FYSMAS1119 Examensarbete 30 hp Juni 2020
Advanced Characterization of Exoplanet Host Stars
Khaled Al Moulla
Masterprogrammet i fysik Master Programme in Physics
Abstract Advanced Characterization of Exoplanet Host Stars
Khaled Al Moulla
Teknisk- naturvetenskaplig fakultet UTH-enheten The spectroscopic determination of stellar properties is important for subsequent studies of exoplanet atmospheres. In this thesis, Besöksadress: HARPS data for 6 exoplanet-hosting, late-type stars is processed to Ångströmlaboratoriet Lägerhyddsvägen 1 achieve an average signal-to-noise ratio of ~105. Together with line Hus 4, Plan 0 data, the SME tool is used to synthesize spectra and interpolate model photospheres with which chi-square minimization is performed. Postadress: Box 536 751 21 Uppsala Fundamental parameters are derived to an overall precision of 191 K in effective temperature, 0.88 dex in surface gravity and 0.21 dex in Telefon: metallicity. For 5 of the stars, the parameters are thereafter used 018 – 471 30 03 to compute specific intensities across the stellar discs.
Telefax: 018 – 471 30 00 Primary improvements could be made in regards to the stellar models, i.a. through the update of atomic properties and inclusion of Hemsida: magnetic fields. The numerical derivation can also be handled more http://www.teknat.uu.se/student carefully by excluding parameter-insensitive spectral regions.
Keywords. stars: exoplanet hosts - fundamental parameters - spectroscopy: HARPS - SME
Handledare: Nikolai Piskunov Ämnesgranskare: Bengt Edvardsson Examinator: Andreas Korn FYSMAS1119 Sammanfattning
Den spektroskopiska bestämningen av stjärnegenskaper är viktig för efterföljande studier av exoplaneters atmosfärer. I denna avhan- ∼dling bearbetas HARPS-data från 6 stjärnor av sen typ som hyser exoplaneter för att uppnå en genomsnittlig signal-till-bruskvot på 105. Tillsammans med linjedata, används SME-programvaran för att syntetisera spektra och interpolera modellfotosfärer med vilka chi- kvadratminimering genomförs. : : Fundamentala parametrar härleds till en medelprecision på 191 K i effektiv temperatur, 0 88 dex i ytgravitation och 0 21 dex i metallicitet. För 5 av stjärnorna används parametrarna till att därefter beräkna specifika intensiteter över stjärnornas projicerade ytor.
Huvudsakliga förbättringar kan göras med avseende på stjärnmod- ellerna, bl.a. genom uppdatering av atomära egenskaper och inklud- ering av magnetiska fält. Den numeriska härledningen kan också hanteras med högre noggrannhet genom att avsiktligt exkludera pa- rameterokänsliga spektralregioner.
Nyckelord. stjärnor: exoplanetvärdar - fundamentala parametrar - spektroskopi: HARPS - SME To Jomana, Sleiman and Mona
Under de dystra månaderna satt själen hopsjunken och livlös men kroppen gick raka vägen till dig. Natthimlen råmade. Vi tjuvmjölkade kosmos och överlevde. Eldklotter
— Tomas Tranströmer, (6–10) Contents
List of Acronymsi
Chapter 1: Introduction1
1.1 Background...... 1 Chapter1.2 2: Purpose Theory...... 2 1
2.1 Stellar spectra ...... 2 2.1.1 Classification...... 2 2.1.2 Radiative transfer...... 3 2.1.3 Line formation and broadening...... 4 2.2 Dependence on ...... 6 2.2.1 ... temperature...... 6 2.2.2 ... gravity...... 7 2.2.3 ... metallicity...... 8 2.3 Instrumentation...... 9 2.3.1 Spectrographs...... 9 2.3.2 Detectors...... 11 Chapter 3:2.3.3 Methods Noise ...... 1213
3.1 Target selection...... 13 3.2 Data processing...... 13 3.2.1 Reduction ...... 13 3.2.2 Wavelength calibration ...... 15 3.2.3 Summation...... 15 3.2.4 Continuum normalization ...... 17 3.2.5 SNR filtration...... 17 3.3 Spectral synthesis ...... 19 Chapter 4: Results 21
4.1 Observed and synthetic spectra ...... 21 4.2 Derived parameters...... 23 Chapter4.3 5: Limb Discussion darkening ...... 2327
5.1 Uncertainties...... 27 Chapter5.2 6: Further Conclusion improvements ...... 2729
Acknowledgements 30
Appendix A: Observations 31
Bibliography 33 List of Acronyms
ABO A B O
ADC a nstee- arklem-d c’Mara
ADU analog-to-digital uonverter
CCD cnalog-to-c igitald nit
EDE Eharged- oupledD E evice
ESO Exoplanet S ata xplorerO
FSR f uropeans outhernr bservatory
GUI gree pectralu angei
HARPS HraphicalA ser Rnterface P S
HWHM h igh-w ccuracyh adialm Velocity lanet earcher
LDC l alf-didth at alf-c aximum
LTE limb tarkening oefficiente
NIR nocal ihermodynamicr quilibrium
NLTE near-LTEnfra ed
PSF pon- s f
QE qoint preade unction
RV r uantumv fficiency
SME Sadial elocityM E
SNR s pectroscopyn rade asy
VALD Vignal-to-A oise LatioD
ienna tomic ine atabase
i 1
Chapter 1
Introduction
1.1 Background
The field of exoplanet research has in recent times grown increasingly topical, with the advancement of precise radial velocity (RV) measurements now enabling the discovery of Earth-sized companions (see e.g. Mayor et al. 2008). In order to carry out in-depth studies (atmospheric composition, habitability, etc.) of these planetary systems, it is of utmost importance to have a detailed description of their stellar hosts. Historically, fundamental stellar parameters have been determined via semi-direct methods of varying reliability (Adibekyan et al. 2018). Temperature, for example, can be obtained empirically through photometric calibrations. Surface gravity can be calculated from the stellar mass and radius; the former is either inferred from mass-luminosity relationships or requires the star to be part of a spectroscopic binary, and the latter is measured with interferometry, binary eclipses or lunar occultations. Whereas chemical composition is impossible to investigate directly. 1.2 Purpose
The approach of spectroscopy is versatile and practical for most types of characterization. The purpose of this thesis is to spectroscopically determine the fundamental parameters for a sample of stars hosting transiting exoplanets. Similar studies (e.g. Santos et al. 2004) have focused on equivalent width measurements of single lines, which heavily rely on the quality of atomic properties, and are sometimes hindered by severe line blending especially in cooler stars where molecules form absorption bands. To mitigate the impact of uncertainty, this work will perform spectral synthesis across wavelength regions containing thousands of lines. Together with stellar models, the derived parameters will be utilized to extract intensity variations along the transit paths, useful for subsequent exploration of exoatmospheric transmission spectra. 2
Chapter 2
Theory
2.1 Stellar spectra
2.1.1 Classification
n In the optical wavelength region, many stars showcase prominent hydrogen lines from the Balmer → α → series, i.e. electron transitions originating in energy level = 2. The series notation consists of the β letter H assigned a subscript from the Greek alphabet, e.g. the transition 2 3 is called H , 2 4 is called H , and so on. When astronomers first started to observe absorption lines in stellar spectra, they did not under- stand what caused them (Böhm-Vitense 1989). Still, they began classifying stars, with capital letters of the English alphabet, based on the strength of these Balmer lines in descending order. Later on, it was discovered that stellar radiation is well-described as a theoretical black body, whose spectral energy distribution is given by the Planck function,hc Bλ hc/λkT ; λ 2 − 2 1 h k = 5 c λ(2.1) e 1 T where and are Planck’s and Boltzmann’s constant,T respectively, the vacuum light speed, the wavelength, and the temperature. Although the temperature of a star depends on the depth, this eff allowed the definition an effective temperature, , equivalent to the temperature of a black body which generates the same wavelength-integratedF flux,σT according; to the Stefan-Boltzmann law, 4 eff σ = (2.2) where is Stefan-Boltzmann’s constant. With decreasing effective temperature, the stellar spectra exhibit a clear transition from hydrogen and helium lines to those of heavier elements, collectively called metals. Some of the old letters were kept, resulting in the sequence OBAFGKM, known as the Harvard system. The spectral types are further subdivided by the numbers 0–9, and followed by a Roman numeral to denote the luminosity class, such as ‘V’ for main-sequence stars. 3
Another misnomer which has survived is the division of early- and late-type stars. The observed range of temperatures was thought to be evolutionarily explained which is incorrect since stars do not evolve along the main sequence, however, the terms are nowadays used to reference OBA-stars as early-type and FGKM-stars as late-type. 2.1.2 Radiative transfer
Iλ
Considering an intensity beam of a certain wavelength, , the various atomic processes inside a l κ stellar photosphere result in theI followingλ − l differentialλ κλ Iλ equationjλ jλ ρ (Carrollx; & Ostlie 2017), ` ˘ x d = ρ ( + ) + + d (2.3)
lλ κλ where is the traveled distance, and l the density.κ The remaining variables represent the mass jλ jλ absorption coefficients (also called opacities) for lines and continuum, and , respectively, and the corresponding emission coefficients, and . Two essential quantities can be introduced. First, l κ the source function is simply the emission to absorptionjλ jλ ratio, Sλ : lλ κλ + = (2.4) +
Under the assumption that temperature variations inside the star occur at distances larger than the Sλ Bλ τλ mean free path of photons, which is referred to as local thermodynamic equilibrium (LTE), the source function is equal to the Planck function,τλ =− l.λ Second,κλ ρ x; the optical depth, , is defined as
d = ( + ) d (2.5) x inwardand can be interpreted as the multiple of mean free paths between the depth of formation and the top of the photosphere. Optical depth—opposite to the geometrical depth —is measured radially Iλ , hence the minus sign. Eq. (2.3) can thenI beλ − rewrittenSλ; into τλ d = (2.6) d known as the radiative transfer equation. The opacity dictates how far into a star thevertical observer sees. This entails another important aspect, namely limb darkening, which is the variation in intensity across the stellar disc. The effect is best illustrated by imagining a surface of equal optical depth, i.e. along the direction to the observer, as in Fig. 2.1. The implication is that progressively shallower layers are viewed closer to theµ edge. Asθ the temperature decreases upward, so does the radiation. From its geometry, the limb darkening can be assumed azimuthally independent, and the intensity is usually given as a function of = cos . For an unresolved light source, the observed quantity is the specific flux, equal to the surface- 4
θ
Figure 2.1
Illustration of limb darkening. For light emerging from a layer of equal optical depth along the line of sight, the observer sees deepest into the star at its disc center.
integrated intensity along the line of sight,Fλ Iλ θ : Z = cos dΩ (2.7)
Apart from recreating the flux, model photospheres have the great advantage of also providing specific intensities. In the study of exoatmosphericR transmission spectra, these are needed to disentangleH the stellar and planetary contributions. An exoplanet can be thought of as having a solid—or at p least completely opaque—core of radius with a semi-transparent atmosphere of height on top (Aronson & Waldén 2015). During a transit, the net spectrum will be Fλ; Fλ − R Iλ µ H R H Iλ µ ; R? A A ˜ 2 Z 2 Z ¸ net 1 p p = 2 p d + ( + 2 ) a d (2.8) R? A πR A π R H − A 2 2 p p a p p where is the stellar radius, and = and = ( + ) are the projected areas of the core and atmosphere, respectively. 2.1.3 Line formation and broadening
In the classical description, absorption lines are formed via the interaction between an electromagnetic iωt wave and a bound, oscillating electronme :x (Mihalasω x 1970eE ), whose− me equationγx9; of motion is 2 0 0 e me x ( + ) = e 2 E ω (2.9) ω γ 0 0 where , and are the electron charge, mass and position, the electric field strength, and the angular frequenciesν of the undamped and driven motions, and the damping parameter. By equating the radiated power of the wave and electron, it can be shown that the absorption coefficient per frequency, , is approximately πe γ αν ≈ ; mec2 ω γ 2 2 2 (2.10) ω ω − ω ∆ + ω
0 0 where ∆ = . The line profile is recognized as a Lorentzian, centered at with half-width at 5 γ half-maximum≤ f ≤ (HWHM) . The total absorption coefficient, integrated over all frequencies, has been found to be overestimated due to quantum mechanical effects for which a dimensionless correction, ∞ πe πe 0 1, called the oscillator strength,α isα introduced,ν ≈ → f : ν m c m c Z e 2 e 2 = 0 d (2.11)
Apart from the natural broadening mentioned above, spectral lines are also subject to collisional and Doppler broadening. The former arises due to the interplay with certain kinds of perturbers. In C the Unsöld(1955) formalism, the induced shiftω is describedn ; by a power law, rn
r Cn ∆ = n (2.12) where is the atom-perturber distance, the interaction constant, and an integer representing a family of broadening effects: n 2 linear Stark (2.13a) = 4 quadratic Stark (2.13b) n 6 van der Waals (2.13c)
Each translates to its own dispersion profile. The total HWHM is then the sum of the individual γ γ γn: contributions, n tot X = + (2.14)
The atom velocities, originating from a Maxwellianω distributionkT or turbulent motion, cause a Doppler ω v ; shift, c d m 0 2 D 2 mic T ∆ m= a + v (2.15)
a mic where is the equilibrium temperature, the atom mass, and the microturbulence. ? The extended absorption coefficientπe becomesγ the convolutionπ − ofω/ aω Lorentzian and Gaussian, known αν f ∗ : as a Voigt function, mec2 ω γ ω 2 tot (∆ ∆ D) 2 2 = 2 tot D e (2.16) ∆ + ∆
The conversion between frequency and wavelengthαν ν unitsαλ λ; is found through
ν c/λ ν/ λ −dc/λ= d (2.17)
2 with the substitutions = and d d = . 6 2.2 Dependence on ...
2.2.1The following ... temperature subsections on various dependencies are based on the textbook by Gray(2005).
∞ The strength of a spectral line is most sensitive to temperature variations. The equivalent width, W − Fc λ λ; defined as Z−∞ Fc λ = 1 ( ) d (2.18) lλ/κλ lλ where ( ) is the continuum normalized flux (cf. Sect. 3.2.4), is proportional to the ratio of line to continuum absorption, . Evident throughlλ theρ definitionNαλ; of ,
= N (2.19)
αλ it can either dominated by the number density of absorbers, , which is true for weak lines, or the broadening effects on the absorption coefficient, , relevant for strong lines. n χn In LTE, the population of an atomic state is governed by two equations. The first, describing
Nn gn the fractional number density of the th energy level,−χ withn/kT ; excitation potential , is the Boltzmann equation, N Z
−χi/kT gn tot = e Z igi (2.20) P I where is the statistical weight of that level, and = e the partition function. The / / second one, describing the fractionalN ionizationπme of somekT stageZ X with ionization potential , is the −I/kT ; N + Pe 3h2 5 2 Z + Saha equation, X X P 2 (2 ) 3( ) e X = X e (2.21) where is the electron pressure. The continuous absorption is, in all stars except the hottest, determined by the negative hydrogen − − / : /kT ion. The optical wavelength region isκλ dominated∝ Pe byT its bound-free: component, 5 2 0 75 bf (H ) e (2.22)
Therefore, neutral species are strengthened with temperature, due to the increased likelihood of excitations, until the thermal energy becomes comparable to the ionization potential. Eventually, the lines from singly ionized elements are weakened too when most absorbers become doubly ionized, and so forth. 7
Figure 2.2
Temperature dependence of weakCredit: metal Gray lines. 2005 The (reproduced strengthof and neutral adapted species with permission). increases with temperature before becoming singly ionized, at which point their ionic counterparts begin to increase until they are overtaken by the next ionization stage. 2.2.2 ... gravity
g
The principle of gravity, , dependence can be laid out similarly as for the temperature. Under the assumption of hydrostatic equilibrium, the gasP pressure∝ g / : is approximately 2 3 g (2.23)
Combined with the ideal gas law, it can be related to the electron pressure. In the high-temperature limit, all hydrogen is ionized, yieldingP ≈ aboutPe twice as many particles in total as free electrons,T
g Pe2 ;P (higher ) (2.24a)
g in temperature regimes where, instead, , the relation reduces to P ∝ Pe : T 2 g (lower ) (2.24b)
To evaluate line strengths, it is important to assess the surroundings of the absorber. First, we consider weak lines. If the line species X has most of its element in the next ionization stage, it lλ ∝ N ∝ N Pe; follows from Eq. (2.21) that + N X X (2.25) + X where is almost the total number density of the element and thus considered constant. When dividing the line and continuum absorptions, the electron pressures cancel, indicating an invariance to changes in gravity. If, on the other hand, the species has most of its element in the same ionization 8
Figure 2.3 Credit: Gray 2005 (reproducedGravity dependence and adapted of an with Fe permission).II line. At Solar temperatures, as in this example, iron is mostly ionized. Thus, the modeled change in equivalent width is consistent with the exponent in Eq. (2.26).
lλ − − / ∝ Pe ∝ g ; κλ stage, then 1 1 3 (2.26) with the last step making use of Eqs. (2.23) and (2.24b). αλ Strong lines follow the same analysis, with the exception of additional gravity dependence in- γ ∝ Pe γ ∝ P troduced via in Eq. (2.19). It can be shown that for e.g. quadratic Stark and van der Waals 4 6 g broadening and . The dominating term governs the resulting dependence, which is best studied in the wings of strong lines. 2.2.3 ... metallicity
Considering the chemical abundance of someA elementN /N X; relative to hydrogen,
X X H A = (2.27) the change in equivalent width with is called a curve of growth (Fig. 2.4). A weak line, dominated by the Doppler core, exhibits linear growth,W ∝ A:
(weak) (2.28a)
The line is said to be saturated when the central depth approaches its maximum, after which the ? growth is slowed down, W ∝ A;
(strong) (2.28b) and allocated to the wings. Although, these phases are somewhat oversimplified. More realistically, if the absorber is a metal, 9
Figure 2.4 Credit: Gray 2005 (reproduced and adapted with permission). Curve of growth. The circles at different abundances (left) correspond to the shown line profiles (right).
Pe it will increase in lock-step with other metallic elements, i.e. prominent electron donors. Continuous absorption, through its dependence on , consequently delays the growth curve. The metallicity, defined as the logarithmic iron abundance/ relativeA to− the Sun,A ;@;
Fe Fe [Fe H] = log log (2.29) becomes a measure through which all other metals may be scaled. 2.3 Instrumentation
The following subsections, which cover the elementary aspects of spectroscopic instrumentation, are 2.3.1based on Spectrographs the textbooks by Chromey(2010) and Kitchin(2013).
d The principles of a diffraction grating is basedα on the interference−β of light. Considering a reflection grating with facet separation , as in Fig. 2.5a, one could trace the paths of two rays, A and B, of the same wavelength. Incident at an angle and reflected at , measured counter-clockwise from the grating normal, the rays interfered constructivelyα β whenmλ; their m ∈ pathZ difference is an integer multiple of the wavelength, m (sin + sin ) = (2.30) known as the Grating Equation, with denoting the spectral order. However, the configuration described above entails three primary issues:
1. A significant amount of the incoming light is blocked, and thus lost, in-between facets. β m 2. If Eq. (2.30) is differentiated to obtain the angular dispersion,; λ d β d = (2.31) d cos 10
β α α A β B
d d (a) (b)
FigureSimple 2.5 grating. Echelle grating.
Different types of diffraction gratings.
it becomes evident that no dispersion occurs in the zeroth order, which is also the order with highest efficiency. θ θ α β
The intensity distribution along the image plane (relatedπD θ to the predefinedNπd θ angles through sin = sin + sin ) λ λ I θ I πd θ ; is given by, 2πD θsin 2 sin « ` λ ˘ff « ` λ ˘ff 0 sin 2 sin 2 sin I ( N) = ` sin ˘ D` ˘ (2.32) sin 0 where is the central intensity, the number of facets, and the width of the feeding slit or fiber. The θ ⇒ α −β ⇒ m expression inside the first pair of square brackets, known as the blaze function, modulates the diffraction pattern, providing maximum intensity when = 0 = = 0. λm λn m n
mλm nλn 3. Some wavelengthsm and from spectral orders and , respectively, will be superimposed if they satisfy = , causing overlap between neighboring regions. The unique interval λ for any given , called the free spectralλ range (FSR),; becomes m max FSR λ ∆ = (2.33) + 1 max where is the largest wavelength which the spectrograph can record. The solution to issues 1 and 2, concerning the light loss, is found through a blazed grating.m > By introducing a periodically saw-toothed◦ structure, inclined at an angle to the plane of the grating, much more of the light can be retained.δλ Simultaneously, the blaze function is shifted toward 0. Gratings operating at mnear 90 are called echelles, and are suitable forR observing high orders. From Eq. (2.31) follows that the resolution, , i.e. the smallest distinguishable separation of wavelengths, improves with higher . A related quantity is the resolving power, , defined as the reciprocal λ relative resolution; it can be shown that R mN: δλ
= = (2.34)
rd The solution to the 3 issue, crucial for high-resolution spectroscopy where the FSR becomes notably limited, is the introduction of a cross-disperser, which separates the orders in a direction perpendicular to the diffraction. Placed after the grating, the cross-disperser is usually a prism; the combination is referred to as a grism. 11
Figure 2.6 m Credit: KitchinBichromatic 2013 (reproduced intensitydistribution with permission). for a diffraction grating. The angular dispersion increases with spectral order; at = 7, adjacent orders begin to overlap. The dashed curve outlines a non-blazed modulation.
Echelles are not entirely unproblematic. The steep angle requires the device to be mounted close to the Littrow configuration, in which the incident light is parallel to the facet normal, to avoid shadowing effects. Furthermore, prism aberrations cause the output spectra to be curved and 2.3.2misaligned Detectors with an orthogonal grid of pixels.
The detector is a device onto which the produced spectra are recorded, and the currently preferred choice among astronomers is the charged-coupled device (CCD). A CCD camera consist of an array of pixels, each equipped with a capacitor in which the semiconductor is most often a layer of silicon. As incident light produces photoelectrons, they become stored in the potential well of each capacitor. After an exposure is terminated, the charges are shifted row by row—known as charge coupling—and converted to a signal through an analog-to-digital converter (ADC). The signal is registered in analog-to-digital∼ units (ADUs), and the gain of a CCD specifies the number of electrons needed to increase5 the output by one unit. This is due to the full well size of a pixel being on the16 order of 10 electrons, whereas the ADC is usually limited to 16-bit data (corresponding to 2 = 65 536 values). If the target is sufficiently luminous, the response of the detector will be linear, i.e. the output signal will be proportional to the input illumination. Saturation could cause so-called blooming,λ < : where electrons spill over to adjacent pixels. The quantum efficiency (QE), i.e. the registered fraction of incoming photons, of modern CCDs can reach 95 % for wavelengths 1 1 µm below the silicon band gap, making them ideal for observations in the optical and near-infrared (NIR). 12
Figure 2.7 Credit: Chromey 2010 (reproduced with permission). Schematic view of an echelle grating with a cross-disperser. The spectral orders are shown to be 2.3.3spatially separated Noise when reaching the detector.
A perfect detector is never noise-less. The counting of photons (or equivalently,N photoelectrons) as independently occurring events is well-described by Poisson statistics. For such a distribution, there ? exists an inherent uncertainty associated withσ the numberN: of events, ,
= (2.35)
N ? In the ideal case, the signal-to-noise ratio (SNR) is equalN: to the noise, σ
SNR = = (2.36)
CCDs are prone to additional noise. If not cooled enough, thermally agitated electrons—known as dark currents, because they can be detected with the shutter closed—degrades the signal. Conversely, temperatures close to absolute zero slow down the diffusion of charges during transfer; the added read-out noise is proportional to the pixel sampling frequency. Scientific-grade detectors, for which the total read-out time may be several seconds, counteract this by being assembled in mosaics of multiple CCDs, each with its own register. 13
Chapter 3
Methods
3.1 Target selection
This work makes: use of data from the HARPS (High-Accuracy Radial Velocity PlanetR Searcher; Mayor et al. 2003) cross-dispersive echelle spectrograph,BLUE installedRED on the ESO (European Southern Observatory)λ −3 6 m Telescopem at− La Silla, Chile.λ HARPS− has am resolving− power of = 115 000 and its detector is divided into two CCDs, dubbed the and modes, covering a spectral range of = 378 530 nm ( = 161 116) and = 533 691 nm ( = 114 89), respectively. All target stars (listed in Table 3.1) are hosts to at least one confirmed exoplanet each, for which transit observations with HARPSJ are available. They have been selected to represent a range in late spectral types on the main sequence as well as in companion masses and sizes, while additionally having sufficiently bright -band magnitudes. 3.2 Data processing
N 1 The interface of the ESO Archive Science Portal allows the user to sort available HARPS observa- obs tions by SNR. For each target,2 the = 10 data sets with highest SNR are downloaded from the ESO Science Archive Facility (see Appendix A). Before any analysis can commence, the raw data must be adjusted for unwanted influences and conveniently formatted. This processing is performed in multiple steps, which are detailed below in 3.2.1separate subsections.Reduction
Data reduction is the collective name for the correction of bias, flat fielding and dark currents; in spectroscopy, it also involves the extraction of spectral orders, all of which is performed with the http://archive.eso.org/scienceportal
1 https://archive.eso.org/eso/eso_archive_main.html 2Available at . Available at . 14 Reference ) 0.0038 0.00058 Carter et al. ( 2011 ) 0.00147 Bonfils et al. ( 2012 ) 0.0069 Crossfield0.0102 et al. ( 2015 ) 0.00087 Bouchy et al. ( 2010 ) 0.00076 Hellier et al. ( 2010 ) 0.00158 Lendl et al. ( 2014 ) AU ± ± ± ± ± ± ± ± ( a 0.0769 0.1399 0.208 0.04566 0.0946 ) J 025 023 021 02 019 0184 056 035 076 065 : : : : : : : : : : 0 0 0.0116 0.01433 0.053 0.0356 0 0 0 0 0.060 0.05211 0 0 0 R ( ± ± ± ± ± ± ± ± p R ) J 0.0023 0.195 0.0004 0.157 0.0034 0.139 0.0121 1.021 0.0031 0.239 0.0052 0.374 0.0134 1.070 0.02 0.792 M ( ± ± ± ± ± ± ± ± p M b 0.0164 d 0.0117 b 0.275 Letter ) 067 059 : : @ 0.068 c 0.01298 0.00970.063 b b 0.0204 0.0440 0.040.044 b0 0 b 0.300 0.243 R ( ± ± ± ± ± ± ? R ) @ 0.089 0.561 0.019 0.2110 0.067 0.503 0.03 1.060 0.033 0.808 0.029 1.170 M ( ± ± ± ± ± ± ? Star Planet M 0.601 0.157 0.541 1.010 0.825 1.126 ) 42 75 79 35 35 14 : : : : : : mag 9 9 8 9 9 ( 10 J Target stars and their planets. The stars are listed alphabetically after their catalog or mission name, and the planets are assigned letters (starting with ‘b’) K2-3 Table 3.1 ordered after their discovery or distance from the host star if several are discovered simultaneously. Stellar/planetaryName masses and radii are given in Solar/Jovian units. GJ 1214 GJ 3470 WASP-21 WASP-29 WASP-117 15 REDUCE
(Piskunov & Valenti 2002) package. For each night of observation, the calibration files are obtained from the preceding evening. The bias level is the intrinsic signal from a zero-time exposure. Several frames are combined to create a master bias, which is subtracted from the raw data. Furthermore, pixels may exhibit sensitivity variations, compensated by sampling some uniform light source to create a flat field, with which the resulting frame from the previous step is divided. Dark currents are not an issue for HARPS which is temperature-controlled and isolated in a vacuum vessel. 3.2.2 Wavelength calibration
After the extraction of spectral orders, each pixel must be assigned a specific wavelength. The calibration is done by illuminating the CCD with a lamp containing elements, commonly thorium- argon, with accurately measured emission lines. k λi;j Each data set then consisti of; 2D; :::; arrays N − for the physical quantities,j ; ; :::; where N the− columns corre- spondk ; to; :::; wavelengths N F andλk the rows to spectral orders. The following notation will be used: i;j pix ord is the wavelength at pixel = 0 1 1 and order index = 0 1 1 of observation obs = 1 2 , and ( ) is the flux at that point. 3.2.3 Summation
N
obs The sets should be combined to yield a higher SNR, however, the summation cannot be applied straightforward since at each time of observation the Earth has a different radial velocity component in the direction of the target. Firstly, the wavelengths are transformed from the observatory reference frame to the barycentric v frame of the Solar System through aλ Dopplerλ shift, ; c bary obs ´ bary ¯ v = 1 + (3.1)
bary where is the barycentricv correction≤ π reaching/ aRC maximum/ ≈ value of/ ;
bary 2 (1 AU yr + (24 h)) 30 km s (3.2) where the two terms account for the Earth’s orbit around the Sun and rotation around its own axis. c λ c This is significant compared to the resolutionv of HARPS,≈ able/ : to detect variations down to λ R lim ∆ = = 3 km s (3.3) ∼ : / The reason for transforming toM? the barycentricM@ frame is that theM radialM velocity of the target remains constant,a : neglecting the influence of its planetary system, which could be on the order of 0 1 km s, p J assuming a stellar mass of = 1 , a planetary mass of = 1 and a semi-major axis of = 0 1 AU. 16 Flux
λk −p ··· −i ··· ··· i ··· p ··· N p ··· N pix pix 0 -1- -1
λ ··· p−i ··· p ··· p i ··· p ··· N pix ref 0 + 2 -1 Figure 3.1 k k λ−p Padded spectrum.λ The illustration showcases the th observation of a target being padded in order to resemble the referenceref scale. The arrays at the bottom indicate the pixel indices. Note that is not necessarily equal to 0 , but rather sufficiently close for Bézier interpolation to remain well-behaved.
M For a star-planet system, the orbital radius of ther star,? arounda the common: center of mass, is given by M? M p = p (3.4) + πr If the orbit is approximated to a circle, the stellar velocityv is easily? ; calculated with ? P 2 P = (3.5)
a G M M where is the period obtained from Kepler’s Third Law: ? : P3 π p ( + ) 2 = 2 (3.6) 4
Secondly, the discrete barycentric wavelengths are different for each data set. Therefore, the wavelength scale of the first observation is chosen as a referencep onto which the succeeding ob- servations are interpolated. In order to avoid diverging extrapolation, the spectra are also mirrored around the out-of-bound endpoints (see Fig. 3.1), i.e. the padded points extending the blueward k k k end become λ−i;j λ ;j − λi;j ; ∀i ; ; :::; p k k F λ−i;j F 0λi;j ; = 2 = 1 2 (3.7a) ( ) = ( ) (3.7b) and similarly for the redward end. 17
N The total spectrum is finally given by F λi;j obs Fk λi;j ; k ref tot X ( ) = =1 ( ) (3.8) Fk λi;j k λi;j ref ref where ( ) is the flux of the th observation interpolated onto the wavelengths of the reference scale. Following a similar treatment, the propagationN of errors is given by σ λ σ λ : i;j g obs k i;j f k fX 2 ref tot e ( ) = =1 ( ) (3.9) 3.2.4 Continuum normalization
C λ
F λ Conventionally, a spectrum is normalized withF λ respect to; its continuum ( ), c C λ ( ) ( ) = (3.10) ( ) rendering wavelength regions void of spectral lines equal to unity and facilitating the measurement of relative line strengths. As a first approximation, stellar continua should resemble black-body curves, however, the com- posite spectrum of an echelle spectrograph appears quite different. Due to the blaze function, the intensity of each spectral order peaks around its central wavelength. To compensate for this (and to also avoidC λ gaps in the spectrum), the grating is usually constructed such that neighboring orders partially overlap, causing additional inconsistencies when co-adding their contributions (see Fig. 3.2). Finding ( ) becomes a numerical effort, with visual assessment needed to determine the rigidity of the fit; it should not forfeit large-scale details by being too exaggerated, nor sink into small-scale details by being too relaxed. Furthermore, telluric emission lines can cause local augmentations, and intervals to be ignored are manually selected around them. 3.2.5 SNR filtration
? N Following Poisson statistics, the SNR of the summed spectrum is expected to increased by a factor of obs (given that all observations have approximately equal exposure times) relative to the average N SNR of its individual observations, : N obs k k avg 1 X obs SNR = =1 SNR (3.11) j 0 The presence of read-out noise mitigates the sought increase, which can be elevated by filtering out noisy spectral orders. This is done by only retaining the orders with an average SNR higher than 18
(a)
The continuum is too rigid.
(b)
FigureThe 3.2continuum is too relaxed.
Incorrect continuum normalization. The upper panels show the spectrum (white) in ADUs, together with the blazeβ function (blue). In order to follow the curvature of overlapping orders, the rigidity of the derived continuum (green) must be tuned in-between the extremes above. Lines with strong wings are often helpful, as with H to the center-right.
N − N − N − the arbitrarily set threshold at 90 %Fofλ thei;j0 SNR of: all orders, in eachF respectiveλi;j mode, pix > pix : 1 1 ord N σ λi;j0 N N 1 σ λi;j i tot i j tot 1 X ( ) 0 9 X X ( ) pix tot pix ord tot (3.12) =0 ( ) =0 =0 ( ) 19 Table 3.2 RED BLUE f RED tot Signal-to-noise ratios. All values are averages of the and modes, except SNR and SNR for M-stars, which only comprise values. Star SNRavg SNRtot f SNR : : : : : : GJ 1214 6:4 66:8 3:3 GJ 3470 12:6 90:5 2:3 K2-3 26:6 132:5 1:6 WASP-21 32:4 109:2 1:1 WASP-29 25 9 81 3 1 0 WASP-117 57 0 148 5 0 8 BLUE k;BLUE <
Additionally for M-stars, the mode is entirely omitted since in most cases SNR 10. N − N0 − The total calculated SNR becomes, F λi;j0 pix ; 0 1 ord 1 N N σ λi;j0 i j0 tot tot 1 X X ( ) SNR = pix ord tot (3.13) N0 =0 =0 ( )
ord where is the number of retained orders. Subsequently, one is then able to constructf ? an enhancement; factor for the SNRs, N tot SNR SNR = obs avg (3.14) SNR indicative of how much the signal improved—or worsened, if the factor is less than 1—compared to theory. 3.3 Spectral synthesis
Line data3 for the trimmed wavelength intervals are obtained from the The Vienna Atomic Line Database (VALD; Piskunov et al. 1995; Ryabchikova et al. 2015). The ‘Extract Stellar’ query is configured to include van der Waals broadening from the theory by Anstee-Barklem-O’Mara (ABO; see Barklem et al. 1998, and references therein). 4 Stellar parameters are derived using Spectroscopy Made Easy (SME; Valenti & Piskunov 1996; Piskunov & Valenti 2017), which is an interface-based software. SME performs spectral synthesis by solving the equilibrium number densities of absorbers, needed for calculating opacities. Together with a model photosphere,MARCS the radiative transfer equation can be iteratively solved andχ disc-integrated to provide a flux spectrum. To find the parameters best matching with observations, SME2 interpolates from a grid of e.g. (Gustafsson et al. 2008) model photospheres, with which -minimization is performed. An initialhttp://vald.astro.uu.se guess for the stellar parameters of each targets is retrieved from the Exoplanet 3 http://www.stsci.edu/~valenti/sme.html 4Available at i.a. . Available at . 20
(a) T (b) : g eff The initial guesses (red) span a range of 1200 K in , Close-up of the results (blue), which have a small spread Figure0 5 dex in 3.3log , and 1 dex in [Fe/H] (denoted as [M/H]). along all three axes, showcasing the robustness of SME.
Credit: PiskunovSME & convergence Valenti 2017 test. (reproduced To illustrate with permission).the optimization capability of SME, regardless of initial estimates, 1000 tests of the Sun’s reflection off asteroid Vesta were carried out across the parameter space.
5 Data Explorer (EDE), or estimated from the most resembling sample star in Lindgren & Heiter (2017). Although, the closeness of the initial guess should not be crucial, as the convergence of SME has been shown to be accurate for a wide range of reasonable values (see Fig. 3.3). Via the graphical user interface (GUI), one can create a mask distinguishing line from continuum points, but also wavelength intervals to be ignored during fitting, which is implemented for observed lines not found in the line list and the cores of strong lines without available non-LTE (NLTE) correction.
http://exoplanets.org
5 Available at . 21
Chapter 4
Results
4.1 Observed and synthetic spectra
Prior to the spectral synthesis, the post-processed data should be previewed to verify that all steps have been void of critical errors. Fig. 4.2 shows a smoothed composition of observations. Ordered after spectral type, the diminishing of Balmer lines becomes evident, as does the wide spread of metallic and molecular lines. On the redward end can be seen the constant presence of contamination by BLUE WASP117_blue_fig telluric oxygen. Another noticeable aspect is the result of the SNR filtration, which has removed the noisiest regions, most obvious in the orders. C2 1 5159.039 C2 1 5159.053 C2 1 5159.186 C2 1 5159.939 C2 1 5159.990 C2 1 5160.098 Fe 1 5160.494 C2 1 5160.877 C2 1 5160.902 C2 1 5161.032 C2 1 5161.642 C2 1 5161.709 C2 1 5161.819 C2 1 5162.456 C2 1 5162.486 C2 1 5163.110 C2 1 5163.170 Fe 1 5163.710 C2 1 5163.775 C2 1 5164.305 Fe 1 5166.849 Fe 1 5167.721 Mg 1 5168.761 Fe 1 5168.927 Ni 1 5170.099 Fe 1 5170.337 Fe 2 5170.468 Fe 1 5173.037 Fe 1 5173.112 Mg 1 5174.125 Ni 1 5174.309 Ti 1 5175.184 Ni 1 5178.002 Fe 1 5178.675 La 2 5184.854 Mg 1 5185.048 Ti 2 5185.155 Fe 1 5185.710 Fe 1 5185.710 Ni 1 5186.003 Fe 1 5187.169 Ti 2 5187.346 Ce 2 5188.903 Fe 1 5189.359 Ti 2 5190.132 Ca 1 5190.289 Nd 2 5192.886 Fe 1 5192.900 Zr 2 5193.038 Fe 1 5193.789 Ni 1 5193.941 Nd 2 5194.056 Ti 1 5194.415 Cr 1 5194.938 Fe 1 5196.388 Fe 1 5196.918 Fe 1 5197.506 Mn 1 5198.037 Fe 2 5199.015 Fe 1 5200.158 Nd 2 5201.569 Y 2 5201.858 Fe 1 5203.704 Fe 1 5203.784 Cr 1 5205.947 Fe 1 5206.032 Y 2 5207.172 Cr 1 5207.473 Cr 1 5209.859 Fe 1 5210.044 Ti 1 5211.835 Ti 2 5212.981 Nd 2 5213.811 Cr 1 5215.583
1.01.0
0.80.8
0.60.6 Intensity
0.40.4
0.20.2
0.00.0 51605160 51705170 51805180 51905190 52005200 52105210 Wavelength
Figure 4.1
Example SME synthesis. The staring synthesis (green) is optimized with respect to the observations (black) to produce the final synthesis (blue). The white wavelength intervals are ignored during the fitting. 22
H H H K H WASP-117
MgI
WASP-21
WASP-29
FeI K2-3 FeI Normalized flux Normalized G CaI
GJ 3470
GJ 1214
TiO
Retained Removed D1+D2 4000 5000 6000 7000
λvac (Å)
Figure 4.2 BLUE RED Composite spectra of targets. The vacuum wavelengths are in the rest frames of the stars. Smoothing has been applied to distinguish characteristic features. The and modes constitute the left and right halves, respectively. The black-colored sections are kept orders satisfying the criterion in Eq. (3.12), whereas red-colored parts are subsequently trimmed off. Prominent spectral lines are indicated by their Fraunhofer names or spectroscopic notation; the TiO marker is placed at the center of its molecular band. 23 4.2 Derived parameters
MARCS v / v / The outcome from the spectral fitting described in Sect. 3.3 is presented in Table 4.1. In the mic mac applied models, the micro- and macroturbulence are fixed as = 1 km s and = 3 km s, respectively, similar to values adopted by Valenti & Fischer(2005). Whereas the rotational velocity of the stars is assumed negligible and set to zero. To mimic the instrumental profile of HARPS, the syntheses are additionally convolved with a corresponding point spread function (PSF). The abundances of elements with strong lines in the studied regions are identified and also set as free parameters, in order compensate for insufficient growth from the metallicity scaling. In Fig. 4.3, the derived parameters and their uncertainties are compared to previous studies of the same stars from the literature. 4.3 Limb darkening
MARCS
The derived parameters are thereafter used to compute new model photospheres, for more accurate retrieval of specific intensities compared to interpolation in a grid of pre-existingµ models. For stars/ ≈ with: dual modes, the new models use parameter averages. The specific intensities are calculated at 49 (the maxmimum number of points allowed by SME) equidistant -values between 1 I µ and 1 49 0 02 across each stellarλ disc. Assuming− a − µ a quadratic− b − µ limb; darkening of the form Iλ 2 ( ) = 1 (1 ) (1 ) (4.1) (1) a b regression is applied to find the limb darkening coefficients (LDCs), and , for a subset of the evaluated wavelengths, shown in Fig. 4.4. Although the coefficients exhibit a global trend, points which coincide with the cores of strong lines are scattered due to their shallow depth of formation. 24 0.28 0.31 0.17 0.35 ± ± ± ± 6.87 5.78 5.91 5.64 − − − − 0.11 0.13 0.24 ± ± ± Na Ca 5.86 5.95 5.88 − − − ] 0.19 0.15 0.11 0.11 0.25 0.20 H ± ± ± ± ± ± / Fe [ . Abundances are given as logarithmic number 1.20 0.73 0.47 0.36 0.17 0.47 a − − − − − − 0.83 1.36 0.97 0.88 0.67 1.16 g ± ± ± ± ± ± log ) 71 3.22 K 280 4.37 257 4.40 107 4.25 105 4.82 198 4.36 ( ± ± ± ± ± ± eff T 0.38 4486 0.82 5885 1.49 6045 ± ± ± Mg 3.73 4.21 4.51 − − − ] 0.58 0.15 0.18 H ± ± ± / Fe [ 0.59 0.32 . − − BLUE RED for Mg. 0.61 0.28 0.66 0.81 g ) ± ± ± tot log /N Mg N ) 303 4.69 172 4.21 229 4.19 K log ( ( ± ± ± eff T http://simbad.u-strasbg.fr/simbad Derived stellar parameters and abundances. The stars are sorted after their spectral types listed on SIMBAD Available at a GJ 1214 M5 V 2854 GJ 3470 M2 V 3305 K2-3 M0 V 3718 WASP-29 K4 V 5180 WASP-21 G3 V 5801 Table 4.1 StarWASP-117 Sp. F9 type V 5872 densities relative to the total, e.g. 25
6.0
5.5
5.0
4.5
4.0 (kK): Others'(kK):work eff
T 3.5
3.0
3.0 3.5 4.0 4.5 5.0 5.5 6.0
Teff (kK): This work
5.5
5.0
4.5
4.0
3.5 : Others'work : g 3.0 log
2.5
2.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 logg: This work
0.4
0.2
0.0
-0.2
-0.4 [Fe/H]:Others'work -0.6
-0.8 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 [Fe/H]: This work
Figure 4.3 BLUE RED
Comparison with previous studies. The horizontal axis shows the ( + averaged) values and errors of this work (from Table 4.1), whereas the vertical axis shows previously determinedg g@M parameters?/R? for the same stars retrieved from the references in Table 3.1. The dotted line indicates a 1:1 relationship.2 Surface gravities were unavailable for GJ 3470 and K2-3, and are instead calculated with = . Two metallicity points are missing because they were unavailable for GJ 1214 and 3470. 26
1.5 WASP-117 a 1.0 0.5
0.0
-0.5 1.5 WASP-21 1.0
0.5
0.0
-0.5 1.5 WASP-29 1.0
0.5 LDCs 0.0
-0.5 1.5 K2-3 1.0
0.5
0.0
-0.5 1.5 GJ 3470 1.0
0.5
0.0
-0.5 4500 5000 5500 6000 6500 (Å)
Figure 4.4
Wavelength dependency of the limb darkening. The quadratic LDCs from Eq. (4.1) are evaluated for the retained spectral region of each star in steps of 10 Å. The color of each coefficient is indicated on the first subplot. 27
Chapter 5
Discussion
5.1 Uncertainties
In the SME solver, numerical errors are of little importance. Instead, the uncertainties arise due to deficiencies in the stellar models, which SME tries to estimate through the sensitivities of unmasked points. The parameter changes are inversely proportional to the partial derivatives of the flux with respect to each parameter. Generally, this works well, however,BLUE forRED parameter-insensitive points the uncertainties couldRED diverge, leading to overestimation. BLUE Regarding the quality of derived parameters, the and modes each have their own benefits. While mode has a higher SNR for late-type stars, the spectral region of the hσT i hσ gi : hσ / i : mode contains many more gravity-sensitive Fe lines. In the derived set of parameters, the average eff log [Fe H] uncertainties are = 191 K, = 0 88 dex and = 0 21 dex. The precision is com- parable to spectroscopic determination of this kind, reflected in the Fig. 4.3 comparison, except for surface gravity which might be overestimated following the discussion above. 5.2 Further improvements
The strive to minimize the difference between observations and syntheses might not be so simple as obtaining additional observations to increase SNR, although admittedly that would help to some extent. One source of several other errors is the inadequacy of the stellar models. The numerical task is made feasible by oversimplifying, at the cost of failure to reproduce finer details in the spectra. The atomic line properties are constantly updated—experimentally in laboratories and theoret- ically through complex modeling. Moreover, the inclusion of non-‘classical’ effects would noticeably improve the outcome. For example, Zeeman broadening could play a significant role in magnetically active stars. The turbulence scales should preferably also be target specific, or at least be assessed from trends based on the stars’ auxiliary characteristics. Neither should the computational aspects be neglected. By fitting numerous parameters simul- taneously, there is a risk of degeneracy which could imply the over- or underestimation of some 28 parameters. Ideally, the partial derivatives of the optimization should be utilized to select wave- lengths regions for which only a subset of the parameters are fitted, to subsequently be used as fixed values in regions suitable for the remaining parameters. Furthermore, the SNR filtration should be evaluated to a non-arbitrary threshold which would not exclude important features while keeping the overall signal statistically significant. 29
Chapter 6
Conclusion
The task of determining stellar parameters is intricate and involves several steps of data handling. The prerequisites are high-resolution spectra which are accurately pipelined and combined to yield a high SNR. The{ processT ; thatg; follows/ } is then facilitated with the aid of easily accessed databases, computationallyχ effective stellar models and user-friendly spectroscopy tools. eff 2 In this study log [Fe H] of 6 late-type stars were determined, using HARPS data and -fitting with SME, to a precision suitable for subsequent studies of their companions. Improvements can be made by considering fine structure effects in the stellar models and through decoupling in the numerical derivation. The future of exoplanet characterization is worthy of a final word. Although the work presented here has been carried out in the optical regime, the fundamental parameters of an individual star are wavelength-independent and essentially constant at the timescale of planetary transits (given the star’s activity level is not too abnormal). Thus they are a powerful tool and can, for in- stance, be utilized to synthesize spectra for regions containing lines of compounds associated with biosignatures—prospectively detecting them in the atmospheres of ever-smaller exoplanets. 30
Acknowledgements
I would like to express my deepest gratitude toward Prof. Nikolai Piskunov for his kind mentorship. Your numerous anecdotes from around the globe have persuaded me to explore it for myself. Thank you to Dr. Bengt Edvardsson for your constructive input on this thesis and for the specific models which were crucial for the project’s completion. Finally, thank you to Dr. Andreas Korn for being helpful throughout my Master’s studies. 31
Appendix A
Observations
Table A.1
HARPS observations. The columns specify the object EDE/ESO identifiers, and the ESO IDs for theObject program (EDE/ESO) in which the observation was carriedProgram out and ID its unique dataset with timestamp.Dataset ID
HARPS.2009-07-27T02:54:44.319 283.C-5022(A) HARPS.2009-07-30T00:41:20.581 HARPS.2009-07-30T02:50:18.712 HARPS.2009-08-29T23:28:52.045 GJ 1214 HARPS.2009-09-03T23:26:05.655 GJ1214 HARPS.2009-09-24T23:21:36.122 183.C-0437(A) HARPS.2010-04-11T08:07:44.823 HARPS.2011-04-28T05:45:46.770 HARPS.2011-06-16T01:54:17.803 198.C-0838(A) HARPS.2018-03-21T08:59:57.096 HARPS.2008-12-25T06:38:34.917 082.C-0718(B) HARPS.2008-12-26T06:34:50.163 HARPS.2011-01-05T05:13:42.300 183.C-0437(A) HARPS.2012-05-12T22:37:16.723 GJ 3470 HARPS.2016-10-28T08:21:45.774 GJ3470 HARPS.2016-11-06T08:34:57.913 HARPS.2016-11-09T08:34:40.547 198.C-0838(A) HARPS.2016-11-11T08:30:14.994 HARPS.2017-04-12T00:17:39.549 HARPS.2018-03-22T02:04:03.171 HARPS.2015-05-04T00:51:10.497 HARPS.2016-02-02T06:06:44.049 HARPS.2016-02-03T06:09:07.758 − HARPS.2016-02-04T05:50:22.869 K2-3 191.C-0873(A) HARPS.2016-02-05T06:02:06.439 2M1129 0127 HARPS.2016-02-06T05:30:57.447 HARPS.2016-02-28T03:58:22.504 HARPS.2016-03-05T03:45:35.537 HARPS.2016-03-06T03:56:04.084 198.C-0838(A) HARPS.2017-02-06T08:18:37.443 32
072.C-0488(E) HARPS.2008-08-31T06:00:07.132 HARPS.2008-10-15T03:03:34.833 HARPS.2008-10-16T03:33:47.405 HARPS.2008-10-21T02:51:03.797 WASP-21 082.C-0608(A) HARPS.2008-10-22T02:42:32.846 SW2309+1823 HARPS.2008-10-24T01:57:51.504 HARPS.2009-10-07T02:55:39.881 HARPS.2009-10-08T02:52:32.865 HARPS.2009-10-09T02:35:54.999 084.C-0185(E) HARPS.2009-10-12T02:56:47.280 085.C-0393(A) HARPS.2010-09-05T09:21:56.485 HARPS.2017-08-18T03:38:17.703 HARPS.2017-08-18T03:53:49.064 − HARPS.2017-08-18T04:24:51.077 WASP-29 HARPS.2017-08-18T04:40:22.089 SW2351 3954 099.C-0898(A) HARPS.2017-08-18T05:57:57.105 HARPS.2017-08-18T06:13:28.076 HARPS.2017-08-18T06:28:59.158 HARPS.2017-08-18T06:44:31.099 HARPS.2017-08-18T07:00:03.141 HARPS.2014-10-24T01:41:59.564 HARPS.2014-10-24T02:02:31.934 HARPS.2014-10-24T04:58:44.926 − HARPS.2014-10-24T05:29:49.926 WASP-117 HARPS.2014-10-24T06:16:24.946 094.C-0090(A) SW0227 5017 HARPS.2014-10-24T06:31:57.037 HARPS.2014-10-24T07:18:35.938 HARPS.2014-10-24T07:34:08.387 HARPS.2014-10-24T07:49:39.907 HARPS.2014-10-24T08:05:13.417 33
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