The MACHO Project Large Magellanic Cloud Variable-Star Inventory. XIII. Fourier Parameters for the First-Overtone RR Lyrae Variables and the LMC Distance

Shapes of RR Lyrae light curves can be described in terms of Fourier coefficients that past research has linked with physical characteristics such as luminosity, mass, and temperature. Fourier coefficients have been derived for the V and R light curves of 785 overtone RR Lyrae variables in 16 MACHO fields near the bar of the LMC. In general, the Fourier phase differences φ₂₁, φ₃₁, and φ₄₁ increase and the amplitude ratio R₂₁ decreases with increasing period. The coefficients for both the V and R magnitudes follow these patterns, but the phase differences for the R curves are on average slightly greater, and their amplitudes are about 20% smaller, than the ones for the V curves. The φ₃₁ and R₂₁ coefficients have been compared with those of the first-overtone RR Lyrae variables in the Galactic globular clusters NGC 6441, M107, M5, M3, M2, ω Centauri, and M68. The results indicate that many of the LMC variables have properties similar to the ones in M2, M3, M5, and the Oosterhoff type I variables in ω Cen, but they are different from the Oosterhoff type II variables in ω Cen. Equations derived from hydrodynamic pulsation models have been used to calculate the luminosity and temperature for the 330 bona fide first-overtone variables. The results indicate that they have logL in the range 1.6-1.8 L_solar and logT_eff between 3.85 and 3.87. Based on these temperatures, a mean color excess E(V-R)=0.08 mag, equivalent to E(B-V)=0.14 mag, has been estimated for these 330 stars. The 80 M5-like variables (selected according to their location in the φ₃₁-logP plot) are used to determine an LMC distance. After correcting for the effects of extinction and crowding, a mean apparent magnitude <V₀>=18.99+/-0.02 (statistical) +/-0.16 (systematic) has been estimated for these 80 stars. Combining this with a mean absolute magnitude M_V=0.56+/-0.06 for M5-like stars derived from Baade-Wesselink analyses, main-sequence fitting, Fourier parameters, and the trigonometric parallax of RR Lyrae, we derive an LMC distance modulus μ=18.43+/-0.06 (statistical) +/-0.16 (systematic) mag. The large systematic error arises from the difficulties of correcting for interstellar extinction and for crowding.