The Determination of Angular Diameters of Stars

Abstract

Ideally the determination of the angular diameter of a star would include the measurement of the distribution of intensity across the stellar disc. However, direct methods of measuring angular diameters have so far lacked adequate ‘signal to noise’ ratio to measure the intensity distribution and it has been the custom, in the first instance, to express the measured angular diameter in terms of the angular diameter of the equivalent uniform disc (θUD). Subsequent use of the angular diameter involves the assumption of a limb-darkening law and the application of an appropriate correction to θUD to find the ‘true’ angular diameter (θLD) of the star (e.g. Hanbury Brown et al., 1967). In this article we will discuss the determination of θUD for single stars and we will not refer further to the more difficult problems of determining intensity distributions involving limb-darkening and rotational effects and of measuring the angular parameters of binary systems.By itself the angular diameter of a star has no intrinsic value but when it is combined with other observational data it enables basic physical properties of the star to be determined. It is then possible to make a direct comparison of the observed properties of the star with the predictions of theoretical models of stellar atmospheres and interiors. For example, the combination of an angular diameter with the absolute monochromatic flux received from the star (ƒν), corrected for interstellar extinction, yields the absolute emergent flux at the stellar surface (). If the spectral energy distribution for the star is known it can be calibrated absolutely by and hence the effective temperature (Te) of the star can be found (this is equivalent to knowing the bolometric correction for the star and using it with the angular diameter to find Te). In addition to leading to the determination of Te, the absolute surface flux distribution may be compared directly with the predicted flux distributions for theoretical model stellar atmospheres (e.g. Davis and Webb, 1970). For O and early B. type stars a large fraction of the emergent flux is in the far ultra-violet and the effective temperatures cannot be determined from the, at present, incomplete empirical flux curves. In these cases it is possible to obtain an estimate of the effective temperatures by using the values of to calibrate a grid of model atmospheres which have Te as a parameter. In this way, by measuring the angular diameters of stars of different spectral types, it is possible to establish an effective temperature scale.