Galaxy rotation curves and the tight scaling relations that accompany them are not easily reproduced by collisionless cold dark matter alone, while modified-gravity descriptions that succeed at galactic scales encounter difficulties elsewhere. We examine a minimal alternative that leaves general relativity untouched and instead gives the dark sector a small internal pressure. The dark component is treated as a barotropic fluid in hydrostatic equilibrium with an isothermal equation of state, so that pressure resists gravitational collapse and halos settle into finite-density cores rather than cusps. The resulting rotation law is analytic and carries two free parameters per galaxy, the same number as a standard halo. Fitting 165 galaxies from the SPARC database under a fixed-baryon protocol applied identically to every model, we obtain a median coefficient of determination R^2 = 0.961 , against 0.924 for the standard halo profile at the same two-parameter count, the comparison that isolates the dark sector. The model is favoured by the Akaike criterion, which penalises parameters, in 99 of the 165 galaxies. Calibrating two population scaling relations on photometry alone and predicting each rotation curve with no per-galaxy fitting reproduces the radial acceleration relation with a scatter of 0.192 dex, matching the zero-parameter modified-gravity value of 0.202 dex on the same points. The model also generates an acceleration scale of order the observed one, but a structured rather than universal one: it correlates with baryonic surface density ( p ∼ 10^-14 ), a correlation forbidden for a universal scale and thus a direct point of separation from modified gravity. It recovers the baryonic Tully-Fisher relation with a slope near four. Pressure support thus accounts for the principal galactic regularities without modifying gravity, as a modest extension of the cold dark matter picture.
In this work, we analyze a spatially homogenous but anisotropic locally rotationally symmetric (LRS) Bianchi type‑I spacetime in order to investigate a cosmological scenario described in the framework of f(R,T) gravity. The modified Einstein field equations, which show a smooth development of the cosmos from an early decelerated expansion to the currently observable accelerated phase, can be solved exactly when the deceleration value is chosen appropriately. The discovered solutions also demonstrate that, in later eras, the cosmos progressively approaches isotropy. We analyze the state-finder diagnostics and discover that the cosmic development moves from an Einstein static phase to an era dominated by ΛCDM. By examining basic cosmological characteristics including the energy density, pressure, equation of state parameter, and different energy conditions, the model’s physical plausibility is evaluated. Additionally, the evolution of temperature and entropy density is used to examine the model’s thermodynamic behavior. In accordance with the second law of thermodynamics, it is found that although the entropy density drops with cosmic time, the overall entropy stays positive. It is discovered that the temperature diverges in the first epoch, then falls and eventually approaches a stable value. These results validate the suggested cosmological framework’s consistency and physical robustness.
We analyze the dependence between magnetic field evolution (HMI magnetograms) and the AIA 94Å, 131Å, 171Å, 193Å, 211Å, 304Å, 335Å, and Fe xviii emissions associated to flares through copula theory, which captures both linear and nonlinear correlations of variables. We utilize the Archimedean copulas to characterize the correlations (dependence structures) between the magnetic field and EUV observations for 66 active regions. The copula parameters are determined using the canonical maximum likelihood estimation method to capture the dependency structure effectively, that verified by goodness of fit which shows the validity of modeling based on Frank copula. We demonstrate that the magnetic field configurations are nonlinearly correlated with the onset of flare emissions, which typically occur 2–5.5h later. Therefore, copula approach provides an effective tool to capture the relationships between solar magnetic fields and emissions, offering new insights into solar flare initiation.
A two-dimensional nonlinear integral equation with vacuum boundary condition, arising in radiative transfer theory is investigated. In addition to the trivial solution, the existence of a nontrivial solution is established, together with its uniqueness within an appropriate class of functions. A uniform estimate between the n-th iteration and the exact solution is obtained, allowing the approximation error to be evaluated with any prescribed level of accuracy. Several examples of nonlinear functions satisfying the assumptions of the main theorem are presented. Numerical computations are carried out for a square-root type nonlinearity. The results reveal a qualitative distinction between linear and nonlinear models: while the linear equation admits only the trivial solution (or solution with unbounded growth in limiting case), the nonlinear problem exhibits bounded, physically meaningful solutions with fundamentally different behavior.
