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MUSIC/plugins/transfer_eisenstein.cc

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/*
transfer_eisenstein.cc - This file is part of MUSIC -
a code to generate multi-scale initial conditions
for cosmological simulations
*/
#include "transfer_function.hh"
// forward declaration of WDM class
class transfer_eisenstein_wdm_plugin;
struct eisenstein_transfer
{
//Cosmology m_Cosmology;
double m_h0;
double omhh, /* Omega_matter*h^2 */
obhh, /* Omega_baryon*h^2 */
theta_cmb, /* Tcmb in units of 2.7 K */
z_equality, /* Redshift of matter-radiation equality, really 1+z */
k_equality, /* Scale of equality, in Mpc^-1 */
z_drag, /* Redshift of drag epoch */
R_drag, /* Photon-baryon ratio at drag epoch */
R_equality, /* Photon-baryon ratio at equality epoch */
sound_horizon, /* Sound horizon at drag epoch, in Mpc */
k_silk, /* Silk damping scale, in Mpc^-1 */
alpha_c, /* CDM suppression */
beta_c, /* CDM log shift */
alpha_b, /* Baryon suppression */
beta_b, /* Baryon envelope shift */
beta_node, /* Sound horizon shift */
k_peak, /* Fit to wavenumber of first peak, in Mpc^-1 */
sound_horizon_fit, /* Fit to sound horizon, in Mpc */
alpha_gamma; /* Gamma suppression in approximate TF */
//! private member function: sets internal quantities for Eisenstein & Hu fitting
void TFset_parameters(double omega0hh, double f_baryon, double Tcmb)
/* Set all the scalars quantities for Eisenstein & Hu 1997 fitting formula */
/* Input: omega0hh -- The density of CDM and baryons, in units of critical dens,
multiplied by the square of the Hubble constant, in units
of 100 km/s/Mpc */
/* f_baryon -- The fraction of baryons to CDM */
/* Tcmb -- The temperature of the CMB in Kelvin. Tcmb<=0 forces use
of the COBE value of 2.728 K. */
/* Output: Nothing, but set many global variables used in TFfit_onek().
You can access them yourself, if you want. */
/* Note: Units are always Mpc, never h^-1 Mpc. */
{
double z_drag_b1, z_drag_b2;
double alpha_c_a1, alpha_c_a2, beta_c_b1, beta_c_b2, alpha_b_G, y;
if (f_baryon<=0.0 || omega0hh<=0.0) {
fprintf(stderr, "TFset_parameters(): Illegal input.\n");
exit(1);
}
omhh = omega0hh;
obhh = omhh*f_baryon;
if (Tcmb<=0.0) Tcmb=2.728; /* COBE FIRAS */
theta_cmb = Tcmb/2.7;
z_equality = 2.50e4*omhh/POW4(theta_cmb); /* Really 1+z */
k_equality = 0.0746*omhh/SQR(theta_cmb);
z_drag_b1 = 0.313*pow((double)omhh,-0.419)*(1+0.607*pow((double)omhh,0.674));
z_drag_b2 = 0.238*pow((double)omhh,0.223);
z_drag = 1291*pow(omhh,0.251)/(1+0.659*pow((double)omhh,0.828))*
(1+z_drag_b1*pow((double)obhh,(double)z_drag_b2));
R_drag = 31.5*obhh/POW4(theta_cmb)*(1000/(1+z_drag));
R_equality = 31.5*obhh/POW4(theta_cmb)*(1000/z_equality);
sound_horizon = 2./3./k_equality*sqrt(6./R_equality)*
log((sqrt(1+R_drag)+sqrt(R_drag+R_equality))/(1+sqrt(R_equality)));
k_silk = 1.6*pow((double)obhh,0.52)*pow((double)omhh,0.73)*(1+pow((double)10.4*omhh,-0.95));
alpha_c_a1 = pow((double)46.9*omhh,0.670)*(1+pow(32.1*omhh,-0.532));
alpha_c_a2 = pow((double)12.0*omhh,0.424)*(1+pow(45.0*omhh,-0.582));
alpha_c = pow(alpha_c_a1,-f_baryon)*
pow(alpha_c_a2,-CUBE(f_baryon));
beta_c_b1 = 0.944/(1+pow(458*omhh,-0.708));
beta_c_b2 = pow(0.395*omhh, -0.0266);
beta_c = 1.0/(1+beta_c_b1*(pow(1-f_baryon, beta_c_b2)-1));
y = z_equality/(1+z_drag);
alpha_b_G = y*(-6.*sqrt(1+y)+(2.+3.*y)*log((sqrt(1+y)+1)/(sqrt(1+y)-1)));
alpha_b = 2.07*k_equality*sound_horizon*pow(1+R_drag,-0.75)*alpha_b_G;
beta_node = 8.41*pow(omhh, 0.435);
beta_b = 0.5+f_baryon+(3.-2.*f_baryon)*sqrt(pow(17.2*omhh,2.0)+1);
k_peak = 2.5*3.14159*(1+0.217*omhh)/sound_horizon;
sound_horizon_fit = 44.5*log(9.83/omhh)/sqrt(1+10.0*pow(obhh,0.75));
alpha_gamma = 1-0.328*log(431.0*omhh)*f_baryon + 0.38*log(22.3*omhh)*
SQR(f_baryon);
return;
}
//! private member function: computes transfer function for mode k (k in Mpc)
inline double TFfit_onek(double k, double *tf_baryon, double *tf_cdm)
/* Input: k -- Wavenumber at which to calculate transfer function, in Mpc^-1.
*tf_baryon, *tf_cdm -- Input value not used; replaced on output if
the input was not NULL. */
/* Output: Returns the value of the full transfer function fitting formula.
This is the form given in Section 3 of Eisenstein & Hu (1997).
*tf_baryon -- The baryonic contribution to the full fit.
*tf_cdm -- The CDM contribution to the full fit. */
/* Notes: Units are Mpc, not h^-1 Mpc. */
{
double T_c_ln_beta, T_c_ln_nobeta, T_c_C_alpha, T_c_C_noalpha;
double q, xx, xx_tilde;//, q_eff;
double T_c_f, T_c, s_tilde, T_b_T0, T_b, f_baryon, T_full;
//double T_0_L0, T_0_C0, T_0, gamma_eff;
//double T_nowiggles_L0, T_nowiggles_C0, T_nowiggles;
k = fabs(k); /* Just define negative k as positive */
if (k==0.0) {
if (tf_baryon!=NULL) *tf_baryon = 1.0;
if (tf_cdm!=NULL) *tf_cdm = 1.0;
return 1.0;
}
q = k/13.41/k_equality;
xx = k*sound_horizon;
T_c_ln_beta = log(2.718282+1.8*beta_c*q);
T_c_ln_nobeta = log(2.718282+1.8*q);
T_c_C_alpha = 14.2/alpha_c + 386.0/(1+69.9*pow(q,1.08));
T_c_C_noalpha = 14.2 + 386.0/(1+69.9*pow(q,1.08));
T_c_f = 1.0/(1.0+POW4(xx/5.4));
T_c = T_c_f*T_c_ln_beta/(T_c_ln_beta+T_c_C_noalpha*SQR(q)) +
(1-T_c_f)*T_c_ln_beta/(T_c_ln_beta+T_c_C_alpha*SQR(q));
s_tilde = sound_horizon*pow(1.+CUBE(beta_node/xx),-1./3.);
xx_tilde = k*s_tilde;
T_b_T0 = T_c_ln_nobeta/(T_c_ln_nobeta+T_c_C_noalpha*SQR(q));
T_b = sin(xx_tilde)/(xx_tilde)*(T_b_T0/(1.+SQR(xx/5.2))+
alpha_b/(1.+CUBE(beta_b/xx))*exp(-pow(k/k_silk,1.4)));
f_baryon = obhh/omhh;
T_full = f_baryon*T_b + (1-f_baryon)*T_c;
/* Now to store these transfer functions */
if (tf_baryon!=NULL) *tf_baryon = T_b;
if (tf_cdm!=NULL) *tf_cdm = T_c;
return T_full;
}
double fb_, fc_;
eisenstein_transfer()
{ }
void set_parameters( const cosmology& cosmo, double Tcmb )
{
m_h0 = cosmo.H0*0.01;
TFset_parameters( (cosmo.Omega_m)*cosmo.H0*cosmo.H0*(0.01*0.01),
cosmo.Omega_b/(cosmo.Omega_m-cosmo.Omega_b), Tcmb);
fb_ = cosmo.Omega_b/(cosmo.Omega_m);
fc_ = (cosmo.Omega_m-cosmo.Omega_b)/(cosmo.Omega_m) ;
}
inline double at_k( double k )
{
double tfb, tfcdm;
TFfit_onek( k*m_h0, &tfb, &tfcdm );
return fb_*tfb+fc_*tfcdm;
}
};
//! Implementation of abstract base class TransferFunction for the Eisenstein & Hu transfer function
/*!
This class implements the analytical fit to the matter transfer
function by Eisenstein & Hu (1999). In fact it is their code.
*/
class transfer_eisenstein_plugin : public transfer_function_plugin
{
protected:
using transfer_function_plugin::cosmo_;
eisenstein_transfer etf_;
public:
//! Constructor for Eisenstein & Hu fitting for transfer function
/*!
\param aCosm structure of type Cosmology carrying the cosmological parameters
\param Tcmb mean temperature of the CMB fluctuations (defaults to
Tcmb = 2.726 if not specified)
*/
transfer_eisenstein_plugin( config_file &cf )//Cosmology aCosm, double Tcmb = 2.726 )
: transfer_function_plugin(cf)
{
double Tcmb = pcf_->getValueSafe("cosmology","Tcmb",2.726);
etf_.set_parameters( cosmo_, Tcmb );
tf_distinct_ = false;
tf_withvel_ = false;
}
//! Computes the transfer function for k in Mpc/h by calling TFfit_onek
inline double compute( double k, tf_type type ){
return etf_.at_k( k );
}
inline double get_kmin( void ){
return 1e-4;
}
inline double get_kmax( void ){
return 1.e4;
}
};
#include <map>
class transfer_eisenstein_wdm_plugin : public transfer_function_plugin
{
protected:
real_t m_WDMalpha, m_h0;
double omegam_, wdmm_, wdmgx_, wdmnu_, H0_, omegab_;
std::string type_;
std::map< std::string, int > typemap_;
eisenstein_transfer etf_;
enum wdmtyp { wdm_bode, wdm_viel, wdm_bode_wrong=99};
public:
transfer_eisenstein_wdm_plugin( config_file &cf )
: transfer_function_plugin(cf), m_h0( cosmo_.H0*0.01 )
{
double Tcmb = pcf_->getValueSafe("cosmology","Tcmb",2.726);
etf_.set_parameters( cosmo_, Tcmb );
typemap_.insert( std::pair<std::string,int>( "BODE", wdm_bode ) );
typemap_.insert( std::pair<std::string,int>( "VIEL", wdm_viel ) ); // add the other types
typemap_.insert( std::pair<std::string,int>( "BODE_WRONG", wdm_bode_wrong ) ); // add the other types
omegam_ = cf.getValue<double>("cosmology","Omega_m");
omegab_ = cf.getValue<double>("cosmology","Omega_b");
wdmm_ = cf.getValue<double>("cosmology","WDMmass");
H0_ = cf.getValue<double>("cosmology","H0");
type_ = cf.getValueSafe<std::string>("cosmology","WDMtftype","BODE");
//type_ = std::string( toupper( type_.c_str() ) );
if( typemap_.find( type_ ) == typemap_.end() )
throw std::runtime_error("unknown transfer function fit for WDM");
m_WDMalpha = 1.0;
switch( typemap_[type_] )
{
//... parameterisation from Bode et al. (2001), ApJ, 556, 93
case wdm_bode:
wdmnu_ = cf.getValueSafe<double>("cosmology","WDMnu",1.0);
wdmgx_ = cf.getValueSafe<double>("cosmology","WDMg_x",1.5);
m_WDMalpha = 0.05 * pow( omegam_/0.4,0.15)
*pow(H0_*0.01/0.65,1.3)*pow(wdmm_,-1.15)
*pow(1.5/wdmgx_,0.29);
break;
//... parameterisation from Viel et al. (2005), Phys Rev D, 71
case wdm_viel:
wdmnu_ = cf.getValueSafe<double>("cosmology","WDMnu",1.12);
m_WDMalpha = 0.049 * pow( omegam_/0.25,0.11)
*pow(H0_*0.01/0.7,1.22)*pow(wdmm_,-1.11);
break;
//.... below is for historical reasons due to the buggy parameterisation
//.... in early versions of MUSIC, but apart from H instead of h, Bode et al.
case wdm_bode_wrong:
wdmnu_ = cf.getValueSafe<double>("cosmology","WDMnu",1.0);
wdmgx_ = cf.getValueSafe<double>("cosmology","WDMg_x",1.5);
m_WDMalpha = 0.05 * pow( omegam_/0.4,0.15)
*pow(H0_/0.65,1.3)*pow(wdmm_,-1.15)
*pow(1.5/wdmgx_,0.29);
break;
default:
wdmnu_ = cf.getValueSafe<double>("cosmology","WDMnu",1.0);
wdmgx_ = cf.getValueSafe<double>("cosmology","WDMg_x",1.5);
m_WDMalpha = 0.05 * pow( omegam_/0.4,0.15)
*pow(H0_*0.01/0.65,1.3)*pow(wdmm_,-1.15)
*pow(1.5/wdmgx_,0.29);
break;
}
}
inline double compute( double k, tf_type type )
{
return etf_.at_k( k )*pow(1.0+pow(m_WDMalpha*k,2.0*wdmnu_),-5.0/wdmnu_);
}
inline double get_kmin( void ){
return 1e-4;
}
inline double get_kmax( void ){
return 1.e4;
}
};
// CDM Bino type WIMP small-scale damped spectrum from Green, Hofmann & Schwarz (2004)
class transfer_eisenstein_cdmbino_plugin : public transfer_function_plugin
{
protected:
real_t m_h0;
double omegam_, H0_, omegab_, mcdm_, Tkd_, kfs_, kd_;
eisenstein_transfer etf_;
public:
transfer_eisenstein_cdmbino_plugin( config_file &cf )
: transfer_function_plugin(cf), m_h0( cosmo_.H0*0.01 )
{
double Tcmb = pcf_->getValueSafe("cosmology","Tcmb",2.726);
etf_.set_parameters( cosmo_, Tcmb );
omegam_ = cf.getValue<double>("cosmology","Omega_m");
omegab_ = cf.getValue<double>("cosmology","Omega_b");
H0_ = cf.getValue<double>("cosmology","H0");
mcdm_ = cf.getValueSafe<double>("cosmology","CDM_mass", 100.0); // bino particle mass in GeV
Tkd_ = cf.getValueSafe<double>("cosmology","CDM_Tkd", 33.0); // temperature at which CDM particle kinetically decouples (in MeV)
kfs_ = 1.7e6 / m_h0 * sqrt( mcdm_ / 100. * Tkd_ / 30. ) / (1.0 + log( Tkd_ / 30. ) / 19.2 );
kd_ = 3.8e7 / m_h0 * sqrt( mcdm_ / 100. * Tkd_ / 30. );
LOGINFO(" bino CDM: k_fs = %g, k_d = %g", kfs_, kd_ );
}
inline double compute( double k, tf_type type )
{
double kkfs = k/kfs_;
double kkfs2 = kkfs*kkfs;
double kkd2 = (k/kd_)*(k/kd_);
// in principle the Green et al. (2004) works only up to k/k_fs < 1
// the fit crosses zero at (k/k_fs)**2 = 3/2, we just zero it there...
if( kkfs2 < 1.5 )
return etf_.at_k( k ) * (1.0-2.0/3.0*kkfs2) * exp( -kkfs2 - kkd2 );
else
return 0.0;
}
inline double get_kmin( void ){
return 1e-4;
}
inline double get_kmax( void ){
return 1.e8;
}
};
namespace{
transfer_function_plugin_creator_concrete< transfer_eisenstein_plugin > creator("eisenstein");
transfer_function_plugin_creator_concrete< transfer_eisenstein_wdm_plugin > creator2("eisenstein_wdm");
transfer_function_plugin_creator_concrete< transfer_eisenstein_cdmbino_plugin > creator3("eisenstein_cdmbino");
}
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