The massive star initial mass function of the Arches cluster

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Volume 501 / No 2 (July II 2009)

A&A, 501 2 (2009) 563-583

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Table 8:

Physical parameters of the Arches cluster.
Parameter		Value	Comments
Core radius	$R_{\rm c}$	$0.14\pm0.05$ pc	Derived by fitting the empirical King density law
			to the observed $\Sigma(R)$
Tidal radius	$R_{\rm t}$	${\sim}1$ pc	Derived by Kim et al. (2000)
Central concentration	$c= \log \frac{R_{\rm t}}{R_{\rm c}}$	0.84	Comparable to the less concentrated galactic globulars
			according to Harris (1996)
Central surface density	$\Sigma_{0}$	$2.2({\pm}0.4)\times10^{3}~{\rm stars~pc}^{-2}$	Derived by fitting the empirical King density law
			to the observed $\Sigma(R)$
Central volume density	$\rho_{0}$	$8.0({\pm}1.5)\times10^{3}~{\rm stars~pc}^{-3}$
Central mass density	$\rho_{\rm m,0}$	$2.0({\pm}0.4)\times10^{5}~M_{\odot}~{\rm pc}^{-3}$	For an average mass of $25.4~M_{\odot}$ in the ${>}10~M_{\odot}$ range
Cluster mass	$M_{\rm cl,1}$	${\sim}2.0(\pm0.6)\times10^{4}~M_{\odot}$	For an extrapolation of the photometric mass down to $1~M_{\odot}$
	$M_{\rm cl,2}$	${\sim}3.1(\pm0.6)\times10^{4}~M_{\odot}$	For an extrapolation down to $0.08~M_{\odot}$ using a Kroupa IMF (2002)
Predicted
velocity dispersion^a	$\sigma=\left(\frac{0.4~GM_{\rm cl}}{R_{\rm hm}}\right)^{1/2}$	$9~{\rm km~s}^{-1}$	Using $M_{\rm cl,1}$ and a half mass radius of 0.4 pc derived in SGB02

^a Equations (4)-(80b) of Binney & Tremaine (1987).

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