The Radial Acceleration Relation (RAR) shows a strong correlation between two accelerations associated to galaxy rotation curves. The relation between these accelerations is given by a nonlinear function which depends on an acceleration scale $a_\dagger$. Some have interpreted this as an evidence for a gravity model, such as Modified Newtonian Dynamics (MOND), which posits a fundamental acceleration scale $a_0$ common to all the galaxies. However, it was later shown, using Bayesian inference, that this seems not to be the case: the $a_0$ credible intervals for individual galaxies were not found to be compatible among themselves. This type of test is a fundamental test for MOND as a theory for gravity, since it directly evaluates its basic assumption and this using the data that most favor MOND: galaxy rotation curves. Here we improve upon the previous analyses by introducing a more robust method to assess the compatibility between the credible intervals, in particular without Gaussian approximations. We directly estimate, using a Monte Carlo simulation, that the existence of a fundamental acceleration is incompatible with the data at more than $5σ$. We also consider quality cuts in order to show that our results are robust against outliers. In conclusion, the new analysis further supports the claim that the acceleration scale found in the RAR is an emergent quantity.
The timing of the Local Group is used to test Modified Newtonian Dynamics (MOND). The result shows that the masses predicted by MOND are well below the baryonic contents of the Milky Way and Andromeda galaxies.
We determine the mean velocity dispersion of six Galactic outer halo globular clusters, AM 1, Eridanus, Pal 3, Pal 4, Pal 15, and Arp 2 in the weak acceleration regime to test classical vs. modified Newtonian dynamics (MOND). Owing to the non-linearity of MOND's Poisson equation, beyond tidal effects, the internal dynamics of clusters is affected by the external field in which they are immersed. For the studied clusters, particle accelerations are much lower than the critical acceleration a_0 of MOND, but the motion of stars is neither dominated by internal accelerations (a_i >> a_e) nor exter…
The extremely small accelerations of objects required for the the onset of modified Newtonian dynamics, or MOND, makes testing the hypothesis in conventional terrestrial laboratories virtually impossible. This is due to the large background acceleration of Earth, which is transmitted to the acceleration of test objects within an apparatus. We show however, that it may be possible to test MOND-type hypotheses with experiments using a conventional apparatus capable of tracking very small accelerations of its components, but performed in locally inertial frames such as artificial satellites and o…
We highlight phenomenological aspects of Verlinde's recent proposal to account for the mass anomalies in galactic systems without dark matter -- in particular in their relation to MOND. Welcome addition to the MOND lore as it is, this approach have reproduced, so far, only a small fraction of MOND phenomenology, and is still rather tentative, both in its theoretical foundations and in its phenomenology. What Verlinde has extracted from this approach, so far, is a formula -- of rather limited applicability, and with no road to generalization in sight -- for the effective gravitational field of …
Modified Newtonian dynamics (MOND) provides a paradigm alternative to dark matter that has been successful in fitting and predicting the rich phenomenology of rotating disc galaxies. There have also been attempts to test MOND in dispersion-supported early-type galaxies, but it remains unclear whether MOND can fit the various empirical properties of early-type galaxies. As a way of rigorously testing MOND in elliptical galaxies we calculate the MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of $\sim 2000$ nearly round SDSS elliptical galaxies under a variety of assumpti…
A sample of Coma cluster ultra-diffuse galaxies (UDGs) are modelled in the context of Extended Modified Newtonian Dynamics (EMOND) with the aim to explain the large dark matter-like effect observed in these cluster galaxies. We first build a model of the Coma cluster in the context of EMOND using gas and galaxy mass profiles from the literature. Then assuming the dynamical mass of the UDGs satisfies the fundamental manifold of other ellipticals, and that the UDG stellar mass-to-light matches their colour, we can verify the EMOND formulation by comparing two predictions of the baryonic mass of …
(doctoral thesis of Michal Bilek, finished on June 19, 2015) MOND is an observational rule for predicting the acceleration of stars and galaxies from the distribution of the visible matter. It possibly stems from a new law of physics. I list the theoretical aspects of MOND, its achievements and problems. MOND has been tested mainly in disc galaxies so far. Its tests in elliptical galaxies are rare because the MOND effects are small for them in the parts observable by the conventional methods. In the thesis, I explain the methods and ideas I developed for testing MOND in the ellipticals using s…
A Quality Framework for Testing Gravity with Wide Binaries: No Evidence for MOND
University of Portsmouth（朴茨茅斯大学）；California Institute of Technology（加州理工学院）；Queen Mary University of London（伦敦大学玛丽女王学院）；Leiden University（莱顿大学）；University of Cambridge（剑桥大学）
This paper is devoted to solve the galactic rotation problem for ESO138-G014 galaxy based on two theories: dark matter and Modified Newtonian Dynamics. Here we did the rotation curve analysis with two possible choices for the dark matter density profile, namely Burkert and Navarro, Frenk and White profiles. The analysis shows the dark matter distribution favored to Burkert profile (cored dark matter). The standard hypothesis for most spiral galaxies are known to be embedded in dark matter haloes has now been overshadowed by Modified Newtonian Dynamics, known as MOND, the leading alternative of…
Modified Gravity (MOG) and Non-Local Gravity (NLG) are two alternative theories to General Relativity. They are able to explain the rotation curves of spiral galaxies and clusters of galaxies without including dark matter (Moffat & Rahvar 2013, 2014; Rahvar & Mashhoon 2014). In the weak-field approximation these two theories have similar forms, with an effective gravitational potential that has two components: (i) Newtonian gravity with the gravitational constant enhanced by a factor $(1+α)$ and (ii) a Yukawa type potential that produces a repulsive force with length scale $1/μ$. In this work …
I limelight and review a potentially crucial aspect of MOND: The near equality of the MOND acceleration constant, $a_0$ -- as deduced from local, galactic phenomena -- and cosmological parameters. To wit, $a_0\sim c H_0\sim c^2Λ^{1/2}\sim c^2/\ell_U$, where $H_0$ is the present value of the Hubble-Lemaître constant, $Λ$ is the `cosmological constant', and $\ell_U$ is a cosmological characteristic length; e.g., the Hubble distance, or the de Sitter radius associated with $Λ$. In itself, this near equality has some important phenomenological consequences, such as the impossibility of black holes…
Modified Newtonian dynamics (MOND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here,we set constraints on MOND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic mo…
This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss's law for gravity as well as other fundamental classical laws are extended to a $D$-dimensional metric space, where $D$ can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical structures without requirin…
We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in MOND, using the N-body code N-MODY, which is a particle-mesh based code with a numerical MOND potential solver developed by Ciotti, Londrillo and Nipoti (2006). We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of $10^4 M_\odot$ to $10^9 M_\odot$ and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND r…
Milgrom's modified Newtonian dynamics (MOND) can explain well the mass discrepancy problem in galaxy without invoking dark matter. The MOND theory predicts a universal constant acceleration scale in galaxy, below which the Newtonian dynamics is no longer valid. Recently, Rodrigues et al. analyzed 193 high-quality disk galaxies by using Bayesian inference and they concluded that the probability of existence of a fundamental acceleration scale is essentially 0. In this paper, we use the same method to revisit the same question: Is there a fundamental acceleration scale in galaxies? We fit each g…
Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration
The classical dwarf spheroidals (dSphs) provide a critical test for Modified Newtonian Dynamics (MOND) because they are observable satellite galactic systems with low internal accelerations and low, but periodically varying, external acceleration. This varying external gravitational field is not commonly found acting on systems with low internal acceleration. Using Jeans modelling, Carina in particular has been demonstrated to require a V-band mass-to-light ratio greater than 5, which is the nominal upper limit for an ancient stellar population. We run MOND N-body simulations of a Carina-like …
We analyse the rotation curves and gravitational stability of a sample of six bulgeless galaxies for which detailed images reveal no evidence for strong bars. We explore two scenarios: Newtonian dark matter models and MOdified Newtonian Dynamics (MOND). By adjusting the stellar mass-to-light ratio, dark matter models can match simultaneously both the rotation curve and bar-stability requirements in these galaxies. To be consistent with stability constraints, in two of these galaxies, the stellar mass-to-light ratio is a factor of ~1.5-2 lower than the values suggested from galaxy colours. In c…
We carry out spherical Jeans modeling of nearly round pure-bulge galaxies selected from the ATLAS$^{\rm 3D}$ sample. Our modeling allows for gradients in the stellar mass-to-light ratio ($M_\star/L$) through analytic prescriptions parameterized with a `gradient strength' $K$ introduced to accommodate any viable gradient. We use a generalized Osipkov-Merritt model for the velocity dispersion (VD) anisotropy. We produce Monte Carlo sets of models based on the stellar VD profiles under both the $Λ$CDM and MOND paradigms. Here, we describe the galaxy data, the empirical inputs, and the modeling pr…
The primary argument levelled against Milgrom's MOND is that it has no theoretical support, even though considerable effort has been expended in attempting to provide it. Against that criticism, MOND irrefutably enjoys an expanding portfolio of success and so is almost certainly tapping into something fundamental. But what? Over roughly the same period that MOND has been a topic of controversy, Baryshev, Sylos Labini and others have been claiming, with equal controversy in earlier years, that, on medium scales at least, material in the universe is distributed in a quasi-fractal $D\approx 2$ fa…
Aiming at discriminating different gravitational potential models of the Milky Way, we perform tests based on the kinematic data powered by the Gaia DR2 astrometry, over a large range of $(R,z)$ locations. Invoking the complete form of Jeans equations that admit three integrals of motion, we use the independent $R$- and $z$-directional equations as two discriminators ($T_R$ and $T_z$). We apply the formula for spatial distributions of radial and vertical velocity dispersions proposed by Binney et al., and successfully extend it to azimuthal components, $σ_θ(R,z)$ and $V_θ(R,z)$; the analytic f…
We test the modified Newtonian dynamics (MOND) theory with the velocity-dispersion profiles of Galactic globular clusters populating the outermost region of the Milky Way halo, where the Galactic acceleration is lower than the characteristic MOND acceleration a_0. For this purpose, we constructed self-consistent, spherical models of stellar systems in MOND, which are the analogues of the Newtonian King models. The models are spatially limited, reproduce well the surface-brightness profiles of globular clusters, and have velocity-dispersion profiles that differ remarkably in shape from the corr…
Intermediate-richness galaxy groups are an important test ground for MOND. First, they constitute a distinct type of galactic systems, with their own evolution histories and underlying physical processes; secondly, they probe little-chartered regions of parameter space, as they have baryonic masses similar to massive galaxies, and similar velocity dispersions, but much larger sizes -- similar to cluster cores (or even to clusters), but much lower dispersions. Importantly in the context of MOND, they have the lowest internal accelerations reachable inside galactic systems. I analyze a sample of…
MOdified Newtonian Dynamics (MOND) is an alternative to the standard Cold Dark Matter (CDM) paradigm which proposes an alteration of Newton's laws of motion at low accelerations, characterized by a universal acceleration scale a_0. It attempts to explain observations of galactic rotation curves and predicts a specific scaling relation of the baryonic and total acceleration in galaxies, referred to as the Rotational Acceleration Relation (RAR), which can be equivalently formulated as a Mass Discrepancy Acceleration Relation (MDAR). The appearance of these relations in observational data such as…
NGC 288 is a diffuse Galactic globular cluster, it is remarkable in that its low density results in internal accelerations being below the critical MOND $a_{0}$ acceleration throughout. This makes it an ideal testing ground for MONDian gravity, as the details of the largely unknown transition function between the Newtonian and modified regimes become unimportant. Further, exact analytical solutions exist for isothermal spherical equilibrium structures in MOND, allowing for arbitrary values of the anisotropy parameter, $β$. In this paper we use observations of the velocity dispersion profile of…
Different formulations of MOND predict somewhat different rotation curves for the same mass distribution. Here I consider a global attribute of the rotation curve that might provide a convenient discriminant between theories when applied to isolated, pure-disk galaxies that are everywhere deep in the MOND regime. This parameter is Q=<V^2>/V0^2, where <V^2> is the mean squared rotational speed of the galaxy, and V0 is the asymptotic (constant) rotational speed. The comparison between the observed and predicted values of Q is oblivious to the distance, the inclination, the mass, and the size of …
Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}ρ^γ$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $ζ(y)$ is (for $γ\not=1$) $[\int_0^y ζ\bar y^2 d\bar y]^{1/2}=-yd(…
We show that in the Dirac-Milne universe (a matter-antimatter symmetric universe where the two components repel each other), rotation curves are generically flat beyond the characteristic distance of about 3 virial radii, and that a Tully-Fisher relation with exponent $\approx 3$ is satisfied. Using 3D simulations with a modified version of the RAMSES code, we show that the Dirac-Milne cosmology presents a Faber-Jackson relation with a very small scatter and an exponent equal to $\approx 3$ between the mass and the velocity dispersion. We also show that the mass derived from the rotation curve…
We consider the feasibility of testing Newtonian gravity at low accelerations using wide binary (WB) stars separated by $\ge 3$ kAU. These systems probe the accelerations at which galaxy rotation curves unexpectedly flatline, possibly due to Modified Newtonian Dynamics (MOND). We conduct Newtonian and MOND simulations of WBs covering a grid of model parameters in the system mass, semi-major axis, eccentricity and orbital plane. We self-consistently include the external field (EF) from the rest of the Galaxy on the Solar neighbourhood using an axisymmetric algorithm. For a given projected separ…
Context. Stellar shells, which form axially symmetric systems of arcs in some elliptical galaxies, are most likely remnants of radial minor mergers. They are observed up a radius of $\sim$100 kpc. The stars in them oscillate in radial orbits. The radius of a shell depends on the free-fall time at the position of the shell and on the time since the merger. We previously verified the consistency of shell radii in the elliptical galaxy NGC 3923 with its most probable MOND potential. Our results implied that an as~yet undiscovered shell exists at the outskirts of the galaxy. Aims. We here extend o…
Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models of rotationally supported galaxies lead to curves with different geometries in $(g_{N},g_{tot})$-space ($g2$-space). Here $g_{tot}$ is the total acceleration and $g_{N}$ is the acceleration as obtained from the baryonic matter via Newtonian dynamics. In MOND modified inertia (MI) models the curves in $g2$-space are closed with zero area and so curve segments at radii $r\geq r_{N}$ (large radii) and $r< r_{N}$ (small radii) coincide, where $r_{N}$ is the radius where $g_N$ is greatest. In DM models with cored density profiles where …
We study the post-Newtonian expansion of a class of Lorentz-violating gravity theories that reduce to khronometric theory (i.e. the infrared limit of Horava gravity) in high-acceleration regimes, and reproduce the phenomenology of the modified Newtonian dynamics (MOND) in the low-acceleration, non-relativistic limit. Like in khronometric theory, Lorentz symmetry is violated in these theories by introducing a dynamical scalar field (the "khronon") whose gradient is enforced to be timelike. As a result, hypersurfaces of constant khronon define a preferred foliation of the spacetime, and the khro…
The bulge dominated galaxy NGC 7814 provides one of the strongest dynamical tests possible for Modified Newtonian Dynamics (MOND). Spitzer 3.6 micron photometry fixes the bulge parameterisation and strongly constrains the properties of the sub-dominant stellar disk. Furthermore, the distance is known to better than 5 percent, virtually eliminating it as a free parameter. The rotation curve is easily measured, since the H I (and stellar) disks are edge on, and both the receding and approaching sides agree very well. In this paper we explore the agreement between the model and observed rotation …
Galaxies are the basic structural element of the universe; galaxy formation theory seeks to explain how these structures came to be. I trace some of the foundational ideas in galaxy formation, with emphasis on the need for non-baryonic cold dark matter. Many elements of early theory did not survive contact with observations of low surface brightness galaxies, leading to the need for auxiliary hypotheses like feedback. The failure points often trace to the surprising predictive successes of an alternative to dark matter, the Modified Newtonian Dynamics (MOND). While dark matter models are flexi…
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 Newton…
We provide constraints on the inclination angle of the H\,{\sc i} disk of the dwarf irregular galaxy Holmberg II (Ho II) from stability analysis of the outer gaseous disk. We point out that a mean inclination angle of 27 degrees and thus a flat circular velocity of ~60 km/s, is required to have a level of gravitational stability similar to that found in other galaxies. Adopting this inclination angle, we find that Ho II lies on the right location in the baryonic Tully-Fisher relation. Moreover, for this inclination, its rotation curve is consistent with MOND. However, the corresponding analysi…
The dark matter (DM) haloes around spiral galaxies appear to conspire with their baryonic content: empirically, significant amounts of DM are inferred only below a universal characteristic acceleration scale. Moreover, the discrepancy between the baryonic and dynamical mass, which is usually interpreted as the presence of DM, follows a very tight mass discrepancy acceleration (MDA) relation. Its universality, and its tightness in spiral galaxies, poses a challenge for the DM interpretation and was used to argue in favour of MOdified Newtonian Dynamics (MOND). Here, we test whether or not this …
Galaxies within galaxy clusters are known to be subject to a wide variety of environmental effects, both gravitational and hydrodynamical. In this study, we examine the purely gravitational interaction of idealised galaxy models falling into a galaxy cluster in the context of Modified Newtonian Dynamics (MOND). This modification of gravity gives rise to an external field effect (EFE), where the internal dynamics of a system are affected by the presence of external gravitational fields. We examine the consequences of the EFE on low and high mass disk galaxies in time-evolving analytic backgroun…
The observed flat rotation curves of galaxies are among a number of astrophysical phenomena which require a larger acceleration than can be provided by the Newtonian gravity of the detected baryons. The main proposed solutions are additional undetected mass in the form of dark matter, or a low-acceleration modification to Newtonian gravity known as Milgromian dynamics (MOND). It is possible to directly test MOND using wide binary stars in the Solar neighbourhood, as these systems should contain a dynamically insignificant amount of dark matter even if it comprises most of the Galaxy. However, …
