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@jwise77
Created December 11, 2023 22:02
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import os\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import h5py as h5\n",
"from scipy import integrate\n",
"from scipy.special import erf, erfc"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import rc\n",
"rc('font', size=18)\n",
"rc('font', family='serif')\n",
"rc('font', style='normal')\n",
"rc('font', serif='DejaVu Serif')\n",
"rc('xtick', direction='in')\n",
"rc('ytick', direction='in')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cosmological parameters (global): WMAP-7 from Renaissance Simulations"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"omega = dict(m=0.266, l=0.734, b=0.0449)\n",
"omega['c'] = omega['m'] - omega['b']\n",
"sigma8 = 0.81\n",
"n = 0.963\n",
"h = 0.71\n",
"z = 15 # Redshift"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"Msun = 1.989e33\n",
"Mpc = 3.086e24"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cosmological formulae for parameter evolution (assuming flat Universe)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def E(z):\n",
" return np.sqrt(omega['l'] + omega['m']*(1+z)**3)\n",
"def Hz(z):\n",
" return (100*h / 3.086e19)*E(z)\n",
"def Omz(z):\n",
" return omega['m'] * (1+z)**3 / E(z)**2\n",
"def Olz(z):\n",
" return omega['l'] / E(z)**2\n",
"def g(z):\n",
" return 2.5 * Omz(z) / (Omz(z)**(4./7) - Olz(z) + \n",
" (1 + 0.5*Omz(z))*(1 + Olz(z)/70.))\n",
"# Growth factor\n",
"def D(z):\n",
" return g(z) / (g(0) * (1+z))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Other parameters: like critical and mean densities"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"G = 6.673e-8\n",
"H0 = 100*h / 3.086e19\n",
"rhoc = 3 * Hz(z)**2 / (8*np.pi * G)\n",
"rhoc0 = 3 * H0**2 / (8*np.pi * G)\n",
"rhom = Omz(z) * rhoc\n",
"rhom0 = omega['m'] * rhoc0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculate $\\sigma$: density fluctuations\n",
" * Save to file\n",
" * Load if already calculated"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Transfer function (Bardeen et al. 1986)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def T(k):\n",
" q = k / (omega['m'] * h**2)\n",
" return np.log(1 + 2.34*q) / (2.34) * \\\n",
" (1 + 3.89*q + (16.1*q)**2 + (5.46*q)**3 + (6.71*q)**4)**(-0.25)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Window function: Fourier transfer of a spherical top-hat filter"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def Wtilde(x):\n",
" return 3 * (np.sin(x) - x*np.cos(x)) / x**3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### CDM Power spectrum"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def P(k):\n",
" return k * T(k)**2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sphere radius to mass conversion"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def RtoM(R):\n",
" return (4*np.pi/3) * rhom0 * (R*Mpc)**3\n",
"def MtoR(M):\n",
" return ((3 * M) / (4 * np.pi * rhom0))**(1./3) / Mpc"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def calc_sigma(filename='sigma.h5', N=1000, force_calc=False):\n",
" def sigma_integrand(k,R):\n",
" return P(k) * Wtilde(k*R)**2\n",
" if os.path.exists(filename) and not force_calc:\n",
" fp = h5.File(filename, 'r')\n",
" sigma = fp['sigma'].value\n",
" fp.close()\n",
" return sigma\n",
" Mrange = (1, 1e20)\n",
" Rrange = (MtoR(Mrange[0]*Msun), MtoR(Mrange[1]*Msun))\n",
" Ra = np.logspace(np.log10(Rrange[0]), np.log10(Rrange[1]), N)\n",
" result = np.zeros((3,N)) # R,M,sigma\n",
" for i,R in enumerate(Ra):\n",
" s2 = integrate.quad(sigma_integrand, 0, 1.0, args=(R), limit=100)[0]\n",
" s2 += integrate.quad(sigma_integrand, 1.0, np.inf, args=(R), limit=100)[0]\n",
" result[0,i] = R\n",
" result[1,i] = RtoM(R) / Msun\n",
" result[2,i] = np.sqrt(s2)\n",
"\n",
" # Normalize at 8 Mpc/h\n",
" s8_int = np.interp(8.0/h, result[0], result[2])\n",
" result[2] *= sigma8/s8_int\n",
" \n",
" fp = h5.File(filename, 'w')\n",
" fp['sigma'] = result\n",
" fp.close()\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"R,M,sigma = calc_sigma(N=1000)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1000x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, figsize=(10,8))\n",
"ax.loglog(M, sigma, lw=3)\n",
"ax.axhline(sigma8, lw=2, ls=':', label='$\\sigma_8$', c='C1')\n",
"ax.set_xlim(1e4, 1e16)\n",
"ax.set_ylim(0.1, 20)\n",
"\n",
"#axr = ax.twiny()\n",
"#x1, x2 = ax.get_xlim()\n",
"#print x1, x2\n",
"#print MtoR(x1*Msun)*h, MtoR(x2*Msun)*h\n",
"#axr.set_xlim(MtoR(x1*Msun)*h, MtoR(x2*Msun)*h)\n",
"#axr.set_xlabel('Radius [Mpc/h]')\n",
"\n",
"ax.grid()\n",
"ax.set_xlabel(r'Halo mass M [M$_\\odot$]')\n",
"ax.set_ylabel(r'$\\sigma(M)$')\n",
"ax.legend(loc='best')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Press-Schechter: Calculate collapse fractions and overdensities"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# Critical overdensities\n",
"def deltac(z):\n",
" return 1.69 / D(z)\n",
"def deltaec(sigma, z, beta=0.47, gamma=0.615):\n",
" dc = deltac(z)\n",
" return dc * (1.0 + beta * (sigma**2 / dc**2)**gamma)\n",
"\n",
"# Collapsed fractions\n",
"def fc_ps(nu):\n",
" return erfc(nu / 2**0.5)\n",
"def fc_ec(nu):\n",
" return 0.4 * (1.0 + 0.4 * nu**(-0.4)) * erfc(0.85*nu / 2**0.5)\n",
"\n",
"# Multiplicity factors\n",
"def f_ps(nu):\n",
" return np.sqrt(2.0/np.pi) * nu * np.exp(-0.5*nu**2)\n",
"def f_ec(nu, A=0.322, q=0.3):\n",
" nu_t = 0.84 * nu\n",
" return A * (1.0 + 1.0/(nu_t)**(2*q)) * f_ps(nu_t)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculate the halo mass function\n",
"\n",
"\\begin{equation}\n",
"n(M,t) dM = \\frac{\\bar{\\rho}}{M^2} \\, f_{i}(\\nu) \\left| \\frac{d\\ln\\nu}{d\\ln M} \\right| dM\n",
"\\end{equation}\n",
"\n",
"where $f_i$ is the multiplicity function\n",
"\n",
"\\begin{equation}\n",
"f_{\\rm PS}(\\nu) = \\sqrt{\\frac{2}{\\pi}} \\, \\nu \\exp(-\\nu^2/2)\n",
"\\end{equation}\n",
"\n",
"\\begin{equation}\n",
"f_{\\rm EC}(\\mu) = A \\left(1 + \\frac{1}{\\tilde{\\nu}^{2q}} \\right) f_{\\rm PS}(\\tilde{\\nu})\n",
"\\end{equation}\n",
"\n",
"for spherical and ellipsoidal collapses, respectively. Here $\\tilde{\\nu} = 0.84\\nu$, $q=0.3$, and $A \\approx 0.322$."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"nu_ps = deltac(z) / sigma\n",
"nu_ec = deltaec(sigma, z) / sigma"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.semilogy(nu_ps, M, label='PS', lw=4)\n",
"plt.semilogy(nu_ec, M, label='EC', lw=4)\n",
"plt.xlim(1,6)\n",
"x1, x2 = plt.xlim()\n",
"y1a = M[np.searchsorted(nu_ps, x1)]\n",
"y1b = M[np.searchsorted(nu_ec, x1)]\n",
"y1 = (y1a*y1b)**0.5\n",
"y2 = M[np.searchsorted(nu_ps, x2)]\n",
"plt.ylim(y1,y2)\n",
"plt.grid()\n",
"plt.xlabel(r'$\\nu$')\n",
"plt.ylabel(r'Halo mass [M$_\\odot$]')\n",
"plt.legend(loc='best')\n",
"plt.title('z = %.1f' % (z))\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"rhobar = rhom0 / Msun * Mpc**3 # Msun / cMpc**3\n",
"def ps_integrand(nu, M): \n",
" lnv = np.log(nu)\n",
" numer = lnv[2:] - lnv[:-2]\n",
" dlnv_dlnM = np.zeros(nu.size)\n",
" dlnv_dlnM[1:-1] = numer / np.log(M[2:]/M[:-2])\n",
" dlnv_dlnM = np.abs(dlnv_dlnM)\n",
" const = rhobar/M**2 * f_ps(nu) * dlnv_dlnM\n",
" return const\n",
"\n",
"def ec_integrand(nu, M): \n",
" lnv = np.log(nu)\n",
" numer = lnv[2:] - lnv[:-2]\n",
" dlnv_dlnM = np.zeros(nu.size)\n",
" dlnv_dlnM[1:-1] = numer / np.log(M[2:]/M[:-2])\n",
" dlnv_dlnM = np.abs(dlnv_dlnM)\n",
" const = rhobar/M**2 * f_ec(nu) * dlnv_dlnM\n",
" return const"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"integrand = ec_integrand(nu_ps, M)\n",
"n_ec = np.zeros(integrand.size)\n",
"for i in range(n_ec.size):\n",
" n_ec[i] = np.trapz(integrand[i:], M[i:])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, figsize=(10,8))\n",
"ax.loglog(M, n_ec, lw=3)\n",
"ax.set_xlabel('Halo Mass [M$_\\odot$]')\n",
"ax.set_ylabel('Number density $n(>M)$ [Mpc$^{-3}$]')\n",
"ax.set_xlim(1e5, 1e11)\n",
"ax.set_ylim(1e-7, 1e4)\n",
"ax.set_title('z = %.1f' % (z))\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Extended Press-Schechter\n",
"* Given a descendent halo at some time $t_2$ with mass $M_2$, what is the number density of halos with mass $M_1$ at an earlier time $t_1$?\n",
"\n",
"\\begin{equation}\n",
"n(M_1, t_1 | M_2, t_2) \\, dM_1 = \\frac{M_2}{M_1^2} \\, f_{\\rm PS}(\\nu_{12}) \\left| \\frac{d\\ln\\nu_{12}}{d\\ln M_1} \\right| \\, dM_1\n",
"\\end{equation}\n",
"\n",
"where $\\nu_{12} = (\\delta_1 - \\delta_2) (S_1 - S_2)^{-1/2}$."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def eps_integrand(M1, M2, z1, z2, method='ps'):\n",
" dd = (deltac(z1) - deltac(z2))\n",
" S1 = np.interp(M1, M, sigma)**2\n",
" S2 = np.interp(M2, M, sigma)**2\n",
" nu12 = dd / (S1-S2)**0.5\n",
" numer = np.log(nu12[2:] / nu12[:-2])\n",
" dlnv_dlnM = np.zeros(M1.size)\n",
" dlnv_dlnM[1:-1] = numer / np.log(M1[2:]/M1[:-2])\n",
" dlnv_dlnM = np.abs(dlnv_dlnM)\n",
" if method.lower() == 'ps':\n",
" result = (M2*Msun) / (M1*Msun)**2 * f_ps(nu12) * dlnv_dlnM\n",
" elif method.lower() == 'ec':\n",
" result = (M2*Msun) / (M1*Msun)**2 * f_ec(nu12) * dlnv_dlnM \n",
" else:\n",
" raise RuntimeError('Unknown method: %s' % method)\n",
" return result\n",
" return"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"M2 = 1e12 # Msun\n",
"Mmin = 1e-7 # minimum progenitor mass ratio (M1 = M2 * Mmin)\n",
"z2 = 0.0\n",
"z1 = 14.0\n",
"N_eps = 250\n",
"\n",
"M1 = np.logspace(np.log10(Mmin*M2), np.log10(M2)-0.01, N_eps)\n",
"integrand = eps_integrand(M1, M2, z1, z2, method='ec')\n",
"n_prog = np.zeros(N_eps)\n",
"for i in range(N_eps):\n",
" n_prog[i] = np.trapz(integrand[i:], M1[i:])\n",
"n_prog *= Msun"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Number density of halos at M2(z2)\n",
"#n2 = np.interp(M2, M, n_ec)\n",
"\n",
"fig, ax = plt.subplots(1, figsize=(10,8))\n",
"ax.loglog(M1, n_prog, lw=3)\n",
"#ax.axhline(n2, lw=3, ls=':', label='$n(< 10^{%.2f} M_\\odot, z = %.1f)$' % (np.log10(M2), z2))\n",
"ax.set_xlabel('Progenitor Halo Mass [M$_\\odot$]')\n",
"ax.set_ylabel('Number of progenitors $n(>M)$')\n",
"ax.set_xlim(Mmin*M2, M2)\n",
"ax.set_ylim(1e-5, 1e10)\n",
"ax.set_title(r'$z = %.1f \\rightarrow %.1f; \\log \\, M_2 = %.2f$' % (z2, z1, np.log10(M2)))\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, figsize=(10,8))\n",
"ax.loglog(M1, integrand * (M1*Msun)**2 / (M2*Msun), lw=3)\n",
"#ax.axhline(n2, lw=3, ls=':', label='$n(< 10^{%.2f} M_\\odot, z = %.1f)$' % (np.log10(M2), z2))\n",
"ax.set_xlabel('Progenitor Halo Mass [M$_\\odot$]')\n",
"ax.set_ylabel('Mass fraction PDF $f\\,(M_1|M_2)$ (per $\\ln M_1$)')\n",
"ax.set_xlim(Mmin*M2, M2)\n",
"ax.set_ylim(1e-3, 1e-1)\n",
"ax.set_title(r'$z = %.1f \\rightarrow %.1f; \\log \\, M_2 = %.2f$' % (z2, z1, np.log10(M2)))\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Halo assembly / formation times\n",
"Given a halo of mass $M_0$ at time $t_0$, we can calculate at what time $t_a < t_0$ it reaches a mass $fM_0$, where $f = [0,1]$. This probability is\n",
"\n",
"\\begin{equation}\n",
"\\mathcal{P}(<t_a | M_0, t_0) = \\int_{fM_0}^{M_0} \\frac{M_0}{M_1} f_{\\rm FU}(S_1, \\delta_1 | S_0, \\delta_0) \\left| \\frac{dS_1}{dM_1} \\right| \\, dM_1\n",
"\\end{equation}\n",
"\n",
"Here $M_1$ is the halo mass in the range $[M_0/2,M_0]$. We can introduce the variables $S_f = S(fM_0)$, $t_1 = t_a$,\n",
"\n",
"\\begin{equation}\n",
"\\tilde{S} \\equiv \\frac{S_1 - S_0}{S_f - S_0} \n",
"\\quad\\mathrm{and}\\quad\n",
"\\tilde{\\omega}(t_1) \\equiv \\frac{\\delta_1 - \\delta_0}{\\sqrt{S_f - S_0}}\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"a = 137281\n",
"b = 1.2e-5"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10.0"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mod(1e2,30)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.6"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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