Detection of thermal radio emission from a single coronal giant

We report the detection of thermal continuum radio emission from the K0 III coronal giant Pollux ($\beta$ Gem) with the Karl G. Jansky Very Large Array (VLA). The star was detected at 21 and 9 GHz with flux density values of $150\pm21$ and $43\pm8\,\mu$Jy, respectively. We also place a $3\sigma_{\mathrm{rms}}$ upper limit of $23\,\mu$Jy for the flux density at 3 GHz. We find the stellar disk-averaged brightness temperatures to be approximately 9500, 15000, and $<71000\,$K, at 21, 9, and 3 GHz, respectively, which are consistent with the values of the quiet Sun. The emission is most likely dominated by optically thick thermal emission from an upper chromosphere at 21 and 9 GHz. We discuss other possible additional sources of emission at all frequencies and show that there may also be a small contribution from gyroresonance emission above active regions, coronal free-free emission and free-free emission from an optically thin stellar wind, particularly at the lower frequencies. We constrain the maximum mass-loss rate from Pollux to be less than $3.7\times 10^{-11}\,M_{\odot}$ yr$^{-1}$ (assuming a wind terminal velocity of 215 km s$^{-1}$), which is about an order of magnitude smaller than previous constraints for coronal giants and is in agreement with existing predictions for the mass-loss rate of Pollux. These are the first detections of thermal radio emission from a single (i.e., non-binary) coronal giant and demonstrate that low activity coronal giants like Pollux have atmospheres at radio frequencies akin to the quiet Sun

Hubble Space Telescope Constraints on the Winds and Astrospheres of Red Giant Stars

We report on an ultraviolet spectroscopic survey of red giants observed by the Hubble Space Telescope, focusing on spectra of the Mg II h & k lines near 2800 A in order to study stellar chromospheric emission, winds, and astrospheric absorption. We focus on spectral types between K2 III and M5 III, a spectral type range with stars that are noncoronal, but possessing strong, chromospheric winds. We find a very tight relation between Mg II surface flux and photospheric temperature, supporting the notion that all K2-M5 III stars are emitting at a basal flux level. Wind velocities (V_w) are generally found to decrease with spectral type, with V_w decreasing from ~40 km/s at K2 III to ~20 km/s at M5 III. We find two new detections of astrospheric absorption, for Sigma Pup (K5 III) and Gamma Eri (M1 III). This absorption signature had previously only been detected for Alpha Tau (K5 III). For the three astrospheric detections the temperature of the wind after the termination shock correlates with V_w, but is lower than predicted by the Rankine-Hugoniot shock jump conditions, consistent with the idea that red giant termination shocks are radiative shocks rather than simple hydrodynamic shocks. A full hydrodynamic simulation of the Gamma Eri astrosphere is provided to explore this further.Comment: 16 pages, 8 figures, to appear in The Astrophysical Journa

Weak Galerkin finite element methods for elasticity and coupled flow problems

Includes bibliographical references.2020 Summer.We present novel stabilizer-free weak Galerkin finite element methods for linear elasticity and coupled Stokes-Darcy flow with a comprehensive treatment of theoretical results and the numerical methods for each. Weak Galerkin finite element methods take a discontinuous approximation space and bind degrees of freedom together through the discrete weak gradient, which involves solving a small symmetric positive-definite linear system on every element of the mesh. We introduce notation and analysis using a general framework that highlights properties that unify many existing weak Galerkin methods. This framework makes analysis for the methods much more straightforward. The method for linear elasticity on quadrilateral and hexahedral meshes uses piecewise constant vectors to approximate the displacement on each cell, and it uses the Raviart-Thomas space for the discrete weak gradient. We use the Schur complement to simplify the solution of the global linear system and increase computational efficiency further. We prove first-order convergence in the L2 norm, verify our analysis with numerical experiments, and compare to another weak Galerkin approach for this problem. The method for coupled Stokes-Darcy flow uses an extensible multinumerics approach on quadrilateral meshes. The Darcy flow discretization uses a weak Galerkin finite element method with piecewise constants approximating pressure and the Arbogast-Correa space for the weak gradient. The Stokes domain discretization uses the classical Bernardi-Raugel pair. We prove first-order convergence in the energy norm and verify our analysis with numerical experiments. All algorithms implemented in this dissertation are publicly available as part of James Liu's DarcyLite and Darcy+ packages and as part of the deal.II library

Evolved Late-Type Star FUV Spectra: Mass Loss and Fluorescence

This proposal was for a detailed analysis of the far ultraviolet (FUV) photoionizing radiation that provides crucial input physics for mass loss studies, e.g., observations of the flux below 10448, allow us to constrain the Ca II/Ca III balance and make significant progress beyond previous optical studies on stellar mass loss and circumstellar photochemistry. Our targets selection provided good spectral-type coverage required to help unravel the Ca II/Ca III balance as the mass-loss rates increase by over three orders of magnitude from K5 III to M5 III. We also explored the relationship between the FUV radiation field and other UV diagnostics to allow us to empirically estimate the FUV radiation field for the vast majority of stars which are too faint to be observed with FUSE, and to improve upon their uncertain mass-loss rates

Compression and Reduced Representation Techniques for Patch-Based Relaxation

Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational domain. The two most common families of patch-based methods are block-Jacobi and Schwarz methods, where the former typically corresponds to non-overlapping domains and the later implies some overlap. We focus on cases where each patch consists of the degrees of freedom within a finite element method mesh cell. Patch methods often capture complex local physics much more effectively than simpler point-smoothers such as Jacobi; however, forming, inverting, and applying each patch can be prohibitively expensive in terms of both storage and computation time. To this end, we propose several approaches for performing analysis on these patches and constructing a reduced representation. The compression techniques rely on either matrix norm comparisons or unsupervised learning via a clustering approach. We illustrate how it is frequently possible to retain/factor less than 5% of all patches and still develop a method that converges with the same number of iterations or slightly more than when all patches are stored/factored.Comment: 16 pages, 5 figure

Multi-wavelength Radio Continuum Emission Studies of Dust-free Red Giants

Multi-wavelength centimeter continuum observations of non-dusty, non-pulsating K spectral-type red giants directly sample their chromospheres and wind acceleration zones. Such stars are feeble emitters at these wavelengths however, and previous observations have provided only a small number of modest S/N measurements slowly accumulated over three decades. We present multi-wavelength Karl G. Jansky Very Large Array thermal continuum observations of the wind acceleration zones of two dust-free red giants, Arcturus (Alpha Boo: K2 III) and Aldebaran (Alpha Tau: K5 III). Importantly, most of our observations of each star were carried out over just a few days, so that we obtained a snapshot of the different stellar atmospheric layers sampled at different wavelengths, independent of any long-term variability. We report the first detections at several wavelengths for each star including a detection at 10 cm (3.0 GHz: S band) for both stars and a 20 cm (1.5 GHz: L band) detection for Alpha Boo. This is the first time single luminosity class III red giants have been detected at these continuum wavelengths. Our long-wavelength data sample the outer layers of Alpha Boo's atmosphere where its wind velocity is approaching its terminal value and the ionization balance is becoming frozen-in. For Alpha Tau, however, our long-wavelength data are still sampling its inner atmosphere, where the wind is still accelerating probably due to its lower mass-loss rate. We compare our data with published semi-empirical models based on ultraviolet data, and the marked deviations highlight the need for new atmospheric models to be developed. Spectral indices are used to discuss the possible properties of the stellar atmospheres, and we find evidence for a rapidly cooling wind in the case of Alpha Boo. Finally, we develop a simple analytical wind model for Alpha Boo based on our new long-wavelength flux measurements

CARMA CO(J = 2 - 1) Observations of the Circumstellar Envelope of Betelgeuse

We report radio interferometric observations of the 12C16O 1.3 mm J = 2-1 emission line in the circumstellar envelope of the M supergiant Alpha Ori and have detected and separated both the S1 and S2 flow components for the first time. Observations were made with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) interferometer in the C, D, and E antenna configurations. We obtain good u-v coverage (5-280 klambda) by combining data from all three configurations allowing us to trace spatial scales as small as 0.9\arcsec over a 32\arcsec field of view. The high spectral and spatial resolution C configuration line profile shows that the inner S1 flow has slightly asymmetric outflow velocities ranging from -9.0 km s-1 to +10.6 km s-1 with respect to the stellar rest frame. We find little evidence for the outer S2 flow in this configuration because the majority of this emission has been spatially-filtered (resolved out) by the array. We also report a SOFIA-GREAT CO(J= 12-11) emission line profile which we associate with this inner higher excitation S1 flow. The outer S2 flow appears in the D and E configuration maps and its outflow velocity is found to be in good agreement with high resolution optical spectroscopy of K I obtained at the McDonald Observatory. We image both S1 and S2 in the multi-configuration maps and see a gradual change in the angular size of the emission in the high absolute velocity maps. We assign an outer radius of 4\arcsec to S1 and propose that S2 extends beyond CARMA's field of view (32\arcsec at 1.3 mm) out to a radius of 17\arcsec which is larger than recent single-dish observations have indicated. When azimuthally averaged, the intensity fall-off for both flows is found to be proportional to R^{-1}, where R is the projected radius, indicating optically thin winds with \rho \propto R^{-2}.Comment: 11 pages, 8 figures To be published in the Astronomical Journal (Received 2012 February 10; accepted 2012 May 25