{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Radio Astronomy and Data Analysis Module\n",
"\n",
"**Lecturer:** Poonam Chandra \n",
"**Jupyter Notebook Authors:** Poonam Chandra, David Kaplan, & Cameron Hummels\n",
"\n",
"This is a Jupyter notebook lesson taken from the GROWTH Winter School 2018. For other lessons and their accompanying lectures, please see: http://growth.caltech.edu/growth-astro-school-2018-resources.html\n",
"\n",
"## Objective\n",
"Investigate radio observations, interferometry, and synthesis imaging\n",
"\n",
"## Key steps\n",
"- Estimate the UV tracks for East-West, North-South or inclined array at the GMRT location\n",
"- Calculate the UV tracks for different duration observations\n",
"- Find the flux density for a bright source or a region covering an extended source\n",
"\n",
"## Required dependencies\n",
"\n",
"See GROWTH school webpage for detailed instructions on how to install these modules and packages. Nominally, you should be able to install the python modules with `pip install `. The external package `FriendlyVRI` can be installed by following the instructions at the associated website below\n",
"\n",
"### Python modules\n",
"* python 3\n",
"* astropy\n",
"* numpy\n",
"* matplotlib\n",
"\n",
"### External packages\n",
"* FriendlyVRI - https://crpurcell.github.io/friendlyVRI/"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"import webbrowser\n",
"cwd = os.getcwd()\n",
"data_dir = os.path.join(cwd, 'data')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from astropy.io import fits\n",
"from astropy.wcs import WCS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"Radio astronomy reveals objects that do not radiate in other parts of the spectrum, and they are able to pass through galactic dust clouds that obscure the view in the optical range. In continuum, radio sky is dominated by non-thermal emission, i.e. the emission which cannot be characterized by a single temperature. The non-thermal radio emission usually are sites of particle acceleration and produce synchrotron, Coherent emission, Masers emission. They also reveal new phenomenon such as Fast Radio Bursts etc. \n",
"\n",
"In this image below, left hand side is the optical image of a galaxy which shows big sidelobes in the radio image in the right hand side. The radio image is dominated by synchrotron emission\n",
"\n",
"![SegmentLocal](data/Images/RadioGal.png \"segment\")\n",
"\n",
"\n",
"Spectral line radiation is generated at specific frequencies by atomic and molecular processes. Neutral atomic hydrogen at 1420.405 MHz, which results from the transition between two energy levels of the atom, the separation of which is related to the spin vector of the electron in the magnetic field of the nucleus. \n",
"\n",
"In the left image of this galaxy, the optical emission is dominated by star light, whereas the extent of Neutral H1 emission, shown in the right side image, is much larger.\n",
"\n",
"![SegmentLocal](data/Images/NGC.png \"segment\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# # Radio Interferometry\n",
"The angular resolution of a single radio antenna is insufficient for many astronomical purposes. For example, at 21cm, to obtain 1 arcsec resolution one needs 42km dish. Thus the concept is that for high resolution, use an antenna array instead of a single antenna. Signals from different antennas are brought to focus electronically. Now resolution is better since in resolution λ/d, d is the largest separation between the antennas in the array. Imagine making an image with mirrors with holes. More antennas means lesser holes. \n",
"![SegmentLocal](data/Images/aper.png \"segment\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Rotation of the Earth helps in filling the gaps between mirrors. This is called aperture synthesis.\n",
"\n",
"In the aniation below, one can see that Y-shaped array, and making use of Earth's rotation. \n",
"\n",
"If you want to play the animation again, double-click in this cell and click Run.\n",
"![SegmentLocal](data/Images/ApertureSynthesisAnimation.gif \"segment\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![SegmentLocal](data/Images/radioast.jpg \"segment\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![SegmentLocal](data/Images/uv2.png \"segment\")\n",
"![SegmentLocal](data/Images/uv1.png \"segment\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hands On session on UV tracks\n",
"\n",
"In this code below, one can estimate the UV tracks for East-West, North-South or inclined array at the GMRT location. You can select differnt numbers of hours and check the UV tracks.\n",
"\n",
"Try different number of hours, and different array and see how UV tracks are different for different arrays. \n",
"RUn the code below and compare 2 hrs and 10 hrs tracks for East-West, North-South and Inclined array.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"This will show the uv tracks for a given baseline for two observing session of different lengths\n",
"Enter the numbers of hours (e.g., 5 10): 5\n",
"Enter the wavelength in metre: 1\n",
"Choose the array type: East-West (press 1), North-South (press 2) or inclined (press 3): 1\n"
]
},
{
"data": {
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\n",
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