tokens: of single vibrational transitions. Row 1 of Fig. 6 shows the temperature measured by the internal sensor (solid line) and determined by our algorithm (data points). There is a linear offset to the sensor temperature, the molecular temperature being systematically higher. This discrepancy can be corrected by a linear function A least-squares fit yields a = 1.414, T off,1 = 292.2 K, and T off,2 = 290.45 K. The dashed line in row 1 of Fig. 6 shows the corrected sensor temperature. The residuals between corrected sensor temperature and molecular temperature (σ = T measured − T alg ) displayed in row 2 show minor systematics during the unheated phases. The real cell temperature can then be determined from the algorithm output by inverting equation ( 24 ). We consider three cases for the origin of the temperature offset and discuss them in the following sections. Figure 6. Determined parameters of the measurements as a function of time. Shaded grey areas mark the time intervals during which the heating was switched on. Row 1: Data points with error bars represent the temperature of each spectrum as derived by our algorithm. The solid line shows the temperature determined with the gas cell sensor and the dashed line is the linearly corrected sensor temperature. Residuals between the corrected sensor temperature and the molecular temperature are given in row 2. Row 3 shows the determined effective RV/wavelength shift of each spectrum. 5.3.1 Erroneous model We assume the energy levels to include two terms, the vibrational and rotational energy (equation 12 ). In reality, there are several other contributors to the energy levels, such as a translational and an electronic term. We do, however, argue that the omission of these terms cannot lead to a bias in temperature determination, since the temperature determination is only dependent on the difference between energy levels Δ E ; hence, any term independent of the quantum numbers ν and J is cancelled out in equation ( 18 ). 5.3.2 Heating by the source lamp The source lamp in our setup is located relatively close to the iodine cell, so heating of the gas cannot be dismissed outright. As can be seen in the lower panel of Fig. 3 , the absorption is in fact temperature dependent. The lamp therefore heats the gas and causes a temperature gradient between the cell centre and the cell wall, where the temperature sensor is located. But if this effect were large enough to be present in the data, the temperature offset would not drop to zero at lower temperatures (see upper panel of Fig. 6 and equation ( 24 )), which is why we can rule it out as the underlying cause. 5.3.3 Heat sensor Equation ( 24 ) shows that the difference between the sensor and algorithm temperatures drops to zero at a temperature of 290.45 K, which was in fact the room temperature inside the laboratory at the time of the measurements. Furthermore, the residuals between corrected sensor temperature and the one determined via our algorithm show
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