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We compare N-body simulations performed in MOND with analogs in Newtonian gravity with dark matter (DM). We have developed a code which solves the Poisson equation in both gravity models. It is a grid solver using adaptive mesh refinement techniques, allowing us to study isolated galaxies as well as interacting galaxies. Galaxies in MOND are found to form bars faster and stronger than in the DM model. In Newton dynamics, it is difficult to reproduce the observed high frequency of strong bars, while MOND appears to fit better the observations. Galaxy interactions and mergers, such as the Antennae, are also simulated with Newton and MOND dynamics. In the latter, dynamical friction is much weaker, and merging time-scales are longer. The formation of tidal dwarf galaxies in tidal tails are also compared in MOND and Newton+DM models.
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The properties of the recently discovered Ultra-Compact Dwarf Galaxies (UCDs) show that their internal acceleration of gravity is everywhere above a0, the MOdified Newtonian Dynamics (MOND) constant of gravity. MOND therefore makes the strong prediction that no mass discrepancy should be observed for this class of objects. This is confirmed by the few UCDs for which virial masses were derived. We argue that UCD galaxies represent a suitable test-bench for the theory, in the sense that even a single UCD galaxy showing evidence for dark matter would seriously question the validity of MOND.
We investigate the possibility of discriminating between Modified Newtonian Dynamics (MOND) and Newtonian gravity with dark matter, by studying the vertical dynamics of disk galaxies. We consider models with the same circular velocity in the equatorial plane (purely baryonic disks in MOND and the same disks in Newtonian gravity embedded in spherical dark matter haloes), and we construct their intrinsic and projected kinematical fields by solving the Jeans equations under the assumption of a two-integral distribution function. We found that the vertical velocity dispersion of deep-MOND disks can be much larger than in the equivalent spherical Newtonian models. However, in the more realistic case of high-surface density disks this effect is significantly reduced, casting doubts on the possibility of discriminating between MOND and Newtonian gravity with dark matter by using current observations.
Tests of MOND in ellipticals are relatively rare because these galaxies often lack kinematic tracers in the regions where the MOND effects are significant. Stellar shells observed in many elliptical galaxies offer a promising way to constrain their gravitational field. Shells appear as glowing arcs around their host galaxy. They are observed up to ~100 kpc. The stars in axially symmetric shell systems move in nearly radial orbits. The radial distributions of shell locations and the spectra of stars in shells can be used to constrain the gravitational potential of their host galaxy. The symmetrical shell systems, being especially suitable for these studies, occur in approximately 3% of all early-type galaxies. Hence the shells substantially increase the number of ellipticals in which MOND can be tested up to large radii. In this paper, we review our work on shell galaxies in MOND. We summarize the paper B{i}lek et al. (2013), where we demonstrated the consistency of shell radii in an elliptical NGC 3923 with MOND, and the work B{i}lek et al. (2014), in which we predicted a giant (~200 kpc), as yet undiscovered shell of NGC 3923. We explain the shell identification method, which was used in these two papers. We further describe the expected shape of line profiles in shell spectra in MOND which is very special due to the direct relation of the gravitational field and baryonic matter distribution (B{i}lek et al., 2014, in preparation).
We extend the MOND analysis to a sample of 17 high surface brightness, early-type disc galaxies with rotation curves derived from a combination of 21cm HI line observations and optical spectroscopic data. A number of these galaxies have asymptotic rotation velocities between 250 and 350 km/s making them among the most massive systems (in terms of baryonic mass) considered in the context of MOND. We find that the general MOND prediction for such galaxies -- a rotation curve which gradually declines to the asymptotic value -- is confirmed, and in most cases the MOND rotation curve, determined from the mean radial light and gas distribution, agrees in detail with the observed rotation curve. In the few cases where MOND appears not to work well, the discrepancies can generally be understood in terms of various observational errors -- such as incorrect orientation angles and/or distances -- or of unmodelled physical effects -- such as non-circular motions. The implied mass-to-light ratios for the stellar disc and bulge constrain the MOND interpolating function; the form recently suggested by Zhao & Famaey (2005) yields more sensible values than the one traditionally used in MOND determinations of galaxy rotation curves.
We consider disk stability in the quasi-linear formulation of MOND (QUMOND), the basis for some $N$-body integrators. We generalize the Toomre criterion for the stability of disks to tightly wound, axisymmetric perturbations. We apply this to a family of thin exponential disks with different central surface densities. By numerically calculating their QUMOND rotation curves, we obtain the minimum radial velocity dispersion required for stability against local self-gravitating collapse. MOND correctly predicts much higher rotation speeds in low surface brightness galaxies (LSBs) than does Newtonian dynamics without dark matter. Newtonian models thus require putative very massive halos, whose inert nature implies they would strongly stabilize the disk. MOND also increases the stability of galactic disks, but in contradistinction to Newtonian gravity, this extra stability is limited to a factor of 2. MOND is thus rather more conducive to the formation of bars and spiral arms. Therefore, observation of such features in LSBs could be problematic for Newtonian galaxy models. This could constitute a crucial discriminating test. We quantitatively account for these facts in QUMOND. We also compare numerical QUMOND rotation curves of thin exponential disks to those predicted by two algebraic expressions commonly used to calculate MOND rotation curves. For the choice that best approximates QUMOND, we find the circular velocities agree to within 1.5% beyond $approx 0.5$ disk scale lengths, regardless of the central surface density. The other expression can underestimate the rotational speed by up to 12.5% at one scale length, though rather less so at larger radii.
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