Lecture 4: Heating and the 2-phase model

Dr Graham M. Harper

School of Physics, SNIAM 3.03a

Office Hours: Monday 14:00-15:00

PY4A04 Senior Sophister

Physics of the Interstellar and

Intergalactic Medium

Heating - sources

Add thermal “translational” energy to the gas

photoionization by stars and background galactic radiation field

depends exactly where you are in the Galaxy

solar environs are not typical

photodissociation of molecules

cosmic rays and X-rays (primary and secondary electrons)

photoelectric:

grains (cool neutral ISM)

polycyclic aromatic hydrocarbon - PAHs (cool neutral ISM)

turbulence

ambipolar diffusion heating (molecular clouds - collapse)

gravitational heating (molecular clouds - collapse)

Heating (photoionization)

Only the excess energy of ejected electron counts towards heating

where ΔE is mean excess energy per ionization

σν is the photoionization cross-section

Jν is the mean intensity of the radiation field

ν0 is the photoionization cross-section

what is the upper frequency-limit for integration?

Ejected electrons must scatter quickly to release excess energy into the

thermal pool – and raise the gas temperature

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dh

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Heating (photoionization)

In H II regions photoionization of H is dominant heating term

Integral limits are between Ionization Potential (IP) of hydrogen (13.6 eV) and infinity, or where the galactic radiation field runs out of photons

If we define 3/2kTH as = mean energy contributed then

TH ~ 0.6Teff (for hot stars 30,000 – 50,000 K)

In HI regions only elements IP < 13.6 eV contribute, i.e., C

Integration limits are IP of hydrogen and that of C (11.3 eV)

Mean typical value ΔE ~1 eV with TC ~ 9000 K

Net Heating (photoionization)

Ionization equilibrium: photoionization=radiative recombination

Radiative recombination rate: Rrec=ne αB (Case B)

ETnn

Tnndh

Jn

Beion

Beionatom

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However, radiative recombination cools the same gas, for equilibrium,

but lower energy electrons are preferentially captured

Average cooling rate Erec per recomb: = Erec nion ne kB then combining

Net heating does not depend on magnitude of Jν, or the ionization rate

Depends on shape of radiation field

recBBeionnet EkEnn

Cosmic Ray Spectrum/IceCube/IceTop

http://icecube.wisc.edu/~fmcnally/index.html

Origin of Cosmic Rays (protons)

Credit: CfA/V.A. Acciari

Credit: NASA/DOE/Fermi LAT

Collaboration

Heating: cosmic rays

Cosmic ray protons -probably Fermi accelerated by strong shocks

in supernovae explosions (Fermi, Veritas): Note in late 1960’s –

there as downward revision in CR rates by a factor of 10-100.

Low energy (1-10MeV) protons dominate the ionization of H, He, H2

p + H(1s) → p’ + H+ + e

e + H(1s) → e + H(2p) → e + H(1s) + hν [Lyman alpha cooling]

e + H(1s) → e + H+ + e (secondary electron)

2 MeV protons yields 35 eV primary electron

Neutral gas yields primary and secondary electrons

Total yield about 3.4 eV per electron

Rate uncertain because of galactic magnetic fields influence

CR’s

Heating: X rays

X-rays generally less important that FUV photo-electric

heating

fewer photons, but helium is important: 1 part in 10 of

hydrogen

ISM absorption is important

same issues with creating primary and secondary electrons

50 eV gives about 6 eV thermal energy

1327 scmerg103 nCR

Heating (molecular photo-dissociation)

Electronic ultraviolet transitions excite molecule

[show figure, x2]

H2 -10% time a photon is emitted which returns the molecule to a

vibrational state which is above the dissociation energy

–shakes itself to pieces

H2 photodissociation dominates because of high abundance

Decays to other vibrational levels also heats via collisional de-excitation

Heating (photoelectric emission)

UV radiation interacts with a dust grain or large molecule freeing an electron from its host site

This electron either escapes directly in molecules, e.g., PAH, or diffuses through the dust grain and may escape

Work Function (W) & Ionization Potential = 5 eV (Dust, PAH)

ϕ electrostatic potential for charged source – dust

important for dense photo-dissociation regions but not diffuse ISM

UV photons = 11 eV

Efficiency factor: y < 0.1 (UV) for dust (very uncertain)

1326 scmerg10 npe

)( cIPWhyE

Heating (turbulence)

Observed ISM turbulence forms part of a cascade of energy from large spatial scales down to the molecular length scale where the energy is dissipated as heat.

Energy flows from parsec spatial scales down to σ=10-15 cm2.

For WNM (warm neutral medium)[v=10 kms-1 200pc]

For molecular cloud cores [v=1 kms-1 1pc]

133028 scmerg10103 nturb

l

nmHturb

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Heating (dust-gas)

When dust temperature is greater than gas, then collisions between the

two can raise the gas temperature

Can be more important if the dust is moving with respect to the gas,

e.g., in young stellar outflows, and evolved cool stars

BUT if gas is warmer than the dust then this process can cool

1323310

scmergTTTn dustdustgas

Heating (ambipolar diffusion)

In a partially ionized gas the ions and neutrals can drift past each other

when there is movement of magnetic field with respect to the cold gas

Occurs during gravitational collapse in star formation

The atom-ion collisions result in frictional heating

For a drift of 0.5 pc in 107 years with typical ionization fractions

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30 scmerg102 nad

Heating (gravitational)

When a gas cloud collapses the compression heats the gas

Occurs during gravitational collapse during initial star formation

For conditions in a dense collapsing cloud core

It becomes larger than the ambipolar diffusion heating as T increases

1323

31 scmerg105 Tngrav

Which processes dominate?

Phase Density

(cm-3)

Temperature (K) Sound Speed

(km s-1)

Hot inter-cloud 0.003 106 130

Warm neutral (WNM) 0.5 8000 10

Warm ionized 0.1 8000 10

Cool diffuse clouds 50 80 1

Molecular clouds >200 10 0.4

H II regions 1 - 105 104 13

Approximate properties of ISM phases

From Tielens (2005) Table 1.1

Which process dominates?

Diffuse Clouds ~100 K

typical galactic radiation field

electrons from photoionized (x=1.4 10-4) metals

Photoelectric effect wins, CR become more important at low densities

Warm Neutral Medium (WNM) ~ 8000 K

typical galactic radiation field

electrons from photoionized (x=3 10-3) metals + weak hydrogen ionization

at lower densities CR wins and above 0.1cm-3 photoelectric effect wins

Molecular cloud cores ~10 K

Very low ionization (x=10-7) because of shielding of ionizing radiation

CR win throughout

Relation between the phases of the ISM

FGH Theory

G. B. Field, D. W. Goldsmith, & H. J. Habing, 1969, ApJ, 155, 49

2 Phase model of ISM

Phase F: low density 8000 K plasma

Phase G: intermediate densities and temperatures

Phase H: low temperature and high densities

We can add Phase W: thermal stability of solar corona (Weymann)

Cosmic ray fluxes was thought to be ~10-15 s-1

Two Phase ISM

Thermal equilibrium: heating equals cooling

Consider the ISM in a state of pressure equilibrium

Noting that

cooling rates proportional to n2

heating rates proportional to n

constant heating rate at constant pressure – single valued f(T)

[Show WNM cooling function, and constant pressure]

Find values that satisfy thermal equilibrium. How do these compare

with what is observed?

Not all equilibria are equal: unstable and stable

This is the origin of the early two-phase ISM model that predicted WNM

and molecular clouds: - no longer favoured but does illustrates physics

Stability Criteria

The general stability criterion for isobaric perturbations is

This model has been extended to a three-phase ISM

Hot stars wind and supernovae drive shock heating and turbulent

heating

generated coronal plasma

But this too looks like it is not the whole picture

0

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Tp d

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Three Phase ISM Model

McKee & Ostriker, 1977, ApJ, 218, 148