Transcript 48 - Documents

-based comparison of methods for the detection of Earth-like planetary transits in the time series of CoRoT and Ke
A. F. Lanza1, U. Becciani1, A. S. Bonomo1,2,3, A. Costa1, A. Grillo1,4
1INAF-Osservatorio
2Dipartimento
Astrofisico di Catania
di Fisica e Astronomia, Università degli Studi di Catania, Via S. Sofia, 78 - 95123 Catania, Italy
3Laboratoire
d’Astrophysique de Marseille, Marseille, France
4Consorzio
COMETA, Catania, Italy
Email: [email protected], [email protected],[email protected], [email protected], [email protected]
Abstract. The space missions CoRoT and Kepler are going to observe between 60,000 and 100,000 late-type mainsequence stars to detect extrasolar planets by means of the transit technique. In other words, they will look for the small
periodic light dips produced by the passage of a planet in front of its host star. Planets having a size comparable to that of
the Earth produce dips of the order of 100 parts per million passing in front of a Sun-like star, which implies that the intrinsic
stellar microvariability must be accounted for to extract the transit signal. We have developed and tested several fitting and
filtering methods to find transits by terrestrial planets in the time series of late-type stars observed by CoRoT and Kepler.
Specifically, large Monte Carlo experiments have been performed on the computational grid of the COMETA consortium to
find out the best data processing technique to detect transits in the presence of photon shot noise and stellar microvariability
for stars of different magnitudes and different parameters of the planet.
1. Introduction. The search for extrasolar planets is one of the most interesting and active fields of modern astronomy with more than 330 giant planets discovered to
date. They are mostly Jupiter-mass objects, 20 per cent of which is orbiting at distances closer than 0.1 AU from their stars. The next frontier is the search for Earthsized objects which is possible by means of space-borne telescopes such as those of the missions CoRoT (launched on 27 December 2006) and Kepler (scheduled in
March 2009). They will detect planets in an indirect way, by looking for the light dips produced by the transits of the planets themselves in front of their parent stars (see
Fig.1). The probability of a transit is R/a where R is the radius of the star and a the semi-major axis of the orbit assumed to be circular. Since R/a < 0.003-0.05 and the
transit duration is of the order of a few hours or tens of hours for a solar-like star accompanied by a planet with an orbital period between 10 and 360 days, a large
number of stars must be monitored for transits. CoRoT will observe about 60,000 stars, while Kepler aims at 100,000 for time intervals ranging from 150 days to 4 years.
The light dips produced by the transits of an Earth-sized planet in front of a solar-like star are smaller than 100 parts per million (ppm), so that intrinsic stellar variability
must be accounted for at 30-50 ppm level in order to be able to detect its transits. Since the transit of a large sunspot group across the disk of the Sun produces a dip of
about 3000 ppm, it is necessary to develop techniques to model the effects of stellar magnetic activity and use them to remove stellar microvariability before performing
any successful search for transits by Earth-like planets.
Fig.1. A planetary transit observed by CoRoT. The radius of the planet is 1.6
times the radius of Jupiter. The next step will be the detection of the transit of
Earth-like planets, at a level of 10-4 in relative flux variation.
2. Detecting transits in the presence of magnetic activity. Several techniques have been recently proposed to reduce the impact of stellar variability due to magnetic
activity (i.e., cool spots, bright faculae and network) on the detection of planetary transits across solar-like stars, see, e.g., Defay et al. (2001), Jenkins (2002), Carpano et
al. (2003), Lanza et al. (2003), Aigrain & Irwin (2004), Bonomo & Lanza (2008). They are based on a variety of methods that make use of filtering in Fourier space or in
the time domain, wavelet decomposition or physical models of the surface brightness inhomogeneities in order to account for the effects of magnetic activity on stellar
light curves. In Fig.2, we show the application of the fitting method developed by Lanza et al. (2003) to the transits by a planet of 2.2 Earth radii across the disk of a Sunlike star, the variability of which has been assumed to be identical to the Total Solar Irradiance time series as observed by the experiment VIRGO on board of the satellite
SoHO (Frohlich & Lean 2004). The transit is not detectable by eye during phases of intermediate and maximum activity, owing to the larger intrinsic stellar variability. It
becomes immediately visible after subtracting the best fit to the stellar variability obtained with the model by Lanza et al. (2003). Different methods have different
performance according to the orbital period of the planet, the ratio between the transit depth and the standard deviation of the photon shot noise and the activity level of
the star. A current area of research is the comparison of methods based on physical models of stellar variability, such as that by Lanza et al. (2003), with those based on
linear or non-linear filtering or fitting techniques (see, e.g., Aigrain & Irwin 2004; Moutou et al. 2005).
Time (years)
3. Testing detection methods through simulated light curves. We have recently designed a large Monte Carlo numerical experiment to compare the performance of
the methods proposed by Lanza et al. (2003) and Aigrain & Irwin (2004) with the best of the method proposed by Moutou et al. (2005) for the analysis of the light curves
that are coming from the space experiment CoRoT. The Moutou et al’s best method was developed at Geneva Observatory and is based on the fitting of the stellar
intrinsic variability with 200 harmonic components. We simulated 32,000 light curves for a Sun-like star, using TSI as a proxy for its optical intrinsic variability, spanning a
large set of planetary parameters (radius, orbital period and epoch of the first transit) with one hundred different realizations of the random photon shot noise for each set
of parameters. Each light curve was then fitted with both the methods of Lanza et al. (2003), Aigrain & Irwin (2004), and of Geneva Observatory’s team, respectively,
before performing a search for transits by means of the algorithm proposed by Kovacs et al. (2002). The large computational load of our experiment is managed by
running our analyses on the grid infrastructure of the project PI2S2, allowing us to use up to 2000 CPUs in parallel (e.g., Becciani 2007). The CPU time for fitting stellar
microvariability with all those methods is on average about 20 minutes, while about 10 days of elapsed time have been necessary to analyse the complete set of 32,000
light curves.
4. Results. We show in Fig.3 a sample of our results for the case of a planet of 1.5 Earth radii with orbital periods of 5, 10, 25 days, as labelled, respectively. The noise
value (standard deviation) corresponds to a star of magnitude V=13 as will be observed by CoRoT with an integration time of one hour. The plots show the frequency
distribution of the detection parameter alpha which measures the depth of a putative transit in a light curve with respect to the standard deviation of the noise (see
Kovacs et al. 2002 for detail). In the present case, 400 light curves with transits have been analysed for each value of the parameters. The vertically dot-dashed lines
indicate the threshold for alpha, i.e., the minimum level above which a transit is detected in the light curve with a false-alarm probability lower than 0.01. The solid blue
histogram shows the fraction of detections obtained with the method by Lanza et al., while the red histogram shows the detection with the Geneva Observatory’s
method. Dotted histograms show the distribution frequency of missed detections. Note that missed detections increases with increasing orbital period because the
number of transits in the light curve becomes smaller giving a lower signal-to-noise ratio. Missed detection are concentrated below the threshold. Note that the method
by Lanza et al. performs significantly better than the method by Geneva Observatory’s team, giving systematically higher values of alpha. Such a conclusion is
confirmed by the analysis of the complete set of our simulated light curves. Specifically, we find that the method of Lanza et al. is always better than that of Geneva
Observatory’s team when the standard deviation of the photon shot noise is at least 2-4 times larger than the depth of the transit, that is the case for stars with
magnitude fainter than 13.0 in the fields of CoRoT (see Bonomo & Lanza 2008 for details). On the other hand, the Iterative Non-Linear Filter (INL) proposed by Aigrain
and Irwin (2004) has a performance superior to that of the method by Lanza et al. (see Fig. 4) when the extension of the window of its sliding boxcar filter is properly
selected, i.e., taking into account the level of magnetic activity of the star (see Bonomo et al. 2009, for details).
Fig.2. Upper panel (a): the time series of the Total Solar Irradiance with
superposed a planetary transit of an Earth-like planet of radius 2.2 times the
radius of the Earth and an orbital period of 30 days. Lower panel (b): the
residuals obtained after subtracting the model for stellar microvariability by
Lanza et al. (2003).
Fig.3. A sample histogram showing the results of the analysis of a subset of our
simulated light curves with the method of Lanza et al. (blue histograms) and that
of Geneva Observatory (red histograms; see the text for explanation).
5. Discussion and conclusions. Bonomo & Lanza (2008) shows that the advantage of the technique by Lanza et al. (2003) depends on the limited number of fitting
functions used to account for stellar variability by means of a suitable physical model in comparison to the large number of harmonic components required by Geneva
Observatory’s method. The latter is therefore significantly affected by the Gibbs phenomenon that reduces the depth of the transits in the filtered light curves thus
lowering the efficiency of detection in the presence of noise (see Fig. 5). The INL filter by Aigrain & Irwin (2004) is not affected by the Gibbs phenomenon and has a
performance that can be better than that of both the other methods. Therefore, it can be the method of choice, provided that its boxcar window extension is properly
fixed; otherwise, the method by Lanza et al. (2003) is recommended (Bonomo et al. 2009).
Acknowledgements. The authors gratefully acknowledge the system managers of the Trigrid and Cometa Consortia for their technical advice and kind assistance during the implementation and running of our numerical
experiments on PI2S2 grid-based high performance computing system.
ASB and AFL are also grateful to Drs. S. Aigrain, R. Alonso, P. Barge, P. Bordé, R. Cautain, M. Deluil, A. Leger, C. Moutou, for useful discussions on
several aspects of the present work. The availability of unpublished data of the VIRGO Experiment on the cooperative ESA/NASA Mission SoHO from the VIRGO Team through PMOD/WRC, Davos, Switzerland, is gratefully
acknowledged. The authors gratefully acknowledge support from the Italian Space Agency (ASI) under contract ASI/INAF I/015/07/0, work package 3170. This work has made use of results produced by the PI2S2 Project managed
by the Consorzio COMETA, a project co-funded by the Italian Ministry of University and Research (MIUR) within the Piano Operativo Nazionale "Ricerca Scientifica, Sviluppo Tecnologico, Alta Formazione" (PON 2000-2006). More
information is available at http://www.pi2s2.it and http://www.consorzio-cometa.it. Active star research and exoplanetary studies at INAF-Catania Astrophysical Observatory and the Department of Physics and Astronomy of Catania
University is funded by MUR (Ministero della Università e Ricerca}), and by Regione Siciliana, whose financial support is gratefully acknowledged. This research has made use of the ADS-CDS databases, operated at the CDS,
Strasbourg, France.
Fig.4. As Fig. 3, but for the comparison between the method of Lanza et al. (blue
histograms) and the INL filter of Aigrain & Irwin (green histograms); see the text for
details on the line style coding.
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Fig.5. The shape of a transit by an Earth-like planet as it appears in the ideal
case (solid black line), in the residuals obtained with the method of Lanza et
al. (dashed blue line) and in those of the method of Geneva Observatory’s
team (dotted red line), respectively. Note the reduction of the depth of the
transit and the overshooting at the edges of the transit dip in the case of the
Geneva method due to the Gibbs phenomenon.