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D. B. Melrose

Publications and source records attributed to D. B. Melrose.

At least 19 recordsLinked to original sources
arXiv2024

Response of a Relativistically Streaming Pulsar Plasma

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame, and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit, and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalised Faraday rotation in pulsars and magnetars.

astro-ph.HE↗
arXiv2020

A rotation-driven pulsar radio emission mechanism

We propose and discuss an alternative pulsar radio emission mechanism that relies on rotation-driven plasma oscillations, rather than on a beam-driven instability, and suggest that it may be the generic radio emission mechanism for pulsars. We identify these oscillations as superluminal longitudinal waves in the pulsar plasma, and point out that these waves can escape directly in the O~mode. We argue that the frequency of the oscillations is $ω_0\approxω_{\rm p}(2\langleγ\rangle)^{1/2}/γ_{\rm s}$, where $γ_{\rm s}$ is the Lorentz factor of bulk streaming motion and $\langleγ\rangle$ is the mean Lorentz factor in the rest frame of the plasma. The dependence of the plasma frequency $ω_{\rm p}$ on radial distance implies a specific frequency-to-radius mapping, $ω_0\propto r^{-3/2}$. Escape of the energy in these oscillations is possible if they are generated in overdense, field-aligned regions that we call fibers; the wave energy is initially refracted into underdense regions between the fibers, which act as ducts. Some implications of the model for the interpretation of pulsar radio emission are discussed.

astro-ph.HE↗
arXiv2020

Pulsar radio emission mechanisms: a critique

We consider critically the three most widely favored pulsar radio emission mechanisms: coherent curvature emission (CCE), beam-driven relativistic plasma emission (RPE) and anomalous Doppler emission (ADE). We assume that the pulsar plasma is one dimensional (1D), streaming outward with a bulk Lorentz factor $γ_{\rm s} \gg \langle γ\rangle -1 \gtrsim 1$, where $\langle γ\rangle $ is the intrinsic spread in the rest frame of the plasma. We argue that the formation of beams in a multi-cloud model is ineffective in the intrinsically relativistic case for plausible parameters, because the overtaking takes too long. We argue that the default choice for the particle distribution in the rest frame is a J{ü}ttner distribution and that relativistic streaming should be included by applying a Lorentz transformation to the rest-frame distribution, rather than the widely assumed relativistically streaming Gaussian distribution. We find that beam-driven wave growth is severely restricted by (a) the wave properties in pulsar plasma, (b) a separation condition between beam and background, and (c) the inhomogeneity of the plasma in the pulsar frame. The growth rate for the kinetic instability is much smaller and the bandwidth of the growing waves is much larger for a J{ü}ttner distribution than for a relativistically streaming Gaussian distribution. No reactive instability occurs at all for a J{ü}ttner distribution. We conclude that none of CCE, RPE and ADE in tenable as the generic pulsar radio emission mechanism for ``plausible'' assumptions about the pulsar plasma.

astro-ph.HE↗
arXiv2019

Wave dispersion in pulsar plasma: 3. Beam-driven instabilities

Beam-driven instabilities are considered in a pulsar plasma assuming that both the background plasma and the beam are relativistic Jüttner distributions. In the rest frame of the background, the only waves that can satisfy the resonance condition are in a tiny range of slightly subluminal phase speeds. The growth rate for the kinetic (or maser) version of the weak-beam instability is much smaller than has been estimated for a relativistically streaming Gaussian distribution, and the reasons for this are discussed. The growth rate for the reactive version of the weak-beam instability is treated in a conventional way. We compare the results with exact calculations, and find that the approximate solutions are not consistent with the exact results. We conclude that, for plausible parameters, there is no reactive version of the instability. The growth rate in the pulsar frame is smaller than that in the rest frame of the background plasma by a factor $2γ_{\rm s}$, where $γ_{\rm s} = 10^2 {\rm -} 10^3$ is the Lorentz factor of the bulk motion of the background plasma, placing a further constraint on effective wave growth. Based on these results, we argue that beam-driven wave growth probably plays no role in pulsar radio emission.

physics.plasm-ph↗
arXiv2019

Wave dispersion in pulsar plasma: 2. Pulsar frame

Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\cal K}$ and the pulsar frame ${\cal K}'$ in which the plasma is streaming with speed $β_{\rm s}$. The effect of a Lorentz transformation on both subluminal, $|z|<1$, and superluminal, $|z|>1$, waves is discussed. It is argued that the preferred choice for a relativistically streaming distribution should be a Lorentz-transformed Jüttner distribution; such a distribution is compared with other choices including a relativistically streaming Gaussian distribution. A Lorentz transformation of the dielectric tensor is written down, and used to derive an explicit relation between the relativistic plasma dispersion functions in ${\cal K}$ and ${\cal K}'$. It is shown that the dispersion equation can be written in an invariant form, implying a one-to-one correspondence between wave modes in any two inertial frames. Although there are only three modes in the plasma rest frame, it is possible for backward-propagating or negative-frequency solutions in ${\cal K}$ to transform into additional forward-propagating, positive-frequency solutions in ${\cal K}'$ that may be regarded as additional modes.

physics.plasm-ph↗
arXiv2019

Wave dispersion in pulsar plasma: 1. Plasma rest frame

Wave dispersion in a pulsar plasma (a 1D, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation these are referred to as the X, A and L modes, with the X and A modes having dispersion relation $z=z_A\approx1-1/2β_A^2$, where $z=ω/k_\parallel c$ is the phase speed and $β_Ac$ is the Alfven speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function, $z^2W(z)$, which is negative for $ z < z_0 $ and has a sharp maximum at $z=z_m$, with $1-z_m<1-z_0\ll1$. We give numerical estimates for the maximum of $z^2W(z)$ and for $z_m$ and $z_0$ for a 1D Juttner distribution. The L and A modes reconnect, for $z_A>z_0$, to form the O and Alfven modes for oblique propagation ($θ\neq0$). For $z_A z_0^2-z_A^2$. The L mode is the nearest counterpart to Langmuir waves in a nonrelativistic plasma, but we argue that there are no `Langmuir-like' waves in pulsar plasma, identifying three features of the L~mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir-like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O~mode around $θ\approx0$. The resonance is also possible for the Alfven mode but only near a turnover frequency that has no counterpart for Alfven waves in a nonrelativistic plasma.

physics.plasm-ph↗
arXiv2018

Rethinking the solar flare paradigm

It is widely accepted that solar flares involve release of magnetic energy stored in the solar corona above an active region, but existing models do not include the explicitly time-dependent electrodynamics needed to describe such energy release. A flare paradigm is discussed that includes the electromotive force (EMF) as the driver of the flare, and the flare-associated current that links different regions where magnetic reconnection, electron acceleration, the acceleration of mass motions and current closure occur. The EMF becomes localized across regions where energy conversion occurs, and is involved in energy propagation between these regions.

astro-ph.SR↗
arXiv2017

Current-driven flare and CME models

Roles played by the currents in the impulsive phase of a solar flare and in a coronal mass ejection (CME) are reviewed. Solar flares are magnetic explosions: magnetic energy stored in unneutralized currents in coronal loops is released into energetic electrons in the impulsive phase and into mass motion in a CME. The energy release is due to a change in current configuration effectively reducing the net current path. A flare is driven by the electromotive force (EMF) due to the changing magnetic flux. The EMF drives a flare-associated current whose cross-field closure is achieved by redirection along field lines to the chromosphere and back. The essential roles that currents play are obscured in the "standard" model and are described incorrectly in circuit models. A semi-quantitative treatment of the energy and the EMF is provided by a multi-current model, in which the currents are constant and the change in the current paths is described by time-dependent inductances. There is no self-consistent model that includes the intrinsic time dependence, the EMF, the flare-associated current and the internal energy transport during a flare. The current, through magnetic helicity, plays an important role in a CME, with twist converted into writhe allowing the kink instability plus reconnection to lead to a new closed loop, and with the current-current force accelerating the CME through the torus instability.

astro-ph.SR↗
arXiv2016

Is Cyclotron Maser Emission in Solar Flares Driven by a Horseshoe Distribution?

Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with the precipitation of auroral electrons in a geomagnetic substorm. Originally, a loss-cone-driven version of ECME, developed for AKR, was applied to spike bursts, but it is now widely accepted that a different, horseshoe-driven, version of EMCE applies to AKR. We explore the implications of the assumption that horseshoe-driven ECME also applies to spike bursts. We develop a 1D model for the acceleration of the electrons by a parallel electric field, and show that under plausible assumptions it leads to a horseshoe distribution of electrons in a solar flare. A second requirement for horseshoe-driven ECME is an extremely low plasma density, referred to as a density cavity. We argue that a coronal density cavity should develop in association with a hard X-ray burst, and that such a density cavity can overcome a long-standing problem with the escape of ECME through the second-harmonic absorption layer. Both the horseshoe distribution and the associated coronal density cavity are highly localized, and could not be resolved in the statistically large number of local precipitation regions needed to explain a hard X-ray burst. The model highlights the "number problem" in the supply of the electrons needed to explain a hard X-ray burst.

astro-ph.SR↗
arXiv2016

Pulsar Electrodynamics: an unsolved problem

Pulsar electrodynamics is reviewed emphasizing the role of the inductive electric field in an oblique rotator and the incomplete screening of its parallel component by charges, leaving `gaps' with $E_\parallel\ne0$. The response of the plasma leads to a self-consistent electric field that complements the inductive electric field with a potential field leading to an electric drift and a polarization current associated with the total field. The electrodynamic models determine the charge density, $ρ$, and the current density, ${\bf J}$, charge starvation refers to situations where the plasma cannot supply $ρ$, resulting in a gap and associated particle acceleration and pair creation. It is pointed out that a form of current starvation also occurs implying a new class of gaps. The properties of gaps are discussed, emphasizing that static models are unstable, the role of large-amplitude longitudinal waves, and the azimuthal dependence that arises across a gap in an oblique rotator. Wave dispersion in a pulsar plasma is reviewed briefly, emphasizing its role in radio emission. Pulsar radio emission mechanisms are reviewed, and it is suggested that the most plausible is a form of plasma emission.

astro-ph.HE↗
arXiv2016

Variations of $P_2$ in subpulse drifting pulsars

We develop a model for subpulse separation period, $P_2$, taking into account both the apparent motion of the visible point as a function of pulsar phase, $ψ$, and the possibility of abrupt jumps between different rotation states in non-corotating pulsar magnetospheres. We identify three frequencies: (i) the spin frequency of the star, (ii) the drift frequency of the magnetospheric plasma in the source region, and (iii) the angular frequency of the visible point around its trajectory. We show how the last of these, which is neglected in traditional models by implicitly assuming the line of sight through the center of the star, affects the interpretation of $P_2$. We attribute the subpulse structure to emission from $m$ anti-nodes distributed uniformly in azimuthal angle about the magnetic axis. We show that variations of $P_2$ as a function of rotational phase or observing frequency arise naturally when the motion of the visible point is taken into account. We discuss possible application of our model in signifying overall field-line distortion at the emitting region. Abrupt changes in $P_2$ can occur during state switching in the magnetosphere. We demonstrate that the unique value of $P_2$ in each rotation state can be used, in principle, to relate the rotation state of the magnetospheres to subpulse drifting.

astro-ph.HE↗
arXiv2014

Visibility of pulsar emission: motion of the visible point

A standard model for the visibility of pulsar radio emission is based on the assumption that the emission is confined to a narrow cone about the tangent to a dipolar field line. The widely accepted rotating vector model (RVM) is an approximation in which the line of sight is fixed and the field line is not strictly tangent to it. We refer to an exact treatment (Gangadhara 2004) as the tangent model. In the tangent model (but not in the RVM) the visible point changes as a function of pulsar rotational phase, $ψ$, defining a trajectory on a sphere of radius $r$. We solve for the trajectory and for the angular velocity of the visible point around it. We note the recent claim that this motion is observable using interstellar holography (Pen et al. 2014). We estimate the error introduced by use of the RVM and find that it is significant for pulsars with emission over a wide range of $ψ$. The RVM tends to underestimate the range of $ψ$ over which emission is visible. We suggest that the geometry alone strongly favors the visible pulsar radio being emitted at a heights more than ten percent of the light-cylinder distance, where our neglect of retardation effects becomes significant.

astro-ph.SR↗
arXiv2013

Bulk Energization of Electrons in Solar Flares by Alfvén Waves

Bulk energization of electrons to $10\,-\,20\,$keV in solar flares is attributed to dissipation of Alfvén waves that transport energy and potential downward to an acceleration region near the chromosphere. The acceleration involves the parallel electric field that develops in the limit of inertial Alfvén waves (IAWs). A two-potential model for IAWs is used to relate the parallel potential to the cross-field potential transported by the waves. We identify a maximum parallel potential in terms of a maximum current density that corresponds to the threshold for the onset of anomalous resistivity. This maximum is of order $10\,$kV when the threshold is that for the Buneman instability. We argue that this restricts the cross-field potential in an Alfvén wave to about $10\,$kV. Effective dissipation requires a large number of up- and down-current paths associated with multiple Alfvén waves. The electron acceleration occurs in localized, transient, anomalously-conducting regions (LTACRs) and is associated with the parallel electric field determined by Ohm's law with an anomalous resistivity. We introduce an idealized model in which the LTACRs are (upward-)current sheets, a few skin depths in thickness, separated by much-larger regions of weaker return current. We show that this model can account semi-quantitatively for bulk energization.

astro-ph.SR↗
arXiv2013

Transfer of Energy, Potential, and Current by Alfvén Waves in Solar Flares

Alfvén waves play three related roles in the impulsive phase of a solar flare: they transport energy from a generator region to an acceleration region; they map the cross-field potential (associated with the driven energy release) from the generator region onto the acceleration region; and within the acceleration region they damp by setting up a parallel electric field that accelerates electrons and transfers the wave energy to them. The Alfvén waves may also be regarded as setting up new closed current loops, with field-aligned currents that close across field lines at boundaries. A model is developed for large-amplitude Alfvén waves that shows how Alfvén waves play these roles in solar flares. A picket-fence structure for the current flow is incorporated into the model to account for the "number problem" and the energy of the accelerated electrons.

astro-ph.SR↗
arXiv2012

Changes in Polarization Position Angle across the Eclipse in the Double Pulsar System

We investigate the changes in polarization position angle in radiation from pulsar A around the eclipse in the Double Pulsar system PSR J0737-3039A/B at the 20 cm and 50 cm wavelengths using the Parkes 64-m telescope. The changes are ~2σ during and shortly after the eclipse at 20 cm but less significant at 50 cm. We show that the changes in position angle during the eclipse can be modelled by differential synchrotron absorption in the eclipse regions. Position angle changes after the eclipse are interpreted as Faraday rotation in the magnetotail of pulsar B. Implied charge densities are consistent with the Goldreich-Julian density, suggesting that the particle energies in the magnetotail are mildly relativistic.

astro-ph.SR↗
arXiv2012

Generic model for magnetic explosions applied to solar flares

An accepted model for magnetospheric substorms is proposed as the basis for a generic model for magnetic explosions, and is applied to solar flares. The model involves widely separated energy-release and particle-acceleration regions, with energy transported Alfvénically between them. On a global scale, these regions are coupled by a large-scale current that is set up during the explosion by redirection of pre-existing current associated with the stored magnetic energy. The explosion-related current is driven by an electromotive force (EMF) due to the changing magnetic flux enclosed by this current. The current path and the EMF are identified for an idealized quadrupolar model for a flare.

astro-ph.SR↗
arXiv2012

Magnetic explosions: role of the inductive electric field

Inclusion of the inductive electric field, ${\bf E}_{\rm ind}$ due to the temporally changing ${\bf B}$, in magnetic explosions is discussed, with emphasis on solar flares. Several roles played by ${\bf E}_{\rm ind}$ are identified: on a global scale, ${\bf E}_{\rm ind}$ produces the EMF that drives the explosion; the associated ${\bf E}_{\rm ind}\times{\bf B}$ drift is identified with the inflow of magnetic field lines into a reconnection region; the polarization current, associated with $\partial{\bf E}_{\rm ind}/\partial t$, implies a ${\bf J}\times{\bf B}$ force that accelerates this inflow; and the component of ${\bf E}_{\rm ind}$ parallel to ${\bf B}$ accelerates the energetic electrons that cause hard X-ray emission and type III radio bursts. Some simple models that describe these effects are presented. A resolution of the long-standing "number problem" in solar flares is suggested.

astro-ph.SR↗