Great Migrations

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Lecture 02, ASTB21
Preliminaries from Ch.1 of the green
book(1) 1. Reasons for assuming spherical
symmetry of a star F_centrif / F_grav
1e-5 2. Reasons for defining r and m as two
equivalent choices of an independent variable
in a spherical star concentration in the
center 3. What do we observe? Distance to the
star d pc from geometry Flux on Earth L/(4
pi d2) gt L (luminosity of a star) From
spectrum, T_eff (that blackbody would emit),
e.g. T_eff5780 K
for the sun Stephan-Boltzmann law gt R (stellar
radius) e.g. 0.7mln km
in rare instances, can measure R directly
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Finally, we measure periods P and orbit sizes a
(semi-major axis) in binary stars gt masses M
from Keplers law 4. What are the observed
L(M) functions? L M3 (high mass), M5 (low
mass) fig1.6 5. Reasons for assuming uniform
composition described by mass fractions X, Y,
Z of H, He, and the metals (XYZ1) Q1 Is
chemistry similar everywhere in the star? Q2 Is
chemistry similar everywhere in the galaxy?
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IMPORTANT DIGRESSION On the similarities of
chemical composition of most pop. I
stars Observations show that many stars are
surrounded by dust and sometimes detectable gas,
in the form of the so-called debris disks or
replenished dust disks, originally called
Vega-type disks. The Sun has a zodiacal light
disk, which is a week manifestation of the same
phenomenon. Beta Pictoris (or b Pic, beta Pic)
is the most prominent one. Its a disk around a
nearby star of spectral type A5V, 1.75 times more
massive than the sun, and only 20 Myr old. The
disk is seen almost edge-on, and extends to gt1000
AU from the star. It is made of solid bodies of
different sizes dust, sand, pebbles,, comets,
planets(?)
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Beta Pictoris, I-band
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Beta Pictoris
B Pic sky(?)
Dust
Dust absent around star (30 AU)
10000 x more comets asteroids than our solar
system now
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comet
Beta Pic
Variable absorption line due to comets head
wavelength
Absorption line variability in the b Pic spectrum
shows that comets of solar abundance of metals
sometimes evaporate near the star
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A rock is a rock is a rock But which one
is from the Earth? Mars? Beta Pic?? Its hard
to tell from spectroscopy, or even close up! Why?
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EQUILIBRIUM COOLING SEQUENCE
Chemical unity of nature and its all thanks to
stellar nucleosynthesis and mixing in ISM!
Silicates
silicates
T(K)
What minerals will precipitate from
a solar-composition, cooling gas? Mainly
Mg/Fe-rich silicates water ice. Planets are
made of those
ices
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Silicates with different crystallinity have been
found in all of these objects. They are like
those found on Earth, regarding chemical
composition and apearence.
Source P. Kalas
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Does this mean we are going to see the same
minerals and the same (H_2 O) rivers in
other worlds?
?
despite the substantial disagreement in types of
orbits and mass of planets.
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Marcy and Butler (2003)
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Lecture L2 agenda Whats inside a star?
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N-body dynamics
Astrophysics of Stars
Stellar Astrophysics
Dynamics of a star Hydrodynamics and
hydrostatics
Gen.Rel.
Radiation transfer
High ener. physics
Thermodynamics of gas
atmospheres
Nuclear physics
Astronomyobservations of stars
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ODEs (ordinary diff. Eqs.) OF 1-D
HYDRODYNAMICS (1) Continuity equation dm
4 pi rho r2 dr m m( r ) mass inside
radius r, dm mass of a layer. (3) Equations of
motion (momentum) Newtons 2nd law Dv/Dt
forces where D/Dt d/dt v grad (1) energy
equation Du/Dt
where u is internal energy /dm (1)
constitutive relations, EOS PP(rho,T) In
general, these are 6 equations for 6 unknowns
rho, T, P, v_x, v_y, v_z (or similar velocity
coordinates) unless gas consists of many
species then more eqs. vars are needed, but a
similar equality holds. Q Does that imply that
these ODEs always have solutions?
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ENERGY EQUATION heat absorption mechanical
work gt internal energy change EQUATION OF
MOTION acceleration dm gravity pressure
force
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The virial theorem total internal en. -(1/2)
tot. grav.energy or total energy (1/2)
tot. grav.energy
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How astrophysical estimates are made The trick
is to get an order-of-magnitude estimates (i.e.,
approximation to with a factor of 10) from the
equations governing the structure of a star.
These equations are typically ODEs (ordinary
differential eqs.) that contain terms like
dP/dr This derivative can be estimated as
dP/dr P(R) - P(0)/(R - 0) Notice that this
would be an exact expression for the
derivative if pressure P were falling from a
large P(0) in the center to P(R)0 at the surface
as a strait line section (linearly). Linear
approximation is not necessarily accurate, but
it needs not to be here. Plugging dP/dr
-P(0)/R into the hydrostatic radial
force equation 0 -Gltm/r2gt -(1/ltrhogt) dP/dr,
and replacing the average gas density ltrhogt with
estimate M/V M/((4/3) pi R3) and ltm/r2gt with
M/R2, we finally arrive at P(0) GM2/R4,
which gives 450 mln atm for the center of the sun.
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(for M 2e33 g 3e30 kg 1 M_sun and R 0.7e6
km) Summary of estimates of central pressure
0.5e9 atm average temperature 4e6 K (hot!)
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Final remark
I would like to remind you that this is a
fast-moving course. Reading ahead from
Prialniks book is essential. Only then will you
be able to focus during the lecture, not on
notation or copying strange-looking things, but
on pointers to which things in the book are most
important, comments widening the scope of the
text etc. And youll have many relevant questions
concepts not clear yet from the book or lecture.
So, please do yourself a big favor and BEFORE
every lecture read the new chapter from the
textbook once. (If you dont have any clue about
what to read, or have questions than please
contact the TA or myself during our office
hours.). Home assignements will be distrbuted
every week to every other week. Happy reading,
and looking forward to your questions!