Fractal analysis of noise buried time series signals with applications to exoplanet spectroscopy and bio-data

摘要

The shape of an exoplanet lightcurve is usually obtained by averaging the noise over multiple datasets. Fractal analysis has been demonstrated to be an effective tool for the detection of exoplanet transits using lightcurves summed over all wavelengths sensitive to the detector (G. Tremberger, Jr et. Al, 2006 Proc SPIE Vol 6265). The detection of spectral features would depend on the extent to which the signal was buried in the noise. Different noise sources would have different fractal characteristics. Also, the signal strength could be discontinuous in time depending on the exoplanet's local atmospheric environment. Such a discontinuity is unlikely to be detected with time integrated data. The lightcurve noise and shape information were characterized with fractal dimension analysis of a noise buried time series signal. Computer simulation revealed that when the noise is three times that of the signal, the fractal algorithm could detect the signal at about the 87% confidence level. Application to noise buried time series datasets (HD 209458b lightcurve, HD 149026b lightcurve) detected discontinuities consistent with the results obtained by averaging datasets. Extension to individual wavelength lightcurves would establish a detection limit for the existence of spectral features at wavelengths important for exoplanet study. Other applications such as pre-implantation genetic screening spectroscopy and spatially varied aneuploidy bio-data could use the same analysis principle as well.