Modified Newtonian dynamics and hadronic scales

In this paper, we use the idea of modified Newtonian dynamics to further support the arguments that important information concerning the nature of space is hidden at hadronic mass and distance scales.

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.

Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

Gaia-DR2 extended kinematical maps

Context. Recent statistical deconvolution methods have produced extended kinematical maps in a range of heliocentric distances that are a factor of two to three larger than those analysed in Gaia Collaboration (2018, A&A, 616, A11) based on the same data. Aims. In this paper, we use such maps to derive the rotation curve both in the Galactic plane and in off-plane regions and to analyse the density distribution. Methods. By assuming stationary equilibrium and axisymmetry, we used the Jeans equation to derive the rotation curve. Then we fit it with density models that include both dark matter and predictions of the MOND (Modified Newtonian dynamics) theory. Since the Milky Way exhibits deviations from axisymmetry and equilibrium, we also considered corrections to the Jeans equation. To compute such corrections, we ran N-body experiments of mock disk galaxies where the departure from equilibrium becomes larger as a function of the distance from the centre. Results. The rotation curve in the outer disk of the Milky Way that is constructed with the Jeans equation exhibits very low dependence on R and z and it is well-fitted both by dark matter halo and MOND models. The application of the Jeans equation for deriving the rotation curve, in the case of the systems that deviate from equilibrium and axisymmetry, introduces systematic errors that grow as a function of the amplitude of the average radial velocity. In the case of the Milky Way, we can observe that the amplitude of the radial velocity reaches ∼10% that of the azimuthal one at R ≈ 20 kpc. Based on this condition, using the rotation curve obtained from the Jeans equation to calculate the mass may overestimate its measurement.