Stellar Structure Section 6 Introduction to Stellar Evolution

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, 1950 s) 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 Teff 1. 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, Ann. Rev. Astroph 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 R 2 (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 -637 X/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