Astron. Astrophys. 356, 1010-1022 (2000)

5. Concluding remarks

• We have investigated the process of para to ortho conversion, driven by H-H₂ nuclear spin-changing reactions, in stationary shocks of both C- and J-type, paying particular attention to the chemistry, ion-neutral coupling within the shock wave, and collision-induced transitions in H₂.

• Chemical conversion of oxygen into water is the main source of atomic H in C-type shocks with 20 km s^-1. At higher shock speeds, dissociation by ion impact further increases the atomic fraction, but by no more than a factor of about 3. In J-type shocks, chemical dissociation dominates for 10 km s^-1; at higher speeds, collisional dissociation by H and H₂ becomes effective, increasing the atomic fraction by orders of magnitudes over the chemical value.

• Over a wide range of densities and velocities, the degree of para to ortho conversion is found to be determined mainly by the maximum temperature attained by the neutrals in the shock, . In C-type shocks, where the flow time is long, significant conversion starts at 700 K and is complete for 1300 K, even though the fraction of atomic hydrogen remains low. In J-type shocks, where the time available for conversion is much less, the ortho:para ratio starts to increase only for 1000 K. Complete conversion requires n(H)/ , which occurs in our models for  K, i.e. for 15 km s^-1.

• Our results for C-type shocks differ significantly from those of Timmermann (1998). We find much lower abundances of H⁺ and and a much lower fraction of atomic H, even when we adopt his (larger) rate coefficient for dissociation of H₂ by ion impact. The net effect is that Timmermann's calculations overestimate the final ortho:para ratio.

• The ortho:para ratio deduced from observations of levels above is always lower than the ratio of the total ortho-H₂ and para-H₂ column densities through the shock wave, which is itself lower than the maximum local value of the ortho:para ratio reached in the postshock gas. In addition, the observed ortho:para ratio depends on the lines that are used. For the same object, the pure rotational lines observed with ISOCAM should yield a higher ortho:para ratio than rovibrational lines.

• We have examined constraints on the initial ortho:para ratio and shock speeds that can be derived from the observed H₂ excitation temperatures and ortho:para ratio, using both pure rotational lines and rovibrational lines. For C-type shocks, there may be a strong dependence on the assumed . Adopting a lower yields a lower initial ortho:para ratio and a higher . For J-type shocks, the H₂ excitation temperatures typically observed in protostellar outflows correspond to low velocity shocks ( 10 km s^-1) in which the observed ortho:para ratio is still close to its initial value, which is then better constrained.

• As an illustration, we have considered observations of H₂ in the knots E,K of the Herbig-Haro object HH 54 (Neufeld et al. 1998; Gredel 1994). The pure rotational lines imply an initial ortho:para ratio 1.0. In the case of a C-type shock with = cm^-3, the initial ratio could be as low as 0.01 (the LTE value at 25 K). As is often the case in protostellar flows, the rovibrational lines require the presence of a hotter component within the observing beam, distinct from that producing the pure rotational lines. The need for a distinct component arises independently in order to account for the higher ortho:para H₂ ratio deduced empirically from the rovibrational lines, as compared to the pure rotational lines. Assuming a uniform initial ortho:para ratio in the preshock gas, we show that either a C-type bow shock or a shock wave which has not reached steady-state (and possesses both C- and J-type characteristics) is a plausible model. Observations of the ortho:para H₂ ratio in various sets of lines seem to provide a useful way of determining the shock structures in protostellar outflows.

© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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