The field of extrasolar planetary transits is one of the most productive and innovative subject in astrophysics in the last decade. Transit observations can be used to measure the size of planets, their orbital parameters (Seager and Mallén-Ornelas 2003), and stellar properties (Mandel & Agol 2002; Howarth 2011), to study the atmospheres of planets (Brown 2001; Charbonneau et al. 2002; Tinetti et al. 2007), and to detect small planets (Miralda-Escudé 2002; Agol et al. 2005) and exomoons (Kipping 2009a, 2009b). In particular, the study of planetary atmospheres requires a high level of photometric precision, i.e., one part in ∼104 in stellar flux (Brown 2001), which is comparable to the effects of current instrumental systematics and stellar activity (Berta et al. 2011; Ballerini et al. 2012), hence the necessity of testable methods for data detrending. In some cases, different assumptions, e.g., using different instrumental information or functional forms to describe them, leed to controversial results even from the same data sets; examples in the literature are Tinetti et al. (2007), Ehrenreich et al. (2007), Beaulieu et al. (2008) and Désert et al. (2009, 2011) for the hot-Jupiter HD 189733b, and Stevenson et al. (2010), Beaulieu et al. (2011) and Knutson et al. (2011, 2014) for the warm-Neptune GJ436b. Some of these controversies are based on Spitzer/IRAC data sets at 3.6 and 4.5 μm. The main systematic effect for these two channels is an almost regular undulation with period ∼3000 s, so called pixel-phase effect, as it is correlated with the relative position of the source centroid with respect to a pixel center (Fazio et al. 2004; Morales-Caldéron et al. 2006). Conventional parametric techniques correct for this effect by dividing the measured flux by a polynomial function of the coordinates of the photometric centroid; some variants may include time-dependence (e.g., Stevenson et al. 2010; Beaulieu et al. 2011). Newer techniques attempt to map the intra-pixel variability at a fine-scale level, e.g., adopting spatial weighting functions (Ballard et al. 2010; Cowan et al. 2012; Lewis et al. 2013) or interpolating grids (Stevenson et al. 2012a, 2012b). The results obtained with these methods appear to be strongly dependent on a few assumptions, e.g., the degree of the polynomial adopted, the photometric technique, the centroid determination, calibrating instrument systematics over the out-of-transit only or the whole observation (e.g., Beaulieu et al. 2011; Diamond-Lowe et al. 2014; Zellem et al. 2014). Also, the very same method, applied to different observations of the same system, often leads to significantly different results. Non-parametric methods have been proposed to guarantee a higher degree of objectivity (Carter & Winn 2009; Thatte et al. 2010; Gibson et al. 2012; Waldmann 2012, 2014; Waldmann et al. 2013). Morello et al. (2014, 2015) reanalyzed the 3.6 and 4.5 μm Spitzer/IRAC primary transits of HD 189733b and GJ436b obtained during the cryogenic regime, so called “cold Spitzer” era, adopting a blind source separation technique, based on an Independent Component Analysis (ICA) of individual pixel timeseries, in this paper called “pixel-ICA”. The results obtained with this method are repeatable over different epochs, and a photometric precision of one part in ∼104 in stellar flux is achieved, with no signs of significant stellar variability as suggested in the previous literature (Désert et al. 2011; Knutson et al. 2011). The use of ICA to decorrelate the transit signals from astrophysical and instrumental noise, in spectrophotometric observations, has been proposed by Waldmann (2012, 2014) and Waldmann et al. (2013). The reason to prefer such blind detrending methods is twofold: they require very little, if any, prior knowledge of the instrument systematics and astrophysical signals, therefore they also ensure a higher degree of objectivity compared to methods based on approximate instrument systematics models. As an added value, they give stable results over several data sets, also in those cases where more conventional methods have been unsuccessful. Recently, Deming et al. (2015) proposed a different pixel-level decorrelation method (PLD) that uses pixel timeseries to correct for the pixel-phase effect, while simultaneously modeling the astrophysical signals and possible detector sensitivity variability in a parametric way. PLD has been applied to some Spitzer/IRAC eclipses and synthetic Spitzer data, showing better performances compared to previously published detrending methods.
Citation: Beaulieu et al. (2011)
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