Analysis of x-ray images and spectra.

Four research projects are reported. They are all concerned with X-ray data analysis techniques and although each project is different there is a common theme which links all four. Part I considers the use of grazing incidence optics to produce two dimensional X-ray pictures with the emphasis on the data analysis and presentation. The mathematical development within this project forms a foundation for the subsequent reports. The research concentrates on viable methods of cleaning up blurred and noisy X-ray images using Fourier filtering and the Maximum Entropy Method including a practical implementation of the theory using digital computers. The major product of this project was a software package for the processing of large matrices and this is documented in Appendix I. This package was used to process astronomical X-ray data from a sounding rocket flight to yield a soft X-ray image of the Cygnus Loop supernova remnant and these results are presented to allow comparison of the analysis techniques developed. The second project presented in Part II applies the deconvolution theory developed in Part I to the problem of decoding data from coded mask telescopes. The design of such devices is described and computer simulations of X-ray burst monitors are reported with analysis and comment to give a realistic estimate of the expected performance of proposed instruments and to compare the different methods of analysis available. Part III reports a small project in which the possibility of analysing anode pulse height data from proportional counters using the Maximum Entropy Method was investigated. A computer program was written to both simulate and analyse real data. The algorithm was used to analyse pulse height spectra from the Cygnus Loop observations. The final project, concerned with the calibration of crystal spectrometers, was somewhat different from the other three and is presented in Part IV. The mathematical description of crystal spectrometers is shown to be very similar to that used for imaging devices but instead of studying data analysis methods which require an accurate description of the instrument response, the more fundamental problem of characterising and calibrating the response is addressed. Both theoretical and practical methods for finding crystal reflection parameters are discussed and then applied to three crystals; Langmuir- Blodgett lead stearate multilayers, gypsum 020 and beryl 1010. Sophisticated theoretical calculations using an atomic model developed by other workers were used to predict the crystal response. Direct measurements of the response at a set of wavelengths through each crystal's range were made using a two crystal X-ray spectrometer. The combination of theory and measurement provide a nearly complete description of current pseudo lead stearate crystal production while the excellent agreement between theory and measurement for both gypsum and beryl demonstrates the power of both the theoretical and practical techniques employed. The results from all three crystal types provide excellent calibration data for use in subsequent spectral analysis using these crystals as Bragg Analysers. Measurement of the response across the sulphur k and aluminium k edges in gypsum and beryl respectively also provided direct experimental evidence of k electron resonance in these two atomic types

Effective collecting area of lobster eye optics and optimal value of effective angle

Effective collecting area represents one of principal parameters of optical systems. The common requirement is to obtain as large effective collecting area as it is possible. The paper presents an analytical method of calculating effective collecting length and its maximization for lobster eye optics. The results are applicable for a Schmidt as well as for an Angel lobster eye geometry used in an astronomical telescope where the source is at infinity such that the incoming rays are parallel. The dependence of effective collecting area vs. geometrical parameters is presented in a form of a simple compact equation. We show that the optimal ratio between mirrors depth and distance (effective angle) does not depend on other geometrical parameters and it is determined only by reflectivity function, i.e. by mirrors (or their coating) material and photon energy. The results can be also used for approximate but fast estimation of performance and for finding the initial point for consequent optimization by ray-tracing simulations

The Pulse Luminosity Function of Swift Gamma-ray Bursts

The complete Swift Burst Alert Telescope and X-Ray Telescope light curves of 118 gamma-ray bursts (GRBs) with known redshifts were fitted using the physical model of GRB pulses by Willingale et al. to produce a total of 607 pulses. We compute the pulse luminosity function utilizing three GRB formation rate models: a progenitor that traces the cosmic star formation rate density (CSFRD) with either a single population of GRBs, coupled to various evolutionary parameters, or a bimodal population of high- and low-luminosity GRBs; and a direct fit to the GRB formation rate excluding any a priori assumptions. We find that a single population of GRB pulses with an evolving luminosity function is preferred over all other univariate evolving GRB models, or bimodal luminosity functions in reproducing the observed GRB pulse L-z distribution and that the magnitude of the evolution in brightness is consistent with studies that utilize only the brightest GRB pulses. We determine that the appearance of a GRB formation rate density evolution component is an artefact of poor parametrization of the CSFRD at high redshifts rather than indicating evolution in the formation rate of early epoch GRBs. We conclude that the single brightest region of a GRB light curve holds no special property; by incorporating pulse data from the totality of GRB emission we boost the GRB population statistics by a factor of 5, rule out some models utilized to explain deficiencies in GRB formation rate modelling, and constrain more tightly some of the observed parameters of GRB behaviour

The spectral-temporal properties of the prompt pulses and rapid decay phase of gamma-ray bursts

The prompt emission from gamma-ray burst is the brightest electromagnetic emission known, yet its origin is not understood. The flux density of individual prompt pulses of a GRB can be represented by an analytical expression derived assuming the emission is from a thin, ultrarelativistically expanding, uniform, spherical shell over a finite range of radii. We present the results of fitting this analytical expression to the light curves from the four standard Swift Burst Alert Telescope energy bands and two standard Swift X-ray Telescope energy bands of 12 bursts. The expression includes the high latitude emission (HLE) component and the fits provide a rigorous demonstration that the HLE can explain the rapid decay phase of the prompt emission. The model also accommodates some aspects of energy-dependent lag and energy-dependent pulse width, but there are features in the data which are not well represented. Some pulses have a hard, narrow peak which is not well fitted or a rise and decay which are faster than expected using the standard indices derived assuming synchrotron emission from internal shocks, although it might be possible to accommodate these features using a different emission mechanism within the same overall framework. The luminosity of pulses is correlated with the peak energy of the pulse spectrum, Lf∝[Epeak(1 +z)]1.8, and anticorrelated with the time since ejection of the pulse, Lf∝[Tf/(1 +z)]−2.0

The dust scattering model cannot explain the shallow X-ray decay in GRB afterglows

A dust scattering model was recently proposed to explain the shallow X-ray decay (plateau) observed prevalently in Gamma-Ray Burst (GRB) early afterglows. In this model, the plateau is the scattered prompt X-ray emission by the dust located close (about 10 to a few hundred pc) to the GRB site. In this paper, we carefully investigate the model and find that the scattered emission undergoes strong spectral softening with time, due to the model's essential ingredient that harder X-ray photons have smaller scattering angle thus arrive earlier, while softer photons suffer larger angle scattering and arrive later. The model predicts a significant change, that is Δβ∼ 2–3, in the X-ray spectral index from the beginning of the plateau towards the end of the plateau, while the observed data show close to zero softening during the plateau and the plateau-to-normal transition phase. The scattering model predicts a big difference between the harder X-ray light curve and the softer X-ray light curve, i.e. the plateau in harder X-rays ends much earlier than in softer X-rays. This feature is not seen in the data. The large scattering optical depths of the dust required by the model imply strong extinction in optical, A[subscript: V]≳ 10, which contradicts current findings of A[subscript: V]= 0.1–0.7 from optical and X-ray afterglow observations. We conclude that the dust scattering model cannot explain the X-ray plateaus

The mass and energy budget of Cassiopeia A

Further analysis of X-ray spectroscopy results (Willingale et al. 2002) recently obtained from the MOS CCD cameras on-board XMM-Newton provides a detailed description of the hot and cool X-ray emitting plasma in Cas A. Measurement of the Doppler broadening of the X-ray emission lines is consistent with the expected ion velocities, ~ 1500 km s -1 along the line of sight, in the post shock plasma. Assuming a distance of 3.4 kpc, a constant total pressure throughout the remnant and combining the X-ray observations with optical measurements we estimate the total remnant mass as 10 $M_{\odot}$ and the total thermal energy as $7\times10^{43}$ J. We derive the differential mass distribution as a function of ionisation age for the hot and cool X-ray emitting components. This distribution is consistent with a hot component dominated by swept up mass heated by the primary shock and a cool component which are ablated clumpy ejecta material which were and are still being heated by interaction with the preheated swept up material. We calculate a balanced mass and energy budget for the supernova explosion giving a grand total of $1.0\times10^{44}$ J in an ejected mass; approximately ~ 0.4 $M_{\odot}$ of the ejecta were diffuse with an initial rms velocity ~ $1.5\times10^{4}$ km s -1 while the remaining ~ 1.8 $M_{\odot}$ were clumpy with an initial rms velocity of ~ 2400 km s -1. Using the Doppler velocity measurements of the X-ray spectral lines we can project the mass into spherical coordinates about the remnant. This provides quantitative evidence for mass and energy beaming in the supernova explosion. The mass and energy occupy less than 4.5 sr ( <40% of the available solid angle) around the remnant and 64% of the mass occurs in two jets within 45 degrees of a jet axis. We calculate a swept up mass of 7.9 $M_{\odot}$ in the emitting plasma and estimate that the total mass lost from the progenitor prior to the explosion could be as high as ~ 20 $M_{\odot}$. We suggest that the progenitor was a Wolf-Rayet star that formed a dense nebular shell before the supernova explosion. This shell underwent heating by the primary shock which was energized by the fast diffuse ejecta

Can X-ray emission powered by a spinning-down magnetar explain some gamma-ray burst light-curve features?

Long-duration gamma-ray bursts (GRBs) are thought to be produced by the core-collapse of a rapidly rotating massive star. This event generates a highly relativistic jet and prompt gamma-ray and X-ray emission arises from internal shocks in the jet or magnetized outflows. If the stellar core does not immediately collapse to a black hole, it may form an unstable, highly magnetized millisecond pulsar or magnetar. As it spins down, the magnetar would inject energy into the jet causing a distinctive bump in the GRB light curve where the emission becomes fairly constant followed by a steep decay when the magnetar collapses. We assume that the collapse of a massive star to a magnetar can launch the initial jet. By automatically fitting the X-ray light curves of all GRBs observed by the Swift satellite, we identified a subset of bursts which have a feature in their light curves which we call an internal plateau – unusually constant emission followed by a steep decay – which may be powered by a magnetar. We use the duration and luminosity of this internal plateau to place limits on the magnetar spin period and magnetic field strength, and find that they are consistent with the most extreme predicted values for magnetars

X-ray spectral imaging and Doppler mapping of Cassiopeia A

We present a detailed X-ray spectral analysis of Cas A using a deep exposure from the EPIC-MOS cameras on-board XMM-Newton. Spectral fitting was performed on a 15 $\times$15 grid of 20{\arcsec} \times 20{\arcsec} pixels using a two component non-equilibrium ionisation model (NEI) giving maps of ionisation age, temperature, interstellar column density, abundances for Ne, Mg, Si, S, Ca, Fe and Ni and Doppler velocities for the bright Si-K, S-K and Fe-K line complexes. The abundance maps of Si, S, Ar and Ca are strongly correlated. The correlation is particularly tight between Si and S. The measured abundance ratios are consistent with the nucleosynthesis yield from the collapse of a progenitor star of 12 $M_{\odot}$ at the time of explosion. The distributions of the abundance ratios Ne/Si, Mg/Si, Fe/Si and Ni/Si are very variable and distinctly different from S/Si, Ar/Si and Ca/Si. This is also expected from the current models of explosive nucleosynthesis. The ionisation age and temperature of both the hot and cool NEI components varies considerably over the remnant. Accurate determination of these parameters has enabled us to extract reliable Doppler velocities for the hot and cold components. The combination of radial positions in the plane of the sky and velocities along the line of sight have been used to measure the dynamics of the X-ray emitting plasma. The data are consistent with a linear radial velocity field for the plasma within the remnant with $v_{\rm s}=2600$ km s -1 at $r_{\rm s}=153$ arcsec implying a primary shock velocity of $4000\pm500$ km s -1 at this shock radius. The Si-K and S-K line emission from the cool plasma component is confined to a relatively narrow shell with radius 100-150 arcsec. This component is almost certainly ejecta material which has been heated by a combination of the reverse shock and heating of ejecta clumps as they plough through the medium which has been pre-heated by the primary shock. The Fe-K line emission is expanding somewhat faster and spans a radius range 110-170 arcsec. The bulk of the Fe emission is confined to two large clumps and it is likely that these too are the result of ablation from ejecta bullets rather than swept up circumstellar medium

The Soft X-ray Imager (SXI) on-board the THESEUS mission

We summarize in this contribution the capabilities, design status, and the en- abling technologies of the Soft X-ray Imager (SXI) planned to be on-board the THESEUS mission. We describe its central role in making THESEUS a powerful machine to probe the physical conditions of the early Universe (close to the reionization era) and to explore the time-domain Universe

New light on the X-ray spectrum of the Crab Nebula

XMM-Newton observations of the Crab provide new information on its integrated X-ray spectrum and the variation of the spectral form across the nebula. The Crab pulsar and its surrounding torus exhibit the hardest spectra with power-law indices of $\Gamma = 1.6$ and 1.8. The jet and outer reaches of the nebula are significantly softer with $\Gamma = 2.1$ and 2.3 respectively. For the whole nebula, the huge number of recorded counts allows a detailed examination of the soft X-ray absorption due to cool gas in the foreground of the Crab. Absorption edges due to oxygen and neon are clearly identified. Oxygen and iron in the interstellar medium are underabundant by a factor of $0.63 \pm 0.01$. The average $N_{\rm H}=3.45\pm0.02 10^{21}$ cm-2 and varies by less than $\pm11\%$ on a scale equal to or larger than 20 arcsec over the face of the nebula. These observations of the Crab provide an excellent demonstration of the power of the EPIC cameras on XMM-Newton for spatial, spectral and timing studies