Of “Cocktail Parties” and Exoplanets

Abstract

The characterization of ever smaller and fainter extrasolar planets requires an intricate understanding of one's data and the analysis techniques used. Correcting the raw data at the 10 −4 level of accuracy in flux is one of the central challenges. This can be difficult for instruments that do not feature a calibration plan for such high precision measurements. Here, it is not always obvious how to de-correlate the data using auxiliary information of the instrument and it becomes paramount to know how well one can disentangle instrument systematics from one's data, given nothing but the data themselves. We propose a non-parametric machine learning algorithm, based on the concept of independent component analysis, to de-convolve the systematic noise and all non-Gaussian signals from the desired astrophysical signal. Such a "blind" signal de-mixing is commonly known as the "Cocktail Party problem" in signal processing. Given multiple simultaneous observations of the same exoplanetary eclipse, as in the case of spectrophotometry, we show that we can often disentangle systematic noise from the original light-curve signal without the use of any complementary information of the instrument. In this paper, we explore these signal extraction techniques using simulated data and two data sets observed with the Hubble Space Telescope NICMOS instrument. Another important application is the de-correlation of the exoplanetary signal from time-correlated stellar variability. Using data obtained by the Kepler mission we show that the desired signal can be de-convolved from the stellar noise using a single time series spanning several eclipse events. Such non-parametric techniques can provide important confirmations of the existent parametric corrections reported in the literature, and their associated results. Additionally they can substantially improve the precision exoplanetary light-curve analysis in the future.

Repeatability of Spitzer/Irac Exoplanetary Eclipses With Independent Component Analysis

“…Ten individual eclipses were observed over six months (2012November 11-2013, including two sets of three consecutive eclipses, and another eclipse is contained within a full-orbit observation on 2013 May 5 (PID: 90032). Each individual observation consists of 14,912 frames over 8.4 hr using IRACʼs sub-array readout mode with 2.0 s integration time.…”

A Gemini ground-based transmission spectrum of WASP-29b: a featureless spectrum from 515 to 720 nm

“…Swain, Vasisht & Tinetti 2008;Gibson, Pont & Aigrain 2011); however, advances in data analysis techniques are starting to resolve the issue (e.g. Gibson et al 2012b;Waldmann 2012), along with the availability of more stable NIR cameras such as WFC3 (e.g. Berta et al 2012;Gibson et al 2012a).…”

On the Current State of Ground-based Transmission Spectroscopy of Planet Atmospheres

“…WASP-31b: For WASP-31b we used the approach recently suggested by Waldmann (2012), which is based on the assumption that the systematic noise can be described as a linear combination of several noise signals, all contributing to the signal measured in each wavelength channel data with different weights. If this is the case, then blind source separation algorithms can be used to de-mix the input data into the individual signal components.…”