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

Loss of mass and stability of galaxies in MOND

The self-binding energy and stability of a galaxy in MOND-based gravity are curiously decreasing functions of its center of mass acceleration towards neighbouring mass concentrations. A tentative indication of this breaking of the Strong Equivalence Principle in field galaxies is the RAVE-observed escape speed in the Milky Way. Another consequence is that satellites of field galaxies will move on nearly Keplerian orbits at large radii (100 - 500 kpc), with a declining speed below the asymptotically constant naive MOND prediction. But consequences of an environment-sensitive gravity are even more severe in clusters, where member galaxies accelerate fast: no more Dark-Halo-like potential is present to support galaxies, meaning that extended axisymmetric disks of gas and stars are likely unstable. These predicted reappearance of asymptotic Keplerian velocity curves and disappearance of "stereotypic galaxies" in clusters are falsifiable with targeted surveys.Comment: 4 pages, 2 figures, ApJ Letter

Quasi integral of motion for axisymmetric potentials

We present an estimate of the third integral of motion for axisymmetric three-dimensional potentials. This estimate is based on a Staeckel approximation and is explicitly written as a function of the potential. We tested this scheme for the Besancon Galactic model and two other disc-halo models and find that orbits of disc stars have an accurately conserved third quasi integral. The accuracy ranges from of 0.1% to 1% for heights varying from z = 0~kpc to z= 6 kpc and Galactocentric radii R from 5 to 15kpc. We also tested the usefulness of this quasi integral in analytic distribution functions of disc stellar populations: we show that the distribution function remains approximately stationary and that it allows to recover the potential and forces by applying Jeans equations to its moments.Comment: 9 pages, 9 figures, accepted for publication in Astron. and Astrophy

Combined Solar System and rotation curve constraints on MOND

The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the external gravitational field in which a system is embedded can produce effects on its internal dynamics. In this communication, we first show that this External Field Effect can significantly improve some galactic rotation curves fits by decreasing the predicted velocities of the external part of the rotation curves. In modified gravity versions of MOND, this External Field Effect also appears in the Solar System and leads to a very good way to constrain the transition function of the theory. A combined analysis of the galactic rotation curves and Solar System constraints (provided by the Cassini spacecraft) rules out several classes of popular MOND transition functions, but leaves others viable. Moreover, we show that LISA Pathfinder will not be able to improve the current constraints on these still viable transition functions.Comment: 13 pages, 7 figures, accepted for publication in MNRA

Potentials and distribution functions to be used for dynamical modeling with GAIA-like data

We present new tools to establish axisymmetric equilibrium models of the Milky Way. The models we wish to establish are pairs (V,F) where V is the gravitational potential generated by the whole mass distribution including the dark matter, and F is the distribution function in phase space for late-type tracer stars. We present a set of Stackel potentials that fit some fundamental parameters of the Milky Way (mass density in the solar neighbourhood and Oort constants). Then we define new component distribution functions that can be combined with these potentials in order to reproduce kinematical data like those that will be provided by GAIA.Comment: 2 pages, 2 figures, Proceeding of Les Houches summer school to appear in J.PhysIV Franc

Is violation of Newton's second law possible?

Astrophysical observations (usually explained by dark matter) suggest that classical mechanics could break down when the acceleration becomes extremely small (the approach known as modified Newtonian dynamics, or MOND). I present the first analysis of MOND manifestations in terrestrial (rather than astrophysical) settings. A new effect is reported: around each equinox date, 2 spots emerge on the Earth where static bodies experience spontaneous acceleration due to the possible violation of Newton's second law. Preliminary estimates indicate that an experimental search for this effect can be feasible.Comment: 10 pages; minor changes to match the published versio

Testing MOND Over a Wide Acceleration Range in X-Ray Ellipticals

The gravitational fields of two isolated ellipticals, NGC 720 and NGC 1521, have been recently measured to very large galactic radii (~100 and ~200 kpc), assuming hydrostatic balance of the hot gas enshrouding them. They afford, for the first time to my knowledge, testing MOND in ellipticals with force and quality that, arguably, approach those of rotation-curve tests in disk galaxies. In the context of MOND, it is noteworthy that the measured accelerations span a wide range, from more than 10a0 to about a0/10, unprecedented in individual ellipticals. I find that MOND predicts correctly the measured dynamical mass runs (apart from a possible minor tension in the inner few kpc of NGC 720, which might be due to departure from hydrostatic equilibrium): The predicted mass discrepancy increases outward from none, near the center, to ~10 at the outermost radii. The implications for the MOND-vs-dark-matter controversy go far beyond the simple fact of two more galaxies conforming to MOND.Comment: 5 pages, 2 figures. Minor changes to match published versio

Three-component Stackel potentials satisfying recent estimates of Milky Way parameters

We present a set of three-component Stackel potentials defined by five parameters and designed to model the Milky Way. We review the fundamental constraints that any model of the Milky Way must satisfy, including the most recent ones derived from Hipparcos data, and we study how the parameters of the presented potentials can vary in order to match these constraints. Five different valid potentials are presented and analyzed in detail: they are designed to be confronted with kinematical surveys in the future, by the construction of three-integral analytic distribution functions.Comment: 13 pages, 5 figures, accepted for publication in MNRA

Modified Newtonian Dynamics in the Milky Way

Both microlensing surveys and radio-frequency observations of gas flow imply that the inner Milky Way is completely dominated by baryons, contrary to the predictions of standard cold dark matter (CDM) cosmology. We investigate the predictions of the Modified Newtonian Dynamics (MOND) formula for the Galaxy given the measured baryon distribution. Satisfactory fits to the observationally determined terminal-velocity curve are obtained for different choices of the MOND's interpolating function mu(x). However, with simple analytical forms of mu(x), the local circular speed v_c(R_0) can be as large as 220 km/s only for values of the parameter a_0 that are excluded by observations of NGC 3198. Only a numerically specified interpolating function can produce v_c(R_0)=220 km/s, which is therefore an upper limit in MOND, while the asymptotic velocity is predicted to be v_c(infty)=170+-5 km/s. The data are probably not consistent with the functional form of mu(x) that has been explored as a toy model in the framework of Bekenstein's covariant theory of gravity.Comment: 7 pages, 4 figures, accepted for publication in MNRA