{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1A. Schechter function:\n", "$$ \\phi(L) = (\\frac{\\phi_*}{L_*}) \\exp(-\\frac{L}{L_*}) (\\frac{L}{L_*})^\\alpha$$\n", "Since we will just be looking for fractions of the cumulative function, the normalization doessn't matter, and we have:\n", "$$ \\phi(L) \\propto (\\frac{L}{L_*})^\\alpha \\exp(-\\frac{L}{L_*}) $$\n", "If we make the approximation that a single power law represents the luminosity function (as was suggested that you can do, but see below for numerical calculation), using $\\alpha$=-1, and removing exponential term:\n", "$$\\int_{L_1/L_*}^{L_2/L_*} (\\frac{L}{L_*})^{-1} dL = \\ln \\frac{L_2}{L_*} - \\ln \\frac{L_1}{L_*}$$\n", "\n", "We have $M_{lo}=-5$, $M_{hi}=-23$, $M_*=-21$, $L/L_* = 10^{(-0.4 (M-M_*))}$\n", "\n", "$$\\int_{L_{lo}/L_*}^{L_{hi}/L_*} L^{-1} dL \\propto \\ln (\\frac{L_{hi}}{L_*}) - \\ln (\\frac{L_{lo}}{L_*}) $$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "total: 16.57861266955713\n" ] } ], "source": [ "#analytic solution assuming power law, get total integral first\n", "mlo=-5\n", "mhi=-23\n", "mstar=-21\n", "lhi = 10**(-0.4*(mhi-mstar))\n", "llo = 10**(-0.4*(mlo-mstar))\n", "tot=np.log(lhi)-np.log(llo)\n", "print('total: ', tot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now get the 25, 50, and 75th percentiles:\n", "$$\\int_{L_{lo}/L_*}^{L_p/L_*} (\\frac{L}{L_*})^{-1} dL = \\ln L_p/L_* - \\ln L_{lo}/L* = (p) (tot)$$\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.25 -9.50\n", "0.50 -14.00\n", "0.75 -18.50\n" ] } ], "source": [ "for perc in [0.25, 0.5, 0.75] :\n", " lum = np.exp(perc*tot + np.log(llo))\n", " m = -2.5*np.log10(lum) + mstar\n", " print('{:.2f} {:.2f}'.format(perc,m))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we include the exponential term, you can do the integral numerically:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.25 -8.84\n", "0.50 -12.69\n", "0.75 -16.55\n", "1.00 -23.00\n" ] } ], "source": [ "def phi(m,mstar=-21,alpha=-1) :\n", " \"\"\"Schechter function in magnitudes\"\"\"\n", " return 10.**(-0.4*(alpha+1)*(m-mstar))*np.exp(-10.**(-0.4*(m-mstar)))\n", " \n", "\n", "# simple integral over full range, using small steps\n", "tot=0.\n", "for m in np.arange(-5,-23,-0.001) :\n", " tot+=phi(m)\n", "\n", "# now do it to get the percentiles to nearest 0.001\n", "tmp=0.\n", "p=0.25\n", "for m in np.arange(-5,-23.001,-0.001) :\n", " tmp+=phi(m)\n", " if tmp/tot > p :\n", " print('{:.2f} {:.2f}'.format(p,m))\n", " p+=0.25\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, note that if you express the Schechter function in magnitudes:\n", "$$\\phi(M) \\propto 10^{-0.4 (\\alpha+1) (M-M_*)} \\exp(-10^{-0.4 (M-M_*)})$$\n", "then, for $\\alpha=-1$, you have\n", "$$\\phi(M) \\propto \\exp(-10^{-0.4 M})$$\n", "and you can integrate analytically" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1B. To get luminosity integral ($\\phi_L$), multiply number at each luminosity by the luminosity:\n", "$$ \\phi_L(L) = L (\\frac{\\phi_*}{L_*}) \\exp(-\\frac{L}{L_*}) (\\frac{L}{L_*})^\\alpha$$\n", "For the case of $\\alpha = -1$, this is particularly easy, since the $L$ cancels:\n", "$$ \\phi_L(L) \\propto \\exp(-\\frac{L}{L_*})$$\n", "So the integral is easy and analytic without any approximation:\n", "\n", "$$\\int_{L_{lo}/L_*}^{L_{hi}/L_*} \\exp(-\\frac{L}{L_*}) dL = -\\exp (-\\frac{L_{hi}}{L_*}) + \\exp(-\\frac{L_{lo}}{L_*}) $$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.25 -19.64\n", "0.50 -20.60\n", "0.75 -21.35\n" ] } ], "source": [ "tot=-np.exp(-lhi)+np.exp(-llo)\n", "\n", "for perc in [0.25, 0.5, 0.75] :\n", " lum = -np.log(-perc*tot + np.exp(-llo))\n", " m = -2.5*np.log10(lum) + mstar\n", " print('{:.2f} {:.2f}'.format(perc,m))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1C. These results show that the bulk of the number of galaxies are at low luminosity, but the bulk of the luminosity comes from higher luminosity galaxies\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "select galaxy properties from SDSS" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/holtz/anaconda3/lib/python3.7/site-packages/requests/__init__.py:91: RequestsDependencyWarning: urllib3 (1.26.9) or chardet (3.0.4) doesn't match a supported version!\n", " RequestsDependencyWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "62710\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/holtz/anaconda3/lib/python3.7/site-packages/astroquery/sdss/core.py:877: VisibleDeprecationWarning: Reading unicode strings without specifying the encoding argument is deprecated. Set the encoding, use None for the system default.\n", " comments='#'))\n" ] } ], "source": [ "from astroquery.sdss import SDSS\n", "zmin=0.015\n", "zmax=0.05\n", "sql=' SELECT \\\n", " objid,ra,dec,petroMag_g,petroMag_r, \\\n", " extinction_g,extinction_r,z,class \\\n", " FROM SpecPhotoAll \\\n", " WHERE \\\n", " z > {:f} AND z < {:f} AND class = \"GALAXY\" \\\n", " AND (ra between 140 and 240) and (dec between 0 and 50)'.format(zmin,zmax)\n", "dr17=SDSS.query_sql(sql, data_release=17) \n", "\n", "print(len(dr17))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine absolute magnitudes, first correcting for foreground extinction, then using distances from Hubble law" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.1, 1.2)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#distances from Hubble law\n", "c=3.e5 # km/s\n", "h0=70 # km/s/Mpc\n", "dist=dr17['z']*c/h0 # distance in Mpc\n", "\n", "# correct for extinction and distance to get absolute magnitude\n", "# in Mpc, m-M = 5 log d + 25\n", "r=dr17['petroMag_r']-dr17['extinction_r']-5*np.log10(dist)-25\n", "g=dr17['petroMag_g']-dr17['extinction_g']-5*np.log10(dist)-25\n", "\n", "\n", "# plot color vs absolute mag, every 10th point to see structure\n", "plt.scatter(r[::10],g[::10]-r[::10],s=1)\n", "plt.xlabel('M_R')\n", "plt.ylabel('g-r')\n", "plt.xlim(-10,-25)\n", "\n", "#color histogram to look for bimodality\n", "plt.figure()\n", "out=plt.hist(g-r,bins=np.arange(-10,10,0.01))\n", "plt.xlabel('g-r')\n", "plt.ylabel('N')\n", "\n", "#plot again limit range in color\n", "plt.figure()\n", "plt.scatter(r[::10],g[::10]-r[::10],s=1)\n", "plt.xlabel('M_R')\n", "plt.ylabel('g-r')\n", "plt.xlim(-10,-25)\n", "plt.ylim(-0.1,1.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Raw luminosity function, uncorrected for selection function" ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Number of galaxies (uncorrected)')" ] }, "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": [ "# hist() returns number of objects per bin, and bin edges (one element more than number of bins)\n", "out=plt.hist(r,bins=np.arange(-25,-16.3,0.1),histtype='step')\n", "plt.xlabel('Mabs')\n", "plt.ylabel('Number of galaxies (uncorrected)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maximum volume as a function of absolute magnitude, given an apparent limiting magnitude:\n", "$$d_{max}=10^{(m_{lim}-m_{abs}-25)/5}$$\n", "$$v_{max}=f d_{max}^3$$\n", "where $f$ depends on the survey geometry, i.e. what fraction of the sky is covered.\n", "\n", "However, we also imposed a maximum redshift." ] }, { "cell_type": "code", "execution_count": 187, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "64.28571428571429 -16.270572368805432\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# center of bins into mabs\n", "mabs=out[1][0:-1]+0.05\n", "\n", "# maximum volume as a function of Mabs\n", "mlim=17.77\n", "dmax=10**((mlim-mabs-25)/5)\n", "# we also have a cutoff in redshift by our query!\n", "dmax[dmax>zmax*c/h0] = zmax*c/h0\n", "\n", "# minimum volume from selection criterion of z>0.015\n", "dmin=.015*3.e5/70\n", "print(dmin,mlim-5*np.log10(dmin)-25)\n", "\n", "# volume probed as a function of mabs\n", "vol = (dmax**3-dmin**3)\n", "plt.plot(mabs,vol)\n", "plt.yscale('log')\n", "plt.xlabel('Mabs')\n", "plt.ylabel('Volume probed')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To account for selection function, divide counts at each absolute magnitude by the volume probed for that absolute magnitude" ] }, { "cell_type": "code", "execution_count": 188, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\phi$')" ] }, "execution_count": 188, "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": [ "# corrected luminosity function\n", "lf=out[0]/vol\n", "plt.plot(mabs,lf)\n", "\n", "plt.xlim(-25,-16.5)\n", "plt.yscale('log')\n", "plt.xlabel('Mabs')\n", "plt.ylabel('$\\phi$')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "V/V_max test is useful to check the completeness of a survey. For every object, calculate the volume in which it is found, as well as the maximum volume in which it could be found. Make a histogram of V/V_max for all objects." ] }, { "cell_type": "code", "execution_count": 247, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/holtz/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: overflow encountered in power\n", " \"\"\"\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ ": 0.46\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#volumen in which object is found\n", "v=dist**3-dmin**3\n", "\n", "# volume in which it could be found\n", "dmax=10**((mlim-r-25)/5)\n", "dmax[dmax>zmax*c/h0] = zmax*c/h0\n", "vmax=dmax**3-dmin**3\n", "\n", "# plot v/vmax\n", "out=plt.hist(v/vmax,bins=np.arange(0,1,0.01))\n", "plt.xlabel('V/Vmax')\n", "gd=np.where((v/vmax > 0) & (v/vmax <=1))[0]\n", "print(': {:.2f}'.format(np.mean(v[gd]/vmax[gd])))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do a Schechter fit to the corrected luminosity function\n" ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Schechter fit:\n", "Mstar: -21.870660 \n", " alpha: -1.347165 \n", " phistar: 0.000100\n", "Schechter fit after remove brightest bins:\n", "Mstar: -21.870794 \n", " alpha: -1.347172 \n", " phistar: 0.000100\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\phi$')" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def schechter(m,mstar=-21,alpha=-1,phistar=1) :\n", " \"\"\"Schechter function in magnitudes\"\"\"\n", " return phistar*10.**(-0.4*(alpha+1)*(m-mstar))*np.exp(-10.**(-0.4*(m-mstar)))\n", " \n", "\n", "# plot the corrected LF\n", "plt.plot(mabs,lf)\n", "plt.yscale('log')\n", "\n", "# do the fit with curve_fit\n", "p0=[-21,-1,1] # starting guess for fit\n", "from scipy.optimize import curve_fit\n", "pars=curve_fit(schechter,mabs,lf,p0=p0)\n", "print('Schechter fit:')\n", "print('Mstar: {:f} \\n alpha: {:f} \\n phistar: {:f}'.format(*pars[0]))\n", "plt.plot(mabs,schechter(mabs,*pars[0]))\n", "plt.xlabel('M_{abs}')\n", "plt.ylabel('$\\phi$')\n", "\n", "# try again removing data with Mabs<-23.5\n", "plt.figure()\n", "gd =np.where(mabs>-23.5)[0]\n", "pars=curve_fit(schechter,mabs[gd],lf[gd],p0=p0)\n", "print('Schechter fit after remove brightest bins:')\n", "print('Mstar: {:f} \\n alpha: {:f} \\n phistar: {:f}'.format(*pars[0]))\n", "plt.plot(mabs[gd],lf[gd])\n", "plt.yscale('log')\n", "\n", "plt.plot(mabs[gd],schechter(mabs[gd],*pars[0]))\n", "plt.xlabel('M_{abs}')\n", "plt.ylabel('$\\phi$')\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 }