ALMA 873 $μ$m Polarization Observations of the PDS~70 Disk

At a 112.4 pc distance, the PDS70 protoplanetary disk is a rare case that has been confirmed to host two accreting planets. This makes it the most important laboratory for studying dust growth in the context of planet formation. Here we present the first deep, full polarization observations at 873 $μ$m wavelength. We detected $\sim$1%-2.5% linear polarization over the bulk of the $\sim$55-100 AU (sub)millimeter ring. The polarization position angles align preferentially with the projected minor axis of the disk. The standard interpretation is that the observed polarization is caused by dust self-scattering, with a maximum dust grain size of $\sim$100 $μ$m. On $\gtrsim$10 AU scales, which can be resolved by the presented 873-3075 $μ$m observations, the ring is marginally optical thick at 873 $μ$m wavelength. Using Monte Carlo radiative transfer simulations, we found that an azimuthally asymmetric, marginally optically thick ring with a maximum dust grain size of $\sim$87 $μ$m can reproduce the observed 873 $μ$m polarization position angles and percentages. This study indicates that the coagulation of ice-coated dust in the protoplanetary disk may be limited by fragmentation or bouncing.

💡 Research Summary

This paper presents the first deep, full‑polarization observations of the PDS 70 protoplanetary disk at a wavelength of 873 µm (ALMA Band 7), complemented by high‑resolution total‑intensity maps at 1226 µm, 1287 µm (Band 6), 2068 µm (Band 4), and 3075 µm (Band 3). The target, located at 112.4 pc, hosts two directly imaged, accreting planets (PDS 70b and c), making it a benchmark system for studying dust evolution in the presence of forming planets.

Observational Results
The 873 µm data resolve an inclined dust ring spanning roughly 55–100 AU. Within this ring, linear polarization is detected at levels of 1 %–2.5 % across most of the azimuth, with the polarization vectors predominantly aligned with the projected minor axis of the disk (mean position angle ≈ 68°). The polarization fraction shows a modest azimuthal variation: it peaks toward the western side of the ring and reaches a minimum near the bright north‑west crescent. The total‑intensity images at the longer wavelengths reveal the same ring structure plus two crescent‑like enhancements (north‑west and south‑west), consistent with previous continuum studies. The north‑west crescent is prominent at λ ≥ 1.2 mm but appears attenuated at 873 µm, indicating higher optical depth at the shorter wavelength.

Spectral Index Analysis
By combining the 873 µm data with the 1226 µm (and 1287 µm) maps, the authors compute spatially resolved spectral indices α_b6‑b7. In the faint outer parts of the wide ring the index is close to the interstellar value (~3.7), implying a maximum grain size a_max ≲ 100 µm. In the brighter inner regions the index drops, suggesting increased optical depth and a possible contribution from larger grains, but still consistent with a_max of order a few × 10² µm at most.

Interpretation via Self‑Scattering
The alignment of polarization vectors with the disk minor axis is a hallmark of dust self‑scattering in inclined disks. The authors therefore adopt the self‑scattering framework, in which grains with sizes near the Mie resonance (a ≈ λ/2π) produce the strongest polarized signal. Using Monte Carlo radiative transfer (MCRT) simulations, they explore a range of disk geometries, optical depths, and grain size distributions. The best‑fit model is an azimuthally asymmetric, marginally optically thick ring (τ ≈ 1) with a maximum grain size a_max ≈ 87 µm. This configuration reproduces both the observed polarization fractions (1 %–2.5 %) and the near‑uniform position angles, as well as the modest azimuthal variation in polarization strength.

Physical Implications
A grain size ceiling of ~80–100 µm suggests that dust growth in the PDS 70 outer ring is limited by fragmentation or bouncing rather than by a lack of material. In the appendix the authors estimate a fragmentation velocity v_frag ≈ 10 m s⁻¹, consistent with laboratory measurements for icy aggregates. This implies that ice‑coated grains, despite being more sticky than silicate grains, still encounter a barrier that prevents them from reaching millimeter or centimeter sizes in the observed region. Consequently, the material feeding the two known planets may be dominated by relatively small, sub‑millimeter particles, influencing models of planetesimal formation and pebble accretion in this system.

Conclusions and Outlook
The study demonstrates that high‑resolution millimeter‑wave polarization is a powerful diagnostic of grain size and optical depth in planet‑forming disks. For PDS 70, the data indicate a marginally optically thick, slightly asymmetric ring populated by grains with a_max ≈ 87 µm, constrained by fragmentation/bouncing limits. This provides a direct observational link between dust evolution and the environment of forming giant planets. Future work—extending polarization measurements to longer wavelengths, improving sensitivity, and employing more sophisticated multi‑wavelength radiative transfer models—will refine the grain‑size distribution and test whether similar growth barriers operate in other planet‑hosting disks.