Dynamical Equilibrium Research Articles

The effects of weather and mobility on respiratory viruses before and during the COVID-19 pandemic

Abstract Background The flu season is caused by a combination of different pathogens, including influenza viruses, which cause the flu, and non-influenza respiratory viruses, that cause common colds or influenza-like illness. These viruses exhibit similar dynamics and, given that outbreaks occur mostly in the winter and there is almost no circulation during the summer, in temperate regions, meteorological conditions have historically been regarded as a principal modulator of their epidemiology. However, after the emergence of SARS-CoV2, in late 2019, the dynamics of these respiratory viruses were strongly perturbed worldwide: some infections displayed near-eradication, while others experienced temporal shifts or occurred “off-season”. This disruption raised questions regarding the dominant role of weather while also providing an unique opportunity to investigate the roles of other determinants in their epidemiological dynamics. Methods Weather, mobility and epidemiological surveillance data was collected for Influenza, RSV, hCOV and hMPV, from Canada and the USA, from 2016 to 2023. Statistical analysis and modeling were employed to test the effects of weather and mobility on viral dynamics, before and during the COVID-19 pandemic. Results Using Beta Regressions, we found that whereas in the pre-COVID-19 pandemic period, weather had a strong effect, in the pandemic period, this effect was strongly reduced post-pandemic with mobility playing a more significant role. Conclusions These results, together with previous studies, dispute the general belief that respiratory viral dynamics are mostly dictated by weather and indicate that behavioral changes resulting from the non-pharmacological interventions implemented to control SARS-CoV2, played a key role. This disruption of past dynamical equilibrium raises important questions regarding the factors that modulate them, particularly in a context of climate change. Key messages • We took advantage of the disruption caused by COVID-19 to study dynamics of other respiratory viruses and to disentangle the effects of weather from those of human behavior. • While before 2020 cold temperatures were highly correlated with incidence, afterwards cold weather was no longer a necessary condition and human mobility became central.

Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego , ; G. M. Buendía , ]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick , ]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point. Published by the American Physical Society 2024

Detection and characterization of detached tidal dwarf galaxies

Tidal interactions between galaxies often give rise to tidal tails, which can harbor concentrations of stars and interstellar gas resembling dwarf galaxies. Some of these tidal dwarf galaxies (TDGs) have the potential to detach from their parent galaxies and become independent entities, but their long-term survival is uncertain. In this study, we conducted a search for detached TDGs associated with a sample of 39 interacting galaxy pairs in the local Universe using infrared, ultraviolet, and optical images. We employed IR colors and UV/optical/IR spectral energy distributions to identify potential interlopers, such as foreground stars or background quasars. Through spectroscopic observations using the Boller and Chivens spectrograph at San Pedro Mártir Observatory, we confirmed that six candidate TDGs are at the same redshift as their putative parent galaxy pairs. We identified and measured emission lines in the optical spectra and calculated nebular oxygen abundances, which range from log(O/H) = 8.10 ± 0.01 to 8.51 ± 0.02. We have serendipitously discovered an additional detached TDG candidate in Arp72 using available spectra from SDSS. Utilizing the photometric data and the CIGALE code for stellar population and dust emission fitting, we derived the stellar masses, stellar population ages, and stellar metallicities for these detached TDGs. Compared to standard mass-metallicity relations for dwarf galaxies, five of the seven candidates have higher than expected metallicities, confirming their tidal origins. One of the seven candidates remains unclear due to large uncertainties in metallicity, and another has stellar and nebular metallicities compatible with those of a preexisting dwarf galaxy. The latter object is relatively compact in the optical relative to its stellar mass, in contrast to the other candidate TDGs, which have large diameters for their stellar masses compared to most dwarf galaxies. The derived stellar population ages range from 100 Myr to 900 Myr, while the inferred stellar masses are between 2 × 106 M⊙ and 8 × 107 M⊙. Four of the six TDGs are associated with the gas-rich M51-like pair Arp 72, one TDG is associated with a second M51-like pair Arp 86, and another is associated with Arp 65, an approximately equal mass pair. In spite of the relatively low stellar masses of these TDGs, they have survived for at least 100–900 Myrs, suggesting that they are stable and in dynamical equilibrium. We conclude that encounters with a relatively low-mass companion (1/10th–1/4th of the mass of the primary) can also produce long-lasting TDGs.

Action-based dynamical models of M31-like galaxies

ABSTRACT In this work, we present an action-based dynamical equilibrium model to constrain the phase-space distribution of stars in the stellar halo, present-day dark matter distribution, and the total mass distribution in M31-like galaxies. The model comprises a three-component gravitational potential (stellar bulge, stellar disc, and a dark matter halo), and a double power-law distribution function (DF), $f(\mathbf {J})$, which is a function of actions. A Bayesian model-fitting algorithm was implemented that enabled both parameters of the potential and DF to be explored. After testing the model-fitting algorithm on mock data drawn from the model itself, it was applied to a set of three M31-like haloes from the Auriga simulations (Auriga 21, Auriga 23, and Auriga 24). Furthermore, we tested the equilibrium assumption and the ability of a double power-law DF to represent the stellar halo stars. The model incurs an error in the total enclosed mass of around 10 per cent out to 100 kpc, thus justifying the equilibrium assumption. Furthermore, the double power-law DF used proves to be an appropriate description of the investigated M31-like haloes. The anisotropy profiles of the haloes were also investigated and discussed from a merger history point of view, however, our approach underscores to capture the non-equilibrium anisotropy information of stellar haloes in Auriga models, which is expected.

Spontaneous symmetry breaking of cooperation between species.

In mutualistic associations, two species cooperate by exchanging goods or services with members of another species for their mutual benefit. At the same time, competition for reproduction primarily continues with members of their own species. In intra-species interactions, the prisoner's dilemma is the leading mathematical metaphor to study the evolution of cooperation. Here we consider inter-species interactions in the spatial prisoner's dilemma, where members of each species reside on one lattice layer. Cooperators provide benefits to neighbouring members of the other species at a cost to themselves. Hence, interactions occur across layers but competition remains within layers. We show that rich and complex dynamics unfold when varying the cost-to-benefit ratio of cooperation, r. Four distinct dynamical domains emerge that are separated by critical phase transitions, each characterized by diverging fluctuations in the frequency of cooperation: (i) for large r cooperation is too costly and defection dominates; (ii) for lower r cooperators survive at equal frequencies in both species; (iii) lowering r further results in an intriguing, spontaneous symmetry breaking of cooperation between species with increasing asymmetry for decreasing r; (iv) finally, for small r, bursts of mutual defection appear that increase in size with decreasing r and eventually drive the populations into absorbing states. Typically, one species is cooperating and the other defecting and hence establish perfect asymmetry. Intriguingly and despite the symmetrical model set-up, natural selection can nevertheless favour the spontaneous emergence of asymmetric evolutionary outcomes where, on average, one species exploits the other in a dynamical equilibrium.

Collisionless Relaxation from Near-equilibrium Configurations: Linear Theory and Application to Tidal Stripping

Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolated N-body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against an N-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system.

PHANGS-MeerKAT and MHONGOOSE HI observations of nearby spiral galaxies: Physical drivers of the molecular gas fraction, Rmol

The molecular-to-atomic gas ratio is crucial to our understanding of the evolution of the interstellar medium (ISM) in galaxies. We investigated the balance between the atomic ( and molecular gas ( surface densities in eight nearby star-forming galaxies using new high-quality observations from MeerKAT and ALMA (for and CO, respectively). We defined the molecular gas ratio as mol and measured how depends on local conditions in the galaxy disks using multiwavelength observations. We find that, depending on the galaxy is detected at out to $20-120$\,kpc in galactocentric radius gal $). The typical radius at which reaches 1 is hi kpc, which corresponds to $1-3$ times the optical radius $). We note that, $R_ mol $ correlates best with the dynamical equilibrium pressure, P$_ DE $, among potential drivers studied, with a median correlation coefficient of $ Correlations between mol $ and the star formation rate surface density, total gas surface density, stellar surface density, metallicity, and (a proxy for the combined effect of the UV radiation field and number density) are present but somewhat weaker. Our results also show a direct correlation between and $ SFR $, supporting self-regulation models. Quantitatively, we measured similar scalings as previous works, and attribute the modest differences that we do find to the effect of varying resolution and sensitivity. At $r_ gal gtrsim 0.4 r_ $, atomic gas dominates over molecular gas among our studied galaxies, and at the balance of these two gas phases ($R_ mol $ = 1), we find that the baryon mass is dominated by stars, with Our study constitutes an important step in the statistical investigation of how local galaxy properties (stellar mass, star formation rate, or morphology) impact the conversion from atomic to molecular gas in nearby galaxies.

Competition between self- and other-regarding preferences in resolving social dilemmas

Evolutionary game theory assumes that individuals maximize their benefits when choosing strategies. However, an alternative perspective proposes that individuals seek to maximize the benefits of others. To explore the relationship between these perspectives, we develop a model where self- and other-regarding preferences compete in public goods games. We find that other-regarding preferences are more effective in promoting cooperation, even when self-regarding preferences are more productive. Cooperators with different preferences can coexist in a new phase where two classic solutions invade each other, resulting in a dynamical equilibrium. As a consequence, a lower productivity of self-regarding cooperation can provide a higher cooperation level. Our results, which are also valid in a well-mixed population, may explain why other-regarding preferences could be a viable and frequently observed attitude in human society.

Feedback and Galaxy Dynamics: A Study of Turbulence and Star Formation in 34 Galaxies Using the PHANGS Survey

The correlation between interstellar turbulent speed and local star formation rate surface density, ΣSFR, is studied using CO observations in the PHANGS survey. The local velocity dispersion of molecular gas, σ, increases with ΣSFR, but the virial parameter, α vir, is about constant, suggesting the molecular gas remains self-gravitating. The correlation arises because σ depends on the molecular surface density, Σmol, and object cloud mass, M mol, with the usual molecular cloud correlations, while ΣSFR increases with both of these quantities because of a nearly constant star formation efficiency for CO. Pressure fluctuations with ΔΣSFR are also examined. Azimuthal variations of molecular pressure, ΔP mol, have a weaker correlation with ΔΣSFR than expected from the power-law correlation between the total quantities, suggesting slightly enhanced star formation rate (SFR) efficiency per molecule in spiral arms. Dynamical equilibrium pressure and SFR correlate well for the whole sample, as PDE∝ΣSFR1.3 , which is steeper than in other studies. The azimuthal fluctuations, ΔP DE(ΔΣSFR), follow the total correlation P DE(ΣSFR) closely, hinting that some of this correlation may be a precursor to star formation, rather than a reaction. Galactic dynamical processes correlate linearly such that ΣSFR∝(ΣgasR)1.0±0.3 for total gas surface density Σgas and galactic dynamical rates, R, equal to κ, A, or Ω, representing epicyclic frequency, shear rate A, and orbit rate Ω. These results suggest important roles for both feedback and galactic dynamics.

Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations.

The rate constants of enzyme-catalyzed reactions (kcat) are often approximated from the barrier height of the reactive step. We introduce an enhanced sampling QM/MM approach that directly calculates the kinetics of enzymatic reactions, without introducing the transition-state theory assumptions, and takes into account the dynamical equilibrium between the reactive and non-reactive conformations of the enzyme/substrate complex. Our computed kcat values are in order-of-magnitude agreement with the experimental data for two representative enzymatic reactions.

Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling.

Inertial effects caused by perturbations of dynamical equilibrium during the flow of soft matter constitute a hallmark of turbulence. Such perturbations are attributable to an imbalance between energy storage and energy dissipation. During the flow of Newtonian fluids, kinetic energy can be both stored and dissipated, while the flow of viscoelastic soft matter systems, such as polymer fluids, induces the accumulation of both kinetic and elastic energies. The accumulation of elastic energy causes local stiffening of stretched polymer chains, which can destabilise the flow. Migrating multicellular systems are hugely complex and are capable of self-regulating their viscoelasticity and mechanical stress generation, as well as controlling their energy storage and energy dissipation. Since the flow perturbation of viscoelastic systems is caused by the inhomogeneous accumulation of elastic energy, rather than of kinetic energy, turbulence can occur at low Reynolds numbers.This theoretical review is focused on clarifying the role of viscoelasticity in the appearance of low-Reynolds turbulence. Three types of system are considered and compared: (1) high-Reynolds turbulent flow of Newtonian fluids, (2) low and moderate-Reynolds flow of polymer solutions, and (3) migration of epithelial collectives, discussed in terms of two model systems. The models considered involve the fusion of two epithelial aggregates, and the free expansion of epithelial monolayers on a substrate matrix.

Machine Learning the Dark Matter Halo Mass of Milky Way-Like Systems

Despite the Milky Way’s proximity to us, our knowledge of its dark matter halo is fairly limited, and there is still considerable uncertainty in its halo mass. Many past techniques have been limited by assumptions such as the Galaxy being in dynamical equilibrium as well as nearby galaxies being true satellites of the Galaxy, and/or the need to find large samples of Milky Way analogs in simulations.Here, we propose a new technique based on neural networks that obtains high precision (<0.14 dex mass uncertainty with perfect measurements of 30 neighboring galaxies; <0.14 dex including fiducial observational errors) without assuming halo dynamical equilibrium or that neighboring galaxies are all satellites, and which can use information from a wide variety of simulated halos (even those dissimilar to the Milky Way) to improve its performance. This method uses only observable information including satellite orbits, distances to nearby larger halos, and the maximum circular velocity of the largest satellite galaxy. In this paper, we demonstrate a proof-of-concept method on simulated dark matter halos; in future papers in this series, we will apply neural networks to estimate the masses of the Milky Way’s and M31’s dark matter halos, and we will train variations of these networks to estimate other halo properties including concentration, assembly history, and spin axis.

The Radial Orbits of Ram-pressure-stripped Galaxies in Clusters from the GASP Survey

We analyze a sample of 244 ram-pressure-stripped candidate galaxy members within the virial radius of 62 nearby clusters to determine their velocity anisotropy profile β(r). We use previously determined mass profiles for the 62 clusters to build an ensemble cluster by stacking the 62 cluster samples in projected phase space. We solve the Jeans equation for dynamical equilibrium by two methods, MAMPOSSt and the Jeans inversion technique, and determine β(r) both in parametric form and nonparametrically. The two methods consistently indicate that the orbits of the ram-pressure-stripped candidates are increasingly radial with distance from the cluster center, from almost isotropic (β ≃ 0) at the center, to very radial at the virial radius (β ≃ 0.7). The orbits of cluster galaxies undergoing ram pressure stripping are similar to those of spiral cluster galaxies but more radially elongated at large radii.

Structural and dynamical equilibrium properties of hard board-like particles in parallel confinement.

We performed Monte Carlo and dynamic Monte Carlo simulations to model the diffusion of monodispersed suspensions composed of impenetrable cuboidal particles, specifically hard board-like particles (HBPs), in the presence of parallel hard walls. The impact of the walls was investigated by adjusting the size of the simulation box while maintaining constant packing fractions, fixed at η = 0.150, for systems consisting of HBPs with prolate, dual-shaped, and oblate geometries. We observed that increasing the distance between the walls led to the recovery of an isotropic bulk phase, while local particle organization near the walls remained stable. Due to their shape, oblate HBPs exhibit more efficient anchoring at wall surfaces compared to prolate shapes. The formation of nematic-like particle assemblies near the walls, confirmed by theoretical calculations based on density functional theory, significantly influenced local particle dynamics. This effect was particularly pronounced to the extent that a modest portion of cuboids near the walls tended to diffuse exclusively in planes parallel to the confinement, even more efficiently than observed in the bulk regions.

The ALMaQUEST Survey XI: a strong but non-linear relationship between star formation and dynamical equilibrium pressure

ABSTRACT We present the extended ALMA MaNGA QUEnching and STar formation survey (ALMaQUEST), a combination of the original 46 ALMaQUEST galaxies plus new ALMA observations for a further 20 interacting galaxies. Three well-studied scaling relations are fit to the 19 999 star-forming spaxels in the extended sample, namely the resolved Schmidt–Kennicutt relation, the resolved star-forming main-sequence and the resolved molecular gas main sequence. We additionally investigate the relationship between the dynamical equilibrium pressure (PDE) and star formation rate surface density (ΣSFR), which we refer to as the resolved PDE (rPDE) relation. Contrary to previous studies that have focussed on normal star-forming galaxies and found an approximately linear rPDE relation, the presence of more vigourously star-forming galaxies in the extended ALMaQUEST sample reveals a marked turnover in the relation at high pressures. Although the scatter around the linear fit to the rPDE relation is similar to the other three relations, a random forest analysis, which can extract non-linear dependences, finds that PDEis unambiguously more important than either $\Sigma _{\rm H_2}$ or Σ⋆ for predicting ΣSFR. We compare the observed rPDE relation to the prediction of the pressure-regulated feedback-modulated (PRFM) model of star formation, finding that galaxies residing on the global SFMS do indeed closely follow the rPDE relation predicted by the PRFM theory. However, galaxies above and below the global SFMS show significant deviations from the model. Galaxies with high SFR are instead consistent with models that include other contributions to turbulence in addition to the local star formation feedback.

The Tully–Fisher relation from SDSS-MaNGA: physical causes of scatter and variation at different radii

ABSTRACT The stellar mass Tully–Fisher relation (STFR) and its scatter encode valuable information about the processes shaping galaxy evolution across cosmic time. However, we are still missing a proper quantification of the STFR slope and scatter dependence on the baryonic tracer used to quantify rotational velocity, on the velocity measurement radius and on galaxy integrated properties. We present a catalogue of stellar and ionized gas (traced by H$\rm {\alpha }$ emission) kinematic measurements for a sample of galaxies drawn from the MaNGA Galaxy Survey, providing an ideal tool for galaxy formation model calibration and for comparison with high-redshift studies. We compute the STFRs for stellar and gas rotation at 1, 1.3 and 2 effective radii (Re). The relations for both baryonic components become shallower at 2Re compared to 1Re and 1.3Re. We report a steeper STFR for the stars in the inner parts (≤1.3Re) compared to the gas. At 2Re, the relations for the two components are consistent. When accounting for covariances with integrated v/σ, scatter in the stellar and gas STFRs shows no strong correlation with: optical morphology, star formation rate surface density, tidal interaction strength or gas accretion signatures. Our results suggest that the STFR scatter is driven by an increase in stellar/gas dispersional support, from either external (mergers) or internal (feedback) processes. No correlation between STFR scatter and environment is found. Nearby Universe galaxies have their stars and gas in statistically different states of dynamical equilibrium in the inner parts (≤1.3Re), while at 2Re the two components are dynamically coupled.

CLASH-VLT: The Inner Slope of the MACS J1206.2-0847 Dark Matter Density Profile

The inner slope (γ DM) of the dark matter (DM) density profile of cosmological halos carries information about the properties of DM and/or baryonic processes affecting the halo gravitational potential. Cold DM cosmological simulations predict steep inner slopes, γ DM ≃ 1. We test this prediction on the MACS J1206.2-0847 cluster at redshift z = 0.44, whose DM density profile has been claimed to be cored at the center. We determine the cluster DM density profile from 2 kpc from the cluster center to the virial radius (∼2 Mpc), using the velocity distribution of ≃500 cluster galaxies and the internal velocity dispersion profile of the Brightest Cluster Galaxy (BCG), obtained from VIMOS@VLT and MUSE@VLT data. We solve the Jeans equation of dynamical equilibrium using an upgraded version of the MAMPOSSt method. The total mass profile is modeled as a sum of a generalized Navarro–Frenk–White profile that describes the DM component, allowing for a free inner slope of the density profile, a Jaffe profile that describes the BCG stellar mass component, and a nonparametric baryonic profile that describes the sum of the remaining galaxy stellar mass and of the hot intra-cluster gas mass. Our total mass profile is in remarkable agreement with independent determinations based on X-ray observations and strong lensing. We find (68% confidence levels), consistent with predictions from recent Lambda cold dark matter cosmological numerical simulations.

The H i-rich ultra-diffuse galaxies follow the extended Schmidt law

ABSTRACT The ${\rm H\, {\small I}}$-rich ultra-diffuse galaxies (HUDGs) offer a unique case for studies of star formation laws as they host low star formation efficiency and low-metallicity environments where gas is predominantly atomic. We collect a sample of six HUDGs in the field and investigate their location in the extended Schmidt law ($\Sigma _{\text{SFR }} \propto \left(\Sigma _{\text{star}}^{0.5} \Sigma _{\text{gas}}\right)^{1.09}$). They are consistent with this relationship well (with deviations of only 1.1σ). Furthermore, we find that HUDGs follow the tight correlation between the hydrostatic pressure in the galaxy mid-plane and the quantity on the x-axis ($\rm log(\Sigma _{star}^{0.5}\Sigma _{gas})$) of the extended Schmidt law. This result indicates that these HUDGs can be self-regulated systems that reach the dynamical and thermal equilibrium. In this framework, the stellar gravity compresses the disc vertically and counteracts the gas pressure in the galaxy mid-plane to regulate the star formation as suggested by some theoretical models.

Gravitomagnetism and galaxy rotation curves: a cautionary tale

We investigate recent claims that gravitomagnetic effects in linearised general relativity can explain flat and rising rotation curves, such as those observed in galaxies, without the need for dark matter. If one models a galaxy as an axisymmetric, stationary, rotating, non-relativistic and pressureless ‘dust’ of stars in the gravitoelectromagnetic (GEM) formalism, we show that gravitomagnetic effects on the circular velocity v of a star are smaller than the standard Newtonian (gravitoelectric) effects and thus any modification of galaxy rotation curves must be negligible, as might be expected. Moreover, we find that gravitomagnetic effects are too small to provide the vertical support necessary to maintain the dynamical equilibrium assumed in such a model. These issues are obscured if one constructs a single equation for v, as considered previously. We nevertheless solve this equation for a galaxy having a Miyamoto–Nagai density profile since this allows for both an exact numerical integration and an accurate analytic approximation. We show that for the values of the mass, M, and semi-major and semi-minor axes, a and b, typical for a dwarf galaxy, the rotation curve depends only very weakly on M, and becomes independent of it for larger M values. Moreover, for aspect ratios , the rotation curves are concave over their entire range, which does not match observations in any galaxy. Most importantly, we show that for the poloidal gravitomagnetic flux ψ to provide the necessary vertical support, it must become singular at the origin and have extremely large values near to it. This originates from the unwitting, but forbidden, inclusion of free-space solutions of the Poisson-like equation that determines ψ and also clearly contradicts the linearised treatment implicit in the GEM formalism, hence ruling out the methodology in the form used as a means of explaining flat galaxy rotation curves. We further show that recent deliberate attempts to leverage such free-space solutions against the rotation curve problem yield no deterministic modification outside the thin disk approximation, and that, in any case, the homogeneous contributions to ψ are ruled out by the boundary value problem posed by any physical axisymmetric galaxy.

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.