Expert-level stellar physics covering stellar structure and evolution, nucleosynthesis, stellar atmospheres, variable stars, binary systems, and stellar populations.
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Hydrostatic equilibrium: pressure gradient balances gravity at each shell. Energy transport: radiative diffusion of photons or convective bulk motion. Mass-luminosity relation: L proportional to M to the power 4 for main sequence. Lane-Emden equation: polytropic models of stellar structure. Convection zones: low-mass stars fully convective, solar-type have outer convection zone.
Pre-main sequence: Hayashi track fully convective, Henyey track radiative. Zero-age main sequence: star settles into stable hydrogen burning phase. Red giant: hydrogen shell burning, core contraction, envelope expansion. Horizontal branch: helium core burning, instability strip contains RR Lyrae. AGB: asymptotic giant branch, thermal pulses, mass loss, planetary nebula formation.
Big Bang nucleosynthesis: H, D, He-3, He-4, Li-7 produced in first minutes. Stellar nucleosynthesis: CNO cycle, triple-alpha process, s-process. Explosive nucleosynthesis: r-process in neutron star mergers, p-process in supernovae. Chemical evolution: enrichment of ISM by stellar winds and supernova ejecta.
Classifications: visual, spectroscopic, eclipsing, astrometric binaries. Roche lobe overflow: mass transfer when star fills its Roche lobe. Cataclysmic variables: white dwarf accreting from companion, novae and dwarf novae. Type Ia supernovae: white dwarf reaching Chandrasekhar mass via accretion.
| Pitfall | Fix |
|---|---|
| Ignoring metallicity effects | Metal-poor stars evolve differently from solar |
| Applying solar-calibrated models to all stars | Low-mass and high-mass stars differ significantly |
| Confusing luminosity classes | Use gravity-sensitive lines to distinguish |
| Missing binary contamination in photometry | Check for variability and composite spectra |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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