Photometric Transformation of Tycho V and 2MASS J to Johnson V for Main Sequence Stars
The Tycho and Tycho-2 catalogs and the SuperWASP survey report photometry for millions of stars on the Tycho V ("V_T") photometric system. The Tycho V_T bandpass is somewhat wider than the classic Johnson V bandpass. Since the Johnson V system has been in common use since 1950s, and many properties reported for stars are in the Johnson V system (e.g. intrinsic colors, absolute magnitudes, etc.), finding photometric transformations to this system can be useful in stellar astronomy research. This figure plots the (V_T - J) color ("Tycho V_T minus 2MASS J") versus the offset between Johnson V and Tycho V_T for main sequence stars. The stars plotted as open circles are taken from the HIPPARCOS catalog, and represent nearby dwarf stars within +-1 magnitude of the main sequence in absolute magnitude, with negligible reddening (distances < 75 pc, parallax errors < 16%), and the smallest photometric errors in V_T and J in three bins across the sequence (so as to give nearly equal weighting between the bluest and reddest stars). This was accomplished starting with a parent sample of dwarf stars from HIPPARCOS with reported V_T and J errors of <= 0.03 mag, but slightly different combined color error thresholds were applied to three color bins:
(V_T - J) < 1.5: error(V_T - J) < 0.019 mag,
1.5 <= (V_T-J) <= 2.5: error(V_T - J) < 0.025 mag,
(V_T - J) > 2.5: error(V_T - J) < 0.050 mag.
This selection yielded 151, 227, and 64 stars in the blue, middle, and red color bins. I fit an unweighted ordinary least-squares fit "OLS(X|Y)" made using the program SLOPES written by Eric Feigelson (see Isobe, Feigelson, Akritas, & Babu 1990, Astrophysical Journal 364, 104).
The transformation between Tycho V_T and 2MASS J magnitudes and Johnson V magnitudes for main sequence dwarf stars with colors (-0.02 < V_T - J < 3.67; roughly A0 to M3 spectral types) can be expressed as:
V_Johnson = (V_Tycho - 0.095+-0.001) + (-0.062+-0.002)(V_Tycho - J_2MASS - 1.631)
