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PreprintCC BY-NC-ND 4.0arXiv

Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants

  • Renzhi Su
  • Minfeng Gu
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Abstract

In this paper, we show that the optical depths of any OH Λ-doublet quartet obey one exact linear relation in every velocity channel. No approximation is needed. The only exception is the 2Π1/2 J=1/2 level, which has three transitions only, because its F=0↔0 line is strictly forbidden. The relation is τS1(v)/μS12+τS2(v)/μS22=τM1(v)/(aμM12)+τM2(v)/(bμM22), where a=2J2+J−1, b=2J2+3J, and the μi2 are reduced transition dipole moments derived from the catalogued Einstein A coefficients. It holds equally for gas in local thermodynamic equilibrium (LTE), for non-LTE gas, for masers and for conjugate gas. We suggest that it is a powerful tool for measuring the variation of fundamental physical constants.

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Cite

BibTeXRIS
BibTeX
@misc{su2026derivation,
  title = {{Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants}},
  author = {Renzhi Su and Minfeng Gu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36007},
  eprint = {2610.36007},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36007},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants
AU  - Renzhi Su
AU  - Minfeng Gu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36007
UR  - https://arxiv.org/abs/2610.36007
AB  - In this paper, we show that the optical depths of any OH Λ-doublet quartet obey one exact linear relation in every velocity channel. No approximation is needed. The only exception is the ^2Π_1/2 J=1/2 level, which has three transitions only, because its F=0↔0 line is strictly forbidden. The relation is τ_S_1(v)/μ_S_1^2+τ_S_2(v)/μ_S_2^2=τ_M_1(v)/(aμ_M_1^2)+τ_M_2(v)/(bμ_M_2^2), where a=2J^2+J−1, b=2J^2+3J, and the μ_i^2 are reduced transition dipole moments derived from the catalogued Einstein A coefficients. It holds equally for gas in local thermodynamic equilibrium (LTE), for non-LTE gas, for masers and for conjugate gas. We suggest that it is a powerful tool for measuring the variation of fundamental physical constants.
ER  -