Transcript Powerpoint of lecture 16

Stellar Structure
Section 6: Introduction to Stellar Evolution
Lecture 16 – Evolution of core after S-C instability
Formation of red giant
Evolution up giant branch
He ignition (low-mass stars: He flash)
Asymptotic giant branch
Double-shell source stars
Thermal pulsing and mixing
Evolution beyond He-burning
Evolution after S-C instability
• Initial core collapse catastrophic – but heating destroys
isothermality, internal pressure gradients build up and core
contraction slows to thermal timescale, with slow release of
gravitational energy
• H-shell very T-sensitive – acts as thermostat:
 if shell contracts, T rises,  grows, causing further T rise
and raising thermal pressure – shell expands again
 if shell expands, T drops → Pthermal drop and contraction
• Hence Tshell ~ constant => rshell ~ constant
• Effect driven by need for Lshell to balance Lsurface
Consequence of constant shell
radius
• Shell radius ‘wants’ to be
constant
• But core inside it is contracting
• This requires the envelope to
expand, to compensate – star
becomes a giant
• L ~ constant (at Lshell), and L 
R2Teff4, so Teff drops as star
expands – becomes red giant
Expansion on thermal timescale, implies evolution across HR
diagram very fast: accounts for Hertzsprung gap
Stars of lower mass
• S-C instability operates in stars with ~2 < M/M < ~6
• Lower-mass stars: isothermal core becomes degenerate
before S-C limit reached, giving extra pressure support
and preventing collapse – can be understood qualitatively
using scaling arguments (see blackboard sketch):
 Boyle’s law: P  +1/R3
 Self-gravity: P  Ω  -M2/R4
 Degeneracy: P  5/3  +M5/3/R5
• Core still contracts on thermal timescale, so thermostatic
effect of shell still causes (slower) envelope expansion
Evolution to the giant branch
• Star evolves on thermal timescale of core
• Higher-mass stars: L roughly constant (Hertzsprung gap)
• Lower-mass stars: L increases, Teff still decreases
• When star reaches Hayashi line, it can’t cross it into
‘forbidden region’
• Again need improved surface boundary conditions
• Star develops deep convective envelope (as in pre-MS)
• Unlike pre-MS star, has a nuclear source, so now moves up
the Hayashi line: the red giant branch (RGB) (Handout 13)
Evolution up the giant branch
• Core shrinks, T rises until He can burn
• He ignition depends strongly on mass:
 M > 2.3 M: core still ideal gas, ignition occurs quietly, at
centre; H-burning continues in shell; star stops climbing RGB
 M < 2.3 M: core has become degenerate, and ignition is
explosive (see blackboard) – helium flash
• Post He-flash: T rises fast until Pion ~ Pel, then Ptot rises, core
expands and cools, settles to steady burning
• Star survives explosion, but moves rapidly in HR diagram from
top of RGB to horizontal branch – see blackboard sketch
He burning and after
• Steady core He burning, star in equilibrium, as on MS
• Timescale for He-burning much shorter than for H-burning,
because burning rate much faster
• After He exhausted at centre (Yc = 0), all stars climb giant
branch again, approaching it asymptotically from somewhat
higher temperatures: Asymptotic Giant Branch (AGB)
• Detailed behaviour depends on mass (Handout 14)
• Shell burning continues on AGB, both He and H: doubleshell source stars
Thermal pulses and mixing
• Shell burning thermally unstable → burning alternating
between H and He shells (discovered numerically ~1965)
• Instability causes
 thermal pulses of luminosity
 mixing of processed material to surface (convective envelope
outside H shell, plus convection between shells)
• Processed material seen in observations
 Excess of C: ‘carbon stars’, with C/O ~ 2-5 (MS: ~0.5)
 Isotope anomalies: 12C/13C ~ 10-20 (solar system ~90;
CNO cycle in equilibrium ~4)
• Later evolution depends crucially on core mass
Post-He-burning – 1 (no WD remnant)
Main Sequence mass > 8 M
• Nuclear burning continues beyond C, mainly by addition of He
nuclei to form O, Ne, Mg, Si etc, as far as Fe: limit of ‘free’ energy
• Core partially supported by degenerate electrons – some electrons
in high-energy states may be captured by Ne or Mg nuclei
• Pressure drops, core cannot support itself, collapses
catastrophically (timescale: 10s of milliseconds!) to nuclear
densities, and bounces, leading to outward-travelling shock wave
• Shock also accelerated by pressure of neutrinos, produced in
explosive nucleosynthesis generated by energy of collapse
• Leads to ejection of outer layers (~90% of mass of star) – Type II
supernova (may leave compact core → NS or BH – see later)
Explosive nucleosynthesis (formation
of elements heavier than iron)
• Very high densities favour neutronisation: e- + p+ → n + 
(Normally, neutron is unstable, timescale ~900 s)
• Neutrino flux helps to accelerate shock
• Neutron flux allows rapid neutron addition to Fe and heavier
elements, forming n-rich nuclei
• Addition very fast compared to -decay timescale – elements
produced called r-process elements (r for rapid) – seen in
supernova remnants
• (AGB evolution: much smaller neutron flux available, n-addition
occurs on timescale long compared to -decay timescale – forms
n-poor nuclei by s-process (s for slow) – s-process elements
seen in atmospheres of red giants and supergiants)
Post-He-burning – 2 (produces WD)
Main Sequence mass < 8 M
• Neutrino processes cool centre, inhibiting C ignition
(needs T ~ 5108 K)
• Degenerate core:
 pure helium (low initial mass)
 He, C, O mixture (higher initial mass)
• On AGB, substantial mass loss by stellar winds (and possibly
thermal pulses) – helps to prevent core heating to C ignition
• Finally, a “superwind” (observed, not understood) ejects entire
outer envelope as coherent shell, revealing hot interior
• Hot remnant ionizes shell → planetary nebula
• Star then cools and fades → white dwarf star (Handout 15)