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Institute
- Institut für Physik und Astronomie (641) (remove)
Stellar magnetic fields, as a crucial component of star formation and evolution, evade direct observation at least with current and near future instruments. However investigating whether magnetic fields are generated by a dynamo process or represent relics from the formation process, or whether they show a behavior similar to the sun or something very different, it is essential to investigate their structure and temporal evolution. Fortunately nature provides us with the possibility to indirectly observe surface topologies on distant stars by means of Doppler shift and polarization of light, though not without its challenges. Based on the mentioned effects, the so called Zeeman-Doppler Imaging technique is a powerful method to retrieve magnetic fields from rapid rotating stars based on measurements of spectropolarimetric observations in terms of Stokes profiles. In recent years, a large number of stellar magnetic field distributions could be reconstructed by Zeeman-Doppler Imaging (ZDI). However, the implementation of this method often relies on many approximations because, as an inversion method, it entails enormous computational requirements. The aim of this thesis is to develop methods for a ZDI, designed to invert time-resolved spectropolarimetric data of active late type stars, and to account for the expected complex and small scale magnetic fields on these stars. In order to reliably reconstruct the detailed field orientation and strength, the inversion method is employed to be able to use of all four Stokes components. Furthermore it is based on fully polarized radiative transfer calculations to account for the intricate interplay between temperature and magnetic field. Finally, the application of a newly developed ZDI code to Stokes I and V observations of II Pegasi (short: II Peg) was supposed to deliver the first magnetic surface maps for this highly active star. To accomplish the high computational burden of a radiative transfer based ZDI, we developed a novel approximation method to speed up the inversion process. It is based on Principal Component Analysis and Artificial Neural Networks. The latter approximate the functional mapping between atmospheric parameters and the corresponding local Stokes profiles. Inverse problems, as we are dealing with, are potentially ill-posed and require a regularization method. We propose a new regularization scheme, which implements a local entropy function that accounts for the peculiarities of the reconstruction of localized magnetic fields. To deal with the relatively large noise that is always present in polarimetric data, we developed a multi-line denoising technique based on Principal Component Analysis. In contrast to other multi-line techniques that extract from a large number of spectral lines a sort of mean profile, this method allows to extract individual spectral lines and thus allows for an inversion on the basis of specific lines. All these methods are incorporated in our newly developed ZDI code iMap, which is based on a conjugated gradient method. An in depth validation of our new synthesis method demonstrates the reliability and accuracy of this approach as well as a gain in computation time by almost three orders of magnitude relative to the conventional radiative transfer calculations. We investigated the influence of the different Stokes components (IV / IVQU) on the ability to reconstruct a known synthetic field configuration. In doing so we validate the capability of our inversion code, and we also assess limitations of magnetic field inversions in general. In a first application to II Peg, a K2 IV subgiant, we derived temperature and magnetic field surface distributions from spectropolarimetric data obtained in 2004 and 2007. It gives for the first time simultaneously the temporal evolution of the surface temperature and magnetic field distribution on II Peg.
X-ray spectroscopy is a sensitive probe of stellar winds. X-rays originate from optically thin shock-heated plasma deep inside the wind and propagate outwards throughout absorbing cool material. Recent analyses of the line ratios from He-like ions in the X-ray spectra of O-stars highlighted problems with this general paradigm: the measured line ratios of highest ions are consistent with the location of the hottest X-ray emitting plasma very close to the base of the wind, perhaps indicating the presence of a corona, while measurements from lower ions conform with the wind-embedded shock model. Generally, to correctly model the emerging Xray spectra, a detailed knowledge of the cool wind opacities based on stellar atmosphere models is prerequisite. A nearly grey stellar wind opacity for the X-rays is deduced from the analyses of high-resolution X-ray spectra. This indicates that the stellar winds are strongly clumped. Furthermore, the nearly symmetric shape of X-ray emission line profiles can be explained if the wind clumps are radially compressed. In massive binaries the orbital variations of X-ray emission allow to probe the opacity of the stellar wind; results support the picture of strong wind clumping. In high-mass X-ray binaries, the stochastic X-ray variability and the extend of the stellar-wind part photoionized by X-rays provide further strong evidence that stellar winds consist of dense clumps.
X-rays are integral to furthering our knowledge of exoplanetary systems. In this work we discuss the use of X-ray observations to understand star-planet interac- tions, mass-loss rates of an exoplanet’s atmosphere and the study of an exoplanet’s atmospheric components using future X-ray spectroscopy.
The low-mass star GJ 1151 was reported to display variable low-frequency radio emission, which is an indication of coronal star-planet interactions with an unseen exoplanet. In chapter 5 we report the first X-ray detection of GJ 1151’s corona based on XMM-Newton data. Averaged over the observation, we detect the star with a low coronal temperature of 1.6 MK and an X-ray luminosity of LX = 5.5 × 1026 erg/s. This is compatible with the coronal assumptions for a sub-Alfvénic star- planet interaction origin of the observed radio signals from this star.
In chapter 6, we aim to characterise the high-energy environment of known ex- oplanets and estimate their mass-loss rates. This work is based on the soft X-ray instrument on board the Spectrum Roentgen Gamma (SRG) mission, eROSITA, along with archival data from ROSAT, XMM-Newton, and Chandra. We use these four X-ray source catalogues to derive X-ray luminosities of exoplanet host stars in the 0.2-2 keV energy band. A catalogue of the mass-loss rates of 287 exoplan- ets is presented, with 96 of these planets characterised for the first time using new eROSITA detections. Of these first time detections, 14 are of transiting exoplanets that undergo irradiation from their host stars that is of a level known to cause ob- servable evaporation signals in other systems, making them suitable for follow-up observations.
In the next generation of space observatories, X-ray transmission spectroscopy of an exoplanet’s atmosphere will be possible, allowing for a detailed look into the atmospheric composition of these planets. In chapter 7, we model sample spectra using a toy model of an exoplanetary atmosphere to predict what exoplanet transit observations with future X-ray missions such as Athena will look like. We then estimate the observable X-ray transmission spectrum for a typical Hot Jupiter-type exoplanet, giving us insights into the advances in X-ray observations of exoplanets in the decades to come.
In this review I briefly summarize our knowledge of the X-ray emission from single WN, WC, and WO stars. These stars have relatively modest X-ray luminosities, typically not exceeding 1L⊙. The analysis of X-ray spectra usually reveals thermal plasma with temperatures reaching a few x10 MK. X-ray variability is detected in some WN stars. At present we don't fully understand how X-ray radiation in produced in WR stars, albeit there are some promising research avenues, such as the presence of CIRs in the winds of some stars. To fully understand WR stars we need to unravel mechanisms of X-ray production in their winds.
Using a code that employs a self-consistent method for computing the effects of photoionization on circumstellar gas dynamics, we model the formation of wind-driven nebulae around massive Wolf-Rayet (W-R) stars. Our algorithm incorporates a simplified model of the photo-ionization source, computes the fractional ionization of hydrogen due to the photoionizing flux and recombination, and determines self-consistently the energy balance due to ionization, photo-heating and radiative cooling. We take into account changes in stellar properties and mass-loss over the star's evolution. Our multi-dimensional simulations clearly reveal the presence of strong ionization front instabilities. Using various X-ray emission models, and abundances consistent with those derived for W-R nebulae, we compute the X-ray flux and spectra from our wind bubble models. We show the evolution of the X-ray spectral features with time over the evolution of the star, taking the absorption of the X-rays by the ionized bubble into account. Our simulated X-ray spectra compare reasonably well with observed spectra of Wolf-Rayet bubbles. They suggest that X-ray nebulae around massive stars may not be easily detectable, consistent with observations.∗
Giacconi et al. (1962) discovered a diffuse cosmic X-ray background with rocket experiments when they searched for lunar X-ray emission. Later satellite missions found a spectral peak in the cosmic X-ray background at ~30 keV. Imaging X-ray satellites such as ROSAT (1990-1999) were able to resolve up to 80% of the background below 2 keV into single point sources, mainly active galaxies. The cosmic X-ray background is the integration of all accreting super-massive (several million solar masses) black holes in the centre of active galaxies over cosmic time. Synthesis models need further populations of X-ray absorbed active galaxy nuclei (AGN) in order to explain the cosmic X-ray background peak at ~30 keV. Current X-ray missions such as XMM-Newton and Chandra offer the possibility of studying these additional populations. This Ph.D. thesis studies the populations that dominate the X-ray sky. For this purpose the 120 ksec XMM-Newton Marano field survey, named for an earlier optical quasar survey in the southern hemisphere, is analysed. Based on the optical follow-up observations the X-ray sources are spectroscopically classified. Optical and X-ray properties of the different X-ray source populations are studied and differences are derived. The amount of absorption in the X-ray spectra of type II AGN, which are considered as a main contributor to the X-ray background at ~30 keV, is determined. In order to extend the sample size of the rare type II AGN, this study also includes objects from another survey, the XMM-Newton Serendipitous Medium Sample. In addition, the dependence of the absorption in type II AGN with redshift and X-ray luminosity is analysed. We detected 328 X-ray sources in the Marano field. 140 sources were spectroscopically classified. We found 89 type I AGN, 36 type II AGN, 6 galaxies, and 9 stars. AGN, galaxies, and stars are clearly distinguishable by their optical and X-ray properties. Type I and II AGN do not separate clearly. They have a significant overlap in all studied properties. In a few cases the X-ray properties are in contradiction to the observed optical properties for type I and type II AGN. For example we find type II AGN that show evidence for optical absorption but are not absorbed in X-rays. Based on the additional use of near infra-red imaging (K-band), we were able to identify several of the rare type II AGN. The X-ray spectra of type II AGN from the XMM-Newton Marano field survey and the XMM-Newton Serendipitous Medium Sample were analysed. Since most of the sources have only ~40 X-ray counts in the XMM-Newton PN-detector, I carefully studied the fit results of simulated X-ray spectra as a function of fit statistic and binning method. The objects revealed only moderate absorption. In particular, I do not find any Compton-thick sources (absorbed by column densities of NH > 1.5 x 10^24 cm^−2). This gives evidence that type II AGN are not the main contributor of the X-ray background around 30 keV. Although bias effects may occur, type II AGN show no noticeable trend of the amount of absorption with redshift or X-ray luminosity.
WR Time Series Photometry
(2015)
We take a comprehensive look at Wolf Rayet photometric variability using the MOST satellite. This sample, consisting of 6 WR stars and 6 WC stars defies all typical photometric analysis. We do, however, confirm the presence of unusual periodic signals resembling sawtooth waves which are present in 11 out of 12 stars in this sample.
For some years now, spectroscopic measurements of massive stars in the amateur domain have been fulfilling professional requirements. Various groups in the northern and southern hemispheres have been established, running successful professional-amateur (ProAm) collaborative campaigns, e.g., on WR, O and B type stars. Today high quality data (echelle and long-slit) are regularly delivered and corresponding results published. Night-to-night long-term observations over months to years open a new opportunity for massive-star research. We introduce recent and ongoing sample campaigns (e.g. ∊ Aur, WR 134, ζ Pup), show respective results and highlight the vast amount of data collected in various data bases. Ultimately it is in the time-dependent domain where amateurs can shine most.
In this review, I discuss the suitability of massive star progenitors, evolved in isolation or in interacting binaries, for the production of observed supernovae (SNe) IIb, Ib, Ic. These SN types can be explained through variations in composition. The critical need of non-thermal effects to produce He I lines favours low-mass He-rich ejecta (in which ^56 Ni can be more easily mixed with He) for the production of SNe IIb/Ib, which thus may arise preferentially from moderate-mass donors in interacting binaries. SNe Ic may instead arise from higher mass progenitors, He-poor or not, because their larger CO cores prevent efficient non-thermal excitation of He i lines. However, current single star evolution models tend to produce Wolf-Rayet (WR) stars at death that have a final mass of > 10 M⊙. Single WR star explosion models produce ejecta that are too massive to match the observed light curve widths and rise times of SNe IIb/Ib/Ic, unless their kinetic energy is systematically and far greater than the canonical value of 10^56 erg. Future work is needed to evaluate the energy/mass degeneracy in light curve properties. Alternatively, a greater mass loss during the WR phase, perhaps in the form of eruptions, as evidenced in SNe Ibn, may reduce the final WR mass. If viable, such explosions would nonetheless favour a SN Ic, not a Ib.
Wolf-Rayet (WR) stars, as they are advanced stages of the life of massive stars, provide a good test for various physical processes involved in the modelling of massive stars, such as rotation and mass loss. In this paper, we show the outputs of the latest grids of single massive stars computed with the Geneva stellar evolution code, and compare them with some observations. We present a short discussion on the shortcomings of single stars models and we also briefly discuss the impact of binarity on the WR populations.
Wolf-Rayet Stars
(2015)
Nearly 150 years ago, the French astronomers Charles Wolf and Georges Rayet described stars with very conspicuous spectra that are dominated by bright and broad emission lines. Meanwhile termed Wolf-Rayet Stars after their discoverers, those objects turned out to represent important stages in the life of massive stars.
As the first conference in a long time that was specifically dedicated to Wolf-Rayet stars, an international workshop was held in Potsdam, Germany, from 1.-5. June 2015. About 100 participants, comprising most of the leading experts in the field as well as as many young scientists, gathered for one week of extensive scientific exchange and discussions. Considerable progress has been reported throughout, e.g. on finding such stars, modeling and analyzing their spectra, understanding their evolutionary context, and studying their circumstellar nebulae. While some major questions regarding Wolf-Rayet stars still remain open 150 years after their discovery, it is clear today that these objects are not just interesting stars as such, but also keystones in the evolution of galaxies.
These proceedings summarize the talks and posters presented at the Potsdam Wolf-Rayet workshop. Moreover, they also include the questions, comments, and discussions emerging after each talk, thereby giving a rare overview not only about the research, but also about the current debates and unknowns in the field. The Scientific Organizing Committee (SOC) included Alceste Bonanos (Athens), Paul Crowther (Sheffield), John Eldridge (Auckland), Wolf-Rainer Hamann (Potsdam, Chair), John Hillier (Pittsburgh), Claus Leitherer (Baltimore), Philip Massey (Flagstaff), George Meynet (Geneva), Tony Moffat (Montreal), Nicole St-Louis (Montreal), and Dany Vanbeveren (Brussels).
I review our current understanding of the interaction between a Wolf-Rayet star's fast wind and the surrounding medium, and discuss to what extent the predictions of numerical simulations coincide with multiwavelength observations of Wolf-Rayet nebulae. Through a series of examples, I illustrate how changing the input physics affects the results of the numerical simulations. Finally, I discuss how numerical simulations together with multiwavelength observations of these objects allow us to unpick the previous mass-loss history of massive stars.
An overview of the known Wolf-Rayet (WR) population of the Milky Way is presented, including a brief overview of historical catalogues and recent advances based on infrared photometric and spectroscopic observations resulting in the current census of 642 (vl.13 online catalogue). The observed distribution of WR stars is considered with respect to known star clusters, given that ≤20% of WR stars in the disk are located in clusters. WN stars outnumber WC stars at all galactocentric radii, while early-type WC stars are strongly biased against the inner Milky Way. Finally, recent estimates of the global WR population in the Milky Way are reassessed, with 1,200±100 estimated, such that the current census may be 50% complete. A characteristic WR lifetime of 0.25 Myr is inferred for an initial mass threshold of 25 M⊙.
A significant number of the central stars of planetary nebulae (CSPNe) are hydrogen-deficient, showing a chemical composition of helium, carbon, and oxygen. Most of them exhibit Wolf-Rayet-like emission line spectra, similar to those of the massive WC Pop I stars, and are therefore classified as of spectral type [WC]. In the last years, CSPNe of other Wolf-Rayet spectral subtypes have been identified, namely PB 8, which is of spectral type [WN/C], and IC 4663 and Abell 48, which are of spectral type [WN]. We review spectral analyses of Wolf-Rayet type central stars of different evolutionary stages and discuss the results in the context of stellar evolution. Especially we consider the question of a common evolutionary channel for [WC] stars. The constraints on the formation of [WN] or [WC/N] subtype stars will also be addressed.
The emission-line dominated spectra of Wolf-Rayet stars are formed in expanding layers of their atmosphere, i.e. in their strong stellar wind. Adequate modeling of such spectra has to face a couple of difficulties. Because of the supersonic motion, the radiative transfer is preferably formulated in the co-moving frame. The strong deviations from local thermodynamical equilibrium (LTE) require to solve the equations of statistical equilibrium for the population numbers, accounting for many hundred atomic energy levels and thousands of line transitions. Moreover, millions of lines from iron-group elements must be taken into account for their blanketing effect. Model atmospheres of the described kind can reproduce the observed WR spectra satisfyingly, and have been widely applied for corresponding spectral analyses.
During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator–inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
What can we learn from climate data? : Methods for fluctuation, time/scale and phase analysis
(2006)
Since Galileo Galilei invented the first thermometer, researchers have tried to understand the complex dynamics of ocean and atmosphere by means of scientific methods. They observe nature and formulate theories about the climate system. Since some decades powerful computers are capable to simulate the past and future evolution of climate. Time series analysis tries to link the observed data to the computer models: Using statistical methods, one estimates characteristic properties of the underlying climatological processes that in turn can enter the models. The quality of an estimation is evaluated by means of error bars and significance testing. On the one hand, such a test should be capable to detect interesting features, i.e. be sensitive. On the other hand, it should be robust and sort out false positive results, i.e. be specific. This thesis mainly aims to contribute to methodological questions of time series analysis with a focus on sensitivity and specificity and to apply the investigated methods to recent climatological problems. First, the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) is studied. It is argued that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires to investigate the local slopes of the fluctuation function. The variability characteristic for stochastic processes is accounted for by calculating empirical confidence regions. The comparison of a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. When aiming to infer short memory by means of DFA, a local slope larger than $\alpha=0.5$ for large scales does not necessarily imply long-memory. Also, a finite scaling of the autocorrelation function is shifted to larger scales in the fluctuation function. It turns out that long-range correlations cannot be concluded unambiguously from the DFA results for the Prague temperature data set. In the second part of the thesis, an equivalence class of nonstationary Gaussian stochastic processes is defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well defined time dependent spectral properties; they allow one to generate realizations of any nonstationary Gaussian process. The dependency of the realizations on the wavelets used for the generation is studied, bias and variance of the wavelet sample spectrum are calculated. To overcome the difficulties of multiple testing, an areawise significance test is developed and compared to the conventional pointwise test in terms of sensitivity and specificity. Applications to Climatological and Hydrological questions are presented. The thesis at hand mainly aims to contribute to methodological questions of time series analysis and to apply the investigated methods to recent climatological problems. In the last part, the coupling between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales is studied by means of Hilbert transformation and a curvature defined phase. This method allows one to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. The performance of the technique is evaluated using a toy model. From the data, distinct epochs are identified, especially two intervals of phase coherence, 1886-1908 and 1964-1980, confirming earlier findings from a new point of view. A significance test of high specificity corroborates these results. Also so far unknown periods of coupling invisible to linear methods are detected. These findings suggest that the decreasing correlation during the last decades might be partly inherent to the ENSO/Monsoon system. Finally, a possible interpretation of how volcanic radiative forcing could cause the coupling is outlined.
To understand the evolution and morphology of planetary nebulae, a detailed knowledge of their central stars is required. Central stars that exhibit emission lines in their spectra, indicating stellar mass-loss allow to study the evolution of planetary nebulae in action. Emission line central stars constitute about 10 % of all central stars. Half of them are practically hydrogen-free Wolf-Rayet type central stars of the carbon sequence, [WC], that show strong emission lines of carbon and oxygen in their spectra. In this contribution we address the weak emission-lines central stars (wels). These stars are poorly analyzed and their hydrogen content is mostly unknown. We obtained optical spectra, that include the important Balmer lines of hydrogen, for four weak emission line central stars. We present the results of our analysis, provide spectral classification and discuss possible explanations for their formation and evolution.
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}