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

Fourier coefficents 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. The $phi_{31}$ and $R_{21}$ coefficients have been compared with those of the first overtone RR Lyrae variables in the Galactic globular clusters NGC 6441, M107, M5, M3, M2, $omega$ 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 $omega$ Cen, but they are different from the Oosterhoff type II variables in $omega$ 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 $log L$ in the range 1.6 to $1.8lsun$ and $log T_{eff}$ 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 $phi_{31}-log P$ plot) are used to determine a LMC distance. After correcting for the effects of extinction and crowding, a mean apparent magnitude $<V_0>=18.99 pm 0.02$ (statistical) $pm 0.16$ (systematic) has been estimated for these 80 stars. Combining this with a mean absolute magnitude $M_V=0.56pm 0.06$ 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 $mu=18.43pm 0.06$ (statistical) $pm 0.16$ (systematic) mag. The large systematic error arises from the difficulties of correcting for interstellar extinction and for crowding.