Three-integral models for axisymmetric galactic discs

Famaey, Benoît; Caelenberg, K. Van; Dejonghe, Herwig

doi:10.1046/j.1365-8711.2002.05642.x

Cited by 11 publications

(14 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By substitution of from into , the equation stands for so that it is either a linear and homogeneous partial differential equation for f , for a given potential , or a linear non‐homogeneous partial differential equation for , where the density function f is already known. Both approaches have been largely studied since Eddington (1921) and Oort (1928), and among other works, those of Vandervoort (1979), de Zeeuw & Lynden‐Bell (1985), Bienaymé (1999) and Famaey, Van Caelenberg & Dejonghe (2002) may be pointed out.…”

Section: Introductionmentioning

confidence: 99%

The nth-order stellar hydrodynamic equation: transfer of comoving moments and pressures

Cubarsi

2007

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

The exact mathematical expression for an arbitrary nth‐order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hydrodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions about symmetries, steadiness or particular kinematic behaviours, so that they can be used in their complete form, and for any order, in future works with improved observational data. Also, in order to work with a finite number of equations and unknowns, which would provide a dynamic model for the stellar system, the nth‐order equation is needed to investigate in a more general way the closure conditions, which may be expressed in terms of velocity distribution statistics. A case example for a Schwarzschild distribution shows how the infinite hierarchy of hydrodynamic equations is reduced to the equations of orders n= 0, 1, 2, 3, owing to the recurrent form of the central moments and to the equations of order n= 2 and 3, which become closure conditions for higher even‐ and odd‐order equations, respectively. The closure example is generalized to a quadratic function in the peculiar velocities, so that the equivalence between moment equations and the system of equations that Chandrasekhar had obtained working from the collisionless Boltzmann equation is borne out.

show abstract

Section: Introductionmentioning

confidence: 99%

The nth-order stellar hydrodynamic equation: transfer of comoving moments and pressures

Cubarsi

2007

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

show abstract

“…Assuming a constant velocity anisotropy σ z /σ R , the radial velocity dispersion becomes Theoretical arguments suggest that a constant velocity anisotropy is a fair approximation in the inner parts of galaxy discs (Cuddeford & Amendt 1992; Famaey, van Caelenberg & Dejonghe 2002). An observational argument for the approximate constancy of the velocity anisotropy is provided by the ages and kinematics of 182 F and G dwarf stars in the solar neighbourhood (Edvardsson et al 1993).…”

Section: The Disc Modelmentioning

confidence: 99%

Structure and kinematics of edge-on galaxy discs - IV. The kinematics of the stellar discs

Kregel¹,

Kruit²

2005

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

The stellar disc kinematics in a sample of 15 intermediate‐ to late‐type edge‐on spiral galaxies are studied using a dynamical modelling technique. The sample covers a substantial range in maximum rotation velocity and deprojected face‐on surface brightness and contains seven spirals with either a boxy‐ or peanut‐shaped bulge. Dynamical models of the stellar discs are constructed using the disc structure from I‐band surface photometry and rotation curves observed in the gas. The differences in the line‐of‐sight stellar kinematics between the models and absorption‐line spectroscopy are minimized using a least‐squares approach. The modelling constrains the disc surface density and stellar radial velocity dispersion at a fiducial radius through the free parameter (σz/σR)−1, where σz/σR is the ratio of vertical and radial velocity dispersion and M/L is the disc mass‐to‐light ratio. For 13 spirals a transparent model provides a good match to the mean line‐of‐sight stellar velocity dispersion. Models that include a realistic radiative transfer prescription confirm that the effect of dust on the observable stellar kinematics is small at the observed slit positions. We discuss possible sources of systematic error and conclude that most of these are likely to be small. The exception is the neglect of the dark halo gravity, which has probably caused an overestimate of the surface density in the case of low surface brightness discs.

show abstract

“…Our long-term goal is to constrain the mass distribution of the Galaxy by using kinematical stellar surveys. We shall choose a Stäckel potential, and use the quadratic programming technique described by Dejonghe (1989) to determine, for the available surveys, distribution functions in the space of the integrals of the motion (see Famaey, Van Caelenberg & Dejonghe 2002). Then we shall compare the resulting predictions with the surveys.…”

Section: Introductionmentioning

confidence: 99%

Three-component Stackel potentials satisfying recent estimates of Milky Way parameters

Famaey

Dejonghe

2003

Monthly Notices of the Royal Astronomical Society

Self Cite

View full text Add to dashboard Cite

We present a set of three‐component Stäckel potentials defined by five parameters and designed to model the Milky Way. We review the fundamental constraints that any model of the Milky Way must satisfy, including the most recent ones derived from Hipparcos data, and we study how the parameters of the presented potentials can vary in order to match these constraints. Five different valid potentials are presented and analysed in detail. These are designed to be confronted with kinematical surveys in the future, by the construction of three‐integral analytic distribution functions.

show abstract

Three-integral models for axisymmetric galactic discs

Cited by 11 publications

References 31 publications

The nth-order stellar hydrodynamic equation: transfer of comoving moments and pressures

The nth-order stellar hydrodynamic equation: transfer of comoving moments and pressures

Structure and kinematics of edge-on galaxy discs - IV. The kinematics of the stellar discs

Three-component Stackel potentials satisfying recent estimates of Milky Way parameters

Contact Info

Product

Resources

About