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Giovanni Covone » 6.Energy balance in the ISM

Magnetic fields in the Orion Molecular Cloud

The Orion Molecular Cloud in the Orion constellation. The inset shows the coils of the helical magnetic field surrounding the filamentary cloud. Credit: NRAO.

Introduction

In the last lecture we have discuss the different physical contributions to the pressure in the ISM.

We express those pressures in terms of the energy density, $u$ . Units: eV per cubic cm.

The six main sources of energy in the ISM are:

thermal energy, $u_{\rm th} = \frac{3}{2} n K T$
hydrodynamic energy, $u_{\rm hydro} \, = \, {1}{2} \rho v^2$
magnetic energy, $u_B \, = \, \frac{B^2}{8 \pi}$
cosmic rays, $u_{\rm cr}$
starlight, $u_{\rm stars}$
far-infrared radiation from dust, $u_{\rm FIR}$
cosmic background radiation, $u_{CBR}$

Energy densities in the local ISM

We compare here the typical values of the main source of energy densities in the local ISM.

cosmic background radiation, $u_{CBR} \simeq 0.265 \, {\rm eV \, cm}^{-3}$

Far-infrared radiation from dust $u_{\rm FIR} \simeq 0.31 \, {\rm eV \, cm}^{-3}$

starlight (photones less energetic than 13.6 eV), $u{\rm stars} = 0.54 \, {\rm eV \, cm}^{-3}$

Thermal kinetic energy, $u_{\rm th } \, = \, 0.49 \, {\rm eV \, cm}^{-3}$

hydrodynamic energy, $u_{\rm hydro} = 0.22 \, {\rm eV \, cm}^{-3}$

magnetic energy, $u_B = 0.89 \, {\rm eV \, cm}^{-3}$

cosmic rays, $u_{\rm cr} = 1.39 \, {\rm eV \, cm}^{-3}$

Note: all these contributions are comparable, within one order of magnitude.

A note on the energy densities

A numerical coincidence: a deeper physical meaning?

Is the near-equipartition of energy densitise coincidental?

The energy density in the CMB is similar to the other energy densities: an accidental fact.

The other energy densities are coupled.

The magnetic energy are built up by ﬂuid motions.

What if the cosmic ray energy density were much larger?

This negative feedback limits the cosmic ray energy density.

Starlight energy and the gas.

Energy balance of the ISM

Energy balance in the ISM. The ISM is far from thermodynamic equilibrium.

Sources of heatings: electrons from dust grain

The dominant heating source is given by the photoelectrons ejected from dust grains.

UV radiation can free electrons out of small dust grains and large molecules, like the Polycyclic Aromatic Hydrocarbons (PAH).

Photons responsible for this mechanism are in the FUV region of the spectrum, below 13.6 eV.

The photoelectric heating rate:

$n \, G_{pe} \, \sim \, 10^{-24} \, \epsilon \, n \, G_0 \, {\rm erg \, cm}^{-3} \, {\rm s}^{-1} \, ,$

where $\epsilon$ is the heating efficiency, $n$ the gas density, $G_0$ the mean intensity of the interstellar ration field.

Heating efficiency: at most about 0.05.

Maximum heating rate per hydrogen atom:
$G / n_H \sim 5 \, \times \, 10^{-26} \, {\rm erg \, s}^{-1} \, {\rm atom}^{-1} \, .$
This value is higher than any other heating mechanisms in large parts of the ISM.

Cosmic rays

The ISM is pervaded by cosmic rays, a population of very energetic nuclei and electrons.

Cosmic rays provide an important heating source for the ISM.

In particular, low energy cosmic rays, such as protons with energy between 1 and 10 MeV, heat the the ISM by means of ionizing collisions:

$H^+ + H \rightarrow H^+ + H^+ + e^- \, .$

Ejected electrons have mean energy of about 35 eV.
The electrons can quickly thermalize, via electron-electron collisions.

Secondary ionization of H and He.

All–sky gamma-ray map

The all-sky gamma-ray map above 100 MeV obtained by the instrument EGRET, on board of the Compton Gamma Ray Observatory satellite. Credit: NASA.

Photoionization heating

Photoionization is the third relevant heating process in the ISM.

Ionizing photons are FUV photons (mostly provided by hot stars) generally with energy between 11 and 13.6 eV

The ionizing mechanism can be written as:

$X^r + h \nu \rightarrow X^{r+1} + e^- \, .$

The electron mean energy is given by the difference of the ionizing photon energy and ionization potentials of the species, and of the order of a few eV.

Ionization states in the ISM and IGM

The gas ionization in the ISM and also the IGM.

In dense molecular clouds, the material is almost entirely neutral, with $x_ e \equiv n_e / n_H < 10^{-6}$

HI regions. elements such as C are photo-ionized by starlight, and the hydrogen is partially ionized by cosmic rays, with resulting ionization fractions in the range $10^{-3} < n_e / n_H < 10^{-1}$ .

H II regions. Around hot O stars, the hydrogen may be mostly ionized, the helium may be mostly singly ionized, and elements like oxygen or neon mainly doubly ionized (O III and Ne III).

Lyman-alpha clouds. $N_{\rm H I} < 10^{17} \, {\rm cm}^{-2}$ in the IGM, the hydrogen and helium may be mostly ionized (H II, He III), with C triply ionized (C IV).

Supernova remnants. Elements up through carbon may be fully ionized. Oxygen or neon may retain only electrons in the innermost atomic shell.

Massive stars in NGC 281

Massive stars in the HII region NGC 281 heat the surrounding ISM. Credit: NASA.

RCW 120, a hot gas region with glowing dust

The system RCW 120, observed by the Spitzer Space Telescope in the infrared. Credit: NASA.

Summary

Most important heating mechanism in the ISM.

Cold neutral clouds ( $T \sim 100 K$ , and $x \sim 10^{-4}$ ).
The most important processes is the photoelectric heating, at all the densities.

Warm neutral medium ( $T \sim 8000 \, {\rm K}$ and $x \sim 3 \times 10^3$ ).
Heating from dust grain is dominant when the density is larger than $0.1 \, {\rm cm}^{-3}$ .
Carbon is ionized: photoionization heating less efficient.

Cold cores of molecular clouds ( $T \sim 10 \, {\rm K}$ and $x < 10^{-7}$ ).
FUV radiation cannot penetrate, thus photoionization is negligible.
Many heating processes are active here, mainly related to gas dynamics, but cosmic ray heating is surely the dominant process, by an order of magnitude.