We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical ...linear algebra community for the development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs). We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability. Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task.
We consider what can be learnt about the processes of gas accretion and depletion from the kinematic misalignment between the cold/warm gas and stars in local early-type galaxies. Using simple ...analytic arguments and a toy model of the processes involved, we show that the lack of objects with counter-rotating gas reservoirs strongly constrains the relaxation, depletion and accretion time-scales of gas in early-type galaxies. Standard values of the accretion rate, star-formation efficiency and relaxation rate are not simultaneously consistent with the observed distribution of kinematic misalignments. To reproduce that distribution, both fast gas depletion (t
dep ≲ 108 yr; e.g. more efficient star formation) and fast gas destruction (e.g. by active galactic nucleus feedback) can be invoked, but both also require a high rate of gas-rich mergers (>1 Gyr−1). Alternatively, the relaxation of misaligned material could happen over very long time-scales (≃100 dynamical times or ≈1–5 Gyr). We explore the various physical processes that could lead to fast gas depletion and/or slow gas relaxation, and discuss the prospects of using kinematic misalignments to probe gas-rich accretion processes in the era of large integral-field spectroscopic surveys.
We here present the first spatially resolved study of the initial mass function (IMF) in external galaxies derived using a dynamical tracer of the mass-to-light ratio (M/L). We use the kinematics of ...relaxed molecular gas discs in seven early-type galaxies (ETGs) selected from the ATLAS super( 3D) survey to dynamically determine M/L gradients. These M/L gradients are not very strong in the inner parts of these objects, and galaxies that do show variations are those with the highest specific star formation rates. Stellar population parameters derived from star formation histories are then used in order to estimate the stellar IMF mismatch parameter, and shed light on its variation within ETGs. Some of our target objects require a light IMF, otherwise their stellar population masses would be greater than their dynamical masses. In contrast, other systems seem to require heavier IMFs to explain their gas kinematics. Our analysis again confirms that IMF variation seems to be occurring within massive ETGs. We find good agreement between our IMF normalizations derived using molecular gas kinematics and those derived using other techniques. Despite this, we do not see find any correlation between the IMF normalization and galaxy dynamical properties or stellar population parameters, either locally or globally. In the future, larger studies which use molecules as tracers of galaxy dynamics can be used to help us disentangle the root cause of IMF variation.
Cosmological models predict that galaxies forming in the early Universe experience a chaotic phase of gas accretion and star formation, followed by gas ejection due to feedback processes. Galaxy ...bulges may assemble later via mergers or internal evolution. Here we present submillimeter observations (with spatial resolution of 700 parsecs) of ALESS 073.1, a starburst galaxy at redshift Formula: see text when the Universe was 1.2 billion years old. This galaxy's cold gas forms a regularly rotating disk with negligible noncircular motions. The galaxy rotation curve requires the presence of a central bulge in addition to a star-forming disk. We conclude that massive bulges and regularly rotating disks can form more rapidly in the early Universe than predicted by models of galaxy formation.
We study the relationship between coronal X-ray emission and stellar age for late-type stars, and the variation of this relationship with spectral type. We select 717 stars from 13 open clusters and ...find that the ratio of X-ray to bolometric luminosity during the saturated phase of coronal emission decreases from 10−3.1 for late K dwarfs to 10−4.3 for early-F-type stars across the range 0.29 ≤ (B−V)0 < 1.41. Our determined saturation time-scales vary between 107.8 and 108.3 yr, though with no clear trend across the whole FGK range. We apply our X-ray emission-age relations to the investigation of the evaporation history of 121 known transiting exoplanets using a simple energy-limited model of evaporation and taking into consideration Roche lobe effects and different heating/evaporation efficiencies. We confirm that a linear cut-off of the planet distribution in the M
2/R
3 versus a
−2 plane is an expected result of population modification by evaporation and show that the known transiting exoplanets display such a cut-off. We find that for an evaporation efficiency of 25 per cent we expect around one in ten of the known transiting exoplanets to have lost ≥5 per cent of their mass since formation. In addition we provide estimates of the minimum formation mass for which a planet could be expected to survive for 4 Gyr for a range of stellar and planetary parameters. We emphasize the importance of the earliest periods of a planet's life for its evaporation history with 75 per cent expected to occur within the first Gyr. This raises the possibility of using evaporation histories to distinguish between different migration mechanisms. For planets with spin-orbit angles available from measurements of the Rossiter-McLaughlin effect, no difference is found between the distributions of planets with misaligned orbits and those with aligned orbits. This suggests that dynamical effects accounting for misalignment occur early in the life of the planetary system, although additional data are required to test this.
In this work we discuss the technique of using molecular gas kinematics (or the kinematics of any dynamically cold tracer) to estimate black hole masses. We present a figure of merit that will be ...useful in defining future observational campaigns, and discuss its implications. We show that, in principle, one can estimate black hole masses using data that only resolve scales ≈2 times the formal black hole sphere of influence, and confirm this by re-analysing lower resolution observations of the molecular gas around the black hole in NGC 4526. We go on to discuss the effect that angular resolution, velocity resolution and the depth of the galaxies potential have on the ability to estimate black hole masses, and conclude by discussing prospects for the future. Once Atacama Large Millimetre/submillimetre Array is fully operational, we find that over 105 local galaxies with massive black holes will be observable, and that given sufficient surface brightness sensitivity one could measure the mass of a ≳4 × 108 M⊙ black hole at any redshift.
Abstract
We use eagle to quantify the effect galaxy mergers have on the stellar specific angular momentum of galaxies, jstars. We split mergers into dry (gas-poor)/wet (gas-rich), major/minor and ...different spin alignments and orbital parameters. Wet (dry) mergers have an average neutral gas-to-stellar mass ratio of 1.1 (0.02), while major (minor) mergers are those with stellar mass ratios ≥0.3 (0.1–0.3). We correlate the positions of galaxies in the jstars–stellar mass plane at z = 0 with their merger history, and find that galaxies of low spins suffered dry mergers, while galaxies of normal/high spins suffered predominantly wet mergers, if any. The radial jstars profiles of galaxies that went through dry mergers are deficient by ≈0.3 dex at r ≲ 10 r50 (with r50 being the half-stellar mass radius), compared to galaxies that went through wet mergers. Studying the merger remnants reveals that dry mergers reduce jstars by ≈30 per cent, while wet mergers increase it by ≈10 per cent, on average. The latter is connected to the build-up of the bulge by newly formed stars of high rotational speed. Moving from minor to major mergers accentuates these effects. When the spin vectors of the galaxies prior to the dry merger are misaligned, jstars decreases by a greater magnitude, while in wet mergers corotation and high orbital angular momentum efficiently spun-up galaxies. We predict what would be the observational signatures in the jstars profiles driven by dry mergers: (i) shallow radial profiles and (ii) profiles that rise beyond ≈10 r50, both of which are significantly different from spiral galaxies.
ABSTRACT In this letter we construct a large sample of early-type galaxies (ETGs) with measured gas-phase metallicities from the Sloan Digital Sky Survey and Galaxy Zoo in order to investigate the ...origin of the gas that fuels their residual star formation. We use this sample to show that star-forming elliptical galaxies have a substantially different gas-phase metallicity distribution from spiral galaxies, with ≈7.4 per cent having a very low gas-phase metallicity for their mass. These systems typically have fewer metals in the gas phase than they do in their stellar photospheres, which strongly suggests that the material fuelling their recent star formation was accreted from an external source. We use a chemical evolution model to show that the enrichment time-scale for low-metallicity gas is very short, and thus that cosmological accretion and minor mergers are likely to supply the gas in ≳ 37 per cent of star-forming ETGs, in good agreement with estimates derived from other independent techniques.
Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for ...solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.
ABSTRACT
In this paper, we study the molecular gas content of a representative sample of 67 of the most massive early-type galaxies (ETGs) in the local universe, drawn uniformly from the MASSIVE ...survey. We present new Institut de Radioastronomie Millimétrique (IRAM) 30-m telescope observations of 30 of these galaxies, allowing us to probe the molecular gas content of the entire sample to a fixed molecular-to-stellar mass fraction of 0.1 per cent. The total detection rate in this representative sample is 25$^{+5.9}_{-4.4}$ per cent, and by combining the MASSIVE and atlas3D molecular gas surveys, we find a joint detection rate of 22.4$^{+2.4}_{-2.1}$ per cent. This detection rate seems to be independent of galaxy mass, size, position on the Fundamental Plane, and local environment. We show here for the first time that true slow rotators can host molecular gas reservoirs, but the rate at which they do so is significantly lower than for fast rotators. Objects with a higher velocity dispersion at fixed mass (a higher kinematic bulge fraction) are less likely to have detectable molecular gas, and where gas does exist, have lower molecular gas fractions. In addition, satellite galaxies in dense environments have ≈0.6 dex lower molecular gas-to-stellar mass ratios than isolated objects. In order to interpret these results, we created a toy model, which we use to constrain the origin of the gas in these systems. We are able to derive an independent estimate of the gas-rich merger rate in the low-redshift universe. These gas-rich mergers appear to dominate the supply of gas to ETGs, but stellar mass loss, hot halo cooling, and transformation of spiral galaxies also play a secondary role.
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