tokens: that sometimes show a periodic structure (one of the most famous example is the Guitar nebula, see e.g. Chatterjee Cordes 2002 , 2004 ; van Kerkwijk Ingle 2008 ). While at present the structures in the vicinity of the bow-shock head are reasonably well understood, the same cannot be said of the structures in the tail (Brownsberger Romani 2014 ; Klingler et al. 2016 ; Pavan et al. 2016 ). The possibility that the dynamics of PWNe can be strongly affected by the mass loading was discussed by Bucciantini and Bandiera ( 2001 ) and Bucciantini ( 2002c ). There the authors have shown that a non-negligible fraction of neutral atoms is expected to penetrate in the bow shock through shocked ISM, and then interact with the pulsar wind, modifying the predicted dynamics. These first models provide a good description of both the hydrogen penetration length-scale and the Hα luminosity. In Morlino, Lyutikov, and Vorster ( 2015 ) a quasi-1D steady-state model has been proposed to investigate the effect of mass loading on the tail morphology of BSPWNe. If a significant fraction of neutral atoms from the ISM penetrate into the bow shock, they can undergo ionization essentially by interacting with the UV photons emitted by the relativistic plasma of the nebula. The resulting protons and electrons interact, in turn, with the wind thorough its magnetic field, leading to a net mass loading of the shocked wind in the tail. The newly formed protons and electrons are at rest in the rest frame of the ISM. Moreover they originate from the cold neutrals of the ISM, which carry negligible thermal energy. Hence they do not add momentum or internal energy to the flow (they however add their rest mass energy). Given that momentum and energy are conserved, the rise in rest mass energy density causes the wind to slow down and the pressure to rise, resulting ultimately in a lateral expansion. This effect indeed produces a shape which resembles the head-and-shoulder morphology. Nevertheless the analytic model by Morlino et al. ( 2015 ) has few shortcomings: being 1D it does not account for the fluid dynamics in the lateral direction, the ISM ram pressure is neglected despite the supersonic motion, and, being stationary, it cannot capture possible instabilities. In this paper we extend this model by means of 2D relativistic HD axisymmetric simulations, with the aim of validating the head–shoulder morphology of BSPWNe predicted by the aforementioned work, and extending it beyond its limitations. Although magnetic field might influence the dynamics of the flow, its response to mass loading, and the expected opening of the tail, in order to avoid a further level of complexity we limit this work to pure HD. This paper is organized as follows: in Section 2 the numerical tool and setup are described; in Section 3 we present and discuss our findings. Conclusions are then drawn in Section 4 . 2 NUMERICAL SETUP The typical length-scale of BSPWNe is the so called stand off distance d
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