void set_NFW_params(double M,
double z,
int mode,
cosmo_info **cosmo,
double *c_vir,
double *R_vir){
double M_o;
double Delta;
double h_Hubble;
double Omega_M;
if(mode!=NFW_MODE_DEFAULT)
SID_trap_error("Unknown mode (%d) in set_NFW_params()",ERROR_LOGIC,mode);
switch(ADaPS_exist(*cosmo,"M_WDM")){
case FALSE:
{
Omega_M =((double *)ADaPS_fetch(*cosmo,"Omega_M"))[0];
h_Hubble=((double *)ADaPS_fetch(*cosmo,"h_Hubble"))[0];
M_o =M_sc(z,cosmo,PSPEC_LINEAR_TF,PSPEC_ALL_MATTER);
// Mass-concentration from Munoz-Cuartas et al 2010
//(*c_vir)=(11./(1.+z))*pow(M/M_o,-0.13); // Bullock et al '01 & Zehavi et al '04
double w = 0.029;
double m = 0.097;
double alpha=-110.001;
double beta =2469.720;
double gamma= 16.885;
double a_z =w*z-m;
double b_z =alpha/(z+gamma)+beta/pow(z+gamma,2.);
(*c_vir) =take_alog10(a_z*take_log10(M/(M_SOL/h_Hubble))+b_z);
Delta =Delta_vir(z,*cosmo);
Delta=200.;
(*R_vir)=R_Delta_z(M,Delta,z,*cosmo); // Bullock et al '01
}
break;
case TRUE:
SID_trap_error("ENS not working.",ERROR_LOGIC);
//(*c_vir)=c_ENS(M,z,*cosmo); // Eke, Navarro and Steinmetz
//(*R_vir)=R_Delta_z(M,200.,z,*cosmo); // R_200
break;
}
}
int compute_group_analysis(halo_properties_info *properties,
halo_profile_info *profile,
double (*p_i_fctn) (void *,int,int),
double (*v_i_fctn) (void *,int,int),
size_t (*id_i_fctn)(void *,int),
void *params,
double box_size,
double particle_mass,
int n_particles,
double expansion_factor,
double *x,
double *y,
double *z,
double *vx,
double *vy,
double *vz,
double *R,
size_t **R_index_in,
int flag_manual_centre,
int flag_compute_shapes,
cosmo_info *cosmo){
size_t *R_index;
int i,j;
int i_profile;
int j_profile;
int k_profile;
int n_profile;
size_t i_particle;
size_t j_particle;
size_t k_particle;
int next_bin_particle;
interp_info *V_R_interpolate;
interp_info *vir_interpolate;
int i_bin;
int n_in_bin;
double n_per_bin;
int n_cumulative;
double V1;
double V2;
double dV;
double dM;
double sigma_r_mean;
double sigma_t_mean;
double sigma_T_mean;
double sigma_P_mean;
double sigma_mean;
double x_COM_accumulator;
double y_COM_accumulator;
double z_COM_accumulator;
double vx_COM_accumulator;
double vy_COM_accumulator;
double vz_COM_accumulator;
double spin_x_accumulator;
double spin_y_accumulator;
double spin_z_accumulator;
double r_xy;
double v_tot,v_rad,v_tan;
double v_x_mean,v_y_mean,v_z_mean,v_rad_mean;
double shape_eigen_values[3];
double shape_eigen_vectors[3][3];
double x_COM,y_COM,z_COM,R_COM;
double r_c[MAX_PROFILE_BINS_P1];
double v_c[MAX_PROFILE_BINS_P1];
double r_interp[MAX_PROFILE_BINS];
double y_interp[MAX_PROFILE_BINS];
size_t n_bins_temp;
double V_max,R_max;
double Delta,Omega;
double norm;
int flag_interpolated=FALSE;
const gsl_interp_type *interp_type;
double sigma_cor,sigma_halo;
double M_cor,M_halo;
double x_vir,gamma;
double h_Hubble=((double *)ADaPS_fetch(cosmo,"h_Hubble"))[0];
double Omega_M =((double *)ADaPS_fetch(cosmo,"Omega_M"))[0];
double redshift=z_of_a(expansion_factor);
Delta=Delta_vir(redshift,cosmo);
Omega=1.;
// Initialize properties
properties->id_MBP =id_i_fctn(params,0);//id_array[index_MBP];
properties->n_particles =n_particles;
properties->position_COM[0]=0.;
properties->position_COM[1]=0.;
properties->position_COM[2]=0.;
properties->position_MBP[0]=(float)p_i_fctn(params,0,0);//(x_array[index_MBP]);
properties->position_MBP[1]=(float)p_i_fctn(params,1,0);//(y_array[index_MBP]);
properties->position_MBP[2]=(float)p_i_fctn(params,2,0);//(z_array[index_MBP]);
properties->velocity_COM[0]=0.;
properties->velocity_COM[1]=0.;
properties->velocity_COM[2]=0.;
properties->velocity_MBP[0]=(float)v_i_fctn(params,0,0);//(vx_array[index_MBP]);
properties->velocity_MBP[1]=(float)v_i_fctn(params,1,0);//(vy_array[index_MBP]);
properties->velocity_MBP[2]=(float)v_i_fctn(params,2,0);//(vz_array[index_MBP]);
properties->M_vir =0.;
properties->R_vir =0.;
properties->R_halo =0.;
properties->R_max =0.;
properties->V_max =0.;
properties->sigma_v =0.;
properties->spin[0] =0.;
properties->spin[1] =0.;
properties->spin[2] =0.;
properties->q_triaxial =1.;
properties->s_triaxial =1.;
for(i=0;i<3;i++){
for(j=0;j<3;j++)
properties->shape_eigen_vectors[i][j]=0.;
properties->shape_eigen_vectors[i][i]=1.;
}
// Set the number of profile bins and the number of particles per bin
profile->n_bins=MAX(MIN_PROFILE_BINS,MIN((int)((6.2*log10((double)n_particles)-3.5)+((double)n_particles/1000.)+1),MAX_PROFILE_BINS));
n_per_bin =(double)(n_particles)/(double)profile->n_bins;
// There's nothing to do if there are no particles
if(n_particles==0)
profile->n_bins=0;
else{
// Create a v_c(0)=0 bin
r_c[0]=0.;
v_c[0]=0.;
// Initialize profiles
for(i_bin=0;i_bin<profile->n_bins;i_bin++){
profile->bins[i_bin].r_med =0.;
profile->bins[i_bin].r_max =0.;
profile->bins[i_bin].n_particles =0;
profile->bins[i_bin].M_r =0.;
profile->bins[i_bin].rho =0.;
profile->bins[i_bin].overdensity =0.;
profile->bins[i_bin].position_COM[0] =0.;
profile->bins[i_bin].position_COM[1] =0.;
profile->bins[i_bin].position_COM[2] =0.;
profile->bins[i_bin].velocity_COM[0] =0.;
profile->bins[i_bin].velocity_COM[1] =0.;
profile->bins[i_bin].velocity_COM[2] =0.;
profile->bins[i_bin].sigma_rad =0.;
profile->bins[i_bin].sigma_tan =0.;
profile->bins[i_bin].sigma_tot =0.;
profile->bins[i_bin].spin[0] =0.;
profile->bins[i_bin].spin[1] =0.;
profile->bins[i_bin].spin[2] =0.;
profile->bins[i_bin].q_triaxial =1.;
profile->bins[i_bin].s_triaxial =1.;
for(i=0;i<3;i++){
for(j=0;j<3;j++)
profile->bins[i_bin].shape_eigen_vectors[i][j]=0.;
profile->bins[i_bin].shape_eigen_vectors[i][i]=1.;
}
}
// Fill temporary arrays for particle positions, radii (all w.r.t MBP) and velocities
// Also, enforce periodic box on particle positions
double x_cen;
double y_cen;
double z_cen;
x_cen=(double)properties->position_MBP[0];
y_cen=(double)properties->position_MBP[1];
z_cen=(double)properties->position_MBP[2];
if(flag_manual_centre){
double x_cen_manual;
double y_cen_manual;
double z_cen_manual;
// Compute a rough comoving centre
for(j_particle=0;j_particle<n_particles;j_particle++){
x[j_particle]=d_periodic(p_i_fctn(params,0,j_particle)-x_cen,box_size);//(double)(x_array[k_particle])-x_cen,box_size);
y[j_particle]=d_periodic(p_i_fctn(params,1,j_particle)-y_cen,box_size);//(double)(y_array[k_particle])-y_cen,box_size);
z[j_particle]=d_periodic(p_i_fctn(params,2,j_particle)-z_cen,box_size);//(double)(z_array[k_particle])-z_cen,box_size);
}
// Refine it with shrinking spheres
int n_iterations;
n_iterations=compute_centroid3D(NULL,
x,
y,
z,
n_particles,
1e-3, // 1 kpc
0.75,
30,
CENTROID3D_MODE_FACTOR|CENTROID3D_MODE_INPLACE,
&x_cen_manual,
&y_cen_manual,
&z_cen_manual);
x_cen+=x_cen_manual;
y_cen+=y_cen_manual;
z_cen+=z_cen_manual;
properties->position_MBP[0]=x_cen;
properties->position_MBP[1]=y_cen;
properties->position_MBP[2]=z_cen;
if(properties->position_MBP[0]< box_size) properties->position_MBP[0]+=box_size;
if(properties->position_MBP[1]< box_size) properties->position_MBP[1]+=box_size;
if(properties->position_MBP[2]< box_size) properties->position_MBP[2]+=box_size;
if(properties->position_MBP[0]>=box_size) properties->position_MBP[0]-=box_size;
if(properties->position_MBP[1]>=box_size) properties->position_MBP[1]-=box_size;
if(properties->position_MBP[2]>=box_size) properties->position_MBP[2]-=box_size;
}
for(j_particle=0;j_particle<n_particles;j_particle++){
// ... halo-centric particle positions ...
x[j_particle]=expansion_factor*d_periodic(p_i_fctn(params,0,j_particle)-x_cen,box_size);//((double)x_array[k_particle])-x_cen,box_size);
y[j_particle]=expansion_factor*d_periodic(p_i_fctn(params,1,j_particle)-y_cen,box_size);//((double)y_array[k_particle])-y_cen,box_size);
z[j_particle]=expansion_factor*d_periodic(p_i_fctn(params,2,j_particle)-z_cen,box_size);//((double)z_array[k_particle])-z_cen,box_size);
// ... velocities ...
vx[j_particle]=v_i_fctn(params,0,j_particle);//(double)(vx_array[k_particle]);
vy[j_particle]=v_i_fctn(params,1,j_particle);//(double)(vy_array[k_particle]);
vz[j_particle]=v_i_fctn(params,2,j_particle);//(double)(vz_array[k_particle]);
// ... particle radii ...
R[j_particle]=sqrt(x[j_particle]*x[j_particle]+y[j_particle]*y[j_particle]+z[j_particle]*z[j_particle]);
}
// Sort particles by radius
merge_sort((void *)R,(size_t)n_particles,R_index_in,SID_DOUBLE,SORT_COMPUTE_INDEX,SORT_COMPUTE_NOT_INPLACE);
R_index=(*R_index_in);
// Use the average of the central 30 particles for the MBP velocity if we are
// manually computing centres
if(flag_manual_centre){
double vx_cen_temp=0.;
double vy_cen_temp=0.;
double vz_cen_temp=0.;
int n_cen =0;
for(i_particle=0;i_particle<MIN(30,n_particles);i_particle++){
vx_cen_temp+=vx[i_particle];
vy_cen_temp+=vy[i_particle];
vz_cen_temp+=vz[i_particle];
n_cen++;
}
properties->velocity_MBP[0]=vx_cen_temp/(double)n_cen;
properties->velocity_MBP[1]=vy_cen_temp/(double)n_cen;
properties->velocity_MBP[2]=vz_cen_temp/(double)n_cen;
}
// We need the COM velocity at R_vir before we can get halo centric velocities. Thus,
// we need the overdensity profile first
x_COM_accumulator =0.;
y_COM_accumulator =0.;
z_COM_accumulator =0.;
vx_COM_accumulator =0.;
vy_COM_accumulator =0.;
vz_COM_accumulator =0.;
V2 =0.;
n_cumulative =0;
for(i_bin=0,i_particle=0;i_bin<profile->n_bins;i_bin++,i_particle+=n_in_bin){
V1=V2; // Volumes
// ... particle numbers ...
if(i_bin<profile->n_bins-1)
n_in_bin=(int)((double)(i_bin+1)*n_per_bin)-i_particle;
else
n_in_bin=n_particles-i_particle;
n_cumulative +=n_in_bin;
profile->bins[i_bin].n_particles =n_in_bin;
// ... mass profile ...
profile->bins[i_bin].M_r=particle_mass*(double)n_cumulative;
// ... binning radii ...
if(n_in_bin%2==1)
profile->bins[i_bin].r_med=(float)R[R_index[i_particle+n_in_bin/2]];
else
profile->bins[i_bin].r_med=0.5*(float)(R[R_index[i_particle+n_in_bin/2-1]]+R[R_index[i_particle+n_in_bin/2]]);
profile->bins[i_bin].r_max=(float)R[R_index[i_particle+n_in_bin-1]];
// ... COM positions and velocities ...
for(j_particle=0;j_particle<n_in_bin;j_particle++){
k_particle=R_index[i_particle+j_particle];
x_COM_accumulator += x[k_particle];
y_COM_accumulator += y[k_particle];
z_COM_accumulator += z[k_particle];
vx_COM_accumulator+=vx[k_particle];
vy_COM_accumulator+=vy[k_particle];
vz_COM_accumulator+=vz[k_particle];
}
profile->bins[i_bin].position_COM[0]=(float)(x_COM_accumulator/(double)n_cumulative);
profile->bins[i_bin].position_COM[1]=(float)(y_COM_accumulator/(double)n_cumulative);
profile->bins[i_bin].position_COM[2]=(float)(z_COM_accumulator/(double)n_cumulative);
profile->bins[i_bin].velocity_COM[0]=(float)(vx_COM_accumulator/(double)n_cumulative);
profile->bins[i_bin].velocity_COM[1]=(float)(vy_COM_accumulator/(double)n_cumulative);
profile->bins[i_bin].velocity_COM[2]=(float)(vz_COM_accumulator/(double)n_cumulative);
// ... density ...
V2=FOUR_THIRDS_PI*profile->bins[i_bin].r_max*profile->bins[i_bin].r_max*profile->bins[i_bin].r_max; // Volume
dV=V2-V1;
dM=particle_mass*(double)n_in_bin;
profile->bins[i_bin].rho =(float)(dM/dV);
profile->bins[i_bin].overdensity=(float)(profile->bins[i_bin].M_r/(V2*Omega*rho_crit_z(redshift,cosmo)));
/// ... triaxiality ...
if(flag_compute_shapes){
compute_triaxiality(x,
y,
z,
(double)profile->bins[i_bin].position_COM[0],
(double)profile->bins[i_bin].position_COM[1],
(double)profile->bins[i_bin].position_COM[2],
box_size,
n_cumulative,
R_index,
shape_eigen_values,
shape_eigen_vectors);
profile->bins[i_bin].q_triaxial=(float)(shape_eigen_values[1]/shape_eigen_values[0]);
profile->bins[i_bin].s_triaxial=(float)(shape_eigen_values[2]/shape_eigen_values[0]);
for(i=0;i<3;i++)
for(j=0;j<3;j++)
profile->bins[i_bin].shape_eigen_vectors[i][j]=(float)shape_eigen_vectors[i][j];
}
}
// Interpolate to get R_vir
flag_interpolated=FALSE;
properties->R_halo=profile->bins[profile->n_bins-1].r_max;
if(profile->n_bins>1){
// Remove any small-radius monotonic increases from the interpolation interval
j_profile=0;
while(profile->bins[j_profile].overdensity<=profile->bins[j_profile+1].overdensity && j_profile<profile->n_bins-2)
j_profile++;
// Only keep decreasing bins
n_bins_temp=0;
r_interp[n_bins_temp]=take_log10((double)profile->bins[j_profile].r_max);
y_interp[n_bins_temp]=take_log10((double)profile->bins[j_profile].overdensity);
n_bins_temp++;
for(i_profile=j_profile+1;i_profile<profile->n_bins;i_profile++){
if(take_log10((double)profile->bins[i_profile].overdensity)<y_interp[n_bins_temp-1]){
r_interp[n_bins_temp]=take_log10((double)profile->bins[i_profile].r_max);
y_interp[n_bins_temp]=take_log10((double)profile->bins[i_profile].overdensity);
n_bins_temp++;
}
}
if(n_bins_temp>1){
// Perform interpolation
if(y_interp[0]>=take_log10(Delta) && y_interp[n_bins_temp-1]<=take_log10(Delta)){
if(n_bins_temp>9)
interp_type=gsl_interp_cspline;
else
interp_type=gsl_interp_linear;
interp_type=gsl_interp_linear;
init_interpolate(y_interp,r_interp,n_bins_temp,interp_type,&vir_interpolate);
properties->R_vir =(float)take_alog10(interpolate(vir_interpolate,take_log10(Delta)));
free_interpolate(SID_FARG vir_interpolate,NULL);
flag_interpolated=TRUE;
}
else if(y_interp[0]<take_log10(Delta)){
properties->R_vir=(float)take_alog10(r_interp[0]);
flag_interpolated=FLAG_INTERP_MIN_BIN;
}
else{
properties->R_vir=(float)take_alog10(r_interp[n_bins_temp-1]);
flag_interpolated=FLAG_INTERP_MAX_BIN;
}
}
else{
properties->R_vir=(float)take_alog10(r_interp[0]);
flag_interpolated=FLAG_INTERP_MIN_BIN;
}
}
else{
properties->R_vir=profile->bins[0].r_max;
flag_interpolated=FLAG_INTERP_MIN_BIN;
}
// Set the interpolation method
if(n_bins_temp>9)
interp_type=gsl_interp_cspline;
else
interp_type=gsl_interp_linear;
interp_type=gsl_interp_linear;
// Compute v_COM(R_vir)
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
r_interp[i_profile]=(double)profile->bins[i_profile].r_max;
if(flag_interpolated==TRUE){
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].velocity_COM[0];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->velocity_COM[0]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].velocity_COM[1];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->velocity_COM[1]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].velocity_COM[2];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->velocity_COM[2]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
}
else{
if(flag_interpolated==FLAG_INTERP_MIN_BIN) i_profile=0;
else if(flag_interpolated==FLAG_INTERP_MAX_BIN) i_profile=profile->n_bins-1;
else SID_trap_error("Unrecognized value for flag_interpolated {%d}.",flag_interpolated);
properties->velocity_COM[0]=(float)profile->bins[i_profile].velocity_COM[0];
properties->velocity_COM[1]=(float)profile->bins[i_profile].velocity_COM[1];
properties->velocity_COM[2]=(float)profile->bins[i_profile].velocity_COM[2];
}
// Compute halo-centric particle velocities
// Subtract COM mean and add Hubble flow
for(j_particle=0;j_particle<n_particles;j_particle++){
vx[j_particle]+=x[j_particle]*H_convert(H_z(redshift,cosmo))-(double)properties->velocity_COM[0];
vy[j_particle]+=y[j_particle]*H_convert(H_z(redshift,cosmo))-(double)properties->velocity_COM[1];
vz[j_particle]+=z[j_particle]*H_convert(H_z(redshift,cosmo))-(double)properties->velocity_COM[2];
}
// Compute remaining profiles ...
spin_x_accumulator=0.;
spin_y_accumulator=0.;
spin_z_accumulator=0.;
V2 =0.;
n_cumulative =0;
for(i_bin=0,i_particle=0;i_bin<profile->n_bins;i_bin++,i_particle+=n_in_bin){
V1=V2; // Volumes
// ... particle numbers ...
if(i_bin<profile->n_bins-1)
n_in_bin=(int)((double)(i_bin+1)*n_per_bin)-i_particle;
else
n_in_bin=n_particles-i_particle;
n_cumulative+=n_in_bin;
// ... spins and mean velocities ...
v_x_mean =0.;
v_y_mean =0.;
v_z_mean =0.;
v_rad_mean=0.;
for(j_particle=0;j_particle<n_in_bin;j_particle++){
k_particle=R_index[i_particle+j_particle];
// ... spins ...
spin_x_accumulator+=(double)(y[k_particle]*vz[k_particle]-z[k_particle]*vy[k_particle]);
spin_y_accumulator+=(double)(z[k_particle]*vx[k_particle]-x[k_particle]*vz[k_particle]);
spin_z_accumulator+=(double)(x[k_particle]*vy[k_particle]-y[k_particle]*vx[k_particle]);
// ... mean velocities (needed below for velocity dispersions) ...
if(R[k_particle]>0.){
v_rad =(x[k_particle]*vx[k_particle]+y[k_particle]*vy[k_particle]+z[k_particle]*vz[k_particle])/R[k_particle];
v_x_mean +=vx[k_particle];
v_y_mean +=vy[k_particle];
v_z_mean +=vz[k_particle];
v_rad_mean+=v_rad;
}
}
profile->bins[i_bin].spin[0]=(float)(spin_x_accumulator)/n_cumulative;
profile->bins[i_bin].spin[1]=(float)(spin_y_accumulator)/n_cumulative;
profile->bins[i_bin].spin[2]=(float)(spin_z_accumulator)/n_cumulative;
v_x_mean /=(double)n_in_bin;
v_y_mean /=(double)n_in_bin;
v_z_mean /=(double)n_in_bin;
v_rad_mean/=(double)n_in_bin;
// ... velocity dispersions ...
for(j_particle=0;j_particle<n_in_bin;j_particle++){
k_particle=R_index[i_particle+j_particle];
if(R[k_particle]>0.){
v_tot=sqrt(pow(vx[k_particle]-v_x_mean,2.)+pow(vy[k_particle]-v_y_mean,2.)+pow(vz[k_particle]-v_z_mean,2.));
v_rad=(x[k_particle]*(vx[k_particle]-v_x_mean)+y[k_particle]*(vy[k_particle]-v_y_mean)+z[k_particle]*(vz[k_particle]-v_z_mean))/R[k_particle];
v_tan=sqrt(v_tot*v_tot-v_rad*v_rad);
profile->bins[i_bin].sigma_tot+=(float)((v_tot)*(v_tot));
profile->bins[i_bin].sigma_rad+=(float)((v_rad-v_rad_mean)*(v_rad-v_rad_mean));
profile->bins[i_bin].sigma_tan+=(float)((v_tan)*(v_tan));
}
}
profile->bins[i_bin].sigma_tot=(float)sqrt((double)profile->bins[i_bin].sigma_tot/(double)n_in_bin);
profile->bins[i_bin].sigma_rad=(float)sqrt((double)profile->bins[i_bin].sigma_rad/(double)n_in_bin);
profile->bins[i_bin].sigma_tan=(float)sqrt((double)profile->bins[i_bin].sigma_tan/(double)n_in_bin);
// ... circular velocity; v_c(R) ...
r_c[i_bin+1]=profile->bins[i_bin].r_max;
v_c[i_bin+1]=sqrt(G_NEWTON*profile->bins[i_bin].M_r/(double)profile->bins[i_bin].r_max);
}
// Determine R_max and V_max from v_c(R)...
R_max=(double)r_c[1]; // default for a monotonically increasing V_c(r)
V_max=(double)v_c[1]; // default for a monotonically increasing V_c(r)
if(profile->n_bins>1){
// Remove any large-radius monotonic increases from the interpolation interval
k_profile=profile->n_bins;
while(v_c[k_profile-1]<=v_c[k_profile] && k_profile>1)
k_profile--;
if(v_c[0]<=v_c[1] && k_profile==1)
k_profile--;
// If the profile is not monotonically increasing ...
if(k_profile>0){
n_bins_temp=k_profile+1;
// ...find the maximum (call its index j_profile)
for(i_profile=0,j_profile=0;i_profile<n_bins_temp;i_profile++){
if(v_c[i_profile]>v_c[j_profile])
j_profile=i_profile;
}
// ...find bottom of range in which to search for maximum (call its index i_profile)
i_profile=j_profile-1;
while(v_c[i_profile]>=v_c[j_profile] && i_profile>0)
i_profile--;
// ...find top of range in which to search for maximum (call its index k_profile)
k_profile=j_profile+1;
while(v_c[k_profile]>=v_c[j_profile] && k_profile<n_bins_temp-1)
k_profile++;
// ... perform interpolation
V_max=(double)v_c[j_profile];
R_max=(double)r_c[j_profile];
if(i_profile<j_profile && j_profile<k_profile){
if(n_bins_temp>9)
interp_type=gsl_interp_cspline;
else
interp_type=gsl_interp_linear;
interp_type=gsl_interp_linear;
init_interpolate(r_c,v_c,n_bins_temp,gsl_interp_cspline,&V_R_interpolate);
interpolate_maximum(V_R_interpolate,
r_c[i_profile],
r_c[j_profile],
r_c[k_profile],
0.05,
&R_max,
&V_max);
free_interpolate(SID_FARG V_R_interpolate,NULL);
}
}
}
properties->R_max=(float)R_max;
properties->V_max=(float)V_max;
if(profile->n_bins>9)
interp_type=gsl_interp_cspline;
else
interp_type=gsl_interp_linear;
interp_type=gsl_interp_linear;
// Perform normal interpolation from profiles to get the rest of the global quantities
if(flag_interpolated==TRUE){
// ... COM positions ...
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].position_COM[0]/expansion_factor;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->position_COM[0]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].position_COM[1]/expansion_factor;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->position_COM[1]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].position_COM[2]/expansion_factor;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->position_COM[2]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
// ... M_vir ...
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].M_r;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->M_vir=interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
// ... sigma_v ...
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].sigma_tot;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->sigma_v=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
// ... spin ...
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].spin[0];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->spin[0]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].spin[1];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->spin[1]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].spin[2];
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->spin[2]=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
// ... triaxial axes ratios ...
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].q_triaxial;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->q_triaxial=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)profile->bins[i_profile].s_triaxial;
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->s_triaxial=(float)interpolate(vir_interpolate,properties->R_vir);
free_interpolate(SID_FARG vir_interpolate,NULL);
// ... shape eigen vectors ...
for(i=0;i<3;i++){
for(j=0;j<3;j++){
for(i_profile=0;i_profile<profile->n_bins;i_profile++)
y_interp[i_profile]=(double)cos(profile->bins[i_profile].shape_eigen_vectors[i][j]);
init_interpolate(r_interp,y_interp,profile->n_bins,interp_type,&vir_interpolate);
properties->shape_eigen_vectors[i][j]=(float)acos(MAX(0,MIN(1.,interpolate(vir_interpolate,properties->R_vir))));
free_interpolate(SID_FARG vir_interpolate,NULL);
}
norm=sqrt(properties->shape_eigen_vectors[i][0]*properties->shape_eigen_vectors[i][0]+
properties->shape_eigen_vectors[i][1]*properties->shape_eigen_vectors[i][1]+
properties->shape_eigen_vectors[i][2]*properties->shape_eigen_vectors[i][2]);
for(j=0;j<3;j++)
properties->shape_eigen_vectors[i][j]/=norm;
}
}
// ... else apply defaults to faulty cases.
else{
if(flag_interpolated==FLAG_INTERP_MIN_BIN) i_profile=0;
else if(flag_interpolated==FLAG_INTERP_MAX_BIN) i_profile=profile->n_bins-1;
else SID_trap_error("Unrecognized value for flag_interpolated {%d}.",flag_interpolated);
// ... COM positions ...
properties->position_COM[0]=(double)(profile->bins[i_profile].position_COM[0])/expansion_factor;
properties->position_COM[1]=(double)(profile->bins[i_profile].position_COM[1])/expansion_factor;
properties->position_COM[2]=(double)(profile->bins[i_profile].position_COM[2])/expansion_factor;
// ... M_vir ...
properties->M_vir=(double)profile->bins[i_profile].M_r;
// ... sigma_v ...
properties->sigma_v=(float)profile->bins[i_profile].sigma_tot;
// ... spin ...
properties->spin[0]=(float)profile->bins[i_profile].spin[0];
properties->spin[1]=(float)profile->bins[i_profile].spin[1];
properties->spin[2]=(float)profile->bins[i_profile].spin[2];
// ... triaxial axes ratios ...
properties->q_triaxial=(float)profile->bins[i_profile].q_triaxial;
properties->s_triaxial=(float)profile->bins[i_profile].s_triaxial;
// ... shape eigen vectors ...
for(i=0;i<3;i++){
for(j=0;j<3;j++)
properties->shape_eigen_vectors[i][j]=(float)profile->bins[i_profile].shape_eigen_vectors[i][j];
norm=sqrt(properties->shape_eigen_vectors[i][0]*properties->shape_eigen_vectors[i][0]+
properties->shape_eigen_vectors[i][1]*properties->shape_eigen_vectors[i][1]+
properties->shape_eigen_vectors[i][2]*properties->shape_eigen_vectors[i][2]);
for(j=0;j<3;j++)
properties->shape_eigen_vectors[i][j]/=norm;
}
}
// Enforce periodic box on COM position
properties->position_COM[0]+=x_cen;
properties->position_COM[1]+=y_cen;
properties->position_COM[2]+=z_cen;
if(properties->position_COM[0]< box_size) properties->position_COM[0]+=box_size;
if(properties->position_COM[1]< box_size) properties->position_COM[1]+=box_size;
if(properties->position_COM[2]< box_size) properties->position_COM[2]+=box_size;
if(properties->position_COM[0]>=box_size) properties->position_COM[0]-=box_size;
if(properties->position_COM[1]>=box_size) properties->position_COM[1]-=box_size;
if(properties->position_COM[2]>=box_size) properties->position_COM[2]-=box_size;
// Perform unit conversions
// ... properties first ...
properties->position_COM[0]*=h_Hubble/M_PER_MPC;
properties->position_COM[1]*=h_Hubble/M_PER_MPC;
properties->position_COM[2]*=h_Hubble/M_PER_MPC;
properties->position_MBP[0]*=h_Hubble/M_PER_MPC;
properties->position_MBP[1]*=h_Hubble/M_PER_MPC;
properties->position_MBP[2]*=h_Hubble/M_PER_MPC;
properties->velocity_COM[0]*=1e-3;
properties->velocity_COM[1]*=1e-3;
properties->velocity_COM[2]*=1e-3;
properties->velocity_MBP[0]*=1e-3;
properties->velocity_MBP[1]*=1e-3;
properties->velocity_MBP[2]*=1e-3;
properties->M_vir *=h_Hubble/M_SOL;
properties->R_vir *=h_Hubble/M_PER_MPC;
properties->R_halo *=h_Hubble/M_PER_MPC;
properties->R_max *=h_Hubble/M_PER_MPC;
properties->V_max *=1e-3;
properties->sigma_v *=1e-3;
properties->spin[0] *=1e-3*h_Hubble/M_PER_MPC;
properties->spin[1] *=1e-3*h_Hubble/M_PER_MPC;
properties->spin[2] *=1e-3*h_Hubble/M_PER_MPC;
// ... then profiles ...
for(i_bin=0;i_bin<profile->n_bins;i_bin++){
profile->bins[i_bin].r_med *=h_Hubble/M_PER_MPC;
profile->bins[i_bin].r_max *=h_Hubble/M_PER_MPC;
profile->bins[i_bin].M_r *=h_Hubble/M_SOL;
profile->bins[i_bin].rho *=M_PER_MPC*M_PER_MPC*M_PER_MPC/(h_Hubble*h_Hubble*M_SOL);
profile->bins[i_bin].position_COM[0]*=h_Hubble/M_PER_MPC;
profile->bins[i_bin].position_COM[1]*=h_Hubble/M_PER_MPC;
profile->bins[i_bin].position_COM[2]*=h_Hubble/M_PER_MPC;
profile->bins[i_bin].velocity_COM[0]*=1e-3;
profile->bins[i_bin].velocity_COM[1]*=1e-3;
profile->bins[i_bin].velocity_COM[2]*=1e-3;
profile->bins[i_bin].sigma_rad *=1e-3;
profile->bins[i_bin].sigma_tan *=1e-3;
profile->bins[i_bin].sigma_tot *=1e-3;
profile->bins[i_bin].spin[0] *=1e-3*h_Hubble/M_PER_MPC;
profile->bins[i_bin].spin[1] *=1e-3*h_Hubble/M_PER_MPC;
profile->bins[i_bin].spin[2] *=1e-3*h_Hubble/M_PER_MPC;
}
}
return(flag_interpolated);
}
double bias_model(double x_in, double delta_c, double z, cosmo_info **cosmo, int mode) {
// Decide what the input is
int flag_Vmax_ordinate = SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_VMAX_ORDINATE);
double M_R;
double V_max;
if(flag_Vmax_ordinate)
V_max = x_in;
else
M_R = x_in;
double bias;
int flag_done = GBP_FALSE;
// Tinker et al 2010
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_TRK)) {
if(flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). Multiple model definitions.", SID_ERROR_LOGIC,
mode);
flag_done = GBP_TRUE;
if(flag_Vmax_ordinate)
M_R = Vmax_to_Mvir_NFW(V_max, z, NFW_MODE_DEFAULT, cosmo);
double y = take_log10(Delta_vir(z, *cosmo));
double A = 1. + 0.24 * y * exp(-pow(4. / y, 4.));
double B = 0.183;
double C = 0.019 + 0.107 * y + 0.19 * exp(-pow(4. / y, 4.));
double a = 0.44 * y - 0.88;
double b = 1.5;
double c = 2.4;
double sigma = sigma_M(cosmo, M_R, z, PSPEC_LINEAR_TF, PSPEC_ALL_MATTER);
double nu = delta_c / sigma;
bias = 1. - A * pow(nu, a) / (pow(nu, a) + pow(delta_c, a)) + B * pow(nu, b) + C * pow(nu, c);
}
// Basilakos and Plionis (2001;2003) w/ Papageorgiou et al 2013 coeeficients
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_BPR)) {
if(flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). Multiple model definitions.", SID_ERROR_LOGIC,
mode);
flag_done = GBP_TRUE;
if(flag_Vmax_ordinate)
M_R = Vmax_to_Mvir_NFW(V_max, z, NFW_MODE_DEFAULT, cosmo);
double alpha_1 = 4.53;
double alpha_2 = -0.41;
double beta_1 = 0.37;
double beta_2 = 0.36;
double I_z;
double C_1;
double C_2;
double Omega_M, Omega_k, Omega_Lambda, h_Hubble;
double Ez;
Omega_M = ((double *)ADaPS_fetch(*cosmo, "Omega_M"))[0];
Omega_k = ((double *)ADaPS_fetch(*cosmo, "Omega_k"))[0];
Omega_Lambda = ((double *)ADaPS_fetch(*cosmo, "Omega_Lambda"))[0];
h_Hubble = ((double *)ADaPS_fetch(*cosmo, "h_Hubble"))[0];
Ez = E_z(Omega_M, Omega_k, Omega_Lambda, z);
I_z = bias_model_BPR_integral(cosmo, z);
C_1 = alpha_1 * pow(M_R / (1e13 * M_SOL / h_Hubble), beta_1);
C_2 = alpha_2 * pow(M_R / (1e13 * M_SOL / h_Hubble), beta_2);
bias = (C_1 + C_2 * I_z) * Ez + 1.;
}
// Poole et al 2014
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_HALO)) {
if(flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). Multiple model definitions.", SID_ERROR_LOGIC,
mode);
flag_done = GBP_TRUE;
if(!flag_Vmax_ordinate)
V_max = V_max_NFW(M_R, z, NFW_MODE_DEFAULT, cosmo) * 1e-3;
else
V_max *= 1e-3;
double V_SF_o;
double V_SF_z;
double s_V_o;
double s_V_z;
double b_o_o;
double b_o_z;
double b_V_o;
double b_V_z;
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_SUBSTRUCTURE)) {
V_SF_o = 5.326176e-02;
V_SF_z = -1.673868e-01;
s_V_o = 4.026941e-01;
s_V_z = 6.096567e-01;
b_o_o = -1.974311e-01;
b_o_z = 2.138219e-01;
b_V_o = 2.707540e-01;
b_V_z = 8.202001e-02;
} else {
V_SF_o = 2.819063e-02;
V_SF_z = -1.381993e-01;
s_V_o = 3.685953e-01;
s_V_z = 6.154695e-01;
b_o_o = -3.793559e-01;
b_o_z = 3.074326e-01;
b_V_o = 3.147507e-01;
b_V_z = 6.072666e-02;
}
double b_o = b_o_o + b_o_z * z;
double b_V = (b_V_o + b_V_z * z) / 220.;
double V_SF = take_alog10(V_SF_o + V_SF_z * z) * 220.;
double s_V = (s_V_o + s_V_z * z) / 220.;
double s = s_V * fabs(V_max - V_SF);
bias = take_alog10(0.5 * (b_o + b_V * V_max));
}
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_ZSPACE)) {
if(flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). Multiple model definitions.", SID_ERROR_LOGIC,
mode);
flag_done = GBP_TRUE;
if(!flag_Vmax_ordinate)
V_max = V_max_NFW(M_R, z, NFW_MODE_DEFAULT, cosmo) * 1e-3;
else
V_max *= 1e-3;
double V_SF_o;
double V_SF_z;
double s_V_o;
double s_V_zz;
double b_o_o;
double b_o_zz;
double b_V_o;
double b_V_z;
double z_b_c;
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_SUBSTRUCTURE)) {
V_SF_o = 3.173152e-01;
V_SF_z = -1.599133e-01;
s_V_o = 5.344408e-01;
s_V_zz = 7.102406e-02;
b_o_o = 2.198795e-01;
b_o_zz = -3.749491e-02;
b_V_o = -4.628602e-02;
b_V_z = -1.832620e-02;
z_b_c = 9.292014e-01;
} else {
V_SF_o = 3.100167e-01;
V_SF_z = -2.026411e-01;
s_V_o = 3.342258e-01;
s_V_zz = 9.233431e-02;
b_o_o = 2.206163e-01;
b_o_zz = -4.419126e-02;
b_V_o = -4.804747e-02;
b_V_z = -1.454479e-02;
z_b_c = 7.852721e-01;
}
double b_o = b_o_o + b_o_zz * (z - z_b_c) * (z - z_b_c);
double b_V = (b_V_o + b_V_z * z) / 220.;
double V_SF = 220. * take_alog10(V_SF_o + V_SF_z * z);
double s_V = (s_V_o + s_V_zz * z * z) / 220.;
double s = s_V * fabs(V_max - V_SF);
bias = take_alog10(0.5 * (b_o + b_V * V_max));
}
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_TOTAL)) {
if(flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). Multiple model definitions.", SID_ERROR_LOGIC,
mode);
flag_done = GBP_TRUE;
if(!flag_Vmax_ordinate)
V_max = V_max_NFW(M_R, z, NFW_MODE_DEFAULT, cosmo) * 1e-3;
else
V_max *= 1e-3;
double V_SF_o;
double V_SF_z;
double s_V_o;
double s_V_z;
double b_o_o;
double b_o_z;
double b_V_o;
double b_V_z;
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_POOLE_SUBSTRUCTURE)) {
V_SF_o = 2.128681e-01;
V_SF_z = -2.280569e-01;
s_V_o = 1.118792e+00;
s_V_z = 6.121383e-01;
b_o_o = 1.198136e-02;
b_o_z = 2.112670e-01;
b_V_o = 2.153513e-01;
b_V_z = 7.763461e-02;
} else {
V_SF_o = 2.041659e-01;
V_SF_z = -2.966696e-01;
s_V_o = 9.408169e-01;
s_V_z = 4.514711e-01;
b_o_o = -1.534952e-01;
b_o_z = 2.799483e-01;
b_V_o = 2.547096e-01;
b_V_z = 6.760491e-02;
}
double b_o = b_o_o + b_o_z * z;
double b_V = (b_V_o + b_V_z * z) / 220.;
double V_SF = V_SF_o + V_SF_z * z;
double s_V = (s_V_o + s_V_z * z) / 220.;
double s = s_V * fabs(V_max - V_SF);
bias = take_alog10(0.5 * (b_o + b_V * V_max));
}
if(!flag_done)
SID_exit_error("Mode flag (%d) is invalid in bias_model(). No model definition.", SID_ERROR_LOGIC, mode);
// Apply the Kaiser '87 model to whatever model has been processed above. Be careful, there
// are some mode flags (such as BIAS_MODE_POOLE_ZSPACE) for which this does not make sence
// and we presently don't check for this.
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_KAISER_BOOST)) {
double Omega_M_z = Omega_z(z, (*cosmo));
double f = pow(Omega_M_z, 0.55);
double beta = f / bias;
double boost = pow(1. + TWO_THIRDS * beta + 0.2 * beta * beta, 0.5);
bias = boost;
}
if(SID_CHECK_BITFIELD_SWITCH(mode, BIAS_MODEL_KAISER)) {
double Omega_M_z = Omega_z(z, (*cosmo));
double f = pow(Omega_M_z, 0.55);
double beta = f / bias;
double boost = pow(1. + TWO_THIRDS * beta + 0.2 * beta * beta, 0.5);
bias *= boost;
}
return (bias);
}