arXiv subjects

Walter Dehnen

Publications and source records attributed to Walter Dehnen.

81 records · Page 5Linked to original sources

arXiv1999

A Dynamical Model of the Inner Galaxy

An extension of Schwarzschild's galaxy-building technique is presented that, for the first time, enables one to build Schwarzschild models with known distribution functions (DFs). The new extension makes it possible to combine a DF that depends only on classical integrals with orbits that respect non-classical integrals. With such a combination, Schwarzschild's orbits are used only to represent the difference between the true galaxy DF and an approximating classical DF. The new method is used to construct a dynamical model of the inner Galaxy. The model is based on an orbit library that contains 22168 regular orbits. The model aims to reproduce the three-dimensional mass density of Binney, Gerhard & Spergel (1997), which was obtained through deprojection of the COBE surface photometry, and to reproduce the observed kinematics in three windows - namely Baade's Window and two off-axis fields. The model fits essentially all the available data within the innermost 3 kpc. The axis ratio and the morphology of the projected density contours of the COBE bar are recovered to good accuracy within corotation. The kinematic quantities - the line-of-sight streaming velocity and velocity dispersion, as well as the proper motions when available - are recovered, not merely for the fitted fields, but also for three new fields. The dynamical model deviates most from the input density close to the Galactic plane just outside corotation, where the deprojection of the surface photometry is suspect. The dynamical model does not reproduce the kinematics at the most distant window, where disk contamination may be severe.

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arXiv1998

The Distribution of Nearby Stars in Velocity Space

From the tangential velocities of stars all over the sky, one can, in a statistical way, infer their 3D velocity distribution. An application to Hipparcos data reveals rich structure in the planar stellar motions: there are several moving groups, increasing in number with stellar type but decreasing in importance. A distinct group of outward moving stars with low rotation velocities might be associated with the Galactic bar: growing a bar in a smooth model for the Galactic disk results in such a group, provided the Sun is outside the outer Lindblad resonance (OLR) and the orientation angle with the bar is in the first quadrant. The vertical motions show less structure, but the mean increases for large rotational velocities, which can be nicely explained by a warp of the outer stellar disk.

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arXiv1998

The Distribution of Nearby Stars in Velocity Space Inferred from Hipparcos Data

(abridged) The velocity distribution f(v) of nearby stars is estimated, via a maximum- likelihood algorithm, from the positions and tangential velocities of a kinematically unbiased sample of 14369 stars observed by the HIPPARCOS satellite. f(v) shows rich structure in the radial and azimuthal motions, v_R and v_phi, but not in the vertical velocity, v_z: there are four prominent and many smaller maxima, many of which correspond to well known moving groups. While samples of early-type stars are dominated by these maxima, also up to 25% of red main-sequence stars are associated with them. These moving groups are responsible for the vertex deviation measured even for samples of late-type stars; they appear more frequently for ever redder samples; and as a whole they follow an asymmetric-drift relation, in the sense that those only present in red samples predominantly have large |v_R| and lag in v_phi w.r.t. the local standard of rest (LSR). The question arise, how these old moving groups got on their eccentric orbits. A plausible mechanism, known from solar system dynamics, which is able to manage a shift in orbit space involves locking into an orbital resonance. Apart from these moving groups, there is a smooth background distribution, akin to Schwarzschild's ellipsoidal model, with axis ratio of about 1:0.6:0.35 in v_R, v_phi, and v_z. The contours are aligned with the $v_r$ direction, but not w.r.t. the v_phi and v_z axes: the mean v_z increases for stars rotating faster than the LSR. This effect can be explained by the stellar warp of the Galactic disk. If this explanation is correct, the warp's inner edge must not be within the solar circle, while its pattern rotates with frequency of about 13 km/s/kpc or more retrograde w.r.t. the stellar orbits.

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arXiv1998

M87 as a Galaxy

I review recent studies about the gravitational potential and stellar dynamics of M87 in particular, and the dynamics of the stars in the presence of a super-massive central black hole, in general. At large radii, investigations of both the X-ray emitting gas and the velocity distribution of globular clusters indicate the presence of large amounts of non-luminous matter, possibly belonging to the inner parts of the Virgo cluster. At small radii, there is no evidence from the stellar kinematics, at most a hint, for the existence of a central point mass, whereas the gas dynamics reveal the presence of a highly concentrated mass in the centre of M87, possibly a super-massive black hole (BH). Given the existence of such a central mass, the stellar kinematics indicate a strong tangential anisotropy of the stellar motion inside a few arcseconds. The implications of this result for the evolution and formation history of M87 and its central BH are discussed. I also discuss in more general terms the structural changes that a highly concentrated central mass can induce in its parent galaxy.

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arXiv1997

Local stellar kinematics from Hipparcos data

(shortened) From a kinematically unbiased subsample of the Hipparcos catalogue we have redetermined as a function of colour the kinematics of main-sequence stars. The stars' mean heliocentric velocity nicely follows the asymmetric drift relation, except for stars blueward of B-V=0.1. Extrapolating to zero dispersion yields for the velocity of the Sun w.r.t. the LSR in km/s: U_0=10.00+/-0.36 (radially inwards), V_0=5.23+/-0.62 (in direction of galactic rotation), and W_0=7.17+/-0.38 (vertically upwards). A plot of velocity dispersion vs. colour beautifully shows Parenago's discontinuity: the dispersion is constant for B-V>0.62 and decreases towards bluer colour. We determine the velocity-dispersion tensor sigma^2_ij as function of B-V. The mixed moments involving vertical motion are zero within the errors, while sigma^2_xy is non-zero at about (10km/s)^2 independent of colour. The resulting vertex deviations are about 20 deg for early-type stars and 10+/-4 deg for old-disc stars. The persistence of the vertex deviation to late-type stars implies that the Galactic potential is significantly non-axisymmetric at the solar radius. If spiral arms are responsible for this, they cannot be tightly wound. Except for stars bluer than B-V=0.1 the ratios of the principal velocity dispersions are 2.2 : 1.4 :1, while the absolute values increase with colour from sigma_1=20km/s at B-V=0.2 to sigma_1=38km/s at Parenago's discontinuity and beyond. These ratios imply significant heating of the disc by spiral structure and that R_0/R_d=3 to 3.5, where R_d is the scale length of the disc.

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arXiv1997

Mass models of the Milky Way

A parameterized model of the mass distribution within the Milky Way is fitted to the available observational constraints. The most important single parameter is the ratio of the scale length R_d* of the stellar disk to R0. The disk and bulge dominate v_c(R) at R > R0. For example, changing the disk slightly from an exponential surface-density profile significantly changes the form of v_c(R) at R >> R0, where the disk makes a negligible contribution to v_c. Moreover, minor changes in the constraints can cause the halo to develop a deep hole at its centre that is not physically plausible. These problems call into question the proposition that flat rotation curves arise because galaxies have physically distinct halos rather than outwards-increasing mass-to-light ratios. The mass distribution of the Galaxy and the relative importance of its various components will remain very uncertain until more observational data can be used to constrain mass models. Data that constrain the Galactic force field at z > R and at R > R0 are especially important.

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arXiv1996

The outer rotation curve of the Milky Way

A straightforward determination of the circular-speed curve vc(R) of the Milky Way suggests that near the Sun, vc starts to rise approximately linearly with R. If this result were correct, the Galactic mass density would have to be independent of radius at R ~> R0. We show that the apparent linear rise in v_c arises naturally if the true circular-speed curve is about constant or gently falling at R0 < R ~< 2 R0, but most tracers that appear to be at R ~> 1.25 R0 are actually concentrated into a ring of radius ~1.6 R0.

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arXiv1996

Dynamical Models for the Milky Way

The only way to map the Galaxy's gravitational potential $Φ({\bf x})$ and the distribution of matter that produces it is by modelling the dynamics of stars and gas. Observations of the kinematics of gas provide key information about gradients of $Φ$ within the plane, but little information about the structure of $Φ$ out of the plane. Traditional Galaxy models {\em assume}, for each of the Galaxy's components, arbitrary flattenings, which together with the components' relative masses yield the model's equipotentials. However, the Galaxy's isopotential surfaces should be {\em determined\/} directly from the motions of stars that move far from the plane. Moreover, from the kinematics of samples of such stars that have well defined selection criteria, one should be able not only to map $Φ$ at all positions, but to determine the distribution function $f_i({\bf x},{\bf v})$ of each stellar population $i$ studied. These distribution functions will contain a wealth of information relevant to the formation and evolution of the Galaxy. An approach to fitting a wide class of dynamical models to the very heterogeneous body of available data is described and illustrated.

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arXiv1994

Modelling Galaxies with f(E,Lz); a Black Hole in M32

A technique for the construction of axisymmetric distribution functions for individual galaxies is presented. It starts from the observed surface bright- ness distribution, which is deprojected to gain the axisymmetric luminosity density, from which follows the stars' gravitational potential. After adding dark mass components, such as a central black hole, the two-integral distribu- tion function (2I-DF) f(E,Lz), which depends only on the classical integrals of motion in an axisymmetric potential, is constructed using the Richardson- Lucy algorithm. This algorithm proved to be very efficient in finding f(E,Lz) provided the integral equation to be solved has been properly modified. Once the 2I-\df\ is constructed, its kinematics can be computed and compared with those observed. Many discrepancies may be remedied by altering the assumed inclination angle, mass-to-light ratio, dark components, and odd part of the 2I-DF. Remaining discrepancies may indicate, that the distribution function depends on the non-classical third integral, or is non-axisymmetric. The method has been applied to the nearby elliptical galaxy M32. A 2I-DF with ~55 degrees inclination and a central black hole (or other compact dark mass inside ~1pc) of 1.6-2*10^6 Msun fits the high-spatial-resolution kinema- tic data of van der Marel et al. remarkably well. 2I-DFs with a significantly less or more massive central dark mass or with edge-on inclination can be ruled out for M32. Predictions are made for HST-observations: spectroscopy using its smallest square aperture of 0.09"*0.09" should yield a non-gaussian central velocity profile with broad wings, true and gaussian-fit velocity dispersion of 150-170km/s and 120-130km/s, respectively.

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