{ "cells": [ { "metadata": {}, "cell_type": "markdown", "source": "# Measure the Milky Way with Stars \n## RR Lyrae Stars as Standard Candles", "attachments": {} }, { "metadata": {}, "cell_type": "markdown", "source": "How can we measure astronomical distances? One technique is to use \"standard candles\", which are astronomical objects that have well-known brightnesses. By measuring how bright an object appears to us and knowing the actual brightness from some analysis, we can work out how far the object is from us. We employ the \"inverse square law\" for light to make this happen and do a bit of math.\n\n
Look for the variable stars. They seem to blink.
Illustration of inverse square law.
\n\nThe physical properties of electromagnetic radiation eminating from a star or other astronomical object is best described using flux which is related to power which is related to energy. Another common way to describe light leaving an astronomical object is through the concept of luminosity. The Stefan-Boltzman relation connections the energy density of a star (how much energy leaves 1 square meter of the star's surfce) and the star's temperature.\n\n\\begin{equation*}\nL=\\sigma{T^4}\\>[\\mathbf{W/m^2}]\n\\end{equation*}\n\nWe can find the power emitted by the star if we include the entire spherical surface of the star\n\n\\begin{equation*}\nL=\\sigma{T^4}(4\\pi{R^2})\\>[\\mathbf{W}]\n\\end{equation*}\n\nDon't forget that astronomers can determine the surface temperature of a star using Wien's law. Once the peak wavelength of the light from the star is found, we can get the temperature using the relation:\n\n\\begin{equation*}\n\\lambda_{peak}\\cdot{T}=constant\\>[\\mathbf{m\\cdot{K}}]\n\\end{equation*}\n\n## Magnitude vs Luminosity\nFor historical and convenience reasons, astronomers use a system called magnitude dating back to Hipparcos which uses the star Vega as a reference star. There are many peculiarlities with magnitude. For example a negative magnitude represents a brighter object than does a positive magnitude. Another useful point is that just using light from an image, astronomers can quickly measure the magnitude as seen from earth, the apparent magnitude. That leaves some work to do to get turn the physical brightness or luminosity of the object into the absolute magnitude. The magnitude scale is clunky but still in use - for now." }, { "metadata": {}, "cell_type": "markdown", "source": "## Globular Clusters\nA globular cluster is a very old grouping of stars usually found in the halo or the central region of a galaxy. NGC 3201 is one such globular cluster found in the Milky Way Galaxy. The images used for this activity were taken using the [Skynet Robitic Telescope Network](https://skynet.unc.edu/) run by the University of North Carolina. Yes... they called a robotic telescope system Skynet. The globular cluster was imaged 5 times in a single night by the system. This way, any star that has a periodic change of a day or so will show up in the series of images.\n\n\n\nGlobular Cluster NGC 3201
\n\nImage loaded into Aladin Sky Atlas with with Simbad source data overlaid.
\n\nList of targets visible in the field above.