William J. Tango

γ2 Velorum: orbital solution and fundamental parameter determination with SUSI

The first complete orbital solution for the double-lined spectroscopic binary system γ 2 Velorum, obtained from measurements with the Sydney University Stellar Interferometer (SUSI), is presented. This system contains the closest example of a Wolf-Rayet star and the promise of full characterization of the basic properties of this exotic high-mass system has subjected it to intense study as an archetype for its class. In combination with the latest radial-velocity results, our orbital solution produces a distance of 336 +8 -7 pc, significantly more distant than the Hipparcos estimation. The ability to fully specify the orbital parameters has enabled us to significantly reduce uncertainties and our result is consistent with the Very Large Telescope Interferometer (VLTI) observational point, but not with their derived distance. Our new distance, which is an order of magnitude more precise than prior work, demands critical reassessment of all distance-dependent fundamental parameters of this important system. In particular, membership of the Vela OB2 association has been re-established, and the age and distance are also in good accord with the population of young stars reported by Pozzo et al. We determine the 0-star primary component parameters to be M v (O) = -5.63 ± 0.10mag, R(O) = 17 ± 2 R ⊙ and M(0) = 28.5 ± 1.1 M ⊙ . These values are consistent with calibrations found in the literature if a luminosity class of II-III is adopted. The parameters of the Wolf-Rayet (WR) component are M v (WR) = -4.33 ±0.17 mag and M(WR) = 9.0 ±0.6M ⊙ .

IV Michelson Stellar Interferometry

Publisher Summary The resolution and accuracy of a modern optical Michelson stellar interferometer are limited principally by atmospheric turbulence. To reach 9th magnitude, the maximum practicable baseline is probably about 100 meters because of large scale long period atmospheric fluctuations in optical path. Longer baselines would require narrower optical bandwidths with an associated loss in signal-to-noise ratio and, therefore, of limiting magnitude. Perhaps more important from the astronomical point of view is the loss in accuracy caused by the atmosphere. If the losses are not too large, it is feasible to estimate them by auxiliary observations, either through the same apertures or by means of seeing monitors placed near the primary apertures. Most of the instrumentation needed for a Michelson stellar interferometer has already been developed, either for the existing prototype interferometers or for other applications, so there is no reason why an interferometer with a baseline of 100 meters and a limiting magnitude of +9 cannot be built.

Dispersion in stellar interferometry

The effects of uncompensated dispersion on the fringe visibility in a two beam interferometer are examined for a long baseline stellar interferometer with a path compensator in air rather than in vacuo. We derive a criterion based on the central fringe visibility for evaluating the effects of dispersion and develop a method for selecting suitable compensating media. By limiting the optical bandwidth to ~100 nm and using a compensating system with two glasses it is possible to achieve high fringe visibility in a stellar interferometer with excess air paths of the order of 500 m. The results are generally applicable to other two beam interferometers.

Dust scattering in the Miras R Car and RR Sco resolved by optical interferometric polarimetry

We present optical interferometric polarimetry measurements of the Mira-like variables R Car and RR Sco, using the Sydney University Stellar Interferometer. By making visibility measurements in two perpendicular polarizations, the relatively low-surface brightness light scattered by atmospheric dust could be spatially separated from the bright Mira photospheric flux. This is the first reported successful use of long-baseline optical interferometric polarimetry. Observations were able to place constraints on the distribution of circumstellar material in R Car and RR Sco. The inner radius of dust formation for both stars was found to be less than 3 stellar radii: much closer than the expected innermost stable location for commonly assumed astrophysical ‘dirty silicate’ dust in these systems (silicate dust with a significant iron content). A model with the dust distributed over a shell which is geometrically thin compared to the stellar radius was preferred over an outflow. We propose dust components whose chemistry and opacity properties enable survival at these extreme inner radii.

The fundamental parameters of the roAp star α Circini

We have used the Sydney University Stellar Interferometer to measure the angular diameter of α Cir. This is the first detailed interferometric study of a rapidly oscillating A (roAp) star, α Cir being the brightest member of its class. We used the new and more accurate Hipparcos parallax to determine the radius to be 1.967 ± 0.066 R⊙ . We have constrained the bolometric flux from calibrated spectra to determine an effective temperature of 7420 ± 170 K . This is the first direct determination of the temperature of an roAp star. Our temperature is at the low end of previous estimates, which span over 1000 K and were based on either photometric indices or spectroscopic methods. In addition, we have analysed two high-quality spectra of α Cir, obtained at different rotational phases and we find evidence for the presence of spots. In both spectra we find nearly solar abundances of C, O, Si, Ca and Fe, high abundance of Cr and Mn, while Co, Y, Nd and Eu are overabundant by about 1 dex. The results reported here provide important observational constraints for future studies of the atmospheric structure and pulsation of α Cir.

The circle polynomials of Zernike and their application in optics

The Zernike polynomials are orthogonal functions defined on the unit circle, which have been used primarily in the diffraction theory of optical aberrations. A summary of their principal properties is given. It is shown that the polynomials, which are closely related to the general spherical harmonics, are especially useful in numerical calculations. In particular, by using the polynomials as a basis to represent the commonly encountered functions of optical theory, it is often possible to avoid numerical quadrature and computations are reduced to the simple manipulation of expansion coefficients.

Orbital parameters, masses and distance to β Centauri determined with the Sydney University Stellar: Interferometer and high-resolution spectroscopy

The bright southern binary star β Centauri (HR 5267) has been observed with the Sydney University Stellar Interferometer (SUSI) and spectroscopically with the European Southern Observatory Coude Auxiliary Telescope and Swiss Euler telescope at La Silla. The interferometric observations have confirmed the binary nature of the primary component and have enabled the determination of the orbital parameters of the system. At the observing wavelength of 442 nm the two components of the primary system have a magnitude difference of 0.15 ± 0.02. The combination of interferometric and spectroscopic data gives the following results: orbital period 357.00 ± 0.07 d, semimajor axis 25.30 ± 0.19 mas, inclination 67. ◦ 4 ± 0. ◦ 3, eccentricity 0.821 ± 0.003, distance 102.3 ± 1.7 pc, primary and secondary masses M 1 = ( ◦ )( ◦ ) .

Orbital solution and fundamental parameters of σ Scorpii

The first orbital solution for the spectroscopic pair in the multiple star system sigma Scorpii, determined from measurements with the Sydney University Stellar Interferometer (SUSI), is presented. The primary component is of beta Cephei variable type and has been one of the most intensively studied examples of its class. The orbital solution, when combined with radial velocity results found in the literature, yields a distance of 174(+23,-18) pc, which is consistent with, but more accurate than the Hipparcos value. For the primary component we determine 18.4+/-5.4 M_sun, -4.12+/-0.34 mag and 12.7+/-1.8 R_sun for the mass, absolute visual magnitude and radius respectively. A B1 dwarf spectral type and luminosity class for the secondary is proposed from the mass determination of 11.9+/-3.1 M_sun and the estimated system age of 10 Myr.

Orbital Solution & Fundamental Parameters of sigma Scorpii

The first orbital solution for the spectroscopic pair in the multiple star system sigma Scorpii, determined from measurements with the Sydney University Stellar Interferometer (SUSI), is presented. The primary component is of beta Cephei variable type and has been one of the most intensively studied examples of its class. The orbital solution, when combined with radial velocity results found in the literature, yields a distance of 174(+23,-18) pc, which is consistent with, but more accurate than the Hipparcos value. For the primary component we determine 18.4+/-5.4 M_sun, -4.12+/-0.34 mag and 12.7+/-1.8 R_sun for the mass, absolute visual magnitude and radius respectively. A B1 dwarf spectral type and luminosity class for the secondary is proposed from the mass determination of 11.9+/-3.1 M_sun and the estimated system age of 10 Myr.

The radius and mass of the subgiant star β Hyi from interferometry and asteroseismology

We have used the Sydney University Stellar Interferometer to measure the angular diameter of β Hydri. This star is a nearby G2 subgiant the mean density of which was recently measured with high precision using asteroseismology. We determine the radius and effective temperature of the star to be 1.814 ± 0.017 R⊙ (0.9 per cent) and 5872 ± 44 K (0.7 per cent) respectively. By combining the radius with the mean density, as estimated from asteroseismology, we make a direct estimate of the stellar mass. We find a value of 1.07 ± 0.03 M⊙ (2.8 per cent), which agrees with published estimates based on fitting in the Hertzsprung–Russell diagram, but has much higher precision. These results place valuable constraints on theoretical models of β Hyi and its oscillation frequencies.