ex12_cooling_heating.ipynb

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    "## Astro 304 \"Galaxies\""
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    "### Cooling and heating processes during galaxy formation"
   ]
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    "# setup notebook for inline figures\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "# import pyplot and set some parameters to make plots prettier\n",
    "import matplotlib.pyplot as plt\n",
    "from code.plot_utils import plot_pretty\n",
    "plot_pretty()"
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    "### Heating processes\n",
    "\n",
    "Compression, ionization, cosmic rays. "
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    "### Re-ionization of the universe and heating of the intergalactic gas\n",
    "\n",
    "At $z_{\\rm rec}\\approx 1100$ the electrons and ions recombined, which allowed photons we know detect as the Cosmic Microwave Background (CMB) to propagate freely. \n",
    "\n",
    "Observations show, however, that by $z\\approx 6$ intergalactic medium in the universe is ionized. So between $z=1100$ and $z\\approx 6$ the gas must have been *re-ionized*. The process is called *reionization* and is almost certainly due to the UV photons emitted by young massive stars in the first galaxies at these high redshifts. \n",
    "\n",
    "The UV photons ionize neutral atoms and freed electrons carry extra energy which gets converted into gas temperature. Ionization by photons with spectrum typical of that of massive stars heats the gas to $T\\approx 5000-10000 K$. This heating raises the *Jeans mass* of the integalactic gas and leads to suppression of gas accretion onto halos with the \"virial\" temperature (where $R=R_\\Delta$; $M=M(<R_\\Delta)$):\n",
    "\n",
    "$$kT=\\mu m_p\\frac{GM}{R}$$\n",
    "\n",
    "less than the temperature of the gas. "
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    "### Suppression of gas accretion on small-mass halos and \"filtering mass\" \n",
    "\n",
    "The mathematical formalism describing effect of such re-heating on the evolution of perturbations is presented in <a href=\"http://adsabs.harvard.edu/abs/2000ApJ...542..535G\">Gnedin (2000).</a> The quantitative effect on accretion of baryons on a collapsing peak is calibrated using\n",
    " numerical simulations of galaxy formation  (e.g., <a href=\"http://adsabs.harvard.edu/abs/2006MNRAS.371..401H\">Hoeft et al 2006</a>, <a href=\"http://adsabs.harvard.edu/abs/2008MNRAS.390..920O\">Okamoto et al 2008</a>). It predicts that baryon fractions in halos of mass $M$ at redshift $z$ is modified from a constant value $\\bar{f}_{\\rm b}$ as:\n",
    "\n",
    "$$\n",
    " f_{\\rm b}(M,z)=\\bar{f}_{\\rm b}\\left\\{1+(2^{\\alpha/3-1}-1)\\left[\\frac{M}{M_{\\rm c}(z)}\\right]^{-\\alpha}\\right\\}^{-3/\\alpha},\n",
    "$$\n",
    " \n",
    "with $\\alpha=2$. \n",
    "\n",
    "The cutoff mass $M_{\\rm c}$ is derived from simulations of galaxy formation.\n",
    "For example, $M_{\\rm c}(z)$, in figures of <a href=\"http://adsabs.harvard.edu/abs/2008MNRAS.390..920O\">Okamoto et al (2008)</a>\n",
    "is well approximated by the following formula:\n",
    "\n",
    "$$\n",
    "    M_{\\rm c}(z) = 6\\times 10^9h^{-1}\\ M_\\odot\\,\\exp(-0.63z),\\ \\ \\mathrm{for}\\ z<9,\n",
    "$$\n",
    "\n",
    "while $M_{\\rm c}$ can be assumed to be $\\approx 10^5-10^6h^{-1}\\ M_\\odot$ at $z>9$, because temperature of the gas is much smaller before reionization."
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    "### Cooling processes\n",
    "\n",
    "Unlike dark matter, baryonic matter radiate away the internal energy it acquires during gravitational collapse thanks to many radiative (i.e. cooling) processes, which can be classified into four main classes:\n",
    "\n",
    "1) <b>Free-free emission (aka brehmsstrahlung)</b>  produced by charged particles moving in the EM field of other changed particles - e.g., electron moving past a proton.\n",
    "\n",
    "2) <b>bound-bound emission</b>: electron transitions from level to level in atoms and ions. As atoms or ions (with bound electrons present) absorb photons or bump into each other, electron(s) can get excited to higher energy levels. Subsequent decay back to ground state and emission of photon(s). If plasma has low optical depth to emitted photons, they will leave the system, carrying the energy with them.\n",
    "\n",
    "3) <b>free-bound emission</b> when an electron recombines with an ion. \n",
    "\n",
    "4) <b>Compton cooling</b>, in which the electrons scatter off the CMB photons which have low energy due to redshifting at the redshifts relevant for galaxies.\n",
    "Free electrons must exist - i.e., gas must be at least partially ionized - for the Compton cooling to operate.\n"
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    "### Cooling: scaling with gas density\n",
    "\n",
    "The Compton cooling depends only on the plasma density and temperature and energy density of the CMB photons (which is set by observations). \n",
    "\n",
    "$$\n",
    "\\mathcal{L}_{\\rm Compon}=\\frac{4kT_e}{m_ec^2}c\\sigma_{\\rm T}n_e aT_{\\rm CMB}^4\n",
    "$$\n",
    "\n",
    "The other relevant processes all involve two particles - i.e., electron and ion, ion-ion, or electron-ion. For neutral or partially ionized gas it could be neutral atoms, neutral-electron, or electron-ionized atoms. Thus, the cooling rate due to these processes is proportional to the square of the gas density. \n",
    "\n",
    "The cooling rates is thus often quantified in terms of the so-called *cooling function* $\\Lambda$:\n",
    "\n",
    "$$\\Lambda(T,Z,...)= \\frac{\\mathcal{L}}{n^2},$$\n",
    "\n",
    "where $\\mathcal{L}$ is the cooling rate in, say, ergs per second. "
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    "### Cooling and heating processes\n",
    "\n",
    "For the hydrogen-helium plasma, the processes that contribute to cooling and heating and the relevant \"chemistry\" of atoms and ions can be written down in a page or so of equation (e.g., see Appendix A.2 in <a href=\"http://adsabs.harvard.edu/abs/2011ApJ...728...88G\">Gnedin & Kravtsov (2011)</a>. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/gk11_primordial_chem.PNG\" width=\"500\" height=\"500\"></img>\n"
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    "### Cooling processes in the primordial (zero metallicity) gas\n",
    "\n",
    "This is Figure 1 from <a href=\"http://adsabs.harvard.edu/abs/1997ApJ...477....8W\">Weinberg et al. (1997)</a>:\n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/weinberg_etal97_cool_func_fig1.png\" width=\"500\" height=\"500\"></img>\n",
    "\n"
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    "### Cooling processes in gas enriched with heavy elements (Z>0)\n",
    "\n",
    "As gas gets enriched with heavy elements, the number of different ions present and possible processes of their mutual interactions becomes large. Here is a figure from <a href=\"http://adsabs.harvard.edu/abs/2009MNRAS.393...99W\">Wiersma et al. (2008)</a> (see also $\\Lambda$ and $H$ tables and movies <a href=\"http://www.strw.leidenuniv.nl/WSS08\">here</a>)\n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/wiersma08_Lambda_Z_dependence.PNG\" width=\"500\"></img>"
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    "### Cooling and heating function tables\n",
    "\n",
    "It is possible to follow reaction rate for dozens, or even hundreds, of atoms and ions and to track their abundance in a model (e.g., <a href=\"http://adsabs.harvard.edu/abs/2014MNRAS.442.2780R\">Richings et al. 2014</a>), but this is most often is not necessary because gas is often in the collisional and ionization equilibrium. Thus, such equilibrium can be assumed and the rates can be pre-computed into interpolation table as a function of metallicity, UV background intensity, and gas density,  using a plasma emission code, such as <a href=\"http://www.nublado.org/\">Cloudy</a>.\n",
    "\n",
    "Given that cooling rates depend trivially on $n^2$, the actual tabulated quantity is so-called *cooling function*: $\\Lambda(T,Z,...)\\equiv \\mathcal{L}/n^2$. "
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    "### Cooling and heating functions: example\n",
    "\n",
    "Cooling and heating functions for the primordial metallicity ($Z=M_{\\rm Z}/M_{\\rm gas}=0$) and solar metallicity, $Z=Z_\\odot=0.02$ and for two gas densities: $n=10^{-3}\\ \\mathrm{cm^{-3}}$ (left) and $n=10\\ \\mathrm{cm^{-3}}$ (right). \n",
    "The heating rate is due to cosmic UV background estimated at $z=0$. \n",
    "\n",
    " The plotted functions were generated using accurate approximations of  <a href=\"http://www.nublado.org/\">Cloudy code</a> calculations by <a href=\"http://adsabs.harvard.edu/abs/2012ApJS..202...13G\">Gnedin & Hollon (2012)</a>. You will find the code that reads the tables and produces this plot in this notebook. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/chf.png\" width=\"600\"></img>"
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    "### Cooling time\n",
    "\n",
    "*The cooling time* is a characteristic time scale over which plasma loses its internal energy: $\\dot{e}=e/t_{\\rm cool}$, where $\\dot{e}=n^2(H-L)$ is the net rate of heating/cooling. \n",
    "The cooling time also depends on the physical gas density: $n(r)=\\rho_{\\rm gas}(r)/(\\mu m_p)=f_{\\rm gas}\\rho_{\\rm tot}/(\\mu m_p)$, where the mean molecular weight for ionized plasma is $\\mu\\approx 0.6$ and $m_p=1.67262\\times 10^{-24}\\ \\rm g$ is the mass of proton: \n",
    "\n",
    "$$\n",
    "t_{\\rm cool}=\\frac{e}{\\dot{e}}=\\frac{nkT}{(\\gamma-1)n^2(H-\\Lambda)},\n",
    "$$\n",
    "\n",
    "where $\\gamma=5/3$ for ionized plasma. \n",
    "\n",
    "The *cooling time* for the Compton cooling of ideal monatomic gas is:\n",
    "$$\n",
    "t_{\\rm Compton}\\approx \\frac{3}{2}\\frac{n_ekT_e}{\\mathcal{L_{\\rm Compton}}}=\\frac{3m_ec}{4\\sigma_Ta_rT_{\\rm CMB}^4},\n",
    "$$\n",
    "\n",
    "i.e., it is independent of density. The Compton cooling is only shorter than or comparable to the Hubble time (current age of the universe) at $z>5-6$ and thus is a significant cooling process at these early epochs. It is subdominant at lower $z.$ \n"
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    "### Cooling time as a function of halo mass\n",
    "\n",
    "When gas accretes onto halos it has $T$ of a few thousand K (set by the cosmic UV background) which corresponds to sound speed: $c_s=\\sqrt{\\gamma kT/(\\mu m_p)}$ of a few km/s. However, it will achieve velocity of order halo circular velocity - i.e., $\\sim 200$ km/s for the Milky Way halo. Its motion, thus, will be highly supersonic. Supersonic flows generally quickly develop *shocks*. \n",
    "\n",
    "Shocks are discontinuities in flow properties - jumps of density, velocity, temperature, entropy - convert gas kinetic energy into internal energy via viscosity. \n",
    "\n",
    "Let's assume that gas gets shocked at the virial radius corresponding to density contrast of $\\delta\\approx 100$ and reaches temperature of $T\\sim T_{\\rm vir}= \\mu m_p/k \\times GM_{\\rm vir}/R_{\\rm vir}$. The density contrast at the virial radius does not depend on halo mass, but $T_{\\rm vir}$ does. Thus, *the cooling time of gas will be a function of halo mass.*\n",
    "\n",
    "$$\n",
    "t_{\\rm cool}=\\frac{e}{\\dot{e}}=\\frac{nkT}{(\\gamma-1)n^2(H-\\Lambda)}=\\frac{\\mu m_p}{(\\gamma-1)n_{\\rm vir}(H-\\Lambda)}\\frac{GM_{\\rm vir}}{R_{\\rm vir}},\n",
    "$$\n",
    "\n",
    "where $\\gamma=5/3$ for non-molecular gas, $n_{\\rm vir}=\\Omega_b\\rho_{\\rm crit}(z)(1+\\delta_{\\rm vir})/(\\mu m_p)$ where $\\mu$ is the mean particle weight per proton mass $m_p$: $\\mu\\approx 0.6$ for fully ionized plasma. "
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    "### Cooling time as a function of halo mass\n",
    "\n",
    "Here is a result of such calculation where I used definition of halo mass to be the mass enclosed within the radius within which density contrast is $200\\rho_{\\rm crit}$. You can find the code that does the calculation and produces this figure using Gnedin & Hollon tables in the notebook. \n",
    "\n",
    "The figure shows that the cooling time is much smaller than the age of the universe for small mass halos, but becomes longer than the age of the universe for $M\\geq 10^{12}\\ M_\\odot$. Thus, the gas that accretes on such massive halos and gets shocked to the virial temperature of such halos cannot cool. This explains why we observe hot, X-ray emitting gas in groups and clusters of galaxies. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/tcool_M200c.png\" align=\"center\" width=\"500\"></img>"
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    "from code.setup.setup import data_home_dir\n",
    "\n",
    "def Lambda_cool(Tgas, Zmet = 0.3, init=True):\n",
    "    \"\"\"\n",
    "    cooling function based on Gnedin & Hollon tables\n",
    "    input: \n",
    "    Tgas = gas temperature in K\n",
    "    Zmet = gas metallicity in units of solar metallicity\n",
    "        metallicity dependence is not implemented yet. calculations done for Z = 0.2Zsun.\n",
    "    output:\n",
    "    Lambda(T,z) = cooling function in ergs*cm^3/s\n",
    "    \"\"\"\n",
    "    if init:\n",
    "        dummy = np.loadtxt(data_home_dir()+'cool_table_n1e-3.dat', unpack=True) \n",
    "        lTgh = dummy[0]; heat = dummy[3]; cool = dummy[4]\n",
    "        Lambda_cool.cfunc = UnivariateSpline(lTgh, np.log10(np.abs(heat-cool)), s=0.0)\n",
    "        print \"cooling function initialized...\"\n",
    "        return 0.0\n",
    "    else:\n",
    "        return  Lambda_cool.cfunc(np.log10(Tgas))\n"
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      "cooling function initialized...\n"
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hojoMzNJ2Bhuqd+Kt18Wtp+rob7z+xmnIGD4k4vFRHYpDSZJEHe1mr3xUh76Z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\noHxq7hivc0gJISSQmEmS9sn+NQActxmFju2tGGN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RWwzDRJ38jmQTsQQEWMlY8fHCM+lq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\nkgQAIIIkCQBAxP8hiD6nO7+PDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbb854e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from colossus.cosmology import cosmology\n",
    "from colossus.halo.mass_so import M_to_R\n",
    "from scipy.interpolate import UnivariateSpline\n",
    "\n",
    "delta_vir = 100.; \n",
    "Zmet = 0.001; z=0.\n",
    "# some relevant constants\n",
    "Msun = 1.989e33; kpc = 3.08568e+21; G = 6.67259e-08; yr = 3.15569e+07\n",
    "mu = 0.6; mp = 1.67262e-24; \n",
    "kB = 1.38066e-16; keV = 1.60219e-09\n",
    "mump = 0.6*mp\n",
    "\n",
    "# define a vector of cosmological parameters:    \n",
    "my_cosmo = {'flat': True, 'H0': 70.0, 'Om0': 0.27, 'Ob0': 0.045714, 'sigma8': 0.82, 'ns': 0.96}\n",
    "# set my_cosmo to be the current cosmology\n",
    "cosmo = cosmology.setCosmology('my_cosmo', my_cosmo) \n",
    "\n",
    "\n",
    "mdef = '200c'\n",
    "lMhmin, lMhmax = 7., 15.\n",
    "lm200c = np.arange(lMhmin, lMhmax, 0.02)\n",
    "m200c = np.power(10.,lm200c)/cosmo.h\n",
    "r200c = M_to_R(m200c, z, '200c')/cosmo.h\n",
    "kT200c = 4.3013e4*m200c/r200c*mump\n",
    "n200c = delta_vir*cosmo.Ob0/cosmo.Om0*cosmo.rho_c(z)*cosmo.h**2*Msun/kpc**3/mump # colossus returns density in h^2 Msun/kpc^3\n",
    "\n",
    "Lambda_cool(kT200c/kB, Zmet = Zmet, init=True)\n",
    "\n",
    "tcool = 3.*kT200c/(5.* n200c*10.**Lambda_cool(kT200c/kB,Zmet=Zmet, init=False))/yr\n",
    "\n",
    "\n",
    "plt.figure(figsize=(2.5,2.5))\n",
    "plt.xscale('log'); plt.yscale('log')\n",
    "plt.xlabel(r'$M_{200c}$'); plt.ylabel(r'$t_{\\rm cool}\\ \\mathrm{(yrs)}$')\n",
    "plt.xlim(1.e9,1e15); plt.ylim(1.e7,1.e12)\n",
    "\n",
    "# mean matter density rho_crit(z)*Omega0 in h^2 Msun/kpc^3\n",
    "dmean = 2.77e2\n",
    "plt.plot(m200c, tcool, c='darkslateblue', lw=2.0, label=r'$\\mathrm{t_{\\rm cool}\\ (yrs)}$')\n",
    "\n",
    "tU = cosmo.age(z)*np.ones_like(m200c)\n",
    "plt.plot(m200c, tU*1e9, '--', c='slateblue', lw=2.0, label=r'$\\mathrm{age\\ of\\ the\\ universe}$')\n",
    "\n",
    "plt.grid(linestyle='dotted', c='lightgray')\n",
    "plt.legend(frameon=False, loc='upper left', fontsize=8)\n",
    "plt.savefig('fig/tcool_M200c.png', bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iFNTVwaWX6jXPOxMVpYd83Hqr7h3TmlgdOAAPPQRPP63fy5VRo3Qy62L1l4jU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\nJe+7D2691fWx5cvhyiv1erU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iYpiZmsrMluR1Vg9aX4OlnoT/SawLfuF8fx44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\nnPT/3w03JaqK1OQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd531588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from code.setup.setup import data_home_dir\n",
    "\n",
    "lTln, cf0ln, hf0ln, cf1ln, hf1ln = np.loadtxt(data_home_dir()+'chf_n1e-3.res',unpack=True) \n",
    "lThn, cf0hn, hf0hn, cf1hn, hf1hn = np.loadtxt(data_home_dir()+'chf_n10.0.res',unpack=True) \n",
    "#\n",
    "# plot\n",
    "#\n",
    "fig, ax = plt.subplots(1,2, figsize=(6, 3))\n",
    "xlims = [10., 1.e8]; ylims = [1.e-32, 1.e-20]\n",
    "ax[0].set_xlabel(r'$T (K)$'); ax[0].set_ylabel(r'$\\Lambda(T),\\ \\mathcal{H}(T)\\ \\ \\mathrm{(cm^3\\,erg\\, s^{-1})}$')\n",
    "ax[0].set_xscale('log'); ax[0].set_yscale('log')\n",
    "ax[0].set_xlim(xlims); ax[0].set_ylim(ylims)\n",
    "ax[1].set_xscale('log'); ax[1].set_yscale('log')\n",
    "ax[1].set_xlim(xlims); ax[1].set_ylim(ylims)\n",
    "ax[1].set_xlabel(r'$T (K)$'); \n",
    "plt.setp(ax[1].get_yticklabels(), visible=False)\n",
    "#ax[1].yaxis.set_label_position('right')\n",
    "\n",
    "\n",
    "ax[0].plot(10.**lTln, cf0ln, c='c', lw=2.0, label=r'$(Z=0)$')\n",
    "ax[0].plot(10.**lTln, cf1ln, c='b', lw=2.0, label=r'$(Z=Z_\\odot)$')\n",
    "ax[0].plot(10.**lTln, hf0ln, '--', c='c', lw=2.0)\n",
    "ax[0].plot(10.**lTln, hf1ln, '--', c='b', lw=2.0, label=r'$\\mathcal{H}(T)$')\n",
    "\n",
    "ax[1].plot(10.**lThn, cf0hn, c='c', lw=2.0, label=r'$Z=0$')\n",
    "ax[1].plot(10.**lThn, cf1hn, c='b', lw=2.0, label=r'$Z=Z_\\odot$')\n",
    "ax[1].plot(10.**lThn, hf0hn, '--', c='c', lw=2.0)\n",
    "ax[1].plot(10.**lThn, hf1hn, '--', c='b', lw=2.0, label=r'$\\mathcal{H}(T)$')\n",
    "\n",
    "ax[0].legend( frameon=False, loc='lower left',fontsize=9)\n",
    "#ax[1].legend( frameon=False, loc='upper left',fontsize=9)\n",
    "# build a rectangle in axes coords\n",
    "bottom = 0.25\n",
    "left = 0.27; height = 0.675\n",
    "top = bottom + height\n",
    "\n",
    "ax[0].text(left, top, r'$n=10^{-3}\\,\\mathrm{cm}^{-3}$',\n",
    "        horizontalalignment='center',\n",
    "        verticalalignment='center',\n",
    "        transform=ax[0].transAxes)\n",
    "ax[1].text(left, top, r'$n=10\\,\\mathrm{cm}^{-3}$',\n",
    "        horizontalalignment='center',\n",
    "        verticalalignment='center',\n",
    "        transform=ax[1].transAxes)\n",
    "\n",
    "ax[0].grid(linestyle='dotted', c='lightgray')\n",
    "ax[1].grid(linestyle='dotted', c='lightgray')\n",
    "plt.savefig('fig/chf.png', bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'codes'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-13f08f362d8c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mcodes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgalaxy_model\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mgm\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mcolossus\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlss\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpeaks\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minterpolate\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mUnivariateSpline\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mcolossus\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhalo\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconcentration\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mconcentration\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mcolossus\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhalo\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmass_defs\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mchangeMassDefinition\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'codes'"
     ]
    }
   ],
   "source": [
    "import code.galaxy_model as gm\n",
    "from colossus.lss import peaks\n",
    "from scipy.interpolate import UnivariateSpline\n",
    "from colossus.halo.concentration import concentration\n",
    "from colossus.halo.mass_defs import changeMassDefinition\n",
    "from scipy.integrate import odeint\n",
    "from code.galaxy_model import R_loss\n",
    "\n",
    "# some relevant constants\n",
    "Msun = 1.989e33; kpc = 3.08568e+21; G = 6.67259e-08; \n",
    "yr = 3.15569e+07; Gyr = 1.e9 * yr;\n",
    "mu = 0.6; mp = 1.67262e-24; \n",
    "kB = 1.38066e-16; keV = 1.60219e-09\n",
    "mump = 0.6*mp\n",
    "delta_vir = 200.\n",
    "\n",
    "class gmodel_tcool(gm.model_galaxy):\n",
    "    def __init__(self, *args, **kwargs):\n",
    "        \n",
    "        # gas halo mass\n",
    "        Mgh = kwargs.pop('Mgh')  # Will use 'dict' as default\n",
    "        if Mgh is not None:\n",
    "            self.Mgh = Mgh\n",
    "        else: \n",
    "            self.Mgh = 0.0\n",
    "        self.Mh = kwargs['Mh']; self.t = kwargs['t']\n",
    "        self.cosmo = kwargs['cosmo']\n",
    "        Mvir = self.Mh * self.cosmo.h \n",
    "        self.z = self.cosmo.age(self.t, inverse=True)        \n",
    "\n",
    "        Lambda_cool(1., Zmet = 0.01, init=True)\n",
    "        self.cvir = concentration(Mvir, 'vir', self.z, model='diemer15')\n",
    "        self.M200c, self.R200c, self.c200c = changeMassDefinition(Mvir, self.cvir, self.z, 'vir', '200c')\n",
    "        self.M200c /= self.cosmo.h; self.R200c /= self.cosmo.h\n",
    "        self.kT200c = 4.3013e4*self.M200c/self.R200c*mump\n",
    "        self.n200c = delta_vir*self.cosmo.rho_b(self.z)*self.cosmo.h**2*Msun/kpc**3/mump # colossus returns density in h^2 Msun/kpc^3\n",
    "        self.tcool = 3.*self.kT200c/(5.* self.n200c*10.**Lambda_cool(self.kT200c/kB, Zmet=0.01, init=False))/Gyr\n",
    "        \n",
    "        # only one model based on total gas density for starters, a better model is to be implemented\n",
    "        super(gmodel_tcool, self).__init__(*args, **kwargs)\n",
    "\n",
    "        return\n",
    "            \n",
    "    def evolve(self, Mcurrent, t):\n",
    "        # first set auxiliary quantities and current masses\n",
    "        self.z = self.cosmo.age(t, inverse=True)        \n",
    "        self.gr = self.cosmo.growthFactor(self.z)\n",
    "        self.dDdz = self.cosmo.growthFactor(self.z,derivative=1)\n",
    "        self.thubble = self.cosmo.hubbleTime(self.z)\n",
    "        self.dDdt = self.cosmo.growthFactor(self.z, derivative=1) * self.cosmo.age(t, derivative=1, inverse=True)\n",
    "\n",
    "        self.Mh = Mcurrent[0]; self.Mg = Mcurrent[1]; \n",
    "        self.Ms = Mcurrent[2]; self.MZ = Mcurrent[3]\n",
    "        self.Mgh = Mcurrent[4]\n",
    "        Mvir = self.Mh * self.cosmo.h\n",
    "        self.cvir = concentration(Mvir, 'vir', self.z, model='diemer15')\n",
    "        self.M200c, self.R200c, self.c200c = changeMassDefinition(Mvir, self.cvir, self.z, 'vir', '200c')\n",
    "        self.M200c /= self.cosmo.h; self.R200c /= self.cosmo.h\n",
    "        self.kT200c = 4.3013e4*self.M200c/self.R200c*mump\n",
    "        self.rhobuni = self.cosmo.rho_b(self.z)\n",
    "        self.fgh = np.maximum(1.e-10, self.Mgh / (self.fbuni*self.Mh))\n",
    "        self.n200 = delta_vir*self.fgh*self.cosmo.rho_b(self.z)*self.cosmo.h**2*Msun/kpc**3/mump # colossus returns density in h^2 Msun/kpc^3\n",
    "        self.tcool = 3.*self.kT200c/(5.* self.n200*10.**Lambda_cool(self.kT200c/kB, Zmet=0.01, init=False))/Gyr\n",
    "        \n",
    "        self.epsout = self.eps_out(); self.Mgin = self.Mg_in(t); \n",
    "        \n",
    "        self.Msin = self.Ms_in(t)\n",
    "        self.Rloss = R_loss(0.); self.Rloss1 = 1.0-self.Rloss\n",
    "        self.sfr = self.SFR(t)\n",
    "        \n",
    "        # calculate rates for halo mass, gas mass, stellar mass, and mass of metals\n",
    "        dMhdtd = self.dMhdt(Mcurrent[0], t)\n",
    "        dMgdtd = self.dMgdt(Mcurrent[1], t)\n",
    "        dMsdtd = self.dMsdt(Mcurrent[2], t)\n",
    "        dMZdtd = self.dMZdt(Mcurrent[3], t)\n",
    "        dMghdtd = self.dMghdt(Mcurrent[4], t)\n",
    "        \n",
    "        if self.verbose:\n",
    "            print(\"evolution: t=%2.3f Mh=%.2e, Mg=%.2e, Ms=%.2e, Z/Zsun=%2.2f,SFR=%4.1f, Mgh=%.2e\"%(t,self.Mh,self.Mg,self.Ms,\n",
    "                                                                                           self.MZ/self.Mg/0.02,\n",
    "                                                                                           self.SFR(t)*1.e-9, self.Mgh))\n",
    "\n",
    "        return [dMhdtd, dMgdtd, dMsdtd, dMZdtd, dMghdtd]\n",
    "\n",
    "    def fg_in(self,t):\n",
    "        return 1.\n",
    "    \n",
    "    def dMghdt(self, Mghcurrent, t):\n",
    "\n",
    "        dummy = self.fbuni*self.fg_in(t)*self.dMhdt(self.Mh,t) - Mghcurrent/self.tcool\n",
    "        return dummy\n",
    "    \n",
    "    def Mg_in(self, t):\n",
    "        dummy = self.Mgh/self.tcool \n",
    "        return dummy\n",
    "        \n",
    "def test_galaxy_evolution(gmodel, Minit, sfrmodel, windmodel, etawind, tausf, cosmo, verbose):\n",
    "    zg = np.linspace(20., 0., 40) # grid of redshifts\n",
    "    t_output = cosmo.age(zg) # and corresponding times\n",
    "\n",
    "    # instantiate a galaxy model at t=tinit assuming a given star fromation model and cosmology\n",
    "    g = gmodel(t = t_output[0], Mh = Minit, Mg = None, Ms = None, MZ = None, Mgh = None, \n",
    "                   sfrmodel = sfrmodel, windmodel = windmodel, etawind = etawind, tausf = tausf,  \n",
    "                   cosmo = cosmo, verbose = verbose)\n",
    "    \n",
    "    # array of quantities to evolve with ODE solver\n",
    "    y0 = np.array([g.Mh, g.Mg, g.Ms, g.MZ, g.Mgh])\n",
    "    # evolve y0 in time\n",
    "    Mout = odeint(g.evolve, y0, t_output, rtol = 1.e-7, mxstep = 4000)\n",
    "    \n",
    "    # let's split the output into arrays with intuitive names\n",
    "    Mhout = np.clip(Mout[:,0],0.0,1.e100)\n",
    "    Mgout = np.clip(Mout[:,1],0.0,1.e100)\n",
    "    Msout = np.clip(Mout[:,2],0.0,1.e100)\n",
    "    MZout = np.clip(Mout[:,3],0.0,1.e100)\n",
    "    Mghout = np.clip(Mout[:,4],0.0,1.e100)\n",
    "\n",
    "    return zg, t_output, Mhout, Mgout, Msout, MZout, Mghout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp2d\n",
    "\n",
    "def compute_mass_grid_tcool(gmodel = None, Nz=81, Nm=60, Z_IGM=2.e-5, \n",
    "                      sfrmodel='gaslinear', tausf=2.0,  cosmo=None):\n",
    "    # grid of redshifts and halo masses\n",
    "    zg = np.linspace(30., 0., Nz)\n",
    "    lzg1 = np.log10(1.0+zg)\n",
    "    t_output = cosmo.age(zg)\n",
    "    \n",
    "    lMh = np.linspace(5.0, 8., Nm)\n",
    "    Mh  = np.power(10, lMh)\n",
    "\n",
    "    # arrays to hold evolutionary grids of halo mass, gas mass, stellar mass and metal mass\n",
    "    Mhout = np.zeros((Nm,Nz)); Mgout = np.zeros((Nm,Nz))\n",
    "    Msout = np.zeros((Nm,Nz)); MZout = np.zeros((Nm,Nz))\n",
    "    Mghout = np.zeros((Nm,Nz)); \n",
    "    #evolve a grid of halo masses\n",
    "    print(\"evolving mass grid...\")\n",
    "    for j, Mhd in enumerate(Mh):\n",
    "        #if not j%5:\n",
    "        #    print \"evolving halo of log10(Mh)=%2.2f ...\"%(lMh[j])\n",
    "        # instantiate a model galaxy with a given halo mass at the initial time\n",
    "        g = gmodel(t = t_output[0], Mh = Mhd, Mg = None, Ms = None, MZ = None, Mgh = None, \n",
    "                       Z_IGM = Z_IGM, verbose = False, tausf = 2.0, \n",
    "                       sfrmodel = sfrmodel,  cosmo = cosmo)\n",
    "        # initial values of masses\n",
    "        y0 = np.array([g.Mh, g.Mg, g.Ms, g.MZ, g.Mgh])\n",
    "        # solve the system of ODEs\n",
    "        Mout = odeint(g.evolve, y0, t_output, rtol = 1.e-5, mxstep = 4000)\n",
    "        # split Mout into arrays for specific masses with more intuitive names for convenience\n",
    "        Mhout[j,:] = Mout[:,0]; Mgout[j,:] = Mout[:,1]\n",
    "        Msout[j,:] = Mout[:,2]; MZout[j,:] = Mout[:,3]\n",
    "        Mghout[j,:] = Mout[:,4]\n",
    "    print(\"done.\")\n",
    "\n",
    "    # \n",
    "    # prepare 2D splines for interpolation\n",
    "    #\n",
    "    Mmin = 1.e-10 # prevent zeros in case no SF occurred\n",
    "    lMhi = interp2d(lzg1, lMh, np.log10(np.maximum(Mmin,Mhout)), bounds_error=True, kind='cubic')\n",
    "    lMgi = interp2d(lzg1, lMh, np.log10(np.maximum(Mmin,Mgout)), bounds_error=True, kind='cubic')\n",
    "    lMsi = interp2d(lzg1, lMh, np.log10(np.maximum(Mmin,Msout)), bounds_error=True, kind='cubic')\n",
    "    lMZi = interp2d(lzg1, lMh, np.log10(np.maximum(Mmin,MZout)), bounds_error=True, kind='cubic')\n",
    "    lMghi = interp2d(lzg1, lMh, np.log10(np.maximum(Mmin,Mghout)), bounds_error=True, kind='cubic')\n",
    "\n",
    "    return lMhi, lMgi, lMsi, lMZi, lMghi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evolving mass grid...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
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      "cooling function initialized...\n",
      "cooling function initialized...\n",
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      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "cooling function initialized...\n",
      "done.\n"
     ]
    }
   ],
   "source": [
    "from colossus.cosmology import cosmology\n",
    "\n",
    "# define a vector of cosmological parameters:    \n",
    "my_cosmo = {'flat': True, 'H0': 70.0, 'Om0': 0.27, 'Ob0': 0.045714, 'sigma8': 0.82, 'ns': 0.96}\n",
    "# set my_cosmo to be the current cosmology\n",
    "cosmo = cosmology.setCosmology('my_cosmo', my_cosmo)    \n",
    "\n",
    "lMhitc, lMgitc, lMsitc, lMZitc, lMghitc = compute_mass_grid_tcool(gmodel = gmodel_tcool, \n",
    "                                                   Nz=41, Nm=60, Z_IGM=2.e-5, \n",
    "                                                   sfrmodel='gaslinear', tausf=2.0, \n",
    "                                                   cosmo=cosmo)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# read in M*-Mh relation derived in hw4\n",
    "\n",
    "mhs, msmh = np.loadtxt(data_home_dir()+'mhmsz0.dat', usecols=(0,1), unpack=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bRO8/ehMeG253nDaV2zDzxZmUD7DiB7F5AFzaaLvzU19B1Y6Zr2/cqJbOO33a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\nBz4NY7XCELjGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbb510b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nm = 81\n",
    "lMh = np.linspace(5.0, 8., Nm)\n",
    "Mh  = np.power(10, lMh)\n",
    "#\n",
    "# plot\n",
    "#\n",
    "\n",
    "fig = plt.figure(figsize=(2.5, 2.5))\n",
    "plot_pretty()\n",
    "plt.xlabel(r'$M_h\\ \\rm (M_\\odot)$')\n",
    "plt.ylabel(r'$M_{\\star}\\ \\rm (M_\\odot)$')\n",
    "plt.xlim(1.e7,1.e15); plt.ylim(1.e4,1.e13)\n",
    "plt.xscale('log'); plt.yscale('log')\n",
    "\n",
    "lMhlin = np.linspace(6., 16, 100); Mhlin = 10.**lMhlin\n",
    "Mslin = Mhlin * cosmo.Ob0/cosmo.Om0\n",
    "plt.plot(Mhlin, Mslin, ':', c='gray', lw=1.5, label=r'$\\Omega_{\\rm b}/\\Omega_{\\rm m}\\, M_{\\rm h}$')\n",
    "\n",
    "z_plot = np.array([0., 2.2, 3.5, 6.0])\n",
    "# colors a la Feldmann for easier comparison\n",
    "zcolors = ['green', 'red', 'blue', 'darkgray']\n",
    "for i, zplot in enumerate(z_plot):\n",
    "    Mhz = 10.**lMhitc(np.log10(1.0+zplot),lMh)\n",
    "    Msz = 10.**lMsitc(np.log10(1.0+zplot),lMh)\n",
    "    plt.plot(Mhz, Msz, c=zcolors[i], lw=2.5, label=r'$z=%1.1f$'%zplot)\n",
    "            \n",
    "\n",
    "plt.plot(mhs, msmh, c='darkorange', lw=2.5, label=r'$z=0\\ \\rm AM$')\n",
    "\n",
    "plt.legend(frameon=False,loc='lower right', fontsize=7)\n",
    "plt.grid(linestyle='dotted', c='lightgray')\n",
    "plt.savefig('fig/mhms_Mhotonly_ex.png',bbox_inches='tight')\n",
    "plt.show()\n"
   ]
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