Neutron Star Magnetosphere Research Articles

Explosive energy release in magnetic shocks.

We show that a magnetic shock whose initial density and/or magnetic perturbation exceeds the Hugoniot limit may lead to substantial and rapid energy release in low beta plasmas (such as occur in the magnetospheres of neutron stars). We illustrate this effect for a fast Magnetohydrodynamic perturbation, as well as for large density perturbations which can be naturally created in low beta plasmas. Using the Riemann solution and simulations, we show that slow modes of finite magnitudes and Alfvénic perturbations can generate strong density perturbations. These perturbations develop into shocks, resulting in efficient energy release.

Gamma‐Ray Emission from an Outer Gap Accelerator: Constraints on Magnetospheric Current, Magnetic Inclination, and Distance for PSR B1055−52

We investigate a stationary pair production cascade in the outer magnetosphere of a spinning neutron star. The charge depletion due to global flows of charged particles, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved, together with the distribution functions of particles and gamma-rays. By solving the Vlasov equations describing this pair production cascade, we demonstrate the existence of a stationary gap in the outer magnetosphere of PSR B1055-52 for a wide range of current densities flowing in the accelerator: From sub to super Goldreich-Julian values. However, we find that the expected GeV spectrum becomes very soft if the current density exceeds the Goldreich-Julian value. We also demonstrate that the GeV spectrum softens with decreasing magnetic inclination and with increasing distance to this pulsar. We thus conclude that a sub-Goldreich-Julian current, a large magnetic inclination, and a small distance (500 pc, say) are plausible to account for EGRET observations. Furthermore, it is found that the TeV flux due to inverse Compton scatterings of infrared photons whose spectrum is inferred from the Rayleigh-Jeans side of the soft blackbody spectrum is much less than the observational upper limit.

Active galactic nuclei and pulsars as cosmic ray sources

Relativistic e± particles and cosmic rays are accelerated in the magnetospheres of supermassive black holes and neutron stars. The possibility of synchrotron radiation with extremely high intensity inside the deepest regions of magnetospheres is investigated. Very high brightness temperatures are expected for such radiation by relativistic protons, which can be made even higher in the presence of non-stationary conditions, Doppler boosting and coherent processes. The main parameters for models of such high-brightness-temperature radiation are determined. Two types of active galactic nuclei (AGNs) are expected. One type is associated with the acceleration and ejection of relativistic e± particles only (probably non-IDV sources and FR-I radio galaxies). The second type of AGN is also associated with e± acceleration, but is dominated by the contribution of relativistic protons (probably IDV sources and FR-II radio galaxies). Analogous objects for pulsars are plerion and shell supernova remnants with neutron stars or pulsars without synchrotron nebulae, respectively.

On the state of low luminous accreting neutron stars

Observational appearance of a neutron star in the subsonic propeller state which is a companion of a wind-fed mass-exchange close binary system is discussed. During the subsonic propeller state the neutron star magnetosphere is surrounded by a spherical quasi-static plasma envelope, which is extended from the magnetospheric boundary up to the star accretion radius. The energy input to the envelope due to the propeller action by the neutron star exceeds the radiative losses and the plasma temperature in the envelope is of the order of the free-fall temperature. Under this condition the magnetospheric boundary is interchange stable. Nevertheless, I find that the rate of plasma penetration from the envelope into the magnetic field of the neutron star due to diffusion and magnetic field line reconnection processes is large enough for the accretion power to dominate the spindown power. I show that the accretion luminosity of the neutron star in the subsonic propeller state is 5*10**{30} - 10**{33} (dM/dt)_{15} erg/s, where dM/dt is the strength of the normal companion stellar wind which is parametrized in terms of the maximum possible mass accretion rate onto the neutron star magnetosphere. On this basis I suggest that neutron stars in the subsonic propeller state are expected to be observed as low luminous accretion-powered pulsars. The magnetospheric radius of the neutron star in this state is determined by the strength of the stellar wind, (dM/dt)_c, while the accretion luminosity is determined by the rate of plasma penetration into the star magnetosphere, (dM/dt)_a, which is (dM/dt)_a << (dM/dt)_c. That is why the classification of the neutron star state in these objects using the steady accretion model (i.e. setting (dM/dt)_a = (dM/dt)_c) can lead to a mistaken conclusion.

Electrodynamic Structure of an Outer Gap Accelerator: Location of the Gap and the Gamma‐Ray Emission from the Crab Pulsar

We investigate a stationary pair-production cascade in the outer magnetosphere of a spinning neutron star. The charge depletion due to global flows of charged particles causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma rays, some of which collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the distribution functions of particles and gamma rays. If no current is injected at either of the boundaries of the accelerator, the gap is located around the conventional null surface, where the local Goldreich-Julian charge density vanishes. However, we first find that the gap position shifts outward (or inward) when particles are injected at the inner (or outer) boundary. Applying the theory to the Crab pulsar, we demonstrate that the pulsed TeV flux does not exceed the observational upper limit for moderate infrared photon density and that the gap should be located near to or outside of the conventional null surface so that the observed spectrum of pulsed GeV fluxes may be emitted via a curvature process. Some implications of the existence of a solution for a super Goldreich-Julian current are discussed.

On the accretion flow geometry in A0535+26

The geometry of accretion flow in the Be/X-ray transient A0535+26 is explored. It is shown that neither moderate nor giant X-ray flaring events observed in the system can be interpreted within the spherically symmetrical accretion model and hence the formation of an accretion disk around the neutron star magnetosphere during the both types of flares is required. The accretion disk can be formed at the periastron if (i) the expansion velocity of the Be star envelope in the equatorial plane is Vwr 0:16 _ M 1=7 17 ,w here _ M17 is the rate of mass capture by the neutron star expressed in units of 10 17 gs 1 . We suggest that the \missing outburst phe- nomenon can be associated with the spherically symmetrical accretion onto the interchange-stable magnetosphere of the neutron star. The average spin up rate of the neutron star during moderate flares <3.5 10 12 Hz s 1 is predicted.

Plasmoid impacts on neutron stars and highest energy cosmic rays.

Particle acceleration by electrostatic polarization fields that arise in plasmas streaming across magnetic fields is discussed as a possible acceleration mechanism of highest energy ( greater, similar10(20) eV) cosmic rays. Specifically, plasmoids arising in planetoid impacts onto neutron star magnetospheres are considered. We find that such impacts at plausible rates may account for the observed flux and energy spectrum of the highest energy cosmic rays.

One-dimensional electric field structure of an outer gap accelerator -- III. Location of the gap and the gamma-ray spectrum

We investigate a stationary particle acceleration zone in the outer magnetosphere of a spinning neutron star. The charge depletion due to a global current causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. As a result of this pair-production cascade, the replenished charges partially screen the electric field, which is self-consistently solved together with the distribution of particles and gamma-rays. If no current is injected at neither of the boundaries of the accelerator, the gap is located around the so-called null surface, where the local Goldreich-Julian charge density vanishes. However, we find that the gap position shifts outwards (or inwards) when particles are injected at the inner (or outer) boundary. We apply the theory to the nine pulsars of which X-ray fields are known from observations. We show that the gap should be located near to or outside of the null surface for the Vela pulsar and PSR B1951+32, so that their expected GeV spectrum may be consistent with observations. We then demonstrate that the intrinsically large TeV flux from the outer gap of PSR B0540-69 is absorbed by the magnetospheric infrared photons to be undetectable. We also point out that the electrodynamic structure and the resultant GeV emission properties of millisecond pulsars are similar to young pulsars.

δ-Invariant for Quasi-periodic Oscillations and Physical Parameters of the 4U 0614+09 Binary

The recently formulated two-oscillator (TO) model interprets the lowest of the kilohertz frequencies of the twin-peak quasi-periodic oscillations in X-ray binaries as the Keplerian frequency νK. The high twin frequency νh in this model holds the upper hybrid frequency relation to the rotational frequency of the neutron star's magnetosphere Ω: ν = ν + 4(Ω/2π)2. The vector Ω is assumed to have an angle δ with the normal to the disk. The first oscillator in the TO model allows one to interpret the horizontal branch observed below 100 Hz as the lower mode of the Keplerian oscillator under the influence of the Coriolis force, with frequency νL being dependent on νh, νK, and δ. For some stars such as 4U 0614+09, Scorpius X-1, and 4U 1702-42, νh, νK, and νL have been observed simultaneously, thus providing the opportunity to check the central prediction of the TO model, i.e., the constancy of δ for a particular source. Given the considerable variation of each of these three frequencies, the existence of an observational invariant with a clear physical interpretation as a global parameter of the neutron star magnetosphere is an important test of the TO model. Using the results of recent observations of 4U 0614+09, we verify the existence of this invariant and determine the angle δ = 156 ± 05 for this star. The second oscillator in the model deals with both a radial (presumably sound) oscillation and a diffuse process in the viscous layer surrounding the neutron star. Our analysis of the viscous oscillation frequency νV and the break frequency νb of the diffusion shows that the spin value of the inner boundary of the transition layer for 4U 0614+09 is at least 2 times more than the values for 4U 1728-34 and Sco X-1.

R‐Mode Oscillations and Spin‐down of Young Rotating Magnetic Neutron Stars

Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including the effects of both gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that given by Owen and colleagues in 1998, in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B 1014(νs/300 Hz)2 G, where νs is the spin frequency, the spin-down rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfven wave emission in the neutron star magnetosphere. The Alfven wave driving of the r-mode becomes more important than the gravitational radiation driving when B 1013(νs/150 Hz)3 G; the electromagnetic wave driving of the r-mode is much weaker. Finally, we study the properties of local Rossby-Alfven waves inside the neutron star and show that the fractional change of the r-mode frequency due to the magnetic field is of order 0.5(B/1016 G)2(νs/100 Hz)-2.

On the Disappearance of Kilohertz Quasi-periodic Oscillations at a High Mass Accretion Rate in Low-Mass X-Ray Binaries.

For all sources in which the phenomenon of kilohertz quasi-periodic oscillation (kHz QPO) is observed, the QPOs disappear abruptly when the inferred mass accretion rate exceeds a certain threshold. Although the threshold cannot at present be accurately determined (or even quantified) observationally, it is clearly higher for bright Z sources than for faint atoll sources. Here we propose that the observational manifestation of kHz QPOs requires direct interaction between the neutron star magnetosphere and the Keplerian accretion disk and that the cessation of kHz QPOs at a high accretion rate is due to the lack of such an interaction when the Keplerian disk terminates at the last stable orbit and yet the magnetosphere is pushed farther inward. The threshold is therefore dependent on the magnetic field strength-the stronger the magnetic field, the higher the threshold. This is certainly in agreement with the atoll/Z paradigm, but we argue that it is also generally true, even for individual sources within each (atoll or Z) category. For atoll sources, the kHz QPOs also seem to vanish at a low accretion rate. Perhaps the "disengagement" between the magnetosphere and the Keplerian disk also takes place under such circumstances because of, for instance, the presence of quasi-spherical advection-dominated accretion flow (ADAF) close to the neutron star. Unfortunately, in this case, the estimation of the accretion rate threshold would require a knowledge of the physical mechanisms that cause the disengagement. If the ADAF is responsible, the threshold is likely dependent on the magnetic field of the neutron star.

ICS as a Limiting Factor for Electron Energies in Pulsar Magnetospheres

AbstractBased on the polar cap model, we investigated in the energy loss of accelerated electrons in a neutron star magnetosphere by inverse Compton scattering of thermal photospheric radiation. An analytical treatment is presented, which turns out ranges in the magnetic field strength and thermal temperature where ultrarelativistic electrons can not survive.

One-dimensional electric field structure of an outer gap accelerator — II. γ-ray production resulting from inverse Compton scattering

We study the structure of a stationary and axisymmetric charge-deficient region (or a potential gap) in the outer magnetosphere of a spinning neutron star. A large electric field along the magnetic field lines is created in this potential gap and accelerates migratory electrons (e 2 ) and/or positrons (e + ) to ultrarelativistic energies. Assuming that the gap is immersed in a dense soft photon field, these relativistic e ^ radiate g-ray photons via inverse Compton (IC) scattering. These g-rays, in turn, produce yet more radiating particles by colliding with ambient soft photons, leading to a pair-production cascade in the gap. The replenished charges partially screen the longitudinal electric field, which is self-consistently solved together with the distribution of e ^ and g-ray photons. It is demonstrated that the voltage drop in the gap is not more than 10 10 V when the background X-ray radiation is as luminous as 10 37 ergs 21 . However, this value increases with decreasing X-ray luminosity and attains 10 12 V when the X-ray radiation is 10 36 ergs 21 . In addition, we find useful expressions of the spatial distribution of the particle fluxes and longitudinal electric field, together with the relationship between the voltage drop and the current density. Amazingly, these expressions are valid not only when IC scattering dominates but also when curvature radiation dominates.

One-dimensional electric field structure of an outer gap accelerator — I. γ-ray production resulting from curvature radiation

We study the structure of a stationary and axisymmetric charge-deficient region (or potential gap) in the outer magnetosphere of a spinning neutron star. Assuming the existence of global current flow patterns in the magnetosphere, the charge depletion causes a large electric field along the magnetic field lines. This longitudinal electric field accelerates migratory electrons and/or positrons to ultrarelativistic energies. These relativistic electrons/positrons radiate g-ray photons by curvature radiation. These g-rays, in turn, produce yet more radiating particles by colliding with ambient X-ray photons, leading to a pair production cascade in the gap. The replenished charges partially screen the longitudinal electric field, which is selfconsistently solved together with the distribution of e ^ and g-ray photons. We find the voltage drop in the gap as a function of the soft photon luminosity. It is demonstrated that the voltage drop is less than 3 � 10 13 V when the background X-ray radiation is as luminous as Vela. However, this value increases with decreasing X-ray luminosity and attains 3 � 10 15 V when the X-ray luminosity is as low as LX ˆ 10 31 ergs 21 .

Aquila X-1 from outburst to quiescence: the onset of the propeller effect and signs of an awaken rotation powered pulsar

According to current evolutionary scenarios, neutron stars in Low Mass X-Ray Binaries (LMXRBs) are spun-up by accretion torques to limiting periods in the millisecond range and give rise to “recycled” millisecond ratio pulsars once accretion stops 1–3. In addition to persistent sources, the X-ray sky is populated by a number of transient sources. Among them, Soft X-Ray Transients (SXRTs), when in outburst, show properties similar to those of LMXRBs 4–6. SXRTs are characterised by luminosities, and therefore mass accretion rates, that vary over many decades: while it is clear that when in outburst their emission is powered by accretion onto the neutron star surface, the origin of the low-level emission detected during quiescence remained uncertain 7,8. Here we report on BeppoSAX pointed observations of Aql X-1, the first to follow the decay of a SXRT outburst down to quiescence. The fast X-ray flux decay that leads to quiescence is most readily interpreted in terms of the propeller effect arising from the very fast rotation of the neutron star magnetosphere. The hard X-ray spectrum that characterises the quiescent emission is probably due to shock emission powered by a turned-on radio pulsar.

On the self-consistent model of an axisymmetric radio pulsar magnetosphere

We consider a model of axisymmetric neutron star magnetospheres. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the stream equation describing the magnetic field structure is linear both in the open and closed regions; the main problem is matching the solutions along the separatrix. We demonstrate that it is the stability condition on the separatrix that allows us to obtain a unique solution of the problem. In particular, the zero point of magnetic field is shown to be located near the light cylinder. Moreover, the hypothesis of the existence of the non-linear Ohm’s Law, connecting the potential drop in the pair creation region and the longitudinal electric current flowing in the magnetosphere, is confirmed.

The neutron stars of Soft X-ray Transients

Soft X–ray Transients (SXRTs) have long been suspected to contain old, weakly magnetic neutron stars that have been spun up by accretion torques. After reviewing their observational properties, we analyse the different regimes that likely characterise the neutron stars in these systems across the very large range of mass inflow rates, from the peak of the outbursts to the quiescent emission. While it is clear that close to the outburst maxima accretion onto the neutron star surface takes place, as the mass inflow rate decreases, accretion might stop at the magnetospheric boundary because of the centrifugal barrier provided by the neutron star. For low enough mass inflow rates (and sufficiently short rotation periods), the radio pulsar mechanism might turn on and sweep the inflowing matter away. The origin of the quiescent emission, observed in a number of SXRTs at a level of \(\sim 10^{32}-10^{33}\, {\rm erg\,s^{-1}}\), plays a crucial role in constraining the neutron star magnetic field and spin period. Accretion onto the neutron star surface is an unlikely mechanism for the quiescent emission of SXRTs, as it requires very low magnetic fields and/or long spin periods. Thermal radiation from a cooling neutron star surface in between the outbursts can be ruled out as the only cause of the quiescent emission. We find that accretion onto the neutron star magnetosphere and shock emission powered by an enshrouded radio pulsar provide far more plausible models. In the latter case the range of allowed neutron star spin periods and magnetic fields is consistent with the values recently inferred from the properties of kHz quasi-periodic oscillation in low mass X–ray binaries. If quiescent SXRTs contain enshrouded radio pulsars, they provide a missing link between X–ray binaries and millisecond pulsars.

Aquila X-1 from Outburst to Quiescence: The Onset of the Propeller Effect and Signs of a Turned-on Rotation-powered Pulsar

We report on the 1997 March-April BeppoSAX observations of Aquila X-1, which were the first to monitor the evolution of the spectral and time-variability properties of a neutron star soft X-ray transient from the outburst decay to quiescence. We observed a fast X-ray flux decay, which brought the source luminosity from ~1036 to ~1033 ergs s-1 in less than 10 days. The X-ray spectrum showed a power-law high-energy tail with a photon index Γ~2, which hardened to Γ~1-1.5 as the source reached quiescence. These observations, together with the detection by the Rossi X-Ray Timing Explorer of a periodicity of a few milliseconds during an X-ray burst, likely indicate that the rapid flux decay is caused by the onset of the propeller effect, which arises from the very fast rotation of the neutron star magnetosphere. The X-ray luminosity and hard spectrum that characterize the quiescent emission can be consistently interpreted as shock emission by a turned-on rotation-powered pulsar.

Magnetohydrodynamics in the extreme relativistic limit

We present two new formulations of magnetohydrodynamics (MHD), in the limit where the inertia of the charge carriers can be neglected. The first employs Lagrangian coordinates and generalizes Newcomb's formalism to allow for a variable time slicing. It contains an extremely simple prescription for generalizing the action of a relativistic Nambu-Goto string to four dimensions. It is also related by a duality transformation to the action presented by Achterberg. This transformation causes the perturbed and unperturbed Lagrangian coordinates to exchange roles as dynamical fields and background spacetime. Our second formulation introduces massless electrically charged fermions as the current carrying modes, and considers long wavelength perturbations with ${\ensuremath{\omega}}^{2}{,k}_{\ensuremath{\perp}}^{2}\ensuremath{\ll}\mathrm{eB}.$ Because the Fermi zero mode can be bosonized separately on each magnetic flux line, the current density may be written in terms of a four-dimensional axion field that acts as a Lagrange multiplier to enforce the MHD condition. The fundamental modes of the magnetofluid in this limit comprise two oppositely directed Alfv\'en modes and the fast mode, all of which propagate at the speed of light. We calculate the nonlinear interaction between two Alfv\'en modes, and show that in both formulations it satisfies the same simple expression. This provides the first exact treatment of the effects of compressibility on nonlinear interactions between MHD waves. We then summarize the interactions between Alfv\'en modes, between Alfv\'en modes and fast modes, and between fast modes in terms of a simplified Lagrangian. The three-mode interaction between fast modes is a magnetohydrodynamic analogue of the QED process of photon splitting, but occurs in background magnetic fields of arbitrary strength. The scaling behavior of an Alfv\'en wave cascade in a box is derived, paying close attention to boundary conditions. This result also applies to nonrelativistic MHD media and differs from those obtained by previous authors in the nonrelativistic regime. Finally, we briefly outline the physical processes which determine the inner scale of such a cascade in neutron star magnetospheres, black hole accretion disks, and \ensuremath{\gamma}-ray burst sources. At low charge density, the waves at the inner scale may become charge starved; whereas Compton drag is the dominant dissipative mechanism at large optical depth to electron scattering. A turbulent cascade leads to effective dissipation even in optically thick media, and in particular can significantly raise the entropy-baryon ratio in the relativistic outflows that power cosmological \ensuremath{\gamma}-ray bursts.

ROSAT observations of A0538–66 during quiescence

We discuss serendipitous ROSAT observations of the Be transient A0538-66, which contains the fastest known accreting X-ray pulsar (69 ms). We show that this transient is detected several times during quiescence at a level of about 10^34-35 erg/s. Considering this low luminosity it is more likely that X-rays are produced by matter falling onto the neutron star magnetosphere, rather than onto the star surface. This could be the first example of an X-ray source in the propeller regime.