A mechanism-independent methodology for modeling γ-ray phaseograms of pulsars in the framework of north-south symmetry

Abstract

Fermi-LAT observations revealed that each GeV phase-folded light-curve (aka. phaseogram) of the Crab, Geminga, Dragonfly and Vela pulsars consists of two pulses (P1 & P2) and a "Bridge" between them. There is clearly a "bump" at the Bridge phase of Vela's pulse profiles, that could also be regarded as the third pulse (P3). Differently, the Crab's, Geminga's & Dragonfly's Bridges relatively resemble a "valley floor". Despite such an apparent difference, it is interesting to investigate whether their Bridge emissions are still within the same general picture as Vela's. Assuming the north-south symmetry, we would expect the fourth component (Bridge2/P4) to exist as well. However, such a hypothetical Bridge2/P4 is not intuitively identified on $\gamma$-ray phaseograms of the Crab, Geminga, Dragonfly and Vela pulsars. It is also intriguing to hint at the rationale for the non-discovery of Bridge2/P4. Our prototypical toy model is free of assumptions on emission regions or radiation mechanisms. Instead, it assumes a north-south symmetric geometry and one circularly symmetric beam per hemisphere, while taking into account Doppler shifts (the most innovative element), time delays and energy-dependent beam shapes. Tentative compatibility of our fitting results with wind models is reported. Notably, for the Crab pulsar, we found a preliminary qualitative correlation between our model predictions and the IXPE results on X-ray polarisation. The softer $\gamma$-ray pulsation of the Geminga pulsar is found to span over its full phase. Prompted by systematic evaluations, we outline some potential improvements for our toy model.

18 pages, 15 figures, 3 tables. Accepted for publication in MNRAS. In original form 2025 April 8

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