On the peculiarities in the rotational frequency evolution of isolated neutron stars

The measurements of pulsar frequency second derivatives have shown that they are 10²−10⁶ times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters ν, and of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between and for both and , as well as between ν and . We interpret these dependencies as evolutionary ones due to being nearly proportional to the pulsars’ age. The derived statistical relations as well as “anomalous” values of are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of ν _ev(t), and according to the power law with n≈5, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that—several decades. This work has been supported by the Russian Foundation for Basic Research (grant No 04-02-17555), Russian Academy of Sciences (program “Evolution of Stars and Galaxies”), and by the Russian Science Support Foundation. The authors would also like to thank the anonymous referee for valuable comments.     

Galaxy rotation curves: the effect of $\vec{j} \times\vec{B}$ force

Using the Galaxy as an example, we study the effect of [(j)\vec] ×[(B)\vec]\vec{j} \times \vec{B} force on the rotational curves of gas and plasma in galaxies. Acceptable model for the galactic magnetic field and plausible physical parameters are used to fit the flat rotational curve for gas and plasma based on the observed baryonic (visible) matter distribution and [(j)\vec] ×[(B)\vec]\vec{j} \times\vec{B} force term in the static MHD equation of motion. We also study the effects of varied strength of the magnetic field, its pitch angle and length scale on the rotational curves. We show that [(j)\vec] ×[(B)\vec]\vec{j} \times\vec{B} force does not play an important role on the plasma dynamics in the intermediate range of distances 6–12 kpc from the centre, whilst the effect is sizable for larger r (r≥15 kpc), where it is the most crucial.     

Recent glitches detected in the Crab pulsar

From 2000 to 2010, monitoring of radio emission from the Crab pulsar at Xinjiang Observatory detected a total of nine glitches. The occurrence of glitches appears to be a random process as described by previous researches. A persistent change in pulse frequency and pulse frequency derivative after each glitch was found. There is no obvious correlation between glitch sizes and the time since last glitch. For these glitches Δν _p and D[(n)\dot]_p\Delta\dot{\nu}_{p} span two orders of magnitude. The pulsar suffered the largest frequency jump ever seen on MJD 53067.1. The size of the glitch is ∼6.8×10⁻⁶ Hz, ∼3.5 times that of the glitch occurred in 1989 glitch, with a very large permanent changes in frequency and pulse frequency derivative and followed by a decay with time constant ∼21 days. The braking index presents significant changes. We attribute this variation to a varying particle wind strength which may be caused by glitch activities. We discuss the properties of detected glitches in Crab pulsar and compare them with glitches in the Vela pulsar.     

New phase-coherent measurements of pulsar braking indices

Pulsar braking indices offer insight into the physics that underlies pulsar spin-down. Only five braking indices have been measured via phase-coherent timing; all measured values are less than 3, the value expected from magnetic dipole radiation. Here we present new measurements for three of the five pulsar braking indices, obtained with phase-coherent timing for PSRs J1846-0258 (n=2.65±0.01), B1509-58 (n=2.839±0.001) and B0540-69 (n=2.140±0.009). We discuss the implications of these results and possible physical explanations for them.      

Braking index diagnostics of pulsars. I. alignment,Counteralignment and slowing-down noise

We show that the strong correlation observed between the braking indices (n) and the slowing-down ages (Τ) of pulsars is inconsistent with counteralignment between their rotation and magnetic axes, but that the data on pulsars with positive braking indices is consistent with alignment. Alternatively, slowing-down noise can quantitatively account for the data on all pulsars except the Crab and the Vela, and so for the apparent|n| ∼ Τ² correlation observed for the older pulsars.     

Effect of fluctuations in Doppler width on the center of strong absorption lines

Stochastic temperatures and turbulence are characterized by average velocities u _th and < u _turb  > ≡ u ₀ and fluctuations u￠_th {u'_{th}} and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component Dl￠_D \Delta {\lambda '_D} . Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <H_λ>. Usually, only the average velocities u _th and u ₀ are taken into account in photospheric models and these yield the Doppler width Dl_D⁽⁰⁾ \Delta \lambda_D^{(0)} of a line in the customary way. The fluctuations Dl￠_D \Delta {\lambda '_D} mean that near a line center the average absorption coefficient < α_λ > is larger than the usual α_λ, which depends only on the average velocities u _th and u ₀. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the average level of fluctuations in the Doppler width, h = á | Dl￠_D | ñ

Accelerated expansion from?a?modified-quadratic gravity

We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f(φ)R+f(R) where f(φ)=φ ² and f(R)=AR ²+BR _μν R ^μν,(A,B)∈ℝ. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w≈−0.2 and is accelerated in time with a scale factor evolving like a(t)∝t ^5/3 and B+3A≈0.036. When, B+3A→∞ which corresponds for the purely quadratic theory, the scale factor evolves like a(t)∝t ^1/2 whereas when B+3A→0 which corresponds for the purely scalar tensor theory we found when a(t)∝t ^1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=hH[(f)\dot]/f,h ? \mathbbRR=\eta H\dot{\phi}/\phi,\eta\in\mathbb{R} and H=g[(f)\dot]^c,(g,c) ? \mathbbRH=\gamma\dot{\phi}^{\chi},(\gamma,\chi)\in\mathbb{R}. It was shown that for some special values of  χ, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.     

Coherent Emission Mechanisms in Radio Pulsars

A theory of pulsar radio emission generation, in which the observed waves are produced directly by the maser-type plasma instabilities on the anomalous cyclotron-Cherenkov resonance and the Cherenkov-drift resonance , is capable of explaining the main observational characteristics of pulsar radio emission. The instabilities are due to the interaction of the fast particles of the primary beam and from the tail of the distribution with the normal modes of a strongly magnetized one-dimensional electron-positron plasma. The waves emitted at these resonances are vacuum-like electromagnetic waves that may leave the magnetosphere directly. The cyclotron-Cherenkov instability is responsible for core emission pattern and the Cherenkov-drift instability produces conal emission. The conditions for the development of the cyclotron-Cherenkov instability are satisfied for the both typical and millisecond pulsars provided that the streaming energy of the bulk plasma is not very high γ _p = 5 ÷ 10. In a typical pulsar the cyclotron-Cherenkov and Cherenkov-drift resonances occur in the outer parts of magnetosphere at r _res ≈ 10⁹cm. This theory can account for various aspects of pulsar phenomenology including the morphology of the pulses, their polarization properties and spectral behavior. This revised version was published online in July 2006 with corrections to the Cover Date.     

Equilibrium points and stability in the restricted three-body problem with oblateness and variable masses

The existence and stability of a test particle around the equilibrium points in the restricted three-body problem is generalized to include the effect of variations in oblateness of the first primary, small perturbations ϵ and ϵ′ given in the Coriolis and centrifugal forces α and β respectively, and radiation pressure of the second primary; in the case when the primaries vary their masses with time in accordance with the combined Meshcherskii law. For the autonomized system, we use a numerical evidence to compute the positions of the collinear points L _2κ , which exist for 0<κ<∞, where κ is a constant of a particular integral of the Gylden-Meshcherskii problem; oblateness of the first primary; radiation pressure of the second primary; the mass parameter ν and small perturbation in the centrifugal force. Real out of plane equilibrium points exist only for κ>1, provided the abscissae x < \fracn(k-1)b\xi<\frac{\nu(\kappa-1)}{\beta}. In the case of the triangular points, it is seen that these points exist for ϵ′<κ<∞ and are affected by the oblateness term, radiation pressure and the mass parameter. The linear stability of these equilibrium points is examined. It is seen that the collinear points L _2κ are stable for very small κ and the involved parameters, while the out of plane equilibrium points are unstable. The conditional stability of the triangular points depends on all the system parameters. Further, it is seen in the case of the triangular points, that the stabilizing or destabilizing behavior of the oblateness coefficient is controlled by κ, while those of the small perturbations depends on κ and whether these perturbations are positive or negative. However, the destabilizing behavior of the radiation pressure remains unaltered but grows weak or strong with increase or decrease in κ. This study reveals that oblateness coefficient can exhibit a stabilizing tendency in a certain range of κ, as against the findings of the RTBP with constant masses. Interestingly, in the region of stable motion, these parameters are void for k = \frac43\kappa=\frac{4}{3}. The decrease, increase or non existence in the region of stability of the triangular points depends on κ, oblateness of the first primary, small perturbations and the radiation pressure of the second body, as it is seen that the increasing region of stability becomes decreasing, while the decreasing region becomes increasing due to the inclusion of oblateness of the first primary.     

Spin-down of millisecond pulsars owing to gravitational wave emission

The gravitational radiation from millisecond pulsars owing to glitches in their angular velocity is examined. It is assumed that the energy transferred from interior superfluid regions to the crust of a neutron star is converted into gravitational wave energy by damping oscillations of the matter in the star. The gravitational wave intensity and amplitude are calculated for fourteen millisecond pulsars. Gravitational radiation can explain the observed spin-down of millisecond pulsars and an estimate is given for the magnetic field at which the proposed mechanism predominates in the spin-down of these pulsars. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 479–486 (August 2008).     

An Analytical Model to Predict the Arrival Time of Interplanetary CMEs

Referring to the aerodynamic drag force, we present an analytical model to predict the arrival time of coronal mass ejections (CMEs). All related calculations are based on the expression for the deceleration of fast CMEs in the interplanetary medium (ICMEs), [(v)\dot]=-\frac115 700(v-V_SW)²\dot{v}=-\frac{1}{15\,700}(v-V_{\mathrm{SW}})^{2} , where V _SW is the solar wind speed. The results can reproduce well the observations of three typical parameters: the initial speed of the CME, the speed of the ICME at 1 AU and the transit time. Our simple model reveals that the drag acceleration should be really the essential feature of the interplanetary motion of CMEs, as suggested by Vršnak and Gopalswamy (J. Geophys. Res. 107, 1019, 2002).     

Periodic orbits in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ _c and unstable for m_c ￡ m < \frac12\mu_{c}\le\mu <\frac{1}{2}, where μ _c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.     

A theoretical qualitatively-explained new-variant of Modified-Newtonian-Dynamics (MOND)

It is surprising that we hardly know only 4% of the universe. Rest of the universe is made up of 73% of dark-energy and 23% of dark-matter. Dark-energy is responsible for acceleration of the expanding universe; whereas dark-matter is said to be necessary as extra-mass of bizarre-properties to explain the anomalous rotational-velocity of galaxy. Though the existence of dark-energy has gradually been accepted in scientific community, but the candidates for dark-matter have not been found as yet and are too crazy to be accepted. Thus, it is obvious to look for an alternative theory in place of dark-matter. Milgrom (Astrophys. J. 270:365, 1983a; 270:371, 1983b) has suggested a ‘Modified Newtonian Dynamics (MOND)’ which appears to be highly successful for explaining the anomalous rotational-velocity. But unfortunately MOND lacks theoretical support. The MOND, in-fact, is (empirical) modification of Newtonian-Dynamics through modification in the kinematical acceleration term ‘a’ (which is normally taken as a=\fracv²ra=\frac{v^{2}}{r}) as effective kinematic acceleration a_effective = a m(\fracaa₀)a_{\mathit{effective}} = a \mu(\frac{a}{a_{0}}), wherein the μ-function is 1 for usual-values of accelerations but equals to \fracaa₀ ( << 1)\frac{a}{a_{0}} (\ll1) if the acceleration ‘a’ is extremely-low lower than a critical value a ₀(10⁻¹⁰ m/s²). In the present paper, a novel variant of MOND is proposed with theoretical backing; wherein with the consideration of universe’s acceleration a _d due to dark-energy, a new type of μ-function on theoretical-basis emerges out leading to a_effective = a(1 -K \fraca₀a)a_{\mathit{effective}} = a(1 -K \frac{a_{0}}{a}). The proposed theoretical-MOND model too is able to fairly explain ‘qualitatively’ the more-or-less ‘flat’ velocity-curve of galaxy-rotation, and is also able to predict a dip (minimum) on the curve.     

Radius of the neutron star magnetosphere during disk accretion

The dependence of the spin frequency derivative \(\dot \nu \) of accreting neutron stars with a strongmagnetic field (X-ray pulsars) on the mass accretion rate (bolometric luminosity, L_bol) has been investigated for eight transient pulsars in binary systems with Be stars. Using data from the Fermi/GBM and Swift/BAT telescopes, we have shown that for seven of the eight systems the dependence \(\dot \nu \) (L_bol) can be fitted by the model of angular momentum transfer through an accretion disk, which predicts the relation \(\dot \nu \) ～ L^6/7_bol. Hysteresis in the dependence \(\dot \nu \) (L_bol) has been confirmed in the system V 0332+53 and has been detected for the first time in the systems KS 1947+300, GRO J1008-57, and 1A 0535+26. Estimates for the radius of the neutron star magnetosphere in all of the investigated systems have been obtained. We show that this quantity varies from pulsar to pulsar and depends strongly on the analytical model and the estimates for the neutron star and binary system parameters.     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

Study of Non-spinning black holes with reference to the change in energy and entropy

In this research paper, we have derived the formula for both the changes in energy (δE) and entropy (δS) and thereafter calculated the change in entropy (δS) with corresponding change in energy (δE) taking account the first law of the black hole mechanics relating the change in mass M, angular momentum J, horizon area A and charge Q, of a stationary black hole, when it is perturbed, given by formula satisfying in the vacuum as dM = \frack8p dA + WdJ - udQ\delta M = \frac{k}{8\pi} \delta A + \Omega\delta J - \upsilon\delta Q, specially for Non-spinning black holes.     

Influence of Neutron Star Parameters on Evolutions of Different Types of Pulsar

Influences of the mass, moment of inertia, rotation, absence of stability in the atmosphere and some other parameters of neutron stars on the evolution of pulsars are examined. It is shown that the locations and evolutions of soft gamma repeaters, anomalous X-ray pulsars and other types of pulsar on the period versus period derivative diagram can be explained adopting values of B < 10¹⁴ G for these objects if they have smaller mass (e.g. about 0.5 Solar mass) compared to the conventionally adopted values of mass. This approach gives the possibility to explain many properties of different types of pulsar.     

Gravitational analysis of V541 Cygni,DI Herculis,and the Pioneer anomaly

Detailed analyses by independent research groups over several decades reveal a significant discrepancy between the observed rate of periastron advance in the detached eclipsing binary star systems DI Herculis and V541 Cygni and the values theoretically predicted from the combined classical and general relativistic effects. A modification to Newton’s gravitational theory is proposed in this investigation to account for these discrepancies, and is represented by

A possible evolutionary track of pulsars

It is usually assumed that the dipole radiation at the spin frequency W_d is the only source of braking torque on pulsars (the POG hypothesis), but certain observations cast doubt on this. In this paper, we discuss the effect of elctromagnetic braking near the light cylinder W_em without using the POG hypothesis. We found W_em ∝ P^?3.2 (P is the pulsar period), and the total power L_t ∝ P^?3.2 (if L_t ∝ W_em). A correlation analysis between L_t and Pⁿ for a sample of 15 pulsars gives n = ?3.1, in agreement with our theoretical expectations.Our analysis based on observations shows that W_em is important or even dominant in some cases. In these cases, the evolutionary path (Fig.2) is very different from that given in /4/ where W_d is assumed to be dominant. The actual braking mechanism could be a superposition of the two (Fig.3).The gap in the $\text{P ～}\text{P}\text{?}$ diagram found by Ferguson /5/ for a sample of 80-odd pulsars persists in a larger sample of 199 pulsars. This gap, if real, implies that, for a certain range of parameter values, a neutron star is unstable, while it is stable on either side of the range.