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The H2 molecule

Potential energy curves of molecular hydrogenFigure 6

The large majority of this thesis deals with observations of infrared emission lines from hydrogen molecules. Before giving an overview of the observational work done on H2 emission in flows from young stars and discussing the relevant excitation mechanisms (and the tools to discriminate between these and to constrain the nature of the emitting gas), it seems mandatory to sketch some of the properties of hydrogen molecules relevant for an understanding of molecular hydrogen near-infrared emission lines (for more detailed information see Field et al. 1966; Shull & Beckwith 1982).

The H2 molecule is the simplest (neutral) molecule one could think of. It consists of two protons plus two electrons. In Figure 6 the potential energy of the H2 molecule is plotted as a function of the separation of the hydrogen nuclei for the ground state and a number of excited states (taken from Field et al. 1966; see this paper for an explanation of the level notation). Each electronic state possesses a set of rotation-vibration levels, usually characterized by a vibrational quantum number v and a rotational quantum number J. The electronic ground state possesses 14 bound vibrational levels (as is indicated in Fig. 6), each of which is split into a number of rotational levels. The dissociation energy of the H2 molecule is 4.48 eV, corresponding to a kinetic velocity of an H2 molecule of ~20 km/s.

The first allowed electronic dipole transitions from the ground state X1+g are to the B1+u and C1u states. They occur at energies between 11 and 14 eV (i.e., at UV wavelengths, ~0.1 µm) and are known as the H2 Lyman and Werner bands.

More important for this work are the rotation-vibrational transitions (ro-vibrational transitions in the following) in the electronic ground state. Since the homonuclear H2 molecule does not possess a permanent dipole moment, dipole transitions between levels of different v and J within the electronic ground state are forbidden. Electric quadrupole transitions, however, may occur. For those, no selection rules exist for transitions between various v states. For the rotational quantum number, transitions between ro-vibrational levels must satisfy J = 0, ± 2, with J = 0 -> 0 also forbidden. Ro-vibrational transitions are usually named giving the vibrational transition, the difference in J (with the letters O, Q, and S indicating J = + 2, 0, and - 2, respectively), and the rotational quantum number J of the final state. For example, the 2.12 µm line used in the present work is the v = 1-0 S(1) line, i.e., the transition from v = 1 to v = 0 and from J = 3 to J = 1.

The pure rotational transitions of the vibrational ground state of H2 are located at wavelengths in the mid-infrared (e.g., J = 2-0: 28.22 µm; J = 3-1: 17.04 µm; ... J = 10-8: 5.05 µm). Ro-vibrational transitions with v of 1 or 2 occur at near infrared wavelengths (J-, H-, K-bands), transitions with higher v are also found at optical wavelengths shortward of 1 µm (see, e.g., Black & Dalgarno 1976; Black & van Dishoeck 1987; Wolfire & Königl 1991; Smith 1995).


next up previous contents
Next:Observations of interstellar H2: Milestones Up:2.3 Molecular hydrogen jets Previous:2.3 Molecular hydrogen jets

Thomas Stanke

Mon Aug 14 17:51:08 CEST 2000
Last modified Thu Jul 12 14:23 CEST 2001