09/06 - 09/10

Thursday Update

Outer Grid Profiles

Raw Profile

Normalized (lowest value)

shows approximate contrast

Normalized (equatorial slope)

As seen in the third plot, slope prior to the wing region is unaffected by wind conditions close to the binary - even if mass is removed and density is lowered.

Contrast Ratio

Contrast ratios using three different methods

   run    |   m0   |   m1   |   m2
   b1e5o  -  39.6  -   7.4  -   6.8
   b1e4o  -  65.9  -  10.0  -  14.0
   a1e5o  -  67.7  -  35.4  -  24.1
   a1e4o  -  12.6  -   7.5  -   7.6
   c1e4o  -  43.0  -   7.0  -   6.3
   d1e4o  -  15.6  -   8.4  -   8.4

m0: high_value / low_value

m1: fit to $$\rho(\theta) = C - A \frac{\exp\left(-2\beta \cos^2 t\right)-1}{\exp\left(-2\beta\right)-1}$$

m2: the ratio of average densities $\bar{\rho}_{d_1} / \bar{\rho}_{d_2}$ of two solid angles $d_1$ and $d_2$ where $$d_1 = 0.1 = \int_{\frac{\pi}{2}-\alpha}^{\frac{\pi}{2}} \sin\theta\ d\theta; \alpha=\sin^{-1}(d)$$ and $$d_2 = 0.3 = \int_0^\beta \sin\theta\ d\theta; \beta=\cos^{-1}(1-d)$$

Altering Wind Profiles

All profiles use the following equation: $$u(r) = v_\infty (1+R_c/r)^{-\beta}$$

velocity

velocity (log-x)

mass flux

$u_{0.1},\ \beta=3.5$ (red)

$u_{0.1},\ \beta=10.$ (cyan)

$u_{0.1},\ \beta=100.$ (green)

$u_{0.1},\ \beta=1.2$ (purple)

$u_{1.0},\ \beta=3.5$ (blue)

$u_{0.1},\ \beta=2.0$ (black)

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