The graphical method to determine proceeds by assuming the value of 3, plotting column density against upper energy level, and then inspecting for systematic offsets between the para and ortho lines. For example, Wright et al (1996) have recently applied this method to ISO data for Cepheus A, finding no measurable offset. To find a distribution in , however, requires an analytical method such as developed here. This method yields ortho/para ratios consistent with 3 in various HH objects as well as across the OMC-1 outflow.
Why are no variations in detected? Either the molecules formed in a warm state (T 200 K) according to the statistical weights, or the molecule fractions have been altered to this value within the gas phase. H2 formation is most efficient on dust in a dense environment with a formation rate of order , or a formation timescale of years where (see Duley 1996). The formation is expected to yield a value of 3.
The H2 can be converted before leaving the grain or later, on colliding with a grain. The conversion rate is then of order of the H2 formation rate (Burton et al) and thus produces strong reductions from the statistical weights, , in cool quiescent molecular clouds. This is a satisfactory explanation for the low values in photon dominated regions such as NGC 2023 where (Hasegawa et al 1987). This mechanism could also, however, be expected to lower wherever the H2 has formed. A secondary warm thermalisation process appears necessary.
Reactions with protons would transform ortho and para, producing thermal equilibrium between the modifications on a timescale of years (Dalgarno et al 1973, Flower & Watt 1984). The predicted very low proton densities in cold clouds e.g. ) cm-3 (Flower & Watt 1984) generally imply this to be an inefficient conversion mechanism, consistent with the observed values. On the other hand, numerous warm shocks or regions of supersonic turbulent dissipation within bipolar outflows could provide the necessary column of protons to convert to the value of 3. Detailed calculations need to be performed.
Atomic H can induce ortho-para conversion when the gas is warm, with an estimated rate of (Burton et al 1992, see also Martin et al 1996). The activation barrier and the need for significant atomic H makes this process important in the shocks themselves. Furthermore, atomic H can be large in 'molecular' hydrodynamic shocks as well as in jet-driven outflows (Suttner et al 1997). Given a cooling time for the vibrationally-excited H2 gas of order of 1 year, then the thermal equilibrium value at high temperatures and densities, , will be generated in the shocks themselves for n(H) above .
Such high atomic densities would be convenient for shock modellers for another reason: to generate LTE (as clearly observed in OMC-1). Local thermodynamic equilibrium is difficult to produce through H2 -H2 collisions alone, unless high densities are admitted (n(H2) . Richter, Graham & Wright (1995) solved this possible problem by proposing that atomic H is the major collision partner. Present collision rates imply that atomic H dominates when present at a level of just a few per cent. This, however, as well as the ortho-para rate, remains to be confirmed through rigorous quantum calculations.
© European Southern Observatory (ESO) 1997
Online publication: April 6, 1998