The Impact of Stellar Magnetic Activity on the Radial Velocity Search of Exoplanets

The impact of stellar magnetic activity on the radial velocity search of exoplanets Ansgar Wehrhahn supervised by: Nikolai Piskunov Oleg Khochukhov ver. 1.0 July 7, 2017 ABSTRACT Radial velocity measurements are critical in finding and confirming exoplanets. To confine the parameters of the planet we naturally want to minimise the errors on the measurement. However the observed measurement error is now on the same order as the precision of the instrument. This so called jitter is related to the stellar activity (Wright 2005), i.e. the magnetic field of the star. In this paper we investigate if we can discover any correlation between the radial velocity variation and the magnetic activity of the star using HARPSpol spectra for the two stars Epsilon Eridani and GJ674. Populärvetenskaplig sammanfattning Radialhastighetsmätningar är ett viktigt verktyg för att hitta och bekräfta exoplaneter. Osäkerheten från mätinstrumenten är dock fortfarande av samma storlek som influenser av olika stjärnatmosfäriska processer. Här undersökar vi konkret hur stjärnans magnetfält påverkar radialhastighetsmätningar. I denna studier använder vi oss av data från det noggranna instrumentet HARPS för att undersöka två stjärnor, Epsilon Eridani och GJ674. Med den föreliggande spek- troskopsika materialet kan vi inte hitta ett samband mellan magnetfältstyrkan och radialhastigheten. 1 The Earth is the cradle of humanity, but one cannot stay in the cradle forever. – Konstantin Tsiolkovsky Contents 1. Introduction4 2. Theory 5 2.1. Radial Velocity Search For Exoplanets......................5 2.2. Intrinsic Stellar Noise...............................6 2.3. Zeeman Effect....................................7 2.4. Stokes Parameters.................................8 3. The Instrument9 3.1. HARPS.......................................9 3.2. HARPSpol..................................... 12 4. Target Selection 13 4.1. Epsilon Eridani................................... 14 4.2. GJ 674........................................ 16 5. Data Reduction 18 5.1. Calibration: Bias- and Flatfield.......................... 19 5.2. Extracting the 1D Spectra............................. 20 5.3. Wavelength Calibration.............................. 22 5.4. Continuum Normalization............................. 23 5.5. Stokes Spectra................................... 24 5.6. Least Squares Deconvolution (LSD)....................... 25 6. Calculation Of The Radial Velocity 27 7. Determination Of Longitudinal Magnetic Field 30 8. Result 32 A. Code 35 A.1. SearchForTargets.py................................ 35 A.2. GetCorrelation.py................................. 37 B. Acknowledgements 48 References 49 3 1. Introduction Since the first discovery of an exoplanet just over two decades ago (Mayor and Queloz 1995), thousands more have been discovered. However most of these planets are large giants, as the detection of smaller earth like planets continues to prove difficult. One of the major methods for the discovery of exoplanets is the radial velocity method, which utilizes the gravitational impact of the planet on its host stars motion and therefore its radial velocity. The key limitation for these observations is the precision of the measurements, which is limited by both the instrument (e.g. readout noise of the detector) and stellar processes (e.g. turbulence). In the past great progress was made in improving the instruments such like HARPS (Mayor et al. 2003), ELODIE (Baranne et al. 1996), and many others. However their precision has now reached the same order of magnitude as the intrinsic stellar noise. Therefore it is necessary to find new ways to filter out stellar influences. Here we correlate the stellar magnetic field with the uncertainty of the radial velocity measurement, using the same measurements to calculate both, to investigate the possibility of using their relation to improve radial velocity measurements. The ambition now is to reach instrumental precision better than 10 cm s−1. Similar studies (Hébrard et al. 2016; Hussain et al. 2016) exits, but use much more com- plex methods to obtain the magnetic field, and to relate this measurement to the radial velocity measurements. Sec. 2 describes the theoretical background, while Sec. 3 goes into detail on the instrument in use here HARPS. It continues with Sec. 4 and Sec. 5, which describe the observed stars and the data reduction respectively. Next in Sec. 7 the calculation of the magnetic field is explained. After that Sec. 6 deals with the problems of getting the radial velocity uncertainties. Finally Sec. 8 discusses the results. 4 2. Theory 2.1. Radial Velocity Search For Exoplanets The radial velocity method is the second most successful method for discovering new exoplanets, after the transit method1. In fact the transit method often only provides candidates that need to be confirmed using the radial velocity measurements. It is also a very important tool for the determination of the planetary parameters like mass and speed. As the name suggests the method uses the minute periodic radial velocity shifts created as the host star rotates around the shared center of gravity of the star-planet system. Fig. 1 shows a sketch of the process. The radial velocity can be measured using the Doppler shift of the stellar spectrum. This way the orbital period P and the minimum mass MP sin(i) can be determined, where i is the inclination of the planet orbit. Only Mp sin(i) can be measured since the inclination is unknown and the radial velocity only describes the fraction of the movement in the direction of the observer (i.e. Earth). However if the planet is transiting the star, that can be used to determine the inclination i. The size of the radial velocity shift scales with the mass fraction MP /M∗ and inversely −1 with the orbital distance dp. For example Earth creates a shift of 0.1 m s while Jupiter causes a shift of 12.4 m s−1. Therefore the method is biased towards giant planets close to the host star (i.e. hot Jupiters), although smaller planets are detectable around small stars (Dumusque et al. 2012). Furthermore the precision of the measurements is currently limited to ∼0.3 m s−1 (Dumusque et al. 2012) by both the instruments and the intrinsic stellar processes, therefore many earth like planets have potentially evaded detection so far. Figure 1: The radial velocity method of planet detection 1as per exoplanets.org 5 2.2. Intrinsic Stellar Noise The radial velocity measurement suffers from various sources of noise, some of which are intrinsic to stellar processes. This so called Jitter is caused by collective movement of the stellar plasma, like turbulences and convection. As the star is basically a fluid the velocity distribution of the particles that make up the star is ultimately the determining factor for the measured Doppler shift of the spectrum. Turbulence will broaden the spectral line, as it is a symmetric effect that affects both sides of the velocity distribution equally, i.e. the average velocity does not change. Convection on the other hand will also shift the center of the spectral line, since the emissivity differs between the rising hot and sinking cold gas. Both of these effects are relatively small however when integrated over the whole stellar disk, as is the case here, as most of it cancels each other out. Both phenomena are influenced by the magnetic activity of the star and while the exact relation is complicated (Saar and Donahue 1997) we will use the mean longitudinal magnetic field as an indicator for the overall stellar activity. Another important effect is asteroseismology, in particular p-mode pulsations, as they affect the whole stellar surface (Carrier, Eggenberger, and Leyder 2008). However this is not related to the magnetic field and therefore outside the scope of this project. 6 2.3. Zeeman Effect Figure 2: Principle of the Zeeman effect. Credit: E. Blackman 2 For the measurement of the magnetic field B the Zeeman effect will be used. The Zeeman effect will cause each spectral line to split up into multiplets (e.g. triplets) as the electron orbits are shifted by ∆E = µmlB, where µ is the magnetic moment and ml is the magnetic quantum number, as shown in Fig. 2. From this one can calculate the wavelength shift ∆λ using Eq. 1 by using the energy of the emitted photon Eph. It is important to note that ∆ml = 0, ±1 due to selection rules of the electron transition and therefore each spectral line only split into groups of three separate lines. 1 1 ∆λ Eph = µ∆mlB = hc − ≈ hc 2 λ1 λ2 λ µ ⇒ ∆λ = ∆m Bλ2 (1) hc l However the shift ∆λ is usually smaller than the width σ of the spectral line, which means that only the measured width of the spectral line will increase and no separated peaks can be observed. Therefore a different property is measured as ∆λ is not the only thing differentiating the spectral lines. The lines also differ in circular polarization as the polarization of the emitted light depends on ∆ml of the transition. In the direction of the magnetic field only right hand circularised light is emitted for transitions with ∆ml = +1 to conserve the angular momentum, similarly for ∆ml = −1 only left hand circularised light is emitted. While for ∆ml = 0 no light is emitted in the direction of the magnetic field some signal is still observed due to magnetic field components in other spatial directions. This light is not polarised however. The split between the two differently circularised polarized peaks is large enough to be measured and can therefore be used to detect the magnetic field. It should be noted that Zeeman broadening in the unpolarised spectrum is sensitive to the disk-averaged magnetic field modulus, while the circular polarisation measurement is sensitive to the line of sight magnetic field component averaged over the stellar disk. The latter can be positive or negative, so polarisation measurements are susceptible to cancellation of opposite polarities. 2http://www.pas.rochester.edu/~blackman/ast104/zeeman-split.html 7 2.4. Stokes Parameters For the description of the polarised light the Stokes parameters will be used here.

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