J/ApJ/747/106 Potential of the finite Mestel disk (Schulz, 2012)
The gravitational force and potential of the finite Mestel disk.
Schulz E.
<Astrophys. J., 747, 106 (2012)>
=2012ApJ...747..106S 2012ApJ...747..106S
ADC_Keywords: Models
Keywords: celestial mechanics - galaxies: kinematics and dynamics -
gravitation - methods: analytical
Abstract:
Mestel determined the surface mass distribution of the finite disk for
which the circular velocity is constant in the disk and found the
gravitational field for points in the z=0 plane. Here we find the
exact closed form solutions for the potential and the gravitational
field of this disk in cylindrical coordinates over all the space. The
finite Mestel disk (FMD) is characterized by a cuspy mass distribution
in the inner disk region and by an exponential distribution in the
outer region of the disk. The FMD is quite different from the better
known exponential disk or the untruncated Mestel disk which, being
infinite in extent, are not realistic models of real spiral galaxies.
In particular, the FMD requires significantly less mass to explain a
measured velocity curve.
Description:
Here we present the explicit expressions for the potential and the
gravitational field of the finite Mestel disk (FMD) which was first
introduced by Mestel (1963MNRAS.126..553M 1963MNRAS.126..553M). Until now the force
vectors of the FMD were only known for points in the plane of the
disk, and there was no analytical solution of the potential.
Throughout this work, (R,z) are the cylindrical coordinates in each
meridional plane. Tables 2-4 provide normalized values of the
potential, radial force, and axial force of the FMD. Normalized
expressions for the potential and force field were defined by choosing
units such that the disk mass, the gravitational constant, and the
disk radius were all 1.0.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table2.dat 21 10201 Potential Φ of the Mestel disk
table3.dat 21 10201 Radial force Fr of the Mestel disk
table4.dat 21 10201 Axial force Fz of the Mestel disk
ori/* . 4 *Original tables and ReadMe files
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Note on ori/*: the "ori" subdirectory contains the data in their original
form of 101 lines and 101 columns; these have been converted into 101*101
lines, each line representing a (r,z) point.
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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2- 5 F4.2 --- z [0/5] The scale height (G1)
7- 10 F4.2 --- r [0/5] The radial coordinate (G1)
12- 21 F10.6 --- Phi [-5.8/-0.1]? The potential Φ of the Mestel
disk (1)
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Note (1): See equation (5). To compute the actual potential, if α
is the disk radius (in kpc) and M its mass (in M☉), multiply
the value by C1*M/α, with C1=G.M☉/kpc=4.30136m2/s2.
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Byte-by-byte Description of file: table3.dat
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Bytes Format Units Label Explanations
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2- 5 F4.2 --- z [0/5] The scale height (G1)
7- 10 F4.2 --- r [0/5] The radial coordinate (G1)
12- 21 F10.6 --- Fr [-31.5/0]? The radial force of the Mestel disk (G2)
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Byte-by-byte Description of file: table4.dat
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Bytes Format Units Label Explanations
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2- 5 F4.2 --- z [0/5] The scale height (G1)
7- 10 F4.2 --- r [0/5] The radial coordinate (G1)
12- 21 F10.6 --- Fz [-30.5/0]? The axial force of the Mestel disk (G2)
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Global notes:
Note (G1): The dimensionless coordinates are relative to the disk radius;
use the symmetry properties for negative z.
Note (G2): See equation (6). To compute the actual force, if α is the
disk radius (in kpc) and M its mass (in M☉), multiply the value by
C2.M/α2, with C2=G.M☉/kpc2=1.39397x10-19m/s2.
A blank means ∞.
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History:
From electronic version of the journal
(End) Greg Schwarz [AAS], Emmanuelle Perret [CDS] 27-Sep-2013