References

Astroph., 12, 240, 1971. 2. C. M. Leung, Ap. J., 199, 340, 1975. 3. M. W. Werner and E. E. Salpeter, M.N.R.A.S., 145, 249, 1969. 4. L. Spitzer and J. L. Greenstein, Ap. J., 114, 407, 1951. 5. D. E. Osterbrock, Astrophysics of Gaseous Nebulae, 1974, W. H. Freeman (San Francisco), Section 4.3. 6. L. Spitzer, Ap. J., 107, 6, 1948. 7. J. Silk and J. R. Burke, Ap. J., 190, 11, 1974. 8. W. D. Watson, Ap. J., 176, 103, 1972. 9. M. Jura, Ap. J., 204, 12, 1976. 10. B....

S sAehkT J323

We omit the subscripts jk from v in the rest of this section. The quantity su is an integrated absorption cross section uncorrected for stimulated emission in terms of the usual upward oscillator strength fjk, If the downward oscillator strength is defined by the relation then from any level j, the sum of all the oscillator strengths obeys the usual sum rule 2 fjk Number of jumping electrons in level j. (3-27) Oscillator strengths have been computed for H 3, 4, S4.2c , H2 5 , and either...

Photon Pumping

After absorption of a photon an atom or molecule will usually cascade back through a variety of states, reaching levels which could not be populated by direct upward radiative transitions from the ground state. Examples of this process, which are considered below, are the excitation of the hyperfine levels of the H I ground state, excitation of the fine structure levels in O I, N II, and similar atoms, and the excitation of H2 rotational levels. This indirect excitation of low-lying levels by...

Shock Fronts

When a pulse of increased pressure, with an appreciable amplitude, propagates through a gas, the front of the pulse tends to steepen because the sound velocity is higher in the compressed region this steepening progresses until a nearly discontinuous shock front is formed. Such shock fronts generally appear whenever supersonic motions are present and must therefore be expected in the interstellar gas, where the cloud velocities are often much greater than the sound speed. We consider here the...

Emission And Absorption Coefficients

To determine in any physical system we must evaluate j, k, in equation (3-3). In this section we consider how jv and k depend on the following more basic physical quantities the particle densities . and nk in the lower and upper levels, respectively, of the transitions involved the frequency of the emitted photon, equal to 1 h times the energy difference involved and three radiative transition probabilities, whose values are interrelated. We consider first the emission of radiation. The...

Info

Ir-B, TR) If T is known and I, is measured, t may be found from equation (4-25). If hv kTR< , equation (3-7) is applicable, and we have the physically plausible result that with increasing t , Tb within the line increases from Tr to T. To determine I, when A2l exceeds nHy2 the equation of radiation transfer must be solved with n2 nl determined at each point by the joint action of radiative and collisional transitions. The photons now tend to be trapped within the cloud, increasing the radiant...

Thermodynamic Equilibrium

As a result of the Maxwellian velocity distribution among the components of the thermal gas (distinguishing these from the high-energy suprathermal or cosmic-ray particles), the relative populations of various atomic and molecular energy levels will have some tendency to approach the values they would have in thermodynamic equilibrium. This tendency is particularly marked where transitions resulting from emission or absorption of photons are relatively unimportant, and collisional excitation...

W

Equation (4-13) is applicable particularly when Ur results from the cosmic blackbody radiation, for which W 1 and 7 2.7 K S1.1J. For optical transitions under interstellar conditions, Ur corresponds roughly to B at a radiation temperature of some lO K, with a dilution factor W of order 1014. Under these conditions the Ur terms are negligible in equation (4-12), which takes the more transparent form When ne is so large that ney2l much exceeds A2t, collisional deexcitation dominates over...

Kinetic Temperature

The kinetic temperature of the gas in a steady state is determined by the condition that the total kinetic energy gained per cm3 per second, which we denote by T, is equal to the corresponding energy lost per cm3 per second, denoted by A. In general, both T and A will depend on the temperature T, as well as on the particle density the value of T at which these two functions are equal will be an equilibrium temperature TE. More generally, the heating and cooling functions, T and A, are related...

Condensation Temperature

Figure 9.1 Dependence of depletion on condensation temperature 17 . The observed values of the depletion for each element observed in J Oph (Table 1.1) are plotted against values of the condensation temperature tc ( K) 16 , defined as the temperature at which half the atoms of an element have condensed out in one form or another in thermodynamic equilibrium. Each vertical bar represents an estimated possible error in the depletion resulting from uncertainties in the various curves of growth...

Ph2U y

SJm is the integrated absorption coefficient per H2 molecule for the transition J to m equation (3-15) . According to equations (3-43) and (5-45), itK m is the value that 1 t would have at the line center if there were no Doppler broadening. The opacity produced by grains, which has been ignored in equation (5-45), has been included in more detailed numerical computations 34 . The equation of dissociation equilibrium, obtained by substituting equations (5-40) and (5-42) into equation (4-1), and...

Electric Charge

In a steady state the electric charge on a grain, like other physical quantities, must be constant on the average. The chief physical processes which tend to modify the charge on a grain and which must therefore cancel out on the average are photoelectric emission and collisions with electrons and positive ions. Because of uncertainties in the various physical constants affecting these processes, we do not give the complete steady-state equation 6 , but consider the two limiting cases where...

J k rl

Where j is summed over all masses within the system, and k is summed over all gravitating masses. If masses outside the system can be ignored, then each interaction will be counted twice in the double sum, with r, and rk interchanged. As a result we have in this case which equals the total gravitational energy of the system. Equation (10-10) may be applied to some components of a system, as, for example, the interstellar gas, magnetic field, and relativistic particles, but excluding the stars....