Cyclotron line evolution revealed with pulse-to-pulse analysis in the 2020 outburst of 1A 0535+262

We present a detailed analysis of the X-ray luminosity (L_X) dependence of the cyclotron absorption line energy (E_cyc) for the X-ray binary pulsar 1A 0535+262 during its 2020 giant outburst based on pulse-to-pulse analysis. By applying this technique to high cadence observations of Insight-Hard X-ray Modulation Telescope, we reveal the most comprehensive E_cyc-L_X correlation across a broad luminosity range of ~(0.03-1.3) × 10³⁸ erg s^-1. Apart from the positive and negative correlations between cyclotron line energy and luminosity at L_X ~ (1-3) × 10³⁷ erg s^-1 and ~(7-13) × 10³⁷ erg s^-1, which are expected from the typical subcritical and supercritical accretion regimes, respectively, a plateau in the correlation is also detected at ~(3-7) × 10³⁷ erg s^-1. Moreover, at the lowest luminosity level (L_X ≲ 10³⁷ erg s^-1), the positive E_cyc-L_X correlation seems to be broken, and the pulse profile also occurs a significant transition. These discoveries provide the first complete view on the correlation between luminosity and the centriod energy of the cyclotron line, and therefore are relevant for understanding how accretion on to magnetized neutron stars depends on luminosity.