High-resolution Spectroscopy

Spectroscopy at high resolving powers (currently $R=25,000-140,000$) from the visible to the NIR allows us to (i) resolve molecular bands into the individual lines (see Figure 8.1), and (ii) use the Doppler shift of the planet spectrum to disentangle it from other sources, such as the transmission spectrum of the Earth's atmosphere and the host star spectrum (Snellen et al. 2010). Spectral information can be extracted through cross-correlation with model spectra or templates derived from them, and the best solutions are found by maximizing the cross-correlation. The method excels at identifying species with numerous spectral lines and can be used for transmission, day/night-side emission, and reflected light spectroscopy. In the latter cases, it is also applicable to non-transiting planets (Brogi et al. 2012). Due to the facts that high-resolution spectroscopy (HRS) is currently exclusively available on ground-based facilities, does not need reference stars or telluric standards, and can observe the brightest stars in the sky, it is the natural complement to lower spectral resolution space-based observations.

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In this chapter, we consider the important questions and goals for HRS, the opportunities it offers and the challenges it faces. We specifically consider this in the context of detecting molecular species. The main science questions that high-resolution spectroscopy can address (either currently or in the future), are:

• Determining the chemical inventory of exoplanet atmospheres, including elemental abundances and metallicity. This is due to the robustness of cross-correlation at isolating the specific fingerprint of each species, and to the sensitivity of HRS to relative line ratios, which constrain abundances.
• Constraining the overall vertical thermal structure of exoplanets, in particular the presence of thermal inversion layers, which produce emission lines in the planet's thermal spectrum. Cross correlating emission lines with an absorption spectrum produces anti-correlation rather than correlation.
• Constraining the atmospheric circulation and energy redistribution of giant planets by measuring their atmospheric winds and rotation, and mapping their atmospheric features. This is due to the sensitivity of the method to the line shape (broadening, asymmetries, shifts).
• Constraining the nature of the most common exoplanets (with radii between 2 and 4 ${R}_{\oplus }$) and disentangling atmospheres with strong aerosol opacity from atmospheres with a high metallicity.
• Remotely detecting molecules commonly associated with life, among which are (but not exclusively) molecular oxygen.

The first attempts at using HRS aimed at detecting reflected optical starlight (Cameron et al. 1999; Charbonneau et al. 1999), but only resulted in upper limits. After a decade of further inconclusive attempts at measuring reflected light (Cameron et al. 2002; Leigh et al. 2003; Rodler et al. 2008, 2010) or signatures of molecular species (Wiedemann et al. 2001; Deming et al. 2005), a novel analysis technique was demonstrated on VLT/CRIRES data and detected CO absorption in the transmission spectrum of HD 209458 b around 2.3 μm (Snellen et al. 2010), and H₂O in the atmosphere of HD 189733 b at 3.2 μm (Birkby et al. 2013). Further application to non-transiting hot Jupiters resulted in multiple detection of CO (Brogi et al. 2012; Rodler et al. 2012; Brogi et al. 2013; de Kok et al. 2013; Rodler et al. 2013) and H₂O (Lockwood et al. 2014; Birkby et al. 2017). While these species were routinely found in exo-atmospheres throughout the last decade, detections of additional species were only recently reported for TiO (Nugroho et al. 2017), HCN (Hawker et al. 2018; Cabot et al. 2019), and CH₄ (Guilluy et al. 2019). With the discovery of the class of ultra-hot Jupiters with temperatures rivaling those of M- and K-dwarfs, more exotic species were detected at optical wavelengths, among which Fe and Ti, also in their ionized state, were revealed from a cross-correlation spectral atlas (Hoeijmakers et al. 2019). There is also evidence with HRS that some of these species condense out again on the night side (Ehrenreich et al. 2020).

Molecular high-resolution spectroscopy managed to constrain wind patterns in hot Jupiter atmospheres, in particular the presence of day-to-night side winds at high altitude and overall equatorial super-rotation. It measured for the first time the spin of directly-imaged planets (Snellen et al. 2014; Schwarz et al. 2016), confirmed the tidal locking of HD 189733b (Brogi et al. 2016), and compared results of general circulation models to observations (Flowers et al. 2019). Near-infrared spectroscopy has also delivered the first direct measurement of a thermal inversion layer through TiO emission lines (Nugroho et al. 2017), more recently confirmed in the optical as well (Pino et al. 2020).

In spite of the initial efforts to detect stellar reflected light, evidence remains tentative, and with several upper limits (Martins et al. 2015; Hoeijmakers et al. 2018). This is likely due to the overall low albedo of hot Jupiters in the optical.

Currently, high-resolution spectroscopy is undergoing a series of developments, including instrumentation, observational strategy and analysis techniques:

• Radial-velocity machines capable of NIR HRS have been built in the past 5 years and are currently available at 3–4 m class telescopes. Despite the smaller telescope mirror, these spectrographs have a higher throughput, much larger spectral range, and much higher stability compared to the instruments used for previous studies. Early demonstration on these instruments show performances at least comparable if not superior to VLT/CRIRES or Keck/NIRSPEC observations (Brogi et al. 2018; Guilluy et al. 2019; Alonso-Floriano et al. 2019).
• There has been substantial work in modeling and retrieving atmospheric properties at high spectral resolution (Brogi et al. 2017; Pino et al. 2018), which resulted in the first applicable Bayesian retrieval on these data and its possible combination with space spectroscopy (Brogi & Line 2019; Gandhi et al. 2019; Gibson et al. 2020).
• There is ongoing research assessing the performances of HRS when combined with high-contrast imaging (HCI). The principle behind this application is that photon noise from the parent star, which is the dominant source of noise in HRS observations of bright sources, can be significantly reduced by using direct-imaging techniques, i.e., by suppressing the starlight at the spatial location of the planet. Cross-correlation with model templates then uses both spatial and RV separation of the planet and host star to extract the planet spectrum. HRS+HCI can be achieved through long-slit high-resolution spectroscopy fed via an adaptive optic system, as in the case of CRIRES (Snellen et al. 2014; Schwarz et al. 2016). Alternatively, it can be achieved through an integral field unit (IFU) such as that planned for the METIS instrument for the Extremely Large Telescope (Snellen et al. 2015). Early demonstration of IFUs (albeit at lower spectral resolution) have been obtained with OSIRIS on Keck (Konopacky et al. 2013) and with SINFONI at the VLT (Hoeijmakers et al. 2018). Even at spectral resolving powers of only 2500–5000, it is still possible to apply cross-correlation techniques typical of HRS to filter out the speckle noise from the star (which has a mismatching spectrum) and enhance the signature of the exoplanet.
• In line with similar theoretical development at low resolution (Feng et al. 2016; Parmentier et al. 2016; Taylor et al. 2020), HRS has been used to demonstrate that exoplanet atmospheres are inherently three-dimensional, and that information about their dynamics can be obtained by studying the shape and shift of the spectral lines, as mentioned above. In the infrared, current research is trying to assess the reliability and predictive power of general circulation models, i.e., three-dimensional model of the fluid-dynamics driving the atmospheric flow. Generally, it is observed that GCMs succeed at reproducing the main flow in hot Jupiter atmospheres, especially the day-to-night side flow at low pressure and the overall eastward jet stream at the level of the photosphere (Flowers et al. 2019).
• The exoplanet spectra extracted directly via HRS with current instrumentation are noisy, with typically ${\rm{S}}/{\rm{N}}\lt 1$ per line (Brogi et al. 2012). Template-matching, such as cross-correlation, instead combines all of the spectral lines to measure the level of correlation with model spectra. Past work has highlighted that this process is somewhat dependent on the choice of line lists (Brogi et al. 2017; Brogi & Line 2019; Webb et al. 2020), however there have been significant advances in the accuracy of line lists. For HRS application, the most important factor is the knowledge of transition frequencies at the 0.01 cm⁻¹ level at least in the NIR. Recent work (Gandhi et al. 2020) has shown that such accuracy has been reached for several molecular species including water vapor, while some uncertainty remains for methane and carbon dioxide.

HRS has been undergoing major development as a technique for characterizing exoplanet atmospheres over the last decade since its first successful detection in 2010 (Snellen et al. 2010). However, as noted in Section 8.5; there has been only a small community with limited suitable instruments driving the field and consequently, there is still significant room for improvement in understanding the scope and power of the technique, its limitations, and its future potential. This makes for an exciting time, with a number of pertinent questions and goals. The key opportunities are described in Section 8.4, but below we highlight (a non-exhaustive list of) important considerations to address.

• Absolute abundances: Unlike low-resolution/broadband secondary eclipse spectra, HRS analysis techniques typically remove the absolute continuum level and thus extract atmospheric information using core-to-continuum line contrast and line-to-line contrast (see Figure 8.1). Initially, there were concerns this would mean only relative abundances would result from HRS observations alone (de Kok et al. 2014), but recent work has shown absolute abundances (i.e., volume mixing ratios) reach the same level of precision and accuracy as their lower resolution counterparts, constraining CO abundance to ± 0.4 dex and C/O ratios to ± 0.2 from emission spectroscopy of a hot Jupiter around a bright host with VLT/CRIRES (Brogi & Line 2019). An important goal is to understand the true limit of precision and accuracy of these measurements, and what is needed to improve them (e.g., observational scope and/or analysis techniques), especially as we consider the physical and chemical diversity of exoplanet atmospheres for both gas giants and terrestrial planets in the future.
• M-dwarfs: Do exoplanet atmospheres survive the harsh M-dwarf environment? This is a question that can be answered with HRS and the technique will likely target many nearby planets orbiting potentially very active small stars. Proxima b's host star has significant flares (Howard et al. 2018) and such extreme activity can cause certain lines in the spectra to change rapidly or even saturate, resulting in unusable sections of wavelength and time series during an observing sequence. Understanding the extent of this impact on HRS analysis is a key issue. For example, recent observations of hot pulsating exoplanet host stars have shown that variations in the stellar spectrum, if it overlaps with lines in the planet spectrum used in cross-correlation, results in regions of velocity space that cannot be accessed (Nugroho et al. 2020). M-dwarf spectrum are also more complex compared to hot A-stars and their spectral features can complicate cleaning the data to the photon noise limit. Better understanding of M-dwarf spectra is needed to assist this (see Section 8.5 for more detail), and to date, no exoplanet orbiting an M-dwarf has had molecules detected in is atmosphere with HRS. In addition, when studying exoplanet atmospheres in reflected light with HRS, it is the stellar spectrum itself that is reflected, albeit modulated by planet's albedo as a function of wavelength. In this case, M-dwarf hosts become the optimal target as their spectra have more lines to detect, thus boosting the detection strength of the cross-correlation. However, this again requires accurate models of M-dwarfs spectra, as well as understanding how to extract the albedo information and how to circumvent degeneracy with planet radius given it is likely that the planets will be non-transiting.
• Necessary resolution: As typical spectral lines have FWHM below the resolution element of infrared spectrographs, there is a concrete possibility of increasing the cross-correlation signal by increasing the resolving power, possibly up to $R=500,000$ (López-Morales et al. 2019). This is important both for detecting species with many weak/shallow spectral lines, as well as measuring the exact shape of the lines in the spectrum. However, technical considerations regarding the physical size and throughput of such instrumentation, as well as the consequences of lowering the signal-to-noise per resolution element, would have to be carefully assessed.
• Detection significance: Early analyses of HRS used signal-to-noise theory to assess the strength of cross-correlation signals, which was shown to be a good proxy for significance from the statistical analysis of the distribution of cross-correlation values (Brogi et al. 2012). While straightforward if cross-correlation values can be considered independent and Gaussian, this method can be biased by the presence of residual red noise, aliases of the cross-correlation function in velocity space, and the unavoidable correlation between neighboring velocity lags due to the finite instrumental resolution. The recent introduction of Bayesian techniques to estimate chemical and physical properties opens up to an alternative method to assess the significance of a detection, that is by comparing the Bayesian evidence of models with and without a certain species (Brogi & Line 2019; Gandhi et al. 2019; Gibson et al. 2020). This approach has the advantage of being consistent with the analysis of low-resolution spectroscopy, however it still needs to be demonstrated on a large scale.

HRS offers a cornucopia of opportunities, both near term and long term:

• TESS and the Sub-Neptunes: The imminent discovery of a sample of planets orbiting bright stars by the TESS mission, opens up the detailed atmospheric characterization of sub-Neptunes in support of deep HST observations and in advance of JWST observations. This has an enormous potential for delivering informative discoveries with a strong legacy aspect, especially if the information at low and high spectral resolution is routinely combined.
• Seeing Above the Clouds: The current availability of high-resolution spectroscopy instrumentation is on medium-class facilities (4–8 m) including some with unprecedented spectral range and throughput. The most performing of these instruments at the moment seems to be CARMENES and SPIRou, with a potential of 3× the S/N per unit observing time when looking for broadband absorbers in the NIR such as water vapor and methane. Such opportunity opens up the possibility of surveying exoplanets that show a flat transmission spectrum at low spectral resolution, e.g., due to aerosols, and to detect the fraction of the spectrum forming above the aerosol deck (Hood et al. 2020; Gandhi et al. 2020).
• Nearest Neighbors: Given that HRS does not need a planet to transit in order to characterize its atmosphere, it offers the best chance in the coming decade to remotely study our nearest neighbors, including rocky worlds such as Proxima b (Anglada-Escudé et al. 2016). METIS/ELT is ideally suited to target this planet in the 3–5 μm region (Snellen et al. 2015), alongside GMTIFS and GMTNIRS at GMT, while other optical high-resolution instruments can target oxygen, such as HARMONI and HIRES at ELT, G-CLEF and GMagAOX at GMT. Similar instruments for studying northern hemisphere counterparts include MICHI, MIDHIS, HROS, WFOS, and PSI at TMT. Given the proximity of our nearest neighbor, it can be studied both in Doppler shift and spatial separation at high spectral resolution, and there is even potential to observe it already with a combination of SPHERE+ESPRESSO or other new instruments for the VLT (Lovis et al. 2017).
• Atmospheric Maps, Biosignatures, and Surfaces: The increased sensitivity of the ELTs means that hot Jupiter and high signal-to-noise systems observed with HRS will give the planet spectrum directly, i.e., cross-correlation will not be needed as the spectral lines will stand out above the noise. With METIS/ELT it is expected that individual lines in hot Jupiter spectra will have S/N∼10 each. With such exquisite quality of high-resolution exoplanet spectra, we will be able to essentially apply stellar spectroscopy techniques to exoplanets. For Hot Jupiters, that means each lines gives information about a different altitude in the planet. With time resolution, a fully 3D and phase-resolved model of the planet can be built, including measuring wind speeds at different altitudes. Excitingly, the ELTs can monitor the detailed line shape over time to enable Doppler imaging of giant planets (Snellen et al. 2014), in a similar manner that starspots are imaged, or indeed as was used to make the atmospheric map of the brown dwarf Luhman 16 B (Crossfield et al. 2014). For smaller planets, the increased sensitivity of the ELTs suggests that low abundances molecules can also be studied. An interesting avenue for study is the potential to detect biosignatures with no false positive, for example phosphine as has recently been suggested (Sousa-Silva et al. 2020; Greaves et al. 2020). Finally, it is important to investigate how distinct the different types of terrestrial worlds will appear in HRS observations and if their surface process can be studied this way too.
• HRS in Space: There is a reasonable case for space-based high-resolution spectroscopy in order to overcome the high thermal background noise and instability of the Earth's atmosphere, and unlock precious observable windows targeting the main water vapor bands and much further into the infrared where spectral features can be larger, less obscured by clouds, and contain additional biosignature features. This does not necessarily need to be a flagship mission, but alternative routes could be exploited such as the use of 24U CubeSats with foldable components (see Chapter 10), however considerations need to be made for pointing stability and cooling.
• Combining ELTs with JWST and the Next Great Observatory: As discussed, the combination of HRS and lower resolution spectra is a power method for building a complete, accurate, and precise view of an exoplanet atmosphere. There is a special opportunity then to combine observations with HRS instruments on ELTs with space-based exoplanet spectra from initially JWST and HST, and eventually the Next Great Observatory (e.g., LUVOIR, OST, HabEx), with even the option for simultaneous monitoring. This is a possible long term avenue for the detailed study of nearby Earth-like exoplanets.

In order to capitalize on the opportunities offered by HRS in the study of exoplanet atmospheres, there are several key challenges to overcome.

• Stellar Spectra and 3D: The stellar spectrum is a non-negligible contaminant when looking for species simultaneously present in the stellar and planet atmospheres. For transmission/emission, these are currently the atomic lines from Na and potentially He, molecular lines of CO for G and K-type stars, TiO and H₂O for M-dwarfs. For reflection, the entire stellar spectrum is reflected, albeit at a different Doppler shift. Stellar lines are non-stationary in the observer's reference frame mostly due to the combined rotational and orbital motion of the Earth, and during transit stellar lines are distorted by Rossiter–McLaughlin effect and center-to-limb variations. One-dimensional stellar models applied to a proper simulation of transit geometry can mitigate these effects, and excellent correction is achieved for photospheric lines (e.g., CO) in main-sequence F to K stars when applying 3D stellar modeling (Chiavassa & Brogi 2019). However, uncertainties in molecular opacities remain an issue for proper modeling and correction of stellar lines, furthermore non-photospheric lines and effects of starspots are still challenging to model, with negative impact especially on the correction of M-dwarf spectra. Additional stellar activity in the form of flares can further influence HRS observations and its impact still needs to be quantified.
• Accuracy and Completeness of Line Lists: Uncertainties in molecular line lists at high spectral resolution will still affect accurate modeling of exoplanet spectra at least for a few years to come. These uncertainties come in two main flavors: completeness and accuracy. While the level of completeness is somewhat secondary for detecting species through cross-correlation, it is still important when retrieving abundances and temperatures, because the myriad of weak molecular lines form a pseudo-continuum capable of altering the line ratios. Accuracy refers to the exact determination of the frequency and intensity of a certain transition, and it is the most crucial aspect of current analysis of high-resolution spectra. In particular, inaccurate transition frequencies redistribute power from the peak to the wings of the cross-correlation function, with damaging effects on the detectability of species, especially at the relatively low S/N of HRS observations. While great progress has been made on some species such as CO, H₂O, TiO, and HCN, other key molecules such as CH₄ and CO₂ still lack the accuracy and completeness sufficient at resolving powers close to 10⁵ (Gandhi et al. 2020).
• Community Size and Instrumentation: The community of HRS users is still too small to process even archival data. This is especially true for spectrographs mounted at smaller telescopes (CARMENES, GIANO, SPIRou), due to the significant amount of telescope time invested by small teams with proprietary access. While instrumentation has begun to ramp up in recent years, especially in the optical, and the imminent return of CRIRES+/VLT remains highly anticipated. One main obstacle to create a wider community is the lack of standardized analysis techniques that are applicable on large scale and over heterogeneous data sets. Currently, the analysis is often optimized on a case-by-case basis and with proprietary codes of each research group. Specialist conferences and data challenges are still rare and do not offer enough support for young academics and group leaders to get involved. It is especially important for the community to explore different avenues within the field of HRS which is still in its relative infancy, but also to consolidate its findings on the best approaches for analysis.

JB acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under grant agreement No 805445.