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Institute
- Institut für Physik und Astronomie (411) (remove)
Subject of this work is the investigation of universal scaling laws which are observed in coupled chaotic systems. Progress is made by replacing the chaotic fluctuations in the perturbation dynamics by stochastic processes. First, a continuous-time stochastic model for weakly coupled chaotic systems is introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck equation scaling relations are derived, which are confirmed by results of numerical simulations. Next, the new effect of avoided crossing of Lyapunov exponents of weakly coupled disordered chaotic systems is described, which is qualitatively similar to the energy level repulsion in quantum systems. Using the scaling relations obtained for the coupling sensitivity of chaos, an asymptotic expression for the distribution function of small spacings between Lyapunov exponents is derived and compared with results of numerical simulations. Finally, the synchronization transition in strongly coupled spatially extended chaotic systems is shown to resemble a continuous phase transition, with the coupling strength and the synchronization error as control and order parameter, respectively. Using results of numerical simulations and theoretical considerations in terms of a multiplicative noise partial differential equation, the universality classes of the observed two types of transition are determined (Kardar-Parisi-Zhang equation with saturating term, directed percolation).
In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find various applications in natural sciences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Another part deals with Hamiltonian lattices. Here, a prominent example in which compactons can be found is the granular chain. In the third part, we study systems which are related to the discrete nonlinear Schrödinger equation describing, for example, coupled optical wave-guides or the dynamics of Bose-Einstein condensates in optical lattices. Our investigations are based on a numerical method to solve the traveling wave equation. This results in a quasi-exact solution (up to numerical errors) which is the compacton. Another ansatz which is employed throughout this work is the quasi-continuous approximation where the lattice is described by a continuous medium. Here, compactons are found analytically, but they are defined on a truly compact support. Remarkably, both ways give similar qualitative and quantitative results. Additionally, we study the dynamical properties of compactons by means of numerical simulation of the lattice equations. Especially, we concentrate on their emergence from physically realizable initial conditions as well as on their stability due to collisions. We show that the collisions are not exactly elastic but that a small part of the energy remains at the location of the collision. In finite lattices, this remaining part will then trigger a multiple scattering process resulting in a chaotic state.
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.
Since their discovery in 1610 by Galileo Galilei, Saturn's rings continue to fascinate both experts and amateurs. Countless numbers of icy grains in almost Keplerian orbits reveal a wealth of structures such as ringlets, voids and gaps, wakes and waves, and many more. Grains are found to increase in size with increasing radial distance to Saturn. Recently discovered "propeller" structures in the Cassini spacecraft data, provide evidence for the existence of embedded moonlets. In the wake of these findings, the discussion resumes about origin and evolution of planetary rings, and growth processes in tidal environments. In this thesis, a contact model for binary adhesive, viscoelastic collisions is developed that accounts for agglomeration as well as restitution. Collisional outcomes are crucially determined by the impact speed and masses of the collision partners and yield a maximal impact velocity at which agglomeration still occurs. Based on the latter, a self-consistent kinetic concept is proposed. The model considers all possible collisional outcomes as there are coagulation, restitution, and fragmentation. Emphasizing the evolution of the mass spectrum and furthermore concentrating on coagulation alone, a coagulation equation, including a restricted sticking probability is derived. The otherwise phenomenological Smoluchowski equation is reproduced from basic principles and denotes a limit case to the derived coagulation equation. Qualitative and quantitative analysis of the relevance of adhesion to force-free granular gases and to those under the influence of Keplerian shear is investigated. Capture probability, agglomerate stability, and the mass spectrum evolution are investigated in the context of adhesive interactions. A size dependent radial limit distance from the central planet is obtained refining the Roche criterion. Furthermore, capture probability in the presence of adhesion is generally different compared to the case of pure gravitational capture. In contrast to a Smoluchowski-type evolution of the mass spectrum, numerical simulations of the obtained coagulation equation revealed, that a transition from smaller grains to larger bodies cannot occur via a collisional cascade alone. For parameters used in this study, effective growth ceases at an average size of centimeters.
The theory of atomic Boson-Fermion mixtures in the dilute limit beyond mean-field is considered in this thesis. Extending the formalism of quantum field theory we derived expressions for the quasi-particle excitation spectra, the ground state energy, and related quantities for a homogenous system to first order in the dilute gas parameter. In the framework of density functional theory we could carry over the previous results to inhomogeneous systems. We then determined to density distributions for various parameter values and identified three different phase regions: (i) a stable mixed regime, (ii) a phase separated regime, and (iii) a collapsed regime. We found a significant contribution of exchange-correlation effects in the latter case. Next, we determined the shift of the Bose-Einstein condensation temperature caused by Boson-Fermion interactions in a harmonic trap due to redistribution of the density profiles. We then considered Boson-Fermion mixtures in optical lattices. We calculated the criterion for stability against phase separation, identified the Mott-insulating and superfluid regimes both, analytically within a mean-field calculation, and numerically by virtue of a Gutzwiller Ansatz. We also found new frustrated ground states in the limit of very strong lattices. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2004 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
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.
The topic of synchronization forms a link between nonlinear dynamics and neuroscience. On the one hand, neurobiological research has shown that the synchronization of neuronal activity is an essential aspect of the working principle of the brain. On the other hand, recent advances in the physical theory have led to the discovery of the phenomenon of phase synchronization. A method of data analysis that is motivated by this finding - phase synchronization analysis - has already been successfully applied to empirical data. The present doctoral thesis ties up to these converging lines of research. Its subject are methodical contributions to the further development of phase synchronization analysis, as well as its application to event-related potentials, a form of EEG data that is especially important in the cognitive sciences. The methodical contributions of this work consist firstly in a number of specialized statistical tests for a difference in the synchronization strength in two different states of a system of two oscillators. Secondly, in regard of the many-channel character of EEG data an approach to multivariate phase synchronization analysis is presented. For the empirical investigation of neuronal synchronization a classic experiment on language processing was replicated, comparing the effect of a semantic violation in a sentence context with that of the manipulation of physical stimulus properties (font color). Here phase synchronization analysis detects a decrease of global synchronization for the semantic violation as well as an increase for the physical manipulation. In the latter case, by means of the multivariate analysis the global synchronization effect can be traced back to an interaction of symmetrically located brain areas.<BR> The findings presented show that the method of phase synchronization analysis motivated by physics is able to provide a relevant contribution to the investigation of event-related potentials in the cognitive sciences.
Galaxies are among the most complex systems that can currently be modelled with a computer. A realistic simulation must take into account cosmology and gravitation as well as effects of plasma, nuclear, and particle physics that occur on very different time, length, and energy scales. The Milky Way is the ideal test bench for such simulations, because we can observe millions of its individual stars whose kinematics and chemical composition are records of the evolution of our Galaxy. Thanks to the advent of multi-object spectroscopic surveys, we can systematically study stellar populations in a much larger volume of the Milky Way. While the wealth of new data will certainly revolutionise our picture of the formation and evolution of our Galaxy and galaxies in general, the big-data era of Galactic astronomy also confronts us with new observational, theoretical, and computational challenges.
This thesis aims at finding new observational constraints to test Milky-Way models, primarily based on infra-red spectroscopy from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and asteroseismic data from the CoRoT mission. We compare our findings with chemical-evolution models and more sophisticated chemodynamical simulations. In particular we use the new powerful technique of combining asteroseismic and spectroscopic observations that allows us to test the time dimension of such models for the first time. With CoRoT and APOGEE (CoRoGEE) we can infer much more precise ages for distant field red-giant stars, opening up a new window for Galactic archaeology.
Another important aspect of this work is the forward-simulation approach that we pursued when interpreting these complex datasets and comparing them to chemodynamical models.
The first part of the thesis contains the first chemodynamical study conducted with the APOGEE survey. Our sample comprises more than 20,000 red-giant stars located within 6 kpc from the Sun, and thus greatly enlarges the Galactic volume covered with high-resolution spectroscopic observations. Because APOGEE is much less affected by interstellar dust extinction, the sample covers the disc regions very close to the Galactic plane that are typically avoided by optical surveys. This allows us to investigate the chemo-kinematic properties of the Milky Way's thin disc outside the solar vicinity. We measure, for the first time with high-resolution data, the radial metallicity gradient of the disc as a function of distance from the Galactic plane, demonstrating that the gradient flattens and even changes its sign for mid-plane distances greater than 1 kpc.
Furthermore, we detect a gap between the high- and low-[$\alpha$/Fe] sequences in the chemical-abundance diagram (associated with the thin and thick disc) that unlike in previous surveys can hardly be explained by selection effects. Using 6D kinematic information, we also present chemical-abundance diagrams cleaned from stars on kinematically hot orbits. The data allow us to confirm without doubt that the scale length of the (chemically-defined) thick disc is significantly shorter than that of the thin disc.
In the second part, we present our results of the first combination of asteroseismic and spectroscopic data in the context of Galactic Archaeology. We analyse APOGEE follow-up observations of 606 solar-like oscillating red giants in two CoRoT fields close to the Galactic plane. These stars cover a large radial range of the Galactic disc (4.5 kpc $\lesssim R_{\rm Gal}\lesssim15$ kpc) and a large age baseline (0.5 Gyr $\lesssim \tau\lesssim$ 13 Gyr), allowing us to study the age- and radius-dependence of the [$\alpha$/Fe] vs. [Fe/H] distributions. We find that the age distribution of the high-[$\alpha$/Fe] sequence appears to be broader than expected from a monolithically-formed old thick disc that stopped to form stars 10 Gyr ago. In particular, we discover a significant population of apparently young, [$\alpha$/Fe]-rich stars in the CoRoGEE data whose existence cannot be explained by standard chemical-evolution models. These peculiar stars are much more abundant in the inner CoRoT field LRc01 than in the outer-disc field LRc01, suggesting that at least part of this population has a chemical-evolution rather than a stellar-evolution origin, possibly due to a peculiar chemical-enrichment history of the inner disc. We also find that strong radial migration is needed to explain the abundance of super-metal-rich stars in the outer disc.
Finally, we use the CoRoGEE sample to study the time evolution of the radial metallicity gradient in the thin disc, an observable that has been the subject of observational and theoretical debate for more than 20 years. By dividing the CoRoGEE dataset into six age bins, performing a careful statistical analysis of the radial [Fe/H], [O/H], and [Mg/Fe] distributions, and accounting for the biases introduced by the observation strategy, we obtain reliable gradient measurements. The slope of the radial [Fe/H] gradient of the young red-giant population ($-0.058\pm0.008$ [stat.] $\pm0.003$ [syst.] dex/kpc) is consistent with recent Cepheid data. For the age range of $1-4$ Gyr, the gradient steepens slightly ($-0.066\pm0.007\pm0.002$ dex/kpc), before flattening again to reach a value of $\sim-0.03$ dex/kpc for stars with ages between 6 and 10 Gyr. This age dependence of the [Fe/H] gradient can be explained by a nearly constant negative [Fe/H] gradient of $\sim-0.07$ dex/kpc in the interstellar medium over the past 10 Gyr, together with stellar heating and migration. Radial migration also offers a new explanation for the puzzling observation that intermediate-age open clusters in the solar vicinity (unlike field stars) tend to have higher metallicities than their younger counterparts. We suggest that non-migrating clusters are more likely to be kinematically disrupted, which creates a bias towards high-metallicity migrators from the inner disc and may even steepen the intermediate-age cluster abundance gradient.
Gravitational-wave (GW) astrophysics is a field in full blossom. Since the landmark detection of GWs from a binary black hole on September 14th 2015, fifty-two compact-object binaries have been reported by the LIGO-Virgo collaboration. Such events carry astrophysical and cosmological information ranging from an understanding of how black holes and neutron stars are formed, what neutron stars are composed of, how the Universe expands, and allow testing general relativity in the highly-dynamical strong-field regime. It is the goal of GW astrophysics to extract such information as accurately as possible. Yet, this is only possible if the tools and technology used to detect and analyze GWs are advanced enough. A key aspect of GW searches are waveform models, which encapsulate our best predictions for the gravitational radiation under a certain set of parameters, and that need to be cross-correlated with data to extract GW signals. Waveforms must be very accurate to avoid missing important physics in the data, which might be the key to answer the fundamental questions of GW astrophysics. The continuous improvements of the current LIGO-Virgo detectors, the development of next-generation ground-based detectors such as the Einstein Telescope or the Cosmic Explorer, as well as the development of the Laser Interferometer Space Antenna (LISA), demand accurate waveform models. While available models are enough to capture the low spins, comparable-mass binaries routinely detected in LIGO-Virgo searches, those for sources from both current and next-generation ground-based and spaceborne detectors must be accurate enough to detect binaries with large spins and asymmetry in the masses. Moreover, the thousands of sources that we expect to detect with future detectors demand accurate waveforms to mitigate biases in the estimation of signals’ parameters due to the presence of a foreground of many sources that overlap in the frequency band. This is recognized as one of the biggest challenges for the analysis of future-detectors’ data, since biases might hinder the extraction of important astrophysical and cosmological information from future detectors’ data. In the first part of this thesis, we discuss how to improve waveform models for binaries with high spins and asymmetry in the masses. In the second, we present the first generic metrics that have been proposed to predict biases in the presence of a foreground of many overlapping signals in GW data.
For the first task, we will focus on several classes of analytical techniques. Current models for LIGO and Virgo studies are based on the post-Newtonian (PN, weak-field, small velocities) approximation that is most natural for the bound orbits that are routinely detected in GW searches. However, two other approximations have risen in prominence, the post-Minkowskian (PM, weak- field only) approximation natural for unbound (scattering) orbits and the small-mass-ratio (SMR) approximation typical of binaries in which the mass of one body is much bigger than the other. These are most appropriate to binaries with high asymmetry in the masses that challenge current waveform models. Moreover, they allow one to “cover” regions of the parameter space of coalescing binaries, thereby improving the interpolation (and faithfulness) of waveform models. The analytical approximations to the relativistic two-body problem can synergically be included within the effective-one-body (EOB) formalism, in which the two-body information from each approximation can be recast into an effective problem of a mass orbiting a deformed Schwarzschild (or Kerr) black hole. The hope is that the resultant models can cover both the low-spin comparable-mass binaries that are routinely detected, and the ones that challenge current models. The first part of this thesis is dedicated to a study about how to best incorporate information from the PN, PM, SMR and EOB approaches in a synergistic way. We also discuss how accurate the resulting waveforms are, as compared against numerical-relativity (NR) simulations. We begin by comparing PM models, whether alone or recast in the EOB framework, against PN models and NR simulations. We will show that PM information has the potential to improve currently-employed models for LIGO and Virgo, especially if recast within the EOB formalism. This is very important, as the PM approximation comes with a host of new computational techniques from particle physics to exploit. Then, we show how a combination of PM and SMR approximations can be employed to access previously-unknown PN orders, deriving the third subleading PN dynamics for spin-orbit and (aligned) spin1-spin2 couplings. Such new results can then be included in the EOB models currently used in GW searches and parameter estimation studies, thereby improving them when the binaries have high spins. Finally, we build an EOB model for quasi-circular nonspinning binaries based on the SMR approximation (rather than the PN one as usually done). We show how this is done in detail without incurring in the divergences that had affected previous attempts, and compare the resultant model against NR simulations. We find that the SMR approximation is an excellent approximation for all (quasi-circular nonspinning) binaries, including both the equal-mass binaries that are routinely detected in GW searches and the ones with highly asymmetric masses. In particular, the SMR-based models compare much better than the PN models, suggesting that SMR-informed EOB models might be the key to model binaries in the future. In the second task of this thesis, we work within the linear-signal ap- proximation and describe generic metrics to predict inference biases on the parameters of a GW source of interest in the presence of confusion noise from unfitted foregrounds and from residuals of other signals that have been incorrectly fitted out. We illustrate the formalism with simple (yet realistic) LISA sources, and demonstrate its validity against Monte-Carlo simulations. The metrics we describe pave the way for more realistic studies to quantify the biases with future ground-based and spaceborne detectors.
During a dark night, it is possible to observe thousands of stars by eye. All these stars are located within the Milky Way, our home. Not all stars are the same, they can have different sizes, masses, temperatures and ages. Heavy stars do not live long (in astronomical terms), only a few million years, but stars less massive than the Sun can get more than ten billion years old. Such small stars that formed in the beginning of the Universe still shine today. These ancient stars are very helpful to learn more about the early Universe, the First Stars and the history of the Milky Way. But how do you recognise an ancient star? Using their chemical fingerprints! In the beginning of the Universe, there were only two chemical elements: hydrogen and helium (and a tiny bit of lithium). All the heavier elements like carbon, calcium and iron were only made later within stars and their explosions. The amount of chemical elements in the Universe increases with the number of stars that are born, evolve and explode. Stars that form later are born with more heavy elements, or a greater metallicity. In the field of astronomy that is called “Galactic Archaeology”, stars of various metallicities are used to study the history of the Milky Way. In this doctoral thesis, the focus is on metal-poor stars because these are expected to be the oldest and can therefore tell us a lot about the early history of our Galaxy.
Until today, we still have not discovered a metal-free star. The most metal-poor stars, however, give us important insights in the lives and deaths of the First Stars. Many of the oldest, most metal-poor stars have an unexpectedly large amount of carbon, compared to for example iron. These carbon-enhanced metal-poor (CEMP) stars tell us something about the very first stars in the Universe: they somehow produced a lot of carbon. If we look at the precise chemical fingerprints of the CEMP stars, we can learn a lot more. But our interpretation depends on the assumption that the chemical fingerprint of a star does not change during its life. In this thesis, new data is presented that shows that this assumption may be too simple: many extremely metal-poor CEMP stars are members of binary systems. Interactions between two stars in a binary system can pollute the surface of the stars. Likely not all of the CEMP stars in binary systems were actually polluted, but we should be very careful in our interpretations of the fingerprints of these stars.
The CEMP stars and other metal-poor stars are also important for our understanding of the early history of the Milky Way. Most researchers who study metal-poor stars look for these stars in the halo of the Milky Way: a huge diffuse Galactic component containing about 1% of the stars in our Galaxy. However, models predict that the oldest metal-poor stars are located in the center of the Milky Way, in the bulge. The metal-poor inner Galaxy is unfortunately difficult to study due to large amounts of dust between us and the center and an overwhelming majority of metal-rich stars. This thesis presents results from the successful Pristine Inner Galaxy Survey (PIGS), a new survey looking for (and finding) the oldest stars in the bulge of the Milky Way. PIGS is using images with a specific color that is sensitive to the metallicity of stars, and can therefore efficiently select the metal-poor stars among millions of other, more metal-rich stars. The interesting candidates are followed up with spectroscopy, which is then analysed using two independent methods. With this strategy, PIGS has discovered the largest sample of metal-poor stars in the inner Galaxy to date. A new result from the PIGS data is that the metal-poor stars rotate more slowly around the Galactic center compared to the more metal-rich stars, and they show larger randomness in their motions as well. Another important contribution from PIGS is the discovery of tens of CEMP stars in the inner Galaxy, where previously only two such stars were known.
The new results from this thesis help us to understand the First Stars and the early history of the Milky Way. Ongoing and future large surveys will provide us with a lot of additional data in the coming years. It is an exciting time for the field of Galactic Archaeology.