Astronomy 114 – Summary of Important Concepts #2 1 Stars: Key
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The Hubble Constant H0 --- Describing How Fast the Universe Is Expanding A˙ (T) H(T) = , A(T) = the Cosmic Scale Factor A(T)
Determining H0 and q0 from Supernova Data LA-UR-11-03930 Mian Wang Henan Normal University, P.R. China Baolian Cheng Los Alamos National Laboratory PANIC11, 25 July, 2011,MIT, Cambridge, MA Abstract Since 1929 when Edwin Hubble showed that the Universe is expanding, extensive observations of redshifts and relative distances of galaxies have established the form of expansion law. Mapping the kinematics of the expanding universe requires sets of measurements of the relative size and age of the universe at different epochs of its history. There has been decades effort to get precise measurements of two parameters that provide a crucial test for cosmology models. The two key parameters are the rate of expansion, i.e., the Hubble constant (H0) and the deceleration in expansion (q0). These two parameters have been studied from the exceedingly distant clusters where redshift is large. It is indicated that the universe is made up by roughly 73% of dark energy, 23% of dark matter, and 4% of normal luminous matter; and the universe is currently accelerating. Recently, however, the unexpected faintness of the Type Ia supernovae (SNe) at low redshifts (z<1) provides unique information to the study of the expansion behavior of the universe and the determination of the Hubble constant. In this work, We present a method based upon the distance modulus redshift relation and use the recent supernova Ia data to determine the parameters H0 and q0 simultaneously. Preliminary results will be presented and some intriguing questions to current theories are also raised. Outline 1. Introduction 2. Model and data analysis 3. -
AS1001: Galaxies and Cosmology Cosmology Today Title Current Mysteries Dark Matter ? Dark Energy ? Modified Gravity ? Course
AS1001: Galaxies and Cosmology Keith Horne [email protected] http://www-star.st-and.ac.uk/~kdh1/eg/eg.html Text: Kutner Astronomy:A Physical Perspective Chapters 17 - 21 Cosmology Title Today • Blah Current Mysteries Course Outline Dark Matter ? • Galaxies (distances, components, spectra) Holds Galaxies together • Evidence for Dark Matter • Black Holes & Quasars Dark Energy ? • Development of Cosmology • Hubble’s Law & Expansion of the Universe Drives Cosmic Acceleration. • The Hot Big Bang Modified Gravity ? • Hot Topics (e.g. Dark Energy) General Relativity wrong ? What’s in the exam? Lecture 1: Distances to Galaxies • Two questions on this course: (answer at least one) • Descriptive and numeric parts • How do we measure distances to galaxies? • All equations (except Hubble’s Law) are • Standard Candles (e.g. Cepheid variables) also in Stars & Elementary Astrophysics • Distance Modulus equation • Lecture notes contain all information • Example questions needed for the exam. Use book chapters for more details, background, and problem sets A Brief History 1860: Herchsel’s view of the Galaxy • 1611: Galileo supports Copernicus (Planets orbit Sun, not Earth) COPERNICAN COSMOLOGY • 1742: Maupertius identifies “nebulae” • 1784: Messier catalogue (103 fuzzy objects) • 1864: Huggins: first spectrum for a nebula • 1908: Leavitt: Cepheids in LMC • 1924: Hubble: Cepheids in Andromeda MODERN COSMOLOGY • 1929: Hubble discovers the expansion of the local universe • 1929: Einstein’s General Relativity • 1948: Gamov predicts background radiation from “Big Bang” • 1965: Penzias & Wilson discover Cosmic Microwave Background BIG BANG THEORY ADOPTED • 1975: Computers: Big-Bang Nucleosynthesis ( 75% H, 25% He ) • 1985: Observations confirm BBN predictions Based on star counts in different directions along the Milky Way. -
1 Kepler's Third
Astronomy 114 { Summary of Important Concepts #1 1 1 Kepler's Third Law Kepler discovered that the size of a planet's orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the orbit. If the size of the orbit (a) is expressed in astronomical units (1 AU equals the average distance between the Earth and Sun) and the period (P) is measured in years, then Kepler's Third Law says P 2 = a3: After applying Newton's Laws of Motion and Newton's Law of Gravity we find that Kepler's Third Law takes a more general form: 4π2 P 2 = a3 "G(m1 + m2)# in MKS units where m1 and m2 are the masses of the two bodies. Let's assume that one body, m1 say, is always much larger than the other one. Then m1 + m2 is nearly equal to m1. We can then use our technique of dividing two instances of this equation derive a general form of Kepler's Third Law: MP 2 = a3 where P is in Earth years, a is in AU and M is the mass of the central object in units of the mass of the Sun. So M = 1 whenever we talk about planets orbiting the Sun. Examples: Q: The Earth orbits the Sun at a distance of 1AU with a period of 1 year. 12 = 13. Suppose a new asteroid is discovered which orbits the Sun at a distance of 9AU. How long does it take this object to orbit the Sun? A: MP 2 = a3 (1)(P 2) = 93 P 2 = 729 P = p729 = 27 years Astronomy 114 { Summary of Important Concepts #1 2 2 Newton's Law of Gravitation Any two objects, no matter how small, attract one another gravitationally. -
Galaxies – AS 3011
Galaxies – AS 3011 Simon Driver [email protected] ... room 308 This is a Junior Honours 18-lecture course Lectures 11am Wednesday & Friday Recommended book: The Structure and Evolution of Galaxies by Steven Phillipps Galaxies – AS 3011 1 Aims • To understand: – What is a galaxy – The different kinds of galaxy – The optical properties of galaxies – The hidden properties of galaxies such as dark matter, presence of black holes, etc. – Galaxy formation concepts and large scale structure • Appreciate: – Why galaxies are interesting, as building blocks of the Universe… and how simple calculations can be used to better understand these systems. Galaxies – AS 3011 2 1 from 1st year course: • AS 1001 covered the basics of : – distances, masses, types etc. of galaxies – spectra and hence dynamics – exotic things in galaxies: dark matter and black holes – galaxies on a cosmological scale – the Big Bang • in AS 3011 we will study dynamics in more depth, look at other non-stellar components of galaxies, and introduce high-redshift galaxies and the large-scale structure of the Universe Galaxies – AS 3011 3 Outline of lectures 1) galaxies as external objects 13) large-scale structure 2) types of galaxy 14) luminosity of the Universe 3) our Galaxy (components) 15) primordial galaxies 4) stellar populations 16) active galaxies 5) orbits of stars 17) anomalies & enigmas 6) stellar distribution – ellipticals 18) revision & exam advice 7) stellar distribution – spirals 8) dynamics of ellipticals plus 3-4 tutorials 9) dynamics of spirals (questions set after -
Apparent and Absolute Magnitudes of Stars: a Simple Formula
Available online at www.worldscientificnews.com WSN 96 (2018) 120-133 EISSN 2392-2192 Apparent and Absolute Magnitudes of Stars: A Simple Formula Dulli Chandra Agrawal Department of Farm Engineering, Institute of Agricultural Sciences, Banaras Hindu University, Varanasi - 221005, India E-mail address: [email protected] ABSTRACT An empirical formula for estimating the apparent and absolute magnitudes of stars in terms of the parameters radius, distance and temperature is proposed for the first time for the benefit of the students. This reproduces successfully not only the magnitudes of solo stars having spherical shape and uniform photosphere temperature but the corresponding Hertzsprung-Russell plot demonstrates the main sequence, giants, super-giants and white dwarf classification also. Keywords: Stars, apparent magnitude, absolute magnitude, empirical formula, Hertzsprung-Russell diagram 1. INTRODUCTION The visible brightness of a star is expressed in terms of its apparent magnitude [1] as well as absolute magnitude [2]; the absolute magnitude is in fact the apparent magnitude while it is observed from a distance of . The apparent magnitude of a celestial object having flux in the visible band is expressed as [1, 3, 4] ( ) (1) ( Received 14 March 2018; Accepted 31 March 2018; Date of Publication 01 April 2018 ) World Scientific News 96 (2018) 120-133 Here is the reference luminous flux per unit area in the same band such as that of star Vega having apparent magnitude almost zero. Here the flux is the magnitude of starlight the Earth intercepts in a direction normal to the incidence over an area of one square meter. The condition that the Earth intercepts in the direction normal to the incidence is normally fulfilled for stars which are far away from the Earth. -
Measurements and Numbers in Astronomy Astronomy Is a Branch of Science
Name: ________________________________Lab Day & Time: ____________________________ Measurements and Numbers in Astronomy Astronomy is a branch of science. You will be exposed to some numbers expressed in SI units, large and small numbers, and some numerical operations such as addition / subtraction, multiplication / division, and ratio comparison. Let’s watch part of an IMAX movie called Cosmic Voyage. https://www.youtube.com/watch?v=xEdpSgz8KU4 Powers of 10 In Astronomy, we deal with numbers that describe very large and very small things. For example, the mass of the Sun is 1,990,000,000,000,000,000,000,000,000,000 kg and the mass of a proton is 0.000,000,000,000,000,000,000,000,001,67 kg. Such numbers are very cumbersome and difficult to understand. It is neater and easier to use the scientific notation, or the powers of 10 notation. For large numbers: For small numbers: 1 no zero = 10 0 10 1 zero = 10 1 0.1 = 1/10 Divided by 10 =10 -1 100 2 zero = 10 2 0.01 = 1/100 Divided by 100 =10 -2 1000 3 zero = 10 3 0.001 = 1/1000 Divided by 1000 =10 -3 Example used on real numbers: 1,990,000,000,000,000,000,000,000,000,000 kg -> 1.99X1030 kg 0.000,000,000,000,000,000,000,000,001,67 kg -> 1.67X10-27 kg See how much neater this is! Now write the following in scientific notation. 1. 40,000 2. 9,000,000 3. 12,700 4. 380,000 5. 0.017 6. -
Spectroscopy of Variable Stars
Spectroscopy of Variable Stars Steve B. Howell and Travis A. Rector The National Optical Astronomy Observatory 950 N. Cherry Ave. Tucson, AZ 85719 USA Introduction A Note from the Authors The goal of this project is to determine the physical characteristics of variable stars (e.g., temperature, radius and luminosity) by analyzing spectra and photometric observations that span several years. The project was originally developed as a The 2.1-meter telescope and research project for teachers participating in the NOAO TLRBSE program. Coudé Feed spectrograph at Kitt Peak National Observatory in Ari- Please note that it is assumed that the instructor and students are familiar with the zona. The 2.1-meter telescope is concepts of photometry and spectroscopy as it is used in astronomy, as well as inside the white dome. The Coudé stellar classification and stellar evolution. This document is an incomplete source Feed spectrograph is in the right of information on these topics, so further study is encouraged. In particular, the half of the building. It also uses “Stellar Spectroscopy” document will be useful for learning how to analyze the the white tower on the right. spectrum of a star. Prerequisites To be able to do this research project, students should have a basic understanding of the following concepts: • Spectroscopy and photometry in astronomy • Stellar evolution • Stellar classification • Inverse-square law and Stefan’s law The control room for the Coudé Description of the Data Feed spectrograph. The spec- trograph is operated by the two The spectra used in this project were obtained with the Coudé Feed telescopes computers on the left. -
Abbreviated Curriculum Vitae
Abbreviated Curriculum Vitae GRANT J. MATHEWS February 20, 2012 ADDRESS Department of Physics Center for Astrophysics University of Notre Dame Notre Dame, IN 46556 email: [email protected] off: (574) 631-6919 , FAX: (574) 631-5952 BIRTHDATE: October 14, 1950 PRESENT POSITION: • Nov. 1994 - Present Professor Department of Physics University of Notre Dame and • Sept. 2000 - Present Director, Center for Astrophysics at Notre Dame University (CANDU) University of Notre Dame PREVIOUS POSITIONS: • Apr. 1993-Nov. 1994 Senior Scientist Physical Sciences & Space Technologies Di- rectorate Physics Research Program/P-Division University of California, Lawrence Livermore National Laboratory and 1 • Sept. 1992-Nov. 1994 Adjunct Professor of Physics and Astronomy University of California, Davis • Oct. 1986-Apr. 1993 Group Leader for Astrophysics Physics Department/E-Division University of California, Lawrence Livermore National Laboratory • Apr. 1981-Oct. 19886 Physicist Physics Department/E-Division University of Cal- ifornia, Lawrence Livermore National Laboratory • Nov. 1979-Apr. 1981 Senior Research Fellow California Institute of Technology, W. K. Kellogg Radiation Laboratory • Sept. 1977- Nov. 1979 Research Associate University of California, Lawrence Berke- ley Laboratory • May-Sept. 1977 Post-Doctoral Research Associate, University of Maryland EDUCATION: • B.S., June 1972, Michigan State University • Ph.D., May 1977, University of Maryland, College Park, MD Dissertation: Re- flections and Research on: I) The Nucleosynthesis of Light and Heavy Nuclei; II) A Generalized Theory of Odd-A Nuclei; III) A Study of Three Heavy-Ion Systems HONORS: • Research Excellence Award of the Society of the Sigma Xi (1976) • Assoc. Western Univ.-ERDA-Fellowship to Lawrence Berkeley Laboratory (1976) • Visiting Scientist: California Institute of Technology (1981) • Guest Scientist: Max Planck Institute for Astrophysics (1984) • Distinguished Visiting Professor: Univ. -
Observations and Properties of Candidate High Frequency GPS
Mon. Not. R. Astron. Soc. 000, 1–21 () Printed 30 October 2018 (MN LATEX style file v2.2) Observations and properties of candidate high frequency GPS radio sources in the AT20G survey Paul J. Hancock1,2, Elaine M. Sadler1, Elizabeth K. Mahony1,2, Roberto Ricci3 1Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia 2Australia Telescope National Facility, CSIRO, PO Box 76, Epping, NSW 1710, Australia 3INAF-Istituto di Radioastronomia, Bologna, Via P. Gobetti, 101, 40129 Bologna, Italy ABSTRACT We used the Australia Telescope Compact Array (ATCA) to obtain 40GHz and 95GHz ob- servations of a number of sources that were selected from the Australia Telescope Compact Array 20GHz (AT20G) survey . The aim of the observations was to improve the spectral cov- erage for sources with spectral peaks near 20GHz or inverted (rising) radio spectra between 8.6GHz and 20GHz. We present the radio observations of a sample of 21 such sources along with optical spectra taken from the ANU Siding Spring Observatory 2.3m telescope and the ESO-New Technology Telescope (NTT). We find that as a group the sources show the same level of variability as typical GPS sources, and that of the 21 candidate GPS sources roughly 60% appear to be genuinely young radio galaxies. Three of the 21 sources studied show evi- dence of being restarted radio galaxies. If these numbers are indicative of the larger population of AT20G radio sources then as many as 400 genuine GPS sources could be contained within the AT20G with up to 25% of them being restarted radio galaxies. -
Gaia Data Release 2 Special Issue
A&A 623, A110 (2019) Astronomy https://doi.org/10.1051/0004-6361/201833304 & © ESO 2019 Astrophysics Gaia Data Release 2 Special issue Gaia Data Release 2 Variable stars in the colour-absolute magnitude diagram?,?? Gaia Collaboration, L. Eyer1, L. Rimoldini2, M. Audard1, R. I. Anderson3,1, K. Nienartowicz2, F. Glass1, O. Marchal4, M. Grenon1, N. Mowlavi1, B. Holl1, G. Clementini5, C. Aerts6,7, T. Mazeh8, D. W. Evans9, L. Szabados10, A. G. A. Brown11, A. Vallenari12, T. Prusti13, J. H. J. de Bruijne13, C. Babusiaux4,14, C. A. L. Bailer-Jones15, M. Biermann16, F. Jansen17, C. Jordi18, S. A. Klioner19, U. Lammers20, L. Lindegren21, X. Luri18, F. Mignard22, C. Panem23, D. Pourbaix24,25, S. Randich26, P. Sartoretti4, H. I. Siddiqui27, C. Soubiran28, F. van Leeuwen9, N. A. Walton9, F. Arenou4, U. Bastian16, M. Cropper29, R. Drimmel30, D. Katz4, M. G. Lattanzi30, J. Bakker20, C. Cacciari5, J. Castañeda18, L. Chaoul23, N. Cheek31, F. De Angeli9, C. Fabricius18, R. Guerra20, E. Masana18, R. Messineo32, P. Panuzzo4, J. Portell18, M. Riello9, G. M. Seabroke29, P. Tanga22, F. Thévenin22, G. Gracia-Abril33,16, G. Comoretto27, M. Garcia-Reinaldos20, D. Teyssier27, M. Altmann16,34, R. Andrae15, I. Bellas-Velidis35, K. Benson29, J. Berthier36, R. Blomme37, P. Burgess9, G. Busso9, B. Carry22,36, A. Cellino30, M. Clotet18, O. Creevey22, M. Davidson38, J. De Ridder6, L. Delchambre39, A. Dell’Oro26, C. Ducourant28, J. Fernández-Hernández40, M. Fouesneau15, Y. Frémat37, L. Galluccio22, M. García-Torres41, J. González-Núñez31,42, J. J. González-Vidal18, E. Gosset39,25, L. P. Guy2,43, J.-L. Halbwachs44, N. C. Hambly38, D. -
PHAS 1102 Physics of the Universe 3 – Magnitudes and Distances
PHAS 1102 Physics of the Universe 3 – Magnitudes and distances Brightness of Stars • Luminosity – amount of energy emitted per second – not the same as how much we observe! • We observe a star’s apparent brightness – Depends on: • luminosity • distance – Brightness decreases as 1/r2 (as distance r increases) • other dimming effects – dust between us & star Defining magnitudes (1) Thus Pogson formalised the magnitude scale for brightness. This is the brightness that a star appears to have on the sky, thus it is referred to as apparent magnitude. Also – this is the brightness as it appears in our eyes. Our eyes have their own response to light, i.e. they act as a kind of filter, sensitive over a certain wavelength range. This filter is called the visual band and is centred on ~5500 Angstroms. Thus these are apparent visual magnitudes, mv Related to flux, i.e. energy received per unit area per unit time Defining magnitudes (2) For example, if star A has mv=1 and star B has mv=6, then 5 mV(B)-mV(A)=5 and their flux ratio fA/fB = 100 = 2.512 100 = 2.512mv(B)-mv(A) where !mV=1 corresponds to a flux ratio of 1001/5 = 2.512 1 flux(arbitrary units) 1 6 apparent visual magnitude, mv From flux to magnitude So if you know the magnitudes of two stars, you can calculate mv(B)-mv(A) the ratio of their fluxes using fA/fB = 2.512 Conversely, if you know their flux ratio, you can calculate the difference in magnitudes since: 2.512 = 1001/5 log (f /f ) = [m (B)-m (A)] log 2.512 10 A B V V 10 = 102/5 = 101/2.5 mV(B)-mV(A) = !mV = 2.5 log10(fA/fB) To calculate a star’s apparent visual magnitude itself, you need to know the flux for an object at mV=0, then: mS - 0 = mS = 2.5 log10(f0) - 2.5 log10(fS) => mS = - 2.5 log10(fS) + C where C is a constant (‘zero-point’), i.e. -
Part 2 – Brightness of the Stars
5th Grade Curriculum Space Systems: Stars and the Solar System An electronic copy of this lesson in color that can be edited is available at the website below, if you click on Soonertarium Curriculum Materials and login in as a guest. The password is “soonertarium”. http://moodle.norman.k12.ok.us/course/index.php?categoryid=16 PART 2 – BRIGHTNESS OF THE STARS -PRELIMINARY MATH BACKGROUND: Students may need to review place values since this lesson uses numbers in the hundred thousands. There are two website links to online education games to review place values in the section. -ACTIVITY - HOW MUCH BIGGER IS ONE NUMBER THAN ANOTHER NUMBER? This activity involves having students listen to the sound that different powers of 10 of BBs makes in a pan, and dividing large groups into smaller groups so that students get a sense for what it means to say that 1,000 is 10 times bigger than 100. Astronomy deals with many big numbers, and so it is important for students to have a sense of what these numbers mean so that they can compare large distances and big luminosities. -ACTIVITY – WHICH STARS ARE THE BRIGHTEST IN THE SKY? This activity involves introducing the concepts of luminosity and apparent magnitude of stars. The constellation Canis Major was chosen as an example because Sirius has a much smaller luminosity but a much bigger apparent magnitude than the other stars in the constellation, which leads to the question what else effects the brightness of a star in the sky. -ACTIVITY – HOW DOES LOCATION AFFECT THE BRIGHTNESS OF STARS? This activity involves having the students test how distance effects apparent magnitude by having them shine flashlights at styrene balls at different distances.