Action-space clustering of tidal streams to infer the Galactic potential

We present a new method for constraining the Milky Way halo gravitational potential by simultaneously fitting multiple tidal streams. This method requires full three-dimensional positions and velocities for all stars to be fit, but does not require identification of any specific stream or determination of stream membership for any star. We exploit the principle that the action distribution of stream stars is most clustered when the potential used to calculate the actions is closest to the true potential. Clustering is quantified with the Kullback-Leibler Divergence (KLD), which also provides conditional uncertainties for our parameter estimates. We show, for toy Gaia-like data in a spherical isochrone potential, that maximizing the KLD of the action distribution relative to a smoother distribution recovers the true values of the potential parameters. The precision depends on the observational errors and the number of streams in the sample; using KIII giants as tracers, we measure the enclosed mass at the average radius of the sample stars accurate to 3% and precise to 20-40%. Recovery of the scale radius is precise to 25%, and is biased 50% high by the small galactocentric distance range of stars in our mock sample (1-25 kpc, or about three scale radii, with mean 6.5 kpc). About 15 streams, with at least 100 stars per stream, are needed to obtain upper and lower bounds on the enclosed mass and scale radius when observational errors are taken into account; 20-25 streams are required to stabilize the size of the confidence interval. If radial velocities are provided for stars out to 100 kpc (10 scale radii), all parameters can be determined with 10% accuracy and 20% precision (1.3% accuracy in the case of the enclosed mass), underlining the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint halo stars observed by Gaia.

An analytical phase-space model for tidal caustics

The class of tidal features around galaxies known variously as shells or umbrellas comprises debris that has arisen from high-mass-ratio mergers with low impact parameter; the nearly radial orbits of the debris give rise to a unique morphology, a universal density profile, and a tight correlation between positions and velocities of the material. As such they are accessible to analytical treatment, and can provide a relatively clean system for probing the gravitational potential of the host galaxy. In this work we present a simple analytical model that describes the density profile, phase-space distribution, and geometry of a shell, and whose parameters are directly related to physical characteristics of the interacting galaxies. The model makes three assumptions: that their orbit is radial, that the potential of the host is spherical at the shell radii, and that the satellite galaxy had a Maxwellian velocity distribution. We quantify the error introduced by the first two assumptions and show that selecting shells by their appearance on the sky is a sufficient basis to assume that these simplifications are valid. We further demonstrate that (1) given only an image of a shell, the radial gravitational force at the shell edge and the phase-space density of the satellite are jointly constrained, (2) that combining the image with measurements of either point line-of-sight velocities or integrated spectra will yield an independent estimate of the gravitational force at a shell, and (3) that an independent measurement of this force is obtained for each shell observed around a given galaxy, potentially enabling a determination of the galactic mass distribution.

The satellites of the Milky Way - Insights from semi-analytic modelling in a LambdaCDM cosmology

We combine the six high-resolution Aquarius dark matter simulations with a semi-analytic galaxy formation model to investigate the properties of the satellites of Milky Way-like galaxies. We find good correspondence with the observed luminosity function, luminosity-metallicity relation and radial distribution of the Milky Way satellites. The star formation histories of the dwarf galaxies in our model vary widely, in accordance with what is seen observationally. Ram-pressure stripping of hot gas from the satellites leaves a clear imprint of the environment on the characteristics of a dwarf galaxy. We find that the fraction of satellites dominated by old populations of stars matches observations well. However, the internal metallicity distributions of the model satellites appear to be narrower than observed. This may indicate limitations in our treatment of chemical enrichment, which is based on the instantaneous recycling approximation. Our model works best if the dark matter halo of the Milky Way has a mass of ~8 x 10^11 Msun, in agreement with the lower estimates from observations. The galaxy that resembles the Milky Way the most also has the best matching satellite luminosity function, although it does not contain an object as bright as the SMC or LMC. Compared to other semi-analytic models and abundance matching relations we find that central galaxies reside in less massive haloes, but the halo mass-stellar mass relation in our model is consistent both with hydrodynamical simulations and with recent observations.

On the identification of merger debris in the {it Gaia} Era

We model the formation of the Galactic stellar halo via the accretion of satellite galaxies onto a time-dependent semi-cosmological galactic potential. Our goal is to characterize the substructure left by these accretion events in a close manner to what may be possible with the {it Gaia} mission. We have created a synthetic {it Gaia} Solar Neighbourhood catalogue by convolving the 6D phase-space coordinates of stellar particles from our disrupted satellites with the latest estimates of the {it Gaia} measurement errors, and included realistic background contamination due to the Galactic disc(s) and bulge. We find that, even after accounting for the expected observational errors, the resulting phase-space is full of substructure. We are able to successfully isolate roughly 50% of the different satellites contributing to the `Solar Neighbourhood by applying the Mean-Shift clustering algorithm in energy-angular momentum space. Furthermore, a Fourier analysis of the space of orbital frequencies allows us to obtain accurate estimates of time since accretion for approximately 30% of the recovered satellites.

Thick-disk evolution induced by the growth of an embedded thin disk

We perform collisionless N-body simulations to investigate the evolution of the structural and kinematical properties of simulated thick disks induced by the growth of an embedded thin disk. The thick disks used in the present study originate from cosmologically-common 5:1 encounters between initially-thin primary disk galaxies and infalling satellites. The growing thin disks are modeled as static gravitational potentials and we explore a variety of growing-disk parameters that are likely to influence the response of thick disks. We find that the final thick-disk properties depend strongly on the total mass and radial scale-length of the growing thin disk, and much less sensitively on its growth timescale and vertical scale-height as well as the initial sense of thick-disk rotation. Overall, the growth of an embedded thin disk can cause a substantial contraction in both the radial and vertical direction, resulting in a significant decrease in the scale-lengths and scale-heights of thick disks. Kinematically, a growing thin disk can induce a notable increase in the mean rotation and velocity dispersions of thick-disk stars. We conclude that the reformation of a thin disk via gas accretion may play a significant role in setting the structure and kinematics of thick disks, and thus it is an important ingredient in models of thick-disk formation.

Orbital Eccentricity as a probe of Thick Disk Formation Scenarios

We study the orbital properties of stars in four (published) simulations of thick disks formed by: i) accretion from disrupted satellites, ii) heating of a pre-existing thin disk by a minor merger, iii) radial migration and iv) gas rich mergers. We find that the distribution of orbital eccentricities are predicted to be different for each model: a prominent peak at low eccentricity is expected for the heating, migration and gas-rich merging scenarios, while the eccentricity distribution is broader and shifted towards higher values for the accretion model. These differences can be traced back to whether the bulk of the stars in each case is formed in-situ or is accreted, and are robust to the peculiarities of each model. A simple test based on the eccentricity distribution of nearby thick disk stars may thus help elucidate the dominant formation mechanism of the Galactic thick disk.

On the nature of the Milky Way satellites

We combine a series of high-resolution simulations with semi-analytic galaxy formation models to follow the evolution of a system resembling the Milky Way and its satellites. The semi-analytic model is based on that developed for the Millennium Simulation, and successfully reproduces the properties of galaxies on large scales, as well as those of the Milky Way. In this model, we are able to reproduce the luminosity function of the satellites around the Milky Way by preventing cooling in haloes with Vvir < 16.7 km/s (i.e. the atomic hydrogen cooling limit) and including the impact of the reionization of the Universe. The physical properties of our model satellites (e.g. mean metallicities, ages, half-light radii and mass-to-light ratios) are in good agreement with the latest observational measurements. We do not find a strong dependence upon the particular implementation of supernova feedback, but a scheme which is more efficient in galaxies embedded in smaller haloes, i.e. shallower potential wells, gives better agreement with the properties of the ultra-faint satellites. Our model predicts that the brightest satellites are associated with the most massive subhaloes, are accreted later (z $lta$ 1), and have extended star formation histories, with only 1 per cent of their stars made by the end of the reionization. On the other hand, the faintest satellites were accreted early, are dominated by stars with age > 10 Gyr, and a few of them formed most of their stars before the reionization was complete. Objects with luminosities comparable to those of the classical MW satellites are associated with dark matter subhaloes with a peak circular velocity $gta$ 10 km/s, in agreement with the latest constraints.

On the common mass scale of the Milky Way satellites

We use a hybrid approach that combines high-resolution simulations of the formation of a Milky Way-like halo with a semi-analytic model of galaxy formation to study the mass content of dwarf galaxies in the concordance $Lambda$CDM cosmology. We find that the mass within 600 pc of dark matter haloes hosting luminous satellites has a median value of $sim 3.2times 10^7$ Msun with very little object-to-object scatter. In contrast, the present day total luminosities of the model satellites span nearly five orders of magnitude. These findings are in very good agreement with the results recently reported in the literature for the dwarf spheroidal galaxies of the Milky Way. In our model, dwarf irregular galaxies like the Small Magellanic Cloud, are predicted to have similar or slightly larger dark matter mass within 600 pc.

Mapping the Galactic Halo VIII: Quantifying substructure

We have measured the amount of kinematic substructure in the Galactic halo using the final data set from the Spaghetti project, a pencil-beam high latitude sky survey. Our sample contains 101 photometrically selected and spectroscopically confirmed giants with accurate distance, radial velocity and metallicity information. We have developed a new clustering estimator: the 4distance measure, which when applied to our data set leads to the identification of 1 group and 7 pairs of clumped stars. The group, with 6 members, can confidently be matched to tidal debris of the Sagittarius dwarf galaxy. Two pairs match the properties of known Virgo structures. Using models of the disruption of Sagittarius in Galactic potentials with different degrees of dark halo flattening, we show that this favors a spherical or prolate halo shape, as demonstrated by Newberg et al. (2007) using SDSS data. One additional pair can be linked to older Sagittarius debris. We find that 20% of the stars in the Spaghetti data set are in substructures. From comparison with random data sets we derive a very conservative lower limit of 10% to the amount of substructure in the halo. However, comparison to numerical simulations shows that our results are also consistent with a halo entirely built up from disrupted satellites, provided the dominating features are relatively broad due to early merging or relatively heavy progenitor satellites.

Simulations of minor mergers. II. The phase-space structure of thick discs

We analyse the phase-space structure of simulated thick discs that are the result of a significant merger between a disc galaxy and a satellite. Our main goal is to establish what would be the characteristic imprints of a merger origin for the Galactic thick disc. We find that the spatial distribution predicted for thick disc stars is asymmetric, seemingly in agreement with recent observations of the Milky Way thick disc. Near the Sun, the accreted stars are expected to rotate more slowly, to have broad velocity distributions, and to occupy preferentially the wings of the line-of-sight velocity distributions. The majority of the stars in our model thick discs have low eccentricity orbits (in clear reference to the pre-existing heated disc) which gives rise to a characteristic (sinusoidal) pattern for their line of sight velocities as function of galactic longitude. The z-component of the angular momentum of thick disc stars provides a clear discriminant between stars from the pre-existing disc and those from the satellite, particularly at large radii. These results are robust against the particular choices of initial conditions made in our simulations, and thus provide clean tests of the disc heating via a minor merger scenario for the formation of thick discs.