SUBARCSECOND ANALYSIS OF THE INFALLING–ROTATING ENVELOPE AROUND THE CLASS I PROTOSTAR IRAS 04365+2535

Figure 1(a) shows an image of the continuum emission at 260 GHz. The peak position derived by the two-dimensional Gaussian fit is (α₂₀₀₀, δ₂₀₀₀) = (04^h39^m352, 25°41'4419). The size of the distribution is 075 × 052 with a position angle of 19°. Hence, the image is marginally resolved (040 × 032 for the deconvolved size). The peak flux is determined to be 166.9 ± 0.9 mJy beam⁻¹ from the Gaussian fit, while the integrated flux is 268.2 ± 2.3 mJy. The integrated flux is almost consistent with those reported by Harsono et al. (2014; 164 mJy at 220 GHz) and Aso et al. (2015; 182.1 mJy at 225 GHz), considering the difference of the frequency and a β index of 1.46 (Chandler et al. 1998).

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Figure 1(b) shows the moment 0 map of CS (J = 5 – 4). The CS distribution is extended toward the northeastern direction, and also shows clear concentration to the protostar with a size scale of 300 au. The distribution is fairly asymmetric even in the centrally concentrated component, where the northeastern part is brighter. The extended component in the northeastern part has a typical velocity of 5.8 km s⁻¹. A systemic velocity of this source is 6.5 km s⁻¹, which is an average of the reported values (Brown & Chandler 1999; Yen et al. 2013; Harsono et al. 2014), and hence the 5.8 km s⁻¹ component traces the blueshifted gas associated with the protostar. The corresponding redshifted component does not appear, probably linked to the asymmetric gas distribution.

Figure 1(b) shows the moment 1 map superposed on contours of the moment 0 map. A clear velocity gradient can be seen, where the northeastern and southwestern parts are blueshifted and redshifted, respectively. This clearly confirms the rotation motion of the disk/envelope system around the protostar. Figure 1(a) shows the distributions of the most blueshifted component and the most redshifted component (3.5 km ${{\rm{s}}}^{-1}\gt |$δV$| \gt$ 2.5 km s⁻¹) on the continuum distribution, where δV denotes the velocity shift from the systemic velocity. The peaks of these two components do not coincide with the peak of the continuum emission, and these three peaks are aligned on a single line. This situation is similar to that observed for the C¹⁸O (J = 2 – 1) emission by Aso et al. (2015). We determined the position angle (PA) of the disk/envelope system to be 70° using this line. It is consistent with that reported by Harsono et al. (2014; −115°, corresponding to 65° in our definition) and that reported by Aso et al. (2015; 73°).

The position–velocity (PV) diagrams along the envelope direction and along the line perpendicular to it through the protostar position (outflow direction) are shown in Figure 2(a). In the PV diagram along the envelope, a clear spin-up feature is seen toward the protostar. The rotation motion traced by CS abruptly disappears around the radius of 50 au from the protostar, while rotation is still evident to smaller radii in the C¹⁸O emission (Aso et al. 2015). In addition, a counter velocity component caused by the infalling motion is seen in the northeastern part. Although the corresponding counter velocity component in the southwestern part is missing, this may be due to the asymmetrical distribution of the infalling gas around the protostar. More importantly, the velocity gradient is evident along the outflow direction. All these characteristic features seen in the CS emission cannot be explained by a Keplerian disk but, in contrast, strongly suggest an infalling–rotating envelope.

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Here, we analyzed the PV diagram with a simple ballistic model of an infalling–rotating envelope, which was previously applied to L1527 (Sakai et al. 2014a, 2014b; Oya et al. 2015) and IRAS15398-3359 (Oya et al. 2014). In the ballistic model, the infalling velocity takes its maximum at the centrifugal radius, r_CR (twice the radius of the centrifugal barrier, r_CB), where the infalling velocity is equal to the rotation velocity. The rotation velocity increases by a factor of 2 from r_CR to r_CB. Toward the protostar position, only the infalling velocity can be measured, and we find that its maximum velocity at the redshifted side is just one-half of the rotation velocity at 50 au (Figure 2(a)). This means that the gas is certainly infalling beyond r_CR, at least in the southwestern side. The radius (50 au), where the CS emission tracing rotation motion abruptly disappears in the southwestern side, is thus interpreted as the radius of the centrifugal barrier r_CB in our model because of the above-a-factor-of-2 relation.

We performed simulations of molecular emission using the simple ballistic model. In the model, the gas motion is approximated by the particle motion under conservation of kinetic energy and angular momentum. Under this assumption, the gas motion depends on the two model parameters, r_CB, and the total mass of the protostar and the inner disk (M) (Oya et al. 2014). Since our main purpose is to account for the velocity structure, we simply assume an r^−1.5 density profile and constant molecular abundances. The lines are assumed to be optically thin, and no excitation effect is considered for simplicity. The only difference from the previous models is that we considered an increase in the envelope thickness toward the outside, as shown in a schematic view of Figure 1(d). The extension angle of the envelope thickness is assumed to be 30°, judging from the K-band (1.92–2.55 μm) image of this source (Ishii & Tamura 2004).

We investigated a fairly large space for the three parameters, r_CB, M, and the inclination angle of the envelope. We assumed an outer radius of the envelope of 350 au, which is the size of the CS emitting region around the protostar (Figure 1(b)). The model image is convolved by the velocity width of 0.5 km s⁻¹ and the beam size of 069 × 040 (PA = 11°). Although we chose this velocity width by considering the turbulent motion expected in front of the centrifugal barrier, the simulation does not change significantly by use of the 0.2 km s⁻¹ line width. We found a set of parameters that can reasonably reproduce the observed PV diagrams. The acceptable range of r_CB is from 40 to 60 au, and that of the mass is from 0.20 M_⊙ to 0.30 M_⊙. The inclination angle (i) is from 10° to 30°, which is consistent with those reported by Harsono et al. (2014) and Aso et al. (2015) (25° and 35°, respectively, in our definition). The result of the simulation with the most probable parameters (r_CB = 50 au, M = 0.25 M_⊙, and i = 20°) is shown in Figures 2(a) and (b). The model well reproduces the characteristic features of the observed PV diagrams.

On the basis of a change in the power-law index of the rotation curve, Harsono et al. (2014) and Aso et al. (2015) reported the radius of the Keplerian disk r_Kep to be about 100 au, which is larger than r_CB derived by our simple model. Since an infalling fluid parcel cannot simply cross the disk to reach r_CB in hydrodynamics, our ballistic model could be oversimplified. Detailed analysis of more realistic (and complex) gas motion in the infalling–rotating envelope and the transition zone to the disk is desirable (e.g., Stahler et al. 1994), but is out of the scope of the present study. Our observation and analysis clearly show, however, an infalling flow down to ∼50 au. Since it is smaller than the r_Kep reported, it could be an accretion flow from the envelope onto the disk. In the following, we still refer to this radius as r_CB for simplicity.

It is also interesting to compare the protostellar mass between our model and Aso et al. (2015). We derived the protostellar mass to be 0.25 M_⊙ from a simple analysis of an infalling–rotating envelope, while Aso et al. (2015) analyzed the Keplerian disk inside the envelope to derive the mass of 0.68 M_⊙ (inclination corrected). This disagreement is in fact consistent with the findings of Aso et al. (2015); in their model using the protostellar mass of 0.68 M_⊙, the infalling speed of the infalling–rotating envelope is evaluated to be higher than their C¹⁸O (J = 2 – 1) observations. Then, they introduce an effective parameter to reduce the infalling speed to explain the kinematics of the infalling–rotating envelope part. Hence, structure and physics of the transition zone from the infalling–rotating envelope to the Keplerian disk still remain to be explored for thorough understandings of disk formation from the envelope.

Figure 1(c) shows the moment 0 map of the SO (J_N = 7₆ – 6₅) line. The critical density of this line calculated from the Einstein A coefficient and the collisional cross section (LAMDA; Schöier et al. 2005; Lique et al. 2006) is ∼10⁷ cm⁻³, which is similar to that of the CS (J = 5 – 4) line. Nevertheless, the distribution is concentrated around the protostar and is more compact than that of CS. The SO intensity is brighter in the southern part of the integrated intensity map in contrast to the CS case. Figures 2(c) and (d) show the PV diagrams along the envelope direction and the direction perpendicular to it. Along the envelope, the SO intensity is brighter in the southeastern part of the PV diagram than in the northeastern part. Since the CS emission is brighter in the northeastern part, the intensity of SO seems to be anticorrelated with that of CS. In the southwestern part, the SO emission is concentrated around the radius of the centrifugal barrier, as in the case of L1527. The SO molecule would be liberated into the gas phase from the ice mantle by a weak accretion shock near the centrifugal barrier. The actual shock would be occurring in a certain range of the radius in front of the centrifugal barrier, possibly between r_CB and r_CR. This situation can be seen in the northeastern side, as described below. Figures 2(c) and (d) show the model of the infalling–rotating envelope with the same parameters mentioned above. Enhancement of SO near the centrifugal barrier can be recognized.

On the other hand, the SO distribution is slightly extended outward of the centrifugal barrier in the northeastern part up to ∼100 au. As indicated by the CS distribution, the envelope gas distribution is asymmetric around the protostar, and a large amount of the gas is stagnated in front of the centrifugal barrier in the northeastern part. As the result, the accretion shock would occur at a larger radius than the radius of the centrifugal barrier. Hence, the shock would be weakened resulting in a weak SO intensity there. Alternatively, a part of SO may originate from thermal evaporation by protostellar heating. According to the model by Brown & Chandler (1999), the "disk" temperature could be as high as 155 ± 99 K at 100 au. This estimate has a large uncertainty, and the actual temperature would be somewhat lower according to the general model for the Class I sources (Whitney et al. 2003). Nevertheless, an inner part of the envelope might have a higher temperature than the evaporation temperature of SO (∼60 K).

The abundance ratio of SO/CS at the centrifugal barrier is derived by using the same non-LTE method described in Sakai et al. (2014b). For this purpose, we used the intensities integrated from 7.9 to 9.3 km s⁻¹ and from 3.7 to 5.1 km s⁻¹ for the redshifted and blueshifted components because the systemic velocity component would suffer from self-absorption. The SO/CS ratio is evaluated to be 4.6–8.8 and 1.9–3.2 for the redshifted and blueshifted components for the H₂ density range from 3 × 10⁶ to 3 × 10⁸ cm⁻³ and the temperature range from 30 to 120 K. The ratio for the redshifted component is comparable to that found in L1527 (4.6–5.9), while that for the blueshifted component is slightly lower. The latter result would reflect the weaker accretion shock mentioned above.

Apart from the asymmetry of the envelope gas, the physical and chemical situation seen in this source is similar to that observed in L1527. Namely, CS is mostly distributed outward of the centrifugal barrier, while SO is enhanced around and in front of the centrifugal barrier. We also observed the CCH and SO₂ lines, whose distributions are similar to that of CS and SO, respectively (N. Sakai et al. 2016, in preparation). Thus, chemistry highlights the centrifugal barrier. Inward of the centrifugal barrier, these molecules would be depleted onto dust grains in the mid-plane of the disk-forming region, although a part of them, particularly those near the surface of the disk, will stay in the gas phase.