We report results on the timing analysis of the 2020 giant outburst of 1A 0535+262, using broadband data from Insight-HXMT. The analysis of the pulse profile evolution from the subcritical-luminosity to the supercritical-luminosity regime is presented for the first time. We found that the observed pulse profile exhibits a complex dependence on both energy and luminosity. A dip structure at the energy of the cyclotron resonant scattering features is found for the first time in the pulse fraction–energy relation of 1A 0535+262, when the outburst evolves in a luminosity range from 4.8 × 1037 to 1.0 × 1038 erg s−1. The observed structure is luminosity dependent and appears around the source critical luminosity (∼6.7 × 1037 erg s−1).

The detection of cyclotron resonance scattering features (CRSFs) is the only way to directly and reliably measure the magnetic field near the surface of a neutron star (NS). The broad energy coverage and large collection area of Insight-HXMT in the hard X-ray band allowed us to detect the CRSF with the highest energy known to date, reaching about 146 keV during the 2017 outburst of the first galactic pulsing ultraluminous X-ray source (pULX) Swift J0243.6+6124. During this outburst, the CRSF was only prominent close to the peak luminosity of ∼2 × 1039 erg s−1, the highest to date in any of the Galactic pulsars. The CRSF is most significant in the spin-phase region corresponding to the main pulse of the pulse profile, and its centroid energy evolves with phase from 120 to 146 keV. We identify this feature as the fundamental CRSF because no spectral feature exists at 60–70 keV. This is the first unambiguous detection of an electron CRSF from an ULX. We also estimate a surface magnetic field of ∼1.6 × 1013 G for Swift J0243.6+6124. Considering that the dipole magnetic field strengths, inferred from several independent estimates of magnetosphere radius, are at least an order of magnitude lower than our measurement, we argue that the detection of the highest-energy CRSF reported here unambiguously proves the presence of multipole field components close to the surface of the neutron star. Such a scenario has previously been suggested for several pulsating ULXs, including Swift J0243.6+6124, and our result represents the first direct confirmation of this scenario.

MAXI J1816–195 is a newly discovered accreting millisecond pulsar with prolific thermonuclear bursts, detected during its outburst in 2022 June by Insight-HXMT and NICER. During the outburst, Insight-HXMT detected 73 bursts in its peak and decay phase, serving as a prolific burst system found in the accreting millisecond pulsars. By analyzing one burst that was simultaneously detected by Insight-HXMT and NICER, we find a mild deviation from the conventional blackbody model. By stacking the Insight-HXMT light curves of 66 bursts that have similar profiles and intensities, a hard X-ray shortage is detected with a significance of 15.7σ in 30–100 keV. The shortage is about 30% of the persistent flux, which is low compared with other bursters. The shortage fraction is energy-dependent: larger in a higher energy band. These findings make the newly discovered millisecond MAXI J1816–195 a rather peculiar system compared with other millisecond pulsars and atoll bursters. In addition, based on the brightest burst, we derive an upper limit of the distance as 6.3 kpc, and therefore estimate the upper limit of the inner-disk radius of the accretion disk to be ∼40 km. Assuming the radius as the magnetospheric radius, the derived magnetic field strength is about 7.1 × 108 G.