Simple Seismic Tests of the Solar Core 1
|
|
- Sydney Roberts
- 6 years ago
- Views:
Transcription
1 DOE/ER/02A INT99-31 UF-IFT-HEP-99-7 July 1999 Simple Seismic Tests of the Solar Core 1 Dallas C. Kennedy Institute for Nuclear Theory, University of Washington and University of Florida ABSTRACT A model-independent reconstruction of hyostatic profiles (density, pressure) of the solar interior is outlined using the adiabatic sound speed and bouyancy frequency profiles. These can be inferred from helioseismology if both p- and g-mode frequencies are measured. With homology applied to the solar core only and some additional assumptions, but without a full solar model, the chemical profile of the evolved core can be deduced from the hyostatic profiles as well. Subject headings: Sun: abundances Sun: interior Sun: oscillations Submitted to Astrophysical Journal Letters Standard solar models (SSMs) are now very accurate, exemplified by the work of Bahcall et al. (Bahcall et al. 1998; Pinsonneault 1998; Bahcall 1999) and Turck-Chièze et al. (Brun et al. 1998). But confidence in predicted solar neutrino fluxes is enhanced by checks of the solar core independent of model details, depending on only a few general assumptions. This can be done with helioseismology, although the g-modes are needed. Serious claims of g-modes observations have been put forward (Hill & Gu 1990; Thomson et al. 1995) but remain controversial (Guenther & Sills 1995; Lou 1996). The Bahcall-Pinsonneault 1998 SSM is used here for specific numerical results. 1 Contribution to the INT Low-Energy Neutrino Physics Workshop, Univ. Washington, Seattle (June- September 1999).
2 2 We assume negligible radiation pressure P γ P gas and no significant departures from an ideal gas (P = P gas = ρrt/µ). Γ=dln P/dln ρ, Γ ad =( ln P/ ρ) ad, (1) = d ln T/dln P, ad =( ln T/ ln P ) ad. Γ ad = 5/3, ad = 2/5 for a monatomic gas. The Brunt-Väisälä (bouyancy) frequency N(r) : N 2 = g [1 λ P Γ 1 ] g = [ ad + µ ], λ 1 P = dln P/, (2) Γ ad λ P with µ = d ln µ/d ln P, is real for propagating g-waves, outside any convective zones. For the Sun, the base of the convective zone R CZ (0.71)R. The adiabatic square sound speed c 2 ad =Γ ad P/ρ. Adiabatic seismology here follows Unno et al. (1989), with some differences in notation. The seismic modes are labeled by radial index n (number of radial nodes) and angular indices l and m; frequencies degenerate in the last if rotation is ignored. The spectrum exhibits middle f (fundamental or n =0,l>1) modes and the p- (g-) modes rising above (falling below) the f mode in ν for n>0, l>0. For large n, thep-andg-modes are concentrated near the surface and the center, respectively. Their frequencies ν p and ν g are ν 1 p (n, l) 2 n + 1 l(l +1) 2 R 0 c ad (r), ν g (n, l) l(l +1) 2nπ 2 RCZ 0 r N(r), (3) for large n. (lcannot be large in ν p.) A large set of measured frequencies allow reconstruction of the c ad (r) andn(r) profiles. Let Ω g the second integral in (3). 1. Some Tests of Hyostatic Equilibrium Correct prediction of the ν g (n, l), n 1, would rule out central convection, although the Sun is not far from this state ( 1.1M ), as N 2 < 0 otherwise (Kippenhahn & Weigert 1990). Present helioseismic data rule out the Γ = 5/3 convective polytrope almost to the center (Basu et al. 1997; Christensen-Dalsgaard 1997). A second test: dc 2 ad = gγ ad (1 1 ) P + Γ ρ dγ ad, 1 1 Γ = µ. (4) In addition, assume dγ ad / = 0 in the core and a non-singular mass distribution, so that g = Gm/r 2 =(4πG/3)ρ c r 0asr 0. (5)
3 3 Thus dc 2 ad(0)/ must vanish. A third test: assume a hyostatic unperturbed state with no convection (N 2 > 0or Γ<Γ ad ). Hyostatic equilibrium, dp = ρg = Gmρ r 2, (6) with 4πr 2 ρ = dm/, implies a static unperturbed state, the simplest case. But a more complex unperturbed state can include a non-zero steady velocity field v 0, taken here as radial for simplicity. Ignoring rotation and magnetic effects, also calculable, the correction linear in v 0 to frequency ν(n, l) is the expectation value in the (n, l) modeofk r v 0 /2π, with k r = radial wavenumber. The related length scale R /few for low-n modes, but for high-n g-modes, is the central scale R 0 : R 2 0 =3P c /2πGρ 2 c, with R 0 /R = 0.12 for the present SSM (Kennedy & Bludman 1999). For large n, k r n R 0 Ω g 8π3 ρ c G 3 ( 1 1 ) Γ c Γ ad. (7) A conservative relative measurement error for ν g is 0.003, while the theoretical uncertainty Thus a direct bound of the core v 0 < 2πν g(n, l)/k r ( msec 1 ) l(l+1)/n 2, or 120 m sec 1 for l =1,n= 30, is feasible, independent of azimuthal splitting by m Mechanical Profiles The N(r) andc ad (r) profiles are sufficient to reconstruct the mechanical (hyostatic) profiles. N(r) anddc ad (r)/ are proportional, either one controlling the ν g : dc ad (r) N(r)/2 = Γ ad /Γ(r) 1 [ 1 1 ] Γad. (8) Γ(r) Assuming dγ ad / = 0, Γ satisfies a quaatic equation, (1 + D)Γ 2 (2 D Γ ad )Γ + 1 = 0, D(r) = [ ] 2 2 dcad (r)/, (9) Γ ad N(r) 2 This is too large by about 10 7 to detect directly the heavy element mixing invoked to solve the solar neutrino deficit (Cumming & Haxton 1996), although such mixing is disfavored by the measured c ad profile (Bahcall et al. 1997).
4 4 with one physical root, Γ(r) = 2 D(r) Γ ad + [2 D(r) Γ ad ] 2 4[1 + D(r)] 2[1 + D(r)]. (10) Thus the Γ(r) profile is reconstructible with N(r) and a numerical derivative of c ad (r). The mass and pressure profiles then follow: Gm(r) = r2 dc 2 ad(r)/ Γ ad [1 1/Γ(r)] 4πGρ c = 6 dc2 ad (0)/2 Γ ad (1 1/Γ c ) P (r) = ρ(r) c2 ad (r), Γ ad,, (11) where ρ(r) is obtained from m(r). Note that m>0forr>0asγ>1ifdc 2 ad/ < 0 and Γ < 1ifdc 2 ad / > 0, the present SSM inner core being an example of the latter case. Dimensionless structure in terms of homology variables can also be derived (Kennedy & Bludman 1999). 3. Chemical Profile of the Evolved Solar Core As the SSM evolves, falls while µ increases from zero, the core becoming more concentrated. Helioseismology is adiabatic and non-evolutionary and thus cannot give the T or chemical profiles without a detailed solar model. However, many SSM core features can be understood via mechanical-thermal core homology without a detailed model (Bludman & Kennedy 1996). Homology applied to the core only is valid for power-law opacity and luminosity generation and does not require a polytrope, not even approximately valid for the present SSM core. Unlike ordinary homology, which relates stars of different mass and luminosity, core homology varies the core properties of one star, leaving the total luminosity and mass fixed. The homology in reality in violated somewhat, as the exponents are not constant and the luminosity is not exclusively produced by one reaction chain. Assume luminosity in equilibrium, with power-law dependences: in erg gm 1 sec 1, ε = ε o ρ λ T η ; and luminosity transported by radiative diffusion, with opacity in cm 2 gm 1 κ = κ o ρ n T s. Reasoning similarly to Section 3 of Bludman & Kennedy (1996) yields the scaling laws r η s+3λ+3n ε o κ o µ η s 4 m η s+λ+n 2, (12)
5 5 µ f [ µ +1 1/Γ] ε o κ o ρ g (c 2 ad) f, (13) f =3 η+s, g = n+λ+1, (14) where (12) is dimensional only (correcting an error in Bludman & Kennedy 1996), and (13) keeps separate track of derivatives. Γ ad is assumed constant. Equation (13) is best solved as a differential equation using the mechanical profiles gleaned in Section 2. The boundary conditions at the core edge are µ µ ZAMS 1.26 and µ = 0. A complication arises from the chemical dependencies of ε o and κ o. With H, He, and metal mass fractions X, Y,and X i, ε o X 2, κ o (1 + X)[X + Y + i X i Z 2 i /A i ], 1 µ = X + Y 4 + i X i A i, (15) A i = nuclear mass number, Z i = nuclear charge number (Kippenhahn & Weigert 1990). X + Y + i X i = 1, and the SSM implies i X i 0.02, although the metal contribution to κ o is non-negligible (Bahcall 1989; Böhm-Vitense 1992) and has to be treated separately by hand. With ρ, P,andµknown, T follows. CNO-dominated fusion can be ruled out, as it would raise, not lower, neutrino fluxes (Bahcall 1989). For ppi-dominated luminosity and realistic OPAL opacity, λ = 1, η = 4, n = 1/2, and s = 5/2 are reasonable approximations (see Böhm-Vitense 1992, Rogers 1994, Iglesias & Rogers 1996, and Bludman & Kennedy 1996 for details), yielding f = 3/2 and g = 5/2. 4. Summary Some solar core tests are proposed, independent of model details. Measured p- and g-modes are needed to reconstruct c 2 ad(r) andn 2 (r). Absence of core convection implies N 2 > 0 in (2) and the existence of ν g (n, l) for high n (3). A non-singular mass distribution implies vanishing of the sound speed slope (4) at the center (5). The high-n ν g can set a direct limit O(10 2 )msec 1 on a central velocity field. Assuming a constant Γ ad allows reconstruction of the solar interior mechanical structure (10-11). Chemical and thermal structure reconstruction requires more detailed assumptions or a full solar model. But many model results are derivable from a simple homology construction applied to the core alone (12-15), with fixed solar mass and luminosity. Truly independent tests of thermal structure and chemical evolution require comparison with other Sun-like stars, in particular via asteroseismology (Deubner et al. 1998). With the appropriate changes, the method outlined here can be used to analyze such stars as well.
6 6 The author thanks John Bahcall (Institute for Advanced Study) and Marc Pinsonneault of (Ohio State Univ.) for the BP98 model tables and Jørgen Christensen-Dalsgaard (Aarhus Univ.) for helioseismic data. This work is partly based on research done in collaboration with Sidney Bludman (Univ. Pennsylvania and DESY) and was supported by the Department of Energy under Grant Nos. DE-FG06-90ER40561 at the Institute for Nuclear Theory (Univ. Washington) and DE-FG05-86ER40272 at the Institute for Fundamental Theory (Univ. Florida). REFERENCES Bahcall, J. N. 1989, Neutrino Astrophysics (Cambridge: Cambridge University Press) Bahcall, J. N. 1999, URL jnb/sndata/solarmodels.html Bahcall, J. N., Basu, S., & Pinsonneault, M. H., 1998, Phys. Lett. B433, 1 Bahcall, J. N., Pinsonneault, M. H., Basu, S., & Christensen-Dalsgaard, J. 1997, Phys. Rev. Lett. 78, 171 Basu, S. et al. (BiSON/LOWL) 1997, Mon. Not. R. Astron. Soc. 292, 243 Bludman, S. A. & Kennedy, D. C. 1996, ApJ 472, 412 Böhm-Vitense, E. 1992, Introduction to Stellar Astrophysics, vol. 3 (Cambridge: Cambridge University Press) Brun, A. S., Turck-Chièze, S., & Morel, P. 1998, ApJ 506, 913 Christensen-Dalsgaard, J. 1997, in T. R. Bedding, A. J. Booth, & J. Davis, eds., Proc. IAU Symp. No. 189 (Dorecht: Kluwer Academic) Cumming, A. & Haxton, W. C. 1996, Phys. Rev. Lett. 77, 4286 Deubner, F.-L., Christensen-Dalsgaard, J., & Kurtz, D., eds., 1998, Proc. IAU Symp. No. 185 (Dorecht: Kluwer Academic) Guenther, D. B. & Sills, K. 1995, in A. B. Balantekin & J. N. Bahcall, eds., Proc. Solar Modeling Workshop, INT, Univ. Washington (Singapore: World Scientific) Hill, H. A. & Gu, Y.-M. 1990, Science in China A37, 854 Iglesias, C. A. & Rogers, F. J. 1996, ApJ 464, 943 Kennedy, D. C. & Bludman, S. A. 1999, ApJ 525(2) Kippenhahn, R. & Weigert, A. 1990, Stellar Structure and Evolution (Berlin: Springer- Verlag)
7 7 Lou, Y.-Q. 1996, Science 272, 521 Pinsonneault, M. H. 1998, private communication Rogers, F. J. 1994, in G. Chabrier & E. Schatzman, eds., Proc. IAU Colloq. No. 147 (Cambridge: Cambridge University Press) Thomson, D. J. et al. 1995, Nature 376, 139 Unno, W., Osaki, Y., Ando, H., Saio, H., & Shibahashi, H. 1989, Nonradial Oscillations of Stars, 2nd ed. (Tokyo: University of Tokyo Press) This preprint was prepared with the AAS L A TEX macros v4.0.
Solar Seismic Model and the Neutrino Fluxes
Solar Seismic Model and the Neutrino Fluxes K. M. Hiremath Indian Institute of Astrophysics Bangalore-560034, India H. Shibahashi and M. Takata University of Tokyo, Japan 4/19/2006 1 Plan of the talk Introduction
More informationThe new solar abundances - Part II: the crisis and possible solutions
Comm. in Asteroseismology Vol. 147, 2006 The new solar abundances - Part II: the crisis and possible solutions J.Montalbán 1, A. Miglio 1, S. Théado 1, A. Noels 1, N. Grevesse 1,2 1 Institut d Astrophysique
More informationThe effect of turbulent pressure on the red giants and AGB stars
Astron. Astrophys. 317, 114 120 (1997) ASTRONOMY AND ASTROHYSICS The effect of turbulent pressure on the red giants AGB stars I. On the internal structure evolution S.Y. Jiang R.Q. Huang Yunnan observatory,
More informationAsteroseismic Study of Red Giant ɛ Ophiuchi
Research in Astron. Astrophys. 2010 Vol. XX No. XX, 000 000 http://www.raa-journal.org http://www.iop.org/journals/raa Research in Astronomy and Astrophysics Asteroseismic Study of Red Giant ɛ Ophiuchi
More informationSeismology of the Solar Convection Zone. Sarbani Basu & Η. Μ. Antia Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay
J. Astrophys. Astr. (1994) 15, 143 156 Seismology of the Solar Convection Zone Sarbani Basu & Η. Μ. Antia Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005 Received 1993 October
More informationA Vivace Introduction to Solar Oscillations and Helioseismology
A Vivace Introduction to Solar Oscillations and Helioseismology Matthew Kerr Department of Physics University of Washington Nuclear Astrophysics, 2007 Outline 1 Introduction and Motivation 2 Non-radial
More informationWhat does helioseismology tell us about the Sun?
What does helioseismology tell us about the Sun? Jørgen Christensen-Dalsgaard Department of Physics and Astronomy, University of Aarhus & Danish AsteroSeismology Centre (DASC) Sir Arthur Stanley Eddington:
More informationFundamental Stellar Parameters. Radiative Transfer. Stellar Atmospheres
Fundamental Stellar Parameters Radiative Transfer Stellar Atmospheres Equations of Stellar Structure Basic Principles Equations of Hydrostatic Equilibrium and Mass Conservation Central Pressure, Virial
More informationThe Standard Solar Model. PHYSUN L'Aquila
The Standard Solar Model Aldo Serenelli Max Planck Institute for Astrophysics PHYSUN L'Aquila 16-17 October, 2008 Outline Overview of Standard Solar Model - BPS08 Two solar compositions SSM, solar compositions
More informationarxiv:astro-ph/ v2 24 May 1998
How Uncertain Are Solar Neutrino Predictions? John N. Bahcall 1 and Sarbani Basu 2 arxiv:astro-ph/9805135v2 24 May 1998 School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540
More information2. Equations of Stellar Structure
2. Equations of Stellar Structure We already discussed that the structure of stars is basically governed by three simple laws, namely hyostatic equilibrium, energy transport and energy generation. In this
More informationarxiv: v1 [astro-ph] 3 Jul 2008
Transiting Planets Proceedings IAU Symposium No. 253, 2008 c 2008 International Astronomical Union DOI: 00.0000/X000000000000000X Measurements of Stellar Properties through Asteroseismology: A Tool for
More informationHelioseismology and screening of nuclear reactions in the Sun. Abstract
INFNFE-05-00 Helioseismology and screening of nuclear reactions in the Sun G. Fiorentini (1,2), B. Ricci (1,2) and F.L. Villante (1,2) (1) Dipartimento di Fisica dell Università di Ferrara,I-44100 Ferrara,
More informationPast, Present, and Future of Solar Neutrino Physics
Past, Present, and Future of Solar Neutrino Physics A.B. Balantekin University of Wisconsin SMU ebubble Workshop January 22, 2008 ...to see into the interior of a star and thus verify directly the hypothesis
More informationTHIRD-YEAR ASTROPHYSICS
THIRD-YEAR ASTROPHYSICS Problem Set: Stellar Structure and Evolution (Dr Ph Podsiadlowski, Michaelmas Term 2006) 1 Measuring Stellar Parameters Sirius is a visual binary with a period of 4994 yr Its measured
More informationASTR 1040 Recitation: Stellar Structure
ASTR 1040 Recitation: Stellar Structure Ryan Orvedahl Department of Astrophysical and Planetary Sciences University of Colorado at Boulder Boulder, CO 80309 ryan.orvedahl@colorado.edu February 12, 2014
More informationEquations of Stellar Structure
Equations of Stellar Structure Stellar structure and evolution can be calculated via a series of differential equations involving mass, pressure, temperature, and density. For simplicity, we will assume
More informationASTM109 Stellar Structure and Evolution Duration: 2.5 hours
MSc Examination Day 15th May 2014 14:30 17:00 ASTM109 Stellar Structure and Evolution Duration: 2.5 hours YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY
More informationIntroduction. Stellar Objects: Introduction 1. Why should we care about star astrophysics?
Stellar Objects: Introduction 1 Introduction Why should we care about star astrophysics? stars are a major constituent of the visible universe understanding how stars work is probably the earliest major
More information9.1 Introduction. 9.2 Static Models STELLAR MODELS
M. Pettini: Structure and Evolution of Stars Lecture 9 STELLAR MODELS 9.1 Introduction Stars are complex physical systems, but not too complex to be modelled numerically and, with some simplifying assumptions,
More informationSummary of stellar equations
Chapter 8 Summary of stellar equations Two equations governing hydrostatic equilibrium, dm dr = 4πr2 ρ(r) Mass conservation dp dr = Gm(r) r 2 ρ Hydrostatic equilibrium, three equations for luminosity and
More informationModeling sub-giant stars. Fernando Jorge Gutiérrez Pinheiro Centro de Astrofísica da Universidade do Porto ESO Visiting Scientist
Modeling sub-giant stars Fernando Jorge Gutiérrez Pinheiro Centro de Astrofísica da Universidade do Porto ESO Visiting Scientist ESO (Santiago), 9th of April of 2008 In collaboration with: J. Fernandes
More informationStandard Solar Models
Nuclear Physics B (Proc. Suppl.) 77 (1999) 64 72 Standard Solar Models John N. Bahcall a a Institute for Advanced Study, Princeton, NJ 08540 I review recent developments that affect standard solar model
More informationAsteroseismology of Red Giants. Josefina Montalbán Université de Liège
Asteroseismology of Red Giants Josefina Montalbán Université de Liège Stellar oscillations Oscillation mode Variations of v r : spectroscopy Variations of luminosity: photometry Basic properties Lamb Frequency:
More informationStar Formation and Protostars
Stellar Objects: Star Formation and Protostars 1 Star Formation and Protostars 1 Preliminaries Objects on the way to become stars, but extract energy primarily from gravitational contraction are called
More informationarxiv: v1 [astro-ph.sr] 27 Apr 2009
Bull. Astr. Soc. India (0000) 00, 000 000 arxiv:0904.4101v1 [astro-ph.sr] 27 Apr 2009 The quest for solar gravity modes: probing the solar interior Savita Mathur Indian Institute of Astrophysics, Bangalore
More informationStellar models for a wide range of initial chemical compositions until helium burning
ASTRONOMY & ASTROPHYSICS NOVEMBER I 1997, PAGE 439 SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 125, 439-443 (1997) Stellar models for a wide range of initial chemical compositions until helium burning
More informationProbing Stellar Structure with Pressure & Gravity modes the Sun and Red Giants. Yvonne Elsworth. Science on the Sphere 14/15 July 2014
Probing Stellar Structure with Pressure & Gravity modes the Sun and Red Giants Yvonne Elsworth Science on the Sphere 14/15 July 2014 Evolving stars are building blocks of the galaxy and their cores are
More informationSeminar: Measurement of Stellar Parameters with Asteroseismology
Seminar: Measurement of Stellar Parameters with Asteroseismology Author: Gal Kranjc Kušlan Mentor: dr. Andrej Prša Ljubljana, December 2017 Abstract In this seminar I introduce asteroseismology, which
More informationarxiv:astro-ph/ v2 16 May 2005
What Is The Neon Abundance Of The Sun? John N. Bahcall Institute for Advanced Study, Einstein Drive,Princeton, NJ 08540 arxiv:astro-ph/0502563v2 16 May 2005 Sarbani Basu Department of Astronomy, Yale University,
More informationPhysics 576 Stellar Astrophysics Prof. James Buckley. Lecture 11 Polytropes and the Lane Emden Equation
Physics 576 Stellar Astrophysics Prof. James Buckley Lecture 11 Polytropes and the Lane Emden Equation Reading/Homework Assignment Makeup class tomorrow morning at 9:00AM Read sections 2.5 to 2.9 in Rose
More informationarxiv:hep-ph/ v1 16 May 1997
Solutions to the Solar Neutrino Anomaly Naoya Hata 1 and Paul Langacker 2 1 Institute for Advanced Study Princeton, NJ 08540 2 Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania
More informationNuclear Reactions and Solar Neutrinos ASTR 2110 Sarazin. Davis Solar Neutrino Experiment
Nuclear Reactions and Solar Neutrinos ASTR 2110 Sarazin Davis Solar Neutrino Experiment Hydrogen Burning Want 4H = 4p è 4 He = (2p,2n) p è n, only by weak interaction Much slower than pure fusion protons
More informationarxiv:astro-ph/ v1 4 Jul 2004
Helioseismological Implications of Recent Solar Abundance Determinations John N. Bahcall Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 arxiv:astro-ph/0407060 v1 4 Jul 2004 Sarbani Basu
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON PHYS3010W1 SEMESTER 2 EXAMINATION 2014-2015 STELLAR EVOLUTION: MODEL ANSWERS Duration: 120 MINS (2 hours) This paper contains 8 questions. Answer all questions in Section A and
More informationDetection of MeV scale neutrinos and the solar energy paradigm
Journal of Physics: Conference Series PAPER OPEN ACCESS Detection of MeV scale neutrinos and the solar energy paradigm To cite this article: Aldo Ianni 2018 J. Phys.: Conf. Ser. 940 012023 View the article
More informationPAPER 68 ACCRETION DISCS
MATHEMATICAL TRIPOS Part III Tuesday, 2 June, 2009 9:00 am to 11:00 am PAPER 68 ACCRETION DISCS There are THREE questions in total Full marks can be obtained by completing TWO questions The questions carry
More informationQUANTITATIVE ANALYSIS OF THE OSCILLATION SPECTRUM OF BOOTIS
The Astrophysical Journal, 612:454 462, 2004 September 1 # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A. QUANTITATIVE ANALYSIS OF THE OSCILLATION SPECTRUM OF BOOTIS D.
More informationPhysics 576 Stellar Astrophysics Prof. James Buckley. Lecture 10
Physics 576 Stellar Astrophysics Prof. James Buckley Lecture 10 Reading/Homework Assignment Makeup class tomorrow morning at 9:00AM Read sections 2.5 to 2.9 in Rose over spring break! Stellar Structure
More informationAy 1 Lecture 8. Stellar Structure and the Sun
Ay 1 Lecture 8 Stellar Structure and the Sun 8.1 Stellar Structure Basics How Stars Work Hydrostatic Equilibrium: gas and radiation pressure balance the gravity Thermal Equilibrium: Energy generated =
More informationSPA7023P/SPA7023U/ASTM109 Stellar Structure and Evolution Duration: 2.5 hours
MSc/MSci Examination Day 28th April 2015 18:30 21:00 SPA7023P/SPA7023U/ASTM109 Stellar Structure and Evolution Duration: 2.5 hours YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL
More informationPAPER 58 STRUCTURE AND EVOLUTION OF STARS
MATHEMATICAL TRIPOS Part III Monday, 31 May, 2010 1:30 pm to 4:30 pm PAPER 58 STRUCTURE AND EVOLUTION OF STARS Attempt no more than THREE questions. There are FOUR questions in total. The questions carry
More informationMass-Radius Relation: Hydrogen Burning Stars
Mass-Radius Relation: Hydrogen Burning Stars Alexis Vizzerra, Samantha Andrews, and Sean Cunningham University of Arizona, Tucson AZ 85721, USA Abstract. The purpose if this work is to show the mass-radius
More informationOverview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy. PHY 688, Lecture 5 Stanimir Metchev
Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy PHY 688, Lecture 5 Stanimir Metchev Outline Review of previous lecture Stellar atmospheres spectral lines line profiles; broadening
More informationPHYS 633: Introduction to Stellar Astrophysics
PHYS 6: Introduction to Stellar Astrophysics Spring Semester 2006 Rich Townsend (rhdt@bartol.udel.edu Convective nergy Transport From our derivation of the radiative diffusion equation, we find that in
More informationUpdated solar models ASTRONOMY AND ASTROPHYSICS. P. Morel 1,J.Provost 1, and G. Berthomieu 1
Astron. Astrophys. 327, 349 360 (1997) ASTRONOMY AND ASTROPHYSICS Updated solar models P. Morel 1,J.Provost 1, and G. Berthomieu 1 Département Cassini, UMR CNRS 6529, Observatoire de la Côte d Azur, BP
More informationCOX & GIULI'S PRINCIPLES OF STELLAR STRUCTURE
COX & GIULI'S PRINCIPLES OF STELLAR STRUCTURE Extended Second Edition A. Weiss, W. Hillebrandt, H.-C. Thomas and H. Ritter Max-Planck-lnstitut fur Astrophysik, Garching, Germany C S P CONTENTS PREFACE
More informationarxiv:astro-ph/ v1 9 Oct 2002
Submitted on December 3, 2017 The Y 2 Stellar Evolutionary Tracks Sukyoung K. Yi arxiv:astro-ph/0210201v1 9 Oct 2002 University of Oxford, Astrophysics, Keble Road, Oxford OX1 3RH, UK yi@astro.ox.ac.uk
More informationNumerical techniques. Chapter Difference equations
Chapter 6 Numerical techniques The differential equations (4.61), (4.62) and (4.64), in combination with boundary conditions such as equations (4.65) (4.68), constitute a two point boundary value problem.
More informationLinear Theory of Stellar Pulsation
Linear Theory of Stellar Pulsation Mir Emad Aghili Department of Physics and Astronomy, University of Mississippi, University, MS, 38677 Introduction The first pulsating star to be discovered was omicron
More informationPhysics 556 Stellar Astrophysics Prof. James Buckley
hysics 556 Stellar Astrophysics rof. James Buckley Lecture 8 Convection and the Lane Emden Equations for Stellar Structure Reading/Homework Assignment Read sections 2.5 to 2.9 in Rose over spring break!
More informationarxiv: v1 [astro-ph.sr] 12 Sep 2011
Mon. Not. R. Astron. Soc. 000, 1 6 (2011) Printed 4 September 2017 (MN LaT E X style file v2.2) Frequency dependence of the large frequency separation of solar-like oscillators: Influence of the Helium
More informationGlobal parameters and evolutionary sequences
CoRoT/ESTA - Model Comparison - Task 1 Global parameters and evolutionary sequences Monteiro M.J.P.F.G. (Porto), Castro M. (Toulouse), Christensen-Dalsgaard J. (Aarhus), Cunha M.S. (Porto), Degl Innocenti
More informationThe structure and evolution of stars
The structure and evolution of stars Lecture 7: The structure of mainsequence stars: homologous stellar models 1 Learning Outcomes Student will learn: How to employ approximate forms for the three equations
More informationOpacity. requirement (aim): radiative equilibrium: near surface: Opacity
(Gray) Diffusion approximation to radiative transport: (assumes isotropy valid only in the deep stellar interior) - opacity is a function of frequency (wave length ). - aim: to reduce the (rather complex)
More informationarxiv:astro-ph/ v1 27 Jan 2004
Updated Toulouse solar models including the diffusioncirculation coupling and the effect of µ-gradients arxiv:astro-ph/0401568 v1 27 Jan 2004 Olivier Richard GRAAL UMR5024, Université Montpellier II, CC072,
More informationdp dr = ρgm r 2 (1) dm dt dr = 3
Week 5: Simple equilibrium configurations for stars Follows on closely from chapter 5 of Prialnik. Having understood gas, radiation and nuclear physics at the level necessary to have an understanding of
More informationStellar Structure. Observationally, we can determine: Can we explain all these observations?
Stellar Structure Observationally, we can determine: Flux Mass Distance Luminosity Temperature Radius Spectral Type Composition Can we explain all these observations? Stellar Structure Plan: Use our general
More informationAstronomy 112: The Physics of Stars. Class 14 Notes: The Main Sequence
Astronomy 112: The Physics of Stars Class 14 Notes: The Main Sequence In the last class we drew a diagram that summarized the basic evolutionary path of stars, as seen from their centers. In this class
More informationDiffusion and helioseismology
Diffusion and helioseismology Jørgen Christensen-Dalsgaard Institut for Fysik og Astronomi, Aarhus Universitet & Danish AsteroSeismology Centre (DASC) Eddington (1926): The internal constitution of the
More informationThe physics of red-giant oscillations
The physics of red-giant oscillations Marc-Antoine Dupret University of Liège, Belgium The impact of asteroseismology across stellar astrophysics Santa Barbara, 24-28 oct 2011 Plan of the presentation
More informationarxiv:astro-ph/ v1 15 Feb 2004
Mon. Not. R. Astron. Soc. 000, 000 000 (0000) Printed 13 May 2017 (MN LATEX style file v2.2) Asteroseismic determination of helium abundance in stellar envelopes arxiv:astro-ph/0402360v1 15 Feb 2004 Sarbani
More informationarxiv:astro-ph/ v1 18 Jul 2002
Helioseismology Jørgen Christensen-Dalsgaard High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, USA, Teoretisk Astrofysik Center, Danmarks Grundforskningsfond, and Institut
More informationResearch paper assignment
Research paper assignment Review of research that interests you, more focused than discussions in class Include references and figures Final format should be PDF (try LaTeX!) Concise! < 5000 words Steps:
More informationThe sun shines 3.85e33 erg/s = 3.85e26 Watts for at least ~4.5 bio years
The sun shines 3.85e33 erg/s = 3.85e26 Watts for at least ~4.5 bio years 1 2 SOHO, 171A Fe emission line 3 4 and its all nuclear physics: 1905 Einstein finds E=mc 2 1920 Aston measures mass defect of helium
More informationThe structure and evolution of stars. Introduction and recap
The structure and evolution of stars Lecture 3: The equations of stellar structure 1 Introduction and recap For our stars which are isolated, static, and spherically symmetric there are four basic equations
More informationEffects of errors in the solar radius on helioseismic inferences
Mon. Not. R. Astron. Soc. 298, 719 728 (1998) Effects of errors in the solar radius on helioseismic inferences Sarbani Basu School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton
More information4p 4 He + 2e + +2ν e. (1)
1 SOLAR NEUTRINOS Revised September 2001 by K. Nakamura (KEK, High Energy Accelerator Research Organization, Japan). 1. Introduction: The Sun is a main-sequence star at a stage of stable hydrogen burning.
More informationSolar Neutrinos and The Sun NEUTEL 11 Venice 15/03/11
Solar Neutrinos and The Sun NEUTEL 11 Venice 15/03/11 A. Serenelli Outline Update on Solar models: abundances and nuclear reaction rates Solar neutrino fluxes from neutrino data: can neutrinos disentangle
More informationConvection and Other Instabilities. Prialnik 6 Glatzmair and Krumholz 11 Pols 3, 10
Convection and Other Instabilities Prialnik 6 Glatzmair and Krumholz 11 Pols 3, 10 What is convection? A highly efficient way of transporting energy in the stellar interior Highly idealized schematic.
More informationDegeneracy and the mode classification of adiabatic oscillations of stars
Degeneracy and the mode classification of adiabatic oscillations of stars Masao Takata Department of Astronomy, University of Tokyo October 26, 2011 Introduction: mode classification and identification
More informationAstronomy 310/510: Lecture 2: In stars, hydrostatic equilbrium means pressure out cancels gravity in.
Astronomy 310/510: Lecture 2: Newton s laws, his second law in particular: F = ma. If a = 0, then no net forces act. In stars, hydrostatic equilbrium means pressure out cancels gravity in. When pressure
More informationConvection. If luminosity is transported by radiation, then it must obey
Convection If luminosity is transported by radiation, then it must obey L r = 16πacr 2 T 3 3ρκ R In a steady state, the energy transported per time at radius r must be equal to the energy generation rate
More informationMetallicities in stars - what solar neutrinos can do
- what solar neutrinos can do Institute for Nuclear and Particle Physics, Technical University Dresden, 01069 Dresden, Germany E-mail: zuber@physik.tu-dresden.de New elemental abundance determinations
More informationHomologous Stellar Models and Polytropes
Homologous Stellar Models and Polytropes Main Sequence Stars Stellar Evolution Tracks and Hertzsprung-Russell Diagram Star Formation and Pre-Main Sequence Contraction Main Sequence Star Characteristics
More informationREVIEWS OF MODERN PHYSICS, VOLUME 74, OCTOBER 2002
REVIEWS OF MODERN PHYSICS, VOLUME 74, OCTOBER 2002 Helioseismology Jørgen Christensen-Dalsgaard High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado 80307; and Teoretisk
More informationEstimate of solar radius from f-mode frequencies
A&A manuscript no. (will be inserted by hand later) Your thesaurus codes are: 09(06.15.1; 06.18.2) ASTRONOMY AND ASTROPHYSICS 1.2.2008 Estimate of solar radius from f-mode frequencies H. M. Antia Tata
More informationdp dr = GM c = κl 4πcr 2
RED GIANTS There is a large variety of stellar models which have a distinct core envelope structure. While any main sequence star, or any white dwarf, may be well approximated with a single polytropic
More informationASTEROSEISMIC ANALYSIS OF THE CoRoT TARGET HD 49933
The Astrophysical Journal, 780:15 (10pp), 014 January 10 C 014. The American Astronomical Society. All rights reserved. Printed in the U.S.A. doi:10.1088/0004-637x/780//15 ASTEROSEISMIC ANALYSIS OF THE
More informationarxiv: v2 [astro-ph] 16 Jul 2008
Astronomy & Astrophysics manuscript no. SV07v9 c ESO 2008 July 16, 2008 arxiv:0806.0235v2 [astro-ph] 16 Jul 2008 Asteroseismology of solar-type stars: signatures of convective and/or helium cores. M. Soriano
More informationThe Importance of Realistic Starting Models for Hydrodynamic. Simulations of Stellar Collisions
The Importance of Realistic Starting Models for Hydrodynamic Simulations of Stellar Collisions Alison Sills Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT, 06520-8101, USA James
More informationThe Sun. The Sun. Bhishek Manek UM-DAE Centre for Excellence in Basic Sciences. May 7, 2016
The Sun Bhishek Manek UM-DAE Centre for Excellence in Basic Sciences May 7, 2016 Outline 1 Motivation 2 Resume of the Sun 3 Structure of the Sun - Solar Interior and Atmosphere 4 Standard Solar Model -
More information11 Neutrino astronomy. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1
11 Neutrino astronomy introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 11.1 The standard solar model As we discussed in stellar evolution III, to obtain a reliable model for the sun, we
More informationHomologous Stellar Models and Polytropes
Homologous Stellar Models and Polytropes Main Sequence Stars Stellar Evolution Tracks and Hertzsprung-Russell Diagram Star Formation and Pre-Main Sequence Contraction Main Sequence Star Characteristics
More informationD. Cardini, R. Ventura, G. Catanzaro, C. Barban,T. R. Bedding, J. Christensen- Dalsgaard, J. De Ridder, S. Hekker, D.Huber, T. Kallinger,A.
Maria Pia Di Mauro INAF-IASF Roma (Italy) D. Cardini, R. Ventura, G. Catanzaro, C. Barban,T. R. Bedding, J. Christensen- Dalsgaard, J. De Ridder, S. Hekker, D.Huber, T. Kallinger,A. Miglio, J. Montalban,
More informationLecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses
Lecture 1 Overview Time Scales, Temperature-density Scalings, Critical Masses I. Preliminaries The life of any star is a continual struggle between the force of gravity, seeking to reduce the star to a
More informationLecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses. I. Preliminaries
I. Preliminaries Lecture 1 Overview Time Scales, Temperature-density Scalings, Critical Masses The life of any star is a continual struggle between the force of gravity, seeking to reduce the star to a
More informationNeutrinos and Solar Metalicity
Neutrinos and Solar Metalicity The solar abundance problem and CN neutrinos Measurement opportunities Wick Haxton INT 8 June 2015 The Standard Solar Model Origin of solar neutrino physics: desire to test
More informationOscillations of the Sun: insights and challenges for the future
Mem. S.A.It. Vol. 74, 564 c SAIt 2003 Memorie della Oscillations of the Sun: insights and challenges for the future M. P. Di Mauro 1 and L. Paternò 2 1 INAF-Osservatorio Astrofisico di Catania via S. Sofia
More informationarxiv:astro-ph/ v1 10 Nov 2005
10,000 Standard Solar Models: a Monte Carlo Simulation John N. Bahcall 1 and Aldo M. Serenelli Institute for Advanced Study, Einstein Drive,Princeton, NJ 08540 and arxiv:astro-ph/0511337 v1 10 Nov 2005
More informationPHAS3135 The Physics of Stars
PHAS3135 The Physics of Stars Exam 2013 (Zane/Howarth) Answer ALL SIX questions from Section A, and ANY TWO questions from Section B The numbers in square brackets in the right-hand margin indicate the
More informationROTATING LOW-MASS STELLAR MODELS WITH ANGULAR MOMENTUM REDISTRIBUTION
ROTATING LOW-MASS STELLAR MODELS WITH ANGULAR MOMENTUM REDISTRIBUTION Luiz Themystokliz Sanctos Mendes Electronics Engineering Department, Universidade Federal de Minas Gerais Belo Horizonte (MG), Brazil
More informationEquations of linear stellar oscillations
Chapter 4 Equations of linear stellar oscillations In the present chapter the equations governing small oscillations around a spherical equilibrium state are derived. The general equations were presented
More informationAsteroseismology of delta Scuti stars - a parameter study and application to seismology of FG Virginis
Asteroseismology of delta Scuti stars - a parameter study and application to seismology of FG Virginis Matthew Templeton, Sarbani Basu, and Pierre Demarque Astronomy Department, Yale University, P.O. Box
More informationPre Main-Sequence Evolution
Stellar Astrophysics: Stellar Evolution Pre Main-Sequence Evolution The free-fall time scale is describing the collapse of the (spherical) cloud to a protostar 1/2 3 π t ff = 32 G ρ With the formation
More informationEVOLUTION OF STARS: A DETAILED PICTURE
EVOLUTION OF STARS: A DETAILED PICTURE PRE-MAIN SEQUENCE PHASE CH 9: 9.1 All questions 9.1, 9.2, 9.3, 9.4 at the end of this chapter are advised PRE-PROTOSTELLAR PHASE SELF -GRAVITATIONAL COLL APSE p 6
More informationPhases of Stellar Evolution
Phases of Stellar Evolution Phases of Stellar Evolution Pre-Main Sequence Main Sequence Post-Main Sequence The Primary definition is thus what is the Main Sequence Locus of core H burning Burning Process
More informationAstrophysics II. Ugeseddel nr. 2.
Jørgen Christensen-Dalsgaard jcd@phys.au.dk 5 eptember 013. The lectures in Q1 take place Mondays 10:15 1 and Thursdays 14:15-16:00. The Exercises will be on Wednesdays 14:15-17:00. Brandon Tingley will
More informationVII. Hydrodynamic theory of stellar winds
VII. Hydrodynamic theory of stellar winds observations winds exist everywhere in the HRD hydrodynamic theory needed to describe stellar atmospheres with winds Unified Model Atmospheres: - based on the
More informationarxiv:astro-ph/ v1 18 Apr 2006
Neutrino-Dominated Accretion Models for Gamma-Ray Bursts: Effects of General Relativity and Neutrino Opacity Wei-Min Gu, Tong Liu, and Ju-Fu Lu arxiv:astro-ph/0604370v1 18 Apr 2006 Department of Physics
More information