*** Bin-integrated one-point PDF of Compton Y (with HSE bias) *** This version uses Planck 2013's pressure profile with a hydrostatic mass bias correction applied, and reproduces the result presented in Dolag, Komatsu & Sunyaev (2015; DKS). June 10, 2016: E.Komatsu Ref: Hill et al., arXiv:1411.8004 Dolag, Komatsu & Sunyaev, arXiv:1509.05134 This code calculates a bin-integrated one-point PDF of the Compton Y (Hill et al.):

(Y) = pi * int dz dV/dz int dlnM dn/dlnM [theta^2(Y)-theta^2(Y+dY)] where dV/dz is the comoving volume element, dn/dlnM is the halo mass function, and theta is the angular radius at which the Compton Y value is equal to a given specified value of Y. The bin-integrated PDF is normalised such that \sum_i

(Y_i) = 1. Dividing

by dY(=1e-6, for example) then gives a bin-averaged PDF. The calculation assumes that halos do not overlap in the sky. This condition imposes a limit on the minimum mass used in the calculation (M1=2d14 in ypdf.f90). A lower minimum mass results in a larger overlapping fraction. Running the code returns an overlapping fraction, F_clust, as defined in Eq.9 of Hill et al. To compute PDF, it is necessary to use the linear matter power spectrum. We provide sample data, "planck15_matterpower.dat," which was generated using the CAMB code for the "TT+lowP+lensing" parameters given in Table 4 of Planck 2015 (arXiv:1502.01589). The input file for CAMB is also provided (planck15_params.ini). NOTE THAT THIS POWER SPECTRUM IS COMPUTED AT Z=0. We also provide the matter power spectrum used by Magneticum Pathfinder Simulation in "wavenumber_pk_at_z=0_magneticum.txt". This power spectrum was generated by Eisentein&Hu's fitting function (which can be computed by one of the codes in CRL). This power spectrum and the associated cosmological parameters need to be chosen in "ypdf.f90" to reproduce the triple-dotted-dashed line in the left panel of Fig.6 of DKS. Finally, we also provide the matter power spectrum of WMAP9 in "wmap9_matterpower.dat". (The CAMB parameter file is "wmap9_params.ini".) This parameter was used by Hill et al., arXiv:1507.01583 << NOTE ON NFW CONCENTRATION PARAMETER >> The default concentration parameter is Duffy et al. (2008): cvir=7.85d0*(mvir/2d12)**(-0.081)/(1d0+z)**0.71 You may also use the concentration parameter of Seljak (2000): cvir=10d0*(mvir/3.42d12)**(-0.2)/(1d0+z) which was originally used by Komatsu&Seljak (2002). << NOTE ON MASS FUNCTION >> The default mass function is Eq.(8)-(12) of Tinker et al. (2010) for Delta=200. Three more mass functions are provided: - Sheth&Tormen (mf_shethtormen.f90) - Jenkins et al. (mf_jenkins.f90; which was originally used by Komatsu&Seljak 2002). - Bocquet et al. with Delta=200m and "Hydro" - Bocquet et al. with Delta=200m and "DM Only" - Tinker et al. (2008) To use these mass functions, change the following: 1. In Makefile, change "mf_magneticum.o" to: "mf_jenkins.o", "mf_shethtormen.o", "mf_magneticum.o", "mf_magneticum_dm.o", "mf_tinker_redshift.o", or 2. For Jenkins et al. and Sherth&Tormen, change "mf(lnnu,z)" to "mf(lnnu)" in integrand.f90 [because Jenkins et al.'s and Sheth&Tormen's functions do not have explicit redshift dependence]. Specifically: dndlnRh=(3d0/4d0/pi)*dlnnudlnRh*mf(lnnu,z)/Rh**3d0 to dndlnRh=(3d0/4d0/pi)*dlnnudlnRh*mf(lnnu)/Rh**3d0 in integrand.f90. 3. Also, since Jenkins et al. use a different mass definition, you need to comment out ! Sheth&Tormen and Tinker et al.'s mass functions are given for the ! overdensity mass M200d (with respect to the mean mass density rather than ! the critical density). CALL mvir2mdel(mvir,rs,cvir,200d0*omega*rhoc,m200d) Rh=(3d0*m200d/4d0/pi/om0/2.775d11)**(1d0/3d0) ! h^-1 Mpc and use ! Alternatively, one may wish to use Jenkins et al.'s mass function, ! which is given for the overdensity mass M180d (with respect to the mean ! mass density rather than the critical density). CALL mvir2mdel(mvir,rs,cvir,180d0*omega*rhoc,m180d) in "integrand.f90". - To compile and use the program, edit Makefile and simply "make" - It will generate executables called "generate_table" and "ypdf" - Running generate_table will generate a dimensionless pressure integrated along the line of sight, f(x), as a function of a dimensionless angular radius, x. The generated file is called "x_fx.txt" and will be used by the main code "ypdf" - Running ypdf will generate the data file called "y_pdf.txt", which contains: 1st: Y 2nd: bin-integrated PDF For your convenience, the result from the default options (Duffy et al.'s concentration parameter and Tinker et al. (2010)'s mass function) is provided as "y_pdf_magneticum_mmin=2e14.txt".