DOCSLIB.ORG

Stellar Atmospheres by R

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Stellar Atmospheres by R Stellar Atmosphere Volume 푉= (Area) (length) Collision = cross section 휎 ⋅ ℓ = 휎 퓋푡 Relative speed 퓋 Number of particles 푁 Number density 푛 = 푁Τ푉 # of collisions = # of (other) particles in the volume = 푁 = 푛 휎 퓋 t # of collisions per unit time = 푁 Τ푡 = 푛 휎 퓋 Time between 2 consecutive collisions (푁=1) (mean-free time), 푡col = 1 Τ (푛 휎 퓋) Distance between 2 consecutive collisions (푁=1) (mean-free path), ℓcol = 퓋푡col = 1 Τ (푛 휎 ) In general “encounters” between particles, or between a particle and a photon. The “cross section” is the key. 2 Opacity −1 ′ 2 −1 −3 휅 cm = 휅 휌 cm g ⋅ g cm = ෍ 푛푖 휎푖 푖 Recall that ׬ 휅 푑푠 is the optical depth If 휅휈 is frequency independent 휅 gray atmosphere Usually an average opacity is used ׬ 휅휈 퐵휈 푑휈 Planck opacity average of frequency 휅P = ׬ 퐵 푑휈 dependent opacity weighted by Planck function 휈 Svein Rosseland −1 Rosseland opacity weighted ׬ 휅휈 푢휈 푑휈 by 푇 derivative, averaging 1Τ휅휈 1Τ휅R = ׬ 푢휈 푑휈 푢 휈, 푇 = 휕퐵휈 푇 Τ휕푇 3 푎+푏+푐 Arithmetic average, , e.g., 1 + 4 + 4 Τ3 = 3 3 Geometric average, 3 푎 ∙ 푏 ∙ 푐, e.g., 3 1 × 4 × 4 ≈ 2.52 1Τ푎 + 1Τ푏 + 1Τ푐 −1 Harmonic average, one of the Pythagorean means, , 3 1Τ1 + 1Τ4 + 1Τ4 −1 e.g., = 2 3 4 Bound-bound absorption Excitation of an electron of an atom to a higher energy state by the absorption of a photon. The excited atom then will be de-excited spontaneously, emitting a photon, or by collision with another particle. Bound-free absorption Photoionization of an electron from an atom (ion) by the absorption of a photon. The inverse process is radiative recombination. 5 • Free-free absorption Transition of a free electron to a higher energy state, via interaction of a nucleus or ion, by the absorption of a photon. The inverse process is bremsstrahlung. • Electron scattering Scattering of a photon by a free electron, also known as Thomson (common in stellar interior) or Compton (if relativistic) scattering. • H− absorption Important when < 104 K, i.e., dominant in the outer layer of low-mass stars (such as the Sun) Hydrogen anion (or protide) Opposite is H cation (or hydron or just proton) 6 • Bound-bound, bound-free, and free-free opacities are collectively called Kramers opacity, named after the Dutch physicist H. A. Kramers (1894-1952). • All have similar dependence 휅 ∝ 휌 푇−3.5. • Kramers opacity is the main source of opacity in gases of 4 6 temperature 10 ~10 K, i.e., in the interior of stars up to ~ 1 M⊙. • In a star much more massive, the electron scattering process dominates the opacity, and the Kramers opacity is important only in the surface layer. Kramers opacity 휅 ≈ 4 × 1025 1 + 푋 푍 + 0.001 휌 푇−3.5 [cm2g−1] 퐾푟 7 X=0.70 Z=0.02 Rosseland mean opacity Data from Iglesias & Rogers (1996) 8 For Thomson scattering, 2 8휋 푟푒 2 −1 휅휈 = = 0.20 1 + 푋 [cm g ] 3 휇푒푚e is frequency independent, so is the Rosseland mean. 2 −1 휅푒푠 = 0.20 1 + 푋 [cm g ] Here 푟푒 is the electron classical (charge; Lorentz) radius, 푋 is the H mass fraction, and 휇푒 = 2Τ(1 + 푋) 푒2 푟 = = 2.82 × 10−15 [m]; experimentally 푟 < 10−18 [m] 푒 푚푐2 푒 −25 2 Classical electron cross section, 휎T = 6.65 × 10 [cm ] = 0.665 barns 9 10 11 Bowers & Deeming12 16 17 Absorption and Emission by Gas Hydrogen as an example … 18 QM versus classical physics Action [energy time] or (momentum distance] is quantized in unit of ℏ Heisenberg’s uncertainty principle, 휎푥 휎푝 ≥ ℏΤ2 Pauli exclusion principle Harwit 19 Lowest state of H, 푝2 푟2 ≈ ∆푝2 ∆푟2 ≈ ℏ2 Virial theorem, 2ℰ퐾 + ℰ푝 = 0 Lowest (ground state) energy 1 1 푍푒2 1 푝2 1 ℏ2 ℰ = − 퐸 = − = − ≈ − 1 2 푝 2 푟 2 휇 2휇 푟2 휇: reduced mass 푍푒2 ℏ2 ℏ2 = ⇒ 푟 = (퐁퐨퐡퐫’퐬 퐫퐚퐝퐢퐮퐬) 푟 휇푟2 휇푍푒2 1 푍푒2휇푍푒2 1 푍2휇푒4 ℰ = − = − 1 2 ℏ2 2 ℏ2 −9 For H, 푍 = 1, ℰ1 = −13.6 eV, 푟 ≈ 5.3 × 10 [cm] = 0.53 Å 20 ℎ ℎ de Broglie matter wavelength, 휆 = = 푝 푚푣 푍푒2 Virial theorem (classical uniform circular motion), 푚푣2 = 푟 Standing waves, 2휋 푟 = 푛휆 ℏ2 For the ground state, 푛 = 1, 푟 = 푚푍푒2 21 Virial theorem relation between (the time average of) the total kinetic energy and the total potential energy of a system in equilibrium Equation of motion (in the Lagragian form) 푑2푟Ԧ 휚 = 푓Ԧ − 훻푃 …… (1) 푑푡2 푑2푟Ԧ In hydrostatic equilibrium, = 0, so 푓Ԧ = 훻P, and assuming 푑푡2 spherical symmetry and the force being self-gravitation 푑푃 퐺 푚 푟 휚 푟 = − (Hydrostatic equilibrium) 푑푟 푟2 푟 2 (and 푚 푟 = ׬0 4휋푟 휚 푑푟 (mass continuity/distribution 22 푑2푟Ԧ 휚 = 푓Ԧ − 훻푃 푑푡2 Take the vector dot of 푟Ԧ of (1), divide by 휚, define 푭 = 풇Τ휚 (force per unit mass, and then integrate, using the boldface for vectors 풅ퟐ풓 푑푚 (׬ 푑푚 풓 ⋅ = ׬ 풓 ⋅ 푭 푑푚 − ׬ 풓 ⋅ 훻푃 …… (2 풅풕ퟐ 휚 푑 푑풓 푑2풓 푑풓 2 1 푑2 Given 풓 ⋅ = 풓 ⋅ + = 풓2 푑푡 푑푡 푑푡2 푑푡 2 푑푡2 풅ퟐ풓 1 푑2 푑풓 2 So, ׬ 푑푚 풓 ⋅ = ׬ 풓2 푑푚 − ׬ 푑푚 풅풕ퟐ 2 푑푡2 푑푡 1 푑2퐼 퐼: moment of inertia = − 2ℰ 2 푑푡2 kin ℰkin: kinetic energy 23 Because 푑푚 = 휚 푑푉, the last term in (2), 푑푚 ׬ 풓 ⋅ 훻푃 = ׬ 풓 ⋅ 훻푃 푑푉 = ׬ 훻 ∙ 풓 ∙ 푷 푑푉 − 3 ׬ 푃 푑푉 휚 Note 풓 ∙ 푷 ∙ 푑푺 − 3 ׬ 푃 푑푉 = න 훻 풓푃 = 훻 ⋅ 풓 푃 + 풓 ⋅ 훻푃 훻 ⋅ 풓 = 3 Assuming spherical symmetry, Gauss’s theorem volume 3 integral of the divergence to 4휋푅 푃푠 − 3 ׬ 푃 푑푉 surface integral = 24 Putting together, we have 1 푑2퐼 = 2ℰ + 3 න 푃 푑푉 + න 풓 ⋅ 푭 푑푚 − ර 푃풓 ⋅ 푑푺 2 푑푡2 kin where 풓 ⋅ 푭 (work) is virial; or 1 푑2퐼 = 2 ℰ + 3 න 푃 푑푉 + ℰ − 4휋푅3푃 2 푑푡2 kinetic potential external For stars, under hydrostatic equilibrium and if 푃ext = 0, 2 ℰk + ℰp = 0 25 1 푑2퐼 LHS = 0 stable = 2 ℰ + ℰ 2 푑푡2 k p LHS < 0 collapsing LHS > 0 expanding 퓔퐤: a variety of kinetic energies 퓔퐩: a variety of potential energies Kinetic energy of molecules Gravitation Bulk motion of clouds Magnetic field Rotation Electrical field … … Note ℰtotal = ℰ푘 + ℰ푝, governs if the system is bound (ℰtotal < 0) For stars, mostly ℰ푝 = Ω (gravitational energy; negative) 26 For higher energy states, 푝푛 푟푛 = 푛ℏ 2 2 2 2 4 푝푛 푛 ℏ 푍 휇 푒 ℰ푛 = − ≈ − 2 = − 2 2 2휇 2휇푟푛 2푛 ℏ For the 푛-th radial state, the phase space volume is 2 2 4휋푝푛 Δ푝푛 4휋푟푛 Δ푟푛 , # of possible states with principle quantum number 푛 Total phase space volume 16휋2푛2ℏ3 = = ∝ 푛2 volume of unit cell ℏ3 The electron spin is either parallel or anti-parallel to that of the nucleus, so the n-th state has 2푛2 different substates, all having the same energy. 27 28 푍2휇 푒4 Note that ℰ ∝ 휇 ℰ = − 푛 푛 2푛2ℏ2 푚푒푚푝 푚푒 For normal H, 휇퐻 = = ≈ 푚푒 1 − 푚푒Τ푚푝 푚푒+푚푝 1+푚푒Τ푚푝 푚푒푚퐷 2푚푒푚푝 For deuteron, 휇퐷 = = ≈ 푚푒 1 − 푚푒Τ2푚푝 > 휇퐻 푚푒+푚퐷 푚푒+2푚푝 So the D lines are 1.5 Å shorter in wavelengths 2 Note also that ℰ푛 ∝ 푍 , so for He II (푍 = 2, with 1 e−) , 푍2 is 4 times larger, and with a different 휇. https://archive.stsci.edu/fuse/scisumm/sci_d2h.html29 푛 Grotrian diagram Lang Gray & Corbally30 31 • For the ground state, the orbital angular momentum is ℓ = 0. The total spin angular momentum is 퐹 = 0 (spin opposite) or 퐹 = 1 (spin parallel) Hyperfine splitting • For 푛 = 2, ℓ =1, and with spin, a total angular momentum of ℓ ℓ + 1 ℏ2 =2ℏ2 3 substates, ℏ, 0, −ℏ, 푚 = 1, 0, −1 (magnetic quantum number) Fine structure, ∆ℰ very small, ~10−5 Ev But if there is an external B field Zeeman splitting 32 Free-free 퐇+ Free-free or free-bound to any level Cascading down emission of photons of different energies − 퐇 Stars: ample supplies of free 푒− from Na, 퐻 + 푒− ⟶ 퐻− + ℎ휈 Ca, Mg, … with low-ionization potentials He atom similar, with the second 푒− weakly bound, shielded by the first 푒− − ℰbinding H = 0.75 eV, only 1 bound state; transitions continuum Absorption by H− immediately followed by reemission − The sunlight we see mostly is due to continuum transitions by 퐻 33 퐇ퟐ • Main constituent of cold clouds, not important in stars, except in the coolest substellar objects (brown dwarfs or planetary- mass objects) • Lacking a permanent electric dipole moment, so very difficult to detect. A rotationally excited molecule would radiate through a relatively slow electric quadrupole transition. • Only detected in a hot medium, where stellar radiation or stellar wind excites vibrational and electronic states which then decay relatively quickly. Zero electric dipole moment 34 Stahler & Palla 35 CO molecules • Simple and abundant, in gaseous or solid form • Strong ℰbinding =11.1 eV self-shielding against UV field • with a permanent electric dipole moment; radiating strongly at radio frequencies. • 12C16O easiest to detect; isotopes 13C16O, 12C18O, 12C17O, 13C18O also useful • Low critical density for excitation CO used to study large- scale distribution of molecules, as a tracer of H2 in dense clouds • 12C16O almost always optically thick; same line from other rare isotopes usually not estimate of column density (total mass) 6 of molecular gas 푁퐻= 10 푁13 퐶푂 36 2.6 mm = 115 GHz Only 5 K above the ground level … can be excited by collisions with ambient molecules or CMB photons Stahler & Palla 37 CO bandheads in the Becklin-Neugebauer (BN) object, an IR-emitting, embedded, massive (~7 M⊙) protostar Gaballe & Persson (1987) Stahler & Palla38 Stahler & Palla 39 Molecules in stars Stellar matter largely gas or plasma.
Load more

Recommended publications
  • THE EVOLUTION of SOLAR FLUX from 0.1 Nm to 160Μm: QUANTITATIVE ESTIMATES for PLANETARY STUDIES
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by St Andrews Research Repository The Astrophysical Journal, 757:95 (12pp), 2012 September 20 doi:10.1088/0004-637X/757/1/95 C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A. THE EVOLUTION OF SOLAR FLUX FROM 0.1 nm TO 160 μm: QUANTITATIVE ESTIMATES FOR PLANETARY STUDIES Mark W. Claire1,2,3, John Sheets2,4, Martin Cohen5, Ignasi Ribas6, Victoria S. Meadows2, and David C. Catling7 1 School of Environmental Sciences, University of East Anglia, Norwich, UK NR4 7TJ; [email protected] 2 Virtual Planetary Laboratory and Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA 3 Blue Marble Space Institute of Science, P.O. Box 85561, Seattle, WA 98145-1561, USA 4 Department of Physics & Astronomy, University of Wyoming, Box 204C, Physical Sciences, Laramie, WY 82070, USA 5 Radio Astronomy Laboratory, University of California, Berkeley, CA 94720-3411, USA 6 Institut de Ciencies` de l’Espai (CSIC-IEEC), Facultat de Ciencies,` Torre C5 parell, 2a pl, Campus UAB, E-08193 Bellaterra, Spain 7 Virtual Planetary Laboratory and Department of Earth and Space Sciences, University of Washington, Box 351310, Seattle, WA 98195, USA Received 2011 December 14; accepted 2012 August 1; published 2012 September 6 ABSTRACT Understanding changes in the solar flux over geologic time is vital for understanding the evolution of planetary atmospheres because it affects atmospheric escape and chemistry, as well as climate. We describe a numerical parameterization for wavelength-dependent changes to the non-attenuated solar flux appropriate for most times and places in the solar system.
    [Show full text]
  • CNSC Research Report 2016-17
    The Science of Safety: CNSC Research Report 2016–17 © Canadian Nuclear Safety Commission (CNSC) 2018 Cat. No. CC171-24E-PDF ISSN 2369-4351 Extracts from this document may be reproduced for individual use without permission provided the source is fully acknowledged. However, reproduction in whole or in part for purposes of resale or redistribution requires prior written permission from the Canadian Nuclear Safety Commission. Également publié en français sous le titre : La science de la sûreté : Rapport de recherche de la CCSN 2016-2017 Document availability This document can be viewed on the CNSC website. To request a copy of the document in English or French, please contact: Canadian Nuclear Safety Commission 280 Slater Street P.O. Box 1046, Station B Ottawa, Ontario K1P 5S9 CANADA Tel.: 613-995-5894 or 1-800-668-5284 (in Canada only) Facsimile: 613-995-5086 Email: [email protected] Website: nuclearsafety.gc.ca Facebook: facebook.com/CanadianNuclearSafetyCommission YouTube: youtube.com/cnscccsn Twitter: @CNSC_CCSN Publishing History June 2018 Edition 1.0 Table of contents Message from the President .......................................................................................................................... 1 Introduction ................................................................................................................................................... 2 Ensuring the safety of nuclear power plants ................................................................................................. 6 Protecting
    [Show full text]
  • Source of Atomic Hydrogen for Ion Trap Experiments: Review and Basic Properties
    WDS'15 Proceedings of Contributed Papers — Physics, 155–161, 2015. ISBN 978-80-7378-311-2 © MATFYZPRESS Source of Atomic Hydrogen for Ion Trap Experiments: Review and Basic Properties A. Kovalenko, Š Roučka, S. Rednyk, T. D. Tran, D. Mulin, R. Plašil, J. Glosík Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. The H-atom source was used to produce atomic hydrogen for study of ion-molecule reactions relevant to astrochemistry at low temperatures. H atoms were cooled and formed into an effusive beam, passing through a 22-pole ion trap. Here we present the basic operating principles of the H-atom source and give a review of this apparatus with some calculations of vacuum conditions and parameters of the produced H-atom beam. Introduction Hydrogen is the most abundant element in the Universe [Field et al., 1966]. It is the main component of stars, giant planets and interstellar clouds. Reactions with atomic or molecular hydrogen are important for understanding the processes which occur in the interstellar medium and during the formation of the new stars. There are three isotopes of hydrogen: protium, deuterium and tritium. The reactions of ions with H atoms have to be studied for better understanding of formation and destruction of more complex ions and molecules observed in interstellar medium. There are regions in space called H I and H II regions where hydrogen is mostly neutral in H I regions, rather than ionized or molecular in the H II regions. The atomic hydrogen plays fundamental role in many astrophysical contexts especially in formation H2 molecules [Habart et al., 2005; Sternberg et al., 2014].
    [Show full text]
  • X-Ray Sun SDO 4500 Angstroms: Photosphere
    ASTR 8030/3600 Stellar Astrophysics X-ray Sun SDO 4500 Angstroms: photosphere T~5000K SDO 1600 Angstroms: upper photosphere T~5x104K SDO 304 Angstroms: chromosphere T~105K SDO 171 Angstroms: quiet corona T~6x105K SDO 211 Angstroms: active corona T~2x106K SDO 94 Angstroms: flaring regions T~6x106K SDO: dark plasma (3/27/2012) SDO: solar flare (4/16/2012) SDO: coronal mass ejection (7/2/2012) Aims of the course • Introduce the equations needed to model the internal structure of stars. • Overview of how basic stellar properties are observationally measured. • Study the microphysics relevant for stars: the equation of state, the opacity, nuclear reactions. • Examine the properties of simple models for stars and consider how real models are computed. • Survey (mostly qualitatively) how stars evolve, and the endpoints of stellar evolution. Stars are relatively simple physical systems Sound speed in the sun Problem of Stellar Structure We want to determine the structure (density, temperature, energy output, pressure as a function of radius) of an isolated mass M of gas with a given composition (e.g., H, He, etc.) Known: r Unknown: Mass Density + Temperature Composition Energy Pressure Simplifying assumptions 1. No rotation à spherical symmetry ✔ For sun: rotation period at surface ~ 1 month orbital period at surface ~ few hours 2. No magnetic fields ✔ For sun: magnetic field ~ 5G, ~ 1KG in sunspots equipartition field ~ 100 MG Some neutron stars have a large fraction of their energy in B fields 3. Static ✔ For sun: convection, but no large scale variability Not valid for forming stars, pulsating stars and dying stars. 4.
    [Show full text]
  • Stellar Magnetic Activity – Star-Planet Interactions
    EPJ Web of Conferences 101, 005 02 (2015) DOI: 10.1051/epjconf/2015101005 02 C Owned by the authors, published by EDP Sciences, 2015 Stellar magnetic activity – Star-Planet Interactions Poppenhaeger, K.1,2,a 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambrigde, MA 02138, USA 2 NASA Sagan Fellow Abstract. Stellar magnetic activity is an important factor in the formation and evolution of exoplanets. Magnetic phenomena like stellar flares, coronal mass ejections, and high- energy emission affect the exoplanetary atmosphere and its mass loss over time. One major question is whether the magnetic evolution of exoplanet host stars is the same as for stars without planets; tidal and magnetic interactions of a star and its close-in planets may play a role in this. Stellar magnetic activity also shapes our ability to detect exoplanets with different methods in the first place, and therefore we need to understand it properly to derive an accurate estimate of the existing exoplanet population. I will review recent theoretical and observational results, as well as outline some avenues for future progress. 1 Introduction Stellar magnetic activity is an ubiquitous phenomenon in cool stars. These stars operate a magnetic dynamo that is fueled by stellar rotation and produces highly structured magnetic fields; in the case of stars with a radiative core and a convective outer envelope (spectral type mid-F to early-M), this is an αΩ dynamo, while fully convective stars (mid-M and later) operate a different kind of dynamo, possibly a turbulent or α2 dynamo. These magnetic fields manifest themselves observationally in a variety of phenomena.
    [Show full text]
  • Crystal Chemistry of Perovskite-Type Hydride Namgh3: Implications for Hydrogen Storage
    Chem. Mater. 2008, 20, 2335–2342 2335 Crystal Chemistry of Perovskite-Type Hydride NaMgH3: Implications for Hydrogen Storage Hui Wu,*,†,‡ Wei Zhou,†,‡ Terrence J. Udovic,† John J. Rush,†,‡ and Taner Yildirim†,§ NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau DriVe, MS 6102, Gaithersburg, Maryland 20899-6102, Department of Materials Science and Engineering, UniVersity of Maryland, College Park, Maryland 20742-2115, and Department of Materials Science and Engineering, UniVersity of PennsylVania, 3231 Walnut Street, Philadelphia, PennsylVania 19104-6272 ReceiVed NoVember 26, 2007. ReVised Manuscript ReceiVed January 11, 2008 The crystal structure, lattice dynamics, and local metal-hydrogen bonding of the perovskite hydride NaMgH3 were investigated using combined neutron powder diffraction, neutron vibrational spectroscopy, and first-principles calculations. NaMgH3 crystallizes in the orthorhombic GdFeO3-type perovskite structure (Pnma) with a-b+a- octahedral tilting in the temperature range of 4 to 370 K. In contrast with previous structure studies, the refined Mg-H lengths and H-Mg-H angles indicate that the MgH6 octahedra maintain a near ideal configuration, which is corroborated by bond valence methods and our DFT calculations, and is consistent with perovskite oxides with similar tolerance factor values. The temperature dependences of the lattice distortion, octahedral tilting angle, and atomic displacement of H are also consistent with the recently observed high H mobility at elevated temperature. The stability and dynamics of NaMgH3 are discussed and rationalized in terms of the details of our observed perovskite structure. Further experiments reveal that its perovskite crystal structure and associated rapid hydrogen motion can be used to improve the slow hydrogenation kinetics of some strongly bound light-metal-hydride systems such as MgH2 and possibly to design new alloy hydrides with desirable hydrogen-storage properties.
    [Show full text]
  • Stars IV Stellar Evolution Attendance Quiz
    Stars IV Stellar Evolution Attendance Quiz Are you here today? Here! (a) yes (b) no (c) my views are evolving on the subject Today’s Topics Stellar Evolution • An alien visits Earth for a day • A star’s mass controls its fate • Low-mass stellar evolution (M < 2 M) • Intermediate and high-mass stellar evolution (2 M < M < 8 M; M > 8 M) • Novae, Type I Supernovae, Type II Supernovae An Alien Visits for a Day • Suppose an alien visited the Earth for a day • What would it make of humans? • It might think that there were 4 separate species • A small creature that makes a lot of noise and leaks liquids • A somewhat larger, very energetic creature • A large, slow-witted creature • A smaller, wrinkled creature • Or, it might decide that there is one species and that these different creatures form an evolutionary sequence (baby, child, adult, old person) Stellar Evolution • Astronomers study stars in much the same way • Stars come in many varieties, and change over times much longer than a human lifetime (with some spectacular exceptions!) • How do we know they evolve? • We study stellar properties, and use our knowledge of physics to construct models and draw conclusions about stars that lead to an evolutionary sequence • As with stellar structure, the mass of a star determines its evolution and eventual fate A Star’s Mass Determines its Fate • How does mass control a star’s evolution and fate? • A main sequence star with higher mass has • Higher central pressure • Higher fusion rate • Higher luminosity • Shorter main sequence lifetime • Larger
    [Show full text]
  • ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (A) Write out the Spectral Classes from Hottest to Coolest Stars. Broadly
    ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (a) Write out the spectral classes from hottest to coolest stars. Broadly speaking, what are the primary spectral features that define each class? (b) What four macroscopic properties in a stellar atmosphere predominantly govern the relative strengths of features? (c) Briefly provide a qualitative description of the physical interdependence of these quantities (hint, don’t forget about free electrons from ionized atoms). 08.1.3 Luminosity Classes: (a) For an A star, write the spectral+luminosity class for supergiant, bright giant, giant, subgiant, and main sequence star. From the HR diagram, obtain approximate luminosities for each of these A stars. (b) Compute the radius and surface gravity, log g, of each luminosity class assuming M = 3M⊙. (c) Qualitative describe how the Balmer hydrogen lines change in strength and shape with luminosity class in these A stars as a function of surface gravity. 10.1.2 Spectral Classes and Luminosity Classes: (a,b,c,d) (a) What is the single most important physical macroscopic parameter that defines the Spectral Class of a star? Write out the common Spectral Classes of stars in order of increasing value of this parameter. For one of your Spectral Classes, include the subclass (0-9). (b) Broadly speaking, what are the primary spectral features that define each Spectral Class (you are encouraged to make a small table). How/Why (physically) do each of these depend (change with) the primary macroscopic physical parameter? (c) For an A type star, write the Spectral + Luminosity Class notation for supergiant, bright giant, giant, subgiant, main sequence star, and White Dwarf.
    [Show full text]
  • Stellar Structure and Evolution
    Lecture Notes on Stellar Structure and Evolution Jørgen Christensen-Dalsgaard Institut for Fysik og Astronomi, Aarhus Universitet Sixth Edition Fourth Printing March 2008 ii Preface The present notes grew out of an introductory course in stellar evolution which I have given for several years to third-year undergraduate students in physics at the University of Aarhus. The goal of the course and the notes is to show how many aspects of stellar evolution can be understood relatively simply in terms of basic physics. Apart from the intrinsic interest of the topic, the value of such a course is that it provides an illustration (within the syllabus in Aarhus, almost the first illustration) of the application of physics to “the real world” outside the laboratory. I am grateful to the students who have followed the course over the years, and to my colleague J. Madsen who has taken part in giving it, for their comments and advice; indeed, their insistent urging that I replace by a more coherent set of notes the textbook, supplemented by extensive commentary and additional notes, which was originally used in the course, is directly responsible for the existence of these notes. Additional input was provided by the students who suffered through the first edition of the notes in the Autumn of 1990. I hope that this will be a continuing process; further comments, corrections and suggestions for improvements are most welcome. I thank N. Grevesse for providing the data in Figure 14.1, and P. E. Nissen for helpful suggestions for other figures, as well as for reading and commenting on an early version of the manuscript.
    [Show full text]
  • Highly Conductive Antiperovskites with Soft Anion Lattices 12 January 2021, by I
    Highly conductive antiperovskites with soft anion lattices 12 January 2021, by I. Mindy Takamiya, Mari Toyama 'cation." They also have numerous intriguing properties, including superconductivity and, in contrast to most materials, contraction upon heating. Lithium- and sodium-rich antiperovskites, such as Li3OCl and Na3OCl, have been attracting much attention due to their high ionic conductivity and alkali metal concentration, making them promising candidates to replace liquid electrolytes used in lithium ion batteries. "But achieving a comparable lithium ion conductivity in solid materials has been challenging," explains iCeMS solid-state chemist Hiroshi Kageyama, who led the study. Soft anions, like sulfur ions (S2-), provide an ideal conduction path for sodium (Na+) and lithium (Li+) ions, Kageyama and his team synthesized a new family with the hydride ions (H-) helping to stabilize the of lithium- and sodium-rich antiperovskites that compound's structure. Credit: Mindy Takamiya/Kyoto begins to overcome this issue. Instead of 'hard' University iCeMS oxygen and halogen anions, their antiperovskites contain a hydrogen anion, called a hydride, and 'soft' chalcogen anions like sulfur. A new structural arrangement of atoms shows The scientists conducted a wide range of promise for developing safer batteries made with theoretical and experimental investigations on solid materials. Scientists at Kyoto University's these antiperovskites, and found that the soft anion Institute for Integrated Cell-Material Sciences lattice provides an ideal conduction path for lithium (iCeMS) designed a new type of 'antiperovskite' and sodium ions, which can be further enhanced by that could help efforts to replace the flammable chemical substitutions. organic electrolytes currently used in lithium ion batteries.
    [Show full text]
  • Chapter 16 the Sun and Stars
    Chapter 16 The Sun and Stars Stargazing is an awe-inspiring way to enjoy the night sky, but humans can learn only so much about stars from our position on Earth. The Hubble Space Telescope is a school-bus-size telescope that orbits Earth every 97 minutes at an altitude of 353 miles and a speed of about 17,500 miles per hour. The Hubble Space Telescope (HST) transmits images and data from space to computers on Earth. In fact, HST sends enough data back to Earth each week to fill 3,600 feet of books on a shelf. Scientists store the data on special disks. In January 2006, HST captured images of the Orion Nebula, a huge area where stars are being formed. HST’s detailed images revealed over 3,000 stars that were never seen before. Information from the Hubble will help scientists understand more about how stars form. In this chapter, you will learn all about the star of our solar system, the sun, and about the characteristics of other stars. 1. Why do stars shine? 2. What kinds of stars are there? 3. How are stars formed, and do any other stars have planets? 16.1 The Sun and the Stars What are stars? Where did they come from? How long do they last? During most of the star - an enormous hot ball of gas day, we see only one star, the sun, which is 150 million kilometers away. On a clear held together by gravity which night, about 6,000 stars can be seen without a telescope.
    [Show full text]
  • STELLAR SPECTRA A. Basic Line Formation
    STELLAR SPECTRA A. Basic Line Formation R.J. Rutten Sterrekundig Instituut Utrecht February 6, 2007 Copyright c 1999 Robert J. Rutten, Sterrekundig Instuut Utrecht, The Netherlands. Copying permitted exclusively for non-commercial educational purposes. Contents Introduction 1 1 Spectral classification (“Annie Cannon”) 3 1.1 Stellar spectra morphology . 3 1.2 Data acquisition and spectral classification . 3 1.3 Introduction to IDL . 4 1.4 Introduction to LaTeX . 4 2 Saha-Boltzmann calibration of the Harvard sequence (“Cecilia Payne”) 7 2.1 Payne’s line strength diagram . 7 2.2 The Boltzmann and Saha laws . 8 2.3 Schadee’s tables for schadeenium . 12 2.4 Saha-Boltzmann populations of schadeenium . 14 2.5 Payne curves for schadeenium . 17 2.6 Discussion . 19 2.7 Saha-Boltzmann populations of hydrogen . 19 2.8 Solar Ca+ K versus Hα: line strength . 21 2.9 Solar Ca+ K versus Hα: temperature sensitivity . 24 2.10 Hot stars versus cool stars . 24 3 Fraunhofer line strengths and the curve of growth (“Marcel Minnaert”) 27 3.1 The Planck law . 27 3.2 Radiation through an isothermal layer . 29 3.3 Spectral lines from a solar reversing layer . 30 3.4 The equivalent width of spectral lines . 33 3.5 The curve of growth . 35 Epilogue 37 References 38 Text available at \tthttp://www.astro.uu.nl/~rutten/education/rjr-material/ssa (or via “Rob Rutten” in Google). Introduction These three exercises concern the appearance and nature of spectral lines in stellar spectra. Stellar spectrometry laid the foundation of astrophysics in the hands of: – Wollaston (1802): first observation of spectral lines in sunlight; – Fraunhofer (1814–1823): rediscovery of spectral lines in sunlight (“Fraunhofer lines”); their first systematic inventory.
    [Show full text]