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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 triplealpha 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 betadecay. 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: rprocess elements synthesized (r for rapid).
Low neutron flux: sprocess 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 1001
l10+10 10702
llU+UT 1003
l10+05 1004
.10104 1005
.10+03 10706 10+02 100? 1mm 10715 10+00 < 1015 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 sprocesses are the primary means to produce
nucleus heavier than the ironpeak 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 HR diagram. The mainsequence 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 zeroage 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
HR 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 (nonrelativistic) 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 pp 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 reemission (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 mezn talcum pub‘lermg 55 new Wadev. 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: (XX11 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 value2‘ cmuw 020m Parana Emimmunoeringumn Wam‘ (from Benneu el al.) ...
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 Simon,M
 Astronomy

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