Toward Spectroscopically Detecting the Global Latitudinal Temperature Variation on the Solar Surface

A very slight rotation-induced latitudinal temperature variation (presumably on the order of several kelvin) on the solar surface is theoretically expected. While recent high-precision solar brightness observations reported its detection, confirmation by an alternative approach using the strengths of spectral lines is desirable, for which reducing the noise due to random fluctuation caused by atmospheric inhomogeneity is critical. Toward this difficult task, we carried out a pilot study of spectroscopically investigating the relative variation of temperature (\(T\)) at a number of points in the solar circumference region near to the limb (where latitude dependence should be detectable, if any exists) based on the equivalent widths (\(W\)) of 28 selected lines in the 5367?–?5393 Å and 6075?–?6100 Å regions. We paid special attention to i) clarifying which types of lines should be employed and ii) how much precision is attainable in practice. We found that lines with strong \(T\)-sensitivity (\(|\log W/\log T|\)) should be used and that very weak lines should be avoided because they inevitably suffer strong relative fluctuations (\(\Delta W/W\)). Our analysis revealed that a precision of \(\Delta T/T \approx 0.003\) (corresponding to ≈?15 K) can be achieved at best by a spectral line with comparatively large \(|\log W/\log T|\), although this can possibly be further improved When a number of lines are used all together. Accordingly, if many such favorable lines could be measured with subpercent precision of \(\Delta W/W\) and by averaging the resulting \(\Delta T/T\) from each line, the random noise would eventually be reduced to ??1 K and detection of a very subtle amount of global \(T\)-gradient might be possible.