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 towards low frequencies; these arise from the source aperiodic variability. Most studies so far adopted the view that the periodic and aperiodic variations are independent. However any aperiodic variability in the emission from the accretion column(s) towards the magnetic neutron star should be modulated at the X-ray pulsar period, by virtue of the same rotation-induced geometric effects which 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 fit to the power spectra of three X-ray pulsars, Vela X-1, 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 testified by a substantialbroadening in the wings of the power spectrum peaks due to the periodic modulation. We find also that these wings can mimick the presence of a knee in the continuum power spectrum components around the fundamental of the periodic modulation, therefore questioning the correlation reported by Takeshima (1992) between the X-ray pulsar frequency and the knee frequency, beyond which the continuum power spectral component steepens. 
Davide Lazzati and Luigi Stella