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In a recent galactic survey, Bizyaev et. al. (2021) modeled the rotation curves for 153 ultra-faint, edge-on galaxies using the 3.5 m telescope at the Apache Point Observatory. One of the interesting features of this survey was that the majority of the distances for the galaxies were inferred using the Tully Fisher Relation. Although there is nothing new about surveys using Tully Fisher for distance estimates, these authors reported drastically different scale lengths for some of these galaxies within a one year time frame. Since rotation curve modeling for any theory is most sensitive to the distance, an opportunity arises in this survey to begin to try to shed some light on how galactic rotation curves are derived for any theory. However, the preliminary analysis shows that this survey may not hold the key to unraveling some of these mysteries, but can provide insight into the methods for a more standard fit for rotation curve physics.

[-5]The applications of Newtonian dynamics in galactic scales have shown that the inverse square law is incompatible with the amount of visible mass in the form of stars and molecular clouds. This manifests as the rotational curves of galaxies being asymptotically flat instead of decaying with the distance to the center of the galaxy. In the context of Newtonian gravity, the standard explanation requires a huge amount of dark mass in the form of hypothetical particles that still remain undetected. A different theory was provided as a modification of Newtonian dynamics (MOND) at low accelerations . This MOND theory still has many supporters and it can easily explain some features of the rotation curves, such as the Tully–Fisher (TF) phenomenological relation between luminosity and velocity. In this paper, we revisit the third approach of a non-Newtonian force, that has resurfaced from time to time, in order to reconcile it with a finite apparent dark mass and the TF relation.

We propose to test the viability of the recently introduced f ( R ) gravity model in the galactic scales. For this purpose we consider test particles moving in stable circular orbits around the galactic center. We study the Palatini approach of f ( R ) gravity via Weyl transformation, which is the frame transformation from the Jordan frame to the Einstein frame. We derive the expression of rotational velocities of test particles in the new f ( R ) gravity model. For the observational data of samples of high surface brightness and low surface brightness galaxies, we show that the predicted rotation curves are well fitted with observations, thus implying that this model can explain flat rotation curves of galaxies. We also study an ultra diffuse galaxy, AGC 242019 which has been claimed in literature to be a dark matter dominated galaxy similar to low surface brightness galaxies with a slowly rising rotation curve. The rotation curve of this galaxy also fits well with the model prediction in our study. Furthermore, we studied the Tully–Fisher relation for the entire sample of galaxies and found that the model prediction shows the consistency with the data.

We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at ≈3σ level for a transition at critical distances Dc≃9 Mpc and Dc≃17 Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance Dc, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For Dc≃9 Mpc and Dc≃17 Mpc, we find a tension between the two subsamples at a level of Δχ2>17(3.5σ). Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than Dc by ΔGG≃−0.1. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions (ΔGG≃−0.1 at the transition redshift of zt≲0.01 (Dc≲40 Mpc)).

A bstract Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes with variable Hausdorff and spectral dimension, originally proposed as descriptions of geometries arising in quantum gravity. We derive the Poisson equation and the Newtonian potential of these theories starting from their covariant modified Einstein’s equations. In particular, in the case of the theory T v with weighted derivatives with small fractional corrections, we find a gravitational potential that grows logarithmically at large radii when the fractional exponent takes the special value α = 4/3. This behaviour is associated with a restoration law for the Hausdorff dimension of spacetime independently found in the dark-energy sector of the same theory. As an application, we check whether this potential can serve as an alternative to dark matter for the galaxies NGC7814, NGC6503 and NGC3741 in the SPARC catalogue. We show that their rotation curves at medium-to-large radii can indeed be explained by purely geometric effects, although the Tully-Fisher relation is not reproduced well. We discuss how to fix the small-radius behaviour by lifting some approximations and how to test the model with other observables and an enlarged galaxy sample.

In the last few years, alternative gravity theories have seen increased interest due to the lack of observational evidence of dark matter. Further, new empirical patterns found in rotation curve data such as the Radial Acceleration Rule (RAR) have given new testable features for gravitational theories. In this paper, we revisit two popular surveys of galaxies (Randriamampandry et al 2013 and Bottema et al 2015) which when published were shown to be problematic for alternative gravity. Here, we apply the most recent observational parameters to the surveys and provide fits of Conformal Gravity, MOND as well as the RAR rotation curve formalism and show how these theories can apply to the new findings. We also provide the fits to the RAR and Tully-Fisher relation for each theory and discuss how the RAR may allow for some confining of parameters in the fitting procedure.

This paper analyzes, within the extended gravitoelectromagnetic (GEM) formulation, the equilibrium of a large scale gravitational system formed by rotating dust. The force balance equation gives the rotation velocity in terms of the GEM fields. Boundary conditions for the fields are introduced using Helmholtz’s decomposition and the virtual casing principle. Hydro-gravitomagnetic Cauchy invariance is implemented to relate the fluid and gravitomagnetic field vorticities. An energy conservation equation gives the rotation velocity in terms of the gravitational field and respective boundary values. A detailed solution is calculated for the case of rotating oblate spheroids. The equilibrium is in the form of a sheared rotational vortex, without introducing dark matter. The results are consistent with the Tully–Fisher relation and the Virginia Trimble correlations.

It has recently been suggested that a gravitational transition of the effective Newton’s constant Geff by about 10%, 50–150 Myrs ago could lead to the resolution of both the Hubble crisis and the growth tension of the standard ΛCDM model. Hints for such an abrupt transition with weaker gravity at times before the transition, have recently been identified in Tully–Fisher galactic mass-velocity data, and also in Cepheid SnIa calibrator data. Here we use Monte-Carlo simulations to show that such a transition could significantly increase (by a factor of 3 or more) the number of long period comets (LPCs) impacting the solar system from the Oort cloud (semi-major axis of orbits ≳104AU). This increase is consistent with observational evidence from the terrestrial and lunar cratering rates, indicating that the impact flux of kilometer sized objects increased by at least a factor of 2 over that last 100 Myrs compared to the long term average. This increase may also be connected with the Chicxulub impactor event that produced the Cretaceous–Tertiary (K-T) extinction of 75% of life on Earth (including dinosaurs) about 66 Myrs ago. We use Monte-Carlo simulations to show that for isotropic Oort cloud comet distribution with initially circular orbits, random velocity perturbations (induced e.g., by passing stars and/or galactic tidal effects), lead to a deformation of the orbits that increases significantly when Geff increases. A 10% increase in Geff leads to an increase in the probability of the comets to enter the loss cone and reach the planetary region (pericenter of less than 10 AU) by a factor that ranges from 5% (for velocity perturbation much smaller than the comet initial velocity) to more than 300% (for total velocity perturbations comparable with the initial comet velocity).

I discuss Local Group galaxies from the perspective of external galaxies that define benchmark scaling relations. Making use of this information leads to a model for the Milky Way that includes bumps and wiggles due to spiral arms. This model reconciles the terminal velocities observed in the interstellar medium with the rotation curve derived from stars, correctly predicts the gradual decline of the outer rotation curve, and extrapolates well out to 50 kpc. Rotationally supported Local Group galaxies are in excellent agreement with the baryonic Tully-Fisher relation. Pressure supported dwarfs that are the most likely to be in dynamical equilibrium also align with this relation. Local Group galaxies thus appear to be normal members of the low redshift galaxy population. There is, however, a serious tension between the dynamical masses of the Milky Way and M31 and those expected from the stellar masshalo mass relation of abundance matching.

We derive the first analytical formula for the density of \"Dark Matter\" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, with inclusion of the OM, the observed coherent gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρD = λgg′2 for the density ρD of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations.