On the structure of tidal tails

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.     

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., 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 disc 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 substructures in the haloes of galaxies.     

The Monitor project: JW 380 – a 0.26-, 0.15-M⊙, pre-main-sequence eclipsing binary in the Orion nebula cluster

We present a general recipe for constructing N -body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N -body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.     

The haloes of merger remnants

We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.     

The graininess of dark matter haloes

We use the recently completed one billion particle Via Lactea II Λ cold dark matter simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as the structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions, the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo cannot be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function.     

The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.     

The distribution function of dark matter in massive haloes

We study the distribution function (DF) of dark matter particles in haloes of mass range  10¹⁴–10¹⁵ M_⊙  . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form     . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β₀ and  β_∞  ) and the scale of transition between them ( L ₀). The energy part   f _E ( E )  is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density   Q =ρ( r )/σ³( r )  .     

nmagic: a fast parallel implementation of a χ2-made-to-measure algorithm for modelling observational data

We describe a made-to-measure (M2M) algorithm for constructing N -particle models of stellar systems from observational data (χ²M2M), extending earlier ideas by Syer & Tremaine. The algorithm properly accounts for observational errors, is flexible, and can be applied to various systems and geometries. We implement this algorithm in a parallel code nmagic and carry out a sequence of tests to illustrate its power and performance. (i) We reconstruct an isotropic Hernquist model from density moments and projected kinematics and recover the correct differential energy distribution and intrinsic kinematics. (ii) We build a self-consistent oblate three-integral maximum rotator model and compare how the distribution function is recovered from integral field and slit kinematic data. (iii) We create a non-rotating and a figure rotating triaxial stellar particle model, reproduce the projected kinematics of the figure rotating system by a non-rotating system of the same intrinsic shape, and illustrate the signature of pattern rotation in this model. From these tests, we comment on the dependence of the results from χ²M2M on the initial model, the geometry, and the amount of available data.     

The dynamics of subhaloes in warm dark matter models

We present a comparison of the properties of substructure haloes ( subhaloes ) orbiting within host haloes that form in cold dark matter (CDM) and warm dark matter (WDM) cosmologies. Our study focuses on selected properties of these subhaloes, namely their anisotropic spatial distribution within the hosts; the existence of a 'backsplash' population; the age–distance relation; the degree to which they suffer mass loss; and the distribution of relative (infall) velocities with respect to the hosts. We find that the number density of subhaloes in our WDM model is suppressed relative to that in the CDM model, as we would expect. Interestingly, our analysis reveals that backsplash subhaloes exist in both the WDM and CDM models. Indeed, there are no statistically significant differences between the spatial distributions of subhaloes in the CDM and WDM models. There is evidence that subhaloes in the WDM model suffer enhanced mass loss relative to their counterparts in the CDM model, reflecting their lower central densities. We note also a tendency for the (infall) velocities of subhaloes in the WDM model to be higher than in the CDM model. Nevertheless, we conclude that observational tests based on either the spatial distribution or the kinematics of the subhalo population are unlikely to help us to differentiate between the CDM model and our adopted WDM model.     

Tailoring triaxial N-body models via a novel made-to-measure method

The made-to-measure N -body method slowly adapts the particle weights of an N -body model, whilst integrating the trajectories in an assumed static potential, until some constraints are satisfied, such as optimal fits to observational data. I propose a novel technique for this adaption procedure, which overcomes several limitations and shortcomings of the original method. The capability of the new technique is demonstrated by generating realistic N -body equilibrium models for dark matter haloes with prescribed density profile, triaxial shape and slowly outwardly growing radial velocity anisotropy.     

Multimass schemes for collisionless N-body simulations

We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f ₀. Our method uses importance sampling to find the sampling DF f _s that minimizes the mean-square formal errors in a given set of projections of the DF f ₀. The result is a multimass N -body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal.