Interactive (statistical) visualisation and exploration of a billion objects with Vaex

With new catalogues arriving such as the Gaia DR1, containing more than a billion objects, new methods of handling and visualizing these data volumes are needed. In visualization, one problem is that the number of datapoints can become so large, that a scatter plot becomes cluttered. Another problem is that with over a billion objects, only a few cpu cycles are available per object if one wants to process them within a second, making traditional methods by rendering glyphs not viable. Instead, we show that by calculating statistics on a regular (N-dimensional) grid, visualizations of a billion objects can be done within a second on a modern desktop computer. This is achieved using memory mapping of hdf5 files together with a simple binning algorithm, which are part of a Python library called vaex. This enables efficient exploration or large datasets interactively, making science exploration of large catalogues feasible. Vaex is a Python library, which also integrates well in the Jupyter/Numpy/Astropy/matplotlib stack. Build on top of this is the vaex application, which allows for interactive exploration and visualization. The motivation for developing vaex is the catalogue of the Gaia satellite, however, vaex can also be used on SPH or N-body simulations, any other (future) catalogues such as SDSS, Pan-STARRS, LSST, WISE, 2MASS, etc. or other tabular data. The homepage for vaex is http://vaex.astro.rug.nl.Comment: 6 pages, 4 figures, conference proceeding for the IAU symposium 325 on Astroinformatics (accepted), webpage http://vaex.astro.rug.n

Vaex: Big Data exploration in the era of Gaia

We present a new Python library called vaex, to handle extremely large tabular datasets, such as astronomical catalogues like the Gaia catalogue, N-body simulations or any other regular datasets which can be structured in rows and columns. Fast computations of statistics on regular N-dimensional grids allows analysis and visualization in the order of a billion rows per second. We use streaming algorithms, memory mapped files and a zero memory copy policy to allow exploration of datasets larger than memory, e.g. out-of-core algorithms. Vaex allows arbitrary (mathematical) transformations using normal Python expressions and (a subset of) numpy functions which are lazily evaluated and computed when needed in small chunks, which avoids wasting of RAM. Boolean expressions (which are also lazily evaluated) can be used to explore subsets of the data, which we call selections. Vaex uses a similar DataFrame API as Pandas, a very popular library, which helps migration from Pandas. Visualization is one of the key points of vaex, and is done using binned statistics in 1d (e.g. histogram), in 2d (e.g. 2d histograms with colormapping) and 3d (using volume rendering). Vaex is split in in several packages: vaex-core for the computational part, vaex-viz for visualization mostly based on matplotlib, vaex-jupyter for visualization in the Jupyter notebook/lab based in IPyWidgets, vaex-server for the (optional) client-server communication, vaex-ui for the Qt based interface, vaex-hdf5 for hdf5 based memory mapped storage, vaex-astro for astronomy related selections, transformations and memory mapped (column based) fits storage. Vaex is open source and available under MIT license on github, documentation and other information can be found on the main website: https://vaex.io, https://docs.vaex.io or https://github.com/maartenbreddels/vaexComment: 14 pages, 8 figures, Submitted to A&A, interactive version of Fig 4: https://vaex.io/paper/fig

Complexity on dwarf galaxies scale: A bimodal distribution function in Sculptor

In previous work we have presented Schwarzschild models of the Sculptor dSph, demonstrating that this system could be embedded in dark matter halos that are either cusped or cored. Here we show that the non-parametric distribution function recovered through Schwarschild's method is bimodal in energy and angular momentum space for all best fitting mass models explored. We demonstrate that this bimodality is directly related to the two components known to be present in Sculptor through stellar populations analysis, although our method is purely dynamical in nature and does not use this prior information. It therefore constitutes independent confirmation of the existence of two physically distinct dynamical components in Sculptor and suggests a rather complex assembly history for this dwarf galaxy.Comment: 4 pages, 4 figures, 1 table, accepted to ApJ Letter

Matching the dark matter profiles of dSph galaxies with those of simulated satellites: a two parameter comparison

We compare the dark matter halos' structural parameters derived for four Milky Way dwarf spheroidal galaxies to those of subhalos found in cosmological $N$-body simulations. We confirm that estimates of the mass at a single fixed radius are fully consistent with the observations. However, when a second structural parameter such as the logarithmic slope of the dark halo density profile measured close to the half-light radius is included in the comparison, we find little to no overlap between the satellites and the subhalos. Typically the right mass subhalos have steeper profiles at these radii than measurements of the dSph suggest. Using energy arguments we explore if it is possible to solve this discrepancy by invoking baryonic effects. Assuming that feedback from supernovae can lead to a reshaping of the halos, we compute the required efficiency and find entirely plausible values for a significant fraction of the subhalos and even as low as 0.1%. This implies that care must be taken not to exaggerate the effect of supernovae feedback as this could make the halos too shallow. These results could be used to calibrate and possibly constrain feedback recipes in hydrodynamical simulations.Comment: 6 pages, 3 figures, submitted to ApJ

A box full of chocolates: The rich structure of the nearby stellar halo revealed by Gaia and RAVE

The hierarchical structure formation model predicts that stellar halos should form, at least partly, via mergers. If this was a predominant formation channel for the Milky Way's halo, imprints of this merger history in the form of moving groups or streams should exist also in the vicinity of the Sun. Here we study the kinematics of halo stars in the Solar neighbourhood using the very recent first data release from the Gaia mission, and in particular the TGAS dataset, in combination with data from the RAVE survey. Our aim is to determine the amount of substructure present in the phase-space distribution of halo stars that could be linked to merger debris. To characterise kinematic substructure, we measure the velocity correlation function in our sample of halo (low metallicity) stars. We also study the distribution of these stars in the space of energy and two components of the angular momentum, in what we call "Integrals of Motion" space. The velocity correlation function reveals substructure in the form of an excess of pairs of stars with similar velocities, well above that expected for a smooth distribution. Comparison to cosmological simulations of the formation of stellar halos indicate that the levels found are consistent with the Galactic halo having been built fully via accretion. Similarly, the distribution of stars in the space of "Integrals of motion" is highly complex. A strikingly high fraction (between 58% and upto 73%) of the stars that are somewhat less bound than the Sun are on (highly) retrograde orbits. A simple comparison to Milky Way-mass galaxies in cosmological hydrodynamical simulations suggests that less than 1% have such prominently retrograde outer halos. We also identify several other statistically significant structures in "Integrals of Motion" space that could potentially be related to merger events.Comment: 19 pages, 16 figures. A&A in pres

Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy

We test the ability of Schwarzschild's orbit superposition method in measuring the mass content, scale radius and shape of a flattened dwarf spheroidal galaxy. Until now, most dynamical model efforts have assumed that dwarf spheroidal galaxies and their host halos are spherical. We use an Evans model (1993) to construct an isothermal mock galaxy whose properties somewhat resemble those of the Sculptor dwarf spheroidal galaxy. This mock galaxy contains flattened luminous and dark matter components, resulting in a logarithmic profile for the global potential. We have tested how well our Schwarzschild method could constrain the characteristic parameters of the system for different sample sizes, and also if the functional form of the potential was unknown. When assuming the true functional form of the potential, the Schwarzschild modelling technique is able to provide an accurate and precise measurement of the characteristic mass parameter of the system and reproduces well the light distribution and the stellar kinematics of our mock galaxy. When assuming a different functional form for the potential, such as a flattened NFW profile, we also constrain the mass and scale radius to their expected values. However in both cases, we find that the flattening parameter remains largely unconstrained. This is likely because the information content of the velocity dispersion on the geometric shape of the potential is too small, since $\sigma$ is constant across our mock dSph. Our results using Schwarzschild's method indicate that the mass enclosed can be derived reliably, even if the flattening parameter is unknown, and already for samples containing 2000 line-of-sight radial velocities, such as those currently available. Further applications of the method to more general distribution functions of flattened systems are needed to establish how well the flattening of dSph dark halos can be determined.Comment: 13 pages, 14 figures. Comments are welcom

Orbit-based dynamical models of the Sculptor dSph galaxy

We have developed spherically symmetric dynamical models of dwarf spheroidal galaxies using Schwarzschild's orbit superposition method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) as well as on the orbital structure of the system (e.g. velocity anisotropy). This method is thus less prone to biases introduced by assumptions in comparison to the more commonly used Jeans modelling, and it allows us to derive the dark matter content in a robust way. Here we present our results for the Sculptor dwarf spheroidal galaxy, after testing our methods on mock data sets. We fit both the second and fourth velocity moment profile to break the mass-anisotropy degeneracy. For an NFW dark matter halo profile, we find that the mass of Sculptor within 1 kpc is M_1kpc = 1.03 \pm 0.07 x 10^8 Msol, and that its velocity anisotropy profile is tangentially biased and nearly constant with radius. The preferred concentration (c ~ 15) is low for its dark matter mass but consistent within the scatter found in N-body cosmological simulations. When we let the value of the central logarithmic slope \alpha{} vary, we find that the best-fit model has \alpha{} = 0, although an NFW cusp or shallower is consistent at 1 \sigma{} confidence level. On the other hand, very cuspy density profiles with logarithmic central slopes \alpha{} < -1.5 are strongly disfavoured for Sculptor.Comment: 18 pages, 12 figures, accepted by MNRAS http://mnras.oxfordjournals.org/content/433/4/317

The dynamically selected stellar halo of the Galaxy with Gaia and the tilt of the velocity ellipsoid

Aims. We study the dynamical properties of halo stars located in the solar neighbourhood. Our goal is to explore how the properties of the halo depend on the selection criteria used to define a sample of halo stars. Once this is understood, we proceed to measure the shape and orientation of the halo’s velocity ellipsoid and we use this information to put constraints on the gravitational potential of the Galaxy. Methods. We use the recently released Gaia DR1 catalogue cross-matched to the RAVE dataset for our analysis. We develop a dynamical criterion based on the distribution function of stars in various Galactic components, using action integrals to identify halo members, and we compare this to the metallicity and to kinematically selected samples. Results. With this new method, we find 1156 stars in the solar neighbourhood that are likely members of the stellar halo. Our dynamically selected sample consists mainly of distant giants on elongated orbits. Their metallicity distribution is rather broad, with roughly half of the stars having [M/H] ≥ −1 dex. The use of different selection criteria has an important impact on the characteristics of the velocity distributions obtained. Nonetheless, for our dynamically selected and for the metallicity selected samples, we find the local velocity ellipsoid to be aligned in spherical coordinates in a Galactocentric reference frame. This suggests that the total gravitational potential is rather spherical in the region spanned by the orbits of the halo stars in these samples

An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

<p>We demonstrate the existence of a distribution function that can be used to represent spherical mass-less cored stellar systems having constant mildly tangential velocity anisotropy embedded in cuspy dark-matter halos. In particular, we derived analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo for beta = -0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile gamma(0) > 2 beta(0). Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group.</p>

Model comparison of the dark matter profiles of Fornax, Sculptor, Carina and Sextans

<p>Aims. We compare dark matter profile models of four dwarf spheroidal galaxies satellites of the MilkyWay using Bayesian evidence. Methods. We use orbit based dynamical models to fit the 2nd and 4th moments of the line of sight velocity distributions of the Fornax, Sculptor, Carina and Sextans dwarf spheroidal galaxies. We compare NFW, Einasto and several cored profiles for their dark halos and present the probability distribution functions of the model parameters.</p><p>Results. For each galaxy separately we compare the evidence for the various dark matter profiles, and find that it is not possible to distinguish between these specific parametric dark matter density profiles using the current data. Nonetheless, from the combined evidence, we find that is unlikely that all galaxies are embedded in the same type of cored profiles of the form PDM 1/(1 + r(2))(beta/2), where beta = 3, 4. For each galaxy, we also obtain an almost model independent, and therefore accurate, constraint on the logarithmic slope of the dark matter density distribution at a radius similar to r-3, i. e. where the logarithmic slope of the stellar density profile is -3.</p><p>Conclusions. For each galaxy, we find that all best fit models essentially have the same mass distribution over a large range in radius (from just below r-3 to the last measured data point). This remarkable finding likely implies much stronger constraints on the characteristics that subhalos extracted from cosmological simulations should have in order to host the dSph galaxies around the Milky Way.</p>