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 semianalytically (without numerical simulations) MOND rotation curves for any density distribution based on AQUAL, applying it to different models of thin disks. The application of this formalism is equivalent to the creation of a fictitious phantom mass whose field may be used in a Newtonian way to calculate iteratively the MOND accelerations. In most cases, the differences between the application of the simple algebraic rule and the AQUAL-MOND calculations are small, $\lesssim 5$%. However, the error of the algebraic solution is larger than 5% when more than half of the mass is in the MONDian regime (where Newtonian and MOND rotation speeds differ by more than 10%), reaching in some cases $>70$% discrepance, such as in Maclaurin disks, representative of galaxies for which the rotational velocity rises to the edge of the disk as is seen in irregular galaxies. The slope of the rotation speed in the dependence with the radius or the vertical distance of the plane is also significantly changed.
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…
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. \cite{Donato}, that the dark matter surface density is not a universal (constant) quantity but correlates with the luminosity as well as with other galactic disc propert…
We present a modified inertia formulation of Modified Newtonian dynamics (MOND) without retaining Galilean invariance. Assuming that the existence of a universal upper bound, predicted by MOND, to the acceleration produced by a dark halo is equivalent to a violation of the hypothesis of locality (which states that an accelerated observer is pointwise inertial), we demonstrate that Milgrom's law is invariant under a new space-time coordinate transformation. In light of the new coordinate symmetry, we address the deficiency of MOND in resolving the mass discrepancy problem in clusters of galaxie…
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…
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…
Unlike Newtonian dynamics which is linear and obeys the strong equivalence principle, in any nonlinear gravitation such as Milgromian dynamics (MOND), the strong version of the equivalence principle is violated and the gravitational dynamics of a system is influenced by the external gravitational field in which it is embedded. This so called External Field Effect (EFE) is one of the important implications of MOND and provides a special context to test Milgromian dynamics. Here, we study the rotation curves (RCs) of 18 spiral galaxies and find that their shapes constrain the EFE. We show that t…
A novel interpretation of MOND is presented. For galactic data, in addition to Newtonian acceleration, there is an attractive acceleration peaking at Milgrom's parameter a_0. The peak lies within experimental error where a_0 = cH_0/2π; H_0 is the present-time value of the Hubble constant and c the velocity of light. The physical interpretation of this relation and its connection to Dark Energy are discussed.
We study the evolution of star clusters located in the outer regions of a galaxy undergoing a sudden mass loss through gas expulsion in the framework of Milgromian dynamics (MOND) by means of N-body simulations. We find that, to leave a bound star cluster, the star formation efficiency (SFE) of an embedded cluster dominated by deep MOND gravity can be reduced down to $2.5\%$. For a given SFE, the star clusters that survive in MOND can bind a larger fraction of mass compared to the Newtonian dynamics. Moreover, the more diffuse the embedded cluster is, the less substantial the size expansion of…
I review the history and development of Modified Newtonian Dynamics (MOND) beginning with the phenomenological basis as it existed in the early 1980s. I consider Milgrom's papers of 1983 introducing the idea and its consequences for galaxies and galaxy groups, as well as the initial reactions, both negative and positive. The early criticisms were primarily on matters of principle, such as the absence of conservation laws and perceived cosmological problems; an important step in addressing these issues was the development of the Lagrangian-based non-relativistic theory of Bekenstein and Milgrom…
The primary argument levelled against Milgrom's MOND is that it has no theoretical support, even though considerable effort has been expended in attempting to provide it. Against that criticism, MOND irrefutably enjoys an expanding portfolio of success and so is almost certainly tapping into something fundamental. But what? Over roughly the same period that MOND has been a topic of controversy, Baryshev, Sylos Labini and others have been claiming, with equal controversy in earlier years, that, on medium scales at least, material in the universe is distributed in a quasi-fractal $D\approx 2$ fa…
Strong constraints on the gravitational law from $Gaia$ DR3 wide binaries
Scottish Universities Physics Alliance, University of Saint Andrews（圣安德鲁斯大学）；The School of Physical and Chemical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院）；Université de Strasbourg, CNRS UMR 7550, Observatoire astronomique de Strasbourg（斯特拉斯堡大学）；European Southern Observatory（欧洲南方天文台）
It is usually believed that MOND can describe the galactic rotational curves with only baryonic matter and without any dark matter very well, while the $Λ$CDM model is expected to have difficulty in reproducing MOND-like behavior. Here, we use EAGLE's data to learn whether the $Λ$CDM model can reproduce MOND-like behavior. EAGLE's simulation result clearly reproduces the MOND-like behavior for $a_b\gtrapprox 10^{-12}\text{m/s}^2$ at $z=0$, although the acceleration constant, $a_0$, is a little larger than the observational data indicate. We find that $a_0$ increases with the redshift in a way …
Alternative gravitations of Milgrom (MOND), Moffat (MOG), and CDM scenarios all simulate rotation curves of spirals with reasonable details. They display significant disparities however in predicting the stellar mass-to-light ($M_*/L$) ratios of the galaxies. We maintain this feature could serve as a distinguishing factor between different alternative theories. We analyze the rotation curves of 46 low- and high-surface brightness galaxies and compare the resulting $M_*/L$s with the predictions of the Stellar Population Synthesis (SPS) scheme. The color-$M_*/L$ correlation obtained for MOND is …
The MOND Depth Index and Dynamical Maturity Clock: Toward a Universal Classification of Galaxies and Star Clusters
Helmholtz-Institut für Strahlen- und Kernphysik (HISKP), Universität Bonn（波恩大学赫尔姆霍兹辐射与核物理研究所）；Astronomical Institute, Faculty of Mathematics and Physics, Charles University in Prague（布拉格查理大学数学物理学院天文研究所）
We study geometries of galactic rotation curves from Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models in $(g_{\rm bar},g_{\rm tot})$-space ($g2$-space) where $g_{\rm tot}$ is the total centripetal acceleration of matter in the galaxies and $g_{\rm bar}$ is that due to the baryonic (visible) matter assuming Newtonian gravity. The $g2$-space geometries of the models and data from the SPARC database are classified and compared in a rescaled $\hat{g}2$-space that reduces systematic uncertainties on galaxy distance, inclination angle and variations in mass to light ratios. We find tha…
A Quality Framework for Testing Gravity with Wide Binaries: No Evidence for MOND
University of Portsmouth（朴茨茅斯大学）；California Institute of Technology（加州理工学院）；Queen Mary University of London（伦敦大学玛丽女王学院）；Leiden University（莱顿大学）；University of Cambridge（剑桥大学）
Dark matter is the generally accepted paradigm in astrophysics and cosmology as a solution to the higher rate of rotation in galaxies, among many other reasons. But since there are still some problems encountered by the standard dark matter paradigm at the galactic scale, we have resorted to an alternative solution, similar to Milgrom's Modified Newtonian dynamics (MOND). Here, we have assumed that: (i) either the gravitational constant, G, is a function of distance (scale): G = G(r), or, (ii) the gravitational-to-inertial mass ratio, mg/mi, is a function of distance (scale): f(r). We have use…
MOND reduces greatly the mass discrepancy in clusters of galaxies, but does leave a consistent global discrepancy of about a factor of two. It has been proposed, within the minimalist and purist MOND, that clusters harbor some indigenous, yet-undetected, cluster baryonic (dark) matter (CBDM). Its total amount has to be comparable with that of the observed hot gas. Following an initial discovery by van Dokkum & al. (2015a), Koda & al. (2015) have recently identified more than a thousand ultra-diffuse galaxy-like objects (UDGs) in the Coma cluster. Robustness of the UDGs to tidal disruption seem…
Using strong lensing data Milgrom's MOdified Newtonian Dynamics (MOND) or its covariant TeVeS (Tensor-Vector-Scalar Theory) is being examined here as an alternative to the conventional $Λ$CDM paradigm. We examine 10 double-image gravitational lensing systems, in which the lens masses have been estimated by stellar population synthesis models. While mild deviations exist, we do not find out that strong cases for outliers to the TeVeS theory.
Milgrom's modified Newtonian dynamics (MOND) can explain well the mass discrepancy problem in galaxy without invoking dark matter. The MOND theory predicts a universal constant acceleration scale in galaxy, below which the Newtonian dynamics is no longer valid. Recently, Rodrigues et al. analyzed 193 high-quality disk galaxies by using Bayesian inference and they concluded that the probability of existence of a fundamental acceleration scale is essentially 0. In this paper, we use the same method to revisit the same question: Is there a fundamental acceleration scale in galaxies? We fit each g…
A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form - dark matter - or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alt…
We explore the possibility that Milgrom's Modified Newtonian Dynamics (MOND) is a manifestation of the modification of inertia at small accelerations. Consistent with the Tully-Fisher relation, dynamics in the small acceleration domain may originate from a quartic (cubic) velocity-dependence of energy (momentum) whereas gravitational potentials remain linear with respect to mass. The natural framework for this interpretation is Finsler geometry. The simplest static isotropic Finsler metric of a gravitating mass that incorporates the Tully-Fisher relation at small acceleration is associated wit…
Kinematically cold tidal streams of globular clusters (GC) are excellent tracers of the Galactic gravitational potential at moderate Galactocentric distances, and can also be used as probes of the law of gravity on Galactic scales. Here, we compare for the first time the generation of such streams in Newtonian and Milgromian gravity (MOND). We first compute analytical results to investigate the expected shape of the GC gravitational potential in both frameworks, and we then run N-body simulations with the Phantom of Ramses code. We find that the GCs tend to become lopsided in MOND. This is a c…
We explore the predictions of Milgromian gravity (MOND) in the Local Universe by considering the distribution of the `phantom' dark matter (PDM) that would source the MOND gravitational field in Newtonian gravity, allowing an easy comparison with the dark matter framework. For this, we specifically deal with the quasi-linear version of MOND (QUMOND). We compute the `stellar-to-(phantom)halo-mass relation' (SHMR), a monotonically increasing power-law resembling the SHMR observationally deduced from spiral galaxy rotation curves in the Newtonian context. We show that the gas-to-(phantom)halo-mas…
The observed flat rotation curves of galaxies are among a number of astrophysical phenomena which require a larger acceleration than can be provided by the Newtonian gravity of the detected baryons. The main proposed solutions are additional undetected mass in the form of dark matter, or a low-acceleration modification to Newtonian gravity known as Milgromian dynamics (MOND). It is possible to directly test MOND using wide binary stars in the Solar neighbourhood, as these systems should contain a dynamically insignificant amount of dark matter even if it comprises most of the Galaxy. However, …
Measurements of the Low-Acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories
提出基于 Gaia 宽双星归一化速度剖面的 Monte Carlo 检验方法，测得低加速度区引力增强因子 1.37，并在 5.8σ 上排除牛顿引力而支持 Milgrom AQUAL。
Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepancy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOdified Newtonian Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc g…
We compare six models (including the baryonic model, two dark matter models, two modified Newtonian dynamics models and one modified gravity model) in accounting for the galaxy rotation curves. For the dark matter models, we assume NFW profile and core-modified profile for the dark halo, respectively. For the modified Newtonian dynamics models, we discuss Milgrom's MOND theory with two different interpolation functions, i.e. the standard and the simple interpolation functions. As for the modified gravity, we focus on Moffat's MSTG theory. We fit these models to the observed rotation curves of …
The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom's MOND. By performing the best-fit procedure to the galaxy rotation curv…
Theories of modified gravity generically violate the strong equivalence principle, so that the internal dynamics of a self-gravitating system in free fall depends on the strength of the external gravitational field (the external field effect). We fit rotation curves (RCs) from the SPARC database with a model inspired by Milgromian dynamics (MOND), which relates the outer shape of a RC to the external Newtonian field from the large-scale baryonic matter distribution through a dimensionless parameter $e_{\rm N}$. We obtain a $>4σ$ statistical detection of the external field effect (i.e. $e_{\rm …
