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Register a new userUsing globular clusters to test gravity in the weak acceleration regime
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We report on the results from an ongoing program aimed at testing Newtons law of gravity in the low acceleration regime using globular clusters. It is shown that all clusters studied so far do behave like galaxies, that is, their velocity dispersion profile flattens out at large radii where the acceleration of gravity goes below 1e-8 cm/s/s, instead of following the expected Keplerian fall off. In galaxies this behavior is ascribed to the existence of a dark matter halo. Globular clusters, however, do not contain dark matter, hence this result might indicate that our present understanding of gravity in the weak regime of accelerations is incomplete and somehow incorrect.
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A test of Newtons law of gravity in the low acceleration regime using globular clusters is presented. New results for the core collapsed globular cluster NGC 7099 are given. The run of the gravitational potential as a function of distance is probed studying the velocity dispersion profile of the cluster, as derived from a set of 125 radial velocities with accuracy better than 1 km/s. The velocity dispersion profile is traced up to ~18 pc from the cluster center. The dispersion is found to be maximal at the center, then decrease until 10+-2 pc from the center, well inside the cluster tidal radius of 42 pc. After that the dispersion remains constant with average value 2.2+-0.3 km/s. Assuming for NGC 7099 a total V mag of M(V)=-7.43 mags and mass-to-light ratio M/L=1, the acceleration at 10 pc from the center is 1.1e-8 cm/s/s. Thus, the flattening of the velocity dispersion profile occurs for a value of the internal acceleration of gravity fully consistent with a_0=1.2e-8 cm/s/s observed in galaxies. This new result for NGC 7099 brings to 4 the clusters with velocity dispersion profile probing acceleration below a_0. All four have been found to have a flat dispersion profile at large radii where the acceleration is below a_0, mimicking qualitatively and quantitatively elliptical galaxies. Whether this indicates a failure of Newtonian dynamics in the low acceleration limit or some more conventional dynamical effect (e.g., tidal heating) is still unclear. However, the similarities emerging between very different globular clusters, as well as between globular clusters and elliptical galaxies seem to favor the first of these two possibilities.
Non-baryonic Dark Matter (DM) appears in galaxies and other cosmic structures when and only when the acceleration of gravity, as computed considering only baryons, goes below a well defined value a0=1.2e-8 cm/s/s. This might indicate a breakdown of Newtons law of gravity (or inertia) below a0, an acceleration smaller than the smallest probed in the solar system. It is therefore important to verify whether Newtons law of gravity holds in this regime of accelerations. In order to do this, one has to study the dynamics of objects that do not contain significant amounts of DM and therefore should follow Newtons prediction for whatever small accelerations. Globular clusters are believed, even by strong supporters of DM, to contain negligible amounts of DM and therefore are ideal for testing Newtonian dynamics in the low acceleration limit. Here, we discuss the status of an ongoing program aimed to do this test. Compared to other studies of globular clsuters, the novelty is that we trace the velocity dispersion profile of globular clusters far enough from the center to probe gravitational accelerations well below a0. In all three clusters studied so far the velocity dispersion is found to remain constant at large radii rather than follow the Keplerian falloff. On average, the flattening occurs at the radius where the cluster internal acceleration of gravity is 1.8+-0.4 x 10^{-8} cm/s/s, fully consistent with MOND predictions.
Stellar kinematics in the external regions of globular clusters can be used to probe the validity of Newtons law in the low acceleration regimes without the complication of non-baryonic dark matter. Indeed, in contrast with what happens when studying galaxies, in globular clusters a systematic deviation of the velocity dispersion profile from the expected Keplerian falloff would provide indication of a breakdown of Newtonian dynamics rather than the existence of dark matter. We perform a detailed analysis of the velocity dispersion in the globular cluster omega Centauri in order to investigate whether it does decrease monotonically with distance as recently claimed by Sollima et al. (2009), or whether it converges toward a constant value as claimed by Scarpa Marconi and Gilmozzi (2003B). We combine measurements from these two works to almost double the data available at large radii, in this way obtaining an improved determination of the velocity dispersion profile in the low acceleration regime. We found the inner region of omega Centauri is clearly rotating, while the rotational velocity tend to vanish, and is consistent with no rotation at all, in the external regions. The cluster velocity dispersion at large radii from the center is found to be sensibly constant. The main conclusion of this work is that strong similarities are emerging between globular clusters and elliptical galaxies, for in both classes of objects the velocity dispersion tends to remain constant at large radii. In the case of galaxies, this is ascribed to the presence of a massive halo of dark matter, something physically unlikely in the case of globular clusters. Such similarity, if confirmed, is best explained by a breakdown of Newtonian dynamics below a critical acceleration.
We study and model the properties of galaxy clusters in the normal-branch Dvali-Gabadadze-Porrati (nDGP) model of gravity, which is representative of a wide class of theories which exhibit the Vainshtein screening mechanism. Using the first cosmological simulations which incorporate both full baryonic physics and nDGP, we find that, despite being efficiently screened within clusters, the fifth force can raise the temperature of the intra-cluster gas, affecting the scaling relations between the cluster mass and three observable mass proxies: the gas temperature, the Compton $Y$-parameter of the Sunyaev-Zeldovich effect and the X-ray analogue of the $Y$-parameter. Therefore, unless properly accounted for, this could lead to biased measurements of the cluster mass in tests that make use of cluster observations, such as cluster number counts, to probe gravity. Using a suite of dark-matter-only simulations, which span a wide range of box sizes and resolutions, and which feature very different strengths of the fifth force, we also calibrate general fitting formulae which can reproduce the nDGP halo concentration at percent accuracy for $0leq zleq1$, and halo mass function with $lesssim3%$ accuracy at $0leq zleq1$ (increasing to $lesssim5%$ for $1leq zleq 2$), over a halo mass range spanning four orders of magnitude. Our model for the concentration can be used for converting between halo mass overdensities and predicting statistics such as the nonlinear matter power spectrum. The results of this work will form part of a framework for unbiased constraints of gravity using the data from ongoing and upcoming cluster surveys.
We present a novel fitting formula for the halo concentration enhancement in chameleon $f(R)$ gravity relative to General Relativity (GR). The formula is derived by employing a large set of $N$-body simulations of the Hu-Sawicki $f(R)$ model which cover a wide range of model and cosmological parameters, resolutions and simulation box sizes. The complicated dependence of the concentration on halo mass $M$, redshift $z$, and the $f(R)$ and cosmological parameters can be combined into a simpler form that depends only on a rescaled mass $M/10^{p_2}$, with $p_2equiv1.5log_{10}left[|{bar{f}_R(z)}|/(1+z)right]+21.64$ and $bar{f}_R(z)$ the background scalar field at $z$, irrespective of the $f(R)$ model parameter. Our fitting formula can describe the concentration enhancement well for redshifts $zleq3$, nearly 7 orders of magnitude in $M/10^{p_2}$ and five decades in halo mass. This is part of a series of works which aims to provide a general framework for self-consistent and unbiased tests of gravity using present and upcoming galaxy cluster surveys. The fitting formula, which is the first quantitative model for the concentration enhancement due to chameleon type modified gravity, is an important part in this framework and will allow continuous exploration of the parameter space. It can also be used to model other statistics such as the matter power spectrum.
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