Energy dependence of Quasi-periodic oscillations in accreting X-ray pulsars

We present the results from an investigation of the energy dependence of Quasi-Periodic Oscillations (QPOs) exhibited by accreting X-ray pulsars using data from archival $\mathit{\text{XMM-Newton}}$, $\mathit{\text{NuSTAR}}$, $\mathit{\text{RXTE}}$, and $\mathit{\text{NICER}}$ observations. In a search for the presence of QPOs in 99 $\mathit{\text{XMM-Newton}}$ and $\mathit{\text{NuSTAR}}$ observations, we detected QPOs in eleven observations of five sources, viz., 4U 1626–67 (48 mHz), IGR J19294+1816 (30 mHz), V 0332+53 (2, 18 and 40 mHz), Cen X–3 (30 mHz), and XTE J1858+034 (180 mHz). A positive correlation of the QPO rms amplitude with energy is exhibited by 4U 1626–67, IGR J19294+1816, Cen X–3 and XTE J1858+034, while no energy dependence is observed in V 0332+53. We also analysed the energy spectrum to decouple thermal (soft-excess) from non-thermal emission and determine if the soft-excess has different QPO properties. We found no evidence for different QPO characteristics of the soft excess. The $\mathit{\text{NuSTAR}}$ observations of V 0332+53 during the Type-I outburst in 2016 show the presence of twin QPOs at 2.5 mHz and 18 mHz, while the $\mathit{\text{XMM-Newton}}$ and $\mathit{\text{NuSTAR}}$ observations during the Type-II outburst in 2015 show a QPO at 40 mHz. We review the observed QPO properties in the context of QPOs found in other types of accreting sources and the models usually used to explain the QPOs in accreting X-ray pulsars.