On the relationship between the periodic and aperiodic variability of accreting X-ray pulsars

Besides the narrow peaks originating from the periodic signal, the power spectra of accreting X-ray pulsars display continuum components usually increasing toward low frequencies; these arise from the source aperiodic variability. Most studies up to the present have adopted the view that the periodic and aperiodic variations are independent. However, any aperiodic variability in the emission from the accretion column(s) toward the magnetic neutron star should be modulated at the X-ray pulsar period, by virtue of the same rotation-induced geometric effects that give rise to the periodic signal. We develop here a simple shot noise model to test the presence of a coupling between the periodic and aperiodic variability of X-ray pulsars. The model power spectrum is fitted to the power spectra of three X-ray pulsars, Vela X-l, 4U 1145-62, and Cen X-3, observed with EXOSAT. In the first two cases, we find that a highly significant coupling is present, as evidenced by a substantial broadening in the wings of the power spectrum peaks which are the result of the periodic modulation. We find also that these wings can mimic the presence of a knee in the continuum power spectrum components around the fundamental of the periodic modulation, therefore bringing into question the correlation reported by Takeshima between the X-ray pulsar frequency and the knee frequency, beyond which the continuum power spectral component steepens.