Weak Star Research Articles

Generic classes defined by neighborhoods assignments and stars

In this article we have a couple of mains. The first one is to make a generic exposure on the classes that are obtained by using neighborhood assignments or applying the star operator to a given topological property P. The second one is to perform an analysis on the classes defined in the first part of the work, for the numerability property.It is important to note that in Example 3.13 we present a Hausdorff weakly star countable space which is not feebly Lindelof, which gives a negative response to the Question 3.14 from [1].

The Chemical Puzzle of Weak G-Band Stars: A Comprehensive Study of HD 54627, HD 105783, HD 198718, and HD 201557

Weak G-band stars (WGBs) are a unique class of objects characterized by weak CH molecular lines in the Fraunhofer G band, indicative of a deficiency in 12C. This peculiar spectral feature is often accompanied by significant enrichments in N and, occasionally, Li and Na abundances. Despite their rarity and recent discoveries of new WGB candidates, the underlying formation mechanism of these stars remains unknown. In this study, we present a comprehensive chemical analysis of four neglected WGBs: HD 54627, HD 105783, HD 198718, and HD 201557. These stars, though identified as WGBs, have been poorly studied to date. Our analysis utilizes high-resolution échelle spectra with a power resolution of R ≈ 48,000, complemented by photometric and astrometric data from the literature. Applying the local thermodynamic equilibrium (LTE) approximation we determine the chemical abundance and then we conduct posterior non-LTE (NLTE) corrections for specific chemical abundances, including Li, O, Na, and Mg. Additionally, we provide details on the projected rotational velocities ( vsini ) and conduct a thorough investigation of the kinematics and orbits of our sample, comparing them with other well-studied WGBs reported in the literature. Our findings indicate that these stars originate from the thin disk, as evidenced by the absence of alpha-element enrichment and kinematics. Notably, half of the WGBs in our sample exhibit Li-rich characteristics, and we identify no rapid rotators ( vsini> 8.0 km s−1) or infrared excess among our studied stars.

Delta shock wave for ternary nonlinear chromatography equations as self-similar viscosity limit

In this paper, we investigate the existence and stability of the delta shock wave in ternary chromatography equations by the self-similar viscosity vanishing approach. Considering the appropriate initial values, we prove the existence of the self-similar solution for the corresponding Riemann problem of the ternary chromatography viscous equations. Furthermore, we rigorously demonstrate that the delta shock wave is the weak star limit of the self-similar solution as viscosity tends to disappear. The result implies that the structure of the delta shock wave is stable under the self-similar viscosity perturbation, which guarantees that the delta shock wave is a unique entropy solution. In addition, we present numerical simulations in agreement with the theoretical analysis.

Neutron Skins: Weak Elastic Scattering and Neutron Stars

The recently completed PREX-2 campaign measured the density distribution of neutrons in the lead nucleus as a function of momentum transfer (the form factor), confirmed a relatively large extent of the neutrons beyond the protons in the nucleus (the neutron skin), and provided a precise determination of the density of protons and neutrons at the center of a heavy nucleus. In turn, the measured form factor can be related to various nuclear and neutron star properties. The NICER X-ray telescope has inferred the masses and radii of some X-ray pulsars (neutron stars), although complications arise when determining these quantities independently. Further improvements in NICER have enabled simultaneous mass–radius determinations that had not previously been possible. During the next decade, measurements in astrophysics, gravitational-wave astronomy, and nuclear physics are expected to provide a wealth of more precise data. In this review, we present an overview of the current state of neutron skin measurements and offer insights into prospects for the future.

Optimization of polarization balance in beam splitter films for weak star simulator.

In the weak star simulator, the background stray light of the self-excited star image and the simulated target star light are mixed with each other, which is difficult to separate and reduces the simulation accuracy of the star position. Therefore, based on the polarized light tracing method, this paper explores the induction mechanism of the polarization effect of the weak star simulator on the background stray light field of the star map, and proposes a polarization balance optimization method for the beam splitter film. At the same time, the mapping model of star position simulation accuracy, polarization parameters of beam splitter and polarization stray light suppression degree is established. Based on this evaluation function, the polarization balance optimization process of beam splitter is constructed to reduce the influence of polarization effect of beam splitter on the background stray light field of star image. The simulation and experimental results show that the stray light suppression ability of the weak star simulator is improved by 2.1 times and the simulation accuracy of the star position is improved by 1.64 times after the polarization balance optimization of the beam splitter film.

Representative Functions, Variational Convergence and Almost Convexity

We develop a new epi-convergence based on the use of bounded convergent nets on the product topology of the strong topology on the primal space and weak star topology on the dual space of a general real Banach space. We study the propagation of the associated variational convergences through conjugation of convex functions defined on this product space. These results are then applied to the problem of construction of a bigger-conjugate representative function for the recession operator associated with a maximal monotone operator on this real Banach space. This is then used to study the relationship between the recession operator of a maximal monotone operator and the normal–cone operator associated with the closed, convex hull of the domain of that monotone operator. This allows us to show that the strong closure of the domain of any maximal monotone operator is convex in a general real Banach space.

Star formation in outer rings of S0 galaxies

Aims. Though S0 galaxies are usually thought to be “red and dead”, they often present weak star formation organized in ring structures in their outer disks. We try to clarify the nature of this phenomenon and its difference from star formation in spiral galaxies. The nearby luminous S0 galaxy NGC 1211 is studied here. Methods. By applying Fabry-Perot scanning interferometry at the Russian 6m telescope, we measured the gas rotation in the outer ring of the galaxy. We studied the pattern and properties of the brightest star formation regions with the tunable filter Mapper of Narrow Galaxy Lines (MaNGaL) at the 2.5 m telescope of the Caucasian Mountain Observatory of the SAI MSU. Results. The gas excitation is strongly inhomogeneous along the ring: in the eastern part, HII-type excitation dominates, while the western part of the ring is partly excited by shocks, as revealed by the emission-line diagnostic diagram. The gas metallicity of the emission clumps in the outer ring also has a broad distribution. The star formation rate is currently falling and is in general too weak for the galaxy gas content. We conclude that the gas in the ring has been accreted recently, about 300 Myr ago, probably from an inclined direction, and that the accretion event has provoked a brief, ineffective starburst.

Comparison Theorems for Weak Topologies (1)

Weak topology on a nonempty set X is defined as the smallest or weakest topology on X with respect to which a given (fixed) family of functions on X is continuous. Let τw be a weak topology generated on a nonempty set X by a family {fα,:α ∈ ∆} of functions, together with a corresponding family {(Xα, τα):α ∈ ∆} of topological spaces. If for some α0 ∈ ∆, τα0 on Xα0 is not the indiscrete topology and fα0 meets certain requirements, then there exists another topology τw1 on X such that τw1 is strictly weaker than τw and fα is τw1-continuous, for all α ∈ ∆. Here in Part 1 of our Comparison Theorems for Weak Topologies it is observed that: (a) the new topology τw1 on X deserves to be called a weak topology (with respect to the fixed family of functions) in its own right. Hence, we call τw1 a strictly weaker weak topology on X, than τw; (b) the usual weak, weak star, and product topologies have chains of pairwise strictly comparable (respectively) weak, weak star, and product topologies around them. All the necessary and sufficient conditions for the existence of τw1 in relation to τw are established. Ample examples are given to illustrate (at appropriate places) the various issues discussed.

Disentangling the two sub-populations of early Herbig Be stars using VLT/X-shooter spectra

Context. Early Herbig Be (HBe) stars are massive, young stars accreting through the boundary layer mechanism. However, given the rapid (<2 Myr) evolution of early Herbig stars to the main-sequence phase, studying the evolution of the circumstellar medium around these stars can be a cumbersome exercise. Aims. In this work, we study the sample of early (B0–B5) HBe stars using the correlation between Hα emission strength and near–infrared excess, complemented by the analysis of various emission features in the X-shooter spectra. Methods. We segregate the sample of 37 early HBe stars based on the median values of Hα equivalent width (EW) and near–infrared index (n(J–H)) distributions. The stars with |Hα EW| > 50 Å and n(J–H) > −2 are classified as intense HBe stars and stars with |Hα EW| < 50 Å and n(J–H) < −2 as weak HBe stars. Using the VLT/X–shooter spectra of five intense and eight weak HBe stars, we visually checked for the differences in intensity and profiles of various HI and metallic emission lines commonly observed in Herbig stars. Results. We propose that the intense HBe stars possess an inner disk close to the star (as apparent from the high near-infrared excess) and an active circumstellar environment (as seen from the high Hα EW value and presence of emission lines belonging to FeII, CaII, OI, and [OI]). However, for weak HBe stars, the inner disk has cleared, and the circumstellar environment appears more evolved than for intense HBe stars. Furthermore, we compiled a sample of ~58 000 emission-line stars published in Gaia DR3 to identify more intense HBe candidates. Further spectroscopic studies of these candidates will help us to understand the evolution of the inner (approximately a few au) disk in early HBe stars.

Operator ranges in Banach spaces with weak star separable dual

We provide several extensions for Banach spaces with weak⁎-separable dual of a theorem of Schevchik ensuring that for every proper dense operator range R in a separable Banach space E, there exists a one-to-one and dense-range operator such that T(E)∩R={0}. These results lead to several characterizations of Banach spaces with weak⁎-separable dual in terms of disjointness properties of operator ranges, which yield a refinement of a theorem of Plichko concerning the spaceability of the complementary set of a proper dense operator range, and an affirmative solution to a problem of Borwein and Tingley for the class of Banach spaces with a separable quotient and weak⁎-separable dual. We also provide an extension to these spaces of a theorem of Cross and Shevchik, which guarantees that for every proper dense operator range R in a separable Banach space E there exist two closed quasicomplementary subspaces X and Y of E such that R∩(X+Y)={0}. Finally, we prove that some weak forms of the theorems of Shevchik and Cross and Shevchik do not hold in any nonseparable weakly Lindelöf determined Banach space.

Star countable subspaces in products of ordinals

In this paper, we discuss the relationships among weakly star countability, almost star countability, star countability and ω1-compactness of subspaces of products of two ordinals. We mainly give the following:(1)For two ordinals ρ and σ, we give a characterization when a subspace X⊆(ρ+1)×(σ+1) is κ-compact, where κ>ω is regular.(2)For a subspace X of ω12, X is almost star countable if and only if it is ω1-compact.(3)There exists a weakly star countable subspace X⊆ω12 such that X is not almost star countable.(4)There exists an almost star countable subspace X⊆(ω1+1)2 such that X is not star countable.(5)For subspaces A and B of an ordinal, A×B is weakly star countable if and only if it is ω1-compact.

Panchromatic Photometry of Low-redshift, Massive Galaxies Selected from SDSS Stripe 82

The broadband spectral energy distribution of a galaxy encodes valuable information on its stellar mass, star formation rate (SFR), dust content, and possible fractional energy contribution from nonstellar sources. We present a comprehensive catalog of panchromatic photometry, covering 17 bands from the far-ultraviolet to 500 μm, for 2685 low-redshift (z = 0.01–0.11), massive (M * > 1010 M ⊙) galaxies selected from the Stripe 82 region of the Sloan Digital Sky Survey, one of the largest areas with relatively deep, uniform observations over a wide range of wavelengths. Taking advantage of the deep optical coadded images, we develop a hybrid approach for matched-aperture photometry of the multiband data. We derive robust uncertainties and upper limits for undetected galaxies, deblend interacting/merging galaxies and sources in crowded regions, and treat contamination by foreground stars. We perform spectral energy distribution fitting to derive the stellar mass, SFR, and dust mass, critically assessing the influence of flux upper limits for undetected photometric bands and applying corrections for systematic uncertainties based on extensive mock tests. Comparison of our measurements with those of commonly used published catalogs reveals good agreement for the stellar masses. While the SFRs of galaxies on the star-forming main sequence show reasonable consistency, galaxies in and below the green valley show considerable disagreement between different sets of measurements. Our analysis suggests that one should incorporate the most accurate and inclusive photometry into the spectral energy distribution analysis, and that care should be exercised in interpreting the SFRs of galaxies with moderate to weak star formation activity.

An asymptotic expansion of eigenpolynomials for a class of linear differential operators

AbstractConsider an M‐th order linear differential operator, ,where is a monic complex polynomial such that and are complex polynomials such that . It is known that the zero counting measure of its eigenpolynomials converges in the weak star sense to a measure μ. We obtain an asymptotic expansion of the eigenpolynomials of in compact subsets out of the support of μ. In particular, we solve a conjecture posed in Masson and Shapiro [On polynomial eigenfunctions of a hypergeometric type operator. Exper Math. 2001;10:609‐618].

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Arp 220: A Post-starburst Galaxy with Little Current Star Formation outside of Its Nuclear Disks

The ultraluminous infrared galaxy Arp 220 is a late-stage merger with several tidal structures in the outskirts and two very compact, dusty nuclei that show evidence for extreme star formation and host at least one active galactic nucleus (AGN). New and archival high-resolution images taken by the Hubble Space Telescope provide a state-of-the-art view of the structures, dust, and stellar clusters in Arp 220. These images cover the near-ultraviolet, optical, and near-infrared in both broad- and narrowband filters. We find that ∼90% of the Hα emission arises from a shock-ionized bubble emanating from the AGN in the western nucleus, while the nuclear disks dominate the Paβ emission. Four very young (∼3–6 Myr) but lower-mass (≲104 M ⊙) clusters are detected in Hα within a few arcseconds of the nuclei, but they produce less than 1% of the line emission. We see little evidence for a population of massive clusters younger than 100 Myr anywhere in Arp 220, unlike previous reports in the literature. From the masses and ages of the detected clusters, we find that star formation took place more or less continuously starting approximately a few gigayears ago with a moderate rate between ≈3 and 12 M ⊙ yr−1. Approximately 100 Myr ago, star formation shut off suddenly everywhere (possibly due to a merging event), except in the nuclear disks. A very recent flicker of weak star formation produced the four young, low-mass clusters, while the rest of the galaxy appears to have remained in a post-starburst state. Cluster ages indicate that the tidal structures on the west side of the galaxy are older than those on the east side, but all appear to predate the shutoff of star formation. Arp 220 has many of the characteristics expected of a “shocked post-starburst galaxy,” since most of the system has been in a post-starburst state for the past ∼100 Myr and the detected Hα emission arises from shocked rather than photoionized gas.

Star formation in outer rings of S0 galaxies

Aims. Though S0 galaxies are usually thought to be ‘red and dead’, they often demonstrate weak star formation organised in ring structures and located in their outer disks. We try to clarify the nature of this phenomenon and its difference from star formation in spiral galaxies. The nearby moderate-luminosity S0 galaxy UGC 4599 is studied here. Methods. By applying long-slit spectroscopy at the Russian 6 m telescope, we have measured stellar kinematics for the main body of the galaxy and strong emission-line flux ratios in the ring. After inspecting the gas excitation in the ring using line ratio diagrams, and having shown that it is ionised by young stars, we determined the gas oxygen abundance by using conventional strong-line calibration methods. We inspected the gas kinematics in the ring with Fabry–Perot interferometer data obtained at the William Herschel Telescope. The pattern and properties of the brightest star formation regions were studied with the tunable filter MaNGaL at the 2.5 m telescope of the Caucasian Mountain Observatory of the SAI MSU. Results. The gas metallicity in the ring is certainly subsolar, [O/H] = −0.4 ± 0.1 dex, which is different from the majority of the outer star-forming rings in S0s we have studied in the past, which typically have nearly solar metallicity. The total stellar component of the galaxy, which is old in the centre, is less massive than its extended gaseous disk. We conclude that the ring and the outer disk of UGC 4599 are probably a result of gas accretion from a cosmological filament.

HD 16424: A new weak G-band star with high Li abundance

ABSTRACT The origin of the so-called weak G-band stars constitutes an unsolved problem in stellar astrophysics. In this context, we present a detailed abundance analysis of a new weak G-band star, HD 16424, which stands out with a very low 12C/13C ratio and Li and Na overabundance. Our work is based on the high-resolution échelle spectrum (R ≈ 48 000) and includes photometric and astrometric data from the literature. The analysis adopted in this work is performed under local thermodynamic equilibrium (LTE) approximation; we determine the atmospheric parameters (Teff, $\log \, g$, [Fe/H], and ξ), abundances for proton-capture elements (C, N, O, Li), s-process elements (Y, Zr, La), and mixing tracers such as the 12C/13C isotopic ratio and sodium abundance, following by NLTE corrections applied to Li, O, and Na abundances. Our results show 12C deficiency ([C/Fe] = −0.57) and N enrichment ([N/Fe] = +0.97), that is typical for weak G-band stars. Also, we notice a carbon isotopic ratio characteristic of the CN-cycle equilibrium (〈12C/13C〉 = 4.0) and high lithium-7 abundance ($\log \, \varepsilon$(Li)NLTE = 2.85). In addition, this study shows a low projected rotational velocity ($v\, \sin \, i$ = 2.0 km s−1) and low mass (1.61 M⊙) of HD 16424, which distinguishes this star from the intermediate-mass objects found in this class of peculiar objects.

Effective Multi-Frame Optical Detection Algorithm for GEO Space Objects

The limited resource of Geostationary Earth Orbit (GEO) is precious and most telecommunication, weather and navigational satellites are placed in this orbit. In order to guarantee the safety and health of active satellites, advanced surveillance and warning of unknown space targets such as space debris are crucial. However, space object detection still remains a very challenging problem because of the weak target characteristics and complex star background. To solve this problem, we conduct a deep-learning-based framework called PP-YOLOv2 for single-frame object detection and design a post-processing algorithm named CFS for further candidate filtration and supplement. First, we transform the label information and generate the according bounding boxes to train the PP-YOLOv2 detector to extract candidate coordinates for each frame. Then, the CFS technique is designed as an effective post-processing procedure to obtain the eventual prediction results. Experiments were conducted over a dataset from the Kelvins SpotGEO challenge, which demonstrate the effectiveness and the comparable detection performance of our proposed pipeline. Finally, the deployment results on NVIDIA Jetson Nano show that the proposed method has a competitive application prospect for a space target monitoring system.

Morpho-kinematic Properties of Wolf–Rayet Planetary Nebulae

The majority of planetary nebulae (PNs) show axisymmetric morphologies, whose causes are not well understood. In this work, we present spatially resolved kinematic observations of 14 Galactic PNs surrounding Wolf–Rayet ([WR]) and weak emission-line stars (wels), based on the Hα and [N ii] emission taken with the Wide Field Spectrograph on the Australian National University 2.3 m telescope. Velocity-resolved channel maps and position–velocity diagrams, together with archival Hubble Space Telescope (HST) and ground-based images, are employed to construct three-dimensional morpho-kinematic models of 12 objects using the program shape. Our results indicate that these 12 PNs mostly have elliptical morphologies, with either open or closed outer ends. The kinematic maps show the on-sky orientations of the interior shells in NGC 6578 and NGC 6629, as well as the compact (≤6″) PNs Pe 1-1, M 3-15, M 1-25, Hen 2-142, and NGC 6567, in agreement with the elliptically symmetric morphologies seen in high-resolution HST images. Point-symmetric knots in Hb 4 exhibit deceleration with distance from the central star, which could be due to shock collisions with the ambient medium. The velocity dispersion maps of Pe 1-1 also disclose the shock interaction between its collimated outflows and the interstellar medium. Collimated bipolar outflows are also visible in the position–velocity diagrams of M 3-30, M 1-32, and M 3-15, which are reconstructed by tenuous prolate ellipsoids extending upward from dense equatorial regions in the kinematic models. The formation of aspherical morphologies and collimated outflows in these PNs could be related to the stellar evolution of hydrogen-deficient [WR] and wels nuclei, which require further investigation.

Morphologies of Wolf–Rayet Planetary Nebulae Based on IFU Observations

Integral field unit (IFU) spectroscopy of planetary nebulae (PNe) provides a plethora of information about their morphologies and ionization structures. An IFU survey of a sample of PNe around hydrogen-deficient stars has been conducted with the Wide Field Spectrograph (WiFeS) on the ANU 2.3-m telescope. In this paper, we present the Hα kinematic observations of the PN M 2-42 with a weak emission-line star (wels), and the compact PNe Hen 3-1333 and Hen 2-113 around Wolf–Rayet ([WR]) stars from this WiFeS survey. We see that the ring and point-symmetric knots previously identified in the velocity [N ii] channels of M 2-42 are also surrounded by a thin exterior ionized Hα halo, whose polar expansion is apparently faster than the low-ionization knots. The velocity-resolved Hα channel maps of Hen 3-1333 and Hen 2-113 also suggest that the faint multipolar lobes may get to a projected outflow velocity of ∼100 ± 20 km s−1 far from the central stars. Our recent kinematic studies of the WiFeS/IFU survey of other PNe around [WR] and wels mostly hint at elliptical morphologies, while collimated outflows are present in many of them. As the WiFeS does not have adequate resolution for compact (≤6 arcsec) PNe, future high-resolution spatially-resolved observations are necessary to unveil full details of their morpho-kinematic structures.