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Distribution of the ISM. 3 February 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low. The Interstellar Medium. Constituents Gas: modern ISM has 90% H, 10% He by number Dust: refractory metals Cosmic Rays: relativistic e - , protons, heavy nuclei - PowerPoint PPT Presentation
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Distribution of the ISM
3 February 2003
Astronomy G9001 - Spring 2003
Prof. Mordecai-Mark Mac Low
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%
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
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.
2
-30.58 cm exp81 pcm
zn
CO distribution in Galaxy
Dame, Hartmann, & Thaddeus 2001
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.
N21/Nα
Lockman, Hobbs, Shull 1986
Vertical Structure of HI
• Overall density distribution (Dickey & Lockman 1990) at radii 4-8 kpc
• “Lockman layer”• Disk flares
substantially beyond solar circle.
2 2-3 -3
-3
( ) 0.395 cm exp / 212 pc 0.107 cm exp /530 pc
0.064 cm exp / 403 pc
n z z z
z
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)
Distribution of HVCs
Wakker et al. 2002 (astro-ph/0208009)
Halo structure• Observations at Galactic
tangent point with Green Bank Telescope reveal clumpy, core-halo structure.
• Distant analogs of intermediate-velocity clouds?
Lockman 2002
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)
Ionization Ratios• Clues to ionization of DIG• 15% of OB ionizing photons sufficient• Ratios of [SII]/Hα, [NII]/Hα 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?
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)
NGC 891Howk & Savage 1997, 2000
Unsharp masked
dust
HII
Correlation between DIG and SFRand, 1996
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
Typical Values for Cold/Warm
Boulares & Cox 1990
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 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.
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.
Discussion
• Ferrière, 2002, Rev Mod Phys, 73, 1031-1066
• First exercise problems, results
Numerical topics
• Shocks (analytic)
• Upwind differencing
• Consistent advection
• Artificial viscosity
• Second order schemes
• Moving grid
• 2D vs 3D (face-centered vs edge-centered)
Shocks
• Discontinuities in flow equations across (stationary) shock front
• Conservation laws still hold1 1 2 2
2 21 1 1 2 2 2
2 21 1 2 2
mass:
momentum:
1 1energy:
2 2
where the specific enthalpy in perfect gas1
v v
p v p v
v h v h
Ph
v1v2
Jump Conditions• If the Mach number is large, the density
jump conditions reduce to:
• The velocity difference across the shock:
• Pressure ratio P2/P1 ->2γM12/(γ+1)
212
21 1 2
1
1 54 if 1
1 31 2
if =1
M
MM
2
111 2 1 12
11
3 5if 2 2 2
4 31 1
if 1
vMv v v v
Mv
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.
1 111 1
1
2 2
n nj jn n n
j j j v tx
11
1 1 12
2
1
2
n n n nj j j
n nj j jjn
vt x t
2 2
22
x
t x
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
11
1
, 0
, 0
n nj j n
n n jj j n
j n nj j n
j
vxv
tv
x
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
0, where D D
v vDt Dt t
3
S
dd V v dS
dt
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)
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
• ρi(w) = ρi+wdρi. How to choose dρi?
1 1 1
1
1
2 0
0 0
where .
i i i i i ii
i i
i i i
d
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”
11 1
2
,2
/ , if / 0where
0 otherwise
n n n ni i i i i iv v q q
t x
C v x v xq
Use of IDL
• Quick and dirty moviesfor 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
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
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