CHAPTER 14 II Stellar Evolution
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Arxiv:0905.1355V2 [Gr-Qc] 4 Sep 2009 Edrt 1 O Ealdrve) Nti Otx,Re- Context, Been Has As This Collapse in Denoted Gravitational of Review)
Can accretion disk properties distinguish gravastars from black holes? Tiberiu Harko∗ Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong Zolt´an Kov´acs† Max-Planck-Institute f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany and Department of Experimental Physics, University of Szeged, D´om T´er 9, Szeged 6720, Hungary Francisco S. N. Lobo‡ Centro de F´ısica Te´orica e Computacional, Faculdade de Ciˆencias da Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal (Dated: September 4, 2009) Gravastars, hypothetic astrophysical objects, consisting of a dark energy condensate surrounded by a strongly correlated thin shell of anisotropic matter, have been proposed as an alternative to the standard black hole picture of general relativity. Observationally distinguishing between astrophysical black holes and gravastars is a major challenge for this latter theoretical model. This due to the fact that in static gravastars large stability regions (of the transition layer of these configurations) exist that are sufficiently close to the expected position of the event horizon, so that it would be difficult to distinguish the exterior geometry of gravastars from an astrophysical black hole. However, in the context of stationary and axially symmetrical geometries, a possibility of distinguishing gravastars from black holes is through the comparative study of thin accretion disks around rotating gravastars and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around slowly rotating gravastars, with all the metric tensor components estimated up to the second order in the angular velocity. -
Supernovae Sparked by Dark Matter in White Dwarfs
Supernovae Sparked By Dark Matter in White Dwarfs Javier F. Acevedog and Joseph Bramanteg;y gThe Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Department of Physics, Engineering Physics, and Astronomy, Queen's University, Kingston, Ontario, K7L 2S8, Canada yPerimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada November 27, 2019 Abstract It was recently demonstrated that asymmetric dark matter can ignite supernovae by collecting and collapsing inside lone sub-Chandrasekhar mass white dwarfs, and that this may be the cause of Type Ia supernovae. A ball of asymmetric dark matter accumulated inside a white dwarf and collapsing under its own weight, sheds enough gravitational potential energy through scattering with nuclei, to spark the fusion reactions that precede a Type Ia supernova explosion. In this article we elaborate on this mechanism and use it to place new bounds on interactions between nucleons 6 16 and asymmetric dark matter for masses mX = 10 − 10 GeV. Interestingly, we find that for dark matter more massive than 1011 GeV, Type Ia supernova ignition can proceed through the Hawking evaporation of a small black hole formed by the collapsed dark matter. We also identify how a cold white dwarf's Coulomb crystal structure substantially suppresses dark matter-nuclear scattering at low momentum transfers, which is crucial for calculating the time it takes dark matter to form a black hole. Higgs and vector portal dark matter models that ignite Type Ia supernovae are explored. arXiv:1904.11993v3 [hep-ph] 26 Nov 2019 Contents 1 Introduction 2 2 Dark matter capture, thermalization and collapse in white dwarfs 4 2.1 Dark matter capture . -
Light Rays, Singularities, and All That
Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition . -
How Supernovae Became the Basis of Observational Cosmology
Journal of Astronomical History and Heritage, 19(2), 203–215 (2016). HOW SUPERNOVAE BECAME THE BASIS OF OBSERVATIONAL COSMOLOGY Maria Victorovna Pruzhinskaya Laboratoire de Physique Corpusculaire, Université Clermont Auvergne, Université Blaise Pascal, CNRS/IN2P3, Clermont-Ferrand, France; and Sternberg Astronomical Institute of Lomonosov Moscow State University, 119991, Moscow, Universitetsky prospect 13, Russia. Email: [email protected] and Sergey Mikhailovich Lisakov Laboratoire Lagrange, UMR7293, Université Nice Sophia-Antipolis, Observatoire de la Côte d’Azur, Boulevard de l'Observatoire, CS 34229, Nice, France. Email: [email protected] Abstract: This paper is dedicated to the discovery of one of the most important relationships in supernova cosmology—the relation between the peak luminosity of Type Ia supernovae and their luminosity decline rate after maximum light. The history of this relationship is quite long and interesting. The relationship was independently discovered by the American statistician and astronomer Bert Woodard Rust and the Soviet astronomer Yury Pavlovich Pskovskii in the 1970s. Using a limited sample of Type I supernovae they were able to show that the brighter the supernova is, the slower its luminosity declines after maximum. Only with the appearance of CCD cameras could Mark Phillips re-inspect this relationship on a new level of accuracy using a better sample of supernovae. His investigations confirmed the idea proposed earlier by Rust and Pskovskii. Keywords: supernovae, Pskovskii, Rust 1 INTRODUCTION However, from the moment that Albert Einstein (1879–1955; Whittaker, 1955) introduced into the In 1998–1999 astronomers discovered the accel- equations of the General Theory of Relativity a erating expansion of the Universe through the cosmological constant until the discovery of the observations of very far standard candles (for accelerating expansion of the Universe, nearly a review see Lipunov and Chernin, 2012). -
Linear Stability of Slowly Rotating Kerr Black Holes
LINEAR STABILITY OF SLOWLY ROTATING KERR BLACK HOLES DIETRICH HAFNER,¨ PETER HINTZ, AND ANDRAS´ VASY Abstract. We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation. Our proof rests on a robust general framework, based on recent advances in microlocal analysis and non-elliptic Fredholm theory, for the analysis of resolvents of operators on asymptotically flat spaces. With the mode stability of the Schwarzschild metric as well as of certain scalar and 1-form wave operators on the Schwarzschild spacetime as an input, we establish the linear stability of slowly rotating Kerr black holes using perturbative arguments; in particular, our proof does not make any use of special algebraic properties of the Kerr metric. The heart of the paper is a detailed description of the resolvent of the linearization of a suitable hyperbolic gauge-fixed Einstein operator at low energies. As in previous work by the second and third authors on the nonlinear stability of cosmological black holes, constraint damping plays an important role. Here, it eliminates certain pathological generalized zero energy states; it also ensures that solutions of our hyperbolic formulation of the linearized Einstein equations have the stated asymptotics and decay for general initial data and forcing terms, which is a useful feature in nonlinear and numerical applications. -
Asymmetric Type-Ia Supernova Origin of W49B As Revealed from Spatially Resolved X-Ray Spectroscopic Study Ping Zhou1,2 and Jacco Vink1,3
A&A 615, A150 (2018) Astronomy https://doi.org/10.1051/0004-6361/201731583 & © ESO 2018 Astrophysics Asymmetric Type-Ia supernova origin of W49B as revealed from spatially resolved X-ray spectroscopic study Ping Zhou1,2 and Jacco Vink1,3 1 Anton Pannekoek Institute, University of Amsterdam, PO Box 94249, 1090 GE Amsterdam, The Netherlands e-mail: p.zhou,[email protected] 2 School of Astronomy and Space Science, Nanjing University, Nanjing 210023, PR China 3 GRAPPA, University of Amsterdam, PO Box 94249, 1090 GE Amsterdam, The Netherlands Received 17 July 2017 / Accepted 23 March 2018 ABSTRACT The origin of the asymmetric supernova remnant (SNR) W49B has been a matter of debate: is it produced by a rare jet-driven core- collapse (CC) supernova, or by a normal supernova that is strongly shaped by its dense environment? Aiming to uncover the explosion mechanism and origin of the asymmetric, centrally filled X-ray morphology of W49B, we have performed spatially resolved X-ray spectroscopy and a search for potential point sources. We report new candidate point sources inside W49B. The Chandra X-ray spectra from W49B are well-characterized by two-temperature gas components ( 0:27 keV + 0.6–2.2 keV). The hot component gas shows a large temperature gradient from the northeast to the southwest and is over-ionized∼ in most regions with recombination timescales 11 3 of 1–10 10 cm− s. The Fe element shows strong lateral distribution in the SNR east, while the distribution of Si, S, Ar, Ca is relatively× smooth and nearly axially symmetric. -
PHY390, the Kerr Metric and Black Holes
PHY390, The Kerr Metric and Black Holes James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University April 1, 2021 Black Holes, Neutron Stars and Gravitational Radiation [email protected] James Lattimer PHY390, The Kerr Metric and Black Holes What Exactly is a Black Hole? Standard definition: A region of space from which nothing, not even light, can escape. I Where does the escape velocity equal the speed of light? r 2GMBH vesc = = c RSch This defines the Schwarzschild radius RSch to be 2GMBH M RSch = 2 ' 3 km c M I The event horizon marks the point of no return for any object. I A black hole is black because it absorbs everything incident on the event horizon and reflects nothing. I Black holes are hypothesized to form in three ways: I Gravitational collapse of a star I A high energy collision I Density fluctuations in the early universe I In general relativity, the black hole's mass is concentrated at the center in a singularity of infinite density. James Lattimer PHY390, The Kerr Metric and Black Holes John Michell and Black Holes The first reference is by the Anglican priest, John Michell (1724-1793), in a letter written to Henry Cavendish, of the Royal Society, in 1783. He reasoned, from observations of radiation pressure, that light, like mass, has inertia. If gravity affects light like its mass equivalent, light would be weakened. He argued that a Sun with 500 times its radius and the same density would be so massive that it's escape velocity would exceed light speed. -
1. Basic Properties of Supernovae During the Past Two Decades, There Has Occurred a Technological Break-Through in Astronomy
PHYSICS of SUPERNOVAE: THEORY, OBSERVATIONS, UNRESOLVED PROBLEMS * D. K. Nadyozhin Institute for Theoretical and Experimental Physics, Moscow. [email protected] The main observational properties and resulting classification of supernovae (SNe) are briefly reviewed. Then we discuss the progress in modeling of two basic types of SNe – the thermonuclear and core-collapse ones, with special emphasis being placed on difficulties relating to a consistent description of thermonuclear flame propagation and the detachment of supernova envelope from the collapsing core (a nascent neutron star). The properties of the neutrino flux expected from the core- collapse SNe, and the lessons of SN1987A, exploded in the Large Magellanic Cloud, are considered as well. 1. Basic Properties of Supernovae During the past two decades, there has occurred a technological break-through in astronomy. The sensitivity, spectral and angular resolution of detectors in the whole electromagnetic diapason from gamma-rays through radio wavelengths has been considerably increased. Hence, it became possible to derive from the observed supernova spectra precise data on dynamics of supernova expansion and on composition and light curves of SNe as well. Moreover, neutrino astronomy overstepped the bounds of our Galaxy to discover the neutrino signal from SN1987A. This epoch- making event had a strong impact on the theory of supernovae. The main indicator for supernova astronomical classification is the amount of hydrogen observed in the SN envelopes. The Type I SNe (subtypes Ia, Ib, Ic) contain no hydrogen in their envelopes. The SN Ia are distinguished by strong Si lines in their spectra and form quite a homogeneous group of objects. On the contrary, Type II SNe (subtypes IIP, IIn, IIL, IIb) have clear lines of hydrogen in their spectra (Fig. -
Pos(GOLDEN2019)046 Model 6 Model May Be Inconsistent 6 Model Can Be Also Progenitors of Peculiar Sne Ia
Progenitor and explosion models of type Ia supernovae PoS(GOLDEN2019)046 Ataru Tanikawa∗ Department of Earth Science and Astronomy, College of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan E-mail: [email protected] Type Ia supernovae (SNe Ia) are important objects in astronomy and astrophysics. They are one of the brightest and common transients in the universe, a standard candle for a cosmic distance, and a dominant origin of iron group elements. It is widely accepted that SNe Ia are thermodynamical explosions of carbon-oxygen (CO) white dwarfs (WDs) in binary systems. Nevertheless, it is yet unclear what the companion stars are, and what the masses of the exploding CO WDs are. Recently, many sub-Chandrasekhar mass explosions in the double-degenerate scenario have been suggested. We have assessed the violent merger and Dynamically-Driven Double-Degenerate Double-Detonation (D6) models by numerical simulations. We have concluded that the violent merger model may not explain normal SNe Ia, since their circum-binary matter is much larger than the size of SN 2011fe, and their event rate is much smaller than the SN Ia rate in our Galaxy by an order of magnitude. However, it can be progenitors of peculiar SNe Ia. The D6 model has roughly consistent features with normal SNe Ia. However, the model has supernova ejecta with an asymmetric shape and low-velocity carbon-oxygen component due to the presence of the surviving companion CO. If these features can be observed, the D6 model may be inconsistent with normal SNe Ia. -
Black Holes - No Need to Be Afraid! Transcript
Black Holes - No need to be afraid! Transcript Date: Wednesday, 27 October 2010 - 12:00AM Location: Museum of London Gresham Lecture, Wednesday 27 October 2010 Black Holes – No need to be afraid! Professor Ian Morison Black Holes – do not deserve their bad press! Black holes seem to have a reputation for travelling through the galaxy “hovering up” stars and planets that stray into their path. It’s not like that. If our Sun were a black hole, we would continue to orbit just as we do now – we just would not have any heat or light. Even if a star were moving towards a massive black hole, it is far more likely to swing past – just like the fact very few comets hit the Sun but fly past to return again. So, if you are reassured, then perhaps we can consider…. What is a black Hole? If one projected a ball vertically from the equator of the Earth with increasing speed, there comes a point, when the speed reaches 11.2 km/sec, when the ball would not fall back to Earth but escape the Earth's gravitational pull. This is the Earth's escape velocity. If either the density of the Earth was greater (so its mass increases) or its radius smaller (or both) then the escape velocity would increase as Newton's formula for escape velocity shows: (0 is the escape velocity, M the mass of the object, r0 its radius and G the universal constant of gravitation.) If one naively used this formula into realms where relativistic formula would be needed, one could predict the mass and/or size of an object where the escape velocity would exceed the speed of light and thus nothing, not even light, could escape. -
Black Hole Math Is Designed to Be Used As a Supplement for Teaching Mathematical Topics
National Aeronautics and Space Administration andSpace Aeronautics National ole M a th B lack H i This collection of activities, updated in February, 2019, is based on a weekly series of space science problems distributed to thousands of teachers during the 2004-2013 school years. They were intended as supplementary problems for students looking for additional challenges in the math and physical science curriculum in grades 10 through 12. The problems are designed to be ‘one-pagers’ consisting of a Student Page, and Teacher’s Answer Key. This compact form was deemed very popular by participating teachers. The topic for this collection is Black Holes, which is a very popular, and mysterious subject among students hearing about astronomy. Students have endless questions about these exciting and exotic objects as many of you may realize! Amazingly enough, many aspects of black holes can be understood by using simple algebra and pre-algebra mathematical skills. This booklet fills the gap by presenting black hole concepts in their simplest mathematical form. General Approach: The activities are organized according to progressive difficulty in mathematics. Students need to be familiar with scientific notation, and it is assumed that they can perform simple algebraic computations involving exponentiation, square-roots, and have some facility with calculators. The assumed level is that of Grade 10-12 Algebra II, although some problems can be worked by Algebra I students. Some of the issues of energy, force, space and time may be appropriate for students taking high school Physics. For more weekly classroom activities about astronomy and space visit the NASA website, http://spacemath.gsfc.nasa.gov Add your email address to our mailing list by contacting Dr. -
Kerr Black Hole and Rotating Wormhole
Kerr Fest (Christchurch, August 26-28, 2004) Kerr black hole and rotating wormhole Sung-Won Kim(Ewha Womans Univ.) August 27, 2004 • INTRODUCTION • STATIC WORMHOLE • ROTATING WORMHOLE • KERR METRIC • SUMMARY AND DISCUSSION 1 Introduction The wormhole structure: two asymptotically flat regions + a bridge • To be traversable: exotic matter which violates the known energy conditions • Exotic matter is also an important issue on dark energy which accelerates our universe. • Requirement of the more general wormhole model - ‘rotating worm- hole’ • Two-dimensional model of transition between black hole and worm- hole ⇒ Interest on the general relation between black hole and wormhole 2 Static Wormhole(Morris and Thorne, 1988) The spacetime metric for static wormhole dr2 ds2 = −e2Λ(r)dt2 + + r2(dθ2 + sin2 θdφ2) 1 − b(r)/r Λ(r): the lapse function b(r): wormhole shape function At t =const. and θ = π/2, the 2-curved surface is embedded into 3-dimensional Euclidean space dr2 d˜s2 = + r2dφ2 = dz2 + dr2 + r2dφ2 1 − b(r)/r Flare-out condition d2r b − b0r = > 0 dz2 2b2 With new radial coordinate l ∈ (−∞, ∞) (proper distance), while r > b ds2 = −e2Λ(l)dt2 + dl2 + r(l)2(dθ2 + sin2 θdφ2) where dl b−1/2 = ± 1 − dr r 3 Rotating Wormhole(Teo, 1998) The spacetime in which we are interested will be stationary and axially symmetric. The most general stationary and axisymmetric metric can be written as 2 2 2 i j ds = gttdt + 2gtφdtdφ + gφφdφ + gijdx dx , where the indices i, j = 1, 2. Freedom to cast the metric into spherical polar coordinates by setting 2 2 g22 = gφφ/ sin x → The metric of the rotating wormhole as: ds2 = −N 2dt2 + eµdr2 + r2K2dθ2 + r2K2 sin2 θ[dφ2 − Ωdt]2 dr2 = −N 2dt2 + + r2K2dθ2 + r2K2 sin2 θ[dφ2 − Ωdt]2, 1 − b(r)/r where Ω is the angular velocity dφ/dt acquired by a particle that falls freely from infinity to the point (r, θ), and which gives rise to the well- known dragging of inertial frames or Lense-Thirring effect in general relativity.