/* 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, 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 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( "BODE", wdm_bode ) ); typemap_.insert( std::pair( "VIEL", wdm_viel ) ); // add the other types typemap_.insert( std::pair( "BODE_WRONG", wdm_bode_wrong ) ); // add the other types omegam_ = cf.getValue("cosmology","Omega_m"); omegab_ = cf.getValue("cosmology","Omega_b"); wdmm_ = cf.getValue("cosmology","WDMmass"); H0_ = cf.getValue("cosmology","H0"); type_ = cf.getValueSafe("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("cosmology","WDMnu",1.0); wdmgx_ = cf.getValueSafe("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("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("cosmology","WDMnu",1.0); wdmgx_ = cf.getValueSafe("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("cosmology","WDMnu",1.0); wdmgx_ = cf.getValueSafe("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; } std::cerr << "WDM alpha = " << m_WDMalpha << std::endl; } 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("cosmology","Omega_m"); omegab_ = cf.getValue("cosmology","Omega_b"); H0_ = cf.getValue("cosmology","H0"); mcdm_ = cf.getValueSafe("cosmology","CDM_mass", 100.0); // bino particle mass in GeV Tkd_ = cf.getValueSafe("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"); }