Old pulsar wind nebulae and the role of the thermal filaments

¹ INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
² Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy
³ INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 March 2026
Accepted: 6 June 2026

Abstract

Context. Old pulsar wind nebulae are among the foremost Galactic high-energy gamma-ray sources. However, we still lack a robust and reliable approach to their modeling, especially in the light of forthcoming high-energy observatories such as the Astri Mini-Array or CTAO. Part of the problem arises from the complex interaction that characterizes these systems. Understanding this complexity has then become mandatory for further advancements.

Aims. We develop a new approach to investigating the possible role that the thermal thick layer of massive filaments (seen in objects such as the Crab nebula and 3C 58, but likely present in all pulsar wind nebulae) can exert on the dynamics of the late reverberation phase and compare results with standard approaches that neglect these layer.

Methods. A new formulation of the one-zone thin-shell plus Lagrangian formalism that we developed in a series of previous papers is extended here to the case of a thick layer of filamentary ejecta. This complements our former work, which was mostly focused on the initial free-expansion phase.

Results. We compared the dynamics of reverberation with and without filaments, and show that in the former case, not only might reverberation be substantially anticipated (~30%), but the following compression takes a much longer time. On the other hand, the total compression of the system does not seem to change much, and the qualitative behavior is preserved.

Conclusions. Our results suggest that the presence or absence of an extended filamentary layer might affect the duration of the free-expansion phase (shortening it) and that of the following compression phase during reverberation (lengthening it), but it does not change the overall compression of the nebula strongly. While this changes the relative number of systems in these two phases and their contribution to high-energy emission, some peculiar radiative effects associated with the level of compression in old systems, such as the super-efficiency, might not be much affected.