oh_einstein_temp_convert

oh_einstein_temp_convert is a Python package which translates temperatures originally calculated from OH*(6-2) transiton spectra using a certain set of Einstein coefficients to a new set of Einstein coefficients with no need of the original data.

It is published on Pypi and kept here, this repo also includes a Jupyter notebook with the same code in a more prose-style with plots to explain the steps.

Pypi package

Author

Rowan Dayton-Oxland University of Southampton Github

Installation

Use the package manager pip to install oh_einstein_temp_convert.

pip install oh_einstein_temp_convert

Requirements

Python >= 3.10
numpy, pandas
OS independent

Einstein A coefficient sources

Ain (int) - Original Einstein coefficient source index (see table)
Aout (int) - Desired output Einstein coefficient source index (see table)

Einstein A Source	Index
Mies et al., 1974	0
Loo and Groenenboom, 2008	1
Langhoff et al., 1986	2
Goldman et al., 1998	3
Turnbull and Lowe, 1989	4

Usage

import oh_einstein_temp_convert as oh

Temperatures = []  # List of temperatures

# Temperatures originally calculated from e.g. Mies et al., 1974 coefficients
Ain_index = 0  # Choose index of input temperatures
# Output temperatures calculated from e.g. Loo and Groenenboom, 2008 coefficients. 
Aout_index = 1  # Choose index of output temperatures

# returns list of converted temperatures
Result = oh.convert_temperatures(Temperatures, Ain_index, Aout_index)

Algorithm

Get the original temperature and original Einstein coefficient set
Calculate $ln(\frac{I}{Ain \cdot 2(2J' + 1)})$ and add a correction term for the new Einstein coefficient set $ln(\frac{Ain}{Aout})$ for each $F(J')$ value in the OH*(6-2) P-branch.
Plot the corrected $ln(\frac{I}{Aout \cdot 2(2J' + 1)})$ term against $F(J')$
Extract the output temperature from the gradient of the line by linear fit

This comes from the following equation; $$ ln(\frac{I}{A \cdot 2(2J' + 1)}) = \frac{-(h c)}{(k T)} * F(J') + ln(\frac{N}{QR}) $$

$I$ The spectral line intensity $A$ The Einstein A coefficient $J'$ The rotational quantum state $h$ The Planck constant $c$ The speed of light in the vacuum $k$ The Boltzmann constant $T$ The rotational temperature $F(J')$ The rotational energy term $ln(\frac{N}{QR})$ The partition function (constant for any single branch in the spectrum)