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Unformatted text preview: Binary Evolution (Kulner, Ch. 12; see also Shu, Ch. 10) AST 203 (Spring 2011) Tidal Forces About 1/2 of all stars are in binary systems. During stellar evolution, interactions between the stars that can
lead to interesting (and explosive) results. Close binary system: a system where one star is able to affect
the evolution of its companion. Gravitational forces between the stars can distort their shapes This is a tidal effect—the gravitational force from the companion
star pulls more on the near side of the star than the far side. AST 203 (Spring 2011) Tidal Forces (Shu cn.10)
Close binaries —> tidal distortions ; 2 (Sm)
dissipate energy /_ \‘\\/O<\ tidal
. _ 1 . _____ __3 _‘.,3 __ l friction
Orbits become Circular \ diss‘iSSuon
Stars always show the same face 2 4 to one another (tidally locked) 4
This IS an equilibrium configuration. ﬂox circulmbit 1030+0103 and Switch to a frame that rotates with \01 syncggﬁized
the system—no motion seen \4 /
No reason for further adjustment. 9 Figure 10.6. When two stars are separated by a distance which
is not much greater than their individual sizes, tidal forces can
raise bulges in the stars. The tidal interactions lead to a slow
change of the orbit shape and the spin rates of the stars. Except
in very unusual circumstances, the long-term evolution tends to bring the system to a state of circular orbits and synchronized
SplIlS. AST 203 (Spring 2011) Equipotentials Consider gravitational force
between the stars + centrifugal _ Equipmema‘s
force (in the rotating frame). Effective gravitational
acceleration is normal to the
equipotentials. ylfa + bl Moving along equipotentials
requires no work. Gravitational acceleration =
gradient of the potential 1&0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
xlfa-i—b) AST 203 (Spring 2011) Equipotentials Gravity dominates near stars Equipotentials Equipotentials spherical
centered on the star Force points inward. Centrifugal force dominates
far from stars. yfia + b) Roche lobe: each half of the
figure-8 The earth-moon system L1 point I
is 84% of the way to the moon. " AsT 203 (spring 2011) Hydrostatic Equilibrium (Shu Ch. 10) Equipotentials: surfaces of constant P Along equipotentials: No effective gravitational force
Nothing to resist a pressure imbalance Horizontal hydrostatic equilibrium. An overpressure expands until P is constant along
equipotentials. HSE says that density must be constant along equipotentials
Shape of star matches equipotentials. AST 203 (Spring 2011) Classification of Binaries
More massive star leaves MS first. R can exceed Roche lobe when red giant
Material flows past the L1 point onto a
Binary system classification: Detached: both stars smaller than Roche
lobes. Interact via gravity only. semi-detached
Semi-detached: one star fills its Roche lobe. Mass can flow to companion. 9
Contact: both stars fill (or exceed) their Roche lobes. Can have a common contact
envelope surrounding both stars. AST 203 (Spring 2011) Binary Evolution Depending on its mass, the first star to evolve off the main
sequence becomes a white dwarf, neutron star, or black hole. Now our binary system is a normal star and a compact object. This is not all that unusual—look at Sirius. Interesting things can happen when the other star evolves. Star fills its Roche lobe —> mass can flow through the L1 point.
Conservation of angular momentum —> accretion disk. AST 203 (Spring 2011) Binary Evolution Very complicated system. Both disk and central star
exhibit activity Hot spot can form where the
mass transfer stream
intersects the disk. (ouvcid '2 KNBH 'v pyma) If the compact object is a... White dwarf: novae and Type la supernovae can result.
Neutron star: X-ray bursts can result.
Black hole: we may see X-ray emission from the accretion disk. We'll consider each of these in turn. AST 203 (Spring 2011) ...
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This note was uploaded on 05/04/2011 for the course AST 203 taught by Professor Simon,m during the Spring '08 term at SUNY Stony Brook.
- Spring '08