Walter Dehnen

University of Leicester, Leiscester, England, United Kingdom

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Publications (65)221.48 Total impact

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    ABSTRACT: Non-axisymmetries in the Galactic potential (spiral arms and bar) induce kinematic groups such as the Hercules stream. Assuming that Hercules is caused by the effects of the Outer Lindblad Resonance of the Galactic bar, we model analytically its properties as a function of position in the Galaxy and its dependence on the bar's pattern speed and orientation. Using data from the RAVE survey we find that the azimuthal velocity of the Hercules structure decreases as a function of Galactocentric radius, in a manner consistent with our analytical model. This allows us to obtain new estimates of the parameters of the Milky Way's bar. The combined likelihood function of the bar's pattern speed and angle has its maximum for a pattern speed of Omega_b=(1.89 +- 0.08) x Omega_0 where Omega_0 is the local circular frequency. Assuming a Solar radius of 8.05 kpc and a local circular velocity of 238 km/s, this corresponds to Omega_b=56 +- 2 km/s/kpc. On the other hand, the bar's orientation phi_b cannot be constrained with the available data. In fact, the likelihood function shows that a tight correlation exists between the pattern speed and the orientation, implying that a better description of our best fit results is given by the linear relation Omega_b/Omega_0=1.905 + 0.0044[phi_b(deg)-47.7], with standard deviation of 0.02. For example, for an angle of phi_b=30deg the pattern speed is 54.0+-0.5km/s/kpc. These results are not very sensitive to the other Galactic parameters such as the circular velocity curve or the peculiar motion of the Sun, and are robust to biases in distance.
    09/2013;
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    ABSTRACT: We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.
    Monthly Notices of the Royal Astronomical Society 06/2012; 431(1). · 5.52 Impact Factor
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    ABSTRACT: Uniquely among the dwarf spheroidal (dSph) satellite galaxies of the Milky Way, Fornax hosts globular clusters. It remains a puzzle as to why dynamical friction has not yet dragged any of Fornax's five globular clusters to the centre, and also why there is no evidence that any similar star cluster has been in the past (for Fornax or any other dSph). We set up a suite of 2800 N-body simulations that sample the full range of globular-cluster orbits and mass models consistent with all existing observational constraints for Fornax. In agreement with previous work, we find that if Fornax has a large dark-matter core then its globular clusters remain close to their currently observed locations for long times. Furthermore, we find previously unreported behaviour for clusters that start inside the core region. These are pushed out of the core and gain orbital energy, a process we call 'dynamical buoyancy'. Thus a cored mass distribution in Fornax will naturally lead to a shell-like globular cluster distribution near the core radius, independent of the initial conditions. By contrast, CDM-type cusped mass distributions lead to the rapid infall of at least one cluster within \Delta t = 1-2Gyr, except when picking unlikely initial conditions for the cluster orbits (\sim 2% probability), and almost all clusters within \Delta t = 10Gyr. Alternatively, if Fornax has only a weakly cusped mass distribution, dynamical friction is much reduced. While over \Delta t = 10Gyr this still leads to the infall of 1-4 clusters from their present orbits, the infall of any cluster within \Delta t = 1-2Gyr is much less likely (with probability 0-70%, depending on \Delta t and the strength of the cusp). Such a solution to the timing problem requires that in the past the globular clusters were somewhat further from Fornax than today; they most likely did not form within Fornax, but were accreted.
    Monthly Notices of the Royal Astronomical Society 05/2012; 426(1). · 5.52 Impact Factor
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    ABSTRACT: Non-axisymmetric components, such as spirals and central bars, play a major role in shaping galactic discs. An important aspect of the disc secular evolution driven by these perturbers is the radial migration of stars. It has been suggested recently that migration can populate a thick-disc component from inner-disc stars with high vertical energies. Since this has never been demonstrated in simulations, we study in detail the effect of radial migration on the disc velocity dispersion and disc thickness, by separating simulated stars into migrators and non-migrators. We apply this method to three isolated barred Tree-SPH N-body galaxies with strong radial migration. Contrary to expectations, we find that as stellar samples migrate, on the average, their velocity dispersion change (by as much as 50%) in such a way as to approximately match the non-migrating population at the radius at which they arrive. We show that, in fact, migrators suppress heating in parts of the disc. To confirm the validity of our findings, we also apply our technique to three cosmological re-simulations, which use a completely different simulation scheme and, remarkably, find very similar results. We believe the inability of migration to thicken discs is a fundamental property of internal disc evolution, irrespective of the migration mechanism at work. We explain this with the approximate conservation of the (average) vertical and radial actions rather than the energy. This "action mixing" can be used to constrain the migration rate in the Milky Way: estimates of the average vertical action in observations for different populations of stars should reveal flattening with radius for older groups of stars.
    Astronomy and Astrophysics 05/2012; · 5.08 Impact Factor
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    Walter Dehnen, Hossam Aly
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    ABSTRACT: The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number NH of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability. Therefore, we investigate the suitability of the Wendland functions as smoothing kernels and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all NH, despite having vanishing derivative at the origin (disproving traditional ideas about the origin of this instability; instead, we uncover a relation with the kernel Fourier transform and give an explanation in terms of the SPH density estimator). The Wendland kernels are computationally more convenient than the higher-order B-splines, allowing large NH and hence better numerical convergence (note that computational costs rise sub-linear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ~= 60 obtains much better convergence then the standard cubic spline.
    Monthly Notices of the Royal Astronomical Society 04/2012; 425(2). · 5.52 Impact Factor
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    ABSTRACT: Disc non-axisymmetrc components, such as spirals and central bars, are nowadays known to play an important role in shaping galactic discs. Here we use Tree-SPH N-body simulations to examine the effect of these perturbers on two aspects: the occurrence of multiple patterns in discs and the effects of radial migration on disc thickening. We find that, in addition to a central bar, multiple spiral patterns and lopsided modes develop in all models. Interaction among these asymmetric features results in a large scale stellar migration. However, we show that, despite the strong radial mixing, discs cannot be thickened sufficiently to match observed thick discs. We relate this to the adiabatic cooling as stars migrate radially outwards. We also find that the bulge contribution to a thick-disc component for an Sa-type galaxy at ~2.5 disc scale-lengths is less than 1% and zero in the case of a Milky Way-like, Sb-type. Our findings cast doubt on the plausibility of thick disc formation via stellar radial migration.
    11/2011;
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    David Cole, Walter Dehnen, Mark Wilkinson
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    ABSTRACT: We consider the infall of a massive clump into a dark-matter halo as a simple and extreme model for the effect of baryonic physics (neglected in gravity-only simulations of large-scale structure formation) on the dark-matter. We find that such an infalling clump is extremely efficient in altering the structure of the halo and reducing its central density: a clump of 1% the mass of the halo can remove about twice its own mass from the inner halo and transform a cusp into a core or weaker cusp. If the clump is subsequently removed, mimicking a galactic wind, the central halo density is further reduced and the mass removed from the inner halo doubled. Lighter clumps are even more efficient: the ratio of removed mass to clump mass increases slightly towards smaller clump masses. This process is the more efficient the more radially anisotropic the initial dark-matter velocities. While such a clumpy infall may be somewhat unrealistic, it demonstrates that the baryons need to transfer only a small fraction of their initial energy to the dark matter via dynamical friction to explain the discrepancy between predicted dark-matter density profiles and those inferred from observations of dark-matter dominated galaxies.
    Monthly Notices of the Royal Astronomical Society 05/2011; 416. · 5.52 Impact Factor
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    W. Dehnen, J. I. Read
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    ABSTRACT: We describe the astrophysical and numerical basis of N -body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N -body simulations and their most important results.
    European Physical Journal Plus 01/2011; 126(5):1-28. · 1.30 Impact Factor
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    ABSTRACT: We follow the dynamical and chemical evolution of isolated systems tuned in their properties on selfgravitating spherical three component (gas+stars+dark matter) dwarf spheroidal galaxies (dSph). The system starts as a strongly dark matter dominated cuspy density profile. It is shown that after few Gyr of evolution the star formation processes are naturally able to reshape the cuspy dark matter profile into a flatter one. The same family of models is then evolved by orbiting in a Milky Way external potential in order to investigate the history of the Carina dwarf galaxy. Structural parameters and the star formation history of Carina are self-consistently determined in good agreement with the observations.
    EAS Publications Series 01/2011; 48:461-462.
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    Lee Cullen, Walter Dehnen
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    ABSTRACT: In smoothed particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial viscosity, which uses the total time derivative of the velocity divergence as shock indicator and aims at completely eliminating viscosity away from shocks. We subject the new scheme to numerous tests and find that the method works at least as well as any previous technique in the strong-shock regime, but becomes virtually inviscid away from shocks, while still maintaining particle order. In particular sound waves or oscillations of gas spheres are hardly damped over many periods.
    Monthly Notices of the Royal Astronomical Society 10/2010; 408(2):669 - 683. · 5.52 Impact Factor
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    Ralph Schönrich, James Binney, Walter Dehnen
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    ABSTRACT: We re-examine the stellar kinematics of the solar neighbourhood in terms of the velocity υ⊙ of the Sun with respect to the local standard of rest. We show that the classical determination of its component V⊙ in the direction of Galactic rotation via Strömberg's relation is undermined by the metallicity gradient in the disc, which introduces a correlation between the colour of a group of stars and the radial gradients of its properties. Comparing the local stellar kinematics to a chemodynamical model which accounts for these effects, we obtain (U, V, W)⊙= (11.1+0.69−0.75, 12.24+0.47−0.47, 7.25+0.37−0.36) km s−1, with additional systematic uncertainties ∼(1, 2, 0.5) km s−1. In particular, V⊙ is 7 km s−1 larger than previously estimated. The new values of (U, V, W)⊙ are extremely insensitive to the metallicity gradient within the disc.
    Monthly Notices of the Royal Astronomical Society 04/2010; 403(4):1829 - 1833. · 5.52 Impact Factor
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    ABSTRACT: The chemodynamical evolution of spherical multi-component self-gravitating models for isolated dwarf galaxies is studied. We compared their evolution with and without feedback effects from star formation processes. We found that initially cuspy dark matter profiles flatten with time without any special tuning conditions as a result of star formation. Thus the seemingly flattened profiles found in many dwarfs do not contradict the cuspy profiles predicted by cosmological models. We also calculated the chemical evolution of stars and gas, to permit comparisons with observational data.
    Astronomy and Astrophysics 01/2010; · 5.08 Impact Factor
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    Walter Dehnen
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    ABSTRACT: The made-to-measure N-body method (Syer & Tremaine 1996) slowly adapts the particle weights of an N-body model, whilst integrating the trajectories in an assumed static potential, until some constraints are satisfied, such as optimal fits to observational data. I propose a novel technique for this adaption procedure, which overcomes several limitations and shortcomings of the original method. The capability of the new technique is demonstrated by generating realistic N-body equilibrium models for dark-matter haloes with prescribed density profile, triaxial shape, and slowly outwardly growing radial velocity anisotropy
    Monthly Notices of the Royal Astronomical Society 02/2009; 395(2). · 5.52 Impact Factor
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    ABSTRACT: We report the discovery of two well-defined tidal tails emerging from the sparse remote globular cluster Palomar 5. These tails stretch out symmetrically to both sides of the cluster in the direction of constant Galactic latitude and subtend an angle of 26 on the sky. The tails have been detected in commissioning data of the Sloan Digital Sky Survey, providing deep five-color photometry in a 25-wide band along the equator. The stars in the tails make up a substantial part (~) of the current total population of cluster stars in the magnitude interval 19.5 ≤ i* ≤ 22.0. This reveals that the cluster is subject to heavy mass loss. The orientation of the tails provides an important key for the determination of the cluster's Galactic orbit.
    The Astrophysical Journal 12/2008; 548(2):L165. · 6.73 Impact Factor
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    ABSTRACT: We present the second data release of the Radial Velocity Experiment (RAVE), an ambitious spectroscopic survey to measure radial velocities (RVs) and stellar atmosphere parameters of up to one million stars using the 6dF multi-object spectrograph on the 1.2-m UK Schmidt Telescope of the Anglo-Australian Observatory (AAO). It is obtaining medium resolution spectra (median R=7,500) in the Ca-triplet region (8,410--8,795 \AA) for southern hemisphere stars in the magnitude range 9<I<12. Following the first data release (Steinmetz et al. 2006) the current release doubles the sample of published RVs, now containing 51,829 RVs for 49,327 individual stars observed on 141 nights between April 11 2003 and March 31 2005. Comparison with external data sets shows that the new data collected since April 3 2004 show a standard deviation of 1.3 km/s, about twice better than for the first data release. For the first time this data release contains values of stellar parameters from 22,407 spectra of 21,121 individual stars. They were derived by a penalized \chi^2 method using an extensive grid of synthetic spectra calculated from the latest version of Kurucz models. From comparison with external data sets, our conservative estimates of errors of the stellar parameters (for a spectrum with S/N=40) are 400 K in temperature, 0.5 dex in gravity, and 0.2 dex in metallicity. We note however that the internal errors estimated from repeat RAVE observations of 822 stars are at least a factor 2 smaller. We demonstrate that the results show no systematic offsets if compared to values derived from photometry or complementary spectroscopic analyses. The data release includes proper motion and photometric measurements. It can be accessed via the RAVE webpage: http://www.rave-survey.org and through CDS. Comment: 85 pages, 23 figures, 14 tables, accepted for publication in the Astronomical Journal
    The Astronomical Journal 06/2008; · 4.97 Impact Factor
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    ABSTRACT: We have investigated the spatial extent and structure of the Draco dwarf spheroidal galaxy by using deep wide-field multicolor CCD photometry from the Sloan Digital Sky Survey (SDSS). Our study covers an area of 27 deg2 around the center of the Draco dwarf and reaches 2 mag below the level of Draco's horizontal branch. The SDSS photometry allows very effective filtering in color-magnitude space. With such filtering the density of the foreground of Galactic field stars is decreased by more than an order of magnitude, and the stellar population of the Draco dwarf galaxy thus stands out with much higher contrast than in former investigations. We show that the spatial distribution of Draco's red giants, red horizontal-branch stars, and subgiants down to i* = 21.7 mag does not provide evidence for the existence of tidally induced tails or a halo of unbound stars. The projected surface density of the dwarf galaxy is flattened with a nearly constant ellipticity of 0.29 ± 0.02 at position angle 88° ± 3°. The radial profile can be fitted by King models, as well as by a generalized exponential. Using the empirical King profile, the core radius and the limiting (or tidal) radius along the major axis are rc = 77 and rt = 401, respectively; the latter means that the size of the Draco dwarf galaxy is 40% larger than previously measured. Fitting the profile of King's theoretical models yields a still larger limiting radius of rt = 495. There is no clear indication of a taillike extension of the Draco population beyond this radius. A break in the radial surface density profile, which might indicate a halo of extratidal stars, is also not found in our Draco data. We conclude that down to the above magnitude limit tidal effects can exist only at a level of 10-3 of the central surface density of Draco or below. The regular structure of Draco found from the new data argues against its being a portion of an unbound tidal stream and lends support to the assumption of dynamical equilibrium, which is the basis for mass estimation. The changes in the values for the core radius and limiting radius imply that the total mass of Draco is higher by more than a factor of 2. Using a King spherical model of equivalent size as a reference and adopting a line-of-sight velocity dispersion of either 10.7 or 8.5 km s-1, we derive estimates of the total mass within radius rt of (3.5 ± 0.7) × 107 M and (2.2 ± 0.5) × 107 M, respectively. From the combined i-band flux of all possible Draco members that lie within major-axis radius rt we determine the total luminosity of the Draco dwarf galaxy as (L/L)i = (2.4 ± 0.5) × 105. This includes corrections for the flux of the foreground stars and the unseen fainter part of the Draco population. We thus obtain overall mass-to-light ratios M/Li of 146 ± 42, or 92 ± 28 in solar units. In summary, our results strengthen the case for a strongly dark matter–dominated, bound stellar system.
    The Astronomical Journal 12/2007; 122(5):2538. · 4.97 Impact Factor
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    ABSTRACT: Using wide-field photometric data from the Sloan Digital Sky Survey (SDSS), we recently showed that the Galactic globular cluster Palomar 5 is in the process of being tidally disrupted. Its tidal tails were initially detected in a 25 wide band along the celestial equator. A new analysis of SDSS data for a larger field now reveals that the tails of Pal 5 have a much larger spatial extent and can be traced over an arc of 10° on the sky, corresponding to a projected length of 4 kpc at the distance of the cluster. The tail that trails behind the Galactic motion of the cluster fades into the field at an angular distance of 65 from the cluster center but shows a pronounced density maximum between 2° and 4° from the center. The leading tail, of length 35, extends down to the border of the available field and thus presumably continues beyond it. The projected width of these tails is small and almost constant (FWHM ~ 120 pc), which implies that they form a dynamically cold and hence long-lived structure. The number of former cluster stars found in the tails adds up to about 1.2 times the number of stars in the cluster, that is, the tails are more massive than the cluster in its present state. The radial profile of stellar surface density in the tails approximately follows a power law rγ with -1.5 ≤ γ ≤ -1.2. The stream of debris from Pal 5 is significantly curved, which demonstrates its acceleration by the Galactic potential. The stream sets tight constraints on the geometry of the cluster's Galactic orbit. We conclude that the cluster is presently near the apocenter but has repeatedly undergone disk crossings in the inner part of the Galaxy leading to strong tidal shocks. Using the spatial offset between the tails and the cluster's orbit, we estimate the mean drift rate of the tidal debris and thus the mean mass-loss rate of the cluster. Our results suggest that the observed debris originates mostly from mass loss within the last 2 Gyr. The cluster is likely to be destroyed after the next disk crossing, which will happen in about 100 Myr. There is strong evidence against the suggestion that Pal 5 might be associated with the Sagittarius dwarf galaxy.
    The Astronomical Journal 12/2007; 126(5):2385. · 4.97 Impact Factor
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    ABSTRACT: The tidal tails of the globular cluster Palomar 5 are analyzed over a 41 deg2 area of the Sloan Digital Sky Survey photometric catalogs. The matched filter algorithm provides the maximum possible signal-to-noise detection of the cluster stars over the measured background, and the expected and actual effectiveness of the technique in the context of this data set is discussed. The stellar background is examined in some detail for systematic variation as a function of Galactic position in order to assess its effect on the detection efficiency. Of the total number of Pal 5 stars detected, 45% are out in the tails. The tails are found as the only additional 3 σ overdensity of cluster stars over the entire 41 deg2 area studied. The annular-averaged density of stars along the tails is fitted to a power law in radius with best-fit index -1.58 ± 0.07, significantly steeper than that predicted from a constant orbit-averaged mass-loss rate.
    The Astronomical Journal 12/2007; 124(1):349. · 4.97 Impact Factor
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    ABSTRACT: We report new constraints on the local escape speed of our Galaxy. Our analysis is based on a sample of high-velocity stars from the RAVE survey and two previously published data sets. We use cosmological simulations of disc galaxy formation to motivate our assumptions on the shape of the velocity distribution, allowing for a significantly more precise measurement of the escape velocity compared to previous studies. We find that the escape velocity lies within the range 498 < vesc < 608 km s−1 (90 per cent confidence), with a median likelihood of 544 km s−1. The fact that v2esc is significantly greater than 2v2circ (where vcirc= 220 km s−1 is the local circular velocity) implies that there must be a significant amount of mass exterior to the solar circle, that is, this convincingly demonstrates the presence of a dark halo in the Galaxy. We use our constraints on vesc to determine the mass of the Milky Way halo for three halo profiles. For example, an adiabatically contracted NFW halo model results in a virial mass of 1.42+1.14−0.54× 1012 M⊙ and virial radius of (90 per cent confidence). For this model the circular velocity at the virial radius is 142+31−21 km s−1. Although our halo masses are model dependent, we find that they are in good agreement with each other.
    Monthly Notices of the Royal Astronomical Society 07/2007; 379(2):755 - 772. · 5.52 Impact Factor
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    Paul J. McMillan, Walter Dehnen
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    ABSTRACT: We present a general recipe for constructing N-body realizations of galaxies comprised of near-spherical and disc components. First, an exact spherical distribution function for the spheroids (halo & bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realisation of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.
    Monthly Notices of the Royal Astronomical Society 04/2007; · 5.52 Impact Factor

Publication Stats

3k Citations
221.48 Total Impact Points

Institutions

  • 2004–2013
    • University of Leicester
      • Department of Physics and Astronomy
      Leiscester, England, United Kingdom
  • 2011
    • University of Rochester
      • Department of Physics and Astronomy
      Rochester, New York, United States
  • 2000–2008
    • Max Planck Institute for Astronomy
      Heidelburg, Baden-Württemberg, Germany
  • 1998–2006
    • University of Oxford
      • Rudolf Peierls Centre for Theoretical Physics
      Oxford, England, United Kingdom