示例#1
0
double rec_HMLA_dxedlna(double xe, double nH, double Hubble, double TM, double TR, double energy_rate, HRATEEFF *rate_table){

   double Alpha[2];
   double Beta[2];
   double R2p2s;
   double matrix[2][2];
   double RHS[2];
   double det, RLya;
   double x2[2];
   double x1s_db;
   double C_2p;
   double chi_ion_H;

   interpolate_rates(Alpha, Beta, &R2p2s, TR, TM / TR, rate_table);

   x1s_db = (1.-xe)*exp(-E21/TR);

   /******** 2s *********/
   matrix[0][0] = Beta[0] + 3.*R2p2s + L2s1s;
   matrix[0][1] = -R2p2s;
   RHS[0]       = xe*xe*nH *Alpha[0] + L2s1s *x1s_db;

   /******** 2p *********/
   RLya = 4.662899067555897e15 *Hubble /nH/(1.-xe);   /*8 PI H/(3 nH x1s lambda_Lya^3) */

   matrix[1][1] = Beta[1] + R2p2s + RLya;
   matrix[1][0] = -3.*R2p2s;
   RHS[1]       = xe*xe*nH *Alpha[1] + 3.*RLya *x1s_db;

   /**** invert the 2 by 2 system matrix_ij * xj = RHSi *****/
   det = matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
   x2[0] = (matrix[1][1] * RHS[0] - matrix[0][1] * RHS[1])/det;
   x2[1] = (matrix[0][0] * RHS[1] - matrix[1][0] * RHS[0])/det;

   C_2p=(RLya+R2p2s*L2s1s/matrix[0][0])/(matrix[1][1]-R2p2s*3.*R2p2s/matrix[0][0]);

   //chi_ion_H = (1.-xe)/3.; // old approximation from Chen and Kamionkowski
    if (xe < 1.)
      chi_ion_H = 0.369202*pow(1.-pow(xe,463929),1.70237); // coefficient as revised by Galli et al. 2013 (in fact it is a fit by Vivian Poulin of columns 1 and 4 in Table V of Galli et al. 2013)
    else
      chi_ion_H = 0.;

   return  (x1s_db*(L2s1s + 3.*RLya) -x2[0]*L2s1s -x2[1]*RLya)/Hubble
     +chi_ion_H/nH*energy_rate*(1./EI+(1.-C_2p)/E21)/Hubble;

}
示例#2
0
double rec_HMLA_dxedlna(double xe, double nH, double Hubble, double TM, double TR, double energy_rate, HRATEEFF *rate_table){

   double Alpha[2];
   double Beta[2];
   double R2p2s;
   double matrix[2][2];
   double RHS[2];
   double det, RLya;   
   double x2[2];   
   double x1s_db;
   double C_2p;
 
   interpolate_rates(Alpha, Beta, &R2p2s, TR, TM / TR, rate_table);
       
   x1s_db = (1.-xe)*exp(-E21/TR);     
   
   /******** 2s *********/
   matrix[0][0] = Beta[0] + 3.*R2p2s + L2s1s;     
   matrix[0][1] = -R2p2s;
   RHS[0]       = xe*xe*nH *Alpha[0] + L2s1s *x1s_db;
                                   
   /******** 2p *********/
   RLya = 4.662899067555897e15 *Hubble /nH/(1.-xe);   /*8 PI H/(3 nH x1s lambda_Lya^3) */
   
   matrix[1][1] = Beta[1] + R2p2s + RLya;
   matrix[1][0] = -3.*R2p2s;
   RHS[1]       = xe*xe*nH *Alpha[1] + 3.*RLya *x1s_db;
                                             
   /**** invert the 2 by 2 system matrix_ij * xj = RHSi *****/
   det = matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
   x2[0] = (matrix[1][1] * RHS[0] - matrix[0][1] * RHS[1])/det;
   x2[1] = (matrix[0][0] * RHS[1] - matrix[1][0] * RHS[0])/det;

   C_2p=(RLya+R2p2s*L2s1s/matrix[0][0])/(matrix[1][1]-R2p2s*3.*R2p2s/matrix[0][0]);
		
   return  (x1s_db*(L2s1s + 3.*RLya) -x2[0]*L2s1s -x2[1]*RLya)/Hubble
     +(1.-xe)/(3.*nH)*energy_rate*(1./EI+(1.-C_2p)/E21)/Hubble;
   
}
示例#3
0
double rec_HMLA_2photon_dxedlna(double xe, double nH, double H, double TM, double TR,
                                HRATEEFF *rate_table, TWO_PHOTON_PARAMS *twog,
                                double zstart, double dlna, double **logfminus_hist, double *logfminus_Ly_hist[],
                                unsigned iz, double z, double energy_rate){
   
   double xr[2];
   double xv[NVIRT];
   double xedot, Pib, feq;
   double fplus[NVIRT], fplus_Ly[3];
   unsigned b, i;
   
   double Trr[2][2];
   double matrix[2][2];
   double *Trv[2];
   double *Tvr[2];
   double *Tvv[3];
   double sr[2];
   double sv[NVIRT];
   double Dtau[NVIRT]; 
   double Alpha[2], Beta[2];

   double RLya;
   double R2p2s;
   double C_2p;

   for (i = 0; i < 2; i++) Trv[i] = create_1D_array(NVIRT);
   for (i = 0; i < 2; i++) Tvr[i] = create_1D_array(NVIRT);
   for (i = 0; i < 3; i++) Tvv[i] = create_1D_array(NVIRT); 

   /* Redshift photon occupation number from previous times and higher energy bins */
   fplus_from_fminus(fplus, fplus_Ly, logfminus_hist, logfminus_Ly_hist, TR,
                     zstart, dlna, iz, z, twog->Eb_tab);
   
   /* Compute real-real, real-virtual and virtual-virtual transition rates */
   populateTS_2photon(Trr, Trv, Tvr, Tvv, sr, sv, Dtau, xe, TM, TR, nH, H, rate_table, 
                      twog, fplus, fplus_Ly, Alpha, Beta, z);
   
   /* Solve for the population of the real and virtual states */   
   solve_real_virt(xr, xv, Trr, Trv, Tvr, Tvv, sr, sv);
	
	
   /*************************************************************/
	
   /* Dark matter annihilation*/
   RLya = 4.662899067555897e15 *H /nH/(1.-xe);   /*8 PI H/(3 nH x1s lambda_Lya^3) */
	
   interpolate_rates(Alpha, Beta, &R2p2s, TR, TM / TR, rate_table);

   matrix[0][0] = Beta[0] + 3.*R2p2s + L2s1s;
   matrix[1][1] = Beta[1] + R2p2s + RLya;
   
   C_2p=(RLya+R2p2s*L2s1s/matrix[0][0])/(matrix[1][1]-R2p2s*3.*R2p2s/matrix[0][0]);
   
   
   /*************************************************************/
 
   /* Obtain xe_dot */
   xedot = -nH*xe*xe*(Alpha[0]+Alpha[1]) + xr[0]*Beta[0] + xr[1]*Beta[1]
	+(1.-xe)/(3.*nH)*energy_rate*(1./EI+(1.-C_2p)/E21);
	
	   
   /* Update fminuses */
   
   for (b = 0; b < NVIRT; b++) {
     if (Dtau[b] != 0) {
         Pib = (1.-exp(-Dtau[b]))/Dtau[b];
         feq  = -xr[0]*Tvr[0][b] - xr[1]*Tvr[1][b];
         feq -= (b == 0       ?  xv[1]*Tvv[2][0]:
                   b == NVIRT-1 ?  xv[NVIRT-2]*Tvv[1][NVIRT-1]:    
                   xv[b+1]*Tvv[2][b] + xv[b-1]*Tvv[1][b]);        
         feq /= (1.-xe)*(1.-Pib)*Tvv[0][b];
                                                
         logfminus_hist[b][iz] = log(fplus[b] + (feq - fplus[b])*(1.-exp(-Dtau[b])));
     }
     else logfminus_hist[b][iz] = log(fplus[b]);
   }
   
   /* log(xnp/(3 x1s)) , n = 2, 3, 4, assuming 3p and 4p in Boltzmann eq. with 2s */
   logfminus_Ly_hist[0][iz] = log(xr[1]/3./(1.-xe));    
   logfminus_Ly_hist[1][iz] = log(xr[0]/(1.-xe)) - E32/TR; 
   logfminus_Ly_hist[2][iz] = log(xr[0]/(1.-xe)) - E42/TR; 
   

   for (i = 0; i < 2; i++) free(Trv[i]);
   for (i = 0; i < 2; i++) free(Tvr[i]);
   for (i = 0; i < 3; i++) free(Tvv[i]);
  
   return xedot/H;
}
示例#4
0
void populateTS_2photon(double Trr[2][2], double *Trv[2], double *Tvr[2], double *Tvv[3], 
                        double sr[2], double sv[NVIRT], double Dtau[NVIRT],
                        double xe, double TM, double TR, double nH, double H, HRATEEFF *rate_table,
                        TWO_PHOTON_PARAMS *twog, double fplus[NVIRT], double fplus_Ly[], 
                        double Alpha[2], double Beta[2], double z) {

   double R2p2s;
   unsigned b;
   double  RLya, Gammab, Pib, dbfact;
  
   double *Aup, *Adn;
   double A2p_up, A2p_dn; 

   Aup = create_1D_array(NVIRT);  
   Adn = create_1D_array(NVIRT);

   RLya = 4.662899067555897e15 *H /nH/(1.-xe);   /*8 PI H/(3 nH x1s lambda_Lya^3) */ 
 
   interpolate_rates(Alpha, Beta, &R2p2s, TR, TM / TR, rate_table); 

   /****** 2s row and column ******/

   Trr[0][0] = Beta[0] + 3.*R2p2s
             + 3.* RLya * (1.664786871919931 *exp(-E32/TR)     /* Ly-beta escape */              
	                          + 1.953125 *exp(-E42/TR));   /* Ly-gamma escape */
			                  
   Trr[0][1] = -R2p2s;
   sr[0]     = nH * Alpha[0] * xe*xe
             + 3.* RLya * (1.-xe) * (1.664786871919931 *fplus_Ly[1] 
                                    + 1.953125 *exp(-E41/TR));
  
   #if (EFFECT_A == 0)
       /* Standard treatment of 2s-->1s two-photon decays */
       Trr[0][0] += L2s1s;
       sr[0]     += L2s1s * (1.-xe) * exp(-E21/TR);
   #endif
  
     
   /****** 2p row and column ******/

   Trr[1][1] = Beta[1] + R2p2s + RLya;			   
   Trr[1][0] = -3.*R2p2s;
   sr[1]     = nH * Alpha[1] * xe*xe + 3.*RLya * (1.-xe) * fplus_Ly[0]; 
                                     
    
   /***** Two-photon transitions: populating Trv, Tvr and updating Trr ******/

   for (b = 0; b < NVIRT; b++) {
       dbfact = exp((twog->Eb_tab[b] - E21)/TR);

       Trr[0][0] -= Tvr[0][b] = -twog->A2s_tab[b]/fabs(exp((twog->Eb_tab[b] - E21)/TR)-1.);
       Trv[0][b]  = Tvr[0][b] *dbfact;
  
       Trr[1][1] -= Tvr[1][b] = -exp(-E32/TR)/3. * twog->A3s3d_tab[b]/fabs(exp((twog->Eb_tab[b] - E31)/TR)-1.)
                                -exp(-E42/TR)/3. * twog->A4s4d_tab[b]/fabs(exp((twog->Eb_tab[b] - E41)/TR)-1.); 
       Trv[1][b] = Tvr[1][b] *3.*dbfact;        
   }

    /****** Tvv and sv. Accounting for DIFFUSION ******/

    populate_Diffusion(Aup, Adn, &A2p_up, &A2p_dn, TM, twog->Eb_tab, twog->A1s_tab); 
   
    /* Updating Tvr, Trv, Trr for diffusion between line center ("2p state") and two neighboring bins */

    Trr[1][1] += (A2p_dn + A2p_up);       
   
    for (b = 0; b < NVIRT; b++) {

      Gammab = -(Trv[0][b] + Trv[1][b]) + Aup[b] + Adn[b];    /* Inverse lifetime of virtual state b */   
      
      /*** Diffusion region ***/
      if (  (b >= NSUBLYA - NDIFF/2 && b < NSUBLYA - 1) 
          ||(b > NSUBLYA && b < NSUBLYA + NDIFF/2)) { 
	  Tvv[1][b] = -Aup[b-1];
          Tvv[2][b] = -Adn[b+1];
      }
      /* Bins neighboring Lyman alpha. */ 
      if (b == NSUBLYA-1)  {
          Tvv[1][b] = -Aup[b-1];
          Tvv[2][b] = 0.;      
          Tvr[1][b] -= A2p_dn;
          Trv[1][b] -= Aup[b];
      }
      if (b == NSUBLYA)  {
          Tvv[1][b] = 0.;      
          Tvv[2][b] = -Adn[b+1];
          Tvr[1][b] -= A2p_up;
          Trv[1][b] -= Adn[b];                        
      }      
      /*********************/

      Dtau[b] = Gammab * (1.-xe) * cube(hPc/twog->Eb_tab[b]) * nH /8. /M_PI /H;

       if (Dtau[b] > 1e-30) {
          Pib = (1.-exp(-Dtau[b]))/Dtau[b];
          Tvv[0][b] = Gammab/(1.-Pib);
          sv[b]  = Tvv[0][b] * (1.-xe) * fplus[b] * Pib;         
       }
       else {  /* Nearly vanishing optical depth: free streaming */
          Tvv[0][b] = 1.;
          Trv[0][b] = Trv[1][b] = Tvr[0][b] = Tvr[1][b] = 0;
          sv[b] = (1.-xe) * fplus[b];
       }
   }

    free(Aup);
    free(Adn);   
}