Early Planet Formation in Embedded Disks (eDisk) V: Possible Annular Substructure in a Circumstellar Disk in the Ced110 IRS4 System

The 1.3 mm dust continuum emission maps are presented in Figure 1. Figure 1(a) shows two compact peaks that are associated with a main protostar, Ced110 IRS4A, and a fainter companion, Ced110 IRS4B, which has not been reported in previous lower-sensitivity observations. The projected distance between the two sources is $\sim$1$\farcs 3$ ($\sim$250 au). In addition to the two compact emission around Ced110 IRS4A and IRS4B, an extended emission ($\sim$2^′′ in radius) is detected at $\sim$5$\sigma$ around ($\Delta\mathrm{RA},~{}\Delta\mathrm{Dec})=(-3^{\prime\prime},7.5^{\prime\prime})$ on the northern side of the protostellar system in a wider view of the 1.3 mm continuum map, presented in Figure 1(b). An arc-like structure with a marginal detection at 3$\sigma$, extending from RA offset of $2\farcs 5$ to $-2\farcs 5$, is connecting to the extended emission.

The primary emission, that is associated with Ced110 IRS4A, exhibits a flattened, disk-like shape (Figure 1(c)), and likely traces the circumstellar disk around the protostar. The peak brightness temperature of the emission is $\sim$79 K. The peak position is measured through the Gaussian fitting to be $(\mathrm{RA},~{}\mathrm{Dec})=(11^{\mathrm{h}}06^{\mathrm{m}}46\fs 3682,~{}-77^{\circ}22\arcmin 32\farcs 882)$. We adopt this position for the coordinates of Ced110 IRS4A and for the map center throughout this paper. The continuum emission does not show any clear substructures such as rings or gaps often found in Class $\mathrm{II}$ disks (e.g., Andrews et al., 2018), despite the angular resolution of $\sim$0$\farcs 05$ ($\sim$10 au).

The secondary emission, that is associated with Ced110 IRS4B, also shows a flattened, disk-like shape (Figure 1(d)) and likely arises from the dust disk around Ced110 IRS4B, whereas it is not spatially well resolved along its minor axis. The emission around Ced110 IRS4B is less bright than the one around Ced110 IRS4A, and the peak brightness temperature is $\sim$9 K. It exhibits three intensity peaks separated by $\sim\negthickspace 0\farcs 05$ (or $\sim\negthickspace 9~{}\mathrm{au}$) along its major axis, but the distinction of these peaks is marginal. The difference in the intensity between the three peaks and the dips between the peaks is $\sim$1–3$\sigma$. The position of Ced110 IRS4B is measured through the Gaussian fitting to be $(\mathrm{RA},~{}\mathrm{Dec})=(11^{\mathrm{h}}06^{\mathrm{m}}46\fs 7718,~{}-77^{\circ}22\arcmin 32\farcs 757)$.

We measured flux densities and dust disk radii to characterize the dust disks of Ced110 IRS4A and IRS4B. The flux densities were measured with elliptical apertures, whose semi-major axes were determined by the curve-of-growth method (Ansdell et al., 2016). In this method, we applied larger apertures until the measured flux density converges. The aperture shapes were assumed based on inclination and position angles of the dust continuum emission, which are derived in Section 4.1. The adopted final apertures and measured flux densities are summarized in Table 3. Uncertainties of the flux densities are statistical errors derived through the error propagation of the rms noise, and do not include the absolute flux calibration error, which is typically 10% for ALMA Band 6 observations. The dust disk radii were also estimated with the curve-of-growth method. We adopted a definition of the dust disk radius that was used in the Lupus Class $\mathrm{II}$  disk survey (Ansdell et al., 2016), where the dust disk radius encloses 90% of the flux density. Following the method of the Lupus survey, uncertainties of the dust disk radii are calculated by taking the range of radii within the uncertainties of the 90% flux densities. The estimated dust disk radii of Ced110 IRS4A and IRS4B are $\sim\negthickspace 91.7\pm 0.2~{}\mathrm{au}$ (or $\sim\negthickspace 0\farcs 485\pm 0\farcs 001$) and $\sim\negthickspace 33.6\pm 0.6~{}\mathrm{au}$ (or $\sim\negthickspace 0\farcs 178\pm 0\farcs 003$), respectively.

Dust masses were calculated from the measured flux densities, assuming that the dust continuum emission is optically thin. We adopt the dust opacity of $2.3~{}\mathrm{cm}^{2}~{}\mathrm{g}^{-1}$ (Beckwith et al., 1990) with the gas-to-dust mass ratio of 100. Two different dust temperatures are adopted: a temperature of 20 K which represents a characteristic temperature of Class $\mathrm{II}$ disks (Andrews & Williams, 2005), and a temperature of 43 K which is derived from an empirical scaling relation of $T_{\mathrm{dust}}=43(L_{\mathrm{bol}}/1~{}L_{\odot})^{0.25}$ representing the averaged temperature of disks embedded in envelopes (Tobin et al., 2020). Note that the peak brightness temperature of the primary emission is much higher than these averaged temperatures of disks, suggesting that an inner part of the emission is optically thick, and thus the derived mass would be a lower limit. The estimated dust masses are presented in Table 3. Uncertainties are calculated through the error propagation of the statistical errors of the flux densities. The dust mass of Ced110 IRS4A of $97.43~{}M_{\oplus}$ assuming 20 K is much larger than the typical dust mass of Class $\mathrm{II}$ disks of $\sim$1 $M_{\oplus}$ adopting the same temperature and a similar dust opacity (Andrews et al., 2013; Ansdell et al., 2016, 2018; Barenfeld et al., 2017; Pascucci et al., 2016; Long et al., 2018b; Ruíz-Rodríguez et al., 2018; Cieza et al., 2019; Williams et al., 2019; Akeson et al., 2019; Andrews, 2020). On the other hand, it agrees with the typical dust mass of Class 0 sources of $\sim$110 $M_{\oplus}$ under similar assumptions on the temperature and dust opacity (Tobin et al., 2020). The flux density and dust mass of Ced110 IRS4B are smaller than those of Ced110 IRS4A approximately by two orders of magnitude and similar to the minimum value among the Orion Class 0 sources (Tobin et al., 2020). As Ced110 IRS4B exhibits very small flux (and dust mass), we also compare its flux density with those measured in protostars with low masses or low luminosities. The flux density of Ced110 IRS4B is smaller than the typical 1.3 mm flux densities measured for disks around substellar-mass or low-mass protostellar objects ($M_{\ast}\lesssim 0.1~{}M_{\odot}$; Lee et al., 2018; Hsieh et al., 2019; Riaz et al., 2019; Aso et al., 2023) by a factor of $\sim\negthickspace 5$, but is comparable to those reported for disk components of very low-luminosity objects ($1.3\pm 0.4~{}\mathrm{mJy}$ in L1521F and $3.6\pm 1~{}\mathrm{mJy}$ in IRAM 04191; Maury et al., 2019). Hence, the dust mass of Ced110 IRS4B is smaller than or comparable to the dust mass of these low-mass or low-luminosity protostellar systems, when the same dust temperature and opacity are adopted.

In order to investigate structures of the continuum emission in more detail, we present one-dimensional intensity profiles along their major and minor axes with the cut width corresponding to the size of one pixel ($\sim$1$/10$ beam size) in Figures 2 and 3. The position angles of $104^{\circ}$ and $85^{\circ}$ were adopted for the primary and secondary continuum emission, respectively, which were derived through fitting of intensity-distribution models in Section 4.1. The intensity profile along the major axis for Ced110 IRS4A, presented in Figure 2(a), interestingly, shows bumpy plateaus at a radius of $\sim$0$\farcs$2–0$\farcs$4, where the intensity distributions are close to flat. It also shows an asymmetry across a radial range of $0\farcs 05$–$0\farcs 4$, where the emission on the eastern side of the protostar is brighter than on the western side by $\sim$6$\sigma$ on average. An asymmetry is also clearly seen along the minor axis in Figure 2(b), where the emission on the southern side is significantly stronger than on the northern side. The intensity profiles for the continuum emission of Ced110 IRS4B are presented in Figure 3. The intensity profile along the continuum major axis for Ced110 IRS4B shows three intensity peaks, although these structures are not significant considering the rms noise level shown as a shaded region. The shape of the intensity profile along the minor axis is not well resolved.

Moment maps of the C¹⁸O, ¹³CO, ¹²CO $J=2$–1 and SO $J_{N}=6_{5}$–$5_{4}$ lines are presented in Figure 4–7. Moment maps of other lines are shown in Appendix A. The moment zero and one maps are calculated by integrating emission detected above $3\sigma$.

The C¹⁸O emission is detected around Ced110 IRS4A, as shown in Figure 4(a). The emission exhibits a flattened shape with a size comparable to that of the continuum emission and an apparent deficit of emission at the protostellar position. The deficit of emission at the center is caused because the cold, foreground line emission absorbs the continuum emission around the line center and thus the continuum is over-subtracted. Indeed, in the velocity channel maps shown in Figure 14, negative emission is clearly seen at the position of Ced110 IRS4A at 3.85–4.52 $\mathrm{km\ s^{-1}}$, where most of the C¹⁸O emission is resolved out. In the moment one map presented in Figure 4(b), a clear velocity gradient is seen along the direction of the continuum elongation across the protostar, suggesting a rotational motion of its disk and/or an envelope. The C¹⁸O emission is also detected around Ced110 IRS4B at $\geq 3\sigma$. Figure 4(c) and (d) show wider views of the moment zero and one maps, respectively. An extended emission at the northern side of the protostar and an arc-like structure connecting to the extended component are observed at $5\sigma$ in the C¹⁸O emission. These structures are very similar to the north-extended and arc-like structures of the 1.3 mm continuum emission. The extended C¹⁸O emission on the northern side has a similar extent to that of the continuum emission ($\sim$2^′′ in semi-major axis). The arc-like structure is more clearly seen in the C¹⁸O emission over a velocity range of 4.85–5.86 $\mathrm{km\ s^{-1}}$ (see also Figure 17), and appears to be one-fourth of a circle across east to north. A clear velocity gradient is seen along the arc-like structure and the northern extended component.

The ¹³CO emission is detected around Ced110 IRS4A as well as the C¹⁸O emission, as seen in moment zero and one maps in Figure 5(a) and (b). The overall features of the ¹³CO emission associated with Ced110 IRS4A are similar to that of the C¹⁸O emission: the ¹³CO emission shows an elongated shape and a velocity gradient in a direction similar to the direction of the continuum elongation, suggesting rotation of a disk and/or an envelope. The moment zero map of the ¹³CO emission also exhibits an apparent deficit of emission at the central, which is likely due to the continuum over-subtraction with the cold, foreground line emission around the line center (see Figure 15). In addition to these structures, the ¹³CO emission exhibits four peaks at the edge of the continuum emission of Ced110 IRS4A, making a dark lane along the continuum major axis at radii of $0\farcs 1$–$0\farcs 5$. These features are not seen in the C¹⁸O emission. The four peaks are slightly asymmetric and the emission on the northern side is brighter. These features suggest that the ¹³CO emission around the Ced110 IRS4A originates mainly from the disk surface. This point is discussed in more detail in Section 5.1.2. The ¹³CO emission is also seen around Ced110 IRS4B, but it is much more extended than the continuum emission and connected to Ced110 IRS4A. Figure 5(c) and (d) show wider views of the moment zero and one maps of the ¹³CO emission. Extended structures of the ¹³CO emission are more complex than those of the C¹⁸O emission. The ¹³CO emission does not show a component corresponding to the arc-like structure found in the C¹⁸O and continuum emission. This could be because the arc-like structure is mostly obscured by optically-thick, extended foreground gas in the ¹³CO emission, as the emission at the velocity range of 3.85–5.52 $\mathrm{km\ s^{-1}}$ is resolved out in the velocity channel maps in Figure 18. The ¹³CO emission shows the arc-like structure only at a velocity of 5.86 $\mathrm{km\ s^{-1}}$ in the velocity channel maps.

The ¹²CO emission shows four intensity peaks around Ced110 IRS4A and a dark lane along the continuum major axis, as the ¹³CO emission does, but more clearly in Figure 6(a). The two intensity peaks on the northern side of the continuum emission are brighter than those on the southern side. In Figure 6(b), a clear velocity gradient appears along the continuum elongation around Ced110 IRS4A, as was seen in the C¹⁸O and ¹³CO emission. The ¹²CO emission is also extended around Ced110 IRS4B. On larger scales, as presented in Figure 6(c) and (d), the ¹²CO emission is extended from east to west around Ced110 IRS4A with a clear velocity gradient. The ¹²CO emission is resolved out over a velocity range of 3.50–5.41 $\mathrm{km\ s^{-1}}$ (see Figure 19), and thus does not show any structures corresponding to the arc-like structures found in the continuum and C¹⁸O emission. No clear outflow from Ced110 IRS4A and IRS4B is seen in the ¹²CO emission, though ¹²CO emission is a typical tracer of outflows around protostars.

The SO emission is not detected around Ced110 IRS4A or IRS4B, but it shows an arc-like structure with a velocity gradient along the structure in Figure 7, as in the case of the C¹⁸O and continuum emission. The SO arc-like structure appears within the same velocity range of 4.85–5.86 $\mathrm{km\ s^{-1}}$ as that of the C¹⁸O emission. The SO emission also exhibits a blue-shifted component at a distance of $\sim\negthickspace 6^{\prime\prime}$ ($\sim\negthickspace 1000~{}\mathrm{au}$) on the southern side of the Ced110 IRS4 system.

Rotational motions are clearly seen in CO isotopologue lines around Ced110 IRS4A. These lines are also detected around Ced110 IRS4B, although they do not show clear velocity gradients around the protostar in the moment one maps. In this subsection, rotational motion around the protostars are investigated in more detail using the C¹⁸O and ¹³CO lines, which are less affected by the absorption by the foreground cloud and imaged with higher velocity resolutions by a factor of four than the ¹²CO line.

The rotation curves derived in Section 4.2 suggest that the inner region within a radius of $\sim$120 au around Ced110 IRS4A is part of a Keplerian disk. Thus, the dust continuum emission of Ced110 IRS4A with a radius of $\sim\negthickspace 91.7~{}\mathrm{au}$ would also originate from a disk rather than a surrounding envelope. In the following subsections, we discuss the structures of the dust disk of Ced110 IRS4A based on the observed dust continuum structures and the orientation of the disk.

The SO and C¹⁸O emission show arc-like structures on the northern side of the protostellar system at a radius of $\sim$1100 au ($\sim$6^′′). A similar structure is also seen in the other lines, H₂CO and $c$-C₃H₂ of our data (see Appendix A) and at near-infrared wavelengths (Pontoppidan & Dullemond, 2005). A possible interpretation of this structure is a shocked shell caused by an outflow, as the SO line is often considered as a shock tracer (Bachiller & Pérez Gutiérrez, 1997; Wakelam et al., 2005). The arc-like structure is seen at LSR velocities of 4.69–6.02 $\mathrm{km\ s^{-1}}$ (see Figure 17 and 20), which are red-shifted with respect to the systemic velocity of 4.67 $\mathrm{km\ s^{-1}}$. This is opposite to the disk orientation inferred from the CO emission but consistent with the orientation of the reflection nebula and the large-scale outflow on scales of $\geq 1000$ au (Zinnecker et al., 1999; Pontoppidan & Dullemond, 2005; Hiramatsu et al., 2007). Thus, the arc-like structure could be formed by the large-scale outflow ejected in past. The LSR velocities of the arc-like structure correspond to velocities of about zero to 1.3 $\mathrm{km\ s^{-1}}$ relative to the systemic velocity. The highest velocity of the arc-like structure is comparable to the escape velocity of 1.37–1.50 $\mathrm{km\ s^{-1}}$ at the radius of $\sim$1130 au, assuming the protostellar mass of 1.21–$1.45~{}M_{\odot}$. Although the inclination angle of the arc-like structure is uncertain as it is not necessarily aligned with the disk normal, the inclination angle of the system is estimated to be $70\pm 5^{\circ}$ to explain the color gradient of the reflection nebula (Pontoppidan & Dullemond, 2005). Assuming $i=70^{\circ}$, the deprojected velocity of the arc-like structure can be up to $\sim$3.8 $\mathrm{km\ s^{-1}}$ with respect to the systemic velocity and much higher than the escape velocity. Thus, this structure could be moving outward to escape from the system.

An infalling flow could be another possible origin of the arc-like structure, as non-axisymmetric, infalling flows are reported in a couple of protostellar systems (e.g., Yen et al., 2014, 2019; Garufi et al., 2022; Thieme et al., 2022). However, the trajectory of the arc-like structure is not connected to the disks associated with either Ced110 IRS4A or IRS4B. Moreover, the largest velocity of the arc-like structure is close to the escape velocity. Considering that the trajectory of the arc-like structure is not quite along the line of sight, the observed velocity would be too high for the arc-like structure to be accreted onto the protostellar system. The arc-like structure could also be a part of a filamentary structure of the foreground cloud. However, previous single-dish observations of the parental cloud in N₂H⁺ show that it has an LSR velocity of around 4.3 $\mathrm{km\ s^{-1}}$, which is smaller than the highest velocity of the arc-like structure by 1.7 $\mathrm{km\ s^{-1}}$. Hence, the arc-like structure would not likely be a part of a filamentary structure in the foreground cloud.

The binary system consisting of Ced110 IRS4A and IRS4B with a projected separation of $\sim$250 au is spatially resolved from the current observations. The properties of the two protostars are summarized in Table 7. The stellar mass ratio ($q=M_{2}/M_{1}$, where $M_{1}$ and $M_{2}$ are the primary and secondary stellar masses, respectively) of $\sim\negthickspace 0.03$ is much smaller than typical values in Class $\mathrm{II}$ multiple systems ($q\gtrsim 0.1$; Woitas et al., 2001; Manara et al., 2019) but similar to those of Class $\mathrm{II}$ binaries with planetary mass companions (e.g., GQ Lup; Wu et al., 2017). Given the relatively close sky separation, structures of the disks might be affected by the dynamical interaction between the two protostars, as it is hinted in Class $\mathrm{II}$ sources (e.g., Manara et al., 2019; Zurlo et al., 2020, 2021). A survey observation of 32 Class $\mathrm{II}$ disks in the Taurus star-forming region has revealed that circumstellar dust disks in multiple systems of their samples ($q\gtrsim 0.1$) tend to be smaller than those around single sources (Manara et al., 2019), which may suggest that the disks in the multiple systems are truncated by the dynamical interaction (e.g., Papaloizou & Pringle, 1977; Artymowicz & Lubow, 1994; Rosotti & Clarke, 2018). The maximum dust disk radius in these multiple systems was $\sim\negthickspace 80~{}\mathrm{au}$ and the ratio between the dust disk radius and the projected separation ($R/a$) was always less than $0.3$ (Manara et al., 2019). Similar trends and maximum dust disk radii have been also observed in the surveys of Class $\mathrm{II}$ disks in the Lupus and Ophiuchus star-forming regions (Zurlo et al., 2020, 2021). In these studies of Class $\mathrm{II}$ disks, the disk radius is defined as the radius enclosing 90% or 95% of the flux density, similar to our study.

The dust disk radius of Ced110 IRS4A is larger than the maximum dust disk radius found in the Class $\mathrm{II}$ multiple systems mentioned above. The ratio between the dust disk radius and the projected separation for Ced110 IRS4A ($R/a\negthinspace\sim\negthinspace 0.37$) is also larger than those reported in the Class $\mathrm{II}$ sources. On the other hand, the disk radius and $R/a$ of Ced110 IRS4B are in the range of those of the Class $\mathrm{II}$ multiple systems. These results could be due to the small stellar mass ratio of $q\negthinspace\sim\negthinspace 0.026$ observed in Ced110 IRS4. In a system with a smaller stellar mass ratio, dynamical interaction is expected to have a stronger effect on the disk around the secondary star but a less impact on the disk around the primary source (Papaloizou & Pringle, 1977; Rosotti & Clarke, 2018). It should be, however, noted that dust disk size can be also smaller than gas disk size due to radial drift of large dust grains (Weidenschilling, 1977). This may also explain the larger dust disk of Ced110 IRS4A compared to those of the Class $\mathrm{II}$ multiple systems, since more radial drift would likely occur in more evolved disks. To estimate the expected truncation radius, we follow an analytic formula in Manara et al. (2019). Assuming the stellar mass ratio of 0.03 and a non-eccentric orbit, we obtain truncation radii for the disks of Ced110 IRS4A and IRS4B to be $\sim\negthickspace 140~{}\mathrm{au}$ and $\sim\negthickspace 30~{}\mathrm{au}$, respectively. The truncation radius calculated for Ced110 IRS4B is comparable with the observed dust disk radius. The expected truncation radius can be smaller approximately by a factor of two if we adopt an eccentricity of $\sim\negthickspace 0.3$ (Manara et al., 2019). Thus, the observed disk radius of Ced110 IRS4A could be also consistent with the tidal truncation if the binary orbit has an eccentricity between zero to 0.3. So far, no observations have constrained the binary orbit of Ced110 IRS4. More observations to reveal orbital motions of the protostars are required in order to evaluate how the disk is affected by the dynamical interaction of two protostars in more detail.

Although the binary orbit is unknown, the line-of-sight velocity difference of the protostars of $\sim$2.1 $\mathrm{km\ s^{-1}}$ agrees with the expected Keplerian velocity of 2.1–2.3 $\mathrm{km\ s^{-1}}$ at a radius of 250 au from Ced110 IRS4A, assuming the protostellar mass of Ced110 IRS4A of 1.21–1.45 $M_{\odot}$ and that the two protostars are gravitationally bound. This may suggest that the orbital plane of the binary system is close to edge-on as well as the circumstellar disks, although more observational constraints on the binary orbit, such as proper motions, are necessary for confirming this. Ced110 IRS4B is on the eastern side of Ced110 IRS4A and has a blue-shifted velocity with respect to Ced110 IRS4A. Similarly, the CO isotopologue lines show blue-shifted velocities on the eastern sides both of Ced110 IRS4A and IRS4B with respect to their systemic velocities. This indicates that the orbital motion of Ced110 IRS4B and rotational motions of the disks/envelopes of Ced110 IRS4A and IRS4B are all in the same direction.

The relatively small projected separation of $\sim$250 au can be consistent with both disk fragmentation due to gravitational instability (Adams et al., 1989; Bonnell & Bate, 1994) and turbulent fragmentation of dense cores (Offner et al., 2010; Lee et al., 2019), as companions formed via turbulent fragmentation can migrate inward from thousands au to less than 100 au within a time scale of a few 10 kyr (Offner et al., 2010; Lee et al., 2019). However, the ordered rotational motions and the large difference in protostellar and disk masses in the Ced110 IRS4 system would favor disk fragmentation over turbulent fragmentation. Although the disks around the two protostars are slightly misaligned by $\sim\negthickspace 19\pm 0.6^{\circ}$, which is naturally expected in turbulent fragmentation of dense cores (Padoan & Nordlund, 2002; Bate et al., 2010; Offner et al., 2010), such small misalignment of $\lesssim 20^{\circ}$ can also appear in multiple systems formed via disk fragmentation (Stamatellos & Whitworth, 2009; Bate, 2018).