Centre-to-Limb Brightness Variations from the Atacama Large Millimeter-Submillimeter Array (ALMA) Full-Disk Solar Images

Science Verification (SV) data of solar observations with the Atacama Large Millimeter-submillimeter Array (ALMA) telescope have been released to the scientific community. Understanding the centre-to-limb brightness function is necessary to compare features in full-disk images. Our goals are to find the empirical centre-to-limb brightness functions in two available spectral bands and create flattened images with centre-to-limb brightness variations removed. We used a second-order polynomial fit of the cosine of incidence angle to data points as a function of radial distance to the centre of the solar disk. The method also includes iterative removal of outliers based on the inter-quartile range. Fitting functions for all available images proved to describe the data adequately with comparatively small errors in the fitting coefficients. In both bands we found brightening towards the limb, which is a consequence of the increase in electron temperature with radial distance in this region of the solar atmosphere. This study found that the brightness temperature \([T_{\mathrm{b}}]\) of an active region has about 180 K difference between estimates with and without the limb brightening at radial distance \({\approx}\,0.75~\mbox{R}_{\odot }\) in Band 6. We also made flattened images with limb brightening removed. The limb-brightening effect in ALMA images is significant enough (of the order of 10% for Band 3 and about 15% in Band 6) that it cannot be neglected in further analyses. Since the effect of the side lobes was not included in this study, these values probably represent the lower limit of the limb brightening. The shape of the limb-brightening function can also be used to constrain electron densities and temperatures in various layers of the solar atmosphere.