{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image\n", "from IPython.display import Video, HTML, YouTubeVideo\n", "width = 600" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to Galaxies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Galaxies are composed of many billions of stars and are tiny islands in this vast Universe. The story of our understanding of galaxies is quite new. About a hundred years ago, there was little clarity on the nature of galaxies themselves. Astronomers knew quite a bit about our own galaxy through star counts. \n", "\n", "When astronomers looked at the night sky with telescopes to find stars, planets and comets, they came across fuzzy patches in the sky. They called them nebulae, and catalogued them, so as to not confuse them with comets. As is often the case, these nebulae turned out to be interesting in themselves. In 1920s there was a great debate between two astronomers: Harlow Shapley and Herber Curtis, about the nature of these nebulae, and the size of the Universe. A summary of the debate can be found in the [wikipedia article](https://tinyurl.com/nga5hm4) and the website linked [here](https://apod.nasa.gov/diamond_jubilee/debate20.html)\n", "\n", "As you can read, this scientific debate was informed by astronomical observations and each side made the case for their point of view. Science often proceeds in ways that can be complicated. But observations (and their confirmations) are crucial to help understand scientific facts." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Galaxies:\n", "\n", "Galaxies are quite pretty to look at, here are a couple of very famous galaxies. First an example of a spiral galaxy:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image(url=\"https://apod.nasa.gov/apod/image/1812/m31_gendler_2700.jpg\", width=width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This galaxy is M31. It is a sister galaxy to the Milky Way. We can see stars arranged in a disk, a very prominent central concentration of stars, a number of dust lanes within the galaxy. The spiral arms in galaxies like M31 are the sites of intense star formation. We can also see that M31 also has a companion dwarf galaxy (M32) which is quite close.\n", "\n", "Next let us look at an example of another spiral galaxy (NGC 1300)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image(url=\"https://upload.wikimedia.org/wikipedia/commons/5/52/Hubble2005-01-barred-spiral-galaxy-NGC1300.jpg\", width=width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The galaxy NGC 1300, has a big bar like structure in the middle, and such structures can be present both in stars and gas. There is evidence that uur galaxy, the Milky Way, also has such a bar like structure.\n", "\n", "Now let us look at an elliptical galaxy." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image(url=\"https://space-facts.com/wp-content/uploads/m87.png\", width=width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This galaxy is M87. It looks like a fuzzy collection of stars. Such galaxies are called elliptical galaxies. There is something funny going on at the center of this galaxy. One can see a nice jet coming out of center of this galaxy. This jet At the center of this galaxy is a massive black hole. It was recently in the news because radio astronomers made the first image of the black hole which lies at the center of this galaxy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then a dwarf irregular galaxy:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image(url=\"https://subarutelescope.org/Pressrelease/2004/02/23/SextansA_200.jpg\", width=width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This galaxy is Sextans-A. It is a dwarf irregular galaxy. Because it is so faint and diffuse it is quite hard to find such galaxies. This particular galaxy lies in the outskirts of our local group of galaxies. It is hard to say whether this galaxy is a satellite galaxy within our local group. The dwarf irregulars are typically rich in their gas content.\n", "\n", "You can read more about these galaxies on wikipedia: [M31](https://en.wikipedia.org/wiki/Andromeda_Galaxy), [M87](https://en.wikipedia.org/wiki/Messier_87) and [SextansA](https://en.wikipedia.org/wiki/Sextans_A).\n", "\n", "Galaxies form a quite diverse population. They do not all look the same, their formation and evolution mechanisms are also quite likely quite different. What sort of different questions come to your mind after seeing some of these images?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Galaxies : Formation\n", "\n", "In our current understanding of the Universe, ordinary matter which makes stars shine, constitutes only a small fraction (about 15 percent) of the matter density of the Universe. The rest is made up of dark matter. The total matter content forms only about 30 percent of the energy density budget of the Universe, today. The rest is in the form of a mysterious component called dark energy, and miniscule amounts of radiation components. The Universe is not static and all physical distances change with time. The rate of change of these physical distances is governed by the energy content of the Universe at any given time. This forms the cosmological context in which galaxies form.\n", "\n", "The early Universe (at the start of the matter dominated era) is not uniform, but has small density fluctuations. These density fluctuations originate in the very early Universe and are a result of quantum fluctuations (and you will learn a lot about it in your cosmology course). These fluctuations set the initial conditions for structure formation.\n", "\n", "The structure in the dark matter distribution grows due to gravitational instabilities and results in the formation of extended dark matter halos. Gas within the dark matter halos is able to collisionally lose its energy and concentrate towards the center. This leads the center of dark matter halos to form stars in a concerted manner and form galaxies. Galaxies, such as the Milky Way, have typical radii of the order of tens of kilo parsecs, where as the dark matter halos are 100s of kilo parsec in size." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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\n", "text/plain": [ "" ] }, "execution_count": 7, "metadata": { "image/png": { "width": 600 } }, "output_type": "execute_result" } ], "source": [ "Image(\"images/halo.png\", width=width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During this course, we will learn a lot about timescales of different physical processes which shape galaxy properties. But most of these time scales are very large compared to that of a human life. This implies that the evolution of galaxies cannot be studied by looking at just one galaxy eveolve over time. This is quite a difficult problem because identifying galaxies which are the counterparts of the galaxies that are observed at one epoch is not easy.\n", "\n", "Galaxies are quite diverse, but their properties are quite correlated and they often obey tight scaling relations (we will study the origin of some of these scaling relations). The evolution of these scaling relations can then help us understand galaxy evolution as a whole as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Big questions\n", "\n", "1. How do galaxies fit in the grand scheme of the Universe?\n", "2. Can they be described by the same laws of physics that we know of in the solar system?\n", "3. How do galaxies evolve?\n", "4. Do galaxy populations obey any statistical properties as a whole and can we understand these properties?\n", "\n", "Throughout these series of lectures we will try to apply some common concepts you would have already learnt in classical mechanics in order to understand the properties of these galaxies." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "0. Think about how you would find the shape and nature of our own galaxy.\n", "1. Look for the period luminosity relation of stars called cepheid variables.\n", "2. Gather data of the periods of Cepheid variables in the Andromeda galaxy (Edwin Hubble compiled this data first, there should be more modern tables) and hence deduce their luminosities\n", "3. Figure out the distance of the Andromeda galaxy from the observed fluxes of Cepheid variables in Andromeda.\n", "4. How can we measure the mass of our galaxy?" ] } ], "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }