Trends in Silicates in the $\beta$ Pictoris Disk

While beta Pic is known to host silicates in ring-like structures, whether the properties of these silicate dust vary with stellocentric distance remains an open question. We re-analyze the beta Pictoris debris disk spectrum from the Spitzer Infrared Spectrograph (IRS) and a new IRTF/SpeX spectrum to investigate trends in Fe/Mg ratio, shape, and crystallinity in grains as a function of wavelength, a proxy for stellocentric distance. By analyzing a re-calibrated and re-extracted spectrum, we identify a new 18 micron forsterite emission feature and recover a 23 micron forsterite emission feature with a substantially larger line-to-continuum ratio than previously reported. We find that these prominent spectral features are primarily produced by small submicron-sized grains, which are continuously generated and replenished from planetesimal collisions in the disk and can elucidate their parent bodies' composition. We discover three trends about these small grains: as stellocentric distance increases, (1) small silicate grains become more crystalline (less amorphous), (2) they become more irregular in shape, and (3) for crystalline silicate grains, the Fe/Mg ratio decreases. Applying these trends to beta Pic's planetary architecture, we find that the dust population exterior to the orbits of beta Pic b and c differs substantially in crystallinity and shape. We also find a tentative 3-5 micron dust excess due to spatially unresolved hot dust emission close to the star. From our findings, we infer that the surfaces of large planetesimals are more Fe-rich and collisionally-processed closer to the star but more Fe-poor and primordial farther from the star.