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Optical frequency combs (OFC) constitute an array of phase-correlated equidistant spectral lines with nearly equal intensities over a broad spectral range. The adaptations of combs generated in mode-locked lasers proved to be highly efficient for the calibration of high-resolution (resolving power > 50000) astronomical spectrographs. The observation of different galaxy structures or the studies of the Milky Way are done using instruments in the low- and medium resolution range. To such instruments belong, for instance, the Multi Unit Spectroscopic Explorer (MUSE) being developed for the Very Large Telescope (VLT) of the European Southern Observatory (ESO) and the 4-metre Multi-Object Spectroscopic Telescope (4MOST) being in development for the ESO VISTA 4.1 m Telescope. The existing adaptations of OFC from mode-locked lasers are not resolvable by these instruments.
Within this work, a fibre-based approach for generation of OFC specifically in the low- and medium resolution range is studied numerically. This approach consists of three optical fibres that are fed by two equally intense continuous-wave (CW) lasers. The first fibre is a conventional single-mode fibre, the second one is a suitably pumped amplifying Erbium-doped fibre with anomalous dispersion, and the third one is a low-dispersion highly nonlinear optical fibre. The evolution of a frequency comb in this system is governed by the following processes: as the two initial CW-laser waves with different frequencies propagate through the first fibre, they generate an initial comb via a cascade of four-wave mixing processes. The frequency components of the comb are phase-correlated with the original laser lines and have a frequency spacing that is equal to the initial laser frequency separation (LFS), i.e. the difference in the laser frequencies. In the time domain, a train of pre-compressed pulses with widths of a few pico-seconds arises out of the initial bichromatic deeply-modulated cosine-wave. These pulses undergo strong compression in the subsequent amplifying Erbium-doped fibre: sub-100 fs pulses with broad OFC spectra are formed. In the following low-dispersion highly nonlinear fibre, the OFC experience a further broadening and the intensity of the comb lines are fairly equalised. This approach was mathematically modelled by means of a Generalised Nonlinear Schrödinger Equation (GNLS) that contains terms describing the nonlinear optical Kerr effect, the delayed Raman response, the pulse self-steepening, and the linear optical losses as well as the wavelength-dependent Erbium gain profile for the second fibre. The initial condition equation being a deeply-modulated cosine-wave mimics the radiation of the two initial CW lasers. The numerical studies are performed with the help of Matlab scripts that were specifically developed for the integration of the GNLS and the initial condition according to the proposed approach for the OFC generation. The scripts are based on the Fourth-Order Runge-Kutta in the Interaction Picture Method (RK4IP) in combination with the local error method.
This work includes the studies and results on the length optimisation of the first and the second fibre depending on different values of the group-velocity dispersion of the first fibre. Such length optimisation studies are necessary because the OFC have the biggest possible broadband and exhibit a low level of noise exactly at the optimum lengths. Further, the optical pulse build-up in the first and the second fibre was studied by means of the numerical technique called Soliton Radiation Beat Analysis (SRBA). It was shown that a common soliton crystal state is formed in the first fibre for low laser input powers. The soliton crystal continuously dissolves into separated optical solitons as the input power increases. The pulse formation in the second fibre is critically dependent on the features of the pulses formed in the first fibre. I showed that, for low input powers, an adiabatic soliton compression delivering low-noise OFC occurs in the second fibre. At high input powers, the pulses in the first fibre have more complicated structures which leads to the pulse break-up in the second fibre with a subsequent degradation of the OFC noise performance. The pulse intensity noise studies that were performed within the framework of this thesis allow making statements about the noise performance of an OFC. They showed that the intensity noise of the whole system decreases with the increasing value of LFS.
We compute spectral libraries for populations of coeval stars using state-of-the-art massive-star evolutionary tracks that account for different astrophysics including rotation and close-binarity. Our synthetic spectra account for stellar and nebular contributions. We use our models to obtain E(B – V ), age, and mass for six clusters in spiral galaxy NGC 1566, which have ages of < 50 Myr and masses of > 5 x 104M⊙ according to standard models. NGC 1566 was observed from the NUV to the I-band as part of the imaging Treasury HST program LEGUS: Legacy Extragalactic UV Survey. We aim to establish i) if the models provide reasonable fits to the data, ii) how well the models and photometry are able to constrain the cluster properties, and iii) how different the properties obtained with different models are.
Observations of the WC9+OB system WR65 in the infrared show variations of its dust emission consistent with a period near 4.8 yr, suggesting formation in a colliding-wind binary (CWB) having an elliptical orbit. If we adopt the IR maximum as zero phase, the times of X-ray maximum count and minimum extinction to the hard component measured by Oskinova & Hamann fall at phases 0.4–0.5, when the separation of the WC9 and OB stars is greatest. We consider WR65 in the context of other WC8–9+OB stars showing dust emission.
The origin of cosmic rays was the subject of several studies for over a century. The investigations done within this dissertation are one small step to shed some more light on this mystery.
Locating the sources of cosmic rays is not trivial due to the interstellar magnetic field. However, the Hillas criterion allows us to arrive at the conclusion that supernova remnants are our main suspect for the origin of galactic cosmic rays. The mechanism by which they are accelerating particles is found within the field of shock physics as diffusive shock acceleration. To allow particles to enter this process also known as Fermi acceleration pre-acceleration processes like shock surfing acceleration and shock drift acceleration are necessary. Investigating the processes happening in the plasma shocks of supernova remnants is possible by utilising a simplified model which can be simulated on a computer using Particle-in-Cell simulations.
We developed a new and clean setup to simulate the formation of a double shock, i.e., consisting of a forward and a reverse shock and a contact discontinuity, by the collision of two counter-streaming plasmas, in which a magnetic field can be woven into. In a previous work, we investigated the processes at unmagnetised and at magnetised parallel shocks, whereas in the current work, we move our investigation on to magnetised perpendicular shocks.
Due to a much stronger confinement of the particles to the collision region the perpendicular shock develops much faster than the parallel shock. On the other hand, this leads to much weaker turbulence. We are able to find indications for shock surfing acceleration and shock drift acceleration happening at the two shocks leading to populations of pre-accelerated particles that are suitable as a seed population to be injected into further diffusive shock acceleration to be accelerated to even higher energies. We observe the development of filamentary structures in the shock ramp of the forward shock, but not at the reverse shock. This leads to the conclusion that the development of such structures in the shock ramp of quasi-perpendicular collisionless shocks might not necessarily be determined by the existence of a critical sonic Mach number but by a critical shock speed.
The results of the investigations done within this dissertation might be useful for further studies of oblique shocks and for studies using hybrid or magnetohydrodynamic simulations. Together with more sophisticated observational methods, these studies will help to bring us closer to an answer as to how particles can be accelerated in supernova remnants and eventually become cosmic rays that can be detected on Earth.
Luminous Blue Variables (LBVs) are stars is a transitional phase massive stars may enter while evolving from main-sequence to Wolf-Rayet stars. The to LBVs intrinsic photometric variability is based on the modulation of the stellar spectrum. Within a few years the spectrum shifts from OB to AF type and back. During their cool phase LBVs are close to the Humphreys-Davidson (equivalent to Eddington/Omega-Gamma) limit. LBVs have a rather high mass loss rate, with stellar winds that are fast in the hot and slower in the cool phase of an LBV. These alternating wind velocities lead to the formation of LBV nebulae by wind-wind interactions. A nebula can also be formed in a spontaneous giant eruption in which larger amounts of mass are ejected. LBV nebulae are generally small (< 5 pc) mainly gaseous circumstellar nebulae, with a rather large fraction of LBV nebulae being bipolar. After the LBV phase the star will turn into a Wolf-Rayet star, but note that not all WR stars need to have passed the LBV phase. Some follow from the RSG and the most massive directly from the MS phase. In general WRs have a large mass loss and really fast stellar winds. The WR wind may interact with winds of earlier phases (MS, RSG) to form WR nebulae. As for WR with LBV progenitors the scenario might be different, here no older wind is present but an LBV nebula! The nature of WR nebulae are therefore manifold and in particular the connection (or family ties) of WR to LBV nebulae is important to understand the transition between these two phases, the evolution of massive stars, their winds, wind-wind and wind-nebula interactions. Looking at the similarities and differences of LBV and WR nebula, figuring what is a genuine LBV and WR nebula are the basic question addressed in the analysis presented here.
The interaction between massive star formation and gas is a key ingredient in galaxy evolution. Given the level of observational detail currently achievable in nearby starbursts, they constitute ideal laboratories to study interaction process that contribute to global evolution in all types of galaxies. Wolf-Rayet (WR) stars, as an observational marker of high mass star formation, play a pivotal role and their winds can strongly influence the surrounding gas. Imaging spectroscopy of two nearby (<4 Mpc) starbursts, both of which show multiple regions with WR stars, are discussed. The relation between the WR content and the physical and chemical properties of the surrounding ionized gas is explored.
Synchronization of large ensembles of oscillators is an omnipresent phenomenon observed in different fields of science like physics, engineering, life sciences, etc. The most simple setup is that of globally coupled phase oscillators, where all the oscillators contribute to a global field which acts on all oscillators. This formulation of the problem was pioneered by Winfree and Kuramoto. Such a setup gives a possibility for the analysis of these systems in terms of global variables. In this work we describe nontrivial collective dynamics in oscillator populations coupled via mean fields in terms of global variables. We consider problems which cannot be directly reduced to standard Kuramoto and Winfree models.
In the first part of the thesis we adopt a method introduced by Watanabe and Strogatz. The main idea is that the system of identical oscillators of particular type can be described by a low-dimensional system of global equations. This approach enables us to perform a complete analytical analysis for a special but vast set of initial conditions. Furthermore, we show how the approach can be expanded for some nonidentical systems. We apply the Watanabe-Strogatz approach to arrays of Josephson junctions and systems of identical phase oscillators with leader-type coupling.
In the next parts of the thesis we consider the self-consistent mean-field theory method that can be applied to general nonidentical globally coupled systems of oscillators both with or without noise. For considered systems a regime, where the global field rotates uniformly, is the most important one. With the help of this approach such solutions of the self-consistency equation for an arbitrary distribution of frequencies and coupling parameters can be found analytically in the parametric form, both for noise-free and noisy cases.
We apply this method to deterministic Kuramoto-type model with generic coupling and an ensemble of spatially distributed oscillators with leader-type coupling. Furthermore, with the proposed self-consistent approach we fully characterize rotating wave solutions of noisy Kuramoto-type model with generic coupling and an ensemble of noisy oscillators with bi-harmonic coupling.
Whenever possible, a complete analysis of global dynamics is performed and compared with direct numerical simulations of large populations.
The Wolf-Rayet (WR) phenomenon is widespread in astronomy. It involves classical WRs, very massive stars (VMS), WR central stars of planetary nebula CSPN [WRs], and supernovae (SNe). But what is the root cause for a certain type of object to turn into an emission-line star? In this contribution, I discuss the basic aspects of radiation-driven winds that might reveal the ultimate difference between WR stars and canonical O-type stars. I discuss the aspects of (i) self-enrichment via CNO elements, (ii) high effective temperatures (Tₑff), (iii) an increase in the helium abundance (Y ), and finally (iv) the Eddington factor Γₑ. Over the last couple of years, we have made a breakthrough in our understanding of Γₑ -dependent mass loss, which will have far-reaching consequences for the evolution and fate of the most massive stars in the Universe. Finally, I discuss the prospects for studies of the WR phenomenon in the highest redshift Lyα and He ii emitting galaxies.
We first give a short historical overview with some key facts of massive star population synthesis with binaries. We then discuss binary population codes and focus on two ingredients which are important for massive star population synthesis and which may be different in different codes. Population simulations with binaries is the third part where we consider the initial massive binary frequency, the RSG/WR and WC/WN and SNII/SNIbc number ratio's, the probable initial rotational velocity distribution of massive stars.
The enigmatic oxygen-sequence Wolf-Rayet stars represent a rare stage in the evolution of massive stars. Their properties can provide unique constraints on the pre-supernova evolution of massive stars. This work presents the results of a quantitative spectroscopic analysis of the known single WO stars, with the aim to obtain the key stellar parameters and deduce their evolutionary state.X-Shooter spectra of the WO stars are modeled using the line-blanketed non-local thermal equilibrium atmosphere code cmfgen. The obtained stellar parameters show that the WO stars are very hot, with temperatures ranging from 150 kK to 210 kK. Their chemical composition is dominated by carbon (>50%), while the helium mass fraction is very low (down to 14%). Oxygen mass fractions reach as high as 25%. These properties can be reproduced with dedicated evolutionary models for helium stars, which show that the stars are post core-helium burning and very close to their eventual supernova explosion. The helium-star masses indicate initial masses or approximately 40 - 60M⊙.Thus, WO stars represent the final evolutionary stage of stars with estimated initial masses of 40 - 60M⊙. They are post core-helium burning and may explode as type Ic supernovae within a few thousand years.