King and Wilson single-mass models with IMBH for Globular Clusters

King Wilson
Wilson model is a variant of the King one. It shows a more extended outer region. See [6]
The central IMBH is included following [5]. The King/Wilson model is generalised by including the Bahcall-Wolf ([1]) distribution function within the IMBH gravitational influence region.
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The first ‘shape’ parameter (see [2]). When the IMBH is present, this is the dimensionless potential at the edge of its gravitational influence radius (see [5]).
This is the second ‘shape’ parameter needed when the IMBH is included. It corresponds to the ratio between the IMBH and the cluster masses (rounded to 2 significant digits).
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[1] Bahcall, J.N. & Wolf, R.A. 1976, ApJ, 209, 214
[2] King, I. R. 1966, AJ, 71, 64
[3] Lanzoni, B. et al., 2007, ApJ, 668, L139
[4] Miocchi, P. 2006, MNRAS, 366, 227
[5] Miocchi, P. 2007, MNRAS, 381, 103
[6] Wilson, C. P. 1975, AJ, 80, 175
Structural parameters:
The basic length parameter for King/Wilson model (in arbitrary units).
The radius at which the density drops to 0.
The radius at which the surface projected density drops to 1/2 its central value (with an IMBH this definition is slightly more complicated, see [5]).
The log of the ratio ‘limiting to core radius’
The radius enclosing half of the integrated surf. density.
The radius enclosing half of the total cluster mass (not including the IMBH mass).
The log slope of the surface density profile in the inner core region (i.e. it goes like r s).
profile preview
model profile.

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Credits. If you use BHKing for scientific work, we kindly ask you to report the following acknowledgment “This research has made use of the products of the Cosmic-Lab project funded by the European Research Council”, and to cite either the paper Miocchi P., 2007, MNRAS, 381, 103 (if the IMBH is included) or Miocchi P., 2006, MNRAS, 366, 227 (without the IMBH).