Physical conditions in astrophysics Axel Brandenburg (Nordita/Stockholm) Kemel+12 Ilonidis+11Brandenburg+11Warnecke+11 Käpylä+12

Temperature/density Temp.c s [km/s]densityurms/cs ISM (CNM)10 2 K110 Sun (upper)10 4 K g/cm ISM (WIM)10 4 K g/cm 3 1 ISM (HIM)10 6 K100~1 Clusters10 8 K1000~1 Early Universe Kc/3 1/ g/cm 3 < 1 2

Fluid approx breaks down wherewhywhat to do Solar windElectric field spectrum below proton gyroradius e.g., gyrokinetics Galaxy clustersLong mean free pathe.g., Braginsky viscosity Dust, planet formationLarge contrastsparticles GRBcollisionlessPIC Earth magnetotailVlasov? 3

Faraday displacement current Displacement current often negligible because of high conductivity 4 Ohm’s law Ampere’s law w/ Maxwell correction

Conductivity, resistivity, viscosity Magnetic Prandtl number small in stars … and large in galaxies and clusters (low density!) O(1) in NS star discs 5

Hydro, and then add physics Never isentropic Specific entropy increases 6 +EOS

Dynamos & shear flow turbulence7 Viscosity often not mentioned Porter, Pouquet, Woodward (1998, Phys. Fluids, 10, 237)

EOS 8 with Perfect gas:

Adding physics Gravity,  stratification –E.g., polytropic Rotation, shear Radiation –Diffusion approximation –Optically thin case and transition Magnetic fields –Vector potential, Euler potentials, gauge issue Active & passive scalars (e.g., CR diffusion) 9

Gravity Self-gravity Fixed potentials, -GM/r, zg, ( W z) 2 /2 Isothermal stratification Polytropic solutions: constant heat flux 10

Turbulence Spectra –Helicity spectra and realizability Energy transfer Forcing Bottleneck mixing 11

Dynamos & shear flow turbulence12 Energy and helicity Incompressible: How  diverges as  0 Inviscid limit different from inviscid case! surface terms ignored

Hydromagnetic equations Induction Equation Magn. Vector potential Momentum equation Lorentz force stirring Magnetic helicity

14 Discs and disc viscosity Magnetorotational instability (MRI) –how does it work? –simulations and experiments Vertical stratification and radiation –Heating near disc surface Star/disc coupling and outflows –Field lines open up, enhanced outflow

15 Alfven and slow magnetosonic waves Vertical field B 0 Dispersion relation Alfven frequency:

16 Alfven and slow magnetosonic waves Alfven slow magnetosonic

17 March 23, 1965: Gemini 3 Gus Grissom & John Young: docking with Agena space craft

18 Analogy with tidal disruption, etc. Space craft experiment MRI (Balbus & Hawley 1991) Tidal disruption of a star