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@bamford
Last active August 10, 2017 09:22
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Ferrer versus Sersic profile
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{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "%matplotlib inline\nfrom matplotlib import pyplot as plt\n# better-looking plots\nplt.rcParams['figure.figsize'] = (8.0, 5.0)\nplt.rcParams['font.family'] = 'serif'\nplt.rcParams['mathtext.fontset'] = 'dejavuserif'\nplt.rcParams['font.size'] = 16",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def ferrer(rout, alpha, beta):\n # Modifed Ferrer profile, normalised to unity at r=0\n def wrapper(r):\n x = np.where(r < rout, r, 0)\n f = (1-(x/rout)**(2-beta))**alpha\n f[r > rout] = 0\n return f\n return wrapper",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def sersic(re, n):\n # Sersic profile, normalised to unity at r=0\n return lambda r: np.exp(-((r/re)**(1.0/n) - 1 ))/exp(1)",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def ferrer_frac(f, rout, alpha, beta):\n # the radius at which the Ferrer profile has value f\n return rout * (1 - f**(1.0/alpha))**(1.0/(2-beta))",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def sersic_frac(f, re, n):\n # the radius at which the Sersic profile has value f\n return re * (1 - np.log(f * exp(1)))**n",
"execution_count": 5,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def rf(f, n):\n # the re for a Sersic profile to cross a Ferrer profile at value f\n return ferrer_frac(f, 1, 2.5, 0)/sersic_frac(f, 1, n)",
"execution_count": 6,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "r = np.linspace(0.0, 1.4, 1000)",
"execution_count": 7,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# plot profiles on linear scale, normalised at half-maximum\nplt.plot(r, ferrer(1, 2.5, 0)(r), label='ferrer (2.5, 0)', c='k', lw=5, alpha=0.3)\nplt.plot(r, sersic(rf(0.5, 0.5), 0.5)(r), label='sersic (0.5)', ls='--')\nplt.plot(r, sersic(rf(0.5, 0.4), 0.4)(r), label='sersic (0.4)', ls='--')\nplt.plot(r, sersic(rf(0.5, 0.25), 0.25)(r), label='sersic (0.3)', ls='--')\nplt.plot(r, sersic(rf(0.5, 0.1), 0.1)(r), label='sersic (0.1)', ls='--')\nplt.hlines(0.5, 0, 1.5, linestyle=':')\nplt.legend()\nplt.ylim(0, 1.1)\nplt.xlim(0, 1.4)\nplt.ylabel('$f\\,/\\,f(r=0)$')\nplt.xlabel('$r\\,/\\,r_{out}$');",
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x116c41048>",
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nZ2c6duxIXFwcHTp0YO3atWRkZNC/f39atWpVbNsOHDhAVlYWLVuafpjx8/Pj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VOsQXG+2lqCHR393kscDlzFxVZ5TQ3BAeMGxOXCVVRklVdXE+zp/3wLW5IL5/jxAHirqjG+AeVu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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# plot profiles on log scale, normalised at tenth-maximum\nplt.plot(r, ferrer(1, 2.5, 0)(r), label='ferrer (2.5, 0)', c='k', lw=5, alpha=0.3)\nplt.plot(r, sersic(rf(0.1, 0.5), 0.5)(r), label='sersic (0.5)', ls='--')\nplt.plot(r, sersic(rf(0.1, 0.4), 0.4)(r), label='sersic (0.4)', ls='--')\nplt.plot(r, sersic(rf(0.1, 0.25), 0.25)(r), label='sersic (0.3)', ls='--')\nplt.plot(r, sersic(rf(0.1, 0.1), 0.1)(r), label='sersic (0.1)', ls='--')\nplt.hlines(0.1, 0, 1.5, linestyle=':')\nplt.legend(loc='lower left')\nplt.yscale('log')\nplt.ylim(1e-3, 2.0)\nplt.xlim(0, 1.4)\nplt.ylabel('$f\\,/\\,f(r=0)$')\nplt.xlabel('$r\\,/\\,r_{out}$');",
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x11865cc50>",
"image/png": 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/Fd9k5qOU4qx+XbhuZDcGpUQcVkuFY+0sAj+/Fh+K3KixbO1yHnWW5ucdMZvN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},
"metadata": {}
}
]
}
],
"metadata": {
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"kernelspec": {
"name": "conda-env-py3.6-py",
"display_name": "Python [conda env:py3.6]",
"language": "python"
},
"language_info": {
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"mimetype": "text/x-python",
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},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"latex_envs": {
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"current_citInitial": 1,
"cite_by": "apalike",
"bibliofile": "biblio.bib",
"LaTeX_envs_menu_present": true,
"labels_anchors": false,
"latex_user_defs": false,
"user_envs_cfg": false,
"report_style_numbering": false,
"autocomplete": true,
"hotkeys": {
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"itemize": "Ctrl-I"
}
},
"gist": {
"id": "6d11b67851c3237829725cef89e480ed",
"data": {
"description": "Ferrer versus Sersic profile",
"public": true
}
},
"_draft": {
"nbviewer_url": "https://gist.github.com/6d11b67851c3237829725cef89e480ed"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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