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The Main Sequence. Projects. Evolve from initial model to establishment of H burning shell after core H exhaustion At minimum do z=0, z=0.1solar, z=solar, z=2solar for z=2solar use hetoz = 2.0 and 3.0 (see genex) Note features in the HR diagram and identify with physical processes
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Projects • Evolve from initial model to establishment of H burning shell after core H exhaustion • At minimum do z=0, z=0.1solar, z=solar, z=2solar • for z=2solar use hetoz = 2.0 and 3.0 (see genex) • Note features in the HR diagram and identify with physical processes • Compare results from different metallicity and YHe
What should a star spend most of its time doing? • 1H4He q>10xq for any other stage, lowest threshold T, largest amount of available fuel
The PP Chain • Actually three reaction branches • PPI: p(p,e+,)d d(p,)3He 3He(3He,2p)4He • PPII 3He(4He, )7Be 7Be(e-,)7Li 7Li(p,)4He • PPIII 7Be(p,)8B 8B(e+ decay)24He • PPII/III dominate at high T, high Yhe • Sun predominantly PPII
CNO Cycle CN: 12C(p,)13N 13N(+)13C decays are weak rather than strong rxns - longer 13C(p,)14N timescales, produce bottlenecks 14N(p,)15O 15O(+)15N 15N(p,)12C 15N(p,)16O NO: Higher coulomb barriers - higher T 16O(p,)17F 17F(+)17O 17O(p,)14N OF: 17O(p,)18F 18F(-,)18O 18O(p,)19F 19F(p,)16O
CNO vs. PP Chain • Equate CNO and PP energy production to find where each dominates • T ~ 1.7x107(XH/50XCN)1/12.1 • Crossover point occurs at ~ 1.1 M for Pop I • At z=0 must reach He burning T and produce CNO catalysts • (PP)~X2H0(T/T0)4.6 ; (CNO) ~XHXCNOfN0(T/T0)16.7 • PP and CNO have to produce same luminosity to support a given mass but CNO works over much narrower T range • Energy from CNO deposited in very small radius - too much to carry by radiation • 1st physical division of stellar types: PP dominated with no convective core and CNO dominated with convective core at ~1.1M
Problems of convective cores • Convective core size determines • Luminosity • Entropy of burning • progress of later burning stages & yields • How do we measure core size? • Indirectly • Binaries (esp. double lined eclipsing binaries) give precise masses and radii. If predicted core size too small model is underluminous. Radius also too small since central condensation fluffy exterior • Cluster ages - turnoff ages lower than ages determined by independent means like Li depletion in brown dwarfs • Width of the main sequence - centrally condensed stars evolve further to the red • Directly - apsidal motion of binaries - stars not point masses tidal torques cause line of apsides of orbit to precess. Rate of precession depends on central condensation
Problems of convective cores • Apsidal motion - stars not point masses so tidal torques cause precession of the line of apsides of the orbit • Rate of precession depends on central condensation of star • Stars with larger convective cores more centrally condensed
Problems of convective cores • Mixing length models always predict core sizes too small • Posit “convective overshooting” and say material mixed some arbitrary distance outside core • Various levels of sophistication, but always observationally calibrated • Amount of overshooting needed varies with mass - calibration for one star won’t work for different ones
Convection Bouyant force per unit volume If the signs of fBand r are opposite fB is a restoring force implies harmonic motion of the form where N is the Brünt-Väisälä frequency N2=-Ag N2<0 implies and exponentially growing displacement - unstable N2>0 oscillatory motion - g-mode/internal waves Locally the acceleration is
Convection • Deceleration of plumes occurs in a region formally stable against convection • Region may still be mixed turbulently if energy in shear > potential across region established by stratification • If less, material displaced by plume, not engulfed or continuing to accelerate, and returns to original position - harmonic lagrangian motion • Richardson number characterizes stability of stratification to energy deposited in shear - real criterion for bulk fluid flow • Stars dominated by radiation pressure have less restoring force - effect of waves & boundary stability INCREASES WITH MASS
Convection • Richardson number characterizes stability of stratification to energy deposited in shear - real criterion for bulk fluid flow • Ri<0.25 fully turbulent, shear from plume spreading & nonlinear waves • Ri<1.0 non-linear waves break & mix • Ri>1.0 linear internal waves
Convection • Richardson number characterizes stability of stratification to energy deposited in shear - real criterion for bulk fluid flow • Ri<0.25 fully turbulent, shear from plume spreading & nonlinear waves • Ri<1.0 non-linear waves break & mix • Ri>1.0 linear internal waves
The Convective Boundary • Boundary characterized by Richardson number Ri = N2 / (∂u/∂r)2 : Ratio of potential energy across a layer to energy in shear • Ri ~ 0.25: • Boundary region. Impact of plumes deposits energy through Lagrangian displacement of overlying fluid. Internal waves propagate from impacts. Ri<0.25 turbulent. • Conversion of convective motion to wave motion. Shear instabilities, nonlinear waves mix efficiently, large luminosity carried by waves. Vorticity XH Velocity
The Convective Boundary • Boundary characterized by Richardson number Ri = N2 / (∂u/∂r)2 : Ratio of potential energy across a layer to energy in shear • Ri ~ 0.25: • Boundary region. Impact of plumes deposits energy through Lagrangian displacement of overlying fluid. Internal waves propagate from impacts. Ri<0.25 turbulent. • Conversion of convective motion to wave motion. Shear instabilities, nonlinear waves mix efficiently, large luminosity carried by waves. Vorticity XH Velocity
The Convective Boundary • Ri > 0.25-1: Linear internal wave spectrum. • Internal waves propagate throughout radiative region • Radiative damping of waves generates vorticity (Kelvin’s theorem) • Slow compositional mixing • Energy transport changes gradients; generates an effective opacity Baroclinicgenerationterm Vorticity
The Convective Boundary • Ri > 0.25-1: Linear internal wave spectrum. • Internal waves propagate throughout radiative region • Radiative damping of waves generates vorticity (Kelvin’s theorem) • Slow compositional mixing • Energy transport changes gradients; generates an effective opacity Baroclinicgenerationterm Vorticity
Internal Waves • Ri>1.0 linear internal (g-mode) mode waves Kelvin’s theorem: lagranigian displacement and oscillatory motion is irrotational unless there is damping Dissipation of waves by radiative damping generates vorticity - mechanism for mixing in radiative regions
(Fewer) Problems of convective cores • Cluster ages match Li depletion ages • Width of main sequence reproduced
Rotation • Changes stellar structure in several ways • Centripedal accelerations mean isobars not parallel with equipotential surfaces • star is oblate • star is hotter at poles than equator (cetripedal acceleration counters some gravity so pressure support can be less) • T has non-radial components - meridional circulation which transports angular momentum and material • Turbulent diffusion along isobars + radiative losses during meridional circulation & wave motion transport J - setting up shear gradients and diffusing composition • evaluating stability against shear gradients: back to Richardson # • Coupled strongly with waves since waves transport J • not well modeled • waves probably have more effect on core sizes, rotation better at transporting material through radiative region
Other outstanding issues in stellar observations • Observations & potential solutions • Weird nucleosynthesis on RGB/AGB - Li,N,13C enhancements, s process - waves (+ rotation) • He enhancements in O stars, He,N enhancements in blue supergiants - rotation (+waves) • Blue/red supergiant demographics - waves (+rotation)? • Primary nitrogen production in early massive stars - waves (+rotation) • Young massive stellar populations, I.e. terrible starburst models - waves + rotation • eruptions in very massive stars - waves + radiation hydro (+radiative levitation?) • mass loss leading to Wolf-Rayet demographics rotation + waves
Mass luminosity relations again 23 M 52 M • 104 change in energy generation rate between 1 and 23 M • 1.5 change in energy generation rate between 23 and 52 M 1 M
Understanding the Mass-Luminosity Relation Relation of pressure to luminosity At low masses ~1 HSE requires fg=-fp T doubling M requires doubling T, so L16L LM4 (ignoring changes in radius with mass & degeneracy)
Understanding the Mass-Luminosity Relation Relation of pressure to luminosity At high masses 0 HSE requires fg=-fp T4 doubling M requires doubling P, T21/4T L2L LM tL/M t M-3at low mass and t const at high mass
Opacity sources • Thompson scattering (non-relativistic limit of Klein-Nishina) e = mean molecular weight per free e-, muin AMU for h > 0.1mec2 (T~108 K) must account for compton scattering Dominates for completely ionized material During H burning Yegoes from ~0.72 0.4994: fewer e- per nucleon, so scattering diminished. Opacity drops so convective cores shrink on the main sequence Free-free Bound-free - ionization Bound-bound - level transitions H- - free e- from metal atoms weakly bound to H - important in sun Conduction energy transport by e- collisions - important under degenerate conditions - note the mantle of the sun is mildly degenerate
Mass loss • Steady mass loss (neither of the cases pictured above) usually driven by absorption of photons in bound-bound transitions of metal lines • most transitions in metal atoms, so is metallicity dependent • depends on current surface z, so self enrichment important • depends on rotation - higher temperatures and increased radiative flux increase mass loss at poles - higher and asymmetry • Kinematic luminosity of O star wind integrated over lifetime can be ~1051 erg - comparable to supernovae • Eruptions in sun driven by magnetic reconnection • To be explored later: • eruptions in massive stars (pulsational and supereddington instability) • dust driven and pulsational mass loss in AGB stars • continuum driven winds in Wolf-Rayet stars