Nonlinear Time Series Analysis of the DB White Dwarf PG 1351+489 Light Intensity Curves

Abstract

A nonlinear time series analysis is performed on light intensity data for the variable DB white dwarf PG 1351+489. The data were collected during the XCov12 campaign of the Whole Earth Telescope. Two data sets integrated to 30 and 10 s, taken at different times during the campaign, were analyzed. The power spectrum of PG 1351+489 is broadband, with a dominant fundamental frequency f 0 , and its harmonics, subharmonics, and other lower amplitude peaks. Our time delay phase-space portrait in 3 dimensions is a rhombohedral shape wrapped around a torus with triangular projections. This differs from earlier reports of a more circular two-dimensional representation. We show that the difference is due to binning and subsequent filtering in the earlier work. A circular phase-space portrait is obtained if only the fundamental frequency is used, the reconstruction subsequently growing in complexity as more and more of the power spectrum is included. Poincaré section return times for the 30 s integrated data correspond to the fundamental period. For the 10 s integrated data, other return times are observed. These are shown to be due to dynamical resetting. An example of dynamical resetting on a theoretical model is given. Since resetting takes the phase-space point off the trajectory, locally projective nonlinear noise reduction was used. Locally projective nonlinear noise reduction results in lower white noise by a factor of $50. Thus, three more harmonics of the fundamental frequency f 0 , four more (n þ 0:47)f 0 subharmonics, and at least 12 other peaks are identified.

Stochastic Brightness Variations in the Central Star of Planetary Nebula NGC 6826

“…An example of the power of nonlinear noise reduction for white dwarf PG 1351+489 can be found in Jevtic et al (2005). The power spectrum for an 11 hr section of its light curve is shown in Figure 2 (gray, upper spectrum).…”

“…time, the focus has shifted to using it for the more general category of nonlinear systems, as in this work. An example of its use to lower noise can be found in Jevtic et al (2005). Noise reduction, in effect, extends the reach of observations, or conversely, shortens observation time.…”

“…For the case of KIC 012071221 and its noisy power spectrum and a two-dimensional phase-space portrait, nonlinear noise reduction gains in efficiency when the number of neighboring points is increased, implying a longerterm periodicity. For the development of a curved surface with the inclusion of more and more frequencies in the power spectrum, please refer to Jevtic et al (2005).…”

Nonlinear time series analysis of the light curves from the black hole system GRS1915+105

“…The scenario has changed in the last few years as enough data are now available through RXTE observations. Recently, a nonlinear time series analysis performed on light intensity data from the white dwarf variable PG1351+489 has enabled much more information regarding the system compared to the conventional power spectrum analysis (Jevtic et al, 2005) and attempts have been made to use these analysis to differentiate between neutron stars and black holes (Karak et al, 2010) Studies on GRS1915+105 have been limited because it became active only over a decade ago. But the system turns out to be unique among all such sources in that it seems to flip from one state to another continuously with each state having its own temporal variability different from the other states.…”

Nonlinear time series analysis of Kepler Space Telescope data: Mutually beneficial progress

“…The time delay d for light curves is chosen at a minimum of the AMI. Jevtić et al (2005Jevtić et al ( , 2012) present a detailed discussion on AMI. This time delay d is an integer number of sampling intervals.…”