Dust production 680-850 million years after the Big Bang

Dust plays an important role in our understanding of the Universe, but it is not obvious yet how the dust in the distant universe was formed. I derived the dust yields per asymptotic giant branch (AGB) star and per supernova (SN) required to explain dust masses of galaxies at z=6.3-7.5 (680-850 million years after the Big Bang) for which dust emission has been detected (HFLS3 at z=6.34, ULAS J1120+0641 at z=7.085, and A1689-zD1 at z=7.5), or unsuccessfully searched for. I found very high required yields, implying that AGB stars could not contribute substantially to dust production at these redshifts, and that SNe could explain these dust masses, but only if they do not destroy most of the dust they form (which is unlikely given the upper limits on the SN dust yields derived for galaxies where dust is not detected). This suggests that the grain growth in the interstellar medium is likely required at these early epochs.
Comment: Accepted to A&A. 6 pages, 1 figure, 2 tables. V2: minor changes to match the published version