slitless.ipynb

{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Thin-disk galaxy kinematics in slitless spectrography\n\n**Author:** Yannick Copin <[email protected]>"
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "# Technical stuff related to the Jupyter notebook\n%matplotlib inline",
   "execution_count": 1,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "import numpy as N\nfrom matplotlib import pyplot as P\ntry:\n    import seaborn\n    seaborn.set_style(\"ticks\", {'axes.grid': True})\nexcept ImportError:\n    pass\n\nRAD2DEG = 180. / N.pi  # ~57 deg/rad\n\nP.rcParams['image.cmap'] = 'gray_r'",
   "execution_count": 2,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## Coordinates\n\nCoordinate cubes:"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "xx = N.linspace(-10, 10, 41)   # Spatial coordinates\nyy = N.linspace(-9, 9, 37)     # yy has a different shape just for debugging purposes\nll = N.linspace(-10, 10, 101)   # Spectral coordinates\nlbda, y_in, x_in = N.meshgrid(ll, yy, xx, indexing='ij')\nprint(x_in.shape)",
   "execution_count": 3,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(101, 37, 41)\n"
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Internal thin-disk coordinates:"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "r_in = N.hypot(x_in, y_in)\ntheta = N.arctan2(y_in, x_in)  # [rad]\n\nP.imshow(r_in[0] < 8, extent=[xx[0], xx[-1], yy[0], yy[-1]])",
   "execution_count": 4,
   "outputs": [
    {
     "execution_count": 4,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xaf2e29ac>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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jx6KpqSm6urrKHqlurV69Oo4fPx4bNmyIiLCWNdDa2hq7d++Otra2qFQqsW/fPrurGnnz\nzTfjrbfeihs3bsSjjz4aL7/88qi38QfkABKTX4DERAAgMREASEwEABITAYDERAAgMREASEwEABL7\nP8ahFsfgXp03AAAAAElFTkSuQmCC\n",
      "text/plain": "<matplotlib.figure.Figure at 0xaf3594ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Projected coordinates:"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "incl = 60. / RAD2DEG    # Disk inclination (0 is face-on) [rad]\n\nx = x_in * N.cos(incl)  # Inclination along the vertical axis\ny = y_in\npsi = N.arctan2(y, x)  # Azimuthal angle\nr = N.hypot(x, y)\nm = N.hypot(x_in / N.cos(incl), y_in)  # Elliptical radius\n\nP.imshow(m[0] < 8, extent=[xx[0], xx[-1], yy[0], yy[-1]])",
   "execution_count": 5,
   "outputs": [
    {
     "execution_count": 5,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xaebba9cc>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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hzpw5E1u3bo2IsJY10NHREfv374/Ozs6oVCpx6NAhR1c18uabb8Zbb70Vt2/fjkceeSRe\nfvnlKbfxB+QAEpNfgMREACAxEQBITAQAEhMBgMREACAxEQBITAQAEvs/vgbpC8/JQvIAAAAASUVO\nRK5CYII=\n",
      "text/plain": "<matplotlib.figure.Figure at 0xaf2c464c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "**TODO:** include position angle."
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## Simple case: uniform disk, no rotation\n\nThe model is restricted to a uniform disk without any internal kinematics: the spectrum is uniform over the disk extent."
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "r0 = 8.      # Disk radius\n\ndisk = N.zeros_like(m)\ndisk[m < r0] = 1\nP.imshow(disk[0], extent=[xx[0], xx[-1], yy[0], yy[-1]])",
   "execution_count": 6,
   "outputs": [
    {
     "execution_count": 6,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xaeb11a8c>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAFXCAYAAABEPvIWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": "<matplotlib.figure.Figure at 0xaeac52ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "**TODO:** include pixel integration (\"antialiasing\")."
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "def disperse_cube(cube):\n    \"\"\"Disperse a cube in a slitless image.\"\"\"\n    \n    nl, ny, nx = cube.shape\n    ima = N.zeros((ny, nx + (nl - 1)))  # Empty image\n    for i, subima in enumerate(cube):  # Loop over constant-wavelength slices\n        ima[:, i:i+nx] += subima\n        \n    return ima",
   "execution_count": 7,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "ima = disperse_cube(disk)\nprint(ima.shape)\nP.imshow(ima)",
   "execution_count": 8,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(37, 141)\n"
    },
    {
     "execution_count": 8,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xae4b312c>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0xaf2b76cc>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Add a spectral component: single Gaussian emission line + constant background."
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "sigma = 2 / 2.355  # Spectral line sigma\nspec = N.exp(-0.5 * (ll / sigma)**2) + 1\nP.plot(ll, spec)",
   "execution_count": 9,
   "outputs": [
    {
     "execution_count": 9,
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0xae3d7a0c>]"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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c37Jli+6880791V/9lZ566qlU1wZkrcHhqA5N80loBiajAckbN7Q3bNigJ554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\nQmCC\n",
      "text/plain": "<matplotlib.figure.Figure at 0xae2c37ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "cube = disk * spec[:, N.newaxis, N.newaxis]  # Spectro-spatial cube \n\nima = disperse_cube(cube)\nprint(ima.shape)\nP.imshow(ima)",
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(37, 141)\n"
    },
    {
     "execution_count": 10,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xae29cecc>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0xae2e15ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false
   },
   "cell_type": "markdown",
   "source": "## Uniform disk, solid rotation\n\nThe model is restricted to a uniform disk with a solid rotation.\n\nVelocity curve:"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "def rot_solid(r, r0=5, v0=5):\n    \"\"\"Solid rotation.\"\"\"\n    \n    return v0 * r / r0",
   "execution_count": 11,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Velocity field:"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "v_sol = rot_solid(r_in) * N.sin(incl) * N.sin(theta)\nv_map = N.ma.masked_array((v_sol * disk), mask=(disk == 0))\nP.contourf(v_map[0], extent=[xx[0], xx[-1], yy[0], yy[-1]], cmap='RdBu_r')\nP.colorbar()",
   "execution_count": 12,
   "outputs": [
    {
     "execution_count": 12,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0xae0c92ac>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0xae27a0ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "spec_sol = N.exp(-0.5 * ((lbda - v_sol) / sigma)**2) + 1\ncube_sol = disk * spec_sol  # Spectro-spatial cube \n\nima_sol = disperse_cube(cube_sol)\nP.imshow(ima_sol)",
   "execution_count": 13,
   "outputs": [
    {
     "execution_count": 13,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xae05b74c>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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ysGfPnsDt2traoHhPnz6Nf//73xg/fjycTieysrIwcOBAXLlyxagmx5Q6/l/8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\n",
      "text/plain": "<matplotlib.figure.Figure at 0xadfff28c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## Uniform disk, keplerian rotation\n\nWe associate a uniform disk to a realistic velocity profile."
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "def rot_plateau(r, r0=2, v0=5):\n    \"\"\"Plateau rotation curve.\"\"\"\n\n    return v0 * N.tanh(r / r0)\n    \ndef rot_kepler(r, r0=2, v0=5):\n    \"\"\"Keplerian rotation curve.\"\"\"\n    \n    return v0 * N.tanh(r / r0) / N.sqrt(0.5 * (1 + r / r0))\n\nrad = N.linspace(0, 10)\nP.plot(rad, rot_plateau(rad), label=\"Plateau\")\nP.plot(rad, rot_kepler(rad), label=\"Keplerian\")\nP.legend()",
   "execution_count": 14,
   "outputs": [
    {
     "execution_count": 14,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0xaddb50ac>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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1uIPv7f8PDAYjX778cySE2gD4xZ+rmJpxcP8thQQH+Hm5SpHTe+/KYh8vuIHx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\n",
      "text/plain": "<matplotlib.figure.Figure at 0xae0b16ec>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "v_kep = rot_kepler(r_in) * N.sin(incl) * N.sin(theta)\nv_map = N.ma.masked_array((v_kep * disk), mask=(disk == 0))\nP.contourf(v_map[0], 11, extent=[xx[0], xx[-1], yy[0], yy[-1]], cmap='RdBu_r')\nP.colorbar()",
   "execution_count": 15,
   "outputs": [
    {
     "execution_count": 15,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0xadfc488c>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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MvYARG7axM9jO9jp16pR+8pOfdOybrZKVlaU33nhDTU1Nhu6fkZGhrKwsS8by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\n5QAAAABJRU5ErkJggg==\n",
      "text/plain": "<matplotlib.figure.Figure at 0xae05562c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "spec_kep = N.exp(-0.5 * ((lbda - v_kep) / sigma)**2) + 1\ncube_kep = disk * spec_kep  # Spectro-spatial cube \n\nima_kep = disperse_cube(cube_kep)\nP.imshow(ima_kep)",
   "execution_count": 16,
   "outputs": [
    {
     "execution_count": 16,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xad44e5ec>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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T4XK5oCgKXC4XHA5Hwseem5uLffv2BR7X1tYGxXvmzBl88sknmDp1KhwOBzIy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\nRU5ErkJggg==\n",
      "text/plain": "<matplotlib.figure.Figure at 0xae07f84c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## Exponential disk, keplerian rotation"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "r0_exp = 4.  # Exponential disk scale length\n\ndisk_exp = N.exp(-m / r0_exp)\nP.imshow(disk_exp[0], extent=[xx[0], xx[-1], yy[0], yy[-1]])",
   "execution_count": 17,
   "outputs": [
    {
     "execution_count": 17,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xad323d8c>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0xae02da2c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "cube_exp = disk_exp * spec_kep  # Spectro-spatial cube \n\nima_exp = disperse_cube(cube_exp)\nP.imshow(ima_exp)",
   "execution_count": 18,
   "outputs": [
    {
     "execution_count": 18,
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0xad34b2ac>"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0xadfa608c>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "",
   "execution_count": null,
   "outputs": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python2",
   "display_name": "Python 2",
   "language": "python"
  },
  "language_info": {
   "mimetype": "text/x-python",
   "nbconvert_exporter": "python",
   "name": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6",
   "file_extension": ".py",
   "codemirror_mode": {
    "version": 2,
    "name": "ipython"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}