arXiv subjects

H. Dejonghe

Publications and source records attributed to H. Dejonghe.

47 records · Page 3Linked to original sources

arXiv1999

Approximate third integrals for axisymmetric potentials using local Stackel fits

We use a set of Stackel potentials to obtain a local approximation for an effective third integral in axisymmetric systems. We present a study on the feasibility and effectiveness of this approach. We have applied it to three trial potentials of various flattenings, corresponding to nearly ellipsoidal, disky and boxy density isophotes. In all three cases, a good fit to the potential requires only a small set of Stackel potentials, and the associated Stackel third integral provides a very satisfactory, yet analytically simple, approximation to the trial potentials effective third integral.

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arXiv1998

Determination of the dynamical structure of galaxies using optical spectra

Galaxy spectra are a rich source of kinematical information since the shapes of the absorption lines reflect the movement of stars along the line-of-sight. We present a technique to directly build a dynamical model for a galaxy by fitting model spectra, calculated from a dynamical model, to the observed galaxy spectra. Using synthetic spectra from a known galaxy model we demonstrate that this technique indeed recovers the essential dynamical characteristics of the galaxy model. Moreover, the method allows a statistically meaningful error analysis on the resulting dynamical quantities.

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arXiv1998

On the kinematic signature of a central Galactic bar in observed star samples

A quasi self-consistent model for a barred structure in the central regions of our Galaxy is used to calculate the signature of such a triaxial structure on the kinematical properties of star samples. We argue that, due to the presence of a velocity dispersion, such effects are much harder to detect in the stellar component than in the gas. It might be almost impossible to detect stellar kinematical evidence for a bar using only l-v diagrams, if there is no a priori knowledge of the potential. Therefore, we propose some test parameters that can easily be applied to observed star samples, and that also incorporate distances or proper motions. We discus the diagnostic power of these tests as a function of the sample size and the bar strength. We conclude that about 1000 stars would be necessary to diagnose triaxiality with some statistical confidence.

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arXiv1996

Numerical calculation of linear modes in stellar disks

We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything is performed in coordinate space instead of using action-angle variables. We show that this approach, though less elegant, is both feasible and straightforward. This approach is then incorporated in a matrix method in order to calculate self-consistent modes, using a set of potential-density pairs which is obtained numerically. We investigated the stability of some unperturbed disks having an almost flat rotation curve, an exponential disk and a non-zero velocity dispersion. The influence of the velocity dispersion, halo mass and anisotropy on the stability is further discussed.

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arXiv1996

On the deprojection of triaxial galaxies with Stäckel potentials

A family of triaxial Stäckel potential-density pairs is introduced. With the help of a Quadratic Programming method, a linear combination of potential-density pairs of this family which fits a given projected density distribution can be built. This deprojection strategy can be used to model the potentials of triaxial elliptical galaxies with or without dark halos. Besides, we show that the expressions for the Stäckel triaxial density and potential are considerably simplified when expressed in terms of divided differences, which are convenient numerically. We present an example of triaxial deprojection for the galaxy NGC~5128 whose photometry follows the de Vaucouleurs law.

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arXiv1995

The dynamics of planetary nebulae in the Galaxy: evidence for a third integral

We present a dynamical analysis of 673 galactic Planetary Nebulae, using a two-integral axisymmetric model with a Kuzmin-Kutuzov Stäckel potential. The method fits the kinematics to the projected moments of a distribution function, by means of Quadratic Programming. The 2.2 $μ$m COBE brightness map has been used after correction for the interstellar extinction as a projected star counts map in the modeling, because it constitutes a galactic distribution view of evolved red populations which are considered to be the progenitors of PNe. The model we have obtained provides a 2-integral distribution function for the COBE 2.2 $μ$m map, and thus {\it a fortiori} a deprojection of it, which allows moreover the identification of all the major Galactic components. We derive the density laws for them. The projected velocity dispersions are not well fitted though, especially in the disk, which points at the likely presence of a third integral. If this result can be confirmed by additional data, this would mean that for the first time the presence and importance of a third integral on a global scale is demonstrated.

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arXiv1995

Probing the halo of Centaurus A: a merger dynamical model for the PN population

Photometry and kinematics of the giant elliptical galaxy NGC~5128 (Centaurus~A) based on planetary nebulae observations (Hui~\etal 1995) are used to build dynamical models which allow us to infer the presence of a dark matter halo. To this end, we apply a Quadratic Programming method. Constant mass-to-light ratio models fail to reproduce the major axis velocity dispersion measurements at large radii: the profile of this kind of models falls off too steeply when compared to the observations, clearly suggesting the necessity of including a dark component in the halo. By assuming a mass-to-light ratio which is increasing with radius, the model satisfactorily matches the observations. The total mass for the best fit model is $\sim4\times10^{11}M_\odot$ of which about 50\% is dark matter. However, models with different total masses and dark halos are also consistent with the data; we estimate that the total mass of Cen~A within 50~kpc may vary between $3\times10^{11}M_\odot$ and $5\times10^{11}M_\odot$. The best fit model consists of 75\% of stars rotating around the short axis $z$ and 25\% of stars rotating around the long axis $x$. Finally, the morphology of the projected velocity field is analyzed using Statler's classification criteria (Statler 1991). We find that the appearance of our velocity field is compatible with a type 'Nn' or 'Nd'.

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arXiv1995

The internal dynamics of very flattened normal galaxies: Stellar distribution functions for NGC 4697

Using the photometry and the kinematic data, part of which acquired with the NTT, we constructed a 2-integral and a 3-integral distribution function for NGC 4697. We detected a nuclear dust lane at $3.4''$ or 0.4 kpc from the centre. A comparison of the Lucy-deprojection method and the multi-gaussian expansion method showed that the latter offers a number of advantages, among which a qualitatively better fit and better controllable convergence. Futhermore, we show that a 2-integral model cannot be excluded for as far as the Satoh parameter $k$ is allowed to vary. The 3-integral model is based on a Stäckel third integral. The original potential is retained where appropriate, in order to minimise errors due to the Stäckel approximation. On the whole, the 3-integral model produces more satisfying results than the 2-integral model, and is better in handling some peculiarities in the kinematic data. For both models we show detailed contour plots for all deprojected moments up to order 2. The mass-to-light ratio appears to be a fairly well determined $(M/L)_B=4.8h_{50}$, and is much better constrained than would be the case for spherical anisotropic models with comparable data.

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arXiv1995

The stability of uniformly rotating stellar disks

We explore a series expansion method to calculate the modes of oscillations for a variety of uniformly rotating finite disks, either with or without a dark halo. Since all models have the same potential, this survey focuses on the role of the distribution function in stability analyses. We show that the stability behaviour is greatly influenced by the structure of the unperturbed distribution, particularly by its energy dependence. In addition we find that uniformly rotating disks with a halo in general can feature spiral-like instabilities.

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arXiv1995

Distribution of proper motions in spherical star clusters

Along with data on radial velocities, more and more data on proper motions of individual stars in globular clusters are becoming available. Their usage was until now rather limited. It was mostly restricted to determining cluster membership of individual stars and to determining the spatial velocity of the cluster. We study the two dimensional distribution of the proper motions, in order to clarify the relation between the projection of the velocities and the dynamical structure. Obviously some assumptions on the dynamics of the system have to be made. In this study we chose a Plummer model. This complements an earlier study about line profiles. The three velocity dispersions in the main directions are determined and compared with the three spherical velocity dispersions. Two parameters analogous to Binney's anisotropy parameter $β$ are defined. Moreover, since the proper motion components are distance dependent and the line of sight velocity dispersion is distance independent, we show explicitly how to determine distances.

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arXiv1995

A method for solving the linearized Boltzmann equation for almost uniformly rotating stellar disks.

We construct analytical phase-space solutions for perturbations of flat disks by performing a power series expansion for the radius and the velocity coordinates. We show that this approach translates into an elegant mathematical formulation which is easy to use for a wide variety of distribution functions, for as far as resonances do not play a role, such as is the case for potentials which are close to quadratic. As a testcase, the method is applied on the Kalnajs disks. The results obtained are in full agreement with the analytical solutions of the mode analysis. The strongest advantages of this method are its independence of the mathematical complexity of the unperturbed distribution, the degree of detail with which the solutions can be calculated and its computational straightforwardness. On the contrary, power series solutions are not suitable for describing regions where resonant orbits occur, which we therefore exclude in this paper. We used the technique to analyse perturbations in the central regions of a galaxy, tracking the dynamical consequences of a Galactic bar on the kinematics of the solar neighbourhood (Hipparcos). We showed how the orientation and strength of the bar is related to the properties of the velocity ellipsoid in our model.

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