© The Authors 2024

1 Introduction

After electrons recombine with ions and enter an excited state, and following the ensuing cascade process, recombination lines are emitted from ionized gas. Photons of recombination lines are produced as the electrons cascade down the energy levels, n, toward the ground state. Transitions with Δn = 1 are called α lines, transitions with Δn = 2 β lines, and so on. For hydrogen, the frequencies of α lines with n ≳ 30 are in the submillimeter/radio regime and are called radio recombination lines (RRLs). They are well-studied tracers used to probe the Galactic ionized environments.

Astrophysical RRLs were first detected in 11 H II regions, including M17 and Orion (Hoglund & Mezger 1965). H II regions are zones of warm (~10⁴ K) plasma ionized by UV photons from massive stars. Therefore, RRLs serve as tracers of ongoing star formation, while dense gases trace the upcoming star formation. RRL surveys for individual H II regions in the Galaxy and follow-up studies have been conducted from meter to (sub)millimeter wavelengths (Lockman 1989; Gordon & Sorochenko 2002; Quireza et al. 2006; Keto et al. 2008; Anderson et al. 2011; Klaassen et al. 2018; Salas et al. 2019).

In the Galaxy, another source of RRL emission is the diffuse ionized component of the interstellar medium (ISM), which is characterized by low densities (~0.1 cm⁻³) and a warm electron temperatures (~10⁴ K), as described by Hoyle & Ellis (1963). This component is referred to as the warm ionized medium (WIM) or diffuse ionized gas (DIG). Although H II regions are the most intense sources of RRL emission, DIGs may contribute more total intensity at low frequencies (Alves et al. 2010; Lee et al. 2012). Due to their diffuse nature, the extended ionized gases traced by low-frequency decimeter RRLs can reveal kinematic information caused mainly by the Galactic dynamics. Thus, the WIM plays a crucial role in our understanding of the life cycle of matter in the ISM and the dynamics of the Galaxy. A blind RRL survey would help to trace the distribution of DIG along the Galactic plane. Furthermore, combined with surveys of other ISM phases such as H I and molecular gas, RRL maps will also contribute to studies of Milky Way structure.

In recent years, extensive blind RRL surveys of the Galactic plane have been conducted using large single-dish radio telescopes. Examples include the HI Parkes All Sky Survey (HIPASS; Alves et al. 2012, 2015), the Survey of Ionized Gas in the Galaxy, Made with the Arecibo Telescope (SIGGMA; Liu et al. 2013, 2019), the GBT Diffuse Ionized Gas Survey (GDIGS; Luisi et al. 2020; Anderson et al. 2021; Linville et al. 2023), and the byproduct RRL survey the Galactic Plane Pulsar Snapshot (GPPS; Hou et al. 2022). These surveys have provided valuable insights into H II regions and DIGs within the disk of the Milky Way.

Alves et al. (2015) find that the distribution of the DIG is strongly correlated with the location of Galactic H II regions. Due to the spatial resolution of ${14}_{.}^{\mathrm{\prime }}4$ and a velocity resolution of 20 km s⁻¹, confirming the relationship between H II regions and DIGs using HIPASS data is very challenging.

SIGGMA provides RRL spectra with a root mean square (RMS) noise of about 1 mJy beam⁻¹ at a spectral resolution of 5 km s⁻¹ and a spatial resolution of approximately $3_{.}^{\mathrm{\prime }}4$. Thanks to its sensitive detections, it has been used to verify additional Galactic H II region candidates from the Wide-field Infrared Survey Explorer (WISE) H II region catalog (Anderson et al. 2014). Furthermore, its smoothed RRL map has confirmed the correlated distribution of H II regions and DIG. However, one should exercise caution when discussing the large-scale structure of the ionized diffuse gas with SIGGMA data due to its observing strategy (Liu et al. 2019).

In contrast to L-band surveys such as HIPASS and SIGGMA, GDIGS offers the most detailed perspective yet on the broad-scale distribution of ionized gas in the Milky Way, achieved through C-band on-the-fly (OTF) observations. Its Nyquist-sampled RRL map, with a spatial resolution of 3′ and RMS noise of approximately 5 mJy beam⁻¹, facilitates comprehensive studies of DIGs and their connections with H II regions. Additionally, multifrequency RRL observations will enable the modeling of the RRL radiation and allow for an accurate determination of the physical properties of the WIM.

Hou et al. (2022) present RRL findings as a byproduct of the GPPS survey conducted using the Five-hundred-meter Aperture Spherical radio Telescope (FAST; Qiu 1998; Nan et al. 2011; Qian et al. 2020). The obtained spectral data have a spatial resolution of approximately 3′, a spectral resolution of 2.2 km s⁻¹, and a typical spectral RMS noise of 0.25 mJy. Their RRL map unveils features predominantly composed of H II regions and DIG areas, demonstrating the efficacy of FAST in detecting faint RRLs. However, similar to SIGGMA, GPPS utilized the snapshot observing mode, resulting in a fully sampled map instead of a Nyquist-sampled one. Inevitably, there are gaps between the footprints of beams in the snapshot mapping mode. Consequently, its datasets may not fully capture the detailed structures of DIG.

To develop a deeper understanding of the diffuse ionized component of the ISM along the Galactic plane and exploit the sensitivity of FAST, we are planning a blind RRL survey. This project will use the FAST multi-beam on-the-fly (MBOTF) mode, made possible by its 19-beam receiver, which will allow us to generate RRL maps with spatial sampling rates exceeding Nyquist. A more detailed examination of the WIM structure on angular scales of a few arcminutes is anticipated. In this paper we report a pilot study of the project. Section 2 introduces the details of the project, including the observation and data reduction, and Sec. 3 presents the main results. In Sec. 4 we present a further analysis of the RRL detection, such as distance estimations and the properties of molecular gases located within these regions. Discussion and conclusions are made in Sects. 5 and 6.

2 Mapping hydrogen radio recombination lines with FAST

2.1 Observation

We conducted a blind RRL mapping observation with a size of about 80′ × 80′ centered at (α=18^h54^m48^s, δ =+01°29′00″) using the L-band 19-beam receiver of FAST. The arrangement of the FAST 19-element feed array (Jiang et al. 2020) enables a high-efficiency sky-mapping technique, the MBOTF observing mode.

The detailed information about the receiver and observing configuration is given in Table 1. In each observing session, we mapped the region twice, with one scanning in right ascension (RA) direction and the other in declination (Dec) direction. During the FAST share-risk stage, we accomplished three sessions in total.

2.2 Data reduction

A software pipeline for data reduction was developed using the Python programming language, with core algorithms taken from the Numpy (Harris et al. 2020) and Astropy (Astropy Collaboration 2018) libraries. Numpy provides support for numerical computing, while Astropy offers tools for related astronomical calculations. The integration of these libraries has streamlined the pipeline, significantly enhanced its efficiency.

Four steps were applied to produce data cubes for individual RRLs, which are radio frequency interference (RFI) excision, calibration, baseline removal, and then cube gridding. The final data cube was produced by averaging data cubes of individual RRLs after convolving them to the same beam size.

The RFI can cause abnormal features to the entire spectra, which may lead to artificial results to flux calibration, baseline and spectral line profile fitting. Therefore, we first searched for and removed the RFI from the individual spectra through all the raw datasets. Then the spectra were calibrated and cut into segments according to the rest frequency of the RRLs within the FAST L-band bandpass. The FAST bandpass contains 20 hydrogen α-RRLs from H165α to H184α. The segments of H172α, H177α, H180α and H181α were affected by RFI and excluded for averaging. To retain possible features of high velocity gases in the Galaxy and to help with the baseline fitting, we kept the bandpass of segments as 5 MHz. For each segment, we converted the frequency to the local standard of rest (LSR) velocity and then resampled the spectra with a uniform velocity range of −400 to +400 km s⁻¹ and a resolution of 0.5 km s⁻¹.

The optics of FAST makes its bandpass suffer from standing-wave ripples with ~1 MHz frequency width (Jiang et al. 2020). In the L band, it is about 200 km s⁻¹ width in velocity. Besides, there are weak but broad RFI, which could survive from the previous RFI excision steps and contribute to the irregular ripples in baselines. We explored and used the asymmetric least squares smoothing method (Eilers & Boelens 2005), which has produced good baseline fitting results (Liu et al. 2022).

Data cubes for each RRLs were made using an OTF gridding technique (Mangum et al. 2007) after baseline removal. They were then convolved to the spatial resolution of 4.7, which is the FAST beam width at rest frequency of H184α. The final step is to produce the stacked data cube by averaging the cubes of all 16 RRLs, with the weighting of $1/T_{\text{sys }}^2$ for data from different beams, resulting one RRL equivalent to H174α at 1237.626 MHz.

Fig. 1 The RMS distribution. Left: RMS map of the observed area. Middle: L-band continuum emission in this region obtained with the THOR project and observed with the JVLA. Right: histogram of the spectral RMS noise. The RMS noise is calculated from the spectrum of each pixel using the line-free channels from −300 to −100 km s−1 with a resolution of 0.5 km s−1. On the RMS map, there are three strong continuum sources (in blue) that introduce high RMS noise. The high noise level in the red region on the left side edge is due to incomplete observing coverage and thus a lack of sampling. The RMS histogram shows that the mode of the noise distribution is about 0.6 mJy beam−1.

Fig. 2 The results of RRL map and spectrum. Left: velocity-integrated map of RRLs from 0 to 120 km s−1. The contour levels are 1, 2, 4, 8, 16, and 32σ, where σ is ~20 mJy beam−1 km s−1. Right: stacked RRL spectrum toward G34.54+0.28, as an example of the RRL spectrum from a position outside of strong emission regions.

3 Main results of RRLs

3.1 Noise distribution of the stacked data cube

Using the stacked data cube, we calculated the RMS noise from the spectrum of each pixel. The line-free channels were chosen within the velocity range from −300 km s⁻¹ to −100 km s⁻¹ with a resolution of 0.5 km s⁻¹. Figure 1 gives the RMS noise map, L-band continuum emission from The H I/OH/Recombination (THOR) line survey of the Milky Way project (Beuther et al. 2016) observed with the Karl G. Jansky Very Large Array (JVLA), and histogram of RMS noise. Within this observed field, three strong continuum sources marked in blue ellipses, including the well-known supernova remnant W44, and the two H II regions G34.87−0.08 and G34.25+0.14, introduce intensive RMS noise spots as expected. The high noise level in the red region on the left side edge is due to incomplete observing coverage and thus a lack of sampling. The noise distribution across the remainder of the observed region is relatively uniform, with a mode value of ~0.6 mJy beam⁻¹. Although high RMS noise is observed in regions such as W44 and G34.25+0.14, it does not impact our scientific results. In the case of W44, no RRL emission was detected, thus yielding no results. For G34.25+0.14, the RRL emission is the most intense in the entire map, ensuring a high signal-to-noise ratio despite the elevated noise level.

3.2 The RRL moment and channel map

Hydrogen RRL detections are seen in a large amount of pixels in the stacked data cube. Searching through the stacked RRL data cube, we see that all hydrogen RRLs are within the velocity range from 0 to 120 km s⁻¹. Figure 2 shows the velocity-integrated map of RRLs from 0 to 120 km s⁻¹ and the spectrum toward one weak RRL emission direction, G34.54+0.28. A few intense RRL emission regions near the middle plane along with extended structures were detected with good signal-to-noise ratio for |b| within 0.5°.

Figure 3 is the RRL channel map made from the stacked data cube. The velocity range is from 25 to 100 km s⁻¹, which is set to fit the hydrogen line. Each channel is integrated over 10 km s⁻¹ range. The central velocity is labeled at top left corner on each map. Two velocity components were detected. The one is between 35 and 65 km s⁻¹ and the other is in range from 75 to 95 km s⁻¹.

Fig. 3 Channel maps of hydrogen RRL, equivalent to H174α at 1237.626 MHz, made from the stacked data cube with a beam size of $4_{.}^{\mathrm{\prime }}7$ (shown in the bottom left as a circle in each channel), which is integrated over a 5 km s−1 range. The central velocity is given at the top-left corner on each map. The RMS noise (σ) is ~0.001 Jy beam−1 km s−1. The contour levels are 5, 10, 20, 40, 80, 120, and 160σ.

3.3 RRL clump identifications

To search for RRL emission regions, we first calculated the dendrogram structures (Rosolowsky et al. 2008) from the stacked data cube. The dendrogram of a data cube is an abstraction of the changing topology of the isosurfaces as a function of contour level. It was originally developed to process molecular line data cubes. Here, we used dendrograms to represent the essential features of the hierarchical structure for RRL data cubes. The ability to track hierarchical structure over a range of scales makes this analysis philosophically different from local segmentation algorithms like “clumpfind” (Williams et al. 1994).

There are two key parameters for calculating the dendrogram structures from the RRL data cube, the minimum value and the minimum delta. The minimum value is set to 5 sigma, which serves as a threshold. Structures peaking below the minimum value were not counted. The minimum delta is set as 1 sigma, which is a minimum significance for structures or the merging point to be considered an independent structure.

The two types of outputs are referenced to as “leaf” and “branch”. A leaf means the detected structure is relative compact and cannot be resolved into substructures according to the dendrograms of the data cube. A branch stands for a complex, which always contains two or more leaves.

Based on the morphology of the RRL emission and the results of dendrogram structures, we defined two different types of structures: “clumps” and “clusters”. A RRL clump is a leaf that shows relatively strong emission center with an extended surrounding. There is no clear substructures of a RRL clump from the dendrogram results. But it may contain multiple spatially separated emission peaks. A RRL cluster is a branch that contains multiple RRL clumps and may spread to a large area with weak and uniform RRL signals.

As a result, there are 21 independent leaves identified in our data cube. Therefore, we cataloged those 21 hydrogen RRL clumps and indexed them by the line peak intensity of the peak pixel of each region, which we call the peak pixel flux (see Col. 4 of Table 2). Those detected clumps are shown as solid line regions in Fig. 4 (Top left). The fitted spectral parameters of the RRL clumps are listed in a catalog in Table 2. We note that there are several clumps with line widths narrower than 18 km s⁻¹, which should be mainly caused by baseline subtraction, when the baseline of spectrum is not flat. Detailed test and discussion had been presented in our technical paper (Liu et al. 2022).

3.4 Velocity distribution of extended ionized gas traced by RRL emission

Besides the 21 identified clumps, there are still remaining extended RRL emission in this region. Based on Fig. 3 and Table 2, it is evident that RRL emissions are concentrated within two distinct velocity ranges: 50 to 60 km s⁻¹ and 80 to 90 km s⁻¹. Hereafter, we refer to the former as the lower velocity component and the latter as the higher velocity component. The lower velocity RRL emission component is more intense and widespread throughout the field, thus garnering the most focus for discussion in this section.

We performed single-component Gaussian fitting within the velocity range of −50 to 150 km s⁻¹ for pixels with peak signals above 3σ across the entire cube. Most of the pixels exhibit only one velocity component, as shown in the channel map (see Fig. 3). However, some pixels, particularly in regions around clump 19, display two velocity components.

We verified the fitting results for the velocity component between 35 and 65 km s⁻¹ in each pixel with two velocity components, which generally agreed well with the spectrum itself. In most of the pixels with two velocity components, the low-velocity one, within 35–65 km s⁻¹, is more intense than the highvelocity ones. Even for pixels with comparable intensity of the two velocity components, the single-component Gaussian fitting can reliably determine the central velocity of the component within 35 to 65 km s⁻¹.

An example spectrum with two velocity components and the fitting results are presented in Fig. 5 from the position marked with a “+”. Another example spectrum for a single velocity component from the position marked with an “×” and the fitting result are also presented in Fig. 5.

The velocity distribution of the extended ionized gas was derived from the RRL line center velocities. The central velocity map of the lower velocity component is presented in Fig. 5, with the identified clumps masked, although the central velocity can still be obtained there. The map provides a continuous velocity distribution over a large region, including clumps 1, 6, 7, 9, 10, and 12, ranging from approximately 54 to 60 km s⁻¹ (shown in red).

4 Distance estimation for the RRL clumps and molecular gas properties

4.1 Distance of the RRL clumps

In general, spiral arms (SAs) manifest continuous traces in Galactic longitude (ℓ)-LSR velocity (υ) diagram of CO or HI emission. By comparing a source’s position to these ℓ. − υ traces of SAs, which have been precisely mapped using very long-baseline interferometry (VLBI) maser parallax measurements (Reid et al. 2019), one can infer its proximity to a SA and thereby estimate its distance. This approach, dependent on a SA model, is referred to as the SA method.

To refine the distance estimates of the RRL clumps, we utilize a parallax-based distance calculator that employs a Bayesian approach (Reid et al. 2016). This method produces a probability density function (PDF) for source distances by integrating all available measurements, including the l-v diagram, Galactic latitude, radio velocity, and proximity to sources with known parallaxes, along with the Galactic SA structure and the rotation curve established through VLBI maser astrometry. The distance estimates derived from the Bayesian method are contingent upon the selected priors. Notably, the default assignment of distance probabilities using the SA method, denoted as P_SA, is set to 0.85. This value has a substantial impact on the resulting distance probability distribution. Nevertheless, evidence from the HI ℓ − υ diagram, which includes the positions of maser sources with VLBI-determined parallaxes (Reid et al. 2019), suggests a discrepancy. Most maser sources near a Galactic longitude of ≈30° with V_lsr around 50 km s⁻¹ align with the distant segment of the Sagittarius-Carina arm according to the ℓ − υ trace. However, their parallaxes indicate they are actually situated in the nearer segment of the Sagittarius-Carina arm. This disparity implies that the ℓ−υ diagram may not reliably assign sources to specific SAs. Consequently, we adjusted P_SA downward to 0.1, thereby reducing the reliance on the SA method and minimizing the dependence on any specific SA model.

Similarly, the user-supplied parameter P_far giving the prior probability (from 0 to 1) that the source is at the far distance to weight the near and far PDFs. As shown in Fig. 6, RRL clump 1 shows conspicuous H I absorption lines with velocities extending to its own velocity (roughly 55 km s⁻¹) rather than that of the tangent point (roughly 100 km s⁻¹). This indicates RRL clump 1 is located at the near distance, according to the 21 cm continuum absorption method (Kuchar & Bania 1994; Kolpak et al. 2003). Additionally, the water maser source G34.41+0.23 is located near RRL clumps 1, 6 and 7, with a measured parallax distance of 3.03 ± 0.17 kpc (Mai et al. 2023). Overall, these observations suggest the RRL clumps likely reside at the near distance end of the range. We hence set P_far = 0.1 to down-weight the PDF at far distance.

To double-check the distances estimated by the Bayesian approach, we also estimated the kinematic distances using the code (Wenger et al. 2018) with the updated Galactic rotation curve (Reid et al. 2019). Figure 7 shows the differences between the distances estimated by the two independent approaches. Notably, the distance differences are within the uncertainties of the estimates themselves.

Accounting for the unknown peculiar motions (noncircular orbit motion) of the RRL clumps, we adopted a conservative uncertainty of 5 km s⁻¹ for LSR velocity, estimated from the Bar and Spiral Structure Legacy (BeSSeL) survey for maser sources at a Galactic longitude about 34° near or on the near portion of Sagittarius-Carina arm (Reid et al. 2019). Table 3 lists the estimated distances of RRL clumps. SgN and AqS denotes the near portion of the Sagittarius arm and the Aquila spur, respectively.

We adopted the Bayesian distances with maximum probabilities for all the RRL clumps in Table 3, except for clumps 3 and 21. We note that these two clumps each have two estimated distances of similar probability. While the distances of the first peak of probability place them in the inter-arm region, there exists an almost equal possibility they may be located on the Sagittarius-Carina arm. However, as shown in the right panel of Fig. 8, their kinematic distances suggest these two clumps likely belong to the Sagittarius-Carina arm, and hence we adopted their closer Bayesian distances. As shown in Fig. 5, the continuity of the extended emission and similar LSR velocities imply that the RRL clumps 1, 6, 7, 9, 10, 12, 16, and 17 are likely associated and located on the off-arm region near the kink on the Sagittarius-Carina arm as shown in the middle panel of Fig. 8.

Fig. 4 RRL clumps over RRL, HNC 1-0, and far-infrared maps. Top left: three groups of RRL clumps – within the Sagittarius-Carina arm (red), AqS (green), and off-arm near the Sagittarius-Carina arm (blue) – overlaid on a velocity-integrated intensity map of RRL from 0 to 120 km s−1. The beam size of FAST ($4_{.}^{\mathrm{\prime }}7$) is presented as circle in the bottom-left corner. Top right: contour of the velocity-integrated intensity map of HNC 1-0 from 53 to 62 km s−1 on the RRL map. The contour levels are 3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0, 27.0, and 30.0σ, where σ is 0.22 K km s−1. The beam of the Taeduk Radio Astronomy Observatory (TRAO) 14 m telescope for HNC 1-0 (57″) is presented as a small circle within that of the FAST beam. Bottom left: same as the top right but with 70 μm emission instead of HNC 1-0. The contour levels are 5, 12.5, 25, 125, 250, 500, and 1000 σ, where σ is 0.04 Jy pixel−1. The beam size of 70 μm (6″) emission is presented within the FAST beam. Bottom right: same as top right and bottom left, but with 160 μm emission. The contour levels are 5, 10, 50, 100, 200 and 400σ, where σ is 0.1 Jy pixel−1. The beam size of 160 μm (12′) emission is shown within the FAST beam.

Fig. 5 The RRL velocity field and spectrum examples. Left: distribution of the central velocity for the component between 35 and 65 km s−1. Middle: Spectrum from the pixel marked with a “+” within clump 19 and at the edge of clump 3. Right: spectrum from the pixel marked with an “×”.

Fig. 6 HI absorption analysis for RRL clump 1. Upper panel: HI absorption lines of RRL clump 1. Lower panel: kinematic distance estimates for sources at the Galactic longitude of RRL clump 1, which has an LSR velocity of 54 km s−1: 3.5 kpc (near) and 9.9 kpc (far). The dashed blue line marks the LSR velocity of the source, and the dotted black line the tangent point velocity.

Fig. 7 Comparison of distances estimated using the Bayesian approach (Reid et al. 2016) and those obtained from the kinematic distance calculator (Wenger et al. 2018).

Fig. 8 RRL clumps on the Galactic plane. Left panel: projected locations of RRL clumps on the Galactic plane, with SAs labeled in different colors. Squares indicate maser sources with VLBI parallaxes, circles RRL clumps with distances estimated from the Bayesian distance calculator provided (Reid et al. 2016), and filled circles RRL clumps located in off-arm regions. The two dashed black lines denote the Galactic longitude range of RRL clumps. Middle panel: zoomed-in view of the region marked by the dashed rectangle in the left panel. Numbers label RRL clumps located on the off-arm and Aquila spur. “K” denotes the kink position on the arm. The filled pink area of the Sagittarius-Carina arm denotes the arm width determined from the BeSSeL survey (Reid et al. 2019). Right panel: same as the middle panel, but the distances are estimated using the kinematics distance code (Wenger et al. 2018).

4.2 Dense gas clumps in this region

4.2.1 HCN and HNC 1-0 mapping observations with TRAO

The HCN and HNC 1-0 OTF mapping observations were carried out from February 2021 to December 2021 using the Taeduk Radio Astronomy Observatory (TRAO) 14m telescope. To cover the observed FAST RRL region, we divided it into 36 sub-regions, each with a size of 15′× 15′. The HCN 1-0 line at 89.087 GHz and HNC 1-0 line at 90.663 GHz lines were simultaneously observed in each subregion with a spectral resolution of 15 kHz, which corresponds to ~ 0.5 km s⁻¹ at 89 GHz. The Second Quabbin Optical Image Array focal plane array receiver and Fast Fourier Transform Spectrometer backend were used. The beam size is 57″, while the typical system temperature is about 170–200 K. The data were re-gridded to a cell size of 20″ and the spectra were smoothed to 0.8 km s⁻¹ per channel to improve the signal-to-noise ratio. Velocity-integrated map of HNC 1-0 shown in Fig. 4 (Top right) is from 53 km s⁻¹ to 62 km s⁻¹.

4.2.2 Virial mass of dense gas clumps

The virial mass was calculated using observational measurements, via $$M_{\mathrm{v}\mathrm{i}\mathrm{r}}=\frac{5{\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}^{2}R}{G},$$(1)

where R is the clump radius, σ_tot is the total velocity dispersion of the gas in the clump, and G is the gravitational constant. The clump radius is given by $R=\sqrt{A/\pi }={86}^{\mathrm{\prime }\mathrm{\prime }}$, where A is the projected area of the clump identified from HNC 1-0 line emission. The total velocity dispersion is the combination of the nonthermal and thermal motions of the gas within the clump, ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}^2={\sigma }_{\mathrm{n}\mathrm{t}}^2+{\sigma }_{\mathrm{t}\mathrm{h},⟨m⟩}^2$. The nonthermal velocity dispersion is given by ${\sigma }_{\mathrm{n}\mathrm{t}}^2={\sigma }_{\mathrm{o}\mathrm{b}\mathrm{s}}^2-{\sigma }_{\mathrm{t}\mathrm{h},\mathrm{m}}^2$. The observed velocity dispersion σ_obs was obtained from clump-averaged HNC 1-0 line emission. We have σ_obs =1.8 km s⁻¹ after deconvolving the channel width by ${\sigma }_{\mathrm{o}\mathrm{b}\mathrm{s}}=\sqrt{({\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^2-{\mathrm{F}\mathrm{W}\mathrm{M}\mathrm{H}}_{\mathrm{c}\mathrm{h}}^2)/8\ln 2}$, where FWHM stands for the full width at half maximum. The thermal velocity dispersion is negligible compared to the line width. The derived virial masses do not show significant differences within a temperature range from 20 to 50 K: 4845 M_⊙ for 20 K, 4892 M_⊙ for 30 K, 4938 M_⊙ for 40 K, and 4984 M_⊙ for 50 K. The distance of 3.03 kpc, determined from the parallax measurement (Mai et al. 2023) for water maser source G34.41+0.23, was used to derive physical size of R.

4.3 Warm dust traced in the far-infrared and molecular gas traced by ¹³CO 1-0 in this region

Far-infrared maps of the targeted region at 70 μm and 160 μm, observed by Herschel Space Observatory (Pilbratt et al. 2010; Molinari et al. 2010), are presented in Fig. 4 (Bottom left & right). These maps reveal warm dust heated by active star formation. Intense 70 μm and 160 μm emissions are detected near RRL clumps 1, 3, and between 6 and 7, indicating active star formation in these areas. Additionally, extended far-infrared emissions are also observed throughout the region.

Molecular gas traced by ¹³CO 1-0 from Boston University-Five College Radio Astronomy Observatory Galactic Ring Survey (Jackson et al. 2006) shows significant different distribution to that of HNC 1-0, which means only part of the molecular gas are dense enough to have upcoming star formation. The velocity-integrated maps of ¹³CO 1-0 from 40 to 52 km s⁻¹, 53 to 62 km s⁻¹, and 63 to 80 km s⁻¹ are presented in top left, middle, and right of Fig. 9, respectively. The corresponding velocity-integrated maps of HNC 1-0 from 40 to 52 km s⁻¹, 53 to 62 km s⁻¹, and 63 to 80 km s⁻¹ are presented in the bottom left, middle, and right of Fig. 9, respectively. The gas with velocity range between 40 and 52 km s⁻¹ is mainly from the Sagittarius-Carina arm, while the gas with velocity range of 53 to 62 km s⁻¹ is mainly from the off-arm regions (Reid et al. 2019). Not only different spatial distribution of total molecular gas traced by velocity-integrated maps of ¹³CO 1-0, but also different dense gas traction traced by ¹³CO 1-0 and HNC 1-0, can be found in these two velocity ranges. In summary, although a substantial amount of molecular gas within the Sagittarius-Carina arm is traced by ¹³CO 1-0 with velocity range of 40 to 52 km s⁻¹ and 63 to 80 km s⁻¹, almost no HNC 1-0 was detected. Conversely, the off-arm gas with a velocity range of 53 to 62 km s⁻¹ is observed with both ¹³CO 1-0 and with HNC 1-0, indicating higher gas density in this region. There are two small areas without HNC 1-0 observations at the top of the map, which are represented in white on the grayscale image.

Fig. 9 Comparison of CO and HNC emission in the field. Top left: velocity-integrated map of 13CO 1-0 from 40 to 52 km s−1. The contour levels are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, and 100σ, where σ is about 0.3 K km s−1. Top middle: velocity-integrated map of 13CO 1-0 from 53 to 62 km s−1. The contour levels are the same as in the top left. Top right: velocity-integrated map of 13CO 1-0 from 63 to 80 km s−1 with the same contour levels. Bottom left: velocity-integrated map of HNC 1-0 from 40 to 52 km s−1. The contour levels are 1, 3, 5, 7, and 9σ, where σ is about 0.25 K km s−1. Bottom middle: velocity-integrated map of HNC 1-0 from 53 to 62 km s−1. The contour levels are 3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0, 27.0, and 30.0σ, where σ is 0.22 K km s−1. Bottom right: velocity-integrated map of HNC 1-0 from 63 to 80 km s−1. The contour levels are the same as in the bottom-left panel.

5 Discussion

5.1 Comparison with the RRL emission detected by THOR

RRL emission near clump 1 has also been detected by THOR (Beuther et al. 2016) in the L band, showing a similar LSR velocity of ~54.0 km s⁻¹ as our results. Figure 10 displays the RRL map from THOR, integrating velocities from 40 to 70 km s⁻¹, overlaid with the 1.4 GHz continuum map depicted in blue contours. In accordance with previous studies (Reid & Ho 1985; Fey et al. 1994), we identified the cometary ultra-compact (UC) H II region as “C” and the ringlike H II region as “D”. An offset of ~15″ is observed between the peak of the continuum emission and the RRLs, although this offset is smaller than the spatial resolution of both the continuum map (25″ × 25″) and the RRL map (40″ × 40″).

Figure 10 indicates that the most intense emissions of both the RRL and the continuum are located near the ring-like H II region D rather than the cometary UC H II region C. Notably, the strongest radio continuum emissions at 3.7 cm and 2 cm originate from region C rather than region D (Fey et al. 1994). Emissions of H93α at 8.046 GHz were detected in both the cometary UC H II region and the ring-like H II region (Fey et al. 1994). The former exhibited a distinct LSR velocity, unlike the latter (~54.0 km s⁻¹), and this LSR velocity was attributed to feedback from young massive stars. These findings are consistent with our understanding of UC HII regions, characterized by their compact physical size and free-free self-absorption, which typically restricts the detection of RRL emissions at low frequencies (≲1 GHz). Conversely, higher-frequency bands, such as short, centimeter to millimeter wavelengths, are expected to provide more favorable conditions for observing RRL emissions from UC H II regions.

However, due to limited sensitivity, no RRL emission other than clump 1 can be detected in this region from THOR observations.

Fig. 10 THOR continuum map (Beuther et al. 2016) near clump 1, overlaid with L-band RRL-integrated intensity contours. The contour levels are 10, 14, 18, 22, 25, and 26σ, where σ is about 100 mJy beam−1 km s−1. The beam sizes of the RRL (40″ × 40″) and continuum (25″ × 25″) are given in the bottom-left corner.

5.2 The known H II REGIONS WITHIN THE FAST RRL MAP

We extracted the average spectra of 28 out of the 31 known H II regions from the FAST RRL data cube, utilizing the locations and dimensions provided by the WISE catalog (Anderson et al. 2014). The remaining three H II regions were not included because their sizes were too small or their spectra were too noisy to detect RRL from the FAST data cube. Subsequently, we compared the LSR velocities of the RRLs to those of the H II regions (see Fig. 11). For the majority of the H II regions, the discrepancies in LSR velocities are within ±10 km s⁻¹. However, six of these HII regions exhibit larger deviations in their LSR velocities, as documented in Table 4, and warrant further investigation.

We then compared the positions of the identified RRL clumps from the FAST data with the known H II regions (see the left panel of Fig. 12). Notably, nearly half of the RRL clumps (10 out of 21) do not overlap with the known H II regions. This suggests that many of the extended RRL features detected by FAST L-band observations are likely dominated by DIG. The known H II regions are also superimposed on the map of the LSR velocity field in the right panel of Fig. 12.

In addition to the large-scale variations in LSR velocity, we detected velocity gradients within some of the evolved H II regions that have larger angular sizes than the FAST beam size. One typical case is the H II region G034.940+00.073 labeled in Fig. 12 (right). Its LSR velocity has an average value of 49.7 km s⁻¹, with a minimum of 45.6 km s⁻¹, a maximum of 53.6 km s⁻¹, and a standard deviation of 2.6 km s⁻¹. The FWHM of this region has an average value of 21.9 km s⁻¹, with a minimum of 18.3 km s⁻¹, maximum of 26.1 km s⁻¹, and standard deviation of 1.7 km s⁻¹.

Fig. 11 Histogram of LSR velocity differences between the known HII in the WISE catalog (Anderson et al. 2014) and the spectra extracted from the FAST data cube toward those H II regions.

5.3 The relation between off-arm massive star-forming regions and the substructure of the Milky Way

VLBI astrometry of about 200 molecular masers (CH₃OH and H₂O) associated with massive star-forming regions have revealed the Milky Way to be a spiral galaxy featuring four primary arms: Norma-Outer, Scutum-Centaurus-OSC, Sagittarius-Carina, and Perseus. These observations also identified additional arm segments and spurs (Reid et al. 2019). As one of the major discoveries in Reid et al. (2019), several kinks of Galactic SAs, with different pitch angles on either side of the kink, were identified. Since kinks of arms were also found in spiral galaxies (Honig & Reid 2015), the formation of such kinks should be important for understanding spiral structures and the evolution of late type galaxies. The kink of the Sagittarius-Carina arm (Reid et al. 2019) is at β=24±2°, which is close to the discovered off-arm active massive star-forming regions (see Fig. 8). This proximity suggests that they may be gravitationally linked.

Dense gas in G34.26+0.15 was estimated to be more than 1.1×10⁴ M_⊙ with a FWHM of 130″ ($2_{.}^{\mathrm{\prime }}2$) (Hill et al. 2005), while the virial mass estimated from HCN 1-0 and HNC 1-0 lines is about 0.49×10⁴ M_⊙, which suggests that the clump is unstable to gravitational collapse and consistent with active star formation there (Reid & Ho 1985; Fey et al. 1994; Bartkiewicz et al. 2016; Elia et al. 2017). The total cold gas mass within the entire region traced by RRL clumps (1, 6, 7, 9, 10, 12, 16, and 17) as well as the neighboring extended RRL emission, will be several times of 10⁴ M_⊙, which may affect the nearby spiral structure where one kink, on either side of which have different pitch angels for an arm (Reid et al. 2019), exists.

6 Conclusions

Deep observations of low-frequency hydrogen RRLs in the L band with large single-dish radio telescopes, such as FAST, or interferometers, such as the Square Kilometre Array (SKA), toward the Galactic plane can provide an unbiased view of active massive star formation distribution, which can be traced via the surrounding low density extended ionized gas. This is because (i) these RRLs are free of dust extinction in the Galactic plane, (ii) there is little influence from the kinematics of local star formation feedback, and (iii) the low-frequency RRL emission from ionized gas can be an ideal probe of SAs, arm segments, and spurs of the Milky Way.

We conducted a pilot project of a blind L-band RRL survey toward the Galactic plane using FAST. The RRL moment map and channel map show the ability of such mapping observations to trace DIGs. Twenty-one RRL clumps are identified and cataloged from the RRL data cube. A comparison with the THOR data was conducted for the most intensive clump (clump 1), indicating that the L-band RRL emission detected by FAST from clump 1 may arise from the evolved H II region instead of the UC H II region. We also compared the RRL clumps and the known H II regions in the WISE catalog (Anderson et al. 2014), finding that many of the extended RRL features detected by FAST L-band observations are likely dominated by DIG.

We further calculated the distances using the Bayesian approach (Reid et al. 2016) and updated Galactic parameters (Reid et al. 2019). According to their distance, the clumps are classified into three groups: ten are within Sagittarius-Carina arm, three in AqS, and eight in the off-arm regions near the Sagittarius-Carina arm. The central radial velocities (V_LSR) of the three groups are below 53 km s⁻¹ for clumps in the Sagittarius-Carina arm, above 80 km s⁻¹ for clumps in AqS, and between 53 and 61 km s⁻¹ for those in the off-arm regions near the Sagittarius-Carina arm. Residual extended RRL emissions with similar central velocities to those of nearby clumps also have high signal-to-noise ratios in most of the regions.

Dense molecular clumps are observed exclusively near RRL clumps in the off-arm regions adjacent to the Sagittarius-Carina arm. In contrast, although molecular gas traced by ¹³CO 1-0 is prevalent throughout this region, the volume densities of the molecular gas near the RRL clumps within the Sagittarius-Carina arm are insufficient to excite HNC 1-0 emission, which requires densities of approximately 10⁵ cm⁻³ at 20 K (Shirley 2015).

The off-arm and in-arm molecular gas within this area present significantly different dense gas fractions, which will directly influence the upcoming star formation in these molecular clouds. By considering the massive star-forming activities and estimating their total mass, we suggest that those offarm clumps could possibly be related to the near kink of the Sagittarius-Carina arm.

Fig. 12 Known H II regions in the field. Left: known H II region from the WISE catalog overlaid on the detected integral RRL map. Right: known H II regions on the velocity field of the diffuse RRL emission.

Acknowledgements

We would like to thank the anonymous referee for his/her valuable comments and suggestions, which helped a lot in improving the quality of our work. This work made use of the data from Five-hundred-meter Aperture Spherical radio Telescope (FAST). FAST is a Chinese national mega-science facility, operated by National Astronomical Observatories, Chinese Academy of Sciences. This work is partially supported by the science and technology innovation program of Hunan province under grant number 2024JC0001.

References

All Tables

All Figures

Fig. 1 The RMS distribution. Left: RMS map of the observed area. Middle: L-band continuum emission in this region obtained with the THOR project and observed with the JVLA. Right: histogram of the spectral RMS noise. The RMS noise is calculated from the spectrum of each pixel using the line-free channels from −300 to −100 km s−1 with a resolution of 0.5 km s−1. On the RMS map, there are three strong continuum sources (in blue) that introduce high RMS noise. The high noise level in the red region on the left side edge is due to incomplete observing coverage and thus a lack of sampling. The RMS histogram shows that the mode of the noise distribution is about 0.6 mJy beam−1.

In the text

	Fig. 2 The results of RRL map and spectrum. Left: velocity-integrated map of RRLs from 0 to 120 km s−1. The contour levels are 1, 2, 4, 8, 16, and 32σ, where σ is ~20 mJy beam−1 km s−1. Right: stacked RRL spectrum toward G34.54+0.28, as an example of the RRL spectrum from a position outside of strong emission regions.
In the text

Fig. 3 Channel maps of hydrogen RRL, equivalent to H174α at 1237.626 MHz, made from the stacked data cube with a beam size of $4_{.}^{\mathrm{\prime }}7$ (shown in the bottom left as a circle in each channel), which is integrated over a 5 km s−1 range. The central velocity is given at the top-left corner on each map. The RMS noise (σ) is ~0.001 Jy beam−1 km s−1. The contour levels are 5, 10, 20, 40, 80, 120, and 160σ.

In the text

Fig. 4 RRL clumps over RRL, HNC 1-0, and far-infrared maps. Top left: three groups of RRL clumps – within the Sagittarius-Carina arm (red), AqS (green), and off-arm near the Sagittarius-Carina arm (blue) – overlaid on a velocity-integrated intensity map of RRL from 0 to 120 km s−1. The beam size of FAST ($4_{.}^{\mathrm{\prime }}7$) is presented as circle in the bottom-left corner. Top right: contour of the velocity-integrated intensity map of HNC 1-0 from 53 to 62 km s−1 on the RRL map. The contour levels are 3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0, 27.0, and 30.0σ, where σ is 0.22 K km s−1. The beam of the Taeduk Radio Astronomy Observatory (TRAO) 14 m telescope for HNC 1-0 (57″) is presented as a small circle within that of the FAST beam. Bottom left: same as the top right but with 70 μm emission instead of HNC 1-0. The contour levels are 5, 12.5, 25, 125, 250, 500, and 1000 σ, where σ is 0.04 Jy pixel−1. The beam size of 70 μm (6″) emission is presented within the FAST beam. Bottom right: same as top right and bottom left, but with 160 μm emission. The contour levels are 5, 10, 50, 100, 200 and 400σ, where σ is 0.1 Jy pixel−1. The beam size of 160 μm (12′) emission is shown within the FAST beam.

In the text

	Fig. 5 The RRL velocity field and spectrum examples. Left: distribution of the central velocity for the component between 35 and 65 km s−1. Middle: Spectrum from the pixel marked with a “+” within clump 19 and at the edge of clump 3. Right: spectrum from the pixel marked with an “×”.
In the text

	Fig. 6 HI absorption analysis for RRL clump 1. Upper panel: HI absorption lines of RRL clump 1. Lower panel: kinematic distance estimates for sources at the Galactic longitude of RRL clump 1, which has an LSR velocity of 54 km s−1: 3.5 kpc (near) and 9.9 kpc (far). The dashed blue line marks the LSR velocity of the source, and the dotted black line the tangent point velocity.
In the text

	Fig. 7 Comparison of distances estimated using the Bayesian approach (Reid et al. 2016) and those obtained from the kinematic distance calculator (Wenger et al. 2018).
In the text

Fig. 8 RRL clumps on the Galactic plane. Left panel: projected locations of RRL clumps on the Galactic plane, with SAs labeled in different colors. Squares indicate maser sources with VLBI parallaxes, circles RRL clumps with distances estimated from the Bayesian distance calculator provided (Reid et al. 2016), and filled circles RRL clumps located in off-arm regions. The two dashed black lines denote the Galactic longitude range of RRL clumps. Middle panel: zoomed-in view of the region marked by the dashed rectangle in the left panel. Numbers label RRL clumps located on the off-arm and Aquila spur. “K” denotes the kink position on the arm. The filled pink area of the Sagittarius-Carina arm denotes the arm width determined from the BeSSeL survey (Reid et al. 2019). Right panel: same as the middle panel, but the distances are estimated using the kinematics distance code (Wenger et al. 2018).

In the text

Fig. 9 Comparison of CO and HNC emission in the field. Top left: velocity-integrated map of 13CO 1-0 from 40 to 52 km s−1. The contour levels are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, and 100σ, where σ is about 0.3 K km s−1. Top middle: velocity-integrated map of 13CO 1-0 from 53 to 62 km s−1. The contour levels are the same as in the top left. Top right: velocity-integrated map of 13CO 1-0 from 63 to 80 km s−1 with the same contour levels. Bottom left: velocity-integrated map of HNC 1-0 from 40 to 52 km s−1. The contour levels are 1, 3, 5, 7, and 9σ, where σ is about 0.25 K km s−1. Bottom middle: velocity-integrated map of HNC 1-0 from 53 to 62 km s−1. The contour levels are 3.0, 6.0, 9.0, 12.0, 15.0, 18.0, 21.0, 24.0, 27.0, and 30.0σ, where σ is 0.22 K km s−1. Bottom right: velocity-integrated map of HNC 1-0 from 63 to 80 km s−1. The contour levels are the same as in the bottom-left panel.

In the text

	Fig. 10 THOR continuum map (Beuther et al. 2016) near clump 1, overlaid with L-band RRL-integrated intensity contours. The contour levels are 10, 14, 18, 22, 25, and 26σ, where σ is about 100 mJy beam−1 km s−1. The beam sizes of the RRL (40″ × 40″) and continuum (25″ × 25″) are given in the bottom-left corner.
In the text

	Fig. 11 Histogram of LSR velocity differences between the known HII in the WISE catalog (Anderson et al. 2014) and the spectra extracted from the FAST data cube toward those H II regions.
In the text

	Fig. 12 Known H II regions in the field. Left: known H II region from the WISE catalog overlaid on the detected integral RRL map. Right: known H II regions on the velocity field of the diffuse RRL emission.
In the text