A Near-Infrared Chemical Inventory of the Atmosphere of 55 Cancri e
Emily K. Deibert, Ernst J. W. de Mooij, Ray Jayawardhana, Andrew Ridden-Harper, Suresh Sivanandam, Raine Karjalainen, Marie Karjalainen
DDraft version February 19, 2021
Typeset using L A TEX twocolumn style in AASTeX62
A Near-Infrared Chemical Inventory of the Atmosphere of 55 Cancri e
Emily K. Deibert,
1, 2
Ernst J. W. de Mooij, Ray Jayawardhana, Andrew Ridden-Harper, Suresh Sivanandam,
1, 2
Raine Karjalainen,
5, 6, 7 and Marie Karjalainen David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St. George Street, ON M5S 3H4, Canada Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, ON M5S 3H4, Canada Astrophysics Research Centre, Queen’s University Belfast, Belfast BT7 1NN, UK Department of Astronomy, Cornell University, Ithaca, New York 14853, USA Astronomical Institute, Czech Academy of Sciences, Friˇcova 298, 25165, Ondˇrejov, Czech Republic Instituto de Astrof´ısica de Canarias, c/ V´ıa L´actea s/n E-38205 La Laguna, Tenerife, Spain Isaac Newton Group of Telescopes, Apartado de Correos 321, Santa Cruz de La Palma, E-38700, Spain (Received November 2, 2020; Revised February 1, 2021; Accepted February 16, 2021)
ABSTRACTWe present high-resolution near-infrared spectra taken during eight transits of 55 Cancri e, a nearbylow-density super-Earth with a short orbital period ( <
18 hours). While this exoplanet’s bulk densityindicates a possible atmosphere, one has not been detected definitively. Our analysis relies on theDoppler cross-correlation technique, which takes advantage of the high spectral resolution and broadwavelength coverage of our data, to search for the thousands of absorption features from hydrogen-,carbon-, and nitrogen-rich molecular species in the planetary atmosphere. Although we are unable todetect an atmosphere around 55 Cancri e, we do place strong constraints on the levels of HCN, NH ,and C H that may be present. In particular, at a mean molecular weight of 5 amu we can rule outthe presence of HCN in the atmosphere down to a volume mixing ratio (VMR) of 0.02%, NH downto a VMR of 0.08%, and C H down to a VMR of 1.0%. If the mean molecular weight is relaxed to2 amu, we can rule out the presence of HCN, NH , and C H down to VMRs of 0.001%, 0.0025%,and 0.08% respectively. Our results reduce the parameter space of possible atmospheres consistentwith the analysis of HST/WFC3 observations by Tsiaras et al. (2016), and indicate that if 55 Cancri eharbors an atmosphere, it must have a high mean molecular weight and/or clouds. Keywords: planets and satellites: atmospheres — planets and satellites: individual (55 Cancri e) —techniques: spectroscopic INTRODUCTIONOver the past several years, our understanding of hotJupiter atmospheres has expanded enormously. Thisis due in large part to high-precision observations oftransiting exoplanets that have enabled the detection ofatomic and molecular species and provided constraintson the atmospheric structures of several gas giants (seee.g. Madhusudhan 2019 for a broad overview of previousdetections).In contrast, the atmospheric properties of lower-mass,super-Earth exoplanets remain largely unconstrained.
Corresponding author: Emily K. [email protected]
Their shallower transit depths and smaller atmosphericscale heights produce weaker spectroscopic signals thatare more challenging to detect given our current obser-vational capabilities. However, these atmospheres areof great scientific interest: in particular, they are pre-dicted to be extraordinarily diverse, potentially beingrich in carbon, silicate, and/or water vapors (e.g. Schae-fer & Fegley 2009; Miguel et al. 2011; Hu & Seager 2014).Their atmospheric compositions are likely to reflect thevaried formation and evolutionary histories that exo-planets in the super-Earth regime have experienced (e.g.Madhusudhan et al. 2016), and can shed light on theseotherwise-elusive worlds.A super-Earth of particular interest is the nearbytransiting planet 55 Cancri e (hereafter referred to as a r X i v : . [ a s t r o - ph . E P ] F e b Deibert et al.
55 Cnc e), the existence of which was first suggestedby McArthur et al. (2004). Dawson & Fabrycky (2010)later determined that its initially-derived period of 2.808days was an alias of its true, much shorter period of ∼ ∼ M ⊕ and radius of ∼ R ⊕ (Crida et al. 2018). It orbits a bright (V=5.95;von Braun et al. 2011) G8V host star. The ultra-shortorbital period of 55 Cnc e results in an equilibrium tem-perature in excess of 2000K (e.g. Demory et al. 2016b),potentially leading to exotic atmospheric properties.While the planet’s bulk density indicates that it couldharbor an atmosphere (see for e.g. Gillon et al. 2012;Bourrier et al. 2018), several observational attemptshave not been able to definitely detect its presence. Inparticular, Ehrenreich et al. (2012) found no evidencefor an extended hydrogen atmosphere, and Esteves et al.(2017) and Jindal et al. (2020) derived limits on waterabsorption consistent with the exoplanet having eithera hydrogen-poor atmosphere or a hydrogen-rich atmo-sphere that is significantly depleted in water vapour.Demory et al. (2016b) measured the photometric phasecurve of 55 Cnc e at 4.5 µ m with the Spitzer Space Tele-scope, finding a large temperature contrast between theexoplanet’s permanent day and night sides and a hot-spot on the day side offset by 40 ◦ from the substellarpoint.Using grism spectroscopy data from the Wide FieldCamera 3 (WFC3) aboard the Hubble Space Telescope(HST), Tsiaras et al. (2016) reported the detection ofan atmosphere around 55 Cnc e and suggested that it islikely hydrogen-rich, with a large scale height and highC/O ratio. They indicate that HCN is the most likelymolecular candidate able to explain features detectedat 1.42 and 1.54 µ m, but caution that additional ob-servations over a broader wavelength range would helpconfirm the results.Hammond & Pierrehumbert (2017) modelled thephase curve of 55 Cnc e using an atmospheric globalcirculation model (GCM) and found that a 90% – 10%mixture of H and N in the atmosphere with cloud-forming species such as SiO can well approximate theobserved phase variations. However, a complementaryanalysis by Angelo & Hu (2017) found that the atmo-sphere is likely dominated by either CO or N with mi-nor abundances of H O or CO . More recently, Miguel(2019) explored the expected chemical composition ofthe atmosphere of 55 Cnc e, and concluded that trans-mission spectra should show strong features of NH and HCN at mid- to long-infrared wavelengths if theatmosphere is nitrogen-rich, as may be expected from the large day-night temperature contrast (Hammond &Pierrehumbert 2017).In this paper, we present high-resolution spectroscopyof 55 Cnc e from 950 – 2350 nm, focusing in particularon absorption features in the near-infrared (NIR) due toHCN. We also investigate the presence of NH , C H ,CO, CO , and H O at NIR wavelengths. Our search forHCN is informed by the observational results of Tsiaraset al. (2016), who suggested that HCN is present in theatmosphere at a high volume mixing ratio (VMR) withacceptable values as low as 10 − . In addition, Zilin-skas et al. (2020) explored plausible VMRs for the caseof a nitrogen-dominated atmosphere (following Miguel2019). They find that CO may be present at relativelyhigh VMRs ( ∼ − . , their Fig. 3) across a wide rangeof pressures and C/O ratios. The expected VMR of H Odepends largely on the C/O ratio, while CO is expectedto have a VMR (cid:46) − . for all pressures and C/O ratiosconsidered. C H is only expected at VMRs > − forC/O >
2; however, tentative results from Tsiaras et al.(2016) suggested that C H may be present with a VMRas high as 10 − at C/O ∼ ∼ OBSERVATIONSWe observed six transits of 55 Cnc e with the CalarAlto high-Resolution search for M dwarfs with Ex-oearths with Near-infrared and optical ´Echelle Spectro-graphs (CARMENES; Quirrenbach et al. 2014) locatedat the Calar Alto Astronomical Observatory. In thispaper we focus on the NIR channel, which spans thewavelength range of 960 – 1710 nm.
IR Spectroscopy of 55 Cancri e Table 1.
Summary of observations.
Night Date (UT) Instrument/Telescope Duration (hr) Frames (In/Out) Exp. Time (s) Avg. SNR Used in Analysis?1 2016 Dec 26 CARMENES/Calar Alto 11.6 363 (80/283) 33.9 91 Y2 2017 Nov 22 CARMENES/Calar Alto 5.7 141 (55/86) 58.0 145 Y3 2017 Nov 24 CARMENES/Calar Alto 5.8 115 (43/72) 87.8 157 Y4 2017 Dec 9 CARMENES/Calar Alto 1.0 26 (9/16) 53.1 108 N5 2017 Dec 11 CARMENES/Calar Alto 5.6 92 (45/47) 86.6 71 Y6 2017 Dec 17 CARMENES/Calar Alto 5.5 59 (14/45) 87.9 74 N7 2019 Feb 14 SPIRou/CFHT 2.6 77 (47/30) 94.7 268 Y8 2019 Feb 25 SPIRou/CFHT 2.5 73 (47/26) 94.7 300 Y9 2019 Apr 17 SPIRou/CFHT 2.7 54 (34/20) 94.7 247 Y10 2019 May 1 SPIRou/CFHT 2.3 73 (46/27) 94.7 250 Y1 (In/Out) refers to the number of in- and out-of-transit frames for each night.2 The exposure times refer to the average exposure time across all observations for each night.
The observations were taken with varying exposuretimes (see Table 1), and in general each observationcovered one full transit of 55 Cnc e (the transit dura-tion being approximately 1.6 hours). We note that theobservations taken on Night 4 and Night 6 (hereafterN and N , respectively) suffered from poor observingconditions and did not cover the full transit. For thisreason, we chose to exclude these nights from our anal-ysis. The spectral resolving power of the instrument inthe NIR is nominally (cid:46) ∼ DATA REDUCTIONThe raw data frames obtained using CARMENESwere initially reduced by the observatory with theCARMENES reduction pipeline CARACAL (Caballeroet al. 2016), while the data obtained using SPIRou wereextracted by the observatory using the SPIRou Data Re-
Table 2.
Stellar and Planetary Parameters Used in This Anal-ysis
Parameter Value ReferenceSpectral Type G8 von Braun et al. (2011)J band Flux 4.59 Ducati (2002)H band Flux 4.14 Ducati (2002)K band Flux 4.015 Cutri et al. (2003) T eff (K) 5172 Yee et al. (2017)log g R ∗ ( R (cid:12) ) 0.980 Crida et al. (2018) K ∗ (m s − ) 6.02 Bourrier et al. (2018) m p ( M ⊕ ) 8.59 Crida et al. (2018) r p ( R ⊕ ) 1.947 Crida et al. (2018) V sys (km s − ) 27.58 Nidever et al. (2002)Orbital Period (days) 0.7365474 Bourrier et al. (2018)Mid-transit (JD) 2457063.2096 Bourrier et al. (2018)Semimajor Axis (au) 0.01544 Bourrier et al. (2018)Inclination (degrees) 83.59 Bourrier et al. (2018) R p /R ∗ a/R ∗ µ µ K ∗ : radial velocity semi-amplitude duction Software (DRS) . Note that while the SPIRouDRS does include a telluric correction, we have chosento carry out this correction ourselves (see Section 3.1);the data products extracted from the SPIRou DRS are Deibert et al. thus wavelength-corrected 2D spectra. Note as well thatboth pipelines supply a Barycentric Earth Radial Veloc-ity (BERV) correction. Examples of extracted spectrafor both CARMENES and SPIRou are shown in the topleft and top right panels of Fig. 1 respectively, whileall extracted and reduced spectra are shown in the firstpanels of the figures presented in Appendix A.The next steps of our data reduction process pro-ceeded similarly to Deibert et al. (2019). We interpo-lated our data to a common wavelength grid with alinear interpolation. We then removed contaminatingcomic rays through median filtering, where points fallingoutside of a threshold of 5 median absolute deviationswere flagged as outliers and masked during subsequentanalyses.To account for the grating-dependent variation inbrightness at different spectral orders in the data (i.e.the “blaze function”), we carried out a blaze correction.Such a correction is necessary for observations taken us-ing ´Echelle spectrographs. The effect was removed sep-arately for each night and each individual order of thedata. To do this, we divided the first science spectrum ofeach night (the “reference spectrum”) from all sciencespectra, and fit this product with a low-order polyno-mial. The polynomial fit was then divided out of eachindividual observation. This removed the effects of theblaze response function, resulting in a normalized spec-trum that could be used for subsequent analysis. Theprocedure additionally corrects for other wavelength-dependent variations such as airmass effects or differ-ential slit losses.The results of these initial data reduction steps on asingle order of N (the 24th order) and N (the 30th or-der) can be seen in the second left and second right pan-els of Fig. 1 for the CARMENES and SPIRou observa-tions, respectively. Additionally, the results of applyingthese corrections to all nights/orders of both datasetsare shown in the second panels of the figures presentedin Appendix A.3.1. Correction of Systematic Effects
After the initial reduction process described above,the resultant spectra were largely dominated by bothstellar and telluric absorption lines, seen as vertical linesin, e.g., the second left and second right panels of Fig.1. However, due to the essentially-stationary nature ofthese lines when compared with absorption due to theexoplanet’s atmosphere (which varies in radial velocityfrom ∼ −
60 km/s to ∼ +60 km/s over the course of thetransit) these features can be removed using the sys-rem algorithm, first described by Tamuz et al. (2005). sysrem allows for linear, systematic effects that appear in many datasets of the same sample to be removedthrough an algorithm that, in the case of equal un-certainties, reduces to a Principal Component Analysis(PCA) algorithm.The correction was determined using both in- and out-of-transit frames, and each order of the data was treatedseparately. For all observations, the average airmass ateach exposure was taken as an initial approximation ofthe systematic effects to be removed. For consistency,we chose to apply the same number of iterations of thealgorithm to each order; to determine this number, wecalculated the root-mean-square (rms) of the residualsafter subsequent iterations of sysrem . We found thaton average, six iterations of the algorithm was the pointat which the rms of the residuals had plateaued andadditional applications of the algorithm did not yield asignificant improvement. The third left and third rightpanels of Fig. 1 show the results of applying 6 iterationsof the sysrem algorithm to CARMENES and SPIRouspectra, respectively. The results of applying six itera-tions to all nights/orders of each data set are shown inthe figures in Appendix A.The algorithm performs poorly around strong orclosely-spaced lines; in particular, several orders of ourobservations (i.e. those at the edges of the Y, J, H,and K photometric bands) suffer from significant tel-luric absorption. These strong lines make the blazeresponse correction difficult, and as a result, nonlineareffects are introduced into the spectra which cannotbe removed using sysrem . To reduce contaminationfrom these poorly-constrained frames, we followed e.g.Snellen et al. (2010), Esteves et al. (2017), and Deibertet al. (2019) in weighting each frame and each pixel byits standard deviation (shown in the fourth panels ofFigs. 1, as well as the figures presented in AppendixA). This step reduces the contribution from the noisierportions of the data. Additionally, we have chosen tofully exclude several particularly-contaminated orders(those located within the gaps between the Y, J, H, andK bands) from further analysis. These are described ingreater detail in Appendix A.3.1.1. Telluric Feature Removal with Molecfit
Although the use of sysrem for the removal of telluricfeatures is well-established (see for e.g. the discussion inBirkby 2018), we repeated the telluric removal processfor a subset of our observations/atmospheric models us-ing Molecfit (Smette et al. 2015; Kausch et al. 2015),a tool originally developed for the European SouthernObservatory (ESO) consortium that corrects telluric ab-sorption based on synthetic modelling of the Earth’s at-mospheric transmission. Molecfit has recently been used
IR Spectroscopy of 55 Cancri e . . O r b i t a l P h a s e − . . . R a w D a t a . . O r b i t a l P h a s e − . . . B l a ze C o rr ec t i o n . . O r b i t a l P h a s e − . . . S Y S R E M . . . S t a nd a r d D e v . . . . S Y S R E M . . O r b i t a l P h a s e − . . . M o l ec fi t . . . S t a nd a r d D e v . . . . M o l ec fi t Figure 1.
An example of the data reduction process described in Section 3, as applied to a single order of Night 2 of theCARMENES data (left) and the SPIRou data (right). In each case, the top panel shows the raw data; the second panel showsthe data after the blaze correction and removal of cosmic rays as described in Section 3; the third panel shows the data after6 iterations of the sysrem algorithm (see Section 3.1); the fourth panel shows the standard deviation across each wavelengthchannel after applying the sysrem algorithm; the fifth panel shows the data (i.e. the second panel) after correcting it withMolecfit (see Section 3.1.1); and the sixth panel shows the standard deviation along each wavelength channel after correctingwith Molecfit and removing residual stellar lines. Note that there are gaps present in the CARMENES orders; this is visible inthe left panels.
Deibert et al. on both high-resolution optical and NIR observations(e.g., Allart et al. 2017, 2018; Salz et al. 2018; Cabotet al. 2020; Seidel et al. 2020, among others).Here, we largely followed the methods laid out in Al-lart et al. (2017) and Salz et al. (2018) to apply Molecfitto our own observations. We used version 2.0.1 of thesoftware, which was the most recent version available atthe time of our analysis. Following Salz et al. (2018),we used a high-resolution synthetic stellar spectrum(PHOENIX; Husser et al. 2013) matching the proper-ties of 55 Cnc A ( T eff ≈ g ≈ ∼ solarmetallicity; Yee et al. 2017) in order to identify and maskstellar features in our spectra. We then checked thesemasked regions by eye, and adjusted where necessary.Following this, we selected narrow regions containingintermediate-strength telluric lines (i.e. not saturated),few or no stellar lines, and a flat continuum distributedthroughout our spectra to fit. The remaining regions ofeach spectrum were corrected with the Calctrans tool,which is used to apply fits from Molecfit to the rest ofthe data. Each individual spectrum was fit and cor-rected separately. The goodness-of-fits for our data arecomparable to those obtained by Allart et al. (2017); inour case, the average χ across all fits is 10.9. We notethat this somewhat large value can likely be explainedby the fact that our fit does not include stellar lines. Ex-amples of this correction can be seen in the fifth panelsof Fig. 1, while an example of the standard deviation ofthis correction across wavelength channels can be seenin the final panels of Fig. 1.Additional details on our fit results, as well as theparameters used for our fits, are presented in AppendixC.1. We discuss the efficacy of Molecfit compared tothat of sysrem in further detail in Section 6.2. ANALYSISOur analysis relies on the Doppler cross-correlationtechnique, which was used to obtain a robust atmo-spheric detection by Snellen et al. (2010). An overviewof the work preceding Snellen et al. (2010), as well as thenumerous detections made since then, is found in Birkby(2018). This technique requires high-resolution datain order to resolve individual absorption features froman atmospheric species, which are then cross-correlatedwith atmospheric models. The precision of the methodincreases with the number of lines included in the cross-correlation (e.g. Birkby 2018). That means molecules(which have rotation-vibration transitions that producethousands of absorption lines) are ideal targets, and arethus the focus of our analysis.Following Snellen et al. (2010) and Deibert et al.(2019), among others, we Doppler-shifted our atmo- spheric models to a range of velocities, and cross-correlated these with each frame of the data. We thenphase-folded the correlations from the in-transit framesto a range of systemic velocities and summed over eachvelocity in order to obtain a grid of correlation strengthsas a function of both systemic and Keplerian velocities.The grids were then summed over all relevant orders andall nights of our observations to increase the detectionstrength. An example of the analysis is shown in Fig. 2,and the method is described in further detail in Section4.2.Note that we have only included orders for which theatmospheric model in question contains absorption fea-tures. Examples of these atmospheric models are dis-played in Appendix B, and the models are described infurther detail in the next section.4.1.
Atmospheric Models
Our analysis involves independently testing for thepresence of various molecules (HCN, NH , C H , CO,CO , and H O) in the atmosphere of 55 Cnc e throughcross-correlation with so-called “parametric models”similar to those used in Jindal et al. (2020). We explorea range of volume mixing ratios (VMRs) and meanmolecular weights ( µ ’s) of each of these molecules, de-scribed in further detail below. We note that thesemodels are not self-consistent, and are instead meant toprovide us with an initial insight into the exoplanet’satmosphere and the limitations of our method. Fur-thermore, various models (i.e. those with low meanmolecular weights; see the top-left panels of the fig-ures in the following section) are non-physical. Suchmodels allow us to test our method, as they are easily-recoverable by the model injection/recovery process (seeSection 4.3). We describe the calculations of all modelsbelow. 4.1.1. Atmospheric Model Calculation
To constrain the volume mixing ratios (VMRs) andmean molecular weights ( µ ’s) of HCN, NH , C H , CO,CO , and H O in the atmosphere of 55 Cnc e, we gener-ated a set of models with varying VMRs and µ ’s for eachof these compounds individually embedded in an inertH atmosphere. The code used to generate these mod-els is an updated version of the line-by-line, plane par-allel radiative transfer code used in, e.g., Esteves et al.(2017); Jindal et al. (2020).Each model was generated on a wavelength grid span-ning the full range of our observations, i.e. between ∼
950 and 2500 nm with a velocity step-size of 1 km/s.The model atmosphere was calculated across 50 at-mospheric layers, and opacities were integrated along
IR Spectroscopy of 55 Cancri e −
200 0 200V sys [km/s] − . . . O r b i t a l P h a s e −
50 0 50V sys [km/s]0100200300 K e p l e r i a n V e l o c i t y [ k m / s ] −
200 0 200V sys [km/s] −
50 0 50V sys [km/s] −
50 0 50V sys [km/s] − . − . − . − . . . C o rr e l a t i o nS t r e n g t h [ A r b i t r a r y U n i t s ] Figure 2.
An example of the data analysis routine used in this work. The top two panels on the left show the results of carryingout the Doppler cross-correlation process as described in Section 4.2. The top-left panel shows the results of cross-correlatingone order of the first night of SPIRou data (N ) with a model containing HCN at a volume mixing ratio of 0.1% and a meanmolecular weight of 2 amu. The top-middle panel shows the same process, but with the atmospheric model injected into thedata at 10 times its nominal strength (see Section 4.3 for a description of the model injection process). The planetary signal isvisible as a diagonal line corresponding to the changing radial velocity of the planet, which varies from ∼ −
60 km/s to ∼ +60km/s over the course of the transit. The bottom two panels on the left show the results of phase-folding the corresponding toppanels, as described in Section 4.2, with the data-only phase-folded plot on the left and the data-plus-model phase-folded ploton the right. The panel on the right shows a horizontal slice of the phase-folded plots at the Keplerian velocity of 55 Cnc e; theblack line shows the data-only slice while the magenta line shows the data-plus-model slice. The dark- and light-grey contoursshow 1 σ and 3 σ confidence levels, respectively; the process used to generate these is described in Section 4.4. We see that thedata-only slice (black line) does not exceed 3 σ whereas the data-plus-model slice (magenta line) does, indicating that if thismodel were present in the atmosphere of 55 Cnc e, we would have been able to detect it at a confidence level of > σ . slanted paths from the direction of the star to the ob-server. Each model includes only a single molecule,and we assume a Voigt profile for the lines with a linewing cutoff of 100/cm. The models were temperature-broadened using standard database parameters and in-cluded pressure-broadening coefficients from HITRAN(Gordon et al. 2017). The line strengths were adjustedfor temperature at each layer. We assume that theVMR is constant throughout the atmosphere. In ad-dition to molecular absorption, Rayleigh scattering andH -H collision-induced absorption were also taken intoaccount in all of our models (Borysow et al. 2001; Bo-rysow 2002). As in Esteves et al. (2017) and Jindalet al. (2020), we account for the geometry during tran-sit when performing the radiative transfer. Like Jindalet al. (2020), we adjust the radius at the bottom of the models iteratively in order to match, on average, themeasured value of R p /R ∗ .In the case of HCN, C H , and NH , we made useof the HITRAN line lists (Gordon et al. 2017). ForCO, CO , and H O, we made use of the HITEMP linelists (Rothman et al. 2010). As in Jindal et al. (2020),we make use of the full line lists for our models. Wenote that as some of these line lists are incomplete (fore.g., the C H line list), the shapes of various molecularbands in our models are not completely accurate: forexample, several of the models presented in AppendixB show sharp cutoffs at both ends of their molecularbands.To compare these models with our data, we convolvedeach of them to the resolution of our observations us-ing a Gaussian kernel. We then spline-interpolated to Deibert et al. the same wavelength grid when calculating the cross-correlation function.Example models for each molecule are displayed inAppendix B.4.2.
Doppler Cross-Correlation
For each night of observations, our data were cross-correlated with models at Doppler shifts spanning −
250 km/s to 250 km/s, with 1 km/s steps betweeneach velocity. This is shown in the top-left panels of Fig.2. Next, we phase-folded the correlation signal from thein-transit frames by shifting each correlation to the ref-erence frame of 55 Cnc e. The in-transit frames weredetermined using a model light curve generated withthe occultquad package from Mandel & Agol (2002).The parameters used for this model light curve, includ-ing limb-darkening parameters from Claret (2004), aresummarized in Table 2. In order to account for the factthat the planetary radial velocity is not known withperfect precision, as well as to better understand thebehavior of the cross-correlation function at velocitiesoutside of the planetary rest frame (e.g. to investigatespurious correlation peaks due to residual telluric lines),we created a correlation map over a wide range of sys-temic velocities (V sys ) and planetary orbital velocities( K p sin 2 πφ ( t ), where φ ( t ) is the orbital phase). Wecreated the map for planetary RV semi-amplitude ( K p )values ranging from 1 to 300 km/s, with a 0.5 km/sstep between each value. An example is shown in thebottom-left panels of Fig. 2.For each model, these correlation grids were summedover orders containing significant molecular absorption,and then summed over all observations.4.3. Model Injection/Recovery Tests
To assess the robustness of our pipeline, and to placeconstraints on the atmospheric composition of 55 Cnc e,we performed injection and recovery tests for each modelused in our analysis. The goal of these tests was to de-termine whether or not our data reduction process, in-cluding the sysrem algorithm, removes any signal thatmay be present, as well as to place sensitivity limits onour results.We carried out these injection/recovery tests by mul-tiplying the in-transit frames of each observation (priorto any data reduction past initial processing at the tele-scope) by an atmospheric model shifted to the frameof the exoplanet to create a synthetic “model + data”data set. Note that the model was only added to the in-transit frames of our data. This was done for each modeldescribed in Section 4.1, each order of every observation,and each night of observation. The synthetic “model + data” spectra were then processed through our data re-duction pipeline described in Section 3, and analyzedusing the Doppler cross-correlation method described inSection 4.2. An example of the process is shown in themiddle two panels of Fig. 2.As a result, we were able to assess the sensitivity limitsof our analysis, by determining which synthetic spectrawere recovered by our pipeline. For example, the top-leftpanel in Fig. 3 shows a case where a correlation betweena model atmosphere and the corresponding syntheticdata set resulted in a detection (magenta line), whereasa correlation between that same model atmosphere andthe true data set (black line) did not result in a detec-tion. Likewise, the top-right panel in Fig. 3 shows a casewhere neither a correlation between a model atmosphereand the corresponding synthetic data set (magenta line)or the correlation between that same model atmosphereand the true data set (black line) resulted in a detection.The model atmosphere in question (HCN with a VMRof 0.1% and a mean molecular weight of 10 amu) wasbeyond the sensitivity limits of our detection pipeline.We note that various models with non-physical, lowmean molecular weights (e.g. the top-left panel in Figure8) allow us to confirm that the model injection/recoveryprocess is working as expected. Such models are easilyrecovered by the injection/recovery process, as seen inthe top-left panels of the figures in the following section.This model injection/recovery process thus allowed usto place constraints on both the atmospheric makeupof the exoplanet as well as the detection limits of ourobservations. 4.4.
Detection Significance
In order to assess the significance of our results, wefollowed the methods described in Esteves et al. (2017)and Deibert et al. (2019). We derived 1 σ and 3 σ con-fidence levels for each feature in each night of the databy randomly selecting a set of out-of-transit frames cor-responding to the number of in-transit frames for eachnight, assigning an in-transit phase to each of these spec-tra, and following through with the cross-correlation andphase-folding process as described in Section 4.2. We re-peated this process 10,000 times, sorted the data, andthen selected the 1 σ and 3 σ confidence levels based onthe outcome. These levels were then compared to thecorrelation strengths of each model in order to assesstheir significance. An example is shown in the right-most panel of Fig. 2. RESULTSIn this section we present the results of applying theDoppler cross-correlation method, as described in Sec-tion 4.2, to our observations. As noted previously, we are
IR Spectroscopy of 55 Cancri e , C H , CO, CO , and H O.Note that the figures in the following sections show onlya subset of the models we analyzed, and all additionalmodels not displayed in the figures did not result in sig-nificant detections or limits. Note as well that we areprobing a grid of mean molecular weights and VMRs,and various combinations result in models that are non-physical. For example, a high ( ∼
10 %) VMR for CO would result in a mean molecular weight higher than 2amu. However, such models allow us to test our methodand ensure that the injection/recovery process is work-ing as expected.5.1. Hydrogen Cyanide
Fig. 3 shows the results of our search for HCN inthe atmosphere of 55 Cnc e. Our aim was to furtherinvestigate the results of Tsiaras et al. (2016), who usedHST/WFC3 observations to report the detection of anatmosphere and suggested that HCN is the most likelymolecule able to account for the observed absorptionfeatures.We analyzed a range of atmospheric models varyingin volume mixing ratio from 0.1% down to 5 × − %,and in mean molecular weight from 2 to 20 amu. Ourmodel spectra were generated using HITRAN2016 (Gor-don et al. 2017). We note that the results depend on theaccuracy of the line list used, thus future studies withupdated line lists may yield different outcomes.As seen in Fig. 3, we can rule out the presence ofHCN in the atmosphere of 55 Cnc e at a mean molecularweight of 2 amu with a volume mixing ratio of 0.001%;if the mean molecular weight is increased to 5 amu, thelowest volume mixing ratio that we can rule out is 0.02%.5.2. Ammonia
Fig. 4 shows the results of our search for NH in theatmosphere of 55 Cnc e.We analyzed a set of models ranging in volume mixingratio from 5% to 10 − %, and mean molecular weightranging from 2 amu to 20 amu.As can be seen in Fig. 4, we are able to rule NH outof the atmosphere at a mean molecular weight of 2 amuwith a volume mixing ratio as low as 0.0025%; if themean molecular weight is increased to 5 amu, we canstill rule NH out with a volume mixing ratio as low as0.08%. 5.3. Acetylene
Fig. 5 shows the results of our search for C H in theatmosphere of 55 Cnc e. We analyzed a set of models ranging in volume mixingratio from 20% to 10 − %, and mean molecular weightranging from 2 amu to 20 amu.As can be seen in Fig. 5, we are able to rule C H out of the atmosphere of 55 Cnc e at a mean molecularweight of 2 amu with a volume mixing ratio as low as0.08%, and at a mean molecular weight of 5 amu with avolume mixing ratio as low as 1.0%.5.4. Carbon Monoxide
The results of our search for CO in the atmosphere of55 Cnc e are summarized in Fig. 6.We analyzed a range of atmospheric models varyingin volume mixing ratio from 10% down to 10 − %, andin mean molecular weight from 2 to 30 amu.As shown in Fig. 6, we are unable to detect atmo-spheric CO in our data. However, we are able to ten-tatively rule out the possibility of CO being present inthe atmosphere of 55 Cnc e at a mean molecular weightof 2 amu and a volume mixing ratio as low as 1.0% atthe 3 σ level. Note however that there are numerous ad-ditional features with peaks > σ that are likely dueto noise in the data (see, e.g., the discussion in Esteveset al. 2017, who noticed a similar phenomenon for opti-cal transit data of 55 Cnc e). For this reason, we cautionthat our limits on the presence of CO are only tentative,and warrant further investigation.5.5. Carbon Dioxide
The results of our search for CO in the atmosphereof 55 Cnc e are summarized in Fig. 7.As was the case with CO (see Section 5.4), we analyzeda range of atmospheric models varying in volume mixingratio from 10% down to 10 − %, and in mean molecularweight from 2 to 30 amu.As can be seen in Fig. 7, we are neither able to detectatmospheric CO in our data nor place any significantconstraints on its presence. We note that while a peakis present in the injected data at a systemic velocity of0 km/s and the orbital velocity of 55 Cnc e, as wouldbe expected for a detection, it does not surpass 3 σ andtherefore is not sufficiently significant to make any con-clusions about the presence or lack of atmospheric CO .5.6. Water
The results of our search for H O in the atmosphereof 55 Cnc e are summarized in Fig. 8.We analyzed a range of atmospheric models varyingin volume mixing ratio from 20% down to 10 − %, andin mean molecular weight from 2 to 20 amu.As was the case with CO (see Section 5.5), none ofthe injected models seen in Fig. 8 surpass the 3 σ confi-dence level, and thus we are unable to place any limits0 Deibert et al. . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu0.1% VMR µ = 5 amu0.1% VMR µ = 10 amu0.1% VMR − . . µ = 2 amu0.05% VMR µ = 5 amu0.05% VMR µ = 10 amu0.05% VMR − . . µ = 2 amu0.02% VMR µ = 5 amu0.02% VMR µ = 10 amu0.02% VMR − . . µ = 2 amu0.01% VMR µ = 5 amu0.01% VMR µ = 10 amu0.01% VMR − . . µ = 2 amu0.005% VMR µ = 5 amu0.005% VMR µ = 10 amu0.005% VMR − . . µ = 2 amu0.002% VMR µ = 5 amu0.002% VMR µ = 10 amu0.002% VMR − . . µ = 2 amu0.001% VMR µ = 5 amu0.001% VMR µ = 10 amu0.001% VMR −
50 0 50 − . . µ = 2 amu0.0005% VMR −
50 0 50 µ = 5 amu0.0005% VMR −
50 0 50 µ = 10 amu0.0005% VMR Figure 3.
Results of injecting HCN models of various strengths into our data, and repeating the Doppler cross-correlationprocess. In all panels, the black line represents the original data and the magenta line represents the data with an atmosphericmodel injected (see Section 4.3). The volume mixing ratio and mean molecular weight of each model are indicated in the bottomright of the panel. The dark- and light-grey contours in each panel correspond to 1 σ and 3 σ confidence levels, respectively, andwere calculated using the process described in Section 4.4. The data have been phase-folded and sliced at the orbital velocityof 55 Cnc e, K p ≈ . IR Spectroscopy of 55 Cancri e . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu5.0% VMR µ = 5 amu5.0% VMR µ = 10 amu5.0% VMR − . . µ = 2 amu1.3% VMR µ = 5 amu1.3% VMR µ = 10 amu1.3% VMR − . . µ = 2 amu0.63% VMR µ = 5 amu0.63% VMR µ = 10 amu0.63% VMR − . . µ = 2 amu0.16% VMR µ = 5 amu0.16% VMR µ = 10 amu0.16% VMR − . . µ = 2 amu0.079% VMR µ = 5 amu0.079% VMR µ = 10 amu0.079% VMR − . . µ = 2 amu0.02% VMR µ = 5 amu0.02% VMR µ = 10 amu0.02% VMR − . . µ = 2 amu0.005% VMR µ = 5 amu0.005% VMR µ = 10 amu0.005% VMR − . . µ = 2 amu0.0025% VMR µ = 5 amu0.0025% VMR µ = 10 amu0.0025% VMR −
50 0 50 − . . µ = 2 amu0.0013% VMR −
50 0 50 µ = 5 amu0.0013% VMR −
50 0 50 µ = 10 amu0.0013% VMR Figure 4.
Results of injecting NH models of various strengths into our data, and repeating the Doppler cross-correlationprocess. The panels are as described in the caption of Fig. 3. We are able to rule out the presence of NH in the atmosphere of55 Cnc e at a mean molecular weight of 2 amu with a volume mixing ratio as low as 0.0025%, and at a mean molecular weightof 5 amu with a volume mixing ratio as low as 0.08%. We note that any additional models with lower VMRs or higher meanmolecular weights which were analyzed but not displayed in this figure did not yield significant detections or limits. Deibert et al. . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu20.0% VMR µ = 5 amu20.0% VMR µ = 10 amu20.0% VMR − . . µ = 2 amu10.0% VMR µ = 5 amu10.0% VMR µ = 10 amu10.0% VMR − . . µ = 2 amu5.0% VMR µ = 5 amu5.0% VMR µ = 10 amu5.0% VMR − . . µ = 2 amu2.5% VMR µ = 5 amu2.5% VMR µ = 10 amu2.5% VMR − . . µ = 2 amu1.3% VMR µ = 5 amu1.3% VMR µ = 10 amu1.3% VMR − . . µ = 2 amu1.0% VMR µ = 5 amu1.0% VMR µ = 10 amu1.0% VMR − . . µ = 2 amu0.63% VMR µ = 5 amu0.63% VMR µ = 10 amu0.63% VMR − . . µ = 2 amu0.32% VMR µ = 5 amu0.32% VMR µ = 10 amu0.32% VMR − . . µ = 2 amu0.16% VMR µ = 5 amu0.16% VMR µ = 10 amu0.16% VMR − . . µ = 2 amu0.1% VMR µ = 5 amu0.1% VMR µ = 10 amu0.1% VMR −
50 0 50 − . . µ = 2 amu0.079% VMR −
50 0 50 µ = 5 amu0.079% VMR −
50 0 50 µ = 10 amu0.079% VMR Figure 5.
Results of injecting C H models of various strengths into our data, and repeating the Doppler cross-correlationprocess. The panels are as described in the caption of Fig. 3. We are able to rule C H out of the atmosphere of 55 Cnc e at amean molecular weight of 2 amu with a volume mixing ratio as low as 0.08%, and at a mean molecular weight of 5 amu with avolume mixing ratio as low as 1.0%. We note that any additional models with lower VMRs or higher mean molecular weightswhich were analyzed but not displayed in this figure did not yield significant detections or limits. IR Spectroscopy of 55 Cancri e . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu10.0% VMR µ = 5 amu10.0% VMR − . . µ = 2 amu1.0% VMR µ = 5 amu1.0% VMR − − −
20 0 20 40 60 − . . µ = 2 amu0.1% VMR − − −
20 0 20 40 60 µ = 5 amu0.1% VMR Figure 6.
Results of injecting CO models of various strengths into our data, and repeating the Doppler cross-correlationprocess. The panels are as described in the caption of Fig. 3. We are able to tentatively rule out the presence of CO in theatmosphere of 55 Cnc e at a mean molecular weight of 2 amu down to a volume mixing ratio of 1.0% at a confidence of 3 σ , ascan be seen in the top two panels on the left. However, we caution that there are many additional peaks surpassing 1 σ in theresults (likely due to noise in the data) and that this may have affected our model injection/recovery process. Deibert et al. . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu10.0% VMR µ = 5 amu10.0% VMR − . . µ = 2 amu1.0% VMR µ = 5 amu1.0% VMR − − −
20 0 20 40 60 − . . µ = 2 amu0.1% VMR − − −
20 0 20 40 60 µ = 5 amu0.1% VMR Figure 7.
Results of injecting CO models of various strengths into our data, and repeating the Doppler cross-correlationprocess. The figures are as described in the caption of Fig. 3. As neither the data (black lines) nor the data with modelsinjected (magenta lines) surpass the 3 σ confidence levels, we have neither detected nor can place limits of the presence of CO in the atmosphere of 55 Cnc e. of the presence of H O in the atmosphere of 55 Cnc ewith these data alone. This is likely due to the imperfectremoval of telluric water lines in the data (see Section3.1 and the additional discussion in Section 6.2 and Ap-pendix D for further details). DISCUSSION6.1.
Comparison with Tsiaras et al. 2016
Our model injection/recovery tests for HCN (seeFig. 3) significantly narrow the parameter space of po-tential atmospheres that are consistent with the resultsreported in Tsiaras et al. (2016). These authors sam-pled volume mixing ratios from 1 to 10 − and meanmolecular weights from 2 to 10 amu. Their analysisindicates that the mean molecular weight of the atmo-sphere peaks at roughly 4 amu, with higher values beingunlikely. Furthermore, strong absorption seen near 1.4and 1.6 µ m in their analysis indicates that the meanmolecular weight is relatively low. They also reportedthat (of the molecules considered in their fit) HCN isthe most likely absorber able to explain their observedabsorption features, and that a scenario with a highvolume mixing ratio for HCN is favoured, though valuesas low as 0.001% are acceptable. While our results do rule out the most likely scenar-ios considered by Tsiaras et al. (2016), they are not incomplete disagreement. A mean molecular weight of 2amu at volume mixing ratios consistent with the Tsiaraset al. (2016) analysis is ruled out by our observations;however, it is possible that the mean molecular weight isslightly greater ( ∼ and C H , and suggests that if any of thesethree molecules are indeed present in the atmosphere of55 Cnc e, they are likely to have high mean molecularweights, low volume mixing ratios, or both. We notethat previous observations (e.g. Ehrenreich et al. 2012;Demory et al. 2016b) do support a high-mean-molecular-weight atmosphere. IR Spectroscopy of 55 Cancri e . . . . . . . . . . . . A r b i t r a r y U n i t s − . . µ = 2 amu20.0% VMR µ = 5 amu20.0% VMR − . . µ = 2 amu10.0% VMR µ = 5 amu10.0% VMR − − −
20 0 20 40 60 − . . µ = 2 amu5.0% VMR − − −
20 0 20 40 60 µ = 5 amu5.0% VMR Figure 8.
Results of injecting H O models of various strengths into our data, and repeating the Doppler cross-correlationprocess. The figures are as described in the caption of Fig. 3. As neither the data (black lines) nor the data with modelsinjected (magenta lines) surpass the 3 σ confidence levels, we have neither detected nor can place limits of the presence of H Oin the atmosphere of 55 Cnc e based on these data. We do, however, note the presence of a peak at the expected location thatapproaches 3 σ for each model displayed with a mean molecular weight of 2 amu, indicating that we may be able to rule thesemodels out with additional observations. Finally, we caution that these constraints rely on theaccuracy of the line lists used to generate our models,and future updates to these line lists could yield differ-ent results. The issue has been discussed in detail in anumber of previous studies. In the case of TiO, for ex-ample, Hoeijmakers et al. (2015) demonstrated that in-accurate line lists can hamper high-resolution retrievals.Likewise, Webb et al. (2020) observed absorption dueto H O in high-resolution VLT/CRIRES spectra of HD179949 b, but found a weak dependence on the line listused for the cross-correlation. Updates to the availableline lists for each of the molecules used in this analysiscould similarly impact our detection capabilities, and wetherefore note that the particulars of line lists should bekept in mind when interpreting our results.6.2.
Comparison with High-Resolution OpticalSpectroscopy
We note that previous studies (Esteves et al. 2017;Jindal et al. 2020) have been able to place significantconstraints on the presence of H O in the atmosphere of55 Cnc e using high-resolution spectra at optical wave-lengths. In particular, recent work by Jindal et al. (2020) resulted in a 3 σ lower limit of 15 amu on themean molecular weight of 55 Cnc e’s atmosphere, as-suming it is water-rich (i.e. has a volume mixing ratioof > . O than the optical wavelength ranges of theseprevious works (e.g. compare our Fig. 28 with Fig. 8 ofEsteves et al. 2017 and Fig. 2 of Jindal et al. 2020), itcould be expected that our data (which cover the samenumber of transits as Jindal et al. 2020) should give thesame or even better constraints than those analyses. Toinvestigate the discrepancy, we carried out a number oftests designed to probe the limits of our technique inthe context of NIR H O (and CO ) absorption. Thefull details of these tests are presented in Appendix D.We conclude that the discrepancies between this workand Esteves et al. (2017) and Jindal et al. (2020) arelargely due to our inability to remove telluric water fea-tures fully from our data. While the overall wavelengthcoverage of the observations used in this work is indeedbroader than that of Jindal et al. (2020), and therefore6 Deibert et al. contains a greater number of absorption lines due toH O, the telluric contamination at these redder wave-lengths is far more severe than at the wavelengths con-sidered in Jindal et al. (2020). As the individual absorp-tion lines due to the exoplanet’s atmosphere are weak,our method relies heavily on our ability to combine thesignals from many absorption lines, which in turn re-lies on our ability to remove telluric contamination ade-quately in the regions where these lines are present. sys-rem is less efficient in regions of strong telluric contam-ination; this can be seen in a comparison between theresiduals after applying sysrem in Jindal et al. (2020)and those in this work (see the plots in Appendix A).While additional iterations of sysrem may aid in re-moving some residual telluric contamination, we showin Appendix D that additional iterations may also be-gin to remove the model itself, and thus will not improveour detection capabilities. We also note that the SNRsof our observations (see Table 1) are in some cases sig-nificantly lower than those of Jindal et al. (2020), whichwould limit our sensitivities further.As mentioned in Section 3.1.1, we also tried correct-ing for telluric absorption using Molecfit. We appliedMolectit and Calctrans to every spectrum in each nightof our CARMENES and SPIRou data. We then in-jected an atmospheric H O model with a VMR of 20%and a mean molecular weight of 2 amu (i.e. the modelshown in Fig. 28; the strongest water model of our sam-ple) into the data and repeated this process. Then, wecarried out the Doppler cross-correlation process as de-scribed in Section 4.2 in order to determine whether ornot we were more readily able to recover an injectedatmospheric H O model with sysrem or with Molecfit.We found that Molecfit does not improve our abilityto detect an injected atmospheric H O model. Instead,the data corrected with Molecfit yielded a weaker de-tection of the injected model than those corrected with sysrem . This is evident in Figs. 9 and 10, where wecompare the two for CARMENES and SPIRou obser-vations, respectively. We tested two separate methodsfor removing stellar lines after applying Molecfit to ourdata: first, we subtracted a mean template of the stellarfeatures remaining; and second, we applied two itera-tions of sysrem to the data after correcting them withMolecfit. In the case of CARMENES observations weare unable to recover the injected model (the middletwo panels of Fig. 9); for SPIRou, on the other hand,we can recover the injected model at a lower significancethan our original analysis (the second panel of Fig. 10).As a check for our CARMENES observations, we alsotested a case where we injected the model at 100 timesits nominal strength into a subset of our data and fol- lowed the same reduction process using Molecfit. In thiscase, we were able to recover the injected model at theexpected location.We note that previous studies which have comparedMolecfit and sysrem in the NIR have had similar re-sults. In particular, S´anchez-L´opez et al. (2019) madea detection of water vapour in the atmosphere of HD209458 b using CARMENES data that had been cor-rected with sysrem . After correcting their data withMolecfit, however, they were unable to recover the plan-etary signal. The authors noted that recent works havefound the scatter in residuals for CRIRES data correctedwith Molecfit to be 3 to 7% (Ulmer-Moll et al. 2019), andconcluded that the fit uncertainties over the wavelengthcoverage of CARMENES are likely too large to detectthe H O features of the planet. Our analysis yields sim-ilar results: although we do not strongly detect the at-mospheric H O model with sysrem , there is a correla-tion peak at the expected location that approaches 3 σ .When running Molefit on our CARMENES data, how-ever, no such peak is present. In the case of SPIRou, apeak is visible at the expected location, but this signalis weaker than the case where sysrem was used instead(Fig. 10).As a final test of what might be impacting our abil-ity to recover injected H O models, we followed Alonso-Floriano et al. (2019) and S´anchez-L´opez et al. (2019)in separately analyzing individual bands of our obser-vations. We separated the CARMENES data into theY, J, and H bands, and separated the SPIRou data intothe Y, J, H, and K bands.Figs. 11 and 12 show these results for CARMENESand SPIRou, respectively. In both cases the contribu-tion to the signal comes almost exclusively from the Jband (and, to a lesser extent, the H band). This sug-gests that although our observations span a wide wave-length range, only a small fraction of that wavelengthrange is contributing to our detection capabilities. Theother water features present (see Fig. 28) were likelynot readily recovered by our model injection/recoverytests because they are comparatively weaker, and be-cause sysrem was not able to remove telluric featurescompletely in these regions (see the figures in AppendixA, particularly the bottom two panels of each).We also ran the individual band analysis on ourstrongest HCN model as a comparison. The results areshown in Figs. 13 and 14 for CARMENES and SPIRou,respectively. In this case we see that a signal is recov-ered in all bands except the K band. For CARMENESthe signal is strongest in the Y and H bands, whereasfor SPIRou the signal is noticeably strongest in the Jand H bands.
IR Spectroscopy of 55 Cancri e . . . . . . sys [km/s]0 . . . K p [ k m / s ] −
50 0 500100200300 −
50 0 50 −
50 0 50 −
50 0 50
Figure 9.
A comparison of our phase-folded CARMENES results for cases where telluric correction is carried out using sysrem (first panel) and Molecfit (second, third, and fourth panels). In all cases, we have injected an atmospheric H O model with aVMR of 20% and a mean molecular weight of 2 amu into our data. In the first panel we have corrected telluric absorption using sysrem (Section 3.1); in the second panel we have corrected telluric absorption using Molecfit and corrected stellar absorptionusing a mean stellar line template; in the third panel we have corrected telluric absorption using Molecfit and corrected stellarabsorption using 2 iterations of sysrem ; and in the fourth panel we have injected the model at 100 × its nominal strength intoa single night of data and corrected for telluric absorption using Molecfit and stellar absorption using 2 iterations of sysrem .In all cases, the correction is followed by the Doppler cross-correlation process as described in Section 4.2. A peak is visiblein the cross-correlation at the expected location for sysrem and Molecfit with a model injected at 100 × its nominal strength;in the cases where Molecfit is used on the model at 1 × its nominal strength, however, we are unable to detect a peak in thecross-correlation. The expected location is indicated by white dotted lines in all panels. . . . . . . sys [km/s]0 . . . . . . K p [ k m / s ] − −
30 0 30 600100200300 − −
30 0 30 60
Figure 10.
A comparison of our phase-folded SPRIou results for cases where telluric correction is carried out using sysrem (left) and Molecfit (right). In both bases, we have injected an atmospheric H O model with a VMR of 20% and a mean molecularweight of 2 amu. In the panel on the right, stellar absorption has been corrected with 2 iterations of sysrem . In this case we seethat the injected model is recovered when the data are corrected with Molecfit; however, the recovered signal is not as strongas in the case where the data are corrected with sysrem . A Nitrogen-Dominated Atmosphere?
Several previous studies have pointed to a nitrogen-dominated atmosphere for 55 Cnc e. Hammond & Pier-rehumbert (2017) used 3D calculations to show that theoffset observed in the phase curve (Demory et al. 2016b;Angelo & Hu 2017), as well as the large day-night tem-perature contrast, may be explained by an N-dominatedatmosphere. The analysis by Angelo & Hu (2017) alsosupports this scenario. To this end, Miguel (2019) ex-plored the observable features in the spectra of an N-dominated atmosphere for 55 Cnc e. Through analyti- cal arguments, equilibrium chemistry calculations, andadopting Titan’s elemental abundances as a potentialcomposition, Miguel (2019) showed that although N isexpected to be the most abundant molecule in the at-mosphere (followed by H and CO), the transmissionspectra should show strong features of NH and HCN.However, a decrease in the N/O ratio would tend toweaken these NH and HCN features.The transmission spectra calculated in Miguel (2019)(their Fig. 3, right panel) range between 3 and 20 µ m,and are thus outside the range of our own observations.Figs. 6 and 7 of Miguel (2019) show the mixing frac-8 Deibert et al. K p [ k m / s ] dataY-75 0 75V sys [km/s]75225 injected 75225 K p [ k m / s ] dataJ-75 0 75V sys [km/s]75225 injected 75225 K p [ k m / s ] dataH-75 0 75V sys [km/s]75225 injected1000 1100 1200 1300 1400 1500 1600 1700 1800Wavelength [nm]246810 σ [ mm ag ] Figure 11.
The results of our model injection/recovery process (see Section 4.3) for the Y, J, and H bands of our CARMENESobservations. These tests use a water model with a VMR of 20% and a mean molecular weight of 2 amu (Fig. 28). The primaryplot shows σ as a function of wavelength for the full wavelength range, and the insets show the phase-folded correlations forthe data alone (top insets) and the data with a model injected (bottom insets). The insets are as described in the caption ofFig. 2. The band is indicated in the title of each inset, and the corresponding region is marked in the primary plot. The whitedotted lines show the expected location of the correlation signal. We see that the majority of the recovered signal comes fromthe J band. tion of the most abundant observable molecules as afunction of temperature at a pressure of ∼ ∼ is less than ∼ − %, while at all pressuresconsidered and for all N/O ratios considered, the volumemixing ratio of NH is less than ∼ − %. Our anal-ysis rules out most low-mean-molecular-weight, high-volume-mixing-ratio scenarios, which is consistent withexpected volume mixing ratios from Miguel (2019), andwith previous work that has combined mass and radiusmeasurements with interior modeling to show that theatmosphere should have a high mean molecular weight(Demory et al. 2011; Winn et al. 2011; Bourrier et al.2018). 6.4. A Cloudy Atmosphere?
We note that the limits we have placed throughoutthis section assume that any signals present in the at- mosphere are not obscured by clouds or hazes. How-ever, the presence of clouds or hazes could act to ob-scure atmospheric signals, limiting our ability to makedetections. Therefore, our results may also be consistentwith a cloudy atmosphere. The limits we have placedthroughout this analysis are only relevant in the caseof a cloud-free atmosphere, as the models were injectedinto the data under the assumption that they were notobscured at any altitude by clouds or hazes. We noteas well that various other investigations into the compo-sition of 55 Cancri e’s atmosphere (Tsiaras et al. 2016;Esteves et al. 2017; Jindal et al. 2020) made similar as-sumptions, meaning that those limits also pertain to thecase in which 55 Cnc e does not harbour clouds.While an in-depth exploration of the effects of cloudsor hazes on the atmosphere could prove insightful, suchan analysis is beyond the scope of this work. However,we note that an analysis by Mahapatra et al. (2017)found that despite 55 Cnc e’s high equilibrium tempera-ture ( ∼ IR Spectroscopy of 55 Cancri e K p [ k m / s ] dataY-75 0 75V sys [km/s]75225 injected 75225 K p [ k m / s ] dataJ-75 0 75V sys [km/s]75225 injected 75225 K p [ k m / s ] dataH-75 0 75V sys [km/s]75225 injected 75225 K p [ k m / s ] dataK-75 0 75V sys [km/s]75225 injected1000 1200 1400 1600 1800 2000 2200 2400Wavelength [nm]246810 σ [ mm ag ] Figure 12.
The same as Fig. 11, but for SPIRou. Here, the recovered signal comes largely from the J and H bands. −
50 0 500100200300 K p [ k m / s ] dataY −
50 0 50V sys [km/s] dataJ −
50 0 50dataH −
50 0 500100200300 K p [ k m / s ] injected −
50 0 50V sys [km/s]injected −
50 0 50injected
Figure 13.
The same as the insets in Fig. 11, but for an HCN model with a VMR of 0.1% and a mean molecular weight of2 amu (Fig. 23). We have omitted the plot of σ as a function of wavelength here as it is the same as the primary plot in Fig.11. We see that the majority of the recovered signal comes from the Y and H bands, but there is a peak present at the expectedlocation in the J band as well. formation is likely only possible in a thin atmosphericregion, and requires strong vertical replenishment (Ma-hapatra et al. 2017). Hammond & Pierrehumbert (2017)also investigated the possibility of clouds and found thatgiven the observed high equilibrium temperature and arange of partial pressures from Miguel et al. (2011), Na isunlikely to condense and form clouds, whereas SiO could potentially condense on the planet’s night-side (both Naand SiO could arise from a day-side magma ocean; e.g.Schaefer & Fegley 2010; Miguel et al. 2011; Hammond& Pierrehumbert 2017).0 Deibert et al. −
50 0 500100200300 K p [ k m / s ] dataY −
50 0 50V sys [km/s]dataJ −
50 0 50dataH −
50 0 50dataK −
50 0 500100200300 K p [ k m / s ] injected −
50 0 50V sys [km/s]injected −
50 0 50injected −
50 0 50injected
Figure 14.
The same as the insets in Fig. 12, but for an HCN model with a VMR of 0.1% and a mean molecular weight of2 amu (Fig. 23). We see that the majority of the recovered signal comes from the J and H bands, with some contribution fromthe Y band; there is no significant correlation peak recovered in the K band.
Refraction
Briefly, we note that while the effects of refractionwere not considered in our model atmosphere calcula-tions (see Section 4.1), it has been shown that refrac-tion can act to mute spectral features in the lower at-mosphere by creating a grey continuum similar to thatproduced by optically thick clouds (B´etr´emieux & Swain2018). For thin atmospheres around terrestrial exoplan-ets, the largest pressure that can be probed may indeedbe the exoplanet’s surface pressure; with increasinglythicker atmospheres, however, refraction may preventobservations of the lower atmosphere.B´etr´emieux & Swain (2018) calculate the refractiveboundaries of several hot Jupiters and terrestrial exo-planets for various atmospheric compositions in orderto assess the impact of refraction on observations. Inmost cases, these refractive boundaries are located atpressures of > ∼ CONCLUSIONWe have presented our analysis of high-resolutionnear-infrared transmission spectroscopy of the transit-ing super-Earth 55 Cnc e. This paper shows the resultsof the Doppler cross-correlation technique, which takesadvantage of the large change in radial velocity of theexoplanet during its transit as well as the high spectralresolution of our observations, allowing us to resolve in- dividual molecular features and disentangle the plane-tary signal from stellar and telluric absorption lines.In the cases of atmospheric HCN, NH , and C H , weare able to place strong upper limits. We can rule HCNout of the atmosphere of 55 Cnc e at a volume mixingratio as low as 0.001% with a mean molecular weight of 2amu; if the mean molecular weight is increased to 5 amu,we can rule HCN out down to a volume mixing ratio of0.02%. Our findings rule out the most likely modelssuggested by the analysis of Tsiaras et al. (2016), butthere remain several models with lower volume mixingratios and a mean molecular weight of ∼ out of the atmosphere at a volumemixing ratio as low as 0.0025% if the mean molecularweight is 2 amu; if it is increased to 5 amu, we can ruleNH out down to a volume mixing ratio of 0.08%. Re-cent work suggests that the atmosphere of 55 Cnc e islikely N-dominated (Angelo & Hu 2017; Hammond &Pierrehumbert 2017). Moreover, Miguel (2019) showedthat both NH and HCN should be present in an N-dominated atmosphere, and that transmission spectrafrom 3 – 20 µ m should show strong features of NH andHCN. Our results rule out low-mean-molecular-weight,high-volume-mixing-ratio scenarios for both molecules;however, they are consistent with calculations suggest-ing that the atmosphere should have a high mean molec-ular weight, thus with the conclusions of Miguel (2019).Finally, we can rule C H out of the atmosphere at avolume mixing ratio as low as 0.08% if the mean molec-ular weight is 2 amu; if the mean molecular weight isincreased to 5 amu, we can rule C H out of the atmo-sphere down to a volume mixing ratio of 1.0%. IR Spectroscopy of 55 Cancri e , and H O, onthe other hand, we are unable to place significant con-straints. We note that while the injections of CO modelswith a VMR of either 10% or 1% and a mean molecu-lar weight of 2 amu do result in > σ detections, thereare many additional features in the data at > σ , andwe thus caution that the peaks seen at > σ in Fig. 6should be treated as tentative and warranting furtherinvestigation.Through several tests designed to probe the limits ofour detection capabilities, we conclude that our inabilityto recover injected H O and CO models stems from thedifficulty of removing telluric absorption lines across thebroad NIR wavelength range of our data. Future anal-yses would benefit from exploring additional avenues oftelluric correction.While we do not detect an atmosphere around55 Cnc e, we do provide improved constraints on thepossible scenarios for one that may exist. Furthermore,we have demonstrated the efficacy of the Doppler cross-correlation method at detecting nitrogen-rich moleculesin particular, which will be of use in future studies ofsuper-Earth atmospheres. Our understanding of thenature of 55 Cnc e’s atmosphere is likely to advance inthe coming years, thanks to the increased wavelengthcoverage of upcoming spectrographs that extend furtherinto the infrared, improved telluric absorption removaltechniques, and the launch of the James Webb SpaceTelescope.We wish to thank Miranda Herman, Yamila Miguel,and Tom´as Cassanelli for the helpful discussions. Wealso wish to thank the anonymous referee for their kind and thorough evaluation, which greatly strengthenedthis work. Finally, we thank the scientific editor MichaelEndl and the anonymous data editor for their helpful in-put.E.K.D was supported by an NSERC Canada Gradu-ate Scholarship-Master’s and a Vanier Canada GraduateScholarship.We acknowledge that this work was conducted on thetraditional land of the Huron-Wendat, the Seneca, andmost recently, the Mississaugas of the Credit River; weare grateful for the opportunity to work here. We alsowish to acknowledge that this work is based on observa-tions obtained at the Canada-France-Hawaii Telescope(CFHT) which is operated from the summit of Mau-nakea by the National Research Council of Canada, theInstitut National des Sciences de l’Univers of the CentreNational de la Recherche Scientifique of France, and theUniversity of Hawaii. The observations at the Canada-France-Hawaii Telescope were performed with care andrespect from the summit of Maunakea, which is a signifi-cant cultural and historic site. This work is also based onobservations collected at the Centro Astron´omico His-pano Alem´an (CAHA), operated jointly by the Max-Planck Institut f¨ur Astronomie and the Instituto de As-trof´ısica de Andalucia (CSIC). Software: astropy (Astropy Collaboration et al. 2013;Price-Whelanetal.2018),Numpy(vanderWaltetal.2011;Harris et al. 2020), CARACAL (Caballero et al. 2016),Molecfit(Smetteetal.2015;Kauschetal.2015),occultquad(Mandel & Agol 2002), Matplotlib (Hunter 2007), SciPy(Virtanen et al. 2020), IPython (Perez & Granger 2007)APPENDIX A. DATA REDUCTIONThe full data reduction process for each night and each order of our observations is presented here. The process isdescribed in Section 3, and examples of the process being applied to specific orders of the CARMENES and SPIRoudatasets are shown in the left and right panels of Fig. 1 respectively. The orders containing significant telluriccontamination (i.e. those between the standard photometric bands) were excluded from further analysis, and areindicated by a greyscale in the figures. A.1.
CARMENES
Figs. 15, 16, 17, and 18 show the results of applying the full data reduction process to the four nights of CARMENESobservations used in this analysis. We chose to exclude several orders from all further analyses due to severe telluriccontamination that prevented the blaze correction or the sysrem algorithm from being able to provide an adequatereduction; these are seen in regions where the standard deviation is much higher than the rest of the spectrum. Notethat we also chose to exclude N and N from our analysis due to poor observing conditions (see Table 1).2 Deibert et al. − . . − . . O r b i t a l P h a s e − . .
00 1000 1100 1200 1300 1400 1500 1600 1700Wavelength [nm]0 . . σ Figure 15.
The data reduction process as applied to the first night of CARMENES observations (N in Table 1). The toppanels show the data after they have been extracted from and reduced by the telescope, the second panels show the data afterapplying a blaze correction and median filtering algorithm (as described in Section 3), the third panels show the data afterapplying 6 iterations of the sysrem algorithm (see Section 3.1), and the fourth panels show the standard deviation along eachwavelength channel after applying the sysrem algorithm. . . . . O r b i t a l P h a s e . . . . σ Figure 16.
The data reduction process as applied to the second night of CARMENES observations (N in Table 1). The panelsare as described in the caption of Fig. 15. . . . . O r b i t a l P h a s e . . . . σ Figure 17.
The data reduction process as applied to the third night of CARMENES observations (N in Table 1). The panelsare as described in the caption of Fig. 15. IR Spectroscopy of 55 Cancri e − . . − . . O r b i t a l P h a s e − . . . . σ Figure 18.
The data reduction process as applied to the fifth night of CARMENES observations (N in Table 1). The panelsare as described in the caption of Fig. 15. We note that sysrem performed poorly in many orders as seen in the third andfourth panels of the plot; however, we have chosen to keep these observations in our analysis. As described in Section 4, weweight each wavelength channel by its standard deviation, and thus we ensure that the areas where sysrem performed poorlydo not negatively impact our results. . . . . O r b i t a l P h a s e . .
05 1000 1200 1400 1600 1800 2000 2200 2400Wavelength [nm]0 . . . σ Figure 19.
The data reduction process as applied to the first night of SPIRou observations (N in Table 1). The panels are asdescribed in the caption of Fig. 15. A.2.
SPIRou
Figs. 19, 20, 21, and 22 show the results of applying the full data reduction process to the four nights of SPIRouobservations. Again, we have excluded regions of severe telluric contamination from our analysis and indicated thesein greyscale. B. MODELSIn this section we present example models for each molecule considered in our analysis (HCN, NH , C H , CO, CO ,and H O; Figs. 23, 24, 25, 26, 27, and 28, respectively). Further details on these models, including a description ofhow they were generated, are available in Section 4.1. Each example model shown here corresponds to the top-leftmodel of each plot in Section 5; e.g. Figs. 3, 4, 5, 6, 7, and 8.For some of the models presented in this work (e.g. the C H model in Fig. 25), the line lists that are currentlyavailable are incomplete. This results in the sharp cutoffs in wavelength visible in numerous bands. Going forward, weexpect that more complete and accurate line list data will become available, which would allow for a more completeand realistic model to be calculated.4 Deibert et al. . . . . O r b i t a l P h a s e . .
05 1000 1200 1400 1600 1800 2000 2200 2400Wavelength [nm]0 . . . σ Figure 20.
The data reduction process as applied to the second night of SPIRou observations (N in Table 1). The panels areas described in the caption of Fig. 15. . . . . O r b i t a l P h a s e . .
05 1000 1200 1400 1600 1800 2000 2200 2400Wavelength [nm]0 . . . σ Figure 21.
The data reduction process as applied to the third night of SPIRou observations (N in Table 1). The panels areas described in the caption of Fig. 15. . . . . O r b i t a l P h a s e . .
05 1000 1200 1400 1600 1800 2000 2200 2400Wavelength [nm]0 . . . σ Figure 22.
The data reduction process as applied to the fourth night of SPIRou observations (N in Table 1). The panels areas described in the caption of Fig. 15. IR Spectroscopy of 55 Cancri e . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 0.1 % Figure 23.
An example HCN model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixing ratioof 0.1%. This model is ruled out of the atmosphere, as seen in the top-left panel of Fig. 3. . . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 5.0 % Figure 24.
An example NH model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixing ratioof 5.0%. This model is ruled out of the atmosphere, as seen in the top-left panel of Fig. 4. . . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 20.0 % Figure 25.
An example C H model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixingratio of 20%. This model is ruled out of the atmosphere, as seen in the top-left panel of Fig. 5.C. MOLECFITIn this section, we present additional details on our telluric feature removal process using Molecfit. Although ouranalysis removes telluric features through the use of the sysrem algorithm, we decided to compare our results withMolecfit in order to determine whether the removal of telluric features was limiting our ability to recover certain6
Deibert et al.
500 750 1000 1250 1500 1750 2000 2250Wavelength [nm]0 . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 10.0 % Figure 26.
An example CO model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixing ratioof 10%. This model is tentatively ruled out of the atmosphere, as seen in the top-left panel of Fig. 6. We caution that thisresult is only tentative, as there are numerous additional peaks at > σ in our results.
500 750 1000 1250 1500 1750 2000 2250Wavelength [nm]0 . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 10.0 % Figure 27.
An example CO model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixing ratioof 10%. This model corresponds to the phase-folded cross correlations shown in the top-left panel of Fig. 7, and is not ruledout of the planet’s atmosphere by our analysis. . . . . . T r a n s i t D e p t h [ ( R p / R ∗ ) ] µ = 2 amuVMR = 20.0 % Figure 28.
An example H O model calculated for 55 Cnc e with a mean molecular weight of 2 amu and a volume mixing ratioof 20%. This model corresponds to the phase-folded correlations shown in the top-left panel of Fig. 8, and is not ruled out ofthe planet’s atmosphere by our analysis.
IR Spectroscopy of 55 Cancri e
Fit Parameters
The initial parameters used with Molecfit for every night are shown in Table 3. Further details on these parametersare available in Smette et al. (2015); Kausch et al. (2015). We allowed Molecfit to fit for a Gaussian kernel that varieswith wavelength, and included fitting for the wavelength solution.
Table 3.
Initial parameters used by Molecfit. We allow Molecfit to fit for molecules with absorptionfeatures present in the wavelength range of our data (see Molecules row below), and apply a second-degree Chebyschev polynomial fit to the wavelength solution ( n λ below). The continuum (cont n below) is fit with a second-degree polynomial, and as the data are normalized, we set an initialconstant term of 1 for the continuum which is then refined through the fit. The instrumental profileis initially assumed to be a Gaussian with a FWHM of 3.5 pixels; however, this too is refined throughthe fit. Molecfit uses the Levenberg-Marquardt technique to quickly solve the least-squares problem(Smette et al. 2015); the χ convergence parameter (ftol below) as well as the parameter convergencecriterion (xtol below) of the Levenberg-Marquardt technique are set to 10 − . Initial parameters Value Notesftol 10 − Relative χ convergence criterionxtol 10 − Relative parameter convergence criterionMolecules H O, CO , O , CO CH , O Molecules included in the fitcont n const . n λ ω Gaussian D. ASSESSING OUR H O AND CO RETRIEVAL CAPABILITIESIn the following sections, we present several additional tests designed to evaluate our H O and CO model recoverycapabilities. D.1. White Noise Test
To test whether residual noise left in the data after the application of the sysrem algorithm was affecting our finalresult, we followed a similar method to Esteves et al. (2017) by simulating a pure white noise data set generated tomatch the rms of each wavelength channel after applying sysrem (see e.g. the bottom panels of the figures in AppendixA). We tried injecting both a model H O atmosphere and a model CO atmosphere into this white noise data set andrepeated our analysis routine as described in Section 4 for each model. This allowed us to assess whether the residualnoise level in the data after applying the sysrem algorithm was the limiting factor in being able to recover H O andCO models. The results of these white noise tests are shown in Figs. 29 (H O) and 30 (CO ) for the CARMENESdata set, and Figs. 31 (H O) and 32 (CO ) for the SPIRou data set.In all cases we see that in a data set comprised of pure white noise, we are unable to recover even the strongest H Oand CO models. This suggests that sysrem did not adequately remove stellar and telluric contamination in the data,and that the data themselves are simply too noisy to allow us to place strong constraints on the presence of H O orCO in the atmosphere of 55 Cnc e. We note that H O and CO contain a significant number of lines throughout thebroad wavelength coverages offered by CARMENES and SPIRou; while these lines can in theory improve the strengthof our detections, there will also be corresponding H O and CO lines present in this wavelength range in the Earth’satmosphere that contaminate the data and pose a challenge to the sysrem algorithm. Future analyses would benefitfrom exploring other avenues of telluric absorption line removal. While we have presented a brief investigation of theefficacy of Molecfit on these data (see Sections 3.1.1 and 6.2, as well as Appendix C), we note that additional insight8 Deibert et al. . . . . . . . . . . . . A r b i t r a r y U n i t s − − −
20 0 20 40 60 − . − . . . . − − −
20 0 20 40 60
Figure 29.
The white noise test for the CARMENES data, as described in Appendix D.1. The panel on the left shows theresults of injecting an atmospheric H O model with a VMR of 20% and a mean molecular weight of 2 amu (i.e. the modelshown in Fig. 28) into our CARMENES data set and repeating the Doppler cross-correlation process. The data with themodel injected is represented by the black line, while the dark- and light-grey contours represent 1 and 3 σ confidence levels,respectively (see Section 4.4) The panel on the right shows the results of injecting this same atmospheric model into a whitenoise dataset as described in Appendix D.1. The model that has been injected into the white noise data set is closer to the3 σ confidence level than that injected into the data; however, in neither case were we able to confidently retrieve the injectedmodel. . . . . . . . . . . . . A r b i t r a r y U n i t s − − −
20 0 20 40 60 − . . . − − −
20 0 20 40 60
Figure 30.
The same as Fig. 29, but for a CO model with a VMR of 10% and a mean molecular weight of 2 amu (i.e. themodel shown in Fig. 27). We were unable to confidently recover the injected model in the original data set (left) or the whitenoise data set (right), but we note that the injected model is closer to the 3 σ confidence level in the white noise data set thanthe original data set. into the strengths of various telluric removal methods on SPIRou observations specifically would be useful. In the caseof CRIRES data, we note that Ulmer-Moll et al. (2019) showed synthetic transmission methods to be preferable to astandard star method. D.2. Wavelength Shift
In addition to the white noise test described in Section D.1, we investigated whether or not a shift was present inthe wavelength solution of the data. Such a shift could potentially impact our ability to recover an injected model. Totest for this, we cross-correlated each spectrum of each night with the first spectrum of the night, and used a centroidalgorithm to fit for the peak of the cross-correlation function. We then compared the difference in measured peaks foreach cross-correlation. This was done on a per-order basis.In the case of the CARMENES data, we find that for each night the majority of orders do not experience a largeshift in the wavelength solution. For most orders, the shift in the fitted centroid of the cross-correlation function
IR Spectroscopy of 55 Cancri e . . . . . . . . . . . . A r b i t r a r y U n i t s − − −
20 0 20 40 60 − . . . − − −
20 0 20 40 60
Figure 31.
The white noise test for the SPIRou data, as described in Appendix D.1. The panels are as described in the captionof Fig. 29. Again, the model that has been injected into the white noise data set here does not pass the 3 σ confidence level. . . . . . . . . . . . . A r b i t r a r y U n i t s − − −
20 0 20 40 60 − . . . − − −
20 0 20 40 60
Figure 32.
The same as Fig. 31, but for a CO model with a VMR of 10% and a mean molecular weight of 2 amu (i.e. themodel shown in Fig. 27). We were unable to confidently recover the injected model in the original data set (left) or the whitenoise data set (right). In the white noise data set, however, the injected model is closer to the 3 σ confidence level. is on average 0.04 pixels. For each night we found that two orders experienced a slightly larger shift (on the orderof ∼ µ . For these individual lines,we also did not find a significant shift in the wavelength solution.Finally, we note that our data reduction procedure (described in Section 3) involves interpolating each frame to acommon wavelength grid.Overall, we do not think that a shift in the wavelength solution impacted our final results, given that the shiftmeasured by the methods described above is significantly less than 1 pixel, and less than the widths of the absorptionlines themselves. D.3. Varying sysrem
Iterations
In addition to the tests described in the preceding sections, we investigated whether applying different numbers ofiterations of sysrem affected our ability to recover injected models. While the methods we used to determine the0
Deibert et al. . . . . . . . . . . . . A r b i t r a r y U n i t s −
50 0 50 − . . . −
50 0 503 iters. −
50 0 504 iters. −
50 0 505 iters. −
50 0 506 iters.
Figure 33.
The results of varying the number of iterations of sysrem used on a data set with a water model injected, asdescribed in Appendix D.3. The model used had a VMR of 20% and a mean molecular weight of 2 amu. Each panel shows adifferent number of iterations of the algorithm, with the number of iterations indicated in the bottom right. As in e.g. Fig. 8, theblack line represents the data, the magenta line represents the data with a model injected, and the dark- and light-grey contoursrepresent 1 and 3 σ confidence levels respectively. After 5 iterations, the strength of the injected model decreases slightly. . . . . . . . . . . . . A r b i t r a r y U n i t s −
50 0 50 − . − . . . −
50 0 503 iters. −
50 0 504 iters. −
50 0 505 iters. −
50 0 506 iters.
Figure 34.