# Rovibrational Excitation of Interstellar Molecules at Low Energies

David R. Flower,
Steven A. Wrathmall

## Molecular astrophysics; linking the very small with the very big!

Atomic and molecular systems play an important role in Astronomy and Astrophysics. In general:

- Molecular emission line data provide information on physical processes in many types of astronomical sources.
- The chemistry can have an important role on small scales as well as on galactic scales.

There are currently over 120 different types of molecule which have been observed in interstellar space.

Understanding atomic and molecular processes allows us to detect, interpret and predict astrophysical observations.

**Far Right:** Possible Glycine detection in the Orion KL region [1].

**Near right:** Warm Molecular Hydrogen Gas in the Orion KL region. (Courtesy of Suburu Telescope, NJAO).

## Astronomical H_{2} Spectra

The image (near left) shows the * ρ* Ophiuchi region [2]. The spectra (far left) show pure rotational transitions of H_{2}
for *ortho* and *para* species. The transitions are in the ultra-violet part of the spectrum and are viewed via
space observatories [3].

### The astrophysical importance of H_{2}

Molecular hydrogen is the most abundant molecule in the universe and plays a fundamental role in many astrophysical contexts:

- Makes the bulk of the mass of the dense gas in galaxies and represents a significant fraction of the total baryonic mass of the universe.
- Plays major roles in the processes regulating star formation and the evolution of galaxies:
1. Formation of H2 on dust grains initiates the chemistry of the interstellar medium,

2. is a major contributor to the cooling of astrophysical media.

- Serves as a probe for a wide range of astrophysical environments.

The H2 molecule has a spectrum comprising rotational, vibrational and electronic state transitions. It can be excited and de-excited among its various energy levels through two main mechanisms:

- Collisions with other atomic and molecular species
- Interaction with a radiation field.

By understanding the radiative and collision properties of H2 we can construct realistic models of its surroundings.

## The rovibrational scattering problem

To understand the observed spectra we need various theoretical quantities:

- Radiative transition probabilities: to derive radiative transition rates.
- When considering transitions between rotational and vibrational energy levels due to inelastic atom-molecule collisions
we solve the Schrdinger equation for the system [4]. This reduces to the following set of coupled differential equations
for the radial functions,
*F(R)*,

where

*R* is the distance between the atom and centre of mass of the molecule,

*μ* is the reduced mass,

*ν* and

*j* are the
vibrational and rotational angular momentum quantum numbers of the molecule respectively,

*k*_{νj} is the wavenumber in the
centre of mass frame relative to level

*νj* of the molecule,

*l* is the atom-molecule relative angular momentum number,
and

**J = j + l** is the total angular momentum of the system.

The matrix elements of the system's interaction potential are given by:

where

*f*_{λ} is a Percival-Seaton coefficient and,

where

*χ(R)*, and

*v*_{λ}(r,R) are the expansion coefficients of the interaction potential,

and

*r* is the internuclear axis vector.

We can derive from the wavefunction solution the **T** matrix , which determine the cross sections, *σ(νj ← ν' j')* .

These cross sections are used to derive the thermally averaged collision rate coefficients.

The radiative and collision rate coefficients are used in radiative transfer models to calculate fractional population
densities for the observed object. The population densities are related to ratios of observed line intensities.

The observed line ratios and calculated population densities can be used to determine/constrain physical parameters of
the observed object (e.g. temperature, density, velocity fields).

## The H_{2} + H system: a not so simple problem.

H_{2} may collide with other atomic and molecular species within the medium.

Some species are more abundant than others and hence are more commonly observed.

H_{2} + H is an important collision system, and being the simplest (in terms of its constituents)
one would assume it is well understood and modeled. This may not be the case.

### Preliminary work

We need the following to proceed with calculations:

**Spectroscopic values** - energy eigenvalues and eigenfunctions for the species we are considering.
**Interaction potential** for the H2 + H system e.g. the potential of Mielke et al. [5]. The interaction
potential is determined through ab initio calculations and comparison with experimental data (when available).
**Computational routines **for calculating theoretical collision quantities e.g. MOLCOL [6].

## What we are doing in Durham

At present we are in the process of determining:

- Rovibrational inelastic cross sections for the H
_{2} + H system.
- Calculation of the respective rate coefficents.

We are also interested in:

- Application of the above analysis to astrophysical modeling.
- Application to more complex systems.
- Calculating the required data for the
Molecular Universe Network project.

## References

- Yi-Hehng Kuan
*et al*. *ApJ*, 593, 848, (2003)
- Harbart
*et al.* *Space Science Review: ISO Special Issue*, Springer, (2005).
- Abergel
*et al.* *A&A*, 315, L329, (1996).
- Flower,
*MNRAS*, 288, 627 (1997).
- Mielke
*et al.* *J. Chem. Phys.*, 116, 4142, (2002).
- Flower, Bourhis, & Launay,
*Computer Phys. Comm.*, 131, 187, (2000).