NICER Spectral and Timing Analysis of 4U 1630$-$47 and its Heartbeat State

We present a spectral and timing analysis of NICER observations of the black hole X-ray binary 4U 1630-47 from 2018 to 2024. We find relativistic reflection features in the hard and soft intermediate states, and disk wind absorption features in the soft intermediate state and soft state. We fit the reflection features with relxillCP and find a stable and untruncated disk in the intermediate states; we fit the wind features with XSTAR and find a stable, highly ionized wind with high column density across different outbursts. Specifically, the heartbeat state is seen in two observations in 2021 and 2023 respectively. Through the phase-resolved spectral fitting, we find the flux of the source to be correlated with the disk parameters while no strong correlation with the coronal parameters is observed, consistent with the scenario given by the inner disk radiation pressure instability. A hard lag on the time scale of 1 s and high coherence is observed near the characteristic frequency of the heartbeat, which can be explained by the viscous propagation of mass accretion fluctuations in the disk. The positive relationship between the heartbeat fractional rms and energy can possibly be explained by a disk-originated oscillation which is then magnified by the corona scattering.