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An IPython notebook generating a curve of growth (rest equivalent width vs column density) for neutral hydrogen.
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"name": "Curve of growth"
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"cell_type": "markdown",
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"source": [
"Here we show how to calculate a curve of growth (the rest equivalent width as a function of column density) for the Lya transition of neutral hydrogen using the Barak package (https://github.com/nhmc/Barak)."
]
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"input": [
"from barak.absorb import calc_iontau, readatom, Nvel_from_tau, Nlam_from_tau\n",
"from barak.constants import c_kms, c, me, e, pi\n",
"from barak.spec import find_bin_edges\n",
"import pylab as plt\n",
"import numpy as np\n",
"\n",
"ATOMDAT = readatom()\n",
"# Lya\n",
"tr = ATOMDAT['HI'][0]\n",
"redshift = 1\n",
"wa0 = np.arange(1200, 1230, 0.01) \n",
"wedge = find_bin_edges(wa0)\n",
"dw0 = np.diff(wedge)\n",
"wa = wa0 * (1 + redshift)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 70
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"Wr = []\n",
"b = 20.\n",
"logNs = np.arange(12, 20.01, 0.2)\n",
"for logN in logNs:\n",
" tau = calc_iontau(wa, ATOMDAT['HI'], 1 + redshift, logN, b, maxdv=10000) \n",
" nfl = np.exp(-tau)\n",
" Wr.append(((1 - nfl) * dw0).sum())\n",
"\n",
"logN_plot = np.array([12, 13, 14, 15, 16, 17, 18, 19, 20], float)\n",
"nflux_plot = []\n",
"Wr_plot = []\n",
"for logN in logN_plot:\n",
" tau = calc_iontau(wa, ATOMDAT['HI'], 1 + redshift, logN, b, maxdv=10000) \n",
" nfl = np.exp(-tau)\n",
" nflux_plot.append(nfl)\n",
" Wr_plot.append(((1 - nfl)*dw0).sum()) \n"
],
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"prompt_number": 71
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"fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\n",
"\n",
"ax = axes[0]\n",
"\n",
"ax.semilogy(logNs, Wr)\n",
"# linear COG approximation\n",
"ax.semilogy(logNs, 10**logNs / 1.13e20 * tr['osc'] * tr['wa']**2, 'b--')\n",
"ax.semilogy(logN_plot, Wr_plot, 'ob')\n",
"ax.set_ylim(10**-2.9, 11)\n",
"ax.set_xlabel('$\\log\\ N\\ \\mathrm{(cm^{-2})}$')\n",
"ax.set_ylabel('Rest equivalent width ($\\AA$)')\n",
"\n",
"ax = axes[1]\n",
"for i,nfl in enumerate(nfluxes):\n",
" ax.plot(wa0, nfl, label=str(logN_plot[i]))\n",
"ax.legend(frameon=False)\n",
"ax.set_xlim(tr['wa'] - 1.5, tr['wa'] + 1.5)\n",
"ax.set_ylabel('Transmission')\n",
"ax.set_xlabel('Wavelength ($\\AA$)')"
],
"language": "python",
"metadata": {},
"outputs": [
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"prompt_number": 72,
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