NEW MASS MEASUREMENT FOR GALAXY CLUSTERS USING POSITION AND RADIAL VELOCITY ____________ A Thesis Presented to The College of Arts and Sciences Ohio University ____________ In Partial Fulfillment Of the Requirements for Graduation With Honors in Physics – Astrophysics ____________ by Kayla Jo Fultz June 2010 ii This thesis has been approved by the Department of Physics and Astronomy and the College of Arts and Sciences ___________________________________________________ Assistant Professor of Physics and Astronomy ____________________________________________________ Dean, College of Arts and Sciences iii Abstract Galaxy clusters are the largest structures in the Universe, and the evolution of galaxy cluster mass profiles is a useful tool for constraining cosmological models. Most methods established for obtaining a mass profile of a cluster of galaxies assumes the clusters obey the virial theorem; however, the majority of clusters are observed to contain non-virialized substructures. Zaritsky outlined a timing argument for obtaining mass profiles (Zaritsky, 1989). The timing argument assumes that at a time t = 0, every galaxy in the cluster was concentrated at one point, and then simultaneously exploded outward. The current position of each galaxy with respect to the cluster center is determined only by Newtonian gravitation. Zaritsky applied this method to the local group and obtained reasonable mass profiles (Zaritsky, 1989). We test this new method for mass measurement and compare our results to values obtained using virialized methods. We apply this timing argument to a sample of galaxy clusters of nearby redshift (from z~0.05 to z~0.2) taken from the Sloan Digital Sky Survey, using a 12 Mpc radius (a region larger than the typical infall radius) for each cluster. We chose clusters from a paper written by Popesso that contained published velocity dispersions for each cluster (Popesso, 2006). The profiles we acquire through the timing argument have a useful astronomical application because they rely only on infalling galaxies in the cluster, forgoing the virial theorem. We estimate a mass based on these profiles and use that mass to calculate a velocity dispersion in each cluster. Our velocity dispersions are compared to published values. Our comparison shows that this method for mass measurement gives reasonable velocity dispersions when applied to a large sample of galaxies. There is no clear systematic offset between our data set and the published data set, and many variables within this method leave room for large errors. iv Table of Contents Introduction . 1 Methods . 5 Data . 14 Analysis . 15 Conclusions . 25 References . 29 Appendix . 30 1 Introduction Galaxy clusters are among the largest celestial structures in the universe. Each cluster contains hundreds of galaxies that, in turn, contain billions of stars. These superstructures have been of great interest to astronomers and have been key components to answering many questions about our universe. The studying the evolution galaxy clusters helps give us a better understanding of the nature of our universe. The study of galaxy clusters has led to recent breakthroughs in the field of study of astrophysics. In studying the universe, we are concerned with two types of matter: baryonic and nonbaryonic. By strict definition, baryonic matter consists of matter made up of three quarks, which include protons and neutrons: the type of matter we can observe. For astronomy, we consider baryonic matter to include objects such as electrons since they constitute a very small portion of the mass in atomic nuclei. Nonbaryonic matter consists of neutrinos--tiny, elementary particles that travel very fast and usually travel through matter without interacting, or other particles that have yet to be discovered. Studying the ratio of baryonic to nonbaryonic matter is essential for cosmologists interested in uncovering specifics about the Big Bang. Models and calculations focusing on the Big Bang require very precise values for the ratio of baryonic to nonbaryonic matter. A fundamental law if physics is the fact that matter can neither be created nor destroyed; therefore, if a value for the current ratio of baryonic to nonbaryonic matter is reached, it is held as a constant even back to the time of the Big Bang. Galaxy clusters have been crucial to developing this ratio of matter. When scientists observed the Coma Cluster, they obtained an unusual mass-to-light ratio. This discrepancy led scientists to conclude that there was more matter than they were 2 observing. When they looked at the cluster through a different filter, they discovered a large amount of hot gas (e.g. Kellogg, Baldwin, & Koch). Since the gas was not producing visible light like the stars in the cluster, it was not readily visible until scientists looked for it specifically. Discoveries such as the large amounts of gas in the Coma Cluster lead to better evaluations of the ratio of baryonic to nonbaryonic matter. Galaxy clusters were also vital in the discovery of dark matter. Dark matter is a very active topic of study for modern astrophysicists. Dark matter was originally proposed by astrophysicist Fritz Zwicky. Zwicky was studying galaxy clusters and the movement of galaxies within these clusters. Based on his observations, Zwicky concluded that there was more mass present in the system than could actually be observed for the galaxies to behave as they did (Zwicky, 1933). Further observations of galaxy clusters proved the existence of dark matter by study of the phenomenon known as gravitational lensing (e.g. Schneider, Ehlers, & Falco, 1992). A gravitational lens occurs when light from a very distant source is bent around a massive object. In most cases, the massive object is a galaxy cluster. By studying the severity of such lensing effects, scientists can calculate the amount of matter in a galaxy cluster and, more specifically, derive an estimate for the amount of dark matter within a given cluster. To qualify as a galaxy cluster, the structure must contain at least 50 galaxies that are gravitationally bound to one another. Galaxy clusters vary in size, number of galaxies, and distance from our solar system. When astronomers discuss distances of astronomical objects, they refer to a celestial structure’s redshift, denoted by the letter “z.” There are two types of redshift we 3 observe in the universe. There is a redshift that corresponds to an object’s movement within the Universe, for instance, galaxies gravitationally bound within a cluster and rotating about its center will have light waves shifted depending on if they’re moving towards us or away from us; however, we live in an expanding universe, so all other celestial objects constantly appear to be moving away from our solar system. Because the Universe is expanding, these objects appear to move away from us, the observer, and the electromagnetic waves emitted by these objects get shifted. Specific colors of light correspond to distinct wavelengths: red has a longer wavelength while blue has a shorter wavelength. Because in an expanding universe these objects are moving away from us, the light emitted becomes “stretched,” and so the phenomenon is called redshift. Redshifts can be used to calculate distances to celestial objects. This relation was first observed by Edwin Hubble. Hubble discovered that the speed at which an object moves away from our solar system could be directly related to the distance from that object to us. These two values are related by a cosmological constant called Hubble’s constant. Theoretical analysis and study of galaxy clusters are constantly updating the value of Hubble’s constant. Determining the mass of a galaxy cluster is a complex task. Traditionally, astronomers use the virial theorem to estimate cluster masses. The virial theorem states that twice the kinetic energy of a virial object is equal to the negative of the object’s potential energy. For galaxy clusters, the virial theorem is thought to hold out to a virial radius. Current estimates of cluster masses must be done assuming the cluster obeys the virial theorem. This method does not hold for nonvirialized substructures within the cluster. 4 The purpose of this project is to determine a lower-mass limit of a selection of galaxy clusters without using the virial theorem. To accomplish this, we utilize a timing argument outlined by Zaritsky (Zaritsky, 1989). This timing argument assumes each galaxy is an infalling galaxy; this means that the galaxy is assumed it is not yet gravitationally bound by the cluster. This argument completely ignores what we know about cosmology and our expanding universe. The timing argument uses pure Newtonian mechanics and the basic laws of gravitation to calculate a minimum cluster mass necessary to have the galaxy at its current distance within the cluster. According to this argument, the galaxy and cluster are on a path towards one another, or an elliptical orbit with eccentricity of 1. Basically, the timing argument goes by the incorrect assumption that at a time t = 0, the galaxy and the cluster were at the same position, and then they simultaneously moved apart, and now are slowly gravitating back towards one another. Their current positions relative to one another are based solely on gravitation. Since this method ignores many cosmological factors, it is surprising that it is a reliable technique; however, this timing argument was used by Zaritsky in 1989 to study objects within the Local Group, the small group of galaxies near to the Milky Way. In Zaritsky’s application, the timing argument yielded remarkably accurate mass estimates. This project will be the first time this technique has been applied to a large survey of galaxy clusters. In order to determine if our mass estimates using the timing argument are good estimates, we will compare our values to Popesso’s published velocity dispersions (Popesso, 2006). 5 Methodology The first step in this project was determining a sample of galaxy clusters.