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125 | //
// Mass funcation and halo bias
//
// Tinker et al (2010) ApJ 724, 878
//
// MF* mf= mf_alloc(); // allocate
// double a= 1.0/(1.0 + z); // scale factor
// mf_set_redshift(mf, a); // set redshift
//
// mf_free(mf);
#include <cstdio>
#include <cmath>
#include <cassert>
#include "mf.h"
#include "const.h" // => delta_c
using namespace std;
static double integrand_mf_normalisation(double nu, void* params);
MF* mf_alloc()
{
MF* const mf= new MF();
mf->z= 0.0;
mf->alpha= 0.0;
return mf;
}
MF* mf_alloc(const double z)
{
MF* const mf= mf_alloc();
const double a= 1.0/(1.0 + z);
mf_set_redshift(mf, a);
return mf;
}
void mf_free(MF* const mf)
{
delete mf;
}
void mf_set_redshift(MF* const mf, const double a)
{
// Integral is necessary to normalise mass function (mf->alpha)
const double z= 1.0/a - 1.0;
if(mf->alpha > 0.0 && mf->z == z)
return;
mf->alpha= 1.0;
mf->z= z;
gsl_integration_cquad_workspace* w=
gsl_integration_cquad_workspace_alloc(100);
gsl_function F;
F.function= &integrand_mf_normalisation;
F.params= (void*) mf;
double result;
gsl_integration_cquad(&F, 1.0e-8, 10.0, 1.0e-5, 1.0e-5, w, &result, 0, 0);
gsl_integration_cquad_workspace_free(w);
mf->alpha = 1.0/result;
}
double mf_f(MF const * const mf, const double nu)
{
#ifdef DEBUG
assert(mf->alpha > 0.0);
#endif
const double z= mf->z;
// Table 4 and Equations (8-12) for Delta=200
// nu= delta_c/sigma
// dn/dM = f(nu) rho_bar/M dln sigma^-1/dM
//const double alpha=0.368;
const double beta=0.589*pow(1.0 + z, 0.20); // (9)
const double phi= -0.729*pow(1.0 + z, -0.08); // (10)
const double eta= -0.243*pow(1.0 + z, 0.27); // (11)
const double gamma= 0.864*pow(1.0 + z, -0.01); // (12)
// normalization constant needs to be determined from
// S b(nu)f(nu)dnu = 1 ... (7)
return mf->alpha*(1.0 + pow(beta*nu, -2.0*phi))*
pow(nu, 2*eta)*exp(-gamma*nu*nu/2.0); // (8)
}
double mf_b(const double nu)
{
// assert(sigma > 0.0);
// halo bias b(M) from Tinker et al (2010) ApJ 724, 878
//double nu= delta_c/sigma;
double y= log10(200.0);
double fy= 4.0/y; double fy2= fy*fy;
double expfy= exp(-fy2*fy2);
// Table 2
double A= 1.0 + 0.24*y*expfy;
double a= 0.44*y - 0.88;
double B= 0.183;
double b= 1.5;
double C= 0.019 + 0.107*y + 0.19*expfy;
double c= 2.4;
return 1.0 - A*pow(nu, a)/(pow(nu, a) + pow(delta_c, a))
+ B*pow(nu, b) + C*pow(nu, c); // (6)
}
static double integrand_mf_normalisation(double nu, void* params)
{
MF const * const mf= (MF const *) params;
return mf_f(mf, nu)*mf_b(nu);
}
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