MOND Predictions Research Articles

Models of a modified-inertia formulation of MOND

Models of "modified-inertia" formulation of MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations of motion. Momentum, angular momentum, and energy are (nonlocally) defined, whose total values are conserved for isolated systems. The models make all the salient MOND predictions. Yet, they differ from existing "modified-gravity" formulations in some second-tier predictions. The models describe correctly the motion of a composite body in a low-acceleration field even when the internal accelerations of its constituents are high. They exhibit a MOND external field effect (EFE) that shows some important differences from what we have come to expect from modified-gravity versions: In one, simple example of the models, what determines the EFE, in the case of a dominant external field, is $\mu(\theta\langle a_{ex}\rangle/a_0)$, where $\mu(x)$ is the MOND `interpolating function' that describes rotation curves, compared with $\mu(a_{ex}/a_0)$ for presently-known modified-gravity formulations. The two main differences are that while $a_{ex}$ is the momentary value of the external acceleration, $\langle a_{ex}\rangle$ is a certain time average of it, and that $\theta>1$ is an extra factor that depends on the frequency ratio of the external- and internal-field variations. Only ratios of frequencies enter, and $a_0$ remains the only new dimensioned constant. For a system on a circular orbit in a galaxy (such as the vertical dynamics in a disc galaxy), the first difference disappears, since $\langle a_{ex}\rangle=a_{ex}$. But the $\theta$ factor can appreciably enhance the EFE in quenching MOND effects, over what is deduced in modified gravity. Some exact solutions are also described, such as for rotation curves, for an harmonic force, and the general, two-body problem, which in the deep-MOND regime reduces to a single-body problem.

Milky Way and M31 rotation curves: ΛCDM versus MOND

We analyze the existing rotation-curve data of the Milky Way and M31 galaxies that extends to very large distances and low accelerations. We find a systematic downward trend in the weak acceleration (large distances) segment of the radial acceleration. A similar downward trend has been noticed in the $\Lambda$CDM EAGLE simulation, while the deviation from the generic MOND prediction would need to be ascribed to an external field effect, or possibly a post facto selected acceleration function $\mu(x)$.

Internal kinematics of GAIA eDR3 wide binaries

Abstract Using the recent GAIA eDR3 catalogue we construct a sample of solar neighbourhood isolated wide binaries satisfying a series of strict signal-to-noise data cuts, exclusion of random association criteria and detailed colour-magnitude diagram selections, to minimize the presence of any kinematic contaminating effects having been discussed in the literature to date. Our final high-purity sample consists of 423 binary pairs within 130 pc of the sun and in all cases high-quality GAIA single-stellar fits for both components of each binary (final average RUWE values of 0.99), both also restricted to the cleanest region of the main sequence. We find kinematics fully consistent with Newtonian expectations for separations, s, below 0.009 pc, with relative velocities scaling with ΔV∝s−1/2 and a total binary mass, Mb, velocity scaling consistent with $\Delta V \propto M_{b}^{1/2}$. For the separation region of s > 0.009 pc we obtain significantly different results, with a separation independent ΔV ≈ 0.5 km/s and a $\Delta V \propto M_{b}^{0.24 \pm 0.21}$. This situation is reminiscent of the low acceleration galactic baryonic Tully-Fisher phenomenology, and indeed, the change from the two regimes we find closely corresponds to the a ≲ a0 transition. These results are at odds not only with Newtonian expectations, but also with MOND predictions, where the presence of an external field effect implies only small deviations from Newtonian dynamics are expected for Solar Neighbourhood wide binaries.

On the absence of a universal surface density, and a maximum Newtonian acceleration in dark matter haloes: Consequences for MOND

Abstract We study the dark matter (DM) surface density using the SPARC sample and compare it to Donato et al. (2009) result. By means of MCMC method, we infer the best-fitting parameters for each galaxy. We reobtain the scaling relation between the surface density and luminosity, and several other scaling laws relating the dark matter halo properties to that of the galactic disc properties. We conclude, in contrast with Donato et al. (2009), that the dark matter surface density is not a universal (constant) quantity but correlates with the luminosity as well as with other galactic disc properties. A derived posterior probability distribution of ρ 0 r 0 shows that the null hypothesis of constancy is rejected at a very high confidence level. These results leave little room for the claimed universality of dark matter surface density. Since MOND has strong prediction on the surface density (Milgrom, 2009), we compared our result with those predictions, finding that MOND predictions are violated by data. To strengthen the previous result, we compared our results to another prediction of MOND (Milgrom and Sanders, 2005), the existence of a maximum Newtonian dark matter acceleration in the halo. Also in this case, MOND predictions are in contradiction with data. The dark matter Newtonian acceleration correlates with all the previously presented galactic disc properties, and data are distributed outside the bound predicted by Milgrom and Sanders (2005). We also find that the null hypothesis (constancy of DM Newtonian acceleration) is rejected at a very high confidence level.

Discussing the first velocity dispersion profile of an ultra-diffuse galaxy in MOND

Using Jeans modeling, we calculated the velocity dispersion profile of the ultra-diffuse galaxy (UDG) Dragonfly 44 in MOND. For the nominal mass-to-light ratio from the literature and an isotropic profile, the agreement with the data is excellent near the center of the galaxy. However, in modified gravity, close to the cluster core, the gravitational environment should bring the galaxy back toward Newtonian behavior. The success of the isolated MOND prediction for the central velocity dispersion could then mean that the galaxy is at a great distance (≫5 Mpc) from the cluster core, as hinted by the fact that nearby UDGs share similar velocities with a dispersion well below that of the cluster itself. There is, however, a 2σ tension in the outer part of the UDG due to an increase in the observed dispersion profile with respect to the flat MOND prediction. This deviation could simply be a measurement error. Other possibilities could be, for a UDG far from the cluster, a higher-than-nominal baryonic mass with a tangentially anisotropic dispersion profile or it could even be a dark baryonic halo. If the UDG is closer to the cluster core, the deviation could be a sign that it is in the process of disruption.

MOND and the dynamics of NGC 1052−DF2

The dwarf galaxy NGC1052-DF2 has recently been identified as potentially lacking dark matter. If correct, this could be a challenge for MOND, which predicts that low surface brightness galaxies should evince large mass discrepancies. However, the correct prediction of MOND depends on both the internal field of the dwarf and the external field caused by its proximity to the giant elliptical NGC1052. Taking both into consideration under plausible assumptions, we find $\sigma_{\rm MOND} = 13.4^{+4.8}_{-3.7}\;\mathrm{km}\,\mathrm{s}^{-1}$. This is only marginally higher than the claimed 90\% upper limit on the velocity dispersion ($\sigma < 10.5\;\mathrm{km}\,\mathrm{s}^{-1}$), and compares well with the observed root mean square velocity dispersion ($\sigma = 14.3\;\mathrm{km}\,\mathrm{s}^{-1}$). We also discuss a few caveats on both the observational and theoretical side. On the theory side, the internal virialization time in this dwarf may be longer that the time scale of variation of the external field. On the observational side, the paucity of data and their large uncertainties call for further analysis of the velocity dispersion of NGC1052-DF2, to check whether it poses a challenge to MOND or is a success thereof.

On the Dark Matter Column Density in Haloes

We study the correlation between the central surface density and the halo core radius of the dark matter haloes of galaxies and clusters of galaxies. We find that the surface density within the halo characteristic radius r* is not an universal quantity as claimed by some authors (e.g., [1]), but it correlates with several physical quantities (e.g., the halo mass M200 and the magnitude M B ). The slope of the surface density—mass relation is 0.18 ± 0.05, leaving small room to the possibility of a constant surface density. Finally, we compare the results with the MOND prediction.

The Surface Density of Haloes

AbstractWe study the correlation between the central surface density and the core radius of the dark matter haloes of galaxies and clusters of galaxies. We find that the surface density within the halo characteristic radius r* is not a universal quantity as claimed by some authors (e.g., Milgrom 2009), but it correlates with several physical quantities (e.g., the halo mass M200, and the magnitude MB). The slope of the surface density-mass relation is 0.18 ± 0.05, leaving small room to the possibility of a constant surface density. Finally, we compare the results with MOND predictions.

MOND prediction of a new giant shell in the elliptical galaxy NGC 3923

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 our study by assuming more general models for the gravitational potential to verify the prediction of the new shell and to estimate its position. Methods. We tested the consistency of the shell radial distribution observed in NGC 3923 with a wide variety of MOND potentials of the galaxy. The potentials differed in the mass-to-light ratio and in distance to the galaxy. We considered different MOND interpolation functions, values of the acceleration constant $a_0$, and density profiles of the galaxy. We verified the functionality of our code on a Newtonian self-consistent simulation of the formation of a shell galaxy. Results. Our method reliably predicts that exactly one new outermost shell exists at a galactocentric radius of about 1900$^{\prime\prime}$ ($\sim$210 kpc) on the southwestern side of the galaxy. Its estimated surface brightness is about 28 mag arcsec$^{-2}$ in $B$ - a value accessible by current instruments. This prediction enables a rare test of MOND in an elliptical down to an acceleration of $a_0/10$. The predictive power of our method is verified by reconstructing the position of the largest known shell from the distribution of the remaining shells.

General virial theorem for modified-gravity MOND

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 in the nonrelativistic, low-acceleration limit. This implies space-dilatation invariance of the static, gravitational-field equations, which, in turn, leads to the above point-mass virial relation. Thus, the various MOND predictions and tests based on this relation hold in any modified-gravity MOND theory. Since we do not know that any of the existing MOND theories point in the right direction, it is important to identify such predictions that hold in a much larger class of theories. Among these predictions are the MOND two-body force for arbitrary masses, and a general mass-velocity-dispersion relation of the form sigma^2=(2/3)(MGa0)^{1/2}[1-\sum_p (m_p/M)^{3/2}], where M is the total mass.

ANDROMEDA DWARFS IN LIGHT OF MODIFIED NEWTONIAN DYNAMICS

We compare the recently published velocity dispersions for seventeen Andromeda dwarf spheroidals with estimates of the MOND predictions, based on the luminosities of these dwarfs, with reasonable stellar M/L values, and no dark matter. We find that the two are consistent within the uncertainties. We further predict the velocity dispersions of another ten dwarfs for which only photometric data are currently available.

MOND--particularly as modified inertia

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 depend on the full trajectory of a system, not only on its instantaneous state, as in MG theories. This may lead to rather different predictions for, e.g., the external-field effect (EFE): A subsystem, such as a globular cluster or a dwarf galaxy, moving in the field of a mother galaxy, or a galaxy in a cluster, may be subject to an EFE that depends on the accelerations all along its orbit, not only on the instantaneous value. And, it is even possible to construct MI theories with practically no EFE. Other predictions that may differ are also discussed. Since we do not yet have a full fledged, modified-inertia formulation, simple, heuristic models have been used to demonstrate these points.

Structure and dynamics of giant low surface brightness galaxies

Giant low surface brightness (GLSB) galaxies are commonly thought to be massive, dark matter dominated systems. However, this conclusion is based on highly uncertain rotation curves. We present here a new study of two prototypical GLSB galaxies: Malin 1 and NGC 7589. We re-analysed existing H I observations and derived new rotation curves, which were used to investigate the distributions of luminous and dark matter in these galaxies. In contrast to previous findings, the rotation curves of both galaxies show a steep rise in the central parts, typical of high surface brightness (HSB) systems. Mass decompositions with a dark matter halo show that baryons may dominate the dynamics of the inner regions. Indeed, a “maximum disk” fit gives stellar mass-to-light ratios in the range of values typically found for HSB galaxies. These results, together with other recent studies, suggest that GLSB galaxies are systems with a double structure: an inner HSB early-type spiral galaxy and an outer extended LSB disk. We also tested the predictions of MOND: the rotation curve of NGC 7589 is reproduced well, whereas Malin 1 represents a challenging test for the theory.

DARK FLUID: A UNIFIED FRAMEWORK FOR MODIFIED NEWTONIAN DYNAMICS, DARK MATTER, AND DARK ENERGY

Empirical theories of Dark Matter like MOND gravity and of Dark Energy like f(R) gravity were motivated by astronomical data. But could these theories be branches rooted from a more general hence natural framework? Here we propose the natural Lagrangian of such a framework based on simple dimensional analysis and co-variant symmetry requirements, and explore various outcomes in a top-down fashion. Our framework preserves the co-variant formulation of GR, but allows the expanding physical metric be bent by a single new species of Dark Fluid flowing in space-time. Its non-uniform stress tensor and current vector are simply functions of a vector field of variable norm, resembling the 4-vector electromagnetic potential description for the photon fluid, but is dark (e.g., by very early decoupling from the baryon-radiation fluid). The Dark Fluid framework naturally branches into a continuous spectrum of theories with Dark Energy and Dark Matter effects, including the $f(R)$ gravity, TeVeS-like theories, Einstein-Aether and $\nu\Lambda$ theories as limiting cases. When the vector field degenerates into a pure Higgs-like scalar field, we obtain the physics for inflaton and quintessence. In this broad setting we emphasize the non-constant dynamical field behind the cosmological constant effect, and highlight plausible corrections beyond the classical MOND predictions. Choices of parameters can be made to pass BBN, PPN, and causality constraints. The Dark Fluid is inspired to unify/simplify the astronomically successful ingredients of previous constructions: the desired effects of inflaton plus quintessence plus Cold DM particle fields or MOND-like scalar field(s) are shown largely achievable by one vector field only.

The central surface density of ‘dark haloes’ predicted by MOND

Prompted by the recent claim, by Donato et al., of a quasi-universal central surface density of galaxy dark matter halos, I look at what MOND has to say on the subject. MOND, indeed, predicts a quasi-universal value of this quantity for objects of all masses and of any internal structure, provided they are mostly in the Newtonian regime; i.e., that their mean acceleration is at or above a0. The predicted value is qSm, with Sm= a0/2 pi G= 138 solar masses per square parsec for the nominal value of a0, and q a constant of order 1 that depends only on the form of the MOND interpolating function. This gives in the above units log(Sm)=2.14, which is consistent with that found by Doanato et al. of 2.15+-0.2. MOND predicts, on the other hand, that this quasi-universal value is not shared by objects with much lower mean accelerations. It permits halo central surface densities that are arbitrarily small, if the mean acceleration inside the object is small enough. However, for such low-surface-density objects, MOND predicts a halo surface density that scales as the square root of the baryonic one, and so the range of the former is much compressed relative to the latter. This explains, in part, the finding of Donato et al. that the universal value applies to low acceleration systems as well. Looking at literature results for a number of the lowest surface-density disk galaxies with rotation-curve analysis, I find that, indeed, their halo surface densities are systematically lower then the above "universal" value. The prediction of Sm as an upper limit, and accumulation value, of halo central surface densities, pertains, unlike most other MOND predictions, to a pure "halo" property, not to a relation between baryonic and "dark matter" properties.

Loss of Mass and Stability of Galaxies in Modified Newtonian Dynamics

The self-binding energy and stability of a galaxy in MOND-based gravity are curiously decreasing functions of its center-of-mass acceleration (of the order of 10-12 to 10-10 m s-2) toward neighboring mass concentrations. A tentative indication of this breaking of the strong equivalence principle in field is the RAVE-observed escape speed in the Milky Way. Another consequence is that satellites of field will move on nearly Keplerian orbits at large radii (100-500 kpc), with a declining speed below the asymptotically constant naive MOND prediction. But the consequences of an environment-sensitive gravity are even more severe in clusters, where member accelerate fast; no dark halo-like potential is present to support galaxies, meaning that extended axisymmetric disks of gas and stars are likely unstable. These predicted reappearances of asymptotic Keplerian velocity curves and disappearances of stereotypic galaxies in clusters are falsifiable with targeted surveys.

Mass Distribution and Bulge Formation in the Milky Way Galaxy

In its first part, this paper summarizes recent work on the mass and shape of the Galactic dark halo. The second part presents a review of the large-scale structure of the Milky Way, and of the evidence that the inner Galaxy is dominated by baryonic matter. This is briefly compared with the predictions of LCDM and MOND. Finally, a summary is given of bulge formation from clumpy, gas-rich disks, a process which may give rise to old, disk-like, alpha-rich bulges similar to the Galactic bulge.

MOND predictions of ‘halo’ phenomenology in disc galaxies

We examine two corollaries of MOND pertaining to properties of the equivalent dark matter halo. MOND predicts for pure exponential discs a tight relation involving the halo and disc scalelengths and the mean acceleration in the disc, which we find to test favourably against the Verheijen sample of Ursa Major galaxies. A correlation between halo and disc length-scales is also apparent when the `maximum disc' contribution is assumed, but we demonstrate that this follows from the more general MOND prediction. The second MOND prediction involves the existence of a maximum halo acceleration, which also tests favourably against the Ursa Major sample for different assumptions on the disc contribution.

Do Modified Newtonian Dynamics Follow from the Cold Dark Matter Paradigm?

In a recent paper, Kaplinghat and Turner (2001) (KT) advertise that MOND can be derived naturally in the CDM paradigm. They actually proceed to produce a more limited result: Every galaxy should have a transition radius, $r_t$, below which baryons dominate, and above which dark matter (DM) takes over; the acceleration at $r_t$ is nearly the same for all galaxies; and due to a coincidences this is of order $a_0\sim cH_0$. This follows from their tacit, intermediate result, whereby CDM halos of galaxies have a very nearly universal acceleration profile $a(r)\approx v^2(r)/r\approx A\hat a(r/\ell)$, where A is universal, and only the scale $\ell$ varies from halo to halo. (This remains so when baryons are added because they assume a universal baryon-collapse factor.) The KT scenario is phenomenologically wrong--observed galaxies are simply not like that. For example, it precludes altogether the existence of LSB galaxies, in which the acceleration is everywhere smaller than $a_0$. The phenomenologically sound outcome--i.e., the role of $a_0$ as a transition acceleration in high-surface-brightness galaxies--pertains to only a small part of the statement of MOND. There are several other, independent roles that $a_0\sim cH_0$ plays in MOND phenomenology, and other predictions of MOND, not related to the value of $a_0$, that are not explainable in the KT scenario. The results of KT also disagree with those of CDM simulations, which, as they now stand, do not reproduce any aspect of MOND phenomenology.

The shape of ‘dark matter’ haloes of disc galaxies according to MOND

Analyses of halo shapes for disc galaxies are said to give incongruous results. I point out that the modified dynamics (MOND) predicts for disc galaxies a distribution of fictitious dark matter that comprises two components: a pure disc and a rounder halo. The former dominates the true disc in regions of small accelerations, where it controls the z-dynamics in the disc (disc flaring etc.); it has a finite total mass. It also dominates the round component near the centre where the geometry is nearly planar. The second component controls motions far from the plane, has a total enclosed mass that diverges linearly with radius, and determines the rotation curve at large radii. Its ellipticity may be appreciable at small radii but vanishes asymptotically. This prediction of MOND differs from what one expects from galaxy-formation scenarios with dark matter. Analyses to date, which, as they do, assume one component--usually with a constant ellipticity, perforce give conflicting results for the best-value ellipticity, depending on whether they probe the disc or the sphere, small radii or large ones.