The radial acceleration relation (RAR) in galaxies describes a tight empirical scaling law between the total acceleration observed in galaxies and that expected from their baryonic mass , with a characteristic acceleration scale of m s⁻². Here, we examine if such a correlation exists in galaxy clusters using weak-lensing, strong-lensing, and X-ray data sets available for 20 high-mass clusters targeted by the Cluster Lensing And Supernova survey with Hubble (CLASH). By combining our CLASH data with stellar mass estimates for the brightest cluster galaxies (BCGs) and accounting for the stellar baryonic component in clusters, we determine, for the first time, an RAR on BCG–cluster scales. The resulting RAR is well described by a tight power-law relation, , with lognormal intrinsic scatter of . The slope is consistent with the low acceleration limit of the RAR in galaxies, , whereas the intercept implies a much higher acceleration scale of m s⁻², indicating that there is no universal RAR that holds on all scales from galaxies to clusters. We find that the observed RAR in CLASH clusters is consistent with predictions from a semianalytical model developed in the standard ΛCDM framework. Our results also predict the presence of a baryonic Faber–Jackson relation ( ) on cluster scales.

A flux of cosmic rays (CRs) propagating through a diffuse ionized gas can excite MHD waves, thus generating magnetic disturbances. We propose a generic model of CR penetration into molecular clouds through their diffuse envelopes, and identify the leading physical processes controlling their transport on the way from a highly ionized interstellar medium to the dense interior of the cloud. The model allows us to describe a transition between a free streaming of CRs and their diffusive propagation, determined by the scattering on the self-generated disturbances. A self-consistent set of equations, governing the diffusive transport regime in an envelope and the MHD turbulence generated by the modulated CR flux, is characterized by two dimensionless numbers. We demonstrate a remarkable mutual complementarity of different mechanisms leading to the onset of the diffusive regime, which results in a universal energy spectrum of the modulated CRs. In conclusion, we briefly discuss implications of our results for several fundamental astrophysical problems, such as the spatial distribution of CRs in the Galaxy as well as the ionization, heating, and chemistry in dense molecular clouds.

Since Bekenstein's creation of his tensor-vector-scalar theory (TeVeS), the modified Newtonian dynamics (MOND) paradigm has been redeemed from the embarrassment of lacking a relativistic version. One primary success of TeVeS is that it provides an enhancement of gravitational lensing, which could not be achieved by other MOND theories. Following Bekenstein's work, we investigate the phenomena of gravitational lensing including deflection angles, lens equations, and time delay. We find that the deflection angle maintains its value, while the distance of closest approach varies in the MOND regime. We also use the deflection angle law to derive magnifications and investigate microlensing light curves. We find that the difference in the magnification of the two images in the point-mass model is not a constant, as in general relativity (GR). Besides, microlensing light curves could deviate significantly from GR in the deep MOND regime. Furthermore, the scalar field, which is introduced to enhance the deflection angle in TeVeS, contributes a negative effect on the potential time delay. Unfortunately, this phenomenon is unmeasurable in lensing systems, where we can only observe the time delay between two images for a given source. However, this measurable time delay offers another constraint on the mass ratio of the dark matter and MOND scenarios, which in general differs from that given by the deflection angle. In other words, for a lensing system, if two masses, m_gN and m_gM, are mutual alternatives for the deflection angles in their own paradigm, regarding the time delay they are in general in an exclusive relation.

We use a semiempirical model to investigate the radial acceleration relation (RAR) in a cold dark matter (CDM) framework. Specifically, we build 80 model galaxies covering the same parameter space as the observed galaxies in the SPARC database, assigning them to dark matter (DM) halos using abundance-matching and halo mass–concentration relations. We consider several abundance-matching relations, finding some to be a better match to the kinematic data than others. We compute the unavoidable gravitational interactions between baryons and their DM halos, leading to an overall compression of the original Navarro–Frenk–White (NFW) halos. Before halo compression, high-mass galaxies lie approximately on the observed RAR, whereas low-mass galaxies display up-bending “hooks” at small radii due to DM cusps, making them deviate systematically from the observed relation. After halo compression, the initial NFW halos become more concentrated at small radii, making larger contributions to rotation curves. This increases the total accelerations, moving all model galaxies away from the observed relation. These systematic deviations suggest that the CDM model with abundance matching alone cannot explain the observed RAR. Further effects (e.g., feedback) would need to counteract the compression with precisely the right amount of halo expansion, even in high-mass galaxies with deep potential wells where such effects are generally predicted to be negligible.

Using strong lensing data, Milgrom’s modified Newtonian dynamics (MOND) and its covariant TeVeS (tensor-vector-scalar theory) are examined here as an alternative to the conventional $\Lambda \mathrm{CDM}$ paradigm. We examine 10 double-image, gravitational lensing systems in which the lens masses have been estimated by stellar population synthesis models. While mild deviations exist, we find no strong case of outliers to the TeVeS theory. DOI: http://dx.doi.org/10.1103/PhysRevD.83.063523 © 2011 American Physical Society

We study the mass discrepancy–acceleration relation (MDAR) of 57 elliptical galaxies by their Einstein rings from the Sloan Lens ACS Survey (SLACS). The mass discrepancy between the lensing mass and the baryonic mass derived from population synthesis is larger when the acceleration of the elliptical galaxy lenses is smaller. The MDAR is also related to surface mass density discrepancy. At the Einstein ring, these lenses belong to high-surface-mass density galaxies. Similarly, we find that the discrepancy between the lensing and stellar surface mass density is small. It is consistent with the recent discovery of dynamical surface mass density discrepancy in disc galaxies where the discrepancy is smaller when surface density is larger. We also find relativistic modified Newtonian dynamics (MOND) can naturally explain the MDAR and surface mass density discrepancy in 57 Einstein rings. Moreover, the lensing mass, the dynamical mass and the stellar mass of these galaxies are consistent with each other in relativistic MOND.