Pulse Profiles, Spectra and Polarization Characteristics of Non-Thermal Emissions from the Crab-Like Pulsars

We discuss non-thermal emission mechanism of the Crab-like pulsars with both a two-dimensional electrodynamical study and a three-dimensional model. We investigate the emission process in the outer gap accelerator. In the two-dimensional electrodynamical study, we solve the Poisson equation of the accelerating electric field in the outer gap and the equation of motion of the primary particles with the synchrotron and the curvature radiation process and the pair-creation process. We show a solved gap structure which produces a consistent gamma-ray spectrum with EGRET observation. Based on the two-dimensional model, we conduct a three-dimensional emission model to calculate the synchrotron and the inverse-Compton processes of the secondary pairs produced outside the outer gap. We calculate the pulse profiles, the phase-resolved spectra and the polarization characteristics in optical to $\gamma$-ray bands to compare the observation of the Crab pulsar and PSR B0540-69. For the Crab pulsar, we find that the outer gap geometry extending from near the stellar surface to near the light cylinder produces a complex morphology change of the pulse profiles as a function of the photon energy. This predicted morphology change is quite similar with that of the observations. The calculated phase-resolved spectra are consistent with the data through optical to the $\gamma$-ray bands. We demonstrate that the 10$\sim$20 % of the polarization degree in the optical emissions from the Crab pulsar and the Vela pulsar are explained by the synchrotron emissions with the particle gyration motion.Comment: 39 pages, 11 figures, Accepted for publication in Ap

A re-visit of the phase-resolved X-ray and \gamma-ray spectra of the Crab pulsar

We use a modified outer gap model to study the multi-frequency phase-resolved spectra of the Crab pulsar. The emissions from both poles contribute to the light curve and the phase-resolved spectra. Using the synchrotron self-Compton mechanism and by considering the incomplete conversion of curvature photons into secondary pairs, the observed phase-averaged spectrum from 100 eV - 10 GeV can be explained very well. The predicted phase-resolved spectra can match the observed data reasonably well, too. We find that the emission from the north pole mainly contributes to Leading Wing 1. The emissions in the remaining phases are mainly dominated by the south pole. The widening of the azimuthal extension of the outer gap explains Trailing Wing 2. The complicated phase-resolved spectra for the phases between the two peaks, namely Trailing Wing 1, Bridge and Leading Wing 2, strongly suggest that there are at least two well-separated emission regions with multiple emission mechanisms, i.e. synchrotron radiation, inverse Compton scattering and curvature radiation. Our best fit results indicate that there may exist some asymmetry between the south and the north poles. Our model predictions can be examined by GLAST.Comment: 35 pages, 13 figures, accepted to publish in Ap

Three-dimensional Two-Layer Outer Gap Model: Fermi Energy Dependent Light Curves of the Vela Pulsar

We extend the two-dimensional two-layer outer gap model to a three-dimensional geometry and use it to study the high-energy emission of the Vela pulsar. In this model, the outer gap is divided into two parts, i.e. the main acceleration region on the top of last-open field lines and the screening region around the upper boundary of the gap. In the main acceleration region, the charge density is much lower than the Goldreich-Julian charge density and the charged particles are accelerated by the electric field along the magnetic field to emit multi-GeV photons. In the screening region, the charge density is larger than the Goldreich-Julian value to close the gap and particles in this region are responsible for multi-100MeV photon emission. We apply this three dimensional two-layer model to the Vela pulsar and compare the model light curves, the phase-averaged spectrum and the phase-resolved spectra with the recent Fermi observations, which also reveals the existence of the third peak between two main peaks. The phase position of the third peak moves with the photon energy, which cannot be explained by the geometry of magnetic field structure and the caustic effects of the photon propagation. We suggest that the existence of the third peak and its energy dependent movement results from the azimuthal structure of the outer gap.Comment: 11 pages, 15 figures, accepted for publication in MNRA

Radiation Mechanism of the Soft Gamma-ray Pulsar PSR B1509-58

The outer gap model is used here to explain the spectrum and the energy dependent light curves of the X-ray and soft gamma-ray radiations of the spin-down powered pulsar PSR B1509-58.In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap's electric field separates the two charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow of particles and that from the null charge surface to the star is dominated by the inflow of particles. The inflow and outflow of particles move along the magnetic field lines and emit curvature photons, and the incoming curvature photons are converted to pairs by the strong magnetic field of the star. These pairs emit synchrotron photons. We suggest that the X-rays and soft gamma-rays of PSR B1509-58 result from the synchrotron radiation of these pairs, and the viewing angle of PSR B1509-58 only receives the inflow radiation. The magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and the second peak appearing at E>10MeV comes from the region near the star, where the stronger magnetic field allows the pair creation to happen with a smaller pitch angle.Comment: 5 pages, 8 figures, 2012 Fermi Symposium proceedings - eConf C12102

Outer gap accelerator closed by magnetic pair-creation process

We discuss outer gap closure mechanism in the trans-field direction with the magnetic pair-creation process near the stellar surface. The gap closure by the magnetic pair-creation is possible if some fraction of the pairs are produced with an outgoing momentum. By assuming that multiple magnetic field will affect the local field near the stellar surface, we show a specific magnetic field geometry near the stellar surface resulting in the outflow of the pairs. Together with the fact that the electric field is weak below null charge surface, the characteristic curvature photon energy emitted by incoming particles, which were accelerated in the outer gap, decreases drastically to $\sim 100$MeV near the stellar surface. We estimate the height measured from the last-open field line, above which 100MeV photons is converted into pairs by the magnetic pair-creation. We also show the resultant multiplicity due to the magnetic pair-creation process could acquire $M_{e^{\pm}}\sim 10^4-10^5$. In this model the fractional outer gap size is proportional to $P^{-1/2}$. The predicted gamma-ray luminosity ($L_{\gamma}$) and the characteristic curvature photon energy ($E_c$) emitted from the outer gap are proportional to $B^2P^{-5/2}$ and $B^{3/4}P^{-1}$ respectively. This model also predicts that $L_{\gamma}$ and $E_c$ are related to the spin down power ($L_{sd}$) or the spin down age of pulsars ($\tau$) as $L_{\gamma} \propto L_{sd}^{5/8}$ or $L_{\gamma} \propto \tau^{-5/4}$, and $E_c \propto L_{sd}^{1/4}$ or $E_c \propto \tau^{-1/2}$ respectively.Comment: 33 pages, 9 figures, Accepted for publication in ApJ

X-ray/GeV emissions from Crab-like pulsars in LMC

We discuss X-ray and gamma-ray emissions from Crab-like pulsars, PSRs~J0537-6910 and~J0540-6919, in Large Magellanic Cloud. Fermi-LAT observations have resolved the gamma-ray emissions from these two pulsars and found the pulsed emissions from PSR~J0540-6919. The total pulsed radiation in the X-ray/gamma-ray energy bands of PSR~J0540-6919 is observed with the efficiency $\eta_{J0540}\sim 0.06$ (in 4$\pi$ sr), which is about a factor of ten larger than $\eta_{Crab}\sim 0.006$ of the Crab pulsar. Although PSR~J0537-6910 has the highest spin-down power among currently known pulsars, the efficiency of the observed X-ray emissions is about two orders of magnitude smaller than that of PSR~J0540-6919. This paper mainly discusses what causes the difference in the radiation efficiencies of these three energetic Crab-like pulsars. We discuss electron/positron acceleration and high-energy emission processes within the outer gap model. By solving the outer gap structure with the dipole magnetic field, we show that the radiation efficiency decreases as the inclination angle between the magnetic axis and the rotation axis increases. To explain the difference in the pulse profile and in the radiation efficiency, our model suggests that PSR~J0540-6919 has an inclination angle much smaller than the that of Crab pulsar (here we assume the inclination angles of both pulsars are $\alpha<90^{\circ}$). On the other hand, we speculate that the difference in the radiation efficiencies between PSRs~J0537-6910 and J0549-6919 is mainly caused by the difference in the Earth viewing angle, and that we see PSR~J0537-6910 with an Earth viewing angle $\zeta>>90^{\circ}$ (or $<<90^{\circ}$) measured from the spin axis, while we see PSR~J0540-6919 with $\zeta\sim 90^{\circ}$.Comment: 23 pages, 7 figures, ApJ in pres

Impact cratering calculations

In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied