Free Parameters Research Articles

Observable ΔNeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {\ extrm{N}}_{\ extrm{eff}}$$\\end{document} in Dirac scotogenic model

We study the possibility of probing the radiative Dirac seesaw model with dark sector particles going inside the loop, popularly referred to as the Dirac scotogenic model via measurements of effective relativistic degrees of freedom ΔNeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {\ extrm{N}}_{\ extrm{eff}}$$\\end{document} at cosmic microwave background (CMB) experiments. The loop suppression and additional free parameters involved in neutrino mass generation allow large (∼O(1))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\sim {\\mathcal {O}}(1))$$\\end{document} coupling of light Dirac neutrinos with the dark sector particles. Such large Yukawa coupling not only dictates the relic abundance of heavy fermion singlet dark matter but also can lead to the thermalisation of the right chiral part of Dirac neutrinos, generating additional relativistic degrees of freedom ΔNeff.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {\ extrm{N}}_{\ extrm{eff}}.$$\\end{document} We find that the parameter space consistent with dark matter phenomenology and neutrino mass bounds can also be probed at future cosmic microwave background experiments like CMB-S4 via precision measurements of ΔNeff.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {\ extrm{N}}_{\ extrm{eff}}.$$\\end{document} The same parameter space, while leading to loop-suppressed direct detection cross-section of dark matter outside future sensitivities, can also have other interesting and complementary observational prospects via charged lepton flavour violation and collider signatures.

Charged spinning fermionic configurations and a mass gap

We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of a minimum positive energy of the system (a mass gap), of a minimum charge (a charge gap), and of a minimum magnetic moment. In turn, the presence of the electric charge results in qualitative changes in the behavior of physical characteristics of the systems under consideration as compared with the case of an electrically neutral spinor field. It is shown that, with a suitable choice of free system parameters, there exists a regular finite-energy particlelike solution describing a localized spinning object whose physical parameters correspond to the main characteristics of an electron/positron (including the spin equal to 1/2), but with the characteristic size comparable to the corresponding Compton wavelength. Also, we show that four local Dirac equations are equivalent to two nonlocal equations.

A scheme to fix multiple solutions in amplitude analyses* *Supported by the National Natural Science Foundation of China (NSFC) (12061141007, 12175005) and by the National Key R&D Program of China (2022YFA1601904)

Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better understanding of the underlying dynamics. In special cases where two spin-1/2 particles and two (pseudo-) scalar particles are present in the process, multiple equivalent solutions are found owing to intrinsic symmetries in the summed probability density function. In this study, the problem of multiple solutions is discussed, and a scheme to overcome this problem is proposed by fixing some free parameters. Toys are generated to validate the strategy. A new approach to align the helicities of initial- and final-state particles in different decay chains is also introduced.

An unrestricted Arnold’s cat map transformation

AbstractThe Arnold’s Cat Map (ACM) is one of the chaotic transformations, which is utilized by numerous scrambling and encryption algorithms in Information Security. Traditionally, the ACM is used in image scrambling whereby repeated application of the ACM matrix, any image can be scrambled. The transformation obtained by the ACM matrix is periodic; therefore, the original image can be reconstructed using the scrambled image whenever the elements of the matrix, hence the key, is known. The transformation matrices in all the chaotic maps employing ACM has limitations on the choice of the free parameters which generally require the area-preserving property of the matrix used in transformation, that is, the determinant of the transformation matrix to be $$\pm 1.$$ ± 1 . This reduces the number of possible set of keys which leads to discovering the ACM matrix in encryption algorithms using the brute-force method. Additionally, the period obtained is small which also causes the faster discovery of the original image by repeated application of the matrix. These two parameters are important in a brute-force attack to find out the original image from a scrambled one. The objective of the present study is to increase the key space of the ACM matrix, hence increase the security of the scrambling process and make a brute-force attack more difficult. It is proved mathematically that area-preserving property of the traditional matrix is not required for the matrix to be used in scrambling process. Removing the restriction enlarges the maximum possible key space and, in many cases, increases the period as well. Additionally, it is supplied experimentally that, in scrambling images, the new ACM matrix is equivalent or better compared to the traditional one with longer periods. Consequently, the encryption techniques with ACM become more robust compared to the traditional ones. The new ACM matrix is compatible with all algorithms that utilized the original matrix. In this novel contribution, we proved that the traditional enforcement of the determinant of the ACM matrix to be one is redundant and can be removed.

Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method

The (3 + 1)-dimensional generalized shallow water equation is a significant mathematical framework for analyzing the dynamic behavior of waves in ocean physics. The purpose of this article is to investigate some more generic soliton solutions of the generalized shallow water-like model in three dimensions. The investigation is conducted utilizing the sophisticated mathematical methodology known as the double variables ( ϕ ′ / ϕ , 1 / ϕ ) expansion technique. With this approach, we produce new propagating wave solutions for this model in the form of hyperbolic, trigonometric, and rational functions. In addition, we offer two- and three-dimensional graphical representations to help visualize the intricate physical phenomena of the system. We have constructed many soliton solutions, such as kink shape soliton solutions, anti-bell shape solutions, single periodic solutions, singular soliton solutions, and anti-kink shape solutions for different values of the free parameters involved in the obtained solutions. These graphical representations are predicated on certain parameter selections, which facilitate the understanding of the complicated general behavior for this model. Through the presentation of new findings in the field of soliton solutions for the aforementioned equation, this paper offers fresh perspectives and highlights hitherto overlooked aspects of this fascinating mathematical challenge. The paper illuminates new results on soliton solutions with different geometrical structures for the given equation, revealing hitherto overlooked facets of this intriguing mathematical challenge.

Solving Large-Scale Unconstrained Optimization Problems with an Efficient Conjugate Gradient Class

The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems. The presented class enjoys the benefits of having three free parameters, its directions are descent, and it can fulfill the Dai–Liao conjugacy condition. Global convergence property of the new class is proved under the weak-Wolfe–Powell line search technique. Numerical efficiency of the proposed class is confirmed in three sets of experiments including 210 test problems and 11 disparate conjugate gradient methods.

Constraining Palatini gravity with GR-independent equations of state for neutron stars

We demonstrate how to construct GR-independent equations of state for a neutron star from the information available in the literature. We emphasize the importance of using theory-based principles instead of relying solely on astrophysical observables and General Relativity. We propose a set of equations of state based on first microscopic principles, including chiral perturbation theory and perturbation theory in quantum chromodynamics. Interpolation methods are employed with assumptions on the thermodynamic stability and causality in the intermediate region. These equations of state are then used to constrain quadratic Palatini f(ℛ) gravity, indicating that its free parameter can at most lie within the range around -6.47 ≲ β ≲ 1.99 km2. Additionally, we briefly discuss the problem of phase transitions and twin stars.

Kindling the First Stars. I. Dependence of Detectability of the First Stars with JWST on the Population III Stellar Masses

The first Population III (Pop III) stars formed out of primordial, metal-free gas, in minihalos at z > 20, and kickstarted the cosmic processes of reionization and enrichment. While these stars are likely more massive than their enriched counterparts, the current unknowns of their astrophysics include when the first Pop III stars ignited, how massive they were, and when and how the era of the first stars ended. Investigating these questions requires an exploration of a multidimensional parameter space, including the slope of the Pop III stellar initial mass function (IMF) and the strength of the nonionizing UV background. In this work, we present a novel model which treats both the slope and maximum mass of Pop III stars as truly free parameters while including the physics of the fragmentation of primordial gas. Our results also hint at a nonuniversal Pop III IMF which is dependent on the efficiency of primordial gas fragmentation. Our relatively simple model reproduces the results from hydrodynamic simulations, but with a computational efficiency which allows us to investigate the observable differences between a wide range of potential Pop III IMFs. In addition, the evolution of the number density of Pop III stars may provide insight into the evolution of the H2 dissociating background. While the slope of the Pop III IMF does not significantly affect the predicted number density of the first stars, more top-heavy IMFs produce Pop III star clusters which are 2–3 magnitudes brighter than their more bottom-heavy counterparts. While the Pop III star clusters are too dim for direct detection by JWST, we find they are within the reach of gravitational lensing.

Revised Constraints on the Fast Radio Burst Population from the First CHIME/FRB Catalog

In this paper, we investigate the fast radio burst (FRB) population using the first CHIME/FRB catalog. We first reconstruct the extragalactic dispersion measure–redshift relation (DME–z relation) from well-localized FRBs, then use it to infer the redshift and isotropic energy of the first CHIME/FRB catalog. The intrinsic energy distribution is modeled by the power law with an exponential cutoff, and the selection effect of the CHIME telescope is modeled by a two-parametric function of specific fluence. For the intrinsic redshift distribution, the star formation history (SFH) model and five other SFH-related models are considered. We construct the joint likelihood of fluence, energy, and redshift, and all the free parameters are constrained simultaneously using the Bayesian inference method. The Bayesian information criterion (BIC) is used to choose the model that best matches the observational data. For comparison, we fit our models with two data samples, i.e., the Full sample and the Gold sample. The power-law index and cutoff energy are tightly constrained to be 1.8 ≲ α ≲ 1.9 and log(Ec/erg)≈42 , which are almost independent of the redshift distribution model and the data sample we choose. The parameters involving the selection effect strongly depend on the data sample but are insensitive to the redshift distribution model. According to BIC, the pure SFH model is strongly disfavored by both the Full sample and Gold sample. For the other five SFH-related redshift distribution models, most of them can match the data well if the parameters are properly chosen. Therefore, with the present data, it is still premature to draw a conclusion on the FRB population.

Strategies for Obtaining Robust Spectral Energy Distribution Fitting Parameters for Galaxies at z ∼ 1 and z ∼ 2 in the Absence of Infrared Data

Robust estimation of star formation rates (SFRs) at higher redshifts (z ≳ 1) using UV–optical–near-infrared (NIR) photometry is contingent on the ability of spectral energy distribution (SED) fitting to constrain the dust attenuation, stellar metallicity, and star formation history (SFH) simultaneously. IR-derived dust luminosities can help break the degeneracy between these parameters, but IR data are often not available. Here, we explore strategies for SED fitting at z ≳ 1 in the absence of IR data using a sample of log M * > 10.2 star-forming galaxies from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) for which 24 μm data are available. We adopt the total IR luminosity (L TIR) obtained from 24 μm as the “ground truth,” which allows us to assess how well it can be recovered (as L dust) from UV–optical–NIR SED fitting. We test a variety of dust attenuation models, stellar population synthesis models, metallicity assumptions, and SFHs separately to identify which assumptions maximize the agreement (correlation and linearity) between L TIR and L dust. We find that a flexible dust attenuation law performs best. For stellar populations, we find that Bruzual & Charlot models are favored over those of Eldridge et al. Fixing the stellar metallicity at solar value is preferred to other fixed values or leaving it as a free parameter. For SFHs, we find that minimizing the variability in the recent (<100 Myr) SFH improves the agreement with L TIR. Finally, we provide a catalog of galaxy parameters (including M * and SFR) for CANDELS galaxies with logM*>8 and 0.7 < z < 1.3, obtained using the models we found to be the most robust.

An Empirical Model for Mercury’s Field‐Aligned Currents Derived From MESSENGER Magnetometer Data

AbstractMercury is the only planetary magnetosphere which does not possess a significantly conducting ionosphere, yet magnetic field observations by the Mariner 10 and MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) missions revealed a stable presence of large‐scale field‐aligned currents (FACs). Several empirical magnetic field models have been developed to describe Mercury’s magnetospheric currents and their associated magnetic fields, but none attempted to include an explicit description of large‐scale FACs. Here, we describe a dynamic FAC magnetic field model for Mercury based on the analytical solution to conical currents, which are shielded by a dynamic magnetopause boundary. The model contains free parameters setting the FACs' latitudinal extent and amplitude as functions of magnetospheric activity. The parameters are fit by minimizing the root‐mean‐square (RMS) differences between the model and MESSENGER Magnetometer data. During magnetically quiet conditions, the modeled FACs have an intensity of ∼10 nA/m2 and extend in latitude from ∼83°N to ∼40°N. They intensify to ∼20 nA/m2 and expand equatorward to ∼28°N during the most active times. The inclusion of the FAC model reduces low‐altitude RMS residuals by 8.1% when compared to prior models. The model effectively captures the azimuthal component of the magnetic field present in the MESSENGER low‐altitude data, but largely misses the radial and co‐latitudinal components, indicating other large‐scale physics remain missing in the mathematical descriptions of Mercury's magnetosphere.

Can Fallback Accretion on the Magnetar Model Power the X-Ray Flares Simultaneously Observed with Gamma Rays of Gamma-Ray Bursts?

The prompt emission, X-ray plateau, and X-ray flares of gamma-ray bursts (GRBs) are thought to be from internal dissipation, and the magnetar as the central engine with propeller fallback accretion is proposed to interpret the observed phenomena of GRBs. In this paper, by systematically searching for X-ray emission observed by Swift/X-ray Telescope, we find that seven robust GRBs include both X-ray flares and plateau emissions with measured redshift. More interestingly, the X-ray flares/bumps for those seven GRBs are simultaneously observed in the gamma-ray band. By adopting the propeller fallback accretion model to fit the observed data, it is found that the free parameters of two GRBs (140512A and 180329B) can be constrained very well, while in the other five cases, more or less, they are not all sufficiently constrained. On the other hand, this requires the conversion efficiency of the propeller to be two or three times higher than that of the spindown dipole radiation of the magnetar. If this is the case, it is contradictory to the expectation from the propeller model: namely, a dirtier ejecta should be less efficient in producing gamma-ray emissions. Our results hint that at least the magnetar central engine with propeller fallback accretion model cannot interpret very well both the GRB X-ray flares simultaneously observed in the gamma-ray band and the X-ray flares of GRBs with a high Lorentz factor.

A Discussion of Implausible Total Solar-Irradiance Variations Since 1700

The Sun plays a role in influencing Earth’s climate, making it important to have accurate information about variations in the Sun’s radiative output. Models are used to recover total solar-irradiance (TSI) variations in the past when direct space-based measurements are not available. One of the most cryptic such TSI reconstructions is the one by Hoyt and Schatten (J. Geophys. Res. 98, 18, 1993, HS93). The rather vague description of the model methodology, the arbitrary selection of solar indices it employs, and the short overlap between the HS93 series and directly measured TSI values has hindered any evaluation of the performance of this model to this day. Here, we aim at rectifying this by updating the HS93 model with new input data. In this way we are also contributing in the discussion on the possible long-term changes in solar irradiance.We find that the analysis by HS93 included a number of erroneous processing steps that led to an artificial increasing trend towards the end of the reconstructed TSI series as well as shifting the peak of the TSI in the mid-twentieth century back in time by about 11 years. Furthermore, by using direct measurements of the TSI we determined that the free parameter of the model, the magnitude of variations (here defined as percentage variations of the difference between the maximum to minimum values), is optimal when it is minimised (being ≤0.05%). This is in stark contrast to the high magnitude of variations, of 0.25%, that was imposed by HS93. However, our result is consistent with more recent estimates, such as those from the Spectral And Total Irradiance REconstruction (SATIRE) model and Naval Research Laboratory TSI (NRLTSI), which were used by the Intergovernmental Panel on Climate Change (IPCC). Overall, we find that the previously reported agreement of the HS93 TSI series to temperature on Earth was purely due to improper analysis and artefacts of the processing.

Imaging Upper-Mantle Anisotropy with Transdimensional Bayesian Monte Carlo Sampling

ABSTRACT Underdetermination is a condition affecting all problems in seismic imaging. It manifests mainly in the nonuniqueness of the models inferred from the data. This condition is exacerbated if simplifying hypotheses like isotropy are discarded in favor of more realistic anisotropic models that, although supported by seismological evidence, require more free parameters. Investigating the connections between underdetermination and anisotropy requires the implementation of solvers which explore the whole family of possibilities behind nonuniqueness and allow for more informed conclusions about the interpretation of the seismic models. Because these aspects cannot be investigated using traditional iterative linearized inversion schemes with regularization constraints that collapse the infinite possible models into a unique solution, we explore the application of transdimensional Bayesian Monte Carlo sampling to address the consequences of underdetermination in anisotropic seismic imaging. We show how teleseismic waves of P and S phases can constrain upper-mantle anisotropy and the amount of additional information these data provide in terms of uncertainty and trade-offs among multiple fields.

Fast Generation of Mock Galaxy Catalogs with COLA

We investigate the feasibility of using the comoving Lagrangian acceleration (COLA) technique to efficiently generate galaxy mock catalogs that can accurately reproduce the statistical properties of observed galaxies. Our proposed scheme combines the subhalo abundance-matching (SHAM) procedure with COLA simulations, using only three free parameters: the scatter magnitude (σ scat) in SHAM, the initial redshift (z init) of the COLA simulation, and the time stride (da) used by COLA. In this proof-of-concept study, we focus on a subset of BOSS CMASS NGC galaxies within the redshift range z ∈ [0.45, 0.55]. We perform GADGET simulation and low-resolution COLA simulations with various combinations of (z init, da), each using 10243 particles in an 800 h −1 Mpc box. By minimizing the difference between COLA mock and CMASS NGC galaxies for the monopole of the two-point correlation function (2PCF), we obtain the optimal σ scat. We have found that by setting z init = 29 and da = 1/30, we achieve a good agreement between COLA mock and CMASS NGC galaxies within the range of 4–20 h −1 Mpc, with a computational cost lower by 2 orders of magnitude than that of the GADGET N-body code. Moreover, a detailed verification is performed by comparing various statistical properties, such as anisotropic 2PCF, three-point clustering, and power spectrum multipoles, which shows a similar performance of the GADGET mock and COLA mock catalogs with the CMASS NGC galaxies. Furthermore, we assess the robustness of the COLA mock catalogs for different cosmological models, demonstrating consistent results in the resulting 2PCFs. Our findings suggest that COLA simulations are a promising tool for efficiently generating mock catalogs for emulators and machine-learning analyses to explore the large-scale structure of the Universe.

Simulations of CO2 Dissolution in Porous Media Using the Volume-of-Fluid Method

Traditional investigations of fluid flow in porous media often rely on a continuum approach, but this method has limitations as it does not account for microscale details. However, recent progress in imaging technology allows us to visualize structures within the porous medium directly. This capability provides a means to confirm and validate continuum relationships. In this study, we present a detailed analysis of the dissolution trapping dynamics that take place when supercritical CO2 (scCO2) is injected into a heterogeneous porous medium saturated with brine. We present simulations based on the volume-of-fluid (VOF) method to model the combined behavior of two-phase fluid flow and mass transfer at the pore scale. These simulations are designed to capture the dynamic dissolution of scCO2 in a brine solution. Based on our simulation results, we have revised the Sherwood correlations: We expanded the correlation between Sherwood and Peclet numbers, revealing how the mobility ratio affects the equation. The expanded correlation gave improved correlations built on the underlying displacement patterns at different mobility ratios. Further, we analyzed the relationship between the Sherwood number, which is based on the Reynolds number, and the Schmidt number. Our regression on free parameters yielded constants similar to those previously reported. Our mass transfer model was compared to experimental models in the literature, showing good agreement for interfacial mass transfer of CO2 into water. The results of this study provide new perspectives on the application of non-dimensional numbers in large-scale (field-scale) applications, with implications for continuum scale modeling, e.g., in the field of geological storage of CO2 in saline aquifers.

The contribution of massive haloes to the matter power spectrum in the presence of AGN feedback

ABSTRACT The clustering of matter, as measured by the matter power spectrum, informs us about cosmology, dark matter, and baryonic effects on the distribution of matter in the universe. Using cosmological hydrodynamical simulations from the cosmo-OWLS and BAHAMAS simulation projects, we investigate the contribution of power in haloes with various masses, to the full power spectrum, as well as the power ratio between baryonic and dark matter only (DMO) simulations for a matched (between simulations) and an unmatched set of haloes. We find that the presence of AGN feedback suppresses the power on all scales for haloes of all masses examined (1011.25 ≤ M500, crit ≤ $10^{14.75}\, \mathrm{M_\odot }/h$), by ejecting matter from within $r_{500,\mathrm{c}}\,$ to $r_{200,\mathrm{m}}\,$ and potentially beyond in massive haloes (M500, crit ≳ $10^{{13}}\, \mathrm{M_\odot }/h$), and likely impeding the growth of lower-mass haloes as a consequence. A lower AGN feedback temperature changes the behaviour of high-mass haloes (M500, crit ≥ $10^{{13.25}}\, \mathrm{M_\odot }/h$), damping the effects of AGN feedback at small scales, $k\, {{\gtrsim }}\, {{4}}\, h\mathrm{\, Mpc^{-1}}$. For $k\, {{\lesssim }}\, {{3}}\, h\mathrm{\, Mpc^{-1}}$, group-sized haloes ($10^{{14\pm 0.25}}\, \mathrm{M_\odot }/h$) dominate the power spectrum, while on smaller scales the combined contributions of lower-mass haloes to the full power spectrum rise above that of the group-sized haloes. Finally, we present a model for the power suppression due to feedback, which combines observed mean halo baryon fractions with halo mass fractions and halo-matter cross-spectra extracted from DMO simulations to predict the power suppression to per cent level accuracy down to $k\, {{\approx }}\, {{10}}\, h\mathrm{\, Mpc^{-1}}$ without any free parameters.

Distinct wave profiles relating to a coupled of Schrödinger equations depicting the modes in optics

Diverse aspects of real-world problems are portrayed through nonlinear Schrodinger equations. This exploration considers a pair of fractional order Schrodinger equations describing important nonlinear instability phenomena which are related to heat pulse, quantum condensates, nonlinear acoustics, hydrodynamics, and nonlinear optics. The improved auxiliary equation and improved tanh schemes are imposed on the governing model which generate a bulk of innovative accurate wave solutions. Plenty of wave solutions achieved in this study could be utilized to characterize the interior mechanisms of intricate phenomena relating to the considered nonlinear models. Some of the solutions are selected to figure out in the sense of contours, 3D and 2D outlines after assigning suitable values to the involved free parameters. The directed techniques are employed to explore appropriate wave solutions of the above-stated nonlinear model for the first time ensuring the unique solutions rather than the results in earlier studies. This present work highlights the competency of used methods celebrating huge appropriate wave solutions of suggested complex nonlinear models and gives a guideline for related future research.

New analytic solutions in f(R)$$ f(R) $$‐cosmology from Painlevé analysis

Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in ‐cosmology. Specifically, for some power‐law ‐theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlevé property. Constraints for the free parameters of the power‐law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions.

Precision MARS Mass Reconstruction of A2744: Synergizing the Largest Strong-lensing and Densest Weak-lensing Data Sets from JWST

We present a new high-resolution free-form mass model of A2744 that combines both weak-lensing (WL) and strong-lensing (SL) data sets from JWST. The SL data set comprises 286 multiple images, presenting the most extensive SL constraint to date for a single cluster. The WL data set, employing photo-z selection, yields a source density of ∼350arcmin−2 , marking the densest WL constraint ever. The combined mass reconstruction enables the highest-resolution mass map of A2744 within the ∼1.8 Mpc × 1.8 Mpc reconstruction region to date, revealing an isosceles triangular structure with two legs of ∼1 Mpc and a base of ∼0.6 Mpc. Although our algorithm, which is called MAximum-entropy ReconStruction (MARS), is entirely blind to the cluster galaxy distribution, the resulting mass reconstruction traces the brightest cluster galaxies remarkably well. The five strongest mass peaks coincide with the five most luminous cluster galaxies within ≲2″. We do not detect any unusual mass peaks that are not traced by the cluster galaxies, unlike the findings in previous studies. Our mass model shows the smallest scatter of SL multiple images in both source (∼0.″05) and image (∼0.″1) planes, which is lower than in previous studies by a factor of ∼4. Although MARS represents the mass field with an extremely large number of free parameters (∼300,000), it converges to a solution within a few hours because we use a deep-learning technique. We make our mass and magnification maps publicly available.