Endpoints of Stellar Evolution
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Generation of Angular Momentum in Cold Gravitational Collapse
A&A 585, A139 (2016) Astronomy DOI: 10.1051/0004-6361/201526756 & c ESO 2016 Astrophysics Generation of angular momentum in cold gravitational collapse D. Benhaiem1,M.Joyce2,3, F. Sylos Labini4,1,5, and T. Worrakitpoonpon6 1 Istituto dei Sistemi Complessi Consiglio Nazionale delle Ricerche, via dei Taurini 19, 00185 Rome, Italy e-mail: [email protected] 2 UPMC Univ. Paris 06, UMR 7585, LPNHE, 75005 Paris, France 3 CNRS IN2P3, UMR 7585, LPNHE, 75005 Paris, France 4 Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy 5 INFN Unit Rome 1, Dipartimento di Fisica, Universitá di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy 6 Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Nonthaburi Campus, 11000 Nonthaburi, Thailand Received 16 June 2015 / Accepted 4 November 2015 ABSTRACT During the violent relaxation of a self-gravitating system, a significant fraction of its mass may be ejected. If the time-varying gravi- tational field also breaks spherical symmetry, this mass can potentially carry angular momentum. Thus, starting initial configurations with zero angular momentum can, in principle, lead to a bound virialised system with non-zero angular momentum. Using numerical simulations we explore here how much angular momentum can be generated in a virialised structure in this way, starting from con- figurations of cold particles that are very close to spherically symmetric. For the initial configurations in which spherical symmetry is broken only by the Poissonian fluctuations associated with the finite particle number N, with N in range 103 to 105, we find that the relaxed structures have standard “spin” parameters λ ∼ 10−3, and decreasing slowly with N. -
Special and General Relativity with Applications to White Dwarfs, Neutron Stars and Black Holes
Norman K. Glendenning Special and General Relativity With Applications to White Dwarfs, Neutron Stars and Black Holes First Edition 42) Springer Contents Preface vii 1 Introduction 1 1.1 Compact Stars 2 1.2 Compact Stars and Relativistic Physics 5 1.3 Compact Stars and Dense-Matter Physics 6 2 Special Relativity 9 2.1 Lorentz Invariance 11 2.1.1 Lorentz transformations 11 2.1.2 Time Dilation 14 2.1.3 Covariant vectors 14 2.1.4 Energy and Momentum 16 2.1.5 Energy-momentum tensor of a perfect fluid 17 2.1.6 Light cone 18 3 General Relativity 19 3.1 Scalars, Vectors, and Tensors in Curvilinear Coordinates 20 3.1.1 Photon in a gravitational field 28 3.1.2 Tidal gravity 29 3.1.3 Curvature of spacetime 30 3.1.4 Energy conservation and curvature 30 3.2 Gravity 32 3.2.1 Einstein's Discovery 32 3.2.2 Particle Motion in an Arbitrary Gravitational Field 32 3.2.3 Mathematical definition of local Lorentz frames . 35 3.2.4 Geodesics 36 3.2.5 Comparison with Newton's gravity 38 3.3 Covariance 39 3.3.1 Principle of general covariance 39 3.3.2 Covariant differentiation 40 3.3.3 Geodesic equation from covariance principle 41 3.3.4 Covariant divergente and conserved quantities . 42 3.4 Riemann Curvature Tensor 45 x Contents 3.4.1 Second covariant derivative of scalars and vectors 45 3.4.2 Symmetries of the Riemann tensor 46 3.4.3 Test for flatness 47 3.4.4 Second covariant derivative of tensors 47 3.4.5 Bianchi identities 48 3.4.6 Einstein tensor 48 3.5 Einstein's Field Equations 50 3.6 Relativistic Stars 52 3.6.1 Metric in static isotropic spacetime 53 -
Stellar Equilibrium Vs. Gravitational Collapse
Eur. Phys. J. H https://doi.org/10.1140/epjh/e2019-100045-x THE EUROPEAN PHYSICAL JOURNAL H Stellar equilibrium vs. gravitational collapse Carla Rodrigues Almeidaa Department I Max Planck Institute for the History of Science, Boltzmannstraße 22, 14195 Berlin, Germany Received 26 September 2019 / Received in final form 12 December 2019 Published online 11 February 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com Abstract. The idea of gravitational collapse can be traced back to the first solution of Einstein's equations, but in these early stages, com- pelling evidence to support this idea was lacking. Furthermore, there were many theoretical gaps underlying the conviction that a star could not contract beyond its critical radius. The philosophical views of the early 20th century, especially those of Sir Arthur S. Eddington, imposed equilibrium as an almost unquestionable condition on theoretical mod- els describing stars. This paper is a historical and epistemological account of the theoretical defiance of this equilibrium hypothesis, with a novel reassessment of J.R. Oppenheimer's work on astrophysics. 1 Introduction Gravitationally collapsed objects are the conceptual precursor to black holes, and their history sheds light on how such a counter-intuitive idea was accepted long before there was any concrete proof of their existence. A black hole is a strong field structure of space-time surrounded by a unidirectional membrane that encloses a singularity. General relativity (GR) predicts that massive enough bodies will collapse into black holes. In fact, the first solution of Einstein's field equations implies the existence of black holes, but this conclusion was not reached at the time because the necessary logical steps were not as straightforward as they appear today. -
Collapse of an Unstable Neutron Star to a Black Hole Matthias Hanauske (E-Mail:[email protected], Office: 02.232)
Experiments in Computer Simulations : Collapse of an unstable Neutron Star to a Black Hole Matthias Hanauske (e-mail:[email protected], office: 02.232) 0 Class Information • application form : { if you want to do this experiment, please register via e-mail to me no later than on the last Wednesday before the week in which you want to do the experiment; your e-mail should include the following information: (1) student number, (2) full name, (3) e-mail address. • intensive course : { 12 [hours] = 6 [hours/week] × 2 [weeks]. • when : { Monday 9-16, two subsequent weeks upon individual arrangement with me; other time slots may be arranged with me individually. • where : { Pool Room 01.120. • preparation : { an account for you on the \FUCHS" cluster of the CSC (http://csc.uni-frankfurt.de/) will be provided; please read the quick starting guide on the CSC web pages before starting the simulation. • required skill : { basic Linux knowledge. • using software : { Einstein Toolkit [5]. { gnuplot (http://www.gnuplot.info/) { pygraph (https://bitbucket.org/dradice/pygraph). { python (https://www.python.org/) and matplotlib (http://matplotlib.org/). { Mathematica (http://www.wolfram.com/mathematica/). 1 1 Introduction Neutron stars are beside white dwarfs and black holes the potential final states of the evo- lution of a normal star. These extremely dense astrophysical objects, which are formed in the center of a supernova explosion, represent the last stable state before the matter collapses to a black hole. Due to their large magnetic fields (up to 1011 Tesla) and fast rotation (up to 640 rotations in one second) neutron stars emit a certain electromagnetic spectrum. -
Detection of Gravitational Collapse J
Detection of gravitational collapse J. Craig Wheeler and John A. Wheeler Citation: AIP Conference Proceedings 96, 214 (1983); doi: 10.1063/1.33938 View online: http://dx.doi.org/10.1063/1.33938 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/96?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Chaos and Vacuum Gravitational Collapse AIP Conf. Proc. 1122, 172 (2009); 10.1063/1.3141244 Dyadosphere formed in gravitational collapse AIP Conf. Proc. 1059, 72 (2008); 10.1063/1.3012287 Gravitational Collapse of Massive Stars AIP Conf. Proc. 847, 196 (2006); 10.1063/1.2234402 Analytical modelling of gravitational collapse AIP Conf. Proc. 751, 101 (2005); 10.1063/1.1891535 Gravitational collapse Phys. Today 17, 21 (1964); 10.1063/1.3051610 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.83.205.78 On: Mon, 02 Mar 2015 21:02:26 214 DETECTION OF GRAVITATIONAL COLLAPSE J. Craig Wheeler and John A. Wheeler University of Texas, Austin, TX 78712 ABSTRACT At least one kind of supernova is expected to emit a large flux of neutrinos and gravitational radiation because of the collapse of a core to form a neutron star. Such collapse events may in addition occur in the absence of any optical display. The corresponding neutrino bursts can be detected via Cerenkov events in the same water used in proton decay experiments. Dedicated equipment is under construction to detect the gravitational radiation. -
Luminous Blue Variables
Review Luminous Blue Variables Kerstin Weis 1* and Dominik J. Bomans 1,2,3 1 Astronomical Institute, Faculty for Physics and Astronomy, Ruhr University Bochum, 44801 Bochum, Germany 2 Department Plasmas with Complex Interactions, Ruhr University Bochum, 44801 Bochum, Germany 3 Ruhr Astroparticle and Plasma Physics (RAPP) Center, 44801 Bochum, Germany Received: 29 October 2019; Accepted: 18 February 2020; Published: 29 February 2020 Abstract: Luminous Blue Variables are massive evolved stars, here we introduce this outstanding class of objects. Described are the specific characteristics, the evolutionary state and what they are connected to other phases and types of massive stars. Our current knowledge of LBVs is limited by the fact that in comparison to other stellar classes and phases only a few “true” LBVs are known. This results from the lack of a unique, fast and always reliable identification scheme for LBVs. It literally takes time to get a true classification of a LBV. In addition the short duration of the LBV phase makes it even harder to catch and identify a star as LBV. We summarize here what is known so far, give an overview of the LBV population and the list of LBV host galaxies. LBV are clearly an important and still not fully understood phase in the live of (very) massive stars, especially due to the large and time variable mass loss during the LBV phase. We like to emphasize again the problem how to clearly identify LBV and that there are more than just one type of LBVs: The giant eruption LBVs or h Car analogs and the S Dor cycle LBVs. -
The Endpoints of Stellar Evolution Answer Depends on the Star’S Mass Star Exhausts Its Nuclear Fuel - Can No Longer Provide Pressure to Support Itself
The endpoints of stellar evolution Answer depends on the star’s mass Star exhausts its nuclear fuel - can no longer provide pressure to support itself. Gravity takes over, it collapses Low mass stars (< 8 Msun or so): End up with ‘white dwarf’ supported by degeneracy pressure. Wide range of structure and composition!!! Answer depends on the star’s mass Star exhausts its nuclear fuel - can no longer provide pressure to support itself. Gravity takes over, it collapses Higher mass stars (8-25 Msun or so): get a ‘neutron star’ supported by neutron degeneracy pressure. Wide variety of observed properties Answer depends on the star’s mass Star exhausts its nuclear fuel - can no longer provide pressure to support itself. Gravity takes over, it collapses Above about 25 Msun: we are left with a ‘black hole’ Black holes are astounding objects because of their simplicity (consider all the complicated physics to set all the macroscopic properties of a star that we have been through) - not unlike macroscopic elementary particles!! According to general relativity, the black hole properties are set by two numbers: mass and spin change of photon energies towards the gravitating mass the opposite when emitted Pound-Rebka experiment used atomic transition of Fe Important physical content for BH studies: general relativity has no intrisic scale instead, all important lengthscales and timescales are set by - and become proportional to the mass. Trick… Examine the energy… Why do we believe that black holes are inevitably created by gravitational collapse? Rather astounding that we go from such complicated initial conditions to such “clean”, simple objects! . -
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 -
The Formation of Brown Dwarfs 459
Whitworth et al.: The Formation of Brown Dwarfs 459 The Formation of Brown Dwarfs: Theory Anthony Whitworth Cardiff University Matthew R. Bate University of Exeter Åke Nordlund University of Copenhagen Bo Reipurth University of Hawaii Hans Zinnecker Astrophysikalisches Institut, Potsdam We review five mechanisms for forming brown dwarfs: (1) turbulent fragmentation of molec- ular clouds, producing very-low-mass prestellar cores by shock compression; (2) collapse and fragmentation of more massive prestellar cores; (3) disk fragmentation; (4) premature ejection of protostellar embryos from their natal cores; and (5) photoerosion of pre-existing cores over- run by HII regions. These mechanisms are not mutually exclusive. Their relative importance probably depends on environment, and should be judged by their ability to reproduce the brown dwarf IMF, the distribution and kinematics of newly formed brown dwarfs, the binary statis- tics of brown dwarfs, the ability of brown dwarfs to retain disks, and hence their ability to sustain accretion and outflows. This will require more sophisticated numerical modeling than is presently possible, in particular more realistic initial conditions and more realistic treatments of radiation transport, angular momentum transport, and magnetic fields. We discuss the mini- mum mass for brown dwarfs, and how brown dwarfs should be distinguished from planets. 1. INTRODUCTION form a smooth continuum with those of low-mass H-burn- ing stars. Understanding how brown dwarfs form is there- The existence of brown dwarfs was first proposed on the- fore the key to understanding what determines the minimum oretical grounds by Kumar (1963) and Hayashi and Nakano mass for star formation. In section 3 we review the basic (1963). -
CHIME and Probing the Origin of Fast Radio Bursts by Liam Dean Connor a Thesis Submitted in Conformity with the Requirements
CHIME and Probing the Origin of Fast Radio Bursts by Liam Dean Connor A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Astronomy and Astrophysics University of Toronto c Copyright 2016 by Liam Dean Connor Abstract CHIME and Probing the Origin of Fast Radio Bursts Liam Dean Connor Doctor of Philosophy Graduate Department of Astronomy and Astrophysics University of Toronto 2016 The time-variable long-wavelength sky harbours a number of known but unsolved astro- physical problems, and surely many more undiscovered phenomena. With modern tools such problems will become tractable, and new classes of astronomical objects will be revealed. These tools include digital telescopes made from powerful computing clusters, and improved theoretical methods. In this thesis we employ such devices to understand better several puzzles in the time-domain radio sky. Our primary focus is on the origin of fast radio bursts (FRBs), a new class of transients of which there seem to be thousands per sky per day. We offer a model in which FRBs are extragalactic but non-cosmological pulsars in young supernova remnants. Since this theoretical work was done, observations have corroborated the picture of FRBs as young rotating neutron stars, including the non-Poissonian repetition of FRB 121102. We also present statistical arguments regard- ing the nature and location of FRBs. These include reinstituting the classic V=Vmax-test @ log N to measure the brightness distribution of FRBs, i.e., constraining @ log S . We find consis- tency with a Euclidean distribution. This means current observations cannot distinguish between a cosmological population and a more local uniform population, unless added assumptions are made. -
The Formation and Early Evolution of Very Low-Mass Stars and Brown Dwarfs Held at ESO Headquarters, Garching, Germany, 11–14 October 2011
Astronomical News and spectroscopic surveys identifying the at the ELTs, together with encouraging emphasised the power of emerging coun- first galaxies, rare quasars, supernovae some explicitly high-risk projects. It was tries and public outreach for investments and gamma-ray bursts. noted that is very important to retain a in astronomical research and that diver- broad range of facilities, including sity in facilities and astronomical capabili- A lively discussion arose on data policy 4-metre- and 8-metre-class telescopes, ties should be retained together with and data mining for surveys and ELTs. to be used as survey facilities, to pro- large-scale projects. Ellis reminded us Most participants agreed that proprietary mote small projects, and to train young that we cannot plan the future in detail time should be at the minimum level but astronomers. All the long-term flagship and so optimism, versatility and creativity sufficient to guarantee intellectual owner- projects should try to involve more stu- remain the key attributes for success. ship and a satisfactory progress of the dents and young researchers, allowing surveys and the ELTs. Others proposed them to attend science working com- All the presentations and the conference to have the data public from the begin- mittees, and communicating the outcome picture are available at the conference ning. In order to facilitate data mining, it of the major high-level decisional meet- website: http://www.eso.org/sci/meetings/ was proposed that all data provided by ings to them. Furthermore, it was pro- 2011/feedgiant. the surveys and the ELTs should be Vir- posed that at least one young astrono- tual Observatory compliant from the out- mer should be included in each of the set. -
AST301 the Lives of the Stars
AST301 The Lives of the Stars A Tale of Two Forces: Pressure vs Gravity I. The Sun as a Star What we know about the Sun •Angular Diameter: q = 32 arcmin (from observations) •Solar Constant: f = 1.4 x 106 erg/sec/cm2 (from observations) •Distance: d = 1.5 x 108 km (1 AU). (from Kepler's Third Law and the trigonometric parallax of Venus) •Luminosity: L = 4 x 1033 erg/s. (from the inverse-square law: L = 4p d2 f) •Radius: R = 7 x 105 km. (from geometry: R = p d) •Mass: M = 2 x 1033 gm. (from Newton's version of Kepler's Third Law, M = (4p2/G) d3/P2) •Temperature: T = 5800 K. (from the black body law: L = 4pR2 σ T4) •Composition: about 74% Hydrogen, 24% Helium, and 2% everything else (by mass). (from spectroscopy) What Makes the Sun Shine? Inside the Sun Far Side Gary Larson Possible Sources of Sunlight • Chemical combustion – A Sun made of C+O: 4000 years • Gravitational Contraction – Convert gravitational potential energy – T = U/L = GM82R8/L8 ~ 107 years • Accretion – Limitless, but M8 increases 3% / 106 years • Nuclear Fusion – Good for ~1010 years How Fusion Works E=mc2 • 4 H ⇒ He4 + energy • The mass of 4 H atoms exceeds the mass of a He atom by 0.7%. • Every second, the Sun converts 6x108 tons of H into 5.96x108 tons of He. • The Sun loses 4x106 tons of mass every second. • At this rate, the Sun can maintain its present luminosity for about 1011 years. • 1010 or 1011 years ??? Nuclear Fusion Proton-Proton (PP I) reaction Releases 26.7 MeV 10 < Tcore < 14 MK How Fusion Works Source: Wikipedia Beyond PP I PP II: dominates for 14 < Tcore < 23 MK • 3He + 4He ⇒ 7Be + g 7 - 7 • Be + e ⇒ Li + ne + g • 7Li +p+ ⇒ 24He + g • 16% of L8 PP III: dominates for Tcore > 23 MK • 3He + 4He ⇒ 7Be + g • 7Be + p+ ⇒ 8B + g 8 8 + • B ⇒ Be + e + ne • 8Be ⇒ 24He • 0.02% of L8 Nuclear Timescale • 1010 years • Sun has brightened by 30% in 4.5 Gyr • Photons take 105 – 106 yrs to diffuse out – Gamma-rays thermalize to optical photons How do we know? • The p-p reaction also produces neutrinos.