Compton polarimeter as a focal plane detector for hard X-ray telescope: sensitivity estimation with Geant4 simulations

X-ray polarimetry can be an important tool for investigating various physical processes as well as their geometries at the celestial X-ray sources. However, X-ray polarimetry has not progressed much compared to the spectroscopy, timing and imaging mainly due to the extremely photon-hungry nature of X-ray polarimetry leading to severely limited sensitivity of X-ray polarimeters. The great improvement in sensitivity in spectroscopy and imaging was possible due to focusing X-ray optics which is effective only at the soft X-ray energy range. Similar improvement in sensitivity of polarisation measurement at soft X-ray range is expected in near future with the advent of GEM based photoelectric polarimeters. However, at energies >10 keV, even spectroscopic and imaging sensitivities of X-ray detector are limited due to lack of focusing optics. Thus hard X-ray polarimetry so far has been largely unexplored area. On the other hand, typically the polarisation degree is expected to increase at higher energies as the radiation from non-thermal processes is dominant fraction. So polarisation measurement in hard X-ray can yield significant insights into such processes. With the recent availability of hard X-ray optics (e.g. with upcoming NuSTAR, Astro-H missions) which can focus X-rays from 5 KeV to 80 KeV, sensitivity of X-ray detectors in hard X-ray range is expected to improve significantly. In this context we explore feasibility of a focal plane hard X-ray polarimeter based on Compton scattering having a thin plastic scatterer surrounded by cylindrical array scintillator detectors. We have carried out detailed Geant4 simulation to estimate the modulation factor for 100 % polarized beam as well as polarimetric efficiency of this configuration. We have also validated these results with a semi-analytical approach. Here we present the initial results of polarisation sensitivities of such focal plane Compton polarimeter coupled with the reflection efficiency of present era hard X-ray optics.     

Characterization of scatterers for an active focal plane Compton polarimeter

In this work we present an active Compton scattering polarimeter as a focal plane instrument able to extend the X-ray polarimetry towards hard X-rays.Other authors have already studied various instrument design by means of Monte Carlo simulations, in this work we will show for the first time the experimental measurements of “tagging efficiency” aimed to evaluate the polarimeter sensitivity as a function of energy. We performed a characterization of different scattering materials by measuring the tagging efficiency that was used as an input to the Monte Carlo simulation. Then we calculated the sensitivity to polarization of a design based on the laboratory set-up. Despite the geometry tested is not optimized for a realistic focal plane instrument, we demonstrated the feasibility of polarimetry with a low energy threshold of 20 keV. Moreover we evaluated a minimum detectable polarization of 10% for a 10 mCrab source in 100 ks between 20 and 80 keV in the focal plane of one multilayer optics module of NuSTAR. The configuration used consisted of a doped p-terphenyl scatterer 3 cm long and 0.7 cm of diameter coupled with a 0.2 cm thick LaBr₃ absorber.     

Optimization of the design of the hard X-ray polarimeter X-Calibur

We report on the optimization of the hard X-ray polarimeter X-Calibur for a high-altitude balloon-flight in the focal plane of the InFOCμS X-ray telescope from Fort Sumner (NM) in Fall 2013. X-Calibur combines a low-Z scintillator slab to Compton-scatter photons with a high-Z Cadmium Zinc Telluride (CZT) detector assembly to photo-absorb the scattered photons. The detector makes use of the fact that polarized photons Compton scatter preferentially perpendicular to the electric field orientation. X-Calibur achieves a high detection efficiency of order unity and reaches a sensitivity close to the best theoretically possible. In this paper, we discuss the optimization of the design of the instrument based on Monte Carlo simulations of polarized and unpolarized X-ray beams and of the most important background components. We calculate the sensitivity of the polarimeter for the upcoming balloon flight from Fort Sumner and for additional longer balloon flights with higher throughput mirrors. We conclude by emphasizing that Compton polarimeters on satellite borne missions can be used down to energies of a few keV.     

Optimising a balloon-borne polarimeter in the hard X-ray domain: From the PoGOLite Pathfinder to PoGO+

PoGOLite is a balloon-borne hard X-ray polarimeter dedicated to the study of point sources. Compton scattered events are registered using an array of plastic scintillator units to determine the polarisation of incident X-rays in the energy range 20–240 keV. In 2013, a near circumpolar balloon flight of 14 days duration was completed after launch from Esrange, Sweden, resulting in a measurement of the linear polarisation of the Crab emission. Building on the experience gained from this Pathfinder flight, the polarimeter is being modified to improve performance for a second flight in 2016. Such optimisations, based on Geant4 Monte Carlo simulations, take into account the source characteristics, the instrument response and the background environment which is dominated by atmospheric neutrons. This paper describes the optimisation of the polarimeter and details the associated increase in performance. The resulting design, PoGO+, is expected to improve the Minimum Detectable Polarisation (MDP) for the Crab from 19.8% to 11.1% for a 5 day flight. Assuming the same Crab polarisation fraction as measured during the 2013 flight, this improvement in MDP will allow a 5σ constrained result. It will also allow the study of the nebula emission only (Crab off-pulse) and Cygnus X-1 if in the hard state.     

A solar flare X-ray polarimeter for the space shuttle

We have recently built and tested an instrument designed to measure the polarization of the hard (5–30 keV) X-ray emission from solar flares, and thereby to investigate the energy release mechanism and constrain flare models. In particular, these measurements will help to determine whether hard X-ray bursts are produced by nonthermal or by thermal electrons. The polarimeter makes use of the angular dependence of Thomson scattering from targets of metallic lithium. It has an energy resolution of a few keV, a time resolution of 5 s, and sufficient sensitivity to measure polarization levels (3) of a few percent in about 10 s for a moderate strength solar flare. The instrumental polarization has been directly measured and found to be within the design goal of 1%. This polarimeter is scheduled to be flown as part of the OSS-1 pallet on an early Space Shuttle mission.     

Measures of the Soft X-ray Excess as an Eigenvector 1 Parameter for Active Galactic Nuclei

We present a preliminary analysis of X-ray data of quasars in the context of the 4D eigenvector 1 parameter space (Sulentic et al. 2000a, b). 4DE1 serves as a surrogate H-R diagram for representing empirical diversity among quasars and identifying the physical drivers of the diversity. The soft X-ray spectral index (Γ_soft) was adopted as one of the key 4DE1 that correlates contrasting extremes in Type 1 properties. 4DE1 motivated the hypothesis of two quasar populations (A and B) divided by L/L _EDD≈0.2. Pop. A is a largely radio-quiet population with FWHM H β<4000 km/s and often showing a soft X-ray excess. Pop. B is a mix of radio-quiet and a majority of RL quasars shows only a hard X-ray power-law SED. The X-ray separation was based upon earlier ROSAT and ASCA data but we now confirm this dichotomy with large samples of X-ray spectra obtained with XMM-Newton and SWIFT. One popular idea connects the soft excess in Pop. A quasars as a signature of thermal emission from a hot accretion disk in sources radiating close to the Eddington limit.     

Polarization, temporal, and spectral parameters of solar flare hard X-rays as measured by the SPR-N instrument onboard the CORONAS-F satellite

The SPR-N polarimeter onboard the CORONAS-F satellite allows the X-ray polarization degree to be measured in energy ranges of 20–40, 40–60, and 60–100 keV. To measure the polarization, the method based on the Thompson scattering of solar X-ray photons in beryllium plates was used; the scattered photons were detected with a system of six CsI(Na) scintillation sensors. During the observation period from August 2001 to January 2005, the SPR-N instrument detected the hard X-rays of more than 90 solar flares. The October 29, 2003, event showed a significant polarization degree exceeding 70% in channels of E = 40–60 and 60–100 keV and about 50% in the 20-to 40-keV channel. The time profile of the polarization degree and the projection of the polarization plane onto the solar disk were determined. For 25 events, the upper limits of the part of polarized X-rays were estimated at 8 to 40%. For all the flares detected, time profiles (with a resolution of up to 4 s), hard X-ray radiation fluxes, and spectral index estimates were obtained.     

Prospects of hard X-ray polarimetry with Astrosat-CZTI

Astrosat is the first Indian satellite mission dedicated for astronomical studies. It is planned for launch during 2014 and will have five instruments for multi-wavelength observations from optical to hard X-rays. Cadmium Zing Telluride Imager (CZTI) is one of the five instruments aiming for simultaneous X-ray spectroscopy and imaging in the energy range of 10 keV to 100 keV (along with all sky photometric capability unto 250 keV). It is based on pixilated CZT detector array with total geometric area of 1024 cm². It will have two-dimensional coded mask for medium resolution X-ray imaging. The CZT detector plane will be realized using CZT detector modules having integrated readout electronics. Each CZT detector module consists of 4 cm × 4 cm CZT with thickness of 5 mm which is further pixilated into 16 × 16 array of pixels. Thus each pixel has size of 2.5 mm × 2.5 mm and thickness of 5 mm. Such pixilated detector plane can in principle be used for hard X-ray polarization measurements based on the principle of Compton scattering by measuring azimuthal distribution of simultaneous events in two adjacent pixels. We have carried out detailed Geant4 simulations for estimating polarimetric capabilities of CZTI detector plane. The results indicate that events in the energy range of 100 keV to 250 keV, where the 5 mm thick CZT detector has significant detection efficiency, can be used for polarimetric studies. Our simulation results indicate the minimum detectable polarization (MDP) at the level of ～ 10% can be achieved for bright Crab like X-ray sources with exposure time of ～500 ks. We also carried out preliminary experiments to verify the results from our simulations. Here we present detailed method and results of our simulations as well as preliminary results from the experimental verification of polarimetric capabilities of CZT detector modules used in Astrosat CZTI.     

A focal plane detector design for a wide-band Laue-lens telescope

The energy range above 60 keV is important for the study of many open problems in high energy astrophysics such as the role of Inverse Compton with respect to synchrotron or thermal processes in GRBs, non thermal mechanisms in SNR, the study of the high energy cut-offs in AGN spectra, and the detection of nuclear and annihilation lines. Recently the development of high energy Laue lenses with broad energy bandpasses from 60 to 600keV have been proposed for a Hard X ray focusing Telescope (HAXTEL) in order to study the X-ray continuum of celestial sources. The required focal plane detector should have high detection efficiency over the entire operative range, a spatial resolution of about 1mm, an energy resolution of a few keV at 500keV and a sensitivity to linear polarization. We describe a possible configuration of the focal plane detector based on several CdTe/CZT pixelated layers stacked together to achieve the required detection efficiency at high energy. Each layer can operate both as a separate position sensitive detector and polarimeter or work with other layers to increase the overall photopeak efficiency. Each layer has a hexagonal shape in order to minimize the detector surface required to cover the lens field of view. The pixels would have the same geometry so as to provide the best coupling with the lens point spread function and to increase the symmetry for polarimetric studies.     

Transition between general relativity and quantum gravity using quark and strange quark matter with some kinematical test

Contemporary piece of writing devotes to the investigation of plane symmetric cosmological model with quark and strange quark matter in the deformations of the Einstein’s theory of General Relativity (GR). At small or large scales (ultraviolet or infrared gravity), deformations of the Einstein’s theory could provide a better handling of cosmic acceleration without magnetism (along with singularities). In particular, a proper deformation of GR in the ultraviolet regime could play the role of describing the transition between GR and quantum gravity. As a matter of fact, although with a different purpose in mind, it was Einstein himself who proposed in the 30’s the reformulation of GR by taking the field of orthonormal frames or tetrads as the dynamical variable instead of the metric tensor (Einstein, Phys. Math. Kl 217, 401, 1928). As per the observation, pressure and energy density of the model approaches the bag constant in negative and positive ways at \(t\rightarrow \infty \), i.e. \(p\rightarrow -B_c \) and \(\rho \rightarrow B_c \), the negative pressure due to the Dark Energy (DE) in the context of accelerated expansion of the universe. So the strange quark matter gives an idea of existence of dark energy in the universe and supports the observations of the SNe-I (Riess et al., Astron. J. 116,1009, 1998; Perlmutter et al., Astrophys. J. 517, 565, 1999). Also these results agree with the study of Aktas and Aygun (Chinese J. Phys. 55, 71, 2017) and Sahoo et al. (New. Astron. 60, 80, 2018).     

Transient Magnetic and Doppler Features Related to the White-Light Flares in NOAA 10486

Rapidly moving transient features have been detected in magnetic and Doppler images of super-active region NOAA 10486 during the X17/4B flare of 28 October 2003 and the X10/2B flare of 29 October 2003. Both these flares were extremely energetic white-light events. The transient features appeared during impulsive phases of the flares and moved with speeds ranging from 30 to 50 km?s^?1. These features were located near the previously reported compact acoustic (Donea and Lindsey, Astrophys. J. 630, 1168, 2005) and seismic sources (Zharkova and Zharkov, Astrophys. J. 664, 573, 2007). We examine the origin of these features and their relationship with various aspects of the flares, viz., hard X-ray emission sources and flare kernels observed at different layers: i) photosphere (white-light continuum), ii) chromosphere (Hα 6563 Å), iii) temperature minimum region (UV 1600 Å), and iv) transition region (UV 284 Å).     

Compton scattered transition radiation from very high energy particles

X-ray transition radiation can be used to measure the Lorentz factor of relativistic particles. At energies approaching γ=E/mc²=10⁵, transition radiation detectors can be optimized by using thick (5–10 mil) foils with large (5–10 mm) spacings. This implies X-ray energies 100 keV and the use of scintillators as the X-ray detectors. Compton scattering of the X-rays out of the particle beam then becomes an important effect. We discuss the design of very high energy detectors, the use of metal radiator foils rather than the standard plastic foils, inorganic scintillators for detecting Compton scattered transition radiation, and the application to the ACCESS cosmic ray experiment.     

天宫2号POLAR探测器的低能X射线在轨定标

伽马暴偏振探测仪(POLAR)是天宫2号实验室上搭载的一个γ射线偏振仪,于2016年9月15日搭载在天宫2号进入低轨运行,主要用于探测在50-500 keV能区的硬X射线辐射的线偏振.POLAR由25个模块组成,每个模块有64个塑料闪烁体棒,总计有1600个塑料闪烁体棒,具有较大的有效探测面积和视场.在轨运行期间探测到多个小耀斑,它们的硬X射线光子能量通常小于50 keV,无法直接使用在轨和地面的高能定标结果来进行能谱分析.结合拉马第太阳高能光谱成像探测器(RHESSI)对耀斑SOL2016112907能谱的观测和蒙特卡洛模拟,对耀斑期间被激活的闪烁体棒进行能量低于50 keV的低能相对定标.虽然定标得到的能量阈值(～10 keV)和转换因子相对稳定,但是和高能定标给出的结果相比有显著差异,并且不同闪烁体棒显示出的差异没有明显的规律性.     

Polarization measurements with an imaging gamma-ray telescope

The proposed Tracking and Imaging Gamma-Ray Experiment (TIGRE), operating in the 0.3–100 MeV energy interval, will be an efficient polarimeter with a modulation factor of 50% at 0.5 MeV. The polarization detection parameters of TIGRE were estimated using a Monte Carlo simulation modified to include the polarization dependence of the Klein-Nishina formula. Using Compton scattering of low energy photons and approximately 3 acceptance angle after scattering, TIGRE will be able to measure strong sources with 20% fractional polarization at 3 significance in a typical balloon-borne exposure and 5% during a 4-week satellite observation.     

A Si/CdTe Compton Camera for gamma-ray lens experiment

Cadmium telluride (CdTe) and cadmium zinc telluride (CdZnTe) have been regarded as promising semiconductor materials for hard X-ray and γ-ray detection. However, a considerable amount of charge loss in these detectors results in a reduced energy resolution. We have achieved a significant improvement in the spectral properties by forming the Schottky junction on the Te side of the CdTe wafer. With the further reduction of leakage current by an adoption of guard ring structure, we have demonstrated a CdTe pixel detector with high energy resolution and full charge collection capabilty. The detector has a pixel size of a few mm and a thickness of 0.5 $-$ 1 mm. We apply this high resolution detector to a new silicon and CdTe Compton Camera which features high angular resolution. We also describe a concept of the stack detector which consists of many thin CdTe layers and provides sufficient efficiency for hard X-rays and gamma-rays up to several hundred keV maintaining good energy resolution. A narrow-FOV Compton telescope can be realized by installing a Si/CdTe Compton Camera inside the deep well of an active shield. This configuration is very suitable as focal plane detector for future focusing gamma-ray missions.     

The fallacy of Oppenheimer Snyder collapse: no general relativistic collapse at all,no black hole,no physical singularity

By applying Birkhoff’s theorem to the problem of the general relativistic collapse of a uniform density dust, we directly show that the density of the dust ρ=0 even when its proper number density n would be assumed to be finite! The physical reason behind this exact result can be traced back to the observation of Arnowitt et al. (Phys. Rev. Lett. 4: 375, 1960) that the gravitational mass of a neutral point particle is zero: m=0. And since, a dust is a mere collection of neutral point particles, unlike a continuous hydrodynamic fluid, its density ρ=mn=0. It is nonetheless found that for k=?1, a homogeneous dust can collapse and expand special relativistically in the fashion of a Milne universe. Thus, in reality, general relativistic homogeneous dust collapse does not lead to the formation of any black hole in conformity of many previous studies (Logunov et al., Phys. Part. Nucl. 37: 317, 2006; Kiselev et al., Theor. Math. Phys. 164: 972, 2010; Mitra, J. Math. Phys. 50: 042502, 2009a; Suggett, J. Phys. A 12: 375 1979b). Interestingly, this result is in agreement with the intuition of Oppenheimer and Snyder (Phys. Rev. 56: 456, 1939) too:“Physically such a singularity would mean that the expressions used for the energy-momentum tensor does not take into account some essential physical fact which would really smooth the singularity out. Further, a star in its early stages of development would not possess a singular density or pressure, it is impossible for a singularity to develop in a finite time.”     

The eccentric Kozai–Lidov effect as a resonance phenomenon

Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719–759, 1962) and, independently, Kozai (Astron J 67:591–598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385–401, 2000; Naoz et al. in Nature 473:187–189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term “eccentric Kozai–Lidov effect” (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of “action-angle” variables emerging in the integrable Kozai–Lidov model. It turns out that for some initial values the resonance is degenerate and the usual “pendulum” approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.     

Plane Symmetric Cosmological Model with Quark and Strange Quark Matter in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Theory of Gravity

We studied plane symmetric cosmological model in the presence of quark and strange quark matter with the help of f(R, T) theory. To decipher solutions of plane symmetric space-time, we used power law relation between scale factor and deceleration parameter. We considered the special law of variation of Hubble’s parameter proposed by Berman (Nuovo Cimento B74, 182, 1983) which yields constant deceleration parameter. We also discussed the physical behavior of the solutions by using some physical parameters.     

VLA Measurements of Faraday Rotation through Coronal Mass Ejections

Coronal mass ejections (CMEs) are large-scale eruptions of plasma from the Sun, which play an important role in space weather. Faraday rotation is the rotation of the plane of polarization that results when a linearly polarized signal passes through a magnetized plasma such as a CME. Faraday rotation is proportional to the path integral through the plasma of the electron density and the line-of-sight component of the magnetic field. Faraday-rotation observations of a source near the Sun can provide information on the plasma structure of a CME shortly after launch. We report on simultaneous white-light and radio observations made of three CMEs in August 2012. We made sensitive Very Large Array (VLA) full-polarization observations using 1?–?2 GHz frequencies of a constellation of radio sources through the solar corona at heliocentric distances that ranged from 6?–?\(15~\mathrm{R}_{\odot}\). Two sources (0842+1835 and 0900+1832) were occulted by a single CME, and one source (0843+1547) was occulted by two CMEs. In addition to our radioastronomical observations, which represent one of the first active hunts for CME Faraday rotation since Bird et al. (Solar Phys., 98, 341, 1985) and the first active hunt using the VLA, we obtained white-light coronagraph images from the Large Angle and Spectrometric Coronagraph (LASCO) C3 instrument to determine the Thomson-scattering brightness [\(\mathrm{B}_{\mathrm{T}}\)], providing a means to independently estimate the plasma density and determine its contribution to the observed Faraday rotation. A constant-density force-free flux rope embedded in the background corona was used to model the effects of the CMEs on \(\mathrm{B}_{\mathrm{T}}\) and Faraday rotation. The plasma densities (\(6\,\mbox{--}\,22\times10^{3}~\mbox{cm}^{-3}\)) and axial magnetic-field strengths (2?–?12 mG) inferred from our models are consistent with the modeling work of Liu et al. (Astrophys. J., 665, 1439, 2007) and Jensen and Russell (Geophys. Res. Lett., 35, L02103, 2008), as well as previous CME Faraday-rotation observations by Bird et al. (1985).     

15-digit accuracy calculations of Ambartsumian-Chandrasekhar’s $$-functions for four-term phase functions with the double-exponential formula

We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar’s \(H\)-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates some advantageous features of the iterative procedure of Kawabata (Astrophys. Space Sci. 358:32, 2015) and the double-exponential integration formula (DE-formula) of Takahashi and Mori (Publ. Res. Inst. Math. Sci. Kyoto Univ. 9:721, 1974), which proved highly effective in Kawabata (Astrophys. Space Sci. 361:373, 2016). Actual calculations of the \(H\)-functions have been carried out employing 27 selected cases of the phase function, 56 values of the single scattering albedo \(\varpi_{0}\), and 36 values of an angular variable \(\mu(= \cos\theta)\), with \(\theta\) being the zenith angle specifying the direction of incidence and/or emergence of radiation. Partial results obtained for conservative isotropic scattering, Rayleigh scattering, and anisotropic scattering due to a full four-term phase function are presented. They indicate that it is important to simultaneously verify accuracy of the numerical values of the \(H\)-functions for \(\mu<0.05\), the domain often neglected in tabulation. As a sample application of the isotropic scattering \(H\)-function, an attempt is made in Appendix to simulate by iteratively solving the Ambartsumian equation the values of the plane and spherical albedos of a semi-infinite, homogeneous atmosphere calculated by Rogovtsov and Borovik (J. Quant. Spectrosc. Radiat. Transf. 183:128, 2016), who employed their analytical representations for these quantities and the single-term and two-term Henyey-Greenstein phase functions of appreciably high degrees of anisotropy. While our results are in satisfactory agreement with theirs, our procedure is in need of a faster algorithm to routinely deal with problems involving highly anisotropic phase functions giving rise to near-conservative scattering.