A second important heating agent for molecular clouds is the diffuse radiation field that permeates interstellar space. We need to understand in detail how these photons impinging on the gas create thermal energy. We should also look to stars embedded within the clouds as additional heating sources.
7.2.1 Major Constituents
Figure 7.4 shows the intensity of the interstellar radiation field as a function of frequency. The form of this distribution is a consequence of the space density and mass spectrum of both stars in the solar neighborhood and of the gas and dust obscuring their light. Thus, we may reliably use Figure 7.4 when considering relatively nearby interstellar clouds, but not to describe conditions out of the plane of the Galaxy or closer to its center. The figure actually plots vJv, where Jv is the specific intensity averaged over all solid angles in the sky. From the discussion in Chapter 2, the latter quantity is related to the monochromatic energy density uv by
cuv 4 n
Integration of the empirical Jv over all frequencies yields, after using this equation, a total radiation energy density of 1.1 eV cm-3. This figure is intriguingly close to that for the cosmic rays.
The energetically dominant components of the radiation field are those at millimeter, far-infrared, and optical wavelengths, peaking at log vmax = 11.3, 12.4, and 14.5, respectively, Here each frequency vmax is measured in Hz. The first component stems from the cosmic background radiation, a blackbody distribution with an associated temperature of 2.74 K. Background photons heat clouds primarily by exciting the lowest rotational transitions in such abundant molecules as CO. The far-infrared component in Figure 7.4 arises from interstellar dust warmed by starlight. Molecular clouds are transparent to this radiation, which is therefore not a heating agent.
The optical component consists of light from field stars. Suppose we crudely model the energy distribution as arising from a diluted blackbody of temperature T. To estimate this temperature, we identify the peak frequency vmax as that for which the blackbody specific intensity
Bv(T) has a maximum. We thus obtain T = hvmax/x0kB = 5400 K, where we have used the result from § 2.3 that xa = 2.82. This temperature is the surface value for a main-sequence G3 star. We may regard this spectral type as an average over the A-dwarfs and K- and M-type red giants that actually dominate the luminosity in the solar neighborhood. A true blackbody radiation field of temperature 5400 K has apeak value for vBv of 9.3 x 109 erg cm-2 s-1 sr-1. To match the observed peak of vJv = 9.1 x 10-4 erg cm-2 s-1 sr-1, the blackbody intensity at every frequency must be multiplied by a dilution factor of W =1 x 10-13. This factor is essentially the fractional solid angle of the sky occupied by stellar surfaces.
Figure 7.4 shows a smaller local maximum in the ultraviolet (log vmax = 15.3). Matching vmax to blackbody values yields an equivalent temperature of 3.4 x 104 K, with a dilution factor of 1 x 10-17. To gauge the effect of massive stars on molecular clouds, theorists often consider an ultraviolet flux that is far above the local background. The convention is to assume an isotropic radiation field in this regime, but with an intensity distribution that is scaled upward by some factor, traditionally denoted Ga.
At the highest frequencies, Figure 7.4 displays a contribution in the soft X-ray regime (16.5 < log v < 16.8) and a conspicuous lack of data in the extreme ultraviolet (15.5 < log v < 16.5). Radiation of both types was first observed through rocket experiments in the 1960s and 1970s. The ultraviolet spectrum was later explored by the EUVE (Extreme Ultraviolet Explorer) satellite. A diffuse gas with temperature of order 106 K can emit photons in these regimes. Within the context of the three-phase model of the interstellar medium, such a hot plasma gains its energy from supernova remnants and fast winds from massive stars. Note that the stars themselves produce extreme ultraviolet photons. However, this contribution is mostly absorbed through its ionization of hydrogen and helium in the stars' own HII regions or in intervening clouds. To avoid such absorption, the inferred 106 K gas must be relatively nearby, probably within a distance of order 100 pc.
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