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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.2:

List of 2D models having a negative initial entropy gradient. 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 rotation law (``d'': differential rotation with $\Omega_0 = 1900 ~{\rm s}^{-1}$ and $\alpha _\Omega = -1.25$; `` ${r}^{\Omega }$'' rigid rotation with an angular velocity of $\Omega $), the adiabatic index of the gas, $\Gamma $, the initial entropy, S0, the radial entropy gradient, $\partial _{\varpi } S$, and the strength of the initially uniform magnetic field, b0z. The next columns give the three quantities $\mathcal{R}_\varpi / \Omega_0^2$, $N^2/\Omega _0^2$ and $\mathcal{C}$ determining the instability regime (see Eq. (24)), followed by the theoretical growth rate, $\sigma _{{\rm th}}$, and the type of the instability. 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 Rot $\Gamma $ S0 $\partial _{\varpi } S$ b0z      $\mathcal{R}_\varpi / \Omega_0^2$ $N^2/\Omega _0^2$ $\mathcal{C}$ $\sigma _{{\rm th}}$ regime $\sigma $ $M_{\varpi \phi }^{{\rm term}}$
          $[{\rm km}^{-1}]$ $\left[10^{12}~{\rm G}\right]$       $\left[ {\rm ms^{-1}} \right]$   $\left[ {\rm ms^{-1}} \right]$ $\left[ 10^{28} ~ {\rm G^2 ~cm^{-3}} \right]$

$100 \times 100$

 d d 1.31 0.20 -0.019 0 -2.5 -0.90 -3.4 1.6 mix 0 0
$100 \times 100$ d d 1.31 0.20 -0.019 10 -2.5 -0.90 -3.4 1.6 mix 1.2 2.6
$100 \times 100$ d d 1.31 0.20 -0.019 20 -2.5 -0.90 -3.4 1.6 mix 1.3 3.4
$100 \times 100$ d d 1.31 0.20 -0.019 40 -2.5 -0.90 -3.4 1.6 mix 1.4 5.7
$100 \times 100$ d d 1.31 0.20 -0.019 80 -2.5 -0.90 -3.4 1.6 mix 1.3 6.0

$ 50 \times 50 $

 d d 1.31 0.20 -0.038 20 -2.5 -1.8 -4.3 2.0 mix 1.6 4.2

$100 \times 100$

 d d 1.31 0.20 -0.038 0 -2.5 -1.8 -4.3 2.0 mix 0 0
$100 \times 100$ d d 1.31 0.20 -0.038 10 -2.5 -1.8 -4.3 2.0 mix 1.5 3.3
$100 \times 100$ d d 1.31 0.20 -0.038 20 -2.5 -1.8 -4.3 2.0 mix 1.7 5.3
$100 \times 100$ d d 1.31 0.20 -0.038 40 -2.5 -1.8 -4.3 2.0 mix 1.7 7.8
$100 \times 100$ d d 1.31 0.20 -0.038 80 -2.5 -1.8 -4.3 2.0 mix 1.7 9.5

$100 \times 100$

 d d 1.31 0.20 -0.075 0 -2.5 -3.6 -6.1 2.8 mix 0 0
$100 \times 100$ d d 1.31 0.20 -0.075 10 -2.5 -3.6 -6.1 2.8 mix 2.4 1.3
$100 \times 100$ d d 1.31 0.20 -0.075 20 -2.5 -3.6 -6.1 2.8 mix 2.6 4.8
$100 \times 100$ d d 1.31 0.20 -0.075 40 -2.5 -3.6 -6.1 2.8 mix 2.5 9.7
$100 \times 100$ d d 1.31 0.20 -0.15 0 -2.5 -7.2 -9.7 4.4 conv 3.0 0
$100 \times 100$ d d 1.31 0.20 -0.15 20 -2.5 -7.2 -9.7 4.4 conv 4.0 1.2
$100 \times 100$ d d 1.31 0.20 -0.15 40 -2.5 -7.2 -9.7 4.4 conv 3.8 3.7
$100 \times 100$ p d 5/3 0.20 -0.019 20 -2.5 -0.70 -3.2 1.5 mix 1.3 6.0
$100 \times 100$ p d 5/3 0.20 -0.019 40 -2.5 -0.70 -3.2 1.5 mix 1.4 50
$ 50 \times 50 $ p d 1.31 0.20 -0.038 20 -2.5 -1.8 -4.3 2.0 mix 1.6 12
$ 50 \times 50 $ p d 1.31 0.20 -0.038 40 -2.5 -1.8 -4.3 2.0 mix 1.7 19.5
$100 \times 100$ p d 1.31 0.20 -0.038 20 -2.5 -1.8 -4.3 2.0 mix 1.7 27
$100 \times 100$ p d 1.31 0.20 -0.038 40 -2.5 -1.8 -4.3 2.0 mix 1.7 22

$100 \times 100$

 d r1000 1.31 0.20 -0.075 0 0 -14 -14 3.4 conv 2.7  
$100 \times 100$ d r1500 1.31 0.20 -0.075 0 0 -5.7 -5.7 2.1 conv 1.6  
$100 \times 100$ d r1900 1.31 0.20 -0.075 0 0 -3.2 -3.2 1.5 MBI 0  
$100 \times 100$ d r1500 1.31 0.20 -0.075 10-8 0 -5.7 -5.7 2.1 conv 1.5 $1.4 \times 10^{-18}$
$100 \times 100$ d r1500 1.31 0.20 -0.075 1 0 -5.7 -5.7 2.1 conv 1.5 0.013
$100 \times 100$ d r1500 1.31 0.20 -0.075 10 0 -5.7 -5.7 2.1 conv 1.8 1.7
$100 \times 100$ d r1900 1.31 0.40 -0.10 4 0 -3.6 -3.6 1.7 MBI 1.1 0.22
$100 \times 100$ d r1900 1.31 0.40 -0.10 8 0 -3.6 -3.6 1.7 MBI 1.2 1.6
$100 \times 100$ d r1900 1.31 0.40 -0.10 10 0 -3.6 -3.6 1.7 MBI 1.1 1.6
$100 \times 100$ d r1900 1.31 0.40 -0.10 20 0 -3.6 -3.6 1.7 MBI 1.4 5.2
$100 \times 100$ d r1900 1.31 0.40 -0.10 40 0 -3.6 -3.6 1.7 MBI    
$200 \times 200$ d r1900 1.31 0.40 -0.10 0 0 -3.6 -3.6 1.7 MBI 0 0
$200 \times 200$ d r1900 1.31 0.40 -0.10 0.01 0 -3.6 -3.6 1.7 MBI $\lesssim $0.006  
$200 \times 200$ d r1900 1.31 0.40 -0.10 4 0 -3.6 -3.6 1.7 MBI 1.0 0.99
$200 \times 200$ d r1900 1.31 0.40 -0.10 8 0 -3.6 -3.6 1.7 MBI 1.4 1.4
$200 \times 200$ d r1900 1.31 0.40 -0.10 10 0 -3.6 -3.6 1.7 MBI 1.4 2.1
$200 \times 200$ d r1900 1.31 0.40 -0.10 20 0 -3.6 -3.6 1.7 MBI 1.5 5.6

Source LaTeX | All tables | In the text

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