A Time Series Study of Rigel, a B8ia Supergiant
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Group Problems #22 - Solutions
Group Problems #22 - Solutions Friday, October 21 Problem 1 Ritz Combination Principle Show that the longest wavelength of the Balmer series and the longest two wavelengths of the Lyman series satisfy the Ritz Combination Principle. The wavelengths corresponding to transitions between two energy levels in hydrogen is given by: n2 λ = λlimit 2 2 ; (1) n − n0 where n0 = 1 for the Lyman series, n0 = 2 for the Balmer series, and λlimit = 91:1 nm for the Lyman series and λlimit = 364:5 nm for the Balmer series. Inspection of this equation shows that the longest wavelength corresponds to the transition between n = n0 and n = n0 + 1. Thus, for the Lyman series, the longest two wavelengths are λ12 and λ13. For the Balmer series, the longest wavelength is λ23. The Ritz combination principle states that certain pairs of observed frequencies from the hydrogen spectrum add together to give other observed frequencies. For this particular problem, we then have: ν12 + ν23 = ν13 =) h(ν12 + ν23) = hν13 (2) 1 1 1 =) hc + = hc (3) λ12 λ23 λ13 1 1 1 =) + = : (4) λ12 λ23 λ13 Inverting Eqn. 1 above gives: 2 2 2 1 1 n − n0 1 n0 = 2 = 1 − 2 : (5) λ λlimit n λlimit n To calculate 1/λ12 and 1/λ13, we use the Lyman series numbers and find 1/λ12 = −1 −1 3=(4 ∗ 91:1) = 0:00823 nm and 1/λ13 = 8=(9 ∗ 91:1) = 0:00976 nm . To compute 1/λ23, we use the Balmer series numbers and find 1/λ23 = 5=(9 ∗ 364:5) = 0:00152 −1 nm . -
HI Balmer Jump Temperatures for Extragalactic HII Regions in the CHAOS Galaxies
HI Balmer Jump Temperatures for Extragalactic HII Regions in the CHAOS Galaxies A Senior Thesis Presented in Partial Fulfillment of the Requirements for Graduation with Research Distinction in Astronomy in the Undergraduate Colleges of The Ohio State University By Ness Mayker The Ohio State University April 2019 Project Advisors: Danielle A. Berg, Richard W. Pogge Table of Contents Chapter 1: Introduction ............................... 3 1.1 Measuring Nebular Abundances . 8 1.2 The Balmer Continuum . 13 Chapter 2: Balmer Jump Temperature in the CHAOS galaxies .... 16 2.1 Data . 16 2.1.1 The CHAOS Survey . 16 2.1.2 CHAOS Balmer Jump Sample . 17 2.2 Balmer Jump Temperature Determinations . 20 2.2.1 Balmer Continuum Significance . 20 2.2.2 Balmer Continuum Measurements . 21 + 2.2.3 Te(H ) Calculations . 23 2.2.4 Photoionization Models . 24 2.3 Results . 26 2.3.1 Te Te Relationships . 26 − 2.3.2 Discussion . 28 Chapter 3: Conclusions and Future Work ................... 32 1 Abstract By understanding the observed proportions of the elements found across galaxies astronomers can learn about the evolution of life and the universe. Historically, there have been consistent discrepancies found between the two main methods used to measure gas-phase elemental abundances: collisionally excited lines and optical recombination lines in H II regions (ionized nebulae around young star-forming regions). The origin of the discrepancy is thought to hinge primarily on the strong temperature dependence of the collisionally excited emission lines of metal ions, principally Oxygen, Nitrogen, and Sulfur. This problem is exacerbated by the difficulty of measuring ionic temperatures from these species. -
Observations of the Lyman Series Forest Towards the Redshift 7.1 Quasar ULAS J1120+0641 R
A&A 601, A16 (2017) Astronomy DOI: 10.1051/0004-6361/201630258 & c ESO 2017 Astrophysics Observations of the Lyman series forest towards the redshift 7.1 quasar ULAS J1120+0641 R. Barnett1, S. J. Warren1, G. D. Becker2, D. J. Mortlock1; 3; 4, P. C. Hewett5, R. G. McMahon5; 6, C. Simpson7, and B. P. Venemans8 1 Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK e-mail: [email protected] 2 Department of Physics & Astronomy, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA 3 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 4 Department of Astronomy, Stockholm University, Albanova, 10691 Stockholm, Sweden 5 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 6 Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 7 Gemini Observatory, Northern Operations Center, N. A’ohoku Place, Hilo, HI 96720, USA 8 Max-Planck Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany Received 15 December 2016 / Accepted 9 February 2017 ABSTRACT We present a 30 h integration Very Large Telescope X-shooter spectrum of the Lyman series forest towards the z = 7:084 quasar ULAS J1120+0641. The only detected transmission at S=N > 5 is confined to seven narrow spikes in the Lyα forest, over the redshift range 5:858 < z < 6:122, just longward of the wavelength of the onset of the Lyβ forest. There is also a possible detection of one further unresolved spike in the Lyβ forest at z = 6:854, with S=N = 4:5. -
Spectroscopy and the Stars
SPECTROSCOPY AND THE STARS K H h g G d F b E D C B 400 nm 500 nm 600 nm 700 nm by DR. STEPHEN THOMPSON MR. JOE STALEY The contents of this module were developed under grant award # P116B-001338 from the Fund for the Improve- ment of Postsecondary Education (FIPSE), United States Department of Education. However, those contents do not necessarily represent the policy of FIPSE and the Department of Education, and you should not assume endorsement by the Federal government. SPECTROSCOPY AND THE STARS CONTENTS 2 Electromagnetic Ruler: The ER Ruler 3 The Rydberg Equation 4 Absorption Spectrum 5 Fraunhofer Lines In The Solar Spectrum 6 Dwarf Star Spectra 7 Stellar Spectra 8 Wien’s Displacement Law 8 Cosmic Background Radiation 9 Doppler Effect 10 Spectral Line profi les 11 Red Shifts 12 Red Shift 13 Hertzsprung-Russell Diagram 14 Parallax 15 Ladder of Distances 1 SPECTROSCOPY AND THE STARS ELECTROMAGNETIC RADIATION RULER: THE ER RULER Energy Level Transition Energy Wavelength RF = Radio frequency radiation µW = Microwave radiation nm Joules IR = Infrared radiation 10-27 VIS = Visible light radiation 2 8 UV = Ultraviolet radiation 4 6 6 RF 4 X = X-ray radiation Nuclear and electron spin 26 10- 2 γ = gamma ray radiation 1010 25 10- 109 10-24 108 µW 10-23 Molecular rotations 107 10-22 106 10-21 105 Molecular vibrations IR 10-20 104 SPACE INFRARED TELESCOPE FACILITY 10-19 103 VIS HUBBLE SPACE Valence electrons 10-18 TELESCOPE 102 Middle-shell electrons 10-17 UV 10 10-16 CHANDRA X-RAY 1 OBSERVATORY Inner-shell electrons 10-15 X 10-1 10-14 10-2 10-13 10-3 Nuclear 10-12 γ 10-4 COMPTON GAMMA RAY OBSERVATORY 10-11 10-5 6 4 10-10 2 2 -6 4 10 6 8 2 SPECTROSCOPY AND THE STARS THE RYDBERG EQUATION The wavelengths of one electron atomic emission spectra can be calculated from the Use the Rydberg equation to fi nd the wavelength ot Rydberg equation: the transition from n = 4 to n = 3 for singly ionized helium. -
The Search for Transiting Extrasolar Planets in the Open Cluster M52
THE SEARCH FOR TRANSITING EXTRASOLAR PLANETS IN THE OPEN CLUSTER M52 A Thesis Presented to the Faculty of San Diego State University In Partial Fulfillment of the Requirements for the Degree Master of Sciences in Astronomy by Tiffany M. Borders Summer 2008 SAN DIEGO STATE UNIVERSITY The Undersigned Faculty Committee Approves the Thesis of Tiffany M. Borders: The Search for Transiting Extrasolar Planets in the Open Cluster M52 Eric L. Sandquist, Chair Department of Astronomy William Welsh Department of Astronomy Calvin Johnson Department of Physics Approval Date iii Copyright 2008 by Tiffany M. Borders iv DEDICATION To all who seek new worlds. v Success is to be measured not so much by the position that one has reached in life as by the obstacles which he has overcome. –Booker T. Washington All the world’s a stage, And all the men and women merely players. They have their exits and their entrances; And one man in his time plays many parts... –William Shakespeare, “As You Like It”, Act 2 Scene 7 vi ABSTRACT OF THE THESIS The Search for Transiting Extrasolar Planets in the Open Cluster M52 by Tiffany M. Borders Master of Sciences in Astronomy San Diego State University, 2008 In this survey we attempt to discover short-period Jupiter-size planets in the young open cluster M52. Ten nights of R-band photometry were used to search for planetary transits. We obtained light curves of 4,128 stars and inspected them for variability. No planetary transits were apparent; however, some interesting variable stars were discovered. In total, 22 variable stars were discovered of which, 19 were not previously known as variable. -
Unique Astrophysics in the Lyman Ultraviolet
Unique Astrophysics in the Lyman Ultraviolet Jason Tumlinson1, Alessandra Aloisi1, Gerard Kriss1, Kevin France2, Stephan McCandliss3, Ken Sembach1, Andrew Fox1, Todd Tripp4, Edward Jenkins5, Matthew Beasley2, Charles Danforth2, Michael Shull2, John Stocke2, Nicolas Lehner6, Christopher Howk6, Cynthia Froning2, James Green2, Cristina Oliveira1, Alex Fullerton1, Bill Blair3, Jeff Kruk7, George Sonneborn7, Steven Penton1, Bart Wakker8, Xavier Prochaska9, John Vallerga10, Paul Scowen11 Summary: There is unique and groundbreaking science to be done with a new generation of UV spectrographs that cover wavelengths in the “Lyman Ultraviolet” (LUV; 912 - 1216 Å). There is no astrophysical basis for truncating spectroscopic wavelength coverage anywhere between the atmospheric cutoff (3100 Å) and the Lyman limit (912 Å); the usual reasons this happens are all technical. The unique science available in the LUV includes critical problems in astrophysics ranging from the habitability of exoplanets to the reionization of the IGM. Crucially, the local Universe (z ≲ 0.1) is entirely closed to many key physical diagnostics without access to the LUV. These compelling scientific problems require overcoming these technical barriers so that future UV spectrographs can extend coverage to the Lyman limit at 912 Å. The bifurcated history of the Space UV: Much the course of space astrophysics can be traced to the optical properties of ozone (O3) and magnesium fluoride (MgF2). The first causes the space UV, and the second divides the “HST UV” (1150 - 3100 Å) and the “FUSE UV” (900 - 1200 Å). This short paper argues that some critical problems in astrophysics are best solved by a future generation of high-resolution UV spectrographs that observe all wavelengths between the Lyman limit and the atmospheric cutoff. -
SATELLITE COMMUNICATION UNIT I OVERVIEW of SATELLITE SYSTEMS, ORBITS and LAUNCHING METHODS Introduction
www.jntuhweb.com JNTUH WEB SATELLITE COMMUNICATION UNIT I OVERVIEW OF SATELLITE SYSTEMS, ORBITS AND LAUNCHING METHODS Introduction – Frequency allocations for satellite services – Intelsat – U.S domsats – Polar orbiting satellites – Problems – Kepler’s first law – Kepler’s second law – Kepler’s third law – Definitions of terms for earth – Orbiting satellites – Orbital elements – Apogee and perigee heights – Orbital perturbations – Effects of a non-spherical earth – Atmospheric drag – Inclined orbits – Calendars – Universal time – Julian dates – Sidereal time – The orbital plane – The geocentric – Equatorial coordinate system – Earth station referred to the IJK frame – The topcentric – Horizon co-ordinate system – The subsatellite point – Predicting satellite position. PART A 1. What is Satellite? Mention the types. An artificial body that is projected from earth to orbit either earth (or) another body of solar systems. Types: Information satellites and Communication Satellites 2. State Kepler’s first law. It states that the path followed by the satellite around the primary will be an ellipse. An ellipse has two focal points F1 and F2. The center of mass of the two body system, termed the barycenter is always centered on one of the foci. e = [square root of ( a2– b2) ] / a 3. State Kepler’s second law. It states that for equal time intervals, the satellite will sweep out equal areas in its orbital Skyupsmediaplane, focused at the barycenter. 4. State Kepler’s third law. It states that the square of the periodic time of orbit is perpendicular to the cube of the mean distance between the two bodies. JNTUH WEB www.jntuhweb.com JNTUH WEB a3= 3 / n2 Where, n = Mean motion of the satellite in rad/sec. -
DSLR PHOTOMETRY: a Citizen Science Project Using a Consumer Camera to Contribute Scientific Data
DSLR PHOTOMETRY: A citizen science project using a consumer camera to contribute scientific data by Mike Durkin Photometry is one of many areas in astronomy where amateurs can make useful contributions. Other areas include astrometry, occultation timings, and recording high quality observations of solar system objects. There are also projects for “armchair astronomers”, such as Galaxy Zoo. What is Photometry? Photometry is the measurement and study of the brightness of objects In astronomy, photometry is used to measure the brightness of stars , supernovae, asteroids , etc. I will be talking mostly about measuring variable stars , which are stars that change brightness over time. By studying the how the brightness of objects change over time, it can help determine physical properties. LIGHT CURVE shows brightness changes over time Cepheids are a type of variable stars that fluctuate in brightness. There is a well defined relationship between brightness and the Period of the brightness variation. Cepheids were used to determine the distance to the Andromeda Galaxy and proved that the universe was much larger than just the Milky Way. Light Curve for an asteroid can be used to show rotational period. Light curve for eclipsing binary The light curve for an eclipsing binary can be used to determine properties such as the diameters, luminosities, and separation of the stars. Eclipsing binary star animation courtesy of Wikimedia Commons THIS SOUNDS LIKE STUFF FOR PROFESSIONAL ASTRONOMERS, WHAT GOOD CAN AMATEURS DO? There are a lot more amateurs than professionals Estimated total number of professional astronomers is 2,080 (U.S. Dept. of Labor, Bureau of Labor Statistics) Estimated total number of amateurs is at least 100,000 based on the circulation numbers of magazines. -
Arxiv:1704.03416V1 [Astro-Ph.GA] 11 Apr 2017 2
Physics of Lyα Radiative Transfer Mark Dijkstra (Institute of Theoretical Astrophysics, University of Oslo) (Dated: April 7, 2017) Lecture notes for the 46th Saas-Fee winterschool, 13-19 March 2016, Les Diablerets, Switzerland. See http://obswww.unige.ch/Courses/saas-fee-2016/ arXiv:1704.03416v1 [astro-ph.GA] 11 Apr 2017 2 Contents 1. Preface 3 2. Introduction 3 3. The Hydrogen Atom and Introduction to Lyα Emission Mechanisms 4 3.1. Hydrogen in our Universe 4 3.2. The Hydrogen Atom: The Classical & Quantum Picture 6 3.3. Radiative Transitions in the Hydrogen Atom: Lyman, Balmer, ..., Pfund, .... Series 8 3.4. Lyα Emission Mechanisms 9 4. A Closer Look at Lyα Emission Mechanisms & Sources 10 4.1. Collisions 10 4.2. Recombination 13 5. Astrophysical Lyα Sources 14 5.1. Interstellar HII Regions 14 5.2. The Circumgalactic/Intergalactic Medium (CGM/IGM) 16 6. Step 1 Towards Understanding Lyα Radiative Transfer: Lyα Scattering Cross-section 22 6.1. Interaction of a Free Electron with Radiation: Thomson Scattering 22 6.2. Interaction of a Bound Electron with Radiation: Lorentzian Cross-section 25 6.3. Interaction of a Bound Electron with Radiation: Relation to Lyα Cross-Section 26 6.4. Voigt Profile of Lyα Cross-Section 27 7. Step 2 Towards Understanding Lyα Radiative Transfer: The Radiative Transfer Equation 29 7.1. I: Absorption Term: Lyα Cross Section 30 7.2. II: Volume Emission Term 30 7.3. III: Scattering Term 30 7.4. IV: ‘Destruction’ Term 36 7.5. Lyα Propagation through HI: Scattering as Double Diffusion Process 38 8. -
Atoms and Astronomy
Atoms and Astronomy n If O o p W H- I on-* C3 W KJ CD NASA National Aeronautics and Space Administration ATOMS IN ASTRONOMY A curriculum project of the American Astronomical Society, prepared with the cooperation of the National Aeronautics and Space Administration and the National Science Foundation : by Paul A. Blanchard f Theoretical Studies Group *" NASA Goddard Space Flight Center Greenbelt, Maryland National Aeronautics and Space Administration Washington, DC 20546 September 1976 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $1.20 Stock No. 033-000-00656-0/Catalog No. NAS 1.19:128 intenti PREFACE In the past half century astronomers have provided mankind with a new view of the universe, with glimpses of the nature of infinity and eternity that beggar the imagination. Particularly, in the past decade, NASA's orbiting spacecraft as well as ground-based astronomy have brought to man's attention heavenly bodies, sources of energy, stellar and galactic phenomena, about the nature of which the world's scientists can only surmise. Esoteric as these new discoveries may be, astronomers look to the anticipated Space Telescope to provide improved understanding of these phenomena as well as of the new secrets of the cosmos which they expect it to unveil. This instrument, which can observe objects up to 30 to 100 times fainter than those accessible to the most powerful Earth-based telescopes using similar techniques, will extend the use of various astronomical methods to much greater distances. It is not impossible that observations with this telescope will provide glimpses of some of the earliest galaxies which were formed, and there is a remoter possibility that it will tell us something about the edge of the universe. -
SYNTHETIC SPECTRA for SUPERNOVAE Time a Basis for a Quantitative Interpretation. Eight Typical Spectra, Show
264 ASTRONOMY: PA YNE-GAPOSCHKIN AND WIIIPPLE PROC. N. A. S. sorption. I am indebted to Dr. Morgan and to Dr. Keenan for discussions of the problems of the calibration of spectroscopic luminosities. While these results are of a preliminary nature, it is apparent that spec- troscopic absolute magnitudes of the supergiants can be accurately cali- brated, even if few stars are available. For a calibration of a group of ten stars within Om5 a mean distance greater than one kiloparsec is necessary; for supergiants this requirement would be fulfilled for stars fainter than the sixth magnitude. The errors of the measured radial velocities need only be less than the velocity dispersion, that is, less than 8 km/sec. 1 Stebbins, Huffer and Whitford, Ap. J., 91, 20 (1940). 2 Greenstein, Ibid., 87, 151 (1938). 1 Stebbins, Huffer and Whitford, Ibid., 90, 459 (1939). 4Pub. Dom., Alp. Obs. Victoria, 5, 289 (1936). 5 Merrill, Sanford and Burwell, Ap. J., 86, 205 (1937). 6 Pub. Washburn Obs., 15, Part 5 (1934). 7Ap. J., 89, 271 (1939). 8 Van Rhijn, Gron. Pub., 47 (1936). 9 Adams, Joy, Humason and Brayton, Ap. J., 81, 187 (1935). 10 Merrill, Ibid., 81, 351 (1935). 11 Stars of High Luminosity, Appendix A (1930). SYNTHETIC SPECTRA FOR SUPERNOVAE By CECILIA PAYNE-GAPOSCHKIN AND FRED L. WHIPPLE HARVARD COLLEGE OBSERVATORY Communicated March 14, 1940 Introduction.-The excellent series of spectra of the supernovae in I. C. 4182 and N. G. C. 1003, published by Minkowski,I present for the first time a basis for a quantitative interpretation. Eight typical spectra, show- ing the major stages of the development during the first two hundred days, are shown in figure 1; they are directly reproduced from Minkowski's microphotometer tracings, with some smoothing for plate grain. -
Balmer and Rydberg Equations for Hydrogen Spectra Revisited
1 Balmer and Rydberg Equations for Hydrogen Spectra Revisited Raji Heyrovska Institute of Biophysics, Academy of Sciences of the Czech Republic, 135 Kralovopolska, 612 65 Brno, Czech Republic. Email: [email protected] Abstract Balmer equation for the atomic spectral lines was generalized by Rydberg. Here it is shown that 1) while Bohr's theory explains the Rydberg constant in terms of the ground state energy of the hydrogen atom, quantizing the angular momentum does not explain the Rydberg equation, 2) on reformulating Rydberg's equation, the principal quantum numbers are found to correspond to integral numbers of de Broglie waves and 3) the ground state energy of hydrogen is electromagnetic like that of photons and the frequency of the emitted or absorbed light is the difference in the frequencies of the electromagnetic energy levels. Subject terms: Chemical physics, Atomic physics, Physical chemistry, Astrophysics 2 An introduction to the development of the theory of atomic spectra can be found in [1, 2]. This article is divided into several sections and starts with section 1 on Balmer's equation for the observed spectral lines of hydrogen. 1. Balmer's equation Balmer's equation [1, 2] for the observed emitted (or absorbed) wavelengths (λ) of the spectral lines of hydrogen is given by, 2 2 2 λ = h B,n1[n2 /(n2 - n 1 )] (1) 2 where n1 and n2 (> n1) are integers with n1 having a constant value, hB,n1 = n1 hB is a constant for each series and hB is a constant. For the Lyman, Balmer, Paschen, Bracket and Pfund series, n1 = 1, 2, 3, 4 and 5 respectively.