Abstract
Transonic (with Mach number \(M_{s}\gtrsim 1\)) motion of a pulsar relative to the external medium can help its compact pulsar wind nebula develop a double-torus X-ray morphology. The double-torus structure can reverberate as a whole under the dynamic pressure of the external flow. For a flow aligned with the symmetry axis of the nebula, the response of the double-torus is uniform in azimuth. For a misaligned flow, the leeward sides of the tori respond with some delay relative to their windward sides. The delay can cause a curious swaying in the short midsection of the leeward jet of the compact X-ray nebula. Within the framework of the relativistic magnetohydrodynamical model of a pulsar wind nebula we study the dynamics of the nebular outflows contributing to the swaying of the jet. When applied to the Vela X-ray nebula, the model allows us to naturally relate two distinct phenomena, the swaying of the bright midsection of the Vela lee jet and the reverberation of its double-torus.
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Notes
Here \(\alpha\) is a tilt of pulsar’s magnetic axis to its rotational axis. The wind magnetization \(\sigma\) is the ratio of the magnetic and kinetic energy densities of the relativistic pulsar wind. In the laboratory frame of reference, this ratio reads as \(\sigma=B^{2}/\left(4\pi\Gamma^{2}\left(\rho c^{2}/\Gamma+4p\right)\right)\), where \(\Gamma\) is the Lorentz factor of the wind flow, and \(p\), \(\rho\) and \(B\) are pressure, mass density, and magnetic field of the wind (in the laboratory frame).
In Vela, this shock is apparently responsible for the X-ray feature at the beginning of the bright midsection of the leeward jet (Fateeva et al. 2023); this feature has the shape of a thin transverse bar, the width of which is greater than the cross-section of the jet (Pavlov et al. 2001; Kargaltsev et al. 2002).
The point of the working surface of the shock closest to the pulsar.
Primarily, on the ambient medium density and the pulsar’s spin-down luminosity, which determine the size of the compact X-ray nebula.
Here we leave aside the discussion of changes in radiation efficiency and spectra of PWNe during the reverberation phase, which, in principle, can be observed; see, e.g., Torres et al. (2019).
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ACKNOWLEDGMENTS
The authors thank the anonymous referee for careful reading of the manuscript and useful comments. We are also grateful to the developers of the PLUTO code (Mignone et al. 2007). The numerical rMHD modeling was performed by A.P. supported by the RSF grant no. 21-72-20020. The Vela PWN observations data were analyzed by K.P. and G.P. supported by the baseline project no. 0040-2019-0025 of Ioffe Institute. The numerical modeling was performed partly at the Tornado subsystem of the Supercomputer Center of Peter the Great St. Petersburg Polytechnic University, and partly using the resources of the JSCC RAS.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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APPENDIX
APPENDIX
Our numerical models of double-torus PWNe are built on the rMHD module of the PLUTO code (Mignone et al. 2007). The models are axisymmetric, with the ‘‘northern’’ and ‘‘southern’’ hemispheres simulated independently (2.5D geometry). The numerical grid is spherical \(\left(r,\theta\right)\), with a logarithmically increasing step in \(r\) and a uniform step in \(\theta\). The simulation box is \(r=(0.0002-R)\) l.y. The basic grid has \(N\) cells in \(r\) and 32 cells in \(\theta\). Level \(L\) Adaptive Mesh Refinement (AMR) is activated at time \(t_{1}\) (in years). The pulsar inclination \(\alpha=80^{\circ}\). The initial wind magnetization: \(\sigma_{0}=0.03\) in model M1 (Fig. 1, top), and \(\sigma_{0}=0.1\) in models M2 (Fig. 1, bottom) and M3 (Fig. 2). The model parameters:
Mass density of the ambient medium \(\rho_{a}=10^{-28}\) g cm\({}^{-3}\). The wind power is normalized on the Vela pulsar spin-down luminosity \(\dot{E}=6.9\times 10^{36}\textrm{ erg}\textrm{ s}^{-1}\). To allow comparison with other PWN models in the literature, we applied the widely used pulsar wind model and the recipe for calculating synthetic maps of synchrotron radiation based on MHD models (Porth et al. 2014; see also Bühler and Giomi 2016); their details are reiterated in Ponomaryov et al. (2023).
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Petrov, A.E., Levenfish, K.P. & Ponomaryov, G.A. Reverberation of the Vela Pulsar Wind Nebula. Astron. Lett. 49, 777–786 (2023). https://doi.org/10.1134/S106377372312006X
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DOI: https://doi.org/10.1134/S106377372312006X