Distribution of the ISM

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Distribution of the ISM

• 3 February 2003
• Astronomy G9001 - Spring 2003
• Prof. Mordecai-Mark Mac Low

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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

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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 Ha relation

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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.

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CO distribution in Galaxy
Dame, Hartmann, Thaddeus 2001
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Vertical distribution of HI

• Measurement of halo HI done by comparing Lya
  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
Lya abs.
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N21/Na
Lockman, Hobbs, Shull 1986
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Vertical Structure of HI

• Overall density distribution (Dickey Lockman
  1990) at radii 4-8 kpc
• Lockman layer
• Disk flares substantially beyond solar circle.

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Local vertical structure

• The sky is falling!
• Most neutral material above below plane of disk
  infalling.
• Material with v gt 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 (Z0.1Z?)
• IVC origin
• Galactic fountain hot gas rises, cools, falls
  (ZZ?)

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

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

Lockman 2002
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Warm ionized gas in halo

• Diffuse warm ionized gas extends to higher than 1
  kpc, seen in Ha (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)

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Ionization Ratios

• Clues to ionization of DIG
• 15 of OB ionizing photons sufficient
• Ratios of SII/Ha, NII/Ha enhanced at high
  altitude compared to HII 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?

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Hot gas in halo

• FUSE observations of extragalactic objects show
  OVI 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 (CIV, NV, OVI) show 2-5 kpc scale
  heights in a very patchy distribution (Savage et
  al 2003)

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NGC 891
Howk Savage 1997, 2000

• HII

Unsharp masked
dust
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Correlation between DIG and SF
Rand, 1996
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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 106 K gas in
  hydrostatic equilibrium reproduce high ions

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Typical Values for Cold/Warm
Boulares Cox 1990
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Interstellar Pressure

• Thermal pressures are very low, P 103k 1.4 x
  10-13 erg cm-3. Perhaps reaches 3000k in plane.
• Magnetic pressures with B3-6µG 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.

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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.

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Discussion

• Ferrière, 2002, Rev Mod Phys, 73, 1031-1066
• First exercise problems, results

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Numerical topics

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

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Shocks
v2
v1

• Discontinuities in flow equations across
  (stationary) shock front
• Conservation laws still hold

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Jump Conditions

• If the Mach number is large, the density jump
  conditions reduce to
• The velocity difference across the shock
• Pressure ratio P2/P1 -gt2?M12/(?1)

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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.

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Upwind Differencing

• Centered differencing takes information from
  regions flow hasnt reached yet.
• Upwind differencing more stable when supersonic
  (Godunov 1959)
• First order donor cell method

velocity
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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

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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)

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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 lt w lt 1/2
• ?i(w) ?iwd?i. How to choose d?i?

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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

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Use of IDL
pause

• Quick and dirty movies
• for i1,30 do begin
• asin(findgen(10000.))
• hdfrd,fzhd_string(i,form(i3.3))aa,dd,
  xx
• plot,x,d4.dat end
• Scaling, autoscaling, logscaling 2D arrays
• tvscl,alog(d)
• tv,bytscl(d,maxdmax,mindmin)
• Array manipulation, resizing
• tvscl,rebin(d,nx,ny,/s) nx, ny multiple
• tvscl,rebin(reform(dj,,),nx,ny,/s)

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More IDL

• plots, contours
• plot,x,di,,k,xtitleTitle,psym-3
• oplot,x,di10,,k
• contour,reform(di,,),nlev10
• slicer3D
• dp ptr_new(alog10(d))
• slicer3D,dp
• Subroutines, functions

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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