We review galaxy formation and dynamics under the MOND hypothesis of modified gravity, and compare to similar galaxies in Newtonian dynamics with dark matter. The aim is to find peculiar predictions both to discriminate between various hypotheses, and to make the theory progress through different constraints, touching the interpolation function, or the fundamental acceleration scale. Galaxy instabilities, forming bars and bulges at longer term, evolve differently in the various theories, and help to bring constraints, together with the observations of bar frequency. Dynamical friction and the predicted merger rate could be a sensitive test of theories. The different scenarios of galaxy formation are compared within the various theories and observations.
MOND is a phenomenological modification of Newton's law of gravitation which reproduces the dynamics of galaxies, without the need for additional dark matter. This paper reviews the basics of MOND and its application to dwarf galaxies. MOND is generally successful at reproducing stellar velocity dispersions in the Milky Way's classical dwarf ellipticals, for reasonable values of the stellar mass-to-light ratio of the galaxies; two discrepantly high mass-to-light ratios may be explained by tidal effects. Recent observations also show MOND describes tidal dwarf galaxies, which form in complex dy…
We have carried out a search for gas-rich dwarf galaxies that have lower rotation velocities in their outskirts than MOdified Newtonian Dynamics (MOND) predicts, so that the amplitude of their rotation curves cannot be fitted by arbitrarily increasing the mass-to-light ratio of the stellar component or by assuming additional undetected matter. With presently available data, the gas-rich galaxies UGC 4173, Holmberg II, ESO 245-G05, NGC 4861 and ESO 364-G029 deviate most from MOND predictions and, thereby, provide a sample of promising targets in testing the MOND framework. In the case of Holmbe…
MOdified Newtonian dynamics (MOND) represents a phenomenological alternative to dark matter (DM) for the missing mass problem in galaxies and clusters of galaxies. We analyze the central regions of a local sample of $\sim 220$ early-type galaxies from the $\rm ATLAS^{3D}$ survey, to see if the data can be reproduced without recourse to DM. We estimate dynamical masses in the MOND context through Jeans analysis, and compare to $\rm ATLAS^{3D}$ stellar masses from stellar population synthesis. We find that the observed stellar mass--velocity dispersion relation is steeper than expected assuming …
The Baryonic Tully-Fisher Relation (BTFR) is an empirical relation between baryonic mass and rotation velocity in disk galaxies. It provides tests of galaxy formation models in LCDM and of alternative theories like MOND. Observations of gas rich galaxies provide a measure of the slope and normalization of the BTFR that is more accurate (if less precise) than that provided by star dominated spirals, as their masses are insensitive to the details of stellar population modeling. Recent independent data for such galaxies are consistent with Mb = AVf^4 with A = 47+/-6 Msun (km/s)^-4. This is equiva…
Generalized Einstein - Aether vector field models have been shown to provide, in the weak field regime, modifications to gravity which can be reconciled with the successfull MOND proposal. Very little is known, however, on the function F(K) defining the vector field Lagrangian so that an analysis of the viability of such theories at the cosmological scales has never been performed. As a first step along this route, we rely on the relation between F(K) and the MOND interpolating function $μ(a/a_0)$ to assign the vector field Lagrangian thus obtaining what we refer to as "MONDian vector models".…
Dwarf and low surface brightness galaxies are ideal objects to test modified Newtonian dynamics (MOND), because in most of these galaxies the accelerations fall below the threshold below where MOND supposedly applies. We have selected from the literature a sample of 27 dwarf and low surface brightness galaxies. MOND is successful in explaining the general shape of the observed rotation curves for roughly three quarters of the galaxies in the sample presented here. However, for the remaining quarter, MOND does not adequately explain the observed rotation curves. Considering the uncertainties in…
The gravitational lensing of Bullet Clusters and early-type galaxies pose serious challenges on the validity of MOND. Recently, Finslerian MOND, a generalization of MOND in the framework of Finsler gravity, has been proposed to explain the mass discrepancy problem of Bullet Cluster 1E 0657\ 558. In this paper, we check the validity of the Finslerian MOND in describing the strong gravitational lensing of early-type galaxies. The investigation on ten strong lenses of the CASTLES samples shows that there is no strong evidence for the existence of dark matter.
I show that Modified Newtonian Dynamics (MOND) is equivalent to assuming an isothermal dark matter density profile, with its density related to the enclosed total baryonic mass. This density profile can be deduced by physical laws if a dark matter core exists and if the baryonic component is spherically-symmetric, isotropic and isothermal. All the usual predictions of MOND, as well as the universal constant $a_0$, can be derived in this model. Since the effects of baryonic matter are larger in galaxies than in galaxy clusters, this result may explain why MOND appears to work well for galaxies …
We comment on arXiv:1112.1320 and point out that baryonic oscillations of the matter power spectrum, while predicted by theories that do not incorporate collisionless cold dark matter, are strongly suppressed by the statistical window function that is used to process finite-sized galaxy samples. We assert that with present-day data sets, the slope of the matter power spectrum is a much stronger indicator of a theory's validity. We also argue that MOND should not be used as a strawman theory as it is not in general representative of modified gravity theories; some theories, notably our scalar-v…
We compare the basic properties and kinematics of two gas-rich dwarf galaxies: KK246 and Holmberg II (HoII). HoII is 20 times more luminous in the blue-band than KK246 and its HI mass is a factor of 6 higher than in KK246. However, the amplitudes of the rotation curves (at the last measured point) of both galaxies are very similar, of about 40 km/s at a galactocentric radius of 7 kpc. This fact is challenging for modified theories of gravity that predict a one-to-one relation between gravity at any radius and the enclosed baryonic mass in galaxies. In particular, MOdified Newtonian Dynamics (M…
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…
Modified Newtonian Dynamics (MOND) at low acceleration has been astonishingly powerful at explaining the flat rotation curve of galaxies and the relation between the baryonic content of the galaxies and their observed circular velocity, known as the Baryonic Tully-Fisher Relationship (BTFR). It is known that MOND fails at explaining the observed velocity dispersion of the ultra-faint dwarf galaxies (UFDs) with the justification that UFDs are more prone to tidal disruption in MOND compared to cold dark matter model. We show that: (i) the ratio of tidal to internal acceleration in UFDs is extrem…
Survival of high-energy cosmic rays (HECRs) against gravitational Cherenkov losses is shown not to cast strong constraints on MOND theories that are compatible with general relativity (GR): theories that coincide with GR in the high-acceleration limit. The energy-loss rate, L, is shown to be many orders smaller than those derived in the literature for theories with no extra scale. The gravitational acceleration produced by a HECR in its vicinity is much higher than the MOND acceleration a0. So, modification to GR, which underlies L, enters only beyond the MOND radius of the particle, within wh…
The gravitational-wave event GW170817 and the near-simultaneous corresponding gamma-ray burst (GRB 170817 A) falsify modified gravity theories in which the gravitational geometry differs non-conformally from physical geometry. Thus, the observations of this event definitively rule out theories, such as TeVeS, a suggested relativistic extension of Milgrom's modified Newtonian dynamics (MOND), that predict a significantly different Shapiro delay for electromagnetic and gravitational radiation. While not falsifying MOND per se, GW170817 severely constrains relativistic extensions of MOND to theor…
A general account of MOND theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration -- below an acceleration constant a0 -- where dynamics become scale invariant. I list some of the salient predictions of these tenets. The special role of a0 and its significance are then discussed. In particular, I stress its coincidence with cosmologically relevant accelerations. The deep-MOND limit and the consequences of its scale invariance are considered in some detail. General aspects of MOND theories are then described, after wh…
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 …
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.
The missing mass problem has not been solved decisively yet. Observations show that if gravity is to be modified, then the MOND theory is its excellent approximation on galactic scales. MOND suggests an adjustments of the laws of physics in the limit of low accelerations. Comparative simulations of interacting galaxies in MOND and Newtonian gravity with dark matter revealed two principal differences: 1) galaxies can have close flybys without ending in mergers in MOND because of weaker dynamical friction, and 2) tidal dwarf galaxies form very easily in MOND. When this is combined with the fact …
We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity. We also prove that a Noethe…
I derive a new MOND relation for pure-disc galaxies: The `dynamical' central surface density, $Σ^0_D$, deduced from the measured velocities, is a universal function of only the true, `baryonic' central surface density, $Σ^0_B$: $Σ^0_D=Σ_M \mathcal{S}(Σ^0_B/Σ_M)$, where $Σ_M\equiv a_0/2πG$ is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. $\mathcal{S}(y)$ is derived: $\mathcal{S}(y)=\int_0^yν(y')dy'$, with $ν(y)$ the interpolating function of the theory. The relation aymptotes to $Σ^0_D=Σ^0_B$ for $Σ^0_B\ggΣ_M$, and to…
We discuss the advantages of using metric theories of gravity with curvature-matter couplings in order to construct a relativistic generalisation of the simplest version of Modified Newtonian Dynamics (MOND), where Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature-matter couplings. Using the simplest two local constructions in a FLRW …
After a succinct review of the MOND paradigm--with its phenomenology, and its various underlying theories--I concentrate on so called modified inertia (MI) formulations of MOND, which have so far received only little attention. These share with all MOND theories the salient MOND predictions, such as asymptotically flat rotation curves, and the universal mass-asymptotic-speed relation. My emphasis here is, however, on the fact that MI theories can differ substantially from their "modified-gravity" (MG) kin in predicting other phenomena. Because MI theories are non local in time, MOND effects de…
A specific modification of Newtonian dynamics known as MOND has been shown to reproduce the dynamics of most astrophysical systems at different scales without invoking non-baryonic dark matter (DM). There is, however, a long-standing unsolved problem when MOND is applied to rich clusters of galaxies in the form of a deficit (by a factor around two) of predicted dynamical mass derived from the virial theorem with respect to observations. In this article we approach the virial theorem using the velocity dispersion of cluster members along the line of sight rather than using the cluster temperatu…
An important and useful relation is known to hold in two specific MOND theories. It pertains to low-acceleration, isolated systems of pointlike masses, m_p, at positions r_p, subject to gravitational forces F_p. It reads sum_p r_p.F_p=-(2/3)(Ga0)^{1/2}[(\sum_p m_p)^{3/2}-\sum_p m_p^{3/2}]; a0 is the MOND acceleration constant. Here I show that this relation holds in the nonrelativistic limit of any modified-gravity MOND theory. It follows from only the basic tenets of MOND (as applied to such theories): departure from standard dynamics at accelerations below a0, and space-time scale invariance…
Two incorrect arguments against MOND in elliptical galaxies could be that the equivalent circular velocity curves tend to become flat at much larger accelerations than in spiral galaxies, and that the Newtonian dark matter halos are more concentrated than in spirals. Here, we compare published scaling relations for the dark halos of elliptical galaxies to the scaling relations expected for MONDian phantom halos. We represent the baryonic content of galaxies by spherical profiles, and their corresponding MONDian phantom halos by logarithmic halos. We then derive the surface densities, central d…
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…
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 …
In the cold dark matter (CDM) paradigm, bulges easily form through galaxy mergers, either major or minor, or through clumpy disks in the early universe, where clumps are driven to the center by dynamical friction. Also pseudo-bulges, with a more disky morphology and kinematics, can form more slowly through secular evolution of a bar, where resonant stars are elevated out of the plane, in a peanut/box shape. As a result, in CDM cosmological simulations, it is very difficult to find a bulgeless galaxy, while they are observed very frequently in the local universe. A different picture emerges in …
An impact model of gravity designed to emulate Newton's law of gravitation is applied to the radial acceleration of disk galaxies. Based on this model (Wilhelm et al. 2013), the rotation velocity curves can be understood without the need to postulate any dark matter contribution. The increased acceleration in the plane of the disk is a consequence of multiple interactions of gravitons (called "quadrupoles" in the original paper) and the subsequent propagation in this plane and not in three-dimensional space. The concept provides a physical process that relates the fit parameter of the accelera…
MOND predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is phi(r)=(MGa0)^{1/2}ln(r); a0 is the MOND constant. Relativistic MOND theories predict that the lensing effects of M are dictated by phi(r) as general-relativity lensing is dictated by the Newtonian potential. Thus, MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have: (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2s^2) that depends only on M: s=(MGa0/4)^{1/4}. I compare these predictions with r…
A sample of 22 spiral galaxies compiled from published data is studied. The galaxy rotation curves pass through a maximum distance of more than $\sim 1$ kpc from the center with a subsequent decrease in the rotation velocity. The galaxy position in the Tully-Fisher (TF) and baryonic Tully-Fisher (BTF) diagrams show that the values of maximum rotation velocities are located on the same sequence with other galaxies, while the velocities at the disk periphery for some galaxies are significantly lower than the expected values for a given mass or luminosity. Thus, the decrease in the rotation curve…
Studies of stellar populations in early-type galaxies (ETGs) show that the more massive galaxies form earlier and have a shorter star formation history (SFH). In this study, we investigate the initial conditions of ETG formation. The study begins with the collapse of non-rotating post-Big-Bang gas clouds in Milgromian (MOND) gravitation. These produce ETGs with star-forming timescales (SFT) comparable to those observed in the real Universe. Comparing these collapse models with observations, we set constraints on the initial size and density of the post-Big-Bang gas clouds in order to form ETGs…
I discuss a novel MOND effect that entails a correction to the dynamics of isolated mass systems even when they are deep in the Newtonian regime: systems whose extent R<<Rm, where Rm=sqrt(GM/a0) is the MOND radius, and M the total mass. Interestingly, even if the MOND equations approach Newtonian dynamics arbitrarily fast at high accelerations, this correction decreases only as a power of R/Rm. The effect appears in formulations of MOND as modified gravity, governed by generalizations of the Poisson equation. The MOND correction to the potential is a quadrupole field G*Pij*Ri*Rj, where R is th…
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 …
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…
Bimetric MOND (BIMOND) theories, propounded recently, predict peculiar gravitational interactions between matter and twin matter (TM). Twin matter is hypothetical matter that might couple directly only to the second metric of the theory. Considerations of cosmology in the BIMOND framework suggest that such TM might exist and copy matter in its attributes. Here I investigate the indirect interactions that BIMOND theories predict between nonrelativistic masses of matter and TM. The most salient result is that in the deep-MOND regime of the matter-TM-symmetric theories, TM behaves as if it has a …
There has been much interest in novel models of dark matter that exhibit interesting behavior on galactic scales. A primary motivation is the observed Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the quartic power of rotation speed. This scaling is not obviously accounted for by standard cold dark matter. This has prompted the development of dark matter models that exhibit some form of so-called MONDian phenomenology to account for this galactic scaling, while also recovering the success of cold dark matter on large scales. A beautiful example of this are the so-ca…
The concordance model of cosmology, LCDM, provides a satisfactory description of the evolution of the universe and the growth of large scale structure. Despite considerable effort, this model does not at present provide a satisfactory description of small scale structure and the dynamics of bound objects like individual galaxies. In contrast, MOND provides a unique and predictively successful description of galaxy dynamics, but is mute on the subject of cosmology. Here I briefly review these contradictory world views, emphasizing the wealth of distinct, interlocking lines of evidence that went…
Detailed knowledge of the different classes of stellar orbits that can be accommodated in a given galactic potential is a prerequisite when building self-consistent models using for instance the Schwazschild technique. Furthermore, observational properties of galaxies depend on what these classes of orbits are and on the presence of chaos in the systems. In the realistic case in which the starting point for modeling is not a gravitational potential, but an observed density distribution, we will require a gravitational theory to make the connection between the stars that we see and the movement…
MOND predicts a number of laws that galactic systems should obey irrespective of their complicated, haphazard, and mostly unknowable histories -- as Kepler's laws are obeyed by planetary systems. The main purpose of this work is to show how, and to what extent, these MOND laws follow from only the paradigm's basic tenets: departure from standard dynamics at accelerations a<~a0, and space-time scale invariance in the limit a<<a0. Such predictions will be shared by all MOND theories that embody these premises. This is important because we do not know which of the existing MOND theories, if any, …
MOND has limelighted the fact that Newtonian dynamics (ND) and general relativity (GR) have not been verified at accelerations below MOND's $a_0$. In particular, we do not know that all the principles underlying ND or GR apply below $a_0$. I discuss possible breakdown of general covariance (GC) in this limit. This resonates well with MOND, which hinges on accelerations. Relaxing GC affords more freedom in constructing MOND theories. I exemplify this with a simplified theory whose gravitational Lagrangian is $\mathcal{L}_M\propto \ell_M^{-2}\mathcal{F}(\ell_M^{2}\mathcal{R})$, where $\mathcal{R…
Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter. These systems should be entirely Newtonian according to standard dark-matter theories, while the predictions for MOND-like theories are distinctly different, if the various observational issues can be overcome. Here we provide an updated version of our 2019 study using the recent GAIA EDR3 data release: we select a large sample of 73 159 candidate wide binary s…
The MOND paradigm to the missing mass problem requires introducing a functional that is to be identified through observations and experiments. We consider AQUAL theory as a realization of the MOND. We show that the accurate value of the Earth GM measured by the Lunar Laser Ranging and that by various artificial Earth satellites, including the accurate tracking of the LAGEOS satellites, constrain this functional such that some of the chosen/proposed functional are refuted.
We propose a unified framework that reconciles the stunning success of MOND on galactic scales with the triumph of the LambdaCDM model on cosmological scales. This is achieved through the physics of superfluidity. Dark matter consists of self-interacting axion-like particles that thermalize and condense to form a superfluid in galaxies, with ~mK critical temperature. The superfluid phonons mediate a MOND acceleration on baryonic matter. Our framework naturally distinguishes between galaxies (where MOND is successful) and galaxy clusters (where MOND is not): dark matter has a higher temperature…
I describe the MOND paradigm, which posits a departure from standard physics below a certain acceleration scale. This acceleration as deduced from the dynamics in galaxies is found mysteriously to agree with the cosmic acceleration scales defined by the present day expansion rate and by the density of `dark energy'. I put special emphasis on phenomenology and on critical comparison with the competing paradigm based on classical dynamics plus cold dark matter. I also describe briefly nonrelativistic and relativistic MOND theories.
In this talk we present a novel framework that unifies the stunning success of MOND on galactic scales with the triumph of the LambdaCDM model on cosmological scales. This is achieved through the rich and well-studied physics of superfluidity. The dark matter and MOND components have a common origin, representing different phases of a single underlying substance. In galaxies, dark matter thermalizes and condenses to form a superfluid phase. The superfluid phonons couple to baryonic matter particles and mediate a MOND-like force. Our framework naturally distinguishes between galaxies (where MON…
