A Study on the X-Ray Pulse Profile and Spectrum of the Crab Pulsar Using NICER and Insight-HXMT's Observations

TL;DR

This study investigates the energy-dependent X-ray pulse profile and spectra of the Crab pulsar using NICER and Insight-HXMT data, revealing phase-dependent spectral curvature and particle energy-loss characteristics.

Contribution

It introduces a detailed phase-resolved spectral analysis with log-parabola and broken-power-law models, highlighting phase-related spectral evolution and energy-loss processes.

Findings

Spectral curvature varies with phase, with two turning points indicating lowest particle energy-loss regions.

Anticorrelations found between spectral indices and curvature, and between indices and broken energies.

Higher broken energies are observed bridging the two pulses, indicating regions of stronger radiation energy loss.

Abstract

We analyze the energy dependence of the X-ray pulse profile and the phase-resolved spectra (PRS) of the Crab pulsar using observations from the Neutron star Interior Composition Explorer (NICER) and the Hard X-ray Modulation Telescope (Insight-HXMT). We parameterize the pulse profiles and quantify the evolution of these parameters in the broad energy band of 0.4-250 keV. A log-parabola function is used to fit the PRS in 2-250 keV, and the curvature of the spectrum, i.e., the evolution of the photon index with energy, as represented by the parameter \{beta} of the log-parabola model, also changes with phase. The relation of \{beta} and phase has two turning points slightly later than those of the pulse intensity profile, where the values of \{beta} are the lowest, suggesting that the energy-loss rate of the particles is the lowest in the corresponding regions. A three-segment broken-power-law model is also used to fit those PRS. The differences between the hard spectral index and the soft ones have a distribution similar to that of \{beta}, confirming the fitting results of the log-parabola model, while the broken energies are generally higher in the region bridging the two pulses. We find anticorrelations between the spectral indices and the curvature of the log-parabola model fitting and a similar anticorrelation between the spectral indices and broken energies of the broken-power-law model fitting, suggesting a scenario where the highest-energy particles are produced in regions where radiation energy loss is strongest.