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How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.
The X-ray emission of O-type stars was first discovered in the early days of the Einstein satellite. Since then many different surveys have confirmed that the ratio of X-ray to bolometric luminosity in O-type stars is roughly constant, but there is a paucity of studies that account for detailed information on spectral and wind properties of O-stars. Recently a significant sample of O stars within our Galaxy was spectroscopically identified and presented in the Galactic O-Star Spectroscopic Survey (GOSS). At the same time, a large high-fidelity catalog of X-ray sources detected by the XMM-Newton X-ray telescope was released. Here we present the X-ray catalog of O stars with known spectral types and investigate the dependence of their X-ray properties on spectral type as well as stellar and wind parameters. We find that, among the GOSS sample, 127 O-stars have a unique XMM-Newton source counterpart and a Gaia data release 2 (DR2) association. Terminal velocities are known for a subsample of 35 of these stars. We confirm that the X-ray luminosities of dwarf and giant O stars correlate with their bolometric luminosity. For the subsample of O stars with measure terminal velocities we find that the X-ray luminosities of dwarf and giant O stars also correlate with wind parameters. However, we find that these correlations break down for supergiant stars. Moreover, we show that supergiant stars are systematically harder in X-rays compared to giant and dwarf O-type stars. We find that the X-ray luminosity depends on spectral type, but seems to be independent of whether the stars are single or in a binary system. Finally, we show that the distribution of log(L-X/L-bol) in our sample stars is non-Gaussian, with the peak of the distribution at log(L-X/L-bol) approximate to -6.6.
The presence of extreme horizontal branch (EHB) and blue hook stars in some Galactic globular clusters (GGCs) constitutes one of the remaining mysteries of stellar evolution. While several evolutionary scenarios have been proposed to explain the characteristics of this peculiar population of evolved stars, their observational verification has been limited by the availability of spectroscopic data for a statistically significant sample of such objects in any single GGC. We recently launched the SHOTGLAS project with the aim of providing a comprehensive picture of this intriguing stellar population in terms of spectroscopic properties for all readily accessible GGCs hosting an EHB. In this first paper, we focus on omega Cen, a peculiar, massive GGC that hosts multiple stellar populations. We use non-LTE model atmospheres to derive atmospheric parameters (Te ff, log g and N(He) / N(H)) and spectroscopic masses for 152 EHB stars in the cluster. This constitutes the largest spectroscopic sample of EHB stars ever analyzed in a GGC and represents similar to 20% of the EHB population of omega Cen. We also search for close binaries among these stars based on radial velocity variations. Our results show that the EHB population of omega Cen is divided into three spectroscopic groups that are very distinct in the Te ff helium abundance plane. The coolest sdB-type stars (Te ff. 30 000 K) have a hydrogen-rich atmosphere, populate the theoretical EHB region in the Te ff log g plane, and form 26% of our sample. The hottest sdO-type stars (Te ff & 42 000 K) make up 10% of the sample, have a hydrogen-rich atmosphere and are thought to be in a post-EHB evolutionary phase. The majority of our sample is found at intermediate temperatures and consists of sdOB stars that have roughly solar or super-solar atmospheric helium abundances. It is these objects that constitute the blue hook at V > 18 : 5 mag in the omega Cen color-magnitude diagram. Interestingly, the helium-enriched sdOBs do not have a significant counterpart population in the Galactic field, indicating that their formation is dependent on the particular environment found in omega Cen and other select GGCs. Another major di ff erence between the EHB stars in omega Cen and the field is the fraction of close binaries. From our radial velocity survey we identify two binary candidates, however no orbital solutions could be determined. We estimate an EHB close binary fraction of similar to 5% in omega Cen. This low fraction is in line with findings for other GGCs, but in sharp contrast to the situation in the field, where around 50% of the sdB stars reside in close binaries. Finally, the mass distribution derived is very similar for all three spectroscopic groups, however the average mass (0.38 M fi) is lower than that expected from stellar evolution theory. While this mass conundrum has previously been noted for EHB stars in omega Cen, it so far appears to be unique to that cluster.
The supernova remnant (SNR) W49B originated from a core-collapse supernova that occurred between one and four thousand years ago, and subsequently evolved into a mixed-morphology remnant, which is interacting with molecular clouds (MC). Gamma-ray observations of SNR-MC associations are a powerful tool to constrain the origin of Galactic cosmic rays, as they can probe the acceleration of hadrons through their interaction with the surrounding medium and subsequent emission of non-thermal photons. We report the detection of a gamma-ray source coincident with W49B at very high energies (VHE; E > 100 GeV) with the H.E.S.S. Cherenkov telescopes together with a study of the source with five years of Fermi-LAT high-energy gamma-ray (0.06-300 GeV) data. The smoothly connected, combined source spectrum, measured from 60 MeV to multi-TeV energies, shows two significant spectral breaks at 304 +/- 20 MeV and 8.4(-2.5)(+2.5) GeV; the latter is constrained by the joint fit from the two instruments. The detected spectral features are similar to those observed in several other SNR-MC associations and are found to be indicative of gamma-ray emission produced through neutral-pion decay.
Context. NGC 253 is one of only two starburst galaxies found to emit gamma-rays from hundreds of MeV to multi-TeV energies. Accurate measurements of the very-high-energy (VHE; E> 100 GeV) and high-energy (HE; E > 60 MeV) spectra are crucial to study the underlying particle accelerators, probe the dominant emission mechanism(s) and to study cosmic-ray interaction and transport. Aims. The measurement of the VHE gamma-ray emission of NGC 253 published in 2012 by H.E.S.S. was limited by large systematic uncertainties. Here, the most up to date measurement of the gamma-ray spectrum of NGC 253 is investigated in both HE and VHE gamma-rays. Assuming a hadronic origin of the gamma-ray emission, the measurement uncertainties are propagated into the interpretation of the accelerated particle population. Methods. The data of H.E.S.S. observations are reanalysed using an updated calibration and analysis chain. The improved Fermi-LAT analysis employs more than 8 yr of data processed using pass 8. The cosmic-ray particle population is evaluated from the combined HE-VHE gamma-ray spectrum using NAIMA in the optically thin case. Results. The VHE gamma-ray energy spectrum is best fit by a power-law distribution with a flux normalisation of (1.34 +/- 0.14(stat) +/- 0.27(sys)) x 10(-13) cm(-2) s(-1) TeV-1 at 1 TeV - about 40% above, but compatible with the value obtained in Abramowski et al. (2012). The spectral index Gamma = 2.39 +/- 0.14(stat) +/- 0.25(sys) is slightly softer than but consistent with the previous measurement within systematic errors. In the Fermi energy range an integral flux of F(E > 60 MeV) = (1.56 +/- 0.28(stat) +/- 0.15(sys)) x 10(-8) cm(-2) s(-1) is obtained. At energies above similar to 3 GeV the HE spectrum is consistent with a power-law ranging into the VHE part of the spectrum measured by H.E.S.S. with an overall spectral index Gamma = 2.22 +/- 0.06(stat). Conclusions. Two scenarios for the starburst nucleus are tested, in which the gas in the starburst nucleus acts as either a thin or a thick target for hadronic cosmic rays accelerated by the individual sources in the nucleus. In these two models, the level to which NGC 253 acts as a calorimeter is estimated to a range of f(cal) = 0.1 to 1 while accounting for the measurement uncertainties. The presented spectrum is likely to remain the most accurate measurements until the Cherenkov Telescope Array (CTA) has collected a substantial set of data towards NGC 253.
We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in Hollander (Isr. J. Math. 163:93-124, 2008), which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BG (con).
Context. SMC AB6 is the shortest-period (P = 6.5 d) Wolf-Rayet (WR) binary in the Small Magellanic Cloud. This binary is therefore a key system in the study of binary interaction and formation of WR stars at low metallicity. The WR component in AB6 was previously found to be very luminous (log L = 6.3 [L-circle dot]) compared to its reported orbital mass (approximate to 8 M-circle dot), placing it significantly above the Eddington limit. Aims. Through spectroscopy and orbital analysis of newly acquired optical data taken with the Ultraviolet and Visual Echelle Spectrograph (UVES), we aim to understand the peculiar results reported for this system and explore its evolutionary history. Methods. We measured radial velocities via cross-correlation and performed a spectral analysis using the Potsdam Wolf-Rayet model atmosphere code. The evolution of the system was analyzed using the Binary Population and Spectral Synthesis evolution code. Results. AB6 contains at least four stars. The 6.5 d period WR binary comprises the WR primary (WN3:h, star A) and a rather rapidly rotating (v(eq) = 265 km s(-1)) early O-type companion (O5.5 V, star B). Static N III and N IV emission lines and absorption signatures in He lines suggest the presence of an early-type emission line star (O5.5 I(f), star C). Finally, narrow absorption lines portraying a long-term radial velocity variation show the existence of a fourth star (O7.5 V, star D). Star D appears to form a second 140 d period binary together with a fifth stellar member, which is a B-type dwarf or a black hole. It is not clear that these additional components are bound to the WR binary. We derive a mass ratio of M-O/M-WR = 2.2 +/- 0.1. The WR star is found to be less luminous than previously thought (log L = 5.9 [L-circle dot]) and, adopting M-O = 41 M-circle dot for star B, more massive (M-WR = 18 M-circle dot). Correspondingly, the WR star does not exceed the Eddington limit. We derive the initial masses of M-i,M-WR = 60 M-circle dot and M-i,M-O = 40 M-circle dot and an age of 3.9 Myr for the system. The WR binary likely experienced nonconservative mass transfer in the past supported by the relatively rapid rotation of star B. Conclusions. Our study shows that AB6 is a multiple - probably quintuple - system. This finding resolves the previously reported puzzle of the WR primary exceeding the Eddington limit and suggests that the WR star exchanged mass with its companion in the past.
Organic semiconductors are of great interest for a broad range of optoelectronic applications due to their solution processability, chemical tunability, highly scalable fabrication, and mechanical flexibility. In contrast to traditional inorganic semiconductors, organic semiconductors are intrinsically disordered systems and therefore exhibit much lower charge carrier mobilities-the Achilles heel of organic photovoltaic cells. In this progress review, the authors discuss recent important developments on the impact of charge carrier mobility on the charge transfer state dissociation, and the interplay of free charge extraction and recombination. By comparing the mobilities on different timescales obtained by different techniques, the authors highlight the dispersive nature of these materials and how this reflects on the key processes defining the efficiency of organic photovoltaics.
Load partitioning between phases in a cast AlSi12CuMgNi alloy was investigated by in-situ compression test during neutron diffraction experiments. Computed tomography (CT) was used to determine volume fractions of eutectic Si and intermetallic (IM) phases, and to assess internal damage after ex-situ compression tests. The CT reconstructed volumes showed the interconnectivity of IM phases, which build a 3D network together with eutectic Si. Large stresses were found in IMs, revealing their significant role as a reinforcement for the alloy. An existing micromechanical model based on Maxwell scheme was extended to the present case, assuming the alloy as a three-phase composite (Al matrix, eutectic Si, IM phases). The model agrees well with the experimental data. Moreover, it allows predicting the principal stresses in each phase, while experiments can only determine stress differences between the axial and radial sample directions. Finally, we showed that the addition of alloying elements not only allowed developing a 3D interconnected network, but also improved the strength of the Al matrix, and the ability of the alloy constituents to bear mechanical load.
The nine-year H.E.S.S. Galactic Plane Survey (HGPS) has yielded the most uniform observation scan of the inner Milky Way in the TeV gamma-ray band to date. The sky maps and source catalogue of the HGPS allow for a systematic study of the population of TeV pulsar wind nebulae found throughout the last decade. To investigate the nature and evolution of pulsar wind nebulae, for the first time we also present several upper limits for regions around pulsars without a detected TeV wind nebula. Our data exhibit a correlation of TeV surface brightness with pulsar spindown power (E) over dot. This seems to be caused both by an increase of extension with decreasing (E) over dot, and hence with time, compatible with a power law R-PWN((E) over dot) similar to(E) over dot(0.65 +/- 0.20), and by a mild decrease of TeV gamma-ray luminosity with decreasing (E) over dot, compatible with L-1 (10 TeV) similar to (E) over dot(0.59 +/- 0.21). We also find that the off sets of pulsars with respect to the wind nebula centre with ages around 10 kyr are frequently larger than can be plausibly explained by pulsar proper motion and could be due to an asymmetric environment. In the present data, it seems that a large pulsar off set is correlated with a high apparent TeV efficiency L1- 10 TeV / (E) over dot. In addition to 14 HGPS sources considered firmly identified pulsar wind nebulae and 5 additional pulsar wind nebulae taken from literature, we find 10 HGPS sources that are likely TeV pulsar wind nebula candidates. Using a model that subsumes the present common understanding of the very high-energy radiative evolution of pulsar wind nebulae, we find that the trends and variations of the TeV observables and limits can be reproduced to a good level, drawing a consistent picture of present-day TeV data and theory.