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Astron. Astrophys. 318, 608-620 (1997)

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5. Upper limits to H [FORMULA]

One of the original aims of our observations was to see if H [FORMULA] could be detected in the regions of OMC-1 which show strong molecular hydrogen emission. In such regions Neufield & Dalgarno (1989) have argued that concentrations of H [FORMULA] might reach as high as 10 [FORMULA] H2), (the density of H2). Values of the ro-vibrational Einstein [FORMULA] coefficients for H [FORMULA] are typically of the order of 102 s-1, some nine orders of magnitude larger than those for H2. This suggests that, were conditions of thermal equilibrium to pertain, H [FORMULA] ought to be observable.

Molecular hydrogen can exist in thermal equilibrium at densities of 10 [FORMULA] cm-3, densities reached easily in shocked interstellar gas. For H [FORMULA] such densities are sufficient for rotational states within a vibrational sub-level to be thermalised. However, the large ro-vibrational [FORMULA] values of H [FORMULA] mean that gas densities around 10 [FORMULA] cm-3 are required to reach full ro-vibrational thermal equilibrium. These densities are typical of the atmosphere of Jupiter, but are reachable only in very localised regions - around masers, for example - in the interstellar medium.

In the K window, at temperatures above 1000 K, the strongest emission line is [FORMULA] R(6), occurring at 2.0933 µm. Our non-detection of this line sets an upper limit of a flux of [FORMULA] erg s-1 cm-2 from the area subtended at OMC-1 by our pixels. This in turn translates into an upper limit on the column density of [FORMULA] cm-2 in the v=2 vibrational level, if we assume zero extinction. Our non-detection of lines belonging to [FORMULA] in the L window sets an upper limit of [FORMULA] in the v=1 level. Under conditions of complete thermal equilibrium, this translates - at temperatures in the range of 2000 to 3000 K - to an upper limit on the column density N (H [FORMULA]) of [FORMULA] cm-2. At the lower temperature of 1000 K, our results produce a total H [FORMULA] column density of no more than [FORMULA] cm-2.

Under non-thermal conditions, the population of H [FORMULA] in the excited vibrational levels is controlled by collisions with the dominant species, H2. No measurements of the cross section, [FORMULA], for this process have been made. Values of 10-16 to 10-15 cm3 s-1 are usually quoted for H2 /H2 collisional excitation. But vibrationally excited H [FORMULA] may additionally be produced by proton-hopping to vibrationally excited H2. This reaction is expected to occur at close to the Langevin rate for ion molecule reactions, of the order of 10 [FORMULA] cm3 s-1. At 2500 K, a median temperature for the entire cloud about 5 % of H2 molecules are in the vibrationally excited, v=1, state. Proton hopping is thus probably the dominant mechanism for vibrationally exciting H [FORMULA]. We can now make use of a simplified equation of balance for ratio between ground state and vibrationally excited H [FORMULA], thus:


where i corresponds to H [FORMULA] in a vibrationally excited level, j to H [FORMULA] in the ground state, and [FORMULA] is that fraction of hydrogen molecules excited to the v=1 vibrational level.

In order to evaluate this equation, we must first assume that the excited H2 and any emitting H [FORMULA] are spatially co-existent. We can then use the values obtained for the column densities of H2 and the upper limit on H [FORMULA] in the v=2 level in place of n (H2) and [FORMULA] respectively. Together with the value of [FORMULA] for v=2 [FORMULA] 0 given by Dinelli et al. (1992), this gives an upper limit for the density of H [FORMULA] in the ground state (which is close to the total H [FORMULA] concentration under non-thermal conditions) of n (H [FORMULA]) = 40 cm-3. This number is clearly highly dependent on the value chosen for [FORMULA]. But the upper limit we set would certainly not rule out relative concentrations as high as 10-7 if total densities of 108 cm-3 were reached locally.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998