The major luminous component of spiral galaxies typically have "exponential" disks, in which the distribution of surface light falls off with galactocentric radius, R, like exp(-R/hR), where hR is the characteristic disk scalelength.
The gravitational potential of the disk component is often modeled using the flattened spheroids of Miyamoto and Nagai (1975). This potential is straightforward to implement for numerical orbital integrations, and has a simple analytical form for the corresponding density distribution, but unfortunately does not produce a particularly exponential falloff of surface mass density as seen in a wide range of R in real disk galaxies.
This problem can be greatly alleviated by simply adding together several Miyamoto-Nagai (MN) disks. For the Milky Way, this has been done using 3 MN disks, by Flynn et al (1996). Smith et al (2015) have generalised this technique to disks with a range of thicknesses, providing fitting formulae to determine the values of the MN scalelength, a and MN disk mass, M, for 3 MN disks. The parameters for these 3 MN disks can be computed below.
To compute the values a1, a2 and a3, and M1, M2 and M3 for a 3 MN fit to an exponential disk, enter the "disk thickness" ratio (i.e. the scaleheight to exponential scalelength ratio) hz/hR, in the range 0 to 3.
hz/hR =
Note well: the valid range is 0 to 3 if negative densities are allowed, and 0 to 1.35 for positive densities only.)
Positive densities only Allow negative densities