Thesis
Reference
New concept of spectral calibration for high resolution astronomical spectrographs
CERSULLO, Maria Federica
Abstract
The current precision of radial-velocity spectrographs is limited by the wavelength calibration and used calibration sources. New types of calibration sources are needed to enable better wavelength calibration. The goal of my thesis work was to test several Fabry-Perots, which are systems that produce a spectrum of nearly-equidistant emission lines over a very large wavelength range. As such, and provided that the lines remain stable in wavelength over time, this source can be used as a wavelength reference. During the the second part of my thesis work, I investigated furthermore possible developments of our Fabry-Perot system as an alternative to current calibration sources. The declared objective was to improve the wavelength calibration accuracy of the HARPS spectrograph by combining the absolute spectral reference provided by the emission lines of a thorium-argon hollow-cathode lamp (HCL) with the spectrally rich and precise information delivered by the Fabry-Perot-based calibration source.
CERSULLO, Maria Federica. New concept of spectral calibration for high resolution astronomical spectrographs. Thèse de doctorat : Univ. Genève, 2018, no. Sc. 5313
DOI : 10.13097/archive-ouverte/unige:114982 URN : urn:nbn:ch:unige-1149825
Available at:
http://archive-ouverte.unige.ch/unige:114982
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U G F S
Département d’Astronomie Professeur Francesco Pepe Dr. Bruno Chazelas
New Concept of Spectral Calibration for High Resolution Astronomical
Spectrographs
T
présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences,
mention Astronomie et Astrophysique
par
Maria Federica C
de
Cosence (Italie)
Thèse No5313
G
Observatoire Astronomique de l’Université de Genève 2018
D
A Matteo,
Tutto mi sembra migliore, ora capisco bene cos’ è.
A Giorgio,
che ha sempre creduto in me e sostenuto con amore e comprensione.
Questo lavoro è dedicato a voi. Grazie infinite per quello che è stato, è, e per quello che ci attende.
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There are lots of people I would like to thank for a huge variety of reasons.
I am particularly grateful to my Supervisor, Prof. Francesco Pepe.
I could not have imagined having a better advisor and mentor for my PhD, and without his commonsense, knowledge, perceptiveness and enthusiasm, I would never have enjoyed so much my work. I have learned a lot. Thanks for having given me this opportunity!
I am grateful for the invaluable support and the priceless help in the laboratory given to me by Dr. Francois Wildi and Dr Bruno Chazelas.
I had the honor to work with two brilliant engineers who have put a lot of effort and patient in showing to me how an ’engineer’ should think and act.
Special thanks go to Adrien Coffinet for our collaboration and for having challenged together that terrible beast called DRS.
Thanks for the valuable discussions, the good time spent together, the patience and for doing with me the past 11pm in the office.. with you I shared more than a publication:
friendship and deep respect!
I would like to specifically thank Helen and Angelo for the very big help as reviewers of my thesis.
Thanks for your precious advices, You saved me!
I would like to thank all the rest of the colleagues and friends gravitating around the observatory.
Living in a foreign country is not always easy, but thanks to a lot of lovely colleagues and friends, I’ve always felt at home. I have a lot of memories shared with you. Thanks, again!
I have to say a big "Grazie" to my family: Mum, Dad, Luca, Maria and my two lovely nieces Elisabetta and Francesca, You are always with me!...and most importantly, to Giorgio and my "ciupetto" Matteo, for... for... for everything and for making me laugh when I don’t even want to smile!
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The study of fixed stars as it has been so far important for the theory of celestial movements, as much as it was limited to physical research. Everything so far has been reduced to examining the color, the intensity of light and the variability. But the discovery of spectrometry made this study one of the most vague, varied and even delectable and important that can be found.
The variety of the colors of the stars is accompanied by a corresponding distinction of their elementary colors, and by a difference of spectral lines and these being admirably connected with the nature of the matter that burns in those asters and constitutes them, giving us the means to know the nature of those substances of which they are formed.
Padre Angelo Secchi.
Centinaia di anni fa l’uomo viveva sulla terra, fra grattacieli e autostrade sopra il mare.
Poi nel 2000 la Convenzione...
Poi nel 2000 la Convenzione...
Molti andarono su Giove, fra pianeti artificiali,
e altri su Venere in cerca di spazio, un po’ restammo quaggiù sotto il mare...
un po’ restammo quaggiù sotto il mare...
Sopra l’acqua... dei segnali di un cervello sconosciuto...
intercettare il linguaggio...
Ricevuto!
Cerchi di luce attraversano il cielo Cerchi di luce attraversano il cielo.
Cerchi di luce attraversano il cielo.
Franco Battiato.
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Dedication iii
Acknowledgements v
Epigraph vii
Contents ix
List of Figures xi
List of Tables xiii
Summary xvii
Résumé xx
Preface xxii
1 Introduction 1
1.1 Rationale . . . 1
1.2 Science case . . . 2
2 Wavelength reference in precise radial-velocity measurements 9 2.1 Echelle Spectrograph . . . 9
2.2 Wavelength Calibration for spectrographs . . . 12
2.3 Referencing methods . . . 14
2.4 Wavelength reference sources. . . 16
3 Fabry-Pérot as a reference for high resolution spectrograph 21 3.1 Theory. . . 21
3.2 Real Fabry-Pérot . . . 25
3.3 Simulation and analysis on variation of the alignment and variation of fibre diameter . . . 27
3.4 Design&Specifications . . . 32
3.5 Measurements in laboratory . . . 34
4 The SPIRou RV-Reference module 41 4.1 Introduction . . . 41
4.2 Fabry-Pérot RV-module Acceptance . . . 56 ix
5.2 Comments and additional results . . . 78
6 Conclusion&future directions 81
Appendix 85
A Appendix 85
A.1 A new infrared Fabry-Pérot-based radial-velocity-reference module for the SPIRou radial-velocity spectrograph . . . 85 A.2 A new wavelength calibration for echelle spectrographs using Fabry-Pérot etalons 99 A.3 List of Publications . . . 115
Bibliography 117
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1.1 On the left, the radial velocity curve of 51 Pegasi of the discovery paper. On the right, precise measurements of RVs over 10 years of observations of Tau Ceti by HARPS.Mayor and Queloz(1995) andPepe et al.(2014). Used with permission. . 5 1.2 Velocity semi-amplitude as function of time for exoplanets discovered with the
radial velocity method. Plot obtained throughhttp://exoplanets.org.. . . 6 2.1 Typically optical layout of echelle spectrograph. The figure is excerpt fromThe fiber
fed echelle spectrograph at the 1.2 meter telescope at Kourovskaya astronomical observatoryofA.F. Punanova, V.V. Krushinsky. . . . 10 2.2 Geometry of the orders in an echelle spectrograph. The near horizontal lines
represent the free spectral range (FSR) whereas the red dots are Th-Ar lines and, the box is the physical size of the CCD. Figure excerpt fromFeger et al.(2014). . . 11 2.3 Example of a raw echellogramme. "True" colors have been superimposed to
show the evolution of the wavelength across the detector. Image taken fromht- tps://homepage.univie.ac.at/michel.breger/lehre/AI2/instrumente2.html. . . 12 2.4 Spectroscopic Data Reduction Steps. . . 13 2.5 HARPS First Light spectrum, recorded on February 11, 2003. Simultaneous
Thorium-Argon spectrum ("white dots") alongside the object spectrum. From ESO archive. . . . 15 2.6 Spectrum of star through iodine cell. From slide presentation Radial Velocity
Detection of Planets: I. Techniquesby Justina King. . . 16 3.1 Scheme of a Fabry-Pérot cavity with incident wave E0, the reflected waves En0
and the transmitted wavesEn. Multiple reflections occurred. Figure excerpt from http://www.physics.iitm.ac.in/ ph5060/manuals. . . 22 3.2 The transmission as a function of the wavelength. A high-finesse (red line, F2)
has sharper peaks and lower transmission minima compared to a low-finesse etalon (blue line,F1). Figure excerpt formWikipedia.. . . 24
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defects, b) Surface Irregularities, c) Parallelism Defects. FromCVI Optical Com- ponents and Assemblies Manual. . . . 25 3.4 The fibre model. A local polar coordinate system (⇢,') is introduced. . . 28 3.5 Simulated transmittance of ESPRESSO Fabry-Pérot for fibre diameters of 200, 400,
and 600µm, assuming the fibre is centred on the optical axis and a focal length of the collimator f =100mm. . . 29 3.6 Simulated transmittance of ESPRESSO Fabry-Pérot for fibre de-centering value of
20, 250, 500, and 1000µmassuming a fixed fibre diameter ofD= 200µmand a focal length of the collimator f =100mm. . . 30 3.7 Finesse for a centred fibre as a function of fibre diameter (left) and as a function
of fibre de-centring (right) for a fixed fibre diameter D = 200µm. The blue line marks the area we are interested in namely a small fibre diameter and an effective finesse close to the nominal valueFR =11. . . 30 3.8 Change in radial velocity for a centred fibre as a function of fibre diameter (left)
and as a function of fibre de-centring (right) for a fixed fibre diameterD=200µm.
The blue line marks the limit area we are interested in. The area is small because small changes introduces shift of several hundreds or more of m s 1in both cases. . 31 3.9 Radial velocity sensitivity to fibre-size change for a centred fibre (left) and to de-
centring for a fixed fibre size ofD=200µm (right). The blue line marks the limit area we are interested in. For 2 mrad fibre size, the RV will change by 350 m s 1 (3.5 m s 1micron 1) for a centred fibre. In the case of de-centring, it changes by 750 m s 1(7.5 m s 1micron 1). . . 32 3.10 General view of the Fabry-Pérot opto-mechanical assembly. FromVLT-TRE-ESP-
13520-0154, Issue 1 - Fabry-Pérot calibrator: Final Design Description and Performances Analysis. . . . 34 3.11 Functional diagram of the RV-reference unit. . . 35 3.12 Above and on the left, the two optical etalons for CORALIE@Euler Telescope (La
Silla) and ESPRESSO@VLT Telescope (Paranal). Above and on the right, the infrared etalon for SPIROU@CHFT (Hawaii). On the bottom, the optical etalon for SOPHIE.. . . 36 3.13 Setup for transmission curve measurements. . . 37 3.14 Curves of transmission for finesse measurements for the four different etalons. . . . 38 3.15 In the top-upper left corner, we see a spectrum of CORALIE; in the top upper-
right corner, we see a spectrum of ESPRESSO; on the bottom, we see aspectrum SOPHIE. Used with permission of F. Pepe and F. Bouchy.. . . 39
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3.16 Differential drift between the two fibers expressed in terms of radial velocity. On the top, drift measurement of CORALIE is shown; on the center, drift measurement of ESPRESSO; on the bottom, drift measurement of SOPHIE. Courtesy of F. Pepe and F. Bouchy.. . . 40 4.1 Portion of a SPIRou frame. Each group of three vertical lines corresponds to one
spectral order. showing side-by-side the spectra of a star and the Fabry-Pérot.
Courtesy of F. Bouchy. . . 56 4.2 Relative Flux as function of wavelength for the full spectrum. Figure excerpt from
SPIRou-High Level AcceptanceTests AT-4&Results. Courtesy of F. Bouchy.. . . . 57 4.3 RV stability of the Spirou spectrograph over 24h measured by the RV-reference
module. The red curve shows the absolute stability expressed in m s 1, while the green curve shows the relative drift between the target and the reference channels.
Figure excerpt from SPIRou-High Level AcceptanceTests AT-4& Results. Used with permission of F. Bouchy. . . 58 4.4 Dispersion curve of the etalon used in the SPIRou RV-reference module. Variation
of the cavity gap is shown as a function of wavelength. Figure excerpt from SPIRou-High Level AcceptanceTests AT-4&Results. Courtesy of F. Bouchy.. . . . 60 5.1 On the left side, the HARPS RV data of HD 10700 obtained between 2004 to
2017 are shown being reduced with the standard (top), C18 (center) and new DRS (bottom). The data set before the change of the fibres is plotted in blue while the data set after the change of the fibres is plotted in red The right-hand plots show the respective LSP of the residuals to the fitted Keplerian model. . . 80 6.1 Effective etalon gap variation2D( ) 2D0as a function of wavelength as computed
for each Fabry-Pérot peak using the initial thorium wavelength solution. . . 84
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1.1 Table of orbital parameters for several planets in the solar system and corresponding radial-velocity induced on the Sun by the planets. . . 4
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3.2 Specifications for all Fabry-Pérot etalons. . . 33 5.1 Comparison of the standard (std), the intermediate (C18)Coffinet et al. 2019and
the new (new) versions of the DRS. The second column indicated the number of data points (nightly averages) per target, the third column the time span tin days and the fourth column the number of planets assumed in the model. The dispersion (rmsin m s 1) of the residuals to the fit of the radial-velocity data is given for all three versions of the DRS, for the full data set (Global), and the data sets before and after the fiber change separately. . . 79
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The proof for the existence of planets orbiting stars other than the Sun was not given until the discovery of 51 Peg b by Michel Mayor and Didier Queloz in 1995. The employed technique was the one of the so-called Doppler spectro-velocimetry, an indirect method that measures the stellar velocity vector projected along the "line of sight" that connects the star to the observer.
Recording the radial-velocity curve, i.e. the change of radial velocity as a function of time, allows us to determine the orbital period, the product of the mass of the planet withsini, where iis the angle of the orbital plane projected on the sky, as well as the eccentricityeof the orbit.
Exoplanets like 51 Peg b induce on their host star a radial-velocity variation of about 100 m s 1 semi-amplitude over a few days of period. Our own Jupiter induces on our Sun a much smaller variation of the order of 13 m s 1, in particular due to the much larger distance to the Sun compared to that of 51 Peg b to its star. The Earth induces a modulation of only 9 cm s 1 onto our Sun over a period of one year. Therefore, a spectrograph able of detecting Earth-like planets will have to achieve precisions at the level of cm s 1. Tiny planets imply thus tiny signals, which require in turn precise measurements. A measurement can however only be as accurate as its calibration, and as precise as its repeatability. The current precision of radial-velocity spectrographs is limited by the wavelength calibration and used calibration sources. New types of calibration sources are needed to enable better wavelength calibration and thus measurements with an increased sensitivity to velocity variations.
In January 2003, HARPS, a fibre-fed spectograph at the Cassegrain focus of ESO’s 3.6 m telescope was installed in La Silla. It is specialized for the measurement of radial velocities reaching the highest accuracy and precision available at present (better than 1 m s 1). The calibration source is a Thorium-Argon (Th-Ar) lamp and the observation mode is the simultan- eous reference; together they provide adequate radial-velocity precision.
The goal of my thesis work was to test several Fabry-Pérots, which are systems that produce a spectrum of nearly-equidistant emission lines over a very large wavelength range. As such, and provided that the lines remain stable in wavelength over time, this source can be used as a wavelength reference. These Fabry-Pérots are used in the CORALIE, ESPRESSO, SOPHIE and SPIRou spectrographs so far. They were built to meet the following requirements: provide
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of the spectrograph; the spectral lines should be isolated, i.e. not be blended; the peak flux of the lines should be as homogeneous as possible across the wavelength range. The first system, currently in use on the HARPS spectrograph, has been performing well and has completely replaced the ThAr spectral lamp for instrumental drift measurement purposes. Nevertheless, its lens-based optical design was not compatible with an infrared version we had to produce for SPIRou, an infrared radial-velocity spectrograph for the Canada-France-Hawaii-Telescope.
During my thesis I have contributed in specifying, designing, building and testing a new infrared Fabry-Pérot system. The only element that needed to be adapted was the etalon itself in terms of material and coatings. We converted the requirements set by SPIRou, into requirements for the ’RV-reference module’ (for simultaneous reference measurements). We verified the as- sumptions by analysis and simulations, designed and manufactured the new module according to the choices we made, and finally tested the key performances in laboratory. The obtained performances are fully compliant with the requirements. In parallel to this work, we designed and built another system of the same new design for the CORALIE spectrograph. I have tested and installed the system in May 2015 on CORALIE on the Swiss EULER 1.2-m Telescope at the La Silla Observatory. The Fabry-Pérot is since in continuous operation and has demonstrated a stability of better than 1 m s 1 per night, such that it has fully replaced the thorium-argon lamp for simultaneous-reference measurements.
During the the second part of my thesis work, I investigated furthermore possible develop- ments of our Fabry-Pérot system as an alternative to current calibration sources. The declared objective was to turn the Fabry-Pérot-based light source into a cost-effective alternative to laser- frequency combs (LFC). The more immediate goal was to improve the wavelength calibration accuracy of the HARPS spectrograph by combining the absolute spectral reference provided by the emission lines of a thorium-argon hollow-cathode lamp (HCL) with the spectrally rich and precise information delivered by the Fabry-Pérot-based calibration source. In collabora- tion with another PhD-student, Adrien Coffinet, I developed a new wavelength solution, which fits simultaneously the thorium emission lines and the Fabry-Pérot lines. The combined fit is anchored to the absolute thorium wavelengths, which provide thezero-pointof the spectrograph, while the Fabry-Pérot lines are used to improve the (spectrally) local precision. I integrated the new wavelength solution into the HARPS data-reduction software (DRS), verified it for self-consistency and successfully tested it against a solution obtained using the HARPS LFC. I finally tested the new calibration concept on the three well-known and ’RV-standard’ stars: HD 10700, HD 20794 and HD 69830. I could demonstrate that the combined wavelength solution produced significantly better performances compared to the thorium-only calibration. Given these very positive results, we considered that the conditions had been met to install the new
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DRS on HARPS and HARPS-N pipelines, and in the future for the ESPRESSO spectrograph.
These results demonstrate that the chosen approach was correct and give prospectives for new and even improved solutions for wavelength calibration of future high-fidelity astronomical spectrographs.
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La preuve de l’existence de planètes en orbite autour d’étoiles autres que le Soleil n’a été démontrée qu’à la découverte de 51Peg b par Michel Mayor et Didier Queloz en 1995. La technique employée était celle de la spectro-vélocimétrie dite Doppler, une méthode indirecte mesurant le vecteur vitesse stellaire projeté le long de la "ligne de mire" qui relie l’étoile à l’observateur. Les exoplanètes comme 51Peg b induisent une variation de vitesse radiale d’environ 100 m s 1semi-amplitude sur quelques jours de la période. Notre propre Jupiter induit sur notre Soleil une variation beaucoup plus petite, de l’ordre de 13 m s 1. La Terre induit une variation de seulement 9 cm s 1sur notre Soleil. Par conséquent, un spectrographe capable de détecter des planètes semblables à la Terre devra obtenir des précisions au niveau du cm s 1. Les petites planètes induisent, donc, des petites variations qui nécessitent alors des mesures plus précises. La précision d’une mesure dépend du calibration de l’instrument et du répétabilité de la mesure. La précision actuelle des spectrographes à vitesse radiale est limitée par l’étalonnage en longueur d’onde et les sources d’étalonnage utilisées. De nouveaux types de sources d’étalonnage sont nécessaires pour permettre un meilleur étalonnage en longueur d’onde et donc des mesures avec une sensibilité accrue aux variations de vitesse.
En janvier 2003, HARPS, un spectographe à fibres optiques, a été installé à La Silla sur le télescope 3.6 m. Il est spécialisé dans la mesure de vitesses radiales, atteignant la plus grande précision disponible à ce jour (meilleure que 1 m s 1). La source d’étalonnage est une lampe Thorium-Argon (Th-Ar) et le mode d’observation est la référence simultanée, offrant ainsi la meilleure précision à court terme.
Un des buts de ma thèse était de tester plusieurs Fabry-Pérot, des systèmes produisant un spectre de raies d’émission presque équidistantes sur une très grande plage de longueurs d’onde. A condition que les lignes restent stables en longueur d’onde dans le temps, cette source peut être utilisée comme référence de longueur d’onde. Ces Fabry Pérot sont jusqu’à présent utilisés dans les spectrographes CORALIE, ESPRESSO, SOPHIE et SPIRou. Ils ont été construits pour répondre aux exigences suivantes: fournir de nombreuses lignes étroites non résolues de longueur d’onde connue et stable; couvrir toute la plage spectrale du spectrographe;
les raies spectrales doivent être isolées, c’est-à-dire ne pas être mélangées; le flux de crête xix
premier système, actuellement utilisé sur le spectrographe HARPS, a bien fonctionné et a complètement remplacé la lampe spectrale Th-Ar pour les mesures de dérive instrumentale.
Néanmoins, sa conception optique à base de lentilles n’était pas compatible avec une version infrarouge que nous devions produire pour SPIRou, un spectrographe dans l’ infrarouge pour le Canada-France-Hawaii Telescope. Au cours de ma thèse, j’ai contribué à la spécification, à la conception, à la construction et au test d’un nouveau système infrarouge. Nous avons converti les exigences définies par SPIRou en exigences du "module de référence RV" pour les mesures de référence simultanées, vérifiant les hypothèses par des analyses et des simulations, et fabriquant le nouveau module en fonction des choix que nous avons testé les performances clés en laboratoire. Parallèlement à ce travail, nous avons conçu et construit un autre système pour le spectrographe CORALIE. J’ai testé et installé ce système en mai 2015 sur CORALIE qu’est installée sur le telescope EULER à l’observatoire de La Silla. Cet Fabry Pérot fonctionne de manière continue et a démontré une stabilité supérieure à 1 m s 1par nuit et il a totalement remplacé la lampe thorium-argon pour les mesures simultanées.
Au cours de la deuxième partie de ma thèse, j’ai étudié d’autres développements possibles de notre système Fabry-Pérot comme alternative aux sources d’étalonnage actuelles. L’objectif déclaré était de transformer cette source de lumière en une alternative économique aux peignes de fréquence laser. L’objectif le plus immédiat était d’améliorer la précision de l’étalonnage en longueur d’onde du spectrographe HARPS en combinant les valeurs absolues de référence spectrale fournie par les raies d’émission d’une lampe à cathode creuse (HCL) à thorium-argon avec les informations spectrales de la source d’étalonnage Fabry-Pérot. En collaboration avec un autre doctorant, Adrien Coffinet, j’ai développé une nouvelle solution de longueur d’onde, qui s’adapte simultanément aux lignes d’émission de thorium et aux lignes de Fabry-Pérot.
L’ajustement combiné est ancré aux longueurs d’onde absolues de thorium, qui fournissent le point zérodu spectrographe, tandis que les lignes du Fabry-Pérot sont utilisées pour améliorer la précision spectrale locale. La nouvelle solution de longueur d’onde a été intégrée sur la DRS de HARPS, vérifiée et testée avec succès par rapport à une solution obtenue à l’aide du peigne laser-fréquence (LFC) de HARPS. Le nouveau concept d’étalonnage a finalement été testé sur trois étoiles connues et "standard RV". J’ai pu démontrer que la solution de longueur d’onde combinée produisait des performances nettement meilleures que l’étalonnage uniquement au Thorium. Compte tenu de ces résultats très positifs, nous avons considéré que les conditions étaient réunies pour modifier les pipelines de HARPS, HARPS-N et, à l’avenir, sur le spectrographe ESPRESSO. Ils démontrent que l’approche choisie était correcte et offrent des perspectives pour des améliorations et de nouvelle solution pour l’étalonnage en longueur d’onde des spectrographes astronomiques à haute fidélité.
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Questions like"Is our Earth unique? Are we alone in the universe? have always fascinated mankind. Epicurus believed that there were infinite inhabited worlds because everything con- sists of an infinite variety of atoms that detach themselves from the Infinite void to temporarily assume a precarious order. The prevailing philosophy in the classical world, inspired by Plato and Aristotle, sustained the uniqueness of the Earth and therefore there could not be other systems of worlds. This has always clearly excluded, a priori, the concept of the possibility of a plurality of worlds in the name of a metaphysical unity of the world itself.
Therefore, Western philosophical thought, especially with the advent of Christianity and the affirmation of a dogmatic reading of the sacred texts, rejected the thesis of the plurality of the worlds and the question of extraterrestrial life. Only a few thinkers supported the existence of other worlds and therefore alien life. Among these, Giordano Bruno (1548-1600), who was condemned as a heretic and burned at the stake in 1600, imagined an infinite universe, populated by an infinity numbers of stars like the Sun, each surrounded by planets, on some of which intelligent beings grow and prosper.
The negationist philosophical theses of a strongly religious character began to be questioned on the basis of the work and scientific discoveries in the astronomical field during the seventeenth century by Nicolaus Copernicus and Galileo Galilei. In fact, these discoveries laid the first scientific basis for the idea of the possible existence of extraterrestrial life, which gradually consolidated with the progress of scientific and astronomical knowledge. In particular, it has began to have great importance with the discovery that the universe is incredibly large, and therefore, besides our solar system, there are many others.
Among the many questions that astrophysics addresses, this is certainly one that has attracted most interest by the wide public. This is true when, at the end of the 19th century, the Italian astronomer Schiaparelli observed with a telescope for the first time the canals on the planet Mars, which were mistakenly recognized as artificial constructions. Schiaparelli’s work in- spired many writers of the time, who wrote numerous science-fiction novels, such as "The War of the Worlds" by H. G. Wells, which attracted popular attention in an incredible way, making famous the term of "Martian", used playfully even today.
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Nevertheless, some of the most fundamental questions are still open for debate. Astronomers have long since discovered that the universe is expanding. Following, the Big Bang, galaxies move away from each other like shards of a bomb. Einstein, applying the general theory of re- lativity (1915), introduced into equations the cosmological constant⇤to represent the repulsive energy necessary to prevent the model of the universe from collapsing under its own gravity.
When Edwin Hubble discovered the expansion of the universe in 1929, Einstein rejected the cosmological constant by boiling it as the greatest mistake of his life. In fact, if the expansion is due to the Big Bang, the explosion from which the cosmos originated, it is not necessary to hypothesize a repulsive force to explain the mutual removal of the "splinters". However, recent observations have established that supernovae are at least ⇠ 15% less luminous than expected even in the most favorable case of uniform expansion not slowed by gravity (in which the distances are maximum). This discovery has restored scientific value to the cosmological constant which would even turn out to be dominant.
Search for extra-solar planets and the direct measurement of the expansion of the universe are the two most prominent examples of topical astronomical science cases, which can be addressed with extremely precise radial-velocity spectrographs. These considerations were among my main motivations me to undertake a PhD in Astrophysics and dedicate my time to improving cutting edge instrumentation and techniques.
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The work presented in this thesis, was conducted at the Department of Astronomical Obser- vatory of the University of Geneva. The main goal of my thesis consisted in studying how to improve the wavelength calibration of astronomical spectrographs in order to fulfill the requirements to detect extra-solar Earth-like planets.
1.1 Rationale
The discovery of Earth-like planets in the habitable zone of their parent stars is one of the main scientific topics of the next decades. Precision radial velocity (PRV) measurements are required to discover potentially habitable worlds, to detect small signals induced by small planets, to confirm and characterize detections from transit programs and to provide mass measurements from other space-based missions. The radial velocity technique consists in exploiting gravitational perturbations induced by a planet on the host star using the variations of velocity induced on it. This challenging objective requires a precision of 10 cm s 1 in terms of radial velocity. To reach such level of precision, we need a more precise wavelength calibration.
Wavelength calibration is the assignment of wavelengths to individual pixels on a CCD detector.
In other words, to perform a wavelength calibration means acquire the obtained spectrum and then, validate the wavelength and intensity assignments. This task needs a comparison with a reference source. One of the most common and spectral references used in the optical domain is the hollow cathode lamps (HCLs) such as He-Ar-Ne, Th-Ar and Ne-Ar-Kr. Th-Ar is the default
1
wavelength reference in the optical spectrograph since it offers a large number of narrow lines, a line position accuracy of 10 - 82 m s 1 (Palmer and Engleman(1983a) andLovis and Pepe (2007)) and, in addition, it is reliable and easy to operate. Mainly, a large electric potential difference, applied between anode and cathode (thorium), ionizes the gas (argon) and transforms it into plasma. Under the effect of the electric field, the positive ions of the gas are accelerated towards the cathode and hit it. Following these collisions, some atoms of the cathode are sputtered and mixed with the inert gas. These atoms pass to an excited state colliding with the other particles produced during ionization and return into the ground state, then emit photons of characteristic wavelengths that are independent from the environment. By the same process also the atoms of the inert gas can emit photons at different characteristic wavelengths. The result is a rich spectrum of thorium and argon emission lines (Kerber et al. 2007).
Therefore, Thorium-Argon (Th-Ar) is suitable for high-precision applications like doppler measurements with a precision of m s 1. On the other hand, there are few issues with HCLs. In fact, they show effects due to age, pressure and operating current. Furthermore, the non-uniform line distribution and the highly different line intensities of the Th-Ar spectrum compromise the wavelength calibration. Last but not least, the high-purity thorium lamps are not anymore in production. Their replacement, thorium-oxide lamps, have quite different spectra and show many (unwanted and perturbing) line blending.
This thesis work aimed at exploring the potential of the Fabry-Pérot-based system, possibly use it for the simultaneous reference technique and the wavelengths calibration at the declared level of precision, and eventually implement it on existing and future high-precision radial- velocity spectrographs.
1.2 Science case
1.2.1 The characterization of exoplanets using radial-velocity technique
Since 1995, when the first exoplanets were identified, more than 3600 planets have been discovered in orbit around stars other than our Sun and almost 2800 planetary systems. Today the improvement of observational methods and the development of special space missions make the research of exoplanets - in particular those that may have favorable conditions for hosting life forms - one of the most exciting topics of astronomy.
The detection of an exoplanet by the radial velocity technique, i.e. Doppler spectroscopy, is a key technique for identifying and characterizing exoplanets. Other techniques like transit photometry, microlensing and direct imaging have been employed for detecting exoplanets.
In fact, while the transit methods can provide the period and the size of the planet, other
. . Science case 3 methods must be employed to study their mass and the remaining orbital elements, possible non-transiting planets in the system and planetary atmospheres. In the current landascape, with the arrival of the TESS and PLATO mission, high-fidelity spectroscopy and precise radial velocities (PRV) will be more needed than ever.
The detection of an exoplanet by the radial velocity technique is based on the observations and measurements of the velocity of the star and its periodic variation caused by the star orbiting around the center of mass of the star-planet system. In a 2-body system, the radial velocity of the star is (Cassen et al. 2006):
V = +K1[cos(⌫+!)+e cos!] (1.1) where is the radial velocity of the center of mass of the system,K1is the velocity amplitude,
⌫ is the true anomaly, ! is the angle between the direction of the ascending node and the periastron, e is the eccentricity of the orbit. The amplitude K1 of the radial velocity curve variation of the primary star is:
K1= 28.4 m s 1 p1 e2
m2 sini MJup
✓m1+m2
M
◆ 1/2⇣ a 1 au
⌘ 1/2
, (1.2)
whereiis the inclination of the orbital plane taking into account the tangent plane of the sky, ais the semi-major axis of the orbit,m1andm2are respectively the masses of the star and the planet. Since by Kepler’s third law the semi-major axis is linked to the orbital period P, the eq.
1.2becomes:
K1 = 28.4 m s 1 p1 e2
m2 sini MJup
✓m1+m2 M
◆ 1/2✓ P 1y
◆ 1/3
. (1.3)
Radial-velocity observations covering all orbital phases provide the measurement of the orbital periodP, the eccentricityeand the radial velocity semi-amplitudeK1. From these observables m2 sini, (the minimum mass or lower limit of the planetary mass) and the semi-major axis a of the elliptical orbit can be computed.
On the celestial sphere, let us define the orthogonal coordinate system by the right ascension (RA), declination (Dec) and the direction along the line of sight (LOS) to the observed object.
The velocity components perpendicular to the LOS (proper motion) is determined through the measurements of the celestial coordinates RA and Dec and their change with time. The radial velocity is the velocity component of an object along the LOS and is determined by the measurement of Doppler effect through spectroscopic observations. According to special relativity, given a velocity v between the object and the observer, the wavelengths of the Doppler-shift spectral lines of the observed star become:
obs = 0
⇣c+3 c 3
⌘1/2
, (1.4)
where obs is the wavelength in the rest-frame of the observer, 0the intrinsic wavelength (i.e.
in the restframe of the emitter) andcis the speed of the light. Defining Doppler shiftszas the relative change in wavelength and using eq. 1.4we obtain:
z:= obs 0
0 = ⇣c+3 c 3
⌘1/2
1. (1.5)
Expanding Eq. 1.5in terms of3/cand considering3 <<c, the relation can be approximated by:
z = obs 0
0 ⇡ 3
c. (1.6)
To get an idea of the order of magnitude of expected Doppler shifts, Table1.1shows the amplitude of the velocity variation imposed that the planets of our solar system on the Sun. The Earth is reported for comparison, however it is noted that Jupiter imposes on the Sun a radial velocity variation of about 12.5 m s 1, while Saturn (farther and smaller) of 2.7 m s 1.
Planet a(Km) Mp(Kg) Ms (Kg) e P(days) 3(m s 1) Earth 1.50·108 5.97·1024 1.99·1030 0,017 365 8.95·10 2 Jupiter 7.78·108 1.90·1027 1.99·1030 0.048 4332.550 12.5 Saturn 14.34·109 5.68·1026 1.99·1030 0.0565 10767.5 2.77
Table 1.1: Table of orbital parameters for several planets in the solar system and corresponding radial-velocity induced on the Sun by the planets.
In 1995,Mayor and Queloz(1995) announced the discovery of the first planet known to orbit another sun-like star. Doppler measurements of 51 Pegasi were made from 1994 September through 1995 January with the fibre-fed echelle spectrograph ELODIE at Haute-Provence Observatory (France), with a precision of 15 m s 1. The results showed a period of 4.231 days, a velocity amplitude of56±1m s 1, and a velocity curve that is essentially sinusoidal.
The following years marked an increase in Doppler and the discovery of many new and even lighter planets. Considering the wide range of orbital parameters of the discovered exoplanets extending from hot-Jupiters to close Earth analogues, the actual measured velocity amplitudes range from⇠ 0.5to100m s 1(i. e. Doppler shifts as low as⇠10 5Å). Since the spectral shifts are very small and difficult to be measured, the spectrographs used must have a precision of m s 1 level and even more. This is a very small value, which is equivalent to a displacement of the stellar spectrum on the CCD detector of a typical radial-velocity spectrograph by⇠ 1/1000 of the size of a pixel, i.e. 15 nm (Mayor et al. 2014; Fischer et al. 2016) (considering the case of HARPS). A spectrograph that has been able to reach sub-m s 1precision is HARPS (High-Accuracy Radial-velocity Planet Searcher), a cross-dispersed echelle spectrograph of resolving powerR=1150000. It operates in a vacuum and temperature-controlled environment
. . Science case 5 and, furthermore, to optimize its performance, many improvements related to wavelength calibration and data reduction process, as well as a new fiber link (Lo Curto et al. 2015) have been implemented over the years..
Fig. 1.1 illustrates the improvements in Doppler measurements, by comparing the radial velocity curve of the discovery paper of 51 Peg b (Mayor and Queloz 1995) to the precise RV measurements taken over 10 years of observations of Tau Ceti by HARPS. While the residuals dispersion to the Keplerian fit in the former case is of about 15 m s 1, in the second case the dispersion is 1 m s 1and can be reduced to 20 cm s 1by time-binning of the data.
Figure 1.1: On the left, the radial velocity curve of 51 Pegasi of the discovery paper. On the right, precise measurements of RVs over 10 years of observations of Tau Ceti by HARPS.
Mayor and Queloz(1995) andPepe et al.(2014). Used with permission.
Technology development and understanding of the stellar physics have led to a deep im- provement in the Doppler precision by 2-3 orders of magnitude. Fig. 1.2shows this progress by plotting the induced semi-amplitude of exoplanets discovered by the radial-velocity technique as a function of the discovery year. Following the example of the HARPS spectrograph (Pepe et al. 2000;Mayor et al. 2003), technological research in precision radial-velocity measure- ments have focused on building extremely stable and precise instruments. ESPRESSO (Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations) aims at achieving precision level at 10 cm s 1(Pepe et al. 2014). ESPRESSO was installed at the Paranal Ob- servatory in 2017 to achieve the required precision and sensitivity such to be able to search for and characterize rocky exoplanets in the habitable zone and to study the possible variability of fundamental physical constants. The improvement are still ongoing and new instruments are currently under development. Other spectrographes like CARMENES (Quirrenbach and
CARMENES Consortium 2012, 3.5m, Cala Alto), GIANO (Carleo et al. 2016, TNG, La Palma, Canaries), SPIRou (Artigau et al. 2014, CFHT, Mauna Kea, Hawaï), NIRPS (Wildi et al. 2017, NIRPS, 3.6 m, La Silla), HPF (10 m, Hobby-Eberly Telescope at McDonald Observatory, Texas) aim also at reaching sub-m s 1precision.
1990 1995 2000 2005 2010 2015
103
100
10
1
0.1
0.01
10-3
First Publication Date
Velocity Semiamplitude [Meters/Seconds]
exoplanets.org | 1/23/2019
Figure 1.2: Velocity semi-amplitude as function of time for exoplanets discovered with the radial velocity method. Plot obtained throughhttp://exoplanets.org.
1.2.2 Exoplanets atmospheres
In the era of a new generation of high resolution spectrographs with a resolving power of R⇠1000000, high-precision spectroscopy represent an efficient method not only for detecting exoplanets but also for characterizing their atmospheres and chemical compositions (Snellen 2013; Narita 2013; Deming et al. 2018). The detection of atmospheric signatures requires
’high-fidelity’, this means the ability of reproducing the spectrum across many observations.
For this, one need a very stable/repeatable spectrograph. Therefore, wavelength calibration is also of great importance in this field of research. This requires stability and precision on the spectrograph at the level of / < 10 9. Several approaches were proposed to detect exoplanets atmospheres. Snellen et al.(2015) proposed to combine ground-based high- dispersion (R = 1000000) spectroscopy (HDS) with high-contrast imaging (HCI) aimed at spatially separating the planet from the star. The HDS+HCI technique allows to detect and characterize temperate rocky planets in their habitable zones. On the other side, Wyttenbach
. . Science case 7 et al.(2017) proposed to resolve exoplanet atmospheres with transit spectroscopy, like HEARTS program that is proposed for the exploration of a large sample of gas giants in different mass and irradiation regimes. Still in this context, (Lovis et al. 2017) proposed the idea to develop a coupling interface between the SPHERE high-contrast imager and the new ESPRESSO spectrograph, both installed at ESO VLT. This was aimed to directly detect the temperate Earth-mass planet Proxima b and characterize its atmosphere. The final goal was to separate the stellar light from the planet light by combining high-contrast imaging with high-resolution spectroscopy. For this aspect, again, high-fidelity is needed and now more than ever wavelength calibration of unprecedented accuracy and stability is required.
1.2.3 Spatial-Temporal Variation of fundamental constants in cosmology
The Standard Model of particle physics introduces fundamental constants, which describe the properties of atoms, stars and the whole Universe. Astrophysical tests for the variability of the constants are based on on the observations of quasar spectra of the transition frequencies of the narrow metal absorption lines which are sensitive to the fine structure constant↵(Bahcall and Schmidt 1967). In addition, the molecular hydrogen clouds is sensitive to the proton-to-electron mass ratioµ(Thompson et al. 2009).
In 1999, observations with the HIRES spectrograph at the Keck Observatory showed that↵had a different value in the early epoch of the universe (smaller than today by roughly ↵↵ ⇠10 6).
In their paper,Webb et al.(1999) affirmed thatOur results should thus be regarded as stringent upper limits on any possible time variation rather than a positive detection of a change.
Carroll and Tam(2010) proposed a different approach looking at the fine-structure constant as a scalar field and if fine-structure constant varies smoothly over the universe, the scalar field must have a very small mass. One year later,Webb et al.(2011) announced for a variation of↵ dependent in spatial direction. Data from Very Large Telescope (VLT) have proved a different direction in the Universe as an inverse evolution of↵which is increasing at high redshift. Next generation of high resolution spectrographs will be able to combine a large light-collecting power and an extreme wavelength precision which will be able to assist this field of research.
To investigate the domain offundamental physicsand to allow for a high significance of the results, we need precision and accuracy approaching on cm s 1-level. HIRES (Maiolino et al.
2013) and, before it, ESPRESSO (Pepe et al. 2010) aimed at providing increased measurement accuracy of these two constants by at least one order of magnitude. This requires in turn again an excellent control of the wavelength calibration.
As characterization of exoplanets, exoplanets atmospheres, fundamental constants in cos- mology show how high-fidelity is necessary and to which extent improvements on the resolution
and wavelength accuracy are mandatory to reach new, ambitious observational objectives.
To facilitate the reader’s task, this thesis is presented as follows. In Chapter 1 and 2, the scientific context and technical problem are presented. In Chapter 3, I will present the theory and the experience in the laboratory. Chapter 4 details the first project achieved in this work:
the implementing of a new infrared Fabry-Pérot-based radial-velocity-reference module for the SPIRou radial-velocity spectrograph. In Chapter 5, the central topic of calibration of high precision astronomical spectrographs and a new solution are presented. Chapter 6 describes the outlook for these new spectrographs, and future ideas and projects.
C 2
W
-
High-fidelity spectroscopy calls for precise and accurate wavelength calibrators. This chapter briefly describes the principles of cross-dispersed echelle spectrographs and how their are calibrated, such to illustrate challenges and limits of current solutions.
2.1 Echelle Spectrograph
In astronomy, most of the instruments required to deliver high spectral resolution are echelle spectrographs because of their advantages compared to other designs in terms of signal-to-noise ratio (SNR) performance. and covering a large spectral band. Compact designs make use of a combination of quasi-Littrow configuration, and a "white" pupil design (Baranne and Duchesne 1972). The Littrow configuration consists in a special geometry in which the grating is used so as to the diffraction angle and incidence angle are identical. The diffracted beam is back- reflected into the direction of the incident beam. However diffraction angle and incidence angle are not perfectly identical, thus the mode of operation is called quasi-Littrow. Quasi-Littrow configuration includes high through-put around the blaze peak, mechanical simplicity due to all the optical component lying in the same plane and no loss of photons. According to the
"white" pupil design, the pupil is imaged on the cross disperser in order to reduce the size of the cross disperser and of the camera. Optical designer can use a relatively small camera.
The schematic of a typical echelle spectrograph is shown in Fig. 2.1. The divergent beam from the entrance slit is collimated by a primary mirror. The dispersed beam is refocused and then
9
reflected to a second collimator that produces a "white" pupil at the cross disperser. Following the Littrow configuration of the echelle grating, the same mirror operates as a camera to produce an intermediate "white" spectrum, where all the echelle orders are superimposed.
Figure 2.1: Typically optical layout of echelle spectrograph. The figure is excerpt fromThe fiber fed echelle spectrograph at the 1.2 meter telescope at Kourovskaya astronomical observatory ofA.F. Punanova, V.V. Krushinsky.
Most of the modern high-resolution spectrographs for exoplanets research are a mounted in a gravity-invariant location and are coupled to the telescope by an optical fiber, which feeds the starlight from the telescope focus to the spectrograph, ensuring this way a stable and uniform illumination of the ’slit’. In order to minimize the thermo-mechanical drifts of the instrument, some high-resolution spectrographs are enclosed in vacuum tanks in order to easily control the pressure (better than 10 2 mbar in the case of HARPS). For an overview of high-resolution spectrographs operating at large telescopes, or under construction we refer to (Pepe et al. 2014).
Figure2.2shows a typical example of spectral format produced by a cross-dispersed echelle spectrograph. The so-called echellogramme consists of a number of spectral orders and ar- ranged side-by-side on the detector. Each horizontal line traces the free-spectral range (FSR) of a given order and represents a portion of the spectrum projected on the detector. The spectrum has maximum intensity at the center of the order where the Blaze condition is satisfied. The flux reaches at the edge of the FSR about 50%of its peak value and decreases even further beyond the limit of the FSR due to lower diffraction efficiency. The missing flux is not lost, however, since the same wavelengths chunk will be found on the preceding or following order on the opposite side of the CCD. In summary, the whole spectrum is drawn with increasing wavelength from left to the right and from bottom to top. In order to ensure full coverage of
. . Echelle Spectrograph 11
Figure 2.2: Geometry of the orders in an echelle spectrograph. The near horizontal lines represent the free spectral range (FSR) whereas the red dots are Th-Ar lines and, the box is the physical size of the CCD. Figure excerpt fromFeger et al.(2014).
the spectral range without any gaps in wavelength, the detector most cover at least the FSR of the longest (reddest) order. If the detector is sufficiently large to cover more that only the FSR, the most of the flux is collected.
Most detectors, and notable CCDs, are however color ’blind’, i.e. they cannot distinguish the wavelength or frequency of the recorded photons. On a stellar spectrum, for instance, it would not be possible to determine whether and by how much the absorption lines are Doppler shifted, due to the simple fact that the wavelength scale is missing. Similarly, on the spectrum of a spec- tral lamp, it would be possible to recognize the emission lines and able to determine the pixel coordinates x and y on the detector, but not to ’measure’ their respective wavelengths. However, the opposite is possible if the wavelength of the emission lines are know e.g. from laboratory measurements or from atomic physics: one can use the knowledge of the wavelengths of the spectral lines to assign to each pixel of the detector where such a line is available a wavelength.
By interpolation, one can finally assign the pixel recording the spectrum a precise wavelength.
This fundamental step of spectroscopy is called wavelength calibration.
2.2 Wavelength Calibration for spectrographs
Wavelength calibration is a fundamental step of spectroscopy in general and astronomical spec- troscopy in particular. It provides the wavelength scale for the recorded astrophysical spectrum.
The wavelength scale, hereafter also called wavelength solution, is obtained by feeding the spec- trograph with a spectral reference, i.e. a light source providing spectral lines of well-known wavelength.
On a raw frame (see Fig. 2.3) the wavelength solution would be described by a 2D- function (x,y), The traces of the spectrum on the detector are bent and several pixel wide, all of these pixels ’carrying’ the same wavelength. Therefore, typical data reduction processes first ’extract’ the spectra by converting them into several 1-D spectra I(x, m), where I is the number of photon-electrons per resolution bin (extracted pixel), x is the pixel coordinate in main-dispersion direction and m the echelle order.
Figure 2.3: Example of a raw echellogramme. "True" colors have been superimposed to show the evolution of the wavelength across the detector. Image taken from ht- tps://homepage.univie.ac.at/michel.breger/lehre/AI2/instrumente2.html.
Currently, most of the optical spectrographs are calibrated using standard light sources with accurately known wavelengths. The emission lines from hollow cathode lamps (HCL) or simple gas discharge tubes are reliable standards for wavelength calibration, as these emission lines are intrinsic to the source and arise from atomic level transition. Thorium-Argon (Th-Ar) lamps, for instance, have large number of these lines. They are narrow, dense, cover the entire visible wavelength range and occur, last but not least, at well-known laboratory wavelength
. . Wavelength Calibration for spectrographs 13 (Palmer and Engleman(1983b);Lovis and Pepe(2007);Coffinet et al.(2018)-submitted and under revision). Once the spectra have been extracted, the position of each spectral linexi,m in all the order m can be determined, e.g. by fitting the individual lines with a Gaussian profile. One obtains a list of lines with known wavelength ito which a positionxi,mi can be associated. The wavelength solution is then the function f which links the line position with the wavelength: i = f(xi,mi). Evidently, both the wavelength and the line positions are affected my measurement error or systematics. The best calibration is therefore usually obtained by chi-quared minimization, while watching that a minimum number of free parameters is used.
Several approaches have been used (Baranne et al. 1996;Hall et al. 1994), but the description of them is out of the scope of this work. It should only be mentioned that for the best accuracy it is mandatory to use absolute wavelength references, while for the best precision one has to aim at optimising the measurement precision on the line position.
01.
Correction of bias and
dark
02.
Correction of flat field
03.
Average of bias, dark
and flat field
04.
Creation of an Order Map and Extraction
05.
Fit pixel- wavelength
map and application to spectrum
Figure 2.4: Spectroscopic Data Reduction Steps.
Figure2.4shows a summary of the data reduction process. It starts with bias subtraction, cosmics removal and background subtraction, flat-field correction and ends with the spectrum extraction. Only after these steps, one can proceed with the wavelength calibration.
2.3 Referencing methods
The association of the pixels to the wavelengths needs extreme precision and stability. The spectrograph is usually calibrated before or after the astronomical measurement. Calibrating the spectrograph at different moments in time means to rely on passive stability of the spectrograph or to track possible drifts that may occur between the calibration and the astronomical meas- urement. Relying on passive stability would imply however that the spectrum remains stable on the detector at sub-m s 1level, which, considered the typical resolving power of astronomical spectrographs, corresponds to a level of stability in the line position of about 1/1000 of the widths. This sets extreme stability requirements to the illumination, the thermo-mechanical stability, as well as the index (or pressure) of the surrounding air. Since this this is hardly guaranteed, methods to measure the instrumental drifts have been developed and employed.
The two most common methods will be presented hereafter.
2.3.1 Simultaneous reference
The ELODIE spectrograph was the first echelle spectrograph which used Thorium-Argon lamp also drift reference (Baranne et al. 1996). The key principle on which this so-called simultaneous-reference technique is based is to use two input channels: a scientific and a ref- erence channel. These channels correspond in practice to two fibers injected with the stellar light and a the light from a spectral reference, respectively. The spectra of both channels are simultaneously formed on the detector side by side (see Fig. 2.5). The spectrum from the reference channel will be compared to the spectrum on the same fiber illuminated by the same spectral reference taken during the calibration exposure. In this way, the instrumental drift is determined and the calibration of the scientific channel corrected for.
The simultaneous thorium exposure assumes that the thorium spectrum is extracted and cal- ibrated with the last thorium by itself. The radial-velocity measurement is performed on each channel independently by applying the cross-correlation function (CCF). The drift on the refer- ence channel is thus computed by comparing the CCFs of the observation exposure to the one on the calibration exposure. Then, the wavelength solution of each channel (sky and star) is performed assuming that their drifts are identical. Therefore, the radial-velocity shift measured on the reference fiber is directly applicable to the object fiber and can be used to corrected the stellar radial velocity from instrumental drifts occurred between the time of calibration and the time of observation.
Simultaneous referencing with a hollow-cathode lamp was validated on several (among the most precise) spectrographs, such as HARPS. Various disadvantages remain though, e.g. the
. . Referencing methods 15
Figure 2.5: HARPS First Light spectrum, recorded on February 11, 2003. Simultaneous Thorium-Argon spectrum ("white dots") alongside the object spectrum. FromESO archive.
uncertainties of the calibration that originate from a dependency of the thorium line positions on operating conditions of the spectral lamp or the fact that instrumental drifts are conceptually measured on a fiber which is not the object fiber. In addition, the quality of the thorium lamps seem to set limits for the sub-m s 1regime. Indeed the "good" thorium lamps are no longer on the market. For this reason, alternative lamps have to be investigated.
2.3.2 Self reference
The self reference or self calibrating-technique, consists in superimposing the stellar spectrum with the spectrum of an iodine absorption cells. HIRES-like instruments (Vogt et al. 1994) use iodine cell as a self reference source (Butler and Marcy 1995), which is the best compromise when an absorptive calibration source for the visible wavelength regime is chosen. Figure2.6 shows the spectrum of a star though iodine gas cell, first proposed byBeckers(1979) for solar studies. Later, Marcy and Butler(1992) proposed the same reference source for their precise radial-velocity program for the Lick Telescope. The gas cell is placed on the telescope light path just before the spectrograph slit, and the absorption lines, (whose wavelength are known), are superimposed to the stellar spectrum providing a ’real-time’ reference on the stellar spec- trum itself. It must be pointed out that even in these spectrographs the wavelength calibration
Figure 2.6: Spectrum of star through iodine cell. From slide presentation Radial Velocity Detection of Planets: I. Techniquesby Justina King.
is normally performed in preceding calibration exposures using a thorium lamp. However, the ’fine’ displacement of the stellar spectrum on the detector due to e.g. a radial-velocity shift, is referred to the iodine spectrum. The self-calibration technique has a strong conceptual advantage with respect to the simultaneous-reference technique: the iodine spectrum and the stellar spectrum being produce through exactly the same optical system, they will experience identical instrumental profile IP and possible variations of it. The IP changes are thus supposed to affect possible shift of the stellar and iodine spectrum in the same way. In practice however, the data reduction and analysis will formally depend on a deconvolution of the product of two spectra from an instrumental profile that by itself cannot be assumed stable (slit spectrograph).
Retrieval of the original stellar spectrum, and thus the correct radial velocity, is therefore non perfect and ’photon-consuming’. Furthermore, absorption cell absorb by definition stellar light and are usually limited in spectral band-width. For this reason, more and more project are considering the application of the simultaneous-reference technique.
2.4 Wavelength reference sources
A stable, well-characterized reference with a large number of spectral lines over the largest possible wavelength range is a mandatory for having stellar spectrum with a precise wavelength calibration. The calibrator determines the precision and the accuracy in the measurements of
. . Wavelength reference sources 17 the stellar features shift. In this section, we present some aspects of these references in more details.
2.4.1 Hollow cathode lamps
Thorium-Argon hollow cathode lamps show rich density lines which cover a large wavelength range (from visible to near-infrared) (Redman 2011). The precise measurement of their line position is impacted by numerous blends and by the large dynamic range in line intensities that the Th-Ar spectra show. In addition, they are affected by the ageing effects, e.g. changes in line intensities and small wavelength shifts produced by the slow pressure variations in the lamps. The most sensitive to these effects are the Ar lines which could drift by several tens of m s 1 during the lifetime of a lamp. During wavelength calibration process, it is man- datory to avoid these lines. Th lines drift by few m s 1 , instead, and they can be corrected if we know the drift of Ar lines with respect to Th lines and the sensitivity ratio between them (Lovis and Pepe 2007). HARPS has demonstrated that the best stability achieved with the thorium-argon lamps as a wavelength calibrator is at a level of 30 cm s 1(Lovis and Pepe 2007).
However, for several years such lamps have not been manufactured anymore due to to the unavailability of pure thorium for to hollow-cathod lamps manufacturer. Instead, pure thorium-oxide is used. Unfortunately, Th-oxide introduces impurities (Fischer et al. 2016) that current Thorium hollow cathode lamps contain. Thorium-oxide lamp spectra show undesirable spectral features, called "grass" of unidentified emission lines. Thus, wavelength calibration of high-accuracy radial-velocity spectrographs is compromised by these features. Uranium-Neon (U-Ne) and Uranium-Argon (U-Ar) have been proposed (Sarmiento et al. 2018) instead of Thorium-Argon (Th-Ar) for the calibration of near-infrared spectrographs.
Wavelength calibration of optical spectrographs becomes increasingly difficult if Thorium cathode lamps are not available and no line-lists are available for alternative cathode materials.
Sarmiento et al.(2018) explored Uranium as an alternative for the established Thorium cathodes in the wavelength range from 500 to 1000 nm. Uranium cathode provided a factor of about two more lines than the Thorium cathode. The spectrum of the Ne filling gas shows fewer strong lines and is therefore preferred with respect to Ar. At the end of the analysis, the U-Ne and U-Ar lamps show comparable performances for wavelength calibration.
2.4.2 Iodine gas cell
Molecular iodine vapor provides a dense forest of absorption lines between 5000 and 6200 Å. It is therefore operated typically in a glass cell at about 50 C, indeed, until this temperature no more
iodine could be evaporated. Its spectrum is made by various overlapping molecular transition which are numerous Doppler-broadened by the gas pressure. Therefore, the iodine spectrum can be affected by short-term or long-term variations in iodine pressure and temperature.
The amount of Doppler information of the iodine itself is a function of the signal-to-noise ratio (SNR) of the spectrum that is determined in turn by stellar flux. The star+iodine exposure must therefore be performed at high SNR observations which set strong constraints on the target magnitude and exposure time, respectively. Moreover, the stellar spectrum and thus its radial velocity must be retrieved by a deconvolution process which introduces additional free parameter and is thus by itself ’photon-consuming’.
2.4.3 Laser frequency comb
Murphy et al.(2007) propose for the first time to use a laser frequency comb (Nobel Prize in Physics in 2005,Hall (2006);Hänsch(2006);Glauber(2007)) for the accurate calibration of astronomical spectrographs. The spectrum of such laser frequency combs is made of equally- spaced emission lines whose frequencies fnare determined by the formula fn = f0+n· fr ep
whereof f0is the so-called carrier-envelope offset frequency and fr ep the repetition frequency of the ultra-short pulsed laser emission and, can be related directly to an atomic clock using well established electronic phase locking techniques. Eventually, by determining and fixing accurately f0and fr ep, all optical frequencies of the LFC will have the accuracy and long-term stability of the atomic clocks. The accuracy and stability of laser comb lines are the same of those of the atomic clock, i.e. better than10 12or less than 1 cm s 1, when expressed in terms of radial velocities.
Nevertheless, the spectrum of a laser frequency comb has today still a few limitation when employed as wavelength calibrator for high-precision radial velocity measurements:
1) The natural spectrum of a laser frequency comb is densely packed with emission lines.
The consecutive comb peaks are so close one to each other, that even the resolution of astronomical spectrographs (typically of R = 1000000) cannot solve the lines. Indeed, the current laser repetition rates (⇠1GHz) are too low (by a factor of 10). Therefore, the modes of the frequency comb must be filtered with Fabry-Pérot etalons (Li et al. 2008;
Steinmetz et al. 2008;Braje et al. 2008;Lo Curto et al. 2012). If only 1 out of 10 modes is transmitted, the resultant comb spectrum becomes resolvable by the spectrograph.
On the other hand, there are few difficulties to deal with, e.g. the instabilities and the imperfections in the filtering cavity that could affect the intrinsic comb accuracy or the varying group-dispersion delay across the spectrum that introduces a line shift
