Xavier Hernandez

In the context of theories of gravity modified to account for the observed dynamics of galactic systems without the need to invoke the existence of dark matter, a prediction often appears regarding low acceleration systems: wherever $a$ falls below $a_{0}$ one should expect a transition from the classical to the modified gravity regime.This modified gravity regime will be characterised by equilibrium velocities which become independent of distance, and which scale with the fourth root of the total baryonic mass, $V^{4} \propto M$. The two above conditions are the well known flat rotation curves and Tully-Fisher relations of the galactic regime. Recently however, a similar phenomenology has been hinted at, at the outskirts of Galactic globular clusters, precisely in the region where $a<a_{0}$. Radial profiles of the projected velocity dispersion have been observed to stop decreasing along Keplerian expectations, and to level off at constant values beyond the radii where $a<a_{0}$. We have constructed gravitational equilibrium dynamical models for a number of globular clusters for which the above gravitational anomaly has been reported, using a modified Newtonian force law which yields equilibrium velocities equivalent to MOND. We find models can be easily constructed having an inner Newtonian region and an outer modified gravity regime, which reproduce all observational constraints, surface brightness profiles, total masses and line of sight velocity dispersion profiles. Through the use of detailed single stellar population models tuned individually to each of the globular clusters in question, we derive estimates of the total masses for these systems. Interestingly, we find that the asymptotic values of the velocity dispersion profiles are consistent with scaling with the fourth root of the total masses, as expected under modified gravity scenarios.

Modified gravity scenarios where a change of regime appears at acceleration scales $a<a_{0}$ have been proposed. Since for $1 M_{\odot}$ systems the acceleration drops below $a_{0}$ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching $10^{4}$ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same $a<a_{0}$ acceleration regime. Our results are suggestive of a breakdown of Kepler's third law beyond $a \approx a_{0}$ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.

The theoretical understanding of density waves in disk galaxies starts from the classical WKB perturbative analysis of tight-winding perturbations, the key assumption being that the potential due to the density wave is approximately radial. The above has served as a valuable guide in aiding the understanding of both simulated and observed galaxies, in spite of a number of caveats being present. The observed spiral or bar patterns in real galaxies are frequently only marginally consistent with the tight-winding assumption, often in fact, outright inconsistent. Here we derive a complementary formulation to the problem, by treating quasi-radial density waves under simplified assumptions in the linear regime. We assume that the potential due to the density wave is approximately tangential, and derive the corresponding dispersion relation of the problem. We obtain an instability criterion for the onset of quasi-radial density waves, which allows a clear understanding of the increased stability of the higher order modes, which appear at progressively larger radii, as often seen in real galaxies. The theory naturally yields a range of pattern speeds for these arms which appears constrained by the condition $\Omega_{p}<\Omega_{0} \pm \kappa /m$. For the central regions of galaxies where solid body rotation curves might apply, we find weak bars in the oscillatory regime with various pattern speeds, including counter rotating ones, and a prediction for $\Omega_{p}$ to increase towards the centre, as seen in the rapidly rotating bars within bars of some numerical simulations. We complement this study with detailed numerical simulations of galactic disks and careful Fourier analysis of the emergent perturbations, which support the theory presented.

Using an extensive sample of galaxies selected from the Sloan Digital Sky Survey Data Release 5, we compare the angular momentum distribution of active galactic nucleus (AGN) with non-AGN hosting late-type galaxies. To this end we characterize galactic spin through the dimensionless angular momentum parameter $\lambda$, which we estimate approximately through simple dynamical considerations. Using a volume limited sample, we find a considerable difference when comparing the empirical distributions of $\lambda$ for AGNs and non-AGN galaxies, the AGNs showing typically low $\lambda$ values and associated dispersions, while non-AGNs present higher $\lambda$ values and a broader distribution. A more striking difference is found when looking at $\lambda$ distributions in thin $M_{r}$ cuts, while the spin of non-AGN galaxies presents an anti-correlation with $M_{r}$, with bright (massive) galaxies having low spins, AGN host galaxies present uniform values of $\lambda$ at all magnitudes, a behavior probably imposed by the fact that most late-type AGN galaxies present a narrow range in color, with a typical constant $\lambda$ value. We also find that the fraction of AGN hosting galaxies in our sample strongly depends on galactic spin, increasing dramatically for decreasing $\lambda$. For AGN host galaxies we compute the mass of their supermassive black holes and find that this value tends to be higher for low spin galaxies, even at fixed luminosity, a result that could account, to a certain extent, for the spread on the luminosity black-hole mass relation.

We study the effects of the cluster environment on galactic morphology by defining a dimensionless angular momentum parameter $\lambda_{d}$, to obtain a quantitative and objective measure of galaxy type. The use of this physical parameter allows us to take the study of morphological transformations in clusters beyond the measurements of merely qualitative parameters, e.g. S/E ratios, to a more physical footing. To this end, we employ an extensive Sloan Digital Sky Survey sample (Data Release 7), with galaxies associated with Abell galaxy clusters. The sample contains 121 relaxed Abell clusters and over 51,000 individual galaxies, which guarantees a thorough statistical coverage over a wide range of physical parameters. We find that the median $\lambda_{d}$ value tends to decrease as we approach the cluster center, with different dependences according to the mass of the galaxies and the hosting cluster; low and intermediate mass galaxies showing a strong dependence, while massive galaxies seems to show, at all radii, low $\lambda_{d}$ values. By analysing trends in $\lambda_{d}$ as functions of the nearest neighbour environment, clustercentric radius and velocity dispersion of clusters, we can identify clearly the leading physical processes at work. We find that in massive clusters ($\sigma>700$ km/s), the interaction with the cluster central region dominates, whilst in smaller clusters galaxy-galaxy interactions are chiefly responsible for driving galactic morphological transformations.