galaxies_hw1_gilbert.ipynb

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   "source": [
    "# Samantha Gilbert\n",
    "## Galaxies HW \\#1\n",
    "## Winter 2021"
   ]
  },
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   "source": [
    "We are given a text file containing the SDSS measurements for about 600,000 stars with $b > 80^{\\circ}$ and $14 < r < 21$. Each row represents a star, while each column represents a variety of observational quantities/measurements for each star. We will start by reading in this file."
   ]
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   "source": [
    "#---------------------------------Import modules----------------------------------# \n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from astropy.table import Table\n",
    "import scipy\n",
    "plt.rcParams[\"font.family\"] = \"Times New Roman\"\n",
    "#sb.set_style('white')\n",
    "\n",
    "\n",
    "#---------------------------------------------------------------------------------# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
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   "source": [
    "#---------------------------------Read in data----------------------------------# \n",
    "\n",
    "with open('/Users/samanthagilbert/Desktop/galaxies_hw1/Astr511HW1data.dat', 'r') as ff:\n",
    "    line1 = ff.readline()\n",
    "    cols = line1.strip('#').split()\n",
    "data = Table.read('/Users/samanthagilbert/Desktop/galaxies_hw1/Astr511HW1data.dat', format='ascii')"
   ]
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   "source": [
    "Now, we want to calculate the absolute magnitude $M_r$. To calculate absolute magnitude, we will need to calculate metallicity $[\\textrm{Fe}/\\textrm{H}]$ and change in absolute magnitude $\\Delta{M_r}$.\n",
    "\n",
    "Using Ivezi$\\acute{c}$ (2008), we define\n",
    "\n",
    "$$\\Delta{M_r}([\\textrm{Fe}/\\textrm{H}]) = 4.50 - 1.11[\\textrm{Fe}/\\textrm{H}] - 0.18[\\textrm{Fe}/\\textrm{H}]^2$$\n",
    "\n",
    "$${M_r}(g-i,[\\textrm{Fe}/\\textrm{H}]) = M_r^0(g-i) + \\Delta{M_r}([\\textrm{Fe}/\\textrm{H}])$$\n",
    "\n",
    "where we are given that metallicity can be expressed as\n",
    "\n",
    "$$([\\textrm{Fe}/\\textrm{H}]) =  A + Bx + Cy + Dxy + Ex^2 + Fy^2 + Gx^2y + Hxy^2 + Ix^3 + Jy^3$$\n",
    "\n",
    "using the fact that $x = (u - g)$ and $y = (g - r)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
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   "source": [
    "# Store filter values.\n",
    "\n",
    "u = np.array(data['u'])\n",
    "g = np.array(data['g'])\n",
    "r = np.array(data['r'])\n",
    "i = np.array(data['i'])\n",
    "z = np.array(data['z'])\n",
    "\n",
    "# Determine photometric color.\n",
    "\n",
    "x = u - g\n",
    "y = g - r\n",
    "g_i = g - i\n",
    "\n",
    "# Identify constants for metallicity function.\n",
    "\n",
    "A = -13.13\n",
    "B = 14.09\n",
    "C = 28.04\n",
    "D = -5.51\n",
    "E = -5.90\n",
    "F = -58.68\n",
    "G = 9.14\n",
    "H = -20.61\n",
    "I = 0\n",
    "J = 58.20 \n",
    "\n",
    "# Calculate metallicity using function provided by Ivezic 2008.\n",
    "\n",
    "def calc_metallicity(x,y):\n",
    "        metallicity = A + B*x + C*y + D*x*y + E*(x**2) + F*(y**2) + G*(x**2)*y + H*x*(y**2) + I*(x**3) + J*y**3\n",
    "        return metallicity\n",
    "\n",
    "# For stars with g - r > 6, set Z = -0.6.\n",
    "    \n",
    "metallicities = np.ones(len(y))*-0.6\n",
    "        \n",
    "# Otherwise, use the function defined above to calculate metallicity.    \n",
    "    \n",
    "for star in range(len(y)):\n",
    "    if y[star] < 0.6:\n",
    "        metallicities[star] = calc_metallicity(x[star],y[star])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
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   "source": [
    "# Calculate change in magnitude.\n",
    "\n",
    "def delta_abs_mag(metallicity):\n",
    "    del_M = 4.50 - 1.11*metallicity - 0.18*metallicity**2\n",
    "    return del_M\n",
    "\n",
    "# Calculate initial magnitude using Ivezic 2008 A7.\n",
    "\n",
    "def M_init(g_i):\n",
    "    M_0 = -5.06 + 14.32*g_i - 12.97*g_i**2 + 6.127*g_i**3 - 1.267*g_i**4 + 0.0967*g_i**5\n",
    "    return M_0\n",
    "\n",
    "# Calculate absolute magnitude using initial magnitude and change in magnitude calculated above.\n",
    "\n",
    "def abs_mag(g_i, metallicity):\n",
    "    M = M_init(g_i) + delta_abs_mag(metallicity)\n",
    "    return M\n",
    "\n",
    "magnitudes = (abs_mag(g-i,metallicities)) # an array for storing our calculated abs. magnitudes"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We are told to assume that Z = D, where\n",
    "\n",
    "$$r - M_r = 5\\log(D/10\\:\\textrm{pc}) $$ \n",
    "\n",
    "Solving for D, we find\n",
    "\n",
    "$$D = 10^{\\frac{r - M_r}{5}+1} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {
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   "source": [
    "# Calculate D.\n",
    "\n",
    "def D_val(r,M):\n",
    "    D = 10**(((r - M) / 5) + 1)\n",
    "    return D\n",
    "\n",
    "D_vals = D_val(r,magnitudes) # an array for storing our distances\n",
    "Z = D_vals # for clarity, rename as \"Z\""
   ]
  },
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   "source": [
    "## Problem 1\n",
    "\n",
    "For stars with $0.2 < g - r < 0.4$, we will plot $\\ln(\\rho)$ vs $Z$, where $\\rho$ is the stellar number density. We can approximate $\\rho(Z) = N(Z)/V(Z)$,where $N(Z)$ is the number of stars in a given bin and $V(Z)$ is the bin volume. We are given that the solid angle $\\Delta\\Omega \\sim 314$ deg$^2$.\n",
    "\n",
    "From Lecture 3, we are given\n",
    "\n",
    "$$dV = \\Delta\\Omega * D^2 *dD $$\n",
    "\n",
    "where $\\Delta\\Omega$ is the solid angle and $dD$ is the bin size. We will use a bin size of 1 kpc based on Ivezi$\\acute{c}$ (2008)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {
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   "source": [
    "# Create new arrays for storing the distances (in kpc) and magnitudes of stars with\n",
    "# 0.2 < g - r < 0.4. I know I did this the \"slow\" way, but I did not find it prohibitively slow, so\n",
    "# I left it as is. \n",
    "\n",
    "cut_1 = []\n",
    "mag_1 = []\n",
    "\n",
    "for star in range(len(y)):\n",
    "    if (y[star] < 0.4) and (y[star] > 0.2):\n",
    "        cut_1.append(Z[star]/1000) # convert to kpc\n",
    "        mag_1.append(magnitudes[star])\n",
    "\n",
    "# Calculate dV using the given solid angel of 314 deg^2. Observing a bin size of 1 kpc based on\n",
    "# Ivezic 2008, we estimate that there are ~25 bins in these plots. We use the same binning\n",
    "# choices here.\n",
    "        \n",
    "volume_bins = (0.09565)*np.arange(1,25,1)**2 # 314 deg^2 converted to steradians       "
   ]
  },
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   "cell_type": "code",
   "execution_count": 411,
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ADCDsAcCA/wKKp42ji+jfugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "relevant_slice = np.logical_and(y<0.4,y>0.2) # A smarter, faster way for storing distances\n",
    "N_z, num_bins, patch_objects = plt.hist(Z[relevant_slice]/1000, bins=np.arange(1,26))"
   ]
  },
  {
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    {
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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.arange(1,25,1),np.log(N_z/volume_bins)) #multiply y by dD/dV??\n",
    "plt.xlabel('Distance [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\ln\\\\frac{dN}{dV}$', fontsize ='larger')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now, we want to determine the distance cutoff $Z$ beyond which we no longer trust our results. There is an inherent bias to our observations in that, the farther we attempt to observe, the dimmer the objects get. This phenomenon results in an apparent decrease in objects with increasing distance. To figure out at what distance this phenomenon takes over, we can plot absolute magnitude with distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.scatter(cut_1, mag_1, s=0.5, alpha=0.1, color='k') \n",
    "plt.xlabel('Distance [kpc]', fontsize='larger')\n",
    "plt.ylabel('Absolute Magnitude', fontsize='larger')\n",
    "plt.title('Number of Stars', fontsize='x-large')\n",
    "plt.axvline(7, color='r',linestyle='--')\n",
    "plt.axvline(10, color='r',linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can see that between $Z = 7$ and $Z = 10$ that the number of stars with distance begins to decrease with an apparently exponential relationship. It is in this region that our luminosity bias becomes applicable. Thus, we might impose a distance limit of $Z=7$ on our survey. \n",
    "\n",
    "We can now replot our stellar number density results with this cutoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.arange(1,25,1),np.log(N_z/volume_bins)) #multiply y by dD/dV??\n",
    "plt.axvline(7, color='k', linestyle='--')\n",
    "plt.xlabel('Distance [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\ln\\\\frac{dN}{dV}$', fontsize ='larger')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Problem 2\n",
    "\n",
    "We now want to overplot the stellar number density for three different color ranges: $0.4 < g - r < 0.6$, $0.6 < g - r < 0.8$, $0.8 < g - r < 1.0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/samanthagilbert/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:22: RuntimeWarning: divide by zero encountered in log\n",
      "/Users/samanthagilbert/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cut_2 = []\n",
    "cut_3 = []\n",
    "cut_4 = []\n",
    "\n",
    "for star in range(len(y)):\n",
    "    if (y[star] < 0.6) and (y[star] > 0.4):\n",
    "        cut_2.append(Z[star]/1000) # convert to kpc\n",
    "        \n",
    "    if (y[star] < 0.8) and (y[star] > 0.6):\n",
    "        cut_3.append(Z[star]/1000) # convert to kpc\n",
    "        \n",
    "    if (y[star] < 1.0) and (y[star] > 0.8):\n",
    "        cut_4.append(Z[star]/1000) # convert to kpc\n",
    "\n",
    "N_z_2, num_bins, patch_objects = plt.hist(cut_2, bins=np.arange(1,26))  \n",
    "N_z_3, num_bins, patch_objects = plt.hist(cut_3, bins=np.arange(1,26))\n",
    "N_z_4, num_bins, patch_objects = plt.hist(cut_4, bins=np.arange(1,26))\n",
    "        \n",
    "fig1 = plt.figure(figsize=(5,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.arange(1,25,1),np.log(N_z/volume_bins), label=\"$0.2 < g - r < 0.4$\") #multiply y by dD/dV??\n",
    "plt.step(np.arange(1,25,1),np.log(N_z_2/volume_bins), label=\"$0.4 < g - r < 0.6$\")\n",
    "plt.step(np.arange(1,25,1),np.log(N_z_3/volume_bins), label=\"$0.6 < g - r < 0.8$\")\n",
    "plt.step(np.arange(1,25,1),np.log(N_z_4/volume_bins), label=\"$0.8 < g - r < 1.0$\")\n",
    "plt.xlabel('Distance [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\ln$(kpc$^{-3}$)', fontsize='larger')\n",
    "plt.legend(fontsize='large')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see that redder stars (higher $g - r$) values have number densities that fall off much faster with distance than for bluer stars (lower $g - r$). Thus, the reddest stars in our sample, with $0.8 < g - r < 1.0$ have a number density that falls off precipitously. In terms of absolute magnitude, bluer stars are also brighter than redder stars. As a result, we can explain this differing behavior between subsamples by recognizing that we are biased towards observing a greater number of bright stars with increasing distances. Similarly, our redder, fainter stars will have higher systematic errors than comparatively bluer, brighter stars."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Problem 3\n",
    "\n",
    "In this exercise, we will separate stars with $0.2 < g - r < 0.4$ by metallicity. We will define high metallicity as stars that have $[\\textrm{Fe}/\\textrm{H}] > -1.0$, while low metallicity stars will have $[\\textrm{Fe}/\\textrm{H}] < -1.0$. We will then plot $\\ln(\\rho)$ versus $Z$ for these subsamples and compare their trends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAD8CAYAAACW/ATfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAADZVJREFUeJzt3T1v29Yex/Ffb64BLzribhDoHNpjEeDMHgR368JXoLWZDBS4QBE0S4F06Vj4DZQZulXlkNUHCDpG9FyUyHA3PQw1IAS5g2Hmoa5E+oYUpf/3M1l/UzEJ5Px0dHjO4Wdv3759KwDAXvvXtk8AANA+wh4ADCDsAcAAwh4ADCDsAcAAwh4ADCDsAcAAwh4ADCDsAcCAf2/7BG49evRIR0dH2z4NANgpr1+/1suXLzce15uwPzo60i+//LLt0wCAnfLVV1/VOo5hHAAwgLAHAAMIewAwgLAHAAMIewAwgLAHAAMIewAwgLAHAAMIewAwgLBHLderN528B0A7erNdAvrt8OCBPv/m10bv+eP7L1s6GwBN0bMHAAMIewAwgLAHAAMIewAwgLAHAAMIe4OYEgnYw9RLg5hGCdhDzx4ADCDsAcAAwh4ADCDsAcAAwh6taTrrh1lCQHuYjYPWNJ31w4wfoD307AHAgI09+6IoVJalJGk0GkmS8jyXc05FUWg8HjeqAQC6t7Fn/9NPP2k0GqksSxVFoaIoJEne+yrI69YAANuxNuzzPNfJyYkkaTweK0kSTSYTOeckSXEcK4RQu4Z2cGMTwCZrh3FevXol6WYoJ4Sg8Xis5XKp4XBYHTObzWrX0A5uhALYZOMwThRFSpJE0k1PHwCwe9b27KMoUhzHkiTnnF69eqXBYKD5fC5JWiwWiqJIkmrXAADdWxv2o9Go6s0vFgudnJwojmNNp1NJUlmW8t5LUu0aAKB7a4dx4jiWc055nms2m2k0GlVDOiEEOeeUJEntGgBgOzbOs0/TVNK7Ofbv1+46blMNANA9VtACgAGEPQAYQNgDgAGEPQAYQNj3DFsfAGgD+9n3TNOtD6T92f7gevVGhwcPWn8PYBFhj96w/EEHtI1hHAAwgLAHAAP2I+xX1928BwB21H6M2R8cSk+Gm49735N5O+cCAD20Hz17AMBahD0AGEDYA4ABhD0AGEDYA4ABhD0AGEDYA4ABhH2L2MESQF/sx6KqnmJjLwB9Qc8eAAwg7AHAgI1h/+zZM0lSlmVVLc9zhRB0cXHRuAYA6N7GsH/+/LlOT08Vx7EkqSgKSZL3Xs45FUVRuwYA2I6NYf/06VO9ePFC3ntJ0mQykXNOkhTHsUIItWsAgO3YGPZlWX4wFLNcLjUcvttOeDab1a4BALZj49TL8XgsSbq8vKR3DgA7am3YZ1mm4XCo0WikKIpUlqUGg4Hm85sHfywWC0VRJEm1a8CndL16o8ODB62/B9h1a8P++Pi4ujFblqXSNNXx8bGm02lVux3Lr1sDPiUWrgH1rA37JEmq3n0cx0qSRNJNiIcQ5JxrXAMAdG/jmH2app+0BgDoHitoAcAAwh4ADCDsAcAAwh4ADCDsG+BhJAB2FQ8vaaDpnG7mcwPoC3r2AGAAYQ8ABhD2AGAAYQ8ABhD2AGAAYQ8ABhD2AGAAYQ8ABhD2AGAAYQ8ABhD2AGAAYQ8ABhD2AGAAYQ8ABhD2AGBA7bC/uLiofs7zXCGEe9UAAN2rFfYhBIUQJElFUUiSvPdyzqkoito1AMB2NB7GmUwmcs5JkuI4Vgihdg3og/s8XpJHUmLXbXwsYVEU8t5XQzHL5VLD4bD6/Ww2q10D+qDp4yUlHjGJ3bexZz+fz7s4DwBAi9b27G979e8bDAbVB8BisVAURZJUu9Yn9O4AWLE27MuyVFmWms/nms/nKopCZ2dnmk6n1e9vPwzq1npjdd08vFfX7ZwLALRsbdiPRiNJUpZlWiwWkqQkSTSdThVCkHNOSZJIUu1abxwcSk+Gm4973xOGtADspo03aCUpTVOlafrB67uOqVMDAHSPFbQAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYABhD9TQ9Bm0PLMWfVNri2PAuqbPreWpZugbevYAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYABhDwAGEPYAYMDGFbQhBEnS5eWlzs/PJUl5nss5p6IoNB6PG9UAAN1b27MPISjPc3nvdXV1paIoVBSFJMl7XwV53RoAYDvWhr33Xt99950kqSxLJUmiyWQi55wkKY5jhRBq1wAA21FrzP7i4qIK/eVyqeFwWP1uNpvVrgEAtqNW2I/HY/38889aLBZtnw8AoAVrb9DejrMnSaI4jpVlmQaDgebzuSRpsVgoiiJJql0DAHRvbdiHEJQkiaSb4ZuTkxN57zWdTiXdjON77yWpdg0A0L21wzhpmqosS2VZJkkajUZV+IcQ5JxTkiS1awCA7Vjbs3fOKU3Tv9X/nxoAoHusoAUAAwh7ADCAsAcAAwh7ADCAsAcAAwh7ADCAsAcAAwh7oAXXqzedvAeoa+PDSwA0d3jwQJ9/82uj9/zx/ZctnQ1Azx4ATCDsAcAAwh4ADCDsAcAAwh4ADCDsAcAAwh4ADCDsAcAAwh4ADCDsAcAAwh4ADCDsAcAAwh4ADNi462WWZZKkP//8U+fn55KkPM/lnFNRFBqPx41qO2113WxnwtV1e+cCAA2sDfsQgrz3iuNYX3/9tUIIGg6HkiTvvcqyVFEU1fGbakmStHQZHTk4lJ4M6x//ZN7euQBAA2uHccqyVAhBkhTHscqy1GQykXOuqoUQatcAANuxtmefpmn189XVlc7OzlQURdW7l6TZbKblclmrBuCfXa/e6PDgQevvgU21nlRVFIUePny4+8MwQI/xdCu0qVbYhxCqm7ODwUDz+c1Y9GKxUBRFklS7BgDoXq3ZOLczaUIIOjs703Q6lXQzpu+9l6TaNQBA99beoA0h6IcfftDp6am++OILSaqGckIIcs4pSZLaNQDAdqzt2Xvv9fvvv/+t/v6N26Y1AED3WEELAAYQ9gBgAGEPAAYQ9gBgAGEPAAYQ9gBgAGEPAAYQ9sAOu169afV47I9ae+MA6Kemm6excZpd9OwBwADCHgAMIOwBwADCHgAMIOwBwABm47Rpdd189sPqup1zAWAaYd+mg0PpyXDzce97Mm/nXACYxjAOABhA2AOG3GcFLatu9wPDOIAhTVfcSqy63Rf07AHAAMIeAAyoFfZFUXzwOs9zhRB0cXHRuAYA6N7GsA8h6PHjx9Xr2+D33ss5p6IoatcAANuxMey994rjuHo9mUzknJMkxXGsEELtGgBgOxqP2S+XSw2H7xYKzWaz2jUAwHYw9bJv2GIBQAsah/1gMNB8frOkf7FYKIoiSapdwwb32WLhP/9t9gHBhwNgTuOwPzs703Q6lSSVZSnvvSTVrqEFTT8g+rr/Dt9qgNZsDPs8zzWdTpXnuUajkZIk0XQ6VQhBzjklSSJJtWsw5D7h3fa3Gkla/cWHSgPXqzc6PHjQ+nvQro1hPxqNNBqNPqilafq34+rWYEgX3zjuu7MoQ2W1scXCfuAGrUX3Gi65R294nzT9ULnXN479+YBA/xD2FnXVG+7rvYEudHGjXeIDArUR9kBf8LAbtIiN0ADAAMIeAAxgGAfYZU1vtnc07bTp1EumaraPsAd22X2mt3ZwX6DpdE3TM706QtgDWI+VzXuBsAewHrOE9gJhD+DTa3wv4frmQwWtIewBfHodbJXBTd1mmHoJYPvuMcZ/qFULJ7K/6NkD2D7uC7SOnj0AGEDYA9hN95neufqr/b/RUwzjANhNXezeukdDRfTsAeCf3OvbQz+/DdCzB4B/cs/nEjTWwToDwh4APqWezixiGAcADCDsAcAAwh4ADCDsAcCAVm/Q5nku55yKotB4PG7zTwEA1mitZ18UhSTJe18FPgBgO1oL+8lkIuecJCmOY4UQ2vpTAIANWgv75XKp4fDdXNPZbNbWnwIAbPDZ27dv37bxD3/77bdK01RJkiiEoMvLS52fn//j8Y8ePdLR0VEbpwIAe+v169d6+fLlxuNau0E7GAw0n9+sClssFoqiaO3xdU4WAHA/rQ3jnJ2dqSxLSVJZlvLet/WnAAAbtBb2SZJIkkIIcs5VrwEA3WttzB4A0B+soAUAAwh7bNXHi+3yPFcIQRcXF1s6o259fP3Pnj2TJGVZto3TwR7rVdhba+gfs9bQQwh6/Phx9draquuPr1+Snj9/rtPTU8VxvKWz6kaWZcqyrPo/L9lq/3ddf9vtvzdhb62h38VKQ7/lvf/gWq2tuv74+iXp6dOnevHixV7PXgshyHuvNE1VlqVCCKba/13XL7Xf/nsT9tYa+l0sNPR1WHWtqvHvc+/2/YCL41hlWZpq/3ddv9R+++9N2NPQbTR0rDcej+W912w229vAS9NUaZpKkq6urnR8fGyq/d91/VL77b83YQ8bDX2dpquu902WZcrzXJIURVHV49tXRVHo4cOHZtfgfHz9bbf/3oQ9Dd1WQ7+L9VXXx8fH1TWXZVn1+PZVCKHaL8ti+3//+rto/70Jexq6rYYu3cy+mE6n1X9ya6uu77r+3377TXmeK47jvb7+LMuqBxqFEMy1/4+vv4v236sVtFmWVTcsbse0LMmyTMPhUGVZ8mQv7K3bKafD4VDz+Vw//vijvPdm2v+662+z/fcq7AEA7ejNMA4AoD2EPQAYQNgDgAGEPQAYQNgDgAGEPQAYQNgDgAGEPQAY8D/B4LecKj5K7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "low_metallicity = []\n",
    "high_metallicity = []\n",
    "r_mags_low = []\n",
    "r_mags_high = []\n",
    "\n",
    "for star in range(len(y)):\n",
    "    if (y[star] < 0.4) and (y[star] > 0.2):\n",
    "        if (metallicities[star]) < -1.0:\n",
    "            low_metallicity.append(Z[star]/1000) # convert to kpc\n",
    "            r_mags_low.append(r[star])\n",
    "        else:\n",
    "            high_metallicity.append(Z[star]/1000)\n",
    "            r_mags_high.append(r[star])\n",
    "\n",
    "volume_bins = (0.09565)*np.arange(1,25,1)**2 # 314 deg^2 converted to steradians, D takes on values 0-25        \n",
    "\n",
    "N_low, num_bins, patch_objects = plt.hist(low_metallicity, bins=np.arange(1,26))\n",
    "N_high, num_bins, patch_objects = plt.hist(high_metallicity, bins=np.arange(1,26))\n",
    "\n",
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.arange(1,25,1),np.log(N_low/volume_bins), label='Low Metallicity ($[\\\\textrm{Fe}/\\\\textrm{H}] < -1.0$)') #multiply y by dD/dV??\n",
    "plt.step(np.arange(1,25,1),np.log(N_high/volume_bins), label='High Metallicity ($[\\\\textrm{Fe}/\\\\textrm{H}] > -1.0$)') \n",
    "plt.xlabel('Distance [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\ln$(kpc$^{-3}$)', fontsize ='larger')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.legend(fontsize='large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We find that initially, the number density of low and high metallicity stars is comparable. As distance increases, we find a higher number density of low metallicity stars compared to high metallicity stars. Eventually, once we reach a distance of 20 kpc, the number density of high metallicity stars actually overtakes that of their low metallicity peers. \n",
    "\n",
    "Up to the first couple of kpc, we are not looking through the disk, so we see a comparable number of low and high metallicity stars. Up to 20 kpc, we observe a higher number density of low metallicity stars because we are probing the halo. Stars in the halo tend to be older and thus lower metallicity since they formed from metal-poor nebulae. After 20 kpc, we are seeing the results of metallicity contamination. Our systematic photometric errors worsen with distance. Thus, at sufficiently large distances, low metallicity stars become classified as high metallicity stars. As a result, low metallicity counts bleed into high metallicity counts, and high metallicity stars appear to overtake low metallicity stars at large distances. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Problem 4\n",
    "\n",
    "We will now plot and compare the differential r band magnitude contributions for the high and low metallicity subsamples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/samanthagilbert/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log10\n",
      "  \"\"\"\n",
      "/Users/samanthagilbert/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in log10\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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eABxA2AOAAwh7AHAAYQ8ADiDsAcABhD0AOICwBwAH/A+WwxSsHwjy7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_low, num_bins, patch_objects = plt.hist(r_mags_low, bins=np.arange(1,26,0.1))\n",
    "N_high, num_bins, patch_objects = plt.hist(r_mags_high, bins=np.arange(1,26,0.1))\n",
    "\n",
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.arange(1,25.9,0.1),np.log10(N_low), label='Low Metallicity ($[\\\\textrm{Fe}/\\\\textrm{H}] < -1.0$)') #multiply y by dD/dV??\n",
    "plt.step(np.arange(1,25.9,0.1),np.log10(N_high), label='High Metallicity ($[\\\\textrm{Fe}/\\\\textrm{H}] > -1.0$)') \n",
    "plt.xlabel('$r$', fontsize='larger')\n",
    "plt.ylabel('$\\log_{10}(N)$', fontsize ='larger')\n",
    "plt.title('Stellar Counts by $r$ Magnitude Contributions', fontsize='x-large')\n",
    "plt.legend(fontsize='large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A linear function should fit the low metallicity line. However, because we are flux-limited at fainter magnitudes for low metallicity stars, the line appears to fall off at fainter magnitudes.\n",
    "\n",
    "The high metallicity line appears to follow a bimodal distribution. However, the second \"bump\" in the line is a spurious product of our photometric errors. The first \"bump\" reflects the population of stars in the disk, which are younger and metal-rich. Thus, the peak of this bump gives us the scale height of the disk by fitting the curve with a power  law between $14 < r < 16$. The second \"bump\" emerges because our systematic photometric errors cause us to misclassify low metallicity stars as high metallicity stars. Without this metallicity contamination, we would anticipate the number of stars after the first bump to decrease directly with magnitude as fainter stars become more difficult to observe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Problem 5\n",
    "\n",
    "We now want to identify the faint r-band limit for a survey to be able to map $\\ln(\\rho)$ vs. $Z$ out to 100 kpc using main sequence stars, as well as estimate the number of stars with $0.2 < g - r < 0.4$ between 90 and 100 kpc.\n",
    "\n",
    "To identify the faint r-band limit, we return to our absolute magnitude plot in Problem 1 and identify the faintest absolute magnitude prior to the Z cutoff we established. From our plot, we find that this $M_r$ = 6.5. Using our equation from problem 1, we can solve for $r$\n",
    "\n",
    "$$ r = 5\\log(D/{10~\\textrm{pc}}) + M_r $$\n",
    "\n",
    "where $D = 100\\times10^3 = 1\\times10^5$ pc and $M_r = 6.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The faint r-band limit is 26.5.\n"
     ]
    }
   ],
   "source": [
    "def r_lim(D,M):\n",
    "    r = (5*np.log10(D/10)) + M\n",
    "    return r\n",
    "\n",
    "print(\"The faint r-band limit is {}.\".format(r_lim(1e5,6.5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We find that the faint r-band limit is 26.5. We can understand $r$ as a proxy for distance for Main Sequence stars, as stars generally become fainter with distance. Our $r$ values only go up to 21, forcing us to extrapolate to longer distances and thus higher $r$ values. If we had a survey with a magnitude depth of 26.5, we would not need to extrapolate like this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To estimate the number of stars with these magnitudes in the halo, we assume the same color distribution as the SDSS sample and a solid angle of $\\Omega = 1$ deg$^2$ = $3.046\\times10^{-4}$ sr. \n",
    "\n",
    "First, we will determine the distance at which stars in this band become flux-limited Z$_{max}$, as well as the distance at which we become dominated by halo stars, Z$_{min}$. We established in Problem 1 that $Z_{max} \\sim 10$ kpc. From Ivezic 2008, we have that halo stars begin to dominate between 3-5 kpc, so we will choose $Z_{min} \\sim 4$ kpc.\n",
    "\n",
    "Next, we will calculate the distance from the galactic center. To do this, we must account for the fact that the earth is located 8 kpc from the galactic center, generating a distance offset. As a result, we must use the Pythagorean theorem to find the radial distance $R$ such that\n",
    "\n",
    "$$R^2 = (8\\:\\:\\textrm{kpc})^2 + Z^2 $$\n",
    "\n",
    "We will then fit a cubic distance-density relation to the number of stars with distance $R$:\n",
    "\n",
    "$$\\rho \\sim \\frac{a}{R^3} $$\n",
    "\n",
    "where $a$ is some normalization constant.\n",
    "\n",
    "Finally, we will use the relation from our fit to extrapolate the number of stars between 90 and 100 kpc, integrating over this distance to produce our final estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z_min = 4 # Starting Z of the halo \n",
    "Z_max = 7 # Flux-limited Z limit\n",
    "\n",
    "# Use the Pythagorean theorem to calculate the radial galactic distance R.\n",
    "# Earth's distance to G.C. = 8 kpc\n",
    "\n",
    "def galactic_rad(Z):\n",
    "    radius = np.sqrt(8**2 + Z**2)\n",
    "    return radius\n",
    "\n",
    "radius_slice=[]\n",
    "\n",
    "for radius in radii:\n",
    "    radius_slice.append((radius > galactic_rad(Z_min)) and (radius < galactic_rad(Z_max)))\n",
    "\n",
    "N_z, num_bins, patch_objects = plt.hist(Z[relevant_slice]/1000, bins=np.arange(4,7.1,0.1))\n",
    "volume_bins = (0.09565)*np.arange(4,7,0.1)**2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.scatter(galactic_rad(np.arange(4,6.9,0.1)),(N_z/volume_bins), color='k', s=5, label='$0.2 < g - r < 0.4$')\n",
    "plt.xlabel('R [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\\\frac{dN}{dV}$', fontsize ='larger')\n",
    "plt.legend(fontsize='large')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "xdata = galactic_rad(np.arange(4,6.9,0.1))\n",
    "ydata = N_z/volume_bins\n",
    "\n",
    "# Fit a cubic function to the data with a normalization constant.\n",
    "\n",
    "def power_law(x, a):\n",
    "    return a*x**-3\n",
    "\n",
    "popt, pcov = scipy.optimize.curve_fit(power_law, xdata, ydata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.scatter(xdata,ydata, color='k', s=5, label='$0.2 < g - r < 0.4$')\n",
    "plt.plot(xdata, power_law(xdata, popt[0]), color='r', label='$\\\\rho$ = {:.2} $\\\\times$ $R^{{-3}}$'.format(popt[0]))\n",
    "plt.xlabel('R [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\\\frac{dN}{dV}$', fontsize ='larger')\n",
    "plt.legend(fontsize='large')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now to extrapolate!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def extrap(R):\n",
    "    num_stars = popt[0]*R**-3\n",
    "    return num_stars\n",
    "\n",
    "rho = extrap(np.linspace(90,100,100)) # Calculate the number density for 90 < R < 100. Bin finely given the sparse number of stars we expect to encounter this far from the disk.\n",
    "\n",
    "volume_bins = (3.046e-4)*np.linspace(90,100,100)**2 # Recalculate volume bins given solid angle = 1 deg^2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of stars between 90 and 100 kpc = 75.8363793438\n"
     ]
    }
   ],
   "source": [
    "fig1 = plt.figure(figsize=(7,5), dpi= 100, facecolor='w', edgecolor='k')\n",
    "plt.step(np.linspace(90,100,100),rho, color='blue', label='$0.2 < g - r < 0.4$')\n",
    "plt.xlabel('R [kpc]', fontsize='larger')\n",
    "plt.ylabel('$\\\\frac{dN}{dV}$', fontsize ='larger')\n",
    "plt.legend(fontsize='large')\n",
    "plt.title('Stellar Number Density', fontsize='x-large')\n",
    "plt.show()\n",
    "\n",
    "N = rho*volume_bins # \n",
    "print\"The number of stars between 90 and 100 kpc = {}\".format(np.sum(N)) # Sum the number of stars in each bin between 90 and 100 kpc to get the total number of stars."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Extrapolating our $\\rho$-$R$ relationship out to 90-100 kpc, we find ~75 stars between 90 and 100 kpc. However, we know this number is contaminated by comparatively brighter disk stars. "
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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