The Three-Dimensional Mass Distribution in NGC 1700

A variety of modeling techniques is used with surface photometry from the literature and recently acquired high-accuracy stellar kinematic data to constrain the three-dimensional mass distribution in the luminous cuspy elliptical galaxy NGC 1700. First, we model the radial velocity field and photometry, and, using a Bayesian technique, estimate the triaxiality T and short-to-long axis ratio c in five concentric annuli between approximately 1 and 3 effective radii. The results are completely consistent with T being constant inside about 2.5 r_e (36 arcsec; 6.7/h kpc). Adding an assumption of constant T as prior information gives an upper limit of T < 0.16 (95% confidence); this relaxes to T < 0.22 if it is also assumed that there is perfect alignment between the angular momentum and the galaxy's intrinsic short axis. Near axisymmetry permits us then to use axisymmetric models to constrain the radial mass profile. Using the Jeans (moment) equations, we demonstrate that 2-integral, constant-M/L models cannot fit the data; but a 2-integral model in which the cumulative enclosed M/L increases by a factor of roughly 2 from the center out to 12/h kpc can. Three-integral models constructed by quadratic programming show that, in fact, no constant-M/L model is consistent with the kinematics. Anisotropic 3-integral models with variable M/L, while not uniquely establishing a minimum acceptable halo mass, imply, as do the moment models, a cumulative M/L_B approximately 10 h at 12/h kpc. We conclude that NGC 1700 represents the best stellar dynamical evidence to date for dark matter in elliptical galaxies.Comment: 26 pages, Latex, AASTeX v4.0, with 11 eps figures. To appear in The Astronomical Journal, January 1999. Figures 1 and 3 are color but are readable in b/

Kinematics of elliptical galaxies with a diffuse dust component

Observations show that early-type galaxies contain a considerable amount of interstellar dust, most of which is believed to exist as a diffusely distributed component. We construct a four-parameter elliptical galaxy model in order to investigate the effects of such a smooth absorbing component on the projection of kinematic quantities, such as the line profiles and their moments. We investigate the dependence on the optical depth and on the dust geometry. Our calculations show that both the amplitude and the morphology of these quantities can be significantly affected. Dust effects should therefore be taken in consideration when interpreting photometric and kinematic properties, and correlations that utilize these quantities.Comment: 12 pages, 9 figures, accepted for publication in MNRA

Generalisations of the Tully-Fisher relation for early and late-type galaxies

We study the locus of dwarf and giant early and late-type galaxies on the Tully-Fisher relation (TFR), the stellar mass Tully-Fisher relation (sTFR) and the so-called baryonic or HI gas+stellar mass Tully-Fisher relation (gsTFR). We show that early-type and late-type galaxies, from dwarfs to giants, trace different yet approximately parallel TFRs. Surprisingly, early-type and late-type galaxies trace a single yet curved sTFR over a range of 3.5 orders of magnitude in stellar mass. Moreover, all galaxies trace a single, linear gsTFR, over 3.5 orders of magnitude in HI gas+stellar mass. Dwarf ellipticals, however, lie slightly below the gsTFR. This may indicate that early-type dwarfs, contrary to the late-types, have lost their gas, e.g. by galactic winds or ram-pressure stripping. Overall, environment only plays a secondary role in shaping these relations, making them a rather ``clean'' cosmological tool. LCDM simulations predict roughly the correct slopes for these relations.Comment: 4 pages, 2 figures, accepted for publication in Astrophysical Journa

Player migration and opportunity: examining the efficacy of the UEFA home-grown rule in six European football leagues.

The introduction of UEFAs home-grown rule occurred for the start of the 2006–2007 season with the full quota in place from the 2008–2009 season, which imposed quotas on European clubs. From 2008, clubs are required to have at least 8 players classified as home-grown in the 25-player squad, up from 4 in 2006–2007 and 6 in 2007–2008. This study examines the efficacy of this rule across the six major European leagues (England, France, Germany, Holland, Italy and Spain) in relation to playing opportunities (minutes played and appearances) between 1999 and 2015. This was also examined in relation to age. Since the home-grown rule was introduced for the six nations hosting the major leagues, the rule had different impacts by nationality. Only Germany saw significant increases in the proportion of minutes played by their players when comparing the periods before and after the home-grown rules were imposed. Holland, albeit seeing a slight decrease overall, saw significant increases for playing time for under 21s and 22- to 25-year olds. England and Italy were the two nations where statistically significant decreases in indigenous playing opportunities were recorded since the home-grown rules were introduced

The Compression of Dark Matter Halos by Baryonic Infall

The initial radial density profiles of dark matter halos are laid down by gravitational collapse in hierarchical structure formation scenarios and are subject to further compression as baryons cool and settle to the halo centers. We here describe an explicit implementation of the algorithm, originally developed by Young, to calculate changes to the density profile as the result of adiabatic infall in a spherical halo model. Halos with random motion are more resistant to compression than are those in which random motions are neglected, which is a key weakness of the simple method widely employed. Young's algorithm results in density profiles in excellent agreement with those from N-body simulations. We show how the algorithm may be applied to determine the original uncompressed halos of real galaxies, a step which must be computed with care in order to enable a confrontation with theoretical predictions from theories such as LCDM.Comment: Revised version for ApJ. 8 pages, 8 figures, latex uses emulateap

Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365

We present a flexible and efficient method to construct triaxial dynamical models of galaxies with a central black hole, using Schwarzschild's orbital superposition approach. Our method is general and can deal with realistic luminosity distributions, which project to surface brightness distributions that may show position angle twists and ellipticity variations. The models are fit to measurements of the full line-of-sight velocity distribution (wherever available). We verify that our method is able to reproduce theoretical predictions of a three-integral triaxial Abel model. In a companion paper (van de Ven, de Zeeuw & van den Bosch), we demonstrate that the method recovers the phase-space distribution function. We apply our method to two-dimensional observations of the E3 galaxy NGC 4365, obtained with the integral-field spectrograph SAURON, and study its internal structure, showing that the observed kinematically decoupled core is not physically distinct from the main body and the inner region is close to oblate axisymmetric.Comment: 21 Pages, 14 (Colour) Figures, Companion paper is arXiv:0712.0309 Accepted to MNRAS. Full resolution version at http://www.strw.leidenuniv.nl/~bosch/papers/RvdBosch_triaxmethod.pd

Constraints on H_0 from the Central Velocity Dispersions of Lens Galaxies

We employ Schwarzschild's method of orbit modeling to constrain the mass profiles of the central lens galaxies in Q0957+561 and PG 1115+080. We combine the measured central projected stellar velocity dispersions of these galaxies with the self-similar radial profiles of the rms velocity and of the Gauss-Hermite moment h_4 observed in nearby galaxies for 0 < R < 2 R_eff. For Q0957+561, we find a 16% uncertainty in the galaxy mass, and formal 2-sigma limits on the Hubble constant of H_0 = (61 +13/-15) km/s/Mpc. For PG 1115+080, we find that none of the viable lens models can be ruled out, so that H_0 is not yet strongly constrained by this system.Comment: Revised version accepted by ApJ: slightly modified results for both lens sytems. 18 pages, with 7 inline Postscript figures, LaTeX, aaspp4.sty; postscript paper w/figs (490 kb) also available at http://cfa-www.harvard.edu/~romanow/orbit.post.v2.ps.g

Internal Dynamics, Structure and Formation of Dwarf Elliptical Galaxies: I. A Keck/HST Study of Six Virgo Cluster Dwarfs

Keck/ESI spectroscopy is presented for six Virgo Cluster dwarf elliptical (dE) galaxies. The mean line-of-sight velocity and velocity dispersion are resolved as a function of radius along the major axis of each galaxy, nearly doubling the total number of dEs with spatially-resolved stellar kinematics. None of the observed objects shows evidence of strong rotation: upper limits on v_rot/sigma are well below those expected for rotationally-flattened objects. Such limits place strong constraints on dE galaxy formation models. Although these galaxies continue the trend of low rotation velocities observed in Local Group dEs, they are in contrast to recent observations of large rotation velocities in slightly brighter cluster dEs. Using WFPC2 surface photometry and spherically-symmetric dynamical models, we determine global mass-to-light ratios 3 < M/L_V < 6. These ratios are comparable to those expected for an intermediate-age stellar population and are broadly consistent with the (V-I) colors of the galaxies. This implies that these dEs do not have a significant dark matter component inside an effective radius. Central black holes more massive than 10^7 M_sun can be ruled out. For the 5 nucleated dEs in our sample, we determine kinematic and photometric properties for the central nucleus separately from the underlying host dE galaxy. These nuclei are as bright or brighter than the most luminous Galactic globular clusters and lie near the region of Fundamental Plane space occupied by globular clusters. In this space, the Virgo dE galaxies lie in the same general region as Local Group and other nearby dEs, although non-rotating dEs appear to have a slightly higher mean mass and mass-to-light ratio than their rotating counterparts.Comment: 31 pages, 11 figures. Accepted in the Astronomical Journa