Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes

The impact of rotation on the line profiles of Wolf-Rayet stars

Massive Wolf-Rayet stars are recognized today to be in a very common, but short, evolutionary phase of massive stars. While our understanding of Wolf-Rayet stars has increased dramatically over the past decades, it remains unclear whether rapid rotators are among them. There are various indications that rapidly rotating Wolf-Rayet stars should exist. Unfortunately, due to their expanding atmospheres, rotational velocities of Wolf-Rayet stars are very difficult to measure. However, recently observed spectra of several Wolf-Rayet stars reveal peculiarly broad and round emission lines. Could these spectra imply rapid rotation? In this work, we model the effects of rotation on the atmospheres of Wolf-Rayet stars. We further investigate whether the peculiar spectra of five Wolf-Rayet stars may be explained with the help of stellar rotation, infer appropriate rotation parameters, and discuss the implications of our results. We make use of the Potsdam Wolf-Rayet (PoWR) non-LTE model atmosphere code. Since the observed spectra of Wolf-Rayet stars are mainly formed in their expanding atmospheres, rotation must be accounted for with a 3D integration scheme of the formal integral. For this purpose, we assume a rotational velocity field consisting of an inner co-rotating domain and an outer domain, where the angular momentum is conserved. We find that rotation can reproduce the unique spectra analyzed here. However, the inferred rotational velocities at the stellar surface are large (~200 km/s), and the inferred co-rotation radii (~10 stellar radii) suggest the existence of very strong photospheric magnetic fields (~20 kG)

Wolf-Rayet stars: recent advances and persisting problems

Wolf-Rayet (WR) stars comprise a class of stars whose spectra are dominated by strong, broad emission lines that are associated with copious mass loss. In the massive-star regime, roughly 90% of the known WR stars are thought to have evolved off the main sequence. Dubbed classical WR (cWR) stars, these hydrogen-depleted objects represent a crucial evolutionary phase preceding core collapse into black holes, and offer a unique window into hot-star wind physics. Their formation is thought to be rooted in either intrinsic mass-loss or binary interactions. Results obtained from analyses using contemporary model atmospheres still fail to reconcile the derived properties of WR stars with predictions from stellar evolution. Importantly, stellar evolution models cannot reproduce the the bulk of cWR stars, a problem that becomes especially severe at subsolar metallicity. Next-generation model atmospheres and upcoming observational campaigns to hunt for undetected companions promise a venue for progress.Comment: Proceedings for IAU Symposium 361: Massive Stars Near and Far, held in Ballyconnell, Ireland, 9-13 May 2022. Based on invited talk on Wolf-Ryaet star

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars

Wolf-Rayet stars in the Small Magellanic Cloud: I. Analysis of the single WN stars

Wolf-Rayet (WR) stars have a severe impact on their environments owing to their strong ionizing radiation fields and powerful stellar winds. Since these winds are considered to be driven by radiation pressure, it is theoretically expected that the degree of the wind mass-loss depends on the initial metallicity of WR stars. Following our comprehensive studies of WR stars in the Milky Way, M31, and the LMC, we derive stellar parameters and mass-loss rates for all seven putatively single WN stars known in the SMC. Based on these data, we discuss the impact of a low-metallicity environment on the mass loss and evolution of WR stars. The quantitative analysis of the WN stars is performed with the Potsdam Wolf-Rayet (PoWR) model atmosphere code. The physical properties of our program stars are obtained from fitting synthetic spectra to multi-band observations. In all SMC WN stars, a considerable surface hydrogen abundance is detectable. The majority of these objects have stellar temperatures exceeding 75 kK, while their luminosities range from 10^5.5 to 10^6.1 Lsun. The WN stars in the SMC exhibit on average lower mass-loss rates and weaker winds than their counterparts in the Milky Way, M31, and the LMC. By comparing the mass-loss rates derived for WN stars in different Local Group galaxies, we conclude that a clear dependence of the wind mass-loss on the initial metallicity is evident, supporting the current paradigm that WR winds are driven by radiation. A metallicity effect on the evolution of massive stars is obvious from the HRD positions of the SMC WN stars at high temperatures and high luminosities. Standard evolution tracks are not able to reproduce these parameters and the observed surface hydrogen abundances. Homogeneous evolution might provide a better explanation for their evolutionary past.Comment: 18+12 pages; 22+8 figures; accepted for publication in A&

Investigating the lack of main-sequence companions to massive Be stars

About 20% of all B-type stars are classical Be stars. The Be phenomenon is strongly correlated with rapid rotation, the origin of which remains unclear. It may be rooted in single- or binary-star evolution. In the framework of the binary channel, the initially more massive star transfers mass and angular momentum to the original secondary, which becomes a Be star. The system then evolves into a Be binary with a post-main-sequence companion, which may later be disrupted in a supernova event. Hence, if the binary channel dominates the formation of Be stars, one may expect a strong lack of close Be binaries with main sequence (MS) companions. Through an extensive, star-by-star review of the literature of a magnitude-limited sample of Galactic early-type Be stars, we investigate whether Be binaries with MS companions are known to exist. Our sample is constructed from the BeSS database and cross-matched with all available literature on the individual stars. Out of an initial list of 505 Be stars, we compile a final sample of 287 Galactic Be stars earlier than B1.5 with V<=12 mag. Out of those, 13 objects were reported as Be binaries with known post-MS companions and 11 as binaries with unknown, uncertain or debated companions. We find no confirmed reports of Be binaries with MS companions. For the remaining 263 targets, no significant reports of multiplicity exist in the literature, implying that they are either Be binaries with faint companions, or truly single. The clear lack of reported MS companions to Be stars, which stands in contrast to the high number of detected B+B MS binaries, strongly supports the hypothesis that early-type Be stars are binary interaction products that spun up after mass and angular momentum transfer from a companion star. Taken at face value, our results may suggest that a large majority of the early-type Be stars have formed through binary mass-transfer.Comment: 15 pages (incl. appendix), 6 figures, 3 tables, accepted for publication in A&

Coupling hydrodynamics with comoving frame radiative transfer: II. Stellar wind stratification in the high-mass X-ray binary Vela X-1

CONTEXT: Vela X-1, a prototypical high mass X-ray binary (HMXB), hosts a neutron star (NS) in a close orbit around an early-B supergiant donor star. Accretion of the donor star's wind onto the NS powers its strong X-ray luminosity. To understand the physics of HMXBs, detailed knowledge about the donor star winds is required. AIMS: To gain a realistic picture of the donor star in Vela X-1, we constructed a hydrodynamically consistent atmosphere model describing the wind stratification while properly reproducing the observed donor spectrum. To investigate how X-ray illumination affects the stellar wind, we calculated additional models for different X-ray luminosity regimes. METHODS: We use the recently updated version of the PoWR code to consistently solve the hydrodynamic equation together with the statistical equations and the radiative transfer. RESULTS: The wind flow in Vela X-1 is driven by ions from various elements with Fe III and S III leading in the outer wind. The model-predicted mass-loss rate is in line with earlier empirical studies. The mass-loss rate is almost unaffected by the presence of the accreting NS in the wind. The terminal wind velocity is confirmed at $v_\infty \approx 600$ km/s. On the other hand, the wind velocity in the inner region where the NS is located is only $\approx 100$ km/s, which is not expected on the basis of a standard $\beta$-velocity law. In models with an enhanced level of X-rays, the velocity field in the outer wind can be altered. If the X-ray flux is too high, the acceleration breaks down because the ionization increases. CONCLUSIONS: Accounting for radiation hydrodynamics, our Vela X-1 donor atmosphere model reveals a low wind speed at the NS location, and it provides quantitative information on wind driving in this important HMXB.Comment: 19 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

A spectroscopic multiplicity survey of Galactic Wolf-Rayet stars. I. The northern WC sequence

It is now well established that the majority of massive stars reside in multiple systems. However, the effect of multiplicity is not sufficiently understood, resulting in a plethora of uncertainties about the end stages of massive-star evolution. In order to investigate these uncertainties, it is useful to study massive stars just before their demise. Classical Wolf-Rayet stars represent the final end stages of stars at the upper-mass end. The multiplicity fraction of these stars was reported to be ${\sim}0.4$ in the Galaxy but no correction for observational biases has been attempted. The aim of this study is to conduct a homogeneous radial-velocity survey of a magnitude-limited ($V$ $\leq 12$) sample of Galactic Wolf-Rayet stars to derive their bias-corrected multiplicity properties. The present paper focuses on 12 northern Galactic carbon-rich (WC) Wolf-Rayet stars observable with the 1.2m Mercator telescope on the island of La Palma. We homogeneously measured relative radial velocities (RVs) for carbon-rich Wolf-Rayet stars using cross-correlation. Variations in the derived RVs were used to flag binary candidates. We investigated probable orbital configurations and provide a first correction of observational biases through Monte-Carlo simulations. Of the 12 northern Galactic WC stars in our sample, seven show peak-to-peak RV variations larger than 10 km s$^{-1}$, which we adopt as our detection threshold. This results in an observed spectroscopic multiplicity fraction of 0.58 with a binomial error of 0.14. In our campaign, we find a clear lack of short-period (P~$<~\sim$100\,d), indicating that a large number of Galactic WC binaries likely reside in long-period systems. Finally, our simulations show that at the 10% significance level, the intrinsic multiplicity fraction of the Galactic WC population is at least 0.72

On the binary nature of massive blue hypergiants: high-resolution X-ray spectroscopy suggests that Cyg OB2 12 is a colliding wind binary

The blue hypergiant Cyg OB2-12 (B3Ia+) is a representative member of the class of very massive stars in a poorly understood evolutionary stage. We obtained its high-resolution X-ray spectrum using Chandra observatory. PoWR model atmospheres were calculated to provide realistic wind opacities and to establish the wind density structure. We find that collisional de-excitation is the dominant mechanism de-populating the metastable upper levels of the forbidden lines of the He-like ions SiXIV and MgXII. Comparison between the model and observations reveals that X-ray emission is produced in a dense plasma, which could reside only at the photosphere or in a colliding wind zone between binary components. The observed X-ray spectra are well fitted by thermal plasma models, with average temperatures in excess of 10 MK. The wind speed in Cyg OB2-12 is not high enough to power such high temperatures, but the collision of two winds in a binary system can be sufficient. We used archival data to investigate the X-ray properties of other blue hypergiants. In general, stars of this class are not detected as X-rays sources. We suggest that our new Chandra observations of Cyg OB2-12 can be best explained if Cyg OB2-12 is a colliding wind binary possessing a late O-type companion. This makes Cyg OB2-12 only the second binary system among the 16 known Galactic hypergiants. This low binary fraction indicates that the blue hypergiants are likely products of massive binary evolution during which they either accreted a significant amount of mass or already merged with their companion.Comment: accepted to Ap