Interstellar Shocks

Tom Hartquist

University of Leeds

Outline

• Thermally Unstable Shocks and Cosmic Ray Moderation – Supernova Remnants

• Shocks and Clumps – Triggering Star Formation

• Shocks in Dense Molecular Regions – Stars Strike Back

Cas A Supernova Remnant

Young Remnant’s Two Shock Structure

Clumpy Ejecta

• Ejecta are rich in heavy elements and observations of their spectra are made to diagnosis nuclear burning in the explosion

• Shock entering the ejecta suffers significant radiative losses

• Density enhancement behind shock entering the ejecta increases from 4 as radiative losses occur

Thermal Instability

• Falle (1975); Langer, Chanmugum, and Shaviv (1981); Imamura, Wolfe, and Durisen (1984) showed that single fluid, non-magnetic, radiative shocks are unstable if the logarithmic temperature derivative (ALPHA) of the energy radiated per unit time per unit volume is less than a critical value

• Pittard, Dobson, Durisen, Dyson, Hartquist, and O’Brien (2005) investigated the dependence of thermal stability on Mach number and boundary conditions

Alpha = -1.5, M = 1.4, 2, 3, and 5

Do Magnetic Fields Affect the Themal Instability?

• Interstellar magnetic pressure is comparable to interstellar thermal pressure (about 1 eV/cc)

• Immediately behind a strong shock propagating perpendicular to the magnetic field, the magnetic pressure increases by a factor of 16

• Immediately behind a strong shock the thermal pressure increases by roughly the Mach number squared

• Magnetic pressure limits the ultimate compression behind a strong radiative shock, but it does not affect the thermal instability

How About Cosmic Rays?

• In interstellar medium the pressure due to roughly GeV protons is comparable to the thermal pressure.

• Krymskii (1977); Axford et al. (1977); Blandford and Ostriker (1978); Bell (1978) showed that shocks are the sites of first order Fermi acceleration of cosmic rays.

• Studies were restricted to adiabatic shocks but indicated that cosmic ray pressure is great enough to modify the thermal fluid flow.

Two Fluid Model of Cosmic Ray Modified Adiabatic Shocks

• Volk, Drury, and McKenzie (1984) used such a model to study the possible cosmic ray acceleration efficiency

• Thermal fluid momentum equation includes the gradient of the cosmic ray pressure

• Thermal fluid equation for its entire energy includes a corresponding term containing cosmic ray pressure

• Equation governing cosmic ray pressure derived from appropriate momentum moment of cosmic ray transport equation including diffusion – diffusion coefficient is a weighted mean

• Concluded that for a large range of parameter space most ram pressure is converted into cosmic ray pressure and that the compression factor is 7 rather than 4 behind a strong shock

Two Fluid Model of Cosmic Ray Modified Radiative Shocks

• Developed by Wagner, Falle, Hartquist, and Pittard (2006)

Cosmic Ray Pressure Held Constant Over Whole Grid Until

t = 0

Problems

• Compression is much less than observed

• Too high of a fraction of ram pressure goes into cosmic ray pressure which is inconsistent with comparable interstellar themal and cosmic ray pressures

Possible Solution

• Drury and Falle (1986) showed that if the length scale over which the cosmic ray pressure changes is too small compared to the diffusion length an acoustic instability occurs

• Wagner, Falle, and Hartquist (2007, 2009) assumed that energy transfer from cosmic rays to thermal fluid then occurs

Including Acoustic Instability Induced Energy Transfer

Starburst Galaxy M82

Do Winds Induce or Halt Star Formation?

• Purely hydrodynamic models of winds interacting with clumps of Pittard, Dyson, Falle, and Hartquist (2005)

Wind Hitting Single Clump

Wind Hitting Multiple Clumps

Pressure Around Clumps

• Hierarchical density structure in molecular clouds

• Emission line maps of the Rosette Molecular Cloud (Blitz 1987)

Shock Induced Formation of a Giant Molecular Cloud

• A GMC typically contains 100 magnetically dominated translucent clumps with number densities of 300 – 1000 molecules/cc and masses of 30 to 3000 solar masses each

• The thermal pressure to magnetic pressure ratio is about 0.03 to 0.1 in such clumps

• Van Loo, Falle, and Hartquist (2007) performed ideal MHD studies of shocks interacting with 10,000K regions in which the thermal and magnetic pressures are initially equal.

• The shocks drive the pressure above the threshold for thermal instability to develop

Dynamical evolutionInteraction of shock with initially warm, thermally stable cloud which is in pressure equilibrium with hot ionised gas

Mach 2.5 (but similar for other moderate values)

Dynamical evolution

• Typical GMC values: n ≈ 20 cm-3 & R ≈ 50 pc• High-mass clumps in boundary and low-mass clumps inside cloud precursors of stars• Similar to observations of e.g. W3 GMC (Bretherton 2003)

12CO

Jets and Bullets

Shocks in Star Forming Regions

– Low ionisation fraction (< 10-7)

– Molecular clouds threaded by magnetic fields

electromagnetic forces act only on charged particles

Significantly changes shock structure

C-type shocks• Different shock structures:

• J-type shock:

• discontinuous compression jump

• C-type shock:

• all flow variables continuous

• depends on vS and vA,I

(B and ρ)

Dust grains

• Makes up ~1% of total mass• Dust grain charging by ions and electrons determines grain charge

Havnes, Hartquist & Pilipp (1987)

Dust is dynamically important

Previous studies

Previous studies of dusty C-type shocks

• Perpendicular steady shocks (Draine, Roberge & Dalgarno

1983) • Oblique steady shocks (Pilipp & Hartquist 1994)

only intermediate-mode shocks • Oblique fast-mode shocks (Wardle 1998)

• Time-dependent models (Ciolek & Roberge 2002)

decouple v// and v

S. Falle (2003) - S. Van Loo et al. (2009) code

• Time-dependent multifluid MHD code» Species: neutrals, ions, electrons + ‘N’ x grains» Mass transfer between fluids

ionisation, recombination, flow onto grains,…» Momentum transfer between fluids

collisions with neutrals» Energy transfer between fluids

line cooling (OI, CO & H2O), cosmic ray heating,…

» Average grain charge

Results

• Oblique shock ~ 45° •

– nH = 106 cm-3

– B = 1 mG

– T = 26.7 K

– rg = 0.4 micron

– ρg = 0.01 ρn

– vs = 25 km/s

Velocity along shock normal

Results: oblique shockFluid temperatureand grain chargeTangential B-field

Results: two grain species

• Inclusion of 2nd grain species

• Mathis-Rumpl-Nordsieck

• distribution (n ~ r-3.5):– rs = 0.04 micron

– ρg + ρs = 0.01ρn

⇒ Smaller shock width

⇒ Large grains move between

ions/electrons and neutrals

Velocity along shock normal

Results: two grain species

Ionisation fraction and grain charge density

Future workSiO emission in YSOs

• SiO frozen onto grains in dense molecular regions

• SiO in gas phase associated with shocks and outflows

grain-grain collisions sputtering of grains

• Expand work of Caselli, Hartquist & Havnes (1997) time dependence of emission inhomogeneous upstream region

Grain-neutral relative speed