The transmission spectrum of WASP-121b in high resolution with HARPS
Jan Philip Sindel
Space Engineering, master's level (120 credits) 2018
Luleå University of Technology
Department of Computer Science, Electrical and Space Engineering
The transmission spectrum of WASP-121b in high resolution with HARPS
Jan Philip Sindel
Supervisors: D. Ehrenreich
∗& J. Hoeijmakers
†September 17, 2018
This report was written as part of an internship at the Observatoire de Geneve1 for the M2 ASEP program at Université Toulouse III - Paul Sabatier2and the Erasmus Mundus SpaceMaster program at Luleå Tekniska Universitet3. The internship was carried out between the 22nd of January and the 29th of June 2018.
Abstract
Transmission spectroscopy is a powerful tool to analyze the atmospheric composition of exoplanets. In this work we examine data gathered with the HARPS instrument at the 3.6m telescope in La Silla, Chile during three transits of the exoplanet WASP-121b in early 2018.
We find evidence for the absorption of sodium at a 5.4σ confidence level. Additionally we investigate the claim of the occurance of VO in this planet byEvans et al.(2017) employing the cross-correlation technique for high resolution but find no evidence. We show that our model transmission spectrum would induce a signal with low significance, concluding that there is neither confirmation, nor disproval of the claim for now.
∗David.Ehrenreich@unige.ch
†Jens.Hoeijmakers@unige.ch
151 Chemin des Maillettes, 1290 Versoix, Suisse
2118 route de Narbonne, 31062 TOULOUSE CEDEX 9, France
397187 Luleå, Sweden
Contents
1 Introduction 3
1.1 Exoplanets: Historical Context and Motivation . . . 3
1.2 Detection methods . . . 4
1.2.1 Radial Velocity . . . 5
1.2.2 Transit photometry . . . 6
1.2.3 Other methods . . . 7
1.3 Exoplanet atmospheres. . . 9
1.3.1 Theory and motivation . . . 9
1.4 Transmission spectroscopy . . . 9
1.4.1 Cross-correlation technique . . . 10
1.4.2 Spectrographs and spectral resolution . . . 11
2 Data analysis 13 2.1 The data-set . . . 13
2.2 Data reduction . . . 13
2.2.1 Extraction from .fits files . . . 13
2.2.2 Blaze correction and normalization . . . 15
2.2.3 Removal of hot pixels . . . 16
2.3 Telluric Correction . . . 17
2.4 BERV correction . . . 18
2.5 Removal of the star signal . . . 19
3 Transmission Spectrum of WASP-121b 19 3.1 Retrieval of transmission spectrum . . . 19
3.2 Detection of Sodium . . . 20
4 Cross-correlation 22 4.1 Search for VO. . . 23
4.2 Injection of an artificial signal . . . 24
4.2.1 Rotational profile of the planet . . . 24
4.2.2 Movement of the planet through the frame . . . 25
4.2.3 Injection to raw data. . . 25
4.3 Retrievability of model templates . . . 25
5 Discussion and Outlook 26 5.1 Sodium . . . 26
5.2 VO . . . 27
6 Acknowledgements 27
7 List of acronyms 29
1 Introduction
1.1 Exoplanets: Historical Context and Motivation
Since ancient times humanity has wondered if we are alone in the universe. We developed different methods and techniques to explore the night sky, and found that our rocky sphere wasn’t the only one to orbit its host sphere of plasma. These so-called planets were the first point of attack for our search for alien life. With our scientific knowledge steadily advancing we were able to know ever more about these places that were, on a cosmic scale, so close to us. We landed probes on the rocky planets Mars and Venus, studied gas giants like Jupiter and Saturn as well as their moons from orbit and concluded that life as we know it does not exist in our immediate neighborhood.
But our sun was not alone, quite the opposite. There are billions of stars in our galaxy, thousands of which can be seen with the naked eye each night. What if these stars also hosted planets and therefore maybe had the ability to support life? This led to the search for extra-solar planets, or exoplanets for short.
The first exoplanet found around a main sequence star was a big surprise, because it is very different from the planets in our solar system. 51 Pegasi b, its discovery attributed toMayor &
Queloz(1995), is a planet with a mass of 0.46MJup (Brogi et al.(2013)) that orbits its host star at distance of 0.0527AU. This means it’s a gas giant type planet that has an orbital period of only a few days and is very close to its host star. Since then, more planets like it around different stars have been discovered and have been dubbed hot Jupiters.
A lot of different surveys for exoplanets have since been conducted with varying degrees of success.
At the date of this work, there are 3725 confirmed exoplanets4, out of which 1559 reside in multi- planet systems. This provides a great statistical sample that allows us to investigate the population of exoplanets.5 One of the first things we realized was that hot Jupiters, even though they were the most common type of exoplanet found early on, were not nearly as prevalent throughout our galaxy as thought and merely a statistical artifact because of how easy they were to detect. One of the main goals of exoplanet science to this day is to find a planet that is as similar to Earth as possible, and can therefore be able to support life as we know it. The most important quality of such a planet is that its surface temperature allows for water to exist in its liquid form, since that is where life formed on Earth. Since stars vary wildly in the amount of energy they give off to their environment each star has its own habitable zone, defined by the distance to the star where the incident flux onto a planet would allow it to have a surface temperature that can support liquid water. This habitable zone can be extended in both direction by introducing atmospheres and thereby positive or negative temperature feedback cycles, extending the borders of the classical habitable zone (Kasting et al. (1993)). These limits for several different stars and discovered sys- tems are pictured in figure3. The search for earth like planets in the habitable zones of foreign starts had already yielded a couple of candidates, for example the second and third planet in the TRAPPIST-1 planetary system (Gillon et al.(2017)). In a statistical analysisPetigura et al.(2013) found that 11 ˘ 4% of sun-like stars have an earth sized planet in their that receives between 1 and 4 earth-equivalent amounts of energy from their host star.
Ever since the apparent prevalence of exoplanets in our galaxy has become known, efforts have been made to find them and analyse them in depth. During the time of this work the TESS (Terrestrial exoplanet survey satellite,Ricker et al.(2015)) spacecraft was launched and is expected to further advance the statistical data-set of exoplanets available to us. The search for a second earth is in full effect and it might not be long until we find it.
4https://exoplanetarchive.ipac.caltech.edu/index.html, visited on 21/05/18
5A database for all known exoplanet can be found onhttp://exoplanet.eu/
Figure 3: The habitable zone for the solar system and several other discovered planetary systems.
Image Credit: Chester Harman / NASA
1.2 Detection methods
In the search for planetary mass objects outside of our solar system several methods have been proposed and used in order to infer their existence from observational data. The first successful method was the observation of the timing of Pulsar name, leading to the discovery of a planetary system around the Pulsar PSR B1257+12 Wolszczan & Frail (1992). The method used during the detection of the first exoplanet orbiting a main-sequence star was the radial velocity method, utilizing the shifts in the star spectrum induced by the motion of the star around the common barycenter with its planet. The most successful method to this day is the transit-method, observing a dip in brightness of the host star when the planet passes in front of it, which has lead to the discovery of 2911 exoplanets. Other methods include direct imaging, microlensing and astrometry.
Figure 4
The evolution of the set of known exoplanets over the years, separated in color by detection technique. The large increase in transit discoveries after 2013 is due to NASAs Kepler mission.6
1.2.1 Radial Velocity
By measuring the position of spectral lines in the spectrum of a star it is possible to infer its velocity in our line of sight. If there is a planet orbiting said star, the latter will also orbit the common barycenter and therefore change its velocity as measured from our line of sight. The amount of displacement ∆λ is dependent of the wavelength of the observed line λ0 and the velocity in our line of sight v˚sin i by the doppler relation:
∆λ λ0
“ v˚
c sin i (1)
Observing the spectrum of a star that is orbited by a planet produces a quasi-sinusodial signal in the observed radial velocity of the star, whose semi-amplitude K˚ and period are directly related to the mass ratio and orbital properties of the system by:
K˚“ˆ 2πG P
˙13
mpsin i m˚23
? 1
1 ´ e2 (2)
This relation can be used to then obtain the period and minimum mass of the system. Since the inclination is generally unknown and cannot be inferred through spectroscopic measurements, there is a degeneracy between it and the planet mass. This presents the biggest disadvantage of the radial velocity technique. Since the velocity amplitude of a Sun-like star induced by a Jupiter-mass planet at a orbital seperation of 1 AU is only 28.44 m s´1, this method needs extremely stable and precise spectrographs that can detect shifts in the wavelength of star lines in the order of millions of nanometers. One of these instruments is the HARPS spectrograph at the 3.6m telescope in La Silla, Chile, that is stable on long timescales, allowing the detection of planets with high orbital periods (Mayor et al.(2003)).
Figure 5
The radial velocity method, detecting a planet by measuring the position of spectral lines in the star, which changes due to the stars motion around the barycenter. 7
6Image source: https: // exoplanetarchive. ipac. caltech. edu/ exoplanetplots/ exo_ dischist_
cumulative. png, from 21/05/18
7Image source: https: // faculty. uca. edu/ njaustin/ PHYS1401/ _Media/ dopplerWobble. gif, from 21/05/18
1.2.2 Transit photometry
When an exoplanet eclipses its host star in our line of sight, it causes a decrease in the stars brightness, proportional to the relative radius of the planet to the star. This makes it possible to determine the radius of the planet, if the radius of the star is known, and several other physical properties of the system. Although the probability of an exoplanet transiting is low, the first transiting exoplanet was found in 1999 by bothHenry et al.(2000) andCharbonneau et al.(2000), observing HD 209458, a star that was known to host an exoplanet from radial velocity measure- ments. Only 3 years later, the first transiting exoplanet was found byKonacki et al.(2003), using photometric measurements for the initial detection and follow-up RV-measurements to confirm its existence. Today most transiting exoplanets are found with extensive ground- (WASP (Street et al.(2003)), HAT-P) and space-based (Kepler, Corot) photometric surveys, observing thousands of stars at once, searching for periodic dips in brightness. The most successful survey to date, the Kepler satellite, was launched in 2009 and observed 150.000 stars at once, detecting more than 2000 now confirmed planets and several thousand that are still treated as candidates, since they have not been independently followed up yet. Similar to the radial velocity method this method is sensitive to large planets that are close to their host stars, since those cause a bigger dip in brightness and have a higher probability to transit in our line of sight. For circular orbits and uniformly distributed inclinations of the orbital plane it can be shown, that (Borucki & Summers (1984)):
ptransit“ R˚
a « 0.005ˆ R˚ Rd
˙´ a 1AU
¯´1
(3) Observing a transit as a time-series of photometric observations yields a transit lightcurve that can be used to infer physical parameters of the system. A mock-up of such a light curve can be found in figure 6. The most important physical properties of the system that can be retrieved are the planet radius in relation to the radius of the star, the inclination of the system and the transit time. In the same way that RV-measurements are unable to provide data on the radius of the planet, transit-detections do not infer anything about the mass of the planet. If we want to measure the density of the planet we therefore need radial velocity follow-up observations for transiting planets or vice versa.
Figure 6
A single transit of a planet in front of its host star and the corresponding light curve is shown.
The transit time is defined as the time between the points b and f. The theoretical light curve for a star with constant brightness is shown in red, whereas the actual light curve is influenced by
the stars limb darkening and shown in blue. 8
1.2.3 Other methods
Imaging The biggest challenge of taking direct images of exoplanets is that their host star outshines them by several orders of magnitude. Many approaches have been made to eliminate the stars influence. One can use a coronograph to mask out the star to see if the signal of the planet exceeds the noise from the stellar residual. This is easier to do in the near infrared since that is where most exoplanets have the peak of their black-body spectrum. A second method is to take two images of the same star but rotating the telescope and camera in between. If you’re viewing the planetary system top down and substract the two exposures therefore eliminating the time- constant star, a planet that has moved in its position and will appear as a positive and negative signature relative to the noise. This approach yields superior results, when using telescopes with good adaptive optics that have very stable point spread functions (PSFs). Figure 7 shows the detection of a brown dwarf using this method. Both of these methods work best for large planets that have a strong signal and large seperations from their host star so they are spatially resolvable.
(Perryman (2014))
Figure 7: SCR 1845 observed with VLT-NACO-SDI. Two 30-minute observations were made at position angles 0 deg and 20 deg. Division of the two images removes most of the signal of the star (A) and reveals the mid-T dwarf SCR 1845b.(Biller et al.(2006))
Microlensing According to general relativity, gravity distorts space-time and can therefore bend light. A body with high gravity, e.g. a star, can therefore act as a lens for background objects, significantly increasing their incoming flux. In the search for exoplanets this is utilized by looking for stars with such lensing effects, but since the lens and the background source have to pass each other within 1mas (Gaudi(2012)) in our line of sight these events happen rather rarely. If the lens has a companion of planetary mass, the observed signal is influenced by its existence (see Figure 8) and one can derive information about the mass-ratio between the planet and the lens star.
Since microlensing events only happen once per system, confirming the planets found through this method is rather difficult.
Figure 8: The OGLE-2005-BLG-390 microlensing event. The solid line shows the best fit of a Paczynski model to the observed light curve. Observations by different telescopes are marked in different colors. The OGLE light curve is shown in the inset on the top left. The enlarged inset on the right shows the deviation caused by the cool 5.5MCplanetary companion. (Beaulieu et al.
(2006))
Astrometry Astrometry is the precise measurement of a stars position and velocity. If a star is orbited by at least one planet, it causes a displacement of the star due to its barycentric motion.
The goal is to measure the position of the star as precisely as possible to observe the displacement.
So far almost no ground- or spacebased telescopes were able to achieve such a precision, which is why to date only one exoplanet has been found using the astrometry method. Therefore the hopes
lie in the GAIA satellite, which was launched in 2013 and is able to measure the position of a billion stars with a precision that makes it possible to find exoplanets via this method. (Perryman et al.(2014))
1.3 Exoplanet atmospheres
1.3.1 Theory and motivation
The atmosphere of a planet and its chemical composition hold a lot of information. A great example is Earths neighboring planet Venus, that despite only being the second closest planet from our host star has the highest surface temperature in the Solar System due to its thick, greenhouse-gas-rich atmosphere. On the other hand Mars could be a lot friendlier to life as we know it, if its atmosphere was thicker and could trap more of the incident radiation. Investigating the atmospheres of Earth- like exoplanets can therefore give us information about how hospitable they might be to human or other carbon-based, Earth-like life.
We can also learn about processes that happen on the surface of an exoplanet by studying the chemical composition of its atmosphere. The combination of high concentrations of molecular oxygen found in an atmosphere together with a reducing agent such as methane, could point to a large oxygen source to build up this supply. The best candidate for such a strong source is photosynthesis as it is down by biotic life forms on Earth. These combinations of chemical components in the atmosphere that infer the existence of biotic life processes are called biomarkers.
If we manage to find these on another planet, we would have encountered the strongest candidate for life outside of our Solar System. (Kaltenegger & Selsis(2010);Snellen et al.(2013))
Some observations indicate that hot Jupiters, analogue to earth, can have a thermal inversion layer. On earth this is cause by the ozone in the atmosphere in between altitudes of 10 and 50 km. Because ozone is such a strong absorber of star-light it heats up more than the layers below it creating a thermal inversion. This inversion leads to molecular lines no longer being present in absorption but rather in emission, which has been observed for some hot Jupiters, for example by Haynes et al.(2015). The molecular species that are theorized to be responsible for the thermal inversion in hot Jupiters are primarily titanium and vanadium oxide (TiO / VO). These species have rich absorption spectra that are known to make up the spectra of cooler dwarf stars. Since the outer atmospheres of hot Jupiters can reach similar temperatures it is logical to pick these species as strong candidates for the thermal inversion layer. The search for TiO and VO in planet transmission spectra that was sparked by this has not been very successful thus far(Désert et al.
(2008),Hoeijmakers et al. (2015)).
Lastly the chemical composition of the atmospheres of gas giants give a lot of information about the chemical properties of the planet. Analyzing these could yield information about the formation of hot Jupiters, since it is currently unclear if they form close-in to their host stars or further out and migrate in, possibly ejecting other members of their planetary system into outer space. The chemical composition which can be traced to the part of the protoplanetary disk where the planet originated could give further information on that question.
1.4 Transmission spectroscopy
If the orbit of the planet intersects the disk of its host star in our line of sight and a transit occurs, the starlight passes through the outer layers of the planet’s atmosphere and interacts with it. At wavelengths where the atmosphere is optically thick, the planet will appear larger than at wavelengths where the atmosphere is optically thin. This difference in apparent planet radius can be used to infer the presence of certain molecules since their absorbing properties can be calculated from first-principle and measured in laboratories. (Seager & Sasselov(2000)). Since the absorption and therefore the opacity are higher in the core of a line than the wings, we can use the fact that the line profile is also dictated by the local temperature and pressure to gain information about the temperature profile of the planets atmosphere (Heng(2017),Sing et al. (2008)).
Another factor that comes into play when analyzing atmospheres is scattering through aerosols and light reflected by optically thick clouds. As on Earth, aerosols scatter more towards the blue, making planets appear larger in the shorter wavelengths. It has also been found in several transmission spectroscopy surveys that transmission spectra of exoplanets are in general rather featureless, a fact that has been attributed to the presence of clouds that block the parts of the
8Image source: https: // futurism. com/ wp-content/ uploads/ 2013/ 04/ transit. jpg, from 21/05/18
atmosphere that act as absorbing layers.(Pont et al.(2008)).
The process of finding the transmission spectrum of a planet through observations proves difficult, since the absorption by the planet is very small compared to the flux of the host star. The big advantage however is that the planet orbits the star, leading to a relative doppler-shift of the absorption lines over the course of the observation. This is shown in a toy model in figure9. We can use the fact that the spectrum star is constant over the time of the transit and easily remove it while the planet signal remains intact because it varies over the time of the observation. The analysis of exoplanet atmospheres, be it through transmission spectroscopy or day-side emission from the planet has yielded interesting results. The first evidence for a exoplanetary atmosphere was found byCharbonneau et al.(2002) who investigated the transit of the hot jupiter HD 209458 and found that the planet appeared larger in a passband centered at the sodium doublet around 589.3 nm than in adjacent passbands. Sodium was also found byWyttenbach et al.(2015) in the atmosphere of HD 189733b as well as WASP-49b (Wyttenbach et al. (2017)). Brogi et al. (2014) found evidence for the presence of CO and water vapor in the atmosphere of HD 179949 b, a non-transiting exoplanet that they observed during the time of superior conjuction at wavelengths corresponding to the thermal emission of the planet. Recently the atmosphere of the ultrahot jupiter WASP-121b has been found by Evans et al. (2017) to exhibit water features in emission, hinting at a stratosphere and therefore a thermal inversion layer. EarlierEvans et al.(2016) already detected H2O in said atmosphere, as well as evidence hinting at VO absorption in the transmission spectrum. However the claim to latter is not as strong since the molecular absorption by VO is spread over a large amount of lines which could not be resolved due to the low resolution of the data. If confirmed, this would constitute the first detection of an absorber relevant for creating thermal inversion layers in hot jupiters.
Figure 9: This figure shows a toy model of the spectrum of HD 209458b, with the clearly visible phase-dependency of the TiO-emission out of transit and the slanted absorption lines that appear during transit around orbital phase φ “ 0. The strength of both emission and absorption has been enhanced dramatically for clarity purposes. The straight lines correspond to the stellar emission lines, which are stable in time. (Hoeijmakers et al.(2015))
1.4.1 Cross-correlation technique
The molecular species that are easily found in exoplanetary often display strong absorption features at single wavelengths, such as the sodium doublet at 589.3 nm in the optical. Other molecules do
not have strong single lines but rather a forest of absorption lines across a range of wavelengths, caused by fine structure effects. These individual lines are often suppressed by the noise of the stellar residuals that arise from the fact that our assumption about the star flux being time- invariant is not exact. Nonetheless, a technique that can be used to extract information from the transmission spectrum is cross-correlation. It is used to compute the degree of similarity between the noisy data yk and a template xk of the spectral absorption for a molecular absorber:
Cpx, yq “
řN
k“0pxk´ ¯xqpyk´ ¯yq b
řN
k“0pxk´ ¯xq2řN ´1
k“0pyk´ ¯yq2
(4)
The value for Cpx, yq varies between a maximum of 1.0 for positive correlation, i.e. y “ ax ` b with a ą 0 and b constants and a minimum of ´1.0 when a ă 0. The template for absorption is then doppler-shifted to different radial velocities and Cpx, yq is calculated at each RV-step. Since the planetary system has a systemic velocity relative to earth, the maximum correlation in case of absorption would be found at said velocity, since all the absorption lines in the spectrum would line up with the template and therefore be co-added. This technique therefore combines the information on the position of all the absorbing lines to increase the S/N-ratio.
1.4.2 Spectrographs and spectral resolution
In order to take advantage of the co-added information of the spectral line positions used in the cross-correlation technique, we need to be able to spectrally resolve these individual lines. The resolving power of a spectrograph is given by:
R “ λ
∆λ (5)
where ∆λ is the smallest difference in wavelengths that can be distinguished at a wavelength of λ. Since the size and therefore weight of the spectrograph grow proportionally to its resolving power, the spectrographs used in space based obervatories like the Hubble Space Telescope do not exceed R « 102 in the optical. Ground-based instruments however can reach far higher, up to the order of R « 105. The HARPS spectrograph (Mayor et al. (2003)), based at the 3.6m telescope in La Silla, Chile has a spectral resolving power of R “ 115000 when used in high accuracy mode. It is stable over very long timescales which makes it an ideal instrument to use for planet-hunting through the RV method. Shown below in figure 10 is the difference of a VO absorption spectrum computed using the Exomol linelist (Tennyson & Yurchenko(2012)) and the Helios opacity calculator (Grimm & Heng (2015)), assuming the analytical formula by Heng &
Kitzmann(2017) at spectral resolutions of 103 and 105. It is easy to see that while only showing rough bands at low resolution, the individual lines are well resolved at the resolution of HARPS and therefore make a great candidate for the cross-correlation technique. Future endeavors in the field of high-resolution spectroscopy include the NIRPS-spectrograph, a sister instrument to HARPS in the infra-red (Wildi et al.(2017)), and ESPRESSO which is the successor to HARPS and is currently being installed at the VLT (Pepe et al.(2010)).
Figure 10: A slice of the calculated VO transmission spectrum for WASP-121b, shown at two spectral resolutions. It becomes apparent that while at lower resolutions the rough shape of the transmission spectrum is still easily seen, the information about the individual lines is lost opposed to the high-resolution spectrum. The latter is therefore beneficial for investigations using the cross- correlation technique.
2 Data analysis
2.1 The data-set
The target WASP-121b was discovered by the WASP survey in 2015 and followed up with the CORALIE spectrograph byDelrez et al. (2016). It was revealed to be a hot Jupiter in a polar orbit around its host star. The following data was taken from the discovery paper and used in this work whenever needed:
Variable Value
Orbital period P [d] 1.2749255 Transit width W [d] 0.1203
T0 [HJD] 635.0832
Orbital semi-major axis a [AU] 0.02544 Orbital inclination i [deg] 87.6
Mass MP [MJ up] 1.183
Radius RP [RJ up] 1.807 Equilibrium temperature [K] 2358
Table 1: Summary of the values adopted fromDelrez et al.(2016) for this work.
The data analyzed in this work consists of three nights of observations, conducted on 31/12/2017, 09/01/2018 and 14/01/2018 with the 3.6m Telescope at the European Southern Observatory (ESO) in La Silla, Chile, using the HARPS spectrograph. A summary of all the data we analyze in this work can be found in the table below.
Night Date Blazeframes λ frames Science Frames
1 31/12/17 2 4 35
2 09/01/18 2 4 55
3 14/01/18 2 4 50
Table 2: The data taken from the 3 nights of observation of transits of WASP-121 in early 2018.
The blazeframes are used to correct for the wavelength dependent dispersion and therefore intensity of the spectrograph, while the λ frames hold the wavelength calibration.
HARPS is an echelle spectrograph, splitting its wavelength range (380 nm to 690 nm) into 72 so- called spectral orders, each spanning 40 ´ 70nm. The spectra retrieved from HARPS are therefore 2D, which can be seen in figure11.
2.2 Data reduction
2.2.1 Extraction from .fits files
In order to obtain the wavelength calibration for the science frames, we combined all the calibration measurements (λ frames) taken the night of the observation using the mean value for each pixel in each spectral order, creating three different wavelength matrices corresponding to the three different nights. The blaze function represents the tendency of the spectrograph to disperse less light towards the edges of each spectral order and more towards the center and has to be corrected for during the reduction of the science frames. We again combined the two blaze calibrations taken each night using the mean and received the sensitivity for all 72 orders. Every science frame consists of 72 orders of the HARPS spectrograph, with 4096 pixels each. We extracted each order individually and put them together in time series. A raw image of one of the science frames can be found in figure11, while the time series for order 57 of the first night can be found in figure 12. We estimated the errors in the pixel-count in each pixel by taking into account the photon noise that corresponds to an error of σ9?
N , where N is the amplitude of the signal and the read-out-noise that is instrumental and is on the order of 10 per px. We add these two errors up by calculating the square root of the sum of their squares. These initial errors get propagated throughout the analysis using gaussian error propagation methods. In addition to the spectra, we
extracted several variables from the header of the .fits files, that are calculated and stored by the HARPS data reduction pipeline:
• The mid observation time of each exposure, which together with the transit mid-point and period was used to calculate the orbital phase of each exposure
• The average airmass during each exposure, by building the mean of airmass at start and end
• The earths barycentric velocity (BERV) respective to the target star in each exposure
Figure 11: The 24th of 35 exposures taken during the first night of observations on 01/01/2018.
We notice higher flux when looking at higher spectral orders, corresponding to longer wavelengths and are able to see several absorption lines in the spectra.
Figure 12: Time series of spectral order 57 of the first day using the extracted phase- and wavelength-axes. We can clearly see the strongly absorbing sodium doublet as well as the in- fluence of the blaze, increasing the flux in the center of the spectra.
2.2.2 Blaze correction and normalization
To account for the dispersion of the spectrograph across each order, we use a mean of the blaze- frames, exposures taken at high intensity at a short exposure time. We remove the variation in sensitivity by dividing each exposure in each order by its respective blaze. Afterwards we nor- malize the spectra to one by dividing them by their mean. The results for the time-series and an indivdual spectrum can be seen in figure13. There is a residual gradient in each spectrum that is not accounted for by the blaze. We eliminate this gradient through binning the spectrum to 8 points using the median for each bin and fitting out the linear trend.
Figure 13: Time series of spectral order 57 after correcting for the influece of the blaze and normalizing the flux. The overall low level according to the colorbar is caused by a few hot pixels that can be seen in the upper right corner.
2.2.3 Removal of hot pixels
There are several causes for hot pixels in the data, from cosmic rays to oversensitivity of individual pixels. We calculate the average out-of-transit spectrum and divide it out of all the spectra. The resulting residuals are scanned for any outliers more than 3σ above the median of each residual.
The values of these outliers are set to the median value of their respective spectrum. The success of the process is documented in figure14.
Figure 14: Time series of spectral order 57 after eliminating hot pixels.
2.3 Telluric Correction
Observations taken from Earth’s surface have to take into account several effects that can influence the data. Since this work relies on absorption by molecules, it is important that any absorption from Earth’s atmosphere is removed before looking for signals from any other source. In our case the strongest contamination happens through telluric water absorption. Since all of our observations are taken in the rest frame of Earth there is no shift in the position of these water lines. A telluric absorption model was obtained using ESO SkyCalc (Noll et al. (2012); Jones et al.(2013)). We treat each spectral order individually, since some have higher amounts of contamination than others and some might suppress their tellurics entirely within their noise. We start by normalizing the telluric absorption model after cutting it to match the wavelength range of each spectral order and check for lines that are deeper than a 3σ deviation from the median. If the spectral order has such lines that are deep enough to be considered contaminating the spectrum the telluric absorption model is fitted to each exposure of the order using a powerlaw. Each exposure corresponds to a certain airmass and we find that the power of the fit and the airmass correlate linearly, if the telluric contamination is stronger than the noise-level. One example for that case can be found in figure15. If we find that correlation to be existent, we fit the power to the airmass using a linear 1D model and subsequently divide out the telluric absorption in each exposure with its power corresponding to the fit. The fit for a single exposure of a single order can be found in figure16.
The removal of the tellurics for one order can be found in figure17. This correction removes the variability of the telluric lines due to the airmass, and therefore eliminates any artificial signals the residuals might have produced.
(a) Timeseries of the airmass and the fitted power for the telluric absorption model for each exposure.
(b) The fitted power as a function of airmass, with a linear fit.
Figure 15: This figure shows the clear correlation between the airmass and the strength of the the telluric absorption and confirms that the time-variation of the airmass is well-accounted for using our method.
Figure 16: Spectrum of exposure 14 of the spectral order 58 of the first night of observations with the fitted telluric absorption model.
Figure 17: Time series of spectral order 57 after the removal of the telluric lines.
2.4 BERV correction
Since our observations were taken during three different nights, the relative motion of Earth towards the observed target was different in each observation, due to the varying orbital motion of Earth as projected along the line of sight. We extracted the magnitude of this shift from the header of the science frames and used that information to shift each spectrum to the same rest frame respective to the star. This shift also includes minor differences in the Earth barycentric velocity during the night of each observation, but these variations are small and only lead to shifts on the sub-pixel
level. The shift to a different radial velocity happens by Doppler-shifting the wavelength axis to a different velocity by multiplying it with the Doppler-factor
b1`β
1´β with β “ Vc and afterwards linearly interpolating the spectrum onto this shifted wavelength axis. We refrain from showing a figure for this process, since it does not yield any visible differences.
2.5 Removal of the star signal
After removing all the time-variant effects, the next step was to remove the time-constant signal of the host star from the data, so that we obtain only the signal of the planet in the residuals.
We took the transit duration W from the discovery paper (see table 1) in combination with the phase information for each exposure to compute the average out-of-transit spectrum which can be viewed as constant since the host star spectrum does not change significantly over the time-scale of the observations and it does not include the variations induced by the moving planet signal in the in-transit frames. We then divided each exposure by this average out of transit spectrum and were left with only residuals with a moving planet signal hiding in them. The result for one spectral order can be seen in figure18.
Figure 18: The residual spectrum of spectral order 57 after the removal of the time-constant star spectrum. This corresponds to the transmission spectrum of WASP-121b in the stellar rest frame.
3 Transmission Spectrum of WASP-121b
3.1 Retrieval of transmission spectrum
Transmission spectroscopy uses the fact that the planets spectrum is doppler-shifted to different wavelengths in each of the exposures due to the planets motion around its host star and therefore is not constant in time. Knowing the relative radial velocity of the planet to the star it is possible to shift all exposures to the planet rest frame and add them up to obtain the planets spectrum. We used the orbital information from the discovery paper together with the phase information from our data to calculate the planets orbital velocity in each frame and shift all the exposures to the planets rest frame. This can be seen in figure19. Subsequently all the in-transit exposures of the individual orders were added up for all three nights of observation and constitute the transmission spectrum of WASP-121b.
Figure 19: The time series of spectral order 57, shifted to the planet rest frame. For visibility reasons this was done before the star removal to display the slope created by the large orbital velocity change of the planet and thereby induced doppler-shift in each exposure.
3.2 Detection of Sodium
One of the most interesting spectral orders is order 57, which ranges from 585 to 591 nm, and therefore includes the sodium doublet around 589.3 nm. Sodium has been discovered in the at- mospheres of several hot Jupiters so far (seeWyttenbach et al.(2017,2015); Charbonneau et al.
(2002)), but not in the atmosphere of WASP-121b. We filter out broad-band spectral variations caused by variations in the Earth’s atmosphere or the instrument by convolving the residuals with a Gaussian kernel with a width of 150 px. The resulting trend curve is divided out of the residual spectra to complete the filtering. The wavelength-axes of the three nights were not identical, we therefore interpolated all exposures to the wavelength calibration of the first night. Afterwards we built a weighted mean from all the in-transit exposures shifted to the planet rest-frame of order 57 for all three nights. The spectrum of each night was weighted with its propagated error. The result can be found in figure20. Even though the noise level is high we can see a downward trend around the positions where we would expect the sodium doublet, which is red-shifted to the systemic ve- locity of the system.To further enhance this part of the spectrum, we binned the data, combining 30 data-points per bin, building the mean and its error. The result for each individual night as well as the average of all three is shown in figure21. We see the absorption in the D2 line is clearly visible and significant in all three nights as well as the average, whereas the D1 line is weaker in the second night, where it is embedded in the much higher noise. To investigate the absorption strength for each night and all the nights combined, we create a passband filter around both lines spanning 12Å from 5888 to 5900 nm. We compare the flux in this passband to two equally broad neighboring bandpasses in the red and blue and thereby construct the relative absorption strength.
To investigate the same feature inside the absorption lines, we create bandpasses of varying sizes, centered on the absorption lines. The reference bandpasses in the blue and red are kept for all bandwidths. The results can be found in table3. We then fit Gaussian absorption profiles to the raw, unbinned data, using a Levenberg-Marquardt algorithm and least squares statistics. The best fit using with the binned data can be found in figure22, the fitting parameters are listed in table 4. The errors for the fit-parameters are determined from the covariance matrix.
∆λ[Å] 0.75 “ 2 ˆ 0.375 1.5 “ 2 ˆ 0.75 3 “ 2 ˆ 1.5 6 “ 2 ˆ 3 12 Night 1 0.423 ˘ 0.124 0.318 ˘ 0.087 0.249 ˘ 0.063 0.128 ˘ 0.045 0.071 ˘ 0.029 Night 2 0.418 ˘ 0.232 0.375 ˘ 0.161 0.251 ˘ 0.115 0.258 ˘ 0.081 0.212 ˘ 0.052 Night 3 0.255 ˘ 0.138 0.196 ˘ 0.097 0.106 ˘ 0.070 0.013 ˘ 0.050 ´0.012 ˘ 0.032 All nights 0.365 ˘ 0.099 0.297 ˘ 0.069 0.202 ˘ 0.050 0.133 ˘ 0.035 0.090 ˘ 0.022 Table 3: The relative combined absorption strength of the sodium doublet in the planet-frame transmission spectrum for several bandwidths ∆λ. We observe that the significance of the detection is constant over all three nights and over the several bandpasses. Outliers lie in the third night, that produces even a negative absorption depth for the 12Åpassband. The cause for this phenomenon is rooted in the behaviour not in the lines but between them, where the transmission spectrum for the third night is high enough on average to diminish the signal of the absorption lines over the range of the passband. when we look at a smaller passband, the absorption is significant again.
Overall is the S/N for All nights on the order of 4σ.
Line Mean [Å] Absorption [%] σ
D1 5896.45 ˘ 0.16 0.179 ˘ 0.068 0.36 ˘ 0.16 D2 5890.76 ˘ 0.04 0.495 ˘ 0.103 0.16 ˘ 0.04
Table 4: The fit parameters for the Gaussians fitted to the transmission spectrum at the positions of the absorption lines. The significance of both lines (2.6σ for D1 and 4.8σ for D2) combines to a significance of the detection of 5.46σ
Figure 20: Average in-transit spectrum in the planet frame of WASP-121b. There is a visible downward trend around the position of the sodium doublet in the system frame.
Figure 21: Average in-transit spectrum in the planet frame of WASP-121b, binned by a factor of 30. We notice the absorption is significant in the D2 sodium line in all 3 nights as well as on average. For the D2 line the absorption is significant for both the first and the third night, while being lost in the higher noise of the second night. However it is still detectable in the average.
Figure 22: Average in-transit spectrum in the planet frame of WASP-121b. It is overplotted with a spectrum that is binned by a factor of 30. The best gaussian fit for both of the absoption lines can be seen in red.
4 Cross-correlation
As discussed in the introduction the cross-correlation technique is very powerful at detecting ab- sorbing species that not only have a few strong absorption features, but, at high resolution, exhibit
entire forests of absorption lines with a very specific shape. We employ this method to search for the evidence of VO absorption in the transmission spectrum of WASP-121b.
4.1 Search for VO
The model transmission spectra were computed by J. Hoeijmakers using the Exomol linelist (Ten- nyson & Yurchenko(2012)) and the Helios opacity calculator (Grimm & Heng (2015)), assuming the analytical formula byHeng & Kitzmann(2017). It corresponds to a nominal cloud-free planet with a VMR of 10 ˆ 10´8, which is roughly in line with the expected metallicity of the planet in the absence of chemical mechanisms that would deplete VO. This is a conservative model. Since we observed the spectra at a lower resolution than the transmission model, it has to be brought to the same resolution as our instrument, so we can interpolate it onto our wavelength grid with- out losing information. This is done by convolving the model spectrum with a gaussian that has the width of a delta-line function observed with HARPS in each order. Subsequently the model spectrum is interpolated onto the wavelength axis of the respective observation. To account for large-scale variations in the residuals caused by instrumental imperfections, they are again filtered through a 150px wide Gaussian, as has been done during the search for sodium. To avoid a bias caused by the higher noise in the lower spectral orders, each pixel of the science-frame residuals was weighted with its respective standard-deviation in time squared, so that highly variable pixels are suppressed. The residuals were then again shifted to the planet frame. We constructed a cross-correlation function that calculates the cross-correlation coefficient of the residuals with the transmission model while the latter was shifted from radial velocities of ´100 km s´1to 100 km s´1. This function was applied to each in-transit exposure of each order for each of the three nights.
Figure23shows the mean CCF of all as well as the individual nights. If there was a signal induced by a planet in the residuals we would expect it to exhibit a cross-correlation peak at the systemic velocity of the system, which is vsys “ 38.35 km s´1. However there is no significant peak in the cross-correlation functions found for any of the days. This leads us to the conclusion that there is no VO in the atmosphere of Wasp-121b at the levels that we are sensitive to.
Figure 23: The co-added cross-correlation coefficients for all exposures and all orders. Interesting is the region around the systemic velocity, since that is where a planetary signal would show up.
However, there are no notable features.
4.2 Injection of an artificial signal
Our non-detection of VO does not necessarily mean that this molecule does not exist in the atmo- sphere of WASP-121b, but that it is either occluded by clouds or similar mechanisms, or does not absorb strongly enough. We want to check how sensitive our data analysis routine is to an artificial transmission spectrum that we inject into the data prior to the start of this analysis. The following section describes how we process the model spectrum to account for all the physical effects that affect the shape, depth and position of the transmission spectrum.
4.2.1 Rotational profile of the planet
Any object that orbits another body in close proximity is subject to tidal forces, which almost always lead to so-called tidal locking of the smaller orbiting body. The most prominent example of tidal locking is earths moon, of which we only see one side, since its orbital period around Earth is equal to its rotation period around its axis. The same happens to hot Jupiters, which is why we assume the rotation period for WASP-121 b to be equal to its orbital period. The rotation of the planet itself influences the shape of the absorption lines, since one half of the planet and therefore also its atmosphere is rotating towards our line-of-sight, blue-shifting its part of the transmission spectrum, while the other part is rotating away from our line-of-sight, red-shifting its part of the spectrum. Since the transmission happens only in the atmosphere a the edge of the planet, the rotational broadening profile is dominated by these quickly rotating edges. To model the broadening profile of a single line due to the rotation of the planet, we constructed a simple 1D model of the atmosphere. The atmospheric scale height for WASP-121b is
H “ kT
µg « 1000 km « 0.008RP (6)
assuming a primarily molecular hydrogen atmosphere, which is common for hot Jupiters. Since the part of the atmosphere responsible for transmission has a typical size of 5-10 atmospheric scale heights, the absorbing part of the atmosphere makes up for approximately 5% of the planet radius. Our transmitting atmosphere model stretches from 0.975 to 1.025 planet radii. We treat the atmosphere as a rigid rotating ring and split this ring into 100 parts of equal surface area.
We then associate each of these areas with their respective rotational velocity. We model a non- broadened line as a Gaussian with an amplitude of one and a standard deviation according to the HARPS spectral resolution in each order. Since each of the 100 slices of atmosphere is responsible for equal amount of transmission, we split the Gaussian into 100 Gaussians with an amplitude of 0.01 and Doppler-shift each of the Gaussians to match their rotational velocity. An example can be found in figure24. This rotational broadening shaped was computed into a convolution Kernel and used to model the effect of the rotational broadening for the transmission spectra, by convolving them with this kernel. Through this method we intrinsically also account for the limiting spectral resolution of HARPS (Brogi et al.(2016)).
Figure 24: The rotational convolution Kernel for spectral order 46. It shows the spread of a delta function that has been broadened to match HARPS resolution (orange) as a result of the planetary rotation. The strong influence of the fast rotating edges of the atmosphere can be seen as most of the flux is doppler-shifted by more than 25 pixels.
4.2.2 Movement of the planet through the frame
The next effect we have to take into account is that during each exposure the planet is still moving with respect to our telescope, shifting the lines continuously through the frame. We calculate the difference in orbital velocity from the start to the end of each frame and use that to construct a box-kernel, modeling the continuous shift of the lines. We convolve our rotationally broadened transmission model with this kernel and receive the transmission spectrum as it has to be injected into the raw data.
4.2.3 Injection to raw data
Since we want the transmission model to originate from the planet, we shift it to the planet rest frame in each exposure and subsequently apply a correction for the berv and the systemic velocity, so that the spectra are in the planet restframe in comparison to the observations taken in earths rest-frame. The transmission models are then injected by multiplying the raw in-transit frames with the model in each order.
4.3 Retrievability of model templates
We reduce the raw frames with the injected models using the same code as for the non-injected models before and cross-correlate them with the same spectral-resolution adjusted templates. To see the difference the injection of the model makes we now overplot the CCFs for the raw data with the ones for the injected data in figure25. Additionally we plot their difference to be able to estimate how much signal strength we gained through the injection. We judge that the injection was a success, since the signal of the CCF is stronger by 5 ˆ 10´3. The problem is that the noise-level of the raw ccf, computed simply by the standard-deviation is of the order 4 ˆ 10´3, leading to the conclusion that our transmission model alone does not induce a significant signal.
It is however also visible, that the additional signal by the injection is broadened, mostly due to the rotation profile of the planet and the movement of the planet during exposures, so that it might be beneficial to bin the data to get more of the broadened signal into the bin closest to the systemic velocity. Additionally while the injection itself is barely of the order of 1σ, the peak at
Vsys is visible and gives further hints towards the non-existence or non-detectability of VO in the atmosphere of WASP-121b.
Figure 25: A comparison of the cross-correlation functions for the raw data in orange and the data with the injected model in blue. The difference is seen in black. We conclude that the injection has been successful as the additional signal is retrieved at the position systemic velocity. However the overall peak induced by the injection is not significant, leading to the conclusion that our sensitivity to the model is limited.
5 Discussion and Outlook
5.1 Sodium
The detection of sodium is a first for WASP-121b, after (Evans et al. 2017) already found evidence for water vapor and CO in emission. Following similar procedures asWyttenbach et al. (2015), we were able to establish a detection significance of 5.46σ for the absorption in the Fraunhofer line doublet. Other time-variable processes that can influence a signal like this are the Rossiter- McLaughlin-effect and telluric sodium. The former arises from the fact that during a transit the planet blocks two differently rotating halves of the star at different times in the observation leading to slightly red- and blueshifted absorption profiles over the course of the night. Here however, the planet is in a polar orbit (Delrez et al.(2016)), we therefore expect no RM-effect, since the parts of the star the planet masks during its transit have the same rotational velocity towards our line of sight. Additionally the planet moves very fast due to its close in orbit, and the relative Doppler- shifts caused by that far exceed the level of RM we expect due to the comparatively slow rotation rate of the star (Delrez et al. (2016)). The second time-variable process is the absorption by telluric sodium. This is where the high systemic velocity of the system of Vsys“ 38.35 km s´1 acts as and advantage since the telluric sodium absorption is shifted out of the for us relevant range by that constant redshift. The following steps to be taken after this discovery are to fit a dedicated absorption model to the lines and retrieve an atmospheric temperature profile as was mentioned in the introduction. The center for the absorption for both lines according to the gaussian fits deviates slightly from the expected value, which could be explained by winds in the transmitting atmosphere. A simulation like this would however not fit the scope of this work, but we report the significant first detection of absorption by sodium in the atmosphere of WASP-121b.
5.2 VO
The trade-off for high-resolution spectrographs lies therein that one has to deal with less flux per wavelength element. While usually exceeding at the search for molecules with absorption line forests like VO, in this case lower-resolution spectroscopy would have been just as effective. The cause for that is the fast rotation of the planet, which broadens absorption lines significantly, as well as the comparatively long exposure times that are needed to obtain high S/N-spectra. These lead to large changes in orbital velocity during the exposure further broadening the spectrum.
This could be counteracted by using ESPRESSO, the successor of HARPS which was recently installed at the VLT. The increase in size of the primary mirror of the telescope from 3.6m for HARPS to 8m for ESPRESSO allows for the same amount of light to be collected within much shorter exposure times. Retaining the high resolution could have the advantage, that for a known absorber the cross-correlation peak could be measured with very high precision and accuracy, giving the opportunity to obtain knowledge on the actual rotation profile of the planet. Evans et al.(2017) have claimed the possibility of VO-absorption from a feature found in low-resolution transmission spectroscopy data. We investigated that claim using a VO transmission model but were unable to find any evidence for its existence. After injecting our model into our own data, we found that the additional signal is barely significant and therefore hard to detect and easily suppressed by noise. However our model made very conservative assumptions, and still makes a visible difference in the cross-correlation function. we can therefore assume, that any better-case scenario would have even higher significance. What still can be done to further investigate the claim is to construct a transmission model that produces a signal analogous to the one Evans et al.(2017) found and check if this model has a higher retrievability from our data. The claim to the detection is primarily doubtful because from element abundances TiO would be expected in higher concentration than VO and would have been easier to find. However, no evidence for TiO absorption has been found. The search for the molecules believed to be responsible for creating thermal inversion layers in hot Jupiters continues for now.
6 Acknowledgements
This project has been funded with support from the European Commission. This thesis reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. Co-funded by the Erasmus+ Programme of the European Union.
First and foremost I want to thank my supervisor Prof. David Ehrenreich, for making this intern- ship and my stay at the observatory possible. Jens, thank you for never being farther than an e-mail away, accepting my at times questionable working hours and answering all my questions as easily understandable as I hope I one day will be able to answer questions asked from me. I want to thank the Planetary Atmospheres group for the highly informative but still super fun weekly WHAMs, that not once didn’t end on time. I want to thank every single person I have met at the observatory during my time here, I have enjoyed talking to each and everyone of you, may it be at or off work, about scientific, social or private topics. I want to say special thanks to: My officemate Leo for amazing Karaoke nights every wednesday and a place to sleep whenever either the observatory or I were too far gone. My other officemate Julia, for indulging my horrible jokes.
And the good ones as well. Aurelien, for making me rediscover my love for error propagation and answering all the questions about sodium that ever came to my mind. Emiliy, for the not-so-rare spontaneous wine sessions on the roof. Heather, Nick and the entire CERN Wildcats Rugby team for teaching me about priorities (and tackles). Manu (Pfrt!), for making me enjoy the excellent french language a bit more. Lorenzo, for teaching me how to properly prepare italian cuisine.
Everyone that I forgot to mention here, for not being mad at me about that. Clement, Lena and Sebastien, for making living at the observatory feel a lot less lonely than I initially feared.
I want to thank my colleagues as well as my lecturers from the M2 ASEP program for teaching me more in a single semester than I thought was possible, while still having fun. I also want to thank my SpaceMaster family for providing me with a place that feels like home, no matter where I go. Thank you, to all my friends back home for not forgetting about me. And last but not least I want to thank my family, for always having my back and pushing me over the finish line, time and time again.
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7 List of acronyms
VO Vanadium Oxide
TiO Titanium Oxide
CO Carbon monOxide
HARPS High Accuracy Radial velocity Planet Searcher NIRPS Near Infra Red Planet Searcher
ESPRESSO Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations WASP Wide Angle Search for Planets
HAT-P Hungarian Automated Telescope - Planet
TRAPPIST TRAnsiting Planets and PlanetesImals Small Telescope TESS Transiting Exoplanet Survey Satellite
VLT Very Large Telescope
ESO European Southern Observatory Mjup Jupiter mass
AU Astronomical Unit
BERV Barycentric EaRth Velocity CCF Cross-Correlation Function RM Rossiter-McLaughlin effect PSF Point Spread Function
RV Radial Velocity
