Calculating the Redshift of Galaxies
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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 . -
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. -
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. -
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. -
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. -
Spectra of Photoionized Regions 1. Introduction
Spectra of Photoionized Regions Friday, January 21, 2011 CONTENTS: 1. Introduction 2. Recombination Processes A. Overview B. Level networks C. Free-bound continuum D. Two-photon continuum E. Collisions 3. Additional Processes A. Lyman-α emission B. Helium processes C. Resonance fluorescence 4. Diagnostics A. Temperature B. Density C. Composition D. Star formation rates 1. Introduction Our next task is to consider the emitted spectrum from an H II region. This is one of the most important subjects observationally since spectroscopy provides our principal set of diagnostics on the physics occurring in the region. This material is (mostly) covered in Chapters 4 and 5 of Osterbrock & Ferland (on which most of these notes are based). The sources of emission we will consider fall into two categories: Cooling: Infrared fine structure lines Optical forbidden lines Free-free continuum Recombination: Free-bound continuum Recombination lines Two-photon continuua 1 Generally, the forbidden lines (optical or IR) come from metals, whereas the recombination features are proportional to abundance and arise mainly from H and He. Since the cooling radiation has already been discussed, we will focus on recombination and then proceed to diagnostics. 2. Recombination Processes A. OVERVIEW We first consider the case of recombination of hydrogen at very low densities where the collision rates are small, i.e. any hydrogen atom that forms can decay radiatively before any collision. Later on we will introduce collisions between particles (electrons, protons) with excited atoms. The recombination process at low density begins with a radiative recombination, H+ + e− → H0(nl) + γ , which populates an excited state of the hydrogen atom. -
The Hydrogen Atom and the Lyman Series Block: ______Answer Each Question in the Space Required
Chemistry Worksheet NAME: _____________________________ The Hydrogen Atom and the Lyman series Block: _________ Answer each question in the space required. Show all work. Pay attention to significant figures and units. 1. Hydrogen is the simplest atom in the universe, thus it is the most commonly used example for delving into the quantum world. The energy levels of hydrogen can be calculated using the 2 principle quantum number, n, in the equation En = −13.6 eV (1/n ), for n = 1, 2, 3, 4 … ∞. Recall that eV stands for the energy unit called the electron volt, which relates to joules (J) by the following conversion: 1 eV = 1.602 × 10−19 J. a. What is the value of principal quantum number, n, for the ground state of hydrogen? b. Calculate the energy (in eV and in joules) for the ground state of hydrogen. c. Calculate the energy, En, for the first four excited states of the hydrogen atom. d. Is the third excited state higher or lower in energy than the ground state? Justify your answer in one or two sentences. e. The ionization energy of hydrogen is defined as the minimum energy required to excite an electron from the ground state to a state where the electron is separated from the nucleus (the proton). From your answers above, what is the ionization energy for hydrogen? Justify your answer in one or two sentences. f. How much energy would be required to ionize an entire mole of hydrogen atoms? Copyright© 2007, Alan D. Crosby, Newton South High School, Newton, MA 02459 Chemistry Worksheet NAME: _____________________________ The Hydrogen Atom and the Lyman series Block: _________ 2. -
A Kinematic Study of the Irregular Dwarf Galaxy NGC 4861 Using HI
Astronomy & Astrophysics manuscript no. 11766.bw c ESO 2021 September 10, 2021 A kinematic study of the irregular dwarf galaxy NGC 4861 using H i and Hα observations J. van Eymeren1;2;3, M. Marcelin4, B. S. Koribalski3, R.-J. Dettmar2, D. J. Bomans2, J.-L. Gach4, and P. Balard4 1 Jodrell Bank Centre for Astrophysics, School of Physics & Astronomy, The University of Manchester, Alan Turing Building, Oxford Road, Manchester, M13 9PL, UK e-mail: [email protected] 2 Astronomisches Institut der Ruhr-Universitat¨ Bochum, Universitatsstraße¨ 150, 44780 Bochum, Germany 3 Australia Telescope National Facility, CSIRO, P.O. Box 76, Epping, NSW 1710, Australia 4 Laboratoire d’Astrophysique de Marseille, OAMP, Universite´ Aix-Marseille & CNRS, 38 rue Fred´ eric´ Joliot-Curie, 13013 Marseille, France Accepted 20 July 2009 ABSTRACT Context. Outflows powered by the injection of kinetic energy from massive stars can strongly affect the chemical evolution of galaxies, in particular of dwarf galaxies, as their lower gravitational potentials enhance the chance of a galactic wind. Aims. We therefore performed a detailed kinematic analysis of the neutral and ionised gas components in the nearby star-forming irregular dwarf galaxy NGC 4861. Similar to a recently published study of NGC 2366, we want to make predictions about the fate of the gas and to discuss some general issues about this galaxy. Methods. Fabry-Perot interferometric data centred on the Hα line were obtained with the 1.93m telescope at the Observatoire de Haute-Provence. They were complemented by H i synthesis data from the VLA. We performed a Gaussian decomposition of both the Hα and the H i emission lines in order to search for multiple components indicating outflowing gas. -
Supernova Remnant N103B, Radio Pulsar B1951+32, and the Rabbit
On Understanding the Lives of Dead Stars: Supernova Remnant N103B, Radio Pulsar B1951+32, and the Rabbit by Joshua Marc Migliazzo Bachelor of Science, Physics (2001) University of Texas at Austin Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Master of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2003 c Joshua Marc Migliazzo, MMIII. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. Author.............................................................. Department of Physics January 17, 2003 Certifiedby.......................................................... Claude R. Canizares Associate Provost and Bruno Rossi Professor of Physics Thesis Supervisor Accepted by . ..................................................... Thomas J. Greytak Chairman, Department Committee on Graduate Students 2 On Understanding the Lives of Dead Stars: Supernova Remnant N103B, Radio Pulsar B1951+32, and the Rabbit by Joshua Marc Migliazzo Submitted to the Department of Physics on January 17, 2003, in partial fulfillment of the requirements for the degree of Master of Science in Physics Abstract Using the Chandra High Energy Transmission Grating Spectrometer, we observed the young Supernova Remnant N103B in the Large Magellanic Cloud as part of the Guaranteed Time Observation program. N103B has a small overall extent and shows substructure on arcsecond spatial scales. The spectrum, based on 116 ks of data, reveals unambiguous Mg, Ne, and O emission lines. Due to the elemental abundances, we are able to tentatively reject suggestions that N103B arose from a Type Ia supernova, in favor of the massive progenitor, core-collapse hypothesis indicated by earlier radio and optical studies, and by some recent X-ray results. -
Celestial Radio Sources Whitham D
Important Celestial Radio Sources Whitham D. Reeve Introduction The list of celestial radio sources presented below was obtained from the National Radio Astronomy Observatory (NRAO) library. Each column heading is defined below. As presented here, the list is sorted in order of flux density as received on Earth. As an aid in visualizing the location of the more powerful radio sources in the sky with respect to the Milky Way galaxy, an annotated radio map also is provided along with explanations of its important features. Listing – Definition of column headings The information below is necessarily brief. Additional information may be found by using an online encyclopedia (for example, http://en.wikipedia.org/wiki/Main_Page ) or visiting other online sources such as the National Radio Astronomy Observatory website ( http://www.nrao.edu/ ). Object Name: Each object is named according its original catalog listing (for celestial object naming conventions, see Tom Crowley’s article “Introduction to Astronomical Catalogs” in the October- November 2010 issue of Radio Astronomy ). Most of the objects in the list originally were listed in the 3rd Cambridge catalog (3C) but some are in NRAO’s catalog (NRAO). Right Ascension and Declination: The right ascension and declination are used together to define the location of an object in the sky according to the equatorial coordinate system . Right ascension is given in hour minute second format and abbreviated RA . RA is the angle measured in hours, minutes and seconds from the Vernal equinox (intersection of celestial equator and ecliptic). The declination, abbreviated Dec , is the number of degrees, minutes and seconds above (0° to +90°) or below (0° to – 90°) the celestial equator. -
Atomic Structure
1 Atomic Structure 1 2 Atomic structure 1-1 Source 1-1 The experimental arrangement for Ruther- ford's measurement of the scattering of α particles by very thin gold foils. The source of the α particles was radioactive radium, a rays encased in a lead block that protects the surroundings from radiation and confines the α particles to a beam. The gold foil used was about 6 × 10-5 cm thick. Most of the α particles passed through the gold leaf with little or no deflection, a. A few were deflected at wide angles, b, and occasionally a particle rebounded from the foil, c, and was Gold detected by a screen or counter placed on leaf Screen the same side of the foil as the source. The concept that molecules consist of atoms bonded together in definite patterns was well established by 1860. shortly thereafter, the recognition that the bonding properties of the elements are periodic led to widespread speculation concerning the internal structure of atoms themselves. The first real break- through in the formulation of atomic structural models followed the discovery, about 1900, that atoms contain electrically charged particles—negative electrons and positive protons. From charge-to-mass ratio measurements J. J. Thomson realized that most of the mass of the atom could be accounted for by the positive (proton) portion. He proposed a jellylike atom with the small, negative electrons imbedded in the relatively large proton mass. But in 1906-1909, a series of experiments directed by Ernest Rutherford, a New Zealand physicist working in Manchester, England, provided an entirely different picture of the atom. -
Postępy Astronomii Nr 3/1969
POSTĘPY ASTRONOMII CZASOPISMO POŚWIĘCONE UPOWSZECHNIANIU WIEDZY ASTRONOMICZNEJ PTA TOM XVII — ZESZYT 3 1969 WARSZAWA • LIPIEC — WRZESIEŃ 1969 POLSKIE TOWARZYSTWO ASTRONOMICZNE POSTĘPY ASTRONOMII KWARTALNIK TOM XVII — ZESZYT 3 1969 WARSZAWA • LIPIEC — WRZESIEŃ 1969 KOLEGIUM REDAKCYJNE Redaktor naczelny: Stefan Piotrowski, Warszawa Członkowie: Józef Witkowski, Poznań Włodzimierz Zonn, Warszawa Sekretarz Redakcji: Jerzy Stodółkiewicz, Warszawa Adres Redakcji: Obserwatorium Astronomiczne UW Warszawa, Al. Ujazdowskie 4 W Y D A W A N E Z ZASIŁKU POLSKIEJ AKADEMII NAUK Printed in Poland Państwowe Wydawnictwo Naukowe Oddział w Łodzi 1969 W ydanie 1. N akład 456 4- 124 egi. Ark. w yd. 9.00 Ark. druk. 8.50 Papier druk sal. kl. Ul. 80 g. 70 x 100. O ddano d o d r u k u 19. VIII. 1909 Druk ukończono w sierpniu 1 9 6 9 r. Zam. 223 B-8 C ena i \ 10,— Zakład Graficzny PWN Łódź, ul. Gdańska 162 PULSARY STANISŁAW GRZĘDZIELSKI nyjibCAPW C. T)KeHaejibCKM CoflepjKaHMe CTaTba coflep»MT o03op flaiiHbix o Ha6jiK)fleHMflx u TeopemuecKMe hh- TepnpeTauMM nyjibcapoB, onyBjiMKOBaHHbisi b TeueHMM nepBoro ro^a nocjie OTKpblTMH 9TMX OÓbeKTOB. PULSARS Summary The article reviews the observational data on pulsars and their theoretical interpretation as published during the first year after the announcement of the discovery. 1. WSTĘP W lutym bieżącego roku minęło dwanaście miesięcy od opublikowania pierwszej wzmianki o odkryciu pulsara CP 1919 (He wish, Bell, P i 1 k i n g- ton, Scott, Collins 1968). Artykuł ukazał się w czasopiśmie „Naturę” , które stało się głównym forum dyskusji o tym fenomenie. W ciągu pierwszych sześciu miesięcy ukazało się w „Naturę” * 51 prac, zarówno teoretycznych jak i obserwacyjnych, w których doniesiono o odkryciu 9 pulsarów.