Table 1
Summary of the properties of the families of models studied in the present paper.
| Family of | Distribution | Dimensionless | Internal | Anisotropy | Isophote | Paper |
| models | function | parameters | rotation | profile | shape | sections |
|
|
||||||
|
Ae − aH0 [e − a(H − H0) − 1] | Ψ, χ | solid-body | (0,0,0) | disky | 2 |
|
Ae − aE0 [e − a(I − E0) − 1 + a(I − E0)] | Ψ, χ,  , c |
differential | (0, > 0, − 2) | boxy | 3, 4, 5, 6 |
|
Ae − aE0e − a(I − E0) | Ψ, χ, , c |
differential | (0, > 0,0) | boxy | 3, 6, Appendix B] |
Notes. The relevant integrals are defined as H = E − ωJz and 
, with the corresponding cut-off constants given by H0 and E0. The dimensionless parameters are defined as follows: Ψ = ψ(0) respresents a measure of the concentration, χ = ω2/(4πGρ0) a measure of the (central) rotation strength, and, for the family of differentially rotating models, 
and c > 1/2 determine the shape of the rotation profile. The pressure anisotropy profiles are characterized in terms of the values of the anisotropy parameter 
in the central, intermediate, and outer regions of a model; values of α greater than, lower than, and equal to zero indicate radially-biased, tangentially-biased anisotropy, and isotropy in velocity space, respectively. For each family of models, the first and third values of α are calculated analytically as the limiting values for small and large radii. For physical reasons discussed in Sect. 3.1, the focus of the paper is on the first two families.
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