Lags of the KiloHertz Quasi-Periodic Oscillations in the transient source XTE J1701$-$462

We analysed 14 observations with kilohertz quasi-periodic oscillations (kHz QPOs) of the neutron star X-ray binary XTE J1701$-$462, the first source to show a clear transition between atoll and Z-like behaviour during a single outburst. We calculated the average cross-spectrum of both atoll and Z-phase observations of XTE J1701$-$462 between a reference/hard band (6.1 - 25.7 keV) and a subject/soft band (2.1 - 5.7 keV) to obtain, using a novel technique, the average time lags of the lower and upper kHz QPOs. During the atoll phase, we found that at the frequency of the lower kHz QPO the soft photons lag behind the hard ones by $18 \pm 8$ $\mu$s, whereas during the Z phase the lags are $33\pm35$ $\mu$s, consistent with zero. This difference in the lags of both phases suggests that in XTE J1701$-$462, as observed in other sources, the lags decrease with increasing luminosity. We found that for both the atoll and Z phase observations the fractional rms amplitude increases with energy up to $\sim$10 keV and remains more or less constant at higher energies. Since these changes in the variability of XTE J1701$-$462 occur within the same outburst, properties like the mass of the neutron star or the inclination of the system cannot be responsible for the differences in the timing properties of the kHz QPOs in the atoll and Z phase. Here we suggest that these differences are driven by a Comptonizing component or corona, possibly oscillating in a coupled mode with the innermost regions of the accretion disc.