A temperature or FUV tracer? The HNC/HCN ratio in M83 on the GMC scale

The data towards SWBE are taken as a part of ALMA project code 2021.1.01195.S (PI: Harada), and consist of the 12-meter array data, as well as the Atacama Compact Array (ACA) data (7-meter and total power). This project covers the field of view of $94\arcsec\times 80\arcsec$ ($2.1\times 1.8\,$kpc) with a position angle of 78 degrees. We imaged the interferometer data (12-meter and 7-meter antennae) with the PHANGS pipeline (ver. 2; Leroy et al., 2021) using CASA (McMullin et al., 2007; CASA Team et al., 2022) version 5.6.3. After the imaging, we used the CASA version 6.6.0. We used the total power data obtained from the ALMA data delivery (QA2), and used the CASA task feather to combine the interferometry data and the total power data. We convolved all the cubes into the angular resolution of $1\farcs 9\times 1\farcs 9$ (=42 pc $\times$ 42 pc) to match the largest beam. Achieved single-channel sensitivities are 30 mK (HCN and HCO⁺) and 13 mK (HNC) over 3.3 km s^-1. Primary beam correction was applied to all the cubes.

We also obtained a 3-mm continuum image at 95.8 GHz. It has an rms of $10\,\mu$Jy beam^-1 to estimate the star formation rate. Most of the 3-mm continuum likely originates from free-free emission in HII regions and has a direct relationship with the star formation rate. Because ALMA does not provide the total power capability for the continuum, spatial filtering may be an issue if the continuum emission is extended. Although we cannot check the exact missing flux in the continuum data, we can at least compare the HCN data with and without total power. The HCN emission is usually more extended than the continuum emission. The missing flux of HCN is less than 10 % even if we take the aperture of 10.7$\arcsec$, which is the beam size used in Section 3.5 to compare with lower-resolution far-infrared data.

Although the 3-mm continuum should be dominated by the free-free emission, it may also contain contamination from the dust emission or synchrotron radiation. We checked the continuum emission at 348.5 GHz to estimate the contribution from the dust emission, which will be presented in our forthcoming paper. The contamination is $\lesssim 10$ % for the region used for our analyses in later sections. The synchrotron radiation should be negligible because there is not many synrotron sources such as supernovae in this region (Long et al., 2022).

The HNC data are taken from the cube produced for Harada et al. (2019) (project code: 2016.1.00164.S), and include 12-meter and 7-meter arrays with a maximum recoverable scale (MRS) of $74\arcsec$ at 90 GHz. HCN and HCO⁺ data are taken from the ALMA archive (project code 2015.1.01177: Callanan et al., 2021), which contains only the 12-meter data with an MRS of 25$\arcsec$. These MRSs should be enough to cover most of the emission in the central region judging from the structure of CO(1–0) (Koda et al., 2023). Although the CO(1–0) emission is expected to be much more extended than HCN, HCO⁺, and HNC, most of the emission comes from regions within the size of 25$\arcsec$. The data were imaged using the same way as Harada et al. (2019) using CASA ver. 5.4 and later processed with CASA ver. 6.6.0. We convolved cubes into a common beam of $2.5\arcsec$(=55 pc), and applied primary beam correction. Single-channel rms noise levels over 10 km s^-1 are 20 mK, 17 mK, and 10 mK for HCN, HCO⁺, and HNC, respectively. The continuum image has an rms of 29 $\mu$Jy beam^-1.

The 3-mm continuum (more precisely, 2.8-mm or 96.9 GHz) may also suffer from the dust contamination in addition to the free-free emission here. By comparing the 2.8-mm and 1.0-mm continuum presented in Harada et al. (2019), we estimate the contamination to be less than 10 % for most emission, but can be up to 30 % for very low-level ($<0.4\,$mJy beam^-1) emission. The star formation rate corresponding to this level of emission is log($\dot{M}_{*}$[$M_{\odot}$ Myr^-1 pc^-2])$<0.5$ (see Section 3.2).

To put the observed region into perspective, we have derived the dense gas surface density ($\Sigma_{\mathrm{dense}}$) and the star formation rate surface density ($\Sigma_{\mathrm{SFR}}$). For the dense gas surface density, we use

where $\alpha_{\rm HCN}$ is the conversion factor of $10\,M_{\odot}$ pc^-2 (K km s^-1)^-1 (Gao & Solomon, 2004), $\int T_{b}\,dv$ is the velocity-integrated intensity, and $i$ is the inclination angle ($i=26^{\circ}$; Koda et al., 2023). We derived the star formation rate surface density by first calculating the star formation rate $\dot{M}_{*}$ within the aperture using the following equation (e.g., Bendo et al., 2016).

where $g_{\rm ff}$ is the Gaunt factor, $\alpha_{B}$ is the effective recombination coefficient, $T_{\rm e}$ is the electron temperature, $D$ is the distance to the galaxy, and $f$ is the flux per beam. We assume the electron temperature to be $T_{\rm e}=5000\,$K. The Gaunt factor is given by

where $\nu$ is the frequency and $Z$ is the electric charge, which can be approximated as $\sim 1$. We approximate the effective recombination coefficient $\alpha_{B}$ using the following formula (Michiyama et al., 2020)

To derive the star formation rate surface density, we take

where $A$ is the aperture size in pc².

Figure 4 shows the relationship between the dense gas surface density and the star formation surface density in the SWBE region and the central region. The data points in the SWBE region lie close to or slightly higher than those in the northern arm of M51 (Querejeta et al., 2019). Data points from both regions lie roughly in the $\Sigma_{\rm SFR}-\Sigma_{\rm dense}$ relationship in star-forming galaxies (García-Burillo et al., 2012; Usero et al., 2015; Sánchez-García et al., 2022). It is fair to say that regions we observe have normal star-forming conditions although the scatter is large due to the high spatial resolution ($\sim 50\,$pc) we used (see the effect of the beam size on the relation in Sánchez-García et al., 2022). As discussed in Section 2, the 3-mm continuum has minor contamination from the dust contribution, and caution is needed to interpret the faint 3mm emission (i.e., low star formation rate surface density) in this relation.

Figure 7 shows spectra from positions 1-7 shown in Figure 3. Some spectra show different line shapes between HCN and HNC, specifically at positions 3, 5, and possibly at 7. At these positions, HCN has either flat-top or double-peak profiles while HNC has single-peak Gaussian-like profiles. This suggests that HCN is optically thick compared with HNC. Meanwhile, at position 1, where the HNC/HCN ratio is relatively low, the line profiles of HCN and HNC are similar. This position is close to the optical nucleus (Thatte et al., 2000), and their line widths are large. Line emission is likely to be optically thinner at this position than others.

Note that the hyperfine structures of HCN($J=$1–0) alone cannot produce the line profiles we see here. Compared to the strongest transition of $F=2-1$, $F=0-1$ and $F=1-1$ have velocity shifts of $-7.1$ km s^-1 and $4.9$ km s^-1, respectively. These hyperfine splittings can cause slightly wider line profiles, but their effect should be small considering the spectral width of our data cube, 10 km s^-1. We note that, due to the large line widths (FWHM) in our observations ($\gtrsim 40$ km s^-1 in the central region, $\gtrsim 20$ km s^-1 in SWBE), we cannot check if there is any excitation anomaly among the hyperfine splitting (e.g., ones reported towards Orion-B by Santa-Maria et al., 2023).

The FIR ratio can be a probe of dust temperature, and an increase in the dust temperature can be caused by UV photons from a star-forming activity. We obtained the FIR data from Herschel at $70\,\mu$m and $160\,\mu$m (Bendo et al., 2012; VNGS team, 2012), which correspond to dust emission peaks at $\sim 40$ and 20 K, respectively. Since currently available far-IR observations only have a coarser resolution than the ALMA data, we convolved our ALMA data into the beam size of the 160-$\mu$m Herschel data using the CASA task imsmooth. Since the Herschel 70-$\mu$m data also has a smaller beam ($5.6\arcsec$) compared with the 160-$\mu$m data, we also convolved the 70-$\mu$m data to the beam size of the 160-$\mu$m data, 10.7$\arcsec$. Figure 8 (left) shows the HNC/HCN ratio at a $10.7\arcsec$ resolution superposed with the ratio of 70$\mu$m over $160\mu$m flux. This HNC/HCN ratio map was created by convolving the HCN and HNC images individually to $10.7\arcsec$, and taking the ratio. The Herschel data have already been presented by Foyle et al. (2012). The HNC/HCN ratio tends to be high when the 70$\mu$m/$160\mu$m ratio is lower. This is an expected result if the UV field both heats the dust and decreases the HNC/HCN ratio. Moreover, the HNC/HCN ratio can be low even if the 70$\mu$m/$160\mu$m ratio is moderately low if it is near the high 70$\mu$m/$160\mu$m ratio region. We can interpret this trend as a global (a few 100 pc scale) effect of the UV field on the HNC/HCN ratio.

Since the FIR data are only available in a lower resolution, it is helpful to compare the HNC/HCN ratio with the star formation rate with the same resolution as the FIR data. Figure 8 (right) is similar to Figure 8 (left), but the contours are the 3-mm continuum convolved to the same resolution as the Herschel beam. The large-scale variation of the 3-mm continuum appears somewhat similar to that of the 70$\mu$m/$160\mu$m ratio, although the 3-mm continuum is more concentrated around regions detected with molecules. The region with the peak of the 70$\mu$m/$160\mu$m ratio has a low HNC/HCN ratio, which may indicate that the global star formation rate impacts the HNC/HCN ratio. At the same time, the HNC/HCN ratio peak at the eastern part of the map has a moderately high star formation rate inferred from the 3mm continuum. There does not seem to be a consistent trend between the star formation rate and the HCN/HCN ratio even globally.

Before discussing the implications of our results, let us summarize the factors that may affect the abundances of HCN and HNC, and the ratio between them.

In the previous sections, we compared the HNC/HCN ratios with the 3-mm continuum and the 70$\mu$m/160$\mu$m ratios. Here we connect these measurable quantities to the physical parameters that could affect the chemistry, namely, the temperature, UV field, and cosmic-ray ionization rates.

The 3-mm continuum emission

As mentioned above, the 3-mm continuum is considered a tracer of SFR. Although continuum flux could contain synchrotron radiation or dust emission, there is no obvious synchrotron source such as supernova remnants (Long et al., 2022). Although there may be unidentified diffuse supernova remnants that cause synchrotron radiation, we do not expect it to be more significant than for normal star-forming galaxies, where synchrotron radiation is insignificant at the 3-mm wavelength. We already discussed the estimate of the dust contamination in Section 2, which tends to be insignificant.

Good spatial correlations with the temperature and SFR have been observed in many regions. Galactic centers have higher temperatures on the GMC scale where the star formation rates are higher (e.g., Ginsburg et al., 2016; Tanaka et al., 2024) according to LVG analyses. An LVG analysis on the data towards the center of M83 using the same method as Tanaka et al. (2024) shows elevated temperatures ($\gtrsim$ a few hundred K) near regions with intense star formation compared to the region without star formation ($\sim 100\,$K)(Kaneko et al. in preparation). Such correlation is also seen in the spiral-arm region of the Galaxy, but the heating is only effective on the scale of 1 pc or so (e.g., Hacar et al., 2020; Murase et al., 2022). Of course, having a higher number of star-forming regions within a GMC should raise the temperature on average, but it is unclear how much the temperature is raised for a given value of SFR in the extragalactic GMCs where the density structure within the beam is unknown.

A high star formation rate also produces a high UV radiation field. While we expect some spatial correlation between the star formation rate and the UV field, the correlation between the star formation rate and the UV radiation field may not be tight if the region has high visual extinction that allows the attenuation of the UV photons.

The correlation between the cosmic-ray ionization rate and the 3-mm continuum should be weak. First, the locations of supernova remnants (Long et al., 2022) do not seem to correlate with the star formation rate on $<100\,$pc scale. Moreover, cosmic rays penetrate high column densities, and variation among GMCs should be small although we do expect $\sim$kpc-scale variations near the galactic center region where supernova remnants are concentrated.

FIR intensity ratio (70$\mu$m/160$\mu$m)

We expect some spatial correlation between the UV radiation field and the FIR intensity ratio. The UV radiation heats the dust, which increases the $70\mu$m/$160\mu$m ratio. If the UV field also heats the gas in addition to the dust, the gas kinetic temperature should also be high where the $70\mu$m/$160\mu$m ratio is high. For the same reasons as the 3-mm continuum, we do not expect a good spatial correlation between the FIR intensity ratio and cosmic-ray ionization rates.

We have seen that the HNC/HCN ratio varies with the large-scale variation of 70/160$\mu$m, but not with the local star formation rates in the bar-end region. We also found that the HNC/HCN ratio is largely determined by the optical depth in the galactic center region. Depending on the driving force of the HNC/HCN chemistry, we can propose the following two scenarios. For each scenario, we add the interpretation of observed trends. The summary of this section is also shown in Figure 9.

1. 1.

   The HNC/HCN ratio changes with the temperature

   SWBE $2\arcsec$ (40 pc) scale: In this case, the increase in the temperature caused by the high star formation rate is not visible in our HNC/HCN observations. A possible reason is that either the star formation does not increase the temperature or that it occurs on a scale far smaller than our beam size (i.e., parsec scale or less). Because it is hard for star formation not to increase the temperature at all, we speculate that the heated regions are small for the embedded star formation traced with the 3-mm continuum emission.

   SWBE $10\arcsec$ scale ($\sim 200\,$pc): There is a gas temperature increase on a large scale as the gas flows through the bar end region, which lowers the HNC/HCN ratio downstream. The heating source is unknown, but possible candidates are photoelectric heating due to UV photons, shock heating, and cosmic-ray heating. If the heating source is UV photons, it is difficult to distinguish whether the driving force of the chemistry is temperature or UV photons. Koda et al. (2020) found that the CO(2–1)/(1–0) ratio is higher downstream around spiral arms, and proposed that this higher ratio is caused by UV or cosmic-ray heating due to star formation that took place when the gas passed through the spiral arms. This star formation causing the temperature increase must be unobscured instead of the embedded one. Cosmic rays are unlikely to be the main driver of chemistry in regions with high CO(2–1)/(1–0) ratios because the cosmic rays increase the HNC/HCN ratio.

   The central region: The center of M83 has a temperature of $>100\,$K according to the LVG analysis by Kaneko et al. (in preparation). Most of the gas is supposed to have HNC/HCN$<0.1$ if this ratio follows the relationship by Hacar et al. (2020). We can interpret the high HNC/HCN ratio with the high cosmic-ray ionization rate. There is still an effect of the optical depth that alters the HNC/HCN ratio locally.

2. 2.

   The HNC/HCN ratio changes with the UV radiation field

   SWBE $2\arcsec$ scale: If the HNC/HCN ratio is affected by the UV radiation field, its effect is limited in highly obscured regions. Star-forming regions traced with the 3mm continuum may not alter the HNC/HCN ratio because these star-forming regions are embedded, providing little dependence of the HNC/HCN on the star formation rate in the bar-end region on the small scale.

   SWBE $10\arcsec$ scale: The global dependence of the HNC/HCN ratio on the far-infrared ratio is caused by the UV radiation field because the UV radiation also heats the dust.

   The central region: In the galactic center region, the HNC/HCN ratio is not very low despite the high star formation rate and high temperature because the density is also high, and the UV radiation field can be attenuated. The high HNC/HCN ratio in the obscured region is caused by both the lack of UV field and the optical depth.

It is difficult to determine which scenario is correct from the observations in the SWBE region alone, especially if the UV photons are the main heating source. To decide which scenario is more likely, it is important to study regions where the heating source is not UV photons, i.e., regions that are obscured from external UV photons. The spatial distribution of the HNC/HCN ratio in the galactic center region can give us a clue, since it generally has high column densities judging from the fact that molecular emission and dust continuum emission are both brighter than the bar-end region by about an order of magnitude. For the HNC/HCN ratio to be high enough in the high-temperature region of the M83 galactic center, cosmic-ray ionization needs to be high according to Scenario 1, where the HNC/HCN ratio is mainly determined by the temperature. While the cosmic-ray ionization rate is expected to be high due to the high supernova rate (Long et al., 2022), it is unlikely to be the main driver of the chemistry. If cosmic rays increase the HNC/HCN ratio, they should have a stronger impact in the low-density region, because the chemistry scales as $\zeta/n$, where $\zeta$ is the cosmic-ray ionization rate and $n$ is the density. This contradicts the observed trend in M83. The HNC/HCN ratios are also high in high-column-density regions in the central region of NGC 253 (Behrens et al., 2022).

Even in Scenario 1, one could also argue that the HNC/HCN ratio is high in the central region simply because of the optical depth despite the high temperature. However, the HNC/HCN ratio is moderately high ($\sim 0.3$) even where a line is broad and likely optically thin around the optical nucleus (near the position 1 in Figure 3). The temperature corresponding to $I$(HNC)/$I$(HCN)=0.3 is about 30 K according to the Hacar et al. (2020) relation, and is too low for a galactic center. Although it appears reasonable to exclude this case, deep maps of H¹³CN and an estimate of ¹²C/¹³C are necessary for confirmation so that the optical depth in this whole region can be derived.

It may sound unreasonable that the HNC/HCN ratio is moderately high in the galactic center region despite the high UV field expected from the high star formation rate if Scenario 2 is true. However, the HNC/HCN ratio is low ($\lesssim 0.2$) in low column density regions, where the UV photons can travel without too much extinction. Near-infrared observations towards the galactic center region reveal higher visual extinction ($A_{\mathrm{V}}\gtrsim 14$; Turner et al., 1987). Molecular regions likely have even higher visual extinction, which would increase the HNC/HCN ratio if the HNC/HCN ratio decreases with the UV field. For these reasons, we believe that Scenario 2 is more plausible.