Stellar Structure
Section 6: Introduction to Stellar Evolution
Lecture 13 – Overview
Pre-main-sequence evolution:
… Henyey track (purely radiative)
… surface boundary conditions
… Hayashi line; forbidden region
Outline of evolution from gas cloud to main
sequence (and links to simulations)
Overview
• MS stars: initially homogeneous composition, slow evolution of
composition until H exhausted
• Look later at what happens after H-burning: what happens
before H-burning?
• Have assumed no other nuclear reactions, and uniform
composition but little else – OK because MS evolution so slow it
is essentially independent of previous history, allowing MS and
pre-MS evolution to be studied separately
• Useful because ideas about pre-MS evolution took much longer
to develop – few observations (but many theories) until IR, mm
and sub-mm astronomy became possible
• Subject now largely observation-led; theory of earliest phases
still much more uncertain than of MS and post-MS phases
Pre-main-sequence evolution
• Omit very early phases: start when gas cloud becomes opaque
– proto-star
• Initial properties: large radius, low surface temperature, low
luminosity – lower RH corner of HR diagram
• Earliest calculations (Henyey et al, 1950s) assumed radiative
energy transport throughout slow (quasi-static) contraction to
main sequence; luminosity supplied by gravitational energy
• R decreases, L and Teff increase monotonically
• Henyey track:
L  Teff1.1
from detailed calculations
Was Henyey right?
• Homology argument (Handout 9) shows that Henyey’s result is
qualitatively what is expected for radiative proto-stars
• Implies that proto-star always less luminous than its final MS
luminosity
• But: luminosity during contraction determined by opacity – low
opacity means high radiation loss, supplied by gravitational
energy – contraction rate adjusts to balance luminosity
• MS luminosity determined by nuclear reaction rates –
completely different mechanism
• No reason for L(grav) to be always less than L(nuc)
• Is the radiative assumption correct?
Hayashi’s alternative
• Two problems with Henyey model:
 as T rises, cool molecular gas is dissociated, then ionised,
and  becomes low enough for convection to occur
 at surface, Hayashi (1961) found (see blackboard) that
radiation was escaping from a region where T >> Teff
• Radiation escapes easily because Teff low and H- absorption
dominates: opacity  T to positive power
• This situation requires the modified surface boundary
conditions of Section 4: T = Teff, P = g at M = Ms
• Models with these boundary conditions turn out to be largely
convective, and to have L >> LMS
Hayashi’s ‘forbidden region’
(Hayashi, AnnRevAstrAstroph 4, 171-192, 1966;
see also Kippenhahn & Weigert, pp.224-233)
• 3-page paper in 1961: there is a region in the HR diagram in which
no quasi-static models can exist (sketch on blackboard)
• Boundary (the Hayashi line) of this ‘forbidden region’ almost vertical
in HR diagram (Teff ~ 4000 K); locus of fully convective models
• No quasi-static models exist to the cool side of the Hayashi line
• Implies that quasi-static evolution confined to proto-stars on or to
the left of the Hayashi line, and that L  R2 (because Teff ≈
constant), so large proto-stars are very luminous: L >> LMS
Approach to main sequence
• On the Hayashi model, proto-stars start fully convective, but a
radiative core can develop (depends on mass), and grow to
make star fully radiative
• Final approach to MS is then along Henyey track (Handout 10,
top)
• Lowest mass stars remain fully convective right to the MS
• Using homology, can compare timescales for Hayashi and
Henyey tracks, from infinity to the point where they meet
• Assuming Kramers’ opacity, the Hayashi timescale is less than
half the Henyey timescale (because L is much larger)
Evolution through the ‘forbidden
region’
• Evolution on cool side of Hayashi line occurs, but on a
dynamical timescale (Handout 10, foot)
• Before gas cloud becomes opaque, it is cool and optically thin,
and collapsing in free fall: negligible internal pressure
• Stays cool because radiation escapes freely
• Once opaque, radiation trapped – moves to adiabatic collapse
• Core forms first, heated by trapped radiation
• Outer layers fall onto core, causing shock, more rapid heating,
molecular dissociation, H ionization and onset of convection
• Very fast evolution: ~20 years A to E, only ~100 days D to E
Pre-opaque phases?
• Perturbations in initial gas cloud cause condensations, which
start to contract under gravity
• Higher density => shorter dynamical timescale => higherdensity regions contract faster, enhancing density contrast
• Core-envelope structure forms (dense cores are observed)
• Complications:
 fragmentation
 non-spherical collapse (rotation, magnetic fields)
• Numerical simulations show filaments, knots, spirals, discs,
formation (and break-up) of binary and multiple systems
• Observations show discs, jets, cocoons of dust and gas
Links to numerical simulations – 1
http://iopscience.iop.org/0004-637X/707/2/1023/fulltext
Look at this from a computer on the university network, and you
should get free access. There are online animations in this
electronic version of the paper – this is a still from Animation 1
Links to numerical simulations – 2
http://www.ukaff.ac.uk/starcluster/
This site has excellent animations available – but beware of their
size, and read the copyright rules! Here is a small set of stills.
Turbulent cloud
Stars form
Stars ejected from cloud
Spirals and discs