Institut für Physik und Astronomie
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Institute
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
The plasmon resonance of metal nanoparticles determines their optical response in the visible spectral range. Many details such as the electronic properties of gold near the particle surface and the local environment of the particles influence the spectra. We show how the cheap but highly precise fabrication of composite nanolayers by spin-assisted layer-by-layer deposition of polyelectrolytes can be used to investigate the spectral response of gold nanospheres (GNS) and gold nanorods (GNR) in a self-consistent way, using the established Maxwell–Garnett effective medium (MGEM) theory beyond the limit of homogeneous media. We show that the dielectric function of gold nanoparticles differs from the bulk value and experimentally characterize the shape and the surrounding of the particles thoroughly by SEM, AFM and ellipsometry. Averaging the dielectric functions of the layered surrounding by an appropriate weighting with the electric field intensity yields excellent agreement for the spectra of several nanoparticles and nanorods with various cover-layer thicknesses.
We have investigated the electrochemical, spectroscopic and electroluminescent properties of a family of aza-aromatic complexes of ruthenium of type [RuII(bpy/phen)2(L)]2+ (4d6) with three isomeric L ligands, where, bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline and the L ligands are 3-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L1), 3-(2-pyridyl[1,2,3])triazolo[1,5-a]pyridine (L2) and 2-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L3). The complexes display two bands in the visible region near 410–420 and 440–450 nm. The complexes are diamagnetic and show well defined 1H NMR lines. They are electroactive in acetonitrile solution and exhibit a well defined RuII/RuIII couple near 1.20 to 1.30 V and −1.40 to −1.50 V due to ligand reduction versus Saturated Calomel Electrode (SCE). The solutions are also luminescent, with peaks are near 600 nm. All the complexes are electroluminescent in nature with peaks lying near 580 nm. L1 and L3 ligated complexes with two bpy co-ligands show weak photoluminescence (PL) but stronger electroluminescence (EL) compared to corresponding L2 ligated analogues.
Biological materials, in addition to having remarkable physical properties, can also change shape and volume. These shape and volume changes allow organisms to form new tissue during growth and morphogenesis, as well as to repair and remodel old tissues. In addition shape or volume changes in an existing tissue can lead to useful motion or force generation (actuation) that may even still function in the dead organism, such as in the well known example of the hygroscopic opening or closing behaviour of the pine cone. Both growth and actuation of tissues are mediated, in addition to biochemical factors, by the physical constraints of the surrounding environment and the architecture of the underlying tissue. This habilitation thesis describes biophysical studies carried out over the past years on growth and swelling mediated shape changes in biological systems. These studies use a combination of theoretical and experimental tools to attempt to elucidate the physical mechanisms governing geometry controlled tissue growth and geometry constrained tissue swelling. It is hoped that in addition to helping understand fundamental processes of growth and morphogenesis, ideas stemming from such studies can also be used to design new materials for medicine and robotics.
Semi-empirical sea-level models (SEMs) exploit physically motivated empirical relationships between global sea level and certain drivers, in the following global mean temperature. This model class evolved as a supplement to process-based models (Rahmstorf (2007)) which were unable to fully represent all relevant processes. They thus failed to capture past sea-level change (Rahmstorf et al. (2012)) and were thought likely to underestimate future sea-level rise. Semi-empirical models were found to be a fast and useful tool for exploring the uncertainties in future sea-level rise, consistently giving significantly higher projections than process-based models.
In the following different aspects of semi-empirical sea-level modelling have been studied. Models were first validated using various data sets of global sea level and temperature. SEMs were then used on the glacier contribution to sea level, and to infer past global temperature from sea-level data via inverse modelling. Periods studied encompass the instrumental period, covered by tide gauges (starting 1700 CE (Common Era) in Amsterdam) and satellites (first launched in 1992 CE), the era from 1000 BCE (before CE) to present, and the full length of the Holocene (using proxy data). Accordingly different data, model formulations and implementations have been used. It could be shown in Bittermann et al. (2013) that SEMs correctly predict 20th century sea-level when calibrated with data until 1900 CE. SEMs also turned out to give better predictions than the Intergovernmental Panel on Climate Change (IPCC) 4th assessment report (AR4, IPCC (2007)) models, for the period from 1961–2003 CE.
With the first multi-proxy reconstruction of global sea-level as input, estimate of the human-induced component of modern sea-level change and projections of future sea-level rise were calculated (Kopp et al. (2016)). It turned out with 90% confidence that more than 40 % of the observed 20th century sea-level rise is indeed anthropogenic. With the new semi-empirical and IPCC (2013) 5th assessment report (AR5) projections the gap between SEM and process-based model projections closes, giving higher credibility to both. Combining all scenarios, from strong mitigation to business as usual, a global sea-level rise of 28–131 cm relative to 2000 CE, is projected with 90% confidence. The decision for a low carbon pathway could halve the expected global sea-level rise by 2100 CE.
Present day temperature and thus sea level are driven by the globally acting greenhouse-gas forcing. Unlike that, the Milankovich forcing, acting on Holocene timescales, results mainly in a northern-hemisphere temperature change. Therefore a semi-empirical model can be driven with northernhemisphere temperatures, which makes it possible to model the main subcomponent of sea-level change over this period. It showed that an additional positive constant rate of the order of the estimated Antarctic sea-level contribution is then required to explain the sea-level evolution over the Holocene. Thus the global sea level, following the climatic optimum, can be interpreted as the sum of a temperature induced sea-level drop and a positive long-term contribution, likely an ongoing response to deglaciation coming from Antarctica.
The high-latitudinal thermospheric processes driven by the solar wind and Interplanetary Magnetic Field (IMF) interaction with the Earth magnetosphere are highly variable parts of the complex dynamic plasma environment, which represent the coupled Magnetosphere – Ionosphere – Thermosphere (MIT) system. The solar wind and IMF interactions transfer energy to the MIT system via reconnection processes at the magnetopause. The Field Aligned Currents (FACs) constitute the energetic links between the magnetosphere and the Earth ionosphere. The MIT system depends on the highly variable solar wind conditions, in particular on changes of the strength and orientation of the IMF.
In my thesis, I perform an investigation on the physical background of the complex MIT system using the global physical - numerical, three-dimensional, time-dependent and self-consistent Upper Atmosphere Model (UAM). This model describes the thermosphere, ionosphere, plasmasphere and inner magnetosphere as well as the electrodynamics of the coupled MIT system for the altitudinal range from 80 (60) km up to the 15 Earth radii.
In the present study, I developed and investigated several variants of the high-latitudinal electrodynamic coupling by including the IMF dependence of FACs into the UAM model. For testing, the various variants were applied to simulations of the coupled MIT system for different seasons, geomagnetic activities, various solar wind and IMF conditions. Additionally, these variants of the theoretical model with the IMF dependence were compared with global empirical models. The modelling results for the most important thermospheric parameters like neutral wind and mass density were compared with satellite measurements. The variants of the UAM model with IMF dependence show a good agreement with the satellite observations. In comparison with the empirical models, the improved variants of the UAM model reproduce a more realistic meso-scale structures and dynamics of the coupled MIT system than the empirical models, in particular at high latitudes. The new configurations of the UAM model with IMF dependence contribute to the improvement of space weather prediction.
Organic bulk heterojunction (BHJ) solar cells based on polymer:fullerene blends are a promising alternative for a low-cost solar energy conversion. Despite significant improvements of the power conversion efficiency in recent years, the fundamental working principles of these devices are yet not fully understood. In general, the current output of organic solar cells is determined by the generation of free charge carriers upon light absorption and their transport to the electrodes in competition to the loss of charge carriers due to recombination.
The object of this thesis is to provide a comprehensive understanding of the dynamic processes and physical parameters determining the performance. A new approach for analyzing the characteristic current-voltage output was developed comprising the experimental determination of the efficiencies of charge carrier generation, recombination and transport, combined with numerical device simulations.
Central issues at the beginning of this work were the influence of an electric field on the free carrier generation process and the contribution of generation, recombination and transport to the current-voltage characteristics. An elegant way to directly measure the field dependence of the free carrier generation is the Time Delayed Collection Field (TDCF) method. In TDCF charge carriers are generated by a short laser pulse and subsequently extracted by a defined rectangular voltage pulse. A new setup was established with an improved time resolution compared to former reports in literature. It was found that charge generation is in general independent of the electric field, in contrast to the current view in literature and opposed to the expectations of the Braun-Onsager model that was commonly used to describe the charge generation process. Even in cases where the charge generation was found to be field-dependend, numerical modelling showed that this field-dependence is in general not capable to account for the voltage dependence of the photocurrent. This highlights the importance of efficient charge extraction in competition to non-geminate recombination, which is the second objective of the thesis.
Therefore, two different techniques were combined to characterize the dynamics and efficiency of non-geminate recombination under device-relevant conditions. One new approach is to perform TDCF measurements with increasing delay between generation and extraction of charges. Thus, TDCF was used for the first time to measure charge carrier generation, recombination and transport with the same experimental setup. This excludes experimental errors due to different measurement and preparation conditions and demonstrates the strength of this technique. An analytic model for the description of TDCF transients was developed and revealed the experimental conditions for which reliable results can be obtained. In particular, it turned out that the $RC$ time of the setup which is mainly given by the sample geometry has a significant influence on the shape of the transients which has to be considered for correct data analysis.
Secondly, a complementary method was applied to characterize charge carrier recombination under steady state bias and illumination, i.e. under realistic operating conditions. This approach relies on the precise determination of the steady state carrier densities established in the active layer. It turned out that current techniques were not sufficient to measure carrier densities with the necessary accuracy. Therefore, a new technique {Bias Assisted Charge Extraction} (BACE) was developed. Here, the charge carriers photogenerated under steady state illumination are extracted by applying a high reverse bias. The accelerated extraction compared to conventional charge extraction minimizes losses through non-geminate recombination and trapping during extraction. By performing numerical device simulations under steady state, conditions were established under which quantitative information on the dynamics can be retrieved from BACE measurements.
The applied experimental techniques allowed to sensitively analyse and quantify geminate and non-geminate recombination losses along with charge transport in organic solar cells. A full analysis was exemplarily demonstrated for two prominent polymer-fullerene blends.
The model system P3HT:PCBM spincast from chloroform (as prepared) exhibits poor power conversion efficiencies (PCE) on the order of 0.5%, mainly caused by low fill factors (FF) and currents. It could be shown that the performance of these devices is limited by the hole transport and large bimolecular recombination (BMR) losses, while geminate recombination losses are insignificant. The low polymer crystallinity and poor interconnection between the polymer and fullerene domains leads to a hole mobility of the order of 10^-7 cm^2/Vs which is several orders of magnitude lower than the electron mobility in these devices. The concomitant build up of space charge hinders extraction of both electrons and holes and promotes bimolecular recombination losses.
Thermal annealing of P3HT:PCBM blends directly after spin coating improves crystallinity and interconnection of the polymer and the fullerene phase and results in comparatively high electron and hole mobilities in the order of 10^-3 cm^2/Vs and 10^-4 cm^2/Vs, respectively. In addition, a coarsening of the domain sizes leads to a reduction of the BMR by one order of magnitude. High charge carrier mobilities and low recombination losses result in comparatively high FF (>65%) and short circuit current (J_SC ≈ 10 mA/cm^2). The overall device performance (PCE ≈ 4%) is only limited by a rather low spectral overlap of absorption and solar emission and a small V_OC, given by the energetics of the P3HT.
From this point of view the combination of the low bandgap polymer PTB7 with PCBM is a promising approach. In BHJ solar cells, this polymer leads to a higher V_OC due to optimized energetics with PCBM. However, the J_SC in these (unoptimized) devices is similar to the J_SC in the optimized blend with P3HT and the FF is rather low (≈ 50%). It turned out that the unoptimized PTB7:PCBM blends suffer from high BMR, a low electron mobility of the order of 10^-5 cm^2/Vs and geminate recombination losses due to field dependent charge carrier generation.
The use of the solvent additive DIO optimizes the blend morphology, mainly by suppressing the formation of very large fullerene domains and by forming a more uniform structure of well interconnected donor and acceptor domains of the order of a few nanometers. Our analysis shows that this results in an increase of the electron mobility by about one order of magnitude (3 x 10^-4 cm^2/Vs), while BMR and geminate recombination losses are significantly reduced. In total these effects improve the J_SC (≈ 17 mA/cm^2) and the FF (> 70%). In 2012 this polymer/fullerene combination resulted in a record PCE for a single junction OSC of 9.2%.
Remarkably, the numerical device simulations revealed that the specific shape of the J-V characteristics depends very sensitively to the variation of not only one, but all dynamic parameters. On the one hand this proves that the experimentally determined parameters, if leading to a good match between simulated and measured J-V curves, are realistic and reliable. On the other hand it also emphasizes the importance to consider all involved dynamic quantities, namely charge carrier generation, geminate and non-geminate recombination as well as electron and hole mobilities. The measurement or investigation of only a subset of these parameters as frequently found in literature will lead to an incomplete picture and possibly to misleading conclusions.
Importantly, the comparison of the numerical device simulation employing the measured parameters and the experimental $J-V$ characteristics allows to identify loss channels and limitations of OSC. For example, it turned out that inefficient extraction of charge carriers is a criticical limitation factor that is often disobeyed. However, efficient and fast transport of charges becomes more and more important with the development of new low bandgap materials with very high internal quantum efficiencies. Likewise, due to moderate charge carrier mobilities, the active layer thicknesses of current high-performance devices are usually limited to around 100 nm. However, larger layer thicknesses would be more favourable with respect to higher current output and robustness of production. Newly designed donor materials should therefore at best show a high tendency to form crystalline structures, as observed in P3HT, combined with the optimized energetics and quantum efficiency of, for example, PTB7.
The lives of more than 1/6 th of the world population is directly affected by the caprices of the South Asian summer monsoon rainfall. India receives around 78 % of the annual precipitation during the June-September months, the summer monsoon season of South Asia. But, the monsoon circulation is not consistent throughout the entire summer season. Episodes of heavy rainfall (active periods) and low rainfall (break periods) are inherent to the intraseasonal variability of the South Asian summer monsoon. Extended breaks or long-lasting dryness can result in droughts and hence trigger crop failures and in turn famines. Furthermore, India's electricity generation from renewable sources (wind and hydro-power), which is increasingly important in order to satisfy the rapidly rising demand for energy, is highly reliant on the prevailing meteorology. The major drought years 2002 and 2009 for the Indian summer monsoon during the last decades, which are results of the occurrence of multiple extended breaks, emphasise exemplary that the understanding of the monsoon system and its intraseasonal variation is of greatest importance. Although, numerous studies based on observations, reanalysis data and global model simulations have been carried out with the focus on monsoon active and break phases over India, the understanding of the monsoon intraseasonal variability is only in the infancy stage. Regional climate models could benefit the comprehension of monsoon breaks by its resolution advantage.
This study investigates moist dynamical processes that initiate and maintain breaks during the South Asian summer monsoon using the atmospheric regional climate model HIRHAM5 at a horizontal resolution of 25 km forced by the ECMWF ERA Interim reanalysis for the period 1979-2012. By calculating moisture and moist static energy budgets the various competing mechanisms leading to extended breaks are quantitatively estimated. Advection of dry air from the deserts of western Asia towards central India is the dominant moist dynamical process in initiating extended break conditions over South Asia. Once initiated, the extended breaks are maintained due to many competing mechanisms: (i) the anomalous easterlies at the southern flank of this anticyclonic anomaly weaken the low-level cross-equatorial jet and thus the moisture transport into the monsoon region, (ii) differential radiative heating over the continental and the oceanic tropical convergence zone induces a local Hadley circulation with anomalous rising over the equatorial Indian Ocean and descent over central India, and (iii) a cyclonic response to positive rainfall anomalies over the near-equatorial Indian Ocean amplifies the anomalous easterlies over India and hence contributes to the low-level divergence over central India.
A sensitivity experiment that mimics a scenario of higher atmospheric aerosol concentrations over South Asia addresses a current issue of large uncertainty: the role aerosols play in suppressing monsoon rainfall and hence in triggering breaks. To study the indirect aerosol effects the cloud droplet number concentration was increased to imitate the aerosol's function as cloud condensation nuclei. The sensitivity experiment with altered microphysical cloud properties shows a reduction in the summer monsoon precipitation together with a weakening of the South Asian summer monsoon. Several physical mechanisms are proposed to be responsible for the suppressed monsoon rainfall: (i) according to the first indirect radiative forcing the increase in the number of cloud droplets causes an increase in the cloud reflectivity of solar radiation, leading to a climate cooling over India which in turn reduces the hydrological cycle, (ii) a stabilisation of the troposphere induced by a differential cooling between the surface and the upper troposphere over central India inhibits the growth of deep convective rain clouds, (iii) an increase of the amount of low and mid-level clouds together with a decrease in high-level cloud amount amplify the surface cooling and hence the atmospheric stability, and (iv) dynamical changes of the monsoon manifested as a anomalous anticyclonic circulation over India reduce the moisture transport into the monsoon region. The study suggests that the changes in the total precipitation, which are dominated by changes in the convective precipitation, mainly result from the indirect radiative forcing. Suppression of rainfall due to the direct microphysical effect is found to be negligible over India. Break statistics of the polluted cloud scenario indicate an increase in the occurrence of short breaks (3 days), while the frequency of extended breaks (> 7 days) is clearly not affected. This disproves the hypothesis that more and smaller cloud droplets, caused by a high load of atmospheric aerosols trigger long drought conditions over central India.
Optical frequency combs (OFC) constitute an array of phase-correlated equidistant spectral lines with nearly equal intensities over a broad spectral range. The adaptations of combs generated in mode-locked lasers proved to be highly efficient for the calibration of high-resolution (resolving power > 50000) astronomical spectrographs. The observation of different galaxy structures or the studies of the Milky Way are done using instruments in the low- and medium resolution range. To such instruments belong, for instance, the Multi Unit Spectroscopic Explorer (MUSE) being developed for the Very Large Telescope (VLT) of the European Southern Observatory (ESO) and the 4-metre Multi-Object Spectroscopic Telescope (4MOST) being in development for the ESO VISTA 4.1 m Telescope. The existing adaptations of OFC from mode-locked lasers are not resolvable by these instruments.
Within this work, a fibre-based approach for generation of OFC specifically in the low- and medium resolution range is studied numerically. This approach consists of three optical fibres that are fed by two equally intense continuous-wave (CW) lasers. The first fibre is a conventional single-mode fibre, the second one is a suitably pumped amplifying Erbium-doped fibre with anomalous dispersion, and the third one is a low-dispersion highly nonlinear optical fibre. The evolution of a frequency comb in this system is governed by the following processes: as the two initial CW-laser waves with different frequencies propagate through the first fibre, they generate an initial comb via a cascade of four-wave mixing processes. The frequency components of the comb are phase-correlated with the original laser lines and have a frequency spacing that is equal to the initial laser frequency separation (LFS), i.e. the difference in the laser frequencies. In the time domain, a train of pre-compressed pulses with widths of a few pico-seconds arises out of the initial bichromatic deeply-modulated cosine-wave. These pulses undergo strong compression in the subsequent amplifying Erbium-doped fibre: sub-100 fs pulses with broad OFC spectra are formed. In the following low-dispersion highly nonlinear fibre, the OFC experience a further broadening and the intensity of the comb lines are fairly equalised. This approach was mathematically modelled by means of a Generalised Nonlinear Schrödinger Equation (GNLS) that contains terms describing the nonlinear optical Kerr effect, the delayed Raman response, the pulse self-steepening, and the linear optical losses as well as the wavelength-dependent Erbium gain profile for the second fibre. The initial condition equation being a deeply-modulated cosine-wave mimics the radiation of the two initial CW lasers. The numerical studies are performed with the help of Matlab scripts that were specifically developed for the integration of the GNLS and the initial condition according to the proposed approach for the OFC generation. The scripts are based on the Fourth-Order Runge-Kutta in the Interaction Picture Method (RK4IP) in combination with the local error method.
This work includes the studies and results on the length optimisation of the first and the second fibre depending on different values of the group-velocity dispersion of the first fibre. Such length optimisation studies are necessary because the OFC have the biggest possible broadband and exhibit a low level of noise exactly at the optimum lengths. Further, the optical pulse build-up in the first and the second fibre was studied by means of the numerical technique called Soliton Radiation Beat Analysis (SRBA). It was shown that a common soliton crystal state is formed in the first fibre for low laser input powers. The soliton crystal continuously dissolves into separated optical solitons as the input power increases. The pulse formation in the second fibre is critically dependent on the features of the pulses formed in the first fibre. I showed that, for low input powers, an adiabatic soliton compression delivering low-noise OFC occurs in the second fibre. At high input powers, the pulses in the first fibre have more complicated structures which leads to the pulse break-up in the second fibre with a subsequent degradation of the OFC noise performance. The pulse intensity noise studies that were performed within the framework of this thesis allow making statements about the noise performance of an OFC. They showed that the intensity noise of the whole system decreases with the increasing value of LFS.
The subject of the present thesis is the one-dimensional Bose gas. Since long-rang order is destroyed by infra-red fluctuations in one dimension, only the formation of a quasi-condensate is possible, which exhibits suppressed density fluctuations, but whose phase fluctuates strongly. It is shown that modified mean-field theories based on a symmetry-breaking approach can even characterise phase coherence properties of such a quasi-condensate properly. A correct description of the transition from the degenerate ideal Bose gas to the quasi-condensate, which is a smooth cross-over rather than a phase transition, is not possible though. Basic conditions for the applicability of the theories are not fulfilled in this regime, such that the existence of a critical point is predicted.
The theories are compared on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, the Stochastic Gross-Pitaevskii equation (SGPE), a non-linear Langevin equation, is analysed numerically by means of Monte-Carlo simulations and the results are compared to those of the mean-field theories. In this context, a lot of attention is payed to the appropriate choice of the parameters. The simulations prove that the SGPE is capable of describing the cross-over properly, but highlight the limitations of the widely used local density approximation as well.
This work investigates the influence of the Coriolis force on mass motion related to the Rheasilvia impact basin on asteroid (4) Vesta's southern hemisphere. The giant basin is 500km in diameter, with a centre which nearly coincides with the rotation axis of Vesta. The Rheasilvia basin partially overlaps an earlier, similarly large impact basin, Veneneia.
Mass motion within and in the vicinity of the Rheasilvia basin includes slumping and landslides, which, primarily due to their small linear extents, have not been noticeably affected by the Coriolis force. However, a series of ridges related to the basin exhibit significant curvature, which may record the effect of the Coriolis force on the mass motion which generated them.
In this thesis 32 of these curved ridges, in three geologically distinct regions, were examined. The mass motion velocities from which the ridge curvatures may have resulted during the crater modification stage were investigated. Velocity profiles were derived by fitting inertial circles along the curved ridges and considering both the current and past rotation states of Vesta. An iterative, statistical approach was used, whereby the radii of inertial circles were obtained through repeated fitting to triplets of points across the ridges. The most frequently found radius for each central point was then used for velocity derivation at that point.
The results of the velocity analysis are strongly supportive of a Coriolis force origin for the curved ridges. Derived velocities (29.6 ± 24.6 m/s) generally agree well with previously published predictions from numerical simulations of mass motion during the impact process. Topographical features such as local slope gradient and mass deposition regions on the curved ridges also independently agree with regions in which the calculated mass motion accelerates or decelerates.
Sections of constant acceleration, deceleration and constant velocity are found, showing that mass motion is being governed by varying conditions of topography, regolith structure and friction. Estimates of material properties such as the effective viscosities (1.9-9.0·10⁶ Pa·s) and coefficients of friction (0.02-0.81) are derived from the velocity profile information in these sections. From measured accelerations of mass motions on the crater wall, it is also shown that the crater walls must have been locally steeper at the time of the mass motion.
Together with these novel insights into the state and behaviour of material moving during the modification stage of Rheasilvia's formation, this work represents the first time that the Coriolis Effect on mass motions during crater formation has been shown to result in diagnostic features preserved until today.
The X-ray observations of the colliding wind binary WR 21a is reported. The first monitoring performed by Swift/XRT in order to reveal the phase-locked variation. Our observations cover 201 different epochs from 2013 October 1 to 2015 January 30 for a total exposure of about 306 ks. It is found for the first time that the luminosity varies roughly in inverse proportion to the separation of the two stars before the X-ray maximum but later drops rapidly toward periastron.
While the majority of very massive stars is clearly found in clusters, there are also very massive objects not associated with any cluster, suggesting they may have been born in isolation. In order to gain more insights, we studied the regions around two WR stars in the Galactic Center region. To understand the nature of the potential cluster around massive stars, photometry alone is not sufficient. We therefore used the ESO VLT/SINFONI integral field spectrograph to obtain photometry and spectra for the whole region around our two candidate stars. In total, more than 60 stars have been found and assigned a spectral type.
We an optically-thick, transonic, steady wind model for a H-free Wolf-Rayet star. A bifurcation is found across a critical mass loss rate Mb. Slower winds M < Mb extend by several hydrostatic stellar radii, reproduce features of envelope in ation from Petrovic et al. (2006) and Gräfener et al. (2012), and are energetically unbound. This work is of particular interest for extended envelopes and winds, radiative hydrodynamic instabilities (eg. wind stagnation, clumping, etc.), and NLTE atmospheric models.
We present 3D numerical simulations of the NGC6888 nebula considering the proper motion and the evolution of the star, from the red supergiant (RSG) to the Wolf-Rayet (WR) phase. Our simulations reproduce the limb-brightened morphology observed in [OIII] and X-ray emission maps. The synthetic maps computed by the numerical simulations show filamentary and clumpy structures produced by instabilities triggered in the interaction between the WR wind and the RSG shell.
We present the first physical characterization of the young open cluster VVVCL041. We spectroscopically observed the cluster main-sequence stellar population and a very-massive star candidate: WR62-2. CMFGEN modelling to our near-infrared spectra indicates that WR62-2 is a very luminous (10^6.4±0.2 L⊙)and massive (∼ 80M⊙) star.
We present results of investigation of spectral variability of one of the most interesting massive stars, Romano's star (M33/V532 or GR290), located in the M33 galaxy. Brightness of the star changes together with its spectral class, which varies from WN11 to WN8. Using CMFGEN code we estimated parameters of stellar atmosphere and found that during last ten years bolometric luminosity of the star changed synchronously with stellar magnitude. Our calculations argue in favor of the hypothesis of a post-LBV status of GR290.
We present the results of the new photometric observations of the famous hypergiant PCygni. New observations were obtained in 2014 using the 48 cm Cassegrain telescope of the Abastumani Astrophysical Observatory, Georgia. We reveal some interesting behaviors of the B,V,R,I light curves, and also report new results on the periodicity of PCygni's variation. The latter result is based on the analysis of the photometric data (U,B,V filters) collected at the Abastumani Observatory between 1937 and 1983.
Under the assumption of spherical symmetry, the run of intensity with impact parameter for a spatially resolved and optically thin bubble can be inverted for an "effective emissivity" as a function of radius. The effective emissivity takes into account instrumental sensitivity and even interstellar absorption. This work was supported by a grant from NASA (G03-14008X).
Using ESPaDOnS optical spectra of WR6, we search variations on the stellar wind parameters during the different phases of the spectral variations. We use the radiative transfer code CMFGEN (Hillier & Miller 1998) to determine the wind parameters. Our work gives mean parameters for WR6, Teff = 55 kK, M = 2.7 × 10^-5 M⊙/yr and v∞ =1700 km/s. Furthermore the line profiles variations at different phases are the consequence of a variation of mass loss rate and temperature un the winds. Effective temperature reaches 59 kK at the highest intensity, whereas the mass-loss rate decreases to 2.5 × 10^-5 M⊙/yr in that case. On the other hand, effective temperature decreases to 52.5 kK and the mass-loss rate increases to 3 × 10^-5 M/⊙yr when the line profile reach its minimum intensity. Results confirm the variable nature of the stellar wind, presented in this case on two of its fundamental parameters: temperature and mass-loss; which could be used to constrain the nature of the instability at the basis of the wind.
The gas cloud G2 is currently being tidally disrupted by the Galactic Centre super-massive black hole, Sgr A*. The region around the black hole is populated by ∼ 30 Wolf-Rayet stars, which produce strong outflows. Here we explore the possibility that gas clumps like G2 originate from the collision of stellar winds via the non-linear thin shell instability.
75 WR stars and 164 RSGs are identified in a single WFC3 pointing of our M101 survey. We find that within it's large star-forming complex NGC 5462 WR stars are preferentially located in the core whilst RSGs are found in the halo, suggesting two bursts of star-formation. A review of our WR candidates reveals that only ∼30% are detected in the archival broad-band ACS imaging whilst only ∼50% are associated with HII regions.
Spectroscopy is the preferred way to study the physical and wind properties of Wolf-Rayet (WR) stars, but with decreasing brightness and increasing distance of the object spectroscopy become very expensive. However, photometry still delivers a high signal to noise ratio. Current and past astronomical surveys and space missions provide large data sets, that can be harvested to discover new WR stars and study them over a wide metallicity range with the help of state of the art stellar atmosphere and evolutionary models.
We found original observations of PCygni by E. Kharadze and N. Magalashvili in the archives of the Abastumani Observatory. These observations were carried out in the period 1951–1983. Initially they used 29 Cygni as a comparison star, and all observations of PCygni were processed using this star. On the basis of their calculations, the authors decided that PCygni may be a WUMa type binary with an orbital period of 0.500565 d, but this hypothesis was not confirmed. The only observations that have been published in the Bulletin of the Abastumani Astrophysical Observatory were those of of 1951–1955. There are whole sets of observational data not only for PCygni and 29 Cygni, but in the majority of cases also for 36 Cygni in the archives. We recalculated all data (where it was possible) using 36 Cygni as a comparison star. We are presenting UBV light curves of the variable, and also observations made by V. Nikonov in Abastumani in the period 1935–1937
Concluding Remarks
(2015)
The interaction between massive star formation and gas is a key ingredient in galaxy evolution. Given the level of observational detail currently achievable in nearby starbursts, they constitute ideal laboratories to study interaction process that contribute to global evolution in all types of galaxies. Wolf-Rayet (WR) stars, as an observational marker of high mass star formation, play a pivotal role and their winds can strongly influence the surrounding gas. Imaging spectroscopy of two nearby (<4 Mpc) starbursts, both of which show multiple regions with WR stars, are discussed. The relation between the WR content and the physical and chemical properties of the surrounding ionized gas is explored.
The feedback from massive stars is important to super star cluster (SSC) evolution and the timescales on which it occurs. SSCs form embedded in thick material, and eventually, the cluster is cleared out and revealed at optical wavelengths – however, this transition is not well understood. We are investigating this critical SSC evolutionary transition with a multi-wavelength observational campaign. Although previously thought to appear after the cluster has fully removed embedding natal material, we have found that SSCs may host large populations of Wolf-Rayet stars. These evolved stars provide ionization and mechanical feedback that we hypothesize is the tipping point in the combined feedback processes that drive a SSC to emerge. Utilizing optical spectra obtained with the 4m Mayall Telescope at Kitt Peak National Observatory and the 6.5m MMT, we have compiled a sample of embedded SSCs that are likely undergoing this short-lived evolutionary phase and in which we confirm the presence of Wolf-Rayet stars. Early results suggest that WRs may accelerate the cluster emergence.
We discuss our most recent findings on the diffuse X-ray emission within Wolf-Rayet (WR) nebulae. The best-quality X-ray observations of these objects are those performed by XMM- Newton and Chandra towards S 308, NGC 2359, and NGC 6888. Even though these three WR nebulae might have different formation scenarios, they all share similar characteristics: i) the main plasma temperatures of the X-ray-emitting gas is found to be T =[1–2]×^K, ii) the diffuse X-ray emission is confined inside the [O iii] shell, and iii) their X-ray luminosities and electron densities in the 0.3–2.0 keV energy range are LX ≈10^33–10^34 erg s-1 and ne ≈0.1–1 cm^-3 . These properties and the nebular-like abundances of the hot gas suggest mixing and/or thermal conduction is taking an important rôle reducing the temperature of the hot bubble.
Using a code that employs a self-consistent method for computing the effects of photoionization on circumstellar gas dynamics, we model the formation of wind-driven nebulae around massive Wolf-Rayet (W-R) stars. Our algorithm incorporates a simplified model of the photo-ionization source, computes the fractional ionization of hydrogen due to the photoionizing flux and recombination, and determines self-consistently the energy balance due to ionization, photo-heating and radiative cooling. We take into account changes in stellar properties and mass-loss over the star's evolution. Our multi-dimensional simulations clearly reveal the presence of strong ionization front instabilities. Using various X-ray emission models, and abundances consistent with those derived for W-R nebulae, we compute the X-ray flux and spectra from our wind bubble models. We show the evolution of the X-ray spectral features with time over the evolution of the star, taking the absorption of the X-rays by the ionized bubble into account. Our simulated X-ray spectra compare reasonably well with observed spectra of Wolf-Rayet bubbles. They suggest that X-ray nebulae around massive stars may not be easily detectable, consistent with observations.∗
Ring Nebulae
(2015)
Preliminary results are presented from spectroscopic data in the optical range of the Galactic ring nebulae NGC 6888, G2:4+1:4, RCW 58 and Sh2-308. Deep observations with long exposure times were carried out at the 6.5m Clay Telescope and at the 10.4m Gran Telescopio Canarias. In NGC 6888, recombination lines of C ii, O ii and N ii are detected with signal-to-noise ratios higher than 8. The chemical content of NGC 6888 is discussed within the chemical enrichment predicted by evolution models of massive stars. For all nebulae, a forthcoming work will content in-depth details about observations, analysis and final results (Esteban et al. 2015, in prep.).
We analyse whether a stellar atmosphere model computed with the code CMFGEN provides an optimal description of the stellar observations of WR 136 and simultaneously reproduces the nebular observations of NGC 6888, such as the ionization degree, which is modelled with the pyCloudy code. All the observational material available (far and near UV and optical spectra) were used to constrain such models. We found that the stellar temperature T∗, at τ = 20, can be in a range between 70 000 and 110 000 K, but when using the nebula as an additional restriction, we found that the stellar models with T∗ ∼ 70 000 K represent the best solution for both, the star and the nebula.
I review our current understanding of the interaction between a Wolf-Rayet star's fast wind and the surrounding medium, and discuss to what extent the predictions of numerical simulations coincide with multiwavelength observations of Wolf-Rayet nebulae. Through a series of examples, I illustrate how changing the input physics affects the results of the numerical simulations. Finally, I discuss how numerical simulations together with multiwavelength observations of these objects allow us to unpick the previous mass-loss history of massive stars.
Colliding Wolf-Rayet (WR) winds produce thermal X-ray emission widely observed by X-ray telescopes. In wide WR+O binaries, such as WR 140, the X-ray flux is tied to the orbital phase, and is a direct probe of the winds’ properties. In the Galactic center, ~30 WRs orbit the super massive black hole (SMBH) within ~10”, leading to a smorgasbord of wind-wind collisions. To model the X-ray emission of WR 140 and the Galactic center, we perform 3D hydrodynamic simulations to trace the complex gaseous flows, and then carry out 3D radiative transfer calculations to compute the variable X-ray spectra. The model WR 140 RXTE light curve matches the data well for all phases except the X-ray minimum associated with periastron, while the model spectra agree with the RXTE hardness ratio and the shape of the Suzaku observations throughout the orbit. The Galactic center model of the Chandra flux and spectral shape match well in the region r ≤ 3”, but the model flux falls off too rapidly beyond this radius.
Two of the main physical parameters that govern the massive star evolution, the mass and the mass-loss rate, are still poorly determined from the observational point of view. Only binary systems could provide well constrained masses and colliding-wind binaries could bring some constraints on the mass-loss rate. Therefore, colliding-wind binaries turn out to be very promising objects. In this framework, we present detailed studies of basic observational data obtained with the XMM-Newton facility and combined with ground-based observations and other data. We expose the results for two particularly interesting WR+O colliding-wind binaries: WR22 and WR21a.
As WR 6 is a putatively single WN4 star, and is relatively bright (V = 6.9), it is an ideal case for studying the wind mechanisms in these extremely luminous stars. To obtain higher resolution spectra at higher energy (above 1 keV) than previously obtained with the XMM/Newton RGS, we have observed WR 6 with the Chandra High Energy Transmission Grating Spectrometer for 450 ks. We have resolved emission lines of S, Si, Mg, Ne, and Fe, which all show a “fin"-shaped prole, characteristic of a self-absorbed uniformly expanding shell. Steep blue edges gives robust maximal expansion velocities of about 2000 km/s, somewhat larger than the 1700km/s derived from UV lines. The He-like lines all indicate that X-ray emitting plasmas are far from the photosphere – even at the higher energies where opacity is lowest { as was also the case for the longer wavelength lines observed with XMM-Newton/RGS. Abundances determined from X-ray spectral modeling indicate enhancements consistent with nucleosynthesis. The star was also variable in X-rays and in simultaneous optical photometry obtained with Chandra aspect camera, but not coherently with the optically known period of 3.765 days.
In this review I briefly summarize our knowledge of the X-ray emission from single WN, WC, and WO stars. These stars have relatively modest X-ray luminosities, typically not exceeding 1L⊙. The analysis of X-ray spectra usually reveals thermal plasma with temperatures reaching a few x10 MK. X-ray variability is detected in some WN stars. At present we don't fully understand how X-ray radiation in produced in WR stars, albeit there are some promising research avenues, such as the presence of CIRs in the winds of some stars. To fully understand WR stars we need to unravel mechanisms of X-ray production in their winds.
Magnetic fields, non-thermal radiation and particle acceleration in colliding winds of WR-O stars
(2015)
Non-thermal emission has been detected in WR-stars for many years at long wavelengths spectral range, in general attributed to synchrotron emission. Two key ingredients are needed to explain such emissions, namely magnetic fields and relativistic particles. Particles can be accelerated to relativistic speeds by Fermi processes at strong shocks. Therefore, strong synchrotron emission is usually attributed to WR binarity. The magnetic field may also be amplified at shocks, however the actual picture of the magnetic field geometry, intensity, and its role on the acceleration of particles at WR binary systems is still unclear. In this work we discuss the recent developments in MHD modelling of wind-wind collision regions by means of numerical simulations, and the coupled particle acceleration processes related.
Wolf-Rayet (WR) stars lose copious amounts of mass and momentum through dense stellar winds. The interaction of these outflows with their surroundings results in highly structured and complex circumstellar environments, often featuring knots, arcs, shells and spirals. Recent improvements in computational power and techniques have led to the development of detailed, multi-dimensional simulations that have given new insight into the origin of these structures, and better understanding of the physical mechanisms driving their formation. We review three of the main mechanisms that shape the outflows of WR stars:
• interaction with the interstellar medium (ISM), i.e., wind-ISM interactions;
• interaction with a stellar wind, either from a previous phase of evolution or the wind from a companion star, i.e., wind-wind interactions;
• and interaction with a companion star that has a weak or insignificant outflow (e.g., a compact companion such as a neutron star or black hole), i.e.,wind-companion interactions.
We also highlight the broader implications and impact of these circumstellar structures for related phenomena, e.g., for X-ray binaries and Gamma-ray bursts.
We look at how the dynamics of colliding wind binaries (CWB) can be investigated in 2D, and how several parameters influence the dynamics of the small scale structures inside the colliding wind and the shocked regions, as well as in how the dynamics influence the shape of the collision region at large distances. The parameters we adopt are based on the binary system WR98a, one of the few Wolf-Rayet (WR) dusty pinwheels known.
Observations of the WC9+OB system WR65 in the infrared show variations of its dust emission consistent with a period near 4.8 yr, suggesting formation in a colliding-wind binary (CWB) having an elliptical orbit. If we adopt the IR maximum as zero phase, the times of X-ray maximum count and minimum extinction to the hard component measured by Oskinova & Hamann fall at phases 0.4–0.5, when the separation of the WC9 and OB stars is greatest. We consider WR65 in the context of other WC8–9+OB stars showing dust emission.
Carbon-rich Wolf-Rayet stars are efficient carbon dust makers. Despite the strong evidence for dust formation in these objects provided by infrared thermal emission from dust, the routes to nucleation and condensation and the physical conditions required for dust production are still poorly understood. We discuss here the potential routes to carbon dust and the possible locations conducive to dust formation in the colliding winds of WC binaries.
Two types of X-ray sources are mostly found in planetary nebulae (PNe): point sources at their central stars and diffuse emission inside hot bubbles. Here we describe these two types of sources based on the most recent observations obtained in the framework of the Chandra Planetary Nebula Survey, ChanPlaNS, an X-ray survey targeting a volume-limited sample of PNe. Diffuse X-ray emission is found preferentially in young PNe with sharp, closed inner
shells. Point sources of X-ray emission at the central stars reveal magnetically active binary companions and shock-in stellar winds.
Nearly 50 post-common-envelope (post-CE) close binary central stars of planetary nebulae (CSPNe) are now known. Most contain either main sequence or white dwarf (WD) companions that orbit the WD primary in around 0.1–1.0 days. Only PN G222.8–04.2 and NGC 5189 have post-CE CSPNe with a Wolf-Rayet star primary (denoted [WR]), the low-mass analogues of massive Wolf-Rayet stars. It is not well understood how H-deficient [WR] CSPNe form, even though they are relatively common, appearing in over 100 PNe. The discovery and characterisation of post-CE [WR] CSPNe is essential to determine whether proposed binary formation scenarios are feasible to explain this enigmatic class of stars. The existence of post-CE [WR] binaries alone suggests binary mergers are not necessarily a pathway to form [WR] stars. Here we give an overview of the initial results of a radial velocity monitoring programme of [WR] CSPNe to search for new binaries. We discuss the motivation for the survey and the associated strong selection effects. The mass functions determined for PN G222.8–04.2 and NGC 5189, together with literature photometric variability data of other [WR] CSPNe, suggest that of the post-CE [WR] CSPNe yet to be found, most will have WD or subdwarf O/B-type companions in wider orbits than typical post-CE CSPNe (several days or months c.f. less than a day).
A significant number of the central stars of planetary nebulae (CSPNe) are hydrogen-deficient, showing a chemical composition of helium, carbon, and oxygen. Most of them exhibit Wolf-Rayet-like emission line spectra, similar to those of the massive WC Pop I stars, and are therefore classified as of spectral type [WC]. In the last years, CSPNe of other Wolf-Rayet spectral subtypes have been identified, namely PB 8, which is of spectral type [WN/C], and IC 4663 and Abell 48, which are of spectral type [WN]. We review spectral analyses of Wolf-Rayet type central stars of different evolutionary stages and discuss the results in the context of stellar evolution. Especially we consider the question of a common evolutionary channel for [WC] stars. The constraints on the formation of [WN] or [WC/N] subtype stars will also be addressed.
In this review, I discuss the suitability of massive star progenitors, evolved in isolation or in interacting binaries, for the production of observed supernovae (SNe) IIb, Ib, Ic. These SN types can be explained through variations in composition. The critical need of non-thermal effects to produce He I lines favours low-mass He-rich ejecta (in which ^56 Ni can be more easily mixed with He) for the production of SNe IIb/Ib, which thus may arise preferentially from moderate-mass donors in interacting binaries. SNe Ic may instead arise from higher mass progenitors, He-poor or not, because their larger CO cores prevent efficient non-thermal excitation of He i lines. However, current single star evolution models tend to produce Wolf-Rayet (WR) stars at death that have a final mass of > 10 M⊙. Single WR star explosion models produce ejecta that are too massive to match the observed light curve widths and rise times of SNe IIb/Ib/Ic, unless their kinetic energy is systematically and far greater than the canonical value of 10^56 erg. Future work is needed to evaluate the energy/mass degeneracy in light curve properties. Alternatively, a greater mass loss during the WR phase, perhaps in the form of eruptions, as evidenced in SNe Ibn, may reduce the final WR mass. If viable, such explosions would nonetheless favour a SN Ic, not a Ib.
The stellar Eddington limit
(2015)
It is often assumed that when stars reach their Eddington limit, strong outflows are initiated, and that this happens only for extreme stellar masses. We discuss here that in models of up to 500 M⊙, the Eddington limit is never reached at the stellar surface. Instead, we argue that the Eddington limit is reached inside the stellar envelope in hydrogen-rich stars above ∼ 30 M⊙ and in Wolf-Rayet stars above ∼ 7 M⊙, with drastic effects for their struture and stability.
The morphological appearance of massive stars across their post-Main Sequence evolution and before the SN event is very uncertain, both from a theoretical and observational perspective. We recently developed coupled stellar evolution and atmospheric modeling of stars done with the Geneva and CMFGEN codes, for initial masses between 9 and 120 M⊙. We are able to predict the observables such as the high-resolution spectrum and broadband photometry. Here I discuss how the spectrum of a massive star changes across its evolution and before death, with focus on the WR stage. Our models indicate that single stars with initial masses larger than 30 M⊙ end their lives as WR stars. Depending on rotation, the spectrum of the star can either be that of a WN or WO subtype at the pre-SN stage. Our models allow, for the first time, direct comparison between predictions from stellar evolution models and observations of SN progenitors.
We compute spectral libraries for populations of coeval stars using state-of-the-art massive-star evolutionary tracks that account for different astrophysics including rotation and close-binarity. Our synthetic spectra account for stellar and nebular contributions. We use our models to obtain E(B – V ), age, and mass for six clusters in spiral galaxy NGC 1566, which have ages of < 50 Myr and masses of > 5 x 104M⊙ according to standard models. NGC 1566 was observed from the NUV to the I-band as part of the imaging Treasury HST program LEGUS: Legacy Extragalactic UV Survey. We aim to establish i) if the models provide reasonable fits to the data, ii) how well the models and photometry are able to constrain the cluster properties, and iii) how different the properties obtained with different models are.
Wolf-Rayet (WR) stars, as they are advanced stages of the life of massive stars, provide a good test for various physical processes involved in the modelling of massive stars, such as rotation and mass loss. In this paper, we show the outputs of the latest grids of single massive stars computed with the Geneva stellar evolution code, and compare them with some observations. We present a short discussion on the shortcomings of single stars models and we also briefly discuss the impact of binarity on the WR populations.