source: Sophya/trunk/Cosmo/SimLSS/hu_power.c@ 3756

/* Fitting Formulae for CDM + Baryon + Massive Neutrino (MDM) cosmologies. */
/* Daniel J. Eisenstein & Wayne Hu, Institute for Advanced Study */

/* There are two primary routines here, one to set the cosmology, the
other to construct the transfer function for a single wavenumber k. 
You should call the former once (per cosmology) and the latter as 
many times as you want. */

/* TFmdm_set_cosm() -- User passes all the cosmological parameters as
        arguments; the routine sets up all of the scalar quantites needed 
        computation of the fitting formula.  The input parameters are: 
        1) omega_matter -- Density of CDM, baryons, and massive neutrinos,
                                in units of the critical density. 
        2) omega_baryon -- Density of baryons, in units of critical. 
        3) omega_hdm    -- Density of massive neutrinos, in units of critical 
        4) degen_hdm    -- (Int) Number of degenerate massive neutrino species 
        5) omega_lambda -- Cosmological constant 
        6) hubble       -- Hubble constant, in units of 100 km/s/Mpc 
        7) redshift     -- The redshift at which to evaluate */

/* TFmdm_onek_mpc() -- User passes a single wavenumber, in units of Mpc^-1.
        Routine returns the transfer function from the Eisenstein & Hu
        fitting formula, based on the cosmology currently held in the 
        internal variables.  The routine returns T_cb (the CDM+Baryon
        density-weighted transfer function), although T_cbn (the CDM+
        Baryon+Neutrino density-weighted transfer function) is stored
        in the global variable tf_cbnu. */

/* We also supply TFmdm_onek_hmpc(), which is identical to the previous
        routine, but takes the wavenumber in units of h Mpc^-1. */

/* We hold the internal scalar quantities in global variables, so that
the user may access them in an external program, via "extern" declarations. */

/* Please note that all internal length scales are in Mpc, not h^-1 Mpc! */

/* -------------------------- Prototypes ----------------------------- */

int TFmdm_set_cosm(double omega_matter, double omega_baryon, double omega_hdm,
        int degen_hdm, double omega_lambda, double hubble, double redshift);
double TFmdm_onek_mpc(double kk);
double TFmdm_onek_hmpc(double kk);

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

/* Convenience from Numerical Recipes in C, 2nd edition
------------ COMPLETEMENT DEBILE (cmv) ????????? ------------
static double sqrarg;
#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
*/
#define SQR(a) (a*a)

/* ------------------------- Global Variables ------------------------ */

/* The following are set in TFmdm_set_cosm() */
double   alpha_gamma,   /* sqrt(alpha_nu) */
        alpha_nu,       /* The small-scale suppression */
        beta_c,         /* The correction to the log in the small-scale */
        num_degen_hdm,  /* Number of degenerate massive neutrino species */
        f_baryon,       /* Baryon fraction */
        f_bnu,          /* Baryon + Massive Neutrino fraction */
        f_cb,           /* Baryon + CDM fraction */
        f_cdm,          /* CDM fraction */
        f_hdm,          /* Massive Neutrino fraction */
        growth_k0,      /* D_1(z) -- the growth function as k->0 */
        growth_to_z0,   /* D_1(z)/D_1(0) -- the growth relative to z=0 */
        hhubble,        /* Need to pass Hubble constant to TFmdm_onek_hmpc() */
        k_equality,     /* The comoving wave number of the horizon at equality*/
        obhh,           /* Omega_baryon * hubble^2 */
        omega_curv,     /* = 1 - omega_matter - omega_lambda */
        omega_lambda_z, /* Omega_lambda at the given redshift */
        omega_matter_z, /* Omega_matter at the given redshift */
        omhh,           /* Omega_matter * hubble^2 */
        onhh,           /* Omega_hdm * hubble^2 */
        p_c,            /* The correction to the exponent before drag epoch */
        p_cb,           /* The correction to the exponent after drag epoch */
        sound_horizon_fit,  /* The sound horizon at the drag epoch */
        theta_cmb,      /* The temperature of the CMB, in units of 2.7 K */
        y_drag,         /* Ratio of z_equality to z_drag */
        z_drag,         /* Redshift of the drag epoch */
        z_equality;     /* Redshift of matter-radiation equality */

/* The following are set in TFmdm_onek_mpc() */
double  gamma_eff,      /* Effective \Gamma */
        growth_cb,      /* Growth factor for CDM+Baryon perturbations */
        growth_cbnu,    /* Growth factor for CDM+Baryon+Neutrino pert. */
        max_fs_correction,  /* Correction near maximal free streaming */
        qq,             /* Wavenumber rescaled by \Gamma */
        qq_eff,         /* Wavenumber rescaled by effective Gamma */
        qq_nu,          /* Wavenumber compared to maximal free streaming */
        tf_master,      /* Master TF */
        tf_sup,         /* Suppressed TF */
        y_freestream;   /* The epoch of free-streaming for a given scale */

/* Finally, TFmdm_onek_mpc() and TFmdm_onek_hmpc() give their answers as */
double   tf_cb,         /* The transfer function for density-weighted
                        CDM + Baryon perturbations. */
        tf_cbnu;        /* The transfer function for density-weighted
                        CDM + Baryon + Massive Neutrino perturbations. */

/* By default, these functions return tf_cb */

/* ------------------------- TFmdm_set_cosm() ------------------------ */
int TFmdm_set_cosm(double omega_matter, double omega_baryon, double omega_hdm,
        int degen_hdm, double omega_lambda, double hubble, double redshift)
/* This routine takes cosmological parameters and a redshift and sets up
all the internal scalar quantities needed to compute the transfer function. */
/* INPUT: omega_matter -- Density of CDM, baryons, and massive neutrinos,
                                in units of the critical density. */
/*        omega_baryon -- Density of baryons, in units of critical. */
/*        omega_hdm    -- Density of massive neutrinos, in units of critical */
/*        degen_hdm    -- (Int) Number of degenerate massive neutrino species */
/*        omega_lambda -- Cosmological constant */
/*        hubble       -- Hubble constant, in units of 100 km/s/Mpc */
/*        redshift     -- The redshift at which to evaluate */
/* OUTPUT: Returns 0 if all is well, 1 if a warning was issued.  Otherwise,
        sets many global variables for use in TFmdm_onek_mpc() */
{
    double z_drag_b1, z_drag_b2, omega_denom;
    int qwarn;
    qwarn = 0;

    theta_cmb = 2.728/2.7;      /* Assuming T_cmb = 2.728 K */

    /* Look for strange input */
    if (omega_baryon<0.0) {
        fprintf(stderr,
          "TFmdm_set_cosm(): Negative omega_baryon set to trace amount.\n");
        qwarn = 1;
    }
    if (omega_hdm<0.0) {
        fprintf(stderr,
          "TFmdm_set_cosm(): Negative omega_hdm set to trace amount.\n");
        qwarn = 1;
    }
    if (hubble<=0.0) {
        fprintf(stderr,"TFmdm_set_cosm(): Negative Hubble constant illegal.\n");
        exit(1);  /* Can't recover */
    } else if (hubble>2.0) {
        fprintf(stderr,"TFmdm_set_cosm(): Hubble constant should be in units of 100 km/s/Mpc.\n");
        qwarn = 1;
    }
    if (redshift<=-1.0) {
        fprintf(stderr,"TFmdm_set_cosm(): Redshift < -1 is illegal.\n");
        exit(1);
    } else if (redshift>99.0) {
        fprintf(stderr,
          "TFmdm_set_cosm(): Large redshift entered.  TF may be inaccurate.\n");
        qwarn = 1;
    }
    if (degen_hdm<1) degen_hdm=1;
    num_degen_hdm = (double) degen_hdm; 
        /* Have to save this for TFmdm_onek_mpc() */
    /* This routine would crash if baryons or neutrinos were zero, 
        so don't allow that */
    if (omega_baryon<=0) omega_baryon=1e-5;
    if (omega_hdm<=0) omega_hdm=1e-5;

    omega_curv = 1.0-omega_matter-omega_lambda;
    omhh = omega_matter*SQR(hubble);
    obhh = omega_baryon*SQR(hubble);
    onhh = omega_hdm*SQR(hubble);
    f_baryon = omega_baryon/omega_matter;
    f_hdm = omega_hdm/omega_matter;
    f_cdm = 1.0-f_baryon-f_hdm;
    f_cb = f_cdm+f_baryon;
    f_bnu = f_baryon+f_hdm;

    /* Compute the equality scale. */
    z_equality = 25000.0*omhh/SQR(SQR(theta_cmb));      /* Actually 1+z_eq */
    k_equality = 0.0746*omhh/SQR(theta_cmb);

    /* Compute the drag epoch and sound horizon */
    z_drag_b1 = 0.313*pow(omhh,-0.419)*(1+0.607*pow(omhh,0.674));
    z_drag_b2 = 0.238*pow(omhh,0.223);
    z_drag = 1291*pow(omhh,0.251)/(1.0+0.659*pow(omhh,0.828))*
                (1.0+z_drag_b1*pow(obhh,z_drag_b2));
    y_drag = z_equality/(1.0+z_drag);

    sound_horizon_fit = 44.5*log(9.83/omhh)/sqrt(1.0+10.0*pow(obhh,0.75));

    /* Set up for the free-streaming & infall growth function */
    p_c = 0.25*(5.0-sqrt(1+24.0*f_cdm));
    p_cb = 0.25*(5.0-sqrt(1+24.0*f_cb));

    omega_denom = omega_lambda+SQR(1.0+redshift)*(omega_curv+
                        omega_matter*(1.0+redshift));
    omega_lambda_z = omega_lambda/omega_denom;
    omega_matter_z = omega_matter*SQR(1.0+redshift)*(1.0+redshift)/omega_denom;
    growth_k0 = z_equality/(1.0+redshift)*2.5*omega_matter_z/
            (pow(omega_matter_z,4.0/7.0)-omega_lambda_z+
            (1.0+omega_matter_z/2.0)*(1.0+omega_lambda_z/70.0));
    growth_to_z0 = z_equality*2.5*omega_matter/(pow(omega_matter,4.0/7.0)
            -omega_lambda + (1.0+omega_matter/2.0)*(1.0+omega_lambda/70.0));
    growth_to_z0 = growth_k0/growth_to_z0;      
    
    /* Compute small-scale suppression */
    alpha_nu = f_cdm/f_cb*(5.0-2.*(p_c+p_cb))/(5.-4.*p_cb)*
        pow(1+y_drag,p_cb-p_c)*
        (1+f_bnu*(-0.553+0.126*f_bnu*f_bnu))/
        (1-0.193*sqrt(f_hdm*num_degen_hdm)+0.169*f_hdm*pow(num_degen_hdm,0.2))*
        (1+(p_c-p_cb)/2*(1+1/(3.-4.*p_c)/(7.-4.*p_cb))/(1+y_drag));
    alpha_gamma = sqrt(alpha_nu);
    beta_c = 1/(1-0.949*f_bnu);
    /* Done setting scalar variables */
    hhubble = hubble;   /* Need to pass Hubble constant to TFmdm_onek_hmpc() */
    return qwarn;
}

/* ---------------------------- TFmdm_onek_mpc() ---------------------- */

double TFmdm_onek_mpc(double kk)
/* Given a wavenumber in Mpc^-1, return the transfer function for the
cosmology held in the global variables. */
/* Input: kk -- Wavenumber in Mpc^-1 */
/* Output: The following are set as global variables:
        growth_cb -- the transfer function for density-weighted
                        CDM + Baryon perturbations. 
        growth_cbnu -- the transfer function for density-weighted
                        CDM + Baryon + Massive Neutrino perturbations. */
/* The function returns growth_cb */
{
    double tf_sup_L, tf_sup_C;
    double temp1, temp2;

    qq = kk/omhh*SQR(theta_cmb);

    /* Compute the scale-dependent growth functions */
    y_freestream = 17.2*f_hdm*(1+0.488*pow(f_hdm,-7.0/6.0))*
                SQR(num_degen_hdm*qq/f_hdm);
    temp1 = pow(growth_k0, 1.0-p_cb);
    temp2 = pow(growth_k0/(1+y_freestream),0.7);
    growth_cb = pow(1.0+temp2, p_cb/0.7)*temp1;
    growth_cbnu = pow(pow(f_cb,0.7/p_cb)+temp2, p_cb/0.7)*temp1;

    /* Compute the master function */
    gamma_eff =omhh*(alpha_gamma+(1-alpha_gamma)/
                (1+SQR(SQR(kk*sound_horizon_fit*0.43))));
    qq_eff = qq*omhh/gamma_eff;

    tf_sup_L = log(2.71828+1.84*beta_c*alpha_gamma*qq_eff);
    tf_sup_C = 14.4+325/(1+60.5*pow(qq_eff,1.11));
    tf_sup = tf_sup_L/(tf_sup_L+tf_sup_C*SQR(qq_eff));

    qq_nu = 3.92*qq*sqrt(num_degen_hdm/f_hdm);
    max_fs_correction = 1+1.2*pow(f_hdm,0.64)*pow(num_degen_hdm,0.3+0.6*f_hdm)/
                (pow(qq_nu,-1.6)+pow(qq_nu,0.8));
    tf_master = tf_sup*max_fs_correction;

    /* Now compute the CDM+HDM+baryon transfer functions */
    tf_cb = tf_master*growth_cb/growth_k0;
    tf_cbnu = tf_master*growth_cbnu/growth_k0;
    return tf_cb;
}

/* ---------------------------- TFmdm_onek_hmpc() ---------------------- */

double TFmdm_onek_hmpc(double kk)
/* Given a wavenumber in h Mpc^-1, return the transfer function for the
cosmology held in the global variables. */
/* Input: kk -- Wavenumber in h Mpc^-1 */
/* Output: The following are set as global variables:
        growth_cb -- the transfer function for density-weighted
                        CDM + Baryon perturbations. 
        growth_cbnu -- the transfer function for density-weighted
                        CDM + Baryon + Massive Neutrino perturbations. */
/* The function returns growth_cb */
{
    return TFmdm_onek_mpc(kk*hhubble);
}