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Stellar Structure Section 6: Introduction to Stellar Evolution Lecture 14 – Main-sequence stellar structure: … mass dependence of energy generation, opacity,

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Presentation on theme: "Stellar Structure Section 6: Introduction to Stellar Evolution Lecture 14 – Main-sequence stellar structure: … mass dependence of energy generation, opacity,"— Presentation transcript:

1 Stellar Structure Section 6: Introduction to Stellar Evolution Lecture 14 – Main-sequence stellar structure: … mass dependence of energy generation, opacity, convection zones, density profile … mass limits … effects of composition changes Post-main-sequence evolution: … calculations and observational tests

2 Mass dependence of opacity and energy generation Central (and mean) temperature of a MS star increases with mass, though not strongly (T ~ M/R, R ~ M 0.6-0.8 ) Bound-free opacity (Kramers’) decreases with temperature, while electron-scattering stays constant, thus becoming relatively more important Energy generation increases with temperature – and CNO cycle much more sensitive than pp chain, so becomes more important Roughly speaking:  M > 1.5 M  : CNO cycle, Thomson scattering dominate  M < 1.5 M  : pp chain, bound-free absorption dominate Transition actually occurs gradually, at slightly different masses

3 Mass dependence of convection CNO cycle has much stronger T-dependence than pp chain, so central temperature gradient steeper in more massive stars Steep gradient unstable to convection → convective core (radiative core in less massive stars with pp chain) Less massive stars have cooler surfaces => ionisation zones in surface regions → convective envelopes (more massive stars ionised right to surface, so have radiative envelopes) Thus convective envelopes are deep at low mass, and shrink to nothing as mass increases, while convective cores grow with mass, from zero at about 1.1 M  (Handout 11, top) Note strong mass-dependence of the concentration of mass to the centre (50% of R contains ~95% M at Sun, <50% at 0.4 M  )

4 Mass dependence of central conditions Seen already that T generally increases slowly with mass – Handout 11 (foot) shows the detail – note the dramatic change of T with density for masses around the Sun Density decreases as mass increases (contributing to decrease of bound-free opacity) – but note almost constant central density (~100 g cm -3 ) over mass range 0.3 to 1.3 M  Ratio of central to mean density at Sun ~100 Radiation pressure increases gradually towards higher mass, and degeneracy towards lower mass

5 Mass limits ( see http://www.sheffield.ac.uk/mediacentre/2010/1713.html for details of R136a1)http://www.sheffield.ac.uk/mediacentre/2010/1713.html Lower mass limit for MS: ~0.08 M , caused by T being too low at centre for H fusion (some D fusion pre-main-sequence) Less massive stars simply cool slowly; seen as brown dwarfs (with degenerate cores, and surface molecules, such as methane); below ~17 Jupiter masses, usually classed as planets High mass limit less clear: cores of 50-100 M  have luminosities large enough for radiation pressure to stop further accretion, so this often taken as upper limit (also: pulsationally unstable) Recent VLT observations suggest more massive stars exist:  eclipsing binary NGC 3603-A1, masses 116 and 89 M  - consistent  R136a1, mass ~265 M , birth mass ~320 M  ! Sun R136a

6 Summary of basic picture For solar composition, model HR diagram agrees satisfactorily with observations, remembering that models are zero age and observed stars have range of ages – see blackboard sketch Changes in assumed composition of models cause small shifts in ZAMS, but little change in shape – see blackboard sketch, which implies giants cannot remain well-mixed as they evolve Theoretical M-L relation agrees reasonably with observation (Handout 2), despite small number of well-determined masses Switchover from convective to radiative envelopes seems to occur at about the right effective temperature, if we are interpreting spectra correctly

7 Post-main-sequence evolution Better understood than pre-MS evolution Pioneering calculations in 1950s and 1960s by 3 main groups:  Icko Iben (USA)  Rudolf Kippenhahn and collaborators (Germany)  Bohdan Paczynski and collaborators (Poland) Results agreed well, despite 3 independent computer codes Many other groups now active, from Switzerland to Japan to USA – results differ from each other only in detail: slightly different assumptions about equation of state, opacity, nuclear reaction rates, treatment of convection etc

8 Observational tests give additional confidence Many observational tests available for MS stars => firm foundation for post-MS studies MS lifetime >> pre-MS timescale => much more data available (even though star formation studies now observation-led) Post-MS timescale also nuclear (except for a few phases) – so again much more data than for pre-MS studies Two kinds of observational constraint  Statistical studies of large numbers of field stars (problem: selection effects, e.g. more luminous stars dominate sample)  Look at star clusters: stars all at ~same distance, and probably all of ~same age. See next lecture


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