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1.
It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function (DF) are not fully independent. Here, we study the interplay between density profile and orbital anisotropy at large radii in physically admissible (consistent) stellar systems. The analysis is carried out by using two-component  ( n - γ, γ1)  spherical self-consistent galaxy models, in which one density distribution follows a generalized γ profile with external logarithmic slope n , and the other a standard  γ1  profile (with external slope 4). The two density components have different 'core' radii, the orbital anisotropy is controlled with the Osipkov–Merritt recipe, and for simplicity we assume that the mass of the  γ1  component dominates the total potential everywhere. The necessary and sufficient conditions for phase-space consistency are determined analytically, also in the presence of a dominant massive central black hole, and the analytical phase-space DF of (   n - γ  ,1) models, and of   n - γ  models with a central black hole, is derived for  γ= 0, 1, 2  . It is found that the density slope in the external regions of a stellar system can play an important role in determining the amount of admissible anisotropy: in particular, for fixed density slopes in the central regions, systems with a steeper external density profile can support more radial anisotropy than externally flatter models. This is quantified by an inequality formally identical to the 'cusp slope-central anisotropy' theorem by An & Evans, relating at all radii (and not just at the centre) the density logarithmic slope and the anisotropy indicator in all Osipkov–Merritt systems.  相似文献   

2.
This is the second in a series of papers dedicated to unveiling the mass structure and orbital content of a sample of flattened early-type galaxies in the Coma cluster. The ability of our orbit libraries to reconstruct internal stellar motions and the mass composition of a typical elliptical in the sample is investigated by means of Monte Carlo simulations of isotropic rotator models. The simulations allow a determination of the optimal amount of regularization needed in the orbit superpositions. It is shown that under realistic observational conditions and with the appropriate regularization, internal velocity moments can be reconstructed to an accuracy of ≈15 per cent; the same accuracy can be achieved for the circular velocity and dark matter fraction. In contrast, the flattening of the halo remains unconstrained. Regularized orbit superpositions are applied to a first galaxy in our sample, NGC 4807, for which stellar kinematical observations extend to  3  r eff  . The galaxy seems dark-matter dominated outside   r > 2  r eff  . Logarithmic dark matter potentials are consistent with the data, as well as NFW profiles, mimicking logarithmic potentials over the observationally sampled radial range. In both cases, the derived stellar mass-to-light ratio ϒ agrees well with independently obtained mass-to-light ratios from stellar population analysis. The achieved accuracy is  Δϒ≈ 0.5  . Kinematically, NGC 4807 is characterized by mild radial anisotropy outside   r > 0.5  r eff  , becoming isotropic towards the centre. Our orbit models hint at either a distinct stellar component or weak triaxiality in the outer parts of the galaxy.  相似文献   

3.
Galactic nuclei are now generally thought to have density cusps in their centres, and the evidence is mounting that as a consequence they are unlikely to be triaxial. Self-consistent stellar dynamical models of non-axisymmetric cusps would be an interesting counter-argument to this conclusion. We consider 2D analogues of triaxial cusps: a sequence of non-axisymmetric, cuspy discs first described by Sridhar & Touma. Scale-free models with potential Φ ∝  r α are examined in detail. It is shown analytically for 0 < α ≲ 0.43 that self-consistent models with positive phase-space density do not exist. Numerical solutions of the combined Vlasov and Poisson equations suggest that the whole sequence of models with 0 < α < 1 are also unphysical. Together with existing work on cusps, we conclude on purely theoretical grounds that galactic nuclei are not expected to be triaxial.  相似文献   

4.
Collisionless stellar systems are driven towards equilibrium by mixing of phase-space elements. I show that the excess-mass function     [where     is the coarse-grained distribution function] always decreases on mixing . D ( f ) gives the excess mass from values of     . This novel form of the mixing theorem extends the maximum phase-space density argument to all values of f . The excess-mass function can be computed from N -body simulations and is additive: the excess mass of a combination of non-overlapping systems is the sum of their individual D ( f ). I propose a novel interpretation for the coarse-grained distribution function, which avoids conceptual problems with the mixing theorem.
As an example application, I show that for self-gravitating cusps (  ρ∝ r −γ  as   r → 0  ) the excess mass   D ∝ f −2(3−γ)/(6−γ)  as   f →∞  , i.e. steeper cusps are less mixed than shallower ones, independent of the shape of surfaces of constant density or details of the distribution function (e.g. anisotropy). This property, together with the additivity of D ( f ) and the mixing theorem, implies that a merger remnant cannot have a cusp steeper than the steepest of its progenitors. Furthermore, I argue that the cusp of the remnant should not be shallower either, implying that the steepest cusp always survives.  相似文献   

5.
We construct a new sample of ∼1700 solar neighbourhood halo subdwarfs from the Sloan Digital Sky Survey (SDSS), selected using a reduced proper-motion diagram. Radial velocities come from the SDSS spectra and proper motions from the light-motion curve catalogue of Bramich et al. Using a photometric parallax relation to estimate distances gives us the full phase-space coordinates. Typical velocity errors are in the range  30–50 km s−1  . This halo sample is one of the largest constructed to date and the disc contamination is at a level of ≲1 per cent. This enables us to calculate the halo velocity dispersion to excellent accuracy. We find that the velocity dispersion tensor is aligned in spherical polar coordinates and that  (σ r , σφ, σθ) = (143 ± 2, 82 ± 2, 77 ± 2) km s−1  . The stellar halo exhibits no net rotation, although the distribution of   v φ  shows tentative evidence for asymmetry. The kinematics are consistent with a mildly flattened stellar density falling with distance like   r −3.75  .
Using the full phase-space coordinates, we look for signs of kinematic substructure in the stellar halo. We find evidence for four discrete overdensities localized in angular momentum and suggest that they may be possible accretion remnants. The most prominent is the solar neighbourhood stream previously identified by Helmi et al., but the remaining three are new. One of these overdensities is potentially associated with a group of four globular clusters (NGC 5466, NGC 6934, M2 and M13) and raises the possibility that these could have been accreted as part of a much larger progenitor.  相似文献   

6.
We discuss the problem of using stellar kinematics of early-type galaxies to constrain the orbital anisotropies and radial mass profiles of galaxies. We demonstrate that compressing the light distribution of a galaxy along the line of sight produces approximately the same signature in the line-of-sight velocity profiles as radial anisotropy. In particular, fitting spherically symmetric dynamical models to apparently round, isotropic face-on flattened galaxies leads to a spurious bias towards radial orbits in the models, especially if the galaxy has a weak face-on stellar disc. Such face-on stellar discs could plausibly be the cause of the radial anisotropy found in spherical models of intermediate luminosity ellipticals such as NGC 2434, 3379 and 6703.
In the light of this result, we use simple dynamical models to constrain the outer mass profiles of a sample of 18 round, early-type galaxies. The galaxies follow a Tully–Fisher relation parallel to that for spiral galaxies, but fainter by at least 0.8 mag ( I -band) for a given mass. The most luminous galaxies show clear evidence for the presence of a massive dark halo, but the case for dark haloes in fainter galaxies is more ambiguous. We discuss the observations that would be required to resolve this ambiguity.  相似文献   

7.
We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.  相似文献   

8.
The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f ( E ). We show that this effect is operative out to a radius of approximately three to four times the hole's influence radius, R bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a 'warm' and 'hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ≃13 per cent the local rms velocity dispersion σ. A study in three dimensions suggests a reduced effect for polar orbits.  相似文献   

9.
We present new Planetary Nebula Spectrograph observations of the ordinary elliptical galaxy NGC 4494, resulting in positions and velocities of 255 planetary nebulae out to seven effective radii (25 kpc). We also present new wide-field surface photometry from MMT/Megacam, and long-slit stellar kinematics from VLT/FORS2. The spatial and kinematical distributions of the planetary nebulae agree with the field stars in the region of overlap. The mean rotation is relatively low, with a possible kinematic axis twist outside  1 R e  . The velocity dispersion profile declines with radius, though not very steeply, down to  ∼70 km s−1  at the last data point.
We have constructed spherical dynamical models of the system, including Jeans analyses with multi-component Λ cold dark matter (CDM) motivated galaxies as well as logarithmic potentials. These models include special attention to orbital anisotropy, which we constrain using fourth-order velocity moments. Given several different sets of modelling methods and assumptions, we find consistent results for the mass profile within the radial range constrained by the data. Some dark matter (DM) is required by the data; our best-fitting solution has a radially anisotropic stellar halo, a plausible stellar mass-to-light ratio and a DM halo with an unexpectedly low central density. We find that this result does not substantially change with a flattened axisymmetric model.
Taken together with other results for galaxy halo masses, we find suggestions for a puzzling pattern wherein most intermediate-luminosity galaxies have very low concentration haloes, while some high-mass ellipticals have very high concentrations. We discuss some possible implications of these results for DM and galaxy formation.  相似文献   

10.
In this paper we investigate the gravothermal instability of spherical stellar systems endowed with a radially anisotropic velocity distribution. We focus our attention on the effects of anisotropy on the conditions for the onset of instability and in particular we study the dependence of the spatial structure of critical models on the amount of anisotropy present in a system. The investigation has been carried out by the method of linear series which has already been used in the past to study the gravothermal instability of isotropic systems._   We consider models described by King, Wilson and Woolley–Dickens distribution functions. In the case of King and Woolley–Dickens models, our results show that, for quite a wide range of the amount of anisotropy in the system, the critical value of the concentration of the system (defined as the ratio of the tidal to the King core radius of the system) is approximately constant and equal to the corresponding value for isotropic systems. Only for very anisotropic systems does the critical value of the concentration start to change and it decreases significantly as the anisotropy increases and penetrates the inner parts of the system. For Wilson models the decrease of the concentration of critical models is preceded by an intermediate regime in which critical concentration increases, reaches a maximum and then starts to decrease. The critical value of the central potential always decreases as the anisotropy increases.  相似文献   

11.
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12.
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13.
A method for inverting the statistical star counts equation, including proper motions, is presented; in order to break the degeneracy in that equation, it uses the supplementary constraints required by dynamical consistency. The inversion gives access to both the kinematics and the luminosity function of each population in three régimes: the singular ellipsoid, the constant ratio Schwarzschild ellipsoid plane-parallel models and the epicyclic model. This more realistic model is tailored to account for the local neighbourhood density and velocity distribution.
The first model is fully investigated, both analytically and by means of a non-parametric inversion technique, while the second model is shown to be formally its equivalent. The effect of noise and incompleteness in apparent magnitude is investigated. The third model is investigated by a     non-parametric inversion technique where positivity of the underlying luminosity function is explicitly accounted for.
It is argued that its future application to data such as the Tycho catalogue (and in the upcoming satellite GAIA ) could lead – provided that the vertical potential and or the asymmetric drift or w ⊙ are known – to a non-parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks. It should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disc from the thick disc or the halo.  相似文献   

14.
It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ρ ∝ r −1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n , of the density profiles, defined as ρ ∝ r − n , changes from n ≈2.1 at intermediate radii to a shallower power than n ≈2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.  相似文献   

15.
We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R −2 distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.  相似文献   

16.
We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sérsic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N -body simulations) with those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter, observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of 1 M⊙/L⊙ is assumed, the required mass of the dark halo is     , two orders of magnitude larger than the mass in stars. The derived MOND acceleration scale is     . In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.  相似文献   

17.
We present two simple dynamical models for Sagittarius based on N -body simulations of the progressive disruption of a satellite galaxy orbiting for 12.5 Gyr within a realistic Galactic potential. In both models the satellite initially has observable properties similar to those of current outlying dwarfs; in one case it is purely stellar while in the other it is embedded in an extended massive halo. The purely stellar progenitor is a King model with a total velocity dispersion of 18.9 km s−1, a core radius of 0.44 kpc and a tidal radius of 3 kpc. The initial stellar distribution in the other case follows a King profile with the same core radius, a slightly larger total velocity dispersion and similar extent. Both these models are consistent with all published data on the current Sagittarius system, they match not only the observed properties of the main body of Sagittarius, but also those reported for unbound debris at larger distances.  相似文献   

18.
We present radial velocities for a sample of 723 planetary nebulae in the disc and bulge of M31, measured using the WYFFOS fibre spectrograph on the William Herschel Telescope. Velocities are determined using the [O  iii ] λ5007 emission line. Rotation and velocity dispersion are measured to a radius of 50 arcmin (11.5 kpc), the first stellar rotation curve and velocity dispersion profile for M31 to such a radius. Our kinematics are consistent with rotational support at radii well beyond the bulge effective radius of 1.4 kpc, although our data beyond a radius of 5 kpc are limited. We present tentative evidence for kinematic substructure in the bulge of M31 to be studied fully in a later work. This paper is part of an ongoing project to constrain the total mass, mass distribution and velocity anisotropy of the disc, bulge and halo of M31.  相似文献   

19.
We present stellar radial velocity data for the Draco dwarf spheroidal (dSph) galaxy obtained using the AF2/WYFFOS instrument combination on the William Herschel Telescope. Our data set consists of 186 member stars, 159 of which have good quality velocities, extending to a magnitude   V ≈19.5  with a mean velocity precision of ≈2 km s−1. As this survey is based on a high-precision photometric target list, it contains many more Draco members at large radii. For the first time, this allows a robust determination of the radial behaviour of the velocity dispersion in a dSph.
We find statistically strong evidence of a rising velocity dispersion consistent with a dark matter halo that has a gently rising rotation curve. There is a <2 σ signature of rotation about the long axis, inconsistent with tidal disruption as the source of the rising dispersion. By comparing our data set with earlier velocities, we find that Draco probably has a binary distribution and fraction comparable to those in the solar neighbourhood.
We apply a novel maximum likelihood algorithm and fit the velocity data to a two parameter spherical model with an adjustable dark matter content and velocity anisotropy. Draco is best fit by a weakly tangentially anisotropic distribution of stellar orbits in a dark matter halo with a very slowly rising rotation law  ( v circ∝ r 0.17)  . We are able to rule out both a mass-follows-light distribution and an extended halo with a harmonic core at the 2.5 to 3 σ significance level, depending on the details of our assumptions about Draco's stellar binary population. Our modelling lends support to the idea that the dark matter in dwarf spheroidals is distributed in the form of massive, nearly isothermal haloes.  相似文献   

20.
We use the integral-field spectrograph SAURON to measure the stellar line-of-sight velocity distribution and absorption line strengths out to four effective radii ( R e) in the early-type galaxies NGC 3379 and 821. With our newly developed observing technique, we can now probe these faint regions in galaxies that were previously not accessible with traditional long-slit spectroscopy. We make optimal use of the large field-of-view and high throughput of the spectrograph: by adding the signal of all ∼1400 lenslets into one spectrum, we obtain sufficient signal-to-noise in a few hours of observing time to reliably measure the absorption line kinematics and line strengths out to large radius.
We find that the line strength gradients previously observed within 1 R e remain constant out to at least 4 R e, which puts constraints on the merger histories of these galaxies. The stellar halo populations are old and metal poor. By constructing orbit-based Schwarzschild dynamical models, we find that dark matter is necessary to explain the observed kinematics in NGC 3379 and 821, with 30–50 per cent of the total matter being dark within 4 R e. The radial anisotropy in our best-fitting halo models is less than in our models without halo, due to differences in orbital structure. The halo also has an effect on the  Mg  b – V esc  relation: its slope is steeper when a dark matter halo is added to the model.  相似文献   

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