Energy-dependent temporal study of GX 13+1 with AstroSat observation

In this work, we performed an energy-dependent study of low-frequency oscillations observed in GX 13+1 using \textit{AstroSat} (Large Area X-ray Proportional Counter and Soft X-ray Telescope). The hardness-intensity diagram (HID) of the observation resembles a `$\nu$'-shaped track, while the color-color diagram exhibits a `$<$'-shaped track, similar to the horizontal and normal branches of the Z source. We conducted flux-resolved temporal studies focusing on low-frequency variability and divided the HID into five regions: A, B, C, D, and E. Low-frequency quasi-periodic oscillations (QPOs) were detected in Regions A, B, and C. The QPO in Region A has a frequency of $5.06^{+0.54}_{-0.48}$ Hz with a quality factor (Q-factor) of 2.80. In Region B, the QPO was detected at $4.52^{+0.14}_{-0.13}$ Hz with a Q-factor of 5.79, while in Region C, it was observed at $4.70^{+0.62}_{-0.42}$ Hz with a Q-factor of 4.35. The QPO frequencies, Q-factors, and low root-mean-square (rms) values (1.32\%, 1.34\%, and 0.7\%) suggest that these oscillations are Normal Branch Oscillations, similar to those reported in GX 340+0. We modeled the rms and lag of the QPOs using a propagative model, considering variations in blackbody temperature, coronal heating rate, and optical depth. Our findings indicate that the observed QPOs are likely driven by interactions between the corona and variations in the blackbody temperature.