Universe

26 pages, 515 KiB

Open AccessArticle

GEMS Embeddings of Hayward Regular Black Holes in Massless and Massive Gravities

by Soon-Tae Hong, Yong-Wan Kim and Young-Jai Park

Universe 2023, 9(11), 486; https://doi.org/10.3390/universe9110486 - 20 Nov 2023

Viewed by 1268

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass [...] Read more.

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call ‘massless’. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher-dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2023—Gravitation)

► Show Figures

Figure 1

31 pages, 4838 KiB

Open AccessArticle

Observational Detection of Higher-Order Secular Perturbations in Tight Hierarchical Triple Stars

by Tamás Borkovits and Tibor Mitnyan

Universe 2023, 9(11), 485; https://doi.org/10.3390/universe9110485 - 20 Nov 2023

Cited by 2 | Viewed by 1014

Abstract

In this work, we search for observational evidence of higher-order secular perturbations in three eclipsing binaries. These are slightly eccentric binaries, and they form the inner pairs of tight, compact, hierarchical triple star systems. Simultaneously, we analyze the high-precision satellite (Kepler and [...] Read more.

In this work, we search for observational evidence of higher-order secular perturbations in three eclipsing binaries. These are slightly eccentric binaries, and they form the inner pairs of tight, compact, hierarchical triple star systems. Simultaneously, we analyze the high-precision satellite (Kepler and TESS) light curves; eclipse timing variations; combined spectral energy distributions (through catalog passband magnitudes); and, where available, radial velocities of KICs 9714358, 5771589, and TIC 219885468. Besides the determination of the robust astrophysical and dynamical properties of the three systems, we find evidence that the observed unusual eclipse timing variations of KIC 9714358 are a direct consequence of the octupole-order secular eccentricity perturbations forced by unusual, resonant behavior between the lines of the apsides of the inner and outer orbital ellipses. We also show that, despite its evident cyclic eclipse depth variations, KIC 5771589 is an almost perfectly coplanar system (to within

0 . 3^{\circ}

), and we explain the rapid eclipse depth variations with the grazing nature of the eclipses. Finally, we find that the inner pair of TIC 219885468 consists of two twin stars; hence, in this triple there are no octupole-order three-body perturbations. Moreover, we show that this triple is also coplanar on the same level as the former one, but due to its deep eclipses, it does not exhibit eclipse depth variations. We intend to follow this work up with further analyses and a quantitative comparison of the theoretical and the observed perturbations. Full article

(This article belongs to the Special Issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets)

► Show Figures

Figure 1

21 pages, 638 KiB

Open AccessArticle

Neutron Star Constraints on Neutron Dark Decays

by Dake Zhou

Universe 2023, 9(11), 484; https://doi.org/10.3390/universe9110484 - 17 Nov 2023

Cited by 2 | Viewed by 1319

Abstract

Motivated by the neutron lifetime puzzle, it is proposed that neutrons may decay into new states yet to be observed. We review the neutron star constraints on dark fermions carrying unit baryon number with masses around 939 MeV, and discuss the interaction strengths [...] Read more.

Motivated by the neutron lifetime puzzle, it is proposed that neutrons may decay into new states yet to be observed. We review the neutron star constraints on dark fermions carrying unit baryon number with masses around 939 MeV, and discuss the interaction strengths required for the new particle. The possibility of neutrons decaying into three dark fermions is investigated. While up to six flavors of dark quarks with masses around 313 MeV can be compatible with massive pulsars, any such exotic states lighter than about 270 MeV are excluded by the existence of low-mass neutron stars around ∼

1.2 M_{⊙}

. Light dark quarks in the allowed mass range may form a halo surrounding normal neutron stars. We discuss the potential observable signatures of the halo during binary neutron star mergers. Full article

(This article belongs to the Special Issue Neutron Lifetime)

► Show Figures

Figure 1

14 pages, 886 KiB

Open AccessReview

Diffractive and Photon-Induced Production of Top Quark

by Michael Pitt

Universe 2023, 9(11), 483; https://doi.org/10.3390/universe9110483 - 16 Nov 2023

Viewed by 1081

Abstract

The top quark plays a central role in particle physics, as many experiments at the Large Hadron Collider scrutinize its properties within the Standard Model. Although most of the measurements of the top quarks today concentrate on production modes initiated by quarks or [...] Read more.

The top quark plays a central role in particle physics, as many experiments at the Large Hadron Collider scrutinize its properties within the Standard Model. Although most of the measurements of the top quarks today concentrate on production modes initiated by quarks or gluons, this review will highlight the lesser-explored modes initiated by pomerons or photons. It aims to provide an in-depth look into both the phenomenological studies and the existing experimental measurements, emphasizing the necessity of exploring the diffractive and photon-induced production of top quarks to enhance the accuracy of top-quark measurements. Full article

(This article belongs to the Special Issue Top Quark at the New Physics Frontier)

► Show Figures

Figure 1

8 pages, 275 KiB

Open AccessArticle

Consistent Couplings between a Massive Spin-3/2 Field and a Partially Massless Spin-2 Field

by Nicolas Boulanger, Guillaume Lhost and Sylvain Thomée

Universe 2023, 9(11), 482; https://doi.org/10.3390/universe9110482 - 15 Nov 2023

Cited by 1 | Viewed by 1170

Abstract

We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (anti) de Sitter (A)dS

_{4}

spacetime. We use the Stueckelberg formulation of the action principle for these fields and find two non-trivial cubic [...] Read more.

We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (anti) de Sitter (A)dS

_{4}

spacetime. We use the Stueckelberg formulation of the action principle for these fields and find two non-trivial cubic vertices with less than two derivatives when moving to the unitary gauge. One of the vertices is reminiscent of the minimal coupling of the massive spin-3/2 field to gravity, except that now the graviton is partially massless. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)

19 pages, 420 KiB

Open AccessArticle

Dynamic Aether as a Trigger for Spontaneous Spinorization in Early Universe

by Alexander Balakin and Anna Efremova

Universe 2023, 9(11), 481; https://doi.org/10.3390/universe9110481 - 14 Nov 2023

Cited by 1 | Viewed by 1013

Abstract

In the framework of the Einstein–Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first [...] Read more.

In the framework of the Einstein–Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first one is the aetheric regulation of behavior of the spinor field; the second mechanism can be related to a self-similarity of internal interactions in the spinor field. The dynamic aether is designed to switch on and switch off the self-similar mechanism of the spinor field evolution; from the mathematical point of view, the key of such a guidance is made of the scalar of expansion of the aether flow, proportional to the Hubble function in the isotropic cosmological model. Two phenomenological parameters of the presented model are shown to be considered as factors predetermining the total number of fermions born in the early Universe. Full article

(This article belongs to the Special Issue The Languages of Physics—A Themed Issue in Honor of Professor Richard Kerner on the Occasion of His 80th Birthday)

► Show Figures

Figure 1

22 pages, 22260 KiB

Open AccessArticle

Molecular-Clump Detection Based on an Improved YOLOv5 Joint Density Peak Clustering

by Jin-Bo Hu, Yao Huang, Sheng Zheng, Zhi-Wei Chen, Xiang-Yun Zeng, Xiao-Yu Luo and Chen Long

Universe 2023, 9(11), 480; https://doi.org/10.3390/universe9110480 - 11 Nov 2023

Viewed by 1164

Abstract

The detection and analysis of molecular clumps can lead to a better understanding of star formation in the Milky Way. Herein, we present a molecular-clump-detection method based on improved YOLOv5 joint Density Peak Clustering (DPC). The method employs a two-dimensional (2D) detection and [...] Read more.

The detection and analysis of molecular clumps can lead to a better understanding of star formation in the Milky Way. Herein, we present a molecular-clump-detection method based on improved YOLOv5 joint Density Peak Clustering (DPC). The method employs a two-dimensional (2D) detection and three-dimensional (3D) stitching strategy to accomplish the molecular-clump detection. In the first stage, an improved YOLOv5 is used to detect the positions of molecular clumps on the Galactic plane, obtaining their spatial information. In the second stage, the DPC algorithm is used to combine the detection results in the velocity direction. In the end, the clump candidates are positioned in the 3D position-position-velocity (PPV) space. Experiments show that the method can achieve a high recall of 98.41% in simulated data made up of Gaussian clumps added to observational data. The efficiency of the strategy has also been demonstrated in experiments utilizing observational data from the Milky Way Imaging Scroll Painting (MWISP) project. Full article

(This article belongs to the Special Issue New Discoveries in Astronomical Data)

► Show Figures

Figure 1

20 pages, 629 KiB

Open AccessArticle

Why Are Some Radio Galaxies Detected by Fermi, but Others Not?

by Danyi Huang, Xuhong Ye, Xiao Ye, Xiulin Huang, Yanjun Qian, Ziyan Li, Chengfeng Li, Jiru Liao, Hengji Zhang, Zhiyuan Pei, Jianghe Yang and Junhui Fan

Universe 2023, 9(11), 479; https://doi.org/10.3390/universe9110479 - 08 Nov 2023

Viewed by 1180

Abstract

Aiming to answer an interesting question on why some radio sources can be detected by Fermi-LAT but others cannot, we compare several parameters of Fermi-detected Fanaroff-Riley radio galaxies (FFRs) and non-Fermi-detected sources (NFFRs), including the optical absolute magnitude, 1.4 GHz [...] Read more.

Aiming to answer an interesting question on why some radio sources can be detected by Fermi-LAT but others cannot, we compare several parameters of Fermi-detected Fanaroff-Riley radio galaxies (FFRs) and non-Fermi-detected sources (NFFRs), including the optical absolute magnitude, 1.4 GHz radio luminosity, radio loudness, core dominance parameter, Doppler factor, and the mass of the central black hole. Significant differences are ascertained within these parameters between FFRs and NFFRs. Our findings suggest that FFRs are jet-dominant while NFFRs are disk-dominant sources, and NFFRs have a weaker beaming effect. Additionally, we predict the observed

γ

-ray flux for NFFRs, establishing that the reason why some NFFRs are not detectable arises from their

γ

-ray flux being below the sensitivity detection threshold of Fermi. We also discuss two sub-types of Fanaroff-Riley galaxies, namely FR I and FR II sources. We first propose a “changing-look” phenomenon in these radio sources and also investigate why FR IIs seem to be exclusive in

γ

-ray emission. Full article

(This article belongs to the Special Issue Multimessenger Studies of Active Galactic Nucleus)

► Show Figures

Figure 1

19 pages, 1623 KiB

Open AccessArticle

Dark Matter in Fractional Gravity III: Dwarf Galaxies Kinematics

by Francesco Benetti, Andrea Lapi, Giovanni Gandolfi, Minahil Adil Butt, Yacer Boumechta, Balakrishna S. Haridasu and Carlo Baccigalupi

Universe 2023, 9(11), 478; https://doi.org/10.3390/universe9110478 - 08 Nov 2023

Viewed by 1189

Abstract

Recently, we put forward a framework where the dark matter (DM) component within virialized halos is subject to a non-local interaction originated by fractional gravity (FG) effects. In previous works, we demonstrated that such a framework can substantially alleviate the small-scale issues of [...] Read more.

Recently, we put forward a framework where the dark matter (DM) component within virialized halos is subject to a non-local interaction originated by fractional gravity (FG) effects. In previous works, we demonstrated that such a framework can substantially alleviate the small-scale issues of the standard

Λ

CDM paradigm, without altering the DM mass profile predicted by N-body simulations, and retaining its successes on large cosmological scales. In this paper, we investigate further, to probe FG via the high-quality data of individual dwarf galaxies, by exploiting the rotation velocity profiles inferred from stellar and gas kinematic measurements in eight dwarf irregulars, and the projected velocity dispersion profiles inferred from the observed dynamics of stellar tracers in seven dwarf spheroidals and in the ultra-diffuse galaxy DragonFly 44. We find that FG can reproduce extremely well the rotation and dispersion curves of the analyzed galaxies, performing in most instances significantly better than the standard Newtonian setup. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2024—"Galaxies and Clusters")

► Show Figures

Figure 1

22 pages, 2283 KiB

Open AccessArticle

Automatic Classification of Spectra with IEF-SCNN

by Jingjing Wu, Yanxia Zhang, Meixia Qu, Bin Jiang and Wenyu Wang

Universe 2023, 9(11), 477; https://doi.org/10.3390/universe9110477 - 08 Nov 2023

Viewed by 1102

Abstract

Telescopes such as the Large Sky Area Multi-Object Spectroscopic Telescope and the Sloan Digital Sky Survey have produced an extensive collection of spectra, challenging the feasibility of manual classification in terms of accuracy and efficiency. To overcome these limitations, machine learning techniques are [...] Read more.

Telescopes such as the Large Sky Area Multi-Object Spectroscopic Telescope and the Sloan Digital Sky Survey have produced an extensive collection of spectra, challenging the feasibility of manual classification in terms of accuracy and efficiency. To overcome these limitations, machine learning techniques are increasingly being utilized for automated spectral classification. However, these approaches primarily treat spectra as frequency domain signals, and lack robustness in low signal-to-noise ratio (S/N) scenarios and for small datasets of rare celestial objects. Moreover, they frequently neglect nuanced expert astronomical understanding. In this study, we draw inspiration from the human spectral discrimination process and propose a new model called the Image-EFficientNetV2-Spectrum Convolutional Neural Network (IEF-SCNN). IEF-SCNN combines spectral images using EfficientNetV2 with one-dimensional (1D) spectra through a 1DCNN. This integration effectively incorporates astronomical expertise into the classification process. Specifically, we plot the spectrum as an image and then classify it in a way that incorporates an attention mechanism. This attention mechanism mimics human observation of images for classification, selectively emphasizing relevant information while ignoring irrelevant details. Experimental data demonstrate that IEF-SCNN outperforms existing models in terms of the F1-score and accuracy metrics, particularly for low S/N (<6) data. Using progressive learning and an attention mechanism, the model trained on 12,000 M-class stars with an S/N below 6 achieved an accuracy of 87.38% on a 4000-sample test set. This surpasses traditional models (support vector machine with 83.15% accuracy, random forest with 65.40%, and artificial neural network with 84.40%) and the 1D stellar spectral CNN (85.65% accuracy). This research offers a foundation for the development of innovative methods for the automated identification of specific celestial objects, and can promote the creation of user-friendly software for astronomers who may not have computational expertise. Full article

(This article belongs to the Section Stellar Astronomy)

► Show Figures

Figure 1

18 pages, 432 KiB

Open AccessArticle

Vacuum Energy, the Casimir Effect, and Newton’s Non-Constant

by Benjamin Koch, Christian Käding, Mario Pitschmann and René I. P. Sedmik

Universe 2023, 9(11), 476; https://doi.org/10.3390/universe9110476 - 08 Nov 2023

Viewed by 1156

Abstract

The idea of quantum mechanical vacuum energy contributing to the cosmological vacuum energy density is not new. However, despite the persisting cosmological constant problem, few investigations have focused on this subject. We explore the possibility that the quantum vacuum energy density contributes to [...] Read more.

The idea of quantum mechanical vacuum energy contributing to the cosmological vacuum energy density is not new. However, despite the persisting cosmological constant problem, few investigations have focused on this subject. We explore the possibility that the quantum vacuum energy density contributes to the (local) gravitational energy density in the framework of a scale-dependent cosmological constant

Λ

and Newton’s constant G. This hypothesis has several important consequences, ranging from quantum scale-dependence to the hypothetical prospect of novel experimental insight concerning the quantum origin of cosmological energy density. Full article

(This article belongs to the Special Issue Quantum Field Theory in Curved Spacetime and Its Implications for Cosmology, Blackholes and Quantum Gravity)

► Show Figures

Figure 1

18 pages, 1485 KiB

Open AccessArticle

Statistical and Radio Analysis of Exoplanets and Their Host Stars

by Baoda Li, Liyun Zhang, Tianhao Su, Xianming L. Han, Prabhakar Misra and Liu Long

Universe 2023, 9(11), 475; https://doi.org/10.3390/universe9110475 - 08 Nov 2023

Viewed by 1200

Abstract

As of February 2022, over 4900 exoplanets have been confirmed. In this study, we conducted statistical analyses on both the exoplanets and their host stars’ parameters. Our findings suggest that the radius and true mass distribution of the exoplanets remain largely unchanged compared [...] Read more.

As of February 2022, over 4900 exoplanets have been confirmed. In this study, we conducted statistical analyses on both the exoplanets and their host stars’ parameters. Our findings suggest that the radius and true mass distribution of the exoplanets remain largely unchanged compared to prior research. However, we observed a correlation between the average eccentricity and the number of planets in a system, and fluctuations in the “size” of the planets may contribute to such variation. Moreover, we discovered that, among planets with precise measurements of radius, true mass, and semi-major axis, the true mass-radius relationship follows a power–law distribution. Interestingly, the power–law index tends to decrease from super-Earths to cold Jupiters, potentially due to atmospheric composition. We also revised the radius valley, and determined that M-type host stars with low mass and metal abundance exhibit high planetary ownership rates or harbor large-mass planets, suggesting a different planet formation mechanism than GK-type stars. Lastly, we assessed the possibility of detecting exoplanets using FAST and found that there are three planets in FAST sky that may be detected, namely CoRoT-3 b, GPX-1 b, and TOI-2109 b. Full article

(This article belongs to the Section Planetary Sciences)

► Show Figures

Figure 1

19 pages, 11549 KiB

Open AccessArticle

Ionospheric Response on Solar Flares through Machine Learning Modeling

by Filip Arnaut, Aleksandra Kolarski, Vladimir A. Srećković and Zoran Mijić

Universe 2023, 9(11), 474; https://doi.org/10.3390/universe9110474 - 07 Nov 2023

Viewed by 1300

Abstract

Following solar flares (SF), the abrupt increase in X-radiation and EUV emission generates additional ionization and higher absorption of, e.g., electromagnetic waves in the sunlit hemisphere of the Earth’s ionosphere. The modeling of the ionosphere under solar flares are motivated by new observations [...] Read more.

Following solar flares (SF), the abrupt increase in X-radiation and EUV emission generates additional ionization and higher absorption of, e.g., electromagnetic waves in the sunlit hemisphere of the Earth’s ionosphere. The modeling of the ionosphere under solar flares are motivated by new observations with spacecrafts, satellites, and ground-based measurements. The estimation of modeling parameters for the ionospheric D-region during SF events poses a significant challenge, typically requiring a trial-and-error approach. This research presents a machine learning (ML) methodology for modeling the sharpness (β) and reflection height (H′) during SF events occurred from 2008 to 2017. The research methodology was divided into two separate approaches: an instance-based approach, which involved obtaining SF parameters during the peak SF, and a time-series approach, which involved analyzing time-series data during SFs. The findings of the study revealed that the model for the instance-based approach exhibited mean absolute percentage error (MAPE) values of 9.1% for the β parameter and 2.45% for the H′ parameter. The findings from the time-series approach indicated that the model exhibited lower error rates compared to the instance-based approach. However, it was observed that the model demonstrated an increase in β residuals as the predicted β increased, whereas the opposite trend was observed for the H′ parameter. The main goal of the research is to develop an easy-to-use method that provides ionospheric parameters utilizing ML, which can be refined with additional and novel data as well as other techniques for data pre-processing and other algorithms. The proposed method and the utilized workflow and datasets are available at GitHub. Full article

(This article belongs to the Section Space Science)

► Show Figures

Figure 1

10 pages, 453 KiB

Open AccessArticle

How Long Does the Hydrogen Atom Live?

by David McKeen and Maxim Pospelov

Universe 2023, 9(11), 473; https://doi.org/10.3390/universe9110473 - 04 Nov 2023

Cited by 2 | Viewed by 1217

Abstract

It is possible that the proton is stable while atomic hydrogen is not. This is the case in models with new particles carrying baryon number which are light enough to be stable themselves, but heavy enough so that proton decay is kinematically blocked. [...] Read more.

It is possible that the proton is stable while atomic hydrogen is not. This is the case in models with new particles carrying baryon number which are light enough to be stable themselves, but heavy enough so that proton decay is kinematically blocked. Models of new physics that explain the neutron lifetime anomaly generically have this feature, allowing for atomic hydrogen to decay through electron capture on a proton. We calculate the radiative hydrogen decay rate involving the emission of a few hundred keV photon, which makes this process experimentally detectable. In particular, we show that the low energy part of the Borexino spectrum is sensitive to radiative hydrogen decay, and turn this into a limit on the hydrogen lifetime of order

10^{30} s

or stronger. For models where the neutron mixes with a dark baryon,

χ

, this limits the mixing angle to roughly

10^{- 11}

, restricting the

n \to χ γ

branching to

10^{- 4}

, over a wide range of parameter space. Full article

(This article belongs to the Special Issue Neutron Lifetime)

► Show Figures

Figure 1

25 pages, 1702 KiB

Open AccessArticle

Neutrino Mixing Sum Rules and the Littlest Seesaw

by Francesco Costa and Stephen F. King

Universe 2023, 9(11), 472; https://doi.org/10.3390/universe9110472 - 31 Oct 2023

Cited by 4 | Viewed by 1220

Abstract

In this work, we study the neutrino mixing sum rules arising from discrete symmetries and the class of Littlest Seesaw (LS) neutrino models. These symmetry-based approaches all offer predictions for the cosine of the leptonic CP phase

cos δ

in terms of the [...] Read more.

In this work, we study the neutrino mixing sum rules arising from discrete symmetries and the class of Littlest Seesaw (LS) neutrino models. These symmetry-based approaches all offer predictions for the cosine of the leptonic CP phase

cos δ

in terms of the mixing angles,

θ_{13}

,

θ_{12}

,

θ_{23}

, while the LS models also predict the sine of the leptonic CP phase

sin δ

, as well as making other predictions. In particular, we study the solar neutrino mixing sum rules, arising from charged lepton corrections to tri-bimaximal (TB), bimaximal (BM), golden ratio (GR) and hexagonal (HEX) neutrino mixing, and the atmospheric neutrino mixing sum rules, arising from preserving one of the columns of these types of mixing—for example, the first or second column of the TB mixing matrix (TM1 or TM2)—and we confront them with an up-to-date global fit of the neutrino oscillation data. We show that some mixing sum rules, such as an atmospheric neutrino mixing sum rule arising from a version of neutrino golden ratio mixing (GRa1), are already excluded at 3

σ

, and we determine the remaining models allowed by the data. We also consider the more predictive LS models (which obey the TM1 sum rules and offer further predictions) based on constrained sequential dominance CSD(n) with

n \approx 3

. We compare for the first time the three cases

n = 2.5

,

n = 3

and

n = 1 + \sqrt{6} \approx 3.45

, which are favored by theoretical models, using a new type of analysis to accurately predict the observables

θ_{12}

,

θ_{23}

and

δ

. We study all the above approaches, solar and atmospheric mixing sum rules and LS models, together so that they may be compared and to give an up-to-date analysis of the predictions of all of these possibilities, when confronted with the most recent global fits. Full article

(This article belongs to the Special Issue CP Violation and Flavor Physics)

► Show Figures

Figure 1

26 pages, 1637 KiB

Open AccessEditor’s ChoiceArticle

Uniform Asymptotic Approximation Method with Pöschl–Teller Potential

by Rui Pan, John Joseph Marchetta, Jamal Saeed, Gerald Cleaver, Bao-Fei Li, Anzhong Wang and Tao Zhu

Universe 2023, 9(11), 471; https://doi.org/10.3390/universe9110471 - 31 Oct 2023

Cited by 1 | Viewed by 1241

Abstract

In this paper, we study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl–Teller (PT) potential, for [...] Read more.

In this paper, we study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl–Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT potential, we find that the upper bounds of the errors of the approximate solutions in general are ≲0.15∼10% for the first-order approximation of the UAA method. The approximations can be easily extended to high orders, for which the errors are expected to be much smaller. Such obtained analytical solutions can be used to study cosmological perturbations in the framework of quantum cosmology as well as quasi-normal modes of black holes. Full article

(This article belongs to the Special Issue Recent Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on His 60th Anniversary)

► Show Figures

Figure 1

26 pages, 647 KiB

Open AccessReview

Revisiting Hansen’s Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements

by Martin Lara and Hodei Urrutxua

Universe 2023, 9(11), 470; https://doi.org/10.3390/universe9110470 - 31 Oct 2023

Viewed by 1276

Abstract

A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane [...] Read more.

A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge. Full article

(This article belongs to the Section Space Science)

► Show Figures

Figure 1

14 pages, 664 KiB

Open AccessArticle

Unimodular Theory of Gravity in Light of the Latest Cosmological Data

by Naveen K. Singh and Gopal Kashyap

Universe 2023, 9(11), 469; https://doi.org/10.3390/universe9110469 - 31 Oct 2023

Cited by 2 | Viewed by 1564

Abstract

The unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of [...] Read more.

The unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of Type Ia Supernovae (SNs) (2018), Baryon Acoustic Oscillations (BAOs), and the observational H(z) data from the Differential Age method (DA). We also used the Cosmic Microwave Background (CMB) distance priors from the Planck 2018 results. We considered a model consisting of a generalized cosmological constant, radiation, and a dark matter component along with normal matter. The considered theory respects only unimodular coordinate transformations. We first fit our model with low-redshift data from SNs and DA and determined the value of the model parameters

(ξ, H_{0})

. We found the best-fit value of parameter

ξ = 6.03 \pm 0.40

, which deviates slightly from 6, for which the theory becomes the standard general theory of relativity. We observed a small deviation in the value of the Hubble constant (

H_{0} = 72.6 \pm 3.5

km s⁻¹ Mpc⁻¹) in the UG model compared with the standard

Λ

CDM model (

H_{0} = 72.2 \pm 1.2

km s⁻¹ Mpc⁻¹). Using the BAO + CMB constraint in the UG model, we obtained

H_{0} = 68.45 \pm 0.66 km s^{- 1} {Mpc}^{- 1}

, and

ξ

is ∼6.029. For the combined datasets (SN + DA + BAO + CMB), the estimated

H_{0} = 69.01 \pm 0.60 km s^{- 1} {Mpc}^{- 1}

with

ξ \sim

6.037, and in standard gravity,

H_{0} = 68.25 \pm 0.40 km s^{- 1} {Mpc}^{- 1}

. Full article

(This article belongs to the Special Issue Advances in Cosmological Models)

► Show Figures

Figure 1

16 pages, 5811 KiB

Open AccessArticle

A Meteor Detection Algorithm for GWAC System

by Yicong Chen, Guangwei Li, Cuixiang Liu, Bo Qiu, Qianqian Shan and Mengyao Li

Universe 2023, 9(11), 468; https://doi.org/10.3390/universe9110468 - 30 Oct 2023

Viewed by 1207

Abstract

Compared with the international meteor surveillance systems, the ground wide angle camera (GWAC) system exhibits characteristics such as images with the resolution of 4K × 4K and single-site observation. These characteristics present challenges for meteor detection in the GWAC system. Consequently, this paper [...] Read more.

Compared with the international meteor surveillance systems, the ground wide angle camera (GWAC) system exhibits characteristics such as images with the resolution of 4K × 4K and single-site observation. These characteristics present challenges for meteor detection in the GWAC system. Consequently, this paper proposes a new meteor detection algorithm for the GWAC system on the base of the solely mini-GWAC system data algorithm. The new algorithm consists of the following key steps: (1) to compare differences between adjacent frames, applying block-based image binarization thresholds, and incorporating median filtering to reduce noise; (2) to adopt the probabilistic Hough transform (PHT) to identify moving objects and cluster them based on the origin moment of the line segments, while assessing the credibility of clustering; (3) to introduce the so-called maximum disappearance frame for moving objects in the tracking algorithm, enhancing the ability to track multi-frame moving objects. The utilization of the line segment inclination angle of the moving object as the direction of movement facilitates the tracking of multiple moving objects, thereby reducing the probability of mistakenly selecting single-frame moving objects; (4) to leverage the light curves of single-frame moving objects to select meteors to enhance the accuracy of meteor detection. Comparative experiments demonstrate that our proposed algorithm processes each frame image in just 0.39 s, achieving an accuracy of 89.8% in the dataset of 5856 adjacent frames. The experimental results indicate that the algorithm achieved an accuracy of 90.27% when applied in the meteor detection of the image data captured by the GWAC system from Dec. 10th to 19th in 2019 and 2021, obtaining excellent detection results. Full article

(This article belongs to the Special Issue New Discoveries in Astronomical Data)

► Show Figures

Figure 1

15 pages, 804 KiB

Open AccessEditor’s ChoiceArticle

Closed Timelike Curves Induced by a Buchdahl-Inspired Vacuum Spacetime in

R^{2}

Gravity

by Hoang Ky Nguyen and Francisco S. N. Lobo

Universe 2023, 9(11), 467; https://doi.org/10.3390/universe9110467 - 30 Oct 2023

Cited by 1 | Viewed by 1402

Abstract

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter

\tilde{k}

of higher-derivative characteristic, and reduces to the Schwarzschild metric, for [...] Read more.

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter

\tilde{k}

of higher-derivative characteristic, and reduces to the Schwarzschild metric, for

\tilde{k} = 0

. For the case

\tilde{k} \in (- 1, 0)

, it was shown that it describes a traversable Morris–Thorne–Buchdahl (MTB) wormhole Eur. Phys. J. C 83, 626 (2023), where the weak energy condition is formally violated. In this paper, we briefly review the special Buchdahl-inspired metric, with focuses on the construction of the Kruskal–Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing two reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points

(T, X)

and

(- T, - X)

on the wormhole throat in the KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli–Lousto metric in Brans–Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli–Lousto solution. Full article

(This article belongs to the Special Issue The Physics of Time Travel)

► Show Figures

Figure 1

16 pages, 2877 KiB

Open AccessReview

Element Abundances in Impulsive Solar Energetic-Particle Events

by Donald V. Reames

Universe 2023, 9(11), 466; https://doi.org/10.3390/universe9110466 - 30 Oct 2023

Cited by 3 | Viewed by 1154

Abstract

Impulsive solar energetic-particle (SEP) events were first distinguished as the streaming electrons that produce type III radio bursts as distinct from shock-induced type II bursts. They were then observed as the surprisingly enhanced ³He-rich SEP events, which were also found to have [...] Read more.

Impulsive solar energetic-particle (SEP) events were first distinguished as the streaming electrons that produce type III radio bursts as distinct from shock-induced type II bursts. They were then observed as the surprisingly enhanced ³He-rich SEP events, which were also found to have element enhancements rising smoothly with the mass-to-charge ratio A/Q through the elements, even up to Pb. These impulsive SEPs have been found to originate during magnetic reconnection in solar jets where open magnetic field lines allow energetic particles to escape. In contrast, impulsive solar flares are produced when similar reconnection involves closed field lines where energetic ions are trapped on closed loops and dissipate their energy as X-rays, γ-rays, and heat. Abundance enhancements that are power laws in A/Q can be used to determine Q values and hence the coronal source temperature in the events. Results show no evidence of heating, implying reconnection and ion acceleration occur early, rapidly, and at low density. Proton and He excesses that contribute their own power law may identify events with reacceleration of SEPs by shock waves driven by accompanying fast, narrow coronal mass ejections (CMEs) in many of the stronger jets. Full article

(This article belongs to the Special Issue Advances in Impulsive Solar Flares and Particle Acceleration)

► Show Figures

Figure 1

21 pages, 6897 KiB

Open AccessArticle

Possible Wormholes in a Friedmann Universe

by Kirill A. Bronnikov, Pavel E. Kashargin and Sergey V. Sushkov

Universe 2023, 9(11), 465; https://doi.org/10.3390/universe9110465 - 29 Oct 2023

Viewed by 3874

Abstract

We study the properties of evolving wormholes able to exist in a closed Friedmann dust-filled universe and described by a particular branch of the well-known Lemaître–Tolman–Bondi solution to the Einstein equations and its generalization with a nonzero cosmological constant and an electromagnetic field. [...] Read more.

We study the properties of evolving wormholes able to exist in a closed Friedmann dust-filled universe and described by a particular branch of the well-known Lemaître–Tolman–Bondi solution to the Einstein equations and its generalization with a nonzero cosmological constant and an electromagnetic field. Most of the results are obtained with pure dust solutions. It is shown, in particular, that the lifetime of wormhole throats is much shorter than that of the whole wormhole region in the universe (which coincides with the lifetime of the universe as a whole), and that the density of matter near the boundary of the wormhole region is a few times smaller than the mean density of matter in the universe. Explicit examples of wormhole solutions and the corresponding numerical estimates are presented. The traversability of the wormhole under study is shown by a numerical analysis of radial null geodesics. Full article

(This article belongs to the Special Issue The Friedmann Cosmology: A Century Later)

► Show Figures

Figure 1

21 pages, 1254 KiB

Open AccessArticle

Exploring Neutrino Mass Orderings through Supernova Neutrino Detection

by Maria Manuela Saez

Universe 2023, 9(11), 464; https://doi.org/10.3390/universe9110464 - 28 Oct 2023

Cited by 1 | Viewed by 1326

Abstract

Core-collapse supernovae (SNe) are one of the most powerful cosmic sources of neutrinos, with energies of several MeV. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the [...] Read more.

Core-collapse supernovae (SNe) are one of the most powerful cosmic sources of neutrinos, with energies of several MeV. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the hot initial to the cold final states. Detecting these neutrinos from Earth and analyzing the emitted signals present a unique opportunity to explore the neutrino mass ordering problem. This research outlines the detection of neutrinos from SNe and their relevance in understanding the neutrino mass ordering. The focus is on developing a model-independent analysis strategy, achieved by comparing distinct detection channels in large underground detectors. The objective is to identify potential indicators of mass ordering within the neutrino sector. Additionally, a thorough statistical analysis is performed on the anticipated neutrino signals for both mass orderings. Despite uncertainties in supernova explosion parameters, an exploration of the parameter space reveals an extensive array of models with significant sensitivity to differentiate between mass orderings. The assessment of various observables and their combinations underscores the potential of forthcoming supernova observations in addressing the neutrino mass ordering problem. Full article

(This article belongs to the Special Issue Neutrinos across Different Energy Scales)

► Show Figures

Figure 1

17 pages, 1288 KiB

Open AccessArticle

Secular Orbital Dynamics of the Possibly Habitable Planet K2-18 b with and without the Proposed Inner Companion

by Valeri V. Makarov and Alexey Goldin

Universe 2023, 9(11), 463; https://doi.org/10.3390/universe9110463 - 28 Oct 2023

Viewed by 1153

Abstract

The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: A single planet orbiting the [...] Read more.

The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: A single planet orbiting the host star, and a two-planet system including the proposed inner planet close to the 4:1 mean motion rationalization. The emphasis is made on the secular changes of eccentricity and orbital inclination, which are important for the climate stability of the planet. It is demonstrated that the secular orbital dynamics of planet K2-18 b with an internal companion are accurately represented by the periodic eccentricity and inclination exchange on the time scales of a few Kyr. A single planet is not expected to experience fast orbital changes, with the much weaker tidal and rotation-driven perturbations mostly reflecting in a slow periastron and nodal precession. The tidal decay of the orbit is too insignificant on the time scale of the stellar age. However, the conditions for the habitability of a single K2-18 b planet are much improved if, like the Earth, it rotates faster than the mean motion and its rotation angle is tilted by a hypothetical moon. Milanković’s cycles of the habitable planet’s climate are discussed for both configurations. Full article

(This article belongs to the Section Planetary Sciences)

► Show Figures

Figure 1

13 pages, 335 KiB

Open AccessArticle

Lorentz Symmetry Violation Effects Caused by the Coupling between the Field f^μγ⁵ and the Derivative of the Fermionic Field on One-Dimensional Potentials

by K. Bakke and H. Belich

Universe 2023, 9(11), 462; https://doi.org/10.3390/universe9110462 - 27 Oct 2023

Viewed by 1132

Abstract

In search of physics beyond the standard model, new phenomena can be relevant in low energies. In view of the Standard Model Extension is an effective field theory, in this study we explore the fermionic sector by showing that the properties of nonrelativistic [...] Read more.

In search of physics beyond the standard model, new phenomena can be relevant in low energies. In view of the Standard Model Extension is an effective field theory, in this study we explore the fermionic sector by showing that the properties of nonrelativistic quantum systems can be modified. We study one-dimensional nonrelativistic quantum systems under Lorentz symmetry violation effects caused by the coupling between the fixed vector field

f^{μ} γ^{5}

and the derivative of the fermionic field. We deal with the quantum bouncer, the attractive inverse-square potential, a modified attractive inverse-square potential, and a scalar exponential potential inside this scenario of the Lorentz symmetry violation. Then, we show that the spectra of energy are influenced by the Lorentz symmetry violation effects. Full article

(This article belongs to the Section Field Theory)

27 pages, 29790 KiB

Open AccessReview

Yutu-2 Radar Observations at the Chang’E-4 Landing Site: The Shallow Geological Structure and Its Dielectric Properties

by Zhonghan Lei and Chunyu Ding

Universe 2023, 9(11), 461; https://doi.org/10.3390/universe9110461 - 27 Oct 2023

Viewed by 1386

Abstract

China has successfully carried out five lunar exploration missions since 2007. These missions indicate that China has successfully implemented a three-step lunar exploration program of “orbiting, landing, and returning”. Among them, the Lunar Penetrating Radar (LPR) carried by the Yutu-2 rover in the [...] Read more.

China has successfully carried out five lunar exploration missions since 2007. These missions indicate that China has successfully implemented a three-step lunar exploration program of “orbiting, landing, and returning”. Among them, the Lunar Penetrating Radar (LPR) carried by the Yutu-2 rover in the Chang’E-4 (CE-4) mission is the only one still operating on the far side of the Moon. Up to now, the Yutu-2 radar has measured a large amount of scientific data, and its observations are of great significance to human cognition of the geological evolution of the lunar surface and the exploration of possible lunar in situ resources. This paper reviews the scientific results obtained by previous researchers based on the radar exploration data of Yutu-2, focusing mainly on three aspects, e.g., the geological structure of the shallow surface at the CE-4 landing site, the dielectric properties of the shallow subsurface materials and the special geological features. Finally, the prospects of Yutu-2 radar research priorities and future exploration, and the application trend of Moon-based ground-penetrating radar are given. Full article

(This article belongs to the Topic Techniques and Science Exploitations for Earth Observation and Planetary Exploration)

► Show Figures

Figure 1

26 pages, 649 KiB

Open AccessArticle

Hořava–Lifshitz

F (\bar{R})

Theories and the Swampland

by Hugo García-Compeán, Daniel Mata-Pacheco and Luis Zapata

Universe 2023, 9(11), 460; https://doi.org/10.3390/universe9110460 - 26 Oct 2023

Cited by 1 | Viewed by 1146

Abstract

The compatibility between the de Sitter Swampland conjecture and Hořava–Lifshitz

F (\bar{R})

theories with a flat FLRW metric is studied. We first study the standard

f (R)

theories and show that the only way in which the dS [...] Read more.

The compatibility between the de Sitter Swampland conjecture and Hořava–Lifshitz

F (\bar{R})

theories with a flat FLRW metric is studied. We first study the standard

f (R)

theories and show that the only way in which the dS conjecture can be made independent of R is by considering a power law of the form

f (R) \sim R^{γ}

. The conjecture and the consistency of the theory puts restrictions on

γ

to be greater but close to one. For

F (\bar{R})

theories described by its two parameters

λ

and

μ

, we use the equations of motion to construct the function starting with an ansatz for the scale factor in the Jordan frame of the power law form. By performing a conformal transformation on the three metric to the Einstein frame, we can obtain an action of gravity plus a scalar field by relating the parameters of the theory. The non-projectable and projectable cases are studied and the differences are outlined. The obtained

F (\bar{R})

function consists of terms of the form

{\bar{R}}^{γ}

with the possibility of having negative power terms. The dS conjecture leads to inequalities for the

λ

parameter; in both versions, it becomes restricted to be greater but close to

1 / 3

. We can also study the general case in which

μ

and

λ

are considered as independent. The obtained F function has the same form as before. The consistency of the theory and the dS conjecture lead to a set of inequalities on both parameters that are studied numerically. In all cases,

λ

is restricted by

μ

around

1 / 3

, and we obtain

λ \to 1 / 3

if

μ \to 0

. We consider the

f (R)

limit

μ, λ \to 1

and we obtain consistent results. Finally, we study the case of a constant Hubble parameter. The dS conjecture can be fulfilled by restricting the parameters of the theory; however, the constraint makes this compatibility exclusive to these kinds of theories. Full article

(This article belongs to the Special Issue Universe: Feature Papers 2023—Gravitation)

► Show Figures

Figure 1

19 pages, 8702 KiB

Open AccessArticle

Rapid Orbit-to-Orbit Transfer to Asteroid 4660 Nereus Using Solar Electric Propulsion

by Alessandro A. Quarta, Giovanni Mengali and Marco Bassetto

Universe 2023, 9(11), 459; https://doi.org/10.3390/universe9110459 - 26 Oct 2023

Viewed by 1126

Abstract

This paper analyzes the rapid rendezvous trajectory of a spacecraft equipped with an advanced solar electric propulsion system towards asteroid 4660 Nereus. In this context, a set of possible minimum-time orbit-to-orbit transfer trajectories is calculated by modeling the propulsion system performance characteristics on [...] Read more.

This paper analyzes the rapid rendezvous trajectory of a spacecraft equipped with an advanced solar electric propulsion system towards asteroid 4660 Nereus. In this context, a set of possible minimum-time orbit-to-orbit transfer trajectories is calculated by modeling the propulsion system performance characteristics on those of NASA’s Evolutionary Xenon Thruster-Commercial (NEXT-C). In particular, the actual NEXT-C ion engine throttle table is used to calculate the optimal thrust control law that ensures the flight time is minimized for an assigned value for the spacecraft’s initial mass and the reference (electric) power at the beginning of the transfer. A baseline scenario that considers the actual inertial characteristics of the NASA’s DART spacecraft is analyzed in detail, and a parametric study is proposed to evaluate the transfer performance as a function of the main design parameters as, for example, the spacecraft’s initial mass and the reference power. Full article

(This article belongs to the Special Issue Space Missions to Small Bodies: Results and Future Activities)

► Show Figures

Figure 1

13 pages, 281 KiB

Open AccessArticle

Diffeomorphism Covariance of the Canonical Barbero–Immirzi–Holst Triad Theory

by Donald Salisbury

Universe 2023, 9(11), 458; https://doi.org/10.3390/universe9110458 - 25 Oct 2023

Viewed by 1061

Abstract

The vanishing phase space generator of the full four-dimensional diffeomorphism-related symmetry group in the context of the Barbero–Immirz–Holst Lagrangian is derived directly, for the first time, from Noether’s second theorem. Its applicability in the construction of classical diffeomorphism invariants is reviewed. Full article

(This article belongs to the Special Issue Recent Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on His 60th Anniversary)

15 pages, 579 KiB

Open AccessArticle

NLTE Analysis of High-Resolution H-Band Spectra, V: Neutral Sodium

by Zeming Zhou, Jianrong Shi, Shaolan Bi, Hongliang Yan, Junbo Zhang, Kaike Pan and Xiaodong Xu

Universe 2023, 9(11), 457; https://doi.org/10.3390/universe9110457 - 25 Oct 2023

Viewed by 1086

Abstract

In order to derive sodium abundances and investigate the effects of non-local thermodynamic equilibrium (NLTE) on the formation of H-band Na I lines, we update the sodium atomic model by incorporating collision rates with hydrogen from new quantum-mechanical calculations. The differential Na [...] Read more.

In order to derive sodium abundances and investigate the effects of non-local thermodynamic equilibrium (NLTE) on the formation of H-band Na I lines, we update the sodium atomic model by incorporating collision rates with hydrogen from new quantum-mechanical calculations. The differential Na abundances for 13 sample stars are obtained by analyzing high-resolution H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and optical spectra under both local thermodynamic equilibrium (LTE) and NLTE conditions. Consistent abundances from both bands suggest that our updated atomic model is valid for studying the formation of H-band Na I lines. Our calculations show that, in our stellar parameter space, NLTE effects are negative and can result in corrections larger than −0.4 dex on optical lines. The corrections on H-band Na I lines are typically small, within about 0.05 dex, but not negligible if accurate sodium abundance is desired. We note that the [Na/Fe] ratios favor the theoretical galactic chemical model. Full article

(This article belongs to the Section Stellar Astronomy)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Universe, Volume 9, Issue 11 (November 2023) – 30 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI