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Interstellar Shock Waves
Mark Wardle
Department of Physics Macquarie University

Outline Shock waves Jump conditions and radiative shocks 1D steady shock models Simulations
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Shock waves
· Rapid motion: fluid cannot move away until overrun by a

disturbance
· Scattering conver ts unshocked gas to shocked gas ­ compresses and heats gas ­ entropy is increased

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Terrestrial shock waves

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Astrophysical shock waves
· Cosmic violence: shock waves are common sound speed: cs = AlfvИn speed: vA = kT m B 4 3 km/s в 2 km/s в T /1000 K m/mp
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B /µ G (nH / cm-3 )1

/2

­ stellar winds, cloud collisions, supernovae, accretion, jets, . . . · Shock waves process the gas ­ change density, velocity and temperature ­ affect ionization state, destroy dust grains, drive chemistry ­ introduce structure into the fluid ­ par ticle acceleration ­ shocked gas radiates!
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Accretion

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Compact HI I region / cloud collisions

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Stellar wind

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IC 443 supernova remnant
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IC 443 ­ 2MASS
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SNR E0102-72
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Protostellar jets
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Jump Conditions

unshocked gas at rest

shock frame

· Conser vation of mass, momentum and energy fluxes across shock

front v B2 8 P B2 v2 + + - 1 4 Bv v2 + P +

1 2

v
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Strong shocks

· For v

s

vA , cs and > 1 the jump conditions reduce to 2 B2 v1 + 1 = = =4 1 B1 v2 - 1 T2
2 3 mvs 1.4 в 10 16 k 5

(for = 5/3) vs 100 km/s
2

K

· Magnetic fields hardly affect the jump ­ but if the gas is ionised, their presence leads to par ticle acceleration which can significantly increase the compression ratio ­ and limits the compression of the gas as it cools ­ you have been warned

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Radiative shocks

· Shocked gas radiates away energy, so T drops · Total pressure, P + B 2 /8 is constant in the postshock gas · Initially, thermal pressure dominates magnetic pressure ­ increases to compensate for drop in T ­ B 2 /8 increases as 2 · Magnetic pressure kicks in and halts fur ther compression ­ cool gas forms a dense layer B2 2vs 2 1 vs = 1 8 1 vA
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Steady, 1D shock models
· Follow a fluid element as it passes through the shock and drifts

downstream
­ ­ ­ ­ , v, T , B dissociation, ionisation, recombination, chemistr y cooling function ( , T ) internal excitation: level populations

· A set of ordinar y differential equations describe structure of

shocked gas
­ local effects only: integrate an initial value problem ­ for vs > 100 km/s, shock-generated radiation gives rise to non-local coupling: iterative methods ­ "trivial" problem compared to fluid simulations · When does the structure of the shock front matter? ­ par ticle acceleration in collisionless shocks ­ vs < 45 km/s shocks in molecular clouds (C-type shocks)
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Atomic shocks

Sutherland & Dopita 1996
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Atomic shock - structure

Sutherland & Dopita 1996

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J-type shocks in molecular clouds

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Hollenbach & Mckee 1989
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C-type shock waves in molecular clouds
· Molecular clouds are strongly magnetised ­ magnetic pressure 100 times the gas pressure ­ vA 2 km/s, cs 0.2 km/s · Molecular clouds are weakly ionised ­ cosmic-ray ionisation vs recombination: ne 10-7 n(H2 ): · Magnetic fields only act on charged par ticles ­ forces charged par ticles to drift through the neutrals ­ collisions communicate magnetic forces to the neutral gas: JвB = i v c ­ "ambipolar diffusion"
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C-shock structure

Kaufmann & Neufeld 1996

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Line emission

Kaufmann & Neufeld 1996

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Instability

Wardle 1990
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Saturated state (2D)

Neufeld & Stone 1997
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Thermal instability

Sutherland et al 2003
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Fig. 12.--Two-dimensional shock time-evolution snapshots. Panels 1­12 show the density variable in the power-law density spectrum shock model at evenly spaced time intervals (2 б 1010 s) throughout the simulation. The postshock gas is at times relatively smooth (1, 5, 8, 10), during the approximately adiabatic buildup of the shock before cooling initiated collapse occurs. The visible fluctuations result from shock compressed initial fluctuations. Subsequently, (2, 6, 9), the fluctuation contrast increases and dense filaments form (3, 7) along with low-density voids. The shock then collapses with the loss of internal pressure support (4).

Sutherland et al 2003
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Shocks hitting clouds

Xu & Stone 1995
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3D

Xu & Stone 1995
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NOVA experiments

Klein et al 2003

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2D vs 3D

Klein et al 2003
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3D AMR

Klein et al 2003

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2D Cartesian with B

Fragile et al 2005
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Fragile et al 2005
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Summary

· Shock simulations: what should you worr y about? ­ Adiabatic vs radiative ­ Magnetohydrodynamics vs hydrodynamics ­ Dimensionality ­ Geometr y ­ Boundar y conditions · If you are involved with large-scale simulations that contain shocks

what should you be really worried about?
­ small-scale shock instabilities ­ subtle aspects of MHD

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