Primer: the Collapsar - Fireball Model
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Negreiros Lecture II
General Relativity and Neutron Stars - II Rodrigo Negreiros – UFF - Brazil Outline • Compact Stars • Spherically Symmetric • Rotating Compact Stars • Magnetized Compact Stars References for this lecture Compact Stars • Relativistic stars with inner structure • We need to solve Einstein’s equation for the interior as well as the exterior Compact Stars - Spherical • We begin by writing the following metric • Which leads to the following components of the Riemman curvature tensor Compact Stars - Spherical • The Ricci tensor components are calculated as • Ricci scalar is given by Compact Stars - Spherical • Now we can calculate Einstein’s equation as 휇 • Where we used a perfect fluid as sources ( 푇휈 = 푑푖푎푔(휖, 푃, 푃, 푃)) Compact Stars - Spherical • Einstein’s equation define the space-time curvature • We must also enforce energy-momentum conservation • This implies that • Where the four velocity is given by • After some algebra we get Compact Stars - Spherical • Making use of Euler’s equation we get • Thus • Which we can rewrite as Compact Stars - Spherical • Now we introduce • Which allow us to integrate one of Einstein’s equation, leading to • After some shuffling of Einstein’s equation we can write Summary so far... Metric Energy-Momentum Tensor Einstein’s equation Tolmann-Oppenheimer-Volkoff eq. Relativistic Hydrostatic Equilibrium Mass continuity Stellar structure calculation Microscopic Ewuation of State Macroscopic Composition Structure Recapitulando … “Feed” with diferente microscopic models Microscopic Ewuation of State Macroscopic Composition Structure Compare predicted properties with Observed data. Rotating Compact Stars • During its evolution, compact stars may acquire high rotational frequencies (possibly up to 500 hz) • Rotation breaks spherical symmetry, increasing the degrees of freedom. -
Exploring Pulsars
High-energy astrophysics Explore the PUL SAR menagerie Astronomers are discovering many strange properties of compact stellar objects called pulsars. Here’s how they fit together. by Victoria M. Kaspi f you browse through an astronomy book published 25 years ago, you’d likely assume that astronomers understood extremely dense objects called neutron stars fairly well. The spectacular Crab Nebula’s central body has been a “poster child” for these objects for years. This specific neutron star is a pulsar that I rotates roughly 30 times per second, emitting regular appar- ent pulsations in Earth’s direction through a sort of “light- house” effect as the star rotates. While these textbook descriptions aren’t incorrect, research over roughly the past decade has shown that the picture they portray is fundamentally incomplete. Astrono- mers know that the simple scenario where neutron stars are all born “Crab-like” is not true. Experts in the field could not have imagined the variety of neutron stars they’ve recently observed. We’ve found that bizarre objects repre- sent a significant fraction of the neutron star population. With names like magnetars, anomalous X-ray pulsars, soft gamma repeaters, rotating radio transients, and compact Long the pulsar poster child, central objects, these bodies bear properties radically differ- the Crab Nebula’s central object is a fast-spinning neutron star ent from those of the Crab pulsar. Just how large a fraction that emits jets of radiation at its they represent is still hotly debated, but it’s at least 10 per- magnetic axis. Astronomers cent and maybe even the majority. -
Neutron Stars
Chandra X-Ray Observatory X-Ray Astronomy Field Guide Neutron Stars Ordinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons. The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% Chandra Image of Vela Pulsar open space! (NASA/PSU/G.Pavlov et al. What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons! Such extreme forces occur in nature when the central part of a massive star collapses to form a neutron star. The atoms are crushed completely, and the electrons are jammed inside the protons to form a star composed almost entirely of neutrons. -
R-Process Elements from Magnetorotational Hypernovae
r-Process elements from magnetorotational hypernovae D. Yong1,2*, C. Kobayashi3,2, G. S. Da Costa1,2, M. S. Bessell1, A. Chiti4, A. Frebel4, K. Lind5, A. D. Mackey1,2, T. Nordlander1,2, M. Asplund6, A. R. Casey7,2, A. F. Marino8, S. J. Murphy9,1 & B. P. Schmidt1 1Research School of Astronomy & Astrophysics, Australian National University, Canberra, ACT 2611, Australia 2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia 3Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, AL10 9AB, UK 4Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 5Department of Astronomy, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden 6Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany 7School of Physics and Astronomy, Monash University, VIC 3800, Australia 8Istituto NaZionale di Astrofisica - Osservatorio Astronomico di Arcetri, Largo Enrico Fermi, 5, 50125, Firenze, Italy 9School of Science, The University of New South Wales, Canberra, ACT 2600, Australia Neutron-star mergers were recently confirmed as sites of rapid-neutron-capture (r-process) nucleosynthesis1–3. However, in Galactic chemical evolution models, neutron-star mergers alone cannot reproduce the observed element abundance patterns of extremely metal-poor stars, which indicates the existence of other sites of r-process nucleosynthesis4–6. These sites may be investigated by studying the element abundance patterns of chemically primitive stars in the halo of the Milky Way, because these objects retain the nucleosynthetic signatures of the earliest generation of stars7–13. -
Introduction to Astronomy from Darkness to Blazing Glory
Introduction to Astronomy From Darkness to Blazing Glory Published by JAS Educational Publications Copyright Pending 2010 JAS Educational Publications All rights reserved. Including the right of reproduction in whole or in part in any form. Second Edition Author: Jeffrey Wright Scott Photographs and Diagrams: Credit NASA, Jet Propulsion Laboratory, USGS, NOAA, Aames Research Center JAS Educational Publications 2601 Oakdale Road, H2 P.O. Box 197 Modesto California 95355 1-888-586-6252 Website: http://.Introastro.com Printing by Minuteman Press, Berkley, California ISBN 978-0-9827200-0-4 1 Introduction to Astronomy From Darkness to Blazing Glory The moon Titan is in the forefront with the moon Tethys behind it. These are two of many of Saturn’s moons Credit: Cassini Imaging Team, ISS, JPL, ESA, NASA 2 Introduction to Astronomy Contents in Brief Chapter 1: Astronomy Basics: Pages 1 – 6 Workbook Pages 1 - 2 Chapter 2: Time: Pages 7 - 10 Workbook Pages 3 - 4 Chapter 3: Solar System Overview: Pages 11 - 14 Workbook Pages 5 - 8 Chapter 4: Our Sun: Pages 15 - 20 Workbook Pages 9 - 16 Chapter 5: The Terrestrial Planets: Page 21 - 39 Workbook Pages 17 - 36 Mercury: Pages 22 - 23 Venus: Pages 24 - 25 Earth: Pages 25 - 34 Mars: Pages 34 - 39 Chapter 6: Outer, Dwarf and Exoplanets Pages: 41-54 Workbook Pages 37 - 48 Jupiter: Pages 41 - 42 Saturn: Pages 42 - 44 Uranus: Pages 44 - 45 Neptune: Pages 45 - 46 Dwarf Planets, Plutoids and Exoplanets: Pages 47 -54 3 Chapter 7: The Moons: Pages: 55 - 66 Workbook Pages 49 - 56 Chapter 8: Rocks and Ice: -
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. -
Hawking Radiation
a brief history of andreas müller student seminar theory group max camenzind lsw heidelberg mpia & lsw january 2004 http://www.lsw.uni-heidelberg.de/users/amueller talktalk organisationorganisation basics ☺ standard knowledge advanced knowledge edge of knowledge and verifiability mindmind mapmap whatwhat isis aa blackblack hole?hole? black escape velocity c hole singularity in space-time notion „black hole“ from relativist john archibald wheeler (1968), but first speculation from geologist and astronomer john michell (1783) ☺ blackblack holesholes inin relativityrelativity solutions of the vacuum field equations of einsteins general relativity (1915) Gµν = 0 some history: schwarzschild 1916 (static, neutral) reissner-nordstrøm 1918 (static, electrically charged) kerr 1963 (rotating, neutral) kerr-newman 1965 (rotating, charged) all are petrov type-d space-times plug-in metric gµν to verify solution ;-) ☺ black hole mass hidden in (point or ring) singularity blackblack holesholes havehave nono hairhair!! schwarzschild {M} reissner-nordstrom {M,Q} kerr {M,a} kerr-newman {M,a,Q} wheeler: no-hair theorem ☺ blackblack holesholes –– schwarzschildschwarzschild vs.vs. kerrkerr ☺ blackblack holesholes –– kerrkerr inin boyerboyer--lindquistlindquist black hole mass M spin parameter a lapse function delta potential generalized radius sigma potential frame-dragging frequency cylindrical radius blackblack holehole topologytopology blackblack holehole –– characteristiccharacteristic radiiradii G = M = c = 1 blackblack holehole -- -
Scattering on Compact Body Spacetimes
Scattering on compact body spacetimes Thomas Paul Stratton A thesis submitted for the degree of Doctor of Philosophy School of Mathematics and Statistics University of Sheffield March 2020 Summary In this thesis we study the propagation of scalar and gravitational waves on compact body spacetimes. In particular, we consider spacetimes that model neutron stars, black holes, and other speculative exotic compact objects such as black holes with near horizon modifications. We focus on the behaviour of time-independent perturbations, and the scattering of plane waves. First, we consider scattering by a generic compact body. We recap the scattering theory for scalar and gravitational waves, using a metric perturbation formalism for the latter. We derive the scattering and absorption cross sections using the partial-wave approach, and discuss some approximations. The theory of this chapter is applied to specific examples in the remainder of the thesis. The next chapter is an investigation of scalar plane wave scattering by a constant density star. We compute the scattering cross section numerically, and discuss a semiclassical, high-frequency analysis, as well as a geometric optics approach. The semiclassical results are compared to the numerics, and used to gain some physical insight into the scattering cross section interference pattern. We then generalise to stellar models with a polytropic equation of state, and gravitational plane wave scattering. This entails solving the metric per- turbation problem for the interior of a star, which we accomplish numerically. We also consider the near field scattering profile for a scalar wave, and the cor- respondence to ray scattering and the formation of a downstream cusp caustic. -
The Sun, Yellow Dwarf Star at the Heart of the Solar System NASA.Gov, Adapted by Newsela Staff
Name: ______________________________ Period: ______ Date: _____________ Article of the Week Directions: Read the following article carefully and annotate. You need to include at least 1 annotation per paragraph. Be sure to include all of the following in your total annotations. Annotation = Marking the Text + A Note of Explanation 1. Great Idea or Point – Write why you think it is a good idea or point – ! 2. Confusing Point or Idea – Write a question to ask that might help you understand – ? 3. Unknown Word or Phrase – Circle the unknown word or phrase, then write what you think it might mean based on context clues or your word knowledge – 4. A Question You Have – Write a question you have about something in the text – ?? 5. Summary – In a few sentences, write a summary of the paragraph, section, or passage – # The sun, yellow dwarf star at the heart of the solar system NASA.gov, adapted by Newsela staff Picture and Caption ___________________________ ___________________________ ___________________________ Paragraph #1 ___________________________ ___________________________ This image shows an enormous eruption of solar material, called a coronal mass ejection, spreading out into space, captured by NASA's Solar Dynamics ___________________________ Observatory on January 8, 2002. Paragraph #2 Para #1 The sun is a hot ball made of glowing gases and is a type ___________________________ of star known as a yellow dwarf. It is at the heart of our solar system. ___________________________ Para #2 The solar system consists of everything that orbits the ___________________________ sun. The sun's gravity holds the solar system together, by keeping everything from planets to bits of dust in its orbit. -
Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 Xxneutron-Star Binaries: X-Ray Bursters
Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 XXNeutron-Star Binaries: X-ray bursters [Look at the slides and the pictures in your book, but I won’t test you on this in detail, and we may skip altogether in class.] 22.4 Gamma-Ray Bursts 22.5 Black Holes 22.6 XXEinstein’s Theories of Relativity Special Relativity 22.7 Space Travel Near Black Holes 22.8 Observational Evidence for Black Holes Tests of General Relativity Gravity Waves: A New Window on the Universe Neutron Stars and Pulsars (sec. 22.1, 2 in textbook) 22.1 Neutron Stars According to models for stellar explosions: After a carbon detonation supernova (white dwarf in binary), little or nothing remains of the original star. After a core collapse supernova, part of the core may survive. It is very dense—as dense as an atomic nucleus—and is called a neutron star. [Recall that during core collapse the iron core (ashes of previous fusion reactions) is disintegrated into protons and neutrons, the protons combine with the surrounding electrons to make more neutrons, so the core becomes pure neutron matter. Because of this, core collapse can be halted if the core’s mass is between 1.4 (the Chandrasekhar limit) and about 3-4 solar masses, by neutron degeneracy.] What do you get if the core mass is less than 1.4 solar masses? Greater than 3-4 solar masses? 22.1 Neutron Stars Neutron stars, although they have 1–3 solar masses, are so dense that they are very small. -
Searching for Gravitational Waves
Astronomy group seminar, University of Southampton, Jan 2015 LIGO-DCC G1500072 1. Gravitational wave (GW) background What are gravitational waves? • Gravitational waves are a direct prediction of Einstein’s General Theory of Relativity • Solutions to (weak field) Einstein equations in vacuum are wave equations 휕2 − + 훻2 ℎ휇휈 = −16휋푇휇휈 휕푡 2 Vacuum so stress- energy tensor 2 휕 푇휇휈 = 0 − + 훻2 ℎ휇휈 = 0 휕푡 2 휇휈 휇휈 휇 ℎ = 퐴 exp 푘휇 푥 • “Ripples in space-time” What are GWs? • Einstein first predicted GWs in 1916 paper • This had a major error – the waves carried no energy! Einstein, “Näherungsweise Integration der Feldgleichungen der Gravitation“, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 1916 What are GWs? • Corrected in 1918 paper which introduced the now famous “quadrupole formula” Einstein, “Über Gravitationswellen“, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 1918 What are GWs Source: Bulk Motion Oscillating Tidal Field Observer Detects Produces Changing Tidal Field Propagates (Unobstructed) Distortion Strain to Observer 푙 + Δ푙 푙 Δ푙 Strain: ℎ = 푙 2 퐺 mass quadruple Quadrupole ℎ(푡) = 퐼( 푡) formula: 푟 푐4 -45 source distance (1/r - ~ 8x10 small number! amplitude not power!) What are GWs? For two 1.4 M⊙ neutron stars 2 퐺 mass near coalescence at a distance of ℎ(푡) = 퐼( 푡) quadruple 10 Mpc ℎ~1.4 × 10−22 푟 푐4 -45 Displacement measured by 4km long ~ 8x10 detector ~5.6 × 10−19m - about 1/10000th source distance (1/r - amplitude not power!) diameter of a proton, or measuring change in distance to α Centauri to ~1/10th diameter of a human hair! • Detectable gravitational waves (GWs) will only come from the most massive and energetic systems in the universe e.g. -
Central Engines and Environment of Superluminous Supernovae
Central Engines and Environment of Superluminous Supernovae Blinnikov S.I.1;2;3 1 NIC Kurchatov Inst. ITEP, Moscow 2 SAI, MSU, Moscow 3 Kavli IPMU, Kashiwa with E.Sorokina, K.Nomoto, P. Baklanov, A.Tolstov, E.Kozyreva, M.Potashov, et al. Schloss Ringberg, 26 July 2017 First Superluminous Supernova (SLSN) is discovered in 2006 -21 1994I 1997ef 1998bw -21 -20 56 2002ap Co to 2003jd 56 2007bg -19 Fe 2007bi -20 -18 -19 -17 -16 -18 Absolute magnitude -15 -17 -14 -13 -16 0 50 100 150 200 250 300 350 -20 0 20 40 60 Epoch (days) Superluminous SN of type II Superluminous SN of type I SN2006gy used to be the most luminous SN in 2006, but not now. Now many SNe are discovered even more luminous. The number of Superluminous Supernovae (SLSNe) discovered is growing. The models explaining those events with the minimum energy budget involve multiple ejections of mass in presupernova stars. Mass loss and build-up of envelopes around massive stars are generic features of stellar evolution. Normally, those envelopes are rather diluted, and they do not change significantly the light produced in the majority of supernovae. 2 SLSNe are not equal to Hypernovae Hypernovae are not extremely luminous, but they have high kinetic energy of explosion. Afterglow of GRB130702A with bumps interpreted as a hypernova. Alina Volnova, et al. 2017. Multicolour modelling of SN 2013dx associated with GRB130702A. MNRAS 467, 3500. 3 Our models of LC with STELLA E ≈ 35 foe. First year light ∼ 0:03 foe while for SLSNe it is an order of magnitude larger.