Millimeter gap contrast as a probe for turbulence level in protoplanetary disks

Abstract

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks. Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data, and an exquisite determination of the temperature. In this work, taking the well-known HD 163296 disk as an example, we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence. With self-consistent radiative transfer models, we simultaneously analyzed the radial brightness profiles along the disk major and minor axes, and the azimuthal brightness profiles of the B67 and B100 rings. By fitting all the gap contrasts measured from these profiles, we constrained the gas-to-dust scale height ratio Λ to be 3.0 +0.3 −0.8 , 1.2 +0.1 −0.1 and 6.5 for the D48, B67 and B100 regions, respectively. The varying gas-to-dust scale height ratios indicate that the degree of dust settling changes with radius. The inferred values for Λ translate into a turbulence level of α turb < 3 × 10 −3 in the D48 and B100 regions, which is consistent with previous upper limits set by gas line observations. However, turbulent motions in the B67 ring are strong with α turb ∼1.2 × 10 −2 . Due to the degeneracy between Λ and the depth of dust surface density drops, the turbulence strength in the D86 gap region is not constrained.

Early Planet Formation in Embedded Disks (eDisk). II. Limited Dust Settling and Prominent Snow Surfaces in the Edge-on Class I Disk IRAS 04302+2247

“…In one extreme, dust settled into an infinitely thin sheet should appear symmetric across the minor axis, and for disks with rings, the rings and gaps should not show azimuthal variation (e.g., Pinte et al 2016;Doi & Kataoka 2021). Several observations of Class II sources show that the dust is predominantly well settled (e.g., Andrews et al 2018;Long et al 2018;Villenave et al 2020;Doi & Kataoka 2021;Liu et al 2022;Villenave et al 2023). One of the clearest cases is SSTC2D J163131.2−242627 (or Oph 163131 for short), whose gaps are resolved even though the disk is nearly edge-on (Villenave et al 2022; i ∼ 84°).…”

Modest Dust Settling in the IRAS04302+2247 Class I Protoplanetary Disk

“…We now aim to look for any trends in the variation of the settling efficiency with different parameters, such as the stellar mass, disk outer radius, and time. In Table 4, we compile various parameters for seven disks at different evolutionary stages, with constraints on the large dust vertical height (HH212, L1527, VLA 1623 W, IRAS04302, HL Tau, HD163296, and Oph163131; Pinte et al 2016;Nakatani et al 2020;Doi & Kataoka 2021;Lin et al 2021;Liu et al 2022;Michel et al 2022;Ohashi et al 2022;Sheehan et al 2022;Villenave et al 2022).…”

“…Finally, the last column of Table 4 reports the dust heights of the different systems. For the most evolved sources, specific radiative transfer modeling were performed, allowing the authors to quantify the vertical extents of the large dust particles and to compare them with those of the gas (Pinte et al 2016;Doi & Kataoka 2021;Wolff et al 2021;Liu et al 2022;Villenave et al 2022). On the other hand, for the younger Class 0 systems, determining the gas height is complex, due to the presence of a dense envelope, and the different papers do not provide quantitative measurements of the gas and dust scale heights.…”

“…Star formation is divided into several classes: Class 0 corresponds to embedded protostars, Class I objects present both a disk and a prominent envelope around the central star, and Class II systems only have the disk left (e.g., Andre et al 2000). Direct measurements of the millimeter dust scale height in several Class I/II and Class II disks have found that the outer regions are very settled, with a typical scale height of less than 1 au at a radius of 100 au (Pinte et al 2016;Villenave et al 2020;Doi & Kataoka 2021;Liu et al 2022;Villenave et al 2022). In contrast, observations of younger systems, such as HH212, VLA 1623 West, and L1527, at the Class 0 and 0/I stages, have revealed much thicker disks, which are possibly not affected by vertical settling (Sakai et al 2017;Lin et al 2021;Lee et al 2022;Michel et al 2022;Ohashi et al 2022;Sheehan et al 2022).…”

Observing Planetesimal Formation under Streaming Instability in the Rings of HD 163296

“…To assess if SI-driven particle clumping in the presence of AD is a viable scenario for HD 163296, we adopted literature measurements of the dust-to-gas coupling in the vertical direction (Doi & Kataoka 2021;Liu et al 2022) to determine the vertical diffusivity in the 67 and 100 au rings of HD 163296 using the Stokes numbers from Table 1. Our results are summarized in Table 3, and, when compared with our estimates of the radial diffusivity in Table 1, they suggest that turbulence is nonisotropic in both rings (see also Doi & Kataoka 2023).…”