1. Tom Hartquist University of Leeds
Interstellar Shocks
Tom Hartquist
University of Leeds

2. Outline
Thermally Unstable Shocks and Cosmic Ray Moderation – Supernova Remnants
Shocks and Clumps – Triggering Star Formation
Shocks in Dense Molecular Regions – Stars Strike Back

3. Cas A Supernova Remnant

4. Young Remnant’s Two Shock Structure

5. 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

6. 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

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

8. 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

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

10. 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.

11. 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

12. 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

13. Two Fluid Model of Cosmic Ray Modified Radiative Shocks
Developed by Wagner, Falle, Hartquist, and Pittard (2006)

14. Cosmic Ray Pressure Held Constant Over Whole Grid Until t = 0

15. 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

16. 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

17. Including Acoustic Instability Induced Energy Transfer

18. Starburst Galaxy M82

19. Do Winds Induce or Halt Star Formation?
Purely hydrodynamic models of winds interacting with clumps of Pittard, Dyson, Falle, and Hartquist (2005)

20. Wind Hitting Single Clump

21. Wind Hitting Multiple Clumps

22. Pressure Around Clumps

23. Hierarchical density structure in molecular clouds
Emission line maps of the Rosette Molecular Cloud (Blitz 1987)

24. 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

25. 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

26. for other moderate values)
Dynamical evolution
Interaction 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)

27. Dynamical evolution Typical GMC values: n ≈ 20 cm-3 & R ≈ 50 pc
12CO
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)

28. Jets and Bullets

29. 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

30. 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)

31. Havnes, Hartquist & Pilipp (1987)
Dust grains
Dust is dynamically important
Havnes, Hartquist & Pilipp (1987)
Makes up ~1% of total mass
Dust grain charging by ions and electrons
 determines grain charge

32. Previous studies

33. 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

34. 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

35. Velocity along shock normal
Results
Velocity along shock normal
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

36. Results: oblique shock
Fluid temperature
and grain charge
Tangential B-field

37. 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

38. Results: two grain species
Ionisation fraction and
grain charge density

39. Grain-neutral relative speed
Future work
Grain-neutral relative speed
SiO 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