How to configure a razor-thin disk

This stanza defines the phase-space components with associated parameters and force methods as a list. Each list element starts with ‘-’ and has four fields:

Key word	Explanation
name	the mnemonic name for the component
parameters	a list of key: value pairs
bodyfile	the name of the ascii phase-space file to initialize this component
force	the method for computing the potential and acceleration

The mnemonic name may contain spaces. The body file is in EXP native formation. EXP has its own hierarchical phase space structure that we call PSP. EXP provides a number of standalone routines to manipulate, visualize and summarize the content of PSP files. EXP uses the list index internally to describe the component. However, there is support for reflection by mnemonic name.

A complete example

FlatDisk uses the empirical orthogonal function method (EOF) described in Two-dimensional cylindrical bases to find potential-density pairs that best fit a target disk density. This method also computes the potential and force above and below the disk plane for coupling to three-dimensional components. The desired target model is specified in the YAML configuration in the force field stanza. A typical force configuration for a razor-thin exponential disk might be:

---
.
.
.
force        :
  id         : flatdisk
  parameters :
    diskconf   : {name: expon, parameters: {acyl: 0.01}}
    nmaxfid    : 40
    rcylmin    : 0.0
    rcylmax    : 10.0
    numx       : 256
    numy       : 128
    scale      : 0.01
    knots      : 400
    Mmax       : 6
    nmax       : 12
    logr       : false
    self_consistent : true
.
.
.
...

Some explanation:

• id is a mnemonic name for the force, flatdisk in this case

• parameters is a list of key-value pairs that define the force

• diskconf defines the target density for basis construction. Here we are using an exponential disk with with a scale length, acyl of 0.01

• nmaxfid is the maximum Bessel function degree for the Bessel function Gram matrix used to construct the EOF basis

• rcylmin and rcylmax define the minimum and maximum radius, respectively, of the table of potential-density pairs in units where the disk scale is unity

• scale maps the cylindrical coordinates to the disk basis. Choosing this to be the same or similar to the acyl parameter is a good choice in this calse

• numx and numy are the number of grid points in the x and z directions, respectively, for the tabulation of the potential and force functions in the meridional plane

• knots is the number of quadrature knots used to compute the inner products in the Gram matrix

• Mmax and nmax are the maximum azimuthal degree and radial order, respectively, for the new basis functions

• logr is a boolean that indicates whether the radial grid is linear or logarithmic

• self_consistent is a boolean that indicates whether the force field is computed from the particle distribution at every time step or fixed to the initial distribution

Please note that many of these parameters have sensible defaults and can be left out of the configuration. They are included here as an example. By default, FlatDisk uses Bessel functions to construct the full three-dimensional fields from the flat-disk density using the Hankel transform (see Two-dimensional cylindrical bases). This method is very accurate when the initial basis set itself are proportional to Bessel functions and that is the default. However, the initial basis may use the Clutton-Brock two-dimensional basis set, optionally. This is experimental and requires recompiling the code. Ask for help if you want to consider this.

Target densities and their parameters

Exponential disk

Name: expon

Parameters:

Key word	Explanation
acyl	scale length

Kuzmin disk

Name: kuzmin

Parameters:

Key word	Explanation
acyl	scale length

Mestel disk

Name: mestel

Parameters:

Key word	Explanation
vrot	rotation speed

Zang disk

Also known as the doubly tapered Mestel disk

Name: zang

Parameters:

Key word	Explanation
vrot	rotation speed
Ninner	inner taper exponent
Mouter	outer taper exponent
Ri	inner taper radius
Ro	outer taper radius