An Application of Hilbert-Huang Transform on the Non-Stationary Astronomical Time Series: The Superorbital Modulation of SMC X-1

Abstract

We present the Hilbert-Huang transform (HHT) analysis on the quasi-periodic modulation of SMC X-1. SMC X-1, consisting of a neutron star and a massive companion, exhibits superorbital modulation with a period varying between ~40 d and ~65 d. We applied the HHT on the light curve observed by the All-Sky Monitor onboard Rossi X-ray Timing Explorer (RXTE) to obtain the instantaneous frequency of the superorbital modulation of SMC X-1. The resultant Hilbert spectrum is consistent with the dynamic power spectrum while it shows more detailed information in both the time and frequency domains. According to the instantaneous frequency, we found a correlation between the superorbital period and the modulation amplitude. Combining the spectral observation made by the Proportional Counter Array onboard RXTE and the superorbital phase derived in the HHT, we performed a superorbital phase-resolved spectral analysis of SMC X-1. An analysis of the spectral parameters versus the orbital phase for different superorbital states revealed that the diversity of nH has an orbital dependence. Furthermore, we obtained the variation in the eclipse profiles by folding the All Sky Monitor light curve with orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip of Her X-1, can be observed only in the superorbital ascending and descending states, while the width is anti-correlated with the X-ray flux.

Keywords

• X-ray binaries
• superorbital modulations
• Hilbert-Huang transform
• SMC X-1 1. INTRODUCTION The high-mass X-ray binary SMC X-1 consists of a 1.06 M⊙ neutron star (van der Meer et al. 2007) and a 17.2 M⊙ supergiant (Reynolds et al. 1993). The orbital period of this system is ~3.89 d obtained from the X-ray eclipse. Gruber & Rothschild (1984) found that the SMC X-1 exhibits an X-ray periodicity with a rough time scale of 60 d. This periodicity was then confirmed by Wojdowski et al. (1998) and the cycle lengths were reported to vary with time. The behavior of the period variation was investigated after several timefrequency analysis techniques
• like the dynamic power spectrum (Clarkson et al. 2003) and the slide Lomb-Scargle periodogram (Trowbridge et al. 2007)
• were applied on the All-Sky Monitor (ASM) light curve. We present our analysis by
• SMC X-1