DOCSLIB.ORG

Thesis Rybizki.Pdf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thesis Rybizki.Pdf INFERENCEFROMMODELLINGTHECHEMODYNAMICAL EVOLUTION OF THE MILKY WAY DISC jan rybizki Printed in October 2015 Cover picture: Several Circles, Wassily Kandinsky (1926) Dissertation submitted to the Combined Faculties of Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Jan Rybizki born in: Rüdersdorf Oral examination: December 8th, 2015 INFERENCEFROMMODELLINGTHECHEMODYNAMICAL EVOLUTION OF THE MILKY WAY DISC Referees: Prof. Dr. Andreas Just Prof. Dr. Norbert Christlieb ZUSAMMENFASSUNG-RÜCKSCHLÜSSEAUSDER MODELLIERUNGDERCHEMODYNAMISCHEN ENTWICKLUNG DER MILCHSTRAßENSCHEIBE In der vorliegenden Arbeit werden die anfängliche Massenfunktion (IMF) von Feldster- nen und Parameter zur chemischen Anreicherung der Milchstraße, unter Verwendung von Bayesscher Statistik und Modellrechnungen, hergeleitet. Ausgehend von einem lokalen Milchstraßenmodell [Just and Jahreiss, 2010] werden, für verschiedene IMF-Parameter, Sterne synthetisiert, die dann mit den entsprechenden Hip- parcos [Perryman et al., 1997](Hipparcos) Beobachtungen verglichen werden. Die abgelei- tete IMF ist in dem Bereich von 0.5 bis 8 Sonnenmassen gegeben durch ein Potenzgesetz mit einer Steigung von -1.49 0.08 für Sterne mit einer geringeren Masse als 1.39 0.05 M ± ± und einer Steigung von -3.02 0.06 für Sterne mit Massen darüber. ± Im zweiten Teil dieser Arbeit wird die IMF für Sterne mit Massen schwerer als 6 M be- stimmt. Dazu wurde die Software Chempy entwickelt, mit der man die chemische Anrei- cherung der Galaktischen Scheibe simulieren und auch die Auswahl von beobachteten Ster- nen nach Ort und Sternenklasse reproduzieren kann. Unter Berücksichtigung des systema- tischen Eekts der unterschiedlichen in der Literatur verfügbaren stellaren Anreicherungs- tabellen ergibt sich eine IMF-Steigung von -2.28 0.09 für Sterne mit Massen über 6 M . ± Dies zeigt, dass die von der chemischen Entwicklung abgeleitete IMF, ähnlich wie die Ergebnissen aus hydrodynamischen Simulationen der Milchstraße, für hohe Massen der Salpeter[1955] IMF entspricht. Aufgrund der geringen Anzahldichte von massereichen Sternen kann dies durch Sternzählungen nur schwer nachgewiesen werden. ABSTRACT-INFERENCEFROMMODELLINGTHE CHEMODYNAMICALEVOLUTIONOFTHEMILKYWAYDISC In this thesis, the eld star Initial Mass Function (IMF) and chemical evolution parameters for the Milky Way (MW) are derived using a forward modelling technique in combination with Bayesian statistics. Starting from a local MW disc model [Just and Jahreiss, 2010], observations of stellar sam- ples in the Solar Neighbourhood are synthesised and compared to the corresponding volume- complete observational samples of Hipparcos [Perryman et al., 1997](Hipparcos) stars. The resulting IMF, derived from observations in the range from 0.5 to 8 M , is a two-slope bro- ken power law with powers of -1.49 0.08 and -3.02 0.06 for the low-mass slope and the ± ± high-mass slope, respectively, with a break at 1.39 0.05 M . ± In order to constrain the IMF for stars more massive than 8 M , a fast and exible chemical enrichment code, Chempy, was developed, which is also able to reproduce spatial and stel- lar population selections of observational samples. The inferred high-mass slope for stellar masses above 6 M is -2.28 0.09, accounting for the systematic eects of dierent yield ± sets from the literature. v This shows that constraints from chemical modelling, similarly to hydrodynamical simu- lations of the Galaxy, demand a Salpeter[1955] high-mass index. This is hard to recover from star count analysis given the rareness of high-mass stars. vi OVERVIEWANDPUBLICATIONS In this thesis, the mass distribution of stars and the evolution of elements in the Milky Way (MW) are investigated. For this, physically motivated models are constructed, their in- put parameters are changed, and the outcome is compared to observational data of discrim- inative power. This forward modelling approach is combined with the concept of Bayesian inference. Central to this technique is the construction of a likelihood function in order to sample the posterior probability distribution, which is performed by means of Markov Chain Monte Carlo (MCMC) methods. The thesis is organised in the following way. The rst chapter is an introduction to the evolution of the MW, with a focus on the processes governing the synthesis of the chemical elements. The statistical methodology will be introduced in chapter2. The rst example of Bayesian model inference, where the true distance of a star will be inferred from a parallax mea- surement, is taken in great detail from Bailer-Jones[2015]. This leads to the question of determining stellar number densities in a specic volume, which will be discussed in the second part of chapter2. The ideas presented in section 2.2.3 have been published in Just et al.[2015] with a contribution from the author. In chapter3, the Initial Mass Function ( IMF) parameters are inferred from Solar Neighbour- hood stars, using a local MW disk model. Most of this chapter has been published in Rybizki and Just[2015]. In chapter4, a chemical evolution model of the local MW disc is presented and impor- tant model parameters, constraining the high-mass IMF, the infall and the SuperNova of type Ia (SN Ia), are inferred from abundances of Solar Neighbourhood stars. Section 4.3 of this chapter contains results, which are submitted as conference proceedings [Just and Ry- bizki, 2015]. The thesis will be concluded with a summary and a concise outlook. vii ACKNOWLEDGEMENTS First and foremost I would like to thank Prof. Andreas Just for his condence in my work and his guidance. The generous nancial support and the freedom to ponder ideas are very much appreciated as well as his positive supervision style. I am much obliged to PD Coryn Bailer-Jones and Dr. Ewan Cameron for their help with statistical questions, which I came across frequently, and for nurturing my fascination of Bayesian statistics. For most enjoyable lunch breaks and for partaking in my science and non-science related challenges I wish to express my deep gratitude to Dr. Robert Schmidt. His presence made the Astronomisches Rechen-Institut (ARI) feel more like a home for me. I am very grateful to Prof. Norbert Christlieb for readily agreeing to referee this thesis. Fur- thermore I wish to thank Prof. Eva Grebel and Prof. Luca Amendola for willingly joining my examination committee. I also want to mention the highly valued advice and helpful strategic planning from my thesis committee consisting of Prof. Eva Grebel, Dr. Glenn van de Ven and Prof. Andreas Just. Special thanks go to PD Christian Fendt who coordinated the International Max Planck Research School (IMPRS) activities that formed a sociable community out of our IMPRS generation. At ARI, I would like to thank Hendrik Heinl for caring about the social activities and for his support especially towards the end of my thesis writing. For numerous entertaining lunch breaks I want to thank Dr. Markus Demleitner and Aksel Alpay who also helped me to master the computationally expensive MCMC simulations. In the same respect Dr. Peter Schwekendiek and Sven Weimann always provided me with helpful computing advice and maintained the excellent Perseus machine. I want to thank the whole ARI administration, especially mentioning Martina Buchhaupt for thoroughly taking care of my administrative issues and Stefan Leitner for mocking me for my poor hand crafting skills. I enjoyed the scientic and non-scientic exchange with Dr. Corrado Boeche with whom I could lament about the intriguing complexity of selection functions. Last but not least I would like to thank Alex Hygate, Carolin Wittmann, Clio Bertelli, PD Coryn Bailer-Jones, Dr. Corrado Boeche, Daniel Haydon, Dr. Frederik Schönebeck, Dr. Ger- not Burkhardt, Hendrik Heinl, Peter Zeidler, Reza Moetazedian, Dr. Robert Schmidt, Timo Hirscher and Tina Gier for proof reading this thesis and for making the ARI a sociable workspace. My PhD project was funded by SFB 881 The Milky Way System. I would also like to acknowledge nancial support from the Heidelberg Graduate School of Fundamental Physics and the IMPRS which allowed me to participate in several interesting summer schools and useful workshops giving me the opportunity to learn from the best in the eld and be an active part of the international community. ix CONTENTS i introduction 1 1 the milky way galaxy 3 1.1 Etymology . .3 1.2 History . .3 1.3 Cosmology . .4 1.4 Elemental synthesis and stellar evolution . .7 1.4.1 Primordial nucleosynthesis . .7 1.4.2 First stars . .7 1.4.3 Reionization . .8 1.4.4 Low-mass stars . .9 1.4.5 Intermediate-mass stars . .9 1.4.6 High-mass stars . 12 1.4.7 Chemical enrichment - a simple model . 12 1.5 Structure of the Milky Way . 14 1.5.1 Halo . 14 1.5.2 Barred bulge . 15 1.5.3 Disc(s) . 16 1.5.4 Formation scenarios . 18 1.6 Deciphering the Milky Way evolution . 18 1.6.1 Extragalactic observations . 18 1.6.2 Simulations . 18 1.6.3 Analytical models . 19 1.6.4 Milky Way observation . 19 2 statistical inference with astronomical data 21 2.1 Bayesian inference . 21 2.1.1 Conditional probability . 21 2.1.2 Parameter estimation using Bayes’ theorem . 22 2.1.3 An example - Inferring distances from parallaxes . 23 2.1.4 Sampling the parameter space . 28 2.1.5 Model comparison . 30 2.2 Stellar number densities from star counts . 31 2.2.1 Magnitude and distance cuts . 32 2.2.2 Binary splitting and analytic extinction correction . 33 2.2.3 Probabilistic distances . 35 2.2.4 Using inhomogeneous extinction data . 36 2.2.5 Probabilistic binary correction . 37 2.2.6 Relaxing completeness . 37 2.2.7 Modelling a magnitude limited sample . 38 ii milky way disc model inference 39 3 the local initial mass function, as derived from star counts 41 3.1 Introduction .
Load more

Recommended publications
  • POSTERS SESSION I: Atmospheres of Massive Stars
    Abstracts of Posters 25 POSTERS (Grouped by sessions in alphabetical order by first author) SESSION I: Atmospheres of Massive Stars I-1. Pulsational Seeding of Structure in a Line-Driven Stellar Wind Nurdan Anilmis & Stan Owocki, University of Delaware Massive stars often exhibit signatures of radial or non-radial pulsation, and in principal these can play a key role in seeding structure in their radiatively driven stellar wind. We have been carrying out time-dependent hydrodynamical simulations of such winds with time-variable surface brightness and lower boundary condi- tions that are intended to mimic the forms expected from stellar pulsation. We present sample results for a strong radial pulsation, using also an SEI (Sobolev with Exact Integration) line-transfer code to derive characteristic line-profile signatures of the resulting wind structure. Future work will compare these with observed signatures in a variety of specific stars known to be radial and non-radial pulsators. I-2. Wind and Photospheric Variability in Late-B Supergiants Matt Austin, University College London (UCL); Nevyana Markova, National Astronomical Observatory, Bulgaria; Raman Prinja, UCL There is currently a growing realisation that the time-variable properties of massive stars can have a funda- mental influence in the determination of key parameters. Specifically, the fact that the winds may be highly clumped and structured can lead to significant downward revision in the mass-loss rates of OB stars. While wind clumping is generally well studied in O-type stars, it is by contrast poorly understood in B stars. In this study we present the analysis of optical data of the B8 Iae star HD 199478.
    [Show full text]
  • Arxiv:1910.04776V2 [Astro-Ph.SR] 2 Dec 2019 Lion Years
    Astronomy & Astrophysics manuscript no. smsmax c ESO 2019 December 3, 2019 Letter to the Editor Maximally accreting supermassive stars: a fundamental limit imposed by hydrostatic equilibrium L. Haemmerle´1, G. Meynet1, L. Mayer2, R. S. Klessen3;4, T. E. Woods5, A. Heger6;7 1 Departement´ d’Astronomie, Universite´ de Geneve,` chemin des Maillettes 51, CH-1290 Versoix, Switzerland 2 Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland 3 Universitat¨ Heidelberg, Zentrum fur¨ Astronomie, Institut fur¨ Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany 4 Universitat¨ Heidelberg, Interdisziplinares¨ Zentrum fur¨ Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany 5 National Research Council of Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada 6 School of Physics and Astronomy, Monash University, VIC 3800, Australia 7 Tsung-Dao Lee Institute, Shanghai 200240, China Received ; accepted ABSTRACT Context. Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; 5 4 5 −1 & 10 M ) by direct collapse because they can trigger mass inflows as high as 10 − 10 M yr on sub-parsec scales. However, the channel of SMBH formation in this case, either dark collapse (direct collapse without prior stellar phase) or supermassive star (SMS; 4 & 10 M ), remains unknown. Aims. Here, we investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium. −1 Methods. We compute hydrostatic models of SMSs accreting at 1 – 1000 M yr , and estimate the departures from equilibrium a posteriori by taking into account the finite speed of sound.
    [Show full text]
  • Abstract a Search for Extrasolar Planets Using Echoes Produced in Flare Events
    ABSTRACT A SEARCH FOR EXTRASOLAR PLANETS USING ECHOES PRODUCED IN FLARE EVENTS A detection technique for searching for extrasolar planets using stellar flare events is explored, including a discussion of potential benefits, potential problems, and limitations of the method. The detection technique analyzes the observed time versus intensity profile of a star’s energetic flare to determine possible existence of a nearby planet. When measuring the pulse of light produced by a flare, the detection of an echo may indicate the presence of a nearby reflective surface. The flare, acting much like the pulse in a radar system, would give information about the location and relative size of the planet. This method of detection has the potential to give science a new tool with which to further humankind’s understanding of planetary systems. Randal Eugene Clark May 2009 A SEARCH FOR EXTRASOLAR PLANETS USING ECHOES PRODUCED IN FLARE EVENTS by Randal Eugene Clark A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Physics in the College of Science and Mathematics California State University, Fresno May 2009 © 2009 Randal Eugene Clark APPROVED For the Department of Physics: We, the undersigned, certify that the thesis of the following student meets the required standards of scholarship, format, and style of the university and the student's graduate degree program for the awarding of the master's degree. Randal Eugene Clark Thesis Author Fred Ringwald (Chair) Physics Karl Runde Physics Ray Hall Physics For the University Graduate Committee: Dean, Division of Graduate Studies AUTHORIZATION FOR REPRODUCTION OF MASTER’S THESIS X I grant permission for the reproduction of this thesis in part or in its entirety without further authorization from me, on the condition that the person or agency requesting reproduction absorbs the cost and provides proper acknowledgment of authorship.
    [Show full text]
  • Lecture 24. Degenerate Fermi Gas (Ch
    Lecture 24. Degenerate Fermi Gas (Ch. 7) We will consider the gas of fermions in the degenerate regime, where the density n exceeds by far the quantum density nQ, or, in terms of energies, where the Fermi energy exceeds by far the temperature. We have seen that for such a gas μ is positive, and we’ll confine our attention to the limit in which μ is close to its T=0 value, the Fermi energy EF. ~ kBT μ/EF 1 1 kBT/EF occupancy T=0 (with respect to E ) F The most important degenerate Fermi gas is 1 the electron gas in metals and in white dwarf nε()(),, T= f ε T = stars. Another case is the neutron star, whose ε⎛ − μ⎞ exp⎜ ⎟ +1 density is so high that the neutron gas is ⎝kB T⎠ degenerate. Degenerate Fermi Gas in Metals empty states ε We consider the mobile electrons in the conduction EF conduction band which can participate in the charge transport. The band energy is measured from the bottom of the conduction 0 band. When the metal atoms are brought together, valence their outer electrons break away and can move freely band through the solid. In good metals with the concentration ~ 1 electron/ion, the density of electrons in the electron states electron states conduction band n ~ 1 electron per (0.2 nm)3 ~ 1029 in an isolated in metal electrons/m3 . atom The electrons are prevented from escaping from the metal by the net Coulomb attraction to the positive ions; the energy required for an electron to escape (the work function) is typically a few eV.
    [Show full text]
  • ASTR3007/4007/6007, Class 10: Low Mass Stellar Evolution 24 March
    ASTR3007/4007/6007, Class 10: Low Mass Stellar Evolution 24 March Our topic for today is the first of three classes about post-main sequence evolution. Today the topic is low mass stars, with the line between low and high mass to be discussed in a bit. I. Leaving the Main Sequence A. Main Sequence Lifetime Stars remain on the main sequence as long as their hydrogen fuel lasts. While on the main sequence, their properties do not change much, but they do change some due to the gradual conversion of H into He. As a result of this conversion, the hydrogen mass fraction X decreases, while the helium mass fraction Y increases. As a result, the mean atomic weight changes. Recall that 1 1 1 − X − Y ≈ X + Y + (1) µI 4 hAi 1 1 ≈ (1 + X) (2) µe 2 1 1 1 = + : (3) µ µI µe Insterstellar gas out of which stars forms has roughly X = 0:74 and Y = 0:24 (in contrast to X = 0:707 and Y = 0:274 in the Sun, which has processed some of its H into He), which gives µ = 0:60. In contrast, once all the H has been turned into He, X = 0 and Y = 0:98, which gives µ = 1:34. In stars like the Sun that are radiative in their cores, the changes occur shell by shell, so different shells have different compositions depending on their rate of burning. In stars that are convective in their cores, convection homogenises the composition of the different shells, so the entire convective core has a uniform composition.
    [Show full text]
  • Hayashi Limit
    HAYASHI LIMIT Let us consider a simple ”model atmosphere” of a star. The equation of hydrostatic equilibrium and the definition of optical depth are dP dτ = −gρ, = −κρ, (s2.24) dr dr and may be combined to write dP g = . (s2.25) dτ κ Assuming κ = const we may integrate this equation to obtain 2 g GM Pτ=2/3 = , g ≡ 2 , (s2.26) 3 κτ=2/3 R where the subscript τ =2/3 indicates that we evaluate the particular quantity at the photosphere. Let us consider a cool star with the negative hydrogen ion H− dominating opacity in the atmosphere. When temperature is low we may neglect radiation pressure in the atmosphere. Adopting k 0.5 7.7 −25 0.5 P = ρT, κ = κ0ρ T , κ0 = 10 Z , (s2.27) µH we may write the equation (s2.26) as k 2 1 GM ρT = 0 5 7 7 2 , (s2.28) µH 3 κ0ρ . T . R which may be rearranged to have 1.5 8.7 2 µH G M ρ T = 2 . (s2.29) 3 k κ0 R We know that a star with the H− opacity in the atmosphere becomes convective below optical depth τ =0.775, i.e. very close to the photosphere. Let us suppose that the convection extends all the way to the stellar center, and let us ignore here all complications due to hydrogen and helium ionization. Convective star is adiabatic, and if it is made of a perfect gas with the equation of state (s2.27) then it is a polytrope with an index n =1.5.
    [Show full text]
  • 3. Stellar Radial Pulsation and Stability
    Rolf Kudritzki SS 2017 3. Stellar radial pulsation and stability mV δ Cephei Teff spectral type vrad ∆R = vdt Z stellar disk Δ from R 1 Rolf Kudritzki SS 2015 1.55 1.50 1.45 1.40 LD Angular diam. (mas) A 1.35 0.04 0.0 0.5 1.0 0.02 0.00 −0.02 res. (mas) B −0.04 0.0 0.5 1.0 Phase Interferometric observations of δ Cep (Mérand et al. 2005) M. Groenewegen2 MIAPP, 17 June 2014 – p.8/50 Rolf Kudritzki SS 2017 instability strip Hayashi limit of low mass fully convective stars main sequence 3 Rolf Kudritzki SS 2017 the instability strip stars in instability strip have significant layers not too deep, not too superficial, where ↵ stellar opacity increases with T. T , ↵ 0 ⇠ ≥ This is caused by the excitation and ionization of H and He. Consider a perturbation causing a local compression à T increase à κ increase à perturbation heat not radiated away but stored à expansion beyond equilibrium point à then cooling and T decreasing à gravity pulls gas masses back à cyclically pulsation 4 Rolf Kudritzki SS 2017 ↵ stars to the left of instability strip T − , ↵ 0 are hotter and H and He are ionized ⇠ ≥ in the interior. The opacity decreases with increasing T. For a perturbation causing a local compression we have again à T increase but now à κ decreases à perturbation heat is quickly radiated away à perturbation is damped, no pulsation To the right of the instability strip the energy transport is dominated by very effective convection and not by radiation transport.
    [Show full text]
  • Understanding Stellar Evolution
    Astronomy 531 University of Washington Spring 2014 Understanding Stellar Evolution Henny J.G.L.M. Lamers Visiting Professor, University of Amsterdam, NL Email: h.j.g.l.m.lamers@uu.nl Tel: 206-543-4858 1 Astronomy 531 University of Washington Spring 2014 Preface These are the lecture notes of my graduate class “Understanding Stellar Evolution” (AST531) that I have been giving at the University of Washington in Seattle in the spring quarter of almost every other year since 2004. These notes have developed over the years due to comments and suggestions by students and requests by the staff. (I am sure they will keep evolving). They are written as “lecture notes” rather than in the form of a book. I have chosen for this form because I find it more easy to teach from them, and I think it is easier for the students to quickly see the important points in explanations and descriptions. I have avoided (long) purely mathematical explanations. Although these may be appealing, straight forward and physically correct, they often obscure the physical processes behind them. So, where possible, I explain concepts in simple (?) or intuitive physical terms, giving the reference where the more rigorous explanations and derivations can be found. My goal is to give the students a “feeling” and “understanding” of stellar evolution. From the reactions of the students, I sense that this is appreciated. I am grateful for my Utrecht colleague Onno Pols, for his lecture notes on “Stellar structure and evolution” and the more recent one on “Binary evolution”. They often formed the skeleton of my lectures.
    [Show full text]
  • ASTR 1010 Homework Solutions
    ASTR 1010 Homework Solutions Chapter 1 24. Set up a proportion, but be sure that you express all the distances in the same units (e.g., centimeters). The diameter of the Sun is to the size of a basketball as the distance to Proxima Centauri (4.2 LY) is to the unknown distance (X), so (1.4 × 1011 cm) / (30 cm) = (4.2 LY)(9.46 × 1017 cm/LY) / (X) Rearranging terms, we get X = (4.2 LY)(9.46 × 1017 cm/LY)(30 cm) / (1.4 × 1011 cm) = 8.51 × 108 cm = 8.51 × 103 km = 8510 km In other words, if the Sun were the size of a 30-cm diameter ball, the nearest star would be 8510 km away, which is roughly the distance from Los Angeles to Tokyo. 27. The Sun’s hydrogen mass is (3/4) × (1.99 × 1030 kg) = 1.49 × 1030 kg. Now divide the Sun’s hydrogen mass by the mass of one hydrogen atom to get the number of hydrogen atoms contained in the Sun: (1.49 × 1030 kg) / (1.67 × 10-27 kg/atom) = 8.92 × 1056 atoms. 8 11 29. The distance from the Sun to the Earth is 1 AU = 1.496 × 10 km = 1.496 × 10 m. The light-travel time is the distance, 1 AU, divided by the speed of light, i.e., 11 8 3 time = distance/speed = (1.496 × 10 m) / (3.00 × 10 m/s) = 0.499 × 10 s = 499 s = 8.3 minutes. 34. Since you are given diameter (D = 2.6 cm) and angle, and asked to find distance, you need to rewrite the small-angle formula as d = (206,265)(D) / (α).
    [Show full text]
  • ASTR 4008 / 8008, Semester 2, 2020
    Class 18: Protostellar evolution ASTR 4008 / 8008, Semester 2, 2020 Mark Krumholz Outline • Models and methods • Timescale hierarchy • Evolution equations • Boundary conditions • The role of deuterium • Qualitative results: major evolutionary phases • Evolution of protostars on the HR diagram • The birthline • The Hayashi and Heyney tracks Timescale hierarchy Similarities and differences to main sequence stars • Protostellar evolution governed by three basic timescales: • Mechanical equilibration: tmech ~ (R / cs) ~ (R3 / GM)1/2 ~ few hours • Energy equilibration (Kelvin-Helmholtz): tKH = GM2 / RL ~ 1 Myr • Accretion: tacc = M / (dM / dt) ~ 0.1 Myr −5 −1 • Numerical values for M = M⊙, R = 3 R⊙, L = 10 L⊙, dM / dt = 10 M⊙ yr • Implication: protostars are always in mechanical equilibrium, but are not generally in energy equilibrium while they are forming • By contrast, main sequence stars in energy equilibrium because tKH ≪ lifetime • This hierarchy applies to low-mass stars; somewhat different for high mass Equations of stellar structure For protostars • Equations describing mass conservation, hydrostatic balance, and energy transport are exactly the same as for main sequence stars: <latexit sha1_base64="zQBTVeYWRUq5mFjggJdG88FmPGo=">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</latexit>
    [Show full text]
  • Astrophysical Wormholes
    universe Article Astrophysical Wormholes Cosimo Bambi 1,* and Dejan Stojkovic 2 1 Center for Field Theory and Particle Physics and Department of Physics, Fudan University, Shanghai 200438, China 2 Department of Physics, State University of New York (SUNY) at Buffalo, Buffalo, NY 14260-1500, USA; ds77@buffalo.edu * Correspondence: bambi@fudan.edu.cn Abstract: Wormholes are hypothetical topologically-non-trivial structures of spacetime. From the theoretical point of view, the possibility of their existence is challenging but cannot be ruled out. This article is a compact and non-exhaustive review of past and current efforts to search for astro- physical wormholes in the Universe. Keywords: wormholes; black holes; spacetime topology; gravity 1. Introduction Wormholes are hypothetical spacetime structures with non-trivial topologies capable of connecting either two distant regions of the same universe or two different universes, as illustrated in Figure1. The entrances of a wormhole are called the “mouths” of the wormhole and the spacetime region connecting the mouths is called the “throat” of the wormhole. The simplest wormhole configuration has two mouths connected by a throat, but more complex structures are also possible [1]. Strictly speaking, wormholes are not a prediction of general relativity or of other theories of gravity. They are spacetime structures Citation: Bambi, C.; Stojkovic, D. that can potentially exist in curved spacetimes, so they exist in a very wide class of gravity Astrophysical Wormholes. Universe models. The formation mechanisms and stability of these spacetime structures depend on 2021, 7, 136. https://doi.org/ 10.3390/universe7050136 the specific gravity theory and often present problems, so the existence of wormholes in the Universe is challenging.
    [Show full text]
  • Lives of Other Stars Russell-Vogt Theorem Henry Norris Russell and Heinrich Vogt Were the first to Note the Influence of a Star’S Mass
    Astronomy 218 Lives of Other stars russell-Vogt Theorem Henry Norris Russell and Heinrich Vogt were the first to note the influence of a star’s mass. “A star’s properties are determined primarily by its mass.” The pre-main sequence behavior is one example. The stellar lifetime is also determined by the star’s mass, τ ∝ M−3. The mass has an even larger impact on the star’s destiny. Leaving the Main Sequence After a main sequence life that varies from 1010 years to 107 years, differences appear from the point of hydrogen exhaustion in the stellar core. Stars more massive than the Sun follow different paths. A 4 M☉ star takes a long looping path before reaching the Hayashi line and climbing in radius. A 10 M☉ star loops smoothly back and forth between blue supergiant and red supergiant. Structural Differences While the post-main sequence events for stars more massive than the Sun follow the same sequence as those in lower- mass stars, the structure of more massive stars respond differently. Stars with M ≳ 1.5 M☉ have convective cores due to the CNO cycle, but radiative envelopes. Envelope opacity changes gradually until the Hayashi limit, where cool temperatures raise the opacity dramatically, is reached. The details of the loops depends on the interplay of opacity, nuclear energy generation, metallicity, and theory of convection, thus models of the loops remain uncertain. Stars with M ≳ 10 M☉ never reach the Hayashi limit. Helium White Dwarf Achieving the temperatures (> 108K) and densities (> 107 kg m−3) needed for helium burning requires the helium core to exceed 0.45 M☉, preventing stars of ≲ 0.5 M☉ from ever burning helium.
    [Show full text]