In this paper, we extend a paper by Milgrom (2009, MNRAS 398, 1023) dealing with the existence of a quasi-universal surface density for object of all mass and structure, if they are in the Newtonian regime, i.e., that their mean acceleration is larger than MOND typical acceleration $a_0$. This result is in agreement with Donato et al. (2009)'s results, claiming the existence of a quasi-universal surface density in all masses in galaxies. The Milgrom paper also predicts that objects with mean inner acceleration smaller than the values discussed do %es not show the quasi-universal behavior of the surface density discussed. In the present paper, we extend the result of Milgrom's paper, based on a point mass model, considering spiral galaxies, modelled with a double exponential disk. Similar to Milgrom's results, we find the existence of a universal surface density for galaxies with large surface density, and a different behavior for galaxies having small surface density.
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…
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 …
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 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…
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…
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…
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 …
Astronomers use to derive MOdified Newtonian Dynamics (MOND) rotation curves using the simple algebraic rule of calculating the acceleration as equal to the Newtonian acceleration ($a$) divided by some factor $μ(a)$. However, there are velocity differences between this simple rule and the calculation derived from more sophisticated MOND versions such as AQUAL or QMOND, created to expand MOND heuristic law and preserve the conservation of momentum, angular momentum, and energy, and follow the weak equivalence principle. Here we provide recipes based on Milgrom's proposal to calculate semianalyt…
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 …
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…
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…
In this talk I summarize a novel framework that unifies the stunning success of MOND on galactic scales with the triumph of the $Λ$CDM 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. This framework naturally distinguishes between galaxies (where MOND…
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…
Milgrom's Modified Newtonian dynamics (MOND) provides an efficient way to summarize phenomenology of galaxies which does not lean on the notion of dark matter; it has great predictive power. Here I briefly review MOND as well as its implementation as a nonrelativistic modified gravity theory, AQUAL. Gravitational lensing and cosmology call for a relativistic gravity theory different from general relativity if dark matter is to be avoided. In recent years such a theory, T$e$V$e$S, has emerged from the marriage of AQUAL with the timelike vector field of Sanders. I discuss its structure and some …
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 MOND (modified Newtonian dynamics)-based theories the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an "external field effect (EFE)". The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies the EFE can induce warps and modify the rotational speeds. Due to the non-linearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two non-relativistic Lagrangian theories of MOND: the `Aquadratic-Lagrangi…
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…
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 me…
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…
Some quantum-cosmic scaling relations indicate that the MOND acceleration parameter a_0 could be a fundamental quantity ruling the self-gravitating structures, ranging from stars and globular clusters up to superclusters of galaxies and the whole observed universe. We discuss such coincidence relations starting from the Dirac quantization condition ruling the masses of primordial black holes.
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…
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 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…
The premier alternative to the dark matter paradigm is modified gravity. Following an introduction to the relevant phenomenology of galaxies, I review the MOND paradigm, an effective summary of the observations which any theory must reproduce. A simple nonlinear modified gravity theory does justice to MOND at the nonrelativistic level, but cannot be elevated to the relativistic level in a unique way. I go in detail into the covariant tensor-vector-theory (TeVeS) which not only recovers MOND but can also deal in detail with gravitational lensing and cosmology. Problems with MOND and TeVeS at th…
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.
It is pointed out that MOND defines a fiducial specific angular momentum (SAM) for a galaxy of total (baryonic) mass $\mathcal{M}$: $j_M(\mathcal{M})\equiv\mathcal{M}^{3/4}(G^3/a_0)^{1/4}\approx 383(\mathcal{M}/10^{10}M_\odot)^{3/4}{\rm kpc~km/s}$. It plays important roles in disc-galaxy dynamics and evolution: It underlies scaling relations in virialized galaxies that involve their angular-momentum. I show that the disc SAM should be $j_D\approx[\langle r\rangle/r_M(\mathcal{M})]j_M(\mathcal{M})=[Σ_M/\langle Σ\rangle]^{1/2}j_M(\mathcal{M})$, with $\langle r\rangle$ the mean radius of the disc…
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…
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 foun…
