A Steeper than Linear Disk Mass-Stellar Mass Scaling Relation

Abstract: The disk mass is among the most important input parameter for every planet formation model to determine the number and masses of the planets that can form. We present an ALMA 887micron survey of the disk population around objects from 2 to 0.03Msun in the nearby 2Myr-old Chamaeleon I star-forming region. We detect thermal dust emission from 66 out of 93 disks, spatially resolve 34 of them, and identify two disks with large dust cavities of about 45AU in radius. Assuming isothermal and optically thin emission, we convert the 887micron flux densities into dust disk masses, hereafter Mdust. We find that the Mdust-Mstar relation is steeper than linear with power law indices 1.3-1.9, where the range reflects two extremes of the possible relation between the average dust temperature and stellar luminosity. By re-analyzing all millimeter data available for nearby regions in a self-consistent way, we show that the 1-3 Myr-old regions of Taurus, Lupus, and Chamaeleon I share the same Mdust-Mstar relation, while the 10Myr-old Upper Sco association has a steeper relation. Theoretical models of grain growth, drift, and fragmentation reproduce this trend and suggest that disks are in the fragmentation-limited regime. In this regime millimeter grains will be located closer in around lower-mass stars, a prediction that can be tested with deeper and higher spatial resolution ALMA observations.

• The paper finds a steeper-than-linear scaling relation between disk dust mass and stellar mass using ALMA 887μm observations.
• It spatially resolved 34 of 66 detected disks and identified large ~45 AU dust cavities, highlighting significant evolutionary processes.
• Comparative analysis with Taurus, Lupus, and Upper Sco supports theoretical models of grain growth, drift, and fragmentation in disks.

Analysis of "A Steeper than Linear Disk Mass-Stellar Mass Scaling Relation" by Pascucci et al.

The paper by Pascucci et al. presents an investigation into the relationship between disk mass and stellar mass in the 2 million-year-old star-forming region of Chamaeleon I. Using data acquired from the Atacama Large Millimeter/submillimeter Array (ALMA) at 887μm, the study aims to elucidate the mass distribution of protoplanetary disks and its correlation with the mass of their host stars. This is of particular importance for developing accurate models of planet formation, as disk mass is a critical parameter influencing the types and quantities of planets that can form.

Key Findings

1. Detection and Spatial Resolution: The study reports thermal dust emission detected from 66 out of 93 surveyed disks, with 34 of these spatially resolved. The research further identifies two disks possessing large dust cavities approximately 45 AU in radius—indicative of significant evolutionary processes within these systems.
2. Disk Mass-Stellar Mass Relation: By converting ALMA flux densities into dust disk masses under the assumption of isothermal-and-optically-thin emission, the authors uncover a steeper-than-linear scaling relation between dust mass ($M_{\text{dust}}$) and stellar mass ($M_*$). The relation is quantified as $M_{\text{dust}} \propto (M_*)^{1.3-1.9}$, determined by different average dust temperature assumptions.
3. Comparative Analysis with Other Regions: The study includes a re-analysis of millimeter data from other regions such as Taurus, Lupus, and Upper Sco. Findings suggest that the 1-3 Myr-old regions of Taurus and Lupus share a similar $M_{\text{dust}}-M_*$ relationship to Chamaeleon I, whereas the older Upper Sco association exhibits a steeper relation.
4. Theoretical Implications: The observed trend is consistent with theoretical models of grain growth, drift, and fragmentation. The research posits that disks are in a fragmentation-limited regime, with predictions that millimeter grains are located closer in around lower-mass stars. This hypothesis can be further examined with future deeper and higher resolution ALMA observations.

Implications and Speculations

The results have several implications for understanding planetary system development:

• Disk Evolution: The steeper relation found in Upper Sco, a region significantly older than Taurus and Chamaeleon I, hints at potential evolutionary pathways that may lead to observed diversity in exoplanetary systems.
• Fragmentation-Limited Disks: If disks are indeed fragmentation-limited, this could explain the rapid depletion of millimeter-sized grains through inward drift, which when coupled with grain fragmentation, affects disk observability at longer wavelengths.
• Mass Discrepancies: The disparity between the disk masses estimated here and the solids budget required to form known planetary systems, particularly around low-mass stars, suggests that a substantial portion of disk solids might be rapidly converted or relocated inwards, potentially accelerating planet formation.

Future Directions

Future research should focus on high-resolution ALMA observations to probe the disk sizes across a variety of host star masses for a more comprehensive understanding of the mass-temperature relationship. Additionally, expanding the scope to include more mature star systems could refine these relationships further. Testing the fragmentation-limited hypothesis through enhanced sensitivity to dust grain sizes and distributions may corroborate the predictions made herein about grain dynamics and their integral role in shaping planetary architectures.

In conclusion, the analysis by Pascucci et al. presents a detailed examination of disk mass scaling relative to stellar mass in the context of a young star-forming region. By comparing these findings with other regions and employing theoretical models, the research offers critical insights that significantly contribute to the discourse on planet formation and disk evolution.