Into the thick of it: ALMA 0.45 mm observations of HL Tau at 2 au resolution

Aims. To comprehend the efficiency of dust evolution within protoplanetary disks, it is crucial to conduct studies of these disks using high-resolution observations at multiple wavelengths with the Atacama Large Millimeter/submillimeter Array (ALMA). Methods. In this work, we present high-frequency ALMA observations of the HL Tau disk using its Band 9 centered at a wavelength of 0.45 mm. These observations achieve the highest angular resolution in a protoplanetary disk to date, 12 milliarcseconds (mas), allowing the study of the dust emission at scales of 2 au. We use these data to extend the previously published multi-wavelength analysis of the HL Tau disk. Results. Our new 0.45 mm data traces mainly optically thick emission, providing a tight constraint to the dust temperature profile. We derive maximum particle sizes of $\sim$1 cm from the inner disk to $\sim$60 au. Beyond this radius, we find particles between 300 $\mu$m and 1 mm. Moreover, an intriguing asymmetry is observed at 32 au in the northeast inner part of the HL Tau disk at 0.45 mm. We propose that this asymmetry is the outcome of a combination of factors including the optically thick nature of the emission, the orientation of the disk, and a relatively large dust scale height of the grains. To validate this, we conducted a series of radiative transfer models using the RADMC-3D software. If this scenario is correct, our measured dust mass within 32 au would suggest a dust scale height H/R> 0.08 for the inner disk. Finally, the unprecedented resolution allowed us to probe for the first time the dust emission down to a few au scales. We observed an increase in brightness temperature inside the estimated water snowline and speculate whether it could indicate the presence of a traffic jam effect in the inner disk. Abridge