First detection of Soft-lag in GRS 1915+105 at HFQPO using AstroSat observations

The Galactic black hole GRS 1915+105 exhibits generic High-Frequency Quasi-periodic Oscillations (HFQPOs) at $\sim$ 67 Hz only during the radio-quiet 'softer' variability classes. We present the time-lag properties associated with HFQPOs in the wide energy band (3$-$60 keV) using all AstroSat observations. For the first time, we detect soft-lag of 6$-$25 keV band w.r.t 3$-$6 keV band for all 'softer' variability classes ($\delta$, $\omega$, $\kappa$ and $\gamma$). Moreover, our findings reveal that soft-lag increases gradually with the energy of the photons. These features are entirely opposite to the previous report of hard-lag obtained with the RXTE observations. The energy-dependent time-lag study exhibits a maximum soft-lag of $\sim$ 3 ms and $\sim$ 2.5 ms for the $\delta$ and $\omega$ classes respectively, whereas the $\kappa$ and $\gamma$ classes both exhibit a maximum soft-lag of $\sim$ 2.1 ms. We find a coherent lag-energy correlation for all four variability classes, where the amplitude of soft-lag increases with energy and becomes maximum at $\sim$ 18 keV. We interpret this observed soft-lag as the reflection of hard photons in the 'cooler' accretion disc. A generic lag-rms correlation implies that the soft-lag increases with the rms amplitude of the HFQPO. The wideband (0.7$-$50 keV) spectral study suggests a high value of the optical depth ($\tau$ $\sim$ 6.90$-$12.55) of the Comptonized medium and the magnitude of the soft-lag increases linearly with the increase in optical depth ($\tau$). We explain the observed time-lag features at the HFQPOs in the context of a possible accretion disc scenario.