High-Resolution Transmission Spectroscopy: Data Reduction and Processing

Table of Links

• Abstract & Introduction
• Observation
• Data Reduction and Processing
• Model Spectra
• Cross-Correlation Method
• Results
• Clouds and Hazes
• Implications for JWST
• Conclusion and Acknowledgement
• Appendix & References

3. DATA REDUCTION AND PROCESSING

The IRD transit data were reduced following the approach of Hirano et al. (2020), which uses a custom code to correct for a known count bias that depends on the readout channel (Kuzuhara et al. 2018). Subsequent reduction steps were performed using the echelle package of IRAF. As these observations did not use the laser frequency comb, the wavelength calibration was based on the Th-Ar lamp. The wavelength solution was stable to within approximately 0.04 km s−1 over the course of the observations. This stability was determined by first cross-correlating every frame with a model telluric spectrum produced using SkyCalc (Noll et al. 2012; Jones et al. 2013) to find the telluric radial velocity of each frame. We then calculated the standard deviation of all telluric radial velocities during the night (after applying a barycentric correction). The model produced by SkyCalc is highly customizable, but the most important parameters are target elevation or airmass and the precipitable water vapor.

The IGRINS transit data were reduced by the IGRINS Pipeline Package (PLP; Sim et al. 2014; Mace et al. 2018). Though this pipeline provides wavelengthcalibrated data, the PLP wavelength calibration drifted by about 1 kms−1 through the course of the observations. To fit and correct this drift, we first crosscorrelated SkyCalc telluric models (as above) with every frame in spectral orders that had no saturated telluric lines. The spectral orders used for these crosscorrelations are shown in Table 3. For each frame, we then summed the cross-correlation functions (CCFs) from all our considered orders to produce a master CCF. Next, we fit a Gaussian to the master CCF of each frame and adopted the Gaussian center as the radial velocity of the observed telluric spectrum. Finally, we fit the telluric radial velocities with a third-degree polynomial as a function of time and used this to shift the data onto a common wavelength grid using linear interpolation. The amplitudes of the corrective shifts were approximately 0.5−1 km s−1 .

The SPIRou transit data were reduced by the observatory using the SPIRou Data Reduction Software (DRS) [4] . This pipeline provides data with and without a telluric correction, and we opted to use the telluric-corrected data.

For all data sets, after the above procedures, we normalized the spectra on a per-order basis to have a continuum flux of 1. We then masked all spectral regions with a normalized flux less than 0.3. For the IGRINS data, we also masked telluric emission lines, as in Rousselot et al. (2000) and Oliva et al. (2015).

We then applied the SYSREM algorithm (Tamuz et al. 2005) to all data sets to remove remaining telluric features and other systematic trends. We applied SYSREM to our data in fluxes (without first converting to magnitudes), as in Gibson et al. (2020) and Nugroho et al. (2021). Because SYSREM incorporates uncertainties, we estimated the uncertainties of the normalized data as

where σt and σλ are the standard deviations in the time and wavelength dimensions, respectively, σt,λ is the standard deviation in both the time and wavelength dimensions, and ⊗ is the outer product operator.

To determine an effective number of SYSREM iterations to use, we followed a well-established approach and examined how each order’s variance decreased as a function of the number of applied SYSREM iterations (e.g., Deibert et al. 2021a; Herman et al. 2022). For each order, we examined plots of the variance as a function of the number of SYSREM iterations and identified by eye the number of iterations where the decrease in data variance began to plateau. We noted the number of SYSREM iterations determined for each order and then used the most common number of iterations as a constant for each data set. This resulted in us applying five SYSREM iterations to all orders of the SPIRou and IRD data and 10 SYSREM iterations to all orders of the IGRINS data. While our chosen values are likely not the formal optimal values, they are a close approximation, as telluric features and other systematic trends were removed effectively. In general, previous studies have found that the exact number of SYSREM iterations has little to no effect on the final results (e.g., Deibert et al. 2021b). Some IGRINS orders, as indicated in Table 3, had near-total telluric extinction across most of their spectral range. Such severe contamination cannot be corrected by SYSREM, so we excluded these orders from the analysis. Finally, for all data sets, we removed any outlying points more than three standard deviations away from the mean.

Barycentric corrections for the IRD and IGRINS data were calculated with the radial velocity correction function in Astropy. The same corrections for the SPIRou data were provided by the DRS.

[4] http://www.cfht.hawaii.edu/Instruments/SPIRou/SPIRou pipeline.php