erinzm · April 26, 2016 21:05
diff --git a/lm test-1 analysis.ipynb b/lm test-1 analysis.ipynb
 {
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SJS lm-test-1 data analysis\n",
    "I thought a spreadsheet was too tedious for what we're doing (working out the Milky Way's macrostructure) so I hacked together some bits of code to make analysis *incredibly easy* (for me at least, YMMV)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "##\n",
    "# setup for the data analysis - pulls in some useful libraries\n",
    "# this code doesn't contribute to the analysis - you don't need to worry about it.\n",
    "\n",
    "# Render our plots inline\n",
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, I'm going to read in the excel file that I prepared from the .cyb.txt from NRAO's site.\n",
    "This puts the data in the computer's memory so I can work on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>XL1</th>\n",
       "      <th>YR1</th>\n",
       "      <th>XL2</th>\n",
       "      <th>YR2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1412.20276</th>\n",
       "      <td>320.4291</td>\n",
       "      <td>266.0175</td>\n",
       "      <td>320.4291</td>\n",
       "      <td>266.0175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1412.21802</th>\n",
       "      <td>320.0437</td>\n",
       "      <td>265.4948</td>\n",
       "      <td>320.0437</td>\n",
       "      <td>265.4948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1412.23328</th>\n",
       "      <td>319.8062</td>\n",
       "      <td>264.9507</td>\n",
       "      <td>319.8062</td>\n",
       "      <td>264.9507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1412.24854</th>\n",
       "      <td>319.7780</td>\n",
       "      <td>264.7801</td>\n",
       "      <td>319.7780</td>\n",
       "      <td>264.7801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1412.26379</th>\n",
       "      <td>320.3440</td>\n",
       "      <td>264.4579</td>\n",
       "      <td>320.3440</td>\n",
       "      <td>264.4579</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 XL1       YR1       XL2       YR2\n",
       "1412.20276  320.4291  266.0175  320.4291  266.0175\n",
       "1412.21802  320.0437  265.4948  320.0437  265.4948\n",
       "1412.23328  319.8062  264.9507  319.8062  264.9507\n",
       "1412.24854  319.7780  264.7801  319.7780  264.7801\n",
       "1412.26379  320.3440  264.4579  320.3440  264.4579"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat = pd.read_excel('Skynet_57504_lm-test-1_19482_20362.spect.cyb.xlsx', sheetname='pandasdata', index_col=0).sort_index()\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first thing I'm going to do to the data is plot the intensity of recieved radio from 1420 MHZ to 1421 MHz to get an idea of what I'm looking at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f7f430ad198>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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RJLEv/w2spWTGP2c6lNSJnjDV2q2nsYeaCL+6FBsKxfe4tjY42AS9S7r1/dPB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\niBhEwSwiImKQX6sX3w3Ofbc4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f430ada20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat['XL1'][1420:1421].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to find the first $n$ maximums, 6 of them in this case, and store them in memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "maximums = dat['XL1'][1420:1421].sort_values(ascending=False).head(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I specified that the telescope should take measurements at galactic latitude and longitude 0,0.\n",
    "When I got my data file I found out that the measurements were taken at 2016-04-26T07:30:01.750 with a RA/Dec of 17:45:37.11/-28:56:09.21.\n",
    "\n",
    "I then got the following result from the [NRAO radial velocity calculator](http://www.gb.nrao.edu/GBT/setups/radvelcalc.html) for V_LSRK, and stored it in memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v_lsrk = -33.411 # km/sec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, I decided to take the maximums I found and plot them on the original graph to get a better understanding of where they actually *were*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f7f42d2c3c8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jHMdtg6mp7J4NHQ7GwWoqWxKgxCySZO21NbD5XTjldEz54EyHk1xebxaMmCNV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f42d14be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat['XL1'][1420:1421].plot(); maximums.plot(style='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximums around that location represent red-or-blueshifts of the hydrogen 21cm line at $\\approx 1420.406$ $MHz$, emitted pretty much only in hydrogen gas clouds.\n",
    "\n",
    "Since we know that the arms of the Milky Way have interiors composed of hydrogen gas clouds, we can map out the distribution of cloud velocities by seeing how far the hydrogen 21cm line has shifted.\n",
    "\n",
    "The following piece of code calculates how fast an object is moving based on an observed and an actual emitted frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c = 3*(10**5) # km/s\n",
    "# v will be negative for blueshift, positive for redshift\n",
    "def vel_from_fshift(f_base, f_measured):\n",
    "    return c * (f_base - f_measured)/(f_base)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I use that piece of code to find the velocities of each of the maximums."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-49.65867261, -46.4356499 , -52.88169532, -20.65358026,\n",
       "       -43.21262718, -17.43055755])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_21cm_line = 1420.405751786 # MHz\n",
    "velocities = maximums.index.map(lambda v_m: vel_from_fshift(h_21cm_line, v_m))\n",
    "velocities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For fun, let's find the distribution of those velocities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f7f42cc07b8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f42ccce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.Series(velocities).hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like they're mostly lumped around $\\approx -47$ $\\frac{km}{s}$, meaning they're *approaching* us at that speed. Interesting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Written by Liam Marshall, April 26 2016\n",
    "\n",
    "Thanks to Geoffrey Holt for being an awesome teacher!"
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
 }