Physics of stars, galaxies, compact objects, and the interstellar medium. Stellar structure/evolution, Chandrasekhar mass, Eddington luminosity, supernovae, neutron stars, black holes, accretion, galactic dynamics.
Astrophysics
Stellar structure equations
Four coupled ODEs (mass, hydrostatic equilibrium, luminosity, energy transport) governing the radial profile of a spherical star.
Hydrostatic equilibrium
Pressure gradient balances gravitational attraction in a static fluid: dP/dr = −Gm(r)ρ(r)/r². Foundation of stellar and planetary interior…
Chandrasekhar limit
Upper mass limit ≈ 1.44 M_☉ for a non-rotating white dwarf, set by relativistic electron-degeneracy pressure. Above it, gravitational…
Eddington luminosity
Upper luminosity at which radiation pressure balances gravity on fully-ionised hydrogen: L_Edd = 4π G M m_p c / σ_T. ~1.3×10³¹ W per M_☉.
White dwarf
Compact stellar remnant supported by electron-degeneracy pressure; typical M ≈ 0.6 M_☉, R ≈ R_⊕, ρ ~ 10⁶ g/cm³.
Neutron star
Compact remnant supported by neutron-degeneracy pressure (and repulsive strong force); M ≈ 1.4–2 M_☉, R ≈ 10 km. Observed as pulsars.
Astrophysical black hole
Region of spacetime from which nothing can escape; bounded by an event horizon. Stellar-mass (3–100 M_☉) and supermassive (10⁶–10¹⁰ M_☉)…
Accretion disk
Rotating disk of matter spiralling onto a compact accretor; angular-momentum transport by viscous stresses (Shakura–Sunyaev α-disk)…
Supernova
Catastrophic stellar explosion: core-collapse (Type II, Ib/c) after iron-core formation, or thermonuclear (Type Ia) from a…
Stellar nucleosynthesis
Fusion processes in stellar interiors building elements up through iron (pp chain, CNO cycle, He-burning, …); heavier elements from…
Galactic dynamics
Collisionless stellar dynamics governed by the Vlasov–Poisson system. Rotation curves, violent relaxation, disk/spheroid structure;…
Initial mass function (IMF)
Empirical distribution dN/dM of stellar masses at birth; approximately Salpeter dN/dM ∝ M^{−2.35} for M > M_☉.
Gravitational wave detection
LIGO/Virgo/KAGRA observe spacetime strain h ~ 10⁻²¹ from BBH/BNS mergers. GW150914 (first, 2015), GW170817 (BNS multi-messenger). Nobel…
Dark matter evidence
Galaxy rotation curves, gravitational lensing, Bullet Cluster, CMB peaks. ΩDM ≈ 0.26. WIMP, axion, sterile neutrino candidates;…
Dark energy & equation of state w
Accelerating expansion from Type Ia supernovae (Perlmutter/Schmidt/Riess 1998, Nobel 2011). Λ (w=-1) vs quintessence (w>−1) vs modified…
Exoplanet detection methods
Radial velocity (Mayor-Queloz 1995 Nobel 2019), transit (Kepler, TESS), direct imaging, microlensing, astrometry. >5000 confirmed;…
CMB polarization (E + B modes)
E-modes from acoustic oscillations at last scattering; B-modes from tensor perturbations (primordial GW) or lensing. Planck, BICEP/Keck,…
AGN jets & blazars
Relativistic jets from accreting supermassive BH; synchrotron + IC emission spanning radio-TeV γ. Blazars have jet aligned to observer.…
Chandrasekhar mass limit
M_Ch ≈ 1.44 M_☉ max white-dwarf mass from relativistic electron-degeneracy pressure; SN Ia thermonuclear explosion near M_Ch.
Tolman–Oppenheimer–Volkoff equation
dP/dr = -(Gρ/r²)(ρ+P/c²)(M+4πr³P/c²)/(1-2GM/(rc²)); sets NS max mass ≈ 2.2 M_☉ (EoS-dependent).
Hertzsprung–Russell diagram
Luminosity vs effective temperature; main sequence, giant branch, white dwarfs; isochrone fitting gives stellar ages.
pp-chain and CNO cycle
Sun's pp-I: 4p → ⁴He + 2e⁺ + 2ν_e + 26.7 MeV; massive stars burn via CNO: rate ~T¹⁶-²⁰ drives convection.
s- and r-process nucleosynthesis
Slow (τ_n > τ_β) in AGB stars produces up to Pb; rapid (τ_n ≪ τ_β) in neutron-star mergers (GW170817) produces actinides.
SN Ia / II / Ib/c classification
Ia: thermonuclear WD, no H; II: core-collapse, H lines; Ib/c: stripped progenitors. SN Ia standard candles; core-collapse drive chemical…
Neutron-star equation of state
Relates P(ρ) from nuclear + QCD phases; hyperons, quark matter; M-R curve from TOV; tidal deformability from GW170817 constrains stiffness.
Pulsar magnetosphere & spin-down
Dipole radiation Ė = -(2/3c³)(μ sin α)²Ω⁴ gives Ω̇∝Ω³; braking index n ≡ Ω̈Ω/Ω̇² (≈3 for pure dipole, ~2-3 observed).
Shakura–Sunyaev α-disk
Thin Keplerian disk; turbulent viscosity ν = α c_s H; radiation-pressure vs gas-pressure regimes; L ∝ Ṁ; thermal instabilities.
Magnetorotational instability
Weak B-field destabilizes differentially rotating disk at MHD level; Balbus–Hawley 1991 mechanism for angular-momentum transport in…
AGN unified model
Type 1/2 Seyferts, quasars, radio galaxies differ only by orientation relative to obscuring torus around central SMBH. Probed by X-ray,…
Flat galactic rotation curves
V(r) plateaus at large r in spiral galaxies; requires halo with M(r)∝r; evidence for dark matter or MOND.
NFW dark-matter halo profile
ρ(r) = ρ_s/[(r/r_s)(1+r/r_s)²]; universal from N-body CDM simulations; concentration c = r_vir/r_s.
Tully–Fisher relation
L ∝ v_flat^4 for spirals; baryonic TF (McGaugh) extends to gas-rich; distance indicator and DM puzzle.
Large-scale structure (LSS)
Filaments, walls, voids on 100-Mpc scale; N-body simulations (Millennium, IllustrisTNG) match SDSS redshift surveys; probes σ_8, Ω_m.
Gamma-ray bursts (long/short)
Long (≳2s) from collapsars (BH+relativistic jet); short from NS–NS mergers (GW170817–GRB170817A). Afterglows across EM spectrum.
Fast radio bursts (FRBs)
ms-duration radio pulses at cosmological distances; repeating sources (FRB 121102) from magnetar activity; probes IGM baryon density.
Multimessenger astronomy
Joint EM + GW + neutrino + cosmic-ray observations: GW170817 (NSM), TXS 0506+056 (blazar neutrino), SN 1987A (ν burst).
Cosmic ray spectrum
dN/dE ∝ E^(-2.7) below knee (3×10¹⁵ eV), steeper to ankle (10¹⁸ eV); GZK cutoff at 5×10¹⁹ eV from CMB p+γ → Δ interactions.
IceCube astrophysical neutrinos
Diffuse ν flux at PeV energies (2013); TXS 0506+056 blazar association (2017); probes hadronic acceleration sites.
Event Horizon Telescope imaging
1.3 mm VLBI of M87* (2019) and Sgr A* (2022) shadows match Kerr metric within 10%; mass, spin constraints.
Globular cluster ages
Main-sequence turnoff + stellar evolution models give τ_GC ≈ 12-13 Gyr; independent age-of-universe check.
Stellar convection (mixing-length)
Schwarzschild criterion for convection; mixing-length theory gives v_conv, energy flux in outer envelopes of Sun-like stars.
Tidal / Jacobi stability eigenstructure (astrophysical N-body)
Astrophysical N-body application of L0 spectral theorem and Jordan canonical form. The tidal field around a point mass M — the traceless…
Velocity-ellipsoid spectral decomposition (galactic-dynamics)
Astrophysical-dynamics application of L0 principal-component analysis and matrix norms. The stellar velocity-dispersion tensor σ²_{ij} =…