First Detection of Submillimeter-wave [¹³C i] ³P₁–³P₀ Emission in a Gaseous Debris Disk of 49 Ceti with ALMA

The top left panel of Figure 1 shows the [C i] integrated intensity map. The velocity range for integration is from −6 to 11.5 km s⁻¹, where the systemic velocity is 2.8 km s⁻¹. Details of its spatial distribution have already been reported by Higuchi et al. (2019). Although a double-peak distribution centered at the star position is seen in the integrated intensity map at a 30 au scale in radius, these two peaks do not correspond to the actual brightness peaks of the [C i] emission. This is because the integrated intensity is largely affected by the velocity width due to the Keplerian motion. The top right panel of Figure 1 shows the velocity dispersion map of the [C i] emission, supporting the effect described above.

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The bottom left panel of Figure 1 shows the [C i] peak intensity map. This map indicates that the region with the bright [C i] emission extends from 30 to 180 au along the major axis. The bottom right panel of Figure 1 shows the position–velocity (P–V) diagram of the [C i] emission along the major axis prepared by using the CASA impv, which has been presented by Higuchi et al. (2019). It is confirmed that the region with bright the [C i] emission extends to the outer part of the disk. Moreover, the line width tends to be narrower in the outer part. Based on the peak intensity map and the P–V diagram, we thought that the F = 3/2–1/2 component of [¹³C i] could be found in the outer part.

The intensity of the F = 3/2–1/2 component of [¹³C i] is estimated to be 1/116 of the [C i] intensity, if the ¹²C/¹³C abundance ratio is that of the interstellar medium (77; Wilson & Rood 1994) and the [C i] line is optically thin. Here, the effect of the hyperfine splitting is considered. Since the S/N of the P–V diagram of [C i] is about 30, it is difficult to identify such a faint line. However, we may be able to find the [¹³C i] line, if the [C i] line is optically thick. With this in mind, we prepared the P–V diagram with contours from 2σ to 30σ (1σ = 5.5 mJy beam⁻¹).

A marginal emission feature is seen in the region where the velocity of −3 to −5 km s⁻¹ (northwest) and that of +3 to +5 km s⁻¹ (southeast) is guided by the pink lines. We thought that this feature might be a hint of the [¹³C i] emission.

To investigate the marginal feature in more detail, we prepared the spectra toward the six circular areas indicated in Figure 1. The results are shown in Figure 2. These spectra are ones averaged over the 05 areas in diameter that correspond to the spatial resolution. Although the observed areas are overlapped with each other by a half-beam, they provide independent information according to the Nyquist sampling theory.

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In Figure 2, the dashed lines indicate the expected velocities of two hyperfine components of [¹³C i]. A faint spectral feature appears just at the expected velocity of the F = 3/2–1/2 component of the [¹³C i] line in the spectra of the northwestern positions (Figures 2(d)–(f)). The overlaid spectra with pink color show the [C i] spectra whose intensity is scaled by 1/12 and whose velocity is blueshifted by 2.2 km s ⁻¹ (the velocity difference between the F = 3/2–1/2 line of [¹³C i] and the [C i] line). The overlaid spectra correspond well to the faint features. From these results, we concluded that the faint feature is the F = 3/2–1/2 component of the [¹³C i] line.

Since the rms noise level of the spectra is 0.11 K at a resolution of 0.1 km s⁻¹, the [C i] lines are detected in the northeastern positions of (d)–(f) of Figure 1 with the 3σ–5σ confidence level (see Table 2). For the southeastern positions, we cannot detect the [¹³C i] line definitively because of the heavy contamination of the wing component of the [C i] emission. Nevertheless the overlaid spectra in pink color could be consistent with the observed spectra even for Figures 2(a)–(c).

Table 2.  Line Parameters of the F = 3/2–1/2 Component of the [¹³C i] ³P₁–³P₀ Line

Position	TB	VLSRa	dv	$\int {T}_{{\rm{B}}}{dv}$
	(K)	(km s−1)	(km s−1)	(K km s−1)
(d)	0.55 (0.11)	1.6 (0.1)	0.28 (0.10)	0.15 (0.08)
(e)	0.33 (0.11)	1.6 (0.1)	0.39 (0.14)	0.13 (0.09)
(f)	0.32 (0.11)	1.9 (0.1)	0.49 (0.16)	0.16 (0.10)

Note. The numbers in parentheses represent the 1σ error.

^aV_LSR for the [¹³C i] emission.

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In the above analysis, we derived the peak intensity ratio of [C i] relative to [¹³C i] to be 12 ± 3. Considering the ¹²C/¹³C abundance ratio in the interstellar medium of 77 (Wilson & Rood 1994), the observed [C i]/[¹³C i] intensity ratio is much lower than the elemental ratio. This result shows that the [C i] emission is optically thick. The peak optical depth (τ) of the [C i] emission is roughly estimated to be 10 ± 3 by considering the relative intensities of the hyperfine components. Here, we assumed the excitation temperature of [¹³C i] is identical to that of [C i]. Since the optical depth that of [C i] is higher than that of [¹³C i], the excitation temperature of [C i] could be higher than that of [¹³C i] in principle. In this case, the peak optical depth measured above is a lower limit, and hence, our conclusion of optically thick [C i] does not change.

The spectral shape is apparently different between the [C i] and [¹³C i] spectra: the velocity width is narrower in [¹³C i] than in [C i]. This can be understood as the optical depth effect at the peak velocity: the optical depth at the intensity peak of the [C i] spectrum is obviously thick, while at other velocities of the [C i] that in the rest part of the [C i] emission could be lower.

Here, we evaluated the column density, N(C), and the gas kinetic temperature, T_K, by using the non-LTE code (RADEX).⁴ We optimized these two parameters to reproduce the [C i] intensity and its optical depth (10 ± 3) derived above. The major collision partner is not well defined for this situation, so that we simply assume the H₂ density of 10⁴ cm⁻³ (critical density of [C i]) for convenience in the calculation. Here, the velocity width is assumed to be 1 km s⁻¹. Although the contribution of electrons is considered for the CO excitation (Kral et al. 2019), we ignored it for [C i] in this calculation. As the result, we obtained the following parameters: T_K = 18 ± 7 K and N(C) = (1.5 ± 1.0) × 10¹⁸ cm⁻². The excitation temperature is derived to be 18 ± 7 K, being comparable to T_K. This indicates that the lines are thermalized. The column density is by an order of magnitude higher than the value derived from the single-dish observations by Higuchi et al. (2017).

In the previous section, we assumed the ¹²C/¹³C elemental abundance ratio of 77 in order to evaluate the optical depth. However, we need to discuss its validity in the debris disk condition, which would be affected by stellar and/or interstellar UV radiation. If the atomic carbon (C) or the ionized carbon (C⁺) is the major reservoir of gaseous carbon, the ¹²C/¹³C ratio of the atomic carbon should be close to 77. This is because the C⁺/C ratio is determined by the ionization process, which is free from the isotope fractionation. On the other hand, the ¹²C/¹³C ratio of the atomic carbon could be higher than 77, if the major reservoir of gaseous carbon is CO. In this case, ¹³C⁺ formed by photodissociation can react with the abundant ¹²CO as (Langer et al. 1984)

$$\begin{eqnarray}&&{}^{13}{{\rm{C}}}^{+}+{}^{12}\mathrm{CO}\to {}^{12}{{\rm{C}}}^{+}+{}^{13}\mathrm{CO}+35\,{\rm{K}}.\end{eqnarray} \tag{ 1 }$$

For this isotope exchange reaction, ¹³C⁺ and ¹³C become deficient (Langer et al. 1984). This mechanism particularly works in cold conditions, where the backward reaction of the Equation (1) is not effective. Later chemical model simulations indeed confirmed this effect (Furuya et al. 2011; Röllig & Ossenkopf 2013). If the ¹²C/¹³C ratio is higher than 77 in 49 Ceti due to this mechanism, the [C i] optical depth evaluated in this study from the [C i] and [¹³C i] intensities would be higher than 10. For confirmation, observations of the ³P₂–³P₁ (809 GHz) lines of [C i] and [¹³C i] are helpful, which can be done with ALMA.

Although observations of [¹³C i] are essential for the accurate evaluation of the column density of atomic carbon, they have been very sparse so far even in the interstellar medium. This is because the [C i] line is believed not to be optically thick. For the ³P₂–³P₁ transition of [¹³C i] (809 GHz), the frequency is shifted from [C i] by 152 MHz (56 km s⁻¹; Klein et al. 1998), providing a chance to detect the [¹³C i] line emissions. In fact, the first detection of the [¹³C i] ³P₂–³P₁ line emission in Orion IRc2 was achieved by Keene et al. (1998), and further observations have been reported by Tieftrunk et al. (2001).

On the other hand, it is difficult to detect the ³P₁–³P₀ transition of [¹³C i] (492 GHz) because its frequency is shifted from the [C i] line emissions only by 3.6 MHz (2.2 km s⁻¹; Yamamoto & Saito 1991). For this reason, no detection has been reported for the ³P₁–³P₀ line of [¹³C i], as far as we know. Since the [C i] line emissions in the 49 Ceti disk are bright and their line widths are narrow, the [¹³C i] line emission was fortunately detected for the first time.

Although we obtained high-resolution images of 49 Ceti in the CO and [C i] lines with ALMA, we are facing a difficulty that we have little information on the spatially resolved optical depths at a resolution of 05. It is thus difficult to derive the spatially resolved column densities of CO and C from the observed intensities based on the current data sets. At this moment, high-quality and high-resolution images are available only for CO(J = 3–2) and [C i] ³P₁–³P₀. To overcome the above difficulty, we need spatially resolved images of the other lines of ¹²CO and [C i], as well as those of ¹³CO and [¹³C i] lines. Such observations are strongly awaited to evaluate the C/CO ratio accurately, which will be key to understanding the origin of the gas in the debris disk of 49 Ceti.