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Collisional Excitation of the [CII] Fine Structure Transition in Interstellar Clouds

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 Added by Paul Goldsmith
 Publication date 2012
  fields Physics
and research's language is English




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We analyze the collisional excitation of the 158 micron (1900.5 GHz) fine structure transition of ionized carbon (C+) in terms of line intensities produced by simple cloud models. The single C+ fine structure transition is a very important coolant of the atomic interstellar medium and of photon dominated regions in which carbon is partially or completely in ionized form. The [CII] line is widely used as a tracer of star formation in the Milky Way and other galaxies. Excitation of the [CII] fine structure transition can be via collisions with hydrogen molecules, atoms, and electrons. Velocity-resolved observations of [CII] have become possible with the HIFI instrument on Herschel and the GREAT instrument on SOFIA. Analysis of these observations is complicated by the fact that it is difficult to determine the optical depth of the [CII] line due to the relative weakness and blending of the components of the analogous transition of 13C$+. We discuss the excitation and radiative transition of the [CII] line, deriving analytic results for several limiting cases and carry out numerical solutions using a large velocity gradient model for a more inclusive analysis. We show that for antenna temperatures up to 1/3 of the brightness temperature of the gas kinetic temperature, the antenna temperature is linearly proportional to the column density of C+ irrespective of the optical depth of the transition, which can be referred to as the effectively optically thin (EOT) approximation. We review the critical densities for excitation of the [CII] line by various collision partners. We briefly analyze C+ absorption and conclude with a discussion of C+ cooling and how the considerations for line intensities affect the behavior of this important coolant of the ISM.



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C$^+$ is a critical constituent of many regions of the interstellar medium, as it can be a major reservoir of carbon and, under a wide range of conditions, the dominant gas coolant. Emission from its 158$mu$m fine structure line is used to trace the structure of photon dominated regions in the Milky Way and is often employed as a measure of the star formation rate in external galaxies. Under most conditions, the emission from the single [CII] line is proportional to the collisional excitation rate coefficient. We here used improved calculations of the deexcitation rate of [CII] by collisions with H$_2$ to calculate more accurate expressions for interstellar C$^+$ fine structure emission, its critical density, and its cooling rate. The collision rates in the new quantum calculation are $sim$ 25% larger than those previously available, and narrow the difference between rates for excitation by atomic and molecular hydrogen. This results in [CII] excitation being quasi-independent of the molecular fraction and thus dependent only on the total hydrogen particle density. A convenient expression for the cooling rate at temperatures between 20 K and 400 K, assuming an LTE H$_2$ ortho to para ration is $Lambda ({rm LTE~OPR}) = left(11.5 + 4.0,e^{-100,mathrm K/T^{rm kin}}right);e^{-91.25,mathrm K/T^{rm kin}},n ({rm C}^{+}),n({rm H}_2)times 10^{-24};{rm ergs}~{rm cm}^{-3}~{rm s}^{-1}$. The present work should allow more accurate and convenient analysis of the [CII] line emission and its cooling.
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Effective collision strengths for forbidden transitions among the 5 energetically lowest finestructure levels of O II are calculated in the Breit-Pauli approximation using the R-matrix method. Results are presented for the electron temperature range 100 to 100 000 K. The accuracy of the calculations is evaluated via the use of different types of radial orbital sets and a different configuration expansion basis for the target wavefunctions. A detailed assessment of previous available data is given, and erroneous results are highlighted. Our results reconfirm the validity of the original Seaton and Osterbrock scaling for the optical O II ratio, a matter of some recent controversy. Finally we present plasma diagnostic diagrams using the best collision strengths and transition probabilities.
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