Interstellar Gas Heating

Abstract

This chapter presents the main heating and cooling processes responsible for the observed kinetic temperatures of the interstellar clouds. The heating and cooling functions are treated in detail, and the chapter ends with a discussion of the thermal instability processes leading to the different phases observed in the interstellar medium.

Exercises

• 7.1 (a) Estimate the cooling time for an H I cloud with T = 100 K, n _H = 10 cm⁻³, and n _e/n _H = 10⁻³. (b) Estimate the recombination time for radiative capture of an electron by an heavy element X^r, defined as 1/t _r = n _e α(X^r), where α(X^r) is the radiative recombination coefficient. Compare the two timescales.

• 7.2 (a) Consider an interstellar cloud with n _H = 20 cm⁻³ heated by cosmic particles coming from H ionization, with rate ζ _H = 10⁻¹⁵ s⁻¹. Estimate the energy per cm³ per second transferred to the gas, supposing that the mean energy of the electrons ejected by the cosmic rays is 3.4 eV. (b) Suppose that the interstellar cloud is cooled by collisional excitation of C II by H atoms. Consider a depletion parameter d _C = 0.2 and obtain the cloud equilibrium temperature.

• 7.3 Suppose that solid dust grains of an interstellar cloud are spherical with a radius a = 100 Å and internal density s = 3 g cm⁻³. (a) What is the geometric cross section of the grains? (b) What is the mass of the grains relative to the H atom mass? (c) Estimate the grains’ projected area per hydrogen nucleus Σ _d , supposing that the ratio between the total mass of the grains and the total mass of the gas (grain-to-gas ratio) is of the order of 1/200. (d) Estimate the energy provided to cloud heating by photoelectric emission, considering a cloud with n _H = 1 cm⁻³. Assume that the photoelectrons flux is F _e = 2 × 10⁶ cm⁻² s⁻¹ and the photoelectron mean energy is 5 eV.

• 7.4 An interstellar cloud is heated by two processes: (1) H ionization by cosmic rays at a rate of 5 × 10⁻¹⁶ s⁻¹, corresponding to photoelectrons with mean energy of 5 eV, and (2) stellar radiation, by means of carbon photoionization. The cloud cooling is exclusively accomplished by C collisional excitation due to electrons. The cloud has a density n _H = 1 cm⁻³ and a fractional ionization n _e/n _H = 0.1. Assume that all carbon atoms are ionized, the carbon abundance is 4 × 10⁻⁴ n _H, and also that 75 % of the C atoms are contained in interstellar dust grains. (a) Estimate the heating function (erg cm⁻³ s⁻¹) by cosmic rays. (b) Estimate the heating function by stellar radiation for typical cloud temperatures. Which one of these processes dominates? (c) Estimate the cooling function by C ions. (d) Estimate the cloud temperature.

• 7.5 Assume that the cooling function for typical temperatures of the intercloud medium is given by $\Lambda /n_{\mathrm{ H}}^2\simeq 3\times {10^{-26 }}\mathrm{ erg}\mathrm{ c}{{\mathrm{ m}}^3}{{\mathrm{ s}}^{-1 }}$. Bakes and Tielens model (1994) predicts a heating rate by hydrogen atoms of the order of 7 × 10⁻²⁷ erg s⁻¹. What is the density of this interstellar region?