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Connor Mooney

Publications and source records attributed to Connor Mooney.

At least 19 recordsLinked to original sources
arXiv2026

A Multiwavelength Study of a Long-Duration VHE Flare from BL Lacertae with VERITAS

We report the first observations of a long-duration very-high-energy (VHE; $E > 100$ GeV) flare from BL Lacertae (VER J2202+422), taken with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). On October 15, 2022, the Fermi-Large Area Telescope (LAT) detected elevated GeV activity originating from this blazar. This triggered a multiwavelength campaign, which includes observations from VERITAS, Swift, NuSTAR, and select optical and radio observatories. VERITAS observed the source for a total of $\sim 9.8$ hours between September 1, 2022 and December 1, 2022. An analysis of these data yields a $\sim 28 \sigma$ detection of the source. While previously observed VHE flares from BL Lacertae have lasted on time-scales of minutes to days, VERITAS continued to detect flaring activity from the source for over a month ($\sim 40$ days) after the original flaring activity was detected with Fermi-LAT. Broadband spectral modeling shows that a synchrotron self-Compton (SSC) model with an external inverse-Compton (EC) component is preferred over a one-zone SSC model.

astro-ph.HE↗
arXiv2025

Semi-convex viscosity solutions of the special Lagrangian equation

We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We show by example that the range of phases we consider and the semi-convexity condition are sharp. As an application, we find a new Liouville theorem for entire such solutions of the special Lagrangian equation with subcritical phase. We also find effective Hessian estimates with exponential dependence, which we show to be optimal.

math.AP↗
arXiv2025

VERITAS Follow-Up Observations of the Ultra-High-Energy Neutrino Event KM3-230213A

The recent announcement of the detection of the ultra-high-energy (UHE) neutrino event KM3-230213A by the KM3NeT telescope represents a critical opportunity to explore the origins of cosmic neutrinos and their potential gamma-ray counterparts. With an inferred neutrino energy exceeding 100 PeV, this event stands as the most energetic neutrino observed to date. The large offset from the galactic plane (11 degrees) and the presence of several blazars with temporally correlated multiwavelength counterparts within the 3 degrees localization region raise the possibility of an extragalactic origin. Additionally, the event's apparent tension with IceCube constraints suggests that it could be transient in nature rather than cosmogenic. VERITAS conducted a targeted follow-up campaign to search for very-high-energy (VHE, greater than 100 GeV) gamma-ray emission associated with KM3-230213A. Observations were performed in February and March 2025, using a four-point wobble strategy centered on the best-fit neutrino position, covering nearly the entire 90 percent confidence region. These observations probe potential hadronic gamma-ray emission from a common origin with the neutrino, placing constraints on particle-acceleration scenarios. We present the results of this search, including upper limits on very-high-energy gamma-ray flux and their implications for possible source models of KM3-230213A.

astro-ph.HE↗
arXiv2025

Remarks on the quadratic Hessian equation

We prove that viscosity solutions to the quadratic Hessian equation $$\sigma_2(D^2u) = 1$$ cannot touch a harmonic function on a minimal surface from below. This can be viewed as a form of strict $2$-convexity. We also prove an a priori interior $C^2$ estimate in terms of the $W^{2,\,p}$ norm, for any $p > 2$. Finally, we discuss how these results rule out certain strategies for constructing counterexamples to regularity.

math.AP↗
arXiv2025

VERITAS and multiwavelength observations of the Blazar B3 2247+381 in response to an IceCube neutrino alert

While the sources of the diffuse astrophysical neutrino flux detected by the IceCube Neutrino Observatory are still largely unknown, one of the promising methods used towards understanding this is investigating the potential temporal and spatial correlations between neutrino alerts and the electromagnetic radiation from blazars. We report on the multiwavelength target-of-opportunity observations of the blazar B3 2247+381, taken in response to an IceCube multiplet alert for a cluster of muon neutrino events compatible with the source location between May 20, 2022 and November 10, 2022. B3 2247+381 was not detected with VERITAS during this time period. The source was found to be in a low-flux state in the optical, ultraviolet and gamma-ray bands for the time interval corresponding to the neutrino event, but was detected in the hard X-ray band with NuSTAR during this period. We find the multiwavelength spectral energy distribution is well described using a simple one-zone leptonic synchrotron self-Compton radiation model. Moreover, assuming the neutrinos originate from hadronic processes within the jet, the neutrino flux would be accompanied by a photon flux from the cascade emission, and the integrated photon flux required in such a case would significantly exceed the total multiwavelength fluxes and the VERITAS upper limits presented here. The lack of flaring activity observed with VERITAS, combined with the low multiwavelength flux levels, and given the significance of the neutrino excess is at 3$\sigma$ level (uncorrected for trials), makes B3 2247+381 an unlikely source of the IceCube multiplet. We conclude that the neutrino excess is likely a background fluctuation.

astro-ph.HE↗
arXiv2024

Solutions to the minimal surface system with large singular sets

Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects called Cartesian currents. Essentially nothing is known about these limits. We show that such limits can have surprisingly large interior vertical and non-minimal portions. This demonstrates a striking discrepancy between the parametric and non-parametric area minimization problems in higher codimension. Moreover, our construction has the smallest possible dimension ($n = 3$) and codimension $(m = 2)$.

math.AP↗
arXiv2024

Bernstein theorems for nonlinear geometric PDEs

In this expository article we revisit the Bernstein problem for several geometric PDEs including the minimal surface, Monge-Amp\`{e}re, and special Lagrangian equations. We also discuss the minimal surface system where appropriate. The article is based on a lecture series given by the author for the inaugural European Doctorate School of Differential Geometry, held in Granada in June 2024.

math.DG↗
arXiv2024

Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is O(1/t) in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.

cs.LG↗
arXiv2024

Counterexamples to maximal regularity for operators in divergence form

In this paper, we present counterexamples to maximal $L^p$-regularity for a parabolic PDE. The example is a second-order operator in divergence form with space and time-dependent coefficients. It is well-known from Lions' theory that such operators admit maximal $L^2$-regularity on $H^{-1}$ under a coercivity condition on the coefficients, and without any regularity conditions in time and space. We show that in general one cannot expect maximal $L^p$-regularity on $H^{-1}(\mathbb{R}^d)$ or $L^2$-regularity on $L^2(\mathbb{R}^d)$.

math.AP↗
arXiv2023

A half-space Bernstein theorem for anisotropic minimal graphs

We prove that an anisotropic minimal graph over a half-space with flat boundary must itself be flat. This generalizes a result of Edelen-Wang to the anisotropic case. The proof uses only the maximum principle and ideas from fully nonlinear PDE theory in lieu of a monotonicity formula.

math.AP↗
arXiv2023

On the Lawson-Osserman conjecture

We prove that if $u : B_1 \subset \mathbb{R}^2 \rightarrow \mathbb{R}^n$ is a Lipschitz critical point of the area functional with respect to outer variations, then $u$ is smooth. This solves a conjecture of Lawson and Osserman from 1977 in the planar case.

math.AP↗
arXiv2023

A VERITAS/Breakthrough Listen Search for Optical Technosignatures

The Breakthrough Listen Initiative is conducting a program using multiple telescopes around the world to search for "technosignatures": artificial transmitters of extraterrestrial origin from beyond our solar system. The VERITAS Collaboration joined this program in 2018, and provides the capability to search for one particular technosignature: optical pulses of a few nanoseconds duration detectable over interstellar distances. We report here on the analysis and results of dedicated VERITAS observations of Breakthrough Listen targets conducted in 2019 and 2020 and of archival VERITAS data collected since 2012. Thirty hours of dedicated observations of 136 targets and 249 archival observations of 140 targets were analyzed and did not reveal any signals consistent with a technosignature. The results are used to place limits on the fraction of stars hosting transmitting civilizations. We also discuss the minimum-pulse sensitivity of our observations and present VERITAS observations of CALIOP: a space-based pulsed laser onboard the CALIPSO satellite. The detection of these pulses with VERITAS, using the analysis techniques developed for our technosignature search, allows a test of our analysis efficiency and serves as an important proof-of-principle.

astro-ph.IM↗
arXiv2023

VERITAS discovery of very high energy gamma-ray emission from S3 1227+25 and multiwavelength observations

We report the detection of very high energy gamma-ray emission from the blazar S3 1227+25 (VER J1230+253) with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). VERITAS observations of the source were triggered by the detection of a hard-spectrum GeV flare on May 15, 2015 with the Fermi-Large Area Telescope (LAT). A combined five-hour VERITAS exposure on May 16th and May 18th resulted in a strong 13$\sigma$ detection with a differential photon spectral index, $\Gamma$ = 3.8 $\pm$ 0.4, and a flux level at 9% of the Crab Nebula above 120 GeV. This also triggered target of opportunity observations with Swift, optical photometry, polarimetry and radio measurements, also presented in this work, in addition to the VERITAS and Fermi-LAT data. A temporal analysis of the gamma-ray flux during this period finds evidence of a shortest variability timescale of $\tau_{obs}$ = 6.2 $\pm$ 0.9 hours, indicating emission from compact regions within the jet, and the combined gamma-ray spectrum shows no strong evidence of a spectral cut-off. An investigation into correlations between the multiwavelength observations found evidence of optical and gamma-ray correlations, suggesting a single-zone model of emission. Finally, the multiwavelength spectral energy distribution is well described by a simple one-zone leptonic synchrotron self-Compton radiation model.

astro-ph.HE↗
arXiv2023

Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows

The level-set curvature G-equation, a well-known model in turbulent combustion, has the following form $G_t + \left(1-d\, \mathrm{dvi}\left({\frac{DG}{|DG|}}\right)\right)_+|DG|+V(X)\cdot DG=0.$ Here the cutoff correction $()_+$ is imposed to avoid non-physical negative local burning velocity. The existence of the effective burning velocity has been established for a large class of physically relevant incompressible flows $V$ in two dimensions [13] via game theory dynamics. In this paper, we show that the effective burning velocity associated with shear flows in dimensions three or higher ceases to exist when the flow intensity surpasses a bifurcation point. The characterization of the bifurcation point in three dimensions is closely related to the regularity theory of two-dimensional minimal surface type equations due to [29]. As a consequence, a bifurcation also exists for the validity of full homogenization of the curvature G-equation associated with shear flows.

math.AP↗
arXiv2022

The anisotropic Bernstein problem

We construct nonlinear entire anisotropic minimal graphs over $\mathbb{R}^4$, completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of entire minimal graphs over $\mathbb{R}^{n},\, n \geq 8$.

math.AP↗
arXiv2022

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$. Combined with the a priori interior Hessian estimates proved in [Bha21, Bha22], this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.

math.AP↗