A Detached Protostellar Disk around a ∼0.2 M_⊙ Protostar in a Possible Site of a Multiple Star Formation in a Dynamical Environment in Taurus

Figure 1(a) shows the intensity maps of the 0.87 mm continuum and ¹²CO (J = 3–2) observations toward MMS-1 at the angular resolution of ∼018 × 010. MMS-1 is marginally resolved in the dust continuum observation. We deconvolved the source in the image plane by using the point spread function (PSF) of the synthesized beam. The deconvolved size of MMS-1 is (91.1 ± 10.1 mas) × (55.8 ± 4.2 mas), corresponding to (12.8 ± 1.4 au) × (7.8 ± 0.6 au). The peak flux and the total flux are 2.8 mJy beam⁻¹ and 3.6 mJy, respectively, corresponding to the peak H₂ column density and the total mass of 3.1 × 10²³ cm⁻² and 8.3 × 10⁻⁵ M_⊙ with the assumptions of the optically thin emission, the uniform dust temperature of 100 K, and the dust opacity per unit (gas + dust) mass column density, ${\kappa }_{345\mathrm{GHz}}$ = 1.2 × 10⁻² cm² g⁻¹ (Hildebrand 1983; Ossenkopf & Henning 1994; Kauffmann et al. 2008; Paper I), which means that gas-to-dust ratio is assumed to be 100. We have clearly detected the blueshifted and redshifted emission of the ¹²CO (J = 3–2) at MMS-1 (Figures 1(a), (b)) for the first time at the present high-angular resolution. The channel map of the ¹²CO (J = 3–2) is shown in Figure 2. A position angle of the line passing through the emission peaks in each velocity channel is −17°, which is measured counterclockwise relative to the north celestial pole. The angle is nearly perpendicular to that of the bipolar nebula seen in the Spitzer observations (Bourke et al. 2006; Terebey et al. 2009). These gas/dust distributions strongly indicate that the rotating disk-like envelope exists around the very low-luminosity protostar, and the disk orientation is consistent with the direction of the outflow and the bipolar nebula (Paper I). The observed gas components around the systemic velocity of this core (6.15–7.85 km s) are not seen due to the optical thickness of the line.

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As indicated by Paper I, II, our present observations also show that MMS-1 does not have extended high-density envelopes connecting to the disk except for the slightly elongated structures seen toward northwest and east directions in the 0.87 mm continuum (Figure 1(a)). It is to be noted that we cannot detect high-density tracers, H¹³CO⁺ (J = 3–2) and C¹⁷O (J = 3–2), toward MMS-1 even with the higher angular resolution compared with Paper II. These results indicate that the disk may be detached from the surrounding environment although it is located at the center of the dense core whose density is ∼10⁶ cm⁻³. We will discuss possible reasons to realize such an detached disk in Section 4.1.

In this section, we estimate the dynamical mass of the central protostar, M_*, and the physical properties of the disk by comparing the observed ¹²CO spatial/velocity distributions with those of simulated models. The observed highest velocity toward MMS-1 is ∼7 km s⁻¹ with respect to the systemic velocity at ∼2 au from the position of the 0.87 mm continuum peak (Figure 3), and it is comparable to the dynamical velocity (e.g., Kepler velocity) for a M_* of ∼0.1 M_⊙ (=[v²r/G]), indicating that there is a sub-solar mass protostar in this source. However, since the present ALMA observations do not have a sufficient resolution to spatially resolve the disk structure, the comparisons with the simulation of rotating disks are needed to remove the effect of the beam dilution.

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In the present study, we assume a Keplerian rotation, as the simplest modeling approach, to estimate the mass of the protostar and the disk properties. The temperature and density profiles of the simulated models are assumed to be ∝${r}^{-0.5}$ and ∝${r}^{-1}$. Expected line emissions along lines of sight were calculated with radiative transfer equations, assuming the local thermal equilibrium (see, e.g., Ohashi et al. 2014), and then we simulated the ALMA observations in ¹²CO (J = 3–2) and 0.87 mm continuum with the C40-6 configuration, which is the same as in our present observations, using tasks "simobserve" and "simanalyze" in CASA. The free parameters of the model are the central stellar mass (M_*), the disk mass (${M}_{\mathrm{disk}}$), the disk radius (${R}_{\mathrm{disk}}$), the position angle (PA), the inclination angle (i), the kinematic temperature at a radius of 1 au (${T}_{1\mathrm{au}}$), and systemic velocity (${V}_{\mathrm{sys}}$). We adopted the ${V}_{\mathrm{sys}}=6.75$ km s⁻¹ because the high-velocity components are symmetric around this velocity (see Figure 1(b) for the mirrored spectrum). This velocity is also consistent with the systemic velocity of the dense core observed with the single-dish observations (e.g., Onishi et al. 1999). We also adopted the inclination angle = 70° derived from the scattered light seen in the Spitzer (Terebey et al. 2009), and the position angle = −17° as described in Section 3.1. Thus, the remaining free parameters are the M_*, ${R}_{\mathrm{disk}}$, ${M}_{\mathrm{disk}}$, and ${T}_{1\mathrm{au}}$. We tuned the parameters to reproduce the ¹²CO profile at the high-velocity parts because the spectrum is affected by the surrounding dense core toward the source. We derived the optimum values with the following three steps. (1) The peak positions of the ¹²CO (J = 3–2) in each channel (Figure 2) with both the ALMA observations and the synthetic observations of Keplerian models are derived by 2D Gaussian fitting. Based on the plots of the relative velocities to the systemic velocity with respect to the projected distances from the 0.87 mm continuum peak in MMS-1, the parameters of the model were adjusted to match the observations (Figure 3). Similar data analysis was carried out in Tobin et al. (2012). The braking of the power law around ∼5 au in Figure 3 is due to the superposition of rotation velocities projected to our line of sight at large radii (see also Tobin et al. 2012). M_* is basically constrained by the highest velocity and ${R}_{\mathrm{disk}}$ is by the breaking distance. These parameters are insensitive to ${M}_{\mathrm{disk}}$ and ${T}_{1\mathrm{au}}$. We initially assumed ${M}_{\mathrm{disk}}$ of 8 × 10⁻⁵ M_⊙ and ${T}_{1\mathrm{au}}$ of 200 K for the simulation, and iterate the simulation after steps (2) and (3). (2) We then fitted the ${T}_{1\mathrm{au}}$ to reproduce the intensity of the spectrum at high-velocity parts. ${M}_{\mathrm{disk}}$ does not affect the intensity, because the disk is optically thick in ¹²CO. (3) The remaining parameter, ${M}_{\mathrm{disk}}$, was calculated to reproduce the observed 0.87 mm continuum flux by assuming the temperature distribution derived in step (2). The derived optimum values of the Keplerian disk model are M_* = 0.18 M_⊙, ${R}_{\mathrm{disk}}=9\,\mathrm{au}$, ${M}_{\mathrm{disk}}=8\times {10}^{-5}\,{M}_{\odot }$ and ${T}_{1\mathrm{au}}=180$ K. Our observation and model agree reasonably well (see also the channel maps in Figure 2 and the P-V diagram in Figure 4). The uncertainty of the M_* in this analysis is roughly ±0.05 M_⊙. The inner slopes of models with the M_* = 0.13, 0.23 M_⊙, which have the same other parameters as shown above, are also plotted in Figure 3 for the comparison.

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We note that we simulated only the disk component, although the source is heavily embedded in a dense core. This difference is seen in the spectrum mainly around the systemic velocity (4.45–9.55 km s⁻¹); the dense core is observed in this velocity range. In the redshifted (>12.10 km s⁻¹) range, ¹²CO (J = 3–2) observations in Paper II also failed to detect a redshifted outflow seen in the HCO⁺ (J = 3–2) (Paper I) in the same velocity range due to the absorption by the foreground gas component of the dense core (see also Section 3.3 in Paper II). It is likely that the redshifted (>12.10 km s⁻¹) gas components of the disk are not seen for the same reason. Our simulation also assumed the symmetric gas distribution of the disk. There is a slight excess in the observed profile against the model at −0.65 km s⁻¹ (Figure 1(b)). This may be due to the asymmetry of the gas distribution or to the existence of the velocity component in the same line of sight. The detailed disk properties is a subject of the future high-angular resolution observations.

Recent interferometric observations have been reporting diversities of Keplerian disks around Class 0/I protostars. Some sources have the disk radii of 50–350 au with the masses of 10⁻³–10⁻¹ M_⊙ (e.g., Tobin et al. 2012; Ohashi et al. 2014; Aso et al. 2017; Yen et al. 2017); however, others have no Keplerian disks (e.g., Yen et al. 2015). While MHD simulations of disk formation (e.g., Tomida et al. 2017) tend to predict heavy disks, young circumstellar disks have various masses and sizes. The natures of disk at early stage of star formation are not fully understood so far.

The central stellar mass of ∼0.2 M_⊙ in MMS-1 is not much different from other Class 0/I objects, and, on the other hand, the disk mass is more than an order of magnitude smaller than those of the Keplerian disks around them. Such small disk mass is normally seen around T Tauri stars (Andrews & Williams 2005). Because MMS-1 is indeed embedded at the center of the centrally concentrated dense core, it is considered to be still at an early stage of star formation rather than evolved objects. The presence of the small disk seen in MMS-1 may be a key to understand the above mentioned diversities of the Keplerian disks around the Class 0/I sources.

The low luminosity of MMS-1 indicates a low mass accretion rate. Even if the luminosity of MMS-1 is dominated by the accretion luminosity, the mass accretion rate is estimated to be quite low as <2 × 10⁻⁸ M_⊙ yr⁻¹ with the assumption of a stellar radius of 1.5 R_⊙. This is consistent with the fact that the outflow activity is quite low (Paper I, II), although a much higher mass accretion rate is needed to form a ∼0.2 M_⊙ protostar within a timescale of the dense core, ∼4 × 10⁵ years (e.g., Onishi et al. 2002). The existence of the large bipolar nebula with the size scale of >1000 au seen in the Spitzer observations (Bourke et al. 2006; Terebey et al. 2009) may be evidence of such large accretion activities in the past. In Paper II, we argued the observed density profile of MC27/L1521F, which follows n(r) ∝ ${r}^{-1.4}$ in the inner 3000 au and ∝${r}^{-2.0}$ outward of 3000 au, cannot be explained by the inside-out collapse model (Shu 1977), as the central protostar was considered to be at a very young evolutionally stage with an age of ≲10⁴ years and the mass of <0.1 M_⊙. We reconsider here the protostar formation with the mass of ∼0.2 M_⊙ in this system. In the inside-out collapse model, the expansion wave propagates outward with a sound speed of 0.2 km s⁻¹ at 10 K. The timescale of the expansion wave reaching the breaking radius of 3000 au becomes 7 × 10⁴ years. If we assume the accretion rate after the protostar core formation to be 1.6 × 10⁻⁶ M_⊙ yr⁻¹ (Shu 1977), the mass of the formed star becomes ∼0.1 M_⊙ within the timescale; the inside-out collapse model can explain the observed density profile in this case. If we assume the higher accretion rate to be 1 × 10⁻⁵ M_⊙ yr⁻¹ (Larson 1969; Hunter 1977), the timescale becomes much shorter to achieve the present observed stellar mass, and the expansion wave cannot reach the slope breaking radius of 3000 au.

Although we cannot clearly describe the mechanisms to create the detached disk without the significant mass accretion at an early stage of star formation so far, a highly dynamical (turbulent) environment seen in this system (Paper I, II) may be a hint to understand the formation of the disk. Several truncated disks with a size scale of ∼10 au toward young brown dwarfs (Ricci et al. 2012; Testi et al. 2016) have been also reported with ALMA. Testi et al. (2016) suggested that such truncated disks created by dynamical interactions (Bate 2009, 2012). They also confirmed the disk sizes in ρOph, a cluster-forming region, are much smaller than those in Taurus, which is a relatively quiescent star-forming region, due to their different environments. Our present target, MC27/L1521F, is also located in Taurus, however, the central region shows highly complex spatial/velocity structures compared to other isolated protostellar cores (e.g., Ohashi et al. 2014; Evans et al. 2015; Yen et al. 2015), indicating that it resides in the dynamical environment (Paper I, II). There is a possibility that the intrinsically larger disk was stripped by the surrounding gas in the turbulent environment (Paper I). The present ¹²CO (J = 3–2) observations also found very high-temperature (∼50 K) gas component at several hundred au away from MMS-1, indicating that there was shock heating possibly caused by interactions among the turbulent gases. The detailed results will be presented in a forthcoming paper (K. Tokuda et al., in preparation).

We discuss future evolution of MMS-1. Recent numerical simulations that follow evolution of an isolated dense core to a protostar predicted that the mass accretion onto the protostar takes place through the surrounding disk structures (e.g., Machida et al. 2008). The observed disk in MMS-1 is very small, indicating that further significant mass accretion through the disk does not occur anymore. Thus, we may be witnessing a stage close to the moment when the accretion activity has been halting.

In this section, we discuss how the low luminosity of <0.1 L_⊙ is possible for a ∼0.2 M_⊙ protostar. According to the classical evolutionary tracks of pre-main-sequence stars (e.g., Baraffe et al. 1998), it takes >1 Myr for a ∼0.2 M_⊙ protostar to reach a luminosity of <0.1 L_⊙. The timescale is much longer than that expected by the present observations as discussed in Section 4.1. The possible scenario to overcome this issue is thus either the accretion mechanism is different from that or the intrinsic luminosity is underestimated. The uncertainty of the luminosity may come from the incomplete modeling in an environment of a high ISRF luminosity (${L}_{\mathrm{bol}}=0.36\,{L}_{\odot }$) and/or an anisotropic radiation from the optically thick disk, although Bourke et al. (2006) and Terebey et al. (2009) claim that it is unlikely that the intrinsic luminosity exceeds 0.07 L_⊙. The stellar luminosity can be very low even just after the accretion ceases when the accreting gas provides very low entropy (cold accretion; Hartmann et al. (1997), Hosokawa et al. (2011), Baraffe et al. (2012), Vorobyov et al. (2017), Kunitomo et al. (2017) and references therein). We calculated the evolution of the stellar luminosity with the cold accretion by using the numerical code described by Hosokawa & Omukai (2009) and Hosokawa et al. (2010, 2011). We used a fixed accretion rate of 10⁻⁵ M_⊙ yr⁻¹ until the star has reached the mass of 0.2 M_⊙, and then we stopped the accretion and tracked the evolution of pre-main-sequence star. For the cold accretion case, the luminosity depends on the initial stellar radius. Our calculation starting with a 0.01 M_⊙ star with the initial radius of 0.65 R_⊙ reproduces the observed luminosity (∼0.07 L_⊙) in <10⁵ years after we stop the mass accretion. In this case, we note that much smaller initial stellar radius than that calculated by Masunaga & Inutsuka (2000), 4 R_⊙, is required to produce the low luminosity. As described above, it is possible, in principle, to make the luminosity of a very young 0.2 M_⊙ protostar less than 0.1 L_⊙ just after the end of mass accretion if we adopt the cold accretion model. Mechanisms to create such small stellar core and environments that enable the cold accretion are currently unknown. Although more observations toward similar objects are required to obtain a conclusive interpretation of these objects, the present observation provides a challenge to the current theory for the formation and early evolution of a protostar.