BHKing

Model:

Kind of model:

King Wilson

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Wilson model is a variant of the King one. It shows a more extended outer region. See [6]

Include a central IMBH:

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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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Central dimensionless potential (W₀): ---select

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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]).

IMBH mass ratio: ---select

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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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References

[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:

King radius:

The basic length parameter for King/Wilson model (in arbitrary units).

limiting radius:

The radius at which the density drops to 0.

core radius:

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]).

concentration:

The log of the ratio ‘limiting to core radius’

half-light radius:

The radius enclosing half of the integrated surf. density.

half-mass radius:

The radius enclosing half of the total cluster mass (not including the IMBH mass).

central log slope:

The log slope of the surface density profile in the inner core region (i.e. it goes like r ^s).

model profile.

Please, feel free to contact us for any questions, comments or suggestions.

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).