Transcript Distribution and Properties of the ISM

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)
nm
2




z

  0.58 cm-3  exp   

  81 pc  


• Layer thickens consistent with confinement by
stellar gravitational field, constant velocity
dispersion.
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)
21 cm emission
Lyα abs.
• Need to watch for stellar contamination, radio beam
sidelobes, varying spin temperatures.
N21/Nα
Lockman, Hobbs, Shull 1986
Vertical Structure of HI
n( z )   0.395 cm
-3
  0.064 cm -3
 exp    z / 212 pc    0.107 cm  exp    z / 530 pc 
 exp    z / 403 pc
• Overall density
distribution (Dickey
& Lockman 1990) at
radii 4-8 kpc
• “Lockman layer”
• Disk flares
substantially
beyond solar circle.
2
-3
2
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
• Dispersion measures and
extends to higher than 1 kpc, distances of pulsars in
seen in Hα (Reynolds 1985)
globular clusters show scale
• “Reynolds layer”, Warm
height of 1.5 kpc (Reynolds
Ionized Medium, or Diffuse
1989). Revision using all
Ionized Gas
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 891
Howk & Savage 1997, 2000
HII
Unsharp masked
dust
Correlation between DIG and SF
Rand, 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, 10311066
• 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
v2
v1
• Discontinuities in flow equations across
(stationary) shock front
• Conservation laws still hold
mass:
1v1   2v2
momentum: p1  1v12  p2   2v22
energy:
1 2
1 2
v1  h1  v2  h2
2
2
where the specific enthalpy h 

P
 1 
in perfect gas
Jump Conditions
• If the Mach number is large, the density
jump conditions reduce to:
   1
5
 4 if  
  1 M

2

3

    1
2
1   1 M 1  2 
2
M
if  =1

1
• The velocity difference across the shock:
5
3
2
2  2M1
2
 v1 if  
v1  v2 
v 
v1   4
3
2 1
 1
  1 M1

 v1 if   1
• Pressure ratio P2/P1 ->2γM12/(γ+1)
2
1
Numerical Viscosity
• Suppose we take the Lax scheme
n
n

 j 1   j 1 
1 n
n 1
n
 j    j 1   j 1   vt 

2
2x


and rewrite it in the form of FTCS + remainder
n
n
n
n
n



 
 j 1   j 1
1  j 1  2  j   j 1 
 v 
 





t
2x
t

 2

n 1
j
n
j
This is just the finite difference representation of a
2
2


x





diffusion term
like a viscosity.
2


x  t2 
Upwind Differencing
• Centered differencing
takes information from
regions flow hasn’t
reached yet.
• Upwind differencing
more stable when
supersonic (Godunov
velocity
n
n




j
j 1
n
1959)
,
v
n 1
n

j 0
j  j
x
n
• First order: “donor
 v j  n
n

t



cell” method:
 j 1
j
n
 x , v j  0
Conservative formulation
• to ensure conservation, take differential
hydro equations, such as mass equation
D
  v  0,
Dt
D

where
  v
Dt t
• Integrate hydro equations over each zone
volume V, with surface S, using divergence
theorem:
d
3
 d V     v  dS

dt
S
• Similarly for momentum and energy
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?
2i i 1  i  i 1  i i 1  0
d i  
0
i i 1  0

where i   i  i 1  .
Artificial Viscosity
• How to spread out a shock enough to prevent numerical
instability?
• Von Neumann & Richtmeyer (1950):
    v v
qi  qi 1

,


2
x

 t
2

C   v / x  , if  v / x   0
where q  
0
otherwise


n
i 1
n
i
n 1
i
n
i
• Similarly for energy. Satisfies conservation laws
• However, cannot resolve multiple shocks: “wall
heating”
Use of IDL
• Quick and dirty movies
pause
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)
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