Exploring a simple method to estimate spot temperatures in weak-lined T Tauri stars

The astronomy literature contains a wealth of photometric measurements of the brightness variations of weak-lined T Tauri stars. Comparing observations through two different filters, the brightness changes of the vast majority of these stars trace straight lines in magnitude-magnitude plots. It is plausible that the slope of the line is determined by a fixed mean starspot temperature, and that changing filling factors cause the linear magnitude-magnitude relations to be described. This is exploited to derive an estimator for the starspot temperature in terms of a linear regression slope, valid for modest starspot filling factors. Simulations are used to demonstrate that such regression slopes first need to be corrected for measurement errors, in order to avoid biased results. The theory is applied to a collection of 45 extensive sets of BVR (and in some cases UBVR) observations of weak-lined T Tauri stars taken from the literature. The results are examined critically, and it is pointed out that there are systematic differences between spot temperatures determined respectively from BV and VR data pairs. The reason for this is not known; possible causes are briefly speculated about. There is generally poor agreement with published spot temperatures, which also vary considerably. The simplest explanation is that the mean temperature of starspots is variable.