The challenge of measuring the phase function of debris discs

Abstract

Context. Debris discs are valuable systems to study dust properties. Because they are optically thin at all wavelengths, we have direct access to the absorption and scattering properties of the dust grains. One very promising technique to study them is to measure their phase function, that is, the scattering efficiency as a function of the scattering angle. Discs that are highly inclined are promising targets as a wider range of scattering angles can be probed. Aims. The phase function (polarised or total intensity) is usually either inferred by comparing the observations to synthetic disc models, assuming a parametrised phase function or estimating it from the surface brightness of the disc. Here, we argue that the latter approach can be biased due to projection effects leading to an increase in column density along the major axis of a non-flat disc. Methods. We present a novel approach to account for those column density effects. The method remains model dependent, as a disc model is still required to estimate the density variations as a function of the scattering angle. This method allows us, however, to estimate the shape of the phase function without having to invoke any parametrised form. Results. We apply our method to SPHERE/ZIMPOL observations of HR 4796 A and highlight the differences with previous measurements only using the surface brightness; the main differences being at scattering angles smaller than ~100°. Our modelling results suggest that the disc is not vertically flat at optical wavelengths; this result is supported by comparing the width along the major and minor axis of synthetic images. We discuss some of the caveats of the approach, mostly that our method remains blind to real local increases in the dust density and that it cannot be readily applied to angular differential imaging observations yet. Conclusions. We show that the vertical thickness of inclined (≥60°) debris discs can affect the determination of their phase functions. Similarly to previous studies on HR 4796 A, we still cannot reconcile the full picture using a given scattering theory to explain the shape of the phase function, the blow-out size due to radiation pressure, and the shape of the spectral energy distribution, which is a long-lasting problem for debris discs. Nonetheless, we argue that similar effects, such as the ones highlighted in this study, can also bias the determination of the phase function in total intensity.