Self-consistent models for galactic halos

Schwarzschild, M.

doi:10.1086/172687

Cited by 149 publications

(237 citation statements)

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“…These families are primarily distinguished by their net angular momentum: short (z) axis tubes have nonzero angular momentum about the short axis ( J 0 z á ñ ¹ ); both families of long-axis tubes have a net angular momentum about the long (x) axis ( J 0 x á ñ ¹ ); boxes and boxlets have no net angular momentum about any axis. In addition, in a realistic triaxial potential, a significant fraction of orbits may be chaotic (e.g., Schwarzschild 1993;Merritt & Fridman 1996).…”

Section: Introductionmentioning

confidence: 99%

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

Valluri

Shen

Abbott

et al. 2016

ApJ

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We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (∼4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (∼7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediateaxis owingto the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (∼2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits thatbelong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH,the inflow of mass and outward transport of angular momentum transformsome x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies.

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Section: Introductionmentioning

confidence: 99%

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

Valluri

Shen

Abbott

et al. 2016

ApJ

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“…His method consists of three steps: (1) represent the stellar system by a smooth density law and divide it into discrete cells, (2) compute a library of orbits in the potential corresponding to the assumed density law and record the time spent by each orbit in the cells, and (3) find a linear combination of orbits that reproduces the cell masses. Using his method, Schwarzschild (1979Schwarzschild ( , 1982 demonstrated self-consistency of triaxial mass models with and without figure rotation. Most of the orbits in his solutions were regular, i.e., nonchaotic (Merritt 1980).…”

Section: Introductionmentioning

confidence: 99%

A Self‐Consistent Study of Triaxial Black Hole Nuclei

Poon

Merritt

2004

ApJ

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We construct models of triaxial galactic nuclei containing central black holes using the method of orbital superposition and then verify their stability by advancing N-body realizations of the models forward in time. We assume a power-law form for the stellar density, / r À , with ¼ 1 and 2; these values correspond approximately to the nuclear density profiles of bright and faint galaxies, respectively. Equidensity surfaces are ellipsoids with fixed axis ratios. The central black hole is represented by a Newtonian point mass. We consider three triaxial shapes for each value of : almost prolate, almost oblate, and maximally triaxial. Two kinds of orbital solution are attempted for each mass model: the first including only regular orbits, the second including chaotic orbits as well. We find that stable configurations exist, for both values of , in the maximally triaxial and nearly oblate cases; however, steady state solutions in the nearly prolate geometry could not be found. A large fraction of the mass, of order 50% or more, could be assigned to the chaotic orbits without inducing evolution. Our results demonstrate that triaxiality may persist even within the sphere of influence of the central black hole and that chaotic orbits may constitute an important building block of galactic nuclei.

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“…For each value of the integral, we selected four sets: 1) Zero initial velocity; 2) x-y plane andż initial velocity; 3) x-z plane andẏ initial velocity; 4) y-z plane andẋ initial velocity. Schwarzschild (1993) proposed the use of the initial conditions 1 and 3 for non-rotating potentials. As we have a rotating potential, we preferred to add also initial conditions 2 and 4.…”

Section: Initial Conditionsmentioning

confidence: 99%

Regular and Chaotic Motion in Globular Clusters

Carpintero¹,

Muzzio²,

Wachlin³

1999

International Astronomical Union Colloquium

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Abstract. As a first step towards a comprehensive investigation of stellar motions within globular clusters, we present here the results of a study of stellar orbits in a mildly triaxial globular cluster that follows a circular orbit inside a galaxy. The stellar orbits were classified using the frequency analysis code of Carpintero and Aguilar and, as a check, the Liapunov characteristic exponents were also computed in some cases.The orbit families were obtained using different start spaces. Chaotic orbits turn out to be very common and while, as could be expected, they are particularly abundant in the outer parts of the cluster, they are still significant in the innermost regions. Their relevance for the structure of the cluster is discussed.

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Self-consistent models for galactic halos

Cited by 149 publications

References 0 publications

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

A Self‐Consistent Study of Triaxial Black Hole Nuclei

Regular and Chaotic Motion in Globular Clusters

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