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e_hernquist.c
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Sun, Dec 29, 05:16

e_hernquist.c
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#include<stdio.h>
#include<math.h>
#include<fonction.h>
#include<constant.h>
#include<dimension.h>
#include<structure.h>
static double hern_f(double x);
static double hern_gamma(double r, double rs, double kappas);
static double hern_kappa(double r, double rs, double kappas);
/****************************************************************/
/* nom: e_hernquist */
/* auteur: Eric Jullo, Carlo Giocoli (MOKA) */
/* date: 06/13 */
/* place: Marseille */
/****************************************************************
* Global variables used :
* - none
* */
double hern_dpl(double r, double rs, double kappas)
{
double x = r / rs;
double dpl = kappas * rs * x * (1. - hern_f(x)) / (x * x - 1.);
return( dpl );
}
/* --------------------------------------------------------------*/
/* Global variables used :
* - none
* */
static double hern_kappa(double r, double rs, double kappas)
{
double x = r / rs;
double kappa = kappas * ((2. + x * x) * hern_f(x) - 3.) / (x * x - 1.) / (x * x - 1.);
return(kappa);
}
/* --------------------------------------------------------------*
* Return kappa for elliptical NFW (cf. Golse & Kneib 2002, eq 17)
* Global variables used :
* - none
* */
double hern_kappa_eps(double r, double rs, double theta, double kappas, double eps)
{
double kappa_eps;
kappa_eps = hern_kappa(r, rs, kappas) + eps * cos(2 * theta) * hern_gamma(r, rs, kappas);
return(kappa_eps);
}
/* --------------------------------------------------------------*
* Return gamma1 and gamma2 for elliptical Hernquist.
* (cf. Drumet-Montoyat et al. 2012 Eq A10-A12, Golse & Kneib 2002, eq 18)
* The formalism is valid independently of the profile, namely NFW or Hernquist
* Global variables used :
* - none
*/
struct point hern_gamma_eps(double r, double rs, double theta, double kappas, double eps)
{
struct point gamma_eps;
double kappa, gamma;
kappa = hern_kappa(r, rs, kappas);
gamma = hern_gamma(r, rs, kappas);
// gamma_eps = sqrt( pow(gamma, 2.) + 2 * eps * cos(2 * theta) * kappa * gamma + eps * eps * ( pow(kappa, 2.) - pow(sin(2 * theta) * gamma, 2.) ) ); //NOT USED ANYMORE
gamma_eps.x = gamma * cos(2. * theta) + eps * kappa; // gamma1
gamma_eps.y = -sqrt(1. - eps * eps) * gamma * sin(2. * theta); // gamma2
return(gamma_eps);
}
/* --------------------------------------------------------------*/
/* Global variables used :
* - none
* */
static double hern_gamma(double r, double rs, double kappas)
{
return( hern_dpl(r, rs, kappas) / r - hern_kappa(r, rs, kappas) );
}
/* --------------------------------------------------------------*/
/* Global variables used :
* Taken from Keeton 2002, Eq 48
* - none
* */
static double hern_f(double x)
{
double f = 0;
if ( x > 1 )
f = atan(sqrt((x - 1.) * (x + 1.))) / sqrt(x * x - 1);
else if ( x < 1 )
f = atanh(sqrt((1. - x) * (1. + x))) / sqrt(1. - x * x);
else
f = 1.;
return(f);
}

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