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Let (Mⁿ,g) be a complete simply connectedn-dimensional Riemannian manifold with curvature bounds Sect_g≤ κ for κ ≤ 0 and Ric_g≥ (n− 1)KgforK≤ 0. We prove that for any bounded domain Ω ⊂Mⁿwith diameterdand Lipschitz boundary, if Ω* is a geodesic ball in the simply connected space form with constant sectional curvature κ enclosing the same volume as Ω, then σ₁(Ω) ≤Cσ₁(Ω*), where σ₁(Ω) and σ₁(Ω*) denote the first nonzero Steklov eigenvalues of Ω and Ω* respectively, andC=C(n, κ,K,d) is an explicit constant. When κ =K, we haveC= 1 and recover the Brock–Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space. 

Abstract This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that$$\alpha $$ $\alpha$-positive/$$\alpha $$ $\alpha$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all$$\alpha \in [1,5]$$ $\alpha \in [1,5]$. 

Abstract We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature. 

Abstract SN 2023ehl, a normal Type Ia supernova with a typical decline rate, was discovered in the galaxy UGC 11555 and offers valuable insights into the explosion mechanisms of white dwarfs. We present a detailed analysis of SN 2023ehl, including spectroscopic and photometric observations. The supernova exhibits high-velocity features in its ejecta, which are crucial for understanding the physical processes during the explosion. We compared the light curves of SN 2023ehl with other well-observed Type Ia supernovae, finding similarities in their evolution. The line strength ratioR(Siii) was calculated to be 0.17 ± 0.04, indicating a higher photospheric temperature compared to other supernovae. The maximum quasi-bolometric luminosity was determined to be 1.52 × 10⁴³erg s⁻¹, and the synthesized⁵⁶Ni mass was estimated at 0.77 ± 0.05M_⊙. The photospheric velocity atB-band maximum light was measured as 10,150 ± 240 km s⁻¹, classifying SN 2023ehl as a normal velocity Type Ia supernova. Our analysis suggests that SN 2023ehl aligns more with both the gravitationally confined detonation, providing a comprehensive view of the diversity and complexity of Type Ia supernovae. 

Abstract Due to their short timescale, stellar flares are a challenging target for the most modern synoptic sky surveys. The upcoming Vera C. Rubin Legacy Survey of Space and Time (LSST), a project designed to collect more data than any precursor survey, is unlikely to detect flares with more than one data point in its main survey. We developed a methodology to enable LSST studies of stellar flares, with a focus on flare temperature and temperature evolution, which remain poorly constrained compared to flare morphology. By leveraging the sensitivity expected from the Rubin system, differential chromatic refraction (DCR) can be used to constrain flare temperature from a single-epoch detection, which will enable statistical studies of flare temperatures and constrain models of the physical processes behind flare emission using the unprecedentedly high volume of data produced by Rubin over the 10 yr LSST. We model the refraction effect as a function of the atmospheric column density, photometric filter, and temperature of the flare, and show that flare temperatures at or above ∼4000 K can be constrained by a singleg-band observation at air massX≳ 1.2, given the minimum specified requirement on the single-visit relative astrometric accuracy of LSST, and that a surprisingly large number of LSST observations are in fact likely be conducted atX≳ 1.2, in spite of image quality requirements pushing the survey to preferentially lowX. Having failed to measure flare DCR in LSST precursor surveys, we make recommendations on survey design and data products that enable these studies in LSST and other future surveys. 

Light echoes give us a unique perspective on the nature of supernovae and nonterminal stellar explosions. Spectroscopy of light echoes can reveal details on the kinematics of the ejecta, probe asymmetry, and reveal details of ejecta interaction with circumstellar matter, thus expanding our understanding of these transient events. However, the spectral features arise from a complex interplay between the source photons, the reflecting dust geometry, and the instrumental setup and observing conditions. In this work, we present an improved method for modeling these effects in light echo spectra, one that relaxes the simplifying assumption of a light-curve-weighted sum, and instead estimates the true relative contribution of each phase of a transient event to the observed spectrum. We discuss our logic, the gains we obtain over light echo analysis methods used in the past, and prospects for further improvements. Lastly, we show how the new method improves our analysis of echoes from Tycho’s supernova (SN 1572) as an example. 

Abstract Light echoes (LEs) are the reflections of astrophysical transients off of interstellar dust. They are fascinating astronomical phenomena that enable studies of the scattering dust as well as of the original transients. LEs, however, are rare and extremely difficult to detect as they appear as faint, diffuse, time-evolving features. The detection of LEs still largely relies on human inspection of images, a method unfeasible in the era of large synoptic surveys. The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will generate an unprecedented amount of astronomical imaging data at high spatial resolution, exquisite image quality, and over tens of thousands of square degrees of sky: an ideal survey for LEs. However, the Rubin data processing pipelines are optimized for the detection of point sources and will entirely miss LEs. Over the past several years, artificial intelligence (AI) object-detection frameworks have achieved and surpassed real-time, human-level performance. In this work, we leverage a data set from the Asteroid Terrestrial-impact Last Alert System telescope to test a popular AI object-detection framework, You Only Look Once, or YOLO, developed by the computer-vision community, to demonstrate the potential of AI for the detection of LEs in astronomical images. We find that an AI framework can reach human-level performance even with a size- and quality-limited data set. We explore and highlight challenges, including class imbalance and label incompleteness, and road map the work required to build an end-to-end pipeline for the automated detection and study of LEs in high-throughput astronomical surveys. 

Abstract Current and future optical and near-infrared wide-field surveys have the potential to find kilonovae, the optical and infrared counterparts to neutron star mergers, independently of gravitational-wave or high-energy gamma-ray burst triggers. The ability to discover fast and faint transients such as kilonovae largely depends on the area observed, the depth of those observations, the number of revisits per field in a given time frame, and the filters adopted by the survey; it also depends on the ability to perform rapid follow-up observations to confirm the nature of the transients. In this work, we assess kilonova detectability in existing simulations of the Legacy Survey of Space and Time strategy for the Vera C. Rubin Wide Fast Deep survey, with focus on comparing rolling to baseline cadences. Although currently available cadences can enable the detection of >300 kilonovae out to ∼1400 Mpc over the 10 year survey, we can expect only 3–32 kilonovae similar to GW170817 to be recognizable as fast-evolving transients. We also explore the detectability of kilonovae over the plausible parameter space, focusing on viewing angle and ejecta masses. We find that observations in redder izy bands are crucial for identification of nearby (within 300 Mpc) kilonovae that could be spectroscopically classified more easily than more distant sources. Rubin’s potential for serendipitous kilonova discovery could be increased by gain of efficiency with the employment of individual 30 s exposures (as opposed to 2 × 15 s snap pairs), with the addition of red-band observations coupled with same-night observations in g or r bands, and possibly with further development of a new rolling-cadence strategy.