The accurate determination of stellar angular diameters using broad-band stellar interferometry

The angular diameter of a star can be estimated from interferometric observations by fitting the data with the visibility function for a uniformly illuminated disc and then using published correction factors to convert the uniform-disc angular diameter to the limb-darkened angular diameter. The correction factors are strictly valid only for monochromatic light. We investigate the effect of using a broad bandwidth, and present a simple method for calculating broad-band correction factors from the monochromatic factors.
The technique of fitting the data with a uniform-disc visibility function is only useful for stars with compact atmospheres and 'typical' limb-darkening profiles. It should not be applied to stars with extended atmospheres or that show extreme limb darkening. These stars have visibility functions that are qualitatively different from a uniform-disc visibility function, so they can be distinguished observationally from compact-atmosphere stars.     

Limb-darkening corrections for interferometric uniform disc stellar angular diameters

Stellar angular diameters determined interferometrically are generally established by fitting the observed visibility data with a curve appropriate for a uniformly illuminated disc. The resulting uniform-disc diameters must be corrected for the effects of limb darkening in order to determine the true angular diameters of the stars. An extensive grid of limb-darkening corrections, based directly on the centre-to-limb intensity variations for Kurucz model stellar atmospheres, has been computed without the intermediate step of a parametrized representation of the centre-to-limb variation. The limitations of this method of correction are discussed.     

High-precision effective temperatures of 161 FGK supergiants from line-depth ratios

Precise effective temperatures ( T _eff) are determined for 161 FGK supergiants using method of line-depth ratios. We obtain a set of 131 relations for temperatures of supergiants as a function of line depths. These relations have been calibrated against previously published accurate temperature estimates. The application range of the method is 3600–7800 K (F0I–K5I). The internal error of a single calibration is less than 110 K, while combination of all calibrations reduces uncertainty to only 5–30 K (standard error). The error in the zero-point is estimated to be less than 100–200 K. A significant advantage of the line ratio method is its independence of the interstellar reddening, and only modest sensitivity to abundance, macroturbulence, rotation and other factors.     

Calibration observations of Fomalhaut with the VLTI

An investigation of the stability of the transfer function of the European Southern Observatory's Very Large Telescope Interferometer has been carried out through observations of Fomalhaut, which was observed over a range in hour angle from 21:50–05:24 on 20 October 2002. No significant variation in the transfer function was found for the zenith angle range 5°–70°. The projected baseline varied between 139.7 m and 49.8 m during the observations and, as an integral part of the determination of the transfer function, a new accurate limb‐darkened angular diameter for Fomalhaut of 2.109 ± 0.013 mas has been established. This has led to improved values for the emergent flux = (3.43 ± 0.10)×10⁸ Wm⁻², effective temperature = 8819 ± 67 K and radius = (1.213 ± 0.011)×10⁹ m (R/R_⊙ = 1.744 ± 0.016). The luminosity has been found to be (6.34 ± 0.20)×10²⁷ W (L/L_⊙ = 16.5 ± 0.5). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Combining optical spectroscopy and interferometry

Modern optical spectrographs and optical interferometers push the limits in the spectral and spatial regime, providing important new tools for the exploration of the Universe. In this contribution I outline the complementary nature of spectroscopic and interferometric observations and discuss different strategies for combining such data. Most remarkable, the latest generation of “spectro‐interferometric” instruments combine the milliarcsecond angular resolution achievable with interferometry with spectral capabilities, enabling direct constraints on the distribution, density, kinematics, and ionization structure of the gas component in protoplanetary disks. I will present some selected studies from the field of star‐ and planet formation and hot star research in order to illustrate these fundamentally new observational opportunities. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenized effective temperatures for metal deficient stars from stellar catalogues

Homogeneous independent subsamples from selected catalogues and libraries of effective temperatures for metal deficient F–G stars are treated here by combining them in triples and pairs for the stars in common to determine their external errors from data intercomparisons. The effective temperatures are then averaged (with the weights inversely proportional to the squared errors) to produce mean homogenized catalogues which may be used for calibration of spectral and photometric data in large Galactic surveys. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The radius and other fundamental parameters of the F9 V star β Virginis

We have used the Sydney University Stellar Interferometer (SUSI) to measure the angular diameter of the F9 V star β Virginis (β Vir). After correcting for limb darkening and combining with the revised Hipparcos parallax, we derive a radius of  1.703 ± 0.022 R_⊙  (1.3 per cent). We have also calculated the bolometric flux from published measurements which, combined with the angular diameter, implies an effective temperature of  6059 ± 49 K  (0.8 per cent). We also derived the luminosity of β Vir to be   L = 3.51 ± 0.08 L_⊙  (2.1 per cent). Solar-like oscillations were measured in this star by Carrier et al. and using their value for the large frequency separation yields the mean stellar density with an uncertainty of about 2 per cent. Our constraints on the fundamental parameters of β Vir will be important to test the theoretical models of this star and its oscillations.     

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  674 ± 03  , eccentricity  0.821 ± 0.003  , distance  102.3 ± 1.7 pc  , primary and secondary masses   M ₁= M ₂= 9.1 ± 0.3 M_⊙  and absolute visual magnitudes of the primary and secondary   M _{1 V} =−3.85 ± 0.05  and   M _{2 V} =−3.70 ± 0.05  , respectively. The high degree of accuracy of the results offers a fruitful starting point for future asteroseismic modelling of the pulsating binary components.     

Orbital solution and fundamental parameters of σ Scorpii

The first orbital solution for the spectroscopic pair in the multiple star system σ Scorpii, determined from measurements with the Sydney University Stellar Interferometer, is presented. The primary component is of β 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_⊙, −4.12 ± 0.34 mag  and  12.7 ± 1.8 R_⊙  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_⊙  and the estimated system age of 10 Myr.     

Intrinsic colour indices of Be stars obtained from 2MASS photometry

This paper is based on 2MASS photometry (J H K_s magnitudes) of 1172 Be stars. The observed mean intrinsic colours have been derived with aid of two‐colour diagrams for Be stars of luminosity classes Ie‐IIe, IIIe and IVe‐Ve. The obtained results are the first determinations of their intrinsic colours in the astronomical literature. The smoothed infrared colours are compared with those obtained for “normal” B stars. Several two‐colour diagrams and plots of observed and smoothed intrinsic colour versus spectral type of luminosity classes Ie‐IIe, IIIe and IVe‐Ve are presented. Generally the determined infrared intrinsic colours of Be stars (V – J)₀, (V – H)₀, and (V – K_s)_o differ substantially from those of “normal” B stars. It is found that the intrinsic colours of B stars are generally bluer than Be stars of corresponding spectral type and luminosity class. The mean absolute visual magnitude M_v of 528 Be stars for luminosity classes Iae, Ibe‐Iabe, IIe, IIIe and IVe‐Ve is derived from HIPPARCOS parallaxes. The M_v calibration is compared with the existing ones. The Be stars are generally brighter than “normal” B stars of corresponding spectral types. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The colours of the Sun

We compile a sample of Sun-like stars with accurate effective temperatures, metallicities and colours (from the ultraviolet to the near-infrared). A crucial improvement is that the effective temperature scale of the stars has recently been established as both accurate and precise through direct measurement of angular diameters obtained with stellar interferometers. We fit the colours as a function of effective temperature and metallicity, and derive colour estimates for the Sun in the Johnson–Cousins, Tycho, Strömgren, 2MASS and SDSS photometric systems. For  ( B − V )_⊙  , we favour the 'red' colour 0.64 versus the 'blue' colour 0.62 of other recent papers, but both values are consistent within the errors; we ascribe the difference to the selection of Sun-like stars versus interpolation of wider colour– T _eff–metallicity relations.