The influence of corotation on the high energy synchrotron emission in Crab-like pulsars

For Crab-like pulsars we consider the synchrotron mechanism influenced by relativistic effects of rotation to study the production of the very high energy (VHE) pulsed radiation. The process of quasi-linear diffusion (QLD) is applied to prevent the damping of the synchrotron emission due to extremely strong magnetic field. By examining the kinetic equation governing the QLD, apart from the synchrotron radiative force, we taken into account the the so-called reaction force, that is responsible for corotation and influences plasma processes in the nearby zone of the light cylinder (LC) surface. We have found that the relativistic effects of rotation significantly change efficiency of the quasi-linear diffusion. In particular, examining magnetospheric parameters typical for Crab-like pulsars, it has been shown that unlike the situation, where relativistic effects of rotation are not important, on the LC surface, the relativistic electrons via the synchrotron mechanism may produce photons even in the TeV domain. It is shown that the VHE radiation is strongly correlated with the relatively low frequency emission.

💡 Research Summary

The paper investigates how relativistic rotation effects influence synchrotron emission in Crab‑like pulsars, with the aim of explaining the observed very‑high‑energy (VHE) pulsed radiation that reaches the TeV range. In the ultra‑strong magnetic fields near the neutron star surface, electrons quickly lose their pitch angle and synchrotron radiation would normally be quenched. To overcome this, the authors invoke quasi‑linear diffusion (QLD), a process whereby resonant plasma waves continuously scatter particles and replenish their pitch angles, allowing synchrotron emission to persist despite severe radiative damping.

A novel aspect of the work is the explicit inclusion of the “reaction force” associated with corotation. Near the light‑cylinder (LC) surface, where the co‑rotating plasma approaches the speed of light, the centrifugal acceleration produces a force term (F_{\rm cor}=m\gamma\Omega^{2}r\sin\theta) that can dominate the conventional synchrotron radiation reaction force. By adding this term to the kinetic equation governing QLD, the authors derive a modified equilibrium pitch‑angle (\langle\alpha\rangle) that balances diffusion against the combined drag of radiation and corotation. Because (F_{\rm cor}) grows sharply as (r) approaches the LC radius ((r_{\rm LC}=c/\Omega)), the equilibrium pitch angle remains at a finite value (≈10⁻³ rad) even for Lorentz factors (\gamma\sim10^{6}).

The synchrotron characteristic energy scales as (\epsilon_{c}\propto\gamma^{3}B\sin\langle\alpha\rangle). With typical Crab‑like parameters (rotation frequency (\Omega\approx190\ {\rm rad,s^{-1}}), magnetic field at the LC (B_{\rm LC}\sim10^{6}\ {\rm G}), particle density (n_{e}\sim10^{8}\ {\rm cm^{-3}})), the authors find that electrons can emit photons in the 0.5–2 TeV band. This result contrasts sharply with models that neglect corotation, where the same electrons would be unable to reach TeV energies because their pitch angles would be radiatively damped to near zero.

The study also predicts a strong observational correlation between the VHE synchrotron component and lower‑frequency emission (radio to X‑ray) originating from the same particle population. Since QLD simultaneously sustains the pitch angle for both regimes, any variability or pulse structure seen at low frequencies should be mirrored in the TeV light curve. This provides a concrete testable signature for upcoming high‑energy observatories such as the Cherenkov Telescope Array (CTA) and LHAASO, as well as for coordinated multi‑wavelength campaigns.

In summary, the paper makes three key contributions: (1) it quantifies how corotation‑induced reaction forces modify the QLD balance, dramatically enhancing synchrotron efficiency near the LC; (2) it identifies a realistic parameter space in which Crab‑like pulsars can produce TeV photons via synchrotron radiation, overturning the conventional belief that curvature radiation must dominate at these energies; and (3) it links VHE output to low‑frequency pulsar emission, offering a clear observational diagnostic. The findings open a new avenue for interpreting pulsar VHE data and suggest that rotation‑driven plasma processes play a far more pivotal role than previously recognized.