Conversion of Tycho-2 to Johnson-Cousins Magnitudes in the Gaia Era

We take advantage of the availability of precision parallax data from Gaia Data Release 2 together with machine learning to develop a set of equations for transforming Tycho-2 (VT, BT) magnitudes into the Johnson-Cousins (J-C) system. Starting with data for 558 standard stars with apparent magnitudes brighter than 11.0, we employed one step supervised learning with weight decay regularization and 10-fold cross validation to produce a set of transformation equations from Tycho-2 into J-C, which in turn were used to derive transformations of the Tycho-2 standard deviations into the J-C system. Both the aggregated cross validation data sets and the in-sample results from the final training were essentially unbiased (average errors << 1 mmag in both B and V) and had error standard deviations comparable to those of the input data. Comparison of errors in- and out-of-sample indicate modest generalization error growth. Moreover, testing of the distributions of the normalized errors indicated that the predicted standard deviations are accurate, enabling them to be reliably employed in the suitability ranking of comparison star candidates. These results thus enable utilization of a substantial portion of the 2.5 million star Tycho-2 data set as comparison stars for two-color bright star ensemble photometry.