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David Merritt

Publications and source records attributed to David Merritt.

At least 181 records · Page 10Linked to original sources
arXiv1997

Self-Consistent Gravitational Chaos

The motion of stars in the gravitational potential of a triaxial galaxy is generically chaotic. However, the timescale over which the chaos manifests itself in the orbital motion is a strong function of the degree of central concentration of the galaxy. Here, chaotic diffusion rates are presented for orbits in triaxial models with a range of central density slopes and nuclear black-hole masses. Typical diffusion times are found to be less than a galaxy lifetime in triaxial models where the density increases more rapidly than 1/r at the center, or which contain black holes with masses that exceed roughly 0.1% of the galaxy mass. When the mass of a central black hole exceeds roughly 0.02 times the mass of the galaxy, there is a transition to global stochasticity and the galaxy evolves to an axisymmetric shape in little more than a crossing time. This rapid evolution may provide a negative feedback mechanism that limits the mass of nuclear black holes to a few percent of the stellar mass of a galaxy.

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arXiv1997

Periodic Orbits in Triaxial Galaxies with Weak Cusps

The orbital structure of triaxial models with weak central density cusps, $ρ\propto r^{-γ}, gamma < 1$, is investigated. The stability of the $x$- (long-) axis orbit -- and hence the existence of box orbits -- depends sensitively on $γ$; the range of model shapes for which the $x$-axis orbit is stable becomes progressively smaller as $γ$ approaches one. The banana and fish boxlets in the $x-z$ (long axis-short axis) plane are stable over a wide range of model parameters. The boxlets in the $x-y$ and $y-z$ planes are generally vertically unstable.

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arXiv1997

Cusps and Triaxiality

Statler (1987) demonstrated that self-consistent triaxial models with the perfect density law could be constructed for virtually any choice of axis ratios. His experiments are repeated here using triaxial mass models based on Jaffe's density law, which has a central density that diverges as 1/r^2, similar to what is observed in low-luminosity elliptical galaxies. Most of the boxlike orbits are found to be stochastic in these models. Because timescales for chaotic mixing are generally shorter than a galaxy lifetime in triaxial models with strong cusps, and because fully-mixed stochastic orbits have shapes that are poorly suited to reproducing a triaxial figure, only the regular orbits are included when searching for self-consistent solutions. As a result of the restriction to regular orbits, self-consistent solutions are found only for mass models with a modest range of shapes, either nearly oblate, nearly prolate or nearly spherical. This result may explain in part the narrow range of elliptical galaxy properties.

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arXiv1996

The Stellar Dynamics of Omega Centauri

The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997). Rather than fit the data to a family of models, we generate estimates of all dynamical functions nonparametrically, by direct operation on the data. The cluster is assumed to be oblate and edge-on but mass is not assumed to follow light. The mean motions are consistent with axisymmetry but the rotation is not cylindrical. The peak rotational velocity is 7.9 km/s at 11 pc from the center. The apparent rotation of Omega Centauri is attributable in part to its proper motion. We reconstruct the stellar velocity ellipsoid as a function of position, assuming isotropy in the meridional plane. We find no significant evidence for a difference between the velocity dispersions parallel and perpendicular to the meridional plane. The mass distribution inferred from the kinematics is slightly more extended than, though not strongly inconsistent with, the luminosity distribution. We also derive the two-integral distribution function f(E,Lz) implied by the velocity data.

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arXiv1996

Dynamics of Triaxial Stellar Systems

Recent work on the dynamics of triaxial stellar systems is reviewed. The motion of boxlike orbits in realistic triaxial potentials is generically stochastic. The degree to which the stochasticity manifests itself in the dynamics depends on the chaotic mixing timescale, which is a small multiple of the crossing time in triaxial models with steep cusps or massive central singularities. Low-luminosity ellipticals, which have the steepest cusps and the shortest dynamical times, are less likely than bright ellipticals to have strongly triaxial shapes. The observational evidence for triaxiality is reviewed; departures from axisymmetry in early-type galaxies are often found to be associated with evidence of recent interactions or with the presence of a bar.

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arXiv1996

The Stellar Dynamics of M87

We extract the shape of the stellar velocity ellipsoid as a function of radius in M87 from van der Marel's (1994) velocity dispersion data. We include the gravitational force of a central black hole with the mass quoted by Harms et al. (1994). The kinematical data are corrected for the effects of seeing and instrumental blurring using a nonparametric algorithm. We find that the stellar motions in M87 are slightly radially anisotropic throughout the main body of the galaxy. However the tangential velocity dispersion exceeds the radial velocity dispersion within the inner 1''-2'' by a statistically significant amount. A number of models for the formation of nuclear black holes predict a tangential anisotropy in the stellar motions, and our results provide evidence for such an effect in M87.

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arXiv1996

The Dynamical Inverse Problem for Axisymmetric Stellar Systems

The standard method of modelling axisymmetric stellar systems begins from the assumption that mass follows light. The gravitational potential is then derived from the luminosity distribution, and a unique two-integral distribution function f(E,Lz) that generates the stellar density in this potential is found. We show that the gravitational potential can instead be generated directly from the velocity data in a two-integral galaxy, thus allowing one to drop the assumption that mass follows light. The rotational velocity field can also be recovered in a model-independent way. We present regularized algorithms for carrying out the inversions and test them by application to pseudo-data from a family of oblate models.

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arXiv1996

Chaos and Mixing in Triaxial Stellar Systems

We investigate the timescales for stochasticity and chaotic mixing in a family of triaxial potentials that mimic the distribution of light in elliptical galaxies. Some of the models include central point masses designed to represent nuclear black holes. Most of the boxlike orbits are found to be stochastic, with mean Liapunov times that are 3-6 times the period of the long-axis orbit. In models with large cores or small black holes, the stochastic orbits mimic regular box orbits for hundreds of oscillations at least. However a small core radius or significant black hole mass causes most of the stochastic orbits to diffuse through phase space on the same timescale, visiting a significant fraction of the volume beneath the equipotential surface. We estimate timescales for chaotic mixing in the more strongly stochastic models by evolving ensembles of 10^4 points until their distribution reaches a nearly steady state. Mixing initially takes place rapidly, with characteristic times of 10-30 dynamical times, as the phase points fill a region similar in shape to that of a box orbit. Subsequent mixing is slower, with characteristic times of hundreds of orbital times. Mixing rates were found to be enhanced by the addition of modest force perturbations. The consequences for the structure and evolution of elliptical galaxies are discussed.

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arXiv1996

Recovering Velocity Distributions via Penalized Likelihood

Line-of-sight velocity distributions are crucial for unravelling the dynamics of hot stellar systems. We present a new formalism based on penalized likelihood for deriving such distributions from kinematical data, and evaluate the performance of two algorithms that extract N(V) from absorption-line spectra and from sets of individual velocities. Both algorithms are superior to existing ones in that the solutions are nearly unbiased even when the data are so poor that a great deal of smoothing is required. In addition, the discrete-velocity algorithm is able to remove a known distribution of measurement errors from the estimate of N(V). The formalism is used to recover the velocity distribution of stars in five fields near the center of the globular cluster Omega Centauri.

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arXiv1996

Evidence from Intrinsic Shapes for Two Families of Elliptical Galaxies

Bright elliptical galaxies have a markedly different distribution of Hubble types than faint ellipticals; the division occurs near M_B=-20 and bright ellipticals are rounder on average. The Hubble types of galaxies in both groups are narrowly clustered, around E1.5 in the case of the bright galaxies and around E3 for the fainter ones. The Hubble-type distribution of the faint ellipticals is consistent with oblate symmetry, but the oblate hypothesis fails for the bright ellipticals. However a distribution of triaxial intrinsic shapes can successfully reproduce the apparent shape data for either group. The distribution of intrinsic, short-to-long axis ratios is peaked around 0.75 for bright galaxies and 0.65 for faint galaxies. Our results provide further evidence that elliptical galaxies should be divided into two, morphologically distinct families.

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arXiv1996

Optimal Smoothing for N-Body Codes

In any collisionless N-body code, there is an optimal choice for the smoothing parameter that minimizes the average error in the force evaluations. We show how to compute the optimal softening length in a direct-summation code and demonstrate that it varies roughly as 1/N^(1/3).

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arXiv1996

Chaos and the Shapes of Elliptical Galaxies

Hubble Space Telescope (HST) observations reveal that the density of stars in most elliptical galaxies rises toward the center in a power-law cusp. Many of these galaxies also contain central dark objects,possibly supermassive black holes. The gravitational force from a steep cusp or black hole will destroy most of the box orbits that constitute the ``backbone'' of a triaxial stellar system. Detailed modelling demonstrates that the resulting chaos can preclude a self-consistent, strongly triaxial equilibrium. Most elliptical galaxies may therefore be nearly axisymmetric, either oblate or prolate.

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arXiv1995

Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's spherical models are presented, which have densities that vary as 1/r^gamma near the center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp); these two models have density profiles similar to those of the core and power-law galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong- cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 100 - 1000 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 1000 dynamical times or longer. Attempts to construct self- consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These ``fully mixed'' solutions were found to exist only for the weak-cusp potential. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density.

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arXiv1995

Dynamical Modelling of Hot Stellar Systems

Estimation of the distribution function f and potential Phi of hot stellar systems from kinematical data is discussed. When the functional forms of f and Phi are not specified a priori, accurate estimation of either function requires very high quality data: either accurate ``line profiles'' at radii extending well beyond an effective radius, or large samples of discrete radial velocities. Estimates of Phi(r) based on much smaller data sets can be very strongly influenced by assumptions, explicit or implicit, about the form of f. The importance of casting the estimation problem into a mathematically determined form is stressed. Some techniques for nonparametric estimation are presented, with some preliminary results of their application to real stellar systems.

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arXiv1995

Equilibrium and Stability of Elliptical Galaxies

Recent work on the equilibrium and stability of ellipsoidal stellar systems is reviewed. The absence of constant-density cores in early-type galaxies implies that chaos and high-order resonances are generic features of the motion in triaxial stellar systems. Bending instabilities are now well understood and may provide the answers to a number of long-standing riddles, including the absence of highly flattened elliptical galaxies and the formation of galactic bulges. Some preliminary results on instabilities in two-integral oblate models are presented.

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arXiv1995

The Frequency Function of Elliptical Galaxy Intrinsic Shapes

We present fully nonparametric estimates of the frequency function of elliptical galaxy intrinsic shapes under the axisymmetric and triaxial hypotheses. If elliptical galaxies are assumed to be oblate or prolate, the frequency function of intrinsic shapes is negative for axis ratios near unity due to the lack of apparently round galaxies. Both axisymmetric hypotheses are found to be inconsistent at the 99 percent level with the data. Triaxial intrinsic shapes are fully consistent with the data; a number of possible triaxial frequency functions are presented, some of which exhibit strong bimodality. We also compute the ``maximum entropy'' distribution of intrinsic shapes under the triaxial hypothesis.

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arXiv1995

Planetary Nebulae as Probes of Dark Matter in NGC 3384

We have obtained radial velocities of 68 planetary nebulae surrounding the SB0 galaxy NGC 3384 in the Leo I group, using the CTIO 4 m telescope and the Rutgers Fabry-Perot interferometer. The PN system exhibits a well-ordered rotation field aligned with the photometric axes of the galaxy. The rotation curve is flat from about 2 kpc until at least 7 kpc. Our results imply that at least a third of the dynamical mass of the NGC 3379/3384 system may be accounted for in the two bright galaxies.

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