Table 1: Growth rate k, with an estimate of the related uncertainty $\Delta k$ , for the radial orbit instability from the simulation of a set of $f^{(\nu )}$ models. Here $\kappa = 2K_{\rm r}/K_{\rm T}$ is the global anisotropy parameter and $\eta = a_3/a_1$ is the axis ratio of the inertia ellipsoid referred to the sphere of radius 3 r_M. For $M = 10^{11}~M_{\odot}$ and $r_M = 5~\rm kpc$ , k is given in units of $10^{-8}~\rm yr^{-1}$ .
$(\nu;\Psi)$ k $\Delta k$ $\kappa (0)$ $\kappa(t_{\rm end})$ $\eta(t_{\rm end})$

(1; 2.0) 0.85 0.1 2.65 1.87 0.65

(1; 3.0) 0.48 0.07 2.17 1.84 0.67

(1; 3.2) 0.37 0.07 2.09 1.84 0.69

(1; 3.4) 0.34 0.07 2.02 1.83 0.74

(1; 3.6) 0.30 0.05 1.95 1.85 0.80

(1; 3.8) 0.16 0.04 1.89 1.82 0.85

(1; 4.0) 0.08 0.05 1.84 1.81 0.91

(1; 4.2) 0.007 0.10 1.78 1.76 0.94

(1; 5.0) 0.001 0.01 1.60 1.60 0.99

(1; 9.0) <10^-4 - 1.32 1.32 0.99

(3/8; 3.0) 0.90 0.10 2.28 1.86 0.73

(3/8; 5.0) 0.45 0.15 1.75 1.71 0.93

(1/2; 3.0) 0.70 0.10 2.21 1.86 0.70

(1/2; 4.0) 0.43 0.05 1.92 1.80 0.85

(1/2; 5.0) 0.1 0.2 1.68 1.67 0.96

(1/2; 6.0) <10^-3 - 1.54 1.54 0.99

(3/4; 3.0) 0.64 0.05 2.20 1.85 0.70

(3/4; 4.0) 0.16 0.02 1.86 1.76 0.84

(3/4; 5.0) < $2\times 10^{-2}$ - 1.63 1.63 0.98

**Table 1:** Growth rate k, with an estimate of the related uncertainty $\Delta k$ , for the radial orbit instability from the simulation of a set of $f^{(\nu )}$ models. Here $\kappa = 2K_{\rm r}/K_{\rm T}$ is the global anisotropy parameter and $\eta = a_3/a_1$ is the axis ratio of the inertia ellipsoid referred to the sphere of radius 3 r_M. For $M = 10^{11}~M_{\odot}$ and $r_M = 5~\rm kpc$ , k is given in units of $10^{-8}~\rm yr^{-1}$ .
$(\nu;\Psi)$	k	$\Delta k$	$\kappa (0)$	$\kappa(t_{\rm end})$	$\eta(t_{\rm end})$
(1; 2.0)	0.85	0.1	2.65	1.87	0.65
(1; 3.0)	0.48	0.07	2.17	1.84	0.67
(1; 3.2)	0.37	0.07	2.09	1.84	0.69
(1; 3.4)	0.34	0.07	2.02	1.83	0.74
(1; 3.6)	0.30	0.05	1.95	1.85	0.80
(1; 3.8)	0.16	0.04	1.89	1.82	0.85
(1; 4.0)	0.08	0.05	1.84	1.81	0.91
(1; 4.2)	0.007	0.10	1.78	1.76	0.94
(1; 5.0)	0.001	0.01	1.60	1.60	0.99
(1; 9.0)	<10^-4	-	1.32	1.32	0.99
(3/8; 3.0)	0.90	0.10	2.28	1.86	0.73
(3/8; 5.0)	0.45	0.15	1.75	1.71	0.93
(1/2; 3.0)	0.70	0.10	2.21	1.86	0.70
(1/2; 4.0)	0.43	0.05	1.92	1.80	0.85
(1/2; 5.0)	0.1	0.2	1.68	1.67	0.96
(1/2; 6.0)	<10^-3	-	1.54	1.54	0.99
(3/4; 3.0)	0.64	0.05	2.20	1.85	0.70
(3/4; 4.0)	0.16	0.02	1.86	1.76	0.84
(3/4; 5.0)	< $2\times 10^{-2}$	-	1.63	1.63	0.98

Source LaTeX | All tables | In the text

	1 Introduction
	2 Model construction and the relevant parameter space
	3 Density profiles
	4 Phase space properties
	5 Stability
	6 A first comparison with the observations
	7 Discussion and conclusions
	Appendix A: Constants and scales
	References