Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical modeling of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.
Deep Dive into MHD models of Pulsar Wind Nebulae.
Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical modeling of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.
When the ultra-relativistic wind from a pulsar interacts with the ambient medium, either the SNR or the ISM, a bubble of non-thermal relativistic particles and magnetic field, known as Pulsar Wind Nebula or "Plerion" (PWN), is formed. The Crab Nebula is undoubtedly the best example of a PWN, and it is often considered the prototype of this entire class of objects, to the point that models of PWNe are, to a large extent, based on what is known in this single case. The first theoretical model of the structure and the dynamical properties of PWNe was presented by Rees & Gun [88], further developed in more details by Kennel & Coroniti [64,65] (KC84 hereafter), and is based on a relativistic MHD description.
The MHD paradigm is based on three key assumptions:
• that the larmor radii of the particles is much smaller than the typical size of the nebula, and particles are simply advected with the magnetic field. This is true up to energies of order of the pulsar’s voltage, where the larmor radius becomes comparable with the typical size of the system. • That radiative losses are negligible, or at least that they can be accounted for by renormalizing the pulsar spin-down luminosity. This again can be proved to be true in the case of Crab Nebula (and to some extent also in other systems with good spectral coverage), where the synchrotron spectrum shows that the particles carrying the bulk of the energy have a typical lifetime for synchrotron cooling longer than the age of the nebula. • That we are dealing with almost pure pair plasma, and dispersive or hybrid effects (separation of scales) due to the presence of heavier ions are absent. While there is no direct evidence for the absence of ions, standard pulsar wind theory, and the success of the MHD model of PWNe suggest that, from a purely dynamical point of view, there is no need for this extra component.
In it simplest form [88] the MHD model of PWNe can be summarized as follow (see Fig. 3): the ultra-relativistic pulsar wind is confined inside the slowly expanding SNR, and slowed down to non relativistic speeds in a strong termination shock (TS). At the shock the plasma is heated, the toroidal magnetic field of the wind is compressed, and particles are accelerated to high energies. These high energy particles and magnetic field produce a post-shock flow which expands at a non relativistic speed toward the edge of the nebula.
Despite its simplicity the MHD model can explain many of the observed properties of PWNe, and until now no observation has been presented that could rule it out. The presence of an under-luminous region, centered on the location of the pulsar, is interpreted as due to the ultra-relativistic unshocked wind. Polarization measures [112,106,93,57,82,42,70,53] show that emission is highly polarized and the nebular magnetic field is mostly toroidal, as one would expect from the compression of the pulsar wind, and it is consistent with the inferred symmetry axis of the system. The pressure anisotropy associated to the compressed nebular toroidal magnetic field [11,101], explains the elongated axisymmetric shape of many PWNe (i.e. Crab Nebula, 3C58). The MHD flow from the TS to the edge of the nebula also leads to the prediction that PWNe should appear bigger at smaller frequencies: high energy X-rays emitting particles are present only in the vicinity of the TS, having a shorter lifetime for synchrotron losses, compared to Radio particles which fill the entire volume, having negligible losses on the age of the nebula. This increase in size at smaller frequencies is observed in the Crab Nebula [105,14,7].
However one must bear to mind that not all properties of PWNe can be explained within the MHD framework, which, ultimately, only provides a description of the flow dynamics. For example, the acceleration of particles at the TS that accounts for the continuous, non-thermal, very broad-band spectrum, extending from Radio to X-rays [105,8,110,111,83], is usually assumed as given. The MHD model provides no hint to the reason why the injection spectrum looks like a broken powelaw, with no sign of a Maxwellian component at lower energies. Moreover the MHD description might prove faulty if applied to particles responsible for the emission in the 10-100 MeV band, whose larmor radii are comparable to the size of the TS, and can lead to wrong conclusion on their expected behavior.
The MHD model of PWNe has been used, by comparing observations with the predictions of numerical simulations, to constrain some of the properties of the pulsar wind, at least at the distance of the TS. While it is not possible to derive the Lorentz factor of the wind, or its multiplicity, it is possible to constrain the ratio between Poynting flux and kinetic energy, the latitudinal dependence of the energy flux, and the presence of a dissipated equatorial current sheet. This shows that nebular properties can be used to derive informations on the conditions of the pulsar wind
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