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After their birth a significant fraction of all stars pass through the tidal threshold (prah) of their cluster of origin into the classical tidal tails. The asymmetry between the number of stars in the leading and trailing tails tests gravitational theory. All five open clusters with tail data (Hyades, Praesepe, Coma Berenices, COIN-Gaia 13, NGC 752) have visibly more stars within dcl = 50 pc of their centre in their leading than their trailing tail. Using the Jerabkova-compact-convergent-point (CCP) method, the extended tails have been mapped out for four nearby 600-2000 Myr old open clusters to dcl>50 pc. These are on near-circular Galactocentric orbits, a formula for estimating the orbital eccentricity of an open cluster being derived. Applying the Phantom of Ramses code to this problem, in Newtonian gravitation the tails are near-symmetrical. In Milgromian dynamics (MOND) the asymmetry reaches the observed values for 50 < dcl/pc < 200, being maximal near peri-galacticon, and can slightly invert near apo-galacticon, and the Küpper epicyclic overdensities are asymmetrically spaced. Clusters on circular orbits develop orbital eccentricity due to the asymmetrical spill-out, therewith spinning up opposite to their orbital angular momentum. This positive dynamical feedback suggests Milgromian open clusters to demise rapidly as their orbital eccentricity keeps increasing. Future work is necessary to better delineate the tidal tails around open clusters of different ages and to develop a Milgromian direct n-body code., 28 pages, 19 figures, MNRAS, published

In the local universe, disk galaxies are generally well evolved and Toomre stable. Their collisions with satellite galaxies naturally produce ring structures, which have been observed and extensively studied. By contrast, at high redshifts, disk galaxies are still developing and clumpy. These young galaxies interact with each other more frequently. However, the products of their collisions remain elusive. Here, we systematically study the minor collisions between a clumpy galaxy and a satellite on orbits with different initial conditions, and find a new structure that is different from the local collisional ring galaxies. The clumpiness of the target galaxy is fine-tuned by the values of Toomre parameter, Q. Interestingly, a thick and knotty ring structure is formed without any sign of a central nucleus in the target galaxy. Our results provide a promising explanation of the empty ring galaxy recently observed in R5519 at redshift z = 2.19. Moreover, we show that the clumpy state of the collided galaxy exists for a much longer timescale compared to isolated self-evolved clumpy galaxies that have been widely investigated.

We study the kinematics of stars in clusters undergoing gas expulsion in standard Newtonian dynamics and also in Milgromian dynamics (MOND). Gas expulsion can explain the observed line-of-sight (LoS) velocity dispersion profile of NGC 2419 in Newtonian dynamics. For a given star formation efficiency (SFE), the shapes of the velocity dispersion profiles, which are normalised by the velocity dispersion at the projected half-mass radius, are almost indistinguishable for different SFE models in Newtonian dynamics. The velocity dispersion of a star cluster in the outer halo of a galaxy can indeed have a strong radial anisotropy in Newtonian dynamics after gas expulsion. MOND displays several different properties from Newtonian dynamics. In particular, the slope of the central velocity dispersion profile is less steep in MOND for the same SFE. Moreover, for a given SFE, more massive embedded cluster models result in more rapidly declining central velocity dispersion profiles for the final star clusters, while less massive embedded cluster models lead to flatter velocity dispersion profiles for the final products. The onset of the radial-orbit instability in post-gas-expulsion MOND models is discussed. SFEs as low as a few percent, typical of molecular clouds, lead to surviving ultra-diffuse objects. Gas expulsion alone is unlikely the physical mechanism for the observed velocity dispersion profile of NGC 2419 in MOND., 15 pages, 7 figures, accepted for publication in MNRAS

The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured globular clusters (GCs) with a line-of-sight velocity dispersion of $\sigma=7.8^{+5.2}_{-2.2}\,$km/s ($\sigma=10.6^{+3.9}_{-2.3}\,$km/s). Our conventional statistical analysis of the original ten GCs gives $\sigma=8.0^{+4.3}_{-3.0}\,$km/s. The overall distribution of velocities agrees well with a Gaussian of this width. Due to the non-linear Poisson equation in MOND, a dwarf galaxy has weaker self-gravity when in close proximity to a massive host. This external field effect is investigated using a new analytic formulation and fully self-consistent live $N$-body models in MOND. Our formulation agrees well with that of Famaey and McGaugh (2012). These new simulations confirm our analytic results and suggest that DF2 may be in a deep-freeze state unique to MOND. The correctly calculated MOND velocity dispersion agrees with our inferred dispersion and that of van Dokkum et al. (2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs of DF2 are however significantly brighter and larger than normal GCs, a problem which disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc makes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc distance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4, finding good agreement with MOND. We also discuss possible massive galaxies near DF2 and DF4 along with their distances and peculiar velocities, noting that NGC 1052 may lie at a distance near 10 Mpc., Comment: 14 pages, 9 figures, 2 Tables, accepted for publication in MNRAS

A great challenge in present-day physics is to understand whether the observed internal dynamics of galaxies is due to dark matter matter or due to a modification of the law of gravity. Recently, van Dokkum et al. reported that the ultra-diffuse dwarf galaxy NGC1052-DF2 lacks dark matter, and they claimed that this would -- paradoxically -- be problematic for modified gravity theories like Milgromian dynamics (MOND). However, NGC1052-DF2 is not isolated, so that a valid prediction of its internal dynamics in MOND cannot be made without properly accounting for the external gravitational fields from neighbouring galaxies. Including this external field effect following Haghi et al. shows that NGC1052-DF2 is consistent with MOND., 15 pages, including supplementary information (the external field formulae), published by Nature: https://rdcu.be/6uZn

Collisional ring galaxies (CRGs) are formed through off-center collisions between a target galaxy and an intruder dwarf galaxy. We study the mass distribution and kinematics of the CRGs by tuning the bulge-to-disk mass ratio ($B/D$) for the progenitor; i.e., the target galaxy. We find that the lifetime of the ring correlates with the initial impact velocity vertical to the disk plane (i.e., $v_{z0}$). Three orbits for the collisional galaxy pair, on which clear and asymmetric rings form after collisions, are selected to perform the \textit{N}-body simulations at different values of $B/D$ for the progenitor. It is found that the ring structures are the strongest for the CRGs with small values of $B/D$. The S\'{e}rsic index, $n$, of the central remnant in the target galaxy becomes larger after collision. Moreover, the S\'{e}rsic index of a central remnant strongly correlates with the initial value of $B/D$ for the progenitor. A bulge-less progenitor results in a late-type object in the center of the ring galaxy, whereas a bulge-dominated progenitor leads to an early-type central remnant. Progenitors with $B/D\in [0.1,~0.3]$ (i.e., minor bulges) leave central remnants with $n\approx 4$. These results provide a possible explanation for the formation of a recently observed CRG with an early-type central nucleus, SDSS J1634+2049. In addition, we find that the radial and azimuthal velocity profiles for a ring galaxy are more sensitive to the $B/D$ than the initial relative velocity of the progenitor., Comment: 21 pages, 17 figures, accepted for publication in ApJ

We study the dark and luminous mass distributions, circular velocity curves (CVC), line-of-sight kinematics, and angular momenta for a sample of 42 cosmological zoom simulations of massive galaxies. Using a temporal smoothing technique, we are able to reach large radii. We find that: (i)The dark matter halo density profiles outside a few kpc follow simple power-law models, with flat dark matter CVCs for lower-mass systems, and rising CVCs for high-mass haloes. The projected stellar density distributions at large radii can be fitted by Sersic functions with n>10, larger than for typical ETGs. (ii)The massive systems have nearly flat total CVCs at large radii, while the less massive systems have mildly decreasing CVCs. The slope of the CVC at large radii correlates with v_circ itself. (iii)The dark matter fractions within Re are in the range 15-30% and increase to 40-65% at 5Re. Larger and more massive galaxies have higher dark matter fractions. (iv)The short axes of simulated galaxies and their host dark matter haloes are well aligned and their short-to-long axis ratios are correlated. (v)The stellar vrms(R) profiles are slowly declining, in agreement with planetary nebulae observations in the outer haloes of most ETGs. (vi)The line-of-sight velocity fields v show that rotation properties at small and large radii are correlated. Most radial profiles for the cumulative specific angular momentum parameter lambda(R) are nearly flat or slightly rising, with values in [0.06,0.75] from 2Re to 5Re. (vii)Stellar mass, ellipticity at 5Re, and lambda(5Re) are correlated: the more massive systems have less angular momentum and are rounder, as for observed ETGs. (viii)More massive galaxies with a large fraction of accreted stars have radially anisotropic velocity distributions outside Re. Tangential anisotropy is seen only for galaxies with high fraction of in-situ stars. (Full abstract in PDF), 17 pages, 15 figures, 2 tables, accepted by MNRAS

A central problem of contemporary physics is whether the law of gravity is non-Newtonian on galaxy scales. Rodrigues et al. argue that Milgromian gravitation, which solves the flat rotation curve problem without the need for dark matter particles, is ruled out at > 10{\sigma} significance. To a large extent, this conclusion relies on galaxies with very uncertain distances and/or nearly edge-on orientations, where dust obscuration often becomes significant. Applying appropriate quality cuts to the data leaves only a handful of outliers to the predictions of Milgromian gravitation according to the analysis of Rodrigues et al., but even these outliers can be explained with Milgromian gravitation., Comment: Author version, published in Nature Astronomy on 13.Nov.2018 (free version: https://rdcu.be/bbuvP) as a Correspondence to the article by Rodrigues et al. http://adsabs.harvard.edu/abs/2018NatAs...2..668R; see also McGaugh et al. for a parallel Correspondence (https://www.nature.com/articles/s41550-018-0615-9); for a reply by Rodrigues et al. see https://www.nature.com/articles/s41550-018-0614-x

Previous studies of globular cluster (GC) systems show that there appears to be a universal specific GC formation efficiency $\eta$ which relates the total mass of GCs to the virial mass of host dark matter halos, $M_{vir}$ (Georgiev et al 2010, Spitler & Forbes2009). In this paper, the specific frequency, $S_N$, and specific GC formation efficiency, $\eta$, are derived as functions of $M_{vir}$ in Milgromian dynamics, i.e., in modified Newtonian dynamics (MOND). In Milgromian dynamics, for the galaxies with GCs, the mass of the GC system, $M_{GC}$, is a two-component function of $M_{vir}$ instead of a simple linear relation. An observer in a Milgromian universe, who interprets this universe as being Newtonian/Einsteinian, will incorrectly infer a universal constant fraction between the mass of the GC system and a (false) dark matter halo of the baryonic galaxy. In contrast to a universal constant of $\eta$, in a Milgromian universe, for galaxies with $M_{vir} 10^{12}\msun$, $\eta$ increases with the increase of $M_{vir}$., Comment: 5 pages, 3 figures, MNRAS accepted

SDSS J1634+2049 is a local (z = 0.1293) infrared-luminous quasar with LIR= 10^11.91 Lsun. We present a detailed multiwavelength study of both the host galaxy and the nucleus. The host galaxy demonstrates violent, obscured star formation activities with SFR ~ 140 Msun yr^-1, estimated from either the PAH emission or IR luminosity. The optical to NIR spectra exhibit a blueshifted narrow cuspy component in Hb, HeI5876,10830 and other emission lines consistently with an offset velocity of ~900 km/s, as well as additional blueshifting phenomena in high-ionization lines , while there exist blueshifted broad absorption lines (BALs) in NaID and HeI*3889,10830, indicative of the AGN outflows producing BALs and emission lines. Constrained mutually by the several BALs with CLOUDY, the physical properties of the absorption-line outflow are derived as follows: 10^4 < n_H, 13 figures, 6 tables; accepted for publication in ApJ

We study the evolution of the phase-space of collisionless N-body systems under repeated stirrings or perturbations. We find convergence towards a limited solution group, in accordance with Hansen 2010, that is independent of the initial system and environmental conditions, paying particular attention to the assumed gravitational paradigm (Newtonian and MOND). We examine the effects of changes to the perturbation scheme and in doing so identify a large group of perturbations featuring radial orbit instability (ROI) which always lead to convergence. The attractor is thus found to be a robust and reproducible effect under a variety of circumstances.

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 the final star cluster is. The density profiles of a surviving star cluster are more cuspy in the centre for more massive embedded clusters, and the central density profiles are flatter for less massive embedded clusters or for lower SFE. This work may help to understand the low concentration and extension of the distant low-density globular clusters (GCs) and ultra-faint and diffuse satellite galaxies around the Milky Way., Comment: 11 pages, 5 figures, accepted for publication in ApJ

We look for observational signatures that could discriminate between Newtonian and modified Newtonian (MOND) dynamics in the Milky Way, in view of the advent of large astrometric and spectroscopic surveys. Indeed, a typical signature of MOND is an apparent disk of "phantom" dark matter, which is uniquely correlated with the visible disk-density distribution. Due to this phantom dark disk, Newtonian models with a spherical halo have different signatures from MOND models close to the Galactic plane. The models can thus be differentiated by measuring dynamically (within Newtonian dynamics) the disk surface density at the solar radius, the radial mass gradient within the disk, or the velocity ellipsoid tilt angle above the Galactic plane. Using the most realistic possible baryonic mass model for the Milky Way, we predict that, if MOND applies, the local surface density measured by a Newtonist will be approximately 78 Msun/pc2 within 1.1 kpc of the Galactic plane, the dynamically measured disk scale-length will be enhanced by a factor of 1.25 with respect to the visible disk scale-length, and the local vertical tilt of the velocity ellipsoid at 1 kpc above the plane will be approximately 6 degrees. None of these tests can be conclusive for the present-day accuracy of Milky Way data, but they will be of prime interest with the advent of large surveys such as GAIA., 5 pages

We compute the Milky Way potential in different cold dark matter (CDM) based models, and compare these with the modified Newtonian dynamics (MOND) framework. We calculate the axis ratio of the potential in various models, and find that isopotentials are less spherical in MOND than in CDM potentials. As an application of these models, we predict the escape velocity as a function of the position in the Galaxy. This could be useful in comparing with future data from planned or already-underway kinematic surveys (RAVE, SDSS, SEGUE, SIM, GAIA or the hypervelocity stars survey). In addition, the predicted escape velocity is compared with the recently measured high proper motion velocity of the Large Magellanic Cloud (LMC). To bind the LMC to the Galaxy in a MOND model, while still being compatible with the RAVE-measured local escape speed at the Sun's position, we show that an external field modulus of less than $0.03 a_0$ is needed.

The Bekenstein-Milgrom gravity theory with a modified Poisson equation is tested here for the existence of triaxial equilibrium solutions. Using the non-negative least square method, we show that self-consistent triaxial galaxies exist for baryonic models with a mild density cusp $\rho \sim {\Sigma \over r}$. Self-consistency is achieved for a wide range of central concentrations, $\Sigma \sim 10-1000\mathrm{M_{\odot}pc^{-2}}$, representing low-to-high surface brightness galaxies. Our results demonstrate for the first time that the orbit superposition technique is fruitful for constructing galaxy models beyond Newtonian gravity, and triaxial cuspy galaxies might exist without the help of Cold dark Matter., Comment: 19 pages, 1 table, 7 figures, Accepted for publication in ApJ

The self-binding energy and stability of a galaxy in MOND-based gravity are curiously decreasing functions of its center of mass acceleration towards neighbouring mass concentrations. A tentative indication of this breaking of the Strong Equivalence Principle in field galaxies is the RAVE-observed escape speed in the Milky Way. Another consequence is that satellites of field galaxies will move on nearly Keplerian orbits at large radii (100 - 500 kpc), with a declining speed below the asymptotically constant naive MOND prediction. But consequences of an environment-sensitive gravity are even more severe in clusters, where member galaxies accelerate fast: no more Dark-Halo-like potential is present to support galaxies, meaning that extended axisymmetric disks of gas and stars are likely unstable. These predicted reappearance of asymptotic Keplerian velocity curves and disappearance of "stereotypic galaxies" in clusters are falsifiable with targeted surveys.

Adopting Schwarzschild's orbit-superposition technique, we construct a series of self-consistent galaxy models, embedded in the external field of galaxy clusters in the framework of Milgrom's MOdified Newtonian Dynamics. These models represent relatively massive ellipticals with a Hernquist radial profile at various distances from the cluster centre. Using $N$-body simulations, we perform a first analysis of these models and their evolution. We find that self-gravitating axisymmetric density models, even under a weak external field, lose their symmetry by instability and generally evolve to triaxial configurations. A kinematic analysis suggests that the instability originates from both box and non-classified orbits with low angular momentum. We also consider a self-consistent isolated system which is then placed in a strong external field and allowed to evolve freely. This model, just as the corresponding equilibrium model in the same external field, eventually settles to a triaxial equilibrium as well, but has a higher velocity radial anisotropy and is rounder. The presence of an external field in MOND universe generically predicts some lopsidedness of galaxy shapes., Comment: 24 pages, 20 figures. Accepted for publication in ApJ

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 galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian., 17 pages, 5 figures, Matches to MNRAS published version, references updated

External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the Strong Equivalence Principle (SEP) and change the dynamics of self-bound stellar systems moving in space-varying background gravitational fields. We study two kinds of re-virialisation of the stellar systems: the violent phase transition and the adiabatic phase transition for systems moving on radial orbits, where the external field evolves from strong to weak and whose corresponding dynamics changes from Newtonian to Milgromian. We find that the time scale for the phase tranformation from Newtonian to Milgromian gravity lies only within one to a few crossing times for low density globular clusters with masses ranging from $10^4\msun$ to $10^6\msun$. Thus a globular cluster can appear frozen in the Newtonian regime despite being in the Milgromian regime for not longer than a few crossing times. We also study the kinematics and anisotropy profiles of the systems. The velocity dispersions of the systems are larger after the phase transitions, especially for the outer regions of the stellar systems. Moreover, the isotropic systems become radially anisotropic, especially for the outer parts, after the process caused by the dynamical phase transition. Deeper Milgromian systems have more radially anisotropic velocity dispersion functions. We also find that the final profiles of density, velocity dispersion and anisotropy do not depend on the details of the phase transition. I.e., the mass distribution and kinematics of the end-states of the globular clusters do not depend on the rapidity of the transition from Newtonian to Milgromian gravity. Thus, the transition from the Newtonian to the Milgromian regime naturally induces a significant radially anisotropic velocity distribution in a globular cluster., Comment: 17 pages, 19 figures, MNRAS accepted

The recent years have seen combined measurements of X-ray and (weak) lensing contours for colliding galaxy clusters such as, for instance, the famous "Bullet" cluster. These observations have revealed offsets in the peaks of the baryonic and (dominant) gravitational matter component of order ~(100-200) kpc. Such discrepancies are difficult to explain using modified theories for gravity other than dark matter. Or are they not? Here we use the concept of "phantom dark matter" that is based upon a Newtonian interpretation of the MONDian gravitational potential. We show that this idea is in fact capable of producing substantial offsets in idealistic density configurations, involving a uniform external field. However, when analysed in a MONDian cosmological framework we deduce that the size (and probablity) of the effect is too small to explain the observed offsets found in the most recent observations, at least in the simplest incarnation of phantom dark matter as discussed here. The lensing centers in merging galaxy clusters are likely very close to the centers of true mass even in a MONDian cosmology. This gives the support to the idea that neutrino-like non-collisional matter might be responsible for the observed offsets of lensing and X-ray peaks., 6 pages, 5 figures, accepted for publication in ApJ

We perform a stability test of triaxial models in MOdified Newtonian Dynamics (MOND) using N-body simulations. The triaxial models considered here have densities that vary with $r^{-1}$ in the center and $r^{-4}$ at large radii. The total mass of the model varies from $10^8\Msun$ to $10^{10}\Msun$, representing the mass scale of dwarfs to medium-mass elliptical galaxies, respectively, from deep MOND to quasi-Newtonian gravity. We build triaxial galaxy models using the Schwarzschild technique, and evolve the systems for 200 Keplerian dynamical times (at the typical length scale of 1.0 kpc). We find that the systems are virial overheating, and in quasi-equilibrium with the relaxation taking approximately 5 Keplerian dynamical times (1.0 kpc). For all systems, the change of the inertial (kinetic) energy is less than 10% (20%) after relaxation. However, the central profile of the model is flattened during the relaxation and the (overall) axis ratios change by roughly 10% within 200 Keplerian dynamical times (at 1.0kpc) in our simulations. We further find that the systems are stable once they reach the equilibrium state., 13 pages, 14 figures

In recent years several hypervelocity stars (HVSs) have been observed in the halo of our Galaxy. Such HVSs have possibly been ejected from the Galactic center and then propagated in the Galactic potential up to their current position. The recent survey for candidate HVSs show an asymmetry in the kinematics of candidate HVSs (position and velocity vectors), where more outgoing stars than ingoing stars (i.e. positive Galactocentric velocities vs. negative ones) are observed. We show that such kinematic asymmetry, which is likely due to the finite lifetime of the stars and Galactic potential structure, could be used in a novel method to probe and constrain the Galactic potential, identify the stellar type of the stars in the survey and estimate the number of HVSs. Kinematics-independent identification of the stellar types of the stars in such surveys (e.g. spectroscopic identification) could further improve these results. We find that the observed asymmetry between ingoing and outgoing stars favors specific Galactic potential models. It also implies a lower limit of ~54+-8 main sequence HVSs in the survey sample (>=648+-96 in the Galaxy), assuming that all of the main sequence stars in the survey originate from the Galactic center. The other stars in the survey are likely to be hot blue horizontal branch stars born in the halo rather than stars ejected from the Galactic center., 7 pages, 3 figures. Added an appendix. Accepted to ApJ

We point out an interesting theoretical prediction for elliptical galaxies residing inside galaxy clusters in the framework of modified Newtonian dynamics (MOND), that could be used to test this paradigm. Apart from the central brightest cluster galaxy, other galaxies close enough to the centre experience a strong gravitational influence from the other galaxies of the cluster. This influence manifests itself only as tides in standard Newtonian gravity, meaning that the systematic acceleration of the centre of mass of the galaxy has no consequence. However, in the context of MOND, a consequence of the breaking of the strong equivalence principle is that the systematic acceleration changes the own self-gravity of the galaxy. We show here that, in this framework, initially axisymmetric elliptical galaxies become lopsided along the external field's direction, and that the centroid of the galaxy, defined by the outer density contours, is shifted by a few hundreds parsecs with respect to the densest point., Comment: accepted for publication in JCAP

Galaxies are natural laboratories for testing fundamental physics on the nature of the dark matter. MOdified Newtonian Dynamics (MOND) has been tested for over 20 years on small and large scales. While there are several versions of how MOND extrapolates to the large scales, and these versions are not yet fully successful, the original Bekenstein-Milgrom version of MOND is fully predictive and works very well on galaxy scales. However, little work has been done to explore this theory beyond fitting the rotation curves and Tully-Fisher relation of isolated disc galaxies. So far little is known of MONDian elliptical galaxies accelerating in any galaxy cluster. A defining feature of MOND is that internal dynamics of the galaxy depends on the overall acceleration of the galaxy. The existence of cuspy triaxial equilibria for elliptical galaxies is the minimal requirement to MOND. With the PhD project here, I constructed and then further studied the evolution and stability of gravitationally bound systems resembling like cuspy elliptical galaxies, both in isolation and when embedded in a uniform external field. I also studied the escape speeds from spiral galaxies, in particular by comparing the potentials of the Milky Way Galaxy in the Cold Dark Matter (CDM) and MOND frameworks.