ALBERT

Description: We perform in-depth dynamical modelling of the luminous and dark matter (DM) content of the elliptical galaxy NGC 1407. Our strategy consists of solving the spherical Jeans equations for three independent dynamical tracers: stars, blue globular clusters (GCs) and red GCs in a self-consistent manner. We adopt a maximum-likelihood Markov Chain Monte Carlo fitting technique in the attempt to constrain the inner slope of the DM density profile (the cusp/core problem), and the stellar initial mass function (IMF) of the galaxy. We find the inner logarithmic slope of the DM density profiles to be  = 0.6 ± 0.4, which is consistent with either a DM cusp ( = 1) or with a DM core ( = 0). Our findings are consistent with a Salpeter IMF, and marginally consistent with a Kroupa IMF. We infer tangential orbits for the blue GCs, and radial anisotropy for red GCs and stars. The modelling results are consistent with the virial mass–concentration relation predicted by cold dark matter (CDM) simulations. The virial mass of NGC 1407 is log M vir  = 13.3 ± 0.2 M , whereas the stellar mass is log M *  = 11.8 ± 0.1 M . The overall uncertainties on the mass of NGC 1407 are only 5 per cent at the projected stellar effective radius. We attribute the disagreement between our results and previous X-ray results to the gas not being in hydrostatic equilibrium in the central regions of the galaxy. The halo of NGC 1407 is found be DM-dominated, with a dynamical mass-to-light ratio of ${\rm M/L}=260_{-100} ^{+174} \,\mathrm{M}_{\odot }/\mathrm{L}_{\odot , B}$ . However, this value can be larger up to a factor of 3 depending on the assumed prior on the DM scale radius.

Description: We carry out controlled N -body simulations that follow the dynamical evolution of binary stars in the dark matter (DM) haloes of ultrafaint dwarf spheroidals (dSphs). We find that wide binaries with semimajor axes a a t tend to be quickly disrupted by the tidal field of the halo. In smooth potentials the truncation scale, a t , is mainly governed by (i) the mass enclosed within the dwarf half-light radius ( R h ) and (ii) the slope of the DM halo profile at R R h , and is largely independent of the initial eccentricity distribution of the binary systems and the anisotropy of the stellar orbits about the galactic potential. For the reported velocity dispersion and half-light radius of Segue I, the closest ultrafaint, our models predict a t values that are a factor of 2–3 smaller in cuspy haloes than in any of the cored models considered here. Using mock observations of Segue I we show that measuring the projected two-point correlation function of stellar pairs with sub-arcsecond resolution may provide a useful tool to constrain the amount and distribution of DM in the smallest and most DM-dominated galaxies.

Description: This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed as a special type of diffusion process in the integral-of-motion space. In time-varying potentials with a fixed spatial symmetry the diffusion coefficients are closely related to virial quantities, such as the specific moment of inertia, the virial factor and the mean kinetic and potential energy of microcanonical particle ensembles. The non-equilibrium distribution function is found by convolving the initial distribution function with the Green function that solves Einstein's equation for freely diffusing particles. Such a convolution also yields a natural solution to the Fokker–Planck equations in the energy space. Our mathematical formalism can be generalized to potentials with a time-varying symmetry, where diffusion extends over multiple dimensions of the integral-of-motion space. The new probability theory is in many ways analogous to stochastic calculus, with two significant differences: (i) the equations of motion that govern the trajectories of particles are fully deterministic, and (ii) the diffusion coefficients can be derived self-consistently from microcanonical phase-space averages without relying on ergodicity assumptions. For illustration we follow the cold collapse of N -body models in a time-dependent logarithmic potential. Comparison between the analytical and numerical results shows excellent agreement in regions where the potential evolution does not depart too strongly from the adiabatic regime.

Description: This paper explores the effect of the Large Magellanic Cloud (LMC) on the mass estimates obtained from the timing argument. We show that accounting for the presence of the LMC systematically lowers the Local Group mass ( M LG ) derived from the relative motion of the Milky Way–Andromeda pair. Motivated by this result, we apply a Bayesian technique devised by Peñarrubia et al. to simultaneously fit (i) distances and velocities of galaxies within 3 Mpc and (ii) the relative motion between the Milky Way and Andromeda derived from HST observations, with the LMC mass ( M LMC ) as a free parameter. Our analysis returns a Local Group mass $M_{\rm LG}=2.64^{+0.42}_{-0.38}\times 10^{12}\,\mathrm{M}_{\odot }$ at a 68 per cent confidence level. The masses of the Milky Way, $M_{\rm MW}=1.04_{-0.23}^{+0.26}\times 10^{12}\,\mathrm{M}_{\odot }$ , and Andromeda, $M_{{\rm M}31}=1.33_{-0.33}^{+0.39}\times 10^{12}\,\mathrm{M}_{\odot }$ , are consistent with previous estimates that neglect the impact of the LMC on the observed Hubble flow. We find a (total) LMC mass $M_{\rm LMC}=0.25_{-0.08}^{+0.09}\times 10^{12}\,\mathrm{M}_{\odot }$ , which is indicative of an extended dark matter halo and supports the scenario where this galaxy is just past its first pericentric approach. Consequently, these results suggest that the LMC may induce significant perturbations on the Galactic potential.

Description: Using a variety of stellar tracers – blue horizontal branch stars, main-sequence turn-off stars and red giants – we follow the path of the Sagittarius (Sgr) stream across the sky in Sloan Digital Sky Survey data. Our study presents new Sgr debris detections, accurate distances and line-of-sight velocities that together help to shed new light on the puzzle of the Sgr tails. For both the leading and the trailing tails, we trace the points of their maximal extent, or apocentric distances, and find that they lie at R L  = 47.8 ± 0.5 kpc and R T  = 102.5 ± 2.5 kpc, respectively. The angular difference between the apocentres is 93 $_{.}^{\circ}$ 2 ± 3 $_{.}^{\circ}$ 5, which is smaller than predicted for logarithmic haloes. Such differential orbital precession can be made consistent with models of the Milky Way in which the dark matter density falls more quickly with radius. However, currently, no existing Sgr disruption simulation can explain the entirety of the observational data. Based on its position and radial velocity, we show that the unusually large globular cluster NGC 2419 can be associated with the Sgr trailing stream. We measure the precession of the orbital plane of the Sgr debris in the Milky Way potential and show that, surprisingly, Sgr debris in the primary (brighter) tails evolves differently from the secondary (fainter) tails, both in the north and the south.

Description: A central tenet of the current cosmological paradigm is that galaxies grow over time through the accretion of smaller systems. Here, we present new kinematic measurements near the centre of one of the densest pronounced substructures, the South-West Cloud, in the outer halo of our nearest giant neighbour, the Andromeda galaxy. These observations reveal that the kinematic properties of this region of the South-West Cloud are consistent with those of PA-8, a globular cluster previously shown to be co-spatial with the stellar substructure. In this sense, the situation is reminiscent of the handful of globular clusters that sit near the heart of the Sagittarius dwarf galaxy, a system that is currently being accreted into the Milky Way, confirming that accretion deposits not only stars but also globular clusters into the haloes of large galaxies.

Description: We study the evolution of the dark matter (DM) halo profiles of dwarf galaxies driven by the accretion of DM substructures through controlled N -body experiments. Our initial conditions assume that early supernova feedback erases the primordial DM cusps of haloes with z  = 0 masses of 10 9 – 10 10 M . The orbits and masses of the infalling substructures are borrowed from the Aquarius cosmological simulations. Our experiments show that a fraction of haloes that undergo 1:3 down to 1:30 mergers are susceptible to reform a DM cusp by z   0. Cusp regrowth is driven by the accretion of DM substructures that are dense enough to reach the central regions of the main halo before being tidally disrupted. The infall of substructures on the mean of the reported mass–concentration relation and a mass ratio above 1:6 systematically leads to cusp regrowth. Substructures with 1:6–1:8, and 1:8–1:30 only reform DM cusps if their densities are 1 and 2 above the mean, respectively. The merging time-scales of these dense, low-mass substructures is relatively long (5 – 11 Gyr), which may pose a time-scale problem for the longevity of DM cores in dwarfs galaxies and possibly explain the existence of dense dwarfs-like Draco. These results suggest that within cold dark matter a non-negligible level of scatter in the mass profiles of galactic haloes acted on by feedback is to be expected given the stochastic mass accretion histories of low-mass haloes and the diverse star formation histories observed in the Local Group dwarfs.

Description: We present a detailed kinematic analysis of the outer halo globular cluster system of the Andromeda galaxy (M31). Our basis for this is a set of new spectroscopic observations for 78 clusters lying at projected distances between R proj  ~ 20–140 kpc from the M31 centre. These are largely drawn from the recent Pan-Andromeda Archaeological Survey globular cluster catalogue; 63 of our targets have no previous velocity data. Via a Bayesian maximum likelihood analysis, we find that globular clusters with R proj  〉 30 kpc exhibit coherent rotation around the minor optical axis of M31, in the same direction as more centrally located globular clusters, but with a smaller amplitude of 86 ± 17 km s –1 . There is also evidence that the velocity dispersion of the outer halo globular cluster system decreases as a function of projected distance from the M31 centre, and that this relation can be well described by a power law of index –0.5. The velocity dispersion profile of the outer halo globular clusters is quite similar to that of the halo stars, at least out to the radius up to which there is available information on the stellar kinematics. We detect and discuss various velocity correlations amongst subgroups of globular clusters that lie on stellar debris streams in the M31 halo. Many of these subgroups are dynamically cold, exhibiting internal velocity dispersions consistent with zero. Simple Monte Carlo experiments imply that such configurations are unlikely to form by chance, adding weight to the notion that a significant fraction of the outer halo globular clusters in M31 have been accreted alongside their parent dwarf galaxies. We also estimate the M31 mass within 200 kpc via the Tracer Mass Estimator (TME), finding (1.2–1.6) ± 0.2 10 12 M . This quantity is subject to additional systematic effects due to various limitations of the data, and assumptions built in into the TME. Finally, we discuss our results in the context of formation scenarios for the M31 halo.

Description: This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the explicit time-dependence from the Hamiltonian of the system. By referring the phase-space locations of particles to a coordinate frame in which the potential remains ‘static’ the dynamical effects introduced by the time evolution vanish. It follows that dynamical invariants correspond to the integrals of motion for the static potential expressed in the transformed coordinates. The main difficulty reduces to solving the differential equations that define the canonical transformation, which are typically coupled with the equations of motion. We discuss a few examples where both sets of equations can be exactly de-coupled, and cases that require approximations. The construction of dynamical invariants has far-reaching applications. These quantities allow us, for example, to describe the evolution of (statistical) microcanonical ensembles in time-dependent gravitational potentials without relying on ergodicity or probability assumptions. As an illustration, we follow the evolution of dynamical fossils in galaxies that build up mass hierarchically. We show that the growth of the host potential tends to efface tidal substructures in the integral-of-motion space through an orbital diffusion process. The inexorable cycle of deposition, and progressive dissolution, of tidal clumps naturally leads to the formation of a ‘smooth’ stellar halo.

Description: We combine the equations of motion that govern the dynamics of galaxies in the local volume with Bayesian techniques in order to fit orbits to published distances and velocities of galaxies within 3 Mpc. We find a Local Group (LG) mass 2.3 ± 0.7 10 12 M that is consistent with the combined dynamical masses of M31 and the Milky Way, and a mass ratio $0.54^{+0.23}_{-0.17}$ that rules out models where our Galaxy is more massive than M31 with ~95 per cent confidence. The Milky Way's circular velocity at the solar radius is relatively high, 245 ± 23 km s –1 , which helps to reconcile the mass derived from the local Hubble flow with the larger value suggested by the ‘timing argument’. Adopting Planck 's bounds on yields a (local) Hubble constant H 0  = 67 ± 5 km s –1 Mpc –1 which is consistent with the value found on cosmological scales. Restricted N -body experiments show that substructures tend to fall on to the LG along the Milky Way–M31 axis, where the quadrupole attraction is maximum. Tests against mock data indicate that neglecting this effect slightly overestimates the LG mass without biasing the rest of model parameters. We also show that both the time dependence of the LG potential and the cosmological constant have little impact on the observed local Hubble flow.