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**Tom Hartquist University of Leeds**

Interstellar Shocks Tom Hartquist University of Leeds

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

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**Cas A Supernova Remnant**

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**Young Remnant’s Two Shock Structure**

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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

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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

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

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**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

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

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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.

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**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

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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

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**Two Fluid Model of Cosmic Ray Modified Radiative Shocks**

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

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

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**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

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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

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**Including Acoustic Instability Induced Energy Transfer**

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Starburst Galaxy M82

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**Do Winds Induce or Halt Star Formation?**

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

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**Wind Hitting Single Clump**

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**Wind Hitting Multiple Clumps**

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**Pressure Around Clumps**

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**Hierarchical density structure in molecular clouds**

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

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**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

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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

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**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)

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**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)

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Jets and Bullets

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**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

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**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)

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**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

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Previous studies

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**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

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**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

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**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

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**Results: oblique shock**

Fluid temperature and grain charge Tangential B-field

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**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

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**Results: two grain species**

Ionisation fraction and grain charge density

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**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

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