The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have also discussed the Poynting-Robertson (P-R) effect which is caused due to radiation pressure. It is found that the collinear points L ₁,L ₂,L ₃ deviate from the axis joining the two primaries, while the triangular points L ₄,L ₅ are not symmetrical due to radiation pressure. We have seen that L ₁,L ₂,L ₃ are linearly unstable while L ₄,L ₅ are conditionally stable in the sense of Lyapunov when P-R effect is not considered. We have found that the effect of radiation pressure reduces the linear stability zones while P-R effect induces an instability in the sense of Lyapunov.     

Effect of oblateness and radiation pressure on angular frequencies at collinear points

In the three-dimensional restricted three-body problem, by considering the more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion as well as source of radiation, it is found that the collinear point L ₁ comes nearer to the primaries with the increase in oblateness and radiation pressure, while L ₂ and L ₃ move away from the more massive primary with the increase in oblateness and come nearer to it with the increase in radiation pressure. It is noted that the angular frequency s ₁ at L ₁ increases with oblateness as well as with radiation pressure. s ₂ increases with oblateness and decreases with radiation pressure and s ₃ decreases with oblateness and increases with radiation pressure. A study on the norms of the characteristic roots λ and s at L ₁, L ₂ and L ₃ is carried out. It is established that for certain oblateness and radiation pressure parameters there is a one-to-one commensurability at the collinear points L ₂, L ₃ between the planar angular frequencies (s _2,3) and the corresponding angular frequency (s _z ) in the z-direction, and that at L ₁ no such commensurability exists. At L ₂ and L ₃, the value of oblateness parameter providing the commensurability decreases with the increase in the radiation pressure. However, the commensurable angular frequencies and eccentricity of the periodic orbits decrease at L ₂ and increase at L ₃, with the increase in the radiation pressure.     

On the mechanism of X-ray emission from radio pulsars

We discuss the correlations between the luminosities of radio pulsars in various frequency ranges and the magnetic fields on the light cylinder. These correlations suggest that the observed emission is generated in outer layers of the pulsar magnetospheres by the synchrotron mechanism. To calculate the distribution functions of the relativistic particles in the generation region, we use a model of quasilinear interactions between the waves excited by cyclotron instability and particles of the primary beam and the secondary electron—positron plasma. We derive a formula for calculating the X-ray luminosity L _x of radio pulsars. A strong correlation was found between L _x and the parameter \(\dot P_{ - 15} /P^{3.5}\), where P is the neutron-star rotation period, in close agreement with this formula. The latter makes it possible to predict the detection of X-ray emission from more than a hundred (114) known radio pulsars. We show that the Lorentz factors of the secondary particles are small (γ _p = 1.5–8.5), implying that the magnetic field near the neutron-star surface in these objects is multipolar. It follows from our model that almost all of the millisecond pulsars must emit X-ray synchrotron radiation. This conclusion differs from predictions of other models and can be used to test the theory under consideration. The list of potential X-ray radiators presented here can be used to search for X-ray sources with existing instruments.     

Motion around the out-of-plane equilibrium points of the perturbed restricted three-body problem

This paper studies the motion of an infinitesimal body near the out-of-plane equilibrium points, L _6,7, in the perturbed restricted three-body problem. The problem is perturbed in the sense that the primaries of the system are oblate spheroids as well as sources of radiation and small perturbations are give to the Coriolis and centrifugal forces. It locates the positions and examines the stability of L _6,7 with a particular application to the binary system Struve 2398. It is observed that their positions are affected by the radiation, oblateness and a small perturbation in the centrifugal force, but is unaffected by that of the Coriolis force. They are also found to be unstable.     

Luminosity–redshift (L−z) relation and the blazar sequence for low power blazars

This paper presents an alternative interpretation for the wide scatter and apparent lack of anti-correlation in the relationship between the spectral luminosity (L _ν ) and synchrotron peak frequency (ν _peak ) in a sample of BL Lac Objects contained in Wu et al. (Astron. Astrophys. 466:43, 2007) compilation. The apparent lack of correlation between the parameters contradicts the blazar sequence proposed by Fossati et al. (in Mon. Not. R. Astron. Soc. 299:433, 1998), which predicts a general decline in L _ν with increasing ν _peak . Analysis of the radio luminosity and synchrotron peak frequency data of the sample reveals a strong selection effect, due to Malmquist bias. We show that a clear anti-correlation (r～?0.7) between the radio luminosity at synchrotron peak (L _peak ) and ν _peak exists for the BL Lac sample above some redshift cut-off (z _c =0.3), which may correspond to the flux limit of the sample. The results are not only in agreement with FRI–BL Lac unification, but also suggest that the present data is consistent with the blazar sequence.     

Precise Synchrotron Radiation Spectrum of Fast-cooling Electrons and the Prompt GRB Emission

It is generally believed that the synchrotron radiation of electrons from the internal shock is the main radiation mechanism of the prompt GRB (gamma-ray burst) emission. However, what this model predicts can not explain observations well. In this paper, we confirm that electrons are quickly cooled due to radiation losses and also point out that the synchrotron radiation spectrum presented in previous papers is a relatively rough estimation. We get the precise synchrotron radiation spectrum of fast-cooling electrons by carrying out a numerical calculation, and thereby reasonably explain the observed distribution of low-energy spectral index (α) of long GRBs based on a unified model. In addition, we fit the correlation between α and the peak energy of the νFν spectrum (E_p).     

Characteristics of activity energetics of the UV cet-type flare stars

A quantitative comparison of energetics of different manifestations of the activity of the UV Cet-type flare stars — sporadic flares, quiet chromospheres and coronae and stellar spots — have been carried out. On the basis of a statistical analysis of about 1800 flares registered for 23 flare stars, the energy spectra of flares have been constructed and time-averaged powers of optical radiation of flares —L _flares — have been estimated. By use of spectroscopic observations of 26 flare stars between flares, the total radiation in Balmer lines of quiet chromospheres —L _Bal — have been found. On the basis of these data and the soft X-ray observations of 29 flare stars, the mean of the ratiosL _flares/L _bol,L _Bal/L _bol andL _X /L _bol have been found to be equal to (1–2)×10^?4. By use of photometric observations for 9 stars, the total starspot radiation deficits —L _spots — have been estimated as (4×10^?3?6×10^?2)×L _bol. Discussions of probable underestimates in the valuesL _flares,L _Bal,L _X , andL _spots leads to the conclusion that the total power of non-equilibrium processes that take place in flare star atmospheres is close to the total starspot radiation deficit in these stars.     

Dust ring formation due to ice sublimation of radially drifting dust particles under the Poynting-Robertson effect in debris disks

In a disk with a low optical depth, dust particles drift radially inward by the Poynting-Robertson (P-R) drag rather than are blown out by stellar radiation pressure following destructive collisions. We investigate the radial distribution of icy dust composed of pure ice and refractory materials in dust-debris disks taking into account the P-R drag and ice sublimation. We find that icy dust particles form a dust ring by their pile-ups at the edge of their sublimation zone, where they sublime substantially at the temperature 100-110 K. The distance of the dust ring is 20-35 AU from the central star with its luminosity L_??30L_⊙ and 65(L_?/100L_⊙)^1/2 AU for L_??30L_⊙, where L_⊙ is the solar luminosity. The effective optical depth is enhanced by a factor of 2 for L_??100L_⊙ and more than 10 for L_??100L_⊙. The optical depth of the outer icy dust disk exceeds that of the inner disk filled with refractory particles, namely, the residue of ice sublimation, which are further subjected to the P-R effect. As a result, an inner hole is formed inside the sublimation zone together with a dust ring along the outer edge of the hole.     

The power-law behaviours of angular spectra of polarized Galactic synchrotron

We study the angular power spectra of polarized Galactic synchrotron in the range 10≲l≤800, at several frequencies between 0.4 and 2.7 GHz and at several Galactic latitudes up to near the North Galactic Pole. Electric- and magnetic-parity polarization spectra are found to have slopes around α_E,B=1.4–1.5 in the Parkes and Effelsberg Galactic-Plane surveys, but strong local fluctuations of α_E,B are found at |b|≃10° from the 1.4 GHz Effelsberg survey. The C_PIl spectrum, which is insensitive to the polarization direction, is somewhat steeper, being α_PI=1.6–1.8 for the same surveys. The low-resolution multifrequency survey of Brouw and Spoelstra [A&AS 26 (1976) 129] shows some flattening of the spectra below 1 GHz, more intense for C_E,Bl than for C_PIl. In no case we find evidence for really steep spectra. The extrapolation to the cosmological window shows that at 90 GHz the detection of E-mode harmonics in the cosmic background radiation should not be disturbed by synchrotron, even around l≃10 for a reionization optical depth τ_ri≳0.05.     

Broad line and multi-wave luminosity relations in Fermi FSRQs

We study broad line and multi-wave luminosity relations for 80 flat-spectrum radio quasars (FSRQs) detected by Fermi LAT. Our results are as follows: for FSRQs, the correlations between logL _γ and logL _BLR, between logL _X and logL _BLR, between logL _O and logL _BLR, between logL _R and logL _BLR are significant; the correlation between logL _IR and logL _BLR (P=0.08) is not significant, but might be refereed as a “trend” of significant correlation. These results support a close link between jet formation and accretion disk, and the L _γ -L _BLR correlation suggests that the radiation mechanism of the γ-ray emission in FSRQs is likely to be inverse Compton scattering of seed photons from BLR or outflowing BLR.     

Dust ring formation due to sublimation of dust grains drifting radially inward by the Poynting-Robertson drag: An analytical model

Dust particles exposed to the stellar radiation and wind drift radially inward by the Poynting-Robertson (P-R) drag and pile up at the zone where they begin to sublime substantially. The reason they pile up or form a ring is that their inward drifts due to the P-R drag are suppressed by stellar radiation pressure when the ratio of radiation pressure to stellar gravity on them increases during their sublimation phases. We present analytic solutions to the orbital and mass evolution of such subliming dust particles, and find their drift velocities at the pileup zone are almost independent of their initial semimajor axes and masses. We derive analytically an enhancement factor of the number density of the particles at the outer edge of the sublimation zone from the solutions. We show that the formula of the enhancement factor reproduces well numerical simulations in the previous studies. The enhancement factor for spherical dust particles of silicate and carbon extends from 3 to more than 20 at stellar luminosities L_?=0.8-500L_⊙, where L_⊙ is solar luminosity. Although the enhancement factor for fluffy dust particles is smaller than that for spherical particles, sublimating particles inevitably form a dust ring as long as their masses decrease faster than their surface areas during sublimation. The formulation is applicable to dust ring formation for arbitrary shape and material of dust in dust-debris disks as well as in the Solar System.     

Search for secular changes in the 3D profile of the synchrotron radiation around Jupiter

We present a summary of Jupiter data taken over an eighteen year span (1981-1998) by the Very Large Array at ∼21.0 cm. At this wavelength the emission is dominated by synchrotron radiation, which is roughly proportional to the product of the electron number density and magnetic field strength (N_eB). At each epoch 8-12 hours of data were taken, which allowed us to examine Jupiter during an entire rotation period. We mapped the longitudinal structure of the synchrotron radiation by using a 3D reconstruction technique developed by Sault et al. [Astron. Astrophys. 324 (1997) 1190] which enabled us to produce plots of the latitude, radial distance, and peak intensity vs. jovian longitude (System III). The results show the shape of the synchrotron radiation has remained stable (except, of course, during the period of comet Shoemaker-Levy 9 impacts). Specifically, the latitudinal structure has remained nearly constant. Furthermore, the general dependence of the radial intensity profile has remained the same throughout the years, though radial distance has slightly, though significantly, changed. This constancy implies that the spatial structure of both the particle distribution and magnetic field have varied little over the eighteen year span. The primary changes in the synchrotron radiation have been seen in the intensity of emission as a function of time. There are certain epochs (e.g., 1987) which show more emissivity than others (e.g., 1981, 1995) at all longitudes. When each epoch is longitudinally averaged, there may be an anti-correlation between the radial distance and corresponding peak intensities of the synchrotron radiation, as one might expect if radial diffusion is important. We examine these trends by comparing the data to plots of the total intensity at 13 cm (by Klein et al., in: Rucker, H.O., et al., Planetary Radio Emissions V. Austrian Acad. Sci. Press, Vienna, p. 221). Overall, variations in our 21-cm data are similar to those measured at 13 cm, but there appears to be a change in spectral index and perhaps in the spatial brightness distribution in 1992. We attribute this to a change in both the spatial and energy distribution of the relativistic electrons.     

Motion in the generalized restricted three-body problem

This paper investigates the motion of an infinitesimal body in the generalized restricted three-body problem. It is generalized in the sense that both primaries are radiating, oblate bodies, together with the effect of gravitational potential from a belt. It derives equations of the motion, locates positions of the equilibrium points and examines their linear stability. It has been found that, in addition to the usual five equilibrium points, there appear two new collinear points L _n1, L _n2 due to the potential from the belt, and in the presence of all these perturbations, the equilibrium points L ₁, L ₃ come nearer to the primaries; while L ₂, L ₄, L ₅, L _n1 move towards the less massive primary and L _n2 moves away from it. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ _c and unstable for $\mu_{c} \le\mu\le\frac{1}{2}$ , where μ _c is the critical mass ratio influenced by the oblateness and radiation of the primaries and potential from the belt, all of which have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near the oblate, radiating binary stars systems surrounded by a belt.     

Supermassive oblique rotator: Electrodynamics,evolution, observational tests

A detailed theory of high-entropy supermassive oblique rotator is developed on the basis of the results of our previous work on the structure and evolution of supermassive rotating magnetic polytropes. Particular attention is paid to the problem of transformation of rotational energy into observable radiation. It is shown that a rather long duration of the quasi-stationary phase in combination with a considerably high value of magnetic dipole radiationL _md in comparison with that of thermal radiationL _th imposes substantial limitations on the character of the model. This combination is realized in the model of an oblique rotator with a rigid rotation and a poloidal magnetic field. Moreover, the magnetic energy must be comparable, in order of magnitude, with the module of the gravitational energy.The magnitude of the torque acting on the rotator by means of the magnetic field is influenced neither by the external plasma thrown out by the low-frequency radiation pressure, nor by the plasma ejected electrostatically, nor by that flowing out due to rotational instability. For definiteness we assume below that the rotational energy is lost by the rotator in the form of a low-frequency magnetic dipole radiation though many of the conclusions drawn in this paper are also valid for the case when the energy is liberated in some other forms (for example, in magnetohydrodynamic waves).Plasma outflow under rotational instability is considered in detail. This is a pulsating outflow. Near the light cylinder the plasma spreads out and begins to interact intensively with the magnetic dipole radiation. As a result, the particles are accelerated up to relativistic energies. Accelerated electrons radiate by synchrotron mechanism with the radiation maximum in the far infra-red region (Figure 4). Compton scattering of this radiation is in the X-ray and gamma regions. The character of the non-thermal radiation calculated accounts for the essential features of the observable radiation from quasars and active galactic nuclei.A secular variation of the magnetic dipole radiation in the course of evolution of a supermassive oblique rotator (Figure 1) with the account taken of the influence of magnetic dipole losses on the value of the angle between magnetic and rotational axes is discussed in the vacuum approximation substantiated in Section 3. For a wide interval of initial values of this angle the non-thermal (synchrotron and Compton) radiation increases in the course of a quasi-static contraction of the rotator, reaches its maximum at whichL _nthL _th, and then decreases considerably due to rapprochement of the magnetic and rotational axes. Such a behaviour ofL _nth corresponds to the expected secular change of the activity of galactic and quasar nuclei as a certain flaring up, reaching the maximum of their activity and subsequent dying out.Some essential properties of quasars and quasar-like phenomena in galactic and quasar nuclei are explained on the basis of the theory presented. As an illustration, the parameters of a supermassive rotator modelling the source of activity in quasar 3C 273 are calculated (Table I). The estimate of the frequency of occurrence of rotators withL _nth>L _th andL _nthL _th is in a reasonable correspondence with the statistics of active phenomena in the nuclei of galaxies of different morphological types.Observational tests for this theory are suggested. The most important one called upon to ascertain the presence in the nuclei of galaxies and quasars of a supermassive body as a source of their activity is the variability of infra-red radiation near its spectral maximum.Similarity and difference between a supermassive oblique rotator and a pulsar, the model of a quasar nucleus as a cluster of pulsars, an axysymmetric rotator and a low-entropy configuration (disk) as stages of the evolution of an oblique rotator as well as the problems of its genesis and fate are discussed at the end of the paper (Section 9). The main results of the paper are listed in Section 10.     

Jupiter’s radio spectrum from 74 MHz up to 8 GHz

We carried out a brief campaign in September 1998 to determine Jupiter’s radio spectrum at frequencies spanning a range from 74 MHz up to 8 GHz. Eleven different telescopes were used in this effort, each uniquely suited to observe at a particular frequency. We find that Jupiter’s spectrum is basically flat shortwards of 1-2 GHz, and drops off steeply at frequencies greater than 2 GHz. We compared the 1998 spectrum with a spectrum (330 MHz-8 GHz) obtained in June 1994, and report a large difference in spectral shape, being most pronounced at the lowest frequencies. The difference seems to be linear with log(ν), with the largest deviations at the lowest frequencies (ν).We have compared our spectra with calculations of Jupiter’s synchrotron radiation using several published models. The spectral shape is determined by the energy-dependent spatial distribution of the electrons in Jupiter’s magnetic field, which in turn is determined by the detailed diffusion process across L-shells and in pitch angle, as well as energy-dependent particle losses. The spectral shape observed in September 1998 can be matched well if the electron energy spectrum at L = 6 is modeled by a double power law E^−a (1+(E/E₀))^−b, with a = 0.4, b = 3, E₀ = 100 MeV, and a lifetime against local losses τ₀ = 6 × 10⁷ s. In June 1994 the observations can be matched equally well with two different sets of parameters: (1) a = 0.6, b = 3, E₀ = 100 MeV, τ₀ = 6 × 10⁷ s, or (2) a = 0.4, b = 3, E₀ = 100 MeV, τ₀ = 8.6 × 10⁶ s. We attribute the large variation in spectral shape between 1994 and 1998 to pitch angle scattering, coulomb scattering and/or energy degradation by dust in Jupiter’s inner radiation belts.     

Effect of radiation pressure on the stability of L 4,5 in the relativistic R3BP

This paper examines the motion of a test particle in the vicinity of the triangular points L _4,5 by considering the more massive primary as a source of radiation in the framework of the relativistic restricted three-body problem (R3BP). It is found that the position and stability of the triangular point are affected by both the relativistic factor and radiation pressure.     

The accretion of matter by a collapsing star in the presence of a magnetic field

The exact nonstationary solution for the variation of the magnetic field in the Schwarzschild metric with a given spherically symmetric flow is obtained. Initially a homogeneous magnetic field increases with time, changing into a quasi-radial field. On the assumption of equipartition between the magnetic and kinetic energies of a falling gas, in the relativistic case, estimates of the stationary field and the intensity of synchrotron radiation are presented. A considerable part of the radiation is formed in the relativistic regionr?(2.5 to 7.7)r _g (r _g is the gravitational radius of a black hole). Estimates are made for radiation from the relativistic region in the case of disc type accretion.     

Correlation between X-ray and γ-ray for Fermi blazars

Using γ-ray band data detected by Fermi Large Area Telescope (LAT) and X-ray band data for 78 blazars, we find a medium correlation between X-ray flux and γ-ray flux in all states. A medium correlation is also found between X-ray (1 keV) mean spectral index α _x and γ-ray mean spectral index α _γ for BL Lacertae objects (BL Lacs), and there is no correlation for Flat Spectrum Radio Quasars (FSRQs). From these results, we suggest that the most likely radiation mechanism for the high energy gamma-rays would be synchrotron self-Compton (SSC), and that the gamma-ray emission mechanism may be somewhat different for BL Lacs and FSRQs.     

The behaviour of outer radiation belt electrons (> 1·5 MeV) during a geomagnetically disturbed time on 8 March 1970 and its relationship to magnetospheric processes

Omnidirectional intensities of electrons with energies E_e > 1·5 MeV detected by a low orbiting polar satellite (GRS-A/AZUR) in the outer radiation belt are examined during disturbed times including the main phase of a very strong geomagnetic storm on 8 March 1970. The particle intensity features are discussed in relationship with proposed magnetospheric processes. It is found that a superposition of the two following effects can explain the particle behavior in the trapping region:(A) Radial diffusion. After the southward turning of the interplanetary field an inward motion of both the energetic electron belt and the plasmapause took place. This effect was observed at L > 3 R_E and we attribute it to enhanced magnetospheric electric field fluctuations. Later, a strong interplanetary shock impinged upon the magnetosphere which was related to the triggering of intense magnetospheric substorms; a further inward diffusion occurred at L ? 3 R_E, accompanied by an inward movement of the electron slot. A rough estimation of the diffusion coefficient leads to a power spectrum of the electric field fluctuations which seems to be consistent with experimentally determined power spectra (Mozer, 1971).(B) Adiabatic response to ring current changes. Large energetic electron intensity decreases within the outer radiation belt are shown to be adiabatic changes due to ring current variations. The influence of the inflation of the magnetosphere due to the developing ring current is simultaneously observed by the decrease of the solar proton outoff (1·7-2·5 MeV).     

Steady-state observations of geomagnetically trapped energetic heavy ions and their implications for theory

Measurements of energetic heavy ions using the Explorer 45 and ATS-6 satellites are reviewed and the resulting implications for theory are evaluated. The measured ions are basically protons and helium ions in the energy range from 0.1 to 1 MeV/nucleon. The equatorial energetic ion distributions inside L = 4.5 are found to be very stable for extended periods of time. These ions are very closely confined to the equatorial plane and are sharply peaked as a function of L around a value designated as L_max. Beyond L = 5.0 the fluxes of these ions are more variable with order of magnitude variations being observed at L = 6.6 on the time scales of minutes, hours, or days. The region inside L = 4.5 appears to be well described by radial diffusive transport driven by fluctuations in the geomagnetic field coupled with losses due to charge exchange and Coulomb interactions with ambient hydrogen geocorona and terrestrial plasma environment. From an analysis relating the position in L-value of the maximum intensity, L_max, observed for a given ion species and energy, it is argued that the influence of fluctuations in the convection electric field as discussed by Cornwall (1972) are not effective in radially diffusing in L ions with energies greater than a few hundred kiloelectron volts per nucleon. The source of these ions remains basically undetermined and its determination must await further measurements.