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Last active December 2, 2015 04:29
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Simple model for radio source counts
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generating Source Counts From HMF"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": true,
"hide_input": true,
"init_cell": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: pylab import has clobbered these variables: ['f', 'gamma']\n",
"`%matplotlib` prevents importing * from pylab and numpy\n"
]
}
],
"source": [
"%pylab inline\n",
"from mrpy.physical_dependence import mrp_b13\n",
"from astropy.cosmology import Planck13"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction/Outline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The primary idea is to develop a physical model, based on structure formation theory (via spherical collapse) to describe the differential source counts of radio galaxies, $\\frac{dN}{dS}$ (units of ${\\rm Jy^{-1} sr^{-1}}$).\n",
"\n",
"To set up the context, consider the following plot from Franzen+15 (in prep.): \n",
"<img src=\"franzen.png\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this image, several surveys are shown to agree on the source counts at approximately 154 MHz (there is of course a frequency dependence as well). Below 0.1 Jy, the counts are well-modelled by a power-law, while above this there is a turnover, seemingly exponential (reminds me of a gamma distribution in fact...). There is also an expected flattening at low flux densities (detected at higher frequencies), but which is not detected as yet at 154 MHz. \n",
"\n",
"Franzen+15 also mentions that the primary categories of sources are AGN and star-forming galaxies (which may overlap). These two categories may have different properties which, when added together, give the above plot. \n",
"\n",
"Our task is to come up with some model, perhaps with free parameters, that can reproduce the above plot, and give insight as to where this power-law and turnover come from. Furthermore, this extended model should give a more precise description of the source counts for use in EoR studies."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Outlook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The way we will approach this problem is analogous to the Halo Occupation Distribution (HOD) framework. We assume that every galaxy is associated with a dark matter halo. Depending on the category of galaxy (AGN or star-forming [hereafter SF]), we might expect each halo to either have 0 or 1 galaxy, or perhaps several galaxies located as satellites. We specify some parametric model, $N_X(m)$ which prescribes the average number of galaxies in halos of a given mass (we will end up using the data to generate the best-fit parameters of this model). The important point is that we know, to fairly good accuracy, the number density of halos of a given mass for a given cosmology, $\\frac{dn}{dm}$. Thus simply by multiplying the two we estimate the number density of galaxies of category $X$ at a given redshift:\n",
"\n",
"\\begin{equation} \\frac{dn_X}{dm}(m,z) = \\frac{dn_h}{dm}(z) N_X(m,z).\\end{equation}\n",
"\n",
"In the end, we want the number of sources a function of *flux density*, not mass. One way about this might be to specify some relation between average intrinsic radio luminosity, $L_\\nu$ and host halo mass:\n",
"\n",
"\\begin{equation}L_\\nu = f_L(m,z). \\end{equation}\n",
"\n",
"For example, a particularly simple relation might be a constant factor, $L_\\nu = A_\\nu m$. \n",
"\n",
"Once this is specified (again, with free parameters), we can calculate the relevant halo mass at each redshift which will contribute to the flux density $S_\\nu'$ (via the luminosity distance). Since we know the number density of sources in category $X$ corresponding to this halo mass, we can integrate over cosmic volume out to the EoR signal, to generate the total source counts at flux $S_\\nu'$. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mathematical Framework"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's start with the most general equation. In essence, what we are interested in is\n",
"\n",
"$$ \\frac{dN}{dS} = \\sum_X \\int_0^{z_{\\rm EoR}} \\frac{dn_X}{dm}(m_S,z)\\frac{dm}{dS} dV_c(z).$$\n",
"\n",
"That is, the total differential number counts will be the sum of different categories of sources (here we only consider AGN and SF), given by the integral over all comoving volume elements multiplied by the number density of sources in each element. This integral in effect is isotropic, so that the angular part drops out as the solid angle, with the differential comoving volume element $dV_c$ a function of $z$ only (the solid angle is in the units for $dN/dS$).\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cosmology"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In all calculations for this work we assume the cosmology of Planck 2013. Any uncertainty in this assumption will be dwarfed by other uncertainties in the analysis. Two quantities are of immediate interest. Firstly, the value of the comoving volume element as a function of redshift, appearing in our general equation. And secondly, the value of the luminosity distance, which will appear in our equation for $m_S$ later. These are shown graphically below."
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {
"collapsed": false,
"hide_input": false
},
"outputs": [
{
"data": {
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mZscmcf6mwHPRy42BJ8zsNkkNgWHALsAc4GwzWxa956/AxcAa4CozGx21twQG\nAPWAEWbWPWqvS1jMcTBh8UaHaEFFYhzeQ+fywtKlcNppsPvu8OijsEnZgmgFrqb3O0/oUrB6NTRo\nEHYG2Lyg1vW6dDIL+xL+5S9w4omheGajRlW/rxClOuQq6S5C0vWmma1NX2S5wxM6lw/mz4e2bcOj\nTx+fh14eH3LNok8/DcNmnsy5VEhhy7Dp08Nww377hVVeq1fHHVmtVI9QZmmxpAGS2knyXSGdy6Lp\n08Ne2J06hWLsnsylh/9nTIHXn3PptNVW4eY2fnwoqnnQQWFOiUsfM+sKNAFOARYCtwBLoqLCF0er\nU51zGVK6+8M//hH2v3bp4wldCjyhc5nQvDmMHh22u+nSBdq1g1mz4o6q9rBgkpn91cz2BQ4AxgMX\nAQskvSHpGkmNKz+Tc64mXnop7P7Qv7/v/pAJVSZ0kupIulBSF0lbRG2nSHop2voro9MYJbWN9jmc\nKem6cn7eINqu5wNJH0vqlMl4EvkKV5cpUkjkPvkkLLhp3RquvTYsnnDpZWazzOwOMzuaULj3UeAo\n4Nx4I3Ou9hgwAC65JCR1vvtDZlS5KELS3YQdIDYirNzqBtwPfEjYNudDM+uWkeCkOsCnwPGEaumT\ngXPMbHrCMX8lbJPTU9J20fGNzGxNmXOlfaLwDjvA5MmFWQDRZdeiRfC3v4WbYa9eoWbTxsns85Ln\n0lWHrjbzRREul5iFRQ/9+sGoUbDPPnFHlD8ysSjiSzM7yMwOIMw76QIcaGbnmtmRwLdJxlodhwGz\nzGyOma0GhhD2P0y0Dtgqer4VYePqjFf1WrIEfvoJmjTJ9JWcC18eHn443BCfeioM9Y8YEW6WruYk\n3SqpSzntXSXdHEdMztU269bB1VfD44+H3R88mcus6iR08yXtDhDVO3qiTML0ZSYCi6zft7A0Fjbs\naVjqPqCFpIWEXsOrMhjPetOmhX3m5H0FLosOOgheeSWUNvnzn8P2Ye+9F3dUeakjUN5/uffYULjX\nOZekVavgvPPC/WnCBGjsM1IzrjqDNiuAzyS1NLMPzax0z9bpwBhgeqXvTk11+h/aAu+Z2bGS9iDs\nn3igmX1f9sB07m/4ySdh43Xnsk0KxThPPjn02p16Khx3XFg1tttucUeXXqnubViJ7YFvymlfAngV\nQOdS8N13cOaZYeX+6NFQzwsDZUW1CgtLamBmy8u0nQysNbMxGQtOak3Yt7Bt9LonsM7Meicc8xJw\nm5m9Gb377qibAAAgAElEQVR+BbjOzKaUOVda55V07x5+ef7pT2k7pXNJ+f77sCfsvffCBRfA9dfD\ndtvFHVVmpHEv15nALWY2oEx7J+AGM9sj1WvExefQuTgtXhy+bB52WNj9pk6duCPKXxkpLFw2mYva\nRiYmc5JaSNo04fV+pUO1KZgCNJO0W3Tu9oS9DBP9l7BoAkmNgL2B2Slet0reQ+dyxZZbQnFxmAaw\nenWYp3LzzSHRcxX6D3CXpMsk7RE9ugD/Ah6MOTbn8tLMmXDEEWGFfr9+nsxlW1rq0Em6GvgYuDqh\n+XPgTEk13hOxVDRX7w/AaGAaMNTMpkclVEonNN8MHCFpKjAOuNbMliZ7zeoqnUPnXK5o1Ajuuw/e\neQdmzIBmzcKOEytXxh1Z7jGzOwlJXV9gZvS4m5DM9YkxNOfy0pQp0KYN9OgBf/+7zy+PQ1r2cpV0\nE+GGON7M5pb52c1mdkPKF0lROochli4Nw63Ll/tfWpe7pk4Nw68ffgg33BC22cn3za/TXbZE0ubA\nIdHL981sRbrOHRcfcnXZNnp0KBT80ENwRtk6FC5pce3lupGZDSqbzEU2Lactr/kKV5cPDjgAXnwR\nhg6FIUPCDhQDB8LaWrklfc0ouBqYAbwePaZL+pMk30HHuWp6/PEwd/e55zyZi1u6blxNJf3PillJ\nWwK1bqbZtGk+f87lj8MPD6VOHn44fIPed1948smCT+x6A70Iw64nRI//ADdEP3POVcIs7D19/fXw\n6qtw5JFxR+TSNeTaCfgj8ADwGbASOIhQE66PmT2c8kVSlM5hiKuugl12CXXAnMsnZjBuXNhtYtmy\nMBR79tn5M3k5jatclwJdzOypMu1nAQ+aWcNUrxEXH3J1mbZuHVxzDYwZE4qde4H9zIhlyDVa+v8E\nYYXYWGBC9PzxXEjm0s0XRLh8JcEJJ4Sq7XfdFUqd7LcfPPEErMn4/io558Ny2j4CfDKFcxVYtQrO\nPTdsezlhgidzuSQtPXTrTyY1JGxqvRHwtpktTtvJU5TOb6077QQTJ4ZeOufymVkYjr3pJvjyS+jZ\nM0xuztXFE2nsobsHwMyuKtN+N1DHzK5M9Rpx8R46lynLl8NvfwvbbBO+BG62WdwR1W41vd+lO6Hb\nlpDQrQXeNLNM7vNaI+m6yX37bUjkvvvOF0W42uX110P9upkz4dpr4eKLc6/CexoTun7AecBCYCKh\nV64VsBPwOLAmajMz657q9bLJEzqXCQsXhoLBRx0FffvmzzSNfBbXKlck/Z1wc3yOUPx3vqSs7Kua\nTb7C1dVWbdqE+XXDhoW5MbvvHvaMXf4/ZcVrheaEfVsXAbsCu0TP34t+tn/Cw7mCNmNGWPTQvn2o\ndenJXG6qzl6uVZLUDbgEKAbeJpQqOQLoKWlh2YnH+Wz69FD+wbnaqlUreOEF+Ogj6N0b9tgDLr00\nLAbaYYe4o0sPMyvKxHkl1SHscDPfzE6LpqEMJSSNc4CzzWxZdGxP4GLCiEb30p13JLUEBgCbASNK\nh4Ul1QUGEurmLQHaV1Aqyrm0efvtMMx6++2hlqXLXenqofsNcICZ3WZmJWY2xsyKgUOBDmm6Rk74\n9FPYe++4o3Au8/bfP9SYmjw5bCPWogV06QKffRZ3ZDntKsKuNqVjnj2AsWa2F/BK9BpJLQhbGbYA\n2gL/ltb3+/cDOptZM8LWh22j9s7Akqj9Lry8isuw4cNDbbn+/T2ZywfpSug+KP3WmcjM5gHvpuka\nOcETOldomjYNwyyffhp66I46Knxjf/PNsKgin0h6UdLw6M+KHmX3i67uuZsApwAPs2Gl7OnAY9Hz\nx4B20fMzgMFmttrM5gCzgFaSdgS2NLNJ0XEDE96TeK5ngOOSidO56njwQejaFV5+Ocydc7kvXQld\nZSVK16+Xk3ROmq4Xm88+84TOFabtt4cbb4Q5c+D44+HCC8NG3E8/nVclT04FDiAMWX4T/VneIxl3\nAX8B1iW0NUpY7b8YaBQ93wmYn3DcfKBxOe0LonaiP+fB+n2ul0dDus6ljVnYi7VPHxg/Hg49NO6I\nXHWlZQ4d8LGkK4EXEtoEnAt8JWkXQvL4R2Bwmq6ZdatXh19me+4ZdyTOxad+fbjiivDtffhwuPPO\nUGS0e3fo3BkaNIg7wkr9E7gAOAZ4FBhgZvMrf0vVJP0G+MrM3pdUVN4xZmaSstKnWVxcvP55UVER\nRUXlhuTcL6xeHf5dT50Kb70F//d/cUdUWEpKSigpKUn6/enaKWIFUL8ah5qZxbI+Jh1L+T/7DNq2\nhdmz0xSUc7XEpEmhUHHpJt1XXpmZLz7pKFsSbVN4KmFBwknAa4Tk7nkzW53kOW8FOhLKnWwGbAU8\nS5hHXGRmi6Lh1NfMbB9JPQDM7Pbo/aMIW5HNjY5pHrWfAxxjZpdHxxSb2cToM3xpZtuXE4uXLXE1\ntmJF2DUGwkr3LbaINx4XX9mS2YQ9W3ev5LEHeT6fzufPOVe+ww6DwYPDN/v69cP+sb/5TSh/sm5d\n1e/PJjNbY2YvmNkZwG5ACXAzsFBSUr/GzOyvZrazmTUlLAR71cw6Eko4XRgddiHwfPR8ONBB0qaS\nmgLNgElmtgj4TlKraJFERzaMfCSe6yzCIgvnUvbVV3DssaFo/vDhnszlq3QldLea2XQzm1PJ4wvg\nzjRdLxY+f865yjVpArfdBv/9b1g48Ze/hNWx994binHnoM2BBsCWwPdpPG9pF9ntwAmSPgN+Hb3G\nzKYBwwgrYkcC3RK61boRFlbMBGaZ2aio/RFgW0kzCdNXeqQxXlegZs4MX8BOOQUeegg2TtdELJd1\nSQ25SrrDzK5J97GZlI5hiMsug4MPhssvT1NQztVyZvDGGyGhGzcOOnSAbt3C/rHJSNOQa33gbMKQ\n668IxdAfNbNa0ePlQ66uut55B9q1CzvEXHJJ3NG4srI15NqmBsceneQ1cs6nn8Jee8UdhXP5Q4Kj\njw5zcj7+GBo1gpNOgmOOCUO0q1ZlOx49TNgR4kpgCLCTmZ1XW5I556pr+PAwLeKhhzyZqy2S7aFb\nRxhSqE7mGNtCiETp+Na6ww4wZUoYVnLOJWf16vDLpF+/sBtFp06h93uPPap+b6o9dNG9ax4wNWpK\nvCmUntfM7PRkrxE376FzVXngASguDjvCHHZY3NG4itT0fpdsQjebsL3NYipP6gRcYGZb1vgiaZbq\nTW75cmjcOFTM931cnUuPmTNDAdPHHoMDDwxbjLVrB5tuWv7xaUjoBlB+EpfIzOyiZK8RN0/oXEXM\n4IYbYMgQGDXKS3DlumwldJsStvtqRFjhOqaiO4ikZ83szBpfJM1SvclNnhy2PXrvvTQG5ZwDwtDr\nc8+F5O7jj+GCC8Iw0D77/PK4dMyhq+08oXPl+fnn8IVpxgx46aVQKNzltqzMoTOzn83sWTPrB3wG\ndJHUNSogXFbfZK6Ra3z+nHOZU7duWDDx6qthS7GNN4aiorDNWP/+oUaWcy45330X5st9+y289pon\nc7VVymVLzOwLM/sPYZn9gZK6SzpT0ibRz0tSvUYu8Bp0zmVHs2Zw++0wb14oe/Lcc7DzznDxxamd\nV9JhUUHe6h7fMhqNcC5vLVgQFiHtuSc8+2yoE+lqp3TVoSst1vmimfUFJgF/lHS7pFqRBnkNOuey\na5NN4IwzwgKK6dOhefOUTzkRqMnepyWAL4FyeeuTT8J+yx06wP33e4252i4tW3/94oRSS+BS4Byg\nLvCEmXVO4XxtgbuBOsDDZta7nGOKCBtjbwJ8Y2ZF5RyT0rySgw8Oy7t/9aukT+GcS1Eqc+iiFa6P\nAj9W53DgMqC5meXVZn8+h84BlJRA+/Zhr+Xzz487GpeMrCyKKOeiWwHnERK5g4DphKrmj5nZkhTO\nWwf4FDgeWABMBs4xs+kJx2wNvAmcZGbzJW1nZt+Uc66kb3JmsNVWYQho662TOoVzLg1STOhK+OUK\n10oPj449z8wWJnO9uHhC5wYPhquuCqtZf/3ruKNxyarp/S6lDlhJRxCSuN9HTU8BfzCzt1I5b4LD\nCFvfzImuNwQ4g5AwljoXeMbM5gOUl8ylavFi2GwzT+acy2fl9dw7V5uYQZ8+YXj1lVdg//3jjshl\nU1Jz6CRdIelj4A1gf+DPwI5mdlHZZC6q+5SsxoQioKXmR22JmgENJb0maYqkjilcr1yzZoWJ2s45\n51wuWrMGrrgCnnwS3n7bk7lClGwP3d3AaOBvwPtR2zaSyk44bgicnOQ1oHrDI5sAhwDHAfWBtyVN\nNLOZZQ8sLi5e/7yoqIiioqJqBTFrlhdgdC4OJSUllJSUxB2Gcznthx/gnHPgp59gwoQwRcgVnmQT\nuh+Ad4EDo0dFtgO2TfIaEObN7ZzwemdCL12ieYSFED8BP0kaH8VUaUJXEzNnekLnXBzKfvG68cYb\n4wvGuRy0eHGoMbfffqEw9yabxB2Ri0uyCd0rZtarOgdKSqUc7xSgmaTdgIVAe8Lq2UQvAPdFCyjq\nAq2Af6Vwzf8xa1Yon+Ccc87lihkz4JRTws4qvXr5tpSFLtmE7o4aHFuc5DUwszWS/kAY3q0DPGJm\n0yV1iX7+gJnNkDSKsNn2OuAhM5uW7DXL40Ouzjnncsn48fD730Pv3tCpU9zRuFyQ9jp0uSrZpfxm\nYXXrF19Aw5qUJHXOpZ3v5Vo1L1tS+w0ZAt27wxNPwAknxB2Ny5SM7uUq6QhJ2yURVJ3ovXk3VfOb\nb0J1bU/mnHPOxcks9Mhde20oS+LJnEtU07IlbwAnJnGdbaL35t0+C74gwrnCI6mhpB3jjsO5UmvW\nwOWXh6LBXpbElSeZOXTbSdqlhu/J2/4tnz/nXGGQtJmZrQQws6WSjpV0o5ldFndsrrB9/33Yxsss\nlCXZcsu4I3K5KJnCwncDc2r4eC/ZAOPmCZ1zBeO0xBdm9hrweXXfLGkzSe9I+kDSx5KKo/aGksZK\n+kzSmGi7wtL39JQ0U9IMSScmtLeU9FH0s3sS2utKGhq1T5S0ayof2OW+hQuhTRto0gSGD/dkzlWs\npj10N6VwLQO+SOH9sZg1C05OpTSycy5f3CZpf2AUMNHM1hH2kq4WM1sp6Vgz+1HSxsAbkkYCvwPG\nmlkfSdcBPYAekloQSjG1IOyAM05Ss2hFQz+gs5lNkjRCUlszGwV0BpaYWTNJ7YHeQIf0/SdwueSj\nj0KNua5doUcPL0viKlejhM7MijMUR86aOTOsJnLO1Xp3AsuArsAjkj4BlgPPV/cEZvZj9HRTwi42\nBpwOtInaHwNKCEndGcBgM1sNzJE0C2glaS6wpZlNit4zEGhHSDRPB0prgD4D3Ffzj+nywdixcN55\n0LcvdPCU3VVDsnXoCoKZL4pwrlCYWb/o6WBJAg4Crq7JOSRtRJhisgdwX9TD1sjMFkeHLAYaRc93\nAiYmvL10r+rV/HJHnAVs2MN6/f7WUZ3O5ZIamtnSmsTpctvDD8Pf/gbPPANHHx13NC5feEJXiaXR\nLXLbVDYvc87lpGj+2f8Bn5dNiKJhz/cl9a7JOaNh2oMkNQCek7Rf2fNKyniRuGT3rXbxWrcuJHJP\nPRUKB++Vyj5LLu+kune1J3SVmDUL9tjD5y04V5tEixKGAqVVvNZKehn4i5n9Yg9oM/skmWuY2XJJ\nrwEnAYsl7WBmi6JSKF9Fh5Xdq7oJoWduQfS8bHvpe3YBFkbz9BqU1zuX7L7VLj4rV4YdH/77X3jr\nLdh++7gjctmW6t7VyaxyLRi+wtW5WukuYDihnNKOQFtgKTBeUlGyJ5W0XekKVkn1CAnj9OhaF0aH\nXciGOXnDgQ6SNpXUFGgGTDKzRcB3klpFQ78dCXtWU+ZcZwGvJBuvyx3ffAPHHx+m+bz6qidzLjne\nQ1eJ2bNDD51zrlYxM7s/4fVi4JVoCPZxSWeb2ZdJnHdH4DFJdQhfloea2QhJE4FhkjoTyjidHQUx\nTdIwYBqwBuiWsGdXN2AAUA8YEa1wBXgEGCRpJrAEX+Ga9z77DE49Fc46C265BTbybhaXJN/LtRKd\nOoUJqZ07ZyYm51zNpGMvV0m9zKzcsYyolMhlZvbHVK4RJ9/LNX+MHw9nnx0SOf8948rK6F6uhebz\nz2H33eOOwjmXZmsq+oGZTSOsMnUuox5/PPTKDRrkyZxLDx9yrcTnn/uQq3O10GGS9jCzinaB+C6r\n0biCYgY33giPPQavvQb77ht3RK62yGgPnaR1kuZJurDqo3PLjz+GsiWNG1d9rHMur/wamCFpjqSH\nJHWQlDgNfV1cgbnabdUq6NgRRo6EiRM9mXPplekh1/8SJvX2l5RX+7l+8QXsthvUqRN3JM65NLsT\n2Ba4ClgFFAOLoj1Y7wQOiTE2V0uVrmRduTL0zDVqVPV7nKuJjCZ0ZrabmW1HqLj+ZCavlW4+3Opc\nrfVPM/vOzF4wsz+Y2T7ArsA9wA7AifGG52qbTz+Fww+HI4+EYcOgfv24I3K1UVbm0JnZVGBqNq6V\nLp7QOVc7mdkP5bTNB/oTRhP+kf2oXG1VUgLt28Ott/riB5dZvsq1ArNn+wpX5wrU0LgDcLVD//4h\nmRs82JM5l3m+yrUCn38OJ/rAi3MFx8w+ijsGl9/WrYPrrw97sr7+OuyzT9wRuUKQ8YRO0s5AczMb\nE73ez8w+zvR1U+VDrs4552rqxx/hggtg8eKwknW77eKOyBWKbAy5ngd0lVS62bRJOiUL103a2rUw\ndy40bRp3JM455/LFl19CmzZh0cO4cZ7MuexKKqGTVFyDwxeb2ZnRpGPM7BMgp7ceXrAg/EOsVy/u\nSJxzzuWDDz6A1q2hXbtQNLhu3bgjcoUm2R66TpI2qeaxu0o6NsnrIKmtpBmSZkq6rpLjDpW0RtKZ\nyV6rlG/55ZxzrrqGD4cTToA77ghz55TSbsPOJSfZOXS7AMMkXWBm31dx7O3AYEl9gBLgJ2Cz6lxE\nUh3gPuB4YAEwWdJwM5teznG9gVFAyv+UfP6cc865qpjBnXfCXXfBiBFw6KFxR+QKWbIJ3SvAH4De\nkl40s5EVHWhmK4HfSjoKOBxYBDxRzescBswyszkAkoYAZwDTyxx3JfA0kJZ/Tp7QOeecq8zPP8Pl\nl8N774XFDzvvHHdErtAlO+R6ipktMLNuwHaS7pa0dWVvMLM3zOyfZjbIzKq7V2JjYF7C6/lR23qS\nGhOSvH6ll6rmuSs0e7YndM4558q3ZEkoa7VkCUyY4Mmcyw1J9dCZ2eqE54MkjQNulzTCzIanLbrq\nJWd3Az3MzCSJSoZci4uL1z8vKiqiqKio3OO8h8653FBSUkJJSUncYTi33vTpcNpp8LvfwW23wUZe\nnt/lCJml3KG14WTS+UBr4O9mtjQN52sNFJtZ2+h1T2CdmfVOOGY2G5K47YAfgUvLJpaSrLqfdZtt\nYOZMX3LuXK6RhJn5lPNK1ORe52pmzBg4/3zo0wc6dYo7Glfb1fR+l9aELgpgR+BGYLSZPZPiuTYG\nPgWOAxYCk4Bzyi6KSDi+P/CimT1bzs+qdZNbujTUn1u2zFcqOZdrPKGrmid06WcG994beuSGDYOj\nj447IlcIanq/S7YOXWWbVy8CbgVOlTRMUtI158xsDWHxxWhgGjDUzKZL6iKpS7LnrUzpcKsnc845\n51avDosfHnoI3nrLkzmXu5Jd5XqapKeBPYCmwO7RY09CSZPE87aO2pISraAdWabtgQqOvSjZ65Ty\nBRHOuWRE2xwOBP6PMP/3QTPrK6khMBTYFZgDnG1my6L39AQuBtYC3RO2SGwJDCCUeBphZldF7XWj\naxwCLAHam9ncbH3GQrNkCZx1FmyxBbz5Jmy1VdwROVexZBO6/YH3El6vJaxA/YJQa252wmNWCvFl\nnRcVds4laTVwtZl9IGkL4F1JY4GLgLFm1icqjt4D6CGpBdAeaEFYvT9OUrNovLQf0NnMJkkaIamt\nmY0COgNLzKyZpPaE+psdsv9Ra7/SxQ9nnhmGWuvUiTsi5yqXbEL3JWGe3BxC0jY3ceVrPvv8c2jV\nKu4onHP5xswWEaacYGYrJE0nJGqnA22iwx4jfOntQSi3NDi6d86RNAtoJWkusKWZTYreMxBoRyic\nfjrQK2p/hlB43aXZiBFh0YMvfnD5JNmEboSZPZjWSHLE55/DuefGHYVzLp9J2g04GHgHaGRmi6Mf\nLQYaRc93AiYmvK20zubq6HmpBWyov7m+NqeZrZG0XFLDdFQVcGHxw7/+FXZ/eP55OOKIuCNyrvpq\nnNBFpUSuyEAsOcFr0DnnUhENtz4DXGVm3ythhVVULzPjS1CrW3PTbbByJXTtCh9+GHZ+2CXpmd/O\nJSfVups1LlsiaTmwCaGEyOvAeOAtM/upzHHXAVsAj5rZF0lHmCbVWcq/ciU0aAA//AAbJ9t36ZzL\nmFwvWyJpE+AlYKSZ3R21zQCKzGxRVNbpNTPbR1IPADO7PTpuFGE4dW50TPOo/RzgGDO7PDqm2Mwm\nRmWdvjSz7cvE4GVLamjRojBXrnFjGDA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USmBlRMxOpyeQhF5R9AWWRcQ7EbEVmEjy/1JE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\nZI58AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87e530b0d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def dVc(z):\n",
" return Planck13.differential_comoving_volume(z)*Planck13.h**3\n",
"\n",
"def Dl(z):\n",
" return Planck13.luminosity_distance(z)*Planck13.h\n",
"\n",
"Z = linspace(0,10,100)\n",
"fig,ax = subplots(1,2,figsize=(10,4),gridspec_kw={\"wspace\":0.3})\n",
"ax[0].plot(Z,dVc(Z))\n",
"ax[0].set_xlabel(\"Redshift\",fontsize=14)\n",
"ax[0].set_ylabel(r\"$dV_c$, [${\\rm Mpc}^3 h^{-3}$]\",fontsize=18)\n",
"ax[1].plot(Z,Dl(Z))\n",
"ax[1].set_xlabel(\"Redshift\",fontsize=14)\n",
"ax[1].set_ylabel(r\"$D_L$ [Mpc/h]\",fontsize=14)\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Number density"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most interesting part of the equation is the calculation of $n_X(m_S,z)$, which we have loosely described above. It is composed of two factors. The second is a category-specific parameterisation which gives the average number of sources per halo, $N_X(m,z)$ (we'll describe that more thoroughly when we look at each category). The first is the Halo Mass Function (HMF), which is well-defined by simulations and theory.\n",
"\n",
"The HMF can be conveniently specified (within less than ~10% up to $z=10$) by the MRP form:\n",
"\n",
"$$ \\frac{dn}{dm}(z) = A \\beta \\left(\\frac{m}{\\mathcal{H_\\star}}\\right)^\\alpha \\exp\\left(-\\left(\\frac{m}{\\mathcal{H}_\\star}\\right)^\\beta\\right), $$\n",
"\n",
"where each parameter $(\\mathcal{H}_\\star,\\alpha,\\beta,A)$ is a function of $z$. This is convenient because it is much more efficient than the usual EPS calculation. We plot the MRP at several redshifts in the figure below."
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {
"collapsed": false,
"hide_input": true
},
"outputs": [
{
"data": {
"image/png": 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rFRWlznNd66iSGsDj46/FPlLpP+rr69m+fTvvvvsu8fHx3Hjjjdxxxx0sWrTo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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87e4f35fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = logspace(10,15,500)\n",
"for z in range(0,7):\n",
" _ =plot(m,mrp_b13(m,z=z),label=\"z=%s\"%z)\n",
"_ = xscale('log')\n",
"_ = yscale('log')\n",
"_ = ylabel(r\"$\\frac{dn}{dm}$\",fontsize=20)\n",
"_ = xlabel(r\"Mass $m$, [$h^{-1}M_\\odot$]\",fontsize=20)\n",
"_ =legend(loc=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Calculation of $m_S$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The last step is to calculate the appropriate halo mass for the desired flux density $S'$ at each redshift, for use in the general equation. Recall that the assumption is that each halo mass has a characteristic luminosity associated with it, given the type of source:\n",
"\n",
"$$ L_\\nu = f_L^X(m,z).$$\n",
"\n",
"Accounting for the $k$-correction between observed and emitted frequencies, the observed flux density of an object with luminosity $L_\\nu$ is\n",
"\n",
"$$ S_\\nu = (1+z)\\frac{L_{(1+z)\\nu}}{4\\pi D_L^2},$$\n",
"\n",
"where the shift in emitted frequency is $(1+z)\\nu$ and $D_L$ is the luminosity distance to $z$. \n",
"\n",
"Assuming that the mean spectrum of any source is\n",
"\n",
"$$S(\\nu) \\propto\\left(\\frac{\\nu}{\\nu_0}\\right)^{-\\xi},$$\n",
"\n",
"we know that the luminosity will follow the same dependence on frequency, and so we find that\n",
"\n",
"$$ L((1+z)\\nu) = (1+z)^{-\\xi} L_\\nu.$$\n",
"\n",
"Thus, we find that\n",
"\n",
"$$ S_\\nu = \\frac{L_\\nu(1+z)^{1-\\xi}}{4\\pi D_L^2}.$$\n",
"\n",
"Finally then, we have\n",
"\n",
"$$ m_S = f_{L,X}^{-1} \\left(\\frac{4\\pi D_L^2 S_\\nu}{(1+z)^{1-\\xi}}\\right).$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### General Definitions"
]
},
{
"cell_type": "code",
"execution_count": 208,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"## Some definitions of general functions\n",
"def nx(m,z,Nx,*args,**kwargs):\n",
" f = Nx(m,z,*args,**kwargs)\n",
" dndm= mrp_b13(m,z=z)\n",
" return dndm*f\n",
"\n",
"def L_of_S(S,z,xi):\n",
" return 4*np.pi*Dl(z)**2*S/(1+z)**(1-xi)\n",
"\n",
"def ms(S,z,xi,ml_rel,inv=True,**kwargs):\n",
" L = L_of_S(S,z,xi)\n",
" if inv:\n",
" return ml_rel(L,z,**kwargs)\n",
" else:\n",
" m = logspace(0,18,600)\n",
" l = ml_rel(m,z,**kwargs)\n",
" s = spline(l,log10(m))\n",
" return 10**s(L)\n",
" \n",
"def dnds(S,zmax,xi,ml_rel,ml_kwargs,Nx,Nx_kwargs,dmds,zmin=0,ml_inv=True):\n",
" \"\"\"\n",
" Return the differential source counts as a function of flux density (units: Jy^{-1}Sr^{-1})\n",
" \"\"\"\n",
" S_mpc = S*9.95e18 #convert to W/Mpc^2/Hz from Jy\n",
" z = linspace(zmin,zmax,400)\n",
" nz = np.zeros((len(z),len(S)))\n",
" for i,Z in enumerate(z):\n",
" if Z==0:\n",
" continue\n",
" else:\n",
" mdash = ms(S_mpc,Z,xi,ml_rel,ml_inv,**ml_kwargs).value\n",
" DMDS = dmds(mdash,S,Z,**ml_kwargs)\n",
" nz[i,:] = nx(mdash,Z,Nx,**Nx_kwargs)*DMDS\n",
" return simps(nz.T*dVc(z),z,axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## AGN"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For each source type, we really have to consider two things: \n",
"\n",
"1. A parameterisation of the average number of sources per halo of a given mass (call it the HOD), $N_X(m,z)$\n",
"2. A parameterisation of the conversion from mass to luminosity, $f_L^X(m,z)$.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### HOD"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For AGN, we should only really expect the central galaxy to host an AGN, or at least that this will dominate the signal. Thus we know that $N_X \\leq 1$. We probably also expect that it will be a non-decreasing function of mass, and for now, we won't worry about redshift evolution. Let's consider three parameterisations:\n",
"\n",
"1. Mass-independent\n",
"2. Power-law\n",
"3. Lognormal-distributed switch mass."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1. Mass-independent"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the mass-independent case, our parameterisation will just be\n",
"\n",
"$$ N_x(m,z) = F \\leq 1. $$\n",
"\n",
"Physically, this would be saying that AGN formation doesn't depend on the halo mass, but that the luminosity of the AGN would. Thus very small halos may host AGN, but they would be inconsequentially faint. I don't think this is very reasonable, but we'l include it as an extreme example. We needn't plot what this looks like, since it only changes the normalisation of the HMF from above."
]
},
{
"cell_type": "code",
"execution_count": 192,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Define the mass-independent case\n",
"def Nx_mass_independent(m,z,F=1):\n",
" return np.ones_like(m)*F"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2. Power-law"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another option is a power law, with some truncation mass, $m_{\\rm min}$ and potentially some saturation mass, $m_{\\rm sat}$. Thus we have\n",
"\n",
"$$ N_X(m,z) = \\begin{cases} 0 & m < m_{\\rm min} \\\\\n",
" (m/m_{\\rm min})^\\gamma-1 & m_{\\rm min} < m < m_{\\rm sat} \\\\\n",
" F & m \\geq m_{\\rm sat}\n",
" \\end {cases},\n",
"$$\n",
"\n",
"where \n",
"\n",
"$$ m_{\\rm sat} = m_{\\rm min}(F+1)^{1/\\gamma}$$\n",
"\n",
"and $F\\leq1$ is the saturated efficiency.\n",
"\n",
"Illustrating this with $m_{\\rm min} = 10^{11} M_\\odot h^{-1}$, $\\gamma = 0.1$ and $F=1$, we show below:"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {
"collapsed": false,
"hide_input": false
},
"outputs": [
{
"data": {
"image/png": 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otWAXgn0NDayurWV1bS27GxoY7e/fKqcUn47n6zsjxcXHxbRhg7zMvGVIb+JE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"text/plain": [
"<matplotlib.figure.Figure at 0x7f87dfd41210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def Nx_powerlaw(m,z,log_mmin,gamma,F):\n",
" m_sat = 10**log_mmin *(F+1)**(1/gamma)\n",
" return np.clip((m/10**log_mmin)**gamma -1,0,F)\n",
"\n",
"for z in range(0,7):\n",
" _ = plot(m,nx(m,z,Nx_powerlaw,11,0.1,1),label=\"z=%s\"%z)\n",
"_ = xscale('log')\n",
"_ = yscale('log')\n",
"_ = ylabel(r\"$n_X(m,z)$\",fontsize=20)\n",
"_ = xlabel(r\"$m$, [$h^{-1}M_\\odot$]\",fontsize=20)\n",
"_ =legend(loc=0)\n",
"_ = xlim((1e11,1e15))\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 3. Lognormal"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a standard HOD prescription for central galaxy populations, but we'll add an extra parameter. We define it as\n",
"\n",
"$$ N_X(m,z) = F\\left(1 + {\\rm erf} \\left(\\frac{\\log m - \\log m_{\\rm min}}{\\sigma_{\\log m}}\\right)\\right). $$\n",
"\n",
"$F$ again is the saturation fraction, $m_{\\rm min}$ is *approximately* the minimum allowed host halo mass, and $\\sigma_{\\log m}$ is the width of the transition from a fraction of 0 to $F$ (it is the width of the lognormal distribution which is integrated to give this distribution). A very small $\\sigma_{\\log m}$ gives a step-like function. \n",
"\n",
"We show the impact of this below:"
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {
"collapsed": false,
"hide_input": false
},
"outputs": [
{
"data": {
"image/png": 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UMMYdNkxnjEfx2JJc+uMmSh45wqzGtTh+LMXtkCKGL8moPdAHWCoii0XkeRG5\nUkSKOBSbCZD0w3S2UKqJdCXPK0XdpRuJPZjEjEtrk3rCypgHgi/J6BHgVeAx4FfgdmA2kOQt13CP\nA/GZALBhOmPOVOaCMlRf/Avn79/DlCaXknrSrjr4my+fQN97S42nEZHqQBvvV1fgbR+On28i0hno\niGd23zggGeiN5/utpaot3IgrWGUcprOFUo2BCy4qR8q8NRRtWZOJrVvTb+FC+93wI196Rme9Laq6\nSVXfUdVeqnq1D8f2iap+oap3A/2Bm1V1kaoOAGYAE9yKK1idSD1hPSNjMlGpeiWKzV5B8/XLGNPB\nVvv2J1+S0cci8qBjkWTCwXpGp/QC3vdHrKFKVa3SqzHZqFqvJkc/W8TV389mTI8+bocTtnya2g3c\nKCJTRKS5iPjjT2tH6hl5X3cRcEBVD/shzpCVqqlESRRRYkvpG5OVeq0b89uEWXT48gMSBj7sdjhh\nyZdPoIlAYTx1gxbhmbgwS0QeF5EmIr5/uqnqQmB/hs1p9YxU9Thwqp5Rgqo+qKq/A/d64+qWbiLF\n7cC7vsYUbmzygjG50+KGdqz67/tcPWEknw59xe1wwo4vn0KrVfU+8awfXhe4wvv1BDAc+Bmo73uI\nZ8lXPSNVHZrTgSOxnpHdY2RM7nW862Y+/HMPbV94kFkXVqT93Te7HVLABWM9o29FZCSwEPhKVVcD\n//MOozUALnAiwExYPSMH2VJAxuRNj6fuZ8Jvv3LVw71YUuFCmnVo6XZIARV09YxU9QvgceAfPOW8\nT20/qarLVXW6A/FlxuoZOciG6YzJu36jX2XOlTdQum87Nq3Z5HY4YcGn6zqqmqKq36jqnpz3dozV\nM3KQDdMZkz/9PvuYFdUv5a/2l/L3n3+5HU7IyzYZeQvo3eZEQ94Zbg/k8TVWz8jPbJjOmPzrsWAR\nfxY/lx9a1OVEynG3wwlp2SYj7wf/IREZJSKF89uIiJQGPgY25OV1Vs/I/2yYzpj8i46Jps3i1RQ7\nephPLm/mdjghLcdhOlWdCnwBLBCR+7yJJVe89/y8BCwAXlbVWfkP1fhDxmE6WyjVmLwpWaYE5Wet\npO7WNUzo2tvtcEJWrv4kVtW5InIV8CSwRUQS8QyfrQGSvF9RQCyeCq+1gFZAOeANoKndbBqcbJjO\nGN/FX1KF78d/RfteV/P+k3Xo9cITbocUcnI9PqOqB4DHReTfeBYhvQq4G4gDSuKZcp0EJOK5CfYB\nYKGqHnOUk95BAAAgAElEQVQ4ZuOgzIbpbDFIY/Ku+fXt+OKZ/3Hlc/fzTZ1aXNnzerdDCil5vljg\n7eFM8X6ZEGez6YxxTufH7mXS2jU0/1dXNl2yhup1L3Y7pJBhC5JFOBumM8ZZt0x6hx9qNmZvhyYc\n/ueQ2+GEjLBLRiLSWUTeEZEPReQqEaklIh+JyGgR6ep2fMHGZtMZ47yb5y/gn0JF+PryRjYrKJfC\nLhllrGWEZ3Xv11T1X8AtrgYXhGyYzhjnxRQsQN1vVlJ193Ym3NjD7XBCQtAmIwdrGSUAPURkBJ6Z\nfiYdG6Yzxj/KV76Qg+9+ybWzp/Lx86+5HU7QC9pkhEO1jFR1r6oOAgYD+wL9TQQ7G6Yzxn9adGrH\n/Ieep8WLD7Bszg9uhxPUHE1GIjLYqWM5VctIRCqJyNt46i+NcCq+cGElx43xr5v/8ySzW7Ynqm87\n/vrzb7fDCVpOfwp1wlPLKFMicp6q7vXh+PmqZQTcQy5EYj2jVE0lWqLdDsOYsNZ3xnRm1qxMYrvL\n6LZ6ExIVzINS2QvGekaZqSYi/VX1rSyefxR4zIfj+3VaSiTWMzLG+F9UdBSXffsjfza4iAk39+a2\nqR+4HVK+BV09oyxcB6wSkTNmrYlIRRF5mVz2ULJhtYyMMSHpvIpl2ff2NDp+9RFf/W+c2+EEHUeT\nkaouVdUfgE3eSQWXestAbMVTktzXxGG1jPzMbokwxn9ad72aL+98gtrP3MOWn60oX3pOT2DoKp4+\nW0XgKWAZUAy4WlUb4Rmmy+2xrJaRMSbs3DbqBeZf0oAd11/O8ZQTbocTNJwepnsV2IZnWvZcoCsw\nVVXnA6jqV7k9kNUyco8tlGqMf3Wf8x3npBxlwrUd3A4laDidjIoDbwMVVfVfqvo5sFpEbnW4HWOM\nCVlFihWl+JS5dPrhWz78z0i3wwkKTiejMar6oqqm3R+kqquBn0TkThEZ5HB7xhgTki65vBEL73ue\ny0c8wi/L17odjuucTkb/yWyjqv4MrAP+53B7xhgTsroPH8y8uk3Z3bUNJ45H9vUjp2fTZVnNVVWX\nAJ872Z4xxoS6brO/pdCJ43zQ4Tq3Q3FVoG8DHh/g9owxJqgVOacwBRNmc9WS2Xw5MnLvP3J6avdF\nItLFu6DpWVT1SyfbyyaOi0XkTRGZKiL9RaSyiIwVkamBaN8YY/KicdsmzLrtEWo+15+dWyLzPn6n\ne0a7gGTgHRFxrd6uqm5Q1QF4boptoaqJqnqnW/EYY0xO+r02guVxVVl2fauIvPk838lIRK4VkR0i\nckhEFnlrC1VQ1a/xLPvzgK/B+VLTSEQ6ATOAXN/bFIk0En/qjQlSV85aQO09vzH29gFuhxJwkt8P\nIxFZiOfDPgqoh6fGUHE8N7tOA9qrakefghNpCRwCJqlqHe+2aGAjcCWetep+BHoCjYCGwMveUhKn\njjFDVa/z/n+qqnbPoi3N7Fw4tQigCSxLsiZUzRn7EfXu78nWT+bRrH1rt8PJkYigqj5/UPqyavci\nVX0pXUAxwLV4SnvfCQzzMTZUdaGIxGXYnFbTyNvuqZpGL+Kp6oqItAZuBAoBX4pILPACUF9EHk8f\nd3pZlZCwD7bQYn9AmFB21Z03M/7jydS4oxMpW/dRsHBBt0M6g79KSPjSMxquqo4V08umnThgerqe\nUTfgGlW9y/u4D9BEVe/1sZ0se0aWjEKLvWcm1B1POcH38eex/eLLuHXO126Hky2neka+TGD4WEQe\n9DWAfLBPGWNMWIspWICi42fR/vs5zHn7PbfDCQhfktFfwI0iMkVEmotIoGpXW00jY0zYa3xlE6bd\ndA8VnryDA/sOuB2O3/kyTPcdUBSoApQGjgCLgHnAfOBHVU31OcCzh+kK4JnA0A74HU+Zip6+lpKw\nYbrwYe+ZCRepJ1P5qmZF9sdWoO8PS90OJ1PBMEy3WlUbA+cCDYAhwDHgCWAJsNLX4KymkTEmkkVF\nR1FjyhyuXLucqS+96XY4fuVLz6gz0AZYCHylqke926PxJKcLVHW6Q3H6nfWMnPX555+zfv16oqKi\nKF++PH379s31Ptm9dtWqVUyePJlXXnkly7btPTPh5r37B9M44VVKrtnF+eXLuh3OGZzqGeU7GXmD\nKAi0Ataq6h5fg3GTJSPnHDhwgLZt27JixQoAmjVrxvTp0zn33HOz3WfGjBkUKFAgy9f+97//ZdGi\nRZQsWZLx47Ne5tDeMxOOPq8Zz+FzzqH38p/dDuUMwTBMh6qmqOo3oZ6IjLMWLFhArVq10h7Xq1eP\nefPm5bjP3Llzs33tQw89ROfOnf0cvTHBqcGn39J64zo+fSE8K/EEagacCQPbtm1jzJgxWT7ftGlT\nOnfuzK5duyhVqlTa9lKlSrF58+Yz9s1qn9jY2Gxfaz0eE6kq1Yxjwl1P0mrEo+zr15tzLzzP7ZAc\nZcnIAU7c8O/LZ+ymTZsYMmQIe/fuZfny5bRp04aOHTvSv39/3wNLp0qVKgwfPjzH/ZKSkihcuHDa\n44IFC3Lo0KFc7SMi2b7WVlcwkazff//Dp7MSSO5yLb2XLXc7HEcFup6R32VSPuKMx/5oU9X3r/z6\n+++/6d+/P5MmTWLevHm0a9eOyZMnU716dVatWuXcN5kHxYsXP6MHk5ycTGxsbK72yem11jMyka7O\nB7Not/4nvvjfBLdDcVTY9YxUdQMwQESigImq+lb6x8BbrgbosDfeeIOBAwem9SaOHTtG0aJFKVu2\nLJ988gn169d3rK3cDtPFx8ezfPnpv9r27dtHw4YNz9g34z5//fUXDRs2pFSpUtm+1npGJtJVq3cx\nk3r2p8Gw/hzs143ipYq5HZIzVDUov4B3gT+ANRm2twc2AJuBx7N4bSc8pSN6ZvY4i9doZrLaHiwe\nffRRXb9+vaqqrl27Vh9++GFVVd2+fbsOHTrUlZgOHTqktWvXTntct25d/eOPP1RVdcuWLZqamprl\nPtm9VlV1/Pjx2q9fv2zbD/b3zBhfpZ48qXMql9WxV1zhdiinft98/sz3aWq3PzldPiKzxxna08zO\nRbBPE05MTGTatGlUqFCBXbt2MXDgQAoUKMCOHTuYMGECzz77LFu2bGHJkiWUKVOGokWLUrp0aebM\nmcOePXuIi4ujRo0azJo1i86dOzNnzhyaN2/O/v37iYmJoXv3TCtu5CghIYEdO3aQmppKfHw8vXv3\nBqBhw4aMGzeOBg0aZLlPVttff/11pkyZws6dO+nXrx8PPvggJUqUOKvtYH/PjHHC6nnLKN+xKT+/\n+zlte1zvWhxBcZ+Rv2WyFFAz4FlVbe99/ASAespHnHpN+vIRq/Gs0pD2WFUzvY05VJNRVtIno9tu\nu42xY8cSHR3NTTfdRKtWrahZsybz5s2jV69elC5dmqeffpqxY8fy6KOPMnjwYNauXcu6desYMCD0\ninyF6ntmTF6N63IzNX+cyWXb/6ZAjDtXXYKhnpEbygM70z3eBTRJv4Oqfgd8l+F1GR9nKqt6RqEo\n/Yfx4cOHSUlJoUiRIhw5coTGjRuTmJhIkyZNqFWrFtu3b6dq1aoA/PPPP8TGxjJz5ky6detGcnIy\nRYoUcevbMMZk45Yp77EirjTv9e7HrVMmB6RNf9UzCrVk5Nc/d+fPn+/PwwfUggUL+Omnnzh8+DDD\nhg0jISGBcuXKMWjQIGJiYpg9ezZxcXFUqlSJzZs3065dO06cOJG2SkJ0dDRJSUmWiIwJYjEFC5A0\nfAIdBnRn449PUKNxbb+3mfEPdacmFYXaMF1TYGi6YbrBQKpmUbk1j22F1TBddkaNGsWAAQNITk5m\n8ODBjB492u2QHBWO75kx2ZnY/DJK7t9Hl1+2BbztoFgOyAXLgWoiEuddF+9mYJrLMYWc+Ph45s6d\ny/Lly2nQoIHb4RhjfHTtR9No8NuvfPDMq26Hkm9B2zPylo9oDZQB/gSeUdXxInIt8D8gGhinqjkv\nCZC79iKmZxTu7D0zkeiDh56kwcRXuXDLPkqULh6wdiNiNl0gWTIKH/aemYikypz4C9gRX5s753wT\nsGYjdZjOGGNMZkSIffMTuiyey7JZuZpAHFSsZ+RlPaPwYe+ZiWTvtruaCok/c/XW3c6s4pwD6xkZ\nY4w5S9cpH3NR0t9Meew5t0PJE0tGxhgTRkqWKcGyu4bQcMwLHNx/0O1wcs2G6bxsmC582HtmDHwd\nfz6/xV/K7bO/8ms7NkyXjUxqGrUWkYXeba3djs8YY/yt+Mj3uH7RLFYt+MntUHIlrHtG6WoYjQGe\nAPYAw1R1ayb7Ws8oTNh7ZozH5BZNKZy0l27rzvrIc0xE9IxE5F0R+UNE1mTY3l5ENojIZhF5PIvX\ndgJm4KljtFBVO+BJSKF1Vc8YY/Lpqvc/o9mv2/ls5Ntuh5KjoO4ZOV3TyLuE0HuqelaRHusZOevz\nzz9n/fr1REVFUb58efr27ZunfVatWsXkyZN55ZVX8ty2vWfGnDax7wBqfTOJhjsPEF3A+bWxI2YF\nBodqGu0BrgFKAaNVdUEm7VgycsiBAwdo27YtK1asAKBZs2ZMnz49bUXwnPb573//y6JFiyhZsiTj\nx4/Pc/v2nhlz2snjJ1lZsSTr2vem3wTne0iRWs8I8l/T6LOcDhxO9YzctGDBAmrVqpX2uF69esyb\nN++MqrHZ7fPQQw9RpkyZsCrpYYxbomOi2fHoSK4a2p99w/7DueXL+nQ8q2d0mt/+5LUPv+xt27aN\nMWPGZPl806ZN6dy5M7t27aJUqVJp20uVKsXmzZvP2DenfaxnY4xzuj18F5+NfZ5/+vTg1nlzfTqW\nv+oZhWIy+g2omO5xRTy9I9fIc76/Gfps/j98N23axJAhQ9i7dy/Lly+nTZs2dOzYkf79+/scV3pV\nqlRh+PCcF0lPSkqicOHCaY8LFizIoUOH8rSPUz/gxhiPC/6bQKsb27D2+9XUbl7P7XDOEorJKK2m\nEfA7nppGPd0MyJdE4qu///6b/v3789VXX1G4cGG6dOnCxIkTWbFiBatWraJ+/foBj6l48eL89ddf\naY+Tk5M5//zz87SP9YyMcVbTa1uR0KARBfvfTO2fN7gdzlmCOhmlr2kkIjs5XdNoEPA1p2sa/eJm\nnG564403GDhwYFov49ixYxQtWpSyZcvyySefOJqMcjtMFx8fz/Lly9O279u3j4YNG56xb077WM/I\nGOe1mTiVQvUr8/XEz7jm1hvcDucMQZ2MVDXTHo+qzgRmBjicoHTw4MG0iQDr1q3jkksuISYmhuLF\nnS+uldthulatWvHYY4+lPV65ciUvveSpDL9161aqVKmS7T5gPSNj/KFitUqMv/JGKgy9G72lS1D9\n0Rf0U7sDJVSndicmJjJt2jQqVKjArl27GDhwIAUKFGDHjh1MmDCBZ599li1btrBkyRLKlClD0aJF\nKV26NHPmzGHPnj3ExcVRo0YNZs2aRefOnZkzZw7Nmzdn//79xMTEnDEDLi8SEhLYsWMHqampxMfH\n07t3bwAaNmzIuHHjaNCgQZb7vP7660yZMoWdO3fSr18/HnzwQUqUKJHrtoP9PTPGTYcPHGZ3pdIs\nu/85ej032OfjRcx9RoESqskoK+mT0W233cbYsWOJjo7mpptuolWrVtSsWZN58+bRq1cvSpcuzdNP\nP83YsWN59NFHGTx4MGvXrmXdunUMGDDA7W8lz0L1PTMmUCb2f5R6n71B7V3/UCDGtwGyiFgOyORf\n+g/jw4cPk5KSAsCRI0do3Lgxe/fupUmTJtSqVYtjx45RtWpVAP755x9iY2OZOXMml112GcnJya7E\nb4zxnz6vv8SxqGg+uOdet0NJE9TXjEz+LViwgJ9++onDhw8zbNgwEhISKFeuHIMGDSImJobZs2cT\nFxdHpUqV2Lx5M+3atePEiRNpqyRER0eTlJREkSJFXP5OjDFOiy4QxbZBL9ByxEMc+u8IipVy/hpz\nXtkwnVe4DdNlZ9SoUQwYMIDk5GQGDx7M6NGj3Q7JUeH4nhnjD7OrlGVnvTbc8dmUfB8jkpcDypGI\nXAzcD5wLfAusBXrj+X5rqWoLF8NzXXx8PHPnziUmJoYGDRq4HY4xxiUnnxxFhwf68MfOPzm/om/L\nBPkqrHtGp+oZqWpf7+POQFlVPetmmUjqGYU7e8+Myb3pF1/EnvI1uevbr/P1+oiYwOBgPaNTegHv\n+y9iY4wJLeeNGEeXJXPYutZ/BfhyI6h7Rk7WMxKRi4Ahqnp3Fm1ZzyhM2HtmTN58XK8mh4qVpN/i\nH/L82oi4ZqSqC71r0KV3GbBFVbcDiMiHQGdvPaME77b09Yy+9L7uduBd/0dtjDGhpdqoBCpcexlr\nf/iJ2k3duY4c1MkoC/mqZ6SqQ3M6sNUzMsZEonptGjG5dkOiB91K7eU/Z7uv1TM6zeoZGWOMwy59\ncxJlW9Zm9dwl1GvbLMv9/FXPKKgnMGQh6OoZGWNMqKvZqBZfNGzK5gfvcKX9UExGafWMRKQgnnpG\n01yOyRhjQl7LtyZyxaYNrJi9OOBtB3Uy8tYz+h6oLiI7ReQ2VT0BnKpntB74KJLrGRljjFOq1anG\n9EbN2PronQFvO6indgeSTe0OH/aeGZN/iWs3U6JxDTZ9soBmHS7PcX8rIeEwS0bO+vzzz1m/fj1R\nUVGUL1+evn37nrXP+++/z+7du1m2bBk33HADPXr0cKRte8+M8U1CqxbEHPibHqtzHnSyZOQwS0bO\nOXDgAG3btmXFihUANGvWjOnTp6etCA6wZcsWZs6cyb333su+ffuoVq0aK1eupHLlyj63b++ZMb7Z\nsX4LxS6tzpbPv6PJNS2z3TcilgMyoWnBggVppdAB6tWrx7x5887YZ926dYwYMQKAc889l6pVq6Yl\nL2OMuyrVqsrMhs1JfPyugLUZivcZGZds27aNMWPOWmM2TdOmTencuTO7du2iVKlSadtLlSrF5s2b\nz9i3Q4cOzJw5E/AUAty9e3dagT9jjPuavzmBkk2qs/Lb72nYrrnf27Nk5AQnbvryYVhp06ZNDBky\nhL1797J8+XLatGlDx44d6d+/v+9xpVOlShWGDx+e435JSUkULlw47XHBggU5dOjQGfvExMRQu3Zt\nAL788ksaNWpE/fr1HY3XGJN/VepWZWKDyyjy6N00XLnW7+2F3TCdiFwsIm+KyFQR6S8itUTkIxEZ\nLSJd/dKoqu9f+fT333/Tv39/Jk2axLx582jXrh2TJ0+mevXqrFq1ysFvMveKFy9+xjWb5ORkYmNj\nM933wIEDTJgwgcmTJwcqPGNMLjUeNY4rf1nPL4tX+r2tsOsZqeoGYMCpWkZAUeA1VV0kIl8An7ga\noMPeeOMNBg4cmNYTOXbsGEWLFqVs2bJ88sknjvY2cjtMFx8fz/Lly9O279u3j4YNG561v6oyYsQI\nxo4dS7FixdixYweVKlVyLF5jjG9qNb6EhNp1iX7obmouXZ7zC3wQtMlIRN4FOgJ/niof4d3eHvgf\nEA2MVdWXMnltJ2AAnlW8vwGeFZHrgTKBiD2QDh48mDZZYN26dVxyySXExMRQvLjzNe1zO0zXqlUr\nHnvssbTHK1eu5KWXPG/T1q1bqVKlCiLC66+/zo033sjRo0dZtmwZycnJloyMCTK1X36bStc2Y+ua\nLcTX8d913aCd2u1kLaN0r/1EVbtk0V5ITu1OTExk2rRpVKhQgV27djFw4EAKFCjAjh07mDBhAs8+\n+yxbtmxhyZIllClThqJFi1K6dGnmzJnDnj17iIuLo0aNGsyaNYvOnTszZ84cmjdvzv79+4mJiaF7\n9+75iishIYEdO3aQmppKfHw8vXv3BqBhw4aMGzeOw4cP07p167RzKyL8+uuvlC9f3udzEuzvmTGh\nZmrdGhwsfQG3fzf/rOfCvp6RU7WMRKQS8CRwDjAiIMEHUOXKlbn//vuz3WfYsGGMHTuW6Ohobrrp\nJlq1akWDBg2YN28ebdu2pXTp0nz00Ue0atWK6dOn06RJE9auXcu6devyHVdmN7mCp5d0ysmTJ/N9\nfGNM4FR4/jWq9mjPrsTdVKh8gV/aCNpklIV81TIC7snNwcOpnlH6nsHhw4dJSUmhSJEiHDlyhMaN\nG5OYmEiTJk2oVasW27dvT5tW/c8//xAbG8vMmTPp1q0bycnJFClSxK1vwxgTBJpdfzUzKlZg98C7\nqPbYI1bPCD/WMoLwqme0YMECfvrpJw4fPsywYcNISEigXLlyDBo0iJiYGGbPnk1cXByVKlVi8+bN\ntGvXjhMnTqStkhAdHU1SUpIlImMMAIUfe5kOD/Si6KTJfqlnFLTXjAC8w3TT010zagoMVdX23seD\ngdTMJjHko62QvGaUH6NGjWLAgAEkJyczePBgRo8e7XZIjgrH98yYYDA3rizbmlzJnR+9n7YtUpcD\nslpGDoiPj2fu3LksX76cBg3cqXdvjAk9++96htazp3L8WIrjxw7anpG3llFrPNOx/wSeUdXxInIt\np6d2j1PVnOca5669iOkZhTt7z4zxD01VllYowZbOd9LnzZGArdrtOEtG4cPeM2P8Z/z9T9Lgg1HU\n3X2QqOioiB2mM8YY46LeI56j0MkTfDF8lKPHtWRkjDEm1woWimHhlTdTfJwjV0jShNrUbmOMMS7r\n9toojlU5l7mTv3DsmHbNyMuuGYUPe8+M8b93r7ySEnt20H3dFpvA4KTskpEJPfZzbYx/Ja7bQslG\n1SlzVG0CQ3ZE5BwR+VFEOopIZREZKyJT83ocVQ3rr/d+fo+eH/dMezxpktKnj/tx+fpljPGvypdU\n5ct6Z5eGya+wTUbAY8BHAKqaqKp3uhxPyNizZ77bIQSNcFoiyld2Lk6zc+HRe/Eyx44V1MlIRN4V\nkT9EZE2G7e1FZIOIbBaRxzN53VXAemBvoGINJ3/8Md/tEIKGfeicZufiNDsXHlHRzqWQoE5GwHig\nffoN3rpEr3u31wJ6ikhNEekrIiNF5EI8Kzc0BXoBd4kLF37y+sOa0/7ZPZ/Zc7nZlv6xP3+57Fxk\nH4sv+zt9LrI7L06zc5H/Y4fjuQjqZKSqC4H9GTan1TRS1ePAqZpGCar6oKr+rqpDVPVB4H3gHaC0\niLwF1M+sJ+UPwf7DlfFxJP+iZXwcyefCPoDnZ/m8nYvct58fQT+bLpOVu7sB16jqXd7HfYAmqnqv\nj+0E94kwxpgg5cRsulC86dUvScOJk2mMMSZ/gnqYLgu/ARXTPa6Ip+KrMcaYEBWKychqGhljTJgJ\n6mTkrWn0PVBdRHaKyG2qegIYBHyNZ/r2R6r6i5txGmOM8U3QT2AwxhgT/oK6Z2SMMSYyWDLKILN1\n7Lzr3E0UkXdEpJeb8QVSFuci3+v8hbIszkVn78/Eh95VP8JeFufhYhF5U0Smikh/N+MLpKx+F9Kv\ni+lWbIGWxc9FGxFZ6P3ZaJ3TMSwZZZDFOnY3AlNU9W7gehfCckVm5yJS1/nL4lx84f2Z6I9nIk3Y\ny+I8bFDVAXjOQQt3Igu8bH4X0tbFjBRZnItU4CBQiFzMeI6IZJTfNe7SKQ/s9P7/pN8CDQAHzkXY\ncPBcDMGzRFVIcuI8iEgnYAbwlT9j9Tdfz0U4rYvpwM/FQlXtADwBPJdTexGRjMjDGndZvH4Xp+9t\nCvVz5uu5CCc+nQvxeAmYqaqr/B2sH/n8M6Gq070fPL39GWgA+HouXF8X00E+nQs9PTsuCU/vKFuh\n/sGaK3lZ405EYjNZx+5ToKuIjCbE72ny9VxkcX5CUj7PRYN03/e9QDugm4jcE7DAHebreRCR1iIy\nyrv9y4AG7zBffz8yrouZ7gM55Djwc3GDd9sk4LWc2gvF5YCckn7oDTy9nyaq+jeeawBpVPUIcHsA\nYwu0vJyLs7aFmbyci/8D/i+AsQVSXs7Dd8B3AYwt0HJ9Lk5R1YmBCMwFefm5+Az4LLcHjoieURZC\n9i8WP7BzcZqdCw87D6fZuTjNb+cikpORrXF3mp2L0+xceNh5OM3OxWl+OxeRnIxsjbvT7FycZufC\nw87DaXYuTvPbuYiIZCS2xl0aOxen2bnwsPNwmp2L0wJ9LmxtOmOMMa6LiJ6RMcaY4GbJyBhjjOss\nGRljjHGdJSNjjDGus2RkjDHGdZaMjDHGuM6SkTHGGNdZMjLGGOM6S0bGhDARKS4iH4tIxZz3NiZ4\nWTIyJkSJyB3AQ8CNQCgXcTPGlgMyJtSJSCoQp6q/uh2LMfllPSNjjDGus2RkjI9EpI2IpKb7OmsV\nYxEpKSJXikhPEbnBjTjdJiLnZjhPqW7HZIJHJJcdN8Zp871f+zJ5Lg7oCAwEppJFOWYRGQBUyaaN\nFar6YX4DFJGJQF2gHnBqeC/L4mgi0hyYDRQEVgC/qOrt+Wz+MDDU+//bgIvyeRwThiwZGeOc+ar6\n78yeUNXVIvI0cC+wMKsDqOqb/grOe/xbRSQemAC0AKqRRaVOEYkBbgAKA6+r6gM+tp0M/Nt77LZY\nMjLp2DCdMYHTEs/v3CI/HDsvs+laAuO9/8+uF3YH8AuemL/NZ1zG5IolI2MCpxWwX1XXOnEwEekl\nIqMBBV4UkYG5fGkL4GPgKFkkIxGpDCQDNbzHz7I3Z4wTbJjOmMBpjaeMsyNU9X3gfeBfeXxpSVX9\nR0S2k3XPqC/wHzzxrlXVpHwHakwuWDIyYUNEOgPt8FycvxUoA3TD85d9c+AVYBbwoPe58/BcmL9N\nVU/4ObaiwKV4ejDPAMWAC/D8DvZT1WP+bD9dHBWAU/cjJQLxmexzA/AFUMQb89uBiM1ENktGJiyI\nSEGgjareJyI/AgnAp6o62Pv8Y8A4YDLwmqpuF5EoIAnoBUzyc4jNgBigLXCzqv4uItHAfm/747N7\nsYNaA995/58INEn/pIiUAKqo6mci0g7PZ8SCAMVmIphdMzLhohWwUEQEz9DTblUdme75E3h6Q++r\n6nYAVU0FTgJlAxBfa+A4cI+q/u5t/ySe6dWxAWj/lBacvv6zDYgVkeLpnr8HeMv7/1befy0ZGb+z\nnt2OLZ4AAANfSURBVJEJF2vx9HLqAqWB/2V4vjGwVFVXnNogIlWAksC6AMTXGpinquvTtV8DKAGs\nDkD7p8Smu/6T6P23CrBaRBoBG1X1sHd7K2Czqv4RwPhMhLKekQkLqrpHVY8CVwBHgGUZdmkNzMuw\nrT2eGWXf4UciUghPMszYfhfggL/bTxfH+UD6xLLN+28V75BhR1Wd5t23IJ4hPOsVmYCwnpEJN1cA\ni9JPSBCR6kA5PKsjpHcDMFNVj4hIZVVNxD+a4LlxNGP7PYFPVPW4n9s/pRVnJr5T7cUD/YB30z3X\nGE/MOSZKEbkSqI5nKDQKTw9wowPxmghiPSMTNrx/3bfi7B5IGzzXaxan2zfWu/0976aH0z03wbt2\n2q0OhdYaOAj8mK6N2niGFE9NXHjQobaycznpejqq+g/wF56bYAuo6s50++Z4vUhECojIw8AeVR2t\nqu+o6lt4elrdnA/fhDNLRiacNMBzDWh+hu1tgGXe5WhOiQOigTki0hpYmu65U78Xxx2KqxWw2Dth\n4pTqeG6AXSwi7fHPqgxpRKQsnpl8f2V4ajueczEmw/YrgF05lKUYBEzMeBOvqs4EtopIS19iNpHF\nkpEJJxcAP5OuB+J1Lp4p3emtwrMKwQighaompHuuDvAP8KVDcZXMpP1ZwI8i8jpQX1WnONTWGUSk\njIjMB7YCtfAkiQHpdlmOZ4Zfqren85WIrACuBMqIyHwRuS+T4xYGDqhqZovCoqo/4Vm9wZhcsWtG\nJmyo6nRgeibbr85kWypwU8btIlIKz/DZy6p6II8hZLo+nKpelsm2I3gmUPiVqv6Fp2eY1fMD0v3/\nBNAhl4e+hHSTRETkFmAYcE26GYNO9SxNBLCekTFnagkcA/6bj9c+m1U9ozCknJl8iwBF8axokan0\n9Yw4fU3KGMB6Rsacwdu7KprHlyUCz+H5gIbM6xmFm7V4Vo5YC6Cqb3P2skEZE9NhzjxPxqQRVfu5\nMMbknXeV8Kmq+mcmz10GFFZVu0/J5IolI2NMvnjX9rsP+FZV16Tbfi1Q3F+TMkx4smRkjPGJd2p8\ndTzr/BUAvrObXk1eWTIyxhjjOptNZ4wxxnWWjIwxxrjOkpExxhjXWTIyxhjjOktGxhhjXGfJyBhj\njOssGRljjHGdJSNjjDGu+3+ehDssO3AMygAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87e4929a50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.special import erf\n",
"def Nx_lognormal(m,z,log_mmin,sigma,F):\n",
" return (F/2.0)*(1 + erf((log10(m) - log_mmin)/sigma))\n",
"\n",
"for sig in [0.001,0.01,0.2]:\n",
" _ = plot(m,nx(m,z,Nx_lognormal,11.0,sig,1.0),label=r\"$\\sigma_{\\log m}=%s$\"%sig)\n",
"_ = xscale('log')\n",
"_ = yscale('log')\n",
"_ = ylabel(r\"$n_X(m,z)$\",fontsize=20)\n",
"_ = xlabel(r\"$m$, [$h^{-1}M_\\odot$]\",fontsize=20)\n",
"_ =legend(loc=0)\n",
"_ = xlim((1e10,1e15))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally we plot each of the parameterisations against each other to show the differences. We try to make them \"line up\" if we can."
]
},
{
"cell_type": "code",
"execution_count": 182,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f87df2b3c10>"
]
},
"execution_count": 182,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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XV0KTvVKe9NprMHAgBAdn+y3nz8MDD8Azz0Dz5m6MTQU0HcZRylPWrrVZ+88/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\npfIATfZKKZUH/D+z575Lfl8rbwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87de781790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(m,Nx_powerlaw(m,z,11,0.1,1.0),label=\"PowerLaw\")\n",
"plot(m,Nx_mass_independent(m,z,1.0)*np.ones_like(m),label=\"Mass Independent\")\n",
"plot(m,Nx_lognormal(m,z,12.7,0.9,1.0),label=\"Lognormal\")\n",
"xscale('log')\n",
"legend(loc=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### M-L relation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probably initially the only good way to go is to assume a power-law model for $L_\\nu$:\n",
"$$ L_\\nu = A_\\nu \\left(\\frac{m_h}{h^{-1}M_\\odot}\\right)^{\\beta_\\nu},$$\n",
"where $m_h\\equiv m$ is the mass of the host halo.\n",
"\n",
"In this case, the inverse function that we requre is\n",
"\n",
"$$ f_{L,X}^{-1}(L_\\nu,z) = \\left(\\frac{L_\\nu}{A_\\nu}\\right)^{1/\\beta_\\nu} $$\n",
"\n",
"and the mass associated with a given flux density at any redshift is\n",
"\n",
"$$ m_S = \\left(\\frac{4\\pi D_L^2 S_\\nu}{A_\\nu(1+z)^{1-\\xi}}\\right)^{1/\\beta_\\nu}.$$\n",
"\n",
"We also need $dm/dS$, which in this case is given by\n",
"\n",
"$$ \\frac{dm}{dS} = \\frac{m_S}{\\beta_\\nu S_\\nu}.$$\n",
"\n",
"**Note about units:** We use $D_L$ in Mpc/h, and SI units for flux density are W$m^{-2}$Hz$^{-1}$. To agree on the units properly, however, we want the flux density in WMpc$^{-2}$Hz$^{-1}$ which is equivalent to approximately $9.55\\times10^{44}$W$m^{-2}$Hz$^{-1}$. In other words, 1Jy= $9.55\\times10^{18}$WMpc$^{-2}$Hz$^{-1}$. Furthermore, the constant $A_\\nu$ has units of WHz$^{-1}$.\n",
"\n",
"**Typical values:** I can't find any typical values for the spectral luminosity, $L_\\nu$ of AGN in the radio. However, I do know what typical masses are, and typical flux densities. So we can kind of work backwards. Note the following plot, which uses $A_\\nu=10^{13}$WHz$^{-1}$. It gives high flux densities to high masses at low redshifts, as we might expect. Thus this should be in the right ballpark."
]
},
{
"cell_type": "code",
"execution_count": 205,
"metadata": {
"collapsed": false,
"hide_input": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f87e491c7d0>"
]
},
"execution_count": 205,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2iEtaakbTNRo9piut1HWIe0RccRaU6HpB7e2pHxFXXAvSiLjyNPOIuFoktez4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\nKRiJiEjiFIxERCRx/x9QFLkag0bY4AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87de49ba10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def flx_pl(m,z,A_nu,beta_nu):\n",
" return A_nu * m**beta_nu\n",
"\n",
"def flx_pl_inv(L,z,A_nu,beta_nu):\n",
" return (L/A_nu)**(1./beta_nu)\n",
"\n",
"def dmds_pl(m,S,z,A_nu,beta_nu):\n",
" return m/beta_nu/S\n",
"\n",
"S = logspace(-3,0,100)\n",
"for z in range(1,6):\n",
" plot(S,ms(S*9.55e18,z,0.8,flx_pl_inv,A_nu=1e13,beta_nu=1.0),label=\"z=%s\"%z)\n",
"legend(loc=0)\n",
"xscale('log')\n",
"yscale('log')\n",
"xlabel(r\"$S_\\nu$, [Jy]\",fontsize=20)\n",
"ylabel(r\"$m_S$, [$h^{-1}M_\\odot$]\",fontsize=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**NOTE: IGNORE THE FOLLOWING FOR NOW**\n",
"\n",
"-----------------------------------------------------------------------------\n",
"With a little algebra, we can calculate the total number density of sources at a given redshift. Basically, we are just solving\n",
"$$ n_X(z) = \\int_0^\\infty \\frac{dn}{dm} f_X(m) dm. $$\n",
"In this case, we can simply split the integral into three parts: the lower part is identically 0, and the upper parts integrate to \n",
"\n",
"$$ n_X(z) = \\frac{A}{\\mathcal{H}_\\star}\\left[\\left(\\frac{\\mathcal{H}_\\star}{m_{\\rm min}}\\right)^\\gamma \\left(\\frac{1}{\\Gamma(z_\\gamma,x_{\\rm sat})} - \\frac{1}{\\Gamma(z_\\gamma,x_{\\rm min})} \\right) + \\left( \\frac{1}{\\Gamma(z_0,x_{\\rm sat})} - \\frac{1}{\\Gamma(z_0,x_{\\rm min})}\\right) + \\frac{F}{\\Gamma(z_0,x_{\\rm sat})} \\right], $$\n",
"\n",
"where $z_k = (\\alpha + k + 1)/\\beta$, $x_k = (m_k/\\mathcal{H}_\\star)^\\beta$, and $\\Gamma$ is the incomplete gamma function. **NOTE: Something's wrong with this formula, proceed with numerical version...**\n",
"\n",
"-----------------------------------------------------------------------------\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"run_control": {
"marked": false
}
},
"source": [
"### Source Counts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we achieve the full source count distribution, which we convert to Euclidean space, as per Franzen+15, by multiplying by $S^{2.5}$. We do this for a range of models to show how parameters affect the results."
]
},
{
"cell_type": "code",
"execution_count": 158,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Just a helper function to plot things nicely\n",
"def suplabel(axis,label,label_prop=None,\n",
" labelpad=5,\n",
" ha='center',va='center'):\n",
" ''' Add super ylabel or xlabel to the figure\n",
" Similar to matplotlib.suptitle\n",
" axis - string: \"x\" or \"y\"\n",
" label - string\n",
" label_prop - keyword dictionary for Text\n",
" labelpad - padding from the axis (default: 5)\n",
" ha - horizontal alignment (default: \"center\")\n",
" va - vertical alignment (default: \"center\")\n",
" '''\n",
" fig = pylab.gcf()\n",
" xmin = []\n",
" ymin = []\n",
" for ax in fig.axes:\n",
" xmin.append(ax.get_position().xmin)\n",
" ymin.append(ax.get_position().ymin)\n",
" xmin,ymin = min(xmin),min(ymin)\n",
" dpi = fig.dpi\n",
" if axis.lower() == \"y\":\n",
" rotation=90.\n",
" x = xmin-float(labelpad)/dpi\n",
" y = 0.5\n",
" elif axis.lower() == 'x':\n",
" rotation = 0.\n",
" x = 0.5\n",
" y = ymin - float(labelpad)/dpi\n",
" else:\n",
" raise Exception(\"Unexpected axis: x or y\")\n",
" if label_prop is None: \n",
" label_prop = dict()\n",
" pylab.text(x,y,label,rotation=rotation,\n",
" transform=fig.transFigure,\n",
" ha=ha,va=va,\n",
" **label_prop)"
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {
"collapsed": false,
"run_control": {
"marked": true
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.00316227766017 1000.0\n"
]
},
{
"data": {
"image/png": 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dHJIQQgghhBBC9DqSiN5HVdWjwFFFUeYDJ7s7HiGEEEIIIYTojXp9aa6iKH9R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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87df015090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"S = logspace(-2.5,3,100)\n",
"print S.min(),S.max()\n",
"# Spectral Index\n",
"xi = 0.8\n",
"\n",
"# Zeor\n",
"zeor = 6\n",
"\n",
"#M-L params\n",
"A_nu = 1e13\n",
"beta_nu = 1.0\n",
"\n",
"#HOD params\n",
"gamma = 0.1\n",
"F = 1\n",
"log_mmin = 11\n",
"\n",
"\n",
"fig,ax = plt.subplots(2,3,sharex=True,sharey=True,subplot_kw={\"xscale\":'log',\"yscale\":'log'},figsize=(15,10),\n",
" gridspec_kw={\"hspace\":0.08,\"wspace\":0.08})\n",
"\n",
"for zmx in range(5,9):\n",
" ax[0,0].plot(S,dnds(S,zmx,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmds_pl)*S**2.5,label=r\"$z_{\\rm EoR}=%s$\"%zmx)\n",
"\n",
"for mmin in linspace(9,13,5):\n",
" ax[0,1].plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":mmin,\"gamma\":gamma,\"F\":F},dmds_pl)*S**2.5,label=r\"$m_{\\rm min}$=%s\"%mmin)\n",
"\n",
"for f in linspace(0.1,1.0,7):\n",
" ax[1,0].plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":f},dmds_pl)*S**2.5,label=r\"$F=%s$\"%f)\n",
" \n",
"for gm in linspace(0.01,1.0,7):\n",
" ax[1,1].plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gm,\"F\":F},dmds_pl)*S**2.5,label=r\"$\\gamma=%s$\"%gm)\n",
" \n",
"for xx in linspace(0.6,1.2,7):\n",
" ax[0,2].plot(S,dnds(S,zeor,xx,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmds_pl)*S**2.5,label=r\"$\\xi=%s$\"%xx)\n",
" \n",
"\n",
"for anu in logspace(11,16,6):\n",
" ax[1,2].plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":anu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmds_pl)*S**2.5,label=r\"$A_\\nu=%1.1e$\"%anu)\n",
" \n",
"suplabel('y',r\"$\\frac{dN}{dS}$, [${\\rm Jy}^{-1}{\\rm sr}^{-1}$]\",label_prop={\"fontsize\":20},labelpad=4)\n",
"suplabel('x',r\"$S_\\nu$, [${\\rm Jy}$]\",label_prop={\"fontsize\":20},labelpad=4)\n",
"for i in range(2):\n",
" for j in range(3):\n",
" ax[i,j].legend(loc=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I note, excitedly, the blue curve in the bottom right: it has a turnover, similar in character to the first plot from Franzen+15. This is caused by a lack of high-luminosity objects, since high-mass haloes are rare. It occurs at much higher flux densities than in the data plot, but this should be fixed when things are tightened up.\n",
"\n",
"The above plots show variations in parameters for just the power-law HOD. The following shows the characteristic differences between the 3 HOD parameterisations:"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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FrmNd0DrCYsN4rc5rfNvlW1pXbv34maGeJjQUVq2C1atJsi7KviqDmFXiCFfu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\nhFmR7h0LlKbS8D7tzbTd06j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0eW4rVjR1NEIIkass4kLuY925o1+4/ewzaNHC1NEIIUSu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\nkaQvhBAWRJK+EEJYkP8DO9DroPa/rYkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87df650b90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmds_pl)*S**2.5,label=\"Power-Law\")\n",
"plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_mass_independent,\n",
" {\"F\":F},dmds_pl)*S**2.5,label=\"Mass-Independent\")\n",
"plot(S,dnds(S,zeor,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_lognormal,\n",
" {\"log_mmin\":12.7,\"sigma\":0.9,\"F\":F},dmds_pl)*S**2.5,label=\"Lognormal\")\n",
"legend(loc=0)\n",
"xscale('log')\n",
"yscale('log')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Derived Quantities"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are several other quantities we can calculate directly using the same framework, which may or may not be helpful in constraining parameters against data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Total source count"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The total source count over all redshifts and flux densities can conceivably be gotten in two ways. The simple way, from first principles, is not to worry about flux densities at all, and just integrate over mass. The second way is to integrate $dN/dS$ over $S$."
]
},
{
"cell_type": "code",
"execution_count": 215,
"metadata": {
"collapsed": false,
"hide_input": false,
"run_control": {
"marked": true
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f87de08dad0>"
]
},
"execution_count": 215,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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cB6aVdRvCxRfDihXwxz8qGYiIZFO2CeHWW+Hxx2HqVOjQIe1oRESKX6JtCGZW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\nDzCJ0rm7AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87de6c4ed0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def nint(z,Nx,**Nx_kwargs):\n",
" m = logspace(12,17,500)\n",
" integ = simps(nx(m,z,Nx,**Nx_kwargs),m)\n",
" extra=integ*1.0\n",
" while extra > 0.01*integ:\n",
" m = logspace(log10(min(m))-2,log10(min(m)),500)\n",
" extra = simps(nx(m,z,Nx,**Nx_kwargs),m)\n",
" integ += extra\n",
" return integ\n",
" \n",
"def ntot_m(zeor,Nx,zmin=0,**Nx_kwargs):\n",
" z = linspace(zmin,zeor,400)\n",
" nz = np.zeros_like(z)\n",
" for i,Z in enumerate(z):\n",
" nz[i] = nint(Z,Nx,**Nx_kwargs)\n",
" return simps(nz*dVc(z),z)\n",
"\n",
"Z = arange(0,10,0.2)\n",
"NTOT_m= np.zeros_like(Z)\n",
"for i,z in enumerate(Z):\n",
" NTOT_m[i] = ntot_m(z,Nx_powerlaw,log_mmin=log_mmin,gamma=gamma,F=F)\n",
" \n",
"plot(Z,NTOT_m)\n",
"xlabel(\"z\")\n",
"ylabel(r\"Total Source Count [1/sr]\")"
]
},
{
"cell_type": "code",
"execution_count": 218,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f87dde34e50>"
]
},
"execution_count": 218,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f87ddbef390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def ntot_s(zmax,xi,ml_rel,ml_kwargs,Nx,Nx_kwargs,dmds,zmin=0,ml_inv=True):\n",
" S = np.logspace(-6,3,500)\n",
" n = dnds(S,zmax,xi,ml_rel,ml_kwargs,Nx,Nx_kwargs,dmds,zmin,ml_inv)\n",
" return simps(n,S)\n",
"\n",
"Z = arange(0,10,0.2)\n",
"NTOT_s= np.zeros_like(Z)\n",
"for i,z in enumerate(Z):\n",
" NTOT_s[i] = ntot_s(z,xi,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmds_pl)\n",
" \n",
"plot(Z,NTOT_s)\n",
"xlabel(\"z\")\n",
"ylabel(r\"Total Num Sources\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, these should be precisely the same:"
]
},
{
"cell_type": "code",
"execution_count": 219,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f87dd9fca50>]"
]
},
"execution_count": 219,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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wM8uv8MHhMQ4zs3wKHRzuqjIzy6/QweGuKjOz/BwcDg4zs1wKHxzr1kFEvWtiZrbtKHRw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\nw8zMcvn/xsGX5Qh4vywAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87ddcd1450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(Z,NTOT_m/NTOT_s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Luminosity Function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The luminosity function is harder to measure, since it requires knowing the redshifts of the sources. However, we can easily model it. Analogously to $dN/dS$, its equation is\n",
"\n",
"$$ \\frac{dN}{dL_\\nu} = \\frac{\\Omega}{V} \\sum_X \\int_{z_{\\rm min}}^{z_{\\rm max}} \\frac{dn_X}{dm}(m_L,z) \\frac{dm}{dL} dV_c(z), $$\n",
"\n",
"where in this case we multiply by the solid angle divided by the total volume to have units of W$^{-1}$HzMpc$^{-3}$. Typically, I expect this would be measured over some smallish range of redshift, so that its evolution can be determined. Assuming slow evolution over the given range, we could approximate this as\n",
"\n",
"$$ \\frac{dN}{dL_\\nu} = \\sum_X \\frac{dn_X}{dm}(m_L,z)\\frac{dm}{dL_\\nu} $$\n",
"\n",
"For our currently adopted model in which the M-L relation is a power-law, this simplifies to\n",
"\n",
"$$ \\frac{dN}{dL_\\nu} = \\sum_X \\frac{dn_X}{dm}(m_L,z)\\frac{m_L}{\\beta L_\\nu} $$\n",
"\n",
"where $m_L = (L_\\nu/A_\\nu)^{1/\\beta_\\nu}$."
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f87e4392190>"
]
},
"execution_count": 228,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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CIUPUY1IS9O+vWpJpnFqccKFoKEQv4OtDhGIc8ISITG24fgRARP7VTNqbgXJgPfBPYDLN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\nhBCiWP8PA/cp+tm0FNgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f87e4932050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def ml(L,z,ml_rel,inv=True,**kwargs):\n",
" if inv:\n",
" return ml_rel(L,z,**kwargs)\n",
" else:\n",
" m = logspace(0,18,600)\n",
" l = ml_rel(m,z,**kwargs)\n",
" s = spline(l,log10(m))\n",
" return 10**s(L)\n",
" \n",
"def dmdl_pl(m,L,z,A_nu,beta_nu):\n",
" return m/beta_nu/L\n",
"\n",
"def luminosity_function_approx(L,z,ml_rel,ml_kwargs,Nx,Nx_kwargs,dmdl,ml_inv=True):\n",
" mdash = ml(L,z,ml_rel,ml_inv,**ml_kwargs)\n",
" DMDL = dmdl(mdash,L,z,**ml_kwargs)\n",
" return nx(mdash,z,Nx,**Nx_kwargs)*DMDL\n",
"\n",
"L = logspace(25,31,300)\n",
"for z in range(7):\n",
" plot(L,luminosity_function_approx(L,z,flx_pl_inv,{\"A_nu\":A_nu,\"beta_nu\":beta_nu},Nx_powerlaw,\n",
" {\"log_mmin\":log_mmin,\"gamma\":gamma,\"F\":F},dmdl_pl),label=\"z=%s\"%z)\n",
"xscale('log')\n",
"yscale('log')\n",
"legend(loc=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Points for further consideration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**SF GALS**: Need to consider what appropriate HOD/ML relations exist for SF galaxies. This shouldn't add too much to what I'm doing here, since they are expected to be more effective at low $S$.\n",
"\n",
"**Spectral Index:** At the moment, I am hardcoding all of this to take a single spectral index which describes all sources. This is almost certainly not true, and at the very least there will be a distribution of spectral indices. However, the main 6-panelled plot above shows that the effectiveness of the spectral index is very small, and so maybe this won't matter.\n",
"\n",
"**Better Models:** The models I have implemented so far (for HOD and ML) are based on nothing more than intuition from HODs with optical galaxies. They're probably missing some of the features needed to be at all accurate. To go anywhere further than this will require motivation from SAMs I would think. \n",
"\n",
"**Redshift Dependence:** This is probably the main aspect which is screwing up results. Both the HOD and ML models that I've got here have no redshift dependence, which is complete rubbish. This will have to be motivated by SAMs as well.\n",
"\n",
"**Fitting:** Once we think we have a realistic handle on some of the above points, we can invert the process and fit the parameters to data (from Franzen+15 or GLEAM or whatever). \n",
"\n",
"**Clustering:** The exact same framework should be able to predict angular clustering, which should also be able to be measured with the same data we already have (I think?). This will give an extra dataset with which to constrain parameters."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Initialisation Cell",
"hide_input": true,
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
},
"latex_envs": {
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 0
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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