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Aims. We aim to characterize the multiwavelength emission from Markarian 501 (Mrk 501), quantify the energy-dependent variability, study the potential multiband correlations, and describe the temporal evolution of the broadband emission within leptonic theoretical scenarios. Methods. We organized a multiwavelength campaign to take place between March and July of 2012. Excellent temporal coverage was obtained with more than 25 instruments, including the MAGIC, FACT and VERITAS Cherenkov telescopes, the instruments on board the Swift and Fermi spacecraft, and the telescopes operated by the GASP-WEBT collaboration. Results. Mrk 501 showed a very high energy (VHE) gamma-ray flux above 0.2 TeV of similar to 0.5 times the Crab Nebula flux (CU) for most of the campaign. The highest activity occurred on 2012 June 9, when the VHE flux was similar to 3 CU, and the peak of the high-energy spectral component was found to be at similar to 2 TeV. Both the X-ray and VHE gamma-ray spectral slopes were measured to be extremely hard, with spectral indices <2 during most of the observing campaign, regardless of the X-ray and VHE flux. This study reports the hardest Mrk 501 VHE spectra measured to date. The fractional variability was found to increase with energy, with the highest variability occurring at VHE. Using the complete data set, we found correlation between the X-ray and VHE bands; however, if the June 9 flare is excluded, the correlation disappears (significance <3 sigma) despite the existence of substantial variability in the X-ray and VHE bands throughout the campaign. Conclusions. The unprecedentedly hard X-ray and VHE spectra measured imply that their low- and high-energy components peaked above 5 keV and 0.5 TeV, respectively, during a large fraction of the observing campaign, and hence that Mrk 501 behaved like an extreme high-frequency-peaked blazar (EHBL) throughout the 2012 observing season. This suggests that being an EHBL may not be a permanent characteristic of a blazar, but rather a state which may change over time. The data set acquired shows that the broadband spectral energy distribution (SED) of Mrk 501, and its transient evolution, is very complex, requiring, within the framework of synchrotron self-Compton (SSC) models, various emission regions for a satisfactory description. Nevertheless the one-zone SSC scenario can successfully describe the segments of the SED where most energy is emitted, with a significant correlation between the electron energy density and the VHE gamma-ray activity, suggesting that most of the variability may be explained by the injection of high-energy electrons. The one-zone SSC scenario used reproduces the behavior seen between the measured X-ray and VHE gamma-ray fluxes, and predicts that the correlation becomes stronger with increasing energy of the X-rays.
Aims. We present an extensive study of the BL Lac object Mrk 501 based on a data set collected during the multi-instrument campaign spanning from 2009 March 15 to 2009 August 1, which includes, among other instruments, MAGIC, VERITAS, Whipple 10 m, and Fermi-LAT to cover the gamma-ray range from 0.1 GeV to 20 TeV; RXTE and Swift to cover wavelengths from UV to hard X-rays; and GASP-WEBT, which provides coverage of radio and optical wavelengths. Optical polarization measurements were provided for a fraction of the campaign by the Steward and St. Petersburg observatories. We evaluate the variability of the source and interband correlations, the gamma-ray flaring activity occurring in May 2009, and interpret the results within two synchrotron self-Compton (SSC) scenarios. Methods. The multiband variability observed during the full campaign is addressed in terms of the fractional variability, and the possible correlations are studied by calculating the discrete correlation function for each pair of energy bands where the significance was evaluated with dedicated Monte Carlo simulations. The space of SSC model parameters is probed following a dedicated grid-scan strategy, allowing for a wide range of models to be tested and offering a study of the degeneracy of model-to-data agreement in the individual model parameters, hence providing a less biased interpretation than the "single-curve SSC model adjustment" typically reported in the literature. Results. We find an increase in the fractional variability with energy, while no significant interband correlations of flux changes are found on the basis of the acquired data set. The SSC model grid-scan shows that the flaring activity around May 22 cannot be modeled adequately with a one-zone SSC scenario (using an electron energy distribution with two breaks), while it can be suitably described within a two (independent) zone SSC scenario. Here, one zone is responsible for the quiescent emission from the averaged 4.5-month observing period, while the other one, which is spatially separated from the first, dominates the flaring emission occurring at X-rays and very-high-energy (> 100 GeV, VHE) gamma-rays. The flaring activity from May 1, which coincides with a rotation of the electric vector polarization angle (EVPA), cannot be satisfactorily reproduced by either a one-zone or a two-independent-zone SSC model, yet this is partially affected by the lack of strictly simultaneous observations and the presence of large flux changes on sub-hour timescales (detected at VHE gamma rays). Conclusions. The higher variability in the VHE emission and lack of correlation with the X-ray emission indicate that, at least during the 4.5-month observing campaign in 2009, the highest energy (and most variable) electrons that are responsible for the VHE gamma rays do not make a dominant contribution to the similar to 1 keV emission. Alternatively, there could be a very variable component contributing to the VHE gamma-ray emission in addition to that coming from the SSC scenario. The studies with our dedicated SSC grid-scan show that there is some degeneracy in both the one-zone and the two-zone SSC scenarios probed, with several combinations of model parameters yielding a similar model-to-data agreement, and some parameters better constrained than others. The observed gamma-ray flaring activity, with the EVPA rotation coincident with the first gamma-ray flare, resembles those reported previously for low frequency peaked blazars, hence suggesting that there are many similarities in the flaring mechanisms of blazars with different jet properties.
The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.
We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar- Parisi-Zhang equation with a growth-limiting term ("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the transition is found to be in the universality class of directed percolation.
Massive stars that become stripped of their hydrogen envelope through binary interaction or winds can be observed either as Wolf-Rayet stars, if they have optically thick winds, or as transparent-wind stripped-envelope stars. We approximate their evolution through evolutionary models of single helium stars, and compute detailed model grids in the initial mass range 1.5-70 M. for metallicities between 0.01 and 0.04, from core helium ignition until core collapse. Throughout their lifetimes some stellar models expose the ash of helium burning. We propose that models that have nitrogen-rich envelopes are candidate WN stars, while models with a carbon-rich surface are candidate WC stars during core helium burning, and WO stars afterwards. We measure the metallicity dependence of the total lifetimes of our models and the duration of their evolutionary phases. We propose an analytic estimate of the wind's optical depth to distinguish models of Wolf-Rayet stars from transparent-wind stripped-envelope stars, and find that the luminosity ranges at which WN-, WC-, and WO-type stars can exist is a strong function of metallicity. We find that all carbon-rich models produced in our grids have optically thick winds and match the luminosity distribution of observed populations. We construct population models and predict the numbers of transparent-wind stripped-envelope stars and Wolf-Rayet stars, and derive their number ratios at different metallicities. We find that as metallicity increases, the number of transparent-wind stripped-envelope stars decreases and the number of Wolf-Rayet stars increases. At high metallicities WC- and WO-type stars become more common. We apply our population models to nearby galaxies, and find that populations are more sensitive to the transition luminosity between Wolf-Rayet stars and transparent-wind helium stars than to the metallicity-dependent mass loss rates.
In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.
The quantification of spatial propagation of extreme precipitation events is vital in water resources planning and disaster mitigation. However, quantifying these extreme events has always been challenging as many traditional methods are insufficient to capture the nonlinear interrelationships between extreme event time series. Therefore, it is crucial to develop suitable methods for analyzing the dynamics of extreme events over a river basin with a diverse climate and complicated topography. Over the last decade, complex network analysis emerged as a powerful tool to study the intricate spatiotemporal relationship between many variables in a compact way. In this study, we employ two nonlinear concepts of event synchronization and edit distance to investigate the extreme precipitation pattern in the Ganga river basin. We use the network degree to understand the spatial synchronization pattern of extreme rainfall and identify essential sites in the river basin with respect to potential prediction skills. The study also attempts to quantify the influence of precipitation seasonality and topography on extreme events. The findings of the study reveal that (1) the network degree is decreased in the southwest to northwest direction, (2) the timing of 50th percentile precipitation within a year influences the spatial distribution of degree, (3) the timing is inversely related to elevation, and (4) the lower elevation greatly influences connectivity of the sites. The study highlights that edit distance could be a promising alternative to analyze event-like data by incorporating event time and amplitude and constructing complex networks of climate extremes.
Accurately predicting total electron content (TEC) during geomagnetic storms is still a challenging task for ionospheric models. In this work, a neural-network (NN)-based model is proposed which predicts relative TEC with respect to the preceding 27-day median TEC, during storm time for the European region (with longitudes 30 degrees W-50 degrees E and latitudes 32.5 degrees N-70 degrees N). The 27-day median TEC (referred to as median TEC), latitude, longitude, universal time, storm time, solar radio flux index F10.7, global storm index SYM-H and geomagnetic activity index Hp30 are used as inputs and the output of the network is the relative TEC. The relative TEC can be converted to the actual TEC knowing the median TEC. The median TEC is calculated at each grid point over the European region considering data from the last 27 days before the storm using global ionosphere maps (GIMs) from international GNSS service (IGS) sources. A storm event is defined when the storm time disturbance index Dst drops below 50 nanotesla. The model was trained with storm-time relative TEC data from the time period of 1998 until 2019 (2015 is excluded) and contains 365 storms. Unseen storm data from 33 storm events during 2015 and 2020 were used to test the model. The UQRG GIMs were used because of their high temporal resolution (15 min) compared to other products from different analysis centers. The NN-based model predictions show the seasonal behavior of the storms including positive and negative storm phases during winter and summer, respectively, and show a mixture of both phases during equinoxes. The model's performance was also compared with the Neustrelitz TEC model (NTCM) and the NN-based quiet-time TEC model, both developed at the German Aerospace Agency (DLR). The storm model has a root mean squared error (RMSE) of 3.38 TEC units (TECU), which is an improvement by 1.87 TECU compared to the NTCM, where an RMSE of 5.25 TECU was found. This improvement corresponds to a performance increase by 35.6%. The storm-time model outperforms the quiet-time model by 1.34 TECU, which corresponds to a performance increase by 28.4% from 4.72 to 3.38 TECU. The quiet-time model was trained with Carrington averaged TEC and, therefore, is ideal to be used as an input instead of the GIM derived 27-day median. We found an improvement by 0.8 TECU which corresponds to a performance increase by 17% from 4.72 to 3.92 TECU for the storm-time model using the quiet-time-model predicted TEC as an input compared to solely using the quiet-time model.