The modified dynamics (MOND) predicts an absolute maximum to the acceleration produced by `dark halos'

We have recently discovered that the modified dynamics (MOND) implies some universal upper bound on the acceleration that can be contributed by a `dark halo'--assumed in a Newtonian analysis to account for the effects of MOND. Not surprisingly, the limit is of the order of the acceleration constant of the theory. This can be contrasted directly with the results of structure-formation simulations. The new limit is substantial and different from earlier MOND acceleration limits (discussed in connection with the MOND explanation of the Freeman law for galaxy disks, and the Fish law for ellipticals): It pertains to the `halo', and not to the observed galaxy; it is absolute, and independent of further physical assumptions on the nature of the galactic system; and it applies at all radii, whereas the other limits apply only to the mean acceleration in the system.Comment: Latex, five pages, final version to be published in Astrophys. J. Let

Refining MOND interpolating function and TeVeS Lagrangian

The phenomena customly called Dark Matter or Modified Newtonian Dynamics (MOND) have been argued by Bekenstein (2004) to be the consequences of a covariant scalar field, controlled by a free function (related to the MOND interpolating function) in its Lagrangian density. In the context of this relativistic MOND theory (TeVeS), we examine critically the interpolating function in the transition zone between weak and strong gravity. Bekenstein's toy model produces too gradually varying functions and fits rotation curves less well than the standard MOND interpolating function. However, the latter varies too sharply and implies an implausible external field effect (EFE). These constraints on opposite sides have not yet excluded TeVeS, but made the zone of acceptable interpolating functions narrower. An acceptable "toy" Lagrangian density function with simple analytical properties is singled out for future studies of TeVeS in galaxies. We also suggest how to extend the model to solar system dynamics and cosmology, and compare with strong lensing data (see also astro-ph/0509590).Comment: accepted for publication in ApJ Letter

Finite Disks with Power-Law Potentials

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff at some radius Ro. First we discuss circular disks whose circular rotation speed v is proportional to r^alpha, with any alpha> -1/2. The surface-density of the disks is expressed in terms of hypergeometric functions of 1-(Ro/r)^2. We give closed expressions for the full 3-D potentials in terms of hypergeometric functions of two variables. We express the potential and acceleration in the plane at r>Ro, and along the rotation axis, in terms of simple hypergeometric functions. All the multipoles of the disk are given. We then generalize to non-axisymmetric disks. The potential in the midplane is given in terms of the hypergeometric function of two variables. For integer values of 2 alpha the above quantities are given in more elementary terms. All these results follow straightforwardly from formulae we derive for the general, cutoff, power-law, triaxial ellipsoid.Comment: 13 pages, Written in LATEX, using aaspp.st

Stability of disk galaxies in the modified dynamics

General analytic arguments lead us to expect that in the modified dynamics (MOND) self-gravitating disks are more stable than their like in Newtonian dynamics. We study this question numerically, using a particle-mesh code based on a multi-grid solver for the (nonlinear) MOND field equation. We start with equilibrium distribution functions for MOND disk models having a smoothly truncated, exponential surface-density profiles and a constant Toomre $Q$ parameter. We find that, indeed, disks of a given ``temperature'' are locally more stable in MOND than in Newtonian dynamics. As regards global instability to bar formation, we find that as the mean acceleration in the disk is lowered, the stability of the disk is increased as we cross from the Newtonian to the MOND regime. The degree of stability levels off deep in the MOND regime, as expected from scaling laws in MOND. For the disk model we use, this maximum degree of stability is similar to the one imparted to a Newtonian disk by a halo three times as massive at five disk scale lengths.Comment: 20 pages, Latex, 8 embedded figures, version to be published in The Astrophys.

The shape of "dark matter" halos in disc galaxies according to the modified dynamics

Analyses of halo shapes for disc galaxies are said to give incongruous results. I point out that the modified dynamics (MOND) predicts for disc galaxies a distribution of fictitious dark matter that comprises two components: a pure disc and a rounder halo. The former dominates the true disc in regions of small accelerations, where it controls the z-dynamics in the disc (disc flaring etc.); it has a finite total mass. It also dominates the round component near the centre where the geometry is nearly planar. The second component controls motions far from the plane, has a total enclosed mass that diverges linearly with radius, and determines the rotation curve at large radii. Its ellipticity may be appreciable at small radii but vanishes asymptotically. This prediction of MOND differs from what one expects from galaxy-formation scenarios with dark matter. Analyses to date, which, as they do, assume one component--usually with a constant ellipticity, perforce give conflicting results for the best-value ellipticity, depending on whether they probe the disc or the sphere, small radii or large ones.Comment: 8 page

The canonical 8-form on manifolds with holonomy group Spin(9)

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained

First Results from the KMOS Lens-Amplified Spectroscopic Survey (KLASS): Kinematics of Lensed Galaxies at Cosmic Noon

We present the first results of the KMOS Lens-Amplified Spectroscopic Survey (KLASS), a new ESO Very Large Telescope (VLT) large program, doing multi-object integral field spectroscopy of galaxies gravitationally lensed behind seven galaxy clusters selected from the HST Grism Lens-Amplified Survey from Space (GLASS). Using the power of the cluster magnification we are able to reveal the kinematic structure of 25 galaxies at $0.7 \lesssim z \lesssim 2.3$, in four cluster fields, with stellar masses $8 \lesssim \log{(M_\star/M_\odot)} \lesssim 11$. This sample includes 5 sources at $z>1$ with lower stellar masses than in any previous kinematic IFU surveys. Our sample displays a diversity in kinematic structure over this mass and redshift range. The majority of our kinematically resolved sample is rotationally supported, but with a lower ratio of rotational velocity to velocity dispersion than in the local universe, indicating the fraction of dynamically hot disks changes with cosmic time. We find no galaxies with stellar mass $<3 \times 10^9 M_\odot$ in our sample display regular ordered rotation. Using the enhanced spatial resolution from lensing, we resolve a lower number of dispersion dominated systems compared to field surveys, competitive with findings from surveys using adaptive optics. We find that the KMOS IFUs recover emission line flux from HST grism-selected objects more faithfully than slit spectrographs. With artificial slits we estimate slit spectrographs miss on average 60% of the total flux of emission lines, which decreases rapidly if the emission line is spatially offset from the continuum.Comment: Accepted for publication in Ap