On the role of the current loss in radio pulsar evolution

The aim of this article is to draw attention to the importance of the electric current loss in the energy output of radio pulsars. We remind that even the losses attributed to the magneto-dipole radiation of a pulsar in vacuum can be written as a result of an Ampere force action of the electric currens flowing over the neutron star surface (Michel, 1991, Beskin et al., 1993). It is this force that is responsible for the transfer of angular momentum of a neutron star to an outgoing magneto-dipole wave. If a pulsar is surrounded by plasma, and there is no longitudinal current in its magnetosphere, there is no energy loss (Beskin et al., 1993, Mestel et al., 1999). It is the longitudinal current closing within the pulsar polar cap that exerts the retardation torque acting on the neutron star. This torque can be determined if the structure of longitudinal current is known. Here we remind of the solution by Beskin, Gurevitch & Istomin (1993) and discuss the validity of such an assumption. The behavior of the recently observed "part-time job" pulsar B1931+24 can be naturally explained within the model of current loss while the magneto-dipole model faces difficulties.Comment: 4 pages, to appear in Astrophysics and Space Science, Special Issue: Isolated Neutron Stars. In the replaced paper we amended several misprints (coefficients in equations 12,14,15) and removed the excessive explanation for the boundary condition (4

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Pulsar Striped Winds

According to magnetohydrodynamic (MHD) models, the rotational energy of a rapidly spinning neutron star is carried away by a relativistic wind and deposited at a large distance, in the nebula, downstream of the wind termination shock. The energy transport in the outflow is mediated by Poynting flux, but it is not clear how the energy stored in the fields is transferred into the energized population of emitting particles. The most plausible dissipation mechanisms are thought to be related to the "striped" structure of the wind, in particular, to the existence of a current sheet, prone to reconnection events. In this model the current sheet is a natural place for internal dissipation and acceleration of particles responsible for pulsed, high-energy emission. Moreover, reconnection is a promising scenario for explaining annihilation of fields at the shock and conversion of their energy into the kinetic energy of particles. The shock structure, however, is likely to differ in the low-density plasmas, in which non-MHD effects intervene. In this regime, the striped wind can dissipate its energy via an electromagnetic precursor of the shock.Comment: invited review at the Workshop on Modelling Nebulae, June 14-17, 2016, Sant Cugat, Spain; submitted book chapte