A Compact Cylindrical Green’s Function Expansion for the Solution of Potential Problems

Cohl, Howard S.; Tohline, J. E.

doi:10.1086/308062

Cited by 120 publications

(130 citation statements)

References 24 publications

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“…f , , and ò k is equal to unity for k=1 and two otherwise (e.g., Morse & Feshbach 1953;Cohl & Tohline 1999;Cohl et al 2000). 6 The gravitational potential is then given by (3) give the semimajor axis and ellipticity of nuclear rings adopted from Comerón et al (2010).…”

Section: A2 Toroidal Coordinatesmentioning

confidence: 99%

Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

Kim

Moon

2016

ApJ

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Nuclear rings at the centers of barred galaxies exhibit strong star formation activities. They are thought to undergo gravitational instability when they are sufficiently massive. We approximate them as rigidly rotating isothermal objects and investigate their gravitational instability. Using a self-consistent field method, we first construct their equilibrium sequences specified by two parameters: α corresponding to the thermal energy relative to gravitational potential energy, and  R B measuring the ellipticity or ring thickness. Unlike in the incompressible case, not all values of  R B yield an isothermal equilibrium, and the range of  R B for such equilibria shrinks with decreasing α. The density distributions in the meridional plane are steeper for smaller α, and well approximated by those of infinite cylinders for slender rings. We also calculate the dispersion relations of non-axisymmetric modes in rigidly rotating slender rings with angular frequency Ω 0 and central density r c . Rings with smaller α are found more unstable with a larger unstable range of the azimuthal mode number. The instability is completely suppressed by rotation when Ω 0 exceeds the critical value. The critical angular frequency is found to be almost constant at ( ) r G 0.7 c 1 2 for α0.01 and increases rapidly for smaller α. We apply our results to a sample of observed star-forming rings and confirm that rings without a noticeable azimuthal age gradient of young star clusters are indeed gravitationally unstable.

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Section: A2 Toroidal Coordinatesmentioning

confidence: 99%

Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

Kim

Moon

2016

ApJ

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“…For computational reasons, only those Fourier components ρ m whose index m ranges between 0 and m max are retained at this stage. For each of them, the procedure is the following: (1) from ρ m , the gravitational potential Φ m S is obtained at the boundary of the computational domain using an expansion in Legendre functions (Cohl & Tohline 1999). (2) Φ m S is calculated everywhere on the computational domain using the Successive Over Relaxation method (Hirsch 1988).…”

Section: Numerical Proceduresmentioning

confidence: 99%

The effect of MHD turbulence on massive protoplanetary disk fragmentation

Fromang

2005

A&A

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Abstract. Massive disk fragmentation has been suggested to be one of the mechanisms leading to the formation of giant planets. While it has been heavily studied in quiescent hydrodynamic disks, the effect of MHD turbulence arising from the magnetorotational instability (MRI) has never been investigated. This paper fills this gap and presents 3D numerical simulations of the evolution of locally isothermal, massive and magnetized disks. In the absence of magnetic fields, a laminar disk fragments and clumps are formed due to the effect of self-gravity. Although they disapear in less than a dynamical timescale in the simulations because of the limited numerical resolution, various diagnostics suggest that they should survive and form giant planets in real disks. When the disk is magnetized, it becomes turbulent at the same time as gravitational instabilities develop. At intermediate resolution, no fragmentation is observed in these turbulent models, while a large number of fragments appear in the equivalent hydrodynamical runs. This is because MHD turbulence reduces the strength of the gravitational instability. As the resolution is increased, the most unstable wavelengths of the MRI are better resolved and small scale angular momentum transport starts to play a role: fragments are found to form in massive and turbulent disks in that case. All of these results indicate that there is a complicated interaction between gravitational instabilities and MHD turbulence that influences disk fragmentation processes.

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“…This mathematical description employs the use of Q-functions, and these functions are predominantly used for problems which exhibit toroidal sym-metry. However, they have not been extensively applied to cylindrical geometries in the engineering world [32,33], and in fact, recent literature only sparsely mentions the restricted class of toroidal functions which are used for cylindrical geometries [34,35,36]. Other formulations, specifically those due to Kildishev [37,38,39], have made contributions to this problem by employing a spheroidal harmonic analysis.…”

Section: Discussionmentioning

confidence: 99%

Multipole Analysis of Circular Cylindircal Magnetic Systems

Selvaggi

2005

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A Compact Cylindrical Green’s Function Expansion for the Solution of Potential Problems

Cited by 120 publications

References 24 publications

Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

The effect of MHD turbulence on massive protoplanetary disk fragmentation

Multipole Analysis of Circular Cylindircal Magnetic Systems

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