Here I breifly summarize how to calibrate the pairwise velocity PDFs of dark matter halos based on the model in Tinker (2007); arXiv:astro-ph/0604217. I suppose that you have a halo catalog produced by the ROCKSTAR algorithm (https://code.google.com/archive/p/rockstar/) and the linear matter power spectrum at z=0 with CAMB (https://camb.info/) or LAMBDA Web Interface (https://lambda.gsfc.nasa.gov/toolbox/tb_camb_form.cfm). More details are found in https://arxiv.org/abs/2008.02960. (1) Setup Run "./set_prog.sh" You have to install The GNU Scientific Library (https://www.gnu.org/software/gsl/). For cleaning up, you will run "./clean_prog.sh". Make sure that you set the current directory in set_prog.sh and clean_prog.sh properly. (2) ./gen_pdf/gen_pdf_rockstar This code produces the histogram of the pairwise velocity for dark matter halos from the input ROCKSTAR halo catalog. HOW TO USE: "./gen_pdf_rockstar arg1 arg2 arg3" where arg1 : the name of input halo catalog arg2 : the name of output file arg3 : sets the box size for the halo catalog. If your catalog is produced from a N-body simulation with the box length of 500 Mpc/h, then set arg3 = 500. (3) ./save_mass_variance/save_mass_variance_EH This code computes the non-linear mass variance assuming the linear matter power spectrum without the BAO feature (Eisenstein and Hu 1998; arXiv:astro-ph/9710252). The non-linear mass variance is needed to set the model of the pairwise velocity PDF, because the model needs to set the log-normal PDF for cosmic mass density. The non-linear mass variance is obtained with the halo-fit fitting formula (Takahashi et al. 2012; arXiv:1208.2701). HOW TO USE: "./save_mass_variance_EH arg1 arg2 arg3 arg4 arg5 arg6" where arg1 : the name of output arg2 : the present-day mean mass density parameter (Omega_{m0}) arg3 : the present-day hubble parameter in unit of km/s/Mpc/100 arg4 : the spectral index for the inital curvarure power spectrum (n_s) arg5 : the top-hat linear variance with 8 Mpc/h at z=0 (sigma_8) arg6 : redshift of interest. (4) ./fit/fit_mean This code performs the fitting of the mean pairwise velocity profiles for various halo masses at a given redshift with the model. Here the model has three parameters, referred to as A1, A2, and A3. Note A1, A2, and A3 depend on the masses of two halos. It holds that A1 = B_{\rho}, A2 = C_{\rho}, and A3 = A_{\rho} in Eq (22) in https://arxiv.org/abs/2008.02960. HOW TO USE: "./fit/fit_mean arg1 arg2 arg3 arg4 arg5 arg6" where arg1 : the histogram given by ./gen_pdf/gen_pdf_rockstar at the step (2) arg2 : the mass variance given by ./save_mass_variance/save_mass_variance_EH at the step (3) arg3 : redshift of interest arg4 : the mean mass density parameter (Omega_{m0}) arg5 : the table for the linear matter power spectrum at z=0 in the CAMB format arg6 : the name of output file (5) ./fit/search_M_z_depend_mean.py This code seeks for appropriate forms of the fitted parameters (A1, A2, and A3) at the step (4). It tries to find the dependence on halo masses. You may need to modify the following parts to have good results: def fit_func_1D_1(...) def fit_func_1D_2(...) HOW TO USE: "python ./fit/search_M_z_depend_mean.py arg1 arg2 arg3" where arg1 : the file produced by ./fit/fit_mean at the step (4). The file name should include "params_list.dat". arg2 : the name of output file (showing if your model can explain the mass dependence of A1, A2, and A3) arg3 : set 0, 1, and 2 for A1, A2, and A3, respectively. (6) ./fit/fit_variance This code performs the fitting of the variance of the pairwise velocity for various halo masses with the model. There are two relevant variances for redshift surveys. For each variance, the model has three parameters. Hence, the code finds six best-fit parameters in total (denoted as B1, B2, B3, C1, C2, and C3). These six parameters depend on halo masses. It holds that B1 = C^{0}_{t}, B2 = C^{1}_{t}, and B3 = p_t in Eq (24) in https://arxiv.org/abs/2008.02960. Also, it holds that C1 = C^{0}_{r}, C2 = C^{1}_{r}, and C3 = C^{2}_{r} in Eq (24) in https://arxiv.org/abs/2008.02960. Before running, you have to change the following part in fit_variance.c: double cond_Prob_delta_param(double r, double m1, double m2, double b1, double b2) This function returns A_1 * [r/r_max(m1, m2)]^{A_2} + A_3 * [b1+b2] where A1(m1,m2), A2(m1,m2) and A3(m1,m2) are set at the step (5). Note that m1 is the mass of halo 1 and b1 is the linear halo bias of halo 1, and so on. The term of r_max is defined by r_max(m1,m2) = MAX [ r_200b(m1), r_200b(m2)] where r_200b(m) is the spherical overdensity radius with respect to 200 times mean mass density for the halo of m. After setting the function of cond_Prob_delta_param(...), you need to run "./set_prog.sh" again. HOW TO USE: "./fit/fit_variance arg1 arg2 arg3 arg4 arg5 arg6" where arg1 : the histogram given by ./gen_pdf/gen_pdf_rockstar at the step (2) arg2 : the mass variance given by ./save_mass_variance/save_mass_variance_EH at the step (3) arg3 : redshift of interest arg4 : the mean mass density parametr (Omega_{m0}) arg5 : the table for the linear matter power spectrum at z=0 in the CAMB format arg6 : the name of output file (7) ./fit/search_M_z_depend_variance.py This codes search for appropriate forms of the fitted parameters (B1, B2, B3, C1, C2, and C3) at the step (6). It tries to find the dependence on halo masses. You may need to modify the following parts to have good results: def fit_func_1D_1(...) def fit_func_1D_2(...) HOW TO USE: "python ./fit/search_M_z_depend_variance.py arg1 arg2 arg3 arg4" where arg1 : the file produced by ./fit/fit_variance at the step (6). The file name should include "params_list.dat". arg2 : the name of output file (showing if your model can explain the mass dependence of B1-B3 or C1-C3) arg3 : set 0 when working with B1-B3, 1 for C1-C3. arg4 : set 0 for B1 or C1, 1 for B2 or C2, and 2 for B3 or C3. --------------------------- Masato Shirasaki masato.shirasaki@nao.ac.jp August 28, 2020