Modelling Of Pulsar Wind Nebulae Research Articles

A self-regulated stochastic acceleration model of pulsar wind nebulae

Abstract Pulsar wind nebulae (PWNe) are clouds of the magnetized relativistic electron/positron plasma supplied from the central pulsar. However, the number of radio-emitting particles inside a PWN is larger than the expectation from the study of pulsar magnetospheres and then their origin is still unclear. A stochastic acceleration of externally injected particles by a turbulence inside the PWN is proposed by our previous studies. In this paper, the previous stochastic acceleration model of the PWN broadband spectra is improved by taking into account the time evolution of the turbulent energy and then the total energy balance inside a PWN is maintained. The turbulent energy supplied from the central pulsar is wasted by the backreaction from the stochastic particle acceleration and the adiabatic cooling according the PWN expansion. The model is applied to the Crab Nebula and reproduce the current broadband emission spectrum, especially the flat radio spectrum although time evolution of the turbulent energy (diffusion coefficient) is a bit complicated compared with our previous studies, where we assumed an exponential behavior of the diffusion coefficient.

Testing a stochastic acceleration model of pulsar wind nebulae: early evolution of a wind nebula associated with SN 1986J

ABSTRACT Over 3000 pulsars have been discovered, but none have been confirmed to be younger than a few hundred years. Observing a pulsar after a supernova explosion will help us understand the properties of newborn ones, including their capability to produce gamma-ray bursts and fast radio bursts. Here, the possible youngest pulsar wind nebula (PWN) at the centre of the SN 1986J remnant is studied. We demonstrate that the 5 GHz flux of ‘PWN 1986J’, increasing with time, is consistent with a stochastic acceleration model of PWNe developed to explain the flat radio spectrum of the Crab Nebula. We obtain an acceleration time-scale of electrons/positrons and a decay time-scale of the turbulence responsible for the stochastic acceleration as about 10 yr and 70 yr, respectively. Our findings suggest that efficient stochastic acceleration and rising radio/submm light curves are characteristic signatures of the youngest PWNe. Follow-up ALMA observations of decades-old supernovae within a few tens of Mpc, including SN 1986J, are encouraged to reveal the origin of the flat radio spectrum of PWNe.

Ion Acoustic Shock Wave Formation and Ion Acceleration in the Interactions of Pair Jets with Electron–ion Plasmas

Astrophysical jets are ubiquitous in the universe and often associated with compact objects, and their interactions with the ambient medium not only dissipate their own energy but also provide ideal circumstances for particle acceleration. By means of theoretical analysis and particle-in-cell simulations, here we study the ion acoustic shock wave (IASW) formation and consequent ion acceleration when electron–positron (e − e +) jets are injected into ambient electron–ion plasmas. It is found that the Buneman instability can be excited first, which induces the formation of an ion acoustic wave (IAW). As the amplitude of the IAW increases, its waveform is steepened and subsequently an IASW is formed. Some ions in the ambient plasmas will be reflected when they encounter the IASW, and thus can be accelerated to form an energetic ion beam. For an initial e − e + jet with the Lorentz factor γ 0 = 100 and the ion–electron mass ratio m i /m e = 1836, the ions can be accelerated up to 580 MeV. This study deepens our understanding of the fireball model of gamma-ray bursts, the shock model of pulsar wind nebulae, the origin of cosmic rays, and other related astrophysical processes.

Multiband nonthermal radiative model of pulsar wind nebulae: Study of the effects of advection and diffusion

Aims. Nonthermal radiation properties of pulsar wind nebulae (PWNe) are studied in the frame of a time-dependent model with particle advection and diffusion. Methods. The dynamical and radiative evolution of a PWN was self-consistently solved in the model. The time-dependent lepton (electrons and positrons) equation is described by particle injection, advection, diffusion, adiabatic loss, and radiative loss. Nonthermal emission from a PWN is mainly produced by the relativistic leptons through synchrotron radiation and inverse Compton process. Results. The effect of particle transport including advection and diffusion was analyzed, showing that the particle transport process induces a decrease in the nebula flux, and that the total flux decreases with the increase in advection velocity and diffusion coefficient. Meanwhile, the particle transport processes may play an important role in modifying the spectrum of the emitted radiation at X-ray and TeV wavelengths, but only have slightly effects in radio and GeV bands. We applied our model to the three PWNe Crab nebula, 3C 58, and G54.1+0.3, and observed that the spectral energy distributions of photon emissions from the three PWNe are reproduced well. Our results indicate that (i) the particle cooling processes are dominated by adiabatic loss in lower-energy bands and synchrotron loss dominates for the higher-energy particles; and (ii) the particle transport processes are advection dominated, and a slow diffusion may occur within the Crab nebula, 3C 58, and G54.1+0.3.

Introducing the HD+B model for pulsar wind nebulae: a hybrid hydrodynamics/radiative approach

ABSTRACT Identification and characterization of a rapidly increasing number of pulsar wind nebulae is, and will continue to be, a challenge of high-energy gamma-ray astrophysics. Given that such systems constitute -by far- the most numerous expected population in the TeV regime, such characterization is important not only to learn about the sources per se from an individual and population perspective, but also to be able to connect them with observations at other frequencies, especially in radio and X-rays. Also, we need to remove the emission from nebulae in highly confused regions of the sky for revealing other underlying emitters. In this paper, we present a new approach for theoretical modelling of pulsar wind nebulae: a hybrid hydrodynamic-radiative model able to reproduce morphological features and spectra of the sources, with relatively limited numerical cost.

Outflow and Emission Model of Pulsar Wind Nebulae with the Back Reaction of Particle Diffusion

Abstract We present a new pulsar wind nebula (PWN) model that solves both advection and diffusion of nonthermal particles in a self-consistent way to satisfy the momentum and energy conservation laws. Assuming spherically symmetric (1D) steady outflow, we calculate the emission spectrum integrating over the entire nebula and the radial profile of the surface brightness. We find that the back reaction of the particle diffusion modifies the flow profile. The photon spectrum and the surface brightness profile are different from the model calculations without the back reaction of the particle diffusion. Our model is applied to the two well-studied PWNe, 3C 58 and G21.5-0.9. By fitting the spectra of these PWNe, we determine the parameter sets and calculate the radial profiles of X-ray surface brightness. For both the objects, obtained profiles of X-ray surface brightness and the photon index are well consistent with observations. Our model suggests that particles that have escaped from the nebula significantly contribute to the γ-ray flux. A γ-ray halo larger than the radio nebula is predicted in our model.

Confinement of the Crab Nebula with tangled magnetic field by its supernova remnant

A pulsar wind is a relativistic outflow dominated by Poynting energy at its base. Based on the standard ideal magnetohydrodynamic (MHD) model of pulsar wind nebulae (PWNe) with the ordered magnetic field, the observed slow expansion $v_{\rm PWN} \ll c$ requires the wind to be dominated by kinetic energy at the upstream of its termination shock, which conflicts with the pulsar wind theory ($\sigma$-problem). In this paper, we extend the standard model of PWNe by phenomenologically taking into account conversion of the ordered to turbulent magnetic field and dissipation of the turbulent magnetic field. Disordering of the magnetic structure is inferred from the recent three-dimensional relativistic ideal MHD simulations, while magnetic dissipation is a non-ideal MHD effect requiring a finite resistivity. We apply this model to the Crab Nebula and find that the conversion effect is important for the flow deceleration, while the dissipation effect is not. Even for Poynting-dominated pulsar wind, we obtain the Crab Nebula's $v_{\rm PWN}$ by adopting a finite conversion time-scale of $\sim 0.3$ yr. Magnetic dissipation primarily affects the synchrotron radiation properties. Any values of the pulsar wind magnetization $\sigma_{\rm w}$ are allowed within the present model of the PWN dynamics alone, and even a small termination shock radius of $\ll 0.1$ pc reproduces the observed dynamical features of the Crab Nebula. In order to establish a high-$\sigma_{\rm w}$ model of PWNe, it is important to extend the present model by taking into account the broadband spectrum and its spacial profiles.

On the Radio Emitting Particles of the Crab Nebula: Stochastic Acceleration Model

AbstractThe standard shock acceleration model of pulsar wind nebulae (PWNe) does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model including the energy diffusion, i.e., the stochastic acceleration, and apply to the Crab Nebula. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock accelerated particles comparable.

Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisp motions as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.

Time-dependent modelling of pulsar wind nebulae: study on the impact of the diffusion-loss approximations

In this work, we present a leptonic, time-dependent model of pulsar wind nebulae (PWNe). The model seeks a solution for the lepton distribution function considering the full time-energy-dependent diffusion-loss equation. The time-dependent lepton population is balanced by injection, energy losses and escape. We include synchrotron, inverse-Compton (IC; with the cosmic-microwave background as well as with IR/optical photon fields), self-synchrotron Compton, and bremsstrahlung processes, all devoid of any radiative approximations. With this model in place we focus on the Crab nebula as an example and present its time-dependent evolution. Afterwards, we analyse the impact of different approximations made at the level of the diffusion-loss equation, as can be found in the literature. Whereas previous models ignored the escape term, e.g. with the diffusion-loss equation becoming advective, others approximated the losses as catastrophic, so that the equation has only time derivatives. Additional approximations are also described and computed. We study what the impact of these approaches is on the determination of the PWN evolution. In particular, we find the time-dependent deviation of the multi-wavelength spectrum and the best-fitting parameters obtained with the complete and the approximate models.

RELAXATION OF PULSAR WIND NEBULA VIA CURRENT-DRIVEN KINK INSTABILITY

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability was excited by a small initial velocity perturbation and developed turbulent structure inside the hot plasma column. We demonstrated that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter "σ", the ratio of the magnetic energy to the thermal energy for a hot plasma, declined from an initial value of 0.3 to about 0.01 when the CD kink instability saturated. Our simulations demonstrated that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. II. RELAXATION OF PULSAR WIND NEBULA

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the current-driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations, the CD kink instability is excited by a small initial velocity perturbation and develops a turbulent structure inside the hot plasma column. We demonstrate that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter σ, the ratio of the Poynting to the kinetic energy flux, declines from an initial value of 0.3 to about 0.01 when the CD kink instability saturates. Our simulations demonstrate that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae does not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.

A high-sigma model of pulsar wind nebulae

Pulsars and central engines of long gamma ray burst -- collapsars -- may produce highly magnetized (Poynting flux dominated) outflows expanding in a dense surrounding (interstellar medium or stellar material). For certain injection conditions, the magnetic flux of the wind cannot be accommodated within the cavity. In this case, ideal (non-dissipative) MHD models, similar to the Kennel and Coroniti (1984) model of the Crab nebular, break down (the so-called sigma problem). This is typically taken to imply that the wind should become particle-dominated on scales much smaller than the size of the cavity. The wind is then slowed down by a fluid-type (low magnetization) reverse shock. Recent Fermi results, indicating that synchrotron spectrum of the Crab nebula extends well beyond the upper limit of the most efficient radiation reaction-limited acceleration, contradict the presence of a low sigma reverse shock. We propose an alternative possibility, that the excessive magnetic flux is destroyed in a reconnection-like process in two regions: near the rotational axis and near the equator. We construct an example of such highly magnetized wind having two distinct reconnection regions and suggest that these reconnection cites are observed as tori and jets in pulsar wind nebulae. The model reproduces, qualitatively, the observed morphology of the Crab nebula. In parts of the nebular the dissipation occurs in a relativistically moving wind, alleviating the requirements on the acceleration rate.