Radial Acceleration Relation Research Articles

Many body gravity and the galaxy rotation curves

A novel theory was proposed earlier to model systems with thermal gradients, based on the postulate that the spatial and temporal variation in temperature can be recast as a variation in the metric. Combining the variation in the metric due to the thermal variations and gravity, leads to the concept of thermal gravity in a 5-D space-time-temperature setting. When the 5-D Einstein field equations are projected on to a 4-D space, they result in additional terms in the field equations. This may lead to unique phenomena such as the spontaneous symmetry breaking of scalar particles in the presence of a strong gravitational field. This theory, originally conceived in a quantum mechanical framework, is now adapted to explain the galaxy rotation curves. A galaxy is not in a state of thermal equilibrium. A parameter called the “degree of thermalization” is introduced to model partially thermalized systems. The generalization of thermal gravity to partially thermalized systems, leads to the theory of many-body gravity. The theory of many-body gravity is now shown to be able to explain the rotation curves of the Milky Way and the M31 (Andromeda) galaxies, to a fair extent. The radial acceleration relation (RAR) for 63 galaxies, with their galactic masses spanning three orders of magnitude, has been replicated. Finally, the wide binary star (WBS) system is touched upon.

A Strong Falsification of the Universal Radial Acceleration Relation in Galaxies

In the past few decades, many studies revealed that there exist some apparent universal relations that can describe the dynamical properties in galaxies. In particular, the radial acceleration relation (RAR) is one of the most popular relations discovered recently that can be regarded as a universal law to connect the dynamical radial acceleration with the baryonic acceleration in galaxies. This has revealed an unexpected close connection between dark matter and baryonic matter in galaxies. In this article, by following the recent robust Galactic rotation curve analyzes, we derive the Galactic RAR (GRAR) and show for the first time that the alleged best-fit universal RAR deviates from the GRAR data at more than 5σ. This provides a strong evidence to falsify the universal nature of RAR in galaxies claimed in past studies.

Hooks & Bends in the radial acceleration relation: discriminatory tests for dark matter and MOND

ABSTRACT The radial acceleration relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, atot(r), with that accounted for by baryons at the same radius, abar(r). The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the cosmological constant + cold dark matter (ΛCDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of M⋆ ≃ 107–11 M⊙ to study the RAR in the FIRE-2 simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that ‘hook’ down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our ΛCDM-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit ‘bends’ off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach atot ≈ abar/fb, where fb is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and ΛCDM.

On the tension between the radial acceleration relation and Solar system quadrupole in modified gravity MOND

ABSTRACT Modified Newtonian dynamics (MOND), postulating a breakdown of Newtonian mechanics at low accelerations, has considerable success at explaining galaxy kinematics. However, the quadrupole of the gravitational field of the Solar system (SS) provides a strong constraint on the way in which Newtonian gravity can be modified. In this paper, we assess the extent to which the AQUAdratic Lagrangian (AQUAL) and QUasilinear MOND (QUMOND) modified gravity formulations of MOND are capable of accounting simultaneously for the radial acceleration relation (RAR), the Cassini measurement of the SS quadrupole and the kinematics of wide binaries in the Solar neighbourhood. We achieve this by inferring the location and sharpness of the MOND transition from the Spitzer Photometry and Accurate Rotation Curves (SPARC) RAR under broad assumptions for the behaviour of the interpolating function and external field effect. We constrain the same quantities from the SS quadrupole, finding that this requires a significantly sharper transition between the deep-MOND and Newtonian regimes than is allowed by the RAR (an 8.7σ tension under fiducial model assumptions). This may be relieved somewhat by allowing additional freedom in galaxies’ mass-to-light ratios – which also improves the RAR fit – and more significantly (to 1.9σ) by removing galaxies with bulges. For the first time, we also apply to the SPARC RAR fit an AQUAL correction for flattened systems, obtaining similar results. Finally, we show that the SS quadrupole constraint implies, to high precision, no deviation from Newtonian gravity in nearby wide binaries, and speculate on possible resolutions of this tension between SS and galaxy data within the MOND paradigm.

Towards galaxy cluster models in Aether-Scalar-Tensor theory: isothermal spheres and curiosities

The Aether-Scalar-Tensor (AeST) theory is an extension of General Relativity (GR) which can support Modified Newtonian Dynamics (MOND) behaviour in its staticweak-field limit, and cosmological evolution resembling ΛCDM.We consider static spherically symmetric weak-field solutions in this theory and show that the resulting equations can be reduced to a single equation for the gravitational potential.The reduced equation has apparent isolated singularities at the zeros of the derivative of the potential and we show how these are removedby evolving, instead, the canonical momentum of the corresponding Hamiltonian system that we find. We construct solutions in three cases: (i) in vacuum outside a bounded spherical object, (ii) within an extended prescribed source, and (iii) for an isothermal gas in hydrostatic equilibrium, serving as a simplified model for galaxy clusters.We show that the oscillatory regime that follows the Newtonian and MOND regimes, obtained in previous works in the vacuum case, also persists for isothermal spheres, and we show that the gas density profiles in AeST can become more compressed than their Newtonian or MOND counterparts.We construct the Radial Acceleration Relation (RAR) in AeST for isothermal spheres and find that it can display a peak, an enhancement with respect to the MOND RAR, at an acceleration range determined by the value of the AeST weak-field mass parameter, the mass of the system and the boundary value of the gravitational potential. For lower accelerations, the AeST RAR drops below the MOND expectation,as if there is a negative mass density. Similar observational features of the galaxy cluster RAR have been reported. This illustrates the potential of AeST to address the shortcomings of MOND in galaxy clusters, but a full quantitative comparison with observations will require going beyond the isothermal case.

Radial acceleration relation of galaxies with joint kinematic and weak-lensing data

We combine kinematic and gravitational lensing data to construct the Radial Acceleration Relation (RAR) of galaxies over a large dynamic range. We improve on previous weak-lensing studies in two ways. First, we compute stellar masses using the same stellar population model as for the kinematic data. Second, we introduce a new method for converting excess surface density profiles to radial accelerations. This method is based on a new deprojection formula which is exact, computationally efficient, and gives smaller systematic uncertainties than previous methods. We find that the RAR inferred from weak-lensing data smoothly continues that inferred from kinematic data by about 2.5 dex in acceleration. Contrary to previous studies, we find that early- and late-type galaxies lie on the same joint RAR when a sufficiently strict isolation criterion is adopted and their stellar and gas masses are estimated consistently with the kinematic RAR.

A distinct radial acceleration relation across the brightest cluster galaxies and galaxy clusters

Recent studies reveal a radial acceleration relation (RAR) in galaxies, which illustrates a tight empirical correlation connecting the observational acceleration and the baryonic acceleration with a characteristic acceleration scale. However, a distinct RAR has been revealed on brightest cluster galaxy (BCG) cluster scales with a seventeen-times-larger acceleration scale due to the gravitational lensing effect. In this work, we systematically explore the acceleration and mass correlations between dynamical and baryonic components in 50 BCGs. To investigate the dynamical RAR in BCGs, we derived their dynamical accelerations from the stellar kinematics using the Jeans equation through Abel inversion and adopted the baryonic mass from Sloan Digital Sky Survey photometry. We explored the spatially resolved kinematic profiles with the largest integral field spectroscopy (IFS) data collected by the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. Our results demonstrate that the dynamical RAR in BCGs is consistent with the lensing RAR on BCG-cluster scales as well as a larger acceleration scale. This finding may imply that BCGs and galaxy clusters have fundamental differences from field galaxies. We also find a mass correlation, but it is less tight than the acceleration correlation.

Examining baryonic Faber–Jackson relation in galaxy groups

ABSTRACT We investigate the baryonic Faber–Jackson relation (BFJR), examining the correlation between baryonic mass and velocity dispersion in galaxy groups and clusters. Originally analysed in elliptical galaxies, the BFJR is derivable from the empirical radial acceleration relation (RAR) and MOdified Newtonian Dynamics (MOND), both showcasing a characteristic acceleration scale $\mathrm{g}_\mathrm{\dagger }=1.2\times 10^{-10}\, \mathrm{m}\, \mathrm{s}^{-2}$. Recent interpretations within MOND suggest that galaxy group dynamics can be explained solely by baryonic mass, hinting at a BFJR with g† in these systems. To explore this BFJR, we combined X-ray and optical measurements for 6 galaxy clusters and 13 groups, calculating baryonic masses by combining X-ray gas and stellar mass estimates. Simultaneously, we computed spatially resolved velocity dispersion profiles from membership data using the biweight scale in radial bins. Our results indicate that the BFJR in galaxy groups, using total velocity dispersion, aligns with MOND predictions. Conversely, galaxy clusters exhibit a parallel BFJR with a larger acceleration scale. Analysis using tail velocity dispersion in galaxy groups shows a leftward deviation from the BFJR. Additionally, stacked velocity dispersion profiles reveal two distinct types: declining and flat, based on two parallel BFJRs. The declining profile, if not due to the anisotropy parameters or the incomplete membership, suggests a deviation from standard dark matter (DM) density profiles. We further identify three galaxy groups with unusually low DM fractions.

The underlying radial acceleration relation

ABSTRACT The radial acceleration relation (RAR) of late-type galaxies relates their dynamical acceleration, gobs, to that sourced by baryons alone, gbar, across their rotation curves. Literature fits to the RAR have fixed the galaxy parameters on which the relation depends – distance, inclination, luminosity, and mass-to-light ratios – to their maximum a priori values with an uncorrelated Gaussian contribution to the uncertainties in gbar and gobs. In reality these are free parameters of the fit, contributing systematic rather than statistical error. Assuming a range of possible functional forms for the relation with or without intrinsic scatter (motivated by modified Newtonian dynamics with or without the external field effect), I use Hamiltonian Monte Carlo to perform the full joint inference of RAR and galaxy parameters for the Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset. This reveals the intrinsic RAR underlying that observed. I find an acceleration scale $a_0=(1.19 \pm 0.04 \, \text{(stat)} \pm 0.09 \, \text{(sys)}) \: \times \: 10^{-10}$ m s−2, an intrinsic scatter $\sigma _\text{int}=(0.034 \pm 0.001 \, \text{(stat)} \pm 0.001 \, \text{(sys)})$ dex (assuming the SPARC error model is reliable), and weak evidence for the external field effect. I make summary statistics of all my analyses publicly available for future SPARC studies or applications of a calibrated RAR, for example direct distance measurement.

On the fundamentality of the radial acceleration relation for late-type galaxy dynamics

ABSTRACT Galaxies have been observed to exhibit a level of simplicity unexpected in the complex galaxy formation scenario posited by standard cosmology. This is particularly apparent in their dynamics, where scaling relations display much regularity and little intrinsic scatter. However, the parameters responsible for this simplicity have not been identified. Using the Spitzer Photometry & Accurate Rotation Curves galaxy catalogue, we argue that the radial acceleration relation (RAR) between galaxies’ baryonic and total dynamical accelerations is the fundamental 1D correlation governing the radial (in-disc) dynamics of late-type galaxies. In particular, we show that the RAR cannot be tightened by the inclusion of any other available galaxy property, that it is the strongest projection of galaxies’ radial dynamical parameter space, and that all other statistical radial dynamical correlations stem from the RAR plus the non-dynamical correlations present in our sample. We further provide evidence that the RAR’s fundamentality is unique in that the second most significant dynamical relation does not possess any of these features. Our analysis reveals the root cause of the correlations present in galaxies’ radial dynamics: they are nothing but facets of the RAR. These results have important ramifications for galaxy formation theory because they imply that to explain statistically late-type galaxy dynamics within the disc it is necessary and sufficient to explain the RAR and lack of any significant, partially independent correlation. While simple in some modified dynamics models, this poses a challenge to standard cosmology.

Measuring galaxy cluster mass profiles into the low-acceleration regime with galaxy kinematics

We probed the dynamical mass profiles of ten galaxy clusters from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS) using galaxy kinematics. We numerically solved the spherical Jeans equation and parameterize the dynamical mass profile and the galaxy velocity anisotropy profile using two general functions to ensure that our results are not biased toward any specific model. The mass-velocity anisotropy degeneracy is ameliorated by using two “virial shape parameters” that depend on the fourth moment of velocity distribution. The resulting velocity anisotropy estimates consistently show a nearly isotropic distribution in the inner regions, with an increasing radial anisotropy toward large radii. We compared our derived dynamical masses with those calculated from X-ray gas data assuming hydrostatic equilibrium, finding that massive and rich relaxed clusters generally present consistent mass measurements, while unrelaxed or low-richness clusters have systematically larger total masses than hydrostatic masses by, on average, 50%. This might help alleviate current tensions in the measurement of σ8, but it also leads to cluster baryon fractions below the cosmic value. Finally, our approach probes accelerations as low as 10−11 m s−2, comparable to the outskirts of individual late-type galaxies. We confirm that galaxy clusters deviate from the radial acceleration relation defined by galaxies.

Testing the Collisionless Nature of Dark Matter with the Radial Acceleration Relation in Galaxy Clusters

The radial acceleration relation (RAR) represents a tight empirical relation between the inferred total and baryonic centripetal accelerations, g tot = GM tot(< r)/r 2 and g bar = GM bar(< r)/r 2, observed in galaxies and galaxy clusters. The tight correlation between these two quantities can provide insight into the nature of dark matter. Here we use BAHAMAS, a state-of-the-art suite of cosmological hydrodynamical simulations, to characterize the RAR in cluster-scale halos for both cold and collisionless dark matter (CDM) and self-interacting dark matter (SIDM) models. SIDM halos generally have reduced central dark matter densities, which reduces the total acceleration in the central region when compared with CDM. We compare the RARs in galaxy clusters simulated with different dark matter models to the RAR inferred from CLASH observations. Our comparison shows that the cluster-scale RAR in the CDM model provides an excellent match to the CLASH RAR obtained by Tian et al. including the high-acceleration regime probed by the brightest cluster galaxies (BCGs). By contrast, models with a larger SIDM cross section yield increasingly poorer matches to the CLASH RAR. Excluding the BCG regions results in a weaker but still competitive constraint on the SIDM cross section. Using the RAR data outside the central r < 100 kpc region, an SIDM model with σ/m = 0.3 cm2 g−1 is disfavored at the 3.8σ level with respect to the CDM model. This study demonstrates the power of the cluster-scale RAR for testing the collisionless nature of dark matter.

A QFT based on Einstein-Hilbert action and hidden dimensions as consistent theory of measurement, dark energy, dark matter and McGaugh’s universal law for rotating galaxies

We present a quantum field theory of gravity in 11 dimensional spacetime, based on Einstein-Hilbert action and expanded up to 4th order in the metric. In the theory the deviation of the local metric from Minkowski metric is a quantum field, called gravonon field. It is responsible for the localization of a matter particle on a definite position in four dimensional spacetime (warp resonance, beable). This is the solution of the measurament problem of Quantum Mechanics coming out as result of the deterministic Schrödinger equation. The quantum gravonon field is also decisive for calculating the expansion of the universe. In lowest order of the metric the interaction of the matter field with the gravonon field is the cause for the expansion of the universe and is the quantum analogue of the often mentioned dark energy. In higher orders of the metric the interaction of ordinary matter and gravonons becomes attractive. The gravonon field then assumes the role of dark matter. McGaugh’s universal radial acceleration relation in rotationally supported galaxies is obtained using this quantum gravitational appoach. The concept of dark matter emerges as do the results of Milgrom’s MOND analysis.

Dark Matter in Fractional Gravity. I. Astrophysical Tests on Galactic Scales

We explore the possibility that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the standard law of inertia continues to hold, but the gravitational potential associated with a given DM density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type) that are meant to describe nonlocal effects. We analytically derive the expression of the potential that in fractional gravity corresponds to various spherically symmetric density profiles, including the Navarro–Frenk–White (NFW) distribution that is usually exploited to describe virialized halos of collisionless DM as extracted from N-body cosmological simulations. We show that in fractional gravity, the dynamics of a test particle moving in a cuspy NFW density distribution is substantially altered with respect to the Newtonian case, mirroring what in Newtonian gravity would instead be sourced by a density profile with an inner core. We test the fractional gravity framework on galactic scales, showing that (i) it can provide accurate fits to the stacked rotation curves of spiral galaxies with different properties, including dwarfs; (ii) it can reproduce to reasonable accuracy the observed shape and scatter of the radial acceleration relation over an extended range of galaxy accelerations; and (iii) it can properly account for the universal surface density and the core radius versus disk scale length scaling relations. Finally, we discuss the possible origin of the fractional gravity behavior as a fundamental or emerging property of the elusive DM component.

Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime

Quantum treatment of physical reference frame leads to the Ricci flow of quantum spacetime, which is a quite rigid framework to quantum and renormalization effect of gravity. The theory has a low characteristic energy scale described by a unique constant: the critical density of the universe. At low energy long distance (cosmic or galactic) scale, the theory modifies Einstein's gravity which naturally gives rise to a cosmological constant as a counter term of the Ricci flow at leading order and an effective scale dependent Einstein-Hilbert action. In the weak and static gravity limit, the framework gives rise to a transition trend away from Newtonian gravity and similar to the MOdified Newtonian Dynamics (MOND) around the characteristic scale. When local curvature is large, Newtonian gravity is recovered. When local curvature is low enough to be comparable with the asymptotic background curvature corresponding to the characteristic energy scale, the transition trend produces the baryonic Tully-Fisher relation. For intermediate general curvature around the background curvature, the interpolating Lagrangian function yields a similar transition trend to the observed radial acceleration relation of galaxies. When the baryonic matter density is much lower than the critical density at the outskirt of a galaxy, there may be a universal "acceleration floor" corresponding to the acceleration expansion of the universe, which differs from MOND at its deep-MOND limit. The critical acceleration constant $a_0$ introduced in MOND is related to the low characteristic energy scale of the theory. The cosmological constant gives a universal leading order contribution to it and the flow effect gives the next order scale dependent contribution, which equivalently induces the "cold dark matter" to the theory. $a_0$ is consistent with galaxian data when the "dark matter" is about 5 times the baryonic matter.

Galaxy Rotation Curves and Universal Scaling Relations: Comparison between Phenomenological and Fermionic Dark Matter Profiles

Galaxies show different halo scaling relations such as the radial acceleration relation, the mass discrepancy acceleration relation (MDAR), or the dark matter (DM) surface density relation. At difference with traditional studies using phenomenological ΛCDM halos, we analyze the above relations assuming that DM halos are formed through a maximum entropy principle (MEP) in which the fermionic (quantum) nature of the DM particles is dully accounted for. For the first time, a competitive DM model based on first physical principles, such as (quantum) statistical-mechanics and thermodynamics, is tested against a large data set of galactic observables. In particular, we compare the fermionic DM model with empirical DM profiles: the Navarro–Frenk–White (NFW) model, a generalized NFW model accounting for baryonic feedback, the Einasto model, and the Burkert model. For this task, we use a large sample of 120 galaxies taken from the Spitzer Photometry and Accurate Rotation Curves data set, from which we infer the DM content to compare with the models. We find that the radial acceleration relation and MDAR are well explained by all the models with comparable accuracy, while the fits to the individual rotation curves, in contrast, show that cored DM halos are statistically preferred with respect to the cuspy NFW profile. However, very different physical principles justify the flat inner-halo slope in the most-favored DM profiles: while generalized NFW or Einasto models rely on complex baryonic feedback processes, the MEP scenario involves a quasi-thermodynamic equilibrium of the DM particles.

On the functional form of the radial acceleration relation

ABSTRACTWe apply a new method for learning equations from data – Exhaustive Symbolic Regression (ESR) – to late-type galaxy dynamics as encapsulated in the radial acceleration relation (RAR). Relating the centripetal acceleration due to baryons, gbar, to the total dynamical acceleration, gobs, the RAR has been claimed to manifest a new law of nature due to its regularity and tightness in agreement with Modified Newtonian Dynamics (MOND). Fits to this relation have been restricted by prior expectations to particular functional forms, while ESR affords an exhaustive and nearly prior-free search through functional parameter space to identify the equations optimally trading accuracy with simplicity. Working with the SPARC data, we find the best functions typically satisfy gobs ∝ gbar at high gbar, although the coefficient of proportionality is not clearly unity and the deep-MOND limit $g_\text{obs}\propto \sqrt{g_\text{bar}}$ as gbar → 0 is little evident at all. By generating mock data according to MOND with or without the external field effect, we find that symbolic regression would not be expected to identify the generating function or reconstruct successfully the asymptotic slopes. We conclude that the limited dynamical range and significant uncertainties of the SPARC RAR preclude a definitive statement of its functional form, and hence that this data alone can neither demonstrate nor rule out law-like gravitational behaviour.

Gravitational orbits in the expanding Universe revisited

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon’s and Titan’s orbit anomalies.

X-ray analysis of JWST’s first galaxy cluster lens SMACS J0723.3−7327

Context. SMACS J0723.3−7327 is the first galaxy cluster lens observed by James Webb Space Telescope (JWST). Based on its early release observation data, several groups have reported the results on strong lensing analysis and mass distribution of this cluster. The new lens model dramatically improves upon previous results, thanks to JWST’s unprecedented sensitivity and angular resolution. However, limited by the angular coverage of the JWST data, the strong lensing models only cover the central region. Conducting an X-ray analysis on the hot intracluster medium (ICM) is necessary to obtain a more complete constraint on the mass distribution in this very massive cluster. Aims. In this work, we perform a comprehensive X-ray analysis of J0723 with an aim to obtain accurate ICM hydrostatic mass measurements, using the X-ray data from Spectrum Roentgen Gamma (SRG)/eROSITA and Chandra X-ray observatories. By comparing the hydrostatic mass profile with the strong lensing model, we aim to provide the most reliable constraint on the distribution of mass up to R500. Methods. Thanks to the eROSITA all-sky survey and Chandra, which provide high signal-to-noise ratio (S/N) and high angular resolution data, respectively, we were able to constrain the ICM gas density profile and temperature profile with good accuracy both in the core and to the outskirts. With the density and temperature profiles, we computed the hydrostatic mass profile, which was then projected along the line of sight to compare with the mass distribution obtained from the recent strong lensing analysis based on JWST data. We also deprojected the strong lensing mass distribution using the hydrostatic mass profile obtained in this work. Results. The X-ray results obtained from eROSITA and Chandra are in very good agreement. The hydrostatic mass profiles we measured in this work, both projected and deprojected, are in good agreement with recent strong lensing results based on JWST data, at all radii. The projected hydrostatic mass within 128 kpc (the estimated Einstein radius) is (8.0 ± 0.7)×1013 M⊙, consistent with the strong lensing mass reported in recent literature. With the hydrostatic mass profile, we measured R2500 = 0.54 ± 0.04 Mpc and M2500 = (3.5 ± 0.8)×1014 M⊙, while the R500 and M500 are 1.32 ± 0.23 Mpc and (9.8 ± 5.1)×1014 M⊙, with a relatively larger error bar due to the rapidly decreasing S/N in the outskirts. We also find that the radial acceleration relation in J0723 is inconsistent with the RAR for spiral galaxies, implying that the latter is not a universal property of gravity across all mass scales.

Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND

General relativity and its Newtonian weak field limit are not sufficient to explain the observed phenomenology in the Universe, from the formation of large-scale structures to the dynamics of galaxies, with the only presence of baryonic matter. The most investigated cosmological model, the ΛCDM, accounts for the majority of observations by introducing two dark components, dark energy and dark matter, which represent ∼95% of the mass-energy budget of the Universe. Nevertheless, the ΛCDM model faces important challenges on the scale of galaxies. For example, some very tight relations between the properties of dark and baryonic matters in disk galaxies, such as the baryonic Tully–Fisher relation (BTFR), the mass discrepancy–acceleration relation (MDAR), and the radial acceleration relation (RAR), which see the emergence of the acceleration scale a0≃1.2×10−10 m s−2, cannot be intuitively explained by the CDM paradigm, where cosmic structures form through a stochastic merging process. An even more outstanding coincidence is due to the fact that the acceleration scale a0, emerging from galaxy dynamics, also seems to be related to the cosmological constant Λ. Another challenge is provided by dwarf galaxies, which are darker than what is expected in their innermost regions. These pieces of evidence can be more naturally explained, or sometimes even predicted, by modified theories of gravity, that do not introduce any dark fluid. I illustrate possible solutions to these problems with the modified theory of gravity MOND, which departs from Newtonian gravity for accelerations smaller than a0, and with Refracted Gravity, a novel classical theory of gravity introduced in 2016, where the modification of the law of gravity is instead regulated by a density scale.