Probing heartbeat oscillations from the black hole X-ray binary GRS 1915+105 using spectral-timing analysis

GRS 1915+105 is a black hole X-ray binary exhibiting quasi-periodic $\rho$-class ("heartbeat") oscillations with periods of $\sim$50-100 s, thought to arise from radiation-pressure-driven instabilities in the inner accretion disk at near-Eddington luminosities. The coupled disk-corona response across this instability cycle has lacked simultaneous broadband phase-resolved observational constraints. We present phase-resolved spectral and timing analysis using 24 Swift XRT observations (2014-2016; 1-10 keV) and AstroSat SXT+LAXPC data (2017; 0.8-30 keV), dividing each cycle into five phases (three rise, two decay). We find a systematic anti-correlation between inner disk temperature ($T_{\rm in}$) and apparent inner radius ($R_{\rm in}$): $T_{\rm in}$ decreases from $\sim$1.7 to $\sim$1.5 keV as $R_{\rm in}$ increases from $\sim$22 to $\sim$38 km through Phases 1-3, before $R_{\rm in}$ decreases to $\sim$23 km at the burst peak (Phase 4) and $\sim$18 km post-burst (Phase 5). The broadband fits reveal that the coronal electron temperature $kT_{\rm e}$ rises from $\sim$10.5 to $\sim$14.5 keV through Phases 1-3 and drops to $\sim$6 keV after the burst, while Hardness-Intensity and Color-Color Diagrams show clear spectral hysteresis, with Phase 3 appearing softest in XRT/SXT but hardest above $\sim$10 keV in LAXPC. This evolution is consistent with radiation-pressure instability driving the cyclic $T_{\rm in} - R_{\rm in}$ variations, with coronal heating naturally explained by seed photon starvation via the Haardt-Maraschi mechanism as $R_{\rm in}$ increases. Our 0.8-30 keV coverage provides the first phase-resolved characterization of both the thermal disk and Comptonized corona within a single $\rho$ cycle, directly revealing the disk-corona coupling that drives the heartbeat oscillation and is inaccessible to narrow-band observations alone.