Motivated by the discovery of prolate rotation of stars in Andromeda II, a dwarf spheroidal companion of M31, we study its origin via mergers of disky dwarf galaxies. We simulate merger events between two identical dwarfs changing the initial inclina
tion of their disks with respect to the orbit and the amount of orbital angular momentum. On radial orbits the amount of prolate rotation in the merger remnants correlates strongly with the inclination of the disks and is well understood as due to the conservation of the angular momentum component of the disks along the merger axis. For non-radial orbits prolate rotation may still be produced if the orbital angular momentum is initially not much larger than the intrinsic angular momentum of the disks. The orbital structure of the remnants with significant rotation is dominated by box orbits in the center and long-axis tubes in the outer parts. The frequency analysis of stellar orbits in the plane perpendicular to the major axis reveals the presence of two families roughly corresponding to inner and outer long-axis tubes. The fraction of inner tubes is largest in the remnant forming from disks oriented most vertically initially and is responsible for the boxy shape of the galaxy. We conclude that prolate rotation results from mergers with a variety of initial conditions and no fine tuning is necessary to reproduce this feature. We compare the properties of our merger remnants to those of dwarfs resulting from the tidal stirring scenario and the data for Andromeda II.
Context. Many ellipticals are surrounded by round stellar shells probably stemming from minor mergers. A new method for constraining gravitational potential in elliptical galaxies has recently been suggested. It uses the spectral line profiles of the
se shells to measure the circular velocity at the edge of the shell and the expansion velocity of the shell itself. MOND is an alternative to the dark matter framework aiming to solve the missing mass problem. Aims. We study how the circular and expansion velocities behave in MOND for large shells. Methods. The asymptotic behavior for infinitely large shells is derived analytically. The applicability of the asymptotic results for finitely sized shells is studied numerically on a grid of galaxies modeled with Sersic spheres. Results. Circular velocity settles asymptotically at a value determined by the baryonic mass of the galaxy forming the baryonic Tully-Fisher relation known for disk galaxies. Shell expansion velocity also becomes asymptotically constant. The expansion velocities of large shells form a multibranched analogy to the baryonic Tully-Fisher relation, together with the galactic baryonic masses. For many - but not all - shell galaxies, the asymptotic values of these two types of velocities are reached under the effective radius. If MOND is assumed to work in ellipticals, then the shell spectra allow many details of the history to be revealed about the formation of the shell system, including its age. The results pertaining to circular velocities apply to all elliptical galaxies, not only those with shells.
Tests of MOND in ellipticals are relatively rare because these galaxies often lack kinematic tracers in the regions where the MOND effects are significant. Stellar shells observed in many elliptical galaxies offer a promising way to constrain their g
ravitational field. Shells appear as glowing arcs around their host galaxy. They are observed up to ~100 kpc. The stars in axially symmetric shell systems move in nearly radial orbits. The radial distributions of shell locations and the spectra of stars in shells can be used to constrain the gravitational potential of their host galaxy. The symmetrical shell systems, being especially suitable for these studies, occur in approximately 3% of all early-type galaxies. Hence the shells substantially increase the number of ellipticals in which MOND can be tested up to large radii. In this paper, we review our work on shell galaxies in MOND. We summarize the paper B{i}lek et al. (2013), where we demonstrated the consistency of shell radii in an elliptical NGC 3923 with MOND, and the work B{i}lek et al. (2014), in which we predicted a giant (~200 kpc), as yet undiscovered shell of NGC 3923. We explain the shell identification method, which was used in these two papers. We further describe the expected shape of line profiles in shell spectra in MOND which is very special due to the direct relation of the gravitational field and baryonic matter distribution (B{i}lek et al., 2014, in preparation).
Using N-body simulations we study the origin of prolate rotation recently detected in the kinematic data for And II, a dSph satellite of M31. We propose an evolutionary model for the origin of And II involving a merger between two disky dwarf galaxie
s whose structural parameters differ only in their disk scale lengths. The dwarfs are placed on a radial orbit towards each other with their angular momenta inclined by 45 deg to the orbital plane and by 90 deg with respect to each other. After 5 Gyr of evolution the merger remnant forms a stable triaxial galaxy with rotation only around the longest axis. The origin of this rotation is naturally explained as due to the symmetry of the initial configuration which leads to the conservation of angular momentum components along the direction of the merger. The stars originating from the two dwarfs show significantly different surface density profiles while having very similar kinematics in agreement with the properties of separate stellar populations in And II. We also study an alternative scenario for the formation of And II, via tidal stirring of a disky dwarf galaxy. While intrinsic rotation occurs naturally in this model as a remnant of the initial rotation of the disk, it is mostly around the shortest axis of the stellar component. The rotation around the longest axis is induced only occasionally and remains much smaller that the systems velocity dispersion. We conclude that although tidal origin of the velocity distribution in And II cannot be excluded, it is much more naturally explained within the scenario involving a past merger event. Thus, in principle, the presence of prolate rotation in dSph galaxies of the Local Group and beyond may be used as an indicator of major mergers in their history or even as a way to distinguish between the two scenarios of their formation.
Stellar shells observed in many giant elliptical and lenticular as well as a few spiral and dwarf galaxies presumably result from radial minor mergers of galaxies. We show that the line-of-sight velocity distribution of the shells has a quadruple-pea
ked shape. We found simple analytical expressions that connect the positions of the four peaks of the line profile with the mass distribution of the galaxy, namely, the circular velocity at the given shell radius and the propagation velocity of the shell. The analytical expressions were applied to a test-particle simulation of a radial minor merger, and the potential of the simulated host galaxy was successfully recovered. Shell kinematics can thus become an independent tool to determine the content and distribution of dark matter in shell galaxies up to ~100 kpc from the center of the host galaxy. Moreover we investigate the dynamical friction and gradual disruption of the cannibalized galaxy during the shell formation in the framework of a simulation with test particles. The coupling of both effects can considerably redistribute positions and luminosities of shells. Neglecting them can lead to significant errors in attempts to date the merger in observed shell galaxies.
Stellar shells observed in many giant elliptical and lenticular as well as a few spiral and dwarf galaxies, presumably result from galaxy mergers. Line-of-sight velocity distributions of the shells could, in principle, if measured with a sufficiently
high S/N, constitute one of methods to constrain the gravitational potential of the host galaxy. Merrifield & Kuijken (1998) predicted a double-peaked line profile for stationary shells resulting from a nearly radial minor merger. In this paper, we aim at extending their analysis to a more realistic case of expanding shells, inherent to the merging process, whereas we assume the same type of merger and the same orbital geometry. We use analytical approach as well as test particle simulations to predict the line-of-sight velocity profile across the shell structure. Simulated line profiles are convolved with spectral PSFs to estimate the peak detectability. The resulting line-of-sight velocity distributions are more complex than previously predicted due to non-zero phase velocity of the shells. In principle, each of the Merrifield & Kuijken (1998) peaks splits into two, giving a quadruple-peaked line profile, which allows more precise determination of the potential of the host galaxy and, moreover, contains additional information. We find simple analytical expressions that connect the positions of the four peaks of the line profile and the mass distribution of the galaxy, namely the circular velocity at the given shell radius and the propagation velocity of the shell. The analytical expressions were applied to a test-particle simulation of a radial minor merger and the potential of the simulated host galaxy was successfully recovered. The shell kinematics can thus become an independent tool to determine the content and distribution of the dark matter in shell galaxies, up to ~100 kpc from the center of the host galaxy.
The model of a radial minor merger proposed by Quinn (1984), which successfully reproduces the observed regular shell systems in shell galaxies, is ideal for a test-particle simulation. We compare such a simulation with a self-consistent one. They ag
ree very well in positions of the first generation of shells but potentially important effects -- dynamical friction and gradual decay of the dwarf galaxy -- are not present in the test-particle model, therefore we look for a proper way to include them.
We present an improved study of the expected shape of the line-of-sight velocity distribution in shell galaxies. We found a simple analytical expression connecting prominent and in principle observable characteristics of the line profile and mass-dis
tribution of the galaxy. The prediction was compared with the results from a test-particle simulation of a radial merger.
Using N-body simulations of shell galaxies created in nearly radial minor mergers, we investigate the error of collision dating, resulting from the neglect of dynamical friction and of gradual disruption of the cannibalized dwarf.
With the goal to refine modelling of shell galaxies and the use of shells to probe the merger history, we develop a new method for implementing dynamical friction in test-particle simulations of radial minor mergers. The friction is combined with a g
radual decay of the dwarf galaxy. The coupling of both effects can considerably redistribute positions and luminosities of shells; neglecting them can lead to significant errors in attempts to date the merger.
