P. A. Maurone

The Large Magellanic Cloud Eclipsing Binary HV 2274: Fundamental Properties and Comparison with Evolutionary Models

We are carrying out an international, multiwavelength program to determine the fundamental properties and independent distance estimates of selected 14th to 15th magnitude eclipsing binaries in the Large and Small Magellanic Clouds (LMC and SMC). Eclipsing binaries with well-defined double-line radial velocity curves and light curves provide valuable information on orbital and physical properties of their component stars. These properties include, among other characteristics, stellar mass and radius. These can be measured with an accuracy and directness unachievable by any other means. The study of stars in the LMC and SMC, where the metal abundances are significantly lower than solar (by one-third to one-tenth) provides an important opportunity to test opacities and stellar atmosphere, interior, and evolution models. For the first time, we can also measure direct mass-luminosity relations for stars outside our Galaxy. In a previous paper we demonstrated how a precise distance to the LMC—corresponding to (V0 - Mv)LMC = 18.30 ± 0.07 mag—could be determined using the 14th magnitude LMC eclipsing binary HV 2274. In this paper we concentrate on the determination of the orbital and physical properties of HV 2274 and its component stars from analyses of light curves and new radial velocity curves formed from Hubble Space Telescope (HST)/Goddard High-Resolution Spectrograph observations. HV 2274 (B1-2 IV-III + B1-2 IV-III; Vmax ≈ +14.2; P = 5.73 days) is a particularly appealing star because it is a detached binary that has an eccentric orbit (e = 0.136) and shows rapid apsidal motion. The results of these analyses yield reliable masses and absolute radii, as well as other physical and orbital properties of the stars and the system. From UV/optical spectrophotometry (1150-4820 A) of HV 2274 obtained with the HST Faint Object Spectrograph, the temperatures and the metallicity ([Fe/H] = -0.45 ± 0.06) of the stars were found, as well as the interstellar extinction of the system. The values of the mass, absolute radius, and effective temperature for the primary and secondary stars are 12.2 ± 0.7 M☉, 9.9 ± 0.2 R☉, 23000 ± 180 K and 11.4 ± 0.7 M☉, 9.0 ± 0.2 R☉, 23110 ± 180 K, respectively. The age of the system (τ = 17 ± 2 Myr), helium abundance (Y = 0.26 ± 0.03), and a lower limit of the convective core overshooting parameter of αov ≈ 0.2 were obtained by fitting the stellar data with evolution models of Claret & Gimenez. HV 2274 has a relatively well determined (and fast) apsidal motion period of U = 123 ± 3 yr. From an analysis of apsidal motion, additional information and constraints on the structure of the stars can be obtained. The apsidal motion analysis corroborates that some amount of convective core overshooting (αov between 0.2 and 0.5) is needed.

The linear potential wavefunctions

We present an exact analytic solution to the Schrodinger equation for two particles interacting via a central linear potential of the from V (r) =V0+kr. The solution is given in terms of the generalized hypergeometric functions, and is especially useful when discussing problems where the radial parameter is small.

On the asymptotic behavior of the derivatives of Airy functions

We present a noniterative functional solution to the three‐term recursion relation satisfied by the higher order derivatives of the Airy function. This solution allows one to obtain the asymptotic behaviors of these derivatives for large argument and also for large order.