Clusters of Galaxies: Spherical Collapse and Virialization
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Dark Matter 1 Introduction 2 Evidence of Dark Matter
Proceedings Astronomy from 4 perspectives 1. Cosmology Dark matter Marlene G¨otz (Jena) Dark matter is a hypothetical form of matter. It has to be postulated to describe phenomenons, which could not be explained by known forms of matter. It has to be assumed that the largest part of dark matter is made out of heavy, slow moving, electric and color uncharged, weakly interacting particles. Such a particle does not exist within the standard model of particle physics. Dark matter makes up 25 % of the energy density of the universe. The true nature of dark matter is still unknown. 1 Introduction Due to the cosmic background radiation the matter budget of the universe can be divided into a pie chart. Only 5% of the energy density of the universe is made of baryonic matter, which means stars and planets. Visible matter makes up only 0,5 %. The influence of dark matter of 26,8 % is much larger. The largest part of about 70% is made of dark energy. Figure 1: The universe in a pie chart [1] But this knowledge was obtained not too long ago. At the beginning of the 20th century the distribution of luminous matter in the universe was assumed to correspond precisely to the universal mass distribution. In the 1920s the Caltech professor Fritz Zwicky observed something different by looking at the neighbouring Coma Cluster of galaxies. When he measured what the motions were within the cluster, he got an estimate for how much mass there was. Then he compared it to how much mass he could actually see by looking at the galaxies. -
Detection of Co Emission in Hydra I Cluster Galaxies
DETECTION OF CO EMISSION IN HYDRA I CLUSTER GALAXIES W.K. Huehtmeier Max- Planek-Ins t it ut fur Radioastr onomie Auf dem Huge1 69 5300 Bonn 1 , W. Germany Abstract A survey of bright Hydra cluster spiral galaxies for the CO(1-0) transition at 115 GHa was performed with the 15m Swedish-ESO submillimeter telescope (SEST). Five out of 15 galaxies observed have been detected in the CO(1-0) line. The largest spiral galaxy in the cluster , NGC 3312, got more CO than any spiral of the Virgo cluster. This Sa-type galaxy is optically largely distorted and disrupted on one side. It is a good candidate for ram pressure stripping while passing through the cluster's central region. A comparison with global CO properties of Virgo cluster spirals shows a relatively good agreement with the detected Hydra cluster galaxies. 0 bservations Observations were performed with the 15m Swedish-ESO submillimeter telescope (SEST) at La Silla in January 1989 under favorable meteorological conditions. At a frequency of 115 GHz the half power beamwidth (HPBW) of this telescope is 43 arcsec. The cooled Schottky heterodyne receiver had a typical receiver temperature of 350 K; the system temperature was typically 650 to 900 K depending on elevation and humidity. An accousto-optic spectrometer (Zensen 1984) with a bandwidth of 500 MHz yielded a channel width of 0.69 MHz or about 1.8 km/s. In order to improve the signal-to-noise ratio of the integrated profiles usually 5 to 10 frequency channels were averaged resulting in a resolution of 9 to 18 km/s. -
Molecular Gas Content of Galaxies in the Hydra-Centaurus Supercluster
MOLECULAR GAS CONTENT OF GALAXIES IN THE HYDRA-CENTAURUS SUPERCLUSTER W.K. Huchtmeier ™ ** <$ '"" & ^ O Max-Planck-Institut fiir Radioastronomie Auf dem Hugel 69 , 5300 Bonn 1 , W. Germany • Abstract A survey of bright spiral galaxies in the Hydra-Centaurus supercluster for the CO(l-O) transition at 115 GHz was performed with the 15m Swedish-ESO submillimeter telescope (SEST). A total of 30 galaxies have been detected in the CO(l-O) transition out of 47 observed, which is a detection rate over 60%. Global physical parameters of these galaxies derived from optical, CO, HI, and IR measurements compare very well with properties of galaxies in the Virgo cluster. The Hydra I cluster (Abell 1060) is one of the nearest clusters and very similar to the Virgo cluster in many global parameters like type, population, size, and shape. Both clusters have comparable velocity dispersions (i.e. total mass) and are spiral rich. Hydra is well isolated in velocity space and appears more circular (Kwast 1966), and might be dynamically more relaxed, although the center may contain significant substructures (Fitchett and Meritt 1988) or projected foreground groups. Both clusters contain low luminosity central X-ray sources. We assume a distance of 68.4 Mpc for Hydra I in order to allow direct comparison with some (nearly) complete galaxy samples. The Centaurus cluster provides a valuable contrast to Virgo and Coma. It is intermediate in distance and in galaxy population type with a relatively well defined SO-dominated core and an extensive S-rich halo. Its richness class in the Abell scale is 1 or 2 which is richer than Virgo and poorer than Coma. -
S Chandrasekhar: His Life and Science
REFLECTIONS S Chandrasekhar: His Life and Science Virendra Singh 1. Introduction Subramanyan Chandrasekhar (or `Chandra' as he was generally known) was born at Lahore, the capital of the Punjab Province, in undivided India (and now in Pakistan) on 19th October, 1910. He was a nephew of Sir C V Raman, who was the ¯rst Asian to get a science Nobel Prize in Physics in 1930. Chandra also went on to win the Nobel Prize in Physics in 1983 for his early work \theoretical studies of physical processes of importance to the structure and evolution of the stars". Chandra discovered that there is a maximum mass limit, now called `Chandrasekhar limit', for the white dwarf stars around 1.4 times the solar mass. This work was started during his sea voyage from Madras on his way to Cambridge (1930) and carried out to completion during his Cambridge period (1930{1937). This early work of Chandra had revolutionary consequences for the understanding of the evolution of stars which were not palatable to the leading astronomers, such as Eddington or Milne. As a result of controversy with Eddington, Chandra decided to shift base to Yerkes in 1937 and quit the ¯eld of stellar structure. Chandra's work in the US was in a di®erent mode than his initial work on white dwarf stars and other stellar-structure work, which was on the frontier of the ¯eld with Chandra as a discoverer. In the US, Chandra's work was in the mode of a `scholar' who systematically explores a given ¯eld. As Chandra has said: \There is a complementarity between a systematic way of working and being on the frontier. -
Virial Theorem and Gravitational Equilibrium with a Cosmological Constant
21 VIRIAL THEOREM AND GRAVITATIONAL EQUILIBRIUM WITH A COSMOLOGICAL CONSTANT Marek N owakowski, Juan Carlos Sanabria and Alejandro García Departamento de Física, Universidad de los Andes A. A. 4976, Bogotá, Colombia Starting from the Newtonian limit of Einstein's equations in the presence of a positive cosmological constant, we obtain a new version of the virial theorem and a condition for gravitational equi librium. Such a condition takes the form P > APvac, where P is the mean density of an astrophysical system (e.g. galaxy, galaxy cluster or supercluster), A is a quantity which depends only on the shape of the system, and Pvac is the vacuum density. We conclude that gravitational stability might be infiuenced by the presence of A depending strongly on the shape of the system. 1. Introd uction Around 1998 two teams (the Supernova Cosmology Project [1] and the High- Z Supernova Search Team [2]), by measuring distant type la Supernovae (SNla), obtained evidence of an accelerated ex panding universe. Such evidence brought back into physics Ein stein's "biggest blunder", namely, a positive cosmological constant A, which would be responsible for speeding-up the expansion of the universe. However, as will be explained in the text below, the A term is not only of cosmological relevance but can enter also the do main of astrophysics. Regarding the application of A in astrophysics we note that, due to the small values that A can assume, i s "repul sive" effect can only be appreciable at distances larger than about 22 1 Mpc. This is of importance if one considers the gravitational force between two bodies. -
Scientometric Portrait of Nobel Laureate S. Chandrasekhar
:, Scientometric Portrait of Nobel Laureate S. Chandrasekhar B.S. Kademani, V. L. Kalyane and A. B. Kademani S. ChandntS.ekhar, the well Imown Astrophysicist is wide!)' recognised as a ver:' successful Scientist. His publications \\'ere analysed by year"domain, collaboration pattern, d:lannels of commWtications used, keywords etc. The results indicate that the temporaJ ,'ari;.&-tjon of his productivit." and of the t."pes of papers p,ublished by him is of sudt a nature that he is eminent!)' qualified to be a role model for die y6J;mf;ergene-ration to emulate. By the end of 1990, he had to his credit 91 papers in StelJJlrSlructllre and Stellar atmosphere,f. 80 papers in Radiative transfer and negative ion of hydrogen, 71 papers in Stochastic, ,ftatisticql hydromagnetic problems in ph}'sics and a,ftrono"9., 11 papers in Pla.fma Physics, 43 papers in Hydromagnetic and ~}.droa:rnamic ,S"tabiJjty,42 papers in Tensor-virial theorem, 83 papers in Relativi,ftic a.ftrophy,fic.f, 61 papers in Malhematical theory. of Black hole,f and coUoiding waves, and 19 papers of genual interest. The higb~t Collaboration Coefficient \\'as 0.5 during 1983-87. Producti"it." coefficient ,,.as 0.46. The mean Synchronous self citation rate in his publications \\.as 24.44. Publication densi~. \\.as 7.37 and Publication concentration \\.as 4.34. Ke.}.word.f/De,fcriptors: Biobibliometrics; Scientometrics; Bibliome'trics; Collaboration; lndn.idual Scientist; Scientometric portrait; Sociolo~' of Science, Histor:. of St.-iencc. 1. Introduction his three undergraduate years at the Institute for Subrahmanvan Chandrasekhar ,,.as born in Theoretisk Fysik in Copenhagen. -
Equipartition Theorem - Wikipedia 1 of 32
Equipartition theorem - Wikipedia 1 of 32 Equipartition theorem In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion. The equipartition theorem makes quantitative Thermal motion of an α-helical predictions. Like the virial theorem, it gives the total peptide. The jittery motion is random average kinetic and potential energies for a system at a and complex, and the energy of any given temperature, from which the system's heat particular atom can fluctuate wildly. capacity can be computed. However, equipartition also Nevertheless, the equipartition theorem allows the average kinetic gives the average values of individual components of the energy of each atom to be energy, such as the kinetic energy of a particular particle computed, as well as the average or the potential energy of a single spring. For example, potential energies of many it predicts that every atom in a monatomic ideal gas has vibrational modes. The grey, red an average kinetic energy of (3/2)kBT in thermal and blue spheres represent atoms of carbon, oxygen and nitrogen, equilibrium, where kB is the Boltzmann constant and T respectively; the smaller white is the (thermodynamic) temperature. More generally, spheres represent atoms of equipartition can be applied to any classical system in hydrogen. -
MACHINE LEARNING in GALAXY GROUPS DETECTION By
MACHINE LEARNING IN GALAXY GROUPS DETECTION by RAFEE TARIQ IBRAHEM A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY School of Computer Science College of Engineering and Physical Sciences The University of Birmingham May 2017 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract The detection of galaxy groups and clusters is of great importance in the field of astrophysics. In particular astrophysicists are interested in the evolution and formation of these systems, as well as the interactions that occur within galaxy groups and clusters. In this thesis, we developed a probabilistic model capa- ble of detecting galaxy groups and clusters based on the Hough transform. We called this approach probabilistic Hough transform based on adaptive local ker- nel (PHTALK). PHTALK was tested on a 3D realistic galaxy and mass assembly (GAMA) mock data catalogue (at close redshift z < 0:1)(mock data: contains information related to galaxies’ position, redshift and other properties). We com- pared the performance of our PHTALK method with the performance of two ver- sions of the standard friends-of-friends (FoF) method. -
Astronomy Astrophysics
A&A 470, 449–466 (2007) Astronomy DOI: 10.1051/0004-6361:20077443 & c ESO 2007 Astrophysics A CFH12k lensing survey of X-ray luminous galaxy clusters II. Weak lensing analysis and global correlations S. Bardeau1,2,G.Soucail1,J.-P.Kneib3,4, O. Czoske5,6,H.Ebeling7,P.Hudelot1,5,I.Smail8, and G. P. Smith4,9 1 Laboratoire d’Astrophysique de Toulouse-Tarbes, CNRS-UMR 5572 and Université Paul Sabatier Toulouse III, 14 avenue Belin, 31400 Toulouse, France e-mail: [email protected] 2 Laboratoire d’Astrodynamique, d’Astrophysique et d’Aéronomie de Bordeaux, CNRS-UMR 5804 and Université de Bordeaux I, 2 rue de l’Observatoire, BP 89, 33270 Floirac, France 3 Laboratoire d’Astrophysique de Marseille, OAMP, CNRS-UMR 6110, Traverse du Siphon, BP 8, 13376 Marseille Cedex 12, France 4 Department of Astronomy, California Institute of Technology, Mail Code 105-24, Pasadena, CA 91125, USA 5 Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany 6 Kapteyn Astronomical Institute, PO Box 800, 9700 AV Groningen, The Netherlands 7 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Dr, Honolulu, HI 96822, USA 8 Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK 9 School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Received 9 March 2007 / Accepted 9 May 2007 ABSTRACT Aims. We present a wide-field multi-color survey of a homogeneous sample of eleven clusters of galaxies for which we measure total masses and mass distributions from weak lensing. -
Large Peculiar Velocities in the Hydra Centaurus Supercluster
LARGE PECULIAR VELOCITIES IN THE HYDRA CENTAURUS SUPERCLUSTER M. Aaronson1*, G.D. Bothun2, K.G. Budge3, JA. Dawe4, R.J. Dickens5, RJ. Hall6, J.R. Lucey7, J.R. Mould3, J.D. Murray6, R.A. Schommer8, A.E. Wright6. 1 Steward Observatory, University of Arizona 2 University of Michigan 3 California Institute of Technology 4 Australian National University 5Rutherford Appleton Laboratory 6 Australian National Radio Astronomy Observatory 7Anglo Australian Observatory 8 Rutgers University ABSTRACT Six clusters forming part of the Hydra-Cen Supercluster and its ex- tension on the opposite side of the galactic plane are under study at 21 cm with the Parkes radiotélescope. The infrared Tully-Fisher relation is used to determine the relative distances of the clusters. These clusters exhibit significant and generally positive peculiar velocities ranging from essentially zero for the Hydra cluster to as much as 1000 km/sec for the Pavo and Centaurus clusters. An upper limit of 500 km/sec was previously found in the study of clusters accessible from Arecibo. Data collection is not yet complete, however, and is further subject to unstud- ied systematic errors due to present reliance on photographic galaxy diameters. Nevertheless, these preliminary results support the notion of a large scale (and pre- sumably gravit at ionally) disturbed velocity field in the second and third quadrants of the supergalactic plane. 1. INTRODUCTION Comparison of the ratios of distances of galaxies with the ratios of their recession velocities allows one to learn something about the "noise" in the Hubble flow on various scales. One is subject to the limitation, however, that distance indicators are imprecise, and the 0.4 mag scatter in the infrared Tully-Fisher (IRTF) relation translates to an uncertainty of 1000 km/sec in an individual galaxy at cz = 5000 km/sec. -
Virial Theorem for a Molecule Approved
VIRIAL THEOREM FOR A MOLECULE APPROVED: (A- /*/• Major Professor Minor Professor Chairman' lof the Physics Department Dean 6f the Graduate School Ranade, Manjula A., Virial Theorem For A Molecule. Master of Science (Physics), May, 1972, 120 pp., bibliog- raphy, 36 titles. The usual virial theorem, relating kinetic and potential energy, is extended to a molecule by the use of the true wave function. The virial theorem is also obtained for a molecule from a trial wave function which is scaled separately for electronic and nuclear coordinates. A transformation to the body fixed system is made to separate the center of mass motion exactly. The virial theorems are then obtained for the electronic and nuclear motions, using exact as well as trial electronic and nuclear wave functions. If only a single scaling parameter is used for the electronic and the nuclear coordinates, an extraneous term is obtained in the virial theorem for the electronic motion. This extra term is not present if the electronic and nuclear coordinates are scaled differently. Further, the relation- ship between the virial theorems for the electronic and nuclear motion to the virial theorem for the whole molecule is shown. In the nonstationary state the virial theorem relates the time average of the quantum mechanical average of the kinetic energy to the radius vector dotted into the force. VIRIAL THEOREM FOR A MOLECULE THESIS Presented to the Graduate Council of the North Texas State University in Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE By Manjula A. Ranade Denton, Texas May, 1972 TABLE OF CONTENTS Page I. -
8.901 Lecture Notes Astrophysics I, Spring 2019
8.901 Lecture Notes Astrophysics I, Spring 2019 I.J.M. Crossfield (with S. Hughes and E. Mills)* MIT 6th February, 2019 – 15th May, 2019 Contents 1 Introduction to Astronomy and Astrophysics 6 2 The Two-Body Problem and Kepler’s Laws 10 3 The Two-Body Problem, Continued 14 4 Binary Systems 21 4.1 Empirical Facts about binaries................... 21 4.2 Parameterization of Binary Orbits................. 21 4.3 Binary Observations......................... 22 5 Gravitational Waves 25 5.1 Gravitational Radiation........................ 27 5.2 Practical Effects............................ 28 6 Radiation 30 6.1 Radiation from Space......................... 30 6.2 Conservation of Specific Intensity................. 33 6.3 Blackbody Radiation......................... 36 6.4 Radiation, Luminosity, and Temperature............. 37 7 Radiative Transfer 38 7.1 The Equation of Radiative Transfer................. 38 7.2 Solutions to the Radiative Transfer Equation........... 40 7.3 Kirchhoff’s Laws........................... 41 8 Stellar Classification, Spectra, and Some Thermodynamics 44 8.1 Classification.............................. 44 8.2 Thermodynamic Equilibrium.................... 46 8.3 Local Thermodynamic Equilibrium................ 47 8.4 Stellar Lines and Atomic Populations............... 48 *[email protected] 1 Contents 8.5 The Saha Equation.......................... 48 9 Stellar Atmospheres 54 9.1 The Plane-parallel Approximation................. 54 9.2 Gray Atmosphere........................... 56 9.3 The Eddington Approximation................... 59 9.4 Frequency-Dependent Quantities.................. 61 9.5 Opacities................................ 62 10 Timescales in Stellar Interiors 67 10.1 Photon collisions with matter.................... 67 10.2 Gravity and the free-fall timescale................. 68 10.3 The sound-crossing time....................... 71 10.4 Radiation transport.......................... 72 10.5 Thermal (Kelvin-Helmholtz) timescale............... 72 10.6 Nuclear timescale..........................