Vibrationally-excited Lines of HC₃N Associated with the Molecular Disk
around the G 24.78+0.08 A1 Hyper-compact H II Region

We show the continuum image ($\lambda=1.38$ mm) toward the G 24 HC H II region in panel (a) of Figure 1, which was first reported by Moscadelli et al. (2021). The angular resolution is 0$\farcs$071 $\times$ 0$\farcs$048, corresponding to $\sim$ 476 au $\times$ 322 au at the source distance of 6.7 kpc. The beam position angle (PA) is 63.9°. Two peaks are located at the center, and the spatial distribution of the continuum emission is slightly elongated along the north-east to south-west direction (PA = 39°). We will discuss a possible reason for the two peaks in the continuum emission in Section 3.4. Another continuum core is located $\sim$0$\farcs$4 (2680 au) south of the strongest continuum core. This position is consistent with A1M (a molecular emission peak position) named by Moscadelli et al. (2018), and they found that column densities of several complex organic molecules (COMs) are abundant here.

Panels (b)–(d) of Figure 1 show the moment 0 maps of three vibrationally-excited molecular lines; (b) HC₃N ($v_{7}=2$, $J=24-23$, $l=0$), (c) HC₃N ($v_{7}=2$, $J=24-23$, $l=2e$), and (d) CH₃CN ($v_{8}=1$, $J_{K,l}=12_{6,1}-11_{6,1}$); toward the G 24 HC H II region. We select two areas for our analysis, namely “Central region” and “Molecular region” (panel (c) of Figure 1). The central position of the Central region corresponds to the middle of the two continuum peaks, and that of the Molecular region is at the peak position of the HC₃N ($v_{7}=2$, $J=24-23$, $l=2e$) line, respectively. Their coordinates are ($\alpha_{\rm{J}2000}$, $\delta_{\rm{J}2000}$) = (18^h36^m12$\fs$556, $-$07°12′10$\farcs$85), and (18^h36^m12$\fs$546, $-$07°12′10$\farcs$80), respectively. The other molecular lines also have peaks within the Molecular region. We selected the two regions to investigate the potential chemical variation induced by different UV fluxes, which is expected to be higher in the Central region. The Central region is the same position that Moscadelli et al. (2021) analyzed. Following their work, we adopt the radii of 0$\farcs$1 for the two regions, which allows us to check the consistency between their and our analyses (see Section 3.3.1).

Figure 2 shows the spectra of the HC₃N and CH₃CN lines at the Central and Molecular regions. Other two CH₃CN lines ($v_{8}=1$, $J_{K,l}=12_{4,-1}-11_{4,-1}$ and $12_{3,-1}-11_{3,-1}$) are also detected near the CH₃CN ($v_{8}=1$, $J_{K,l}=12_{6,1}-11_{6,1}$) line. We checked molecular lines in the Splatalogue database³³3https://splatalogue.online//advanced1.php, and found that no other lines are likely to contaminate the spectra. In addition, the two vibrationally-excited lines of HC₃N show similar intensities and spatial distributions as expected. We thus concluded that line contamination does not occur.

In the moment 0 maps (panels (b) – (d) of Figure 1), we can recognize the overall similarities in the spatial distributions of the HC₃N and CH₃CN emissions. Their emission regions have similar extents of $\sim 1000{\rm\>au}$, because they have almost the same upper state energies of $771-777$ K (Table 1; see also Figure 6 of Moscadelli et al., 2021). Also, all three emissions are dimmer in the Central region, probably due to photodissociation by intense UV flux (see also Section 3.3.2). These similarities suggest that the vibrationally-excited HC₃N and CH₃CN lines trace the same hot, dense region surrounding the central ionized region, i.e., the molecular disk reported by Moscadelli et al. (2021). We note, despite these similarities, the HC₃N and CH₃CN lines also show a difference in their emission morphology. The CH₃CN emission surrounds the Central region, while the two HC₃N lines are mainly located in the northwest. We can explain this spatial difference if the UV flux from the Central region is stronger toward the south direction, because HC₃N would be more efficiently photodissociated than CH₃CN (Section 3.3.2). Unresolved asymmetric innermost structures, e.g., clumpy density structure and a presence of a binary system (Section 3.4), could be at the origin of such an anisotropic UV radiation field.

Having confirmed the similarity of the spatial distributions, we next investigate the kinematical similarity of the vibrationally-excited HC₃N and CH₃CN lines. Moscadelli et al. (2021) reported the Keplerian disk of G 24 using the P-V diagrams of the CH₃CN lines, including its vibrationally-excited line and ¹³C isotopologue line. In order to confirm that the vibrationally-excited HC₃N line also traces the same molecular disk, we constructed P-V diagrams of HC₃N ($v_{7}=2$, $J=24-23$, $l=2e$) and CH₃CN ($v_{8}=1$, $J_{K,l}=12_{6,1}-11_{6,1}$) along the disk major axis of PA=133°(shown in Figure 1). We used “impv” task in CASA, and averaged the emission over three pixels across the positional cut. The center position (offset = 0″) is set at the coordinate of the Central region. Panels (a) and (b) of Figure 3 show the P-V diagrams of the vibrationally-excited HC₃N and CH₃CN lines, respectively. Their channel maps in Figures 11 and 12 in Appendix B. For comparison, we also provide the P-V diagram of the vibrational ground-state line of CH₃CN ($J_{K}=12_{4}-11_{4}$), which clearly shows the Keplerian feature with $20\>M_{\odot}$ but becomes dimmer in the innermost region (panel (c) of Figure 3).

In the P-V diagrams, we could confirm that the HC₃N emission has kinematic similarities with the vibrationally-excited and ground-state CH₃CN lines, but the resemblance is stronger to the vibrationally-excited line of CH₃CN. The brightest features appear in the northwest and redshifted side, and the dimmest features are in the northwest and blueshifted side in all three panels of Figure 3. On the brightest side, the HC₃N emission covers the innermost region of $+0\farcs 0-+0\farcs 1$ like the vibrationally-excited CH₃CN line, which has almost the same upper-state energy (panels (a) and (b)). Moreover, on the same side, the HC₃N emission shows the consistent profile as the Keplerian rotation seen in the ground-state CH₃CN emission (panels (a) and (c)). Hence, we conclude the vibrationally-excited HC₃N line associated with the same Keplerian disk reported by Moscadelli et al. (2021). Although the HC₃N emission shows some resemblance to that of CH₃CN in the P-V diagrams (Figure 3), the degree of this resemblance is still debatable. Future higher-angular resolution observations including other transitions are necessary for further discussions.

The other similarity is that these HC₃N and CH₃CN lines show emission features on the southwest and redshifted side of the P-V diagrams (see also Figure 4 of Moscadelli et al., 2021). The distribution of the HC₃N emission lines is intermediate between those of the vibrationally-excited and ground-state CH₃CN lines. This again supports that the HC₃N line traces the same gas as CH₃CN. We note that such a kinematical feature cannot be reproduced by a pure Keplerian disk (Sakai et al., 2014; Zhang et al., 2019a). Contamination from an infalling, rotating envelope is able to create this feature, even though we used the lines with the high upper-state energies, which can be excited only in hot dense gas (cf., $E_{\rm{up}}/k=777$ K and the critical density of $\gtrsim 4\times 10^{8}{\rm\>cm}^{-3}$ for the HC₃N line; Wyrowski et al., 1999). One difference between the HC₃N and ground-state CH₃CN lines appears on the southeast and blueshifted sides in their P-V diagrams (panels (a) and (c)). The HC₃N emission is darker on the southwest side, making it difficult to trace that side of the Keplerian feature (see also Figure 1). An anisotropic UV radiation field could create this HC₃N depletion, which we also mentioned in Section 3.1. This would imply that fast chemical processes change the chemical composition of the molecular disk with a shorter timescale than the rotational timescale for the disk (e.g., Cleeves et al., 2017).

As mentioned in Section 1, HC₃N and CH₃CN trace different layers of disks around Herbig Ae and T Tauri stars (Ilee et al., 2021), suggesting that these species trace different physical conditions in disk structures. In order to investigate the physical and chemical conditions of the molecular disk around the G 24 HC H II region, we will evaluate the CH₃CN/HC₃N abundance ratios.

As shown in panel (a) of Figure 1, the two peaks with the separation of $\sim 0.1\arcsec$ are detected in the 1.38 mm continuum emission. Panel (a) of Figure 9 shows the P-V diagram of the H30$\alpha$ emission along a direction connecting the two continuum peaks ($\mathrm{PA}=-31^{\circ}$). It clearly shows that the H30$\alpha$ emission associated with the southeast peak is blueshifted by $\sim 10{\rm\>km\>s^{-1}}$ from the northwest peak.

Moscadelli et al. (2021) interpreted this velocity gradient as the ionized disk rotation around a massive protostar. Assuming an edge-on orientation, they derived the dynamical mass of $\sim 17~{}M_{\odot}$, which should be the minimum mass considering the possible inclination. Consistent with this dynamical mass evaluation, Cesaroni et al. (2019) suggested an O9.5 star based on the derived Lyman continuum rate of $5.3\times 10^{47}{\rm\>s}^{-1}$. We also constructed the spectral energy distribution (SED) toward this source to retrieve the stellar mass and other physical properties, using infrared data from Spitzer, WISE, and Herschel (Table 4 in Appendix C) and fitting the SED with the Zhang & Tan (2018) model (see Appendix C for the details). The best models of the SED fitting suggested the stellar masses of $16$–$24\>M_{\odot}$ with the bolometric luminosities of a few times $10^{5}\>L_{\odot}$ (see Figure 13 and Table 5 in Appendix C), which is also consistent with the dynamical mass estimation with the Keplerian disk by Moscadelli et al. (2021). The agreement of the independent analyses supports the presence of a $\sim 20\>M_{\odot}$ star with the ionized-gas disk in the center of the G 24 HC H II region.

However, this ionized disk scenario does not explain the presence of the two continuum peaks well. An alternative interpretation would be that the kinematic structure of H30$\alpha$ consists of two ionized disks associated with two massive young stars orbiting around each other, i.e., a binary system. In fact, instead of one single velocity gradient across $\sim 0.1\arcsec$, the P-V diagram appears to be more consistent with two separate components with the velocity offset (i.e., the orbital motion), each of which has its own velocity gradient (i.e., the rotation of each disk). It is worth briefly discussing the possibility of the binary system in G 24, considering its asymmetric structures and the high binary rate of massive stars.

We can derive the total mass of the binary system assuming that the protostars locate at the continuum peaks and their velocity offset is due to the orbital motion. The peak separation is $0.08\arcsec$ or $\Delta S\simeq 540{\rm\>au}$, which is a project separation. We estimate their velocity offset as $\Delta V\simeq 8.4{\rm\>km\>s^{-1}}$ from the H30$\alpha$ spectra at the peak locations (panel (b) of Figure 9). Considering a circular Kepler orbit, we derive the total dynamical mass as $M_{\rm tot}=\Delta V^{2}\Delta S/G\simeq 43\>M_{\odot}$, where $G$ is the gravitational constant. This formula is different from that in the disk scenario by a factor of 8, i.e., $M_{\rm c}=\Delta V^{2}\Delta S/(8G)$ (where $M_{c}$ is the stellar mass at the disk center; see Sec. 4.1 of Moscadelli et al., 2021), because $\Delta S$ represents the separation of the two sources while it is the diameter of the ionized disk in the disk scenario. Since free-free and H30$\alpha$ emissions trace the surrounding ionized gas rather than the protostar itself, the actual positions of the protostars might be slightly off the continuum emission peaks. Considering such $\Delta S$ uncertainty of $\sim 100{\rm\>au}$ (or $0.015\arcsec$) and the $\Delta V$ fitting error of $0.36{\rm\>km\>s^{-1}}$, we estimate that the mass range of $M_{\rm tot}\simeq 34$–$51\>M_{\odot}$ is consistent with the binary scenario. We note that the circular orbit perpendicular to the plane of sky are assumed here, and thus we consider those as the minimum masses.

The total values of the Lyman continuum rate and the infrared luminosity can also provide constraints on the stellar masses of the binary. Moscadelli et al. (2018) and Cesaroni et al. (2019) estimated a total Lyman continuum rate of $(5.3$–$7.2)\times 10^{47}~{}\mathrm{s}^{-1}$ by fitting the radio to millimeter SED. Since the two peaks have similar brightness in continuum and H30$\alpha$ total emissions, the two massive stars in the binary should have similar masses, and therefore similar Lyman continuum rate of $\sim 3\times 10^{47}~{}\mathrm{s}^{-1}$. Such a Lyman continuum rate corresponds to a zero-age main sequence (ZAMS) mass of $18~{}M_{\odot}$, making a total mass of $36~{}M_{\odot}$ for the binary, which is close to the minimum dynamical mass estimated above. If the binary stars have not reached the ZAMS phase, their masses can be higher because their Lyman continuum rate would be lower than those in the ZAMS phase at the same masses (e.g., Tanaka et al., 2016). As discussed in Appendix C, we conducted the infrared SED fitting. The mass estimation from this fitting is not applicable for the binary system because it assumed a single-star system. However, the obtained total bolometric luminosity of a few $\times 10^{5}~{}L_{\odot}$ is reasonable even for the multiple-source system (Table 5). Considering the protostellar evolution, the luminosity of a massive protostar with $\sim 15$–$20~{}M_{\odot}$ would be as bright as $10^{5}~{}L_{\odot}$ (e.g., Zhang & Tan, 2018), which is again consistent with the estimation of the dynamical mass.

The systemic velocity of G 24 measured from the outer molecular emissions is $\sim$112 km s^-1. If we assume that the line-of-sight velocity of the mass center of the binary is $112{\rm\>km\>s^{-1}}$, the mass ratio between the primary and secondary would be about 2:1 from the central velocity of each continuum peak. Considering the dynamical mass of $>37~{}M_{\odot}$, we evaluate $\gtrsim 24~{}M_{\odot}$ for A1-SE and $\gtrsim 12~{}M_{\odot}$ for A1-NW. However, such analysis is susceptible to the determination of the line center velocities of H30$\alpha$, which have FWHMs of $30-35$ km s^-1, as well as the binary system velocity. Therefore, it is still difficult to accurately determine the masses of the individual stars via dynamics.

We note that the binary scenario does not necessarily contradict the other features of G 24. In the case of the binary star scenario, the rotating structure traced by CH₃CN and HC₃N is a circumbinary disk surrounding the two massive stars. The P-V diagrams of the molecular lines are roughly consistent with the Keplerian rotation with $\sim 20\>M_{\odot}$, but the disk is assumed to be perpendicular to the sky in these diagrams (Figure 3; Figure 4 of Moscadelli et al., 2021). Hence, the value of $20\>M_{\odot}$ is the minimum enclosed mass, and the total dynamical mass of $>37~{}M_{\odot}$ from the H30$\alpha$ emission is acceptable. The presence of a single jet perpendicular to the molecular disk reported by Moscadelli et al. (2018, 2021) does not exclude the binary scenario. For example, in the forming massive binary system IRAS 16547–4247, one of the binary stars launches a single jet nearly perpendicular to the circumbinary disk, while the other star shows no jet feature, despite both protostars show almost the same levels of continuum and line emissions (Tanaka et al., 2020). If this is also happening in G 24, one star may be supplied with more material from the circumstellar disk. Such an asymmetric infalling structure at $<1000{\rm\>au}$ could cause the asymmetric UV field suggested in the larger scale.

Similar to the binary scenario for G 24, Zhang et al. (2019b) reported a forming massive binary IRAS 07299–1651 with each member traced by hydrogen recombination lines showing velocity offset caused by orbital motion. In IRAS 07299-1651, the line emissions from the two stars are well separated that allows analyzing the circumstellar disk rotation of the primary star. However, in G 24, the H30$\alpha$ emissions from the continuum peaks have already spread out and merged together, making it difficult to analyze the detailed kinematic structures of the ionized gas, i.e., the circumstellar disks and their circumbinary disk. We speculate that G 24 is more massive than IRAS 07299-1651, and thus the ionized gas is more extended. Therefore, although we suggest the possibility of the binary system in G 24, we cannot confirm such a scenario with the current data set. Future higher-angular-resolution observations may help to confirm this point.