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

Cubarsi, Rafael

doi:10.1111/j.1365-2966.2007.12141.x

Cited by 5 publications

(6 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The other case involves a continuous mixture of Gaussian distributions with nearly the same mean takes place, by producing a positive excess of kurtosis. In that case, the resulting distribution is also quadratic (Cubarsi 2007) and, therefore, is consistent with the current model.…”

Section: Discussionsupporting

confidence: 68%

See 1 more Smart Citation

Conditions of consistency for multicomponent axisymmetric stellar systems

Cubarsi

2014

A&A

Self Cite

View full text Add to dashboard Cite

Solving the Boltzmann collisionless equation under the axisymmetric hypothesis introduces serious limitations on describing the kinematics of a single stellar system according to the local Galactic observables. Instead of relaxing the hypothesis of axisymmetry, one alternative is to assume a mixture model. For a finite mixture of ellipsoidal velocity distributions, the coexistence of several stellar populations sharing a common potential introduces a set of conditions of consistency that may also constrain the population kinematics. For only a few potentials, the populations may have independent mean velocities and unconstrained velocity ellipsoids. In this paper, we determine which axisymmetric potentials are connected with a more flexible superposition of the stellar populations. The conditions of consistency are checked against recent results derived from kinematic surveys of the solar neighbourhood that include RAdial Velocity Experiment (RAVE) data. Several key observables are used to determine whether the axisymmetric mixture model is able to account for the main features of the local velocity distribution, such as the vertex deviation associated with the second central moment μ θ , the population radial mean velocities, the radial gradient of the moment μ z , the tilt of the velocity ellipsoids, and the existence of stars with no net rotation. In addition, the mixture moments for an arbitrary number of populations are derived in terms of the one-to-one mean velocity differences in order to study whether a more populated mixture could add any new features to the velocity distribution that remain unnoticed in a two-component mixture. According to this analysis, the quasi-stationary potential is the only potential allowing arbitrary directions of the population mean velocities. Then, the apparent vertex deviation of the total velocity distribution is due to the difference of the mean velocities of the populations whose velocity ellipsoids have no vertex deviation. For a non-separable potential, the population velocity ellipsoids have the same orientation and point towards the Galactic centre. For a potential separable in addition in cylindrical coordinates, the population velocity ellipsoids may have arbitrary tilt.

show abstract

Section: Discussionsupporting

confidence: 68%

“…These equations are equivalent to the infinite hierarchy of the stellar hydrodynamic equations, which can be reduced to equations of orders n = 0, 1, 2, 3, for the sake of a set of closure conditions (Cubarsi 2007(Cubarsi , 2010a.…”

Section: Single Populationmentioning

confidence: 99%

Conditions of consistency for multicomponent axisymmetric stellar systems

Cubarsi

2014

A&A

Self Cite

View full text Add to dashboard Cite

show abstract

“…The literature is full of alternatives to overcome these two limitations, e.g., N-body simulations, the Schwarzschild method, the Made-to-Measure method, full theoretical methods (e.g, Hunt & Kawata 2013;Hunt et al 2015;Cubarsi 2007;Bienaymé, Robin & Famaey 2015;Bienaymé & Traven 2013) etc. whose review is beyond the goal of this paper.…”

Section: Introductionmentioning

confidence: 99%

Spiral arm kinematics for Milky Way stellar populations

Pasetto

Natale

Kawata

et al. 2016

Mon. Not. R. Astron. Soc.

View full text Add to dashboard Cite

We present a new theoretical population synthesis model (the Galaxy Model) to examine and deal with large amounts of data from surveys of the Milky Way and to decipher the present and past structure and history of our own Galaxy.We assume the Galaxy to consist of a superposition of many composite stellar populations belonging to the thin and thick disks, the stellar halo and the bulge, and to be surrounded by a single dark matter halo component. A global model for the Milky Way's gravitational potential is built up self-consistently with the density profiles from the Poisson equation. In turn, these density profiles are used to generate synthetic probability distribution functions (PDFs) for the distribution of stars in colour-magnitude diagrams (CMDs). Finally, the gravitational potential is used to constrain the stellar kinematics by means of the moment method on a (perturbed)-distribution function. Spiral arms perturb the axisymmetric disk distribution functions in the linear response framework of density-wave theory where we present an analytical formula of the so-called 'reduction factor' using Hypergeometric functions.Finally, we consider an analytical non-axisymmetric model of extinction and an algorithm based on the concept of probability distribution function to handle colour magnitude diagrams with a large number of stars. A genetic algorithm is presented to investigate both the photometric and kinematic parameter space.This galaxy model represents the natural framework to reconstruct the structure of the Milky Way from the heterogeneous data set of surveys such as Gaia-ESO, SEGUE, APOGEE2, RAVE and the Gaia mission.

show abstract

“…For the above generalised Schwarzschild velocity distribution, the BCE yields the Chandrasekhar equations (Chandrasekhar 1960), which are equivalent to the moment equations (Cubarsi 2007(Cubarsi , 2010. Their solution provides the tensor A, the function σ, the mean velocity u, and the potential U.…”

Section: Point-axial Systemmentioning

confidence: 99%

Conditions of consistency for multicomponent stellar systems

Cubarsi

2014

A&A

Self Cite

View full text Add to dashboard Cite

Under a common potential, a finite mixture of ellipsoidal velocity distributions satisfying the Boltzmann collisionless equation provides a set of integrability conditions that may constrain the population kinematics. They are referred to as conditions of consistency and were discussed in a previous paper on mixtures of axisymmetric populations. As a corollary, these conditions are now extended to point-axial symmetry, that is, point symmetry around the rotation axis or bisymmetry, by determining which potentials are connected with a more flexible superposition of stellar populations. Under point-axial symmetry, the potential is still axisymmetric, but the velocity and mass distributions are not necessarily. A point-axial stellar system is, in a natural way, consistent with a flat velocity distribution of a disc population. Therefore, no additional integrability conditions are required to solve the Boltzmann collisionless equation for such a population. For other populations, if the potential is additively separable in cylindrical coordinates, the populations are not kinematically constrained, although under point-axial symmetry, the potential is reduced to the harmonic function, which, for the Galaxy, is proven to be non-realistic. In contrast, a non-separable potential provides additional conditions of consistency. When mean velocities for the populations are unconstrained, the potential becomes quasi-stationary, being a particular case of the axisymmetric model. Then, the radial and vertical mean velocities of the populations can differ and produce an apparent vertex deviation of the whole velocity distribution. However, single population velocity ellipsoids still have no vertex deviation in the Galactic plane and no tilt in their intersection with a meridional Galactic plane. If the thick disc and halo ellipsoids actually have non-vanishing tilt, as the surveys of the solar neighbourhood that include RAdial Velocity Experiment (RAVE) data seem to show, the point-axial model is unable to fit the local velocity distribution. Conversely, the axisymmetric model is capable of making a better approach. If, in the end, more accurate data confirm a negligible tilt of the populations, then the point-axisymmetric model will be able to describe non-axisymmetric mass and velocity distributions, although in the Galactic plane the velocity distribution will still be axisymmetric.

show abstract

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

Cited by 5 publications

References 35 publications

Conditions of consistency for multicomponent axisymmetric stellar systems

Conditions of consistency for multicomponent axisymmetric stellar systems

Spiral arm kinematics for Milky Way stellar populations

Conditions of consistency for multicomponent stellar systems

Contact Info

Product

Resources

About