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Home All issues Volume 498 / No 1 (April IV 2009) A&A, 498 1 (2009) 241-271 Full HTML
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Table B.1:

List of 2D models having a positive entropy gradient and an initial rotation profile given by $\Omega_0 = 1900 ~{\rm s}^{-1}$ and $\alpha _\Omega = -1.25$. The columns give (from left to right) the number of grid zones $m_{\varpi } \times m_z$ (the box has an edge length $L_{\varpi} = L_z = 1 ~{\rm km}$), the type of boundary condition which was applied (d: velocity damping; p: periodic), the adiabatic index of the gas, $\Gamma $ (models computed with an ideal-gas equation of state instead of the hybrid one are marked ``id''), the initial entropy, S0, and the radial entropy gradient, $\partial _{\varpi } S$. The next three columns give the parameter $\mathcal{C}$ determining the instability regime (see Eq. (24)), the theoretical growth rate, $\sigma _{{\rm th}}$, and the strength of the initially uniform magnetic field, b0z. The last two columns list the numerical growth rate, $\sigma $, and the value of the Maxwell stress component $M^{{\rm term}}_{\varpi \phi }$ at MRI termination.
$m_{\varpi } \times m_z$ BC $\Gamma $ S0 $\partial _{\varpi } S$ $\mathcal{C}$ $\sigma _{{\rm th}}$ b0z $\sigma $ $M_{\varpi \phi }^{{\rm term}}$
        $[{\rm km}^{-1}]$   $\left[ {\rm ms^{-1}} \right]$ $\left[10^{12}~{\rm G}\right]$ $\left[ {\rm ms^{-1}} \right]$ $\left[ 10^{28} ~ {\rm G^2 ~cm^{-3}} \right]$

$100 \times 100$

 d 1.31 0.20 0.020 -1.7 0.73 10 0.72 1.1
$100 \times 100$ d 1.31 0.20 0.020 -1.7 0.73 20 0.71 1.3
$100 \times 100$ d 1.31 0.20 0.020 -1.7 0.73 40 0.70 1.6
$100 \times 100$ d 1.31 0.20 0.020 -1.7 0.73 80 0.60 1.8

$200 \times 200$

 d 1.31 0.20 0.020 -1.7 0.73 10 0.71 1.3

$ 400 \times 400 $

 d 1.31 0.20 0.020 -1.7 0.73 10 0.67 1.2
$ 400 \times 400 $ d 1.31 0.20 0.020 -1.7 0.73 20 0.69 1.5
$ 50 \times 50 $ d 5/3 0.20 0.040 -1.1 0.49 10 0.46 0.97
$ 50 \times 50 $ d 5/3 0.20 0.040 -1.1 0.49 20 0.61 1.7
$ 50 \times 50 $ d 5/3 0.20 0.040 -1.1 0.49 40 0.48 0.87
$ 50 \times 50 $ d 5/3 0.20 0.040 -1.1 0.49 80 0.39 0.93
$ 50 \times 50 $ d 1.31, id 0.20 0.040 -0.69 0.32 20 0.50 0.53
$ 50 \times 50 $ d 1.31, id 0.20 0.040 -0.69 0.32 40 0.30 0.27
$ 50 \times 50 $ d 1.31, id 0.20 0.040 -0.69 0.32 80 0.28 0.22
$ 50 \times 50 $ d 1.31 0.20 0.040 -0.69 0.32 4 0.25 0.21
$ 50 \times 50 $ d 1.31 0.20 0.040 -0.69 0.32 20 0.49 0.50
$ 50 \times 50 $ d 1.31 0.20 0.040 -0.69 0.32 40 0.28 0.24
$ 50 \times 50 $ d 1.31 0.20 0.040 -0.69 0.32 80 0.28 0.22
$100 \times 100$ d 1.31 0.20 0.040 -0.69 0.32 10 0.49 0.55
$100 \times 100$ d 1.31 0.20 0.040 -0.69 0.32 20 0.30 0.29
$100 \times 100$ d 1.31 0.20 0.040 -0.69 0.32 40 0.30 0.29
$100 \times 100$ d 1.31 0.20 0.040 -0.69 0.32 80 0.28 0.22
$200 \times 200$ d 1.31 0.20 0.040 -0.69 0.32 4 0.53 0.40
$200 \times 200$ d 1.31 0.20 0.040 -0.69 0.32 10 0.30 0.20
$200 \times 200$ d 1.31 0.20 0.040 -0.69 0.32 20 0.30 0.22
$200 \times 200$ d 1.31 0.20 0.040 -0.69 0.32 40 0.30 0.30
$200 \times 200$ d 1.31 0.20 0.040 -0.69 0.32 80 0.26 0.18
$100 \times 100$ d 1.31 0.20 0.080 1.1 0 20 <0.01  
$200 \times 200$ d 1.31 0.20 0.080 1.1 0 10 <0.05  

$100 \times 100$

 p 5/3 0.20 0.020 -1.8 0.82 20 0.79 4.9
$100 \times 100$ p 1.31 0.20 0.020 -1.7 0.73 10 0.73 1.9
$100 \times 100$ p 1.31 0.20 0.020 -1.7 0.73 20 0.71 33
$100 \times 100$ p 1.31 0.20 0.020 -1.7 0.73 40 0.72 202
$100 \times 100$ p 1.31 0.20 0.020 -1.7 0.73 80 0.62 411
$ 50 \times 50 $ p 1.31 0.20 0.040 -0.69 0.32 20 0.51 1.7
$ 50 \times 50 $ p 1.31 0.20 0.040 -0.69 0.32 40 0.31 90
$ 50 \times 50 $ p 1.31 0.20 0.040 -0.69 0.32 80 0.32 159
$100 \times 100$ p 1.31 0.20 0.040 -0.69 0.32 10 0.53 0.64
$100 \times 100$ p 1.31 0.20 0.040 -0.69 0.32 20 0.30 6.8
$100 \times 100$ p 1.31 0.20 0.040 -0.69 0.32 40 0.30 98
$100 \times 100$ p 1.31 0.20 0.040 -0.69 0.32 80 0.31 201
$ 50 \times 50 $ p 5/3 0.20 0.040 -1.1 0.49 10 0.45 0.55
$ 50 \times 50 $ p 5/3 0.20 0.040 -1.1 0.49 20 0.59 3.1
$ 50 \times 50 $ p 5/3 0.20 0.040 -1.1 0.49 40 0.47 201
$ 50 \times 50 $ p 5/3 0.20 0.040 -1.1 0.49 80 0.38 139

$100 \times 100$

 p 5/3 0.20 0.040 -1.1 0.49 4 0.40 0.43
$100 \times 100$ p 5/3 0.20 0.040 -1.1 0.49 10 0.63 0.83
$100 \times 100$ p 5/3 0.20 0.040 -1.1 0.49 20 0.49 5.0
$100 \times 100$ p 5/3 0.20 0.040 -1.1 0.49 40 0.47 262
$100 \times 100$ p 5/3 0.20 0.040 -1.1 0.49 80 0.45 978


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