On the anomalously large extension of the Pulsar Wind Nebula HESS J1825-137

Abstract: The very high energy (VHE) gamma-ray emission reported from a number of pulsar wind nebulae (PWNe) is naturally explained by the inverse Compton scattering of multi-TeV electrons. However, the physical dimensions of some gamma-ray-emitting PWNe significantly exceed the scales anticipated by the standard hydrodynamical paradigm of PWN formation. The most "disturbing" case in this regard is HESS J1825-137, which extends to distances $r\approx70\rm\,pc$ from the central pulsar PSR J1826-1334. If the gamma-ray emission is indeed produced inside the PWN, but not by electrons that escaped the nebula and diffuse in the interstellar medium (ISM), the formation of such an anomalously extended plerion could be realized, in a diluted environment with the hydrogen number density $n_{ism}\le10^{-2}\rm\,cm^{-3}$. In this paper, we explore an alternative scenario assuming that the pulsar responsible for the formation of the nebula initially had a very short rotation period. In this case, the sizes of both the PWN and the surrounding supernova remnant depend on the initial pulsar period, the braking index, and the ISM density. To check the feasibility of this scenario, we study the parameter space that would reproduce the size of HESS J1825-137. We show that this demand can be achieved if the braking index is small, $n\leq2$ and the pulsar birth period is short, $P_{\rm b}\simeq1\rm\,ms$. This scenario can reproduce the wind termination position, which is expected at $R_{ts}\simeq0.03\rm\,pc$, only in a dense environment with $n_{ism}\geq\rm1\,cm^{-3}$. The requirement of the dense surrounding gas is supported by the presence of molecular clouds found in the source vicinity.