DOCSLIB.ORG

Readingsample

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Readingsample Principles and Perspectives in Cosmochemistry Lecture Notes of the Kodai School on 'Synthesis of Elements in Stars' held at Kodaikanal Observatory, India, April 29 - May 13, 2008 Bearbeitet von Aruna Goswami, B. Eswar Reddy 1. Auflage 2010. Buch. x, 440 S. Hardcover ISBN 978 3 642 10351 3 Format (B x L): 15,5 x 23,5 cm Gewicht: 899 g Weitere Fachgebiete > Physik, Astronomie > Astronomie: Allgemeines > Astrophysik Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Nucleosynthesis of Low and Intermediate-mass Stars Amanda I. Karakas Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Weston Creek ACT 2611, Australia [email protected] Summary. The asymptotic giant branch (AGB) is the last nuclear-burning phase for low and intermediate-mass stars with initial masses between about 0.8 to 8 solar masses. The AGB phase of evolution is very short, comprising less than 1 per cent of the main-sequence lifetime, nevertheless, it is on the AGB that the richest nucleosynthesis occurs for this mass range. The nucleosynthesis is driven by thermal instabilities of the helium-burning shell, the products of which are dredged to the stellar surface by recurrent mixing episodes. Hot bottom burning occurs in the most massive AGB stars, and this also alters the surface composition. I review the evolution and nucleosynthesis from the main sequence through to the tip of the AGB. The nucleosynthesis that occurs during the AGB is explored in detail, including a discussion of the effects of hot bottom burning. I finish with a brief review of the slow-neutron-capture process that produces elements heavier than iron. Keywords: stars: AGB and post-AGB stars — planetary nebulae: general — nuclear reactions, nucleosynthesis, abundances 1 Introduction All stars in the mass range 0.8M to ∼ 8M, including our own Sun, will become asymptotic giant branch (AGB) stars (see Herwig [1] for a recent review). The AGB is the last nuclear burning phase of stellar evolution for this mass range, and is brief, lasting much less than 1% of the time spent during core hydrogen (H) burning on the main sequence. AGB stars are evolved objects and are found in the high-luminosity, low temperature region of the Hertzsprung-Russell (HR) diagram. AGB stars have evolved through core H and helium (He) burning and are now sustained against gravitational collapse by alternate H-shell and He-shell burning. The He-burning shell is thermally unstable and flashes or pulses every 104 years, depending on the stellar mass. AGB stars are often observed to be chemically different from their less evolved counterparts, and show enrichments in carbon and heavy elements synthesized A. Goswami and B.E. Reddy (eds.), Principles and Perspectives in Cosmochemistry, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-10352-0 2, c Springer-Verlag Berlin Heidelberg 2010 108 Amanda I. Karakas by the slow neutron-capture process (the s-process). AGB stars are observed with spectral classes M, MS, S, SC and C, where C-type stars are carbon- rich and have C/O ratios exceeding unity. AGB stars are observed to be long-period Mira, semi-regular or irregular variables with periods ≥ 100 days. Many AGB stars are also observed to be losing mass rapidly (typical mass- −5 −1 loss rates M˙ ∼ 10 M year ) through slow, dense outflows (velocities ∼ 10 km/second). After the ejection of the envelope, the AGB phase is terminated and the star quickly evolves (in ≈ 105 years) to become a post-AGB star, before finally ending its life as a dense white dwarf. For a review of the post- AGB and planetary nebulae phase of evolution, we refer to [2] and [3]. The range of bolometric luminosities and masses of AGB stars can be estimated from the large sample of long-period variables observed in the Large Magellanic Cloud (LMC). The luminosities range from Mbol ≈−3.8 to a maximum of ≈−7.1, that corresponds to current masses between about ≈ 1M to 8M [4]. In Figure 1 we show the colour-magnitude diagram (CMD) for the globular cluster M3. A CMD is just a type of HR diagram in which we use colour index rather than spectral class on the horizontal axis; and use the apparent visual magnitude, V , for the vertical axis. While most of the stars in Figure 1 are located on the main sequence, there are distinct bands to the top right of the diagram and an almost horizontal band above the main sequence. Each of these bands, including the main sequence, represents a distinct phase in the life of low to intermediate-mass stars. In the luminous red part of the diagram (top-right corner) there are a few AGB stars. Very few of the AGB stars in globular clusters are more luminous than the tip of the first giant branch which occurs at a bolometric luminosity of Mbol ≈−3.6[5]. AGB stars are particularly important because they are a significant site of nucleosynthesis. The nucleosynthesis during the AGB leads to the production of carbon, nitrogen, fluorine and heavy elements such as barium and lead. Recurrent mixing episodes bring the freshly synthesized material from the core to the envelope, and strong stellar winds ensure that this material is expelled into the interstellar medium (ISM). For these reasons, AGB stars are major factories for the production of the elements in the Universe [7,1]. Knowledge of AGB evolution and nucleosynthesis is vital to obtain an estimate of the contribution of low and intermediate-mass stars to the chemical evolution of galaxies and stellar systems such as M3. For example, a third of the carbon in our Galaxy today is estimated to have been produced in AGB stars [8]. In these lecture notes, we are primarily interested in the changes to the sur- face composition of low and intermediate mass stars during the AGB. Before we get to the AGB stage, it is necessary that we first examine the evolution and nucleosynthesis that occurs prior to the AGB and we cover this material in Sect. 3. AGB evolution is discussed next in Sect. 4, and the nucleosynthe- sis in Sect. 5. We briefly review the s-process in Sect. 6. We begin with some important preliminaries. Nucleosynthesis of Low and Intermediate-mass Stars 109 12 M3 AGB 141618 HB FGB V 2022 main sequence – 0.5 0 0.5 11.5 B–V Fig. 1. Colour-magnitude diagram for M3, using data from [6]. The approximate positions of the main sequence, first giant branch (FGB), horizontal branch (HB), and asymptotic giant branch (AGB) are labelled 2 Some preliminaries In the following lecture notes, it is assumed that the reader has an under- standing of the basics of stellar evolution and nucleosynthesis. We refer to other lectures given at the Kodai School, along with the following textbooks: Clayton [9], Rolfs & Rodney [10], and Iliadis [11] cover all aspects of nuclear astrophysics. Stellar interiors and evolution are covered by Hansen, Kawaler, & Trimble [12]. The chemical evolution of galaxies and stellar systems are discussed by Pagel [13], along with an overview of stellar evolution and nu- clear astrophysics. The topic of AGB stars is covered in detail in [14]. Lugaro [15] reviews stardust in meteorites, with an emphasis on pre-solar grains that originated in AGB stars. Before we begin, it is important to make a few definitions. In the following we will refer to low-mass stars as stars with initial masses between 0.8 to ∼ 2.25M,andintermediate-mass stars as stars with an initial masses be- tween 2.25 and ∼ 8M. Stars in the range 0.8M to 8M evolve through central hydrogen and helium burning and enter the AGB with an electron- degenerate carbon oxygen (C-O) core. The cores of these stars do not reach 110 Amanda I. Karakas the ≈ 800 million K temperatures required for carbon burning. Stars with initial masses between 9–11M may also become AGB stars after core carbon burning; these objects are referred to as super-AGB stars. Stars more massive than about 11M evolve through the central carbon, neon, oxygen and silicon burning stages and end their lives as core collapse supernovae. We do not dis- cuss these massive stars and refer the reader to the lecture notes by Arnould, see also Woosley, Heger, & Weaver [16] and references therein for details. The dividing mass which separates low and intermediate mass is not ar- bitrarily chosen but corresponds to the transition from degenerate to non- degenerate core helium ignition (which is at about 2.25M). The lower mass limit of 0.8M is the minimum mass required to ignite helium and evolve through central helium burning. The upper mass limit of 8M is the maxi- mum mass which avoids core carbon ignition. The mass ranges above are valid for stars with a composition similar to that of our Sun, which is composed of approximately 70% hydrogen by mass, 28% helium (or more precisely, 4He), and about 2% metals. The metal content is referred to as the global metal- licity, Z, and is comprised of about half 16O. Using the solar abundances of Anders & Grevesse [17], we obtain a global solar metallicity of Z =0.019. The revised solar abundances of Asplund, Grevesse & Sauval [18] has reduced the global metallicity to Z ≈ 0.015, primarily because the oxygen abundance of the Sun has been reduced by about a factor of ∼ 2[19].
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]
  • 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: [email protected] 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]
  • 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 .
    [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]
  • 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]
  • Pre-Main Sequence Star Is Optically Visible, but Has No Central Hydrogen Burning
    Definitions • A protostar is the object that forms in the center of a collapsing molecular cloud core, before it finishes the main accretion phase and becomes “optically visible". • A pre-main sequence star is optically visible, but has no central hydrogen burning. • A main sequence star is the result after subsequent contraction and significant increase in central density and temperature, when the star begins to burn hydrogen in its core. Trueism: Gravity always wins • Free-fall time = time for protostellar collapse 1/ 2 $ 3π ' t ff = & ) % 32Gρ( 7 −1/ 2 t ff = 3.4 ×10 n yrs n = 102 cm-3 => free-fall time = 3 x 106 yrs n = 106 cm-3 => free-fall time = 3 x 104 yrs • Too short!! What else can hold up the cloud? € 2 – Magnetic field threading the cloud has pressure Pmag = B /8π 2 – Turbulent velocities in cloud provide pressure Pturb ~ ρvturb Hosokawa Protostellar Infall dM/dt ~ M / tff core is isothermal (n è ∞ polytrope) until it becomes optically thick to own radiation, increasing central temperature. We have ideal gas at this stage, but not yet polytropic. M is increasing with time as object gains mass from infall. van der Tak * van der Tak Recall E = (4-3 γ)U van der Tak Time Scales and Luminosities (as usual, dynamical timescale is the shortest) 5 (few 10 years for 1 Mo) 7 (few 10 years for 1 Mo) (star evolves normally towards the main sequence) = Hosokawa Hosokawa Hosokawa (shock boundary condition) van der Tak van der Tak Hayashi Limit – The Classic Picture Pols Initial Radius – The Classic Picture 3/10 x x 3/10 (R = 36 Rsun at 1 Msun) However, protostellar accretion geometry and accretion history modifies this simple picture.
    [Show full text]
  • 1. Hydrostatic Equilibrium and Virial Theorem Textbook: 10.1, 2.4 § Assumed Known: 2.1–2.3 §
    1. Hydrostatic equilibrium and virial theorem Textbook: 10.1, 2.4 § Assumed known: 2.1–2.3 § Equation of motion in spherical symmetry d2r GM ρ dP ρ = r (1.1) dt2 − r2 − dr Hydrostatic equilibrium dP GM ρ = r (1.2) dr − r2 Mass conservation dM r =4πr2ρ (1.3) dr Virial Theorem 1 E = 2E or E = E (1.4) pot − kin tot 2 pot Derivation for gaseous spheres: multiply equation of hydrostatic equilibrium by r on both sides, integrate over sphere, and relate pressure to kinetic energy (easiest to verify for ideal gas). For next time – Read derivation of virial theorem for set of particles ( 2.4). – Remind yourself of interstellar dust and gas, and extinction§ ( 12.1). – Remind yourself about thermodynamics, in particular adiabatic§ processes (bottom of p. 317 to p. 321). Fig. 1.1. The HRD of nearby stars, with colours and distances measured by the Hipparcos satellite. Taken from Verbunt (2000, first-year lecture notes, Utrecht University). Fig. 1.2. Observed HRD of the stars in NGC 6397. Taken from D’Antona (1999, in “The Galactic Halo: from Globular Clusters to Field Stars”, 35th Liege Int. Astroph. Colloquium). Fig. 1.3. HRD of the brightest stars in the LMC, with observed spectral types and magnitudes transformed to temperatures and luminosities. Overdrawn is the empirical upper limit to the luminosity, as well as a theoretical main sequence. Taken from Humphreys & Davidson (1979, ApJ 232, 409). 2. Star formation Textbook: 12.2 § Jeans Mass and Radius 1/2 3/2 3/2 3/2 1/2 3 5k T 2 T n − MJ = 1/2 = 29 M µ− 4 3 , (2.1) 4π GµmH ρ ⊙ 10K 10 cm− 1/2 1/2 1/2 1/2 3 5k T 1 T n − RJ = 1/2 =0.30pc µ− 4 3 .
    [Show full text]
  • 4.2 Stellar Evolution After the Giant Branch
    I*M*P*R*S on ASTROPHYSICS at LMU Munich Astrophysics Introductory Course Lecture given by: Ralf Bender and Roberto Saglia in collaboration with: Chris Botzler, Andre Crusius-Wätzel, Niv Drory, Georg Feulner, Armin Gabasch, Ulrich Hopp, Claudia Maraston, Michael Matthias, Jan Snigula, Daniel Thomas Powerpoint version with the help of Hanna Kotarba Fall 2007 IMPRS Astrophysics Introductory Course Fall 2007 1 Chapter 4 Stellar Evolution IMPRS Astrophysics Introductory Course Fall 2007 2 4.1 Stellar evolution from the main sequence to the giant branch Immediately after the contraction phase during stellar formation (before nuclear burning sets in) stars have a homogeneous chemical composition. The location of the stars in the HRD where they for the first time start with nuclear fusion in hydrostatic equilibrium is called Zero Age Main Sequence (ZAMS) For the period of central hydrogen burning the stars remain on the main sequence near the ZAMS. As the chemical composition changes slowly, the main sequence is not a line but a strip. Massive metal rich stars (M > 20MΘ) in addition loose a significant fraction of their mass due to stellar winds, which moves them a large distance away from the ZAMS even during the hydrogen burning phase. (Lower mass stars also develop winds but only in the later phases of their evolution.) How does a star move ’inside’ the main sequence? As shown above we have: IMPRS Astrophysics Introductory Course Fall 2007 3 Evolutionary paths in the HRD up to the point where He burning sets in (from Iben 1967, ARAA 5). The shade of the line segments indicates the time spent in the corresponding phases.
    [Show full text]