Hsiang-Kuang Chang

A two-dimensional electrodynamical outer gap model for γ-ray pulsars: γ-ray spectrum

A two-dimensional electrodynamical model is used to study particle acceleration in the outer magnetosphere of a pulsar. The charge depletion from the Goldreich-Julian charge density causes a large electric field along the magnetic field lines. The charge particles are accelerated by the electric field and emit γ-rays via the curvature process. Some of the emitted γ-rays may collide with X-ray photons to make new pairs, which are accelerated again on the different field lines in the gap and proceed similar processes. We simulate the pair creation cascade in the meridional plane using the pair creation mean-free path, in which the X-ray photon number density is proportional to inverse square of radial distance. With the space charge density determined by the pair creation simulation, we solve the electric structure of the outer gap in the meridional plane and calculate the curvature spectrum. We investigate in detail relation between the spectrum and total current, which is carried by the particles produced in the gap and/or injected at the boundaries of the gap. We demonstrate that the hardness of the spectrum is strongly controlled by the current carriers. Especially, the spectrum sharply softens if we assume a larger particle injection at the outer boundary of the outer gap. This is because the mean-free path of the pair creation of the inwardly propagating γ-ray photons is much shorter than the light radius so that the many pairs are produced in the gap to quench the outer gap. Because the two-dimensional model can link both gap width along the magnetic field line and trans-field thickness with the spectral cut-off energy and flux, we can diagnose both the current through the gap and inclination 2 J. Takata, S. Shibata, K. Hirotani & H.-K. Chang angle between the rotational and magnetic axes. We apply the theory to the Vela pulsar. By comparing the results with the EGRET data, we rule out any cases that have a large particle injection at the outer boundary. We also suggest the inclination angle of αinc >65 ◦. The present model predicts the outer gap starting from near the conventional null charge surface for the Vela pulsar.

Pulse Profiles, Spectra, and Polarization Characteristics of Nonthermal Emissions from the Crab-like Pulsars

We discuss nonthermal emission mechanisms of the Crab-like pulsars with both a two-dimensional electrodynamic study and a three-dimensional model. We investigate the emission process in the outer gap accelerator. In the two-dimensional electrodynamic 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 processes and the pair-creation process. We show a solved gap structure that produces a γ-ray spectrum consistent with EGRET observations. Based on the two-dimensional model, we construct 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 through γ-ray bands for comparison with 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 to that of the observations. The calculated phase-resolved spectra are consistent with the data from the optical to the γ-ray bands. We demonstrate that the 10%-20% of the polarization degree in the optical emissions from the Crab pulsar and the Vela pulsar is explained by the synchrotron emissions from the particle gyration motion. For PSR B0540-69, the observed pulse profile with a single broad pulse is reproduced for an emission region thicker and an inclination angle between the rotational axis and the magnetic axis smaller than the Crab pulsar.

Polarization of High-Energy Emission from the Crab Pulsar

We investigate the polarization of the high-energy emission from the Crab pulsar within the framework of the outer gap accelerator, following previous studies by Cheng and coworkers. A recent version of the outer gap, in which the gap extends from inside the null charge surface to the light cylinder, is used to examine the synchrotron radiation from the secondary and tertiary pairs that are produced outside the gap. We are able to simultaneously reproduce the light curve, the spectrum, and the polarization characteristics by taking into account the gyration of the particles. The polarization position angle curve and the degree of polarization are calculated and compared with the Crab optical data. We demonstrate that the radiation from inside the null charge surface produces the outer wing and off-pulse portions of the light curve and that the tertiary pairs contribute to the bridge emission. The emission from the secondary pairs explains the main features of the observed light curve and spectrum. On the other hand, the emissions both from inside the null charge surface and from the tertiary pairs are required in order to explain the optical polarization behavior of the Crab pulsar. The energy dependence of the polarization features is predicted by the model. The polarization position angle curve indicates that our viewing angle as measured from the pulsars rotational axis is greater than 90°.

Ambient acoustic imaging in helioseismology

The increasing availability of high spatial resolution data of velocity and intensity variations on the Sun has stimulated the development of helioseismological techniques that probe the solar interior in localized regions. The techniques developed so far have yielded information on physical quantities (such as the flow velocity and magnetic field) below the surface, but are still far from providing a detailed picture of local subsurface inhomogeneities. Here we report the development and application of a new method for constructing three-dimensional solar images, utilizing acoustic noise (or stochastic P-mode oscillations) in the Sun. We treat a region of the solar surface as a phased array of acoustic sensors, which acts as a computational ‘lens’; acoustic waves ‘scattered’ by local inhomogeneities, such as sunspots, are collected and summed in phase, based on the knowledge of how (on average) they travel within the Sun. In this way, we are able to construct a three-dimensional image of a region of the solar interior.

Particle acceleration and non-thermal emission in the pulsar outer magnetospheric gap

A two-dimensional electrodynamic model is used to study particle acceleration and non-thermal emission mechanisms in the pulsar magnetosphere. We solve the distribution of the accelerating electric field with the emission process and the pair-creation process in the meridional plane, which includes the rotational and magnetic axes. By solving the evolutions of the Lorentz factor, and of the pitch angle, we calculate the spectrum in optical through γ-ray bands with the curvature radiation, synchrotron radiation and inverse-Compton process, not only for outgoing particles but also for ingoing particles, which have been ignored in previous studies. We apply this theory to the Vela pulsar. We find that the curvature radiation from the outgoing particles is the major emission process above 10 MeV bands. In soft γ-ray to hard X-ray bands, the synchrotron radiation from the incoming primary particles in the gap dominates in the spectrum. Below hard X-ray bands, the synchrotron emissions from both outgoing and ingoing particles contribute to the calculated spectrum. The calculated spectrum is consistent with the observed phase-averaged spectrum of the Vela pulsar. Taking into account the predicted dependence of the emission process and the emitting particles on the energy bands, we compute the expected pulse profile in X-ray and γ-ray bands with a three-dimensional geometrical model. We show that the observed five-peak pulse profile in the X-ray bands of the Vela pulsar is reproduced by the inward and outward emissions, and the observed double-peak pulse profile in γ-ray bands is explained by the outward emissions. We also apply the theory to PSR B1706−44 and PSR B1951+32, for which X-ray emission properties have not been constrained observationally very well, to predict the spectral features with the present outer-gap model.

DETECTION AND IMAGING OF THE CRAB NEBULA WITH THE NUCLEAR COMPTON TELESCOPE

The Nuclear Compton Telescope (NCT) is a balloon-borne Compton telescope designed for the study of astrophysical sources in the soft gamma-ray regime (200 keV–20 MeV). NCT’s 10 high-purity germanium crossedstrip detectors measure the deposited energies and three-dimensional positions of gamma-ray interactions in the sensitive volume, and this information is used to restrict the initial photon to a circle on the sky using the Compton scatter technique. Thus NCT is able to perform spectroscopy, imaging, and polarization analysis on soft gamma-ray sources. NCT is one of the next generation of Compton telescopes—the so-called compact Compton telescopes (CCTs)—which can achieve effective areas comparable to the Imaging Compton Telescope’s with an instrument that is a fraction of the size. The Crab Nebula was the primary target for the second flight of the NCT instrument, which occurred on 2009 May 17 and 18 in Fort Sumner, New Mexico. Analysis of 29.3 ks of data from the flight reveals an image of the Crab at a significance of 4σ . This is the first reported detection of an astrophysical source by a CCT.

Occultation of X-rays from Scorpius X-1 by small trans-neptunian objects

Since the discovery of the trans-neptunian objects (TNOs) in 1992, nearly one thousand new members have been added to our Solar System, several of which are as big as—or even larger than—Pluto. The properties of the population of TNOs, such as the size distribution and the total number, are valuable information for understanding the formation of the Solar System, but direct observation is only possible for larger objects with diameters above several tens of kilometres. Smaller objects, which are expected to be more abundant, might be found when they occult background stars, but hitherto there have been no definite detections. Here we report the discovery of such occultation events at millisecond timescales in the X-ray light curve of Scorpius X-1. The estimated sizes of these occulting TNOs are ≤100 m. Their abundance is in line with an extrapolation of the distribution of sizes of larger TNOs.

Probing the subsurface structure of active regions with the phase information in acoustic imaging

We present the phase information of solar p-mode waves constructed with an acoustic imaging technique in the solar interior. There exists a phase shift between the time series constructed with ingoing waves and outgoing waves. We find that this phase shift is different in an active region and the quiet Sun. The p-mode travel time is shorter in the magnetic regions than in the quiet Sun. We construct a three-dimensional phase shift map of the solar interior. As with the acoustic absorption images, the phase shift features of the active region in maps at the surface correlate with magnetic fields. The vertical extension of phase shift features in the active region is smaller in the phase maps constructed with shorter wavelengths. This indicates the vertical spatial resolution of these three-dimensional phase maps is sensitive to the range of modes used in constructing the signal. The actual depths of the phase shift features in the active region may be smaller than those shown in the three-dimensional phase maps.

Measuring neutron star mass and radius with three mass-radius relations

We propose to determine the mass and radius of a neutron star (NS) using three measurable mass‐radius relationships, namely the ‘apparent’ radius inferred from the NS thermal emission, the gravitational redshift inferred from the absorption lines, as well as the averaged stellar mass density inferred from the orbital Keplerian frequency derived from the kilohertz quasi-periodic oscillation data. We apply the method to constrain the NS mass and radius of the X-ray sources, 1E 1207.4−5209, Aql X-1 and EXO 0748−676.

Acoustic Imaging in Helioseismology

The time-variant acoustic signal at a point in the solar interior can be constructed from observations at the surface, based on the knowledge of how acoustic waves travel in the Sun: the time-distance relation of the p-modes. The basic principle and properties of this imaging technique are discussed in detail. The helioseismic data used in this study were taken with the Taiwan Oscillation Network (TON). The time series of observed acoustic signals on the solar surface is treated as a phased array. The time-distance relation provides the phase information among the phased array elements. The signal at any location at any time can be reconstructed by summing the observed signal at array elements in phase and with a proper normalization. The time series of the constructed acoustic signal contains information on frequency, phase, and intensity. We use the constructed intensity to obtain three-dimensional acoustic absorption images. The features in the absorption images correlate with the magnetic field in the active region. The vertical extension of absorption features in the active region is smaller in images constructed with shorter wavelengths. This indicates that the vertical resolution of the three-dimensional images depends on the range of modes used in constructing the signal. The actual depths of the absorption features in the active region may be smaller than those shown in the three-dimensional images.