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Table 1:

Characteristics of a 7 $M_\odot $ star rotating at critical speed.
Parameter ZAMS $X_{\rm c}=0.30$ $X_{\rm c}=0.02$
No rotation      
radius ($R_\odot$) 4.348 4.953 5.857
quadrupolar moment J2 3.370 $\times$ 10 $^{-3}\!\!\!$ 2.766 $\times$ 10 $^{-3}\!\!\!\!$ 2.013 $\times$ 10 $^{-3}\!\!\!\!$
Uniform rotation      
quadrupolar moment J2 8.411 $\times$ 10 $^{-3}\!\!\!$ 7.136 $\times$ 10 $^{-3}\!\!\!\!$ 5.171 $\times$ 10 $^{-3}\!\!\!\!$
mean radius R0 5.125 5.803 6.852
equatorial radius $R_{\rm E}$ 5.821 6.591 7.783
polar radius $R_{\rm P}$ 3.814 4.329 5.133
flattening $R_{\rm E}/R_{\rm P}$ 1.526 1.522 1.516
Differ. rotation      $\Omega_{\rm c}/\Omega_s=4$      
quadrupolar moment J2 1.900 $\times$ 10 $^{-2}\!\!\!$ 1.550 $\times$ 10 $^{-2}\!\!\!\!$ 1.123 $\times$ 10 $^{-2}\!\!\!\!$
mean radius R0 5.773 6.671 7.902
equatorial radius $R_{\rm E}$ 6.557 7.577 8.846
polar radius $R_{\rm P}$ 4.204 4.889 5.846
flattening $R_{\rm E}/R_{\rm P}$ 1.560 1.550 1.535

Notes. J2 is the quadrupolar moment defined in Eq. (17). $R_{\rm E}$, $R_{\rm P}$ and R0 are respectively the equatorial, polar and mean radius. Taking the quadrupolar moment into account increases the flattening $R_{\rm E}/R_{\rm P}$ of the stellar surface beyond the value 1.50 of the Roche model, and even more so when the rotation is non-uniform (with the profile of Eq. (32)); this is illustrated here with a center-to-surface contrast of 4. In the ``no rotation'' case, the non rotating model was used as reference, while uniform rotation (h(x)=1) was assumed when solving the Poisson Eq. (29).


Source LaTeX | All tables | In the text

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