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## Interstellar Shocks

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**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**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**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**Do Winds Induce or Halt Star Formation?**• Purely hydrodynamic models of winds interacting with clumps of Pittard, Dyson, Falle, and Hartquist (2005)**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 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)**Dynamical evolution**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)**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**Dust is dynamically important Havnes, Hartquist & Pilipp (1987) • Makes up ~1% of total mass • Dust grain charging by ions and electrons • determines grain charge**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**Velocity along shock normal**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**Results: oblique shock**Fluid temperature and grain charge Tangential B-field**Velocity along shock normal**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**Results: two grain species**Ionisation fraction and grain charge density**Grain-neutral relative speed**Future work • 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