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The stellar shells surrounding an elliptical galaxy, as remnants of a dwarf galaxy disrupted during merging, reveal the distribution of energy and angular momentum of the progenitor dwarf galaxy. We develop a semi-analytical model to describe the changes in energy Δ E _i and angular momentum Δ Lz _i for particles during the first infall. We show that these changes, induced by the self-gravity of the progenitor, are important in broadening the initial energy distribution of the Plummer or Hernquist progenitor model. Consequently, these changes are crucial in shaping the shells. In the freefall stage following the disintegration of the progenitor potential, particles are no longer bound by self-gravity but move within the gravitational potential of the target galaxy. We investigate the relationship between the radial period and the energy of particles undergoing radial motion. We show that an accurate model of the energy range of the dwarf galaxy at disruption is essential to predict the number of observable shells.

Galaxies are observed to be lopsided, meaning that they are more massive and more extended along one side than the opposite side. In this work, we provide a statistical analysis of the lopsided morphology of 1780 isolated satellite galaxies generated by the TNG50-1 simulation, incorporating the effect of tidal fields from halo centers. The isolated satellites are galaxies without nearby substructures whose mass is over 1% of the satellites within their virial radii. We study the radial alignment (RA) between the major axes of satellites and the radial direction of their halo centers in radial ranges of 0–2, 2–5, and 5–10 R _h , with R _h being the stellar half-mass radius. According to our results, the RA is virtually undetectable in inner and intermediate regions, yet it is significantly evident in outer regions. We also calculate the far-to-near-side semiaxial ratios of the major axes, denoted by a _− / a _+ , which measure the semiaxial ratios of the major axes in the hemispheres between those facing away from (far side) and facing toward (nearside) halo centers. In all the radial bins of the satellites, the numbers of satellites with longer semiaxes on the far side are found to be almost equal to those with longer semiaxes on the near side. Therefore, the tidal fields from halo centers play a minor role in the generation of lopsided satellites. The long semimajor-axes radial alignment (LRA), i.e., an alignment between the long semimajor axes of satellite galaxies and the radial directions to their halo centers, is further studied. No clear evidence of LRA is found in our sample within the framework of ΛCDM Newtonian dynamics. Finally, we briefly discuss the possible origins of the asymmetry of galaxies in TNG50-1.

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 in the centre and at large radii. The total mass of the model varies from 108 to , 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 per cent (20 per cent) after relaxation. However, the central profile of the model is flattened during the relaxation and the (overall) axis ratios change by roughly 10 per cent within 200 Keplerian dynamical times (at 1.0 kpc) in our simulations. We further find that the systems are stable once they reach the equilibrium state. [ABSTRACT FROM AUTHOR]

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 axial 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 is needed. [ABSTRACT FROM AUTHOR]