Helioseismology

Remarks

Example: the splitting $\nu_{n\ell m} - \nu_{n\ell 0}$ of a multiplet is to first order $m / (2\pi)$ times an integral of $\Omega(r, \theta)$ against a kernel concentrated in the region sampled by the mode. Inverting many splittings gives the internal rotation profile. Non-example: inferring the interior of the Sun only from its luminosity and radius through a stellar model is not helioseismology, because no oscillation data enter. For high radial order $n$ and low degree $\ell$, the p-mode frequencies follow the asymptotic relation $\nu_{n\ell} \approx \Delta\nu \, (n + \ell/2 + \varepsilon)$. Here $\Delta\nu = \big(2 \int_0^R dr / c(r)\big)^{-1}$ is the large separation, $R$ is the solar radius and $\varepsilon$ is a constant of order $1$. Local helioseismology studies wave travel times and local wave fields instead of global mode frequencies.