Incorporating Spectra Into Periodic Timing

The Chandra surveys have resulted in a wealth of data on low-luminosity X-ray sources (Lx 10³⁰-34 erg/s) of Galactic scales beyond the local solar neighborhood. Many of these are compact binaries, in particular, cataclysmic variables, often identified by their periodic X-ray variability and spectra. Hong et al. (2009, 2011) have used energy quantiles (Hong, Schlegel & Grindlay, 2004) as a fast, robust indicator of spectral hardness and absorption of the X-ray sources. Energy quantiles also enable a simple but effective illustration of spectral changes with phase in these periodic systems: e.g. absorption by the accreting material is understood to drive the periodic light-curves. An interesting question is how to best make use of the information encapsulated in the periodic change in energy spectrum, along with the periodic change in intensity, especially for cases of ambiguous period determination? And, how to do it computationally efficiently?

A first approach is to do the period search in intensity, as is standard; and then use a criterion of spectral variation to verify possible periods. Huijse, Zegers & Protopapas (2011) recently demonstrated a powerful period estimation technique using information potential and correntropy embedded in the light curve. Similar quantities based on energies (or energy quantiles) of X-ray photons can serve as criteria of spectral variation. A different approach treats the spectrum variations and intensity variations completely independently, searching through period-space in each, and then combining the results. A more general method would include both at the same time, looking for statistically significant variations above what is expected for a constant (in intensity and spectrum).