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

Abstract

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 $β$ 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.

Figures (15)

• Figure 1: Imagery of $\beta$ Pic used in this study. The mid-infrared images were taken by Gemini/T-ReCS Telesco2005Li2012 and VLT/VISIR Han2023. The millimeter dust continuum images were observed with ALMA Band 7 Hull2022 and Band 6 Matra2019. The mid-infrared images are displayed on a linear scale capped at 0.12, 0.12, 0.12, 0.37 and 1.9 Jy/arcsec$^2$ respectively from the shortest to longest wavelength. The white ellipses indicate the half-maximum contour of the PSF (mid-infrared) or synthetic beam (ALMA) when modelled as a 2D Gaussian.
• Figure 2: Rotationally subtracted ALMA images of $\beta$ Pic obtained by subtracting each image rotated by 180$^\circ$ about the star from the original image to emphasize any asymmetric features in the disk. Both images were UV-tapered to achieve an effective beam FWHM of 23 au for both images, as indicated by the white ellipses. Arrows are drawn at 30, -70 and 150 au from the star along the major axis.
• Figure 3: Mean projected surface brightness profile of the smoothed and rotationally subtracted ALMA images displayed in Fig. \ref{['fig:image180_alma']} within 15 au from the disk's major axis as a function of projected separation. Sample points separated by the effective (smoothed) beam FWHM are plotted to indicate the spatial correlation scale. The uncertainties plotted correspond to those for individual binned regions indicated by the sample points and are estimated based on the rms noise per beam of each image. The arrows are at the same location as those shown in Fig. \ref{['fig:image180_alma']}.
• Figure 4: Difference image obtained by subtracting the Band 7 image from the Band 6 image rescaled to the Band 7 flux. Both images have been imaged to achieve the same resolution (with a robust value of 2.0 and the Band 6 image UV-tapered to match Band 7). Contours of the Band 7 image are drawn at 0.3, 0.8, 1.3, 1.8 and 2.3 mJy/arcsec$^2$. The beam is shown in the lower left corner.
• Figure 5: De-projected and deconvolved radial surface brightness profiles of $\beta$ Pic fitted non-parametrically with rave. The left and centre panels display the radial profiles in the mid-infrared and millimeter respectively, with each profile vertically scaled by the factor shown in parentheses in the legend following the wavelength in $\mu$m. The right panel displays the same radial profiles but on a logarithmic scale without scaling. The shaded regions indicate the 1$\sigma$ range of possible models, within which a profile can be drawn while still reasonably reproducing the data. The corresponding fitted central component (star + potential unresolved inner dust) fluxes are shown in Table \ref{['tab:starflux']}, which are not displayed in the radial profiles shown. From the shortest to longest wavelength, the number of annuli used in the fitting are 10, 10, 10, 10, 5, 10 and 7 respectively, which were chosen based on the S/N and resolution of each image.