The multi-wavelength vertical structure of the archetypal $\beta$ Pictoris debris disk

Thermal imaging of debris disks is resolving the vertical height in an increasing number of systems, enabling the use of the vertical structure to decode the dynamical state of the planetary system. In this study, we examine the multi-wavelength structure of the archetypical edge-on debris disk of $\beta$ Pic, extensive imaging of which across mid-infrared to millimeter wavelengths makes it the prime system to study the vertical height across different grain size populations. We non-parametrically modelled the radial profiles and constrained the vertical height at each wavelength while taking into account the vertical warping, finding the disk to be on average 1.5 times thicker vertically in the mid-infrared compared to the millimeter and the scale height to be relatively constant across radius. The decreasing scale height with wavelength is in contrast to predictions from collisional damping, and could be a result of the combined effect of radiation pressure and random collisions. We also show that the disk is warped at millimeter wavelengths and find tentative evidence for clumps in ALMA images which will require follow-up observations to confirm. The millimeter vertical warping is consistent with findings in scattered light and the secular perturbation interpretation due to the inner giant planets, which could also explain the relatively constant apparent scale height across radius, and potentially earlier findings of a non-Gaussian vertical profile which this study confirms.