Centroid Energy Research Articles

Luminosity dependence of the multiple cyclotron lines in 4U 0115+63

Context. The Be X-ray binary 4U 0115+63 underwent a giant outburst in 2023 with the X-ray luminosity of the source reaching 1038 erg s−1. During the outburst, two target of opportunity observations were made with NuSTAR. Aims. The main goal of this work is to model the multiple cyclotron scattering features (CRSFs) present in 4U 0115+63 and study their dependence on the luminosity of the source. Methods. The 3–79 keV broadband X-ray coverage of NuSTAR allowed us to properly model the continuum and investigate the nature of the multiple cyclotron resonance scattering features present in the source spectrum. We used the epoch-folding technique to find the pulsation from the source and also studied the changes in the cyclotron line energy with an order of magnitude variation in the source luminosity. Results. We detected five cyclotron lines during the 2023 outburst near 12, 16, 24, 34, and 47 keV. The ∼16 keV cyclotron line cannot be harmonically related to the other cyclotron lines at ∼12 keV and ∼24 keV. This indicates the presence of two fundamental lines in the spectrum of 4U 0115+63 at 12 keV and 16 keV. Conclusions. With the inclusion of the two latest NuSTAR observations, we have expanded the data set of the CRSF line center to encompass a broad range of luminosity. This enables us to comprehensively investigate the relationship between the centroid energy of the cyclotron lines and luminosity. The CRSF line center shows no anticorrelation with luminosity, unlike previously reported. Instead, a weak positive correlation is found in four out of the five detected cyclotron lines of 4U 0115+63. The luminosity variation of the two fundamental CRSFs could be well explained with the prediction from the collisionless shock model. A tentative negative correlation was observed in the fundamental CRSF at 16 keV and its harmonics beyond a “critical luminosity” of 1038 erg/s. This behavior was not present for the 12 keV fundamental CRSF and its harmonic at 24 keV.

A quantitative explanation of the cyclotron-line variation in accreting magnetic neutron stars of super-critical luminosity

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to be generated in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid (ECRSF) and X-ray luminosity (LX). Aims. It has been pointed out that the observed ECRSF − LX smooth anti-correlation in high-luminosity NSs is in tension with the theoretically predicted one, if the radiative shock is the site of cyclotron-line formation. The shock height increases approximately linearly with luminosity, while the dipolar magnetic field drops as the cubic power of distance, thereby implying that the cyclotron-line energy ought to decrease significantly when the luminosity increases by, say, an order of magnitude, which is contrary to observations. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. Methods. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front’s height, including both the relativistic boosting and the gravitational redshift effects in our considerations. The relativistic boosting effect is due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock’s reference frame. Reults. We find that the cyclotron-line energy varies with (a) the shock height due to the dipolar magnetic field, (b) the Doppler boosting between the shock and bulk-motion frames, and (c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted ECRSF − LX anti-correlation. We use our model to fit the data of the X-ray source V0332+53 that exhibits a weak negative correlation and demonstrate that the model fits the data impressively well, thereby alleviating the tension between observations and theory. Conclusions. The reported weak anti-correlation between cyclotron-line centroid and X-ray luminosity in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. As a result of these effects, the actual magnetic field on the surface of the neutron star may be a factor of ∼2 larger than the naively inferred value from the observed CRSF.

The electric dipole characteristics of well-deformed 171,173Yb

The electric dipole response of well-deformed 171,173Yb in the giant dipole resonance (GDR) and pygmy dipole resonance (PDR) range has been theoretically analyzed using the translation and Galileo invariant quasiparticle phonon nuclear model (TGI-QPNM). The TGI-QPNM consists of an axially symmetric Woods-Saxon Potential, monopole pairing, dipole-dipole residual interaction, and the restoration terms for broken translation and Galilean symmetries. Numerical calculations show the existence of considerable E1 excitations around the neutron separation threshold (S n ) in both isotopes. The TGI-QPNM results of the photoabsorption cross-section give a double-humped shape in both nuclei, consistent with the available experimental data. The integrated moments (σ 0, σ −1) and the centroid energies in the GDR region are also reproduced well.

Ab initio description of monopole resonances in light- and medium-mass nuclei

The paper is the third of a series dedicated to the ab initio description of monopole giant resonances in mid-mass closed- and open-shell nuclei via the so-called projected generator coordinate method. The present focus is on the computation of the moments mk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_k$$\\end{document} of the monopole strength distribution, which are used to quantify its centroid energy and dispersion. First, the capacity to compute low-order moments via two different methods is developed and benchmarked for the m1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_1$$\\end{document} moment. Second, the impact of the angular momentum projection on the centroid energy and dispersion of the monopole strength is analysed before comparing the results to those obtained from consistent quasi-particle random phase approximation calculations. Next, the so-called energy weighted sum rule (EWSR) is investigated. First, the appropriate ESWR in the center-of-mass frame is derived analytically. Second, the intrinsic EWSR is tested in order to quantify the (unwanted) local-gauge symmetry breaking of the presently employed chiral effective field theory (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT) interactions. Finally, the infinite nuclear matter incompressibility associated with the employed χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT interactions is extracted by extrapolating the finite-nucleus incompressibility computed from the monopole centroid energy.

Temporal and spectral variations of the X-ray pulsar Cen X-3 observed by NuSTAR

We report a time-resolved analysis of the accreting X-ray pulsar Cen X-3 using observations carried out by NuSTAR, which cover approximately two binary orbits in different intensity states. The pulse profile is relatively stable over the orbital phase and shows energy dependence. It has an obvious double-peaked shape in the energy band below 15 keV –with the second pulse peak decreasing as energy increases– and is gradually dominated by a single peak in higher energy bands. We find that the pulse profile in the energy band of 3–5 keV at high-intensity states shows a subtle triple-peaked shape, with the main peak divided into two subpeaks. We also find a positive correlation between the pulse fraction and both energy and flux. Our spectral analysis reveals that the spectra can be well described by the continuum of Fermi-Dirac cutoff and NPEX models, and the cyclotron line is detected with the centroid energies varying from 26 keV to 29 keV, along with the iron emission line around 6.4 keV. We investigated the dependence between the cyclotron resonant scattering feature (CRSF) centroid energy and luminosity and discuss the theoretical critical luminosity. Although the variation of Ecyc − LX is not distinct, there is a possibility that the critical luminosity lies within the range of ∼(0.5 − 4)×1037 erg s−1 in the band of 4–78 keV. The photon index shows a strong positive correlation with luminosity. Our orbital-phase analysis reveals that the spectral parameters show orbital variability, and the highly variable photoelectric absorption may indicate the existence of clumpy stellar winds.

Reverse Shock Revisited in Cassiopeia A with Chandra

Using data from the Chandra X-ray Observatory, we revisit the reverse shock in the supernova remnant (SNR) Cassiopeia A. Based on spectroscopy of a series of annuli in the northwest (NW) and southeast (SE), we get the radial profiles of the S/Si Kα line flux ratio and Fe Kα line centroid energy. They both show monotonic increase, confirming that the Si- and Fe-rich ejecta are heated by the reverse shock. The abrupt change of the S and Si line flux ratio is clearly observed in Cassiopeia A, leading to the determination of the reverse-shock location (∼1.′71 ± 0.′16 and ∼1.′35 ± 0.′18 in the NW and SE, with respect to the central source). By comparing the radial profiles of the S and Si line flux, we find that the reverse shock is moving outward in the frame of the observer, and the velocities are ∼3950 ± 210 km s−1 and ∼2900 ± 260 km s−1 in the NW and SE, respectively. In contrast, the velocities become ∼1150 km s−1 (NW) and ∼1300 km s−1 (SE) in the ejecta frame. Our measured reverse-shock velocities are quite consistent with those obtained from the X-ray and/or optical images. They therefore supply a cross-check of the accuracy for the two available methods for measuring the reverse-shock velocity in SNRs. Both the location and the velocity of the reverse shock show apparent asymmetry, suggesting that the asymmetric explosion of the progenitor plays a key role in the interaction between the reverse shock and the ejecta, ultimately shaping the complex features observed in SNRs.

Detection of a cyclotron line in the Be X-ray pulsar IGR J06074+2205

Context. IGR J0607.4+2205 is a transient Be X-ray binary discovered two decades ago. IGR J0607.4+2205 underwent an outburst in 2023 during which it was observed twice with NuSTAR. Aims. The main goal of this work is to model the broadband X-ray spectrum of IGR J0607.4+2205 during the outburst and to study the variations of the spectral and timing features at different intensities. Methods. We extracted the light curve and spectrum of the source from the two NuSTAR observations carried out during the recent outburst in the energy range of 3−78 keV. We used the epoch folding technique to find pulsation from the source and to study the changes in emission characteristics from the source with energy across an order of magnitude variation in source luminosity. Results. IGR J0607.4+2205 shows pulsations with a period of ∼347.6 s during both the observations, with a pulse fraction of ≥50%. The broadband spectrum of the source was modelled using a power-law continuum with a high-energy cutoff. During the first observation, a cyclotron absorption line at ∼51 keV was also present in the source with an optical depth of ∼1.3. However, no cyclotron line feature was detected in the second observation when the source was an order of magnitude fainter. Additionally, soft excess was detected in the second observation, which was modelled with a black body component emerging from close to the neutron star (NS). Conclusions. We report the first ever detection of a cyclotron line in the broadband spectrum of IGR J0607.4+2205 centred at 51 ± 1 keV. The magnetic field strength of the NS is estimated to be ∼4 × 1012 G from the centroid energy of the absorption line. A significant change is observed in the pulse profile with luminosity during the decay of the outburst, indicating an associated change in the beaming pattern.

Cyclotron line formation in the radiative shock of an accreting magnetized neutron star

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Accretion onto their magnetic poles is responsible for the emergence of X-rays, but the site of the CRSF formation is still a puzzle. A promising candidate for high-luminosity sources has always been the radiative shock in the accretion column. Nevertheless, no quantitative calculations of spectral formation at the radiative shock have been performed so far. Aims. It is well accepted that, in the accretion column of a high-luminosity, accreting magnetic NS, a radiative shock is formed. Here, we aim to explore the scenario where the shock is the site of the cyclotron-line formation. We studied spectral formation at the radiative shock and the emergent spectral shape across a wide range of the parameter space and determined which parameters hold an important role in shaping a prominent CRSF. Methods. We developed a Monte Carlo (MC) code based on the forced first collision numerical scheme to conduct radiation transfer simulations at the radiative shock. The seed photons were due to bremsstrahlung and were emitted in the post-shock region. We properly treated bulk-motion Comptonization in the pre-shock region, thermal Comptonization in the post-shock region, and resonant Compton scattering in both regions. We adopted a fully relativistic scheme for the interaction between radiation and electrons, employing an appropriate polarization-averaged differential cross-section. As a result, we calculated the angle- and energy-dependent emergent X-ray spectrum from the radiative shock, focusing on both the CRSF and the X-ray continuum, under diverse conditions. The accretion column was characterized by cylindrical symmetry, and the radiative shock was treated as a mathematical discontinuity. Results. We find that a power law, hard X-ray continuum, and a CRSF are naturally produced by the first-order Fermi energization as the photons criss-cross the shock. The depth and the width of the CRSF depend mainly on the transverse optical depth and the post-shock temperature. We show that the cyclotron-line energy centroid is shifted by ∼(20 − 30)% to lower energies compared to the classical cyclotron energy; this is due to the Doppler boosting between the shock reference frame and the bulk-motion frame. We demonstrate that a “bump” feature arises in the right wing of the CRSF due to the up-scattering of photons by the accreting plasma and extends to higher energies for larger optical depths and post-shock temperatures. Conclusions. We conclude that resonant Compton scattering of photons by electrons in a radiative shock is efficient in producing a power-law X-ray continuum with a high-energy cutoff accompanied by a prominent CRSF. The implications of the Doppler effect on the centroid of the emergent absorption feature must be considered if an accurate determination of the magnetic field strength is desired.

Theoretical Analysis of the RX J0209.6−7427 X-Ray Spectrum during a Giant Outburst

We model the spectral formation occurring in the binary X-ray pulsar (XRP) RX J0209.6−7427 during the 2019 super-Eddington outburst. Using a theoretical model previously developed by the authors, we are able to produce spectra that closely resemble the phase-averaged X-ray spectra observed using the Nuclear Spectroscopic Telescope Array and Insight-HXMT during low- and high-luminosity states of the outburst, respectively. The theoretical model simulates the accretion of fully ionized gas in a dipole magnetic field and includes a complete description of the radiation hydrodynamics, matter distribution, and spectral formation. Type II X-ray outbursts provide an opportunity to study accretion over a large range of luminosities for the same neutron star. The analysis performed here represents the first time both the outburst low and high states of an accretion-powered XRP are modeled using a physics-based model rather than standard phenomenological fitting with arbitrary mathematical functions. We find that the outer polar cap radius remains constant and the column is more fully filled with increasing luminosity, Comptonized bremsstrahlung dominates the formation of the phase-averaged X-ray spectrum, and a negative correlation exists between cyclotron centroid energy and luminosity, as expected. The super-Eddington nature of the outburst is rendered possible owing to the low scattering cross section for photons propagating parallel to the magnetic field. We also find that emission through the column top dominates in both the low and high states, implying that the pulse profiles should have a roughly sinusoidal shape, which agrees with observed properties of ultraluminous XRPs.

NuSTAR detection of a broad absorption line in IGR J06074+2205

BeXRB pulsar IGR J06074+2205 using NuSTAR observations. The temporal and spectral characteristics of the source are investigated. We detect coherent X-ray pulsations of the source and determine the spin period evolution. Using the current spin period data of the source, we show that the source is spinning down at 0.0202(2) sday−1. The pulse profiles are found to evolve with energy and luminosity. Another interesting feature of the source is that the pulse profiles are dual peaked. The dual-peaked pulse profile is characterized by a decreasing secondary peak amplitude with increasing energy. We also observed a proportionate increase in the primary peak amplitude as the energy increases. The pulse fraction exhibits an overall increasing trend with the energy. The X-ray continuum of the source indicates the existence of a characteristic absorption feature with a centroid energy ∼55 keV, which may be interpreted as a cyclotron line. We estimate the corresponding magnetic field strength to be ∼4.74×1012 G. A peculiar ‘10 keV’ absorption feature is observed in the X-ray spectra of the second observation. The luminosity measurements predict that the source may be accreting in the sub-critical regime.

Evidence for a nearly orthogonal rotator in GX 301–2 with phase-resolved cyclotron resonant scattering features

Abstract Cyclotron resonant scattering features (CRSFs) are the absorption features in the X-ray spectra of strongly magnetized accretion neutron stars (NSs), which are probably the most reliable probe to the surface magnetic fields of NSs. The high mass X-ray binary GX 301–2 exhibits a very wide, variable and complicated CRSF in the average spectra, which should be two absorption lines based on NuStar and Insight-HXMT observations. With the Insight-HXMT frequent observations, we performed the phase-resolved spectroscopy and confirmed two cyclotron absorption lines in the phase-resolved spectra, with their centroid energy ratio ∼1.6 − 1.7 in the super-critical luminosity case. A major hindrance in understanding those CRSFs is the very poorly constrained magnetic inclination angle, which is also a fundamental property of a NS and key to understanding the emission characteristics of a pulsar. Comparing the phase-resolved CRSF with simulated X-ray spectra, the magnetic inclination angle is found to be ≳ 70○, i.e., nearly orthogonal between the NS’s spin and magnetic axies. The implications of an orthogonal rotator and magnetic structure evolution in the accreting X-ray binary are also discussed.

Isoscalar giant quadrupole resonance of even-even 112-124Sn isotopes using BCS-QRPA

Using self-consistent Bardeen - Cooper - Schriffer + Hartree - Fock and quasiparticle random phase approximation, the isoscalar giant quadrupole resonance in the isotopes of 112,114,116,118,120,122,124Sn has been studied in this work. Five sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM and effective mass m*/m are used in the calculations. Additionally, the impact of different types of pairing forces (i.e., volume, surface, and mixed) is examined. Comparisons are made between the computed strength distributions, centroid energies Ecen, scaled energies Es, and constrained energies Econ of the isoscalar giant quadrupole resonance and the available experimental data. Analysis is done on the relationships between KNM and m*/m, and the estimated properties.

Chandra/HETG Doppler velocity measurements in stellar coronal sources

ABSTRACT Stellar coronal sources have been observed in the past not only for their astrophysical interest in the field of binary system evolution and interaction but also for their invaluable roles as benchmarks for plasma spectral models and as calibration sources for high resolution spectroscopic X-ray instruments. These include the gratings on-board Chandra and XMM-Newton, as well as the new generation of high resolution capable-detectors recently flown on-board XRISM and planned for the future also onboard the Athena and the LEM missions. In our previous paper exploiting Chandra/HETG observations of the prototypical coronal source Capella, it has been shown that the centroid energies of the many X-ray emission lines detected in the spectrum of this object change as a function of time due to the Doppler modulation within the binary. This is an effect that needs to be corrected while performing calibrations of high-resolution X-ray instruments. In this paper, we extend our previous work on Capella to other known stellar coronal sources that have been observed with the Chandra/HETG (11 objects in total). We measure in several objects clear trends in the velocity shifts along the orbit of the primary star, meaning that in these sources one of the two star components is largely dominating the high energy emission. In a number of systems the trend in the velocity shift is not obvious. This can be ascribed to the fact that both stellar components contribute significantly to the X-ray emission.

Fe Kα XANES, Fe Kβ HERFD XANES and EPMA flank method determinations of the oxidation state of Fe in garnet

The ferric to total iron ratios (Fe3+/∑Fe) of garnets can be paired with thermodynamic mineral activity models to quantify the oxygen fugacity of garnet-bearing rocks. However, techniques with a high analytical and spatial resolution are necessary to distinguish differences in garnet Fe3+/∑Fe ratios at the percent level and to accurately measure garnets that are zoned or contain inclusions. We acquired conventional Fe Kα and high-resolution energy fluorescence detection (HERFD) Fe Kβ X-ray absorption near edge structure (XANES) spectra and electron microprobe flank method analyses on a suite of 27 peridotitic and eclogitic garnets with Fe3+/∑Fe ratios previously determined by Mössbauer spectroscopy to evaluate the precision of each technique. We examined variations in the energy and intensity of three XANES spectral features as a function of Fe3+/∑Fe ratios: 1) the intensity ratio of two-post edge features (I-ratio; Fe Kα only); 2) the energy of the Fe edge at 90% normalized intensity (E0.9; Fe Kα only) and 3) the pre-edge centroid energy (Fe Kα and HERFD Fe Kβ). In accordance with previous work, we find the energies of garnet pre-edge centroids are relatively insensitive to Fe3+/∑Fe ratios. The I-ratios of peridotitic and eclogitic garnets are offset from each other at low Fe3+/∑Fe ratios (≤0.13); I-ratio garnet XANES calibrations are composition-specific. The E0.9 feature is independent of garnet major element composition in spectra that have been corrected for the effects of self-absorption. We produce two Fe Kα garnet XANES calibrations based on variations in the E0.9 feature; one calibration with all garnet reference materials included (Fe3+/∑Fe up to 1.0; “all garnet calibration”) and another calibration specific to garnets with low Fe3+/∑Fe ratios (“low ferric calibration”). Fe3+/∑Fe ratios calculated from the mean of up to 25 flank method measurements on eight garnet reference materials fall within 4% absolute of a one-to-one correlation with Fe3+/∑Fe ratios measured by Mössbauer. The standard error of the mean Fe3+/∑Fe ratio calculated from flank method approaches the Mössbauer-determined Fe3+/∑Fe ratio within estimated error (3%) after three analyses. Flank method precision is enhanced at higher beam current; however, the precision of the flank method does not approach the precision of XANES under any microprobe analytical condition tested here. Garnet reference materials detailed here are available by request to the Smithsonian Institution.

Isoscalar monopole response in the neutron-rich molybdenum isotopes using self-consistent QRPA

The isoscalar giant monopole resonance (ISGMR) of even molybdenum isotopes 92,94,96,98,100Mo has been studied within the Skyrme self-consistent Hartree - Fock - Bardeen, Cooper, and Schrieffer and quasi-particle random phase approximation. Ten sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM are used in the calculations. The calculated strength distributions, centroid energies Ecen, scaled energies Es and constrained energies Econ of ISGMR are compared with available experimental data. Due to the appropriate value of the nuclear matter incompressibility KNM, several types of Skyrme interactions were successful in describing the ISGMR strength distribution in the 92,94,96,98,100Mo isotopes. As a result, high correlations between Ecen and KNM were found.

Energy efficient gateway based routing with maximized node coverage in a UAV assisted wireless sensor network.

Ad-hoc wireless sensor networks face challenges of optimized node deployment for maximizing coverage and efficiently routing data to control centers in post disaster events. These challenges impact the outcome for extending the lifetime of wireless sensor networks. This study presents a uav assisted reactive zone based EHGR (energy efficient hierarchical gateway routing protocol) that is deployed in a situation where the natural calamity has caused communication and infrastructure damage to a major portion of the sensor network. EHGR is a hybrid multi layer routing protocol for large heterogeneous sensor nodes (smart nodes, basic nodes, user handheld devices etc.) EHGR is tailored to meet two important concerns for a disaster hit wsn ie. optimized deployment and energy efficient routing. The first part of EGHR focuses on maximized coverage during node deployments. Maximized coverage is an important aspect to be considered during the event of disaster since most of the nodes loose coverage and are detached from the wireless sensor network. The first part of EHGR uses state of the art game theory approach to build a model that maximizes the coverage of nodes during the deployment phase from all participating entities i.e. nodes and uavs. Rather than fixing the cluster head as is the case in traditional cluster-based approaches EHGR uses the energy centroid nodes. Energy centroid nodes evolve on the basis of aggregated energy of the zone. This approach is superior to simply electing cluster head nodes on the basis of some probability function. The nodes that fail to achieve any successful outcome from the game theory matching model fail to get any association. These nodes will use multi hop d2d relay approach to reach the energy centroid nodes. Gateway relay nodes used with the game theory approach during the deployment of the uav assisted wsn improves the overall coverage by 25% against traditional leach based hierarchical approaches. Once the optimum deployment phase is completed the routing phase is initiated. Aggregated data is sent by the energy centroid nodes from the ECN nodes to the servicing micro controller enabled un manned aerial vehicles. The routing process places partial burden of zone formation and data transmission to the control center for each phase on the servicing uavs. Energy centroid nodes engage only in the data aggregation process and transmission of data to servicing uav. Servicing-uavs reduce energy dissipated of the entire zone which result in gradual decrease of energy for the zone thus increasing the network lifetime. Node deployment phase and the routing phase of EHGR utilize the computations provide by the mirco controller enabled unmanned aerial vehicles such that the computationally intensive calculations are offloaded to the servicing uav. Experiment results indicate an increase in the first dead node report, half dead node report, and last dead node report. Network lifetime is extended to approximately 1800 rounds which is an increase by ratio of 100% against the traditional leach approach and increase by 50% percent against the latest approaches as highlighted in the literature.

Studying the variations of the cyclotron line in Cen X-3 using Insight-HXMT

We investigate the cyclotron resonant scattering features (CRSFs) of the accreting X-ray pulsar Cen X-3 and significantly detect the 29 keV cyclotron line features in the hard X-ray averaged spectroscopy studies based on the recent Insight-HXMT observations in 2022, when Cen X-3 has X-ray luminosity LX>∼5×1037 erg s−1 in the bands of 2 – 60 keV. We do not find a harmonic line in the average spectra based on different continuum models. We showed that the CRSF energies have no correlation with time or luminosity in the average spectra. In addition, by performing a pulse phase-dependent spectral analysis, we revealed the fundamental line with the centroid energy ranging from 25 to 29 keV with a high significance over the spin phases. The evolution of the cyclotron line centroid energies over pulse phase is similar to the shape of pulse profiles, illustrating a positive correlation between the energy of CRSFs and the pulse phase flux.

Weak secondary cyclotron line in eclipsing high-mass X-ray binary Cen X-3

ABSTRACT We report the time-resolved spectroscopy results from two observations of Centaurus X-3, over one binary orbit with AstroSat and two binary orbits with Nuclear Spectroscopic Telescope Array (NuSTAR). NuSTAR covered two intensity states where the light curve showed transition in count rate from first to second binary orbit by a factor of ∼3. A phenomenological model comprising of partially absorbed power law with smoothed high energy cutoff, cyclotron absorption ∼24 and 6.4 keV iron emission gave good fit for AstroSat observation. NuSTAR spectra required two additional emission components, a broad one ∼5.7 keV and a narrow one ∼6.9 keV. A weak secondary absorption feature at ∼11.6 and ∼ 14.5 keV was seen in the residuals of the spectral fit for AstroSat and NuSTAR data, respectively. The secondary absorption energy showed no correlation with the cutoff energy. Its strength varied within 0.1–0.6 keV with its width ∼1.6 keV. Its energy and optical depth showed linear positive correlation with the fundamental cyclotron line energy and depth, respectively. The cyclotron line energy showed anticorrelation to flux described by a power law with negative index and the secondary absorption also showed similar trend to flux. Depth of secondary absorption was ∼45 per cent and centroid energy was ∼54 per cent of fundamental. Depth and energy ratio of secondary to fundamental lied within 2σ deviation from 0.5. We suggest this secondary absorption to be a redshifted dipolar cyclotron resonance feature exhibiting sub-harmonic behaviour.

Investigating the strength of the scissors mode in 151Sm

Change in nuclei deformation leads to changes in statistical properties such as the nuclear level density (NLD) and γ-ray strength function (γSF). The NLD and γSF of 151Sm were extracted using the Oslo method. The strength of the scissors resonance (SR) and its centroid energy for 151Sm were found to be 2.13 ± 0.60 and 2.48 ± 0.25 MeV, respectively. These results were used to place the SR of 151Sm and its magnetic dipole strength B(M1)SR into the context of previously measured Sm isotopes.

Photon centroids and their subluminal propagation

We examine properties of the energy-density and photon-probability centroids of electromagnetic wavepackets in free space. In the second-order paraxial approximation, both of these centroids propagate with the same subluminal velocity because of the transverse confinement of the wavepacket and its diffraction. The tiny difference between the energy and probability centroid velocities appears only in the fourth order. We consider three types of wavepackets: Gaussian, Bessel, and non-diffracting Bessel. In all these cases, the subluminal propagation is clearly visible in the intensity distributions and can be measured experimentally in both classical-light and single-photon regimes. For Gaussian wavepackets, the half-wavelength delay is accumulated after propagation over about 12 Rayleigh lengths.