The study of the atmospheres of transiting exoplanets requires a photometric precision, and repeatability, of one part in $sim 10^4$. This is beyond the original calibration plans of current observatories, hence the necessity to disentangle the instr
umental systematics from the astrophysical signals in raw datasets. Most methods used in the literature are based on an approximate instrument model. The choice of parameters of the model and their functional forms can sometimes be subjective, causing controversies in the literature. Recently, Morello et al. (2014, 2015) have developed a non-parametric detrending method that gave coherent and repeatable results when applied to Spitzer/IRAC datasets that were debated in the literature. Said method is based on Independent Component Analysis (ICA) of individual pixel time-series, hereafter pixel-ICA. The main purpose of this paper is to investigate the limits and advantages of pixel-ICA on a series of simulated datasets with different instrument properties, and a range of jitter timescales and shapes, non-stationarity, sudden change points, etc. The performances of pixel-ICA are compared against the ones of other methods, in particular polynomial centroid division (PCD), and pixel-level decorrelation (PLD) method (Deming et al. 2014). We find that in simulated cases pixel-ICA performs as well or better than other methods, and it also guarantees a higher degree of objectivity, because of its purely statistical foundation with no prior information on the instrument systematics. The results of this paper, together with previous analyses of Spitzer/IRAC datasets, suggest that photometric precision and repeatability of one part in $10^4$ can be achieved with current infrared space instruments.
We analyzed four Spitzer/IRAC observations at 3.6 and 4.5 {mu}m of the primary transit of the exoplanet GJ436b, by using blind source separation techniques. These observations are important to investigate the atmospheric composition of the planet GJ4
36b. Previous analyses claimed strong inter-epoch variations of the transit parameters due to stellar variability, casting doubts on the possibility to extract conclusively an atmospheric signal; those analyses also reported discrepant results, hence the necessity of this reanalysis. The method we used has been proposed in Morello et al. (2014) to analyze 3.6 {mu}m transit light-curves of the hot Jupiter HD189733b; it performes an Independent Component Analysis (ICA) on a set of pixel-light-curves, i.e. time series read by individual pixels, from the same photometric observation. Our method only assumes the independence of instrumental and astrophysical signals, and therefore guarantees a higher degree of objectivity compared to parametric detrending techniques published in the literature. The datasets we analyzed in this paper represent a more challenging test compared to the previous ones. Contrary to previous results reported in the literature, our results (1) do not support any detectable inter-epoch variations of orbital and stellar parameters, (2) are photometrically stable at the level 10e-4 in the IR, and (3) the transit depth measurements at the two wavelengths are consistent within 1{sigma}. We also (4) detect a possible transit duration variation (TDV) of 80 s (2 {sigma} significance level), that has not been pointed out in the literature, and (5) confirm no transit timing variations (TTVs) >30 s.
