Isotopic Ratios in the Disk of HD 163296

TL;DR

The paper addresses how to measure isotopic ratios in protoplanetary disks despite optical depth and excitation degeneracies. It uses high-S/N ALMA observations of rare CO isotopologues, notably $^{13}$C$^{18}$O(2-1), along with archival C$^{17}$O and C$^{18}$O transitions, to identify an optically thin outer disk where flux ratios trace intrinsic isotopic abundances. Through RADEX-based ratio versus optical-depth modeling and an MCMC fit to beam-averaged intensities, the authors derive $^{12}$C/$^{13}$C = $75.3^{+14.7}_{-11.4}$ and $^{18}$O/$^{17}$O = $3.28^{+0.31}_{-0.26}$, both consistent with local ISM values, while $^{16}$O/$^{18}$O remains less constrained. The results establish HD 163296 as a benchmark for isotopic studies in disks and provide a robust, model-independent framework for extending such measurements to other systems with resolved snowlines.

Abstract

Isotopic abundance ratios in protoplanetary disks are critical for understanding volatile inheritance and chemical evolution in planet-forming environments. We present Atacama Large Millimeter/submillimeter Array observations of the rare isotopologue 13C18O(2-1) at approximately 0.3 arcsec resolution from the disk around the Herbig Ae star HD 163296, combined with archival observations of C17O(2-1), C18O(1-0), and C17O(1-0), to empirically constrain carbon and oxygen isotopic ratios without detailed disk modeling. Both the C17O/13C18O(2-1) and C18O/C17O(1-0) flux ratios rise sharply across the CO snowline and flatten beyond 1.5 arcsec (r >= 150 au), where the emission becomes optically thin. This transition, reflecting a steep drop in CO column density set by the disk's thermal structure, makes HD 163296 an optimal case for isotopic analysis. Using beam-averaged intensities of the four transitions measured in this optically thin region, we derive isotopic ratios of 12C/13C = 75.3 (+14.7/-11.4) and 18O/17O = 3.28 (+0.31/-0.26), both consistent with local interstellar medium values. The 16O/18O ratio remains weakly constrained due to moderate optical depth in the C18O(1-0) line and degeneracy with CO column density. These results demonstrate that rare CO isotopologues can provide robust, empirical constraints on isotopic ratios in disks when sharp structural transitions allow for the identification of optically thin regions, and establish HD 163296 as a benchmark for extending such studies to other systems with resolved snowline structures.

Figures (8)

• Figure 1: Radial profile (top) and derivative (bottom) of the $^{13}$C$^{18}$O(2--1) integrated intensity toward HD 163296. The derivative profile shows a clear local minimum at $\sim$0.75, consistent with the location of the sharp CO snowline transition observed in C$^{17}$O and C$^{18}$O lines Qi2024.
• Figure 2: Radial profiles of the same-transition isotopologue intensity ratios. Left: C$^{17}$O/$^{13}$C$^{18}$O(2--1) ratio, flat at small radii, rising steeply across the CO snowline, and converging to $\sim$20 beyond 15. Uncertainties include both statistical errors and a 7.1% systematic calibration term, as the two lines were observed in different bands and epochs. Right: C$^{18}$O/C$^{17}$O(1--0) ratio, showing similar radial behavior and approaching $\sim$2.7 beyond 15. Only statistical uncertainties are shown, since both lines were observed in the same band and share a common amplitude calibration. In both panels, the rapid increase followed by a flat plateau indicates the sharp decline in CO column density across the snowline and identifies the outer disk as an optically thin region suitable for isotopic ratio analysis.
• Figure 3: RADEX-calculated same-transition isotopologue flux ratios as a function of line-center optical depth for a range of $n_{\rm H_2}$ and $T_{\rm kin}$. Upper: C$^{17}$O/$^{13}$C$^{18}$O(2--1) ratio versus C$^{17}$O(2--1) optical depth. Lower: C$^{18}$O/C$^{17}$O(1--0) ratio versus C$^{18}$O(1--0) optical depth. In the optically thin regime ($\tau \ll 1$), the ratios converge to the values set by ISM isotopic abundances (19.2 and 3.6, respectively), and decline rapidly once the more abundant line becomes optically thick ($\tau \gtrsim 1$). The shaded regions indicate the plateau ranges of the ratios measured in HD 163296 beyond 15 (see Figure \ref{['fig:ratio_profiles']}), where all transitions are optically thin. This comparison shows that the observed plateau values fall squarely in the optically thin regime, confirming their suitability for constraining isotopic ratios.
• Figure 4: Velocity field (moment-1, color) of the $^{13}$C$^{18}$O $J$=2--1 emission overlaid with white contours of the integrated intensity (moment-0), both derived using the bettermoments package Teague2018. The intensity-weighted velocity was calculated with a $2\sigma$ clip to minimize noise bias.
• Figure 5: Test A: sensitivity of the C$^{17}$O/$^{13}$C$^{18}$O(2--1) ratio to independent variations in isotopic abundances. Top left: Absolute ratio as a function of C$^{17}$O(2--1) optical depth when varying $^{12}$C/$^{13}$C by $\pm$30% at fixed $^{18}$O/$^{17}$O. Top right: Same, but varying $^{18}$O/$^{17}$O at fixed $^{12}$C/$^{13}$C. Bottom: All curves normalized by their optically thin limits. The nearly identical shapes confirm that the ratio–$\tau$ response is insensitive to these variations.