Sidebands to mHz QPOs in 4U 1626-67 in the second spin-down state

We report results from an AstroSat target-of-opportunity (ToO) observation of 4U 1626 -67, performed on 2023 May 18, soon after the discovery of torque reversal to spin-down in the source. The X-ray emission exhibited significant dependence on both energy and torque state. This work highlights the comparison of timing features of 4U 1626 -67 with a previous AstroSat observation from 2018, when the neutron star was in the spin-up state. The power density spectrum (PDS) of the 2023 observation comprised a sharp peak corresponding to vNS '130 mHz X-ray pulsations along with a prominent quasi-periodic oscillation (QPO) feature at vQPO '46 mHz with '20 per cent rms amplitude, which was positively correlated with energy. We also report the detection of sidebands to QPO occurring at a beat frequency (v(NS) - v(QPO)) of '83 mHz with '8 per cent rms amplitude, having > 3cr detection significance. Additionally, we utilized Nuclear Spectroscopic Telescope ARray (NuSTAR) observations from the same torque state (2023 May-July) to analogize the presence and energy dependence of sidebands. The source retains timing properties in this spin-down torque state, similar to those seen in the previous spin-down phase. In sharp contrast, PDS from the 2018 observation was dominated by red noise, an absence of QPOs and a broadening in the wings of the pulse frequency peak, indicating a coupling between periodic and low-frequency aperiodic variability. Furthermore, we detected the known cyclotron resonance scattering feature (CRSF) at 37 keV in the Large Area X-ray Proportional Counter (LAXPC) spectrum. We explore various mechanisms that could possibly explain the presence of QPOs exclusively during the spin-down state.