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Grain growth in protoplanetary disks in the Upper Scorpius revealed by millimeter-wave spectral indices

Tau Bito, Akimasa Kataoka, Takahiro Ueda, Luca Ricci, Tilman Birnstiel, John Carpenter

TL;DR

This study uses ALMA Band 3 (2.9 mm) observations of 23 Upper Scorpius disks, together with Band 7 data, to measure millimeter spectral indices and constrain dust grain growth in an older (5–10 Myr) protoplanetary-disk population. By comparing observed $\alpha_{\mathrm{mm}}$ with simple disk-evolution models that vary inner/outer radii, surface density, and dust opacity index $\beta$, the work shows that reproducing the low $\alpha_{\mathrm{mm}}$ values in USco requires $\beta \le 0.5$, implying maximum grain sizes up to mm–cm scales in many disks. The results indicate that substantial dust mass persists in the outer, cooler regions of disks at late stages, consistent with continued grain growth over time and inside-out disk evolution. These findings have important implications for planetesimal formation timescales and place quantitative constraints on dust evolution models, highlighting the need for longer-wavelength and higher-resolution follow-ups to separate thermal and non-thermal emission components.

Abstract

The measurement of dust size from millimeter-wavelength spectra provides direct constraints on grain growth in protoplanetary disks. The spectral indices between 0.88 mm and 2.9 mm have been measured in multiple young star-forming regions, such as Taurus, Ophiuchus, and Lupus, which have ages of 1-3 Myr. These spectral indices are as low as 2-3, suggesting that grains in disks are much larger than those in the interstellar medium. In this study, we analyze the ALMA archival data of 23 disks in the Upper Scorpius region. The observed wavelength is 2.9 mm in Band 3, the angular resolution is 3.3 arcsec x 2.1 arcsec, which is not high enough to resolve the targets, and the rms noise is below 0.075 mJy beam$^{-1}$ for almost all sources. Together with the literature values of the Band 7 fluxes of the same targets, we find that the average spectral index of the disks in the Upper Scorpius region is $α_\mathrm{mm}=2.09 \pm 0.10$, which is equal to or slightly smaller than those at the other younger regions. To explain the relationship between the fluxes and spectral indices of the disks in the Taurus, Ophiuchus, Lupus, and Upper Scorpius regions, we construct simple disk evolution models. The observations are best reproduced by models in which the inner radius of the disk increases. This suggests that a substantial amount of dust mass must persist in the outer disk regions where the dust temperature is lower than 20 K even at late evolutionary stages. These findings offer key insights into the grain growth and the temporal evolution of protoplanetary disks.

Grain growth in protoplanetary disks in the Upper Scorpius revealed by millimeter-wave spectral indices

TL;DR

This study uses ALMA Band 3 (2.9 mm) observations of 23 Upper Scorpius disks, together with Band 7 data, to measure millimeter spectral indices and constrain dust grain growth in an older (5–10 Myr) protoplanetary-disk population. By comparing observed with simple disk-evolution models that vary inner/outer radii, surface density, and dust opacity index , the work shows that reproducing the low values in USco requires , implying maximum grain sizes up to mm–cm scales in many disks. The results indicate that substantial dust mass persists in the outer, cooler regions of disks at late stages, consistent with continued grain growth over time and inside-out disk evolution. These findings have important implications for planetesimal formation timescales and place quantitative constraints on dust evolution models, highlighting the need for longer-wavelength and higher-resolution follow-ups to separate thermal and non-thermal emission components.

Abstract

The measurement of dust size from millimeter-wavelength spectra provides direct constraints on grain growth in protoplanetary disks. The spectral indices between 0.88 mm and 2.9 mm have been measured in multiple young star-forming regions, such as Taurus, Ophiuchus, and Lupus, which have ages of 1-3 Myr. These spectral indices are as low as 2-3, suggesting that grains in disks are much larger than those in the interstellar medium. In this study, we analyze the ALMA archival data of 23 disks in the Upper Scorpius region. The observed wavelength is 2.9 mm in Band 3, the angular resolution is 3.3 arcsec x 2.1 arcsec, which is not high enough to resolve the targets, and the rms noise is below 0.075 mJy beam for almost all sources. Together with the literature values of the Band 7 fluxes of the same targets, we find that the average spectral index of the disks in the Upper Scorpius region is , which is equal to or slightly smaller than those at the other younger regions. To explain the relationship between the fluxes and spectral indices of the disks in the Taurus, Ophiuchus, Lupus, and Upper Scorpius regions, we construct simple disk evolution models. The observations are best reproduced by models in which the inner radius of the disk increases. This suggests that a substantial amount of dust mass must persist in the outer disk regions where the dust temperature is lower than 20 K even at late evolutionary stages. These findings offer key insights into the grain growth and the temporal evolution of protoplanetary disks.

Paper Structure

This paper contains 11 sections, 6 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Sample Selection and Observation
  3. Results
  4. Flux at $2.9~\mathrm{mm}$ and spectral indices
  5. Comparison to other regions
  6. Discussion
  7. Simple disk models
  8. Result of model calculations
  9. Evidence of grain growth
  10. Effect of non-thermal emission
  11. Summary

Figures (3)

  • Figure 1: Spectral indices between $0.88$ and $2.9~\mathrm{mm}$ as a function of integrated $1~\mathrm{mm}$ flux for USco disks (blue), Lupus (red; Tazzari2021) , Taurus (orange; Ricci2010Taurus) and Ophiuchus (brown; Ricci2010Ophiuchus). The uncertainties in the flux measurements, shown as blue horizontal bars in the figure, are due to a 10% calibration uncertainty. The errors on the spectral indices, shown as blue vertical bars, are propagated from the flux uncertainties at the two wavelengths. The dark shaded region represents the sensitivity cut-off of our ALMA observations which is caused by the difference between the fluxes at $0.88$ and $2.9~\mathrm{mm}$.
  • Figure 2: Calculated spectral indices between $0.88$ and $2.9~\mathrm{mm}$. The upper left panel shows case A, corresponding to a model with decreasing Rmax. The upper right panel shows case B, corresponding to a model with increasing Rmin. The lower panels show cases C and D, corresponding to models with decreasing $\Sigma_0$. case C (lower left) has no gap in the disk, while case D (lower right) has. In each panel, different colored lines indicate different values of $\beta$. The stars ($\star$) indicate the reference model, with $0.1~\mathrm{au}$ for the inner edge, $100~\mathrm{au}$ for the outer edge, and $100 M_\oplus$ for the dust mass. Moving from one marker to the next corresponds to a tenfold change in dust mass.
  • Figure 3: Observation vs. Model Comparison. Figures \ref{['spectral_index']} and \ref{['dust_model_x2']} are combined. For figure \ref{['dust_model_x2']}, the horizontal axis is converted from flux at $0.88~\mathrm{mm}$ to at $1 \mathrm{mm}$.