How Accurately Can We Calculate the Depth of the Solar Convective Zone?

Details How Accurately Can We Calculate the Depth of the Solar Convective Zone? How Accurately Can We Calculate the Depth of the Solar Convective Zone?

2004-03-26

arxiv.org/abs/astro-ph/0403604v2

Astrophys.J. 614 (2004) 464

Astronomy and Astrophysics

Astrophysics

Accepted for ApJ. Corrected numerical error in size of required opacity increase. Figures and table unchanged. Extrapolation d

Scientific paper

10.1086/423027

We evaluate the logarithmic derivative of the depth of the solar convective zone with respect to the logarithm of the radiative opacity. We use this expression to show that the radiative opacity near the base of the solar convective zone (CZ) must be known to an accuracy of +- 1% in order to calculate the CZ depth to the accuracy of the helioseismological measurement, R(CZ) = (0.713 +- 0.001)R(Sun). The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by about 21% in the Bahcall-Pinsonneault (2004) solar model if one wants to invoke opacity errors in order to reconcile recent solar heavy abundance determinations with the helioseismological measurement of R(CZ). We show that the radiative opacity near the base of the convective zone depends sensitively upon the assumed heavy element mass fraction, Z. The uncertainty in the measured value of Z is currently the limiting factor in our ability to calculate the depth of the CZ. Different state-of-the-art interpolation schemes using the existing OPAL tables yield opacity values that differ by 4% . We describe the finer grid spacings that are necessary to interpolate the radiative opacity to 1%. Uncertainties due to the equation of state do not significantly affect the calculated depth of the convective zone.

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