{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Set 2, Problem 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Field Color Magnitude Diagram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this problem is to make a color magnitude diagram for all stars within a certain distance using Gaia data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (a) Make a CMD ($BP − RP$ vs. $M_{G}$)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Select the subset of all stars within 25 pc from Gaia with good colors (S/N in the blue and red bands ≥ 5) and excellent parallaxes (S/N > 20)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "40.0\n" ] } ], "source": [ "# Compute the parallax (in mas) corresponding to 25 pc\n", "parallax = 1000./(25.)\n", "print(parallax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Download from the Gaia archive at https://gea.esac.esa.int/archive/. Make sure you download all the necessary data for the steps below. You'll need the following: ra, dec, parallax, phot_g_mean_mag, bp_rp, teff_val, lum_val\n", "\n", "(if considering extinction corrections, also need: a_g_val, e_bp_min_rp_val)\n", "\n", "I've saved all stars to a file called 'gaia_25pc.csv'" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Load the file with data\n", "import pandas as pd\n", "import numpy as np\n", "\n", "data = pd.read_csv('gaia_25pc.csv')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"\\ndata = data[~np.isnan(data['a_g_val'])]\\ndata = data[~np.isnan(data['e_bp_min_rp_val'])]\\n\"" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get rid of any stars that don't have all the measurements we need\n", "data = data[~np.isnan(data['parallax'])]\n", "data = data[~np.isnan(data['phot_g_mean_mag'])]\n", "\n", "# In case we want to consider reddening/extinction\n", "'''\n", "data = data[~np.isnan(data['a_g_val'])]\n", "data = data[~np.isnan(data['e_bp_min_rp_val'])]\n", "'''" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 42, "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 matplotlib.pyplot as plt\n", "\n", "# Convert G magnitude to absolute magnitude (accounting for extinction)\n", "g = data['phot_g_mean_mag'] + 5. - 5.*np.log10(1000./data['parallax']) #- data['a_g_val']\n", "'''\n", "# Correct B-R for reddening\n", "br = data['bp_rp'] - data['e_bp_min_rp_val']\n", "'''\n", "br = data['bp_rp']\n", "\n", "plt.plot(br, g, marker='.', linestyle='None', label='N='+str(len(data['bp_rp'])))\n", "plt.xlabel(r'$(B-R)$ (mag)')\n", "plt.ylabel(r'$G$ (mag)')\n", "plt.ylim(16,-3)\n", "plt.legend(loc='best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (b) Make an H-R diagram using the effective temperature and luminosity given by Gaia. Remark on the similarities and differences between the CMD and H-R diagram." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(np.log10(data['teff_val']), np.log10(data['lum_val']), marker='.', linestyle='None', label='N='+str(len(data['teff_val'])))\n", "plt.xlabel(r'log($T_{\\mathrm{eff}}$) [K]')\n", "plt.ylabel(r'log($L/L_{\\odot}$)')\n", "plt.xlim(3.95,3.50)\n", "plt.legend(loc='best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarities: \n", "- can identify a \"main sequence\" from bottom right to top left on both plots\n", "- a \"branch\" of stars above this sequence\n", "\n", "Differences:\n", "- no stars below the main sequence on the HR diagram (probably because Gaia hasn't measured temp or luminosity for these stars)\n", "- concentrations of lots of stars with the same effective temps -- possibly an artifact of how Gaia measures temperatures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (c) Using the data for the effective temperature and BP−RP, find an approximation for temperature given a color, of the form $T = T_{0} − T_{1}(BP − RP)$, and estimate reasonable values of $T_{0}$ and $T_{1}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In other words, we want to find a linear relationship between effective temperature and BP-RP: $T = -T_{1}(BP-RP) + T_{0}$\n", "\n", "Plot these quantities against each other and fit a line." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T0 = 7096.246842461395\n", "T1 = 1701.2009002734594\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, '$(B-R)$ (mag)')" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+YYypTxZIIujUU09FVdm2bRvdunUD4IUXXiAmJob09HT27q3dwo9jB6Yw5cIT+WXvjtw4tCd/OLcPD47qS7A+Ywr8lFd42LgUY4wJlXX/bUSKiooYM2YM8+fPD0hfvXo1aWlpdb7+qY9+yk95RUH3TbnwRFZvz0eAi/onB0wEWXFySGNM82Ddf5ugli1bMm/ePNxuNw888IAvvW/fvojIYQGmpm4+vVel+15bsoU3VmxjxrIsxkxbQubWPJubyxgTEgskjZCIcP/996OqvP322770UaNGISI8+OCD1KYkOXZgCsd3bRN03+Y9P/vm6iotV/752aaA8Sk2N5cxpjJhDSQi0l5E3hSR70VknYgMFpEOIrJQRDY4vxOcY0VEnhGRjSLynYj097vOlc7xG0TkynA+Q7hdeOGFqCqrVq3ypU2aNAmXy8UFF1zAwYMHQ77WzGVZrKtkWpQ2LQK7DG/efSBgfIrNzWWMqUy4SyR/Az5Q1eOAk4F1wETgE1XtDXzifAYYAfR2fiYAzwGISAfgfmAgMAC43xt8jmR9+/ZFVcnNzeWUU04BYN68ebRs2ZKUlBR++umnaq8RbBR7bJRw49Ce3HFOn4D0rXs9I/AnjUxjSK+OTBqZZm0kxpigwhZIRKQtMBR4CUBVS1R1HzAK8K4cNR24wNkeBbyqHkuB9iKSBJwLLFTVvaqaBywEhofrOSKtQ4cOrFy5ktLSUq699loAtm3bRnJyMiLCkiVLKj3XO4rdX5lb2V9cRp+ubRh2Qhdfenm58tbKbCYvWMNXG/fwwP+t4Z53Vlk7iTHmMOEskfQEdgOviMh/ReRFEWkFdFHVHADnd2fn+G7ANr/zs520ytKblejoaF588UVUlalTp/rShwwZgojwyiuvHHbO2IEp3Di0Z8CARbd6qrzGvbiUnh1bHUoH/rM5N2DFxVnLshj9zyXMXJZlU6oYY3zCGUiigf7Ac6p6CvAzh6qxgqls2ENl6YEni0wQkRUismL37t21yW+TcdNNN6GqLFq0yJd2zTXXICL89re/pby8HPB05f3Xki2UlrkPu8bBUjcLvtsekLZx988B/2EVTwnmvrmruOyfX/P4h+sZ/c+vLZgY08yFM5BkA9mq6l2v9k08gWWnU2WF83uX3/Hd/c5PBrZXkR5AVaepaoaqZnTq1KleH6SxOv3001FVfvzxRzp27AjAs88+S3R0NKeeeiqLvtvimwolmOx9hzfcuwROTm5HlF/4Llcod2JRmRue/2xTPT+JMaYpCVsgUdUdwDYR8bbqngWsBeYD3p5XVwLznO35wHin99YgIN+p+voQGCYiCU4j+zAnzTh69OjB7t27OXDgAMOGDQPg66+/5g+/6s+Wxy+kPO8nYqOEk5PbVXstEZj0v2k8eMGJRLs8qytWLBLu2h96z7FgrJrMmKatxiPbnXaNg6paXuObifQDXgRigc3A1XiC2RwgBcgCLlXVveJZBepZPA3phcDVqrrCuc41wD3OZR9W1cMbBPw0lZHtDUVVuffeewNWcQT42yuzeXZjG0qCVHX5i3ZBt/bxlLvdtIiJQoANu3/27U/tEM+To/vVqleX/6JcsdEuZlw3yHqHGdNIhDqyvdpAIiIuYAwwDvgfoBiIw9Nw/h4wTVU31DnHDai5BxJ/s2fPZsyYMQFp7U+/irYDLq7TCo4tYmoXBO55ZxWzlmWhQJTAHcP6cPMZlY/AN8aET31OkbIIOAa4G+iqqt1VtTPwS2Ap8IiI/LpOuTVhM3r0aFSV//73v760fYv/RdZj/8vueY+iZaW1um5tRr5nbs3jzcxsX5tNlEts0KMxTVDwFZACna2qh71dVHUv8BbwlojE1HvOTIPq168fz366gcfeWUbOzHsozc2i8PsvyPr+C6ITkug69jGiWodeuhChxkFg6eZcypxWewEuzehu1VrGNEGhlEi6VLZDRP4XIFigMY3foJ6JxLVJ4Kjr/kHK79+hVdoZAJTl5ZA99Qq2PjqS4pzQai27tGsZMGNwKI3n/lOwxMW4uMimrzemSQqljWQ9cK6qbqmQfg1wr6oe03DZqx/WRlK5e99ZxYxlgevH9971GR+/8nhAWuLIO2ntBJpgenVuzcd3nMbMZVlMmrcat2pIjec2Tb0xjVd9tpHcDiwUkd5+F7/bST+t9lk0jcFF/ZOJjgpsZL/6hltYsWUvR13+kC8td8ETbH10JHmfvoTq4b28WsdGkbk1j0nzVlPmVt9o+GDtJv4llvTUBBLiY3n64x+YWSGgGWOahmrbSFT1PREpBt4XkQuA6/D03hrqzHVlmrD01ARGZ3T3lUpcAnmFJSzdnEtcaj9S71pAad52cv71O7SkiP3L32H/8neISzmJzhffhyu2JQDfZufz1spsyv3W83XJ4Y3nFbv7XjW4B89/vhmALzbsISv3Zyaed3yYnt4YUx9CGpCoqp8AVwGL8cyZdZYFkSPHRf2TaRHjaauIdaaL92+/iO1wFCm3v0H32+YQ170vAMVZ37HtqUvJeuoySvft8M1dExfjwgVEu4TJo/oGVFdlbs3j6Y9/8M3fVVrm5oM1OwLy8s/PN9vARGOamGpLJCJSwKE5ruLwjEjf5QwYVFVt27BZNA1t/Y4C+nRpQ5e2LbjhtGN8L/8Z1w1i6eZcCopKef7zzbji4uk69hFU3eQtepmC5XPRkkK2//M6APTvM5hx3QiWbs4lIT6W1dvzufedVb5GdG9JRPH8BRMT7aJf9/ZsyS305UWBt1ZmW3uJMU1IKFVbwZfUM0eEmcuyuOcd76JZ+Zzep7PvJZ6emuDbTklsxWMffM++olJEXHQ48zo6nHkdB1Z/Su67TwLwl9+O4y+/hV/fNoll8QMpcVZcfCMzm0vSk32rLQqQkhjPhKHHkFdYclieaj8s0hgTCdVWbUkIw51DOcY0ThUXuwq2+BV4pqA/McjcXK37nknqXQvoOv5JX9q/n57Mhinns3v+Y2hZKaVlbgRPtZkLT6kja28hkxesoaCoNOB/wpgosW7AxjQxIY1sF5HfikiKf6KIxIrImSIynUOTLpompuJiV8EWvwplX1zSsaTetYBuN79KdPuuABSu+5ysJy5ky6MjGdLFU1V2au+OCJ51UIpL3bzwxWa8fcBcAn/+VV+r1jKmiQllZPtw4BpglogcDewDWgBRwEfAU6r6TcNl0TSksQM9fx+8vzqHEX2TfJ+rOvblr35k064DQaejj27dgW43vIiWlbLt72PRkiIARp56EgC3/v1tlFjAUzIp97uIKkGruowxjVuNZv91pkLpCBQ5y+Q2CTYgsf5lbs3j1y8upai06pmDVZXdb02maNPygPSOoybS6rhfHHb8lAtPrDKYGWPCpz4HJPqoaqmq5jSlIGIaRnpqAj0SW1V7nIjQ+ZL7Sb1rAZ0uud+XvmfeI54Bjp+/iv8fM7OXZx3W/dfWKzGmcavxeiRNkZVIqjZzWVbQqq3qpi8JNr1KKEpzt7H9ld9CeZkvrcXR6XS68G5cMS2IdsHsG4aQnppg65UYE0GhlkhCaSMxRzD/7r9fbNgDeNpCQnmBX9Q/mTcys6tdGKuimMTupP5+Lu6DB9j5xv2UbF/PwR8z2fbkJbji25E0/infWJKlm3N93Ya9U9VbIDGmcanxUrsicrGz9K05AlTW/TfYC7yi9NQEZl0/iF/27lire7tatCbpiidI+cM8Wp9yPgDuwnx+ev4a/nLRSXz++ecBI+xjnFH3xpjGpTZrto8H/iQiN3l/6jtTJnwq6/4b6gs8PTWB284+lmhX7YcSiSuKxGG/IfWuBXQY/ltf+mmnnUZGjw702P01YwakVFqtZW0oxkRWbdZs/yMwDJiMZxCyqurnDZC3emNtJFWrbRuJv0feW+ebfLE+XHVMMX+ecHFA2oWXj2fOqy8RHX2oRrayKrjGMj19Y8mHMbVRb2u2B7nwPDxjSN7jUCD5R61yGSYWSBrePe+sOmwa+OO7tuHH3J85WE0X4WC6to3jxOT2fLhsDdtfvZPyA4eq1vr378/ChQvp0KEDUxdt5ImP1uNWT/H61N4dGdE3ickL1lBS5iY6ysUxHVuRV1jCBf261Xpm4doEBOsoYJq6hmxsvx34DbAaJ5DUIFNbgAKgHChT1QwR6QDMBnoAW4DLVDXPmXblb8B5QCFwlaqudK5zJfAn57IPqer0WjyHqUfBKrauGNwDwLdGSU3s2F/MjrU7cbXpSPLN03GXFrNn/mMUbVzGypUrSUz0VLXNWfg1sdEuSkrduIGvNu5hyaZcyt2K4lkTZd2OAgCe/3wzn2/YTb+UBPoe1Y68wpKQAkNtA4J1FDDNRY0DiapuFpFs4ApVvV5E7gNqUrV1hqru8fs8EfhEVR8RkYnO57uAEUBv52cg8Bww0Ak89wMZeIJYpojMt2ntI+ui/sm8vnybbz0S4dAodXc9dDF3xcTR+eL7UFXyv5pF/lczAbjsnCEAnHbzY2S1OQG3egZBVnbHtTkFrM0p8H2OjXYx6/qqA0NtA4K3nam0zG0dBcwRrbbdf48BtjnbdZ0deBRwurM9Hc+aJ3c56a+qp+5tqYi0F5Ek59iFqroXQEQW4pnGZVYd82HqID01gQdH9fUss+tWYmMOvTijXeKbCbiuRIT2vxhLx6Fj2f/91+x+ZwoAn039IwDtfzGOdkPGQIjziJaUubnh3yvo1q4lg3smsjIrj6y9hQHVYLUNCOmpCb6p+K2NxBzJahtIFGgpIn2Bo2p43kciosA/VXUa0EVVcwBUNUdEOjvHduNQsALIdtIqSzcRNnZgCn26tjnsxXlpRndmLsvyrUMiEjjHVm2UuSH+2CGk3rWAkt1byHn5FgD2fTmDfV/OoGXvQXT61R+R6Nhqr7WnoIQ9BSV8m53vS/N2HJh43vF1Cgj+U/Ebc6QKZRr5vwZJfgJP7cUVwD01uN+pqtofT7XVzSIytKpbB0nTKtIDTxaZICIrRGTF7t27a5BFUxfpqQncfEavgJfnRf2TifOuwBjj4sELTmRAj/p7ucZ26kHqXQtIvnUWsV2OAaBow1KynriI7H9cTVnBnmquENz0JVt8XYqDPZcxxqPaXlsistJ5+dfvjUUeAA4A1wOnO6WRJGCxqvYRkX8627Oc49fjqdY63Tn+Bic94LhgrNdW5FXs9TR10UYe/3B9g9xL3eXs/XAqB777KCC966//Sly342p0Lf/pWoxpbhpk0sa6EJFWItLGu41nLMpqYD6H1jO5EpjnbM8HxovHICDfqQL7EBgmIgkikuBc58NwPYepnYp/0Q/qmUhs1KHCZWy0ixuH9qyXe4krisQRt3oGOJ7zG1/6jn//nq2PjuTAdwtDvlaZ27P0rzGmcqGUSMqBLGAVnhe/9/f3qloa8o1EegLvOB+jgZmq+rCIJAJzgBTnPpeq6l6n+++zeBrSC4GrVXWFc61rOFSl9rCqvlLVva1E0jhlbs3jrZXZCJ7qr/TUhHof2Oh1MGsVO2fdHZDWpv9IEs66HnFFVXlucvsW/O3y/lYqMc1OvQ1IFJH/AucDfYET/X73Brapat+6Z7dhWSBpWh55bx2vLtlCYS0GMlanLH8nOdNvx12035cWd9RxdL7sz7jiKp8WPyZKuDSjOxc7Ac+Y5qBeA4mqnhIkXYBeqrqh9tkMDwskTdMj761j7jc/IUDO/uJ6vba75CC7507h4I8rDyVGxXDUNc8S06HyToAtYupvGpbKpqYxprGoz0Bynaq+WG85iwALJE2fN6gkxMdySqpnZPpTC9ez+0DdluZVVfZ98Rr7l8wJSO98yQO0PCb4v59xA1O4qH8yl7+w1De2pLpBjRX5T98Poa8MaXN3mXBqsLm2miILJEcm79Ql3pf58LSufLNtH/26t+fdVTmU1nCwys/rvmDP/EcD0tqffhVtB1yM+A1wjHLB0R1bs3HXAV/auIEpPHzhiSHf64qXlvnWfwH4Ze+OvHbtwCrPsbm7TLjZwlbmiFfVQMErBvdg6eZcCopKQ268b3X8L2l1/C8p2bmZnH/dCsC+xf9i3+J/EX/cL+l4/h1IdAzlbgKCCASfcK6q0kNiq9gqPwdjc3eZxsoCiWnSKhs57p+ektiKl7/czOY9PxPK3JGxXXqo0ZpwAAAfaklEQVSSetcCygvz2Tnzbkpzsyj8/guyvv+C6IQkuo57jKhWh+4pQN+j2gVco7rSQ+7PgVVyFT8HY3N3mcbKAok54o0dmOJbPvjtldnM+k9WSAElKr4dR133D7S8jNz3/8bPaxZRlpdD9rNXANB1/FPEJfVGgUnzV9OnaxtfsKiu9DCib1JA1VbFBcaCsbm7TGNlbSSm2fGvclq/o4A/zV0VUmAB2L98LnmfBvY9SRx5J63TzuAP5/bh5jN6MXNZFrOXZ7E2Zz9utxJTSXuG9doyjZ01tvuxQGKq4g0sBUWlLNmcy9bcn9lXVFblOUVbvmHX7D8FpP3ywquIGXwFm3KLfGnDTujCDacd06hLD9YTzFTGAokfCySmOt42jeJSd+grtQGleTnk/Ot3aEmhLy0u5SQ6X/QnXHHxAb2xGmMJxHqCmapYry1jasDbplHTP6tiEpJIuX0O7uJCdr39IMVZqyjO+o5tT1+GxMaz7nfPc8VLnl5Zc7/ZDuBrG2kMwcR6gpn6YIHEGA71iKrN+vIArrh4ul7+F1Td5C16mYLlc9GSQjIfH08m0Hn0Q7Ts0c93/OzlWazZno+Cb9qVSFQxWU8wUx+sassYh7dXl3cRrro6sPpTct99MiAt4azraZsxKiAtSuCs47uwaP0uysq1ypHywYJNKAGoqmOqO9/aUJovayPxY4HE1MTMZVn86Z1V1NeUkcU5P7Dj1TsC0lqlnUHiiN8hUcErBYad0IVp4wP//c5cluVZyljV154BVNvGUZd2EGtDad4a3XokxjQVYwem8MZvhjB2YAoDeiQEXZKzJuKSjvWs4Hjza0S394wX+XnNIrL+egHbX7qJ8sL8w875ZN1O3+qM4HmhT5q3mjK34lbPWvNLN+cGbeOoKJRjKuN/bkmZm6c//iEgX+GUuTWPqYs21vn+9XUdc4i1kRgThP/IeP91U34uLmPBd9spq0VxJap1At1ueAEtK2XPu09S+P0XlO7JIvvv4wBIuvoZYjt7FvcqV7jrzW959JKTAXj64x8o8xvs4hLxtWdU1caRuTWP7fuKiHYJ5c6Ylpq0g3jbULzB5MsNe1i+ZW+Dlkwqq76rj5KRlbAahgUSY6pRcRqWKwb3qFVXYS+JjqHTqLvQX/2R/cveYt9n/wIg5xXP/F4dR02k1XG/YOPun7n4ua+Dloiu+8XRvjxVNtrd/6UZHeVi9IDD11Oprv3DO5r+6Y9/4MsNe1AatndXZS/6+updZr3UGoYFEmNqyH+qkoKiUtbk7CctqS37i8uYuSwr5OuICO0GXUK7QZdQtGk5u978MwB75j3CnnnQdvBltP/lFSCHh5L/W5XDOWldASoNBP4vzfJyN93atzwsiFw+bQml5UpMlDBrwuBKg8ltZx/L8i17G7x3V2Uv+vrqXWa91BqGBRJjaqGyySLbxkXXaqnglsf8D6l3LaA0N5vtr9wC5WXsXzKH/Uvm0OLo/nS68B5cMS18x/+UV8Slz3tKK24lIBB4SxkJ8bG+l2aUS9i+r4jMrXm+fL+1MpsSZ6r9knLlrZXZlf51Xtd5vkLt+VXZi76+5hmz+coahvXaMqaePfLeOqZ9sRm3emYG7tWpFRt2/1yja7iLf2bXnPsp3v69L80V346k8U8R3a5z0HPGDkzh4v7JAVVDk0amsXp7Pm9mZvsCyuRRfRk7MIV731nFDL8SVK9OrRjYM5G0o9qxens+AlxUh6WF/QPa5AVrQm6XsO7GjYd1//VjgcSEW8WX4W2v/9c3sh3AJYQ0UaS6y8n7ZBoFK98NSO8y9hFadO8bkDagRwJxMVF8tXEPbvWMT7ljWB8A/vrhel97TpTAnBuHAHD5C56gU5noKGF0Rnd+Li7jm237GJ7WlYnnHR/S83sDmks8Df3KoTzdfEav6h/eRFyjDCQiEgWsAH5S1ZEicjTwOtABWAlcoaolIhIHvAqkA7nAaFXd4lzjbuBaoBy4VVU/rO6+FkhMY1Bxri3vAMhlm3PZGEKJpeDbj9j7wTMBaR2G3USbU84D8DXKK55A5T/W5NLnvw4IXN5xKplb8wIa0kNx49Ce1QaTqYs28sRH63GrJy8uEVQrnwk5VFZaCa/GOtfW74B1QFvn86PAU6r6uog8jydAPOf8zlPVXiIyxjlutIicAIwB0oCjgI9F5FhVLQ/zcxhTY951Uby87SzeRu+SapYGbnPyMNqcPIyD2evYOeMPAOz96B/s/egftD5pGB3OvRlxRQHQuU0cJya3B2Dhmh2HlX6841TSUxMY0TeJrzfuIdSViT9YsyMgkAR7uVds65g0Mo28wpKQAkBlwcK67jZeYQskIpIMnA88DNwhnkWwzwTGOodMBx7AE0hGOdsAbwLPOsePAl5X1WLgRxHZCAwAloTpMYypd+mpCcyaMNjXnpBXWOKb0n7L3p/JLwyc0r5F8vGk3rWAsv172PHv31NesIcD333Ege8+IrbLMXQe/RA7gB1rd7Jw7c6g9yxXeHtlNgCTF6wJGkRcAi6XUFZhZ7/u7X3blb3ca9uoXVWwsK67jVc4SyRPA38E2jifE4F9qur9V5INdHO2uwHbAFS1TETyneO7AUv9rul/jjFNVmW9wEY9+yXfBhn5DhDdtiPJN/0Ld2kxe+Y/RtHGZZTs3ET2M5cDkHTNVGI7pVZ6zzdWbEOh0jYSt8LZfTpTVFoesJpj7y5tfKWGn/YVBbzc31qZfVjw8I6kD6WBfXuF6/kHC+u623iFJZCIyEhgl6pmisjp3uQgh2o1+6o6p+I9JwATAFJSIj9dtzG1Mfp/Uvg2e1WVx7hi4uh88X2oKvlfv07+lzMAyHn5ZgA6XfQn4nsPOuy8knJl484CYqNdlQ6uVCClQzyxUYdGxifExwYMdPSOmo9yCW9mZlNWfqjHWCi9tfznEIt2CdFRLsrL3URFufjJr8tyKKUca0OJjHCVSE4FfiUi5wEt8LSRPA20F5Fop1SSDHi7tWQD3YFsEYkG2gF7/dK9/M8JoKrTgGngaWyv9ycyJgy8bSrvr84hLaltlWNURIT2p15O+1Mvp/CHJex+52EAdr/9EADtfjGOdkPGIH4DHP+zJY8BPRJoHx/Lx2t3HjZR5eL1uyh3a8DI+IoDHccMSOGo9i35dts+Fq7d6Rv9/v7qnGqrovznEAMocytjBnRH8JSYXv9PFm+vzA6oMqtqhuP6akOxgFQzYZm0UVXvVtVkVe2Bp7H8U1UdBywCLnEOuxKY52zPdz7j7P9UPd3L5gNjRCTO6fHVG/hPOJ7BmEgZOzCF164dyMTzjufGoT0D9g3t3THoOfHHDib1rgUkXTPVl5b/5QyyHvtfdr31IFpW4kv/z5Y8Pll3eBABKC33TBJZVnZoZHxCfCwuEVwCMdEuLuqfzKCeiSxev+tQF+MoFyP6JhEb7SLKOS5YVdTSzbmUV5hD7OL+yRzVvqVvgspQJ5qsy+SU/rwB6YmP1jPuxaU2uWMIIj2y/S7gdRF5CPgv8JKT/hLwmtOYvhdP8EFV14jIHGAtUAbcbD22THMy8bzjSUlsFdCNuOIYFX+xnVJJvWsB5UUF7Jr9J0p2bqJo4zKynriIqDYd6XrFX4lu07HaHltuICE+lsyteTww31OCiBKYNDKN9NQEpi7a6CtVCHBJejJjB6bQp2ubKtdB2b6viJgoT4O+yxks6T2usvaQykoLtWlDCXYta9SvORuQaMwRYOayLKa8u5YDJVX/XaXucvZ+OJUD330UkN71148T163qsSHjBqagzr28xg5MYcqFJwZdK6W6xnX/dpZL0pNDmlCyuuqrmlRJea9VXBo44t+b7g1Ikepm3Biq1xrrOBJjTAPwjlHxn5Ykr7DE9/vbbfv4aO1OxBVF4ohbSRxxKwUr32XvwucA2PFvz7iUxBG30vqkYbRpEU3BwcBux2+s2Eavzq0D0gTPC2/ygjW+BvdJI9MAz6DEyl6CFf/qFwi63LD3XO9gzpYxUVWWFqpqQwmWB28ngzK3Mmneavp0bdMo5uNqamNmLJAYcwSp7EWauTWPzzfsDuid1ab/+bTpfz4Hs1axc9bdAOS+/wy57z/DoJFj2X/8aN8AR/C0l6zNKQi47q6CYt5emU1Jmee6qsrq7fnV9tYa1DOR6CiX77w3Vmwj7ah2Qc+buSyLe9451HMtJkqQWqytUtGgnolEucRXJedW9QWmmgSkhtDUqtcskBjTDPj/lZ0QH8vq7fnsKShm8fpduFJP9AxwzN9Fzqu34y7MZ+mCmbBgJnFHHUfny/6MK65V0O7BC9fuJDbqUJfdmGgXAtW+BNNTE7gkPZlZy7JQoNytlfbyen91TsC5JyS1ZVha1zqXFtJTE5g8qm9AlVxjGZvS1MbMWCAxppkI9le2/1xb0e060+PWGQzo3oq5f72Tgz+upHj792x7ejRERXPU1c8Sk5h82HVLypVhJ3Tm5O7tfS+8t1ZmV/sSvLh/Mm/7HTeib1LQNU9G9E0KGBA5+n8Cp5qpi+o6BERKY6heqwlrbDemmavYuDxpZBqT5q2itFzZ98Vr7F8yJ+D4zpc8QMtjAttfXQIPXXCi7wXvbdNIS2pLm5YxIQ8grKyBueKElyY8GuXsv5FigcSYqgV7oT//2SbW5uwnZ18RB9Z+we75jwac0/60q2g78GLfAMdolzD7hsEAAUsRi/NzVPsWtGkRQ2y0K6RSRWPotdTcWSDxY4HEmNrzf6GvX7OKceefFrA//rhf0vH8O4iKjuHOcz3rn3inkK/KlAtPrDSYNLVeS0eqUANJWEa2G2OarvTUBG4+oxfpqQmMPW8oqsquXbvoeexxABR+/wVZT1xI9rTr6dW6zNdQXN3LpWIjuj9v11y3Qklp7Uepm/CwQGKMqbFOnTqxaf06SkpKOP+iMQCU5uUwfMDxZPTowL0D4rjz3D7cOLRnpS+ZEX2TKr1+Qnysr5eYd1S9abwskBhjai0mJoYFb81CVXnqqad86eN/dRa3nNmb7nkreeM3QzjnhC706tya47u24eTkdlVWawHkFZbgcuaWdInncygyt+YxddFGmx+L8P63sDYSY0y9+vjjjznnnHMC0u644w4ef/xxXK7Q/natzTQlNWlXOdIb8uurjcnaSIwxEXH22WejqmzcuJG2bT2raj/55JNERUVxxhlnUFBQUM0VDo2juGNYn5BfgqHO/tscZvetr5mQQ2WBxBjTII455hjy8/PZv38/Z5xxBgCLFy+mbdu2tG3blk2bNlV5vn8jfyi8jfxVTVsP4X/JRkKo/y3qiwUSY0yDatOmDZ9++inl5eXceeedABQUFNCrVy9EhE8++aRe7hNqKSbcL9lI8P63GD0ghYv7Hz4bQX2zNhJjTNjNmDGDX//61wFpTz31FLfddltY7n+kt5FA/bSTWBuJMabRGjduHKrK8uXLfWm33347IsL48eMpLS1t0PvXtNqsKQpnFZ4FEmNMxGRkZKCq5OTk0KtXLwBee+01YmNjSUtLY/fu3RHOYdMVzio8q9oyxjQaxcXFjB8/njlzAieK/Oabbzj55JMjlKumq65VeFa1ZYxpcuLi4pg9ezZut5tHHz00SWS/fv0QEd54440I5q7pCVcVngUSY0yjIyL88Y9/RFV57733fOmXXXYZIsK9995Lc6hNaSrCFkhEpIWI/EdEvhWRNSLyZyf9aBFZJiIbRGS2iMQ66XHO543O/h5+17rbSV8vIueG6xmMMeE3YsQIVJXvv/+euLg4AKZMmYLL5WL48OEUFhZGOIcmnCWSYuBMVT0Z6AcMF5FBwKPAU6raG8gDrnWOvxbIU9VewFPOcYjICcAYIA0YDvxDRKIwxhzR+vTpw8GDB9m3bx9DhgwB4MMPP6RVq1Z06tSJrVu3RjiHzVfYAol6HHA+xjg/CpwJvOmkTwcucLZHOZ9x9p8lnhV0RgGvq2qxqv4IbAQGhOERjDGNQLt27fjqq68oKyvjlltuAWDPnj306NEDEeGzzz6LcA6bn7C2kYhIlIh8A+wCFgKbgH2qWuYckg10c7a7AdsAnP35QKJ/epBzjDHNRFRUFH//+99RVV566SVf+umnn46I8Nxzz0Uwd81LWAOJqparaj8gGU8p4vhghzm/pZJ9laUHEJEJIrJCRFZYX3RjjmzXXHMNqsrXX3/tS7vpppsQEa6//nrKysqqONvUVUR6banqPmAxMAhoLyLRzq5kYLuznQ10B3D2twP2+qcHOcf/HtNUNUNVMzp16tQQj2GMaWQGDx6MqpKdnU337p7XxIsvvkhMTAzp6ens3bs3wjk8MoWz11YnEWnvbLcEzgbWAYuAS5zDrgTmOdvznc84+z9VT3+/+cAYp1fX0UBv4D/heQpjTFPQrVs3srKyKCoqYtSoUQCsXLmSxMRERIQ1a9ZEOIdHlnCWSJKARSLyHbAcWKiqC4C7gDtEZCOeNhBvZedLQKKTfgcwEUBV1wBzgLXAB8DNqloexucwxjQRLVq0YO7cubjdbiZPnuxL79u3LyLC3LlzI5i7I4dNkWKMaVbmzZvHBRdcEJD25z//mfvuuw9Px1DjZVOkGGNMEKNGjUJVWb16tS/t/vvvx+VyMWrUKIqKiiKYu6bJAokxpllKS0tDVcnNzaV///4AzJ8/n/j4eLp3785PP/0U4Rw2HRZIjDHNWocOHcjMzKS0tJTrr78egOzsbJKTkxERlixZEuEcNn4WSIwxBoiOjmbatGmoasBgxiFDhiAivPzyyxHMXeNmgcQYYyq48cYbUdWA6VauvfZaRIRbbrmF8nLrKOrPAokxxlRi6NChqCpbtmyhc+fOAEydOpXo6GgGDx5Mfn5+hHPYOFggMcaYaqSmprJz504OHDjA8OHDAVi6dCnt27cnLi6O9evXRziHkWWBxBhjQtSqVSvef/993G4399xzDwAlJSUcd9xxiAjvv/9+hHMYGRZIjDGmhkSEhx9+GFVl9uzZvvTzzjsPEeHRRx9tVis4WiAxxpg6uOyyy1BVvvnmG1/axIkTcblcjB49muLi4gjmLjwskBhjTD04+eSTUVV27dpFWloaAHPmzKFFixb06tWLHTt2RDiHDccCiTHG1KNOnTqxevVqSkpKGD9+PACbNm0iKSkJEWH58uURzmH9s0BijDENICYmhunTp6OqPPXUU770AQMGICL8+9//jmDu6pcFEmOMaWC33XYbqsrHH3/sS7viiisQEe68807cbncEc1d3FkiMMSZMzjrrLFSVTZs20a5dOwCefPJJoqKiOOOMMygoKIhwDmvHAokxxoRZz5492bdvHwUFBZx55pkALF68mLZt29K2bVs2bdoU4RzWjAUSY4yJkNatW/PJJ59QXl7O73//ewAKCgro1asXIhJQFdaYWSAxxpgIc7lcPP7446hqQCP8Oeecg4jw9NNPRzB31bNAYowxjci4ceNQ1YBuwrfffjsiwvjx4yktLY1g7oKzQGKMMY1QRkYGqsqOHTvo3bs3AK+99hqxsbGkpaWxe/fuCOfwkLAFEhHpLiKLRGSdiKwRkd856R1EZKGIbHB+JzjpIiLPiMhGEflORPr7XetK5/gNInJluJ7BGGPCrUuXLvzwww8UFxczZswYANauXUvnzp0RkYCpWSIlnCWSMuBOVT0eGATcLCInABOBT1S1N/CJ8xlgBNDb+ZkAPAeewAPcDwwEBgD3e4OPMcYcqWJjY5k1axZut5vHHnvMl37KKacgIrzxxhsRy1vYAomq5qjqSme7AFgHdANGAdOdw6YDFzjbo4BX1WMp0F5EkoBzgYWquldV84CFwPBwPYcxxkSSiPCHP/wBVeW9997zpV922WWICPfee2/YZx6OSBuJiPQATgGWAV1UNQc8wQbo7BzWDdjmd1q2k1ZZujHGNCsjRoxAVVm/fj0tWrQAYMqUKbhcLoYPH05hYWFY8hH2QCIirYG3gNtUdX9VhwZJ0yrSK95ngoisEJEVjalRyhhj6tuxxx5LUVER+/btY8iQIQB8+OGHtGrVKiyN8mENJCISgyeIzFDVt53knU6VFc7vXU56NtDd7/RkYHsV6QFUdZqqZqhqRqdOner3QYwxphFq164dX331FWVlZfz2t7/ltNNOo1WrVg1+33D22hLgJWCdqj7pt2s+4O15dSUwzy99vNN7axCQ71R9fQgME5EEp5F9mJNmjDEGiIqK4plnnmHx4sXEx8c3+P2iG/wOh5wKXAGsEhFvf7V7gEeAOSJyLZAFXOrsew84D9gIFAJXA6jqXhF5EPCO1pmsqnvD8wjGGGMqkuawrnBGRoauWLEi0tkwxpgmRUQyVTWjuuNsZLsxxpg6sUBijDGmTiyQGGOMqRMLJMYYY+rEAokxxpg6sUBijDGmTppF918R2Q1sjXQ+aqAjsCfSmWgg9mxNz5H6XGDPVp1UVa12apBmEUiaGhFZEUrf7abInq3pOVKfC+zZ6otVbRljjKkTCyTGGGPqxAJJ4zQt0hloQPZsTc+R+lxgz1YvrI3EGGNMnViJxBhjTJ1YIIkgERkuIutFZKOITAyy/yoR2S0i3zg/10UinzUlIi+LyC4RWV3JfhGRZ5zn/k5E+oc7j7UVwrOdLiL5ft/ZpHDnsTZEpLuILBKRdSKyRkR+F+SYJvm9hfhsTfV7ayEi/xGRb51n+3OQY+JEZLbzvS1zljqvX6pqPxH4AaKATUBPIBb4FjihwjFXAc9GOq+1eLahQH9gdSX7zwPex7Ns8iBgWaTzXI/PdjqwINL5rMVzJQH9ne02wA9B/n9skt9biM/WVL83AVo72zHAMmBQhWNuAp53tscAs+s7H1YiiZwBwEZV3ayqJcDrwKgI56leqOrnQFWLjY0CXlWPpUB773LLjV0Iz9YkqWqOqq50tguAdUC3Coc1ye8txGdrkpzv4oDzMcb5qdjwPQqY7my/CZzlrFhbbyyQRE43YJvf52yC/899sVON8KaIdA+yvykK9dmbqsFOVcP7IpIW6czUlFP1cQqev279NfnvrYpngyb6vYlIlLPq7C5goapW+r2pahmQDyTWZx4skEROsL8IKv4l8X9AD1U9CfiYQ39VNHWhPHtTtRLPtBInA38H5kY4PzUiIq2Bt4DbVHV/xd1BTmky31s1z9ZkvzdVLVfVfkAyMEBE+lY4pMG/NwskkZMN+JcwkoHt/geoaq6qFjsfXwDSw5S3hlbtszdVqrrfW9Wgqu8BMSLSMcLZComIxOB50c5Q1beDHNJkv7fqnq0pf29eqroPWAwMr7DL972JSDTQjnqunrVAEjnLgd4icrSIxOJpBJvvf0CF+udf4anbPRLMB8Y7vYAGAfmqmhPpTNUHEenqrX8WkQF4/o3lRjZX1XPy/BKwTlWfrOSwJvm9hfJsTfh76yQi7Z3tlsDZwPcVDpsPXOlsXwJ8qk7Le32Jrs+LmdCpapmI3AJ8iKcH18uqukZEJgMrVHU+cKuI/Aoow/MXxFURy3ANiMgsPL1gOopINnA/nkZAVPV54D08PYA2AoXA1ZHJac2F8GyXAL8RkTKgCBhT3/9oG8ipwBXAKqe+HeAeIAWa/PcWyrM11e8tCZguIlF4gt8cVV1Q4T3yEvCaiGzE8x4ZU9+ZsJHtxhhj6sSqtowxxtSJBRJjjDF1YoHEGGNMnVggMcYYUycWSIwxxtSJBRJjjDF1YoHEGGNMnVggMc2aiLQUkc+cie9uEJEcZz2KjSIy15l1oLbXvkFEdjgTAW4SkfEiEisinztTVVSbp9reO4S8VZsPY0JlgcQ0d9cAb6tqOXAScI8zAd6xQF8nrbZOAh5wJgK8HHjSWTLgE2B0iHlqECHmw5iQWCAxzd04YJ6zfSLwX2e7F55ZU3+ow7VPBNY72z8CJc72XOe+VeZJRHqIyPci8qKIrBaRGSJytoh8JSIbnDmhAHBKT5nOKnkT/NLvc66xUERmicjv/e5TXT6MCYlNkWKaLafaKktVuzqfc4Gf8MydlQyc7yxkVdvr5wFpQA7wALBFVV9xqqx2qGqnqvLkrJ2xEc/6GWvwTPT5LXAtnkk8r1bVC5zzOqjqXmfivuXAacDRwIvAYDzz6q0E/qmqf3XOqTQfxtSE1Y+a5qwjsA8863oDu5y1XxCR8cB9wDn+J4jIx0DXINe6V1Xn+R3XHc+yru/hWVjoOzzBBFUtF5ESEWnjrNgXNE+OH1V1lXPNNcAnqqoisgro4XfcrSJyobPdHeiNZznceapa5Jz/f/43qiYfxoTMAolpzoqAFs72ScBav33fAndWPEFVzw7x2icBn6vqmSKSAKzGUzL42tkfBxysJk8AxX7bbr/Pbpx/vyJyOp7pwweraqGILHauEcpyqpXlw5iQWRuJabZUNQ+IEpEWeNoz1oFv/Yor8axKWVu+9hbnPjOB853rJwK7VbW0mjyFqh2Q5wSR4/CURAC+BP5XRFo4qwOe739SVfkwpiYskJjm7iPgF3he/FeJyH+BTDx/0d9Xh+v6N9yDZ9nk85ztM/BUeVWXp1B9AESLyHfAg8BSAFVdjmdRo2+Bt4EVeNbr9qouH8aExBrbTbMmIqcAd6jqFWG859vA3aq6vpL99ZYnEWmtqgdEJB74HJigqitDyYcxobI2EtOsqep/RWSRiEQ15LgNL6dX1tyqXt71nKdpInICnhLWdL8gUm0+jAmVlUiMMcbUibWRGGOMqRMLJMYYY+rEAokxxpg6sUBijDGmTiyQGGOMqRMLJMYYY+rEAokxxpg6sUBijDGmTv4f/y6Um3rLxrAAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Clean up data (remove NaNs)\n", "data2 = data[~np.isnan(data['bp_rp'])]\n", "data2 = data2[~np.isnan(data2['teff_val'])]\n", "\n", "x = np.asarray(data2['bp_rp'])\n", "y = np.asarray(data2['teff_val'])\n", "\n", "# Fit data with linear model\n", "fit = np.polyfit(x,y,1)\n", "T0 = fit[1]\n", "T1 = -1*fit[0]\n", "print('T0 = '+str(fit[1]))\n", "print('T1 = '+str(-1*fit[0]))\n", "fit_fn = np.poly1d(fit) \n", "\n", "# plot the results\n", "plt.plot(x, y, marker='.', linestyle='None')\n", "plt.plot(x, fit_fn(x), '-k')\n", "plt.ylabel(r'$T_{\\mathrm{eff}}$ (K)')\n", "plt.xlabel(r'$(B-R)$ (mag)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (d) Using the data for MG, luminosity, and effective temperature, find a relationship for luminosity given $M_{G}$ and $BP − RP$, of the form $L = L_{\\odot}10^{((M_G−M_0)/M_1)}$, and estimate values of $M_0$ and $M_1$. What should these numbers be if $M_G$ was a bolometric absolute magnitude?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In other words, we want to find a linear relationship between $\\log(L/L_{\\odot})$ and $M_{G}$: $M_{G} = M_{0} + \\log(L/L_{\\odot})M_{1}$\n", "\n", "Plot these quantities against each other and fit a line." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "M0 = 4.859305762769101\n", "M1 = -2.54773050268098\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$G$ (mag)')" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Clean up data (remove NaNs)\n", "data2 = data[~np.isnan(data['phot_g_mean_mag'])]\n", "data2 = data2[~np.isnan(data2['lum_val'])]\n", "\n", "y = data2['phot_g_mean_mag'] + 5. - 5.*np.log10(1000./data2['parallax'])\n", "x = np.asarray(np.log10(data2['lum_val']))\n", "\n", "# Fit data with linear model\n", "fit = np.polyfit(x,y,1)\n", "M0 = fit[1]\n", "M1 = fit[0]\n", "print('M0 = '+str(fit[1]))\n", "print('M1 = '+str(fit[0]))\n", "fit_fn = np.poly1d(fit) \n", "\n", "# plot the results\n", "plt.plot(x, y, marker='.', linestyle='None')\n", "plt.plot(x, fit_fn(x), '-k')\n", "plt.xlabel(r'log($L/L_{\\odot}$)')\n", "plt.ylabel(r'$G$ (mag)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $M_{G}$ was a bolometric magnitude: $M_{\\mathrm {bol,\\star } }-M_{\\mathrm {bol,\\odot } }=-2.5\\log _{10}\\left({\\frac {L_{\\star }}{L_{\\odot }}}\\right)$\n", "\n", "Solving this for $L/L_{\\odot}$, we find $M_{1} = -2.5$ and $M_{2} = 4.74$ is the bolometric magnitude of the Sun." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (e) Using your relations for luminosity and temperature given $M_G$ and $BP−RP$, derive a relationship using these Gaia parameters to determine the radius of a star. Plot your inferred radius compared to the Gaia measured values for stars where you have a radius measurement, and comment on the difference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Start with the relationship between luminosity, temperature, and radius: $L = 4\\pi R^2 \\sigma T^4$\n", "\n", "Solve for radius: $R = \\left(4\\pi\\sigma\\right)^{-1/2}L^{1/2}T^{-2}$\n", "\n", "Plug in our expressions for $L$ and $T$: $R = \\left(4\\pi\\sigma\\right)^{-1/2}(L_{\\odot}10^{((M_{G}−M_{0})/M_{1})})^{1/2}(T_{0} − T_{1}(BP − RP))^{-2}$" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 68, "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": [ "# Define some units in cgs\n", "Rsun = 7.0e10 # cm\n", "Lsun = 4.0e33 # erg s-1\n", "sigma = 0.567e-4 # erg cm-2 K-4 s-1\n", "pi = np.pi\n", "\n", "# Clean up data (remove NaNs)\n", "data2 = data[~np.isnan(data['phot_g_mean_mag'])]\n", "data2 = data2[~np.isnan(data2['bp_rp'])]\n", "data2 = data2[~np.isnan(data2['radius_val'])]\n", "\n", "# Define all parameters\n", "g = data['phot_g_mean_mag'] + 5. - 5.*np.log10(1000./data['parallax'])\n", "bprp = data['bp_rp']\n", "\n", "# Infer radius from MG, BP-RP\n", "r_infer = (4.*pi*sigma)**(-0.5) * (Lsun * 10**((g-M0)/M1))**(0.5) * (T0 - T1*bprp)**(-2.)\n", "\n", "# Convert to solar radius\n", "r_infer = r_infer/Rsun\n", "\n", "# Plot against actual radius\n", "plt.plot(np.log10(r_infer), np.log10(data['radius_val']), marker='.', linestyle='None', label='N='+str(len(data['radius_val'])))\n", "plt.xlabel(r'Inferred $\\log(R/R_{\\odot})$')\n", "plt.ylabel(r'Gaia $\\log(R/R_{\\odot})$')\n", "plt.plot([-0.5,2.5],[-0.5,2.5],'r-',label='One-to-one line')\n", "plt.legend(loc='best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inferred radius tends to overpredict the true measured radius -- probably because the relationship between Teff, BP-RP isn't a perfect line (we tend to underpredict Teff and therefore overpredict radius)" ] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }