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