Over the past decade, runaway stars have been identified, believed to originate either as surviving donors of Type Ia supernovae or as partially deflagrated accretors producing Type Iax supernovae. While the former have been extensively studied recently, the origins of the latter (also called LP 40-365 type stars) remain under-explored and therefore less well understood. So far seven such objects are known. In this paper, we report the discovery of a new LP 40-365 type runaway star, notably hotter than previously studied members of this class. Spectral analysis confirms that its atmosphere is neon- and oxygen-dominated, consistent with earlier analyses of other LP 40-365 type stars. Kinematic analysis indicates that the star has a high probability of being unbound from the Galaxy and was most likely ejected from the Galactic disk approximately 2.8 Myr ago with an ejection velocity exceeding 600 km/s. This result further emphasizes the discrepancy between the abundance yields and kick velocities predicted by white dwarf deflagration models and those observed in stars of LP 40-365 type, underscoring the need for a reassessment of such systems.

X-ray timing of active galactic nuclei (AGN) provides a unique probe of gas accretion onto supermassive black holes (SMBHs). Quasi-periodic oscillations (QPOs), which trace gas dynamics in the strongly curved spacetime around SMBHs, are rare in AGN. These signals often are analogs of high-frequency QPOs occasionally seen in some black-hole X-ray binaries, and their scarcity in AGN can partly be attributed to the low frequencies expected for typical SMBH masses. Intriguingly, robust X-ray QPO detections in SMBH systems have so far been reported only in narrow-line Seyfert 1 galaxies (NLS1s) and tidal disruption events (TDEs). Here we report the discovery of a QPO candidate during the 2018 outburst of the changing-look AGN (CL-AGN) NGC 1566. Numerical simulations indicate that the disk epicyclic oscillations responsible for high-frequency QPOs are damped by magnetohydrodynamic turbulence unless the accretion flow is misaligned and/or eccentric. In TDEs, the stellar debris stream is naturally misaligned with the SMBH spin, while NLS1s may host misaligned disks due to their youth. Motivated by the QPO candidate in NGC 1566, we propose that CL-AGN accretion is also misaligned -- potentially fueled by captured, free-falling broad-line region clouds. This model naturally explains why CL-AGN transition timescales are much shorter than the standard disk viscous timescale. This picture can be tested by searching for QPOs or quasi-periodic eruptions in other CL-AGN.

The Perseus Cluster has been precisely measured by the legacy Hitomi telescope on the Si-group (Si, S, Ar, Ca) and Fe-group elements (Cr, Mn, Ni). These element abundance ratios provide insight into the typical behaviour of supernovae. In Paper II, we presented new massive star explosion models at various metallicity, assuming spherical explosions. We show that while the fitting is improved, some features (e.g., Ni/Fe) remain to be improved. In this article, we extend our calculation to an aspherical explosion using the jet-induced explosion mechanism. The detailed pre- and post-explosion chemical profiles are calculated with a large post-processing network to capture the production of odd-number elements (V, Mn, Cu) and iron-group elements. We further explore how the jet-driven explosions create the diversity of models which could be compatible with the observed diversity in terms of $^{56}$Ni-mass vs ejecta mass, Ti-V relation, and stellar abundances. Finally, we apply the new collapsar models in the Galactic Chemical Evolution context. We study how the galactic stars, including the Zn-enriched star HE 1327-2326, can put constraints on the relative rates of collapsar and some of its model parameters. We show that collapsar could lead to significant changes in some elements, e.g., Zn. Our study shows that the collapsar is a necessary component to explain multiple elemental trends observed in the Milky Way Galaxy.

The legacy Hitomi telescope has delivered the precise measurements of the chemical abundances in the Perseus Cluster, covering the Si-group (Si, S, Ar, Ca) and Fe-group elements (Cr, Mn, Ni). In Paper I (Leung et al., ApJ 2025), we examined the role of convection parameters and presented new core-collapse supernova (CCSN) explosion models at solar metallicity, which fit the observed abundance pattern. In this article, we extend our calculation for the stellar evolutionary models and CCSN models of the initial mass $15 - 60M_{\odot}$ and the metallicity $Z = 0 - Z_{\odot}$. The detailed pre- and post-explosion chemical profiles are calculated with a large post-processing network to capture the production of $α$-chain elements (e.g., Si, S, Ar), odd-number elements (e.g., P, K, Cl), and iron-group elements (e.g., Mn, Ni). We study the role of CCSNe in the production of these elements. We compare the galactic chemical evolution model based on the nucleosynthesis yield of the new massive stars and other yield tables from the literature. For each supernova yield, we perform parameter surveys and search for configurations that produce the best-fit model and best-rate model using the Perseus Cluster as the reference. From the survey, we study how individual chemical elements affect the contributions of massive stars and Type Ia supernovae in the cosmic chemical enrichment

We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is played in this context by a certain root stack over the local model for parahoric level. The construction of this root stack is based on the "divisor theorem" (a foundational fact about local models) and on the theory of toric varieties in this context, both of which are of independent interest. We prove our conjecture in the case of Shimura varieties of PEL type when the parahoric is an Iwahori (under some additional conditions).

A fast simulation method is presented for a depleted monolithic active pixel sensor, which uses a data driven parameterization of the charge collection and propagation. This approach provides an efficient alternative to TCAD simulations, particularly for sensors whose proprietary process details - such as doping profiles or implant geometries - are unavailable. Data was obtained with a MALTA2 sensor fabricated in a 180 nm CMOS imaging technology on 30 μm epitaxial silicon using the MALTA beam telescope at CERN SPS. The model reproduces the measured inpixel efficiency with high accuracy and enables a realistic yet computationally lightweight analog pixel simulation. This method will be further employed in optimizing the digital sensor design for applications in high-rate particle tracking and high-granularity calorimetry.

Newly formed stars have a profound impact on their environment by depositing energy and momentum into the surrounding gas. However, only a fraction of the stellar feedback is retained in the cloud and observational constraints are needed to further our understanding of this process. In a sample of 19 nearby galaxies, we match HII regions from PHANGS$\unicode{x2013}$MUSE to their ionizing stellar source from PHANGS$\unicode{x2013}$HST and measure the percentage of ionizing radiation that is leaking into the surrounding diffuse ionized gas (DIG). Based on a catalogue, where each HII region is powered by a single young and massive stellar association, we measure a photon escape fraction of $f_\mathrm{esc}=82^{+12}_{-24}$ per cent. Comparable results are obtained when different procedures are used to match the ionized gas to its source. All samples we study contain a substantial fraction of objects (up to 20 per cent), where the stellar source is not sufficient to produce the H$α$ flux observed from the nebula. Many of them are probably related to uncertain age estimates, but we also find numerous regions, where a significant fraction of the ionizing photon budget is contributed by stars that reside outside the boundaries of the HII region. This motivates the use of an alternative galaxy-wide approach, in which we include all HII regions and stellar sources, not just the ones that show a clear overlap. When summing up the ionization budget over entire galaxies, we measure slightly lower, but consistent values.

In 1977, Makanin established the decidability of equations in free monoids. A key ingredient in his proof is the exponent of periodicity: for a word $w$, it is the largest exponent $e$ such that $w$ contains a nonempty factor of the form $p^e$. Makanin showed the following for a system of equations in free monoids: if the system has a solution with a sufficiently large exponent of periodicity, then it has infinitely many solutions. However, the converse -- whether the existence of infinitely many solutions implies the existence of solutions with arbitrarily large exponent of periodicity -- remains open. In this paper, we investigate the analogous problem for quadratic equations in finitely generated groups. We use normal forms to define the exponent of periodicity. We then identify structural conditions on groups and their normal forms that guarantee that infinite solution sets of quadratic systems have an unbounded exponent of periodicity. We prove that these conditions are preserved under graph products and, in particular, hold for all finitely generated right-angled Artin groups. In addition, we show that they also hold for finitely generated (graph products of) torsion-free nilpotent and hyperbolic groups, and we characterize the Baumslag-Solitar groups satisfying them.

On the periphery of galaxy clusters, moderately high galaxy densities and velocity dispersions favour interactions and mergers that influence galaxy evolution prior to cluster infall. Observational studies of this phase in dwarfs remain rare. We present a high-resolution study of the merger remnant VCC 693 in the outskirts of Virgo cluster, using observations from the Atomic gas in Virgo Interacting Dwarf galaxies (AVID) project. We explore the origin of VCC 693 and the consequences of the merger on its star formation and structure through a joint analysis of VLA and FAST HI emission line observations, together with complementary optical imaging and spectroscopy. We employ hydrodynamical simulations to help interpret the observations. Our analysis favours a near-major merger between two dwarfs with a stellar mass ratio of 3:1-4:1, with one likely gas-poor progenitor (i.e., a damp merger). The optical appearance of VCC 693 is dominated by complex tidal structures throughout the system, whereas the HI gas has settled to a regular rotating disk. Compared with similar-mass dwarfs, the central star formation and gas-phase metallicity are moderately enhanced. The global star formation rate, HI gas content, and HI-to-optical size ratio of VCC 693 are broadly consistent with those of typical dwarfs of similar mass, albeit somewhat lower. Decomposition of the HI rotation curve into baryonic and dark matter indicates a high halo concentration, suggesting post-merger relaxation into a more centrally peaked configuration. Together with two recent studies of AVID post-merger systems, these results support the view that even major dwarf mergers can produce remnants with overall stellar structures indistinguishable from ordinary dwarfs, and that the environmental effects in cluster outskirts can promote damp or mixed mergers, constituting an integral part of galactic pre-processing.

An accurate model of the point spread function is required in order to estimate positions and brightnesses of stars in digitized images. The PSF of the Gaia space telescope is unusual due to the use of drift-scan mode and time-delayed integration, in which the satellite spins and precesses while images are captured. This induces several systematic and periodic distortions in the PSF that are unique to Gaia. These include systematic variations in the stellar image drift rate with respect to the charge transfer rate, and spatial variations in the CCD response that are, contrary to expectations, not marginalised by the use of TDI mode. These must be incorporated into the PSF model in order to reduce systematic errors in Gaia's data products. We have developed a semi-analytic model of the PSF, in which the blurring effects of along- and across-scan stellar image motion are modelled analytically, and dependences of the PSF shape on source colour and position within the CCD are calibrated empirically. Constraints on the PSF origin are introduced in order to break a degeneracy with the geometric instrument calibration. Our new PSF model leads to significant improvements in the modelling of observations, particularly around the 11-13 magnitude range in G. This will contribute to reductions in the astrometric and photometric uncertainties in the derived data products. Our PSF model was deployed in the Gaia cyclic data processing systems and used in the production of the forthcoming Data Release 4. The linear part of Gaia's PSF is now well understood. Future development work will focus on the handling of several nonlinear effects that depend on the signal level, including charge transfer inefficiency and the brighter-fatter effect. This work will provide a useful reference for users of Gaia data and for other missions that use the same observing principles, such as the proposed GaiaNIR mission.

The radiolysis effect of cosmic rays (CRs) plays an important role in the chemistry in molecular clouds. CRs can dissociate the molecules on dust grains, producing reactive suprathermal species and radicals which facilitate the formation of large molecules. We add the radiolysis process and some relevant reactions into the Nautilus astrochemical code. By adjusting some parameters, we investigate the sensitivity of the simulation results of the H2O ice on the removal of reaction-diffusion competition, the removal of non-diffusive chemistry, and the desorption energies of the suprathermal species. We find the model, with a few adjustments of the chemistry, can reproduce the steady-state [H2O2]/[H2O] and [O3]/[O2]_0 abundance ratios in the H2O and O2 radiolysis experiments at any CR flux in the experiments. These adjustments in the model do not fully reproduce the fluence required to reach the steady state. It tends also to overestimate the destruction of H2O as measured in H2O radiolysis experiments. We show that reducing the G-values of H2O radiolysis, which implies an increase in the efficiency of immediate reformation of water locally after ion impact, leads to simulated H2O destruction rates closer to the experiments. The effect of reaction-diffusion competition on the simulation results of H2O ice is significant at $ζ\lesssim 10^{-14}\ \rm s^{-1}$. The non-diffusive chemistry affects the simulation results at 16 K but not 77K, while the results are sensitive to the desorption energies of suprathermal H, O, O3 and OH at 77 K. Our results show that the steady-state [H2O2]/[H2O] and [O3]/[O2]_0 in experiments can be reproduced by fine-tuning the chemical model, but still call for more constraints on the intermediate pathways in the radiolysis processes, especially the ion chemistry in the ice bulk, as well as activation barriers and branching ratios of the reactions in the network.

We provide context for Apophis' 2029 Earth passage by analyzing its possible source populations, in particular, the Flora family, which has a similar composition, corresponding to LL chondrite meteorites. Out of ${\sim}3380$ NEOs larger or equal than Apophis (${\ge}420\,{\rm m}$), $610\pm 140$ are LL-like NEOs from Flora. Their mean encounter probability is $p = 86\times 10^{-18}\,{\rm km}^{-2}\,{\rm y}^{-1}$, corresponding to once per 13000 y frequency of encounters closer than 38000 km. However, this does not apply to Apophis alone, for which the specific encounter probability is higher, $p' = 1603\times 10^{-18}\,{\rm km}^{-2}\,{\rm y}^{-1}$, but the frequency is lower, only once per 430000 y, when we consider it as a single object. Our simulation of the Flora family over $\sim$1 billion years indicates that Apophis-like bodies have orbits that are particularly persistent in near-Earth space. The temporal distribution of encounter probabilities exhibits peaks (up to ${>}10^4$ in the same units) and the specific value for Apophis is not unusual (occurring ${\sim}70\%$ of time). In other words, there is always at least one Apophis-like body among NEOs. We find that such persistence also creates favorable opportunities for temporary capture as Earth coorbitals. Apophis-like bodies are ultimately removed from the inner solar system by approaching the Sun or by impact into one of the terrestrial planets, where the relative split between these outcomes is $(45\pm 2)\,\%$ and $(50\pm 2)\,\%$. While our current knowledge of Apophis' orbit guarantees no threat from Apophis in the next few centuries, we cannot predict any specific outcome for Apophis in the coming thousands or millions of years. Evaluating this statistically over the long term, we find that objects in Apophis-like orbits have a $(19\pm 2)\,\%$ chance of Earth impact over their lifetime of ${\sim}30\,{\rm My}$.

Dwarf galaxies are important laboratories for studying cosmic magnetism because they can maintain strong magnetic fields via the action of turbulent dynamo despite their low mass and weak gravitational potential. The Magnetic-field Evolution in Dwarf galaxies from Ultra-deep SKA Analysis (MEDUSA) survey is the first SKA-pathfinder programme designed to obtain deep continuum, polarisation, and HI data for dwarf galaxies, enabling a comprehensive study of their radio spectra, magnetic fields, and gas kinematics across a representative population. By analysing the radio continuum spectra and polarisation of the dwarf-dwarf galaxy merger NGC 1487 from the MEDUSA sample, we aim to determine its magnetic field strength and to characterise the large-scale and turbulent components of its magnetic field. We utilise highly sensitive multi-band radio continuum data from MeerKAT L-band (1.28 GHz) and Australia Telescope Compact Array (ATCA) L/S (2.1 GHz), C (5.5 GHz), and X-bands (9 GHz). We analysed the magnetic field configuration using polarisation and rotation measure (RM) synthesis. The integrated spectral energy distribution has a non-thermal spectral index of $α_{\rm nth} = -0.678\pm0.085$. Synchrotron and inverse Compton losses cause a spectral break at $ν_{\rm b} = 6.2\pm1.3$ GHz. In star-forming regions, the magnetic field exhibits strong small-scale fluctuations in RM, suggesting the action of a small-scale dynamo. Conversely, the field becomes more ordered, aligning with the tidal arms toward the galaxy's outskirts, showing a large-scale magnetic field over $\approx3$ kpc. Observations of the dwarf-dwarf merger NGC 1487 show that even low-mass galaxy mergers, likely the building blocks of larger galaxies in the early Universe, can rapidly amplify and produce coherent large-scale magnetic field structures, highlighting their key contribution in the early magnetisation of galaxies.

Type II supernovae (SNe II) have been traditionally separated into several subgroups based on their photometric and spectroscopic properties, but whether these represent distinct progenitors or a continuous distribution remains debated. Over the past decade, growing observational evidence has suggested a possible continuity between slow- (IIP) and fast-declining (IIL) SNe. We investigate the continuity of the SNe IIP/L subclasses through a data-driven statistical analysis of spectral time series, aiming to determine whether significant correlations exist between overall spectral shapes and light-curve decline rates. We introduce a novel standardization method for SN II spectra. After empirically flattening the spectra via continuum normalization, we interpolate the resulting "feature spectra" onto a fixed grid of epochs using Gaussian Process regression. The interpolated spectra are then analyzed using Principal Component Analysis to explore correlations. We find that SNe IIP and IIL form a continuum spectroscopically, though some clustering remains. The spectral diversity is characterized mainly by two components: one continuous group with well-defined P-Cygni profiles and another with "less-regular" features likely driven by enhanced circumstellar material (CSM) interaction. Our results reveal that the spectral diversity of SNe IIP/L diminishes over time. We confirm observational correlations: steeper light-curve declines correspond to weaker spectral features, indicating that SNe IIL tend to show weaker emission and, in some cases, a lack of distinct absorption lines. These trends seemingly break down by enhanced CSM interaction that affects the P-Cygni profiles. Our data-driven method reveals underlying spectral correlations and supports a continuous distribution between IIP and IIL subtypes. This method paves the way for more refined classification algorithms.

In this paper we present PSR J0024$-$7204ai, a 13.026-ms binary pulsar recently discovered in the globular cluster 47 Tucanae by the MeerKAT radio telescope. This is the slowest spinning pulsar known in this globular cluster, and has a $\sim1.67$-day orbit with an eccentricity of $e\approx0.18$. Although it was not yet possible to derive an unambiguous phase-connected timing solution, by combining detections obtained from MeerKAT and archival Parkes data we were able to measure the rate of advance of periastron to high significance, $\dotω$ = 0.1601 $\pm 0.0046$ deg yr$^{-1}$. This value implies a total system mass of $2.41 \pm 0.11\, \mathrm{M}_\odot$ (68.3\% C. L.), which, when combined with the binary mass function, gives a maximum pulsar mass of $\sim 1.7 \, \mathrm{M}_\odot$ and a minimum companion mass of $\sim 0.7\, \mathrm{M}_\odot$. Apart from being the slowest pulsar in 47~Tucanae, its orbit is by far the most eccentric and its companion is the most massive among all known binary pulsars in this globular cluster. One possibility is that system is an old MSP - Carbon-Oxygen White Dwarf binary, whose orbit was perturbed by stellar dynamical interactions in the cluster core. Further follow-up observations of this system will be essential for a more detailed characterisation of this system and its evolution.

We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equations. The approach introduces a notion of generalized Coriolis force, whose spectrum underlies the construction of these solutions. We recover classical exact solutions such as Kelvin and Rossby-Haurwitz waves, while also producing new explicit examples on curved surfaces and three-dimensional manifolds including the round three-sphere. Furthermore, we obtain a complete classification in two dimensions and a partial classification in three dimensions of the Riemannian manifolds that admit such solutions. The method is in fact formulated in the general Euler-Arnold setting and yields a simple criterion for non-stationarity.

Galaxies evolve within vast gaseous halos that fuel star formation and carry signatures of feedback-driven outflows. Deep integral field data have enabled the study of MgII halos, which trace galaxy-scale outflows in emission, but their faintness has limited studies to single-object analyses. Here, we present the first statistical study of MgII-emitting halos using deep MUSE observations of 47 star-forming galaxies at $0.7<z<2.0$. Building on our previous work, where we developed and applied an outflow modeling framework for a single MgII halo, we now extend this approach to a larger sample, enabling robust population-level insights on the properties of circumgalactic outflows traced by their extended MgII emission. We detect extended emission out to tens of kiloparsecs and model the outflows as an ensemble of radially accelerating shells. Galaxies with MgII outflows tend to have higher SFRs, sSFRs, and younger stellar populations, consistent with star-formation-driven winds. The observations are consistent with winds that accelerate linearly with radius, from launching velocities of ~60 km/s up to maximum velocities that correlate with stellar mass and reach ~490 km/s. Their inner regions are highly opaque, and we find a tentative trend between stellar mass and central optical depth. The opening angle of the outflow shows some dependency on the host-galaxy stellar mass, with less massive galaxies showing primarily wide opening angles, and more massive galaxies showing a broader range of values, with both wide and narrow opening angles. The distribution of the spatial extent of MgII halos exhibits a clear peak at half-light radius (HLR) of ~5 kpc, with an extended tail of larger HLR values, up to ~20 kpc. Compact halo sizes (HLR $< 8$ kpc) correlate with stellar mass, but extended halos do not, which could suggest a difference in the powering mechanism between compact and extended halos.

We construct a family of test kernels for use in spectral trace formulas on locally symmetric spaces. The key innovation is the factorization $h_T = g_T \star \widetilde{g}_T$, which simultaneously achieves: (i) automatic positive semi-definiteness of the spectral multiplier $m_{h_T}(π) = |m_{g_T}(π)|^2 \ge 0$; (ii) $J$-fold moment annihilation via a multi-scale Vandermonde construction, yielding super-polynomial decay of all error terms; (iii) uniform spectral parameter bounds (Master-Bound) $\mathfrak{E}_{\mathrm{tot}}(T) \ll T^{d+1-δ}$ with $δ> 0$ depending only on the symmetry order $k$ and the annihilation depth $J \asymp \sqrt{(\log T)/k}$, representing a power saving over the main term $\asymp T^{d+1}$. The cost is a controlled polynomial growth $T^{c_0^2/2+o(1)}$ in the Vandermonde coefficients (with exponent strictly less than 1), which is dominated by the super-polynomial decay of the off-diagonal terms. The construction is axiomatized over two analytic hypotheses -- a Weyl law and Bessel/Airy asymptotics -- making it applicable beyond the classical $\mathrm{GL}(2)$ setting.

Observational extragalactic catalogs over wide sky areas are essential for uncovering the large-scale structure of the Universe. They allow, among others, cosmological studies and density analyses that impose strong constraints on models of galaxy formation and evolution. By taking advantage of the wide field images and the 12 optical bands of the Southern Photometric Local Universe Survey (S-PLUS), we aim at providing a catalog of galaxies located, in projection, towards the Fornax galaxy cluster, within $\sim$ 5 virial radii in right ascension (R.A.) and $\sim$ 3 virial radius in declination (Dec) around NGC,1399, the dominant galaxy of the cluster. Such a catalog will allow unprecedented large-scale structure studies in that sky region. Supervised deep learning algorithms have been developed, utilizing neural networks complemented with dimensionality reduction techniques, to classify and separate spurious objects, stars and galaxies in a photometric catalog previously built for the S-PLUS Fornax Project (S+FP). That catalog was built using a combination of SExtractor configurations optimized for galaxy detection and characterization. A catalog of 119,580 galaxies was obtained in the direction of the Fornax cluster containing photometric information in the 12 optical bands of S-PLUS complemented with GALEX (UV), VHS-VISTA (NIR) and AllWISE (MIR) data. We estimate photometric redshifts (σ_ NMAD $\sim$ 0.0219) with a lower limit of z_ lim $\sim$ 0.03. Stellar masses, star formation rates (SFRs) and D4000_N index estimates were obtained through a machine learning approach, by matching S-PLUS photometric data to SDSS spectroscopic data. The completeness of the catalog (72%) was calculated by comparing with mock catalogs ...

Modern telescopes generate increasingly large and diverse datasets, often consisting of complex and morphologically rich structures. To efficiently explore such data requires automated methods that can extract and organize physically meaningful information, ideally without the need for extensive manual interaction. We aim to provide a user-friendly implementation of a self-supervised machine learning framework to explore morphological properties of large datasets, based on the BYOL (Bootstrap Your Own Latents) method. By enabling the generation of meaningful image embeddings without manually labelled data, the framework will enable key tasks such as clustering, anomaly detection, and similarity based exploration. In contrast to existing BYOL implementations, astromorph accommodates data of varying dimensions and resolutions, including both single-channel FITS images and multi-channel spectral cubes. The package is built with usability in mind, offering streamlined pipeline scripts for ease of use as well as deeper customization options via PyTorch-based classes. To demonstrate the utility of astromorph, we apply it in two contrasting science cases representing different astronomical domains: images of protoplanetary disks observed with ALMA, and infrared dark clouds observed with Spitzer and Herschel. In both cases, we demonstrate how astromorph produces scientifically meaningful embeddings that capture morphological differences and similarities across large samples. astromorph enables users to apply a robust, label-free approach for uncovering morphological patterns in astronomical datasets. The successful application to two markedly different datasets suggest that the pipeline is broadly applicable across a wide range of imaging-rich astronomical context, providing a user friendly tool for advancing discovery in observational astronomy.

Let $a,b,c\in\mathbb C$ with $\re(a)<0$, we show that the extended Gaussian $e^{ax^2+bx+c}$ has maximal frame set (i.e., its frame set consists of precisely all positive pairs $(α,β)$ with $αβ<1$), and its Zak transform has a unique simple zero in the unit square $[0,1)^2$ (in particular, the zero is at the center of the unit square if $b=0$). These statements extend the same results of the usual Gaussian (the cases when $a<0$ and $b,c\in\mathbb R$), and add more instances to the observation that if a continuous Wiener function has maximal frame set, then its Zak transform has a unique simple zero in the unit square. The proof of the maximality of the frame set combines metaplectic representation with a classical density result of the standard Gaussian. The proof of the uniqueness of the zero relies on properties of the theta function.

This paper introduces a novel characteristics-based specification for linear demand to investigate endogenous product design. Characteristics are allowed to affect both consumers' product valuations and to what extent these compete. I demonstrate how such a specification can help linear demand deliver fresh insights in how firms may optimally design existing goods, as well as predict demand for new products. The framework is novel in its broad applicability to settings with any finite number of goods, firms, and product characteristics, with both vertical and horizontal differentiation across different market structures, and under asymmetry.

Recent studies suggest that chemical abundances hold the key to disentangling halo substructure, providing a more reliable tracer than dynamics alone. We aim to probe the Milky Way stellar halo using high-dimensional chemical abundances from GALAH DR4. By leveraging multiple nucleosynthesis channels in synergy with integrals of motion (IoM), we extract information hidden in the raw abundance space to perform chemical tagging. With a graph attention autoencoder, we reconstruct a dynamics-informed, denoised chemical space and identify coherent stellar substructures by applying ensemble clustering. Our method successfully recovers the three largest globular clusters hidden in the dataset, estimates the in-situ fraction to be approximately 41\%, and chemically characterizes several dynamical halo substructures. Strikingly, stars dynamically associated with Gaia-Sausage-Enceladus (GSE) separate into two chemically distinct clusters. By examining their abundances, energy ($E$) and angular momentum ($L_z$) distributions, together with the metallicity trend with $E$, we connect these clusters to their birthplace within the progenitor by proposing a simple infall scenario: one cluster traces the metal-poor, less evolved outskirts, while the other traces the metal-rich, chemically evolved core.

Stellar fly-bys can have multiple dynamical effects on protoplanetary disks, including warping and the excitation of spiral arms. Since observations indicate that warps are common, we aim to investigate these effects for different fly-by trajectories. We further link our models to observations by applying them to the RW Aur system, which is a fly-by candidate with a relatively well constrained trajectory. We investigate the disk dynamics in grid-based hydrodynamical simulations, which allow for a lower disk viscosity than commonly used SPH models. We post-process our simulations of the RW Aur system with radiative transfer models to create synthetic images of the dust continuum and gas kinematics. Fly-bys inclined with respect to the original disk plane can excite warps of a few degrees: the exact outcome depends on the specific geometry of the encounter. Specifically, we find that the position of the periastron with respect to the initial disk plane plays a role for the resulting warp strength. Within our parameter set, the strongest warp is excited for a retrograde fly-by with a periastron that is not in the same plane as the disk. Our models show that the warp can persist even after the perturber can no longer be clearly linked to the system, implying that past fly-bys are a possible origin of observed warps. Excited spirals arms, on the other hand, are much more short-lived than the warp. The RW Aur system presents a perfect opportunity to apply these results: we find that a warp of about 5° can be excited, and that the strong spiral arms have already disappeared at the current time of observation 300 years after periastron). This compares well with existing continuum observations, and our synthetic kinematic evaluations hint at remnant structures in the gas density that may be detectable.

We uncover an effective and communicative set of agents working with MadGraph. Agentic installation, learning-by-doing training, and user support provide easy access to state-of-the-art simulations and accelerate LHC research. We show in detail how MadAgents interact with inexperienced and advanced users, support a range of simulation tasks, and analyze results. In a second step, we illustrate how MadAgents automatize event generation and run an autonomous simulation campaign, starting from a pdf file of a paper. The updated Claude Code implementation includes a self-improvement loop.

This paper investigates the geometric inverse problem of recovering the bottom shape from surface measurements of water waves. Using the general water-waves system on a bounded subdomain of the fluid domain, we address this inverse problem, focusing on the identifiability and the stability issues. We establish uniqueness and derive logarithmic stability estimates in the determination of the bathymetry on any fixed smooth, bounded, open domain ${\mathcal O}\subset {\mathbb R} ^d$, $d=1,2$, from the knowledge of the free surface, its first time derivative, and the trace of the velocity potential on the free surface, at a given instant $t_0$ within $\mathcal O $, together with the knowledge of the bottom along $\partial \mathcal O$. No further assumptions are required for uniqueness. For stability, we impose only a \textit{local fatness} condition on the region between the bottom profiles, allowing us to adapt the size estimates method.

We set up and solve the initial value problem for equivariant harmonic maps of cohomogeneity one manifolds, i.e. we show the local existence of a harmonic map in the neighborhood of a singular orbit. Furthermore, we present some theory of regular-singular systems of first order.

The Galactic Be star binary MWC 656 was long considered the only known Be star+black hole (BH) system, making it a critical benchmark for models of massive binary evolution and for the expected X-ray emission of Be+BH binaries. However, recent dynamical measurements cast doubt on the presence of a BH companion. We present new multi-epoch ultraviolet spectroscopy from the Hubble Space Telescope, combined with high-resolution optical spectra, to reassess the nature of the companion. The far-ultraviolet spectra reveal high-ionisation features -- including prominent N v and He ii lines -- which are absent in the spectra of normal Be stars and are indicative of a hot, luminous companion. Spectral modelling shows that these features cannot originate from the Be star or from an accretion disc around a compact object. Instead, we find that the data are best explained by a hot ($T_\mathrm{eff} \approx 85$ kK), compact, hydrogen-deficient star with strong wind signatures, consistent with an intermediate-mass stripped star. Our revised orbital solution and composite spectroscopic modelling yield a companion mass of $M_2 = 1.48^{+0.55}_{-0.46}\,\mathrm{M}_\odot$, definitively ruling out a BH and disfavouring a white dwarf. MWC 656 thus joins the growing class of Be+stripped star binaries. The system's unusual properties -- including a high companion temperature and wind strength -- extend the known parameter space of such binaries. The continued absence of confirmed OBe+BH binaries in the Galaxy highlights a growing tension with population synthesis models.

Notoriously hard to detect and study, isolated neutron stars (NS) could provide valuable answers to fundamental questions about stellar evolution and explosion physics. With the upcoming Roman Space Telescope, scheduled for launch in 2026, a new and powerful channel for their detection - astrometric microlensing - will become available. We set out to create a realistic sample of simulated gravitational microlensing events as observed by Roman with the Galactic Bulge Time Domain Survey. We focus in particular on the population of NS lenses, which has until now been largely understudied. We use state-of-the-art Galactic models tailored for application to microlensing by compact objects. We simulate four different NS populations with Maxwellian natal kick distributions: $\bar{v} = (150, \ 250, \ 350, \ 450)$ km/s. We apply projected Roman precision, cadence, and detectability criteria. We find the parameter space $\log_{10} t_{\rm E}$ - $\log_{10} θ_{\rm E}$, which will be accessible to Roman observations, to be maximally efficient for classification of stellar remnants. We find a feature in this space that is characteristic to NS; using this feature, optimal samples of NS candidates can be constructed from Roman-like datasets. We describe the dependence of observable parameter distributions on the assumed mean kick velocities. As the effects of natal kicks are very complex and mutually counteracting, we suggest more detailed studies focused on the dynamics of NS are needed in anticipation of Roman and future surveys. We estimate Roman will observe approximately $11\,000$ microlensing events - including $\sim100$ with NS lenses - whose both photometric and astrometric signal are detectable; the event yield decreases by $38\%$ if gap-filling low-cadence observations are not included. We make all simulated microlensing event datasets publicly available in preparation for Roman data.

The ongoing Euclid mission aims to measure spectroscopic redshifts for approximately two million galaxies using the H $α$ line emission detected in near-infrared slitless spectroscopic data from the Euclid Deep Fields (EDFs). These measurements will reach a flux limit of $5\times 10^{-17}\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ in the redshift range $0.4<z<1.8$, opening the door to numerous investigations involving galaxy evolution, extending well beyond the mission's core objectives. The achieved H $α$ luminosity depth will lead to a sufficiently high sampling, enabling the reconstruction of the large-scale galaxy environment. We assess the quality of the reconstruction of the galaxy cosmic web environment with the expected spectroscopic dataset in EDFs. The analysis is carried out on the Flagship and GAEA galaxy mock catalogues. The quality of the reconstruction is first evaluated using geometrical and topological statistics measured on the cosmic web, namely the length of filaments, the area of walls, the volume of voids, and its connectivity and multiplicity. We then quantify how accurately gradients in galaxy properties with distance from filaments can be recovered. As expected, the small-scale redshift-space distortions, have a strong impact on filament lengths and connectivity, but can be mitigated by compressing galaxy groups before skeleton extraction. The cosmic web reconstruction is biased when relying solely on H $α$ emitters. This limitation can be mitigated by applying stellar mass weighting during the reconstruction. However, this approach introduces non-trivial biases that need to be accounted for when comparing to theoretical predictions. Redshift uncertainties pose the greatest challenge in recovering the expected dependence of galaxy properties, though the well-established stellar mass transverse gradients towards filaments can still be observed.