{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(a) (5 points) Calculate the relative total mass of stars below 1 solar mass to stars above 1 solar mass in a Salpeter IMF versus a Kroupa et al. (1993) IMF ( a 3 power law segment IMF, see slide 13 in presentation Download slide 13 in presentationfor details), normalizing them to have the same number of stars above 1 solar mass. Use a lower cutoff mass of 0.07 solar masses and an upper cutoff mass of 100 solar masses. Remember that an IMF is a continuous function, and do this analytically. What are the implications for estimating a total stellar mass based on galaxy luminosity?\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Salpeter IMF, \n", "$$dN/dM = A M^{-2.35}$$ \n", "where we'll set the normalization $A=1$ and work in solar masses.\n", "We'll integrate from 0.07 to 100 solar masses to get total mass:\n", "$$\\int_{0.07}^{100} M dN/dM dM = \\int_{0.07}^{100} M^{-1.35} dM = {1.\\over -0.35} 100^{-0.35}-0.07^{-0.35} = 6.68$$\n", "\n", "For KTG IMF, we have \n", "$$dN/dM = A M^{-2.7}$$ for M>1, \n", "$$dN/dM = A M^{-2.2}$$ for $0.5" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "def salpeter(m, slope=-2.35) :\n", " \"\"\" Salpeter IMF, single power law\n", " \"\"\"\n", " return m**slope\n", "\n", "def ktg(m) :\n", " \"\"\" KTG IMF, 3-segment power law\n", " \"\"\"\n", " # for efficiency, initialize output array and fill 3 sections separately\n", " imf = np.zeros(np.shape(m))\n", " j=np.where(m>1)[0]\n", " imf[j] = m[j]**-2.7\n", " j=np.where((m>0.5)&(m<=1))[0]\n", " imf[j] = m[j]**-2.2\n", " j=np.where(m<=0.5)[0]\n", " imf[j] = 0.5**(-2.2+1.3)*m[j]**-1.3\n", " return imf\n", " \n", "mass=np.arange(0.07,100,0.01)\n", "plt.plot(mass,salpeter(mass),label='Salpeter')\n", "plt.plot(mass,ktg(mass),label='KTG')\n", "plt.legend()\n", "plt.loglog()\n", "plt.xlabel('Mass')\n", "plt.ylabel('dN/dM')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The question actually suggested normalizing the IMFs to be equal number of stars above 1 solar mass. This doesn't really make for an obvious meaningful comparison, where what we're really be interested in is having the same total light from the two IMFs, but that would require applying an age and having to have luminosity as a function of mass. So, just going with what was asked, calculate the nummber of stars above 1 solar mass:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.7392627686555786 0.5880011134290861 1.2572472258502532\n" ] } ], "source": [ "nsalpeter = (100**-1.35 - 1**-1.35) / -1.35\n", "nktg = (100**-1.7 - 1**-1.7 ) / -1.7\n", "print(nsalpeter,nktg,nsalpeter/nktg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This says we'd have to scale the KTG up by about 25 percent to match the total number of stars above 1 solar mass." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question asked about fraction of mass below and above 1 solar mass for the two IMFs. This is actually independent of the normalization! But, again, it's not really an especially meaningful quantity, I'm afraid.\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.676747846301279 0.6574577979194078\n" ] } ], "source": [ "msalpeter = (100**-0.35 - .07**-0.35) / -0.35\n", "msalpeterlow = (1**-0.35 - .07**-0.35) / -0.35\n", "print(msalpeter, msalpeterlow/msalpeter)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Salpeter IMF has 66% of mass below 1 solar mass" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.3418095474777094 0.5895340664549453\n" ] } ], "source": [ "mktg = 0.5**(-2.2+1.3)* (0.5**0.7 - 0.07**0.7) / 0.7 +\\\n", " (1**-0.2 - 0.5**-0.2) / -0.2 +\\\n", " (100**-0.7 - 1**-0.7) / -0.7\n", "mktglow = 0.5**(-2.2+1.3)* (0.5**0.7 - 0.07**0.7) / 0.7 +\\\n", " (1**-0.2 - 0.5**-0.2) / -0.2 \n", "print(mktg, mktglow/mktg)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "KTG IMG has 59% of mass below 1 solar mass.\n", "\n", "Compare the two:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.1154499151103567" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ ".657/.589" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Only 11% more mass in Salpeter!! Not the standard result.\n", "\n", "Total mass is quite different, however:\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.242161434702641" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "6.67/(3.34*nsalpeter/nktg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Really, the physical point that I was trying to make is that, for the same luminosity, there is significantly more mass in the Salpeter IMF, i.e. the M/L ratio is higher. But's it's hard to demonstrate that without bringing in luminosities! But that's the next problem....\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Contributions to total mass and light of different stars

\n", "\n", "(b) (10 points) An isochrone will typically include luminosity/magnitude, temperature, and a range of colors for each stellar mass at the specified age. Download isochrones for a solar metallicity population at ages of roughly 100 Myr, 1 Gyr, and 5 Gyr (possible sources: Padova isochrones Links to an external site., MIST isochrones Links to an external site., YaPSI isochrones Links to an external site.). Choose an IMF and calculate the contributions to the total integrated luminosity and to the total integrated mass as a function of stellar mass for each age. Make sure to pay attention to the size of the implied mass bins for each isochrone point when summing up the total luminosity and mass. Make a plot showing your results and discuss the implications in terms of estimating the total stellar mass of a galaxy based on the observed luminosity for different age populations.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I read in Padova isochrone file for solar metallicity:" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [], "source": [ "from astropy.io import ascii\n", "import os\n", "solar=ascii.read(os.environ['HOME']+'/isochrones/zp00.dat')\n", "mass_col='col3'\n", "age_col='col2'\n", "teff_col='col6'\n", "logl_col='col5'" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "image/png": 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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": [ "def isochrone(iso,age) :\n", " \"\"\" Plot isochrone\n", " \"\"\"\n", " #select points of requested age\n", " gd=np.where(a[age_col] == age)[0]\n", " \n", " # plot isochrones\n", " plt.figure()\n", " plt.plot(iso[teff_col][gd],iso[logl_col][gd])\n", " plt.xlim(plt.xlim()[::-1])\n", " plt.xlabel('log Teff')\n", " plt.ylabel('log L/Lsun')\n", " plt.suptitle('Age: {:f}'.format(age))\n", "\n", "isochrone(solar,8.0)\n", "isochrone(solar,9.0)\n", "isochrone(solar,9.7)" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [], "source": [ "def contrib(iso,age,imf=salpeter) :\n", " \"\"\" Determine contribution to cumulative mass and luminosity as a function of mass for an isochrone\n", " \n", " Plot isochrone\n", " Plot cumulative fractions\n", " \"\"\"\n", " #select points of requested age\n", " gd=np.where(iso[age_col] == age)[0]\n", " \n", " # get contibutions to cumulative fractions\n", " mtot=[]\n", " ltot=[]\n", " # the following loop implicitly assumes that entries are sorted by mass! Could sort explicitly if needed...\n", " for index in gd[1:-1] :\n", " # bin width at this isochrone point\n", " dm = (iso[mass_col][index+1]-iso[mass_col][index-1])/2.\n", " \n", " # number of stars for this bin\n", " n = imf(np.atleast_1d(iso[mass_col][index]))*dm\n", " \n", " # contributions to cumulative mass and luminosity\n", " mtot.append(n*iso[mass_col][index])\n", " ltot.append(n*10.**iso[logl_col][index])\n", "\n", " # get the cumulative sums\n", " mcum = np.cumsum(mtot)\n", " lcum = np.cumsum(ltot)\n", " \n", " #plot fractional contributions\n", " plt.figure()\n", " plt.plot(a[mass_col][gd[1:-1]],mcum/mcum[-1],label='mass')\n", " plt.plot(a[mass_col][gd[1:-1]],lcum/lcum[-1],label='luminosity')\n", " plt.xlabel('Mass')\n", " plt.ylabel('Fractional contribution to sum')\n", " plt.suptitle('Age: {:f}'.format(age))\n", " plt.legend()" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "image/png": 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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": [ "#100Myr\n", "contrib(solar,8,imf=salpeter)\n", "#1 Gyr\n", "contrib(solar,9,imf=salpeter)\n", "# 5 Gyr\n", "contrib(solar,9.7,imf=salpeter)\n", "# 5 Gyr KTG\n", "contrib(solar,9.7,imf=ktg)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Composite stellar spectrum

\n", "\n", "(c) (5 points) A professional SPS model will incorporate stellar spectra in order to build the predicted spectrum for the stellar population. Here we will simplify this step by making the assumption that stars are all perfect blackbody sources, emitting a Planck spectrum at a given temperature. Using the isochrones and IMF used in part (b), “synthesize” a predicted spectrum for this simplified simple\n", "stellar population at 100 Myr, 1 Gyr, and 5 Gyr. Make a plot of the results and discuss the implications, including how your predicted spectra compare to actual SPS model spectra at roughly these same ages and what stars are dominating different parts of the predicted spectra at different times." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For composite spectrum, calculate spectral contribution of each point, using Teff/logg/[M/H] to determine spectrum (for blackbody approximation, only depends on Teff). Weight each spectrum by the total luminosity of stars of each mass. For blackbody spectra that are normalized to give correct flux ($\\sigma T_{eff}^4$):\n", "$$ L = N 4 \\pi R^2 BB(T_{eff}) $$" ] }, { "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 }