main-sequence-part3

main-sequence-part3 - A due today ritiCal for these...

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Unformatted text preview: A due today ritiCal for these lectures .- ..9 and 10 in your text (Kutner) :1 14, S4 and 17 in the recommended book -' et al.) .9 ' Recitations Fri. March 18‘“, we will talk about/review stellar evolution NASA, NOAO, ESAand The Hubble Heritage Team (STSCI/ Main Sequence continued... (Kutner, Ch. 9; see also Canoll and Osllie, Ch. 10; Shu, Ch. 6, Hester el al. Ch. 14) AST 203 (Spring 2011) Triple-(x (Shu) Burning H to He only releases some of the binding energy available. What about the He? (uolssulsed/Elpedlml Average binding energy per nucleon (MeV) 30 60 90 120 150 180 210 240 27‘0 Number of nucleons ln nucleus AST 203 (Spring 2011) Triple-(x (Shu) Consider 4He 8'39 4H9 §He+§He—>§1Be+’y 8Be has less binding energy/ nucleon than the two alphas 8Be rapidly decays Salpeter & Hoyle: equilibrium— some 8Be always around. 0 Neutron (\Mkipedia) At p ~ 105 g cm'3,T ~ 108 K: one 8Be for every 109 4He nuclei: iBe + §He a 1620 —l— *y Net result is 3 3H6 —> 1gC + 27 This reaction is called the triple-alpha process. AST 203 (Spring 2011) Heavier Elements It is easy to imagine many other subsequent reactions. For example, we can make oxygen via: §He+ 13C a 130 +7 Two carbon nuclei can fuse to make magnesium: Simulation codes carry large reaction networks that evaluate the rates for all these reactions to determine what elements are synthesized as a function of T, density, and composition. AST 203 (Spring 2011) R- and S—Process If there are lots of neutrons around, heavy elements can be made Independent of T. Neutrons have no charge—no Coulomb barrier to overcome. Neutron is absorbed by a nucleus —> A increases by 1 baryon. Too many neutrons—it may become unstable to beta-decay. Lots of neutrons around—the nucleus may capture another neutron before it has time to beta decay. If the rate is slow, then the nucleus can decay first. High neutron flux: r-process elements synthesized (r for rapid). Low neutron flux: s-process elements synthesized (s for slow) Likely takes place in stellar explosions AST 203 (Spring 2011) Chart of Nuclides number of protons (Z) Seconds I) 1u+15 10-01 l10+10 10702 llU+UT 10-03 l10+05 1004 .101-04 10-05 .10+03 10706 10+02 10-0? 1mm 10715 10+00 < 10-15 UNKNOWN —> MS number of neutrons (N) (Taken from National Nuclear Data Center/BNL) Reaction Summary We call any element other than H and He a metal. We also refer to thermonuclear reactions as burning. As we burn heavier and heavier elements, we need higher temperatures to overcome the Coulomb barrier. Reaction rates are strongly sensitive to T—can be as T7 or T”! Gravity provides the mechanism to get the high T. The r- and s-processes are the primary means to produce nucleus heavier than the iron-peak elements. All of the heavy elements in our bodies are synthesized in stars. AST 203 (Spring 2011) Main Sequence As reactions take place in the star, its composition is changing Can affect spectral class and luminosity The star will evolve in the H-R diagram. The main-sequence is more of a band than a thin line. The line connecting the set of points where stars first appear on the main sequence is the zero-age main sequence or ZAMS. AST 203 (Spring 2011) Stellar Structure We apply the laws of physics as we understand them on earth to the Universe at large. We use computers to solve the equations describing a star and vary parameters (mass, composition, ...) to match the range of objects we observe. These models allow us to predict the path a star will take on the H-R diagram as it exhausts its hydrogen fuel and looks for other energy sources. AST 203 (Spring 2011) Stellar Structure Divide the star up into shells Look at the forces on each shell Follow the energy flow through each shell Yields the structure of the star. J’F‘FW‘W As we saw previously, the mass in a shell is just dM = 47rr2p(r)dr The rate at which mass changes through the shell is then just dM W : 47rr2p(r) AST 203 (Spring 2011) Stellar Structure This is the first equation of stellar structure—it is called the mass continuity equation. Statement of how the mass, M(r), interior to radius 1" changes with density. We already used MO") in computing gravity in a star. Unless there is some resistance to the gravitational pull, the star will collapse. AST 203 (Spring 2011) Hydrostatic Equilibrium Hydrostatic equilibrium: The weight of each layer is supported by the pressure difference across that layer. Applies to any gravitational stratified medium,. Consider a cylindrical element in our shell. The mass of the cylinder is dm : p(r) dr dA The gravitational force on that mass is just GM(r)dm (Hi/[(77) FG : r2 2 r2 p0“) d7“ dA F0 is negative because it is pointing down. AsT 203 (Spring 2011) Hydrostatic Equilibrium Pressure is just force/unit area The pressure force on the cylinder top is just FPVHdT : —P(r —l— dr)dA The pressure force on the cylinder bottom is F1377. = P(r)dA The net pressure force is then Fp : P(r)dA — P(r + dr)dA : [P(r) — P(r + dr)j dA Defining the pressure differential - dP E P(r + dr) — P(r) we have Fp = —dP dA AsT 203 (Spring 2011) FP,r—l—dr 6L dm FP,r—l—dr 9L dm Hydrostatic Equilibrium Hydrostatic equilibrium means no net acceleration, i.e., _ GM(r) T2 d7“ — Z 0 is just or F : ma dP _ GM(r) E _ — T2 Usually we define the local acceleration of gravity as GM (r) 90“) = T2 and we have dP E * —p(r)g(r) This is one of the fundamental equations of stellar structure. AST 203 (Spring 2011) Hydrostatic Equilibrium Hydrostatic equilibrium: everywhere in the star, the pressure gradient exactly balances the weight of the material above it. pressure —> The mum/ardm/sh gravity {—7 ofpressure. ‘ . V . preclse/y ‘ 1 1‘ """""" -- balances the ‘ inwa/d pull of ' gravity O..- . Pressure [5 greatest deep in tile Sun (from Benneu er a.) W ' Where Hie over/My I weight is greatest. AST 203 (Spring 2011) Hydrostatic Equilibrium Using HSE, we can estimate the central pressure in the Sun. The pressure gradient can be approximated simply as dP PC dT RQ (since the pressure at the _ _ surface of the star is 0) The graVItational force as GM(r) T2 W) N GMQ (MG) RE) RE; Together, we have AST 203 (Spring 2011) Central Pressure and EDS A more accurate calculation yields PC : 2.1 x 1017 dyn our2 Equation of state: relation connecting P to T and density An essential ingredient in any stellar model. Ideal gas law: P: flsznkT m Here, m is the average mass of the particles in the gas. Applicable when the 1) << 0 (non-relativistic) and the density is small, so quantum mechanical effects are not important. In high school chemistry, you may have used the gas constant, B = NAk: AST 203 (Spring 2011) Number Density vs. Mass Density We are used to mass density: mass M” volume V In Astronomy, we often encounter number density: number of particles N n : — : _ volume V we can relate the total mass, M, and the number of particles, N, as M : Nm, where m is the mass of a particle. AST 203 (Spring 2011) Central Temperature With the equation of state, we can estimate the central T: mPC TC : pk Considering just H at the center of the Sun, H is ionized, so the average mass per particle is 1 m m : §(mp+me) % 7” Taking the central density to be _ _ Me pa N p — (4/3)ng we have 3 TZWZ44X107K Mgk: AST 203 (Spring 2011) Central Temperature The actual value, from detailed models is 1.5 X 107 K. Difference results from more accurate central density, ,0C ~ 110p, better central P, and accounting for heavier ions in the center. This temperature is just right for H fusion via the p-p chain. Final piece: how energy is generated and transported through the layers of the star. We'll talk about the remaining ideas on stellar structure in conceptual terms. Your book goes deeper in this part. AsT 203 (Spring 2011) Energy Transport (Zelik and Smith Ch. 16) Conduction: atoms collide with nearby atoms, transport energy. No net movement of the atoms. Think about metals. In normal stars, atoms are too far apart for this to be an efficient. Convection: hot buoyant parcels of fluid rise upward/ cool parcels fall. The fluid exchanges its heat with the environment. Think of a hot air balloon rising. Requires a steep T gradient—occurs in a limited region in most stars. Radiative transport: photons scatter off of and are absorbed by the ions and atoms in the stellar interior. ln stars, the most important opacity processes are electron scattering (photons scattering off free electrons) and photoionization. AST 203 (Spring 2011) Stellar Structure A star's structure is governed by: Mass Continuity Hydrostatic Equilibrium: the pressure everywhere supports the weight of the material above it. Energy Transfer: Photons carry the energy outward from the center through absorption and re-emission (the random walk). lfthe luminosity is too large to be carried by photons, convection takes over. Energy Generation: Thermal equilibrium tells us that the energy carried outward by radiation and/or convection through any spherical surface is balanced by the thermonuclear energy release inside that surface. AST 203 (Spring 2011) Stellar Structure Stellar structure codes solve these equations, together with boundary conditions (P = 0 at the surface, L = 0 at the center, ...) to produce a model of a star at an instance in time, with a given mass and chemical composition. Stars are not static Nuclear reactions —> composition is changing. To chart the evolution of a star, the composition can be updated and a new stellar model can be produced This process is repeated over and over. AST 203 (Spring 2011) The Structure of the Sun Theoretical calculations of the Sun's structure match helioseismology observations. l ~ ; Ke l Key l — — - model i [GD Gala 10 radiation zons convection zcn a turn pc ralurc (K) density (glmnfl) : mmsclron zone a 031 D 0.2 0‘4 06 0.8 1.0 D 0.2 0.4 I 0.6 0.9 1.0 I’acnon or me Sun‘s radius traclion DI the SUITS radius (from Bennett el al.) cwrrghl mam m-ezn talc-um pub‘lermg 55 new Wade-v. Helioseismology: sun quakes—pressure waves that move through the Sun, from the deep interior to the surface. They can be measured via Doppler shifts. AST 203 (Spring 2011) (from Bennelt et al.) More on Fusion... We can create fusion on Earth: (XX-11 IW MIKE/DOE) The difference is that in the Sun, it is controlled thermonuclear fusion. The stability of the Sun's energy output is important for the existence of life on earth. AST 203 (Spring 2011) Equilibrium Why doesn't the Sun explode? AST 203 (Spring 2011) large rise m Siigh: rise in raie oi fusion Slig'll dec’ease in core temperalwe core temperature '\ ialge decrslaae ir- rate oi fusion Because the energy supply is diminished gravizy slarls in uvcrcumc Ihcrmai Solar Thermuslal: Gravilaliunul Equliibnum \ Increased energy a“ uulml enables |hermal pressuna |O mcmumc glavily. pressuta. increased Inermai pressure causes Ina Cure in expand and man can, which restores Iusnm rala lo nurmai value, 1‘ Gravlly ccmprasses ,- Ihemre, heals il up, mu resiures lusian rale la mrmai value-2‘ cmuw 020m Parana Emimmunoeringumn Wam‘ (from Benneu el al.) ...
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