The Ophiuchus DIsk Survey Employing ALMA (ODISEA): Complete Size Distributions for the 100 Brightest Disks Across Multiplicity and SED Classes

Our Band 8 (410 GHz/0.73 mm) sample was selected from the ODISEA survey and is flux-limited. We selected all $\sim$100 targets brighter than 4 mJy in Band 6 (230 GHz/1.3 mm) from Williams et al. (2019), corresponding to M_dust $\gtrsim$ 2 M_⊕. Since $\sim$200 objects were detected by ODISEA in Band 6 (down to a 3-$\sigma$ detection limit of $\sim$0.5 mJy), the Band 8 program is essentially restricted to the brightest half of all detected objects. Given the strong correlation between disk size and disk mass, the Band 8 observations were performed at two different resolutions. The 45 objects brighter than 20 mJy in Band 6 were observed in Band 8 at 0.15^′′ (21 au) because they were already known to be resolved at those spatial scales from the lower-resolution Band 6 data. The 55 objects with Band 6 fluxes between 4 and 20 mJy were observed at 0.05^′′ (7 au) angular resolution in Band 8. Some binary systems were observed at both resolutions because the different components fall in different flux ranges. In the end, a total of 105 disks were observed when counting the individual components in binary systems. The full sample of disks is listed in Table 1.

The observations at 0.15^′′ resolution were taken during ALMA Cycle 8 under program 2021.1.00378.S (PI: L. Cieza) between August 4th and 11th, 2022, and have baselines between 15 m and 1300 m. The 0.05^′′ angular resolution data were obtained between May 23rd and 29th, 2023, in ALMA Cycle 9, under program 2022.1.00480.S (PI: L. Cieza) with baselines ranging from 27 m to 3637 m. The continuum bandwidth was 7.5 GHz in both programs. The precipitable water vapor was around 2.3 mm during the Cycle 8 observations but stayed below 1 mm for the long-baseline observations in Cycle 9.

In order to investigate the continuum disk sizes in our sample, the angular measurements from Table 1 were converted to physical sizes in au adopting the distance from Gaia Collaboration et al. (2018), when available. For objects without a Gaia distance, a mean distance of 139.4 pc (from Williams et al. (2019)) was assumed. The full-size distribution for the 105 disks in the sample is shown in Figure 1 (top-left panel), adopting the Gaussian measurements. We find that the HWHM values range from 1.7 au to 177 au. The distribution is log-normal, with a median value of 13 au and a logarithmic standard deviation of $\sigma_{\log}=0.46$ (corresponding to a factor of 2.9 in linear space), see Table 2).

Since stellar companions are expected to truncate each other’s disks at 0.3-0.5 times the orbital separation (Papaloizou & Pringle, 1977; Artymowicz & Lubow, 1994), disks around close binary systems are expected to be significantly smaller than those around single stars (or wide-separation binaries). To examine the effect of stellar companions on disk sizes, we divide the sample into two groups: stars belonging to close-binary systems (projected sep. $<$ 200 au) and stars lacking close companions. The binary systems were identified from two sources, our own ALMA images and the Near-IR Adaptive Optics survey performed by Zurlo et al. (2020), which detected binary systems down to $\sim$ 6 au projected separations. Overall, our sample includes a total of 30 disks in 20 binary systems because only in $10$ cases the disks were detected around both components of the system. Of these 30 disks in multiple systems, 17 belong to close binaries and 13 are part of wide separation systems and are treated as single stars for statistical purposes.

In Figure 1, we also show the size distribution of disk sizes excluding disks in close binary systems (top-right panel) and the size distribution for close binaries alone (middle-left panel). The cumulative distribution of the full sample and the two sub-samples are plotted in the middle-right panel, together with the Gaussian fits for the observed distributions. We find that removing the close binaries has a minor effect on the full distribution, increasing the the median disk size from $\sim$14 au to $\sim$16 au and decreasing the standard deviation from $\sigma_{\log}$ = 0.46 to $\sigma_{\log}$ = 0.39. According to the Kolmogorov-Smirnov (K-S) test, the distributions of disk sizes including or excluding close binaries are very similar (see Table LABEL:tab:_table3). On the other hand, the size distribution of close binaries alone is clearly different with a median disk size of 4.6 au and a logarithmic standard deviation of $\sigma_{\log}=0.25$ (corresponding to a factor of 1.8 in linear space). We note that the binary systems include secondary disks that do not necessarily meet the flux requirements in our flux-limited sample or that were only detected in the Band 8 high-resolution observations. To correct for this bias, we define a “restricted binary sample” which excludes 4 secondary disks fainter than 4 mJy x [B8/B6], where [B8/B6] is equal to 3.34, the mean Band 8 to Band 6 ratio of the entire sample. This restricted binary sample is also shown in Fig. 1 (middle panels) and included in Table 2. As shown in Table 3, the K-S test confirms a significant difference with respect to the sample excluding close binaries, although with a slightly lower significance. We note that the results remain essentially the same if separation thresholds of 100 au or 300 au are used to define close binary systems, instead of the 200 au we adopted.

Another potential bias when comparing disk sizes is the difference in the underlying distributions of host stellar masses between single stars and binaries, given the known correlations between disk luminosity and stellar mass Manara et al. (2019) and between disk luminosity and disk sizes (Hendler et al., 2020). In particular, secondary objects in binary systems are likely to be biased toward lower host masses and disk luminosities and hence toward smaller disk sizes. To disentangle these dependencies, we plot the disk sizes as a function of flux for all disks and close-binary systems (See Fig. 1, bottom-left panel). We find that disks in binary systems indeed span a smaller range of disk fluxes. However, it is also clear that for a given mm flux, disks in binary systems are systematically smaller.

The Ophiuchus molecular cloud is characterized by a significant population of embedded stars (Class I and Flat Spectrum sources), with an estimated age of $\lesssim$ 0.5-1 Myr, and mostly located in the L1688 cluster (Evans et al., 2009). It also contained a more distributed population of Class II and Class III sources sources with a significant age spread, with stars as old as 6 Myr according to Esplin & Luhman (2020). We note however that most of the embedded and Class II sources in our sample are associated with the L1688 Cluster.

In order to investigate how continuum disk sizes evolve with time, we conducted a size distribution analysis for both groups (embedded stars vs. Class II sources). Figure 2 presents the size distribution of the two SED groups using the Gaussian measurements including close binaries and excluding them (top-left and middle-left panels, respectively). The bottom-left panel corresponds to the size distribution adopting the R_68% values from Frank (only available for non-binary disks).

We further plot cumulative distribution functions for all cases with their corresponding Gaussian fits (panels on the right). As with the previous analysis, we performed K-S tests to compare the distributions between the two SED groups. The results of the K-S test are shown in Table LABEL:tab:_table3. These tests show that the distributions remain statistically indistinguishable from each other, regardless of the inclusion or exclusion of the binary systems, or whether we adopt Gaussian sizes or R_68% values from Frank profiles. Our results indicate that disk sizes are not becoming smaller between the embedded stage and the Class II phase as expected from the radial drift of mm-sized particles. In fact, at face value, Class II disks are slightly larger than disks around embedded sources (see Table 2). Given the strong dependence of disk size on mm flux, this result would be expected if the Class II disks in our sample were significantly brighter than the embedded disks. However, we have verified that this is not the case as we find that the flux distributions of the two samples are indistinguishable from each other according to the K-S test (see Table 3 and left of Figure 4 in the Appendix). Another potential bias that we investigated is the possibility that the sample of embedded sources is contaminated by more evolved, but highly inclined, Class II objects (Ohashi et al., 2023). To test for this possibility we compare the observed distribution of inclinations to that expected for an isotropic distribution of disk orientations (see Figure 4, right panel in the appendix). However, we find that the observed inclination distribution of embedded sources is indistinguishable from random orientations (see K-S in Table 3) and conclude that our sample of embedded sources is not significantly contaminated by highly-inclined older objects.

In our analysis of the $\sim$100 brightest protoplanetary disks in Ophiuchus, we examined how multiplicity influences size distribution. In our flux-limited sample, we find that the stars in close binary systems (sep. $<$ 200 au) have disks that are, on average, more than a factor of two smaller than disks around single stars or wide binary systems (HWHM $\sim$ 5 vs $\sim$ 13 au). The most straightforward implication is that the formation of Uranus and Neptune analogs should be strongly inhibited in close binary systems, which should be prone to producing compact planetary configurations. However, models by Zagaria et al. (2021b) recently suggested that stellar companions might also affect the formation of planets in additional ways. In particular, they find that dust grains should undergo more efficient radial drift in close binaries with respect to wide binaries and single stars. This would very quickly ($<$ 1 Myr) reduce the amount of solids available for the formation of the cores of gas giants unless disk substructures can trap the dust and prevent its inward migration at the very early stages of disk evolution.

The bottom-left panel of Figure 1 shows that, for a given flux (a proxy for dust mass), disks in close binary tend to be smaller than the rest. This is consistent with a more efficient radial drift and supports the notion that dust evolution, and not only tidal truncation, play a role on the continuum disk sizes in binary systems. This idea can be tested by comparing binary separations to the expected truncation radius. The truncation radii are expected to be 0.3-0.5 $\times$ the orbital separations (Papaloizou et al., 1997; Artymowicz & Lubow, 1994). Instead, we find that the continuum radii are $<$ 0.1 $\times$ the projected orbital separations (see Figure 1, bottom-right panel), confirming the result found by Manara et al. (2019) for Taurus binaries. The tidal truncation radius depends strongly on eccentricity, but Manara et al. (2019) already demonstrated that the eccentricity values would need to be unrealistically high to explain the observed disk sizes by tidal truncation alone.

The observational results presented herein should allow more detailed comparisons to numerical models as those of Zagaria et al. (2021b), which can in principle explain disks smaller than the truncation radii in terms of grain growth and radial drift in binary systems. They compared the observed disk sizes in binary systems in Taurus (from Manara et al. (2019)) and Ophiuchus (from Cox et al. (2017)) and obtained good agreement with their models (Zagaria et al., 2021a), but concluded that more resolved disks were needed to derive more robust conclusions. We note that our results in Ophiuchus are highly complementary to those studied by Zagaria et al. (2021b) because our disk sizes come from binaries with projected separations smaller than 200 au, while resolved disk from Manara et al. (2019) and Cox et al. (2017) correspond to disks in binaries with separations larger than 200 au (see Figure 1, bottom-right panel).²²2 With the exception of Elias 2-33 (a.k.a ODISEA$\_$C4$\_$94), all the disks in binaries were known and had ALMA observations (e.g., from Cox et al. 2017 and Zurlo et al. 2021). However, most disks in close binaries were previously unresolved and lacked disk measurements.

Detailed comparisons of disk sizes to the outer architectures of extrasolar planetary systems are also highly desirable, but our ability to detect extrasolar planets at separations beyond $\sim$5 au remains very limited, especially around binary systems. For instance, the detection of Uranus and Neptune analogos in extrasolar binary systems is currently restricted to the microlensing technique and few examples exist e.g., Poleski et al. (2014). However, the Nancy Grace Roman Space Telescope will dramatically change this situation (Penny et al., 2019) and should provide statistics on exoplanets at 1-30 au separations around binary systems that could be compared to disk demographic results.

The lack of evolution in continuum disk sizes between embedded objects and Class II sources found in Section 3.3 is very interesting in the context of pressure bumps, grain growth and radial drift. Pressure bumps can trap dust particles, preventing inward drift and enabling growth into larger bodies (Pinilla et al., 2012, 2020). These pressure bumps are consistent with the rings around most of the massive Class II disks observed at high resolutions (Andrews et al., 2018; Long et al., 2018; Cieza et al., 2021) and with the relatively slow evolution of disk sizes seen between 1–10 Myr old systems (Hendler et al., 2020). Our new ALMA observations includes younger, less massive, and smaller disks than the previous studies mentioned above and suggest that these bumps are ubiquitous and must be present from the early stages of disk evolution (age $\lesssim$ 1 Myr). Additional observational evidence supports this idea. For instance, our Band 8 data has enough resolution and signal to noise to show gaps and rings in several disks that were previously considered smooth (Bhowmik et. in prep). The nearby disk around TW Hydra also shows gaps at au scales (Andrews et al., 2016), and even objects at the deuterium fusion limit can show substructures when observed at sufficiently high-enough resolution, e.g., González-Ruilova et al. (2020).

Future observations with ALMA and the ngVLA (Wu et al., 2024) at even higher angular resolution should be able to search for substructures in all the disks that remain smooth in our study. Meanwhile, the observed continuum size distribution can already provide constraints on the locations of the pressure bumps. As shown by Rosotti et al. (2019), disk sizes derived from ALMA continuum observations mostly trace the radius up to which the disks retain grains large enough to emit significantly at (sub)millimeter wavelengths (e.g., the locations of the outermost dust traps). Furthermore, if dust traps are assumed to be caused by the formation of planets (e.g. Zhang et al. (2018), numerical models that combine viscous evolution, planet-disk interactions, grain growth, and radial drift can be used to investigate the observed (lack of) evolution in disk sizes. The output of such models can be postprocessed with radiative transfer to allow for direct comparison to ALMA observations. Such comparisons can then constrain the underlying populations of planets (in terms of masses and semi-major axes) that are needed to reproduce the observed size distribution in our sample of Ophiuchus disks (Orcajo et al. in prep.), bridging the gap between disk demographics and planet population studies.

It is important to consider that our sample excludes all disks with dust masses $\lesssim$ 2 M_⊕. Such disks might have a different population of planets (e.g., mostly terrestrial planets within $\lesssim$ 1 au). Therefore, to obtain a more complete picture and to test the idea that dust disk sizes are mostly regulated by planet formation that halts dust drift, it would be very beneficial to explore the full size distribution of disk in nearby molecular clouds. This is within current capabilities, as ALMA can reach a resolution of $\sim$1 au at 140 pc using its most extended configuration in Band 8.

The measurement of disk sizes as a function of age can also provide valuable constraints on disk evolution models. In particular, viscous models predict that the disk will expand with time, while models of disks driven by magnetic winds find that the disk sizes should remain close to constant (Tabone et al., 2022). However, most continuum ALMA surveys, including ours, lack the sensitivity to detect the faint emission from the outer disk (arising from small dust) to distinguish between the scenarios (Zagaria et al., 2022). Measuring the sizes of the gaseous disk might be a more direct way to distinguish between viscous and magnetic wind models. Trapman et al. (2023) recently found that gas disk sizes are significantly smaller in Upper Sco (age $>$ 5 Myr) than in Lupus and Taurus (Age $<$ 3 Myr). This seems to contradict both viscous and wind-driven evolution and suggests that external photoevaporation could also play an important role on the evolution of disk sizes. Investigating disk sizes as a function of time is one of the main goals of the AGE-PRO ALMA Large Program (ALMA Survey of Gas Evolution of PROtoplanetary Disks; Zhang et al. submitted). Thanks to very deep continuum and molecular line observations, AGE-PRO will help to constrain the importance of viscous spreading, magnetic winds and photoevaporation in disk evolution (Tabone et al. 2024, submitted; Anania et al. 2024, submitted).