Stellar Structure and Evolution
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PHYS 633: Introduction to Stellar Astrophysics Spring Semester 2006 Rich Townsend ([email protected])
PHYS 633: Introduction to Stellar Astrophysics Spring Semester 2006 Rich Townsend ([email protected]) Governing Equations In the foregoing analysis, we have seen how a star usually maintains a state of hydrostatic equilibrium. We have seen how the energy created in the star through nuclear reactions, or released through contraction, makes its way out in the form of the star’s luminosity. We have seen how the physical processes responsible for transporting this energy can either be radiation or convection. And, finally, we have seen how nuclear reactions within the star, and transport processes such as convective mixing, can alter the stars chemical composition. These four key pieces of physics lead to 3 + I of the differential equations governing stellar structure (here, I is the number of elements whose evolution we are following). Let’s quickly review these equations. First, we have the most general (spherically-symmetric) form for the equation governing momen- tum conservation, ∂P Gm 1 ∂2r = − − . (1) ∂m 4πr2 4πr2 ∂t2 If the second term on the right-hand side vanishes, then we recover the equation of hydrostatic equilibrium, expressed in Lagrangian form (i.e., derivatives with respect to the mass coordinate m, rather than the radial coordinate r). If this term does not vanish at some point in the star, then the mass shells at that point will being to expand or contract, with an acceleration given by ∂2r/∂t2. Second, we have the most general form for the energy conservation equation, ∂l ∂T δ ∂P = − − c + . (2) ∂m ν P ∂t ρ ∂t The first and second terms on the right-hand side come from nuclear energy gen- eration and neutrino losses, respectively. -
Used Time Scales GEORGE E
PROCEEDINGS OF THE IEEE, VOL. 55, NO. 6, JIJNE 1967 815 Reprinted from the PROCEEDINGS OF THE IEEI< VOL. 55, NO. 6, JUNE, 1967 pp. 815-821 COPYRIGHT @ 1967-THE INSTITCJTE OF kECTRITAT. AND ELECTRONICSEN~INEERS. INr I’KINTED IN THE lT.S.A. Some Characteristics of Commonly Used Time Scales GEORGE E. HUDSON A bstract-Various examples of ideally defined time scales are given. Bureau of Standards to realize one international unit of Realizations of these scales occur with the construction and maintenance of time [2]. As noted in the next section, it realizes the atomic various clocks, and in the broadcast dissemination of the scale information. Atomic and universal time scales disseminated via standard frequency and time scale, AT (or A), with a definite initial epoch. This clock time-signal broadcasts are compared. There is a discussion of some studies is based on the NBS frequency standard, a cesium beam of the associated problems suggested by the International Radio Consultative device [3]. This is the atomic standard to which the non- Committee (CCIR). offset carrier frequency signals and time intervals emitted from NBS radio station WWVB are referenced ; neverthe- I. INTRODUCTION less, the time scale SA (stepped atomic), used in these emis- PECIFIC PROBLEMS noted in this paper range from sions, is only piecewise uniform with respect to AT, and mathematical investigations of the properties of in- piecewise continuous in order that it may approximate to dividual time scales and the formation of a composite s the slightly variable scale known as UT2. SA is described scale from many independent ones, through statistical in Section 11-A-2). -
THE EVOLUTION of SOLAR FLUX from 0.1 Nm to 160Μm: QUANTITATIVE ESTIMATES for PLANETARY STUDIES
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by St Andrews Research Repository The Astrophysical Journal, 757:95 (12pp), 2012 September 20 doi:10.1088/0004-637X/757/1/95 C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A. THE EVOLUTION OF SOLAR FLUX FROM 0.1 nm TO 160 μm: QUANTITATIVE ESTIMATES FOR PLANETARY STUDIES Mark W. Claire1,2,3, John Sheets2,4, Martin Cohen5, Ignasi Ribas6, Victoria S. Meadows2, and David C. Catling7 1 School of Environmental Sciences, University of East Anglia, Norwich, UK NR4 7TJ; [email protected] 2 Virtual Planetary Laboratory and Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA 3 Blue Marble Space Institute of Science, P.O. Box 85561, Seattle, WA 98145-1561, USA 4 Department of Physics & Astronomy, University of Wyoming, Box 204C, Physical Sciences, Laramie, WY 82070, USA 5 Radio Astronomy Laboratory, University of California, Berkeley, CA 94720-3411, USA 6 Institut de Ciencies` de l’Espai (CSIC-IEEC), Facultat de Ciencies,` Torre C5 parell, 2a pl, Campus UAB, E-08193 Bellaterra, Spain 7 Virtual Planetary Laboratory and Department of Earth and Space Sciences, University of Washington, Box 351310, Seattle, WA 98195, USA Received 2011 December 14; accepted 2012 August 1; published 2012 September 6 ABSTRACT Understanding changes in the solar flux over geologic time is vital for understanding the evolution of planetary atmospheres because it affects atmospheric escape and chemistry, as well as climate. We describe a numerical parameterization for wavelength-dependent changes to the non-attenuated solar flux appropriate for most times and places in the solar system. -
14 Timescales in Stellar Interiors
14Timescales inStellarInteriors Having dealt with the stellar photosphere and the radiation transport so rel- evant to our observations of this region, we’re now ready to journey deeper into the inner layers of our stellar onion. Fundamentally, the aim we will de- velop in the coming chapters is to develop a connection betweenM,R,L, and T in stars (see Table 14 for some relevant scales). More specifically, our goal will be to develop equilibrium models that describe stellar structure:P (r),ρ (r), andT (r). We will have to model grav- ity, pressure balance, energy transport, and energy generation to get every- thing right. We will follow a fairly simple path, assuming spherical symmetric throughout and ignoring effects due to rotation, magneticfields, etc. Before laying out the equations, let’sfirst think about some key timescales. By quantifying these timescales and assuming stars are in at least short-term equilibrium, we will be better-equipped to understand the relevant processes and to identify just what stellar equilibrium means. 14.1 Photon collisions with matter This sets the timescale for radiation and matter to reach equilibrium. It de- pends on the mean free path of photons through the gas, 1 (227) �= nσ So by dimensional analysis, � (228)τ γ ≈ c If we use numbers roughly appropriate for the average Sun (assuming full Table3: Relevant stellar quantities. Quantity Value in Sun Range in other stars M2 1033 g 0.08 �( M/M )� 100 × � R7 1010 cm 0.08 �( R/R )� 1000 × 33 1 3 � 6 L4 10 erg s− 10− �( L/L )� 10 × � Teff 5777K 3000K �( Teff/mathrmK)� 50,000K 3 3 ρc 150 g cm− 10 �( ρc/g cm− )� 1000 T 1.5 107 K 106 ( T /K) 108 c × � c � 83 14.Timescales inStellarInteriors P dA dr ρ r P+dP g Mr Figure 28: The state of hydrostatic equilibrium in an object like a star occurs when the inward force of gravity is balanced by an outward pressure gradient. -
X-Ray Sun SDO 4500 Angstroms: Photosphere
ASTR 8030/3600 Stellar Astrophysics X-ray Sun SDO 4500 Angstroms: photosphere T~5000K SDO 1600 Angstroms: upper photosphere T~5x104K SDO 304 Angstroms: chromosphere T~105K SDO 171 Angstroms: quiet corona T~6x105K SDO 211 Angstroms: active corona T~2x106K SDO 94 Angstroms: flaring regions T~6x106K SDO: dark plasma (3/27/2012) SDO: solar flare (4/16/2012) SDO: coronal mass ejection (7/2/2012) Aims of the course • Introduce the equations needed to model the internal structure of stars. • Overview of how basic stellar properties are observationally measured. • Study the microphysics relevant for stars: the equation of state, the opacity, nuclear reactions. • Examine the properties of simple models for stars and consider how real models are computed. • Survey (mostly qualitatively) how stars evolve, and the endpoints of stellar evolution. Stars are relatively simple physical systems Sound speed in the sun Problem of Stellar Structure We want to determine the structure (density, temperature, energy output, pressure as a function of radius) of an isolated mass M of gas with a given composition (e.g., H, He, etc.) Known: r Unknown: Mass Density + Temperature Composition Energy Pressure Simplifying assumptions 1. No rotation à spherical symmetry ✔ For sun: rotation period at surface ~ 1 month orbital period at surface ~ few hours 2. No magnetic fields ✔ For sun: magnetic field ~ 5G, ~ 1KG in sunspots equipartition field ~ 100 MG Some neutron stars have a large fraction of their energy in B fields 3. Static ✔ For sun: convection, but no large scale variability Not valid for forming stars, pulsating stars and dying stars. 4. -
Stellar Populations in a Standard ISOGAL Field in the Galactic Disc
A&A 493, 785–807 (2009) Astronomy DOI: 10.1051/0004-6361:200809668 & c ESO 2009 Astrophysics Stellar populations in a standard ISOGAL field in the Galactic disc, S. Ganesh1,2,A.Omont1,U.C.Joshi2,K.S.Baliyan2, M. Schultheis3,1,F.Schuller4,1,andG.Simon5 1 Institut d’Astrophysique de Paris, CNRS and Université Paris 6, 98bis boulevard Arago, 75014 Paris, France e-mail: [email protected] 2 Physical Research Laboratory, Navrangpura, Ahmedabad-380 009, India e-mail: [email protected] 3 Observatoire de Besançon, Besançon, France 4 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, 53121 Bonn, Germany 5 GEPI, UMS-CNRS 2201, Observatoire de Paris, France Received 28 February 2008 / Accepted 3 September 2008 ABSTRACT Aims. We identify the stellar populations (mostly red giants and young stars) detected in the ISOGAL survey at 7 and 15 μmtowards a field (LN45) in the direction = −45, b = 0.0. Methods. The sources detected in the survey of the Galactic plane by the Infrared Space Observatory were characterised based on colour−colour and colour−magnitude diagrams. We combine the ISOGAL catalogue with the data from surveys such as 2MASS and GLIMPSE. Interstellar extinction and distance were estimated using the red clump stars detected by 2MASS in combination with the isochrones for the AGB/RGB branch. Absolute magnitudes were thus derived and the stellar populations identified from their absolute magnitudes and their infrared excess. Results. A standard approach to analysing the ISOGAL disc observations has been established. We identify several hundred RGB/AGB stars and 22 candidate young stellar objects in the direction of this field in an area of 0.16 deg2. -
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 -
A Stripped Helium Star in the Potential Black Hole Binary LB-1 A
A&A 633, L5 (2020) Astronomy https://doi.org/10.1051/0004-6361/201937343 & c ESO 2020 Astrophysics LETTER TO THE EDITOR A stripped helium star in the potential black hole binary LB-1 A. Irrgang1, S. Geier2, S. Kreuzer1, I. Pelisoli2, and U. Heber1 1 Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander University Erlangen-Nuremberg (FAU), Sternwartstr. 7, 96049 Bamberg, Germany e-mail: [email protected] 2 Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany Received 18 December 2019 / Accepted 1 January 2020 ABSTRACT +11 Context. The recently claimed discovery of a massive (MBH = 68−13 M ) black hole in the Galactic solar neighborhood has led to controversial discussions because it severely challenges our current view of stellar evolution. Aims. A crucial aspect for the determination of the mass of the unseen black hole is the precise nature of its visible companion, the B-type star LS V+22 25. Because stars of different mass can exhibit B-type spectra during the course of their evolution, it is essential to obtain a comprehensive picture of the star to unravel its nature and, thus, its mass. Methods. To this end, we study the spectral energy distribution of LS V+22 25 and perform a quantitative spectroscopic analysis that includes the determination of chemical abundances for He, C, N, O, Ne, Mg, Al, Si, S, Ar, and Fe. Results. Our analysis clearly shows that LS V+22 25 is not an ordinary main sequence B-type star. The derived abundance pattern exhibits heavy imprints of the CNO bi-cycle of hydrogen burning, that is, He and N are strongly enriched at the expense of C and O. -
ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (A) Write out the Spectral Classes from Hottest to Coolest Stars. Broadly
ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (a) Write out the spectral classes from hottest to coolest stars. Broadly speaking, what are the primary spectral features that define each class? (b) What four macroscopic properties in a stellar atmosphere predominantly govern the relative strengths of features? (c) Briefly provide a qualitative description of the physical interdependence of these quantities (hint, don’t forget about free electrons from ionized atoms). 08.1.3 Luminosity Classes: (a) For an A star, write the spectral+luminosity class for supergiant, bright giant, giant, subgiant, and main sequence star. From the HR diagram, obtain approximate luminosities for each of these A stars. (b) Compute the radius and surface gravity, log g, of each luminosity class assuming M = 3M⊙. (c) Qualitative describe how the Balmer hydrogen lines change in strength and shape with luminosity class in these A stars as a function of surface gravity. 10.1.2 Spectral Classes and Luminosity Classes: (a,b,c,d) (a) What is the single most important physical macroscopic parameter that defines the Spectral Class of a star? Write out the common Spectral Classes of stars in order of increasing value of this parameter. For one of your Spectral Classes, include the subclass (0-9). (b) Broadly speaking, what are the primary spectral features that define each Spectral Class (you are encouraged to make a small table). How/Why (physically) do each of these depend (change with) the primary macroscopic physical parameter? (c) For an A type star, write the Spectral + Luminosity Class notation for supergiant, bright giant, giant, subgiant, main sequence star, and White Dwarf. -
A Secondary Clump of Red Giant Stars: Why and Where
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server A secondary clump of red giant stars: why and where L´eo Girardi Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, D-85740 Garching bei M¨unchen, Germany E-mail: [email protected] submitted to Monthly Notices of the Royal Astronomical Society Abstract. Based on the results of detailed population synthesis models, Girardi et al. (1998) recently claimed that the clump of red giants in the colour–magnitude diagram (CMD) of composite stellar populations should present an extension to lower luminosities, which goes down to about 0.4 mag below the main clump. This feature is made of stars just massive enough for having ignited helium in non- degenerate conditions, and therefore corresponds to a limited interval of stellar masses and ages. In the present models, which include moderate convective over- shooting, it corresponds to 1 Gyr old populations. In this paper, we go into∼ more details about the origin and properties of this feature. We first compare the clump theoretical models with data for clusters of different ages and metallicities, basically confirming the predicted behaviours. We then refine the previous models in order to show that: (i) The faint extension is expected to be clearly separated from the main clump in the CMD of metal-rich populations, defining a ‘secondary clump’ by itself. (ii) It should be present in all galactic fields containing 1 Gyr old stars and with mean metallicities higher than about Z =0:004.