Improved Hexahedral Meshing on Biological Models

Certain applications of the finite element method require hexahedral meshes for the underlying discretization. A procedure, known as THexing, which is guaranteed to produce an all-hex mesh is to begin with a tetrahedral mesh and then subdivide each element into four hexahedra. This research presents a method for improving the THex approach, known as Diced THexing, or DTHexing. The DTHex approach is based on general coarsening tools. An initial triangle surface mesh is coarsened and smoothed iteratively until a coarse mesh of reasonable quality is obtained. The volume is then easily meshed using a tetrahedral scheme, then refined using ’h’ type modifications. The goal of this method is to 1) improve the quality of elements in the finite element mesh and 2) decrease the number of overall nodes. The DTHex approach has been successful at improving models on biological meshes without increasing node count. This research was conducted using the CUBIT software

230 GHz VLBI OBSERVATIONS OF M87: EVENT‐HORIZON‐SCALE STRUCTURE DURING AN ENHANCED VERY‐HIGH‐ENERGY γ‐RAY STATE IN 2012

We report on 230 GHz (1.3 mm) very long baseline interferometry (VLBI) observations of M87 with the Event Horizon Telescope using antennas on Mauna Kea in Hawaii, Mt. Graham in Arizona, and Cedar Flat in California. For the first time, we have acquired 230 GHz VLBI interferometric phase information on M87 through measurement of the closure phase on the triangle of long baselines. Most of the measured closure phases are consistent with 0° as expected by physically motivated models for 230 GHz structure such as jet models and accretion disk models. The brightness temperature of the event-horizon-scale structure is ~1 X 10[superscript 10] K derived from the compact flux density of ~1 Jy and the angular size of ~40 µas ~ 5.5 R[subscript s], which is broadly consistent with the peak brightness of the radio cores at 1–86 GHz located within ~10[superscript 2] R[subscript s]. Our observations occurred in the middle of an enhancement in very-high-energy (VHE) γ-ray flux, presumably originating in the vicinity of the central black hole. Our measurements, combined with results of multi-wavelength observations, favor a scenario in which the VHE region has an extended size of ~20–60 R[subscript s]

Superresolution Full-polarimetric Imaging for Radio Interferometry with Sparse Modeling

We propose a new technique for radio interferometry to obtain superresolution full-polarization images in all four Stokes parameters using sparse modeling. The proposed technique reconstructs the image in each Stokes parameter from the corresponding full-complex Stokes visibilities by utilizing two regularization functions: the ℓ 1 norm and the total variation (TV) of the brightness distribution. As an application of this technique, we present simulated linear polarization observations of two physically motivated models of M87 with the Event Horizon Telescope. We confirm that ℓ 1+TV regularization can achieve an optimal resolution of ~25%–30% of the diffraction limit λ/D[subscript max], which is the nominal spatial resolution of a radio interferometer for both the total intensity (i.e., Stokes I) and linear polarizations (i.e., Stokes Q and U). This optimal resolution is better than that obtained from the widely used Cotton–Schwab CLEAN algorithm or from using ℓ 1 or TV regularizations alone. Furthermore, we find that ℓ 1+TV regularization can achieve much better image fidelity in linear polarization than other techniques over a wide range of spatial scales, not only in the superresolution regime, but also on scales larger than the diffraction limit. Our results clearly demonstrate that sparse reconstruction is a useful choice for high-fidelity full-polarimetric interferometric imaging

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling

We propose a new imaging technique for radio and optical/infrared interferometry. The proposed technique reconstructs the image from the visibility amplitude and closure phase, which are standard data products of short-millimeter very long baseline interferometers such as the Event Horizon Telescope (EHT) and optical/infrared interferometers, by utilizing two regularization functions: the ℓ_1-norm and total variation (TV) of the brightness distribution. In the proposed method, optimal regularization parameters, which represent the sparseness and effective spatial resolution of the image, are derived from data themselves using cross-validation (CV). As an application of this technique, we present simulated observations of M87 with the EHT based on four physically motivated models. We confirm that ℓ_1 + TV regularization can achieve an optimal resolution of ~20%–30% of the diffraction limit λ/D_(max), which is the nominal spatial resolution of a radio interferometer. With the proposed technique, the EHT can robustly and reasonably achieve super-resolution sufficient to clearly resolve the black hole shadow. These results make it promising for the EHT to provide an unprecedented view of the event-horizon-scale structure in the vicinity of the supermassive black hole in M87 and also the Galactic center Sgr A*

1.3 mm Wavelength VLBI of Sagittarius A*: Detection of Time-Variable Emission on Event Horizon Scales

Sagittarius A*, the ~4 x 10^6 solar mass black hole candidate at the Galactic Center, can be studied on Schwarzschild radius scales with (sub)millimeter wavelength Very Long Baseline Interferometry (VLBI). We report on 1.3 mm wavelength observations of Sgr A* using a VLBI array consisting of the JCMT on Mauna Kea, the ARO/SMT on Mt. Graham in Arizona, and two telescopes of the CARMA array at Cedar Flat in California. Both Sgr A* and the quasar calibrator 1924-292 were observed over three consecutive nights, and both sources were clearly detected on all baselines. For the first time, we are able to extract 1.3 mm VLBI interferometer phase information on Sgr A* through measurement of closure phase on the triangle of baselines. On the third night of observing, the correlated flux density of Sgr A* on all VLBI baselines increased relative to the first two nights, providing strong evidence for time-variable change on scales of a few Schwarzschild radii. These results suggest that future VLBI observations with greater sensitivity and additional baselines will play a valuable role in determining the structure of emission near the event horizon of Sgr A*.Comment: 8 pages, submitted to ApJ

Detection of intrinsic source structure at ~3 Schwarzschild radii with Millimeter-VLBI observations of SAGITTARIUS A*

We report results from very long baseline interferometric (VLBI) observations of the supermassive black hole in the Galactic center, Sgr A*, at 1.3 mm (230 GHz). The observations were performed in 2013 March using six VLBI stations in Hawaii, California, Arizona, and Chile. Compared to earlier observations, the addition of the APEX telescope in Chile almost doubles the longest baseline length in the array, provides additional {\it uv} coverage in the N-S direction, and leads to a spatial resolution of $\sim$30 $\mu$as ($\sim$3 Schwarzschild radii) for Sgr A*. The source is detected even at the longest baselines with visibility amplitudes of $\sim$4-13% of the total flux density. We argue that such flux densities cannot result from interstellar refractive scattering alone, but indicate the presence of compact intrinsic source structure on scales of $\sim$3 Schwarzschild radii. The measured nonzero closure phases rule out point-symmetric emission. We discuss our results in the context of simple geometric models that capture the basic characteristics and brightness distributions of disk- and jet-dominated models and show that both can reproduce the observed data. Common to these models are the brightness asymmetry, the orientation, and characteristic sizes, which are comparable to the expected size of the black hole shadow. Future 1.3 mm VLBI observations with an expanded array and better sensitivity will allow a more detailed imaging of the horizon-scale structure and bear the potential for a deep insight into the physical processes at the black hole boundary.Comment: 11 pages, 5 figures, accepted to Ap