The MACHO Project Large Magellanic Cloud Variable-Star Inventory. XIII. Fourier Parameters for the First-Overtone RR Lyrae Variables and the LMC Distance
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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 $1.8\lsun$ 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 $=18.99 \pm 0.02$ (statistical) $\pm 0.16$ (systematic) has been
estimated for these 80 stars. Combining this with a mean absolute magnitude
$M_V=0.56\pm 0.06$ 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 $\mu=18.43\pm 0.06$ (statistical) $\pm
0.16$ (systematic) mag. The large systematic error arises from the difficulties
of correcting for interstellar extinction and for crowding.