Energy-resolved pulse profiles of accreting pulsars: Diagnostic tools for spectral features

We introduce a method for extracting spectral information from energy-resolved light curves folded at the neutron star spin period (known as pulse profiles) in accreting X-ray binaries. Spectra of these sources are sometimes characterized by features superimposed on a smooth continuum, such as iron emission lines and cyclotron resonant scattering features. We address here the question on how to derive quantitative constraints on such features from energy-dependent changes in the pulse profiles. We developed a robust method for determining in each energy-selected bin the value of the pulsed fraction using the fast Fourier transform opportunely truncated at the number of harmonics needed to satisfactorily describe the actual profile. We determined the uncertainty on this value by sampling through Monte Carlo simulations a total of 1000 faked profiles. We rebinned the energy-resolved pulse profiles to have a constant minimum signal-to-noise ratio throughout the whole energy band. Finally we characterize the dependence of the energy-resolved pulsed fraction using a phenomenological polynomial model and search for features corresponding to spectral signatures of iron emission or cyclotron lines using Gaussian line profiles. We apply our method to a representative sample of NuSTAR observations of well-known accreting X-ray pulsars. We show that, with this method, it is possible to characterize the pulsed fraction spectra, and to constrain the position and widths of such features with a precision comparable with the spectral results. We also explore how harmonic decomposition, correlation, and lag spectra might be used as additional probes for detection and characterization of such features.