Collision calculations refine estimates for a tentative molecular ion in TMC-1

From radio lines to molecular abundance

Seven radio lines observed in TMC-1 have been tentatively attributed to HC₅NH⁺, the protonated form of the carbon-chain molecule HC₅N. Their nearly harmonic frequency spacing and agreement with theoretical molecular properties support that assignment. However, laboratory rotational spectroscopy is still missing, so the identification remains a working hypothesis rather than a confirmed detection.

Ziyu Xiang and colleagues investigate how collisions change the ion’s rotational motion and, consequently, its radio emission. Their study is an arXiv preprint, revised on 6 November 2026; the supplied record does not establish peer-reviewed publication.

The central problem is that molecular brightness depends on how molecules are distributed among rotational energy levels. In sufficiently sparse gas, collisions may not maintain the distribution expected at the gas temperature. Assuming local thermodynamic equilibrium, or LTE, can therefore affect an abundance estimate.

Calculating collisions from the interaction energy

The researchers first calculated how the interaction energy between HC₅NH⁺ and a helium atom changes with their separation and orientation. They used an explicitly correlated coupled-cluster method, CCSD(T)-F12B, with the cc-pVTZ-F12 basis set, evaluating 2,553 geometries.

They treated the ion as a rigid rotor: its internal geometry stayed fixed while its overall rotation could change. This neglects vibrational excitation, which the authors argue is small under the cold conditions considered.

The resulting potential energy surface is strongly direction-dependent. Its deepest attractive region lies near the protonated end, with a depth of about 195 inverse centimetres, an energy unit commonly used in spectroscopy.

Using this surface, the team performed quantum close-coupling scattering calculations with MOLSCAT. These determine cross sections describing the likelihood of particular rotational changes during a collision. Averaging over a thermal distribution of collision energies produced rate coefficients between 3 and 50 kelvin for rotational levels up to quantum number j = 19.

The calculations reveal an energy-dependent preference. At very low collision energies, some transitions decreasing j by one have the largest cross sections. At higher energies and temperatures, decreases by two become dominant among the channels examined. The authors connect this behaviour to the angular structure of the interaction potential, rather than proposing an absolute rule for every collision.

Applying the rates to TMC-1

Helium is computationally simpler to model, but the astronomical analysis requires collisions with molecular hydrogen. Because direct HC₅NH⁺–hydrogen calculations are unavailable, the researchers multiplied their helium rates by 2.7, accounting approximately for differences in reduced mass and electrical polarisability. These are proxy rates, not direct hydrogen collision results.

The team then used RADEX, a non-LTE radiative-transfer code, assuming a uniform spherical cloud and an escape-probability treatment of radiation. They jointly fitted the integrated intensities of the seven previously observed lines, with the gas temperature fixed at 7.8 kelvin.

The best-fitting hydrogen density was 163,000 molecules per cubic centimetre. The best-fitting HC₅NH⁺ column density—the number along the viewing direction per unit area—was 5.09 × 10¹¹ ions per square centimetre. A reduced chi-squared value of 0.87 indicates that the model reproduces the intensities within the adopted observational uncertainties.

The column-density estimate is about 1.5 times lower than the central value from the earlier LTE analysis. That difference does not, by itself, demonstrate that the approximate collision rates are free of systematic error.

What the fit can and cannot establish

The density result is less decisive than its precise best-fit number suggests. At sufficiently high densities, collisions bring rotational excitation close to the gas temperature. Line intensities then change little with further density increases, leaving a broad range of higher densities compatible with the observations.

Accordingly, the fit mainly supplies a lower constraint on density, while more tightly constraining column density. Its interpretation remains conditional on the proposed molecular identification, fixed temperature, cloud model and helium-to-hydrogen scaling.

The work provides a calculated foundation for excitation modelling, not laboratory confirmation of HC₅NH⁺ in TMC-1. The authors also describe public deposition of the collision rates and associated molecular data as a future step upon publication acceptance, rather than an already completed release.