1. The Three-Phase Interstellar Medium
ISM Lecture 10
The Three-Phase Interstellar Medium

2. 10.1 Why necessary? Two-phase model (see Sect. 8.3) FGH model:
Heating by cosmic rays => p.e. effect UV from stars: G(T)
Cooling by [C II] fine-structure emission: L(T)
Thermal equilibrium: G(T)=L(T) => two stable solutions
Cold Neutral Medium T= K, nH=10 cm-3
Warm Neutral Medium T~8000 K, nH=0.2 cm-3
But….. SN explosions destroy FGH model on timescales <106 yr => need new theory which includes SN activity
Also, vertical scale height of CNM,WNM can only be explained if the medium is turbulent, ~7 km s-1 => something must be stirring up the ISM continuously (mechanical rather than radiative energy)
Note that all theories of ISM are global theories, which try to explain ISM on average, but not locally

3. Overview of SNR evolution

4. Why do SN destroy 2-phase ISM?
Frequency S of SN events (not well known)
Probability Q that SN#2 goes off before #1 disappears
Recall
FGH model: no=0.2, vS,fade=10 km/s => tfade=5.2106 yr, Rfade=138 pc => Q=6.(S/10-13)
=> SN events destroy FGH model in 106 yr => need better theory of ISM!

5. 10.2 Overview of three-phase model
McKee & Ostriker 1977, ApJ
Cox 2005, ARAA
Tielens Chap
Q: what is ‘steady-state’ (in global statistical sense) of ISM subject to SN explosions at rate S10-13 pc-3 yr-1?
MO paper is difficult to read; simplified summaries of main ideas given in Appendix

6. Effect of supernovae on ISM
Overlapping SNRs create “tunnel” system of hot ionized (“coronal”) gas threading through HI clouds, much like the “holes”in a “swiss cheese”
SNR evolves in isolation until it intersects a tunnel and connects to coronal gas; then pressure drops suddenly as SNR “vents” to tunnel system and contributes to pressure of coronal gas
Characterize topology by a “porosity” parameter Q with the fraction of the ISM occupied by coronal gas is f1-exp(-Q), with Q1

7. Supershells in 21-cm survey of high-latitude gas => large SNR
Colomb et al. 1980

8. Three-phase MO model of ISM
Cold H I clouds
CNM: filling factor f~0.025
Warm cloud envelopes
WNM f~0.1, ionization by very soft X-rays (?)
WIM f~0.2, ionization by hot B stars
Hot ionized medium
HIM f~0.7
All three phases are in approximate pressure equilibrium P/k=nT3000 cm-3 K
There is no explicit discussion of dense molecular clouds in MO model, since these have filling factor f10-3

9. Cross section of a characteristic small cloud
x = ne / n (ionization fraction)
Cold cloud cores give rise to optical absorption lines
Warm neutral medium has low ionization fraction, which is maintained by soft X-ray background (?)
Outer layer is largely ionized by stellar UV background

10. Small-scale structure of the ISM
A supernova blast wave is expanding into region shown
Small clouds within SNR evaporate

11. Large-scale structure of the ISM
Only SNRs and large clouds are shown
Altogether 9000 clouds occur in this volume

12. 10.3 Physical ideas underlying MO model a. Pressure-balance
Various phases are in pressure equilibrium
Pressure is maintained by SNRs
Suppose pressure is initially low  SNRs overlap with internal pressure larger than ISM pressure  pressure in ISM increases until SNRs overlap just when they fade
Pressure balance requires
Note that actual value of Q uncertain especially if magnetic fields taken into account; current estimates range form
This equation can be used to determine PISM

13. Calculation PISM
Use expressions for Rfade and tfade with vfade=cISM=velocity dispersion ISM in 105 cm/s; no=nH= density into which SNR expands =>
PISMnHx1.4mHc2 =>
Use

14. Result PISM Substitute in above equations =>
This result is about a factor of two higher than the average observed insterstellar pressure of 3500 cm-3 K. Above discussion did not include effects of evaporation of clouds which will slow SNR

15. b. Mass balance
The various phases of the MO model exchange mass. In steady state, these mass flows must balance
Cloud material is lost by “thermal evaporation” due to heat conduction into clouds located within hot young SNR
Cloud material is created in dense cool shell of radiative SNR: clouds make holes in shell and collect material by condensation
Cloud evaporation
WIM
HIM
Ionization
Radiative
SNR
WNM
Heating
Cool dense
shell
Cold cloud
cores
Shell fragmentation

16. Thermal evaporation What happens to cold cloud inside SNR?
Conductive heat flux
into cloud
Hot medium
Cold
cloud
Mass flow away
from cloud
If cloud small => evaporates
If cloud large => survives + condensation of material on top of it
=> There is a critical radius for which evaporation = condensation
Rcrit strong function of T: RcritnT2
For T>107 K, Rcrit~1020 cm => 30 pc => most clouds evaporate
For T<106 K, Rcrit much smaller => less evaporation
MO assume cloud size distribution

17. Supernova density vs. diameter
T higher in young SNRs 
More clouds evaporate in young SNRs 
n(HIM) should be greater in young SNRs than in old (larger) SNRs

18. c. Energy balance
MO assume that most SN energy leaves system as radiation. This is satisfied if SNRs enter cooling (radiative) phase before they overlap (which they do, both by radiation and cloud evaporation)
A small fraction of SN energy remains as kinetic energy of shells at time of SNR overlap. This source of energy input serves to maintain random motions of clouds. Ultimately, this energy is also converted to radiation following cloud-cloud collisions

19. d. Summary Input parameters for MO three-phase model
Supernova rate S
Energy per supernova E51
Mean density of gas in disk
Ionizing EUV photon production rate per volume
Cloud size distribution and geometries
There are uncertainties associated with all these parameters

20. 10.4 Successes of the MO model
Predicts pressure of the ISM correctly “ab initio”
n vs. age (or R) relation observed for SNRs: younger SNRs are denser
O VI absorption lines: probably produced in cloud evaporation interfaces, where cloud material is heated to T  5105 K

21. Successes of the MO model (cont’d)
Observed soft X-ray background in rough agreement with T  5105 K expected for cooling SNR gas = HIM
Electron densities in WIM envelopes  0.04 cm–3 agree with observations (pulsar dispersion measures)
Predicted cloud velocity dispersion  7 km s–1 agrees with observations

22. 10.5 Problems with MO model
MO model does not predict enough WNM; prediction f  0.1 vs. observation f =
Cold H I distribution is observed to be much smoother than in MO model
Clouds are more sheet-like than spherical
Type II SNe are not random but occur in clusters of stars => superbubbles which create galactic fountain (see Sect. 10.6)?
Large fraction of type I SNe occur in disk only and overall SN rate uncertain

23. Problems with MO Model (cont’d)
For Q  1, expect  3000 supershells covering  50% of disk area on sky – where are they?
O VI absorption lines from cloud interfaces require large energy injection rate – where does it go?
Grain destruction in shocks very effective – how does enough dust survive?
Q  1 requires mean gas density n < 1 cm–3 – is n really that low?

24. 10.6 Recent developments and modifications of MO model
Scale height of WNM and HIM larger than thought previously
Expect ~20 pc from pressure equilibrium vs. ~200 observed (see following tables)
McKee 1990: This increased “weight” of ISM can be maintained if porosity Q is high, fHIM  0.5
Filling factors may vary with R and z in the Galaxy, with mostly WIM at large z, not HIM?
External galaxies (e.g., NGC 891) have thick ionized disk

25. Filling factors with z
WIM constrained by new Ha observations by Reynolds (1999) at high
latitudes => scale height ~1 kpc. Need O stars whose photons can travel
over large distances (kpc) to ionize such a thick layer
within MO model

26. Scale height ISM
Blitz 1990

27. “The Galactic corona”
Savage 1995

28. Recent developments (cont’d)
COBE / FIRAS all-sky survey  surprisingly strong [N II] fine structure lines, consistent with large filling factor and scale height of WIM
Fixsen et al. 1999

29. Three-phase model revisited: disk
Purple= mol. clouds
Solid green= cold H I clouds
Hatched green= warm H I
Hatched green on yellow=
diffuse warm H II
Orange= Hotter gas with OVI
Red=Hot gas emitting X-rays
Blue= star
Top three panels show common
(mis)conceptions, bottom panels
show features that need to be
added.
Cox 2005

30. Three-phase ISM: vertical
Same colors as before;
Top three panels have
difficulties.

31. Three-phase ISM: global
Same colors as before;
Top two panels have
problems

32. Summary filling factors in ISM
Little doubt that CNM, WNM, WIM, and HIM are all present in ISM, but filling factors are still controversial
fWNM 
fWIM 
fHIM  MO
FGH

33. 10.6 Gaseous Galactic halo and fountain
Some SNe occur well above Galactic plane and cannot cool efficiently if Thalo  106 K
Can also happen with large OB clusters
This SN energy will be pumped into halo; it can only be removed mechanically  Galactic wind
Thus there may be a Galactic wind with 1 Msun/yr and a halo with Thalo  106 K, nhalo  510–4 cm–3
Halo would contribute to X-ray background

34. Observational evidence
High velocity clouds: large number of H I clouds at high latitudes with large velocities  falling into Galaxy?
HVCs may condense from Galactic wind and fall back towards its point of origin
Presence of ions: C3+, Si3+, N4+, … lines seen towards stars in LMC and SMC (see Sect. 6.2)  originate in boundary layers of halo gas and condensing clouds? Or in tenuous gas of T 12000 K?
Bregman 1980

35. 10.7 The local ISM (within  200 pc from the Sun)
Interstellar absorption lines towards nearby stars  very little neutral matter within 100 pc of the Sun, N(H)  1019 H atoms cm–2
Confirmed by polarization data  n < 0.3 cm–3
Soft X-ray emission mostly of local origin
O VI absorption lines also indicate that there is a lot of hot gas locally
=> The Sun is inside a “local bubble” of hot, ionized gas!

36. Local bubble Where did bubble come from? SN 107 yr ago?
Is Sun located in unique surroundings?
Is there cold cirrus (as seen by H I, CO, dust) inside bubble? If so, how are they formed and how long do they survive?

37. Galactic neighborhood
100 pc
Orange=
Mol. clouds
P. Frisch

39. 10.8 Summary regions in ISM 1. H II regions
Traditional H II regions surrounding early type stars
T  104 K, n  cm-3, f small
Heated and ionized by photons with hn>13.6 eV, l<912 Å
Cooled by forbidden lines of atoms + ions [O III], [O II], [N II], ….
Observed by optical lines of atoms and ions, radio continuum, radio recombination lines
Coronal gas: very hot, tenuous gas pervading ISM (=HIM)
T3x105 K, n 0.003 cm-3, f 0.6?
Heated by shocks from SN and collisionally ionized
Cooled by adiabatic expansion and X-ray emission
Observed by X-ray emission, optical emission, non-thermal radio emission, UV absorption lines of OVI

40. H II regions (cont’d)
Warm ionized gas: warm diffuse gas throughout ISM (=WIM)
T 8000 K, nH 0.25 cm-3, ne/nH 0.7, f0.2?
Heated and ionized by stray photons from O and B stars l<912 Å
Cooled by forbidden lines of atoms and ions
Observed by broad optical and radio recombination lines (e.g. H166a) and pulsar dispersion measures

41. 2. H I regions Cold neutral clouds: H I clouds throughout ISM (=CNM)
T 80 K, nH 40 cm-3, f=0.025, ne/nH 10-4
Heated by UV photons with l>912 Å through p.e. effect
Cooled by [C II] fine-structure emission at 157 mm
Observed by H I 21cm emission + absorption, optical and UV absorption lines of atoms (e.g. Na)
Warm neutral gas: warm diffuse gas throughout ISM (=WNM)
T 8000 K, nH 0.4 cm-3, ne/nH 0.15, f  ?
Heated + partly ionized by soft X-rays + stray photons
Cooled by atomic lines
Observed by H I 21 cm emission

42. 3. H2 regions
Diffuse molecular clouds: includes translucent and high-latitude clouds
T 30-80 K, nH  cm-3, ne/nH 10-4, f0.01
Heated by UV photons with l>912 Å through p.e. effect
Cooled by [C II] fine-structure emission
Observed by H I 21 cm emission, CO mm emission, optical + UV absorption lines, IRAS 100 mm
Dense molecular clouds: dark clouds + GMCs
T  K, nH  cm-3, ne/nH 10-6, f0.0005
Heated by cosmic rays + newborn stars
Cooled by mm emission from molecules such as CO
Observed by mm lines from molecules, FIR and submm continuum emission from dust
Most regions are in approximate pressure equilibrium. Traditional H II regions may
be expanding. Dense molecular clouds are self-gravitating