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Relativistic pair beams produced in the cosmic voids by TeV gamma rays from blazars are expected to produce a detectable GeV-scale cascade emission missing in the observations. The suppression of this secondary cascade implies either the deflection of the pair beam by intergalactic magnetic fields (IGMFs) or an energy loss of the beam due to the electrostatic beam-plasma instability. IGMF of femto-Gauss strength is sufficient to significantly deflect the pair beams reducing the flux of secondary cascade below the observational limits. A similar flux reduction may result in the absence of the IGMF from the beam energy loss by the instability before the inverse Compton cooling. This dissertation consists of two studies about the instability role in the evolution of blazar-induced beams.
Firstly, we investigated the effect of sub-fG level IGMF on the beam energy loss by the instability. Considering IGMF with correlation lengths smaller than a few kpc, we found that such fields increase the transverse momentum of the pair beam particles, dramatically reducing the linear growth rate of the electrostatic instability and hence the energy-loss rate of the pair beam. Our results show that the IGMF eliminates beam plasma instability as an effective energy-loss agent at a field strength three orders of magnitude below that needed to suppress the secondary cascade emission by magnetic deflection. For intermediate-strength IGMF, we do not know a viable process to explain the observed absence of GeV-scale cascade emission and hence can be excluded.
Secondly, we probed how the beam-plasma instability feeds back on the beam, using a realistic two-dimensional beam distribution. We found that the instability broadens the beam opening angles significantly without any significant energy loss, thus confirming a recent feedback study on a simplified one-dimensional beam distribution. However, narrowing diffusion feedback of the beam particles with Lorentz factors less than 1e6 might become relevant even though initially it is negligible. Finally, when considering the continuous creation of TeV pairs, we found that the beam distribution and the wave spectrum reach a new quasi-steady state, in which the scattering of beam particles persists and the beam opening angle may increase by a factor of hundreds. This new intrinsic scattering of the cascade can result in time delays of around ten years, thus potentially mimicking the IGMF deflection. Understanding the implications on the GeV cascade emission requires accounting for inverse Compton cooling and simulating the beam-plasma system at different points in the IGM.
Actin is one of the most highly conserved proteins in eukaryotes and distinct actin-related proteins with filament-forming properties are even found in prokaryotes. Due to these commonalities, actin-modulating proteins of many species share similar structural properties and proposed functions. The polymerization and depolymerization of actin are critical processes for a cell as they can contribute to shape changes to adapt to its environment and to move and distribute nutrients and cellular components within the cell. However, to what extent functions of actin-binding proteins are conserved between distantly related species, has only been addressed in a few cases. In this work, functions of Coronin-A (CorA) and Actin-interacting protein 1 (Aip1), two proteins involved in actin dynamics, were characterized. In addition, the interchangeability and function of Aip1 were investigated in two phylogenetically distant model organisms. The flowering plant Arabidopsis thaliana (encoding two homologs, AIP1-1 and AIP1-2) and in the amoeba Dictyostelium discoideum (encoding one homolog, DdAip1) were chosen because the functions of their actin cytoskeletons may differ in many aspects. Functional analyses between species were conducted for AIP1 homologs as flowering plants do not harbor a CorA gene.
In the first part of the study, the effect of four different mutation methods on the function of Coronin-A protein and the resulting phenotype in D. discoideum was revealed in two genetic knockouts, one RNAi knockdown and a sudden loss-of-function mutant created by chemical-induced dislocation (CID). The advantages and disadvantages of the different mutation methods on the motility, appearance and development of the amoebae were investigated, and the results showed that not all observed properties were affected with the same intensity. Remarkably, a new combination of Selection-Linked Integration and CID could be established.
In the second and third parts of the thesis, the exchange of Aip1 between plant and amoeba was carried out. For A. thaliana, the two homologs (AIP1-1 and AIP1-2) were analyzed for functionality as well as in D. discoideum. In the Aip1-deficient amoeba, rescue with AIP1-1 was more effective than with AIP1-2. The main results in the plant showed that in the aip1-2 mutant background, reintroduced AIP1-2 displayed the most efficient rescue and A. thaliana AIP1-1 rescued better than DdAip1. The choice of the tagging site was important for the function of Aip1 as steric hindrance is a problem. The DdAip1 was less effective when tagged at the C-terminus, while the plant AIP1s showed mixed results depending on the tag position. In conclusion, the foreign proteins partially rescued phenotypes of mutant plants and mutant amoebae, despite the organisms only being very distantly related in evolutionary terms.
The increasing number of known exoplanets raises questions about their demographics and the mechanisms that shape planets into how we observe them today. Young planets in close-in orbits are exposed to harsh environments due to the host star being magnetically highly active, which results in high X-ray and extreme UV fluxes impinging on the planet. Prolonged exposure to this intense photoionizing radiation can cause planetary atmospheres to heat up, expand and escape into space via a hydrodynamic escape process known as photoevaporation. For super-Earth and sub-Neptune-type planets, this can even lead to the complete erosion of their primordial gaseous atmospheres. A factor of interest for this particular mass-loss process is the activity evolution of the host star. Stellar rotation, which drives the dynamo and with it the magnetic activity of a star, changes significantly over the stellar lifetime. This strongly affects the amount of high-energy radiation received by a planet as stars age. At a young age, planets still host warm and extended envelopes, making them particularly susceptible to atmospheric evaporation. Especially in the first gigayear, when X-ray and UV levels can be 100 - 10,000 times higher than for the present-day sun, the characteristics of the host star and the detailed evolution of its high-energy emission are of importance.
In this thesis, I study the impact of stellar activity evolution on the high-energy-induced atmospheric mass loss of young exoplanets. The PLATYPOS code was developed as part of this thesis to calculate photoevaporative mass-loss rates over time. The code, which couples parameterized planetary mass-radius relations with an analytical hydrodynamic escape model, was used, together with Chandra and eROSITA X-ray observations, to investigate the future mass loss of the two young multiplanet systems V1298 Tau and K2-198. Further, in a numerical ensemble study, the effect of a realistic spread of activity tracks on the small-planet radius gap was investigated for the first time. The works in this thesis show that for individual systems, in particular if planetary masses are unconstrained, the difference between a young host star following a low-activity track vs. a high-activity one can have major implications: the exact shape of the activity evolution can determine whether a planet can hold on to some of its atmosphere, or completely loses its envelope, leaving only the bare rocky core behind. For an ensemble of simulated planets, an observationally-motivated distribution of activity tracks does not substantially change the final radius distribution at ages of several gigayears. My simulations indicate that the overall shape and slope of the resulting small-planet radius gap is not significantly affected by the spread in stellar activity tracks. However, it can account for a certain scattering or fuzziness observed in and around the radius gap of the observed exoplanet population.
The icosahedral non-hydrostatic large eddy model (ICON-LEM) was applied around the drift track of the Multidisciplinary Observatory Study of the Arctic (MOSAiC) in 2019 and 2020. The model was set up with horizontal grid-scales between 100m and 800m on areas with radii of 17.5km and 140 km. At its lateral boundaries, the model was driven by analysis data from the German Weather Service (DWD), downscaled by ICON in limited area mode (ICON-LAM) with horizontal grid-scale of 3 km.
The aim of this thesis was the investigation of the atmospheric boundary layer near the surface in the central Arctic during polar winter with a high-resolution mesoscale model. The default settings in ICON-LEM prevent the model from representing the exchange processes in the Arctic boundary layer in accordance to the MOSAiC observations. The implemented sea-ice scheme in ICON does not include a snow layer on sea-ice, which causes a too slow response of the sea-ice surface temperature to atmospheric changes. To allow the sea-ice surface to respond faster to changes in the atmosphere, the implemented sea-ice parameterization in ICON was extended with an adapted heat capacity term.
The adapted sea-ice parameterization resulted in better agreement with the MOSAiC observations. However, the sea-ice surface temperature in the model is generally lower than observed due to biases in the downwelling long-wave radiation and the lack of complex surface structures, like leads. The large eddy resolving turbulence closure yielded a better representation of the lower boundary layer under strongly stable stratification than the non-eddy-resolving turbulence closure. Furthermore, the integration of leads into the sea-ice surface reduced the overestimation of the sensible heat flux for different weather conditions.
The results of this work help to better understand boundary layer processes in the central Arctic during the polar night. High-resolving mesoscale simulations are able to represent temporally and spatially small interactions and help to further develop parameterizations also for the application in regional and global models.
Organic-inorganic hybrids based on P3HT and mesoporous silicon for thermoelectric applications
(2024)
This thesis presents a comprehensive study on synthesis, structure and thermoelectric transport properties of organic-inorganic hybrids based on P3HT and porous silicon. The effect of embedding polymer in silicon pores on the electrical and thermal transport is studied. Morphological studies confirm successful polymer infiltration and diffusion doping with roughly 50% of the pore space occupied by conjugated polymer. Synchrotron diffraction experiments reveal no specific ordering of the polymer inside the pores. P3HT-pSi hybrids show improved electrical transport by five orders of magnitude compared to porous silicon and power factor values comparable or exceeding other P3HT-inorganic hybrids. The analysis suggests different transport mechanisms in both materials. In pSi, the transport mechanism relates to a Meyer-Neldel compansation rule. The analysis of hybrids' data using the power law in Kang-Snyder model suggests that a doped polymer mainly provides charge carriers to the pSi matrix, similar to the behavior of a doped semiconductor. Heavily suppressed thermal transport in porous silicon is treated with a modified Landauer/Lundstrom model and effective medium theories, which reveal that pSi agrees well with the Kirkpatrick model with a 68% percolation threshold. Thermal conductivities of hybrids show an increase compared to the empty pSi but the overall thermoelectric figure of merit ZT of P3HT-pSi hybrid exceeds both pSi and P3HT as well as bulk Si.
Additive manufacturing (AM) processes enable the production of metal structures with exceptional design freedom, of which laser powder bed fusion (PBF-LB) is one of the most common. In this process, a laser melts a bed of loose feedstock powder particles layer-by-layer to build a structure with the desired geometry. During fabrication, the repeated melting and rapid, directional solidification create large temperature gradients that generate large thermal stress. This thermal stress can itself lead to cracking or delamination during fabrication. More often, large residual stresses remain in the final part as a footprint of the thermal stress. This residual stress can cause premature distortion or even failure of the part in service. Hence, knowledge of the residual stress field is critical for both process optimization and structural integrity.
Diffraction-based techniques allow the non-destructive characterization of the residual stress fields. However, such methods require a good knowledge of the material of interest, as certain assumptions must be made to accurately determine residual stress. First, the measured lattice plane spacings must be converted to lattice strains with the knowledge of a strain-free material state. Second, the measured lattice strains must be related to the macroscopic stress using Hooke's law, which requires knowledge of the stiffness of the material. Since most crystal structures exhibit anisotropic material behavior, the elastic behavior is specific to each lattice plane of the single crystal. Thus, the use of individual lattice planes in monochromatic diffraction residual stress analysis requires knowledge of the lattice plane-specific elastic properties. In addition, knowledge of the microstructure of the material is required for a reliable assessment of residual stress.
This work presents a toolbox for reliable diffraction-based residual stress analysis. This is presented for a nickel-based superalloy produced by PBF-LB. First, this work reviews the existing literature in the field of residual stress analysis of laser-based AM using diffraction-based techniques. Second, the elastic and plastic anisotropy of the nickel-based superalloy Inconel 718 produced by PBF-LB is studied using in situ energy dispersive synchrotron X-ray and neutron diffraction techniques. These experiments are complemented by ex situ material characterization techniques. These methods establish the relationship between the microstructure and texture of the material and its elastic and plastic anisotropy. Finally, surface, sub-surface, and bulk residual stress are determined using a texture-based approach. Uncertainties of different methods for obtaining stress-free reference values are discussed.
The tensile behavior in the as-built condition is shown to be controlled by texture and cellular sub-grain structure, while in the heat-treated condition the precipitation of strengthening phases and grain morphology dictate the behavior. In fact, the results of this thesis show that the diffraction elastic constants depend on the underlying microstructure, including texture and grain morphology. For columnar microstructures in both as-built and heat-treated conditions, the diffraction elastic constants are best described by the Reuss iso-stress model. Furthermore, the low accumulation of intergranular strains during deformation demonstrates the robustness of using the 311 reflection for the diffraction-based residual stress analysis with columnar textured microstructures. The differences between texture-based and quasi-isotropic approaches for the residual stress analysis are shown to be insignificant in the observed case. However, the analysis of the sub-surface residual stress distributions show, that different scanning strategies result in a change in the orientation of the residual stress tensor. Furthermore, the location of the critical sub-surface tensile residual stress is related to the surface roughness and the microstructure. Finally, recommendations are given for the diffraction-based determination and evaluation of residual stress in textured additively manufactured alloys.
The origin and structure of magnetic fields in the Galaxy are largely unknown. What is known is that they are essential for several astrophysical processes, in particular the propagation of cosmic rays. Our ability to describe the propagation of cosmic rays through the Galaxy is severely limited by the lack of observational data needed to probe the structure of the Galactic magnetic field on many different length scales. This is particularly true for modelling the propagation of cosmic rays into the Galactic halo, where our knowledge of the magnetic field is particularly poor.
In the last decade, observations of the Galactic halo in different frequency regimes have revealed the existence of out-of-plane bubble emission in the Galactic halo. In gamma rays these bubbles have been termed Fermi bubbles with a radial extent of ≈ 3 kpc and an azimuthal height of ≈ 6 kpc. The radio counterparts of the Fermi bubbles were seen by both the S-PASS telescopes and the Planck satellite, and showed a clear spatial overlap. The X-ray counterparts of the Fermi bubbles were named eROSITA bubbles after the eROSITA satellite, with a radial width of ≈ 7 kpc and an azimuthal height of ≈ 14 kpc. Taken together, these observations suggest the presence of large extended Galactic Halo Bubbles (GHB) and have stimulated interest in exploring the less explored Galactic halo.
In this thesis, a new toy model (GHB model) for the magnetic field and non-thermal electron distribution in the Galactic halo has been proposed. The new toy model has been used to produce polarised synchrotron emission sky maps. Chi-square analysis was used to compare the synthetic skymaps with the Planck 30 GHz polarised skymaps. The obtained constraints on the strength and azimuthal height were found to be in agreement with the S-PASS radio observations.
The upper, lower and best-fit values obtained from the above chi-squared analysis were used to generate three separate toy models. These three models were used to propagate ultra-high energy cosmic rays. This study was carried out for two potential sources, Centaurus A and NGC 253, to produce magnification maps and arrival direction skymaps. The simulated arrival direction skymaps were found to be consistent with the hotspots of Centaurus A and NGC 253 as seen in the observed arrival direction skymaps provided by the Pierre Auger Observatory (PAO).
The turbulent magnetic field component of the GHB model was also used to investigate the extragalactic dipole suppression seen by PAO. UHECRs with an extragalactic dipole were forward-tracked through the turbulent GHB model at different field strengths. The suppression in the dipole due to the varying diffusion coefficient from the simulations was noted. The results could also be compared with an analytical analogy of electrostatics. The simulations of the extragalactic dipole suppression were in agreement with similar studies carried out for galactic cosmic rays.
Organic solar cells (OSCs) represent a new generation of solar cells with a range of captivating attributes including low-cost, light-weight, aesthetically pleasing appearance, and flexibility. Different from traditional silicon solar cells, the photon-electron conversion in OSCs is usually accomplished in an active layer formed by blending two kinds of organic molecules (donor and acceptor) with different energy levels together.
The first part of this thesis focuses on a better understanding of the role of the energetic offset and each recombination channel on the performance of these low-offset OSCs. By combining advanced experimental techniques with optical and electrical simulation, the energetic offsets between CT and excitons, several important insights were achieved: 1. The short circuit current density and fill-factor of low-offset systems are largely determined by field-dependent charge generation in such low-offset OSCs. Interestingly, it is strongly evident that such field-dependent charge generation originates from a field-dependent exciton dissociation yield. 2. The reduced energetic offset was found to be accompanied by strongly enhanced bimolecular recombination coefficient, which cannot be explained solely by exciton repopulation from CT states. This implies the existence of another dark decay channel apart from CT.
The second focus of the thesis was on the technical perspective. In this thesis, the influence of optical artifacts in differential absorption spectroscopy upon the change of sample configuration and active layer thickness was studied. It is exemplified and discussed thoroughly and systematically in terms of optical simulations and experiments, how optical artifacts originated from non-uniform carrier profile and interference can manipulate not only the measured spectra, but also the decay dynamics in various measurement conditions. In the end of this study, a generalized methodology based on an inverse optical transfer matrix formalism was provided to correct the spectra and decay dynamics manipulated by optical artifacts.
Overall, this thesis paves the way for a deeper understanding of the keys toward higher PCEs in low-offset OSC devices, from the perspectives of both device physics and characterization techniques.
Supernova remnants are considered to be the primary sources of galactic cosmic rays. These cosmic rays are assumed to be accelerated by the diffusive shock acceleration mechanism, specifically at shocks in the remnants. Particularly in the core-collapse scenario, these supernova remnant shocks expand inside the wind-blown bubbles structured by massive progenitors during their lifetime. Therefore, the complex environment of wind bubbles can influence the particle acceleration and radiation from the remnants. Further, the evolution of massive stars depends on their Zero Age Main Sequence mass, rotation, and metallicity. Consequently, the structures of the wind bubbles generated during the lifetime of massive stars should be considerably different. Hence, the particle acceleration in the core-collapse supernova remnants should vary, not only from the remnants evolving in the uniform environment but also from one another, depending on their progenitor stars.
A core-collapse supernova remnant with a very massive 60 𝑀 ⊙ progenitor star has been considered to study the particle acceleration at the shock considering Bohm-like diffusion. This dissertation demonstrates the modification in particle acceleration and radiation while the remnant propagates through different regions of the wind bubble by impacts from the profiles of gas density, the temperature of the bubble and the magnetic field structure. Subsequently, in this thesis, I discuss the impacts of the non-identical ambient environment of core-collapse supernova remnants on particle spectra and the non-thermal emissions, considering 20 𝑀 ⊙ and 60 𝑀⊙ massive progenitors having different evolutionary tracks. Additionally, I also analyse the effect of cosmic ray streaming instabilities on particle spectra.
To model the particle acceleration in the remnants, I have performed simulations in one-dimensional spherical symmetry using RATPaC code. The transport equation for cosmic rays and magnetic turbulence in test-particle approximation, along with the induction equation for the evolution of the large-scale magnetic field, have been solved simultaneously with the hydrodynamic equations for the expansion of remnants inside the pre-supernova circumstellar medium.
The results from simulations describe that the spectra of accelerated particles in supernova remnants are regulated by density fluctuations, temperature variations, the large-scale magnetic field configuration and scattering turbulence. Although the diffusive shock acceleration mechanism at supernova remnant shock predicts the spectral index of 2 for the accelerated non-thermal particles, I have obtained the particle spectra that deviate from this prediction, in the core-collapse scenario. I have found that the particle spectral index reaches 2.5 for the supernova remnant with 60 𝑀 ⊙ progenitor when the remnant resides inside the shocked wind region of the wind bubble, and this softness persists at later evolutionary stages even with Bohm-like diffusion for accelerated particles. However, the supernova remnant with 20 𝑀 ⊙ progenitor does not demonstrate persistent softness in particle spectra from the influence of the hydrodynamics of the corresponding wind bubble. At later stages of evolution, the particle spectra illustrate softness at higher energies for both remnants as the consequence of the escape of high-energy particles from the remnants while considering the cosmic ray streaming instabilities. Finally, I have probed the emission morphology of remnants that varies depending on the progenitors, particularly in earlier evolutionary stages. This dissertation provides insight into different core-collapse remnants expanding inside wind bubbles, for instance, the calculated gamma-ray spectral index from the supernova remnant with 60 𝑀 ⊙ progenitor at later evolutionary stages is consistent with that of the observed supernova remnants expanding in dense molecular clouds.
Stars under influence: evidence of tidal interactions between stars and substellar companions
(2023)
Tidal interactions occur between gravitationally bound astrophysical bodies. If their spatial separation is sufficiently small, the bodies can induce tides on each other, leading to angular momentum transfer and altering of evolutionary path the bodies would have followed if they were single objects. The tidal processes are well established in the Solar planet-moon systems and close stellar binary systems. However, how do stars behave if they are orbited by a substellar companion (e.g. a planet or a brown dwarf) on a tight orbit?
Typically, a substellar companion inside the corotation radius of a star will migrate toward the star as it loses orbital angular momentum. On the other hand, the star will gain angular momentum which has the potential to increase its rotation rate. The effect should be more pronounced if the substellar companion is more massive. As the stellar rotation rate and the magnetic activity level are coupled, the star should appear more magnetically active under the tidal influence of the orbiting substellar companion. However, the difficulty in proving that a star has a higher magnetic activity level due to tidal interactions lies in the fact that (I) substellar companions around active stars are easier to detect if they are more massive, leading to a bias toward massive companions around active stars and mimicking the tidal interaction effect, and that (II) the age of a main-sequence star cannot be easily determined, leaving the possibility that a star is more active due to its young age.
In our work, we overcome these issues by employing wide stellar binary systems where one star hosts a substellar companion, and where the other star provides the magnetic activity baseline for the host star, assuming they have coevolved, and thereby provides the host's activity level if tidal interactions have no effect on it. Firstly, we find that extrasolar planets can noticeably increase the host star's X-ray luminosity and that the effect is more pronounced if the exoplanet is at least Jupiter-like in mass and close to the star. Further, we find that a brown dwarf will have an even stronger effect, as expected, and that the X-ray surface flux difference between the host star and the wide stellar companion is a significant outlier when compared to a large sample of similar wide binary systems without any known substellar companions. This result proves that substellar hosting wide binary systems can be good tools to reveal the tidal effect on host stars, and also show that the typical stellar age indicators as activity or rotation cannot be used for these stars. Finally, knowing that the activity difference is a good tracer of the substellar companion's tidal impact, we develop an analytical method to calculate the modified tidal quality factor Q' of individual host stars, which defines the tidal dissipation efficiency in the convective envelope of a given main-sequence star.
Late-type stars are by far the most frequent stars in the universe and of fundamental interest to various fields of astronomy – most notably to Galactic archaeology and exoplanet research. However, such stars barely change during their main sequence lifetime; their temperature, luminosity, or chemical composition evolve only very slowly over the course of billions of years. As such, it is difficult to obtain the age of such a star, especially when it is isolated and no other indications (like cluster association) can be used. Gyrochronology offers a way to overcome this problem.
Stars, just like all other objects in the universe, rotate and the rate at which stars rotate impacts many aspects of their appearance and evolution. Gyrochronology leverages the observed rotation rate of a late-type main sequence star and its systematic evolution to estimate their ages. Unlike the above-mentioned parameters, the rotation rate of a main sequence star changes drastically throughout its main sequence lifetime; stars spin down. The youngest stars rotate every few hours, whereas much older stars rotate only about once a month, or – in the case of some late M-stars – once in a hundred days. Given that this spindown is systematic (with an additional mass dependence), it gave rise to the idea of using the observed rotation rate of a star (and its mass or a suitable proxy thereof) to estimate a star’s age. This has been explored widely in young stellar open clusters but remains essentially unconstrained for stars older than the sun, and K and M stars older than 1 Gyr.
This thesis focuses on the continued exploration of the spindown behavior to assess, whether gyrochronology remains applicable for stars of old ages, whether it is universal for late-type main sequence stars (including field stars), and to provide calibration mileposts for spindown models. To accomplish this, I have analyzed data from Kepler space telescope for the open clusters Ruprecht 147 (2.7 Gyr old) and M 67 (4 Gyr). Time series photometry data (light curves)
were obtained for both clusters during Kepler’s K2 mission. However, due to technical limitations and telescope malfunctions, extracting usable data from the K2 mission to identify (especially long) rotation periods requires extensive data preparation.
For Ruprecht 147, I have compiled a list of about 300 cluster members from the literature and adopted preprocessed light curves from the Kepler archive where available. They have been cleaned of the gravest of data artifacts but still contained systematics. After correcting them for said artifacts, I was able to identify rotation periods in 31 of them.
For M 67 more effort was taken. My work on Ruprecht 147 has shown the limitations imposed by the preselection of Kepler targets. Therefore, I adopted the time series full frame image directly and performed photometry on a much higher spatial resolution to be able to obtain data for as many stars as possible. This also means that I had to deal with the ubiquitous artifacts in Kepler data. For that, I devised a method that correlates the artificial flux variations with the ongoing drift of the telescope pointing in order to remove it. This process was a large success and I was able to create light curves whose quality match and even exceede those that were created by the Kepler mission – all while operating on higher spatial resolution and processing fainter stars. Ultimately, I was able to identify signs of periodic variability in the (created) light curves for 31 and 47 stars in Ruprecht 147 and M 67, respectively. My data connect well to bluer stars of cluster of the same age and extend for the first time to stars redder than early-K and older than 1 Gyr. The cluster data show a clear flattening in the distribution of Ruprecht 147 and even a downturn for M 67, resulting in a somewhat sinusoidal shape. With that, I have shown that the systematic spindown of stars continues at least until 4 Gyr and stars continue to live on a single surface in age-rotation periods-mass space which allows gyrochronology to be used at least up to that age. However, the shape of the spindown – as exemplified by the newly discovered sinusoidal shape of the cluster sequence – deviates strongly from the expectations.
I then compiled an extensive sample of rotation data in open clusters – very much including my own work – and used the resulting cluster skeleton (with each cluster forming a rip in color-rotation period-mass space) to investigate if field stars follow the same spindown as cluster stars. For the field stars, I used wide binaries, which – with their shared origin and coevality – are in a sense the smallest possible open clusters. I devised an empirical method to evaluate the consistency between the rotation rates of the wide binary components and found that the vast majority of them are in fact consistent with what is observed in open clusters. This leads me to conclude that gyrochronology – calibrated on open clusters – can be applied to determine the ages of field stars.
The Lyman-𝛼 (Ly𝛼) line commonly assists in the detection of high-redshift galaxies, the so-called Lyman-alpha emitters (LAEs). LAEs are useful tools to study the baryonic matter distribution of the high-redshift universe. Exploring their spatial distribution not only reveals the large-scale structure of the universe at early epochs, but it also provides an insight into the early formation and evolution of the galaxies we observe today. Because dark matter halos (DMHs) serve as sites of galaxy formation, the LAE distribution also traces that of the underlying dark matter. However, the details of this relation and their co-evolution over time remain unclear. Moreover, theoretical studies predict that the spatial distribution of LAEs also impacts their own circumgalactic medium (CGM) by influencing their extended Ly𝛼 gaseous halos (LAHs), whose origin is still under investigation. In this thesis, I make several contributions to improve the knowledge on these fields using samples of LAEs observed with the Multi Unit Spectroscopic Explorer (MUSE) at redshifts of 3 < 𝑧 < 6.
The near-Earth space environment is a highly complex system comprised of several regions and particle populations hazardous to satellite operations. The trapped particles in the radiation belts and ring current can cause significant damage to satellites during space weather events, due to deep dielectric and surface charging. Closer to Earth is another important region, the ionosphere, which delays the propagation of radio signals and can adversely affect navigation and positioning. In response to fluctuations in solar and geomagnetic activity, both the inner-magnetospheric and ionospheric populations can undergo drastic and sudden changes within minutes to hours, which creates a challenge for predicting their behavior. Given the increasing reliance of our society on satellite technology, improving our understanding and modeling of these populations is a matter of paramount importance.
In recent years, numerous spacecraft have been launched to study the dynamics of particle populations in the near-Earth space, transforming it into a data-rich environment. To extract valuable insights from the abundance of available observations, it is crucial to employ advanced modeling techniques, and machine learning methods are among the most powerful approaches available. This dissertation employs long-term satellite observations to analyze the processes that drive particle dynamics, and builds interdisciplinary links between space physics and machine learning by developing new state-of-the-art models of the inner-magnetospheric and ionospheric particle dynamics.
The first aim of this thesis is to investigate the behavior of electrons in Earth's radiation belts and ring current. Using ~18 years of electron flux observations from the Global Positioning System (GPS), we developed the first machine learning model of hundreds-of-keV electron flux at Medium Earth Orbit (MEO) that is driven solely by solar wind and geomagnetic indices and does not require auxiliary flux measurements as inputs. We then proceeded to analyze the directional distributions of electrons, and for the first time, used Fourier sine series to fit electron pitch angle distributions (PADs) in Earth's inner magnetosphere. We performed a superposed epoch analysis of 129 geomagnetic storms during the Van Allen Probes era and demonstrated that electron PADs have a strong energy-dependent response to geomagnetic activity. Additionally, we showed that the solar wind dynamic pressure could be used as a good predictor of the PAD dynamics. Using the observed dependencies, we created the first PAD model with a continuous dependence on L, magnetic local time (MLT) and activity, and developed two techniques to reconstruct near-equatorial electron flux observations from low-PA data using this model.
The second objective of this thesis is to develop a novel model of the topside ionosphere. To achieve this goal, we collected observations from five of the most widely used ionospheric missions and intercalibrated these data sets. This allowed us to use these data jointly for model development, validation, and comparison with other existing empirical models. We demonstrated, for the first time, that ion density observations by Swarm Langmuir Probes exhibit overestimation (up to ~40-50%) at low and mid-latitudes on the night side, and suggested that the influence of light ions could be a potential cause of this overestimation. To develop the topside model, we used 19 years of radio occultation (RO) electron density profiles, which were fitted with a Chapman function with a linear dependence of scale height on altitude. This approximation yields 4 parameters, namely the peak density and height of the F2-layer and the slope and intercept of the linear scale height trend, which were modeled using feedforward neural networks (NNs). The model was extensively validated against both RO and in-situ observations and was found to outperform the International Reference Ionosphere (IRI) model by up to an order of magnitude. Our analysis showed that the most substantial deviations of the IRI model from the data occur at altitudes of 100-200 km above the F2-layer peak. The developed NN-based ionospheric model reproduces the effects of various physical mechanisms observed in the topside ionosphere and provides highly accurate electron density predictions.
This dissertation provides an extensive study of geospace dynamics, and the main results of this work contribute to the improvement of models of plasma populations in the near-Earth space environment.
This thesis discusses heat and charge transport phenomena in single-crystalline Silicon penetrated by nanometer-sized pores, known as mesoporous Silicon (pSi). Despite the extensive attention given to it as a thermoelectric material of interest, studies on microscopic thermal and electronic transport beyond its macroscopic characterizations are rarely reported. In contrast, this work reports the interplay of both.
PSi samples synthesized by electrochemical anodization display a temperature dependence of specific heat 𝐶𝑝 that deviates from the characteristic 𝑇^3 behaviour (at 𝑇<50𝐾). A thorough analysis reveals that both 3D and 2D Einstein and Debye modes contribute to this specific heat. Additional 2D Einstein modes (~3 𝑚𝑒𝑉) agree reasonably well with the boson peak of SiO2 in pSi pore walls. 2D Debye modes are proposed to account for surface acoustic modes causing a significant deviation from the well-known 𝑇^3 dependence of 𝐶𝑝 at 𝑇<50𝐾.
A novel theoretical model gives insights into the thermal conductivity of pSi in terms of porosity and phonon scattering on the nanoscale. The thermal conductivity analysis utilizes the peculiarities of the pSi phonon dispersion probed by the inelastic neutron scattering experiments. A phonon mean-free path of around 10 𝑛𝑚 extracted from the presented model is proposed to cause the reduced thermal conductivity of pSi by two orders of magnitude compared to p-doped bulk Silicon. Detailed analysis indicates that compound averaging may cause a further 10-50% reduction. The percolation threshold of 65% for thermal conductivity of pSi samples is subsequently determined by employing theoretical effective medium models.
Temperature-dependent electrical conductivity measurements reveal a thermally activated transport process. A detailed analysis of the activation energy 𝐸𝐴𝜎 in the thermally activated transport exhibits a Meyer Neldel compensation rule between different samples that originates in multi-phonon absorption upon carrier transport. Activation energies 𝐸𝐴𝑆 obtained from temperature-dependent thermopower measurements provide further evidence for multi-phonon assisted hopping between localized states as a dominant charge transport mechanism in pSi, as they systematically differ from the determined 𝐸𝐴𝜎 values.
Reflexion und Reflexivität
(2023)
Reflexion gilt in der Lehrkräftebildung als eine Schlüsselkategorie der professionellen Entwicklung. Entsprechend wird auf vielfältige Weise die Qualität reflexionsbezogener Kompetenzen untersucht. Eine Herausforderung hierbei kann in der Annahme bestehen, von der Analyse schriftlicher Reflexionen unmittelbar auf die Reflexivität einer Person zu schließen, da Reflexion stets kontextspezifisch als Abbild reflexionsbezogener Argumentationsprozesse angesehen werden sollte und reflexionsbezogenen Dispositionen unterliegt. Auch kann die Qualität einer Reflexion auf mehreren Dimensionen bewertet werden, ohne quantifizierbare, absolute Aussagen treffen zu können.
Daher wurden im Rahmen einer Physik-Videovignette N = 134 schriftliche Fremdreflexionen verfasst und kontextspezifische reflexionsbezogene Dispositionen erhoben. Expert*innen erstellten theoriegeleitet Qualitätsbewertungen zur Breite, Tiefe, Kohärenz und Spezifität eines jeden Reflexionstextes. Unter Verwendung computerbasierter Klassifikations- und Analyseverfahren wurden weitere Textmerkmale erhoben. Mittels explorativer Faktorenanalyse konnten die Faktoren Qualität, Quantität und Deskriptivität gefunden werden. Da alle konventionell eingeschätzten Qualitätsbewertungen durch einen Faktor repräsentiert wurden, konnte ein maximales Qualitätskorrelat kalkuliert werden, zu welchem jede schriftliche Fremdreflexion im Rahmen der vorliegenden Vignette eine computerbasiert bestimmbare Distanz aufweist. Diese Distanz zum maximalen Qualitätskorrelat konnte validiert werden und kann die Qualität der schriftlichen Reflexionen unabhängig von menschlichen Ressourcen quantifiziert repräsentieren. Abschließend konnte identifiziert werden, dass ausgewählte Dispositionen in unterschiedlichem Maße mit der Reflexionsqualität zusammenhängen. So konnten beispielsweise bezogen auf das Physik-Fachwissen minimale Zusammenhänge identifiziert werden, wohingegen Werthaltung sowie wahrgenommene Unterrichtsqualität eng mit der Qualität einer schriftlichen Reflexion in Verbindung stehen können.
Es wird geschlussfolgert, dass reflexionsbezogene Dispositionen moderierenden Einfluss auf Reflexionen nehmen können. Es wird empfohlen bei der Erhebung von Reflexion mit dem Ziel der Kompetenzmessung ausgewählte Dispositionen mit zu erheben. Weiter verdeutlicht diese Arbeit die Möglichkeit, aussagekräftige Quantifizierungen auch in der Analyse komplexer Konstrukte vorzunehmen. Durch computerbasierte Qualitätsabschätzungen können objektive und individuelle Analysen und differenzierteres automatisiertes Feedback ermöglicht werden.
Planets outside our solar system, so-called "exoplanets", can be detected with different methods, and currently more than 5000 exoplanets have been confirmed, according to NASA Exoplanet Archive. One major highlight of the studies on exoplanets in the past twenty years is the characterization of their atmospheres usingtransmission spectroscopy as the exoplanet transits. However, this characterization is a challenging process and sometimes there are reported discrepancies in the literature regarding the atmosphere of the same exoplanet. One potential reason for the observed atmospheric inconsistencies is called impact parameter degeneracy, and it is highly driven by the limb darkening effect of the host star. A brief introductionto those topics in presented in chapter 1, while the motivation and objectives of thiswork are described in chapter 2.The first goal is to clarify the origin of the transmission spectrum, which is anindicator of an exoplanet’s atmosphere; whether it is real or influenced by the impactparameter degeneracy. A second goal is to determine whether photometry from space using the Transiting Exoplanet Survey Satellite (TESS), could improve on the major parameters, which are responsible for the aforementioned degeneracy, of known exoplanetary systems. Three individual projects were conducted in order toaddress those goals. The three manuscripts are presented, in short, in the manuscriptoverview in chapter 3.More specifically, in chapter 4, the first manuscript is presented, which is an ex-tended investigation on the impact parameter degeneracy and its application onsynthetic transmission spectra. Evidently, the limb darkening of the host star isan important driver for this effect. It keeps the degeneracy persisting through different groups of exoplanets, based on the uncertainty of their impact parameter and on the type of their host star. The second goal, was addressed in the second and third manuscripts (chapter 5 and chapter 6 respectively). Using observationsfrom the TESS mission, two samples of exoplanets were studied; 10 transiting inflated hot-Jupiters and 43 transiting grazing systems. Potentially, the refinement or confirmation of their major system parameters’ measurements can assist in solving current or future discrepancies regarding their atmospheric characterization.In chapter 7 the conclusions of this work are discussed, while in chapter 8 itis proposed how TESS’s measurements can be able to discern between erroneousinterpretations of transmission spectra, especially on systems where the impact parameter degeneracy is likely not applicable.
Control over spin and electronic structure of MoS₂ monolayer via interactions with substrates
(2023)
The molybdenum disulfide (MoS2) monolayer is a semiconductor with a direct bandgap while it is a robust and affordable material.
It is a candidate for applications in optoelectronics and field-effect transistors.
MoS2 features a strong spin-orbit coupling which makes its spin structure promising for acquiring the Kane-Mele topological concept with corresponding applications in spintronics and valleytronics.
From the optical point of view, the MoS2 monolayer features two valleys in the regions of K and K' points. These valleys are differentiated by opposite spins and a related valley-selective circular dichroism.
In this study we aim to manipulate the MoS2 monolayer spin structure in the vicinity of the K and K' points to explore the possibility of getting control over the optical and electronic properties.
We focus on two different substrates to demonstrate two distinct routes: a gold substrate to introduce a Rashba effect and a graphene/cobalt substrate to introduce a magnetic proximity effect in MoS2.
The Rashba effect is proportional to the out-of-plane projection of the electric field gradient. Such a strong change of the electric field occurs at the surfaces of a high atomic number materials and effectively influence conduction electrons as an in-plane magnetic field. A molybdenum and a sulfur are relatively light atoms, thus, similar to many other 2D materials, intrinsic Rashba effect in MoS2 monolayer is vanishing small. However, proximity of a high atomic number substrate may enhance Rashba effect in a 2D material as it was demonstrated for graphene previously.
Another way to modify the spin structure is to apply an external magnetic field of high magnitude (several Tesla), and cause a Zeeman splitting, the conduction electrons.
However, a similar effect can be reached via magnetic proximity which allows us to reduce external magnetic fields significantly or even to zero. The graphene on cobalt interface is ferromagnetic and stable for MoS2 monolayer synthesis. Cobalt is not the strongest magnet; therefore, stronger magnets may lead to more significant results.
Nowadays most experimental studies on the dichalcogenides (MoS2 included) are performed on encapsulated heterostructures that are produced by mechanical exfoliation.
While mechanical exfoliation (or scotch-tape method) allows to produce a huge variety of structures, the shape and the size of the samples as well as distance between layers in heterostructures are impossible to control reproducibly.
In our study we used molecular beam epitaxy (MBE) methods to synthesise both MoS2/Au(111) and MoS2/graphene/Co systems.
We chose to use MBE, as it is a scalable and reproducible approach, so later industry may adapt it and take over.
We used graphene/cobalt instead of just a cobalt substrate because direct contact of MoS2\ monolayer and a metallic substrate may lead to photoluminescence (PL) quenching in the metallic substrate. Graphene and hexagonal boron nitride monolayer are considered building blocks of a new generation of electronics also commonly used as encapsulating materials for PL studies. Moreover graphene is proved to be a suitable substrate for the MBE growth of transitional metal dichalcogenides (TMDCs).
In chapter 1,
we start with an introduction to TMDCs. Then we focus on MoS2 monolayer state of the art research in the fields of application scenario; synthesis approaches; electronic, spin, and optical properties; and interactions with magnetic fields and magnetic materials.
We briefly touch the basics of magnetism in solids and move on to discuss various magnetic exchange interactions and magnetic proximity effect.
Then we describe MoS2 optical properties in more detail. We start from basic exciton physics and its manifestation in the MoS2 monolayer. We consider optical selection rules in the MoS2 monolayer and such properties as chirality, spin-valley locking, and coexistence of bright and dark excitons.
Chapter 2 contains an overview of the employed surface science methods: angle-integrated, angle-resolved, and spin-resolved photoemission; low energy electron diffraction and scanning tunneling microscopy.
In chapter 3, we describe MoS2 monolayer synthesis details for two substrates: gold monocrystal with (111) surface and graphene on cobalt thin film with Co(111) surface orientation.
The synthesis descriptions are followed by a detailed characterisation of the obtained structures: fingerprints of MoS2 monolayer formation; MoS2 monolayer symmetry and its relation to the substrate below; characterisation of MoS2 monolayer coverage, domain distribution, sizes and shapes, and moire structures.
In chapter~4, we start our discussion with MoS2/Au(111) electronic and spin structure. Combining density functional theory computations (DFT) and spin-resolved photoemission studies, we demonstrate that the MoS2 monolayer band structure features an in-plane Rashba spin splitting. This confirms the possibility of MoS2 monolayer spin structure manipulation via a substrate.
Then we investigate the influence of a magnetic proximity in the MoS2/graphene/Co system on the MoS2 monolayer spin structure.
We focus our investigation on MoS2 high symmetry points: G and K.
First, using spin-resolved measurements, we confirm that electronic states are spin-split at the G point via a magnetic proximity effect. Second, combining spin-resolved measurements and DFT computations for MoS2 monolayer in the K point region, we demonstrate the appearance of a small in-plane spin polarisation in the valence band top and predict a full in-plane spin polarisation for the conduction band bottom.
We move forward discussing how these findings are related to the MoS2 monolayer optical properties, in particular the possibility of dark exciton observation. Additionally, we speculate on the control of the MoS2 valley energy via magnetic proximity from cobalt.
As graphene is spatially buffering the MoS2 monolayer from the Co thin film, we speculate on the role of graphene in the magnetic proximity transfer by replacing graphene with vacuum and other 2D materials in our computations.
We finish our discussion by investigating the K-doped MoS2/graphene/Co system and the influence of this doping on the electronic and spin structure as well as on the magnetic proximity effect.
In summary, using a scalable MBE approach we synthesised
MoS2/Au(111) and MoS2/graphene/Co systems. We found a Rashba effect taking place in MoS2/Au(111) which proves that the MoS2 monolayer in-plane spin structure can be modified. In MoS2/graphene/Co the in-plane magnetic proximity effect indeed takes place which rises the possibility of fine tuning the MoS2 optical properties via manipulation of the the substrate magnetisation.
In recent decades, astronomy has seen a boom in large-scale stellar surveys of the Galaxy. The detailed information obtained about millions of individual stars in the Milky Way is bringing us a step closer to answering one of the most outstanding questions in astrophysics: how do galaxies form and evolve? The Milky Way is the only galaxy where we can dissect many stars into their high-dimensional chemical composition and complete phase space, which analogously as fossil records can unveil the past history of the genesis of the Galaxy. The processes that lead to large structure formation, such as the Milky Way, are critical for constraining cosmological models; we call this line of study Galactic archaeology or near-field cosmology.
At the core of this work, we present a collection of efforts to chemically and dynamically characterise the disks and bulge of our Galaxy. The results we present in this thesis have only been possible thanks to the advent of the Gaia astrometric satellite, which has revolutionised the field of Galactic archaeology by precisely measuring the positions, parallax distances and motions of more than a billion stars. Another, though not less important, breakthrough is the APOGEE survey, which has observed spectra in the near-infrared peering into the dusty regions of the Galaxy, allowing us to determine detailed chemical abundance patterns in hundreds of thousands of stars. To accurately depict the Milky Way structure, we use and develop the Bayesian isochrone fitting tool/code called StarHorse; this software can predict stellar distances, extinctions and ages by combining astrometry, photometry and spectroscopy based on stellar evolutionary models. The StarHorse code is pivotal to calculating distances where Gaia parallaxes alone cannot allow accurate estimates.
We show that by combining Gaia, APOGEE, photometric surveys and using StarHorse, we can produce a chemical cartography of the Milky way disks from their outermost to innermost parts. Such a map is unprecedented in the inner Galaxy. It reveals a continuity of the bimodal chemical pattern previously detected in the solar neighbourhood, indicating two populations with distinct formation histories. Furthermore, the data reveals a chemical gradient within the thin disk where the content of 𝛼-process elements and metals is higher towards the centre. Focusing on a sample in the inner MW we confirm the extension of the chemical duality to the innermost regions of the Galaxy. We find stars with bar shape orbits to show both high- and low-𝛼 abundances, suggesting the bar formed by secular evolution trapping stars that already existed. By analysing the chemical orbital space of the inner Galactic regions, we disentangle the multiple populations that inhabit this complex region. We reveal the presence of the thin disk, thick disk, bar, and a counter-rotating population, which resembles the outcome of a perturbed proto-Galactic disk. Our study also finds that the inner Galaxy holds a high quantity of super metal-rich stars up to three times solar suggesting it is a possible repository of old super-metal-rich stars found in the solar neighbourhood.
We also enter into the complicated task of deriving individual stellar ages. With StarHorse, we calculate the ages of main-sequence turn-off and sub-giant stars for several public spectroscopic surveys. We validate our results by investigating linear relations between chemical abundances and time since the 𝛼 and neutron capture elements are sensitive to age as a reflection of the different enrichment timescales of these elements. For further study of the disks in the solar neighbourhood, we use an unsupervised machine learning algorithm to delineate a multidimensional separation of chrono-chemical stellar groups revealing the chemical thick disk, the thin disk, and young 𝛼-rich stars. The thick disk is shown to have a small age dispersion indicating its fast formation contrary to the thin disk that spans a wide range of ages.
With groundbreaking data, this thesis encloses a detailed chemo-dynamical view of the disk and bulge of our Galaxy. Our findings on the Milky Way can be linked to the evolution of high redshift disk galaxies, helping to solve the conundrum of galaxy formation.
The Antarctic ice sheet is the largest freshwater reservoir worldwide. If it were to melt completely, global sea levels would rise by about 58 m. Calculation of projections of the Antarctic contribution to sea level rise under global warming conditions is an ongoing effort which
yields large ranges in predictions. Among the reasons for this are uncertainties related to the physics of ice sheet modeling. These
uncertainties include two processes that could lead to runaway ice retreat: the Marine Ice Sheet Instability (MISI), which causes rapid grounding line retreat on retrograde bedrock, and the Marine Ice Cliff Instability (MICI), in which tall ice cliffs become unstable and calve off, exposing even taller ice cliffs.
In my thesis, I investigated both marine instabilities (MISI and MICI) using the Parallel Ice Sheet Model (PISM), with a focus on MICI.
Search for light primordial black holes with VERITAS using gamma γ-ray and optical observations
(2023)
The Very Energetic Radiation Imaging Telescope Array System (VERITAS) is an array of four imaging atmospheric Cherenkov telescopes (IACTs). VERITAS is sensitive to very-high-energy gamma-rays in the range of 100 GeV to >30 TeV. Hypothesized primordial black holes (PBHs) are attractive targets for IACTs. If they exist, their potential cosmological impact reaches beyond the candidacy for constituents of dark matter. The sublunar mass window is the largest unconstrained range of PBH masses. This thesis aims to develop novel concepts searching for light PBHs with VERITAS. PBHs below the sublunar window lose mass due to Hawking radiation. They would evaporate at the end of their lifetime, leading to a short burst of gamma-rays. If PBHs formed at about 10^15 g, the evaporation would occur nowadays. Detecting these signals might not only confirm the existence of PBHs but also prove the theory of Hawking radiation. This thesis probes archival VERITAS data recorded between 2012 and 2021 for possible PBH signals. This work presents a new automatic approach to assess the quality of the VERITAS data. The array-trigger rate and far infrared temperature are well suited to identify periods with poor data quality. These are masked by time cuts to obtain a consistent and clean dataset which contains about 4222 hours. The PBH evaporations could occur at any location in the field of view or time within this data. Only a blind search can be performed to identify these short signals. This thesis implements a data-driven deep learning based method to search for short transient signals with VERITAS. It does not depend on the modelling of the effective area and radial acceptance. This work presents the first application of this method to actual observational IACT data. This thesis develops new concepts dealing with the specifics of the data and the transient detection method. These are reflected in the developed data preparation pipeline and search strategies. After correction for trial factors, no candidate PBH evaporation is found in the data. Thus, new constraints of the local rate of PBH evaporations are derived. At the 99% confidence limit it is below <1.07 * 10^5 pc^-3 yr^-1. This constraint with the new, independent analysis approach is in the range of existing limits for the evaporation rate.
This thesis also investigates an alternative novel approach to searching for PBHs with IACTs. Above the sublunar window, the PBH abundance is constrained by optical microlensing studies. The sampling speed, which is of order of minutes to hours for traditional optical telescopes, is a limiting factor in expanding the limits to lower masses. IACTs are also powerful instruments for fast transient optical astronomy with up to O(ns) sampling. This thesis investigates whether IACTs might constrain the sublunar window with optical microlensing observations. This study confirms that, in principle, the fast sampling speed might allow extending microlensing searches into the sublunar mass window. However, the limiting factor for IACTs is the modest sensitivity to detect changes in optical fluxes. This thesis presents the expected rate of detectable events for VERITAS as well as prospects of possible future next-generation IACTs. For VERITAS, the rate of detectable microlensing events in the sublunar range is ~10^-6 per year of observation time. The future prospects for a 100 times more sensitive instrument are at ~0.05 events per year.