On the Validity of Collider-Mass Scaling for Molecular Rotational Excitation

Abstract

Rate coefficients for collisional processes such as rotational and vibrational excitation are essential inputs in many astrophysical models. When rate coefficients are unknown, they are often estimated using known values from other systems. The most common example is to use He-collider rate coefficients to estimate values for other colliders, typically H 2 , using scaling arguments based on the reduced mass of the collision system. This procedure is often justified by the assumption that the inelastic cross section is independent of the collider. Here we explore the validity of this approach focusing on rotational inelastic transitions for collisions of H, para-H 2 , 3 He, and 4 He with CO in its vibrational ground state. We compare rate coefficients obtained via explicit calculations to those deduced by standard reduced-mass scaling. Not surprisingly, inelastic cross sections and rate coefficients are found to depend sensitively on both the reduced mass and the interaction potential energy surface. We demonstrate that standard reduced-mass scaling is not valid on physical and mathematical grounds, and as a consequence, the common approach of multiplying a rate coefficient for a molecule-He collision system by the constant factor of ∼1.4 to estimate the rate coefficient for para-H 2 collisions is deemed unreliable. Furthermore, we test an alternative analytic scaling approach based on the strength of the interaction potential and the reduced mass of the collision systems. Any scaling approach, however, may be problematic when low-energy resonances are present; explicit calculations or measurements of rate coefficients are to be preferred.

Collisional quenching of highly rotationally excited HF

“…Walker et al (2014) demonstrated on both theoretical and numerical grounds that this standard reduced-mass scaling approach is typically invalid. We therfore do not recommend here that such an approach be adopted with the present HF-He rate coefficients.…”

“…Given the availability of HF-H 2 and HF-He collisional data, we can test various scaling methods, including the reduced-potential approach introduced in Walker et al (2014). In the reducedpotential method, the collisional data are scaled by the reduced potentials µ X ε X according to…”

“…Standard reduced-mass scaling results in an estimate for para-H 2 collisions that is a factor of 10 too small, while the reduced-potential method with an exponent of C = 1.7 agrees well. Given its better performance, the reduced-potential scaling approach of Walker et al (2014) was therefore used to predict unknown rate coefficients for para-H 2 and H colliders with HF. We adopted the He collision data computed here and the smaller set of para-H 2 rate coefficients for j ≤ 5 calculated by Guillon & Stoecklin (2012) for T = 10−150 K. The rate coefficients are very sensitive to the presence of quasibound resonances over this temperature range, which may partially be accounted for with the reduced-potential approach since it takes into the account the different interaction well-depths.…”

“…We adopted the He collision data computed here and the smaller set of para-H 2 rate coefficients for j ≤ 5 calculated by Guillon & Stoecklin (2012) for T = 10−150 K. The rate coefficients are very sensitive to the presence of quasibound resonances over this temperature range, which may partially be accounted for with the reduced-potential approach since it takes into the account the different interaction well-depths. Compared to the reducedmass scaling technique, where the rate coefficients simply scale as the square root of the ratio of the reduced masses, the reducedpotential scaling approach offers an improvement for predicted HF rate coefficients, much like the improved CO and H 2 O rate coefficient predictions of Walker et al (2014). While the value of C for CO rate coefficients ranged from −0.2 to 1.3 and from 0.5 to 1.2 for H 2 O, it was noted that symmetries were involved in obtaining the best value of C. The accuracy of the reduced-potential scaling approach can be further tested here with the heteronuclear molecule HF.…”

Mutual vibrational quenching in CO + H2 collisions

“…In particular, high-resolution observations of star-forming regions and protoplanetary disks of young stellar objects have shown evidence of rovibrational transitions for states where rate coefficients are currently lacking. In order to model such environments, current simulations have relied on approximate scaling methods which are known to be unreliable 17,18 .…”