Jean-Philippe Bruneton

Insight into the baryon-gravity relation in galaxies

Observations of spiral galaxies strongly support a one-to-one analytical relation between the inferred gravity of dark matter at any radius and the enclosed baryonic mass. It is baffling that baryons manage to settle the dark matter gravitational potential in such a precise way, leaving no “messy” fingerprints of the merging events and “gastrophysical” feedbacks expected in the history of a galaxy in a concordance Universe. This correlation of gravity with baryonic mass can be interpreted from several non-standard angles, especially as a modification of gravity called TeVeS, in which no galactic dark matter is needed. In this theory, the baryon-gravity relation is captured by the dieletric-like function µ of Modified Newtonian Dynamics (MOND), controlling the transition from 1/r 2 attraction in the strong gravity regime to 1/r attraction in the weak regime. Here, we study this µ-function in detail. We investigate the observational constraints upon it from fitting galaxy rotation curves, unveiling the degeneracy between the stellar mass-to-light ratio and the µ-function as well as the importance of the sharpness of transition from the strong to weak gravity regimes. We also numerically address the effects of non-spherical baryon geometry in the framework of non-linear TeVeS, and exhaustively examine how the µ-function connects with the free function of that theory. In that regard, we exhibit the subtle effects and wide implications of renormalizing the gravitational constant. We finally present a discontinuity-free transition between quasi-static galaxies and the evolving Universe for the free function of TeVeS, inevitably leading to a return to 1/r 2 attraction at very low accelerations in isolated galaxies.

Escaping from modified Newtonian dynamics

We present a new test of modified Newtonian dynamics (MOND) on galactic scales, based on the escape speed in the solar neighbourhood. This test is independent from other empirical successes of MOND at reproducing the phenomenology of galactic rotation curves. The galactic escape speed in MOND is entirely determined by the baryonic content of the Galaxy and the external field in which it is embedded. We estimate that the external field in which the Milky Way must be embedded to produce the observed local escape speed of 550 km/s is of the order of a_0/100, where a_0 is the dividing acceleration scale below which gravity is boosted in MOND. This is compatible with the external gravitational field actually acting on the Milky Way.

Non-standard baryon-dark matter interactions

After summarizing the respective merits of the Cold Dark Matter (CDM) and Modified Newtonian Dynamics (MOND) paradigms in various stellar systems, we investigate the possibility that a non-standard interaction between baryonic and dark matter could reproduce the successes of CDM at extragalactic scales while making baryonic matter effectively obey the MOND field equation in spiral galaxies.

The two body problem : analytical results in a toy model of relativistic gravity

The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstrom’s theory of gravity (1913). The gravitational field can be exactly solved for any configuration of point‐particles. We then derive the exact equations of motion of two inspiraling bodies including the exact self‐forces terms. We prove that there is no innermost circular orbit (ICO) in the exact theory whereas we find (order‐dependent) ICOs if post‐Newtonian (PN) truncations are used. We construct a solution of the two body problem in an iterative (non‐PN) way, which can be viewed as a series in powers of (v/c)5. Besides this rapid convergence, each order also provides non‐perturbative information. Starting from a circular Newtonian‐like orbit, the first iteration already yields the 4.5 PN radiation reaction. These results not only shed light on some non‐perturbative effects of relativistic gravity, but may also be useful to test numerical codes.

CAUSALITY AND SUPERLUMINAL FIELDS

JEAN-PHILIPPE BRUNETONGReCO, Institut d’Astrophysique de Paris, UMR 7095-CNRS,Universit´e Pierre et Marie Curie - Paris 6, 98 bis boulevard Arago F-75014, Paris, Francebruneton@iap.frThe expression of causality depends on an underlying choice of chronology. Sincea chronology is provided by any Lorentzian metric in relativistic theories, there are asmany expressions of causality as there are non-conformally related metrics over space-time. Although tempting, a definitive choice of a preferred metric to which one may referto is not satisfying. It would indeed be in great conflict with the spirit of general covari-ance. Moreover, a theory which appear to be non causal with respect to (hereafter, w.r.t)this metric, may well be causal w.r.t another metric. In a theory involving fields thatpropagate at different speeds (e.g. due to some spontaneous breaking of Lorentz invari-ance), spacetime is endowed with such a finite set of non-conformally related metrics. Inthat case one must look for a new notion of causality, such that 1. no particular metricis favored and 2. there is an unique answer to the question : “is the theory causal?”.This new causality is unique and defined w.r.t the metric drawing the wider cone in thetangent space of a given point of the manifold. Moreover, which metric defines the widercone may depend on the location on spacetime. In that sense, superluminal fields aregenerically causal, provided that some other basic requirements are met.