Timing and spectral analysis of the 2025 outburst of 4U 1630$-$47 with $\mathit{\text{NICER}}$

We analyzed $\mathit{\text{NICER}}$ observations of the 2025 outburst of the black hole X-ray binary 4U~1630$-$47 to investigate the spectral–timing properties of its transient low-frequency quasi-periodic oscillations (QPOs) and millihertz-scale quasi-regular modulation (QRM). During the rising phase of the outburst, the QPO centroid frequency increased from $\sim 0.24$ Hz to $\sim 3.43$ Hz. Wavelet-based state separation shows that the with-QPO intervals are associated with a higher inner disk temperature and a lower $\mathtt{\text{diskbb}}$ normalization than the without-QPO intervals, while the photon index ($\mathrm{\Gamma }$) shows weaker changes within the uncertainties. Near the outburst peak, the source displayed a weak QRM at $\sim 0.07$ Hz with a fractional rms amplitude of $\sim 4.7\mathrm{\%}$, lower than that of the heartbeat state observed in 2023. Phase-resolved Hilbert–Huang analysis shows that the inner disk temperature is positively correlated with the X-ray flux, the $\mathtt{\text{diskbb}}$ normalization is anticorrelated, and $\mathrm{\Gamma }$ varies only weakly. Overall, the short-timescale spectral–timing variability is expressed most clearly through the disk-related parameters. The transient QPOs are therefore consistent with short-timescale disk-related variability during the rising phase, whereas the millihertz-scale QRM may represent a weaker heartbeat-like variability mode appearing near the outburst peak.