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We investigate the epicyclic motion of stars escaping from star clusters. Using streaklines, we visualise the path of escaping stars and show how epicyclic motion leads to over- and underdensities in tidal tails of star clusters moving on circular and eccentric orbits about a galaxy. Additionally, we investigate the effect of the cluster mass on the tidal tails, by showing that their structure is better matched when the perturbing effect of the cluster mass is included. By adjusting streaklines to results of N-body computations we can accurately and quickly reproduce all observed substructure, especially the streaky features often found in simulations which may be interpreted in observations as multiple tidal tails. Hence, we can rule out tidal shocks as the origin of such substructures. Finally, from the adjusted streakline parameters we can verify that for the star clusters we studied escape mainly happens from the tidal radius of the cluster, given by x_L = (GM/(Omega^2-partial^2Phi/partial R^2))^{1/3}. We find, however, that there is another limiting radius, the edge radius, which gives the smallest radius from which a star can escape during one cluster orbit about the galaxy. For eccentric cluster orbits the edge radius shrinks with increasing orbital eccentricity (for fixed apocentric distance) but is always significantly larger than the respective perigalactic tidal radius. In fact, the edge radii of the clusters we investigated, which are extended and tidally filling, agree well with their (fitted) King radii, which may indicate a fundamental connection between these two quantities.
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We examine the longitudinal distribution of the stars escaping from a cluster along tidal tails. Using both theory and simulations, we show that, even in the case of a star cluster in a circular galactic orbit, when the tide is steady, the distribution exhibits maxima at a distance of many tidal radii from the cluster.
We report the detection of a pair of degree-long tidal tails associated with the globular cluster Palomar 14, using images obtained at the CFHT. We reveal a power-law departure from a King profile at large distances to the cluster center. The density map constructed with the optimal matched filter technique shows a nearly symmetrical and elongated distribution of stars on both sides of the cluster, forming a S-shape characteristic of mass loss. This evidence may be the telltale signature of tidal stripping in action. This, together with its large Galactocentric distance, imposes strong constraints on its orbit and/or origin: i) it must follow an external orbit confined to the peripheral region of the Galactic halo and/or ii) it formed in a satellite galaxy later accreted by the Milky Way.
We report the discovery of tidal structures around the intermediate-aged ($sim$ 700--800~Myr), nearby ($sim85$~pc) star cluster Coma Berenices. The spatial and kinematic grouping of stars is determined with the {it Gaia} DR2 parallax and proper motion data, by a clustering analysis tool, textsc{StarGO}, to map 5D parameters ($X, Y, Z$, $mu_alpha cosdelta, mu_delta$) onto a 2D neural network. A leading and a trailing tails, each with an extension of $sim50$~pc are revealed for the first time around this disrupting star cluster. The cluster members, totaling to $sim115^{+5}_{-3},rm {M_odot}$, are clearly mass segregated, and exhibit a flat mass function with $alpha sim 0.79pm0.16$, in the sense of $dN/dm propto m^{-alpha}$, where $N$ is the number of member stars and $m$ is stellar mass, in the mass range of $m=0.25$--$2.51~{rm M_odot}$. Within the tidal radius of $sim$6.9~pc, there are 77 member candidates with an average position, i.e., as the cluster center, of R.A.= 186.8110~deg, and decl.= 25.8112~deg, and an average distance of 85.8~pc. Additional 120 member candidates reside in the tidal structures, i.e., outnumbering those in the cluster core. The expansion of escaping members lead to an anisotropy in the velocity field of the tidal tails. Our analysis also serendipitously uncovers an adjacent stellar group, part of which has been cataloged in the literature. We identify 218 member candidates, 10 times more than previously known. This star group is some 65~pc away from, and $sim400$~Myr younger than, Coma Ber, but is already at the final stage of disruption.
Based on recent findings of a formation mechanism of substructure in tidal tails by Kuepper, Macleod & Heggie (2008) we investigate a more comprehensive set of N-body models of star clusters on orbits about a Milky-Way-like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up. The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case. We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disk shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark-matter sub-structures in the haloes of galaxies.
The tidal tails of stellar clusters provide an important tool for studying the birth conditions of the clusters and their evolution, coupling, and interaction with the Galactic potential. We present the N-body evolution of a Hyades-like stellar cluster with backward-integrated initial conditions on a realistic 3D orbit in the Milky Way computed within the AMUSE framework. For the first time, we explore the effect of the initial cluster rotation and the presence of lumps in the Galactic potential on the formation and evolution of tidal tails. We show that the tidal tails are not naturally clustered in any coordinate system. Models with initial rotation result in significant differences in the cluster mass loss and follow different angular momentum time evolution. The orientation of the tidal tails relative to the motion vector of the cluster and the current cluster angular momentum constrain the initial rotation of the cluster. We highlight the use of the convergent point (CP) method in searches for co-moving groups and introduce a new compact CP (CCP) method that accounts for internal kinematics based on an assumed model. Using the CCP method, we are able to recover candidate members of the Hyades tidal tails in the Gaia DR2 and eDR3 reaching a total extent of almost 1kpc. We confirm the previously noted asymmetry in the detected tidal tails. In the eDR3 data we recovered spatial overdensities in the leading and trailing tails that are kinematically consistent with being epicyclic overdensities and thus present candidates for the first such detection in an open star cluster. We show that the epicyclic overdensities are able to provide constraints not only on the cluster properties, but also on the Galactic potential. Finally, based on N-body simulations, a close encounter with a massive Galactic lump can explain the observed asymmetry in the tidal tails of the Hyades.(abriged)
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