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Here we report the spectral-timing results of the black hole X-ray binary 4U 1630–47 during its 2021 outburst using observations from the Hard X-ray Modulation Telescope (Insight-HXMT). Type C quasi-periodic oscillations (QPOs) in ∼1.6–4.2 Hz and quasi-regular modulation (QRM) near 60 mHz are detected during the outburst. The mHz QRM has a fractional rms of ∼10%–16% in the 8–35 keV energy band with a Q factor (frequency/width) of ∼2–4. Benefiting from the broad energy band of Insight-HXMT, we study the energy dependence of the ∼60 mHz QRM in 1–100 keV for the first time. We find that the fractional rms of the mHz QRM increases with photon energy, while the time lags of the mHz QRM are soft and decrease with photon energy. Fast recurrence of the mHz QRM, in a timescale of less than 1 hr, has been observed during the outburst. During this period, the corresponding energy spectra moderately change when the source transitions from the QRM state to the non-QRM state. The QRM phenomenon also shows a dependence with the accretion rate. We suggest that the QRM could be caused by an unknown accretion instability aroused from the corona.

We describe the timing system and the timing calibration results of the three payloads on-board the Insight-Hard X-ray Modulation Telescope (Insight-HXMT). These three payloads are the High Energy X-ray telescope (HE, 20-250 keV), the Medium Energy X-ray telescope (ME, 5-30 keV) and the low Energy X-ray telescope (LE, 1-10 keV). We present a method to correct the temperature-dependent period response and the long-term variation of the on-board crystal oscillator, especially for ME that does not carry a temperature-compensated crystal oscillator. The time of arrivals (ToAs) of the Crab pulsar are measured to evaluate the accuracy of the timing system. As the ephemeris of the Crab pulsar given by Jodrell Bank observatory has systematic errors around 40 {\mu}s (Rots et al. 2014), we use the quasi-simultaneous observations of the X-ray Timing Instrument (XTI) on-board the Neutron star Interior Composition Explorer (NICER) to produce the Crab ephemerides and to verify the timing system of Insight-HXMT. The energy-dependent ToAs' offsets relative to the NICER measurements including physical and instrumental origins are about 24.7{\mu}s, 10.1{\mu}s and 864.7{\mu}s, and the systematic errors of the timing system are determined as 12.1{\mu}s, 8.6{\mu}s, and 15.8{\mu}s, for HE, ME and LE respectively., Comment: 29 pages, 14 figures, accepted for publication in ApJS