Observations in the UV-regime are very important for exoplanet research, because many diagnostically important lines for studying stellar activity are in this regime. Studying stellar activity is not only important because of its negative effects on
the determination planetary parameters, but also because the XUV-radiation from the host stars affects the photochemistry and the erosion of planetary atmospheres . Unfortunately, the XUV-region is only accessible from space. However, since the XUV-radiation is correlated with the CaII,HK-lines, we can use these lines to study the XUV radiation indirectly. The CaIIHK lines for relatively bright stars can be observed with PLATOspec, a new high-resolution echelle spectrograph in development for the ESO 1.5m telescope at La Silla. One advantage compared to instruments on larger telescopes will be that large programs can be carried out. There will be two modes for obtaining precise RV-measurements. In the future, the CUBES instrument on the VLT will be able to study the same lines to probe the XUV-radiation in much fainter targets.
Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns out that if
Studentizing is accompanied by estimating the location parameter in a suitable way, then the $t$-statistic regains the exponential tail behavior. Motivated by this example, the paper analyzes other ways of empirically standardizing sums and establishes tail bounds that are sub-Gaussian or even closer to normal for the following settings: Standardization with Studentized contrasts for normal observations, standardization with the log likelihood ratio statistic for observations from an exponential family, and standardization via self-normalization for observations from a symmetric distribution with unknown center of symmetry. The latter standardization gives rise to a novel scan statistic for heteroscedastic data whose asymptotic power is analyzed.
We prove that both the Laplacian on functions, and the Lichnerowicz Laplacian on symmetric 2-tensors with respect to asymptotically hyperbolic metrics, are sectorial maps in weighted Holder spaces. As an application, the machinery of analytic semigro
ups then applies to yield well-posedness results for parabolic evolution equations in these spaces.
Flares are known to play an important role for the evolution of the atmospheres of young planets. In order to understand the evolution of planets, it is thus important to study the flare-activity of young stars. This is particularly the case for youn
g M-stars, because they are very active. We study photometrically and spectroscopically the highly active M-star 2MASS J16111534-1757214. We show that it is a member of the Upper Sco OB association, which has an age of 5-10 Myrs. We also re-evaluate the status of other bona-fide M-stars in this region and identify 42 members. Analyzing the K2-light curves, we find that 2MASS J16111534-1757214 has, on average, one super-flare with E > 1.0E35 erg every 620 hours, and one with E >1.0E34 erg every 52 hours. Although this is the most active M-star in the Upper Sco association, the power-law index of its flare-distribution is similar to that of other M-stars in this region. 2MASS J16111534-1757214 as well as other M-stars in this region show a broken power-law distribution in the flare-frequency diagram. Flares larger than E >3E34 erg have a power-law index beta=-1.3+/-0.1 and flares smaller than that beta=-0.8+/-0.1. We furthermore conclude that the flare-energy distribution for young M-stars is not that different from solar-like stars.
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynam
ics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.
Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $mu_B geq (2-2.5)T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second, higher order
coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio. In this work, we present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to $mu_B/Tle3.5$.
We present a new approach for inference about a log-concave distribution: Instead of using the method of maximum likelihood, we propose to incorporate the log-concavity constraint in an appropriate nonparametric confidence set for the cdf $F$. This a
pproach has the advantage that it automatically provides a measure of statistical uncertainty and it thus overcomes a marked limitation of the maximum likelihood estimate. In particular, we show how to construct confidence bands for the density that have a finite sample guaranteed confidence level. The nonparametric confidence set for $F$ which we introduce here has attractive computational and statistical properties: It allows to bring modern tools from optimization to bear on this problem via difference of convex programming, and it results in optimal statistical inference. We show that the width of the resulting confidence bands converges at nearly the parametric $n^{-frac{1}{2}}$ rate when the log density is $k$-affine.
Cepheids in multiple systems provide information on the outcome of the formation of massive stars. They can also lead to exotic end-stage objects. This study concludes our survey of 70 galactic Cepheids using the {it Hubble Space Telescope} (HST) Wid
e Field Camera~3 (WFC3) with images at two wavelengths to identify companions closer than $5arcsec$. In the entire WFC3 survey we identify 16 probable companions for 13 Cepheids. The seven Cepheids having resolved candidate companions within $2$ all have the surprising property of themselves being spectroscopic binaries (as compared with a 29% incidence of spectroscopic binaries in the general Cepheid population). That is a strong suggestion that an inner binary is linked to the scenario of a third companion within a few hundred~AU ull. This characteristic is continued for more widely separated companions. Under a model where the outer companion is formed first, it is unlikely that it can anticipate a subsequent inner binary. Rather it is more likely that a triple system has undergone dynamical interaction, resulting in one star moving outward to its current location. {it Chandra} and {it Gaia} data as well as radial velocities and HSTSTIS and {it IUE} spectra are used to derive properties of the components of the Cepheid systems. The colors of the companion candidates show a change in distribution at approximately 2000~AU separations, from a range including both hot and cool colors for closer companions, to only low-mass companions for wider separations.
BD And is a fairly bright (V = 10.8), active and close (P = 0.9258 days) eclipsing binary. The cyclic variability of the apparent orbital period as well as third light in the light curves indicate the presence of an additional late-type component. Th
e principal aim is the spectroscopic testing of the third-body hypothesis and determination of absolute stellar parameters for both components of the eclipsing binary. First medium and high-resolution spectroscopy of the system was obtained. The broadening-function technique appropriate for heavily-broadened spectra of close binaries was used. The radial velocities were determined fitting the Gaussian functions and rotational profiles to the broadening functions. A limited amount of photometric data has also been obtained. Although the photometric observations were focused on the obtaining the timing information, a cursory light-curve analysis was also performed. Extracted broadening functions clearly show the presence of a third, slowly-rotating component. Its radial velocity is within error of the systemic velocity of the eclipsing pair, strongly supporting the physical bond. The observed systemic radial-velocity and third-component changes do not support the 9 year orbit found from the timing variability. Masses of the components of the eclipsing pair are determined with about 0.5% precision. Further characterization of the system would require long-term photometric and spectroscopic monitoring.
We analyze the properties of an impurity in a dilute Bose-Einstein condensate (BEC). First the quasiparticle residue of a static impurity in an ideal BEC is shown to vanish with increasing particle number as a stretched exponential, leading to a boso
nic orthogonality catastrophe. Then we introduce a variational ansatz, which recovers this exact result and describes the macroscopic dressing of the impurity including its back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs for mobile impurities, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with experimental results.
