1. Jonathan Slavin Harvard-Smithsonian CfA
Evaporation and Thermal Balance of Tiny-scale Structure in the Diffuse Interstellar Medium
Jonathan Slavin
Harvard-Smithsonian CfA

2. Types of Small Scale Structure
Cold neutral clouds – possibly embedded in a warm (neutral or ionized) envelope
Warm neutral clouds – possibly embedded in an ionized envelope
Warm ionized medium – possibly surrounded by hot ionized medium
Different heating/cooling rates apply depending on the temperature and ionization state of the cloud

3. Cloud Creation and Destruction
Creation: cooling of small regions that become thermally unstable after compression (e.g. Audit & Hennebelle 2005)
Destruction:
Turbulent mixing
Thermal evaporation
Photoionization/photo-evaporation
Shock heating

4. Destruction of a CNM Cloud by Turbulent Stripping
Time evolution of a CNM cloud embedded in a WNM flow. Cold gas is mixed, expands and warms to join the warm gas.
5 km/s
Timescale for destruction of the cloud is ~106 yr.

5. Thermal Balance and Cloud Destruction
Phase properties of CNM cloud being destroyed by turbulent mixing.
Points are gas parcels from hydro-dynamical
simulation at t = 3.5×105 yr
thermal
equilibrium
cooling > heating
warm
medium
cold cloud
cold cloud
heating > cooling
adiabatic
expansion/contraction

6. Thermal Conduction and Cloud Destruction
Comparison of CNM cloud destruction with (right) and without (left) thermal conduction. Contours show pressure, colors show log density. Though conduction smears out some of the small scale structure the overall effect is small – turbulence is the dominant destruction mechanism.

7. Evaporation vs. Turbulence for Warm Clouds in Hot Gas
Pressure distribution for a warm cloud in a hot medium flow. Contours are density.
Cloud with thermal conduction (left) is much less disrupted than cloud with conduction turned off (right).
The evaporative outflow prevents instabilities from developing at the interface with the flow. But the less disrupted cloud loses mass faster.

8. Thermal Conductivity - Dependencies
Heat flux is carried by electrons in hot/ionized gas; H0 in cold/warm neutral gas
Mean free path determines temperature dependence, κ ~ T 5/2 for electron conductivity, κ ~ T 0.8 for H0
Charge transfer strongly limits H0 mean free path – ionization reduces conductivity in partially ionized warm gas
Magnetic field channels electron conductivity along field lines – magnetic topology very important for conduction for clouds in hot gas

9. Dependence of Thermal Conductivity on Temperature and Ionization
Conductivity vs. temperature – a moderate amount of ionization ~ 20%, substantially reduces the conductivity in warm gas.
Here a photo-ionization rate of
10-13 s-1 causes the ionization in gas at a pressure of
3000 cm-3 K

10. σ0=3.2(Th /106K)3/[(P /104kB)Rcl(pc)]
Heat Flux Saturation
Limitation on heat flux – heat can only be transferred as fast as the carriers can diffuse – important for clouds in hot gas
Saturation for spherical clouds parameterized by (Cowie & McKee 1977)
σ0=3.2(Th /106K)3/[(P /104kB)Rcl(pc)]
If σ0> 1 then mass loss rate is reduced relative to “classical” rate
Small clouds have strong saturation, so evaporation rate is far below classical rate

11. Evaporation Timescales
The timescale for evaporation is calculated as (cloud mass)/(mass loss rate)
For CNM clouds evaporating into WNM envelope, conduction is by H0:
τ = 5.8×107 (Rcl/0.1 pc)2 (Tw/104 K)-0.8 (ncl/50 cm-3) yr
For clouds (cold or warm) evaporating into hot gas (electron conduction) in high σ0 limit:
τ = 2.2×106 (Rcl/0.1 pc)7/6 (ncl/50 cm-3) (Pcl/104)-5/6 yr
For typical conditions, CNM clouds would evaporate in ~3×107 yr in warm gas and ~5×106 yr when embedded in hot gas

12. Details of Heating and Cooling in Cold and Warm Clouds
Dust – ordinary carbonaceous & silicate grains plus PAHs; in WNM/CNM PAHs may dominate
Photoionization – EUV/soft X-ray ionization of H0 and He0 can dominate in partially ionized warm gas (WPIM)
Critical factors are dust content and the radiation field. Note: evaporative interface between cloud and hot gas can generate substantial EUV

13. Heating and Cooling (cont’d)
[C II] 157μm line is important coolant in both warm and cold gas – though not in highly ionized warm gas
Many other IR and optical forbidden lines contribute as well, e.g. [Si II] 34.8μm, [S II] 6731Å depending on temperature, ionization
If n(e)/n(H0) < 0.3 – 2 % (depending on T ) excitation of C+ by H0 dominates

14. The Local Interstellar Cloud as an Example of Warm Partially Ionized Medium
The LIC surrounds the Solar System and is:
Warm, T = 6300 K
Low density, n = 0.26 cm-3
Partially ionized, X(H+) = 20 – 30%
Low HI column density, N(HI) = 0.3 – 2×1018 cm-2
Is the LIC characteristic of WNM gas? Is the WPIM a significant phase of the ISM?

15. Heating and Cooling in the LIC
We have calculated photoionization models using observed and modeled components of the interstellar radiation field
Heating in the LIC is dominated by H0 and He0 photoionization – dust is minor contributor
Primary coolant is [C II] 157μm line, but only accounts for ~40%; rest is spread among many IR and optical lines
C gas phase abundance is high to account for absorption line observation of [C II*] Å
Stellar radiation alone cannot account for the heating necessary to balance cooling by C+

16. Local Interstellar Radiation Field
EUV from nearby white dwarfs and B stars
FUV from O, B, A stars
Soft X-rays from hot gas in the Local Bubble
EUV/soft X-rays from evaporative boundary of the LIC

17. Photoionization Heating and the LIC
Just the line of sight integrated C+ cooling requires more heating than can be provided by stellar sources – without extra heating, cooling time for LIC is ~4×105 yr
Soft X-rays from the Local Bubble can provide enough heating – but under restrictive conditions
Emission from the boundary of the cloud, assuming it’s evaporating helps make up the needed EUV flux

18. Phase Evolution in the n-P Plane
The local interstellar radiation field is hard, but weak leading to a thermal equilibrium curve that is lower than the one from Wolfire et al. (2003)
Dynamical processes lead to departures from equilibrium

19. Summary
Turbulent flow can destroy as well as create CNM clouds – shear causes expansion and mixing
Thermal conduction is a minor effect for CNM clouds in WNM, but is important for cold/warm clouds in hot gas
Evaporation suppresses mixing/disruption of clouds but is slowed by saturation effects in small clouds

20. Summary (cont’d)
Primary heating source depends on dust content, ionization, temperature and radiation field – for CNM/WNM it’s dust (especially PAH), for WPIM/WIM it’s photoionization
C+ cooling is primary coolant for CNM/WNM/WPIM but many other lines contribute
LIC may be typical example of WPIM/WNM – low carbonaceous dust content and hard radiation field determine thermal equilibrium
Creation/destruction of tiny clouds depends on their environment – turbulent velocity field, radiation field, pressure and composition.