Computational insight into diatomic molecules as probes to measure the variation of the proton-to-electron mass ratio
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Computational insight into diatomic molecules as probes to measure the variation of theproton-to-electron mass ratio
Anna-Maree Syme and Laura K. McKemmish School of Chemistry, University of New South Wales,2052 Sydney, Australia (Received August 26, 2020; Revised; Accepted)
Submitted to Research Notes of the AASABSTRACTAstrophysical molecular spectroscopy is an important means of searching for new physics throughprobing the variation of the proton-to-electron mass ratio, µ . New molecular probes could providetighter constraints on the variation of µ and better direction for theories of new physics. Here wesummarise our previous paper (Syme et al. 2019) for astronomers, highlighting the importance ofaccurate estimates of peak molecular abundance and temperature as well as spectral resolution andsensitivity of telescopes in different regions of the electromagnetic spectrum. Whilst none of the 11astrophysical diatomic molecules we investigated showed enhanced sensitive rovibronic transitions atobservable intensities for astrophysical environments, we have gained a better understanding of thefactors that contribute to high sensitivities. From our results, CN, CP, SiN and SiC have shownthe most promise of all astrophysical diatomic molecules for further investigation, with further workcurrently being done on CN. INTRODUCTIONCurrently, only 5% of the observable Universe is understood by the standard model and general relativity. Theincompatibility of these two theories has limited our understanding of the remaining 95% of the universe. Severaltheories have been proposed to bridge this gap (Uzan 2011), with some predicting a temporal variation of fundamentalconstants, which can be tested by high accuracy measurements of observables that depend on these constants. As-trophysically, the proton-to-electron mass ratio, µ , is observed across cosmological time through spectroscopy (Jansenet al. 2014); where the currently the tightest constraint is d µ d t /µ < × − yr − , assuming a linear change in time(Kanekar et al. 2015).The variation of µ is described by; ∆ νν = ν obs − ν ref ν ref = K ∆ µµ , (1)where ∆ µµ is the fractional change in µ , K is the sensitivity coefficient, ∆ νν is the fractional change in the transitionfrequencies, ν obs and ν ref are observed and reference transition frequencies respectively. Equation 1 assumes a variationin other fundamental constants will not affect ∆ µµ , which is suitable for the work done here (Beloy et al. 2011). K is a theoretical value based on the transitions dependence on µ . We assume that all baryonic matter will vary inthe same manner, such that variations in molecular mass and µ (Dent 2007) are synonymous. While pure rotational,vibrational, and electronic transitions can easily be shown to have a sensitivity of -1, -0.5, and 0 respectively, we aresearching for transitions that have enhanced sensitivities ( | K | >
5) from mixing of states or unusual features.Previously the molecules used to constrain the variation in µ are H , HD, CO, NH , and CH OH (Jansen et al.2014). NH and CH OH are preferred for their observed transitions with enhanced sensitivities, whereas H , HD, andCO are considered for their high abundance in astrophysical environments (Syme et al. 2019). Corresponding author: Laura K. [email protected] a r X i v : . [ phy s i c s . a t o m - ph ] A ug Syme and McKemmish
SCREENING DIATOMICSA key aspect of our research was to bring together knowledge from chemistry and astronomy to optimise potentialmolecular probes. The selection criteria we devised has factors from both disciplines; • Molecular properties and sensitivity coefficients of transitions; • Intensity of the transitions and observational constraints; • Resolution and the spectral range of required telescopes; • Abundance and distribution of molecules in various astrophysical environments..Use of these criteria was carried out in our previous publication (Syme et al. 2019), however, our analysis was limitedby the poor availability of consistently tabulated peak molecular abundance and temperatures as well as the spectralresolution and sensitivity at different wavelengths of telescopes. Sensitivity coefficients of the transitions, as well asfrequency and intensity, were calculated from spectroscopic models (Syme et al. 2019). Information of spectral range oftelescopes was fairly accessible, however we found the lack of clarity for the resolution and sensitivity to be a obstacle,especially how that applied to the resolution of the spectral transitions observed and transition intensity requirements.The abundance and distribution of diatomics was arduously consolidated, and the scattered data sources made itdifficult to have high confident in these abundances. With the understanding that astrophysical environments willhave different distributions of molecules, we provided a guide to molecular prevalence.
Figure 1.
Relation between term energy, T e and the maximum | ∆ K | for each diatomic examined, as well as the data points of Al O where the spectroscopic model was altered by shifting the term energy, denoted with filled crosses. Also included is acombination of external data for CO, HD, and H . Figure adapted from Syme et al. (2019). The 11 different diatomic molecules considered here are; C , S H, N O, N S, P O, P S, Si H, Sc H, Ti O, V O, and Al O including its isotopolgues Al O and Al O. Due to difficulties in observingastrophysical low-intensity transitions intensities less than 10 − cm/molecule were omitted. Of the 11 diatomicsconsidered here, none of them showed enhanced transitions at temperatures (10 K, 20 K, and 100 K) of astrophysical nsight for diatomic molecules to constrain µ µ . When considering transitions within our intensity requirementat 1000 K we found SiH, ScH, C , TiO, VO, and all isotopologues of AlO contained at least 1 transition with enhancedsensitivity.A minimum of two transitions are required to account for other astrophysical factors, therefore the relative sensitivitycoefficients, | ∆ K | , must be maximised to constrain the variation of µ (Jansen et al. 2014). We observed the ‘termenergy’ T e (energy between the ground and excited electronic states) is consequential in the prevalence and extent oftransitions with enhanced sensitivities by creating opportunities for more near-degenerate vibronic states. A correlationbetween T e and the maximum | ∆ K | (figure 1) for the diatomics with available data. The data for CO, HD, and H is possibly incomplete, with T e well-known, however the range of K for these diatomics is limited by previouslycalculated values (Ubachs et al. 2016; Salumbides et al. 2012). Figure 1 provides a guide to investigating otherdiatomics as potential probes for testing the variation of µ . Lambda doubling, while shows promise is not explored,however diatomics that fit this criterion are also noted.Curiously, none of our considered diatomics have significant abundance in molecular clouds, with 4 of them lackingany abundance estimate. Only NO and NS have been observed in extragalactic environments and neither showedenhanced sensitivities. All of the transitions that showed enhanced sensitivities were below 1000 cm − necessitatingutilisation of infrared/radio telescopes and interferometers.The relationship between T e and maximum | ∆ K | allows screening of all astrophysical diatomics and identify potentialprobes for further investigation. Of 43 known interstellar diatomics, we have identified; • , CN) that show promise for enhanced rovibronic transitions from low-frequency transitions between near degenerate vibronic states; •
10 molecules (SO + , PO, OH, CH, SH, NO, NS, HCl + , SiC, SiH) with potential lambda doubling transitions; • •
25 molecules (HD, HF, NO + , N , PN, CS, SO, AlCl, O , NH, OH + , CH + , CO + , FeO, TiO, SiH, AlF, KCl,CF + , HCl, NS + , ArH + , NaCl, SH + , CN − ) with low potential for transitions with enhanced sensitivity, eitherlacking or low astronomical abundance.The creation of a spectroscopic model for the extra-galactically observed CN radical (Syme & McKemmish 2020),intent on discerning transitions with enhanced sensitivities and higher intensities at lower temperatures, is underway.REFERENCES) with low potential for transitions with enhanced sensitivity, eitherlacking or low astronomical abundance.The creation of a spectroscopic model for the extra-galactically observed CN radical (Syme & McKemmish 2020),intent on discerning transitions with enhanced sensitivities and higher intensities at lower temperatures, is underway.REFERENCES