Upon entering a molecular cloud, a gyrating cosmic-ray proton interacts with ambient nuclei and electrons through both the Coulomb and nuclear forces. The nuclear excitations principally decay through emission of 7-rays, which promptly escape. Elastic scattering due to the Coulomb repulsion between the proton and H2 is negligible at cosmic ray energies. Instead, the proton scatters inelastically, exciting H2 to a higher electronic state that leads to dissociation. On average, each scattering transfers 1.6 eV to the gas as kinetic energy. The most common result of proton impact, however, is ionization:
Besides heating the cloud, ionization supplies the electric current that couples the gas to any internal magnetic field. This coupling occurs even though the net fractional ionization is quite low. The presence of charged species also serves to initiate the ion-molecule reactions described in Chapter 5.
It is the secondary electron in (7.2) that actually provides heat through its subsequent interactions with ambient hydrogen molecules. Let us denote the rate of heat deposition in the cloud per unit volume as rCR(H2). We may write this quantity as rcR(H2)= c(H2) nn2 AE(H2) . (7.3)
Here, C(H2) is the ionization rate (probability per unit time) for a single hydrogen molecule, nH2 is the volume density of these molecules, and AE(H2) is the thermal energy added to the gas as a result of each ionization event.
To obtain AE(H2), we must consider the energy of the secondary electron, which naturally depends on that of the cosmic-ray proton. Protons with energy E > 1 GeV have no heating effect at all. Instead of ionizing H2, these produce nuclear excitation and 7-rays. One might have expected that the electron production and heating from lower-energy protons would peak and then fall off significantly with diminishing E. However, it is a peculiarity of the long-range Coulomb interaction involved in the p-H2 collision that the energy of the secondary electron is very insensitive to that of the incident proton. Thus, we can focus on a "typical" electron of 30 eV, which is produced by a 10 MeV proton.
There are a number of routes this electron can take. One possibility is the further ionization of ambient molecules:
This reaction does not itself supply thermal energy, but produces an additional electron that can heat the cloud. Although the incident electron is much less energetic than the original cosmic ray proton, the cross section for ionization of H2 by electrons peaks at an energy several times the threshold value of 15.4 eV. Thus, the process described by equation (7.4) is significant. For our 10 MeV proton, this reaction enhances the total ionization rate Z(H2) by a factor of 1.6 over that from the protons alone.
However it is produced, the electron may elastically scatter off a hydrogen molecule. Such a collision imparts relatively little kinetic energy to the gas because of the tiny electron-to-proton mass ratio. The electron may also scatter inelastically, exciting internal energy levels in H2. If the excited level is a rotational one within the ground electronic and vibrational state, there is time to transfer energy to neighboring molecules through collisions. More commonly, it is the higher electronic and vibrational states that are populated. These have such large A-values that they always decay radiatively rather than collisionally. However, most of these energetic photons are absorbed by dust. If the emitting H2 molecule is left in a high vibrational level of the ground electronic state, it continues to decay until it ends up in an excited rotational level within the ground state. Once again, these higher J-states heat the gas collisionally.
The most important means for the electron to provide heating is dissociation:
The energy of the incoming electron beyond that required to dissociate H2 goes into motion of the two hydrogen atoms. Collisions quickly disperse this energy throughout the gas. After summing all possible processes with the appropriate branching ratios, we find that AE(H2) is 7.0 eV. For comparison, the corresponding figures for 1 and 100 MeV cosmic ray proton are 6.3 and 7.6 eV, respectively.
Within diffuse clouds, the heating of atomic hydrogen by cosmic rays is also important. As in the molecular case, the most common result of proton impact is ionization:
It is again the electron, now ejected at a typical energy of 35 eV, that actually heats the gas, at a rate tcr(hi) = Z (HI) nni AE (HI) . (7.7)
In a weakly ionized HI gas, the secondary electron initially slows down by ionization and excitation of additional hydrogen atoms. The effect of secondary ionizations is to increase the total ionization rate by a factor of 1.7. The excited and ionized atoms quickly radiate away their excess energy. Thus, true heating cannot begin until the energy of the electron falls below the 10.2 eV needed to excite hydrogen to its first excited (n = 2) electronic state. From then on, the electron gradually loses its remaining energy through many elastic collisions. Numerical calculation reveals that AS(HI), the average thermal energy transfer per ionization event, is 6.0 eV.
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