ASTC22. Lecture L14

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ASTC22. Lecture L14 The formation of the Local
Group
Jacobi radius in flat-Vc galaxies Chemical
evolution models G-dwarf problem
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Computation of Roche lobe in R3B (Restricted 3
Body) equations of motion ( , a
semi-major axis of the binary)




Point masses only!
L
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Jacobi radius rJ We consider one large and one
small, massive stellar systems, circling each
other. The larger one might represent the Milky
Way, the small either a globular cluster, or a
dwarf galaxy merging with the Galaxy. The
derivation of tidal radius proceeds along the
lines of the Roche lobe size derivation in R3B
(see Lecture 11). One difference is that force of
the Galaxy is not 1/r2. Three forces acting
on a test particle placed at the Lagrange point
L1 are summed up and equated with zero two
gravitational pulls toward the two
massive bodies, plus the centrifugal force.
Lets denote as r_J the Jacobi or tidal radius
(m2-L1 distance), and as r_0 the distance
between bodies 1 and 2 point L1 is then at r
r_0 - r_J (we count the r from body m1). (1)
force from body 1 -G M(r_0 - r_J) /(r_0 -
r_J)2 -GM(r_0)/r_02 (1 r_J/r_0)
where we took into account M(r_0-r_J) M(r_0)
(1 - r_J/r_0) in a flat-Vc galaxy. (2) force
from body 2 Gm/ r_J2 (3) centrifugal force
v_c2 /(r0-r_J) GM(r_0)/r_02 (1 -
r_J/r_0) because this force is a constant
rotation speed Omega2 times the distance r, so
its linearly scaling with r, thus being (1-
r_J/r_0) times smaller at L1 than at
rr_0. Dividing by the unit force (acceleration)
GM(r_0)/r_02 we obtain, equating the sum of the
three terms to zero, and denoting xr_J/r_0, and
M_0M(r_0), we obtain -(1 x) (m/M_0)/x2
(1 - x) 0, therefore 2x (m/M_0)/x2, or
r_J/r_0 m/(2M_0)(1/3) Example globular
cluster mass 1e6 M_sun, Galactic bulge mass
1e10 M_sun gt r_J r_0 (500.333)1e-2 0.04.
Stars beyond 0.04r_0 from the globular cluster
are evaporating.
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M31 Andromeda galaxy
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Local Group Only 3 spirals Only 1 elliptical
(!) Lots of dwarf, irregular galaxies How did
they form?
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Z 1000 epoch of recombination
beginning of structure/galaxy/clusters
formation At t0.3 Myr after Big Bang,
the electron opacity of plasma drops a lot,
because of recombination of p and e into H. The
universe becomes transparent, loses radiation
pressure support. Z 6.5 epoch of first
star formation
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Metallicity - age relation for F-stars in the
solar neighborhood heavy element enrichment with
time, but also a great scatter above the lower
envelope...
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Closed-box model of heavy element enrichment of
ISM/stars
definitions
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Def.!
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Consider some gas turned into stars, and at the
same time enriched in heavy elements by dying
stars
chain differentiation rule
change input - output of Mh
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Like in a closed-box model, metallicity Z is
lower in regions where gas content is lower
(LMC, dwarf Irr, or outer radii of M33)
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So far so good...
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but lets compute in our closed-box the mass of
stars with metallicity less than a given
value Z
(observations give 10 times fewer low-Z stars)
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LMC Large Magellanic Cloud, a neighbor bound to
the Milky Way
Rotation speed 80 km/s
SMC Small Magellanic Cloud
No rotation
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Fornax dwarf spheroidal galaxy
Foreground MW star
Know the differences between dwarf ellipticals,
dwarf spheroidals, and dwarf irregulars (read
Ch.4 of textbook)!