dErgPerGmUnit, double dSecUnit, double dMassFracHelium, int bUVTableUsesTime)
{
assert(cl!=NULL);
cl->dGmPerCcUnit = dGmPerCcUnit;
cl->dComovingGmPerCcUnit = dComovingGmPerCcUnit;
cl->dErgPerGmUnit = dErgPerGmUnit;
cl->dSecUnit = dSecUnit;
cl->dErgPerGmPerSecUnit = cl->dErgPerGmUnit / cl->dSecUnit;
cl->diErgPerGmUnit = 1./dErgPerGmUnit;
cl->Y_H = 1.0-dMassFracHelium;
cl->Y_He = dMassFracHelium/4;
cl->Y_eMAX = cl->Y_H + cl->Y_He*2;
cl->bUVTableUsesTime = bUVTableUsesTime;
cl->bUVTableLinear = bUVTableUsesTime; /* Linear if using time */
/* Derivs Data Struct */
{
clDerivsData *Data = cl->DerivsData;
assert(Data != NULL);
Data->cl = cl;
Data->Y_Total0 = (cl->Y_H+cl->Y_He)*.9999; /* neutral */
Data->Y_Total1 = (cl->Y_eMAX+cl->Y_H+cl->Y_He)*1.0001; /* Full Ionization */
Data->dlnE = (log(EMUL)-log(1/EMUL));
}
}
void clInitUV(CL *cl, UVSPECTRUM *UV, int nUV)
{
int i;
assert(cl!=NULL);
assert(cl->UV == NULL);
cl->nUV = nUV;
cl->UV = (UVSPECTRUM *) malloc(nUV*sizeof(UVSPECTRUM));
assert(cl->UV!=NULL);
for (i=0;i<nUV;i++) {
(cl->UV)[i] = UV[i];
if (i) assert ((UV[i-1].zTime > UV[i].zTime && !cl->bUVTableUsesTime) ||
(UV[i-1].zTime < UV[i].zTime && cl->bUVTableUsesTime));
}
}
void clInitRatesTable( CL *cl, double TMin, double TMax, int nTable ) {
/*-----------------------------------------------------------------
* Function of ln(T) tables:
* cl assumed to be predefined (allocated)
* A table spacing of 1.23e-3 in log(T) eg. nTable=15001 10->1e9 K
* Maximum 1% errors except at discontinuities in the functions.
* Storage for such a table is (15001*15*4|8b) => 0.9|1.7 Mb
*-----------------------------------------------------------------*/
int i;
double DeltaTln, Tln, T;
assert(cl!=NULL);
assert(cl->RT == NULL);
cl->R.Cool_Coll_HI = CL_eHI*CL_B_gm;
cl->R.Cool_Coll_HeI = CL_eHeI*CL_B_gm;
cl->R.Cool_Coll_HeII = CL_eHeII*CL_B_gm;
cl->R.Cool_Diel_HeII = (CL_E2HeII+CL_eHeI)*CL_B_gm;
cl->nTable = nTable;
cl->TMin = TMin;
cl->TMax = TMax;
cl->TlnMin = log( TMin );
cl->TlnMax = log( TMax );
DeltaTln = ( cl->TlnMax-cl->TlnMin )/( nTable - 1 );
cl->rDeltaTln = 1./DeltaTln;
cl->RT = (RATES_T *) malloc( nTable * sizeof(RATES_T) );
assert(cl->RT != NULL);
for ( i=0; i<nTable; i++ ) {
Tln = cl->TlnMin + DeltaTln*(i-1);
T=exp(Tln);
(cl->RT+i)->Rate_Coll_HI = clRateCollHI( T );
if ( (cl->RT+i)->Rate_Coll_HI < CL_RT_MIN ) (cl->RT+i)->Rate_Coll_HI = CL_RT_MIN;
(cl->RT+i)->Rate_Coll_HeI = clRateCollHeI( T );
if ( (cl->RT+i)->Rate_Coll_HeI < CL_RT_MIN ) (cl->RT+i)->Rate_Coll_HeI = CL_RT_MIN;
(cl->RT+i)->Rate_Coll_HeII = clRateCollHeII( T );
if ( (cl->RT+i)->Rate_Coll_HeII < CL_RT_MIN ) (cl->RT+i)->Rate_Coll_HeII = CL_RT_MIN;
(cl->RT+i)->Rate_Radr_HII = clRateRadrHII( T );
(cl->RT+i)->Rate_Radr_HeII = clRateRadrHeII( T );
(cl->RT+i)->Rate_Radr_HeIII = clRateRadrHeIII( T );
(cl->RT+i)->Rate_Diel_HeII = clRateDielHeII( T );
(cl->RT+i)->Cool_Brem_1 = clCoolBrem1( T );
(cl->RT+i)->Cool_Brem_2 = clCoolBrem2( T );
(cl->RT+i)->Cool_Radr_HII = clCoolRadrHII( T );
(cl->RT+i)->Cool_Radr_HeII = clCoolRadrHeII( T );
(cl->RT+i)->Cool_Radr_HeIII = clCoolRadrHeIII( T );
(cl->RT+i)->Cool_Line_HI = clCoolLineHI( T );
(cl->RT+i)->Cool_Line_HeI = clCoolLineHeII( T );
(cl->RT+i)->Cool_Line_HeII = clCoolLineHeII( T );
}
}
void clRatesTableError( CL *cl ) {
/* This estimates the error for a table of half the size of
* the current one.
* The collisional, dielectric and line cooling rates can all go to
* zero (minimum) and will even for double precision (exp(-1e5/T))
* the critical values that must never get down to zero
* are the radiative recombination rates: Check this before using
* CL_RT_FLOAT float for the table.
*/
int i,j,ierr[15];
double min[15],max[15];
double err,maxerr[15];
CL_RT_FLOAT *p,*p1,*p2;
for (j=0;j<15;j++) {
maxerr[j]=0.0;
min[j]=1e300;
max[j]=-1e300;
}
for ( i=1; i<cl->nTable-1; i+=2 ) {
p = (CL_RT_FLOAT *) &((cl->RT+i)->Rate_Coll_HI);
p1 = (CL_RT_FLOAT *) &((cl->RT+i-1)->Rate_Coll_HI);
p2 = (CL_RT_FLOAT *) &((cl->RT+i+1)->Rate_Coll_HI);
if (i==10001) {
printf(" Comp %i %i %e %e\n",i,(int) sizeof(CL_RT_FLOAT),p[1],(cl->RT+i)->Rate_Coll_HeI);
}
for (j=0;j<15;j++) {
if (p[j] < min[j]) min[j]=p[j];
if (p[j] > max[j]) max[j]=p[j];
err= fabs((0.5*(p1[j]+p2[j])-p[j])/(p[j]+1e-30));
if (err > maxerr[j] ) {
maxerr[j]=err;
ierr[j]=i;
}
}
}
for (j=0;j<15;j++) {
printf("Col %i Max Error: %e at T=%e dlnT=%e (min %e max %e)\n",j,
maxerr[j],exp(cl->TlnMin+ierr[j]/cl->rDeltaTln),2/cl->rDeltaTln,min[j],max[j]);
}
}
#define CL_Ccomp0 0.565e-9
#define CL_Tcmb0 2.735
#define CL_Ccomp (CL_Ccomp0*CL_Tcmb0)
void clRatesRedshift( CL *cl, double zIn, double dTimeIn ) {
int i;
double xx;
double zTime;
UVSPECTRUM *UV,*UV0;
cl->z = zIn;
cl->dTime = dTimeIn;
cl->dComovingGmPerCcUnit = cl->dGmPerCcUnit*pow(1.+zIn,3.);
cl->R.Cool_Comp = pow((1+zIn)*CL_Ccomp,4.0)*CL_B_gm;
/* Photo-Ionization rates */
UV = cl->UV;
if (cl->bUVTableUsesTime) {
/*
** Table in order of increasing time
*/
zTime = dTimeIn;
for ( i=0; i < cl->nUV && zTime >= UV->zTime ; i++,UV++ );
}
else {
/*
** Table in order of high to low redshift
*/
zTime = zIn;
for ( i=0; i < cl->nUV && zTime <= UV->zTime ; i++,UV++ );
}
if (i == 0) {
cl->R.Rate_Phot_HI = CL_RT_MIN;
cl->R.Rate_Phot_HeI = CL_RT_MIN;
cl->R.Rate_Phot_HeII = CL_RT_MIN;
cl->R.Heat_Phot_HI = 0.0;
cl->R.Heat_Phot_HeI = 0.0;
cl->R.Heat_Phot_HeII = 0.0;
return;
}
UV0=UV-1;
if (i == cl->nUV ) {
cl->R.Rate_Phot_HI = UV0->Rate_Phot_HI;
cl->R.Rate_Phot_HeI = UV0->Rate_Phot_HeI;
cl->R.Rate_Phot_HeII = UV0->Rate_Phot_HeII;
cl->R.Heat_Phot_HI = UV0->Heat_Phot_HI*CL_B_gm;
cl->R.Heat_Phot_HeI = UV0->Heat_Phot_HeI*CL_B_gm;
cl->R.Heat_Phot_HeII = UV0->Heat_Phot_HeII*CL_B_gm;
}
else {
if (cl->bUVTableLinear) { /* use Linear interpolation */
xx = (zTime - UV0->zTime)/(UV->zTime - UV0->zTime);
cl->R.Rate_Phot_HI = UV0->Rate_Phot_HI*(1-xx)+UV->Rate_Phot_HI*xx;
cl->R.Rate_Phot_HeI = UV0->Rate_Phot_HeI*(1-xx)+UV->Rate_Phot_HeI*xx;
cl->R.Rate_Phot_HeII = UV0->Rate_Phot_HeII*(1-xx)+UV->Rate_Phot_HeII*xx;
cl->R.Heat_Phot_HI = (UV0->Heat_Phot_HI*(1-xx)+UV->Heat_Phot_HI*xx)*CL_B_gm;
cl->R.Heat_Phot_HeI = (UV0->Heat_Phot_HeI*(1-xx)+UV->Heat_Phot_HeI*xx)*CL_B_gm;
cl->R.Heat_Phot_HeII = (UV0->Heat_Phot_HeII*(1-xx)+UV->Heat_Phot_HeII*xx)*CL_B_gm;
}
else { /* use Log interpolation with 1+zTime */
xx = log((1+zTime)/(1+UV0->zTime))/log((1+UV->zTime)/(1+UV0->zTime));
cl->R.Rate_Phot_HI = pow(UV0->Rate_Phot_HI,1-xx)*pow(UV->Rate_Phot_HI,xx);
cl->R.Rate_Phot_HeI = pow(UV0->Rate_Phot_HeI,1-xx)*pow(UV->Rate_Phot_HeI,xx);
cl->R.Rate_Phot_HeII = pow(UV0->Rate_Phot_HeII,1-xx)*pow(UV->Rate_Phot_HeII,xx);
cl->R.Heat_Phot_HI = pow(UV0->Heat_Phot_HI,1-xx)*pow(UV->Heat_Phot_HI,xx)*CL_B_gm;
cl->R.Heat_Phot_HeI = pow(UV0->Heat_Phot_HeI,1-xx)*pow(UV->Heat_Phot_HeI,xx)*CL_B_gm;
cl->R.Heat_Phot_HeII = pow(UV0->Heat_Phot_HeII,1-xx)*pow(UV->Heat_Phot_HeII,xx)*CL_B_gm;
}
}
if (cl->R.Rate_Phot_HI < CL_RT_MIN) cl->R.Rate_Phot_HI = CL_RT_MIN;
if (cl->R.Rate_Phot_HeI < CL_RT_MIN) cl->R.Rate_Phot_HeI = CL_RT_MIN;
if (cl->R.Rate_Phot_HeII < CL_RT_MIN) cl->R.Rate_Phot_HeII = CL_RT_MIN;
/*
printf("Cooling Rates for t(%1i)=%g, Z=%g: %g %g %g %g %g %g\n",cl->bUVTableUsesTime,dTimeIn,zIn,cl->R.Rate_Phot_HI,cl->R.Rate_Phot_HeI,cl->R.Rate_Phot_HeII,cl->R.Heat_Phot_HI,cl->R.Heat_Phot_HeI,cl->R.Heat_Phot_HeII);
*/
return;
}
void clRates ( CL *cl, RATE *Rate, double T ) {
double Tln;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
if (T >= cl->TMax) T=cl->TMax*(1.0 - EPS);
if (T < cl->TMin) T=cl->TMin;
Tln = log(T);
Rate->T = T;
Rate->Tln = Tln;
xTln = (Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = xTln-iTln;
wTln0 = 1-wTln1;
Rate->Coll_HI = (wTln0*RT0->Rate_Coll_HI+wTln1*RT1->Rate_Coll_HI);
Rate->Coll_HeI = (wTln0*RT0->Rate_Coll_HeI+wTln1*RT1->Rate_Coll_HeI);
Rate->Coll_HeII = (wTln0*RT0->Rate_Coll_HeII+wTln1*RT1->Rate_Coll_HeII);
Rate->Radr_HII = (wTln0*RT0->Rate_Radr_HII+wTln1*RT1->Rate_Radr_HII);
Rate->Radr_HeII = (wTln0*RT0->Rate_Radr_HeII+wTln1*RT1->Rate_Radr_HeII);
Rate->Diel_HeII = (wTln0*RT0->Rate_Diel_HeII+wTln1*RT1->Rate_Diel_HeII);
Rate->Totr_HeII = Rate->Radr_HeII + Rate->Diel_HeII;
Rate->Radr_HeIII = (wTln0*RT0->Rate_Radr_HeIII+wTln1*RT1->Rate_Radr_HeIII);
}
double clHeatTotal ( CL *cl, PERBARYON *Y ) {
/* erg /gram /sec
Note: QQ_* premultiplied by (CL_B_gm*erg_ev) */
return Y->HI * cl->R.Heat_Phot_HI * cl->R.Rate_Phot_HI +
Y->HeI * cl->R.Heat_Phot_HeI * cl->R.Rate_Phot_HeI +
Y->HeII * cl->R.Heat_Phot_HeII * cl->R.Rate_Phot_HeII;
}
double clCoolTotal ( CL *cl, PERBARYON *Y, RATE *Rate, double rho ) {
/* Assumes clRates called previously */
/* erg /gram /sec */
double en_B=rho*CL_B_gm;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
xTln = (Rate->Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = xTln-iTln;
wTln0 = 1-wTln1;
/* PUT INTO erg/gm/sec */
return Y->e * (
cl->R.Cool_Comp * ( Rate->T-CL_Tcmb0 ) * ( 1 + cl->z ) +
en_B * (
(wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HII + Y->HeII ) +
(wTln0*RT0->Cool_Brem_2+wTln1*RT1->Cool_Brem_2) * Y->HeIII +
(wTln0*RT0->Cool_Radr_HII+wTln1*RT1->Cool_Radr_HII) * Y->HII * Rate->Radr_HII +
(wTln0*RT0->Cool_Radr_HeII+wTln1*RT1->Cool_Radr_HeII) * Y->HeII * Rate->Radr_HeII +
(wTln0*RT0->Cool_Radr_HeIII+wTln1*RT1->Cool_Radr_HeIII) * Y->HeIII * Rate->Radr_HeIII +
cl->R.Cool_Coll_HI * Y->HI * Rate->Coll_HI +
cl->R.Cool_Coll_HeI * Y->HeI * Rate->Coll_HeI +
cl->R.Cool_Coll_HeII * Y->HeII * Rate->Coll_HeII +
cl->R.Cool_Diel_HeII * Y->HeII * Rate->Diel_HeII +
(wTln0*RT0->Cool_Line_HI+wTln1*RT1->Cool_Line_HI) * Y->HI +
(wTln0*RT0->Cool_Line_HeI+wTln1*RT1->Cool_Line_HeI) * Y->HeI +
(wTln0*RT0->Cool_Line_HeII+wTln1*RT1->Cool_Line_HeII) * Y->HeII ) );
}
COOL_ERGPERSPERGM clTestCool ( CL *cl, PERBARYON *Y, RATE *Rate, double rho ) {
/* Assumes clRates called previously */
/* erg /gram /sec */
double en_B=rho*CL_B_gm;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
COOL_ERGPERSPERGM ret;
xTln = (Rate->Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = xTln-iTln;
wTln0 = 1-wTln1;
/* PUT INTO erg/gm/sec */
ret.compton = Y->e * (
cl->R.Cool_Comp * ( Rate->T-CL_Tcmb0 ) * ( 1 + cl->z ));
ret.bremHII = Y->e * en_B * (
(wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HII ));
ret.bremHeII = Y->e * en_B * (
(wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HeII ));
ret.bremHeIII = Y->e * en_B * (
(wTln0*RT0->Cool_Brem_2+wTln1*RT1->Cool_Brem_2) * Y->HeIII );
ret.radrecHII = Y->e * en_B *
(wTln0*RT0->Cool_Radr_HII+wTln1*RT1->Cool_Radr_HII) * Y->HII * Rate->Radr_HII;
ret.radrecHeII = Y->e * en_B *
(wTln0*RT0->Cool_Radr_HeII+wTln1*RT1->Cool_Radr_HeII) * Y->HeII * Rate->Radr_HeII;
ret.radrecHeIII = Y->e * en_B *
(wTln0*RT0->Cool_Radr_HeIII+wTln1*RT1->Cool_Radr_HeIII) * Y->HeIII * Rate->Radr_HeIII;
ret.collionHI = Y->e * en_B *
cl->R.Cool_Coll_HI * Y->HI * Rate->Coll_HI;
ret.collionHeI = Y->e * en_B *
cl->R.Cool_Coll_HeI * Y->HeI * Rate->Coll_HeI;
ret.collionHeII = Y->e * en_B *
cl->R.Cool_Coll_HeII * Y->HeII * Rate->Coll_HeII;
ret.dielrecHeII = Y->e * en_B *
cl->R.Cool_Diel_HeII * Y->HeII * Rate->Diel_HeII;
ret.lineHI = Y->e * en_B *
(wTln0*RT0->Cool_Line_HI+wTln1*RT1->Cool_Line_HI) * Y->HI;
ret.lineHeI = Y->e * en_B *
(wTln0*RT0->Cool_Line_HeI+wTln1*RT1->Cool_Line_HeI) * Y->HeI;
ret.lineHeII = Y->e * en_B *
(wTln0*RT0->Cool_Line_HeII+wTln1*RT1->Cool_Line_HeII) * Y->HeII;
return ret;
}
void clPrintCool ( CL *cl, PERBARYON *Y, RATE *Rate, double rho ) {
/* Assumes clRates called previously */
/* erg /gram /sec */
double en_B=rho*CL_B_gm;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
xTln = (Rate->Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = xTln-iTln;
wTln0 = 1-wTln1;
/* PUT INTO erg/gm/sec */
printf("Compton: %e\n",
Y->e * (
cl->R.Cool_Comp * ( Rate->T-CL_Tcmb0 ) * ( 1 + cl->z )));
printf("Cool Brem HII %e\n",
Y->e * en_B * (
(wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HII )) );
printf("Cool Brem HeII %e\n",
Y->e * en_B * (
(wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HeII )) );
printf("Cool Brem HeIII %e\n",
Y->e * en_B * (
(wTln0*RT0->Cool_Brem_2+wTln1*RT1->Cool_Brem_2) * Y->HeIII ) );
printf("Radiative Recombination HII %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Radr_HII+wTln1*RT1->Cool_Radr_HII) * Y->HII * Rate->Radr_HII );
printf("Radiative Recombination HeII %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Radr_HeII+wTln1*RT1->Cool_Radr_HeII) * Y->HeII * Rate->Radr_HeII);
printf("Radiative Recombination HeIII %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Radr_HeIII+wTln1*RT1->Cool_Radr_HeIII) * Y->HeIII * Rate->Radr_HeIII);
printf("Collisional Ionization HI %e\n",
Y->e * en_B *
cl->R.Cool_Coll_HI * Y->HI * Rate->Coll_HI);
printf("Collisional Ionization HeI %e\n",
Y->e * en_B *
cl->R.Cool_Coll_HeI * Y->HeI * Rate->Coll_HeI);
printf("Collisional Ionization HeII %e\n",
Y->e * en_B *
cl->R.Cool_Coll_HeII * Y->HeII * Rate->Coll_HeII);
printf("Dielectric Recombination HeII %e\n",
Y->e * en_B * cl->R.Cool_Diel_HeII * Y->HeII * Rate->Diel_HeII);
printf("Line cooling HI %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Line_HI+wTln1*RT1->Cool_Line_HI) * Y->HI);
printf("Line cooling HeI %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Line_HeI+wTln1*RT1->Cool_Line_HeI) * Y->HeI);
printf("Line cooling HeII %e\n",
Y->e * en_B *
(wTln0*RT0->Cool_Line_HeII+wTln1*RT1->Cool_Line_HeII) * Y->HeII );
}
void clAbunds( CL *cl, PERBARYON *Y, RATE *Rate, double rho ) {
double en_B=rho*CL_B_gm;
double rcirrHI = (Rate->Coll_HI)/(Rate->Radr_HII);
double rcirrHeI = (Rate->Coll_HeI)/(Rate->Totr_HeII);
double rcirrHeII = (Rate->Coll_HeII)/(Rate->Radr_HeIII);
double rpirrHI = (cl->R.Rate_Phot_HI)/(Rate->Radr_HII * en_B);
double rpirrHeI = (cl->R.Rate_Phot_HeI)/(Rate->Totr_HeII * en_B);
double rpirrHeII = (cl->R.Rate_Phot_HeII)/(Rate->Radr_HeIII * en_B);
double yHI = 0.;
double yHeI = 0.;
double yHeII = 0.;
double yH = cl->Y_H;
double yHe = cl->Y_He;
double yeMAX = cl->Y_eMAX;
double rye,ye;
double fHI,fHeI,fHeII,rfHe,yHI_old,yHeII_old;
int i;
for ( i=0 ; i<MAXABUNDITERATIONS ; i++ ) {
yHI_old = yHI;
yHeII_old = yHeII;
ye = (yeMAX-(yHI + 2 * yHeI + yHeII));
if (ye <= 0) {
Y->e = 0;
Y->HI = yH;
Y->HII = 0;
Y->HeI = yHe;
Y->HeII = 0;
Y->HeIII = 0;
Y->Total = yH + yHe;
return;
}
rye = 1/ye;
fHI = rcirrHI + rpirrHI * rye;
fHeI = rcirrHeI + rpirrHeI * rye;
rfHe = 1 / ( 1 + fHeI * (1+rcirrHeII+rpirrHeII*rye) );
yHI = yH / (1.0+fHI);
yHeI = yHe * rfHe;
yHeII = yHe * fHeI * rfHe;
/* fprintf(stderr,"Abund %g %g %g %g\n",yHI,yHeI,yHeII,ye);
fprintf(stderr," Rates %g %g %g \n",rcirrHI,rcirrHeI,rcirrHeII); */
if ( fabs(yHeII_old-yHeII) < EPS * yHeII && fabs(yHI_old-yHI) < EPS * yHI ) break;
}
Y->e = ye;
Y->HI = yHI;
Y->HII = yH / (1.0/fHI+1.0);
Y->HeI = yHeI;
Y->HeII = yHeII;
fHeII = rcirrHeII + rpirrHeII*rye;
Y->HeIII = yHe / ((1.0/fHeI+1.0)/fHeII+1.0);
Y->Total = Y->e + yH + yHe;
}
#define CL_Rgascode 8.2494e7
#define CL_Eerg_gm_degK CL_Rgascode
#define CL_ev_degK 1.0/1.1604e4
#define CL_Eerg_gm_ev CL_Eerg_gm_degK/CL_ev_degK
#define CL_Eerg_gm_degK3_2 1.5*CL_Eerg_gm_degK
/*
* Though 13.6eV is lost to the Gas as radiation during H recombination, calculating the
* Energy using u = E per unit mass = 3/2 n/rho k T requires we don't subtract it there.
* This formulation is useful because then pressure = 2/3 u rho.
* Instead we subtract the 13.6eV for H collisional ionization which actually
* removes no energy from the Gas ( similarly for Helium )
* It also means photoionization doesn't add the 13.6eV, only the excess.
*/
double clThermalEnergy( double Y_Total, double T ) {
return Y_Total*CL_Eerg_gm_degK3_2*T;
}
double clTemperature( double Y_Total, double E ) {
return E/(Y_Total*CL_Eerg_gm_degK3_2);
}
double clTemperaturePrimordial( CL *cl, double Y_HI, double Y_HeI, double Y_HeII, double E ) {
return clTemperature( 2*cl->Y_H - Y_HI + 3*cl->Y_He - 2*Y_HeI - Y_HeII, E );
}
/*-----------------------------------------------------------------
* Collisional Ionization rates
*-----------------------------------------------------------------*/
/* H + e- -> H+ + 2e- Janev et al. 1987 (Abel 1996) */
double clRateCollHI( double T ) {
double TL,arg;
TL = log(T*CL_eV_per_K);
arg = -32.713967867 + TL*(13.536556 + TL*(-5.73932875 +
TL*(1.56315498 +
TL*(-0.2877056 + TL*(3.48255977e-2 + TL*(-2.63197617e-3 +
TL*(1.11954395e-4 + TL*(-2.03914985e-6))))))));
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return exp ( arg );
}
/* He + e- -> He+ + 2e- Janev et al. 1987 (Abel 1996) */
double clRateCollHeI( double T ) {
double TL,arg;
TL = log(T*CL_eV_per_K);
arg = -44.09864886 + TL*(23.91596563 + TL*(-10.7532302 +
TL*(3.05803875 +
TL*(-0.56851189 + TL*(6.79539123e-2 + TL*(-5.00905610e-3 +
TL*(2.06723616e-4 + TL*(-3.64916141e-6))))))));
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return exp( arg );
}
/* He+ + e- -> He++ + 2e- Aladdin Database 1989 (Abel 1996) */
double clRateCollHeII( double T ) {
double TL,arg;
TL = log(T*CL_eV_per_K);
arg = -68.71040990 + TL*(43.93347633 + TL*(-18.4806699 +
TL*(4.70162649 +
TL*(-0.76924663 + TL*(8.113042e-2 + TL*(-5.32402063e-3 +
TL*(1.97570531e-4 + TL*(-3.16558106e-6))))))));
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return exp( arg );
}
/*-----------------------------------------------------------------
* Radiative Recombination rates
*-----------------------------------------------------------------*/
/* H+ + e- -> H + gam Verner & Ferland 1996 */
double clRateRadrHII( double T ) {
double Tsq = sqrt(T);
return 7.982e-11/( Tsq*0.563615 *
pow(1+Tsq*0.563615,0.252) * pow(1+Tsq*1.192167e-3,1.748));
}
/* He+ + e- -> He + gam radiative Verner & Ferland 1996 */
double clRateRadrHeII( double T ) {
/*
* Note that these functions do not meet perfectly at 1e6 -- 2% difference
* The derivatives are different there also: So the apparent error is large
*/
double Tsq = sqrt(T);
if (T < 1e6)
return 3.294e-11/( Tsq*0.253673 *
pow(1+Tsq*0.253673,0.309) * pow(1+Tsq*1.649348e-4,1.691));
else
return 9.356e-10/( Tsq*4.841607 *
pow(1+Tsq*4.841607,0.2108) * pow(1+Tsq*4.628935e-4,1.7892));
}
/* He+ + e- -> He + gam dielectronic Aldovandi&Pequignot 1973 (Black 1981) */
double clRateDielHeII( double T ) {
double T_inv = 1.0/T,arg;
arg = -4.7e5*T_inv;
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return 1.9e-3*pow(T,-1.5)*exp(arg)*(1+0.3*exp(-9.4e4*T_inv));
}
/* He++ + e- -> He+ + gam Verner & Ferland 1996 */
double clRateRadrHeIII( double T ) {
double Tsq = sqrt(T);
return 1.891e-10/( Tsq*0.326686 *
pow(1+Tsq*0.326686,0.2476) * pow(1+Tsq*6.004084e-4,1.7524));
}
/*-----------------------------------------------------------------
* Bremsstrahlung
*-----------------------------------------------------------------*/
#define CL_Cbremss1 1.426e-27
#define CL_al 0.79464
#define CL_bl 0.1243
#define CL_ar 2.13164
#define CL_br (-0.1240)
double clCoolBrem1( double T ) {
double Tlog10, Tsq;
Tlog10 = log10(T);
Tsq = sqrt(T);
if (T < 3.2e5)
return Tsq*CL_Cbremss1*(CL_al+CL_bl*Tlog10)*CL_B_gm;
else
return Tsq*CL_Cbremss1*(CL_ar+CL_br*Tlog10)*CL_B_gm;
}
#define CL_alog4 0.602059991
#define CL_alII (4.0*(CL_al-CL_bl*CL_alog4))
#define CL_blII (4.0*CL_bl)
#define CL_arII (4.0*(CL_ar-CL_br*CL_alog4))
#define CL_brII (4.0*CL_br)
double clCoolBrem2( double T ) {
double Tlog10, Tsq;
Tlog10 = log10(T);
Tsq = sqrt(T);
if (T<12.8e5)
return Tsq*CL_Cbremss1*(CL_alII+CL_blII*Tlog10)*CL_B_gm;
else
return Tsq*CL_Cbremss1*(CL_arII+CL_brII*Tlog10)*CL_B_gm;
}
/*-----------------------------------------------------------------
* Cooling multiplier for radiative recombination
*-----------------------------------------------------------------*/
#define CL_aHII 0.0215964
#define CL_b 0.270251
double clCoolRadrHII( double T ) {
double Tpow;
Tpow=pow(T,CL_b);
/* return CL_B_gm*(CL_eHI+exp(-CL_aHII*Tpow)*CL_k_Boltzmann*T); */
/* Though 13.6eV is lost to the Gas as radiation, calculating the
* Energy using u = 3/2 k T requires we don't subtract it here.
*/
return CL_B_gm*(exp(-CL_aHII*Tpow)*CL_k_Boltzmann*T);
}
double clCoolRadrHeII( double T ) {
double Tpow;
Tpow=pow(T,CL_b);
/* return CL_B_gm*(CL_eHeI+exp(-(CL_aHII*pow(13.6/24.59,CL_b))*Tpow)*CL_k_Boltzmann*T); */
return CL_B_gm*(exp(-(CL_aHII*pow(13.6/24.59,CL_b))*Tpow)*CL_k_Boltzmann*T);
}
double clCoolRadrHeIII( double T ) {
double Tpow;
Tpow=pow(T,CL_b);
/* return CL_B_gm*(CL_eHeII+exp(-(CL_aHII*pow(13.6/54.42,CL_b))*Tpow)*CL_k_Boltzmann*T); */
return CL_B_gm*(exp(-(CL_aHII*pow(13.6/54.42,CL_b))*Tpow)*CL_k_Boltzmann*T);
}
/*-----------------------------------------------------------------
* Line Cooling
*-----------------------------------------------------------------*/
/* CEN (1992, Ap.J.Suppl 78,341) ADVOCATES MULTIPLYING EACH OF
* THESE RATES BY Cen_correctn - HE CLAIMS THIS GIVES THE RIGHT
* HIGH T LIMIT FOR PROCESSES INVOLVING A FREE EL INTERACTING
* WITH AN ORBITAL ELECTRON ?? */
#define CL_aHI 7.5e-19
#define CL_bHI 1.18348e05
double clCoolLineHI( double T ) {
double T_inv, arg;
double Cen_correctn = 1.0/(1.0+sqrt(T/1.0e5));
T_inv=1.0/T;
arg = -CL_bHI*T_inv;
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return CL_B_gm*CL_aHI*exp( arg )*Cen_correctn;
}
#define CL_aHeI 9.10e-27
#define CL_bHeI 1.3179e04
#define CL_p_HeI 0.1687
double clCoolLineHeI( double T ) {
double T_inv,arg;
double Cen_correctn = 1.0/(1.0+sqrt(T/1.0e5));
T_inv=1.0/T;
arg = -CL_bHeI*T_inv;
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return CL_B_gm*CL_aHeI*exp(-CL_bHeI*T_inv)*pow(T_inv,CL_p_HeI)*Cen_correctn;
}
#define CL_aHeII 5.54e-17
#define CL_bHeII 4.73638e05
#define CL_p_HeII 0.397
double clCoolLineHeII( double T ) {
double T_inv,arg;
double Cen_correctn = 1.0/(1.0+sqrt(T/1.0e5));
T_inv=1.0/T;
arg = -CL_bHeII*T_inv;
if (arg < CL_MAX_NEG_EXP_ARG) return 0;
return CL_B_gm*CL_aHeII*exp(-CL_bHeII*T_inv)*pow(T_inv,CL_p_HeII)*Cen_correctn;
}
double clEdotInstant( CL *cl, PERBARYON *Y, RATE *Rate, double rho )
{
double en_B = rho*CL_B_gm;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
double Edot,ne;
ne = Y->e*en_B;
xTln = (Rate->Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = (xTln-iTln);
wTln0 = (1-wTln1);
Edot =
-
Y->e * cl->R.Cool_Comp * ( Rate->T-CL_Tcmb0 ) * ( 1 + cl->z )
-
ne * ((wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HII + Y->HeII ) +
(wTln0*RT0->Cool_Brem_2+wTln1*RT1->Cool_Brem_2) * Y->HeIII +
cl->R.Cool_Diel_HeII * Y->HeII * Rate->Diel_HeII +
(wTln0*RT0->Cool_Line_HI+wTln1*RT1->Cool_Line_HI) * Y->HI +
(wTln0*RT0->Cool_Line_HeI+wTln1*RT1->Cool_Line_HeI) * Y->HeI +
(wTln0*RT0->Cool_Line_HeII+wTln1*RT1->Cool_Line_HeII) * Y->HeII +
(wTln0*RT0->Cool_Radr_HII+wTln1*RT1->Cool_Radr_HII) * Y->HII * Rate->Radr_HII +
(wTln0*RT0->Cool_Radr_HeII+wTln1*RT1->Cool_Radr_HeII) * Y->HeII * Rate->Radr_HeII +
(wTln0*RT0->Cool_Radr_HeIII+wTln1*RT1->Cool_Radr_HeIII) * Y->HeIII * Rate->Radr_HeIII +
cl->R.Cool_Coll_HI * Y->HI * Rate->Coll_HI +
cl->R.Cool_Coll_HeI * Y->HeI * Rate->Coll_HeI +
cl->R.Cool_Coll_HeII * Y->HeII * Rate->Coll_HeII )
+
Y->HI * cl->R.Heat_Phot_HI * cl->R.Rate_Phot_HI +
Y->HeI * cl->R.Heat_Phot_HeI * cl->R.Rate_Phot_HeI +
Y->HeII * cl->R.Heat_Phot_HeII * cl->R.Rate_Phot_HeII;
return Edot;
}
/*
* This ugly function adds in the heating and cooling associated with
* sudden changes in ionization (unlike most Equlibrium codes).
*/
#define SIGFRAC 1e-7
double clEdot( CL *cl, PERBARYON *Y, RATE *Rate, double rho,
PERBARYON *Y1, PERBARYON *Y2, double dt) {
double en_B = rho*CL_B_gm;
double xTln,wTln0,wTln1;
RATES_T *RT0,*RT1;
int iTln;
double Edot,ne,ndot,ndot_Phot,ndot_Coll,ndot_Radr_in,ndot_Radr,ndot_Diel,add;
ne = Y->e*en_B;
xTln = (Rate->Tln-cl->TlnMin)*cl->rDeltaTln;
iTln = xTln;
RT0 = (cl->RT+iTln);
RT1 = RT0+1;
wTln1 = (xTln-iTln);
wTln0 = (1-wTln1);
Edot = - Y->e * cl->R.Cool_Comp * ( Rate->T-CL_Tcmb0 ) * ( 1 + cl->z ) -
ne * ((wTln0*RT0->Cool_Brem_1+wTln1*RT1->Cool_Brem_1) * ( Y->HII + Y->HeII ) +
(wTln0*RT0->Cool_Brem_2+wTln1*RT1->Cool_Brem_2) * Y->HeIII +
cl->R.Cool_Diel_HeII * Y->HeII * Rate->Diel_HeII +
(wTln0*RT0->Cool_Line_HI+wTln1*RT1->Cool_Line_HI) * Y->HI +
(wTln0*RT0->Cool_Line_HeI+wTln1*RT1->Cool_Line_HeI) * Y->HeI +
(wTln0*RT0->Cool_Line_HeII+wTln1*RT1->Cool_Line_HeII) * Y->HeII );
/*
* In equilibrium ndot_Phot + ndot_Coll - ndot_Radr = 0
* However, there has been a net change ndot so we adjust the rates
* so that ndot_Phot + ndot_Coll - ndot_Radr = ndot
* and the change in Sum_i (log(ndot_i)-log(ndot_i_in))^2 is minimized
* We do this for HI,HeI and HeII
*/
ndot = (Y1->HI - Y2->HI)/dt;
ndot_Phot = cl->R.Rate_Phot_HI * Y->HI + NDOT_MIN;
ndot_Coll = Rate->Coll_HI * ne * Y->HI;
ndot_Radr_in = Rate->Radr_HII * ne * Y->HII + NDOT_MIN;
add = ndot_Phot*ndot_Radr_in + ndot_Coll*ndot_Radr_in;
if ( add < ndot*fabs(ndot)*SIGFRAC )
ndot_Radr = add/ndot;
else
ndot_Radr = (-.5*ndot + sqrt( 0.25*ndot*ndot + add ));
/*
printf("HI %e ndot %e %e %e -> %e %e %e\n",ndot,ndot_Phot,ndot_Coll,ndot_Radr_in,
ndot_Phot*ndot_Radr_in/ndot_Radr,ndot_Coll*ndot_Radr_in/ndot_Radr, ndot_Radr );
*/
ndot_Phot = ndot_Phot*ndot_Radr_in/ndot_Radr;
ndot_Coll = ndot_Coll*ndot_Radr_in/ndot_Radr;
Edot += ndot_Phot * cl->R.Heat_Phot_HI
- ndot_Coll * cl->R.Cool_Coll_HI
- ndot_Radr * (wTln0*RT0->Cool_Radr_HII+wTln1*RT1->Cool_Radr_HII);
ndot = (Y1->HeI - Y2->HeI)/dt;
ndot_Phot = cl->R.Rate_Phot_HeI * Y->HeI + NDOT_MIN;
ndot_Coll = Rate->Coll_HeI * ne * Y->HeI;
ndot_Radr_in = Rate->Radr_HeII * ne * Y->HeII + NDOT_MIN;
ndot_Diel = Rate->Diel_HeII * ne * Y->HeII;
add = ndot_Phot*ndot_Radr_in + ndot_Coll*ndot_Radr_in;
if ( add < ndot*fabs(ndot)*SIGFRAC )
ndot_Radr = add/( ndot* ( 1 + ndot_Diel/ndot_Radr_in ) );
else
ndot_Radr = (-.5*ndot + sqrt( 0.25*ndot*ndot + add ))/( 1 + ndot_Diel/ndot_Radr_in );
/*
printf("HeI %e ndot %e %e %e %e -> %e %e %e %e\n",ndot,ndot_Phot,ndot_Coll,ndot_Radr_in,ndot_Diel,
ndot_Phot*ndot_Radr_in/ndot_Radr,ndot_Coll*ndot_Radr_in/ndot_Radr, ndot_Radr, ndot_Radr*ndot_Diel/ndot_Radr_in);
*/
ndot_Phot = ndot_Phot*ndot_Radr_in/ndot_Radr;
ndot_Coll = ndot_Coll*ndot_Radr_in/ndot_Radr;
ndot_Diel = ndot_Diel*ndot_Radr/ndot_Radr_in;
Edot += ndot_Phot * cl->R.Heat_Phot_HeI
- ndot_Coll * cl->R.Cool_Coll_HeI
- ndot_Radr * (wTln0*RT0->Cool_Radr_HeII+wTln1*RT1->Cool_Radr_HeII)
- ndot_Diel * cl->R.Cool_Diel_HeII;
ndot = (Y2->HeIII - Y1->HeIII)/dt; /* note: Use HeIII to get HeII rates */
ndot_Phot = cl->R.Rate_Phot_HeII * Y->HeII + NDOT_MIN;
ndot_Coll = Rate->Coll_HeII * ne * Y->HeII;
ndot_Radr_in = Rate->Radr_HeIII * ne * Y->HeIII + NDOT_MIN;
add = ndot_Phot*ndot_Radr_in + ndot_Coll*ndot_Radr_in;
if ( add < ndot*fabs(ndot)*SIGFRAC )
ndot_Radr = add/ndot;
else
ndot_Radr = (-.5*ndot + sqrt( 0.25*ndot*ndot + add ));
/*
printf("HeII %e ndot %e %e %e -> %e %e %e\n",ndot,ndot_Phot,ndot_Coll,ndot_Radr_in,
ndot_Phot*ndot_Radr_in/ndot_Radr,ndot_Coll*ndot_Radr_in/ndot_Radr, ndot_Radr );
*/
ndot_Phot = ndot_Phot*ndot_Radr_in/ndot_Radr;
ndot_Coll = ndot_Coll*ndot_Radr_in/ndot_Radr;
Edot += ndot_Phot * cl->R.Heat_Phot_HeII
- ndot_Coll * cl->R.Cool_Coll_HeII
- ndot_Radr * (wTln0*RT0->Cool_Radr_HeIII+wTln1*RT1->Cool_Radr_HeIII);
/*
printf("Edot %e %e\n",Edot,Edot*dt);
*/
return Edot;
}
/*
* We solve the implicit equation:
* Eout = Ein + dt * Cooling ( Yin, Yout, Ein, Eout )
*
* E erg/gm, PdV erg/gm/s, rho gm/cc, dt sec
*
* Brent's method is fine but you need a bracketing
* I bracket using Ein and Ein+Edot(Ein)*dt*A
* where A is some power of 2
*/
#define MAXBRACKET 10
#define ITMAX 100
#define BRENTEPS 1e-5
#define BRENTTOL 1e6
typedef struct {
PERBARYON Y;
double E,T,F;
} BRENT;
double clEdotHarmonic( CL *cl, RATE *R1, RATE *R2, PERBARYON *Y1, PERBARYON *Y2,
double rho, double PdV, double dt) {
double Edot1,Edot2;
double Prod;
Edot1 = clEdot( cl, Y1, R1, rho, Y1, Y2, dt ) + PdV;
Edot2 = clEdot( cl, Y2, R2, rho, Y1, Y2, dt ) + PdV;
Prod = Edot1*Edot2;
if (Prod < 0) return Edot2; /* Revert to First order always stable endpoint derivative */
return Prod/(0.5*(Edot1+Edot2)); /* Second order Harmonic mean derivative */
}
double clfTemp( void *Data, double T )
{
clDerivsData *d = Data;
d->its++;
clRates( d->cl, &d->Rate, T );
clAbunds( d->cl, &d->Y, &d->Rate, d->rho );
return d->E-clThermalEnergy( d->Y.Total, T );
}
void clTempIteration( clDerivsData *d )
{
double T,TA,TB;
d->its = 0;
if (d->E <= 0) T=d->cl->TMin;
else {