MOND Research Articles

Accelerated Structure Formation: The Early Emergence of Massive Galaxies and Clusters of Galaxies

Galaxies in the early Universe appear to have grown too big too fast, assembling into massive, monolithic objects more rapidly than anticipated in the hierarchical Lambda cold dark matter (ΛCDM) structure formation paradigm. The available photometric data are consistent with there being a population of massive galaxies that form early (z ≳ 10) and quench rapidly over a short (≲1 Gyr) timescale, consistent with the traditional picture for the evolution of giant elliptical galaxies. Similarly, kinematic observations as a function of redshift show that massive spirals and their scaling relations were in place at early times. Explaining the early emergence of massive galaxies requires either an extremely efficient conversion of baryons into stars at z > 10 or a more rapid assembly of baryons than anticipated in ΛCDM. The latter possibility was explicitly predicted in advance by modified Newtonian dynamics (MOND). We discuss some further predictions of MOND, such as the early emergence of clusters of galaxies and early reionization.

Jeans analysis in fractional gravity

It has recently been demonstrated (Giusti in Phys Rev D 101:124029, 2020, https://doi.org/10.1103/PhysRevD.101.124029) that characteristic traits of Milgrom’s modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scenarios. Here, we investigate its implications on Jeans gravitational instability and related phenomena. We examine scenarios involving classical matter confined by gravity and extend our analysis to the quantum domain, through a Schrödinger–Newton approach. We also derive a generalized Lane–Emden equation associated with fractional gravity. Through comparisons between the derived stability criteria and the observed stability of Bok globules, we establish constraints on the theory’s parameters to align with observational data.

Elucidating the z-dependence of the MOND acceleration (a0) within the scale invariant vacuum (SIV) paradigm

ABSTRACT In a recent paper: “On the time dependency of $a_0$” the authors claim that they have tested “one of the predictions of the Scale Invariant Vacuum (SIV) theory on MOND” by studying the dependence of the Modified Newtonian Dynamics (MOND) acceleration at two data sets, low-z ($3.2\times 10^{-4}\le z\le 3.2\times 10^{-2}$) and high-z ($0.5\le z\le 2.5$). They claim “both samples show a dependency of $a_0$ from z”. Here, the work mentioned above is revisited. The explicit analytic expression for the z-dependence of the $a_0$ within the SIV theory is given. Furthermore, the first estimates of the $\Omega _m$ within SIV theory give $\Omega _{m}=0.28\pm 0.04$ using the low-z data only, while a value of $\Omega _{m}=0.055$ is obtained using both data sets. This much lower $\Omega _m$ leaves no room for non-baryonic matter! Unlike in the mentioned paper above, the slope in the z-dependence of $A_0=\log _{10}(a_0)$ is estimated to be consistent with zero Z-slope for the two data sets. Finally, the statistics of the data are consistent with the SIV predictions; in particular, the possibility of change in the sign of the slopes for the two data sets is explainable within the SIV paradigm; however, the uncertainty in the data is too big for the clear demonstration of a z-dependence yet.

Field equation of thermodynamic gravity and galactic rotational curves

The rotational velocity curve (RC) of galaxy NGC 3198 is modelled in various theoretical frameworks: Thermodynamic Gravity (TG) is compared to Dark Matter (DM) and Modified Newtonian Dynamics (MOND). The nonlinear gravitational field equation of TG is solved using the baryonic mass density as the source of the gravitational field. In this paper, first, a dissipation motivated numerical method is verified with the help of exact solutions. Then, the obtained optimal velocity curve is compared to DC14 model DM and MOND EFE (Modified Newtonian Dynamics-External Field Effect aspect) parametrisations for the RC of the galaxy.

Critical analysis of replacing dark matter and dark energy with a model of stochastic spacetime

We analyze consequences of trying to replace dark matter and dark energy with models of stochastic spacetime. In particular, we analyze the model put forth by ref. [1], in which it is claimed that “post-quantum classical gravity” (PQCG), a stochastic theory of gravity, leads to modified Newtonian dynamics (MOND) behavior on galactic scales that reproduces galactic rotation curves, and leads to dark energy. We show that this analysis has four basic problems: (i) the equations of PQCG do not lead to a new large scale force of the form claimed in the paper, (ii) the form claimed is not of the MONDian form anyhow and so does not correspond to observed galactic dynamics, (iii) the spectrum of fluctuations is very different from observations, and (iv) we also identify some theoretical problems in these models.

Galaxy clusters in Milgromian dynamics: Missing matter, hydrostatic bias, and the external field effect

We study the mass distribution of galaxy clusters in Milgromian dynamics, or modified Newtonian dynamics (MOND). We focus on five galaxy clusters from the X-COP sample, for which high-quality data are available on both the baryonic mass distribution (gas and stars) and internal dynamics (from the hydrostatic equilibrium of hot gas and the Sunyaev–Zeldovich effect). We confirm that galaxy clusters require additional ‘missing matter’ in MOND, although the required amount is drastically reduced with respect to the non-baryonic dark matter in the context of Newtonian dynamics. We studied the spatial distribution of the missing matter by fitting the acceleration profiles of the clusters with a Bayesian method, finding that a physical density profile with an inner core and an outer r−4 decline (giving a finite total mass) provide good fits within ∼1 Mpc. At larger radii, the fit results are less satisfactory but the combination of the MOND external field effect and hydrostatic bias (quantified as 10%–40%) can play a key role. The missing mass must be more centrally concentrated than the intracluster medium (ICM). For relaxed clusters (A1795, A2029, A2142), the ratio of missing-to-visible mass is around 1 − 5 at R ≃ 200 − 300 kpc and decreases to 0.4 − 1.1 at R ≃ 2 − 3 Mpc, showing that the total amount of missing mass is smaller than or comparable to the ICM mass. For clusters with known merger signatures (A644 and A2319), this global ratio increases up to ∼5 but may indicate out-of-equilibrium dynamics rather than actual missing mass. We discuss various possibilities regarding the nature of the extra mass, in particular ‘missing baryons’ in the form of pressure-confined cold gas clouds with masses of < 105 M⊙ and sizes of < 50 pc.

A critical review of recent Gaia wide binary gravity tests

ABSTRACT Over the last couple of years, the appearance of the third data release from the Gaia satellite has triggered various wide binary low acceleration gravity tests. Wide binaries with typical total masses $\approx 1.0 - 1.6\,\mathrm{ M}_{\odot }$ and separations above a few thousand au probe the low acceleration $a \lesssim a_{0}$ regime, where at galactic and larger scales gravitational anomalies typically attributed to the presence of an as yet undetected dark matter component appear, where $a_{0} \approx 1.2\times 10^{-10}$ m s$^{-2}$ is the acceleration scale of Modified Newtonian Dynamics (MOND). Thus, studies of the relative velocities and separations on the plane of the sky, $v_{2\mathrm{ D}}$ and $s_{2\mathrm{ D}}$, respectively, of wide binary stars extending to separations above a few kau, provide an independent approach on the empirical study of gravity in the interesting $a \lesssim a_{0}$ acceleration range. Two independent groups, through complementary approaches, have obtained evidence for a departure from Newtonian predictions in the low acceleration regime, in consistency with MOND expectations for wide binary orbits in the Solar Neighbourhood. Two other groups however, have instead reported results showing a clear preference for Newtonian gravity over various MOND alternatives tested, over the same low acceleration regime. We here take a critical look at the various studies in question, from sample selection to statistical treatment of the wide binary relative velocities obtained. We discover a couple of critical problems in the formal design and statistical implementation shared by the two latter groups, and show explicitly how these yield biased conclusions.

Globular cluster orbital decay in dwarf galaxies with MOND and CDM: Impact of supernova feedback

Dynamical friction works very differently for Newtonian gravity with dark matter and in modified Newtonian dynamics (MOND). While the absence of dark matter considerably reduces the friction in major galaxy mergers, analytic calculations indicate the opposite for very small perturbations, such as globular clusters (GCs) sinking in dwarf galaxies. Here, we study the decay of GCs in isolated gas-rich dwarf galaxies using simulations with the Phantom of Ramses code, which enables both the Newtonian and the QUMOND MOND gravity. We modeled the GCs as point masses, and we simulated the full hydrodynamics, with star formation and supernovae feedback. We explored whether the fluctuations in gravitational potential caused by the supernovae can prevent GCs from sinking toward the nucleus. For GCs of typical mass or lighter, we find that this indeed works in both Newtonian and MOND simulations. The GC can even make a random walk . However, we find that supernovae cannot prevent massive GCs ($M from sinking in MOND. The resulting object looks similar to a galaxy with an offset core, which embeds the sunk GC. The problem is much milder in the Newtonian simulations. This result thus favors Newtonian over QUMOND gravity, but we note that it relies on the correctness of the difficult modeling of baryonic feedback. We propose that the fluctuations in the gravitational potential could be responsible for the thickness of the stellar disks of dwarf galaxies and that strong supernova winds in modified gravity can transform dwarf galaxies into ultra-diffuse galaxies.

Simulations of cluster ultra-diffuse galaxies in MOND

Ultra-diffuse galaxies (UDGs) in the Coma cluster have velocity dispersion profiles that are in full agreement with the predictions of modified Newtonian dynamics (MOND) in isolation. However, the external field effect (EFE) from the cluster seriously undermines this agreement. It has been suggested that this could be related to the fact that UDGs are out-of-equilibrium objects whose stars have been heated by the cluster tides or that they recently fell onto the cluster on radial orbits; thus, their velocity dispersion may not reflect the EFE at their instantaneous distance from the cluster centre. In this work, we simulated UDGs within the Coma cluster in MOND, using the Phantom of Ramses ( por ) code. We show that if UDGs are initially at equilibrium within the cluster, tides are not sufficient to increase their velocity dispersions to values as high as the observed ones. On the other hand, if they are on a first radial infall onto the cluster, they can keep high-velocity dispersions without being destroyed until their first pericentric passage. We conclude that in the context of MOND, and without alterations (e.g. a screening of the EFE in galaxy clusters or much higher baryonic masses than currently estimated), we find that UDGs must be out-of-equilibrium objects on their first infall onto the cluster, .

Apparent dark matter inspired by the Einstein equation of state

The purpose of this article is twofold. First, by means of Padmanabhan's proposal on the emergence nature of gravity, we recover the ΛCDM model and the effect of the dark matter in the context of cosmology. Toward this goal, we use the key idea of Padmanabhan that states cosmic space emerges as the cosmic time progresses and links the emergence of space to the difference between the number of degrees of freedom on the boundary and in the bulk. Interestingly enough, we show that the effect of the cold dark matter in the cosmological setup can be understood by assuming an interaction between the numbers of degrees of freedom in the bulk. In the second part, we follow Jacobson's argument and obtain the modified Einstein field equations with additional dark matter component emerging due to the interaction term between dark energy and baryonic matter related by , where α is a coupling constant. Finally, a correspondence with the Yukawa cosmology is pointed out, and the role of massive gravitons as a possibility in explaining the nature of the dark sector as well as the theoretical origin of the Modified Newtonian Dynamics (MOND) are addressed. We speculate that the interaction coupling α fundamentally measures the entanglement between the gravitons and matter fields and there exists a fundamental limitation in measuring the gravitons wavelength.

Testing MOND using the dynamics of nearby stellar streams

The stellar halo of the Milky Way is built up at least in part from debris from past mergers. The stars from these merger events define substructures in phase space, for example in the form of streams, which are groups of stars that move on similar trajectories. The nearby Helmi streams discovered more than two decades ago are a well-known example. Using 6D phase-space information from the Gaia space mission, recent work showed that the Helmi streams are split into two clumps in angular momentum space. This substructure can be explained and sustained in time if the dark matter halo of the Milky Way takes a prolate shape in the region probed by the orbits of the stars in the streams. Here, we explore the behaviour of the two clumps identified in the Helmi streams in a modified Newtonian dynamics (MOND) framework to test this alternative model of gravity. We performed orbit integrations of Helmi streams member stars in a simplified MOND model of the Milky Way and using the more sophisticated phantom of RAMSES simulation framework. We find with both approaches that the two Helmi streams clumps do not retain their identity and dissolve after merely Myr. This extremely short timescale would render the detection of two separate clumps very unlikely in MONDian gravity. The observational constraints provided by the streams, which MOND fails to reproduce in its current formulation, could potentially also be used to test other alternative gravity models.

Einstein-Gauss-Bonnet dark matter halo: negative masses, rotation curves and the origin of dark matter effects

This work presents a novel approach to address the longstanding challenge posed by the rotation curves of galaxies and the associated missing mass problem. Utilizing the four-dimensional modified gravity framework of Einstein-Gauss-Bonnet (EGB), we develop a new model that integrates the concept of dark matter featuring negative mass due to the Gauss-Bonnet term. Our methodology involves using the action of EGB with boundary terms to derive the Israel junction condition, allowing the formulation of a model featuring a spherical dark halo. The mass expression of this dark halo exhibits a remarkable proportionality to the radius r at large distances, forming the basis for subsequent analyses. The model’s implications extend to the dynamics of the early Universe, where we introduce a dynamic scalar field classified as Chameleon. Posting this scalar field as the origin of dark matter effects, we establish a crucial link between the coupling constant α and the scalar field through Z2 symmetry breaking via the effective potential. This connection enables a subtle description of velocity, reminiscent of Modified Newtonian Dynamics (MOND), providing insights into the gravitational interplay and dark matter dynamics. A pivotal aspect of our study involves a particular comparison of the model’s predictions with observational data sourced from SPARC datasets. The alignment of our theoretical outcomes with empirical evidence underscores the model’s efficiency and its potential contribution to our understanding of galactic rotation dynamics.

Exploring the nature of dark matter with the extreme galaxy AGC 114905

i ) morphology, remains somewhat uncertain. We present unmatched ultra-deep optical imaging of AGC 114905 reaching surface brightness limits $ r,lim 32$ mag/arcsec$^2$ ($3 10 arcsec times 10 arcsec) obtained with the 10.4 m Gran Telescopio Canarias. With the new imaging, we characterise the galaxy's optical morphology, surface brightness, colours, and stellar mass profiles in great detail. The stellar disc has a similar extent to the i disc, presents spiral arms-like features, and shows a well-defined edge. Stars and gas have a similar morphology, and crucially, we find an inclination of $31 in agreement with the previous determinations. We revisit the rotation curve decomposition of the galaxy, and we explore different mass models in the context of CDM, self-interacting dark matter (SIDM), fuzzy dark matter (FDM) or Modified Newtonian dynamics (MOND). We find that the last does not fit the circular speed of the galaxy, while CDM only does so with dark halo parameters rarely seen in cosmological simulations. Within the uncertainties, SIDM and FDM remain feasible candidates to explain the observed kinematics of AGC 114905.

Testing MOND on Small Bodies in the Remote Solar System

Modified Newtonian dynamics (MOND), which postulates a breakdown of Newton's laws of gravity/dynamics below some critical acceleration threshold, can explain many otherwise puzzling observational phenomena on galactic scales. MOND competes with the hypothesis of dark matter, which successfully explains the cosmic microwave background and large-scale structure. Here we provide the first solar system test of MOND that probes the subcritical acceleration regime. Using the Bekenstein–Milgrom “aquadratic Lagrangian” (or AQUAL) formulation, we simulate the evolution of myriads of test particles (planetesimals or comets) born in the trans-Neptunian region and scattered by the giant planets over the lifetime of the Sun to heliocentric distances of 102–105 au. We include the effects of the Galactic tidal field and passing stars. While Newtonian simulations reproduce the distribution of binding energies of long-period and Oort-cloud comets detectable from Earth, MOND-based simulations do not. This conclusion is robust to plausible changes in the migration history of the planets, the migration history of the Sun, the MOND transition function, effects of the Sun's birth cluster, and the fading properties of long-period comets. For the most popular version of AQUAL, characterized by a gradual transition between the Newtonian and MOND regimes, our MOND-based simulations also fail to reproduce the orbital distribution of trans-Neptunian objects in the detached disk (perihelion q > 38 au). Our results do not rule out some MOND theories more elaborate than AQUAL, in which non-Newtonian effects are screened on small spatial scales, at small masses, or in external gravitational fields comparable in strength to the critical acceleration.

Geometric interpretation of Tensor-Vector-Scalar theory in a Kaluza–Klein reference fluid

Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully–Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the cosmic microwave background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, a generalized TeVeS from Kaluza–Klein theory in one extra dimension is derived as a consequence of n = 0 Kaluza–Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D Arnowitt–Deser–Misner formalism enforced by a reference fluid as in the Isham-Kuchař method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza–Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles, the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza–Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it provides a symmetry breaking motivation for the interpolating function in MOND.

Aether Scalar Tensor (AeST) theory: quasistatic spherical solutions and their phenomenology

ABSTRACT There have been many efforts in the last three decades to embed the empirical Modified Newtonian Dynamics (MOND) programme into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution of the primordial fluctuations and the formation of large-scale structures in the Universe. The Aether Scalar Tensor theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here, we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealized case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND, and a third regime characterized by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealized case of spherical isolated sources.

Simulations of galaxies in an expanding Universe with modified Newtonian dynamics (MOND) and with modified gravitational attractions (MOGA)

The stability of galaxies is either explained by the existence of dark matter or caused by a modification of Newtonian acceleration (MOND). Here, we show that the modification of the Newtonian dynamics can equally well be obtained by a modification of Newton’s law of universal gravitational attraction (MOGA) when Newton’s inverse square attraction from a distant object is replaced with an inverse attraction. This modification is often proposed in the standard model, and with the modification of the attraction caused by dark matter. The recently derived algorithm, Eur Phys J Plus, 137:99, 2022; Class Quantum Grav, 39:225006, 2022, for classical celestial dynamics is used to simulate models of the Milky Way in an expanding universe and with either MOND or MOGA. The simulations show that the galaxies with MOND dynamics are unstable, whereas MOGA stabilizes the galaxies. The rotation velocities for objects in galaxies with classical Newtonian dynamics decline inversely proportional to the square root of the distance r to the center of the galaxy. But the rotation velocities is relatively independent of r for MOGA and qualitatively in agreement with experimentally determined rotation curves for galaxies in the Universe. The modification of the attractions may be caused by the masses of the objects in the central part of the galaxy by the lensing of gravitational waves from far-away objects in the galaxy.

Hooks & Bends in the radial acceleration relation: discriminatory tests for dark matter and MOND

ABSTRACT The radial acceleration relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, atot(r), with that accounted for by baryons at the same radius, abar(r). The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the cosmological constant + cold dark matter (ΛCDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of M⋆ ≃ 107–11 M⊙ to study the RAR in the FIRE-2 simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that ‘hook’ down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our ΛCDM-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit ‘bends’ off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach atot ≈ abar/fb, where fb is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and ΛCDM.

Towards galaxy cluster models in Aether-Scalar-Tensor theory: isothermal spheres and curiosities

The Aether-Scalar-Tensor (AeST) theory is an extension of General Relativity (GR) which can support Modified Newtonian Dynamics (MOND) behaviour in its staticweak-field limit, and cosmological evolution resembling ΛCDM.We consider static spherically symmetric weak-field solutions in this theory and show that the resulting equations can be reduced to a single equation for the gravitational potential.The reduced equation has apparent isolated singularities at the zeros of the derivative of the potential and we show how these are removedby evolving, instead, the canonical momentum of the corresponding Hamiltonian system that we find. We construct solutions in three cases: (i) in vacuum outside a bounded spherical object, (ii) within an extended prescribed source, and (iii) for an isothermal gas in hydrostatic equilibrium, serving as a simplified model for galaxy clusters.We show that the oscillatory regime that follows the Newtonian and MOND regimes, obtained in previous works in the vacuum case, also persists for isothermal spheres, and we show that the gas density profiles in AeST can become more compressed than their Newtonian or MOND counterparts.We construct the Radial Acceleration Relation (RAR) in AeST for isothermal spheres and find that it can display a peak, an enhancement with respect to the MOND RAR, at an acceleration range determined by the value of the AeST weak-field mass parameter, the mass of the system and the boundary value of the gravitational potential. For lower accelerations, the AeST RAR drops below the MOND expectation,as if there is a negative mass density. Similar observational features of the galaxy cluster RAR have been reported. This illustrates the potential of AeST to address the shortcomings of MOND in galaxy clusters, but a full quantitative comparison with observations will require going beyond the isothermal case.

Dissipationless collapse and the dynamical mass–ellipticity relation of elliptical galaxies in Newtonian gravity and MOND

Context. Recent observational studies proposed an empirical relation between the dark-to-total mass ratio and ellipticity in elliptical galaxies based on their observed total dynamical mass-to-light ratio data M/L = (14.1 ± 5.4)ϵ. In other words, the larger the content of dark matter in the galaxy, the more the stellar component will be flattened. If true, this observation appears to be in stark contrast with the commonly accepted galaxy formation scenario, whereby this process takes place inside dark halos with reasonably spherical symmetry. Aims. Comparing the processes of dissipationless galaxy formation in different theories of gravity and the emergence of the galaxy scaling relations therein provides an important framework within which, in principle, one can discriminate between these processes. Methods. By means of collisionless N-body simulations in modified Newtonian dynamics (MOND) and Newtonian gravity with and without active dark matter halos, with both spherical and clumpy initial structure, I study the trends of intrinsic and projected ellipticities, Sérsic index, and anisotropy with the total dynamical-to-stellar mass ratio. Results. I show that the end products of both cold spherical collapses and mergers of smaller clumps show an increasing departure from spherical symmetry for increasing values of the total dynamical-to-stellar mass ratio, at least in a range of halo masses. The equivalent Newtonian systems of the end products of MOND collapses show a similar behaviour. However, the M/L relation obtained from the numerical experiments in both gravities is rather different from that reported by Deur and coauthors.