1. Distribution of the ISM 3 February 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low

2. The Interstellar Medium Constituents –Gas: modern ISM has 90% H, 10% He by number –Dust: refractory metals –Cosmic Rays: relativistic e -, protons, heavy nuclei –Magnetic Fields: interact with CR, ionized gas Mass –Milky Way has 10% of baryons in gas –Low surface brightness galaxies can have 90%

3. Vertical Distribution Cold molecular gas has 100 pc scale height HI has composite distribution-Lockman layer Reynolds layer of diffuse ionized gas Hot halo extending into local IGM High ions Edge-on galaxies: FIR vs Hα relation

4. Molecular Hydrogen Molecular gas very inhomogeneous Azimuthal average shows (Clemens et al. 1988) Layer thickens consistent with confinement by stellar gravitational field, constant velocity dispersion.

5. CO distribution in Galaxy Dame, Hartmann, & Thaddeus 2001

6. Vertical distribution of HI Measurement of halo HI done by comparing Lyα absorption against high-Z stars to 21 cm emission (Lockman, Hobbs, Shull 1986) Need to watch for stellar contamination, radio beam sidelobes, varying spin temperatures. 21 cm emission Lyα abs.

7. N 21 /N α Lockman, Hobbs, Shull 1986

8. Vertical Structure of H I Overall density distribution (Dickey & Lockman 1990) at radii 4-8 kpc “Lockman layer” Disk flares substantially beyond solar circle.

9. Local vertical structure The sky is falling! –Most neutral material above & below plane of disk infalling. –Material with |v| > 90 km/s called high velocity clouds (HVC), slower gas called intermediate velocity clouds (IVC) HVC origins –Primordial gas (only Type II SN enrichment) –Magellanic stream material (Z~0.1Z  ) IVC origin –Galactic fountain: hot gas rises, cools, falls (Z~Z  )

10. Distribution of HVCs Wakker et al. 2002 (astro-ph/0208009)

11. Halo structure Observations at Galactic tangent point with Green Bank Telescope reveal clumpy, core-halo structure. Distant analogs of intermediate-velocity clouds? Lockman 2002

12. Warm ionized gas in halo Diffuse warm ionized gas extends to higher than 1 kpc, seen in Hα (Reynolds 1985) “Reynolds layer”, Warm Ionized Medium, or Diffuse Ionized Gas Dispersion measures and distances of pulsars in globular clusters show scale height of 1.5 kpc ( Reynolds 1989). Revision using all pulsars by Taylor & Cordes (1993), Cordes & Lazio (2002 astro-ph)

14. Ionization Ratios Clues to ionization of DIG 15% of OB ionizing photons sufficient Ratios of [S II ]/Hα, [N II ]/Hα enhanced at high altitude compared to H II regions dilution of photoionization (Domgörgen & Mathis 1994) part of the answer additional heating must be present –shocks –turbulent mixing layers in bubbles (Slavin, Shull & Begelman 1993) –galactic fountain clouds?

15. Hot gas in halo FUSE observations of extragalactic objects show O VI absorption lines from halo (Wakker et al. 2003, Savage et al. 2003, Sembach et al. 2003). Primordial extragalactic gas, halo supernovae, galactic fountain High ions (C IV, N V, O VI ) show 2-5 kpc scale heights in a very patchy distribution (Savage et al 2003)

16. NGC 891 Howk & Savage 1997, 2000 Unsharp masked dust H II

17. Correlation between DIG and SF Rand, 1996

18. Galactic Fountain Originally referred to buoyant flow of hot gas out of disk followed by radiative cooling (Shapiro & Field 1976) Now refers to any model of flow of hot gas from the plane into the halo, followed by cooling and fall in the form of cold clouds. Computations of cooling of 10 6 K gas in hydrostatic equilibrium reproduce high ions

19. Typical Values for Cold/Warm Boulares & Cox 1990

20. Interstellar Pressure Thermal pressures are very low, P ~10 3 k = 1.4 x 10 -13 erg cm -3. Perhaps reaches 3000k in plane. Magnetic pressures with B=3-6μG reach 0.4-1.4 x 10 -12 erg cm -3. CR pressures 0.8-1.6 x 10 -12 erg cm -3. Turbulent motions of up to 20 km/s contribute as well ~10 -12 erg cm -3. Boulares & Cox (1990) show that total weight may require as much as 5 x 10 -12 erg cm -3 to support.

21. Vertical Support Thermal pressure of gas insufficient to support in hydrostatic equilibrium with observed scale heights Boulares & Cox (1990) suggest that magnetic tension could support gas--a suspension bridge Alternatively, cool gas may not be in static equilibrium, but dynamically flowing? ( eg Avillez 2000 ) Remains to be shown.

22. Discussion Ferrière, 2002, Rev Mod Phys, 73, 1031- 1066 First exercise problems, results

23. Numerical topics Shocks (analytic) Upwind differencing Consistent advection Artificial viscosity Second order schemes Moving grid 2D vs 3D (face-centered vs edge-centered)

24. Shocks Discontinuities in flow equations across (stationary) shock front Conservation laws still hold v1v1 v2v2

25. Jump Conditions If the Mach number is large, the density jump conditions reduce to: The velocity difference across the shock: Pressure ratio P 2 /P 1 ->2γM 1 2 /(γ+1)

26. Numerical Viscosity Suppose we take the Lax scheme and rewrite it in the form of FTCS + remainder This is just the finite difference representation of a diffusion term like a viscosity.

27. Upwind Differencing Centered differencing takes information from regions flow hasn’t reached yet. Upwind differencing more stable when supersonic (Godunov 1959) First order: “donor cell” method: velocity

28. Conservative formulation to ensure conservation, take differential hydro equations, such as mass equation Integrate hydro equations over each zone volume V, with surface S, using divergence theorem: Similarly for momentum and energy

29. Order of Interpolation How to interpolate from cell centers to cell edges? First order, donor cell Second order, piecewise linear Third order, piecewise parabolic (PPA)

30. Monotonicity Enforcing monotonic slopes improves numerical stability. Van Leer (1977) second-order scheme does this Take w to be normalized distance from zone center: -1/2 < w < 1/2 ρ i (w) = ρ i +wdρ i. How to choose dρ i ?

31. Artificial Viscosity How to spread out a shock enough to prevent numerical instability? Von Neumann & Richtmeyer (1950): Similarly for energy. Satisfies conservation laws However, cannot resolve multiple shocks: “wall heating”

32. Use of IDL Quick and dirty movies for i=1,30 do begin & $ a=sin(findgen(10000.)) & $ hdfrd,f=’zhd_’+string(i,form=’(i3.3)’)+’aa’,d=d,x=x & $ plot,x,d[4].dat & end Scaling, autoscaling, logscaling 2D arrays tvscl,alog(d) tv,bytscl(d,max=dmax,min=dmin) Array manipulation, resizing tvscl,rebin(d,nx,ny,/s) ; nx, ny multiple tvscl,rebin(reform(d[j,*,*]),nx,ny,/s) pause

33. More IDL plots, contours plot,x,d[i,*,k],xtitle=’Title’,psym=-3 oplot,x,d[i+10,*,k] contour,reform(d[i,*,*]),nlev=10 slicer3D dp = ptr_new(alog10(d)) slicer3D,dp Subroutines, functions

34. Assignments For next class read for discussion: –Heiles, 1990, ApJ, 354, 483-491 Finish reading –Stone & Norman, 1992, ApJ Supp, 80, 753-790 Complete Exercise 2 –Modification of ZEUS –properties of 1D shocks and waves