Algebraic Solution for the Forward Displacement Analysis of the General 6-6 Stewart Mechanism

The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.

The Synchrotron-self-Compton Radiation Accompanying Shallow Decaying X-Ray Afterglow:the Case of GRB 940217

High energy emission （〉 tens MeV） of Gamma-Ray Bursts （GRBs） provides an important clue on the physical processes occurring in GRBs that may be correlated with the GRB early afterglow. A shallow decline phase has been well identified in about half of Swift Gamma-ray Burst x-ray afterglows. The widely considered interpretation inv.olves a significant energy injection and possibly time-evolving shock parameter（s）. We calculate the synchrotron-self-Compton （SSC） radiation of such an external forward shock and show that it could explain the well-known long term high energy （i.e., tens MeV to GeV） afterglow of GRB 940217. We propose that cooperation of Swift and GLAST will help to reveal the nature of GRBs.

A low-latency pipeline for GRB light curve and spectrum using Fermi/GBM near real-time data

Rapid response and short time latency are very important for Time Domain Astronomy, such as the observations of Gamma-ray Bursts（GRBs） and electromagnetic（EM） counterparts of gravitational waves（GWs）. Based on near real-time Fermi/GBM data, we developed a low-latency pipeline to automatically calculate the temporal and spectral properties of GRBs. With this pipeline, some important parameters can be obtained, such as T_（90） and fluence, within ～ 20 min after the GRB trigger.For ～ 90% of GRBs, T90 and fluence are consistent with the GBM catalog results within 2σ errors.This pipeline has been used by the Gamma-ray Bursts Polarimeter（POLAR） and the Insight Hard Xray Modulation Telescope（Insight-HXMT） to follow up the bursts of interest. For GRB 170817 A, the first EM counterpart of GW events detected by Fermi/GBM and INTEGRAL/SPI-ACS, the pipeline gave T90 and spectral information 21 min after the GBM trigger, providing important information for POLAR and Insight-HXMT observations.

Gamma-Ray Bursts: Afterglows and Central Engines

Gamma-ray bursts (GRBs) are the most intense transient gamma-ray events in the sky; this, together with the strong evidence (the isotropic and inhomogeneous distribution of GRBs detected by BASTE) that they are located at cosmological distances, makes them the most energetic events ever known. For example, the observed radiation energies of some GRBs are equivalent to the total convertion into radiation of the mass energy of more than one solar mass. This is thousand times stronger than the energy of a supernova explosion. Some unconventional energy mechanism and extremely high conversion efficiency for these mysterious events are required. The discovery of host galaxies and association with supernovae at cosmological distances by the recently launched satellite of BeppoSAX and ground based radio and optical telescopes in GRB afterglow provides further support to the cosmological origin of GRBs and put strong constraints on their central engine. It is the aim of this article to review the possible central engines, energy mechanisms, dynamical and spectral evolution of GRBs, especially focusing on the afterglows in multi-wavebands.

Cylindrical Jet - Wind Interaction Model of Gamma-Ray Burst Afterglows

Observations on relativistic jets in radio galaxies, active galactic nuclei, and 'microquasars' revealed that many of these outflows are cylindrical, not conical. So it is worthwhile to investigate the evolution of cylindrical jets in gamma-ray bursts. We discuss afterglows from cylindrical jets in a wind environment. Numerical results as well as analytic solutions in some special cases are presented. Our light curves are steeper compared to those in the homogeneous interstellar medium case, carefully considered by Cheng, Huang & Lu. We conclude that some afterglows, used to be interpreted as isotropic fireballs in a wind environment, can be fitted as well by cylindrical jets interacting with a wind.

Polarization of GRB prompt emission and its application to POLAR’s data

Synchrotron emission polarization is very sensitive to the magnetic field configuration.Recently,polarization of synchrotron emission with a mixed(SM)magnetic field in the gamma-ray burst(GRB)afterglow phase has been developed.Here,we apply these SM models to the GRB prompt phase and compare their polarization properties with that of synchrotron emission in purely ordered(SO)magnetic field.We find that the polarization properties in an SM model are very similar to these in a corresponding SO model(e.g.,synchrotron emission in a mixed magnetic field with an aligned ordered part(SMA)and synchrotron emission with a purely ordered aligned magnetic field(SOA)),only with a lower polarization degree(PD).We also discuss the statistical properties of the models.We find PDs of the simulated bursts are concentrated around 25%for both SOA and synchrotron emission in a purely ordered toroidal magnetic field(SOT),while they can range from 0%to 25%for SMA and synchrotron emission in a mixed magnetic field with a toroidal ordered part(SMT),depending onξ_B value,i.e.,the ratio of magnetic reduction of the ordered magnetic field over that of random magnetic field.From statistics,if PDs of majority GRBs are non-zero,then it favors SO and SM models.Further,if there are some bright GRBs with prominently lower PDs than that of the majority GRBs,it favors SOT(SMT)models;if all the bright GRBs have comparable PDs with the majority ones,it favors SOA(SMA)models.Finally,we apply our results to POLAR’s data and find that~10%time-integrated PDs of the observed bursts favor SMA and SMT models,and theξ_B parameter of these bursts is constrained to be around 1.135.

Can the bump in the composite spectrum of GRB 910503 be an emission line feature of gamma-ray bursts?

Appearing in the composite spectral data of BATSE, EGRET and COMPTEL for GRB 910503, there is a bump at around 1600keV. We perform a statistical analysis on the spectral data, trying to find out if the bump could be accounted for by a blue-shifted and significantly broadened rest frame line due to the Doppler effect of an expanding fireball surface. We made an F-test and adopted previously proposed criteria. The study reveals that the criteria are well satisfied and the feature can be interpreted as the blue shifted 6.4 keV line. From the fit with this line taken into account, we find the Lorentz factor of this source to be F = 116-9^＋9 （at the 68% confident level, △X^2 = 1） and the rest frame spectral peak energy to be E0,p=2.96-0.18^＋0.24 ke V.Although the existence of the emission line feature requires other independent tests to confirm, the analysis suggests that it is feasible to detect emission line features in the high energy range of GRB spectra when taking into account the Doppler effect of fireball expansion.

Aggregate dust model to study the polarization properties of comet C/1996 B2 Hyakutake

The observed linear polarization data of comet Hyakutake are studied at wavelengths λ=0.365 μm,λ=0.485 μm and 0.684μm through simulations using Ballistic Particle-Cluster Aggregate and Ballistic Cluster-Cluster Aggregate aggregates of 128 spherical monomers.We first found that the size parameter of the monomer,x ～ 1.56-1.70,turned out to be the most suitable which provides the best fits to the observed dust scattering properties at three wavelengths：λ=0.365 μm,0.485μm and 0.684μm.Thus,the effective radius of the aggregate （r） lies in the range 0.45 μm ≤ r ≤ 0.49 μm at λ=0.365 μm;0.60 μm ≤ r ≤ 0.66 μm at λ=0.485 μm and 0.88 μm ≤ r ≤ 0.94 μm at λ=0.684 μm.Now using superposition T-MATRIX code and the power-law size distribution,n（r） ～ r-3,the best-fitting values of complex refractive indices are calculated for the observed polarization data at the above three wavelengths.The best-fitting complex refractive indices （n,k） are found to be （1.745,0.095） at λ=0.365 μm,（1.743,0.100） at λ=0.485 μm and （1.695,0.100） at λ=0.684 μm.The refractive indices derived from the present analysis correspond to a mixture of both silicates and organics,which are in good agreement with the in situ measurement of comets by different spacecraft.

Modeling the rail surface unevenness of a high-precision radio telescope

This study proposed a coarse-fine mixed model for describing the rail surface unevenness of an ultra-large fully steerable radio telescope （Qi Tai Telescope） with a diameter of 110 meters. The rail surface unevenness includes information on error arising from two different scales, i.e., the long-period- short-change and the short-period-long-change. Consequently, in this study an idea of a mixed model was proposed, in which trigonometric and fractal functions were, respectively, used to describe infor- mation on error from two scales. Key parameters were determined by using the least squares method and the wavelet transform method, and finally, a specific mathematical expression of the model was obtained by optimization. To validate the effectiveness of the new modeling method, the mixed model was then used to describe the rails of the Green Bank Telescope, the Large Millimeter Telescope, and a radio telescope in Miyun, Beijing. A comparative study revealed that the maximum error was less than 15 %, thus the result was superior to those of existing modeling methods.

f and g series solutions to a post-Newtonian two-body problem with parameters β and γ

Classical Newtonian f and g series for a Keplerian two-body problem are extended for the case of a post-Newtonian two-body problem with parameters β and γ. These two parameters are introduced to parameterize the post-Newtonian approximation of alternative theories of gravity and they are both equal to1 in general relativity. Up to the order of 30, we obtain all of the coefficients of the series in their exact forms without any cutoff for significant figures. The f and g series for the post-Newtonian two-body problem are also compared with a Runge-Kutta order 7 integrator. Although the f and g series have no superiority in terms of accuracy or efficiency at the order of 7, the discrepancy in the performances of these two methods is not quite distinct. However, the f and g series have the advantage of flexibility for going to higher orders.Some examples of relativistic advance of periastron are given and the effect of gravitational radiation on the scheme of f and g series is evaluated.

Circular Polarization in Pulsar Integrated Profiles: Updates

We update the systematic studies of circular polarization in integrated pulse profiles by Han et al. Data of circular polarization profiles are compiled. Sense reversals can occur in core or cone components, or near the intersection between components. The correlation between the sense of circular polarization and the sense of position angle variation for conal-double pulsars is confirmed with a much large database. Circular polarization of some pulsars has clear changes with frequency. Circular polarization of millisecond pulsars is marginally different from that of normal pulsars.

More Emission Cones: Multi-frequency Simulation of the Pulse Profiles of PSR J0437-4715

Pulsar radio emission beams have been studied observationally for a long time, and the suggestion is that they consist of the so-called core and conal components. To reproduce these components is a challenge for any emission model, and that the pulse profile of pulsars changes with frequency presents even a greater challenge. Assuming a local surface magnetic structure (to produce the core or central beam) and a global dipole magnetic field (to produce the conal beams), Gil & Krawczyk (1997) applied curvature radiation to the pulse profile simulation of PSR J0437-4715 (hereafter the GK model). Here we present an alternative multi-frequency simulation of the same profiles within the framework of the Inverse Compton Scattering (ICS) model. It is obtained from our simulation (1) that besides the core, the inner cone and the outer cone, there is an outer-outer cone; (2) that the emission components of the core and cones evolve strongly with frequency. Some important differences between the ICS model and the GK model are discussed, which need to be tested by further observations.

A synchrotron self-Compton scenario for the very high energy γ-ray emission of the intermediate BL Lacertae object W Comae

W Comae has significant variability in multi-wavelengthes, from radio to gamma-ray bands. A bright outburst in optical and X-ray bands was observed in 1998, and most recently, a strong TeV flare was detected by VERITAS in 2008. It is the first TeV intermediate-frequency-peaked BL Lacertae source. I find that both the broadband spectral energy distributions （SEDs） which were quasi-simultaneously obtained during the TeV flare and during the optical/X-ray outburst are well fit by using a single-zone synchrotron ＋ synchrotron-self-Compton model. The satisfactory fitting requires a large beaming factor, i.e., δ- 25 and δ- 20 for the TeV flare and the optical/X-ray outburst, respectively, suggesting that both the optical/X-ray outburst and the TeV flare are from a relativistic jet. The size of the emission region of the TeV flare is three times larger than that of the optical/X-ray outburst, and the strength of the magnetic field for the TeV flare is - 14 times smaller than that of the X-ray/optical outburst, likely indicating that the region of the TeV flare is more distant from the core than that of the X-ray/optical outburst. The inverse Compton component of the TeV flare peaks around 1.3 GeV, but it is around 20 MeV for the X-ray/optical outburst, lower than that for the TeV flare by two orders of magnitude. The model predicts that the optical/X-ray outburst might be accompanied by a strong MeV/GeV emission, but the TeV flare may be not associated with the X-ray/optical outburst. The GeV emission is critical for characterizing the SEDs of the optical/X-ray outburst and the TeV flare. The predicted GeV flux is above the sensitivity of Fermi/LAT, and it could be verified with the observations by Fermi/LAT in the near future.

An Annular Gap Acceleration Model for γ-ray Emission of Pulsars

If the binding energy of the pulsar＇s surface is not so high （the case of a neutron star）, both negative and positive charges will flow out freely from the surface of the star. An annular free flow model for 7-ray emission of pulsars is suggested. It is emphasized that： （1） Two kinds of acceleration regions （annular and core） need to be taken into account. The annular acceleration region is defined by the magnetic field lines that cross the null charge surface within the light cylinder. （2） If the potential drop in the annular region of a pulsar is high enough （normally the case for young pulsars）, charges in both the annular and the core regions could be accelerated and produce primary gamma-rays. Secondary pairs are generated in both regions and stream outwards to power the broadband radiations. （3） The potential drop grows more rapidly in the annular region than in the core region. The annular acceleration process is a key process for producing the observed wide emission beams. （4） The advantages of both the polar cap and outer gap models are retained in this model. The geometric properties of the 7-ray emission from the annular flow are analogous to that pre-sented in a previous work by Qiao et al., which match the observations well. （5） Since charges with different signs leave the pulsar through the annular and the core regions respectively, the current closure problem can be partially solved.

Multi-wavelength emission from 3C 66A: clues to its redshift and gamma-ray emission location

The quasi-simultaneous multi-wavelength emission of TeV blazar 3C 66A is studied by using a one-zone multi-component leptonic jet model. It is found that the quasi-simultaneous spectral energy distribution of 3C 66A can be well reproduced; in particular, the first three months of its average Fermi-LAT spectrum can be well reproduced by the synchrotron self-Compton component plus external Compton component of the broad line region （BLR）. Clues to its redshift and gamma-ray emission location are obtained. The results indicate the following. （i） On the redshift： The theoretical intrinsic TeV spectra can be predicted by extrapolating the reproduced GeV spectra. Through comparing these extrapolated TeV spectra with the corrected observed TeV spectra from extragalactic background light, it is suggested that the redshift of 3C 66A could be between 0.1 and 0.3, with the most likely value being ~ 0.2. （ii） On the gamma-ray emission location： To well reproduce the GeV emission of 3C 66A under different assumptions on the BLR, the gamma-ray emission region is always required to be beyond the inner zone of the BLR. The BLR absorption effect on gamma-ray emission confirms this point.

A Possible Pumping Mechanism for Interstellar Class Ⅱ107 GHz Methanol Masers

It is recognized that the interstellar methanol-107GHz masers and OH-4.765 GHz masers towards Class II sources are associated with each other and coexist towards ultracompact HII regions. Therefore we suggest a new pumping mechanism - methanol masers without population inversion. It can explain the formation of 107GHz methanol masers, with the 4.765 GHz OH masers acting as a driving coherent microwave field. It is argued that this mechanism is compatible with the astronomical conditions.

The Doppler Effect and Spectral Energy Distribution of Blazars

The relativistic beaming model is adopted to discuss quantitatively the observational differences between radio-selected BL Lac objects (RBLs) and X-ray- selected BL Lac objects (XBLs), and between BL Lac objects and flat spectrum radio quasars (FSRQs). The main results are the following: (1) In the Doppler corrected color-color ( ) diagram, XBLs and FSRQs occupy separated regions, while RBLs bridge the gap between them. These properties suggest that similar intrinsic physical processes operate in all the objects under a range of intrinsic physical conditions. (2) Our results are consistent with the results of Sambruna, Maraschi and Urry (1996) from other methods. We show the ■xox introduced by Sambruna to be a good index for describing the energy distribution because it represents the intrinsic energy distribution and includes the Doppler correction. (3) The Doppler effect of relativistic beaming is the main mechanism, and the physical differences (such as magnetic fields, electron energies) are also important complementary factors for understanding the relation between XBLs and RBLs;

Resonant cyclotron scattering in pulsar magnetospheres and its application to isolated neutron stars

Resonant cyclotron scattering （RCS） in pulsar magnetospheres is considered. The photon diffusion equation （Kompaneets equation） for RCS is derived. The photon system is modeled three dimensionally. Numerical calculations show that there exist not only up scattering but also down scattering of RCS, depending on the parameter space. RCS＇s possible applications to spectral energy distributions of magnetar candidates and radio quiet isolated neutron stars （INSs） are pointed out. The optical/UV excess of INSs may be caused by the down scattering of RCS. The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data. In our model, the INSs are proposed to be normal neutron stars, although the quark star hypothesis is still possible. The low pulsation amplitude of INSs is a natural consequence in the RCS model.

Extension of the rotating dipole model with oblateness of both primaries

A rotating mass dipole can be used to understand the dynamical behaviors around elongated asteroids as well as binary asteroids. In this paper an improved dipole model with oblateness in both primaries is investigated. The dynamical equations of a particle around the improved model are first derived by introducing the oblateness coefficients. The characteristic equations of equilibrium points are obtained, resulting in the emergence of new equilibria in the equatorial plane and the plane xoz de- pending on the shape of the spheroid. Numerical simulations are performed to illustrate the distribution of these equilibrium points. Significant influence from the oblateness of the primaries on the topological structure is also analyzed via zero-velocity curves.

What determines the observational differences of blazars？

We examine the scenario that the Doppler factor determines the observational differences of blazars. Significantly negative correlations are found between the observational synchrotron peak frequency and the Doppler factor. After correcting the Doppler boosting, the intrinsic peak frequency has a tight linear relation with the Doppler factor. It is interesting that this relation is consistent with the scenario that the black hole mass governs both the bulk Lorentz factor and the synchrotron peak frequency. In addition, the distinction between the kinetic jet powers of BL Lac objects and fiat spectrum radio quasars disappears after the boosting factor δ2 is considered. The negative correlation between the peak frequency and the observational isotropic luminosity, known as the blazar sequence, also disappears after the Doppler boosting is corrected. We also find that the correlation between the Compton dominance and the Doppler factor exists for all types of blazars. Therefore, this correlation is unsuitable for examining the external Compton emission dominance.