Atmospheric correction for high-resolution near-infrared spectroscopy

Atmospheric

correction for

high-resolution

near-infrared

spectroscopy

Solène Ulmer-Moll

Tese de Doutoramento apresentada à

Faculdade de Ciências da Universidade do Porto

Astronomia

2020

PhD

PPPPPPPP

P

hhhhhhhh

h

DDDDDDDD

D

PPPPPPPP

P

hhhhhhhh

h

D

PPPPPPPP

P

hhhhhhhh

h

D

Atmospheric

correction

for high-resolution

near-infrared

spectroscopy

Solène Ulmer-Moll

Programa Doutoral em Astronomia

Departamento de Física e Astronomia 2020

Orientador

Pedro R. L. Figueira, Investigador, European Southern Observatory Coorientador

Nuno M. C. Santos, Professor Auxiliar, Faculdade de Ciências

PPPPPPPP

P

hhhhhhhh

h

Abstract

The absorption by the Earth’s atmosphere is a major limiting factor for near-infrared spectroscopy. To detect exoplanets with precise radial velocities and charaterize their atmospheres, it is essential to correct for the telluric absorption. Historically, this correction has been done with the standard star method, by observing a rapidly rotating and featureless star close in time and airmass to the target star. In principle, the spectrum of the standard star only contains telluric lines and can be used to correct the target spectrum.

However, this method has several limitations: differences in airmass and time of obser-vation can introduce artifacts in the corrected spectrum and the different light paths lead to different water vapor contents between the standard star and target spectra. To solve these problems, several codes which produce a synthetic transmission spectra of the Earth’s atmosphere at the time of the observations have been developed.

My thesis aims at better understanding the performance of the synthetic transmission methods in the near-infrared region. I compare three telluric correction packages with the standard star technique to evaluate which one delivers the most precise correction. I find that synthetic transmission methods correct best the water lines in the J band but the oxygen lines are better corrected with the standard star method. The use of a tailored atmospheric profile for synthetic transmission methods improves the correction level. Furthermore, I aim at confirming the presence of planetary companions around ξ Aql and HD 192263 using archive spectra taken in the near-infrared, after correcting for the telluric contamination.

Finally, while learning about statistical analysis and looking for methods to improve these codes, I committed some time to other research within the extrasolar planet domain. I used a machine learning algorithm to estimate the radius of exoplanets based on other planetary and stellar parameters. My code forecasts exoplanet radii more accurately than previously published methods.

Resumo

A absorção pela atmosfera da Terra é um fator importante e limitante para a espectro-scopia no infravermelho próximo. Para detetar exoplanetas com o método das velocidades radiais e caracterizar as suas atmosferas, é essencial corrigir a absorção telúrica. O método histórico para fazer esta correção é o método da estrela padrão, que consiste em observar uma estrela de rotação rápida e sem riscas estelares, próxima no tempo e na massa de ar da estrela alvo. Em princípio, o espectro da estrela padrão contém apenas riscas telúricas e pode ser usado para remover as riscas telúricas do espectro alvo, dividindo o alvo pelo espectro telúrico.

No entanto, este método tem várias limitações: diferenças na massa de ar e no tempo de observação podem introduzir artefatos no espectro corrigido. Além disso, os diferentes caminhos de luz na atmosfera levam a diferentes conteúdos de vapor de água entre os espectros da estrela padrão e do alvo. Para resolver estes problemas, foram desenvolvidos vários códigos que produzem espectros de transmissão sintéticos da atmosfera da Terra no momento das observações.

A minha tese visa entender o desempenho dos métodos de transmissão sintética na região do infravermelho próximo. Atravês da comparação de três métodos de correção telúrica com a tecnica da estrela padrão, consegui avaliar qual consegue uma correção mais precisa. Os resultados demonstrão que os métodos de correção com transmissão sintética corrigem melhor as riscas de água na banda J, mas as riscas de oxigénio são melhor corrigidas pelo método da estrela padrão. O use de um perfil atmosférico adequado para o cálculo da transmissão sintética melhora a correção. Para além disso, quis confirmar a presença de planetas em órbita das estrelas ξ Aql e HD 192263 usando espectros no infravermelho depois da correção telúrica.

Por fim, ao aprender sobre análise estatística e procurar métodos para melhorar esses códigos, dediquei algum tempo a outro trabalho no domínio dos planetas extra-solares. Usei um algoritmo de aprendizagem automática para estimar o raio de exoplanetas com base noutros parâmetros do planeta e da estrela. Desenvolvi um código para prever os raios dos exoplanetas com maior exatidão do que os métodos publicados anteriormente.

Acknowledgement

I would like to deeply thank Nuno Santos and Pedro Figueira who provided me with a lot of advice and guided me during this PhD, while giving me a lot of freedom. Now that it is over, I can finally say that I enjoyed it and I would do it again. Thank you to my friends and colleagues from CAUP, who made the difficult moments more cheerful. To Julie Rouzaud, Norine Dumas, and Océane Rennesson, my friends from France who came to visit me several times in Portugal, thank you so much. The time we spent together was amazing and I hope we will keep this friendship going against the adversity of life. To João Faria for all his help with my work and this manuscript. Thank you for all the Sunday walks on the beach, you made me feel at home and I am sure more unforgettable adventures will come.

Finally I want to thank my parents, Eliane and Jean-François Ulmer-Moll for always encouraging me to pursue astronomy and supporting me financially. I hope one day I will get to give you back all I received from you.

Contents

1 Introduction 1

1.1 Exoplanets . . . 1

1.2 Detection methods . . . 2

1.3 Exoplanet detection in the near-infrared . . . 7

1.4 Thesis Structure . . . 10

2 Telluric contamination and correction 13 2.1 Earth’s atmosphere . . . 13

2.1.1 Atmospheric scattering . . . 13

2.1.2 Atmospheric emission . . . 14

2.1.3 Atmospheric absorption and transmission . . . 15

2.1.4 Spectral telluric contamination . . . 16

2.2 Telluric standard star method . . . 16

2.3 Synthetic transmission methods . . . 18

2.3.1 TAPAS . . . 19 2.3.2 Molecfit . . . 20 2.3.3 TelFit . . . 23 2.3.4 Other methods . . . 25 2.4 Data-driven methods . . . 25 2.4.1 Wobble . . . 26

2.4.2 PCA-based telluric correction . . . 28

2.5 Conclusions . . . 29

3 Comparison of telluric correction methods 31 3.1 Observations and data reduction . . . 31

3.1.1 Observations . . . 31

3.1.2 Data reduction . . . 33

3.2 Telluric correction . . . 33

3.2.1 Adaptation of telluric correction methods . . . 33

3.2.2 Difference between the synthetic transmission methods . . . 40

3.2.3 Criteria to compare telluric correction methods . . . 40

3.3 Comparison of the telluric correction . . . 42

3.3.1 Water and oxygen absorption . . . 42

3.3.2 Sensitivity to airmass and precipitable water vapour . . . 49

3.3.3 Effect of the atmospheric profile . . . 51

3.4 Conclusion . . . 56

4 Impact of the telluric absorption on radial velocities 59

4.1 The measurement of Doppler radial velocities . . . 59

4.1.1 Doppler effect . . . 59

4.1.2 Radial velocity in the near-infrared . . . 62

4.1.3 Wavelength calibration in the near-infrared . . . 63

4.2 Impact of telluric absorption on radial velocities . . . 64

4.2.1 Formalism for radial velocity precision . . . 65

4.2.2 Measuring radial velocity precision in the near-infrared . . . 66

4.3 Conclusion . . . 69

5 Radial velocity measurements for exoplanet search 71 5.1 ξ Aql and HD 192263 . . . 71

5.2 CRIRES data analysis . . . 73

5.2.1 Observations and data reduction . . . 73

5.2.2 Telluric correction with Molecfit . . . 76

5.3 Exoplanet detection with radial velocities . . . 77

5.3.1 Radial velocity measurements . . . 77

5.3.2 Analysis of the radial velocities . . . 80

5.4 Conclusion . . . 88

6 Conclusions 89 6.1 Thesis outputs . . . 89

6.2 Future prospects . . . 90

Appendix A Telluric correction of high resolution spectra 93

Appendix B Beyond the exoplanet mass-radius relation 99

Bibliography 125

1

Introduction

„

— Nelson Mandela (Peace Nobel Prize)

This thesis deals with the properties of exoplanets and the challenges posed on their detection by the effects of the Earth’s atmosphere. This first chapter presents an introduction to the research field of exoplanets. Exoplanets are planets orbiting another star than the Sun and an incredible diversity of exoplanets has been found in our galaxy. Section 1.1 summarizes the exoplanet field, from the first detections to the different exoplanet populations known to date. The methods for detecting exoplanets and their current challenges are presented in Section 1.2 and 1.3. The structure of the thesis is shown in Section 1.4.

1.1 Exoplanets

In 2019, the exoplanet count from the NASA exoplanet archive passed the 4000 mark. This same year, the Nobel prize in physics was attributed to astrophysics and half of it was awarded to Michel Mayor and Didier Queloz for “the discovery of an exoplanet orbiting a Solar-like star”. Indeed, their discovery of 51 Pegasi b, a hot-Jupiter orbiting a G2 IV star (Mayor and Queloz, 1995) launched the quest for exoplanets of the last decades.

A few years prior to the historical detection of 51 Peg b, several detections of low mass exoplanets orbiting pulsars were claimed and some confirmed later on (Wolszczan and Frail, 1992; Backer et al., 1993). The measured masses of these first exoplanets are shown in Figure 1.1 along with all the exoplanets detected every year since then. This plot shows us that the mass of the detected planets, clearly decreased towards the Earth regime but seems to have stagnated in the last few years. This plateau is probably due to a combination of factors limiting the achievable precision of the detection methods. I will briefly discuss the detection methods and the associated challenges in the Section 1.2. One incredible aspect of the exoplanets detected so far is their diversity. The Solar system already has a variety of planets from the small rocky Mercury to the gas giant

1990 1995 2000 2005 2010 2015 2020 Discovered year 10−3 10−2 10−1 100 101 102 103 104 Planet Mass (M ⊕ )

Fig. 1.1.: Planet masses as a function of the year of detection from the Encyclopaedia Exoplanets catalogue queried on December 4, 2019.

Jupiter. But from the 4000 exoplanets we already know of puffed gas giant exoplanets orbiting their star only in a few days and planets a few times the size of Earth (Cochran et al., 2011), called super-Earths, which are rocky and potentially have an atmosphere. These numerous detections already allow us to study in detail how planets form and what they are made of. And, fortunately, there are probably many more discoveries to come. The search for an Earth twin around a Solar type star is still on-going, but we are also starting an era of in-depth characterization of exoplanets.

1.2 Detection methods

The two most prolific methods for detecting exoplanets are the transit method and the radial velocity method. I will start by presenting these two methods, followed by direct imaging, microlensing, and astrometry. According to the NASA exoplanet archive on December 4, 2019, 3134 planets were discovered by the transit method, 781 planets by the radial velocity method, 86 planets by gravitational microlensing, 47 by direct imaging, and 1 planet was discovered by astrometry.

Transit The transit method consists in monitoring the brightness of stars in order to

observe an exoplanet passing in front of its host star. The transit method is by far the

one with the largest number of detected exoplanets. This method is, however, prone to a large fraction of false positives since several configurations can lead to an apparent exoplanetary transit. For example, double or multiple star systems can lead to a decrease in the star brightness, mimicking a planetary transit (e.g. Cameron, 2012; Santerne et al., 2013).

The decrease in stellar brightness during transit gives a direct measure of the ratio between the planetary radius and the stellar radius (e.g. Kipping, 2011), with the geometric transit depth given by

δ = R

2

P

R2_?. (1.1)

From this equation, it is clear that larger planets induce a deeper transit. The necessary alignment to observe a transit occurs with a probability that depends, for circular orbits, on the stellar radius and the semi-major axis (e.g. Perryman, 2018):

p = R? a ' 0.005 _R ? R   _a 1AU −1 . (1.2)

One can see that p is small for planets in the habitable zone of Solar-like stars. From the transit it is also possible to measure the orbital inclination of the planet relative to the plane of the sky, which gives us access to the true mass of the exoplanet when it is also detected with radial velocity.

The first transiting planet was reported by Charbonneau et al. (2000) and Henry et al. (2000) around the star HD 209458. It is a gas giant of 1.32 times the mass of Jupiter and 0.69 times its mass with an orbital period of about 3.5 days. This planet was the subject of numerous other studies, in particular atmospheric studies. For example, the He I infrared triplet has been recently detected in the atmosphere of this exoplanet (Alonso-Floriano et al., 2019).

Space-based missions dedicated to high-precision photometry started with CoRoT, followed by Kepler and K2. Photometric campaigns like CoRoT (Baglin et al., 2007) or Kepler (Borucki et al., 2008) performed blind searches and mainly observed Solar-type stars. The CoRoT mission discovered the first exoplanet with a rocky core, called CoRoT-7-b (Léger et al., 2009) and the Kepler mission reported its first rocky exoplanet, Kepler 10b, in 2011 (Batalha et al., 2011). TESS is the latest on-going mission (Ricker et al., 2015). These missions detected and continue to discover myriads of exoplanets and have allowed to compute occurrence rates (e.g. Burke et al., 2015; Hardegree-Ullman et al., 2019) and perform population studies.

Transit timing variations Transit timing variations is a by-product of the transit method.

Once a transiting planet is detected, repeated measures of the time of transit can show

variations of the time between consecutive transits. If it is the case, the presence of additional exoplanets can be deduced and planetary masses can be determined through gravitation interaction (Becker et al., 2015). One of the first exoplanets found thanks to transit timing variations is Kepler-19 c (Ballard et al., 2011). The detection was done by measuring the variation of the time of transit of Kepler-19 b, which has an amplitude of 5 minutes. This method can be used to detect additional, and potentially non-transiting planets, in a system with transiting planets.

Radial velocity The radial velocity method consists in observing the wobble of a star

around the centre of mass of the star-planet system. This wobble is detectable by observing repeatedly the spectrum of the star (e.g. Lovis and Fischer, 2010). The light emitted by the moving star is shifted in wavelength by the Doppler effect: when the star is moving away from the observer the stellar lines in its spectrum are shifted towards longer (redder) wavelengths, and when the star is moving towards the observer the stellar lines are shifted towards shorter (bluer) wavelengths.

An orbiting planet in a circular orbit induces sinusoidal radial velocity variations on the star. The semi-amplitude (K) of the radial velocity curve is given by

 _K m/s  = 28.4  _P 1year −1/3 _M Psini MJ  _M ? M −2/3 (1.3) resulting in K ∼ 12 m/s for a Jupiter-like planet and ∼ 9 cm/s for an Earth-like planet (e.g. Perryman, 2018). From Equation 1.3, we see that more massive planets at shorter orbital periods produce larger radial velocity variations.

The exoplanet 51 Peg b was detected thanks to the radial velocity method, with observations done with the spectrograph ELODIE at the Observatory of Haute-Provence, in France (Mayor and Queloz, 1995). The radial velocity method allows to measure the minimum mass of the planet. If the exoplanet is detected with the transit method, then the inclination is known and the true mass can be determined. This method will be explained in more detail in Section 4.1.

Direct imaging Direct imaging can be summed up as taking a picture of an exoplanet.

This is the most intuitive method to explain to the public and usually provides the most compelling images of exoplanet detections. The first exoplanet to be detected with the direct imaging technique was 2M1207 b with about five times the mass of Jupiter and orbiting a brown dwarf (Chauvin et al., 2004). Direct imaging is a challenging technique in the optical and infrared, since the star is several orders of magnitude brighter than the planet. Direct imaging is performed with a combination of two techniques: an adaptive optics system, which corrects for the effect of the Earth’s atmosphere, and a coronograph which blocks most of the light coming from the central star (Sivaramakrishnan et al.,

2001; Oppenheimer and Hinkley, 2009). One of the high-constrast imaging techniques is the angular differential imaging which allows the field of view around the central star to rotate over the course of several consecutive observations while the instrument and optics are aligned (Marois et al., 2006). Recent instruments such as SPHERE (Beuzit et al., 2019) and GPI (Macintosh et al., 2008) are detecting young exoplanets (e.g. Macintosh et al., 2015; Chauvin et al., 2017), but also characterizing exoplanets in terms of physical and chemical properties (e.g. Bonnefoy et al., 2016). In the future, direct imaging will be key to characterize exoplanets since new instrumentation might allow one to map the atmosphere or even the surface of exoplanets.

Gravitational microlensing Gravitational microlensing detects planets by measuring

the effect of gravity on the light of a background object (Gaudi, 2012). An object with a large mass, such as a star with one or more planets, is able to bend the light coming from a background object. The light from the background star will be amplified by the foreground system, which acts as a lens, hence the name microlensing. If the foreground system is only composed of a star, the light increases slowly and then decreases as the star passes in front of the background object. If there is a planet in the system, the planet will create a sharp peak in the light curve. For reference, the timescale of the peak produced by the planet is of a few hours, while the one produced by the host star is of about a month. This technique does not rely on detecting the light emitted by the host star or the planet and thus can probe exoplanets throughout the Galaxy (Gaudi, 2012).

The first planet detected with gravitational microlensing is 1.5 times the mass of Jupiter and orbits its host star at a distance of 3 AU, assuming that the host is a main-sequence star (Bond et al., 2004). Gravitational microlensing is able to probe exoplanets at larger distances from Earth than other techniques but also small planets. Unfortunately it is almost always a single time event and no follow-up can be performed with ground-based instrumentation.

Astrometry Astrometry relies on measuring the star’s position on the sky. Repeated

measurements of the star’s position can reveal perturbations due to a stellar or planetary companion (Sozzetti, 2005). If the star is in a multiple stellar system or hosts planetary companions, the star will then orbit the centre of mass of the system, like it is observed with the radial velocity method. Its movement around the centre of mass results in perturbations on the motion of the star in the plane of the sky. With ground-based observations, one of the first companions to be detected with astrometric measurements is a very massive object, about 28.5 times the mass of Jupiter located 0.36 AU from its host star (Sahlmann et al., 2013). Launched in December 2013, the Gaia mission (Perryman et al., 2001) measures very precisely the position of over one billion stars in

10−3 10−2 10−1 100 101 102 103 Distance to the star (AU)

10−4 10−3 10−2 10−1 100 101 102 103 Planetary mass (M J ) Transit RV Imaging TTV

Fig. 1.2.: Planetary mass as a function of the distance from the star. The colour code corre-sponds to the detection method: transit method is in orange, radial velocity in green, direct imaging in red, and transit timing variations in black.

our Galaxy. These measurements are expected to lead to the detection of thousands of long-period exoplanets in the next few years (Perryman et al., 2014).

Each detection method allows to access certain types of planets. The radial velocity method is most sensitive to massive planets located close to their host star. But longer-period planets (P ∼ 10 years) can also be found through long-term monitoring from the ground. The transit method preferentially detects large planets close to their host star, with a fast decrease in sensitivity for longer orbital periods. On the contrary, direct imaging has so far only detected planets further away from the host star (semi-major axis a & 10 AU) and young planets. The sensitivity of each detection method can be seen in Figure 1.2 where I present the masses and semi-major axes of planets detected with the first four methods explained in the previous paragraphs.

Several small rocky exoplanets, also called terrestrial planets, are precisely characterized. This type of exoplanets are still a minority compared to the impressive number of exoplanets already found. Moreover, to host life these small rocky exoplanets should be located at a specific distance from their host star to support liquid water on their surface given a sufficient atmospheric pressure which defines the circumstellar habitable zone

(Cruz and Coontz, 2013). The peculiarity of the terrestrial planets is not the reason of this shortage but rather the methods employed to search for exoplanets.

For the radial velocity method, which has been proven to be successful in detecting exoplanets (Mayor et al., 2014), one of the new challenges is to achieve precise radial velocity measurements in the near-infrared. As detailed in the next section, the search and characterization of exoplanets is now moving towards the infrared thanks to a successful transfer of technology.

1.3 Exoplanet detection in the near-infrared

The scientific motivation to detect and characterize exoplanets in the near-infrared is explained in the next paragraphs as well as the challenges encountered when working in the near-infrared.

Scientific motivation

Finding planets around M dwarfs In the quest for Earth-like planets, some focus tends

to be given to M stars for several reasons. M stars are the most numerous in the Universe. These lower mass stars represent about 72% of the stars in our Galaxy (Henry et al., 2006). Their radii vary between 0.075 and 0.5 Solar radii and their masses between 0.08 to 0.6 Solar masses.These last two physical properties of M stars ease the detection of Earth-like planets around them. The ratio between the radius of a transiting planet and an M star is larger than for Solar-type star. And the radial velocity shift induced by a planet is also larger on the M star than on a Solar-type star. Finally, the habitable zone of an M star, which corresponds to the region where liquid water can be maintained at the surface of a planet with an Earth-like atmosphere, is located closer to the star than for a Solar-type star (Kasting et al., 1993). Thus, a planet in the habitable zone of an M star induces again a larger radial velocity shift.

M stars are promising targets to search and characterize Earth-like planets in the habitable zone.They led the development of a new generation of near-infrared spectrographs such as NIRPS (Wildi et al., 2017), SPIRou (Moutou et al., 2015), CARMENES (Quirrenbach et al., 2014), CRIRES+, and HZPF (Mahadevan et al., 2012). Hence, we need to understand the characteristics of these wavelength regions, in order to perform efficient observations and reduction of the infrared data.

Detecting planets in the presence of stellar activity The detection of orbiting planets

can be impeded by stellar activity. Indeed, stellar phenomena can induce radial velocity and flux variations challenging the detection of planets by the radial velocity and transit

methods. Stellar activity ranges from timescales of minutes originating from the short term stellar pulsations (Bouchy et al., 2005), to timescales of several years with activity linked to the stellar magnetic cycle (Santos et al., 2010). The surfaces of Solar-type and M stars present dark spots, which are cooler than the stellar photosphere. These active regions at the surface of the stars also create signals in the timescales of hours or days. These signals have a period which can mimic the one of planetary companions (Queloz et al., 2001; Bonfils et al., 2007). The impact of stellar activity on radial velocity measurements is extensively studied for example with numerical simulations (Boisse et al., 2011; Dumusque et al., 2014). For radial velocity measurements, spectral activity indicators are widely used in order to identify periodicities originating from stellar signals (e.g. Lovis et al., 2011) and new techniques are developed to disentangle stellar activity signals from planetary ones as proven for the active star CoRoT-7 by Faria et al. (2016).

In the case of M stars, they are most luminous in the infrared and the contrast between the stellar spots and the quiet photosphere is lower. Thus, stellar activity could be easier to mitigate for M dwarfs than for FGK stars. The stellar activity of M dwarfs is less well understood than the one of Solar-types, but Astudillo-Defru et al. (2017a) show that emission lines such as the Ca II H and K doublet are correlated with the short-term variability of the activity for a sample of M dwarfs observed with HARPS. The radial velocity variations induced by stellar spots is known to decrease when looking in the redder part of the spectrum and a comparison of the radial velocity variations between the blue and red orders of a spectrum (e.g. the chromatic index) can be used to investigate stellar active regions (Zechmeister et al., 2018) . However, a larger fraction of M stars show Hα chromospheric activity (Delfosse et al., 1998) and numerous flares

(Hawley et al., 2014) compared to higher mass stars.

Detecting exoplanetary atmospheres Transiting exoplanets allow us to determine

precise radii but also to study the atmosphere of these exoplanets. Transit photometry gave the first hints of molecules in an exoplanet atmosphere (Vidal-Madjar et al., 2003). The atmospheres of gas giants and super-Earths are studied with observations from space. For example, one of the latest discoveries is the presence of water in the atmosphere of K2-18 b, an 8 M⊕ exoplanet located in the habitable zone of its host star (Tsiaras et al.,

2019).

High-resolution spectroscopy is also able to provide detailed information on the atmo-sphere of these exoplanets. Transmission spectroscopy is used to probe the atmoatmo-sphere of exoplanets; for example sodium was detected in the atmosphere of a hot gas giant (Seidel et al., 2019) with HARPS observations in the visible. Near-infrared observations are also very valuable. Allart et al. (2018) detected the triplet of neutral helium in the atmosphere of HAT-P-11 b, an exoplanet with the mass of Neptune. In that case, the

correction for the Earth’s atmospheric features is essential because the telluric lines can change the level of the continuum. For cooler planets, the molecules in the exoplanetary atmosphere can be essentially the same species as the ones present in Earth’s atmosphere. Shulyak et al. (2019) argue that the accuracy required in the telluric removal should attain a minimum of 10−3. The authors demonstrate that high-resolution spectroscopy in the near-infrared with new instruments, like CRIRES+, will allow a detailed analysis of various species in the atmosphere with a potential measure of the volume mixing ratios and the temperature profiles.

Observational and scientific challenges

Near-infrared observations face several challenges. I will focus here on near-infrared spectroscopy and will briefly also discuss the challenges of measuring precise radial velocity shifts in the near-infrared.

Detectors Firstly, detectors used to register the spectrum in the infrared are CMOS

detectors (Composite Metal Oxide Semiconductors) and they operate differently than the detectors usually used in the visible. In general, the detectors operating in the visible are CCDs (Charge-Coupled Device) and they are composed of silicon and allow to electronically transfer charges. The photons are converted into charges which are collected in each pixel of the detector. Each row of charges is shifted horizontally and the charges accumulated in one pixel are converted to voltage, amplified and transformed into a digital number. Contrary to the CCD detector, the charge to voltage conversion and the amplification are carried out in each pixel for the CMOS detector. Then the data of each pixel is read line by line in the case of the CMOS sensor. The material of the CMOS detector varies from the CCD one and these materials need to be cooled at lower temperature. The lower temperature avoids that the thermal excitation of electrons creates a small current, called dark current, even though no photon is arriving at the surface of the detector. The conversion of the charges in each pixel can introduce some artefacts and differences between each pixel which have to be quantified, (e.g. pixel-to-pixel non-uniformities) but it also allows to read the pixel several times and at different integrations times, for example. More details on CMOS detectors are available in Glass (1999) and Figueira (2018).

Wavelength calibration Precise wavelength calibration is also challenging in the

near-infrared. For example the Thorium-Argon (Th-Ar) lamp, widely used in the optical, has less lines in the near-infrared and thus is not adequate to perform the wavelength calibration. Several methods to obtain a reliable wavelength calibration in the near-infrared are explained in Section 4.1.3.

Telluric contamination The Earth’s atmosphere imprints absorption and emission lines

in spectra observed from the ground. While the telluric contamination is concentrated in small regions of the optical wavelengths, it is predominant in the near-infrared wavelengths. The telluric lines greatly impact the amount of information which can be retrieved from the spectra and thus need to be corrected for. I detail in Chapter 2 the nature of the telluric contamination and the available methods to perform its removal.

Radial velocity content One current subject of debate in the near-infrared is the

amount of radial velocity information achievable in different wavelength bands. The estimates differ depending on the method used to calculate the radial velocity content (e.g. Figueira et al. 2016; Artigau et al. 2018; Reiners et al. 2017). This argument led to the design of spectrographs with different resolution and wavelength coverage like NIRPS (Wildi et al., 2017) and SPIRou (Delfosse et al., 2013; Moutou et al., 2015) for example. Chapter 4 presents in more detail the computation of the radial velocity information from a spectrum and the impact of telluric lines on the radial velocity content.

1.4 Thesis Structure

Chapter 2

The second chapter presents the absorption by the Earth’s atmosphere in the optical and the near-infrared wavelength ranges and the case for correcting for the atmospheric absorption. The chapter also details the different methods to correct for the Earth’s atmosphere absorption from the historical telluric standard star method to synthetic atmospheric transmission methods and new data-driven methods.

Chapter 3

The third chapter is dedicated to the comparison of existing telluric correction methods. The telluric methods considered in this study are the standard star method, and three synthetic atmospheric transmission methods. The three synthetic transmission methods are Molecfit, TelFit, and TAPAS. This work shows that the level of correction attainable in the near infrared is between 3% and 7% and depends on the molecules corrected. Using a tailored atmospheric profile for the synthetic transmission methods improves the telluric correction.

Chapter 4

The fourth chapter presents the radial velocity method and the challenges of performing radial velocity measurements in the near-infrared regime. The impact of the telluric lines on the precision achievable with the radial velocity method is also explored.

Chapter 5

The fifth chapter has the goal to confirm or refute planetary companion detection around two stars, ξ Aql and HD 192263, with near-infrared spectroscopic data. I use two datasets of CRIRES spectra to derive radial velocity. An essential step in this work is to perform the telluric correction of the near-infrared spectra and perform the wavelength calibration with the telluric lines.

Chapter 6

The conclusions and future prospects are presented in the last chapter. I showed that the telluric correction of near-infrared spectra is a challenging but essential task to achieve the expected radial velocity precision to detect extra-solar planets in the near-infrared domain.

2

Telluric contamination and

correction

2.1 Earth’s atmosphere

The atmosphere is a layer of gases essential to life on Earth. But astronomers would sometimes do without it: “the atmosphere is the greatest single natural impediment for ground-based astronomy” (Wamsteker et al., 2012). In an introductory article, Michard (1953) lists the four main ways in which the atmosphere impacts astronomical observations: refraction, turbulence, absorption and airglow. At its origin probably constituted with carbon dioxide and some water vapour, the atmosphere has evolved since the formation of the Earth, and is now composed of 78% of N2, 21% of O2 and

1% of other gases such as Ar, CO2, Ne, He, H2O (Gargaud et al., 2012). All these

molecules are present in different proportions, which vary with height in the atmosphere. They absorb and scatter the light entering the atmosphere in several wavelength regions (Glass, 1999). The variations in temperature and wind are some of the factors that blur the astronomical observations. This section describes three interactions of the incoming light with the Earth’s atmosphere and how the location of astronomical sites can be chosen in order to minimize the effect of the atmosphere.

2.1.1 Atmospheric scattering

Particles in the atmosphere can redirect the incoming electromagnetic radiation in a phenomenon called scattering. According to the size of the interacting particle, three types of scattering can be differentiated. Rayleigh scattering occurs when particles are smaller than the wavelength of the light. These particles can be oxygen or nitrogen molecules for example. Rayleigh scattering is more efficient for shorter wavelengths (blue light) than for longer wavelengths (red light) and is not isotropic. The blue colour of the sky during daytime is due to the scattering of Sun light in the atmosphere. At sunset, the sky appears redder because the path length covered by the light in the atmosphere is longer and all the blue light has been scattered and only red light reaches the surface (Emery and Camps, 2017).

When particles are about the same size as the wavelength of the incoming light, the scattering process is called Mie scattering. The particles are water vapour and other gases but also particles of dust. This type of scattering is larger in the forward direction.

It occurs in the lower part of the atmosphere where the larger particles are present and affects generally the near-ultraviolet to the mid-infrared light.

Particles which size is much larger than the wavelength of the incoming light also create scattering, called non selective scattering because in this case all optical wavelengths are affected in the same way. These particles are water droplets or dust particles. The white colour of the clouds comes from the water droplets in the cloud which scatter all the incoming light. In general this scattering is isotropic (Emery and Camps, 2017).

2.1.2 Atmospheric emission

Thermal emission The contribution to the thermal emission in astronomical

observa-tions at infrared wavelengths comes from two main components: the atmosphere and the telescope with its associated optics. The emissivity is the ratio of thermal radiation emitted by the material at a given temperature to the thermal radiation emitted by a blackbody at the same temperature. The maximum emissivity is 1 and corresponds to the emitted electromagnetic radiation of a blackbody at a given temperature. Real objects are graybodies which means they reflect part of the incident light. Objects with a temperature different from 0 K have an emissivity lower than 1, and this is the case for the atmosphere. The emissivity of the atmosphere also varies according to its opacity, itself mostly governed by the water vapour (McLean, 2008). The emissivity of the telescope and optics depends on their temperature but also on the nature of their surface (e.g. mirror coating, dust). For wavelengths shorter than 13 µm, the thermal emission is dominated by the telescope, while at longer wavelength it is dominated by the atmosphere. Near-infrared spectrographs are designed to keep the emissivity and the temperature of the optics low in order to decrease the contribution of the thermal radiation.

Non thermal emission The airglow and the aurora are faint luminescences generated

by photochemical reactions in the upper atmosphere, above 70 km. Aurorae are mostly located at polar latitudes and are negligible at mid latitudes where astronomical observa-tories are usually located. Airglow occurs at mid and low latitudes and produces emission lines in the spectra.The airglow is present at different wavelengths and corresponds to several photochemical reactions. Atomic oxygen and sodium can create airglow, but the strongest source is OH, which produces emission lines in the near-infrared between 0.8 and 2.5 µm (McLean, 2008). OH molecules are excited by ultraviolet photons from the Sun in a layer of the atmosphere called the mesopause. The OH airglow occurs when the molecules are relaxing to lower vibrational or rotational states, thus creating the OH airglow in the infrared or at longer wavelengths, respectively. Airglow emission lines are variable in the short time scales (i.e order of minutes) to much longer time scales. Airglow can be corrected for with plain sky spectra taken at the same time as the target

spectra or with modelling tools such as Skycorr (Noll et al., 2014), available on the ESO website1_.

2.1.3 Atmospheric absorption and transmission

Incoming light from astronomical objects is partly absorbed by the Earth’s atmosphere. An atmospheric transmission spectrum computed for the optical and near-infrared ranges is presented in Figure 2.1.

Optical Telluric absorption in the optical is dominated by water, oxygen, and ozone

absorption. The absorption bands in the optical have been studied extensively. For example, the two large oxygen bands at 690 nm and 760 nm are called the B and A oxygen bands. A smaller oxygen band, the γ band, absorbs part of the light around 630 nm. In the bluer part of the spectrum, the large O3 absorption band ranging from

500 to 700 nm with a maximum absorption around 600 nm is called the Chappuis band (Andrews, 2000). The effect of the Rayleigh scattering is not represented in Figure 2.1. Apart from the large absorption bands mentioned above, the optical range is also polluted with shallow absorption lines, called micro-telluric lines. These telluric lines absorb less than 2% of the continuum and they can have an impact on different science cases. For example, their impact on radial velocity measurements have been estimated to be around 10 cm.s−1 _{(Cunha et al., 2014), which is the level of precision expected for}

the ESPRESSO (Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations) spectrograph (Pepe et al., 2014a).

Infrared The infrared sky is quite different from the visible one, as some parts of the

sky obscured by clouds are revealed in infrared light, as well as objects which were too faint to be observed in the visible. We can see the light from hot giant planets (Deming et al., 2005), and cool red stars have their peak of emission in the infrared (Merrill and Ridgway, 1979). The infrared is usually divided in three main regions called near, mid and far infrared. The near-infrared ranges from 0.7 to 5 µm and at these wavelengths the interstellar dust is mostly transparent. In the mid-infrared, ranging from 5 to 30 µm, the sources of emission are planets, comets and asteroids, dust and protoplanetary disks. The far-infrared ranges from 40 up to 300 µm, where the submillimeter wavelengths start. In the far-infrared, there is emission from the cold dust in molecular clouds. Unfortunately, the infrared light is also in some part of the spectrum absorbed by the Earth’s atmosphere which reduces the information we can extract from infrared observations (Emery and Camps, 2017).

1

eso.org/sci/software/pipelines/skytools/skycorr

The near infrared wavelengths after 1.1 µm start to be strongly affected by water bands: in some parts of the spectrum all the light is absorbed. These atmospheric windows are linked with several photometric bands where a good average throughput can be expected. Some useful bands in the near-infrared and their central wavelength are: the J band at 1.25 µm, the H band at 1.65 µm, and the K band at 2.2 µm (McLean, 2008).

Earth’s atmosphere is in constant evolution, from its original composition to the present increase of greenhouse gases such as CO2 and CH4 caused by human activities and

leading to global warming. The absorption lines of different species also change on time scales of months or even hours. It is the case for the water vapour content in the atmosphere, which varies during a night of observations. The water vapour is concentrated in the lower part of the atmosphere (∼ 5 km), thus observatories are often located in dry sites and at high altitude to avoid some of the telluric contamination coming from water lines. Seasonal, daily, and hourly variations are also observed for

CH4 (Schneising et al., 2009), CO2 (Thoning et al., 1989), and O3 (Ramanathan and

Murthy, 1953).

2.1.4 Spectral telluric contamination

The contamination of high-resolution spectra by the Earth’s atmosphere is a limiting factor for various science cases such as stellar characterization, the study of exoplanetary atmospheres or exoplanet detection, to name a few. Several methods are available to correct for the telluric contamination in the optical and near-infrared. Thus, a careful examination of their performance is a necessary step in order to design possible improvements and before foreseeing an automatic implementation of telluric correction as a step of data reduction pipelines for the current and future near-infrared spectrographs. A review of existing telluric correction methods is presented in the next paragraphs.

2.2 Telluric standard star method

The telluric standard star technique is the historical method to correct for telluric contamination in the visible and in the near-infrared. This technique relies on the observation of a hot rapidly rotating star, called a telluric standard, close in time and sky position to the science target (Vacca et al., 2003). The proximity in space and time is motivated by a characterization of the sky as similar as possible to that of the science observations; the temperature of the star is deliberately high and the v.sin(i) (with v the rotational velocity and i the inclination angle) large so that the star shows few spectral lines. The fast rotation implies that the stellar lines are broad, thus only low frequency structures exist in the stellar spectrum. The telluric standard star is usually of spectral type A or B because their spectra contain few metal lines (Abt and Morrell,

0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 H2O 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 T ransmission O2 0.5 1.0 1.5 2.0 2.5 Wavelength (µm) 0.2 0.4 0.6 0.8 1.0 CH4 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 CO2 0.5 1.0 1.5 2.0 2.5 0.97 0.98 0.99 1.00 T ransmission O3 0.5 1.0 1.5 2.0 2.5 Wavelength (µm) 0.94 0.96 0.98 1.00 N2O

Fig. 2.1.: Synthetic atmospheric transmission from the visible to the middle of the near-infrared: 0.35 µm to 2.5 µm calculated with TAPAS using the atmospheric profile from Cerro Paranal. The different panels show the absorption from the six molecules with the largest contribution.

1995) and their rapid rotation broadens the remaining stellar lines. The spectrum of a telluric standard star records the sharp lines produced by the Earth’s atmosphere, and thus provides the atmospheric transmission almost contemporaneous to the science observations. The spectrum of the science target is then divided by the spectrum of the telluric standard star, creating a science spectrum free of telluric lines.

However, several problems arise when using the telluric standard star technique, as summed up in Bailey et al. (2007). The first problem comes from the few remaining stellar features which can pollute the spectrum of the telluric standard star. These features introduce artefacts in the telluric corrected science spectrum which are hard to pinpoint. The second difficulty is that the telluric spectrum is not taken at exactly the same time or position in the sky as the science spectrum. The difference in sky position leads to an airmass difference which translates to differences in the strength of the absorption features. These differences can be well corrected for in the optical wavelengths but not in the near-infrared wavelengths. This is because, in the optical the relation between the extinction, dominated by the Rayleigh and aerosol scattering, and the airmass is linear. On the contrary, the near-infrared wavelengths are polluted with molecular absorption features which saturate, and as such the relation between airmass and extinction loses its linearity. A third challenge is that the light paths probed by the telluric standard star and the target star are different, leading to different atmospheric properties, especially for water vapour, along the two paths. Finally, there is a large loss in telescope time spent to observe telluric standard stars (Seifahrt et al., 2010). That is why several authors turned to model the Earth’s atmospheric transmission in order to attempt to solve these issues. The next Section presents various techniques that build a model atmospheric transmission.

2.3 Synthetic transmission methods

The rise of synthetic transmission spectra emerged to avoid the pitfalls of the telluric standard star method. Bailey et al. (2007) modelled transmission spectra of the Earth’s atmosphere to correct near-infrared high-resolution spectra. The authors used the radiative transfer model SMART (Spectral Mapping Atmospheric Radiative Transfer) described in Meadows and Crisp (1996) to model the atmospheric molecular absorption. The spectroscopic data came from the HITRAN molecular database and the following molecules were considered: H2O, CO₂, O₂, O₃, CH₄, CO and N₂O. The Earth’s

atmosphere description was based on the mid-latitude summer atmospheric profile (see below). Bailey et al. (2007) demonstrate, with simulated spectra, that the correction of telluric lines is more accurate with modelled transmission spectra than with the telluric standard star method. For observations of solar-type stars, the standard star method can lead to errors up to a few percent higher compared with the synthetic transmission

method. In the case of observations of the Martian atmosphere, the error increases up to 50%. This very large error is due to molecular features (e.g. CO2) in the Martian

atmosphere which are similar to the ones in the Earth’s atmosphere. The presence of molecular absorption features in the spectra of cool stars in the near-infrared is also a challenge for telluric correction methods.

After this publication, Seifahrt et al. (2010) started to improve this first synthetic transmission method with the Line by Line Radiative Transfer Model (LBLRTM, Clough and Iacono, 1995) and a complete molecular database HITRAN (Rothman et al., 2009). Seifahrt et al. (2010) show that their technique corrects the telluric contamination in the optical and the near-infrared, where they obtained residuals around 2%. They present the modelling of the telluric absorption but also the telluric emission features. Finally, they use the telluric lines as wavelength calibrators for the near-infrared spectra. All the synthetic transmission methods have common elements, namely a description of the Earth’s atmosphere, a spectroscopic database, and a radiative transfer code. The description of the Earth’s atmosphere contains the distribution of molecule abundances with height for several molecules, between 6 and 30 molecules depending on the model, as well as the temperature and pressure profiles. Most of the codes use the HITRAN database and the LBLRTM radiative transfer code. In 2016, at the beginning of my work on telluric correction for near-infrared high-resolution spectra, three software packages are mainly used to perform the telluric correction: TAPAS (Bertaux et al., 2014), Molecfit (Smette et al., 2015), and TelFit (Gullikson et al., 2014). I detail these three software packages in the following sections.

2.3.1 TAPAS

One of the widely used synthetic transmission methods is the web interface Transmissions of the AtmosPhere for AStronomical data, TAPAS, presented in Bertaux et al. (2014). TAPAS is an online interface2 _{which can be queried to obtain a transmission spectrum}

of the Earth’s atmosphere.

TAPAS retrieves the atmospheric profile through the ESPRI Data Centre (formerly Ether) atmospheric database3_{, which is based on data updated every 6 hours from the}

European Centre for Medium-Range Weather Forecasts (ECMW)4_{. The atmospheric}

profile describes the variation of pressure, temperature, and volume mixing ratio of molecules with the altitude in the atmosphere. The atmospheric profile can be specific to the time and date of the astronomical observations or a yearly averaged profile for a given latitude. 2 cds-espri.ipsl.fr/tapas/ 3_{cds-espri.ipsl.upmc.fr/etherTypo/} 4 https://www.ecmwf.int/

TAPAS uses the radiative transfer code LBLRTM and the high-resolution molecular absorption database HITRAN 2016 (Gordon, 2017) to compute the atmospheric trans-mission. The input data of the TAPAS interface are the following: the location of the observatory, the date and time of the measurement, the spectral unit of the output transmission, spectral range, instrumental function, atmospheric model, resolution power, sampling ratio, and the right ascension and declination of the target. The location of the observatory is used to choose the point in the ECMWF meteorological field which describes best the atmospheric conditions above the observatory. The altitude of the observatory defines the starting point of the atmospheric profile: the atmospheric transmission will be computed from the top of the atmosphere to the altitude of the observatory. By default, TAPAS includes the following molecules: H2O, O₃, O₂, CO₂, CH4, and N2O, but the user can choose to include or not these molecules in the

calculation of the atmospheric transmission.

Atmospheric transmissions derived with TAPAS can be used for three purposes. The first one is to identify the telluric lines present in a spectrum by comparing the atmospheric transmission with a science spectrum. This is useful to probe the completeness and accuracy of the HITRAN spectroscopic database or to identify contaminated regions in the science spectrum. The second purpose is to correct the telluric contamination, either by directly diving the science spectrum by the TAPAS transmission, or by fitting the TAPAS transmission to the spectrum and then dividing. The third way is to incorporate the TAPAS transmission, thus the telluric contamination, in simulated stellar spectra to obtain a more realistic model of observed spectra.

In a first work, I corrected archival spectra taken in November 1998 at the Utrecht Echelle Spectrograph (UES). The sample contains about 20 spectra from T Tauri stars and the goal is to correct the telluric absorption in the wavelength range of two emission lines: [OI] and [SII] at 630.0 nm and 673.1 nm. The UES spectra have a resolution of 55,000. The spectra were observed with no telluric standard and using one of the synthetic transmission methods is the only way to correct for the telluric absorption. I used the TAPAS interface to download the synthetic atmospheric transmission spectra. Figure 2.2 presents the telluric correction performed with TAPAS. The TAPAS transmission matches all the telluric lines found in the spectrum of DG Tau. However, the synthetic telluric lines are too deep compared to the observed telluric lines. Thus we can identify in the spectrum of DG Tau divided by the TAPAS transmission some peaks which correspond to an over-correction of the telluric lines.

2.3.2 Molecfit

Molecfit is a public tool developed at the European Southern Observatory (ESO) and published by Smette et al. (2015). Molecfit performs the telluric correction of the Earth’s

6275 6280 6285 6290 6295 6300 6305 6310 Wavelength (˚A) 1.0 1.5 2.0 2.5 3.0 3.5 Normalized Flux DG Tau spectrum TAPAS transmission

Telluric corrected spectrum

Fig. 2.2.: Utrech Echelle Spectrograph spectrum of the T Tauri star DG Tau centred on the [OI] forbidden emission line (in blue), the TAPAS transmission spectrum is convoluted to a resolution of 55 000 (in orange), and the telluric corrected spectrum (in green). The telluric absorption is the γ band of O2 and the TAPAS atmospheric transmission

is based on an average atmospheric profile.

atmospheric absorption. Based on the same concepts as TAPAS, Molecfit computes the atmospheric transmission using the LBLRTM code version 12.8 (Clough et al., 2005) and the spectroscopic database HITRAN 2008 (Rothman et al., 2009) with some updates linked to the LBLRTM code. I refer the reader to the LBLRTM website5 _{for details on}

the updates of the line parameters. The code retrieves the atmospheric profiles from the Air Resources Laboratory (ARL)6_{. The atmospheric profiles are computed with the online}

database Global Data Assimilation System (GDAS), given that the date and location of the observations are provided. The profiles are also stored in an ESO repository7

which is updated every week. In case an observatory is not in the list8 _{of the ESO}

repository, one can ask ESO to add this observatory. The radiative transfer code takes as inputs the atmospheric profile and the airmass of the observation to compute the atmospheric transmission spectrum. The benefit of Molecfit is that the atmospheric transmission spectrum is then fitted to the input science spectrum provided by the user. The fitting process allows to adjust several parameters, in particular the parameters associated with the wavelength solution, the continuum fitting, the spectral resolution and the molecular content of the atmospheric profile. The line shape, and thus the effect of the instrumental profile, can also be fitted with Molecfit. Once the fit is successful on selected fitting regions of a few Angströms of the input spectrum, the atmospheric transmission is calculated for the whole wavelength range covered by the input science spectrum.

As a comparison with Figure 2.2, I present in Figure 2.3 the telluric correction of the same DG Tau spectrum with Molecfit. Since the ARL archive of GDAS atmospheric profiles only started in 2004, I used an average equatorial atmospheric profile. Since Molecfit fits the transmission to the DG Tau spectrum, there is no over correction of the telluric lines.

Molecfit has an additional mode, called expert mode, which allows the user to parametrize several spectral orders with different wavelength solutions and continuum normalizations, while the molecule abundances are kept consistent between all the orders. This mode is presented and tested for CRIRES spectra in the Molecfit User Manual9_{. In the expert}

mode, the interaction with Molecfit is done thanks to an input parameter file. The parameter file specifies how the fitting will be performed. The continuum and the wavelength solution can be fitted or fixed with a polynomial of a chosen degree. The starting values (offset and coefficients of the polynomial) for the fit can also be written in the parameter file. The expert mode allows one to control the fitting parameters on the different detectors but the fitting is done for all the detector at once.

5 rtweb.aer.com/lblrtm_frame.html 6 ready.noaa.gov/gdas1.php 7 eso.org/pub/dfs/pipelines/skytools/molecfit/gdas 8_{eso.org/pub/dfs/pipelines/skytools/molecfit/Observatories.txt} 9 VLT-MAN-ESO-19550-5772_Molecfit_User_Manual.pdf

6275 6280 6285 6290 6295 6300 6305 6310 Wavelength (˚A) 1.0 1.5 2.0 2.5 3.0 3.5 Normalized Flux DG Tau spectrum Molecfit transmission

Telluric corrected spectrum

Fig. 2.3.: Telluric correction done with Molecfit using an average atmospheric profile. The four telluric lines present in the [OI] forbidden emission line are well corrected. Same colour code as Figure 2.2.

During the course of my PhD, I used Molecfit extensively to correct numerous spectra taken in the optical and near-infrared wavelengths. Molecfit is a versatile and relatively easy-to-use software package with a graphical user interface, which allows one to perform straightforward telluric correction. I present in Appendix A examples of telluric correction done with Molecfit, within the framework of several science cases.

2.3.3 TelFit

TelFit is a publicly available software package10 _{which aims at correcting telluric}

ab-sorption in spectra. The TelFit code is presented in Gullikson et al. (2014); written in Python, it uses the radiative transfer code LBLRTM to produce a synthetic transmission of the Earth’s atmosphere. TelFit makes the interaction with the radiative transfer code more user-friendly. TelFit provides two main Python functions: the function MakeModel generates a telluric model and the function TelluricFitter fits the telluric model to the spectroscopic data. From the TelFit Manual 11_{, there are a few main steps the}

code performs to correct for telluric absorption. The first step is to define the input parameters such as pressure, temperature, wavelength range, abundances of molecule in

10_{github.com/kgullikson88/Telluric-Fitter}

11

http://www.as.utexas.edu/ kgulliks/media/pdfs/TelFit_Manual.pdf

1.175 1.176 1.177 1.178 1.179 1.180 0.5 0.6 0.7 0.8 0.9 1.0 Normalized Flux TelFit model Telluric corrected Input spectrum 1.175 1.176 1.177 1.178 1.179 1.180 Wavelength (µm) −0.05 0.00 0.05 Residuals

Fig. 2.4.: TelFit correction of the water bands in the near-infrared of a telluric standard star. Top panel: The input spectrum is in light blue, the TelFit telluric model is in red, and the telluric corrected spectrum is in green. Bottom panel: Residuals between the input spectrum and the telluric model, the residuals are within the 5% lines relative to the continuum.

the atmosphere, time and location of the observations. The second step is the fitting process, TelFit fits the spectral continuum, and also adjusts the molecule abundances within the ranges provided by the user. The fit of the resolution and the wavelength solution is also performed. The fit results in a telluric model adjusted to the input spectrum. The last step is to divide the input spectrum by the telluric model, which results in the telluric corrected spectrum.

Figure 2.4 presents an example of telluric correction with the TelFit code. The input spectrum is from the telluric standard star HIP100090 taken with the CRIRES spectro-graph. The residuals are within 5% of the continuum for the correction of the water bands. Gullikson et al. (2014) compared the TelFit method with the standard star method and found that TelFit gives better results than the standard star method for the correction of the water bands and gives similar results for the correction of the O2

bands. The telluric correction of a hot B9V stellar spectrum, such as HIP100090, is the easiest case to model, since the input spectrum is almost free of stellar features and mainly contains telluric features.

2.3.4 Other methods

Other software packages are available to perform telluric correction based on the calculation of a synthetic transmission of the Earth’s atmosphere.

Firstly, Tellrem, published by Rudolf et al. (2016), also uses the radiative transfer code LBLRTM to compute the telluric model. Tellrem, similarly to TelFit, fits the telluric model to the observed spectrum. Some characteristics of the Tellrem code are that only a Gaussian line shape is available to fit the line profile and that the wavelength solution is fitted with a first order polynomial, even though the user can choose to implement changes. Other noticeable differences are that Tellrem is less user-friendly and is designed to process X-shooter spectra. The installation procedure is more complicated than TelFit or Molecfit because it requires installing separately the different resources used by the code, such as the radiative transfer code, the line databases and atmospheric profiles. In Chapter 3, the comparison study does not include Tellrem because its principles are very similar to the studied codes, in particular TelFit.

Secondly, the Planetary Spectrum Generator (PSG), published by Villanueva et al. (2018) models planetary spectra via an online radiative transfer suite. The authors present a versatile software package which combines several radiative transfer codes, as well as spectroscopic and planetary databases. Their goal is to model spectra from planets but also comets, exoplanets, and other Solar system planetary objects. In the case of telluric correction, PSG can synthesize the Earth transmission for different astronomical observatories. This transmission spectrum can then be used to perform the telluric correction of spectra. The online interface also allows one to upload their spectra and perform the fitting of the atmospheric transmission remotely.

2.4 Data-driven methods

Specific sequences of observations can lead to ingenuous ways to correct for the telluric absorption. The telluric lines are stable down to 10 to 20 m.s−1 _{in the Earth referential}

(Figueira et al., 2010a), but when a star is observed from Earth, the telluric lines follow the same radial velocity variation as the barycentric radial velocity of the Earth. In this case, the spectra are imprinted with telluric lines whose radial velocity can vary from -30 to 30 km.s−1_{. This particularity allows one to recognize and identify the telluric lines}

against stellar lines.

2.4.1 Wobble

A recent paper published by Bedell et al. (2019) presents a novel method to correct the telluric absorption and derive radial velocity measurements at the same time. Wobble is a data-driven method which does not rely on a stellar template nor an atmospheric transmission to retrieve the stellar spectrum free of telluric lines. The method uses an input data set of 1D wavelength calibrated spectra from a stabilized high-resolution spectrograph with no additional gas cell imprinted in the science spectrum (e.g. iodine cell). To ensure that the telluric correction is efficient, the input spectra should cover different observing epochs during the year, allowing spectra to be registered at different barycentric radial velocities of the Earth.

Wobble assumes that each spectrum can be represented as the product of a telluric spectrum and a stellar spectrum. In the reference frame of the observatory, the telluric spectrum is supposed to be fixed which means that the telluric lines are found at the same wavelengths, but the stellar spectrum varies in position through the RV imprinted by Earth’s rotation around the Sun. In terms of shape, the stellar spectrum has a fixed shape which means for example that the stellar lines have the same absorption, while the telluric spectrum has a shape which can vary over time. The contrast of the telluric lines is a function of the airmass measured at the time of the observation. The first guess for the stellar spectrum is provided by computing the median combined spectrum of the input spectra corrected for the barycentric radial velocity of the Earth (BERV). The telluric spectrum is initialized by computing the median combined spectrum of the input data not corrected for the BERV. Then, the model is optimized with the maximum likelihood estimation method. Both the stellar and telluric spectra are subject to a combination of L1 and L2 regularizations to avoid over-fitting. The use of regularization assumes that the logarithm of the flux of both the telluric and stellar spectra are close to zero. Applying regularization terms will guarantee that the optimization of the free parameters will push both spectra close to zero in case there is no other evidence (Bedell et al., 2019).

After optimization, Wobble derives a radial velocity measurement for each order of the echelle spectrum and delivers a decomposition of the original spectral order into a telluric spectrum and a stellar spectrum. Figure 2.5 presents one order of the HARPS spectrum of 51 Pegasi with the two resulting spectra. The Hα absorption feature is identified as

part of the stellar spectrum and even small telluric lines are identified as part of the telluric spectrum. Wobble is a promising method to derive radial velocity and correct for the telluric contamination for datasets which verify the initial assumptions of the method such as the large BERV coverage of the spectra. The authors have plans to extend Wobble to be able to handle spectra from several spectrographs.

6555 6560 6565 6570 6575 Wavelength (˚A) 0.2 0.4 0.6 0.8 1.0 Normalized Flux Input spectrum Telluric spectrum Stellar spectrum

Fig. 2.5.: The HARPS input spectrum of 51 Peg is plotted in black. The modelled telluric spectrum is plotted in red. The modelled stellar spectrum, thus a telluric free spectrum is plotted in purple. Figure made with the code and dataset from Wobble GitHub repository12_.

2.4.2 PCA-based telluric correction

The telluric correction published by Artigau et al. (2014) is based on Principal Component Analysis (PCA). Principal component analysis is used as a dimensionality reduction technique, aiming at describing a high-dimension dataset with a reduced number of dimensions. The original dataset is projected on a new basis of vectors, where the variables are linearly uncorrelated and called principal components. In this new basis, the first principal component describes the largest possible variance, and the second principal component is orthogonal to the first and describes the second largest variance. The following components are built with the same principles. In the case of the telluric correction, the idea is to build a basis of components reflecting the absorption of the Earth’s atmosphere.

In general, the transmission of the Earth’s atmosphere is the ratio between the incident intensity (I0) at the top of the atmosphere and the transmitted intensity (I) at the

bottom of the atmosphere:

T = I I0

The opacity of the atmosphere O is then defined as the inverse of the transmission, and the atmospheric absorbance A as:

A = −log(T )

The atmospheric absorption spectrum is considered a finite sum of absorbances by different atmospheric molecules such as H20 and O₂. The telluric absorption spectrum can be decomposed as a linear combination of absorbance components. An absorption by one molecule such as water vapour can be found in several absorbance components. Artigau et al. (2014) identify the absorbance components by running a principal com-ponent analysis on a dataset of telluric standard star spectra observed under various weather conditions and airmasses. As an example, the telluric correction of the τ Ceti dataset used about 200 observations of 30 different telluric standard stars to build the database of individual absorbances. The dataset of science spectra which need the telluric correction is composed of several spectra of the same target observed at different epochs so that the position of the telluric lines relative to the stellar lines is varying with the barycentric velocity of the Earth. Using these data, the telluric correction takes place in two steps. The first step is to fit the science spectra with a linear combination of the first absorbance components of the database and a star spectrum initialized to 1 at all wavelengths. The result of the fit is an approximation to the telluric absorption present in the spectra. This approximation is subtracted from all the science spectra. The science spectra are then corrected for the BERV so that the stellar lines are all aligned. Then the spectra are median combined to create a new estimate of the stellar