Bulk metals with helical surface states

In the flurry of experiments looking for topological insulator materials, it has been recently discovered that some bulk metals very close to topological insulator electronic states, support the same topological surface states that are the defining characteristic of the topological insulator. First observed in spin-polarized ARPES in Sb (D. Hsieh et al. Science 323, 919 (2009)), the helical surface states in the metallic systems appear to be robust to at least mild disorder. We present here a theoretical investigation of the nature of these "helical metals" - bulk metals with helical surface states. We explore how the surface and bulk states can mix, in both clean and disordered systems. Using the Fano model, we discover that in a clean system, the helical surface states are \emph{not} simply absorbed by hybridization with a non-topological parasitic metallic band. Instead, they are pushed away from overlapping in momentum and energy with the bulk states, leaving behind a finite-lifetime surface resonance in the bulk energy band. Furthermore, the hybridization may lead in some cases to multiplied surface state bands, in all cases retaining the helical characteristic. Weak disorder leads to very similar effects - surface states are pushed away from the energy bandwidth of the bulk, leaving behind a finite-lifetime surface resonance in place of the original surface states

Spark Model for Pulsar Radiation Modulation Patterns

A non-stationary polar gap model first proposed by Ruderman & Sutherland (1975) is modified and applied to spark-associated pulsar emission at radio wave-lengths. It is argued that under physical and geometrical conditions prevailing above pulsar polar cap, highly non-stationary spark discharges do not occur at random positions. Instead, sparks should tend to operate in well determined preferred regions. At any instant the polar cap is populated as densely as possible with a number of two-dimensional sparks with a characteristic dimension as well as a typical distance between adjacent sparks being about the polar gap height. Our model differs, however, markedly from its original 'hollow cone' version. The key feature is the quasi-central spark driven by pair production process and anchored to the local pole of a sunspot-like surface magnetic field. This fixed spark prevents the motion of other sparks towards the pole, restricting it to slow circumferential drift across the planes of field lines converging at the local pole. We argue that the polar spark constitutes the core pulsar emission, and that the annular rings of drifting sparks contribute to conal components of the pulsar beam. We found that the number of nested cones in the beam of typical pulsar should not excced three; a number also found by Mitra & Deshpande (1999) using a completely different analysis.Comment: 31 pages, 8 figures, accepted by Ap

Hall drift in the crust of neutron stars - necessary for radio pulsar activity?

The radio pulsar models based on the existence of an inner accelerating gap located above the polar cap rely on the existence of a small scale, strong surface magnetic field $B_s$. This field exceeds the dipolar field $B_d$, responsible for the braking of the pulsar rotation, by at least one order of magnitude. Neither magnetospheric currents nor small scale field components generated during neutron star's birth can provide such field structures in old pulsars. While the former are too weak to create $B_s \gtrsim 5\times 10^{13}$G$\;\gg B_d$, the ohmic decay time of the latter is much shorter than $10^6$ years. We suggest that a large amount of magnetic energy is stored in a toroidal field component that is confined in deeper layers of the crust, where the ohmic decay time exceeds $10^7$ years. This toroidal field may be created by various processes acting early in a neutron star's life. The Hall drift is a non-linear mechanism that, due to the coupling between different components and scales, may be able to create the demanded strong, small scale, magnetic spots. Taking into account both realistic crustal microphysics and a minimal cooling scenario, we show that, in axial symmetry, these field structures are created on a Hall time scale of $10^3$-$10^4$ years. These magnetic spots can be long-lived, thereby fulfilling the pre-conditions for the appearance of the radio pulsar activity. Such magnetic structures created by the Hall drift are not static, and dynamical variations on the Hall time scale are expected in the polar cap region.Comment: 4 pages, 5 figures, contribution to the ERPM conferences, Zielona Gora, April 201

Frequency dependence of pulsar radiation patterns

We report on new results from simultaneous, dual frequency, single pulse observation of PSR B0329+54 using the Giant Metrewave Radio Telescope. We find that the longitude separation of subpulses at two different frequencies (238 and 612 MHz) is less than that for the corresponding components in the average profile. A similar behaviour has been noticed before in a number of pulsars. We argue that subpulses are emitted within narrow flux tubes of the dipolar field lines and that the mean pulsar beam has a conal structure. In such a model the longitudes of profile components are determined by the intersection of the line of sight trajectory with subpulse-associated emission beams. Thus, we show that the difference in the frequency dependence of subpulse and profile component longitudes is a natural property of the conal model of pulsar emission beam. We support our conclusions by numerical modelling of pulsar emission, using the known parameters for this pulsar, which produce results that agree very well with our dual frequency observations.Comment: 24 pages, 8 figures. Accepted for publication in Ap

Nature of eclipsing pulsars

We present a model for pulsar radio eclipses in some binary systems, and test this model for PSRs B1957+20 and J2051-0827. We suggest that in these binaries the companion stars are degenerate dwarfs with strong surface magnetic fields. The magnetospheres of these stars are permanently infused by the relativistic particles of the pulsar wind. We argue that the radio waves emitted by the pulsar split into the eigenmodes of the electron-positron plasma as they enter the companion's magnetosphere and are then strongly damped due to cyclotron resonance with the ambient plasma particles. Our model explains in a natural way the anomalous duration and behavior of radio eclipses observed in such systems. In particular, it provides stable, continuous, and frequency-dependent eclipses, in agreement with the observations. We predict a significant variation of linear polarization both at eclipse ingress and egress. In this paper we also suggest several possible mechanisms of generation of the optical and $X$-ray emission observed from these binary systems.Comment: 12 pages, 5 figures, submitted to Ap

The spark-associated soliton model for pulsar radio emission

We propose a new, self-consistent theory of coherent pulsar radio emission based on the non-stationary sparking model of Ruderman & Sutherland (1975), modified by Gil & Sendyk (2000) in the accompanying Paper I. According to these authors, the polar cap is populated as densely as possible by a number of sparks with a characteristic perpendicular dimension D approximately equal to the polar gap height scale h, separated from each other also by about h. Each spark reappears in approximately the same place on the polar cap for a time scale much longer than its life-time and delivers to the open magnetosphere a sequence of electron-positron clouds which flow orderly along a flux tube of dipolar magnetic field lines. The overlapping of particles with different momenta from consecutive clouds leads to effective two-stream instability, which triggers electrostatic Langmuir waves at the altitudes of about 50 stellar radii. The electrostatic oscillations are modulationally unstable and their nonlinear evolution results in formation of ``bunch-like'' charged solitons. A characteristic soliton length along magnetic field lines is about 30 cm, so they are capable of emitting coherent curvature radiation at radio wavelengths. The net soliton charge is about 10^21 fundamental charges, contained within a volume of about 10^14 cm^3. For a typical pulsar, there are about 10^5 solitons associated with each of about 25 sparks operating on the polar cap at any instant. One soliton moving relativisticaly along dipolar field lines with a Lorentz factor of the order of 100 generates a power of about 10^21 erg/s by means of curvature radiation. Then the total power of a typical radio pulsar can be estimated as being about 10^(27-28) erg/s.Comment: 27 pages, 5 figures, accepted by Ap

XMM-Newton Observations of Radio Pulsars B0834+06 and B0826-34 and Implications for Pulsar Inner Accelerator

We report the X-ray observations of two radio pulsars with drifting subpulses: B0834 + 06 and B0826 - 34 using \xmm\. PSR B0834 + 06 was detected with a total of 70 counts from the three EPIC instruments over 50 ks exposure time. Its spectrum was best described as that of a blackbody (BB) with temperature $T_s=(2.0^{+2.0}_{-0.9}) \times 10^6$ K and bolometric luminosity of $L_b=(8.6^{+14.2}_{-4.4}) \times 10^{28}$ erg s$^{-1}$. As it is typical in pulsars with BB thermal components in their X-ray spectra, the hot spot surface area is much smaller than that of the canonical polar cap, implying a non-dipolar surface magnetic field much stronger than the dipolar component derived from the pulsar spin-down (in this case about 50 times smaller and stronger, respectively). The second pulsar PSR B0826 - 34 was not detected over 50 ks exposure time, giving an upper limit for the bolometric luminosity $L_b \leq 1.4 \times 10^{29}$ erg s$^{-1}$. We use these data as well as the radio emission data concerned with drifting subpulses to test the Partially Screened Gap (PSG) model of the inner accelerator in pulsars.Comment: Accepted for publication by The Astrophysical Journa

Multiple cyclical fractional structures in financial time series

This paper analyses multiple cyclical structures in financial time series. In particular, we focus on the monthly structure of the Nasdaq, the Dow Jones and the Standard&Poor stock market indices. The three series are modelled as long-memory processes with poles in the spectrum at multiple frequencies, including the long-run or zero frequency

Pulsar Radio Emission Altitude from Curvature Radiation

We assume that the relativistic sources moving along the dipolar magnetic field lines emit curvature radiation. The beamed emission occurs in the direction of tangents to the field lines, and to receive it, the sight line must align with the tangent within the beaming angle 1/gamma, where gamma is the particle Lorentz factor. By solving the viewing geometry in an inclined and rotating dipole magnetic field, we show that, at any given pulse phase, observer tends to receive radiation only from the specific heights allowed by the geometry. We find outer conal components are emitted at higher altitudes compared to inner components including the core. At any pulse phase, low frequency emission comes from higher altitudes than high frequency emission. We have modeled the emission heights of pulse components of PSR B0329+54, and estimated field line curvature radii and particle Lorentz factors in the emission regions.Comment: 14 pages, 3 figures. Accepted for Astrophysical Journal, 200

Generalized information entropies depending only on the probability distribution

Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and $F$-distributions of $\beta$. It is assumed that they depend only on $p_l$, the probability associated with the microscopic configuration of the system. For each of the three $\beta-$distributions we calculate the Boltzmann factors and show that they coincide for small variance of the fluctuations. For the Gamma distribution it is possible to calculate the entropy in a closed form, depending on $p_l$, and to obtain then an equation relating $p_l$ with $\beta E_l$. We also propose, as other examples, new entropies close related with the Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in this work do not depend on a constant parameter $q$ but on $p_l$. For the $p_l$-Gamma distribution and its corresponding $B_{p_l}(E)$ Boltzmann factor and the associated entropy, we show the validity of the saddle-point approximation. We also briefly discuss the generalization of one of the four Khinchin axioms to get this proposed entropy.Comment: 13 pages, 3 figure