Unlike late-type (cool and low-mass) stars such as Sun, early-type stars such as Vega (Teff > 10,000K and Mass > 2 solar masses) rotate rapidly, faster than 50% breakup of a star. However, the role of rotation has been greatly underestimated, and thus, there have been numerous discrepancies between the models and the observations. Since rotation obscures the interpretation of the observed data, my main work was to numerically simulate rapidly rotating stars (so-called gravity-darkened Roche models, von Zeipel 1924) and predict both interferometric and spectroscopic observables for comparison with the observed data. Then I decoupled rotational effects from the physical properties such as temperature, radius, composition, mass, and in turn age by measuring accurate and precise true rotational velocity of Vega, a rapid rotator, by using both high angular resolution interferometry and high-resolution spectroscopy.

A rotating star can be modeled by a gravity-darkened Roche spheroid (von Zeipel 1924), allowing us to predict measurable interferometric quantities (visibility amplitude and closure phase) that are related to oblateness, temperature gradients, and surface brightness asymmetries. By adding observational data such as parallax, B-V color, projected rotational velocity, and V magnitude to the modeling, I computed not only all the required physical parameters but also the probabilities of detection of oblateness and asymmetry of early-type stars and to produce lists of potential targets for such instruments as the Navy Precision Optical Interferometer (NPOI) and the Very Large Telescope Interferometer (VLTI). But rotation can also introduce uncertainty when one estimates the visibilities of early-type stars that are used as standard stars for calibration of all sorts of astronomical observations. Therefore, I estimated the effects of rotation on potential calibrators by constructing probability distributions of the predicted visibility for the individual objects. This lets astronomers judge the adequacy of their interferometry calibrators. I calculated for a number of configurations of existing long-baseline interferometers such as CHARA, NPOI, SUSI, and VLTI. The detailed description can be found in Yoon et al. (2006, 2007)).

With the detections of the interferometric signature of rapid rotation in Vega (~93% break-up velocity of the star and yet almost pole-on, (Peterson et al. 2006, Aufdenberg et al. 2006), as well as studies of peculiar line shapes in its spectrum (Hill, Gulliver, & Adelman 1994), a number of questions were raised about this fundamental standard, such as its composition, mass, and age. A full synthesis of the spectrum using gravity-darkened Roche models was necessary to reproduce the peculiar line profiles, and this called into question whether a composition analysis based on standard plane-parallel model atmospheres is adequate.

To resolve some of these questions, I have modeled Vega as a Roche spheroid seen nearly pole-on with a temperature gradient across the surface, using ATLAS9 model atmospheres locally. Integrating over the disk, I computed the synthetic spectra for comparison with the observations. These models appear to reproduce the peculiar line profiles very nicely and give confidence to the abundances I obtain for Vega. For observational data, I have utilized spectra from the ELODIE database and co-added 49 spectra, resulting in improving the SNR from about 250 for a typical spectrum to about 1,800 for the combination, critical to fit Vega's unusual peculiar weak lines.

In order to get a good fit to the shapes of the weak lines, I found that I needed to convolve the spectrum with a Gaussian that is substantially broader than the nominal resolution of the ELODIE spectra (R ~ 42,000), amounting to what would be interpreted as adding 10 km/s of macro-turbulence (which can be considered as weather pattern in Vega's atmosphere). I also found that the peculiar appearance of the lines depends on how the excitation potentials amplify the temperature gradient, which is substantially large in rapid rotators (for Vega, the temperature difference between the pole and the equator is about 2,500K.). From the abundance analysis, I found that Vega shows the peculiar abundance pattern of a λ Bootis star, which is a class of metal-poor Population I A−type stars with normal rotation, as previously suggested (e.g., Venn & Lambert 1990). I studied the effects of rotation on the deduced abundances and showed that the dominant ionization states are only slightly affected compared to analyses using non-rotating models. I argued that the rapid rotation requires the star to be well mixed and in turn, the deduced composition is a bulk property not limited to the surface. The deduced composition (Z~0.009) led to mass (M~2.1 solar masses) and particularly age (540 million years) that are quite different compared to what is usually assumed (M~2.3 solar masses and age~360 million years). The increased age I obtained would make Vega an unlikely member of the Castor moving group. The details of this analysis were reported in Yoon et al. (2008).

As my final doctoral analysis, I had done a simultaneous fit of interferometric data (triple-phase of the NPOI) with spectrophotometric data (spectral energy distribution), metal line profiles of Ca I λ6162 and Mg I λ4702 from the ELODIE archive having the peculiar line shapes, and hydrogen wings of three Balmer lines which provides the maximum number of possible constraints on the models and thus gives a more reliable determination of physical characteristics, especially mass. Based on this simultaneous fitting of a Roche model to the data, I discovered not only that Vega's rotation rate is somewhat slower (angular rotation rate of ω~0.88) than the previously determined (ω~0.93, Peterson et al. 2006, Aufdenberg et al. 2006)) but also that the derived mass directly from Balmer lines is less massive (M~2.14 solar masses) than the currently assumed value. By locating its derived mass, radius, and luminosity here on an evolutionary track, I obtained its metallicity of Z~0.008 consistent with the value derived from surface composition and in particular is significantly less than solar. In turn, the lower mass suggests that it is nearly 470 million years and older than previously assumed (360 million years). The low bulk metallicity strongly argues that Vega was formed with a metal-poor composition. The agreement between the bulk and the surface compositions argues that it remains well mixed, consistent with its rapid rotation. But most importantly, the low bulk metallicity creates a significant challenge to identify a process that could produce a relatively young star this depleted in heavy elements. I also note that if Vega is representative, this question could extend to the formation of λ Boo stars generally where the abundance anomalies have until now been assumed to be confined to the surface layers. This analysis was reported in Yoon et al. (2010).