{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Data simulation and cross correlation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we are going to start with the stellar simulation from last, where we took a template spectrum and convolved it with a smoothing kernel. Now we are going to finish it by adding noise.\n", "

\n", "After that, we'll simulate a spectrum with a radial velocity, and see if we can recover it using cross-correlation, experimenting with different S/N." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The keymap.all_axes rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The animation.avconv_path rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n", "The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Spectrum simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start with our simulation of a stellar spectrum from last time." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "minimum dispersion: 0.300000 maximum dispersion: 0.300000\n", "using dispersion: 0.300000\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#read in stellar model, plot and determine dispersion\n", "from astropy.io import ascii\n", "a=ascii.read('star.txt')\n", "\n", "wave=a['WAVE']\n", "plt.plot(wave,a['FLUX'])\n", "dispersion=wave[1:]-wave[0:-1]\n", "print('minimum dispersion: {:f} maximum dispersion: {:f}'.format(dispersion.min(),dispersion.max()))\n", "disp=dispersion.mean()\n", "print('using dispersion: {:f}'.format(disp))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we'll simulate a low resolution spectrum with $\\delta\\lambda=2.5$ Angstrom. Create the smoothing kernel for this resolution, in the pixel units of our model spectrum." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dlambda = 2.5 # delta(lambda) in Angtroms\n", "sig = 2.5/2.354 # corresponding sigma in Angstyroms\n", "sig_pixels = sig / disp # corresponding sigma in pixels, given disp\n", "\n", "def gauss(x,mean=0,sig=1) :\n", " \"\"\" Return normalized Gaussian function here\"\"\"\n", " return 1/sig/np.sqrt(2*np.pi)*np.exp(-(x-mean)**2/2/sig**2) # add code here\n", "\n", "# create a gaussian kernel with this sigma. Let this extend from -5*sig to 5*sig. Note that we want this to be an odd \n", "# number to prevent the convolution from shifting the spectrum.\n", "x=np.arange(-5*sig_pixels,5*sig_pixels+1)\n", "kernel= gauss(x,0,sig_pixels) #use your gauss routine to fill the kernel array\n", "\n", "# plot it\n", "plt.plot(kernel)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now convolve our spectrum with the smoothing kernel using numpy.convolve()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000.0, 5050.0)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tEH0QtIlLrg34+kZbGt8zjmHdCrgYfUosbH8XQhaQ6ebD+JTJXHBtwpIJ7ahdxc3in7O4Pt4UiuvOGUx2+BFGLDMv2VdIaw5HM2vrOS5cS8XZwY7hbXx5/p4GVCpl3+/YhOs4ftaUmMpBNHxmjeV3YDKR8Ek7EpJSYMp+6lUt2jUVpVSI1rqAX7gClFfWwl1rTWhMMvvDE2jqU57WNSva/C/lnO3n+L9fQhnayoe3BjehvIsj5GRB8mXzL7lbFahY5y9DrY5HJ3H/f/fQLcCbr8a2KTV/3Ysq16TZfvQcx3esxCs+mOYOkdR3iMUlJxmFBufy4OkHNduBf08I6Ie2c2B7aCzPrjiKk4MdC8a1pUkNy3YJTP/xJAv3RrDkXkc6Hn0V4sOg2QPQ5QXwbnj7NyfHwMnV6KMrUFcOk6sVSdU7UandKKjT1dyF85dGyDb/QTi+Eg4vAVM2FxuMY9DJLlSsUJElE9pR3bOI0/ZaWUhkAiP+u4vgqu/hmRMPk38r1G34aw5H8+yKozSpUZ7HOtXhYEQCqw5F09KvAksntsexFF2o3bHiM7qf/jeXBq3Ap3U/q+wjYf8yKm14gi1NP6T38MeLVMZdHe5nrt7gySWHCI9L/eO5BlU9+GBYM1rVrGjx/eXn9y/14JY1+OTBltglnIMDc+Hocsi8aY4JNy9oMhS6PA8e1QD4Zs8F3lp3ircGNeGRjrVtUl9LysjOZXdoDFEH11Ev6js6mA7jqHLJdHDHwacl9l4NoFxl811/6dfhWhhcPABZyeBeFQIfgw5PEZaoGfv1AdKycln/dGeLHcGfuXqD+2btZqb/UYZe/ti8z4GfQb1ehS4r9fIpflj4KV0ztuGr8sYwe1Q3/zi7mxeivh4BWSlg7wQtR7GzykgmrL+Ov7c7344PKtXdFLkmTdC7W7jf9wavXXoSqjYxL9PndOezjPNxKQz8fDdNa3iydGI7HPKC/Icjl5i6/AjjO9fhjQGNrf0RCkRrzekZ7fEkGZ/XTxZvbPvtmHKJntGMHDtnar92qEj7KRvh3qa1Dg45ZNEyfzt/jccXhVDO2Z5/9Q6gQ93K7AuP5/Nt58jMyeWHpzrjU8G6R0mXEtPp9dEOWvpVYOGjbXA+MAe2vWv+H9l4CNTtBm7ecCMaIvbAqbVg5wjdp0Gnf6GBsV8f4MSlJHZN63nLbpzSJCk9m00nr7Ll5GXKn/+RJ1iFv90VbthXJN5/KH4dH8ShZtCtb+POzYHz28zziof9Yg7c3tOJ9B3EgNl7qFmpHKsmd8TFsXgXm7XWjJ77G/ddmc1ofoa6PWD411Cu6KNTLiemM2T2bhrbRfFJhzQqJp6C1FjITDb/ESvvYz6ir9uNFceTeHXNCZr7erLg0SA8yzkW6/PYwsurjrH+2BUOP5iF4/djof498NASsL/19zI718Sg2Xu4mpTOz1O7/OPM5M0fTrBwbyRzH27DPU2qWfsj3NHZkyEErOxJSMBztBn1plX39dO3H3Hf+bdJHb4Ut6aFv/vV0uGO1triP21qe2qdla4tJSQyQdd/9Wfd+6MdOvp62l9eC4tJ1k3/vVH3/2ynTsvMsdg+8/PU0kM64LWf9aWYWK0XDtL6zfJaLx+jdXJM/m+IP6/1slHm7ZaN0jo9SR+Ouq5rTVuv52wPs2pdiys1M1vP3hamm765UQ97eaYOnd5c6zfL65SPA3X2ke+0zs4sfKFRB7T+qvcf7bHj8Glda9p6/dLKo8Wu7y9HLuifXs8re8PLWuda5rtwPDpRN3tzo+74/lZ9IS7lH6/n5pr0fzaYP8fD8/frlIxsi+zXFradjtG1pq3X207HaL1/rrntFgzUOjn2lu/5dm+ErjVtvd5w/Eq+r2dm5+reH+3QPWZu19k5udaqeoHt+u8Unf3vCjoxJsrq+woOv6qj3vDXCZ921tpkKvT7gWBtwRy2TsdYZgr6u4chJ7PYRcUlZzJ5cQhVPZ357vEO/zg6r+ftzqxRrTh15QafbDlb7P3dSnBEAuuOXuaZjl7U+HEkXNgFA2fBg4tu3VdZqS48tBj6vgehG2DhAFpW0fRo4MVXO8NJycyxWn2LIzI+lYGf7+aLX47whfs3fO/8NvU9cmD417hN3Y9DiwfAoQgXzfzawmO/wD0z4OwvdNs6lA9aXWdF8EV2hRX99m1TagLVfxxFf/sDmO55F/q9X7QJofLR1MeTpRPbk5aVw/D/7WXp/igyc3Ix5Y0SGfLFHr7YcZ6RQTWZ/0ggbmXgbOx3HetVxt3ZgV9OXoWgiTBoNlzcD192MS8InZX2l+0zsnOZtTWMwFoV6dukar5lOjnY8fw9DQiPS2V1Ca/Zmp2dTcDVnzjlFoSntwXuXbiDlrW8WWQ/hIrXj8GFX62+vzuxSrdM9erV9JXH06FWZxixGFyL1h+ek2ti1Lz9HItOZPXkTjSuceur0M+uOMKGE1fY+VIPi984pLVmyBe/kZSYwNYqH2EfcwIeWACNCrFuydlNsGI0eDfmeK9FDJx3gpf6NeDJ7vUsWtfiCo5IYOKiYJrqs8x1+xLX1GjzAgXdphWoP7bALh+BVePR8edZ4ng/C5xG8dOzPQp/L0BiFCnzh+B4I5Kjbf9D0IAJlqvjTc7GJPPi98c4ejGRck72ZOWYyDFpqpV3Ydq9DRjS0qdMXiR/etlhfjt3jQOv9cbeTsGVY7B2MsScAGdP83qseReSwy/HEnn1Gq19yuFZobL5ulKdrhDQD5z+vG6itWbwnD3Ep2Sx7YVuJXZ/x6Ftq2i98zGOdphFi76P2GSfLy3bzwuhD+Hl1xD12IZC9b1bulvGKkfuua6VmJo9BdPF/TCvD8SeKVI5czafxDVyO2sa76TxzsmweBgsHQE7PoDoEPNQtjxTe9UnO1fz3x3nLfUx/rA3PJ7jFxNYXHEe9lePwkPfFi7YAQLy+jNjT9Hs14n09Pdg0W+R5OSaLF7fogqLSWbcNwd4xHEri9R0XB2AcRvMCxpYMtjBPM/J4ztRrcYwJnsV/0l+mWW/7ClcGRG70XO7Q8pVXnKdTut7rXe3ZUBVD9Y+2ZHF49sxrLUvk7rW5b2hzdj2QjeGtvItk8EO0LdJVeJTswiOyFsLtHpzeGK3+f97k8FgyoELuzBF7EHHhVLLNR1PJyDhApxcDd+Pg5n1YdfHYMoFQCnFi30bcCkxne+Co0vss+UeWkwS7jTu/qDN9tmlsR+fZt+PurgXzqy32X7zY5Uj99Zt2uha42fhenkfC9w+xyknDXq8Ch2mgP0dLjTlZkP4DuL2LsXl/AY8VDooO6hcD5zcITsN4kIBDb5tod9/wLcNAC99f5S1Ry7z64vdLToEbfyCg/SI/Iwxeh30n2k+hS2qUz/Ad48Q49uX9ufG8N8xgfRrWt1idS2q+JRM7p+zk2cy5jJMbzJfXLt/bpHPugrl+Pekr3manFxNbq/pVOg86fZzf+Rmw57PYMf7pLrXZEDcFCYP68uDgdY/9Taa1Mwc2r23lV6NvPlsRKtbbvfxplBmbTvH+qc709Qnb/iqKRci98D+L81BVrOD+SJ2+Rrms905e0jJzGHzs91sN7VxnqTEeJw/acAxr4EEPfWN7fabnk3bdzbym+cbVHFV8OT+AndhlokjdzulWPBoEIleQfRIe5/4Gt1gy5vwWQvzL+W1sL8cdZORBOe3w7p/wcwAWDIcl/CN7HbsSMaDK+Dli/DUQZi0HabshxfPw4BPIDEK5vWEzf8GUy5P96yPyaT5evcFi32W8LgUyp1daw72oEnFC3aAxoPhnhlUjd7Iu24r+XZfpGUqWgwmk+b5Zft5NfVDc7B3+heMXGGbYAdoNpzEsds4oetSYds0mN8bTq/740jwD7k55msXc7vDtnfQDQcwwfFDsjzrMrSVj23qajBuzg48EOjLT8euEJPPXcVgvuN33u4L3Nes+p/BDubrGnW6mq8rDf0Srh6HRUMgLQGlFI92qs35uFR2n7tmmw9zk7Cti3BR2Xh2fNSm+/V0daRNbS8+YgwkhJvvjC4hVrvTwLOcI9+OD8KtUg06XhjHsW7zzBcYN/8bZgfCB7Xg4yYwswF8UBO+HQLHVmCq252ZlabTPudLfB/9BpfG/czjim/mVtk8ZvrpEGgzzvwHY/ko/Nxy6dO4Kt+HRJOZk5tftQpt3dbtfOD4Fdk1gswXRi2hwxQImsSo3B+oe2EZ52JLdk3L7347xaSoafS1OwD9PoA+b1lm1rxCqF67ETs7zOf5rCfISoqBFWPg40bmbrj1z8Ly0fBpU1g2wjyGfsRS9rT6iL2Xspjc3b9U3TRT1jzasTa5WrPkFgca/91xnozsXJ7tE5B/AUpBixEwcrl57P+SByArlf7NqlPF3ZkFv0VYre63Uj70OyKULwEtu9h83wNaVGfZ9Yak+HaFbTPgeskcwFn1N6KyuzPLJ3XA38uD4VvcWddqLjwVbJ7Lotlw87jwer2h179h1Ep48RzvuLzA7MsBvD209Z0nWnL2MK9c3n8mhG2GJQ8yurUX19Oy2XjiarHrf+PGde47PQ2TQzkcRyy8c5dSQSkF/T4g078f0x0WcmDjEsuUWwSXoqNotnk0Qfah6KFfQvvJJVaXJ3vUY4drb8a6f4l+YKH5qPB6BJxcA/HnwTfQfN1i6lFoeB+z8qZ/eCDQt8TqbAS1KrvRq6E3S/JGAt3sbEwy3+6LZHgbX+p5u9+ihDx1upi7ZS4fgp9ewNnBntHtarI9NJaIa6m3f68FxUedIiDrFFE1h6BsfJAC0L9pdRzs7Pi2yrOAMk8iZ7L9tTWrf/JKbk4sm9ie5r6ePL3sMJ8dAd3qYRjwMQz5AobMgS7PY6rXhxmbIvlmTwTjOtVmWJtC/MIGTTT3D0ftpVPIv6hTwYFlB6KKV3GtiV82mTpcJu6e2VC+RvHK+zs7e5wf+ppLrgEMOf8GGZEHLVt+AZgSIrD7ph91uUTi4IWoFhacCrUIPFwcef6eBuyLSGJtViAMmwdT9sG0CPO/Dy02X8i2d2R/eDwHLiTweLe6d81sm9b0aMc6xKdm8fnWPydWS8nM4YnFIXi6OvJC3wYFK6jRAOj8LBxdCmd+ZnS7mtgrxdLi/j4WQvT2+eRqhW+3R222z5tVdHOiS/0qLD4Duu+7ELEL9v/X5vWwyZ81z3KOLJnYjvtb+/DJlrMM/99ejlxM/OP1c7HJPLnkEPN2X+DRjrV5/b4i3LrcbDgMmoU6v5V57v/jYHgc4XHF6O44OI86Vzaw2HUMdYKKuNbinTi5kTD4W+J1efSSh2x7+hZ7mowv+1Au5zq7OsyjSquBttv3bYxo60dLvwrMWH+apLTsfLfJzjXx5o8nqVremZFBNW1cQ2PqVK8yDwX6MXv7OebtCicsJpnnVhwh4loqn49sVbjhxd2mQdWmsG4q3g5pdG/gzdrDl2wzMsxkokbkDxxybE3duvWtv79bGNiiBpcS0zlUeQA06G+effPUjzatg83OWZwd7PnogRZ8OLw5UQlpDJmzh1Zvb6LHzB30/ngnW07H8Gr/hrw5sLF5vG1RtB4L/T7A/9o2ZjrOZcWBIoZl5G+YNr7CttyW2HV9zqrD3Fo0DOCdCm+Tk52BXvKAuT/Z2i4eIHd+P1Iysvmg2if06TvI+vssIDs7xbtDm3I9LYsPNp7Od5u5O8M5czWZdwY3Lfa0BcJMKcV79zfj3qbVmPHTafp8spNNp2J4+d6GtK9buXCFOTjD0P9BegJsmc6w1j7EJmey53y8dSp/k/iTW/AyxZFQf7jV93U79zSphrODHT8evWI+A/UJhFXj4dxWm9XBph1SSikeDPRj+wvdeXNgY/o3q46/lzuv9W/E3ld6Mamrf/GDtP1k6PE6Q+13ERAynZzCXli9HgkrxhDvWI2XeYrBra07vE4pRfdOnZmQ8Rw64QIsH2ORO3tvKWwzetFg4nLK8TDv8NTIwaVujHaTGp6M71yHZQcu/mPkU1hMMp9tDaN/s2qlYu4SI7G3U3w6oiVvDGjM/w1vzo4XujOpq3/RCqvWDNpOgMPf0qtKPJ6ujqw+ZP0x74l7F3JDl6NeF9uNbc+Pu7MDfZtUY/WhSySbnGD0d1C5PiwZbj6Kz07/6xusMCS9RO6Vdnd2YFynOtbbQdcXCL8cw7DQr7i48jn8RnxasDvF0hJg2Qi0KYdHM56nS7MA83S+Vja4ZQ3e/7kZC71eZFzku/D9Y+YLU5ZcMUZr8+yVG18mwSOAAbFTeW6o9SdbK6pp/RoSlZDG2+tPoYH7W/kQEnmd51cexc3JnumDmpR0FQ3J2cGe8Z0t9LvZbRocWYbTtrcY2OLffB8STXJGNh7W+p3KTMbnymY2O3VnYI2SXxFpQpc6/Hj0MisOXmRCl7rw2EbY/IZ5fYFD35rXF6hY23yGc2GXxfdvzPFjSuE7/D8soT9+oQvg5xfMY6RvJzUeFg6EhHB+bfERJzO9GRlkm5ti3JwdeKRjbd6KbMLVDtPNN4QsHgYZN+743gLJSoUfn4YNL5FWpw99E1+hUX1/m32+onCwt2PWyFZ0C/DinfWnaPXOZiYsCsa3oitrp3SStWnLgnKVoOsLELaJR6pFkpFtYoMFRrHdStqR1bjoTJICSrZL5nfNfSvQrk4lvtkTQXauCVzKm6egfmQ9NBxgng5772w4+wtUsPy1ozI1n3thTf/hBD4hHzDRbp15wYhh8/OfAvbqcVg1wTzsbuQyhmx0zruzrqvNuiyS0rPp8p9ttK1difmtwuGHJ80LfgyfD9VbFL3gy0dg9US4FkZu5+cYFdaLk1dT+OXZrqX2qP1mObkmDkQkcCw6Ca1hXKfa0s9elmRnwOdt0BX86HZtGnWquLHwsSCr7Cru894kx10kafxeWtUq4YXI82w9HcP4hcF8NqIlg1vmc6Od1qAUuSaNg71d6b9DtbQYHujHu1kj+a3JdPNpz2ctYddH5jHTOZnm4Nv8pvmOx7QEGL2SM26BHLmYyIi2fjbti/Z0deTxbv5sPRNLSIU+8PAa80IQX/Uyz6WTmVy4AlNiYd1U82fLuAFj1/JO2jD2RyYyY0jTMhHsYD6C7+hfhSe6+TO5u78Ee1nj6AKdpqKi9jKp5hX2nLt2y1FQxXI9Aq/4g/zi2IMWfja6s7oAejTwxt/LjU82nyU1v1lg8zLmvZ/zHzxQHIYO9yY1ytOkRnneim6DnrQDanWErW/D561hhjfM7QZ7PjWvmDRlP9TpyvIDF3Gyt+P+1ra/MWZcp9pUcXfmtTUnSKnR0bz0WaMBsON989QNOz4wT91wK7nZ5kVC1kyGT5rC4cXmC8xT9vH99Xos+M18D8EQuVVf2FLrh8HNm0E3lpJj0mw+HWPxXeQcXopJK5IDhtl8HpvbsbNTzBjSjMiENN5adzLfbRbsucB8C06Z8ruyM/l0ESileKRDbV5adYz9aU1oP2q5eTHkq8fNXTCV6phX7PEwz02dmpnD6kPR9G1arUQW+S3n5MDHD7Zg3IKDPLPsMF+NDcT+gQXQ4SnY/p453He8T255P5I86pPhWhU3V1c8VBp2SdFw5Yj5aN/RzfwL1W4yVKnH4n2RvPHDCTrUrcyr/RvZ/HOJu5yjK3SYQvktb9LLYwAbjnszvDA3Kd6J1uQcWkaIqTGtmjW3XLkW0sG/MlO612P29nO0rV2JB/ImuDOZNDM3hfLFjvP0buSNpWehMXS4AwxqWYP3Npxm0d4I83jdak3NP/lYuj+KGxk5PNaptm0reZOuAV5MH9SEN9aeYNyCgzzasRZ+FRsQ3voLjrucxu7MOvyvn6ZBYhiVVQiQTSyupJSrgb3PALxb3otbg57gUp6Ia6l8teY4S/ZH0bOhN3NGtZY5WETJaDsedn/CSy4/MTCsFjcysi03Ei1qLy4pUazRk3mzbunoa/+7qb3rsy88nhe/P8baI5do5VeRnWFxHItOYmSQH28Pbsr8Ry27zzuGu1LKBdgJOOdt/73W2rqLEVqQi6M9Dwb6MX/3Ba4mZVDNM/9RFpk5uXy1K5yO/pVtttj2rTzcvhZpmTl8uTOcxxb8eWHaxdGOrvVHUcm/MgnVPEi2tyMqPo2DEQlsOR3LtdOZOIQqfCqGoDVcvJ6GvVI80qEWrw9oLMEuSo6zB7SfTIMd71PH1J9tp2Mt1z14ZClpuBLj09d6wyyLydHejsUT2rFkfxRztp9jX3gCTX08eWdIU8a0q2mV63t3HC2jzHt101qnKKUcgd3AVK31vlu9p7SMlvldVHwa3WZu57FOt16Vfen+KF5dc5wlE9rRqV7Jj5EFyMox8evZOFIys6lTxZ0GVT1wdcr/gqLJpDkSnciWUzFcSjTfIFG3ijsjg/zwLi/DBkUpkJaA/rQZm7Jb8GO9GcwZ3br4ZWYmY/qoIavSWhPT82Oe6llyUw4UVGZOLjm5+h9LMlp6Pvc7HrnnLdz6+yQtjnk/lh8/aUU1K5fjwTZ+LPwtgpFBNf8xu116Vi7//fUcLfwq0NG/kLdaW5GTgx19Gue/VuXf2dkpWtesSOsSPusQ4pbKVUK1nUCfPbP47OwxsnJa4uRQzLPJY99hl5XC0txeTK/vZZl6Wpmzgz22WGq3QC2rlLJXSh0BYoHNWuv9+WwzSSkVrJQKjosr+mLH1vJivwa4Otnz1rqT/P1s5Z2fThF9PZ1p/RqUulvxhTCUDk+h7Rx5NHc1By4kFK8srSH4a6Jd6hHh0uivC4mIgoW71jpXa90S8AWClFL/uCKptZ6rtQ7UWgd6eZW+v6BV3J15tncAu8Ku/WX60Y0nrrJ0fxSTutalo3/p6I4RwrDcvTC1foSh9rsJPnKkeGVd3A8xJ1iY3ZtO9b2KPuGgQRXq5EBrnaiU2gH0A05YpUZW9HCHWmw+FcNra06wLzwBRzvF+uNXaO7ryfN9CjhftRCiWBy7/Ivs4G+oHToXrXsV/Wz54HxynTxYfCOIt8pIl4wt3fHIXSnlpZSqkPfYFegNnLFyvazC0d6Ob8cH8WzvAH4+foXNp2J4KNCPr8YGFr/vTwhRMJ4+XPAbwr3ZW7kQfpub8m4n6RKcXMMp7wGk40KXADnr/ruCHLlXBxYqpewx/zH4Tmu93rrVsh4Hezum9q7PqHY1cXO2p5yT4Yf6C1HqVOjzAvbzV5G29UPwn1f4An6bBWjm5/anvrc71T3LxnQatlSQ0TLHgFY2qItNeXlYcDpdIUSheNdsyE8u/eh7eTXEvwKVCzFvfEochCwkp+kD/HzIkYfbS5dMfqQvQghRIi42f4ZM7UDWL4W8J3LfHMjJ4FDNcWTlmOhSX7pk8iPhLoQoER1bNGJuzgCczq4zz21eEEmX4MBX0Hgwm6564ORgR7s6pefelNJEwl0IUSKa1vBkjetQEu0rmxeTyc6485s2TgNTDvSezq6wawTVrnTLu7bvdhLuQogSYWen6NioFtNyHoe4M7Dtndu/IXQDnF4H3V7iqn11QmOSpUvmNiTchRAlplejqvyS2ZTL9ceYl5wL25L/holRsP458GoEHZ5mV5j5LvguMr79liTchRAlpnO9Kjg72PFNuXHg3QSWjzQfnd8s6ZJ5fePsVLh/Ljg4sSvsGlXcnWlU3aNkKl4GSLgLIUqMq5M9nepVYWPYDfSj683rBX83Fn54Ck6uhW3vwlc9zctgPrwGqjfHZNLsPneNrvWryFxQtyHhLoQoUb0aeXMxIZ2wZEcY+wO0HAWnfoCVj8CumVC1sfl5nzYAnLx8g4TULLkr9Q7k9kwhRInq1bAqr3GCLadjCOheDwbPgfs+gcuHoYIflK/xl+135vW3d64n/e23I0fuQogSVc3ThaY+5dl6OvbPJx2coGa7fwQ7wM6zcTSuXl7uMr8DCXchRInr1bAqh6KuE5+SedvtElKzCIm8TrcGctR+JxLuQogS16uRN1rD9tDbL/Tz8/Er5Jg0A5pXt1HNyi4JdyFEiWtawxOfCq6sORx92+1+PHoZfy83Glcvb6OalV0S7kKIEmdnpxjR1o895+KJuJaa7zaXE9M5GJHA4JY+MgSyACTchRClwgOBftjbKZYfvJjv6+uPXUZrGNTinxdZxT9JuAshSoVqni70bOjN9yEXycox/eU1rTVrD1+mha8ntau4lVANyxYJdyFEqTGqXU2upWSx8eTVvzy//tgVTl25wYigmiVUs7JHwl0IUWp0re9FQFV33l53kpgb5imAUzJzmPHTKZr6lOfBQL8SrmHZIeEuhCg17O0Uc0a1JjUzl6eWHuJ8XAoz1p8i5kYm7wxuir2dXEgtKJl+QAhRqtSv6sEHw5oxdfkRen30KwCj29WkVc2KJVyzskXCXQhR6gxu6QNAZo6JgKoeNPfxLOEalT0S7kKIUun3gBdFI33uQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQBLuQghhQHcMd6WUn1Jqu1LqtFLqpFJqqi0qJoQQougKMnFYDvC81vqQUsoDCFFKbdZan7Jy3YQQQhTRHY/ctdZXtNaH8h4nA6cBma5NCCFKsUL1uSulagOtgP35vDZJKRWslAqOi4uzUPWEEEIURYHDXSnlDqwC/qW1vvH317XWc7XWgVrrQC8vL0vWUQghRCEVKNyVUo6Yg32J1nq1daskhBCiuAoyWkYB84HTWuuPrV8lIYQQxVWQI/dOwMNAT6XUkbyf/laulxBCiGK441BIrfVuQNmgLkIIISxE7lAVQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDknAXQggDumO4K6W+VkrFKqVO2KJCQgghiq8gR+4LgH5WrocQQggLumO4a613Agk2qIsQQggLkT53IYQwIIuFu1JqklIqWCkVHBcXZ6lihRBCFIHFwl1rPVdrHai1DvTy8rJUsUIIIYpAumWEEMKACjIUchmwF2iglIpWSo23frWEEEIUh8OdNtBaj7RFRYQQQliOdMsIIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBSbgLIYQBFSjclVL9lFKhSqlzSqmXrV0pIYQQxXPHcFdK2QNzgHuBxsBIpVRja1dMCCFE0RXkyD0IOKe1DtdaZwHLgcHWrZYQQojiKEi4+wAXb/rv6Lzn/kIpNUkpFayUCo6Li7NU/YQQQhRBQcJd5fOc/scTWs/VWgdqrQO9vLyKXzMhhBBFVpBwjwb8bvpvX+CydaojhBDCEgoS7geB+kqpOkopJ2AE8KN1qyWEEKI4HO60gdY6Ryn1FPALYA98rbU+afWaCSGEKLI7hjuA1vpn4Gcr10UIIYSFyB2qQghhQBLuQghhQErrf4xqLH6hSiUDoRYvuGyqAlwr6UqUAtIOf5K2+JO0xZ8aaK09LFVYgfrciyBUax1opbLLFKVUsLSFtMPNpC3+JG3xJ6VUsCXLk24ZIYQwIAl3IYQwIGuF+1wrlVsWSVuYSTv8SdriT9IWf7JoW1jlgqoQQoiSJd0yQghhQBLuQghhQAUOd6VUhFLquFLqyO9DdpRSlZRSm5VSYXn/Vrxp+1fyluULVUr1ven5NnnlnFNKzVJK5TelcKlWmLZQSlVWSm1XSqUopWb/rZy7rS36KKVC8rYPUUr1vKmcu60tgvK2O6KUOqqUGnpTOWW6LQqbFXmv18z7HXnhpufKdDtAob8TtZVS6Td9L/53UzmFbwutdYF+gAigyt+e+xB4Oe/xy8B/8h43Bo4CzkAd4Dxgn/faAaAD5nniNwD3FrQOpeWnkG3hBnQGngBm/+09d1tbtAJq5D1uCly6i9uiHOCQ97g6EHvTf5fptihMO9z0+ipgJfDCXfydqA2cuEU5hW6L4nbLDAYW5j1eCAy56fnlWutMrfUF4BwQpJSqDpTXWu/V5hovuuk9ZV2+baG1TtVa7wYybt74Lm2Lw1rr39cCOAm4KKWc79K2SNNa5+Q970LeAjgGbotbZQVKqSFAOObvxO/PGbUd4DZtkZ+itkVhwl0Dm/JOpyflPVdVa30FIO9f77znb7U0n0/e478/X9YUpi1u5W5vi2HAYa11JndpWyil2imlTgLHgSfywt4IbVHgdlBKuQHTgLf+VoYR2gEK//tRRyl1WCn1q1KqS95zRWqLwkw/0ElrfVkp5Q1sVkqduc22t1qar0BL9pUBhWmLW7lr20Ip1QT4D3DP70/ls5nh20JrvR9oopRqBCxUSm3AGG1RmHZ4C/hEa53yt25kI7QDFK4trgA1tdbxSqk2wNq835UitUWBw/3302mtdaxSag0QBMQopaprra/knTrE5m1+q6X5ovMe//35MqWQbXErd2VbKKV8gTXAWK31+byn78q2uOl9p5VSqZivQ5T5tihkO7QDhiulPgQqACalVAbmPvgy3Q5QuLbIO4vNzHscopQ6DwRQxO9EgbpllFJuSimP3x9jPuI6gXm5vUfyNnsE+CHv8Y/AiLz+1DpAfeBA3ilIslKqfd7V3rE3vadMKEJb5OtubAulVAXgJ+AVrfWe38u5S9uijlLKIe9xLaABEFHW26Kw7aC17qK1rq21rg18CryntZ5d1tsBivSd8FJK2ec9ros5N8OL3BYFvOJbF/Pol6OYL3q8lvd8ZWArEJb3b6Wb3vMa5lEyodx0ZRcIzPuA54HZ5N0lW1Z+itgWEUACkIL5r3Dju7EtgNeBVODITT/ed2lbPJy33RHgEDDkprLKbFsU5ffjpvdO56+jZcpsOxTxOzEsb7ujed+JgcVpC5l+QAghDEjuUBVCCAOScBdCCAOScBdCCAOScBdCCAOScBdCCAOScBdCCAOScBdCCAP6fzduIbLNyPZCAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sim=np.convolve(a['FLUX'],kernel,mode='same')\n", "plt.clf()\n", "plt.plot(wave,a['FLUX'])\n", "plt.plot(wave,sim)\n", "plt.xlim(5000,5050)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, let's add noise to the image. Suppose we want to generate a spectrum with some specified median S/N. For a S/N target, what do we need to scale the median flux level to, given Poisson statistics?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sntarg=3 # Choose a S/N here\n", "fluxtarg=sntarg**2 # what does the flux need to be to reach this target S/N?\n", "\n", "# scale the model spectrum to the desired target flux\n", "sim=sim/np.median(sim)*fluxtarg\n", "# plot should have a median of the desired level\n", "plt.plot(sim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now add Poisson noise using np.random.poisson() " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4000.0, 5000.0)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "noisesim = np.random.poisson(sim) # get a Poisson sampling of the spectrum\n", "\n", "#plot both the spectrum with noise and the noiseless one\n", "plt.plot(wave,noisesim)\n", "plt.plot(wave,sim)\n", "plt.xlim(4000,5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will add in some readout noise, which is represented by a Gaussian distribution with zero mean and a $\\sigma$ corresponding to the readout noise level of the detector, let's say 10 units here." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rn=10 # desired readout noise\n", "\n", "noisesim2=noisesim+np.random.normal(0.,rn,size=len(noisesim)) # add in Gaussian noise\n", "plt.plot(wave,noisesim2,label='spectrum+Poisson+readout')\n", "plt.plot(wave,noisesim,label='spectrum+Poisson')\n", "plt.plot(wave,sim,label='spectrum')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For later use, let's write a routine that scale an input spectrum and adds the noise" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def addnoise(spec,sn=100,rn=10) :\n", " fluxtarg=sn**2 # what does the flux need to be to reach this target S/N?\n", " # scale the model spectrum to the desired target flux\n", " sim=spec/np.median(spec)*fluxtarg\n", " \n", " return np.random.poisson(sim)+np.random.normal(0,rn,len(sim))\n", "\n", "plt.plot(wave,addnoise(sim,sn=100,rn=10),label='spectrum+Poisson+readout')\n", "plt.plot(wave,addnoise(sim,sn=100,rn=0),label='spectrum+Poisson')\n", "plt.plot(wave,sim,label='spectrum')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's simulate a spectrum with a radial velocity of 200 km/s. To do this, you can just shift the wavelengths by the Doppler shift:\n", "$$\\lambda_{shifted} - \\lambda_{rest} = \\lambda_{rest} \\frac{v}{c}$$\n", "To do this, we will initialize an interpolator with these shifted wavelengths using scipy.interpolate() , which we can then use to get a simulated spectrum at any desired wavelengths. We are also going to want to interpolate the rest spectrum to resampled wavelengths as well, so we can cross correlate them, so initialize an interpolator for that as well." ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 5050)" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rv=200 # set desired radial velocity here (in km/s)\n", "\n", "#instantiate an interpolation for the rest spectrum\n", "interp=scipy.interpolate.CubicSpline(wave,sim)\n", "\n", "#instatiate a interpolator given the input (shifted) wavelengths and the spectrum\n", "rvinterp=scipy.interpolate.CubicSpline(wave+wave*rv/3.e5,sim)\n", "\n", "# plot the rest spectrum (here the interpolator is doing nothing!)\n", "plt.plot(wave,interp(wave),color='g',label='rest')\n", "\n", "# plot the shifted spectrum\n", "plt.plot(wave,rvinterp(wave),color='r',label='shifted')\n", "plt.legend()\n", "\n", "#plot a small segment of both\n", "plt.figure()\n", "plt.plot(wave,interp(wave),color='g',label='rest')\n", "plt.plot(wave,rvinterp(wave),color='r',label='shifted')\n", "plt.legend()\n", "plt.xlim(5000,5050)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, to get the radial velocity by cross correlation, we need to resample the spectra to a $\\log\\lambda$ scale, so that the shift is independent of the wavelengths. Let's choose a $\\log\\lambda$ array with the same number of pixels and the same wavelength range as the original wavelengths." ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 6000)" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy\n", "wave=a['WAVE']\n", "# set up a log(wavelength) array with the same number of pixels as the original\n", "#numpy.linspace returns a uniformly spaced array between a starting and ending values with the \n", "# specified number of pixels\n", "logwave=np.linspace(np.log(wave[0]),np.log(wave[-1]),len(wave))\n", "#dlog_lambda is the spacing in log(lambda)\n", "dlog_lambda=logwave[1]-logwave[0]\n", "\n", "# interpolate to the new wavelength scale. Remember that we need to give the interpolator the wavelengths\n", "# not the log(wavelengths)\n", "sim_logwave = interp(np.exp(logwave))\n", "\n", "# plot the old and new, demonstrate they are similar, i.e. interpolator works well here\n", "plt.plot(wave,sim)\n", "plt.plot(np.exp(logwave),sim_logwave)\n", "plt.xlim(5000,6000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll be a little unrealistic (cheat!) and interpolate the rv shifted spectrum first, then add noise" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 5050)" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# need to be careful around edges that cubic spline interpolation doesn't give negative values,\n", "# because they will cause the Poisson routine to fail (why?). Set negatives to 0.\n", "rvsim_logwave = rvinterp(np.exp(logwave))\n", "\n", "rvsim_logwave[rvsim_logwave<0]= 0.\n", "\n", "# now add noise using the addnoise routine from above\n", "out=addnoise(rvsim_logwave,sn=100,rn=10)\n", "plt.clf()\n", "plt.plot(np.exp(logwave),sim_logwave,label='noiseless rest')\n", "plt.plot(np.exp(logwave),out,label='RV shifted with noise')\n", "plt.plot(np.exp(logwave),rvsim_logwave,label='RV shifted, no noise')\n", "plt.legend()\n", "plt.xlim(5000,5050)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now we will see if we can recover the radial velocity using cross correlation.\n", "

\n", "Apart from sampling on a $\\log\\lambda$ grid, another thing we need to be careful of in cross correlation is the continuum level. If the signal has a mean value greater than 0, the cross correlation will be \"diluted\" by the continuum contribution, and edge effects will be very significant; imagine that the signal drops to zero off the edges, which will lead to a big change in cross-correlation as the edges slide relative to each other. As a result, the mean level is typically removed before cross-correlation. Here, the continuum level is clearly a function of wavelength. We'll remove an approximate continuum by subtracting a \"median-filtered\" version of the spectrum: imagine running a window across the spectrum and taking the median value in the window around each pixel. We will use scipy.signal.medfilt() to do this, although the principle is simple.\n", "\n", "We will build this continuum subtraction into a short cross-correlation function, using numpy.correlate to do the actual cross-correlation of the continuum-removed spectra. numpy.correlate() will cross-correlate two spectra across a large range of shifts, depending on the mode keyword, but even the smallest of these is likely overkill for the RV problem, if we expect that the shift is small (pixels or tens of pixels). Here, we use it with the mode='same' option, which will produce a cross-correlation function of the same size as the first array, which means it is computing shifts from the second array being shifted one half of its length to the left up through one half of its length to the right: zero lag will be in the middle of cross-correlation array.\n", "\n", "It would be very straightforward, and possibly simpler to understand, to write your own (perhaps one-line!) cross correlation routine that returned the cross-correlation function as a function of shift (lag)." ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-20, 20)" ] }, "execution_count": 186, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.signal\n", "def xcorr(a,b,filter=401) :\n", " \"\"\" Cross correlate two spectra, but remove the median levels first\n", " \n", " filter gives the width for the median filtering\n", " \n", " returns the lag array and the cross correlation function\n", " \"\"\"\n", " xc=np.correlate(a-scipy.signal.medfilt(a,filter),b-scipy.signal.medfilt(b,filter),mode='same')\n", " # with mode='same', the zero shift cross-correlation is in the middle of the output array\n", " if len(xc)%2 == 0 :\n", " lag=np.arange(len(xc))-len(xc)/2\n", " else :\n", " lag=np.arange(len(xc))-(len(xc)-1)/2\n", "\n", " return lag, xc \n", "\n", "# cross correlate template with itself as a check\n", "lag,xc=xcorr(sim_logwave,sim_logwave)\n", "\n", "# cross correlate template with object\n", "lag,xc2=xcorr(out,sim_logwave)\n", "\n", "# plot cross correlation as a function of lag\n", "plt.plot(lag,xc/xc.max())\n", "plt.plot(lag,xc/xc.max(),'bo', label='autocorrelation')\n", "plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n", "plt.legend()\n", "plt.xlim(-20,20)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can look for the peak of the cross correlation, which will give us the pixel shift in the $\\log\\lambda$ data arrays. To turn that into a velocity, we need to determine the velocity shift per pixel, which is just $d\\log\\lambda \\times c$" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dloglambda: 0.000064 velocity per pixel: 19.068622\n", "peak pixel: 6671 corresponding lag: 10.000000\n", "corresponding RV: 190.686222\n" ] } ], "source": [ "print('dloglambda: {:f} velocity per pixel: {:f}'.format(dlog_lambda,dlog_lambda*3.e5))\n", "# get the peak pixel, the lag corresponding to this pixel, and the corresping RV\n", "imax=xc2.argmax()\n", "print('peak pixel: {:d} corresponding lag: {:f}'.format(imax,lag[imax]))\n", "print('corresponding RV: {:f}'.format(lag[imax]*dlog_lambda*3.e5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How well does this match the input radial velocity? Note that we can do (much) better by fitting for the peak: if you look carefully you can see that the cross-correlation is not symmetric around the peak pixel. Write this as a function so we can use it later (always good to write things as function!)" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot around peak\n", "plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n", "plt.xlim(lag[imax-5],lag[imax+5])\n", "plt.ylim(0.8,1.05)\n", "print(lag[imax])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see by eye that the maximum is probably closer to a lag of 10.5. Getting a little ahead of ourselves, let's do a quick quadratic fit to the peak." ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "peak lag: 10.470327 corresponding RV: 199.654714\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def fitpeak(lag,xcorr,plot=True) :\n", " imax=xcorr.argmax()\n", " x=lag[imax-5:imax+6]\n", " y=xcorr[imax-5:imax+6]/xcorr.max()\n", " fit=np.polyfit(x,y,2)\n", " if plot :\n", " plt.plot(x,y,'ro',label='cross correlation of shifted and rest')\n", " plt.xlim(lag[imax-5],lag[imax+5])\n", " xx=np.linspace(x[0],x[-1],100)\n", " plt.plot(xx,fit[0]*xx**2+fit[1]*xx+fit[2])\n", "\n", " #for a quadratic fit y = ax**2 + bx + c, the peak is where the derivative, 2ax +b, equals 0, so xpeak=-b/2a\n", " return -fit[1]/2/fit[0]\n", "\n", "peak=fitpeak(lag,xc2)\n", "\n", "#convert this to a velocity as above\n", "print('peak lag: {:f} corresponding RV: {:f}'.format(peak,peak*dlog_lambda*3.e5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Better? Try doing this at different S/N for the input spectrum, and report your results. See how compact it is if we use functions for the different steps!" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "S/N: 5.000000 peak lag: 10.004497 corresponding RV: 190.771965\n", "S/N: 10.000000 peak lag: 10.428714 corresponding RV: 198.861203\n", "S/N: 50.000000 peak lag: 10.449020 corresponding RV: 199.248410\n", "S/N: 100.000000 peak lag: 10.469787 corresponding RV: 199.644413\n", "S/N: 1000.000000 peak lag: 10.466854 corresponding RV: 199.588477\n" ] }, { "data": { "image/png": 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MjgMmLUJq05q22aA3jDBa7FMYGccadn4n2F3DuJIXftiEp75aH7bdmYIinA+aLPtCNmnnZdeFFtGaQHQDC7d7oDa0jZ9TFnkm6uiJVf/fir26Il86vDwPN7z/Z8A2eSji8sxjuEohXbAfL4wCmdjH6nTMcljkmehg48Tr5v3aC1S2a9QqnW4i46KbiYEMBUyUYJFnoo4QwNYDuSGhlGlZx/HtGvO5t123qtUBWOMZPyzyTNQ5c74IQ95dgseCcr4Pn7Icz3xjPpRMSeP9q2xZ/xm3Ytf6ERZ5xlYyjpzGv+ZtD5hY8tdLXbvXnqIcSjq+IAqJoFwF+2tijqe/CR9oEAks8iYoLhF445d014WUuYk7PlqJyQszSvOzRAOl0bqe5e0M4yTr95605bws8iZYtOMI/vPHLrz4w2anTXEtfnGV6244j0kkce47ZJOrcxQSc/mXw7uleAnDRAsWeRMUFfsEI55iko0T6jYINzF63eQ/NfcrMeitxaV+d6VoGqvy0jBMrMEibxPj52zD2/OtrQofy/y65VDINjWxl5dbM4JSThA/WcfOckw842rsesZkkVfhsRnr8Hv64YiPn7o4E2/P32mhRbGJf/5PXgHHqTJzE+ZuM5SAKpbhaVfGD4u8Cj9tOIB7/5tm2fnW7T2BBdsiv2lYycy12TiSZ66C/bHTBXh3wc6IYtKdimMXAnjiy3XhGzKMh2CRjxJ/+c8y3DfduptGpBw9XYDRX2/AfSZvYM9+twmTftuBlbvVC0gD5keUfj/7BzoLjWQc0a4EpFVFyEtwBCXjxzKRJ6JEIlpHRD9L75sT0Uoi2klEXxFReav6YiLHP1lsdiR/9rzP7WF36bJPl2fh2OkCTJirr4j1gEnqeWp4IRTjZuz6fFo5kn8CwDbZ+9cBvCWEaA3gBID7LOzLlazfdxKnzgVWBTqcm48eExY4ZJF96P1Aao0oT+iooFRUIqB0H9l3/KxqEWs1dhzO06xj6iUyjpx22gTGJVgi8kTUCMBQAB9J7wlAPwDfSk2mA7jeir7cihAC17/3J+76JDDf908bDuDgKXOjZjs4nKu+OGnvsbO6C1xH4hVQOnNalrLbRwjl2PbL31iIAW8tMtRv5tH4cNUAxiocMd7GqpH82wD+DsAfMF4bwEkhhP+Tlg2godKBRDSKiNKIKC0nJ/bzQm/YZ8+qtWiRfigXfd5ciKlLMjXb6V1UpFSXVP4UkH4oFy/N2ozhU5YrHv/mvO1QW6zqL4bNMF7gUK49g0HTIk9E1wA4IoRYI9+s0FRRFYQQU4UQqUKI1JSUFLPmMCbJPu6robk6zIRqKWGG8uF8/4PfXoJPw6T7zcvX55aZvTF0pSvDxDtWjOR7AbiOiLIAfAmfm+ZtADWIyF9esBEA+8qRO0S05/FWZh7D3mPuXtBz/Mx5tH1hLtbs8d0krJiXPVeoz4/+zgJel8AwwZgWeSHEWCFEIyFEMwAjAPwuhLgdwEIAw6VmIwHMMttXLGLlwp9bpq5AnzcXGj7u9/TD+DPDWGX5cNqsNvG6avdxFBSV4J+ztyk30HHuYCbM0RdZwzBMKHbGyT8LYDQRZcDno//Yxr4cwclQ5Fnr9+Phz9eEbwjg3v+m4faPVupqa/SepORzB4B1FmbUW555zLJzMUy8kRS+iX6EEH8A+EN6nQmgm5XnZ8p44kt7ck/rxT8azy8qhhDC0BPLTxs857ljGNfCK15jECNpAfJ1+rO1+jh7vghXv7NEMXLonmmr8cWqvYrnaDZmdkR9MwxjHSzyJti8/5Qj/U5ZpB3eKGdjtjEblQbkG7NPYdvBXLw2R9nP/svm0AyTDMO4AxZ5E7z7ewYA4HxxieGc8kII/Gveduw/ec5wv8t2qU+i5uUXWrbacdvBXPUnAU4RwDAxAYu8BSzekYN2L/5i6JhtB/MweWEGHvl8raW23PHxKgyYVLYSVD4y7//vP3SfJzff56J50rDvn9WfYdxE3It8Tl4B5m+1LwWw2nRkieTzPq/jCaCgqBh7jmkvyRdCoLhEaK643WUgA+OaPb4i22l7ZIuihPxl2ZslO4/iTAEvo2cYNxL3In/HRytx/6dpEU9QmkXPuHfsd5twxZt/lL5XimR5d0EGWj43xzrDJIpLhK5Q0ckLMyzvm2EY88SVyGefOBtShi4rzAjZLozEoy/RsZDpi1XaqQEipUSE3ohy8wuxOutEwLZCrnPLMK4krkR+yDtLMOozfQuIzBCcblgLu6skBd9LtOqgAsD9QYVNlLJRPv31BgM9MgzjJHEj8ueLSpBrYfrVzBz1CJZeE38vfa02YpevFN2UfQoDJy3CiTPnVdpqvw8+nxa3fbhCc3+wppeIUHfNgQgighiGcYa4EflxP22x9Hz9/q2ey/y0bBJSz0D92slLsfPIabwwa7Ouvo08KQRTJFPxSCdLlf6mj5bujtQkhmFsJG5EfsUu/flP7Iy20eKczqpF6y3KWd/h5Xmlr0tKhGIpPxHwOvwdq7CYffMM4ybiRuSNsCD9iGXnUnXXKGxX889rTdJeNG6epvtE7wTvozPWKkbnnD1fbCgvzafLs3S3ZRjGfuJe5P2yujzzGEZ9miZNNEZvQY8IiD0PpPnY2ZiyaJfm8Xn5RZakFZizSf0cwTefg6fUbypcdo5h3EXci7yfB6an4deth3E2KF5+7MyNhgtG60HP4FgIYOLcdF2Tqhamrddk2a6jqgW4m42ZbWq+gGEY64lLkVdaFSqfkJQPXGes2oe35u+IhlkB/b71m/4+X/l5a4D9ViN312w9kKvZ1o1FyxkmnolLkR/23p9R68vIAFsu00ZL2QUXtX5sxjpcNG5eWAtOnlUO22QYxhvEpchHk3wDK0EjmXhV46cNB5CXX4T3/9D26Y+ducn4yRmGiRniRuTVnBlK+qmktR1e+gWfLc/C7qNncOP7y3T3O3Gucn3SGSt9hTbsDjmcv007HNTIRKnNi3MZhrEBS8v/eQEhBL5K2xey7cz5Yrw4awuGdqpfmqExUgqLSzB9uS/XTObR0Nw5RUHCX+KwuvqLo5w8V2gokyXDMM4T9yIfLJ+rs46HtPELsmV9amj2zsN5eP2X7QHbDucWqLQ2jx5X0Cd/+lazZhw5bVlBEoZhokPciLxet/ZZnatO7UAIYOBbi6PeZziyT3CuGoaJVTzlk39t9lZ0e22+rrZLduag2ZjZIUU7wsWk77JgJKuWHmCpjpTCdnDstH1PCgzDOIunRvIfLglMkrUy8xjOFRajb9u6IW3v/HiV4jkCKiEpkH4oL3IDXQgRcPU7S5w2g2EYm/CUyAdzy1RfWt1Vz/XXfcy0P7Nsssa9HMnjkTzDeBXPuGv2yYph3PnxShzJK1t52W38AsUoFqfgUESGYaKFZ0byl7+xsPT1kp1H8dESd+Y3P5ybHzY1QDTRm96YYZjYxDMiHysMfXcJjp52TyqBNJMx/wzDuBvT7hoiakxEC4loGxFtIaInpO21iOg3Itop/a5p3lz9TF2cGc3udOMmgWcYxvtY4ZMvAvC0EOJCAN0BPEJE7QGMAbBACNEawALpPcMwDBNFTIu8EOKgEGKt9DoPwDYADQEMAzBdajYdwPVm+2IYhmGMYWl0DRE1A9AFwEoA9YQQBwHfjQBAaLA6wzAMYyuWiTwRVQHwHYAnhRC6w0eIaBQRpRFRWk5OjlXmMAzDMLBI5ImoHHwC/7kQYqa0+TAR1Zf21wegWB1bCDFVCJEqhEhNSUmxwhyGYRhGworoGgLwMYBtQohJsl0/AhgpvR4JYJbZvhiGYRhjWBEn3wvAnQA2EdF6adtzACYC+JqI7gOwF8BNFvTFMAzDGMC0yAshlkI9k6/+pDEMwzCM5Xgmdw3DMAwTCos8wzCMh2GRZxiG8TAs8gzDMB6GRZ5hdFC5fKLTJjBMRLDIM4wOrmzHWTmY2IRFnmEYxsOwyDMMg2cGtXHaBMYmPCHyXMKOYcxRt1qy0yYwNuEJkd9+OM9pExiP40vR5GG4uLxn8YTIMwzDMMp4QuSF4GEIw5hBxMBQfsnfr3TahBBSm0ZWurpiueiF5HpD5J02gGEY22lcq5LTJoRQr3pkcxmNala02BJ1vCHyrPIMY4ralSsYPiaaQuVWyiVENldTrWI5iy1RxxMiz2N5xg0Mvai+0yZETP8L6+KDOy8xdMyAC+tF3F8sXys5kSrPtZ1C//6alewRfk+IPI/kmWjz/u1dQ7Y1r1PZAUusgYhwVYcLDB1jZi7s5ksbR3ysEjVsEki7iGa0ljdE3mkDmLjg1m5NSl9frTASHXVFC9yc2iiaJpmmbb2q6Naslq19tLugasi2K9qkYMs/rrKsj5evbW/ZucLx82O9o9aXFXhD5FnlmSjw6rAOmvurJZfDG8MvjpI11jDtnkvx9UM9bO3jxq6N0LVJjZDtsbr0oGPD6qWvrdSe0QPtWXVsRY1Xx+EQSsZuCECCiip9/3DP6BqjQmICobjE2HfB6Den3QVVkX7It/hQy+XQvUUtrMg8bvDskeOUBFjVbdbEoRadKRRPjOSLWeQZi7ju4gYB798Y3insMV2a1ESXJpHFSztNA4MhgL882SdsmwvrV8MHd6aWvjczYq9ZqRxeGdYBmy107cQbnhD5aX9mOW0C4xE6Naoe8L5CUux8RTo3DnWJhMPIBOC7t3YJeK/2BD35ti6obmGI4F09mqFKBW2ng5X9RcI1nepjnMa8wO9PXxFFawKJnU+wBtknzjltAuNRrHxI7Ns2RXN/uURzTuqeLWubOj4cwU85atSJIOY+Uu7t1RzvjOiMfg7l+/ff6Aa2r6cZMdQipYpjmT49IfIFRZyFkjHPh3elqoq6FZOE/aW48t6t6pg/mQtQegqYcMNFqK4Qzqh0Wa24gZZLIgzr3DDikMR3RnTG5/dfptmmWnJS6RPdlDuU1xLo6f/Rfq2NG2gBnhD5FnWqOG0C4wEGtte3uCdSwU+pUh7prw7Gs4PbRXYCl6HkrpGHmUYDgrm777DODdEr6Kb7eP9AMV730iDMH30FPrwrFYM7Bq4lkF+BSuWT8NQA7dH6z4/1xjc2RzMF4wmRb1OPRZ6xHys8N8nlEnFRkN+/9PwejR9QG+Va8XQU7hx/7dtS0Q120yWNsPTZsoRnHRpUK339wOXNA2r6JiYQGteqpDwIkP5n/h6eGKA9Wu/YsDoutXldQjCeEHmGsYrrOof3OxvRpk/uTsWgUnFwJjC8TpXytpy3UpjJUDlW/+XT7+0GAOjTWnueo0Wdyljz4sCQ7bUql0ejmmUJz777a1kYbCT3WqM3rGiGfXtC5D06AGIcoF615IBRnRz/99jI8n8CoUENXyKvahW1RVHtcyyPodZKnaCkG/f1bo7yidZ+zW+/zOeSqV058ObRtHZglsi7ezYrs03HeZNkyb4urO/7H5RXiW66ok0Kdk8Ygh46JpurJZcLG4eeXC4RVWU3LS9pijdE3kv/EcYR1CbU5CQkEFY+1x9vj+is+7wNalTEmKvb4b3buqJnS/MTrpNuvtjQsvoXr2lvSZ4UeS73ZCkXevD37s0IV/squVP8k6FP9Ff3cbuhWlejWr4beK1K6k9L4fLqDNI5FxQptq94JaLBAN4BkAjgIyHERKv7iIWCB4y7kU+oacVc1zNQC3XhM31LR95DFbIOBqPnEb5GpfKqo3krvwdZE4ei2ZjZpe/ludzl0rpx3CB0Gverb7uK5kYixbUql7d1FagSkVy9pwe2RWrTWuipEDH1/u1d0b5BNVRL1hb5cGsAzGLrSJ6IEgG8B+BqAO0B3EpE0cskxDARELzoR435o/tg/mj1RS52ZKWM5JxG/L//ub0rvvur/uiPcAIG+MT/llRrs05GwroXB+LBPi10tdV7yconJahGZV19UX00rV0ZNStrz4lUsLlKlN3umm4AMoQQmUKI8wC+BDDM8l54IM9YSJ0qZYt5tEbHrepWRau6ypFdF6tE0ChxQ5eGAICPRqbi8tb6XTrBfac2NR+1MeSi+rgkzHl6SzZ2DSp9Fzxil99cRnRrEjIyT5R88D0kN5aa/90qalYujxoabhWrnD939Wgato3c1fTcEHtDau0W+YYA9sneZ0vbSiGiUUSURkRpOTk5EcL3BdMAABQaSURBVHXCGs/I6dMmBbXCjJ6MYkQAfn2qD/4XZoGNnDeGd8KmcYPQr109fHafvuOWj+2HHx7pFbAtIcIqRUbp27Yu0l8djEsirG/qp0JSIuaP7oMP7rgEf7uqLb5/uFf4g3Sgy81j46X6x3UdkDl+iO72VXU8DZnBbpFXupQBmiyEmCqESBVCpKakaIdDqcFZKJlggnPQRJM29aoa+uImJSYY/qLXr14xxJdrV3FopRz5yQp9RTIP2qpuVVQsn4hHrmyFtgp5582iqgxhJOO1v3QEAMx6xPiNh4iidsPVg90inw1A7oxrBOCAzX0yDN67LbRykxF+f/oKTX+7Wa5oE9mARotLm9UsFSegrLiF2SGQ2Rz57pE77RtR8xTffEciEW7o2ghZE4fi4giSvrkNu0V+NYDWRNSciMoDGAHgR6s74YE8E7wUvbLJiIUWKVXQqm4V2z5b/sU8VkJEuP2yMn+w1sjYrKtFxYKAd7H2tZx296X4eGSq6c+OHqLpfbD1rxFCFBHRowDmwRdC+YkQYovl/Vh9QibmGD2wDd5dsBOA9sixRqVyOHm2EA/2aYF29aviqa826Dq/0zHZPz/WG1sOnDJ0jJbFn93XDcdOnzdnVBAXBOWm9+uYk9fOSM+1q1QoTSLnJWy/ZQkh5gCYY3c/jDdIqVoBOXkFtp2/S+MaWLg9B5e1qIV+7erpFnmn6diwekDZOT0kaax0rVQ+CZVqaX/9p91zacAq1HA0lFb2BhOs8XrWDETKqKAQyeABYDw+9Xui/B/jHd65pTN+2ngAM1btC984DEkJhCJZObwLDCxk8hKRCtuVbc3laL+kaU18tmIP2tYrcxtljh9iW21XQ4un3DRRYDOc1oBxFQkJhPt661uwEo7gj8Xsx3vHtWtvZpRr0V7fpSGWjemHy1qU5ZdJSCDHXV/xhidG8pzWwFvYNSlVW7bISW8ecn+u8Tt1LHBxO/UN1nPVy6vXd8SaLOWi3Q1UXDjRgm8nHhnJFxaXOG0CY5JuUo5tgvmJ9EubqUeOGL1/1KuWjKyJQ9HV5YW6tfLtyAdBD1zeHC1SrE23cGf3pnh7hL5UENGGh39eEfki/ld6CbMD+RsvCV28E4LHhnizHy/LTKk6AQrC80Pb4/en+0bJKue4Mkw93XjCE+4aHsnHPi9f1x7jftyCixvXwP6T6oXZicLfBPyuGCW3j3/EW8HiHOtW0qlRddzbqzme/Gq97mPkBTB+eqw3Dp6KzeL23z/cE7tyzqjuX/S3vsg9VxT2PHLXXLzj3k+6AZrZkO2PsYa0FwboatehQXV881BPJJdLRMuUKqWFKYLRKoBRr1r4L/ar13fEi9e011Vswil+fLQ3ru/SMHxDFWpVLo8ODZxL62CGLk1qYrjGk1jT2pVVyyfq4dZujdGnTQrut2By30wxFqXUxHbhCZF3S5qIvw9u67QJrqOOwohq3LXhs03f1aOZDdb4RvL39W7uigiPO7o3Qc8o3Gz8he6VinPEGzUqlcen93ZDSlVzI/3p93bDgqcjT3vRpp71eXrU8IS7xi083LcV3vhlu9NmuJYHr2iBVilVMPySRhj301bNtlZosNtnav55/UWmzzGwfT3knivUbDPljkuwdt8JdmFYiB25h+zCEyN5J+Pk/32TvuRNQy7SXxfUq1Qsl4ibUhvrGkXLUwVXkOUZV8p+6Mdr6yVeuqY9fnpUu9Tfh3el4qsHtYt8VK9UzvTCJiZ28YbIO9h3/Rr6Yo9fGdYxfCOPY0SE5W6e12/sVPr6u79GtqDHydTDkXJv7+am/M/xjD8kV62oSzzhCZG/uiOPkmMBszfjYZ0bhHxp29SrgmVj+mked/tlTfB/Okv6Md7gptRGWDamn+vXN0QDT4h86yhOYkSK11wJTvKybOL2gztTQ1ZV+r1B/mv+6rCOaFqbI7DiCSJyfLWtW/CEyLsJ/2NiMF5JvdC+frXIDzZ4p1OLBrmnV/PS1/LC1mpnd0EgDcOE0KRWpfCNLIBF3mJevCZ8eKDXWPrslbacd9mY/pg/+grP3CAZRs6sR3oFrFS2CxZ5i1GdKIthnfpcVpT67p7NQvbLV1taSUrVCgE+ePmAvHmdygGl7oL3A0C1ZF+EMLvKGDdSM0qL1jhOPk6oUiEJpwvCLwdXQp4L5eZLG+Pv320sfS+/AYSjlYVzJwuf6RuyLVjLf3ikF5bsPOqqosoME214JG8SvbUy7RhM3ivzTYfj92ciX52n5dPupbA8+6oOyiXUrru4QcQ2GMFvbouUKhip8OQhZ/HfrsSiv/W12ySGcQwWeRO0SKmMCkmhi3N+fLRXyDYrXQZt6lXB2KvbYfSgNrqPqVtVfy7xRjUDoxIqlldfgKTEhBs6BbyvbPD4SPHfRIwUYm5SuxJH3jCeht01JvCPGKslJyE3v8wV0qlRDVv7TUxIwINXtERxSeR3juDSeHK6NKmJ7BNlWQyN3CAAoFKQqG95ZXBIm6oVkpAXoftIjeeGXIgnBrQ2JPIM43V4JG8Cv0TOH30FfngkdPQe2Fa/IKtlYDRKRY0UAHailXrAz2AbFrAlJhCqJasXz2CYeMQzIj+4Q+Si0SDSsmiSbtetlozOja0bvTerXVmXQIcrk9e9hXLMPqBdSSgajL/hIlysc8k+R8cwTOR4RuQvMFG/ckB75YlCM3RtEij6akKV/upg7J4wJGS7nbHhj1zZMuIcMFZRLjEB428wloXRDemBGSbW8IzIu40vHuiONToKZiSXSzQsXv7Wkd4Gbr+sqWKhlVtSG2PGA93DHv/zY9Ys4IjVwhYME0uwyMMnmo/3a4UH+xisFqOhzcnlEg3l755+bzdjfZtA7Z7y+vBOARWT6ldPxgtDLwxp17Fhdcx+vDc2/+Mqu0xkGMYiWOThGxGPHtQW7RsYy8tiZPwdbtR9RZsU3N+7LO5djx86KYHwwOVlx/ztqsDKVE8PCnx/QTVjLq0xV7fD/Zcr3/g6NKiOKlGKYmld17eISmuOgWEYZeJK5NtdoL3i0ugEn5Hm4SZJI4GI8PzQslw5tWWFNgDfiNsLXNSoOlY91x83pzZ22hSGiTlMiTwRvUlE6US0kYi+J6Iasn1jiSiDiLYTkauf68t83O4J49CyZNItytWovDwvWbdaMk+8MkwEmB3J/wagoxCiE4AdAMYCABG1BzACQAcAgwH8h4gcCdqWl44Lh52hepGe+zaFmPl2Fyi7lSqWD3WfTLjhItwijYD13sT8TwTRcscwDGMfpkReCPGrEMK/bHEFgEbS62EAvhRCFAghdgPIABCVmcWeLWtj+diySkEDLtQfHmlUiDvbvLIVAF4YeiHGXds+IG+6GnUVKtDf2q0JXh8emGaAwswmjLm6HSbecBH6teO6oAwT61jpk78XwFzpdUMA+2T7sqVtIRDRKCJKI6K0nJwc00YMbF8P9avrrwjTo0VtPNS3JQDjIYmRrtpsmaI/V0oCEe7u1RxddCy26ty4hiWTk8nlEjGiWxND7pHgVAYMw7iDsCJPRPOJaLPCzzBZm+cBFAH43L9J4VSKGiqEmCqESBVCpKakpETyNwSdz1j7GaO6l94USqK0tPK5IaFhiSEEmXKXlE1RqyB1crlEfDmqhwnLIuexfq0jOu7BPi3w4V2pFlvDMIyfsE5XIYTmih4iGgngGgD9RVkISTYAeShEIwAHIjXSFBHGOSYmEB64vAWa1KqE577fZNoM+f3DSNSLfzAda1OOTw1og5W7j4VtN1bPDY9hmIgxG10zGMCzAK4TQpyV7foRwAgiqkBEzQG0BrDKTF9GeeNGnx+6VUoVxf3t61fDfb0D87FXqlDmciD4fNNKE5+lbQy4M+STnv6j1GqY2kWCZG80ooieGNAaX+hYPcswjL2YDZ+YDKACgN8kwVshhHhICLGFiL4GsBU+N84jQohik30Z4qbURhjUoR6W7/KNJgd3uAB7jpfdhybdcnFIlMqQjvXx0jUFeOXnrWFl8O6ezXBl2wjdSwRsGjeoVHSVCBZif26egQYmkoP59N5u+DptX+miqJ8e7Y1rJy8FoF6AnGGY2MZsdE0rIURjIURn6ech2b7XhBAthRBthRBztc5jB0SEGpXKq+5XEtiEBMJdPZqGbP/lyctDto27rgOSEiO/fFWTy+nKe+6PhKlXLRnrXxqIR65sFXGfretVxfND25c+gcjr0X79kDO+fIZh7CVuAqHlI+OhneqjdV1lN44S7S6ohrUvDgQAdH31t8j6lw3Ma1RUv/kotS89TuOmFQ2a1lYv2O2mhWQMw5TheZFX8og83LdlWH96cBqCWpUjE9ialcphRLcyv37T2pVQ3sACLbcs8tw0bhDKmXhyYRjGGTwj8n/t2xIZR07jxq6NwrbVipS0eun8upcGAQAOnvKV0wuun6rGxY1rYM2eE66JqqnKFZcYJibxjMjXq5aM/91/mWYbJwWzfvWKmHJHV/RoUUdX+2n3XIpdR07r8vv/+lQfbDuYG5FdVSok4bTFtVYZhnEPnhH5cAhhjetj0s0X40yEoji4Y33dbasll0OXJjV1tW1Tryra1CvLsHntxQ2w++hpXccufKYvjp85r9suhmFiizgQeWPKniA1H3N1O8X9N+hwBznN/93aRXfblKoVkKKQ84ZhGG/AM2lBEBGyJg7FqD4tnTYlprjpEs71zjBuJC5FPkopauIKfhpgGHcSVyLvlnBENVpIKRga19KfRZNhGEYLz4v85a3r4NJmNfH3wco+djdxa7fG+OahHoYmaN1Gf85BzzCuwvMTr5UrJOGbh3o6bYYuiAiXxnAOmayJQ502gWGYIDw/kmcYholn4lLkOc8KwzDxQlyJfLjapgzDMF4jrkSeYRgm3mCRZxiG8TBxJfIVy/nK+7HbhmGYeMHzIZRy3r21C75YtRcdG1YL35hhGMYDxJXIX1A9GaMHtnHaDIZhmKgRV+4ahmGYeINFnmEYxsOwyDMMw3gYFnmGYRgPwyLPMAzjYVjkGYZhPAyLPMMwjIdhkWcYhvEwJFxU8JSIcgDsifDwOgCOWmhOtGC7o0cs2gyw3dEmFu1uKoRIUdrhKpE3AxGlCSFSnbbDKGx39IhFmwG2O9rEqt1qsLuGYRjGw7DIMwzDeBgvifxUpw2IELY7esSizQDbHW1i1W5FPOOTZxiGYULx0kieYRiGCYJFnmEYxsN4QuSJaDARbSeiDCIa47AtjYloIRFtI6ItRPSEtL0WEf1GRDul3zWl7URE70q2bySirrJzjZTa7ySikVGyP5GI1hHRz9L75kS0UrLhKyIqL22vIL3PkPY3k51jrLR9OxFdFQWbaxDRt0SULl33Hm6/3kT0lPT52ExEM4go2Y3Xmog+IaIjRLRZts2ya0tElxDRJumYd4nIktqcKna/KX1GNhLR90RUQ7ZP8TqqaYva/8qVCCFi+gdAIoBdAFoAKA9gA4D2DtpTH0BX6XVVADsAtAfwBoAx0vYxAF6XXg8BMBcAAegOYKW0vRaATOl3Tel1zSjYPxrAFwB+lt5/DWCE9HoKgL9Krx8GMEV6PQLAV9Lr9tL/oAKA5tL/JtFmm6cDuF96XR5ADTdfbwANAewGUFF2je9247UG0AdAVwCbZdssu7YAVgHoIR0zF8DVNto9CECS9Pp1md2K1xEa2qL2v3Ljj+MGWPDP7AFgnuz9WABjnbZLZs8sAAMBbAdQX9pWH8B26fUHAG6Vtd8u7b8VwAey7QHtbLK1EYAFAPoB+Fn64h2VfTFKrzWAeQB6SK+TpHYUfP3l7WyyuRp8gklB2117veET+X2S6CVJ1/oqt15rAM2CxNKSayvtS5dtD2hntd1B+/4C4HPpteJ1hIq2aH0v3PjjBXeN/wvjJ1va5jjSY3UXACsB1BNCHAQA6XddqZma/U78XW8D+DuAEul9bQAnhRBFCjaU2iftPyW1j7bdLQDkAJgmuZk+IqLKcPH1FkLsB/AvAHsBHITv2q2B+6+1H6uubUPpdfD2aHAvfE8OgHG7tb4XrsMLIq/kw3M8LpSIqgD4DsCTQohcraYK24TGdlsgomsAHBFCrJFv1rDBFXbDN7LtCuB9IUQXAGfgcyGo4bjdkg97GHyugQYAKgO4WqN/x23WiVE7HbGfiJ4HUATgc/8mFTtcZXekeEHkswE0lr1vBOCAQ7YAAIioHHwC/7kQYqa0+TAR1Zf21wdwRNquZn+0/65eAK4joiwAX8LnsnkbQA0iSlKwodQ+aX91AMcdsDsbQLYQYqX0/lv4RN/N13sAgN1CiBwhRCGAmQB6wv3X2o9V1zZbeh283TakSd9rANwuJF9LGPuUth+F+v/KdXhB5FcDaC3NdpeHb2LqR6eMkaIDPgawTQgxSbbrRwD+qIKR8Pnq/dvvkiITugM4JT0CzwMwiIhqSiO/QdI2WxBCjBVCNBJCNIPvGv4uhLgdwEIAw1Xs9v89w6X2Qto+QooIaQ6gNXyTa3bZfQjAPiJqK23qD2Ar3H299wLoTkSVpM+L32ZXX2sZllxbaV8eEXWXrsNdsnNZDhENBvAsgOuEEGeD/h6l66ioLdK1V/tfuQ+nJwWs+IFvVn8HfDPhzztsS2/4Ht02Algv/QyBz4+3AMBO6XctqT0BeE+yfROAVNm57gWQIf3cE8W/oS/KomtawPeBzwDwDYAK0vZk6X2GtL+F7Pjnpb9nOyyKlghjb2cAadI1/wG+CA5XX28A/wCQDmAzgM/gi+xw3bUGMAO+eYNC+Ea291l5bQGkStdgF4DJCJpAt9juDPh87P7v5ZRw1xEq2qL2v3LjD6c1YBiG8TBecNcwDMMwKrDIMwzDeBgWeYZhGA/DIs8wDONhWOQZhmE8DIs8wzCMh2GRZxiG8TD/D6j3AX+GoliaAAAAAElFTkSuQmCC\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for sn in [5,10,50,100,1000] :\n", " # get the simulated spectrum for this S/N\n", " out=addnoise(rvsim_logwave,sn=sn,rn=10)\n", " plt.figure()\n", " plt.plot(out)\n", " \n", " # do the cross correlation including continuum removal\n", " lag,xc2=xcorr(out,sim_logwave)\n", " \n", " # fit the cross correlation peak and report results\n", " peak=fitpeak(lag,xc2,plot=False)\n", "\n", " #convert this to a velocity as above\n", " print('S/N: {:f} peak lag: {:f} corresponding RV: {:f}'.format(sn,peak,peak*dlog_lambda*3.e5))\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.11" } }, "nbformat": 4, "nbformat_minor": 2 }