# Connection between Nonaxisymmetric Structures and Neutral Gas Distribution in Disk Galaxies

Ze-Zhong Liang, Jing Wang, Hua Gao, Luis C Ho, E. Athanassoula

► To cite this version:

Ze-Zhong Liang, Jing Wang, Hua Gao, Luis C Ho, E. Athanassoula. Connection between Nonaxisymmetric Structures and Neutral Gas Distribution in Disk Galaxies. The Astrophysical Journal, 2025, 983 (1), pp.61. 10.3847/1538-4357/ad87f1. hal-05470446

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# Connection between Nonaxisymmetric Structures and Neutral Gas Distribution in Disk Galaxies

Ze-Zhong Liang¹,², Jing Wang², Hua Gao³, Luis C. Ho¹,², and E. Athanassoula⁴

¹Department of Astronomy, School of Physics, Peking University, Beijing 100871, People's Republic of China

²Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People's Republic of China; jwang_astro@pku.edu.cn

³Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

⁴Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France

Received 2024 May 27; revised 2024 October 5; accepted 2024 October 15; published 2025 April 4

## Abstract

Nonaxisymmetric structures, such as bars and spiral arms, are known to concentrate molecular gas and star formation in galaxy centers, actively building up the pseudobulges. However, the direct link between the neutral (i.e., molecular and atomic) gas distribution and the exerted torque forces over a broader radial range of galactic disks still remains to be explored. In the present work, we investigate this link by carefully evaluating the torque force field using the 3.6 µm images for 17 The H I Nearby Galaxy Survey galaxies, and measuring neutral gas distribution on resolved atomic and molecular line maps. We find that galaxies with stronger torque forces show a more concentrated neutral gas distribution over the disk scale, defined as half the isophotal radius at $25.5 \ \text{mag arcsec}^{-2}$. The correlation holds regardless of whether the neutral gas fraction or the effective stellar mass surface density is controlled for. In addition, kiloparsec-scale neutral gas overdensities tend to be located close to the local maxima of torque forces. Most of these correlations involving the torque forces are comparatively stronger than those using the traditional Fourier amplitudes to quantify the nonaxisymmetric structures. These results are consistent with the scenario that nonaxisymmetric structures exert torque forces and trigger dissipative processes to transport gas inward, not only to build the pseudobulges but also to fuel the inner disk growth. In this regard, nonaxisymmetric structures inducing stronger torque forces appear to be more efficient in these processes.

*Unified Astronomy Thesaurus concepts: Galaxy evolution (594); Galaxy structure (622); Disk galaxies (391); Galaxy bars (2364); Spiral arms (1559); Interstellar medium (847)*

*Materials only available in the online version of record: figure set*

## 1. Introduction

As redshift decreases, galaxy evolution becomes much slower (Kraljic et al. 2012), and nonaxisymmetric structures, such as bars and spiral arms, are expected to play a significant role in this secular phase of galaxy evolution (J. Kormendy & R. C. Kennicutt 2004; T. Kim et al. 2016; J. A. Sellwood & K. L. Masters 2022).

Bars, for example, have long been considered to be a major driver of galaxy evolution. Observations have demonstrated that bars are ubiquitous in the local Universe (e.g., K. Sheth et al. 2008; P. Erwin 2018; H. Gao et al. 2018). Moving to higher redshifts, recent James Webb Space Telescope (JWST) observations have found bars up to $z \approx 3$, suggesting that the bar-related processes might have already started at these early epochs (e.g., Y. Guo et al. 2023; S. Huang et al. 2023; Z. A. Le Conte et al. 2024). Theories have predicted that the interaction between bars and gas would significantly impact the galaxy evolution (E. Athanassoula 2003; V. P. Debattista et al. 2006; K. Saha et al. 2010). Forces exerted by bars could induce shock processes that effectively transport the gas inward (e.g., E. Athanassoula 1992; W.-T. Kim et al. 2012a; M. C. Sormani et al. 2015). In simulations, this inflow could have an inflow rate of $\sim(0.01–100) M_{\odot} \text{ yr}^{-1}$, depending on the bar strength and pattern speed (E. Athanassoula 1992; M. W. Regan &

P. J. Teuben 2004; W.-T. Kim et al. 2012a). This gas inflow might fuel central star formation, and a central mass concentration of gas and stars formed out of the gas with mass up to $\sim10^{10} M_{\odot}$ might form in the form of disk-like pseudobulges (e.g., E. Athanassoula 2005; E. Athanassoula et al. 2013; D. R. Cole et al. 2014). Note that H. Gao et al. (2020) have found neither more abundant nor more prominent pseudobulges in barred galaxies compared to the nonbarred counterparts, likely because of the self-limit nature of these fueling processes, though one needs to keep in mind the uncertainties in classifications of bulges due to disagreement in the adopted criteria (D. A. Gadotti 2009; J. Neumann et al. 2017; H. Gao et al. 2022). The gas might also stall due to dynamical resonances, shocks, increased centrifugal force, or reduced shear (e.g., P. Rautiainen & H. Salo 2000; M. W. Regan & P. Teuben 2003; W.-T. Kim et al. 2012a; M. R. Krumholz & J. M. D. Kruijssen 2015), leading to local accumulation of gas in the form of rings and other gas morphological features (R. Buta & F. Combes 1996; W.-T. Kim et al. 2012b).

Previous observations focusing on barred galaxies have indeed found kinematic evidence supporting the inward motion of gas (T. M. Schmidt et al. 2016; E. M. Di Teodoro & J. E. G. Peek 2021). Both the molecular gas distribution (e.g., K. Sakamoto et al. 1999; K. Sheth et al. 2005; R. Chown et al. 2019) and star formation rate at timescales of up to $\sim2 \text{ Gyr}$ (e.g., S. L. Ellison et al. 2011; J. Wang et al. 2012; L. Lin et al. 2017; J. Wang et al. 2020a) have been observed to be elevated in barred galaxy center, likely explaining the origin of central disk-like components (e.g., J. Méndez-Abreu et al. 2014;

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P. Erwin et al. 2015; D. A. Gadotti et al. 2020). While most previous works focused on the concentration of molecular gas and star formation, molecular gas has a short depletion time (~(1–2) Gyr), particularly in the galactic central regions (A. K. Leroy et al. 2008). The molecular gas needs to be replenished by the atomic gas that is not only of similar masses as the molecular gas within the star-forming disks (J. Wang et al. 2020b), but is also (1.5–4) times more extended than the star-forming disks (R. A. Swaters et al. 2002; J. Wang et al. 2020b). The atomic gas should be susceptible to the same inflow-driven mechanisms as the molecular gas, and its inflow should benefit the growth of not only bulge masses but also the disk mass on its way (X. Chen et al. 2020). Interestingly, both simulations and observations support that bars would simultaneously lead to a central hole in atomic gas (HI) distribution (E. Athanassoula et al. 2013; L. Newnham et al. 2020). Therefore, the net effect of bars in funneling the neutral (atomic and molecular) gas remains elusive. Observations have also revealed rich gas morphological features in barred galaxies (S. E. Meidt et al. 2021; S. K. Stuber et al. 2023); yet their link with the nonaxisymmetric structures and their association with disk growth remains to be unveiled.

Spiral arms, being another generic morphological feature in the local Universe, could also play a role in driving galaxy secular evolution (J. A. Sellwood & K. L. Masters 2022). Spiral arms are also expected to induce shock processes and funnel the gas inward (Y. Kim & W.-T. Kim 2014). Y. Kim & W.-T. Kim (2014) have estimated the average inflow rate induced by spiral potential to be ~((0.05–0.3) M<sub>☉</sub> yr<sup>-1</sup>), also depending on the spiral strength and the pattern speed. Observations have demonstrated that the force of spiral arms might compress the gas dissipatively (S. E. Meidt et al. 2021), and could transport the gas inward (S. García-Burillo et al. 2005; S. Haan et al. 2009; M. Querejeta et al. 2016). More active galaxy star formation, more active central star formation, and a higher fraction of pseudobulges have also been observed in galaxies with stronger spirals (S.-Y. Yu et al. 2021, 2022a, 2022b).

In a sense, various nonaxisymmetric structures (bars, spiral arms, also ovals, etc.) share a uniformity in terms of inducing the gas inflow to affect galaxy evolution (J. Kormendy & R. C. Kennicutt 2004), with the efficiency presumably dependent upon the strength, i.e., the degree they are able to perturb the regular motion of disk neutral gas. While this uniformity has already been tested observationally using, e.g., stellar mass surface density as a strength proxy (S.-Y. Yu et al. 2022a), torque force offers comparatively a more direct characterization (e.g., F. Combes & R. H. Sanders 1981; E. Athanassoula 1992; A. C. Quillen et al. 1994; E. Athanassoula & A. Misiriotis 2002; E. Laurikainen & H. Salo 2002; S. Díaz-García et al. 2016b). This is because the latter not only offers a more physical measure of the effects due to nonaxisymmetric structures but could also better accounts for (through a normalization by the centrifugal force) the stabilizing effects of the symmetric part of disk, the bulge (E. Laurikainen et al. 2004), and the dark matter halo (S. Díaz-García et al. 2016b), which counters the action of nonaxisymmetric structures. Yet, direct correlations between torque forces and the neutral gas distribution almost remain elusive (but see N. Kuno et al. 2007). Furthermore, it is conjectured that different nonaxisymmetric structures could in principle work together or in relay to transport the gas across the disk (I. Minchev & B. Famaey 2010; W.-Y. Seo & W.-T. Kim 2013; J. Wang et al. 2020a). In this regard, it is possible that the radially average strength of the nonaxisymmetric structures, rather than the maximal force

corresponding to the strongest component, is more important in determining the effectiveness of global gas transport processes; yet this still remains to be tested.

The present work would therefore aim to revisit the link between nonaxisymmetric structures characterized by the force they exert, and the distribution of the neutral gas, i.e., the atomic plus the molecular gas. Both atomic and molecular data with resolution that is able to resolve the stellar disk are therefore necessary for undertaking this investigation. To this aim, we refer to the HI Nearby Galaxy Survey (THINGS; F. Walter et al. 2008) sample, for which uniform measurements of their HI and molecular gas content, as well as the stellar mass distribution from the 3.6 µm mid-infrared images, are available (R. C. Kennicutt et al. 2003; A. K. Leroy et al. 2009; K. Sheth et al. 2010). An inevitable cost for this is naturally a small sample size (17), which calls for careful statistical analysis as well as meticulous uncertainty estimation. We note that the present work could be expanded in the future, either with a uniform reduction of the archival, high-resolution HI imaging data, or when more data from Square Kilometre Array pathfinder surveys, including MONGODB (W. J. G. de Blok et al. 2024) and WALLABY (B. S. Koribalski et al. 2020), are available.

The present work is organized as follows. In Section 2, we briefly describe the sample and the data. In Section 3, we explain how we evaluate the torque forces and quantify the neutral gas distribution. In Section 4, we present our results, which are further discussed in Section 5 and summarized in Section 6.

## 2. Sample and Data

### 2.1. Sample

As mentioned in the previous section, we select our sample galaxies from the THINGS sample, which consists of 34 nearby ($D \lesssim 15$ Mpc), late-type (Hubble type $T > 0$) galaxies that cover a wide range of galactic properties (F. Walter et al. 2008). We further select a disk galaxy sample that satisfies (i) $T < 9$, and (ii) inclination $i \lesssim 65^\circ$, according to Table 1 of F. Walter et al. (2008). The latter criterion ensures that deprojection would not introduce significant uncertainties in characterizing the disk structures (Y. Zou et al. 2014).

In addition, we consider NGC 4826 not an ideal case to study the secular evolution driven by nonaxisymmetric structures, since NGC 4826 has been observed to possess counterrotating gaseous disks, which should signify a transient state due to external perturbation (R. Braun et al. 1992, 1994). Our sample therefore consists of 17 disk galaxies as listed in Table 1.

### 2.2. 3.6 µm Imaging Data

We mainly use the 3.6 µm IRAC 1 imaging data from the Spitzer Infrared Nearby Galaxies Survey (SINGS; R. C. Kennicutt et al. 2003; SINGS Team 2020)<fnref n="5" /> to trace the stellar mass distribution, wherever available. The SINGS IRAC 1 imaging data feature a point-spread function (PSF) FWHM of $\gamma_{PSF} \approx 1.66$ or typically $\sim 70$ pc,<fnref n="6" /> and reach a depth typically of $\sim 0.003$ MJy sr$^{-1}$ or $\sim 0.7 M_{\odot} \text{ pc}^{-2}$. For NGC 2903, NGC 5236, and NGC 5457, we use the 3.6 µm IRAC 1

<footnote n="5">⁵ https://irsa.ipac.caltech.edu/data/SPITZER/SINGS/</footnote>

<footnote n="6">⁶ The PSF properties for the Spitzer cryogenic mission are quoted. See Section 2.2.2 of IRAC Instrument & Instrument Support Teams (2021).</footnote>
<table><caption>**Table 1**
Sample Galaxies</caption><thead><tr><th>Index<br>(1)</th><th>Object<br>(2)</th><th>α<br>(h m s)<br>(3)</th><th>δ<br>(deg arcmin arcsec)<br>(4)</th><th>i<br>(deg)<br>(5)</th><th>φ<sub>PA</sub><br>(deg)<br>(6)</th><th>Note<br>(7)</th></tr></thead><tbody><tr><td>1</td><td>NGC 628</td><td>1 36 41.7</td><td>+15 47 01.1</td><td>28.4 ± 1.7</td><td>81 ± 36</td><td><sup>a</sup></td></tr><tr><td>2</td><td>NGC 925</td><td>2 27 16.5</td><td>+33 34 43.5</td><td>63.3 ± 0.4</td><td>106 ± 2</td><td>...</td></tr><tr><td>3</td><td>NGC 2403</td><td>7 36 51.1</td><td>+65 36 02.9</td><td>62.9 ± 1.1</td><td>124 ± 2</td><td>...</td></tr><tr><td>4</td><td>NGC 2903</td><td>9 32 10.1</td><td>+21 30 04.3</td><td>65.4 ± 2.7</td><td>24 ± 4</td><td>...</td></tr><tr><td>5</td><td>NGC 2976</td><td>9 47 15.3</td><td>+67 55 00.0</td><td>64.8 ± 1.8</td><td>154 ± 12</td><td>...</td></tr><tr><td>6</td><td>NGC 3031</td><td>9 55 33.1</td><td>+69 03 54.7</td><td>58.7 ± 2.6</td><td>150 ± 2</td><td>...</td></tr><tr><td>7</td><td>NGC 3184</td><td>10 18 16.9</td><td>+41 25 27.6</td><td>31.8 ± 2.9</td><td>146 ± 24</td><td><sup>a</sup></td></tr><tr><td>8</td><td>NGC 3351</td><td>10 43 57.8</td><td>+11 42 13.2</td><td>45.6 ± 2.4</td><td>12 ± 4</td><td><sup>a</sup></td></tr><tr><td>9</td><td>NGC 3621</td><td>11 18 16.5</td><td>-32 48 50.9</td><td>64.7 ± 1.0</td><td>165 ± 3</td><td><sup>b</sup></td></tr><tr><td>10</td><td>NGC 3627</td><td>11 20 15.0</td><td>+12 59 29.6</td><td>61.1 ± 4.6</td><td>172 ± 3</td><td>...</td></tr><tr><td>11</td><td>NGC 4736</td><td>12 50 53.0</td><td>+41 07 13.2</td><td>37.6 ± 1.2</td><td>125 ± 5</td><td><sup>c</sup></td></tr><tr><td>12</td><td>NGC 5055</td><td>13 15 49.2</td><td>+42 01 45.3</td><td>64.8 ± 1.7</td><td>100 ± 2</td><td><sup>c</sup></td></tr><tr><td>13</td><td>NGC 5194</td><td>13 29 52.7</td><td>+47 11 42.4</td><td>42.3 ± 4.7</td><td>41 ± 5</td><td><sup>a</sup></td></tr><tr><td>14</td><td>NGC 5236</td><td>13 37 00.9</td><td>-29 51 55.9</td><td>19.9 ± 0.6</td><td>7 ± 8</td><td><sup>a</sup>, <sup>b</sup></td></tr><tr><td>15</td><td>NGC 5457</td><td>14 03 12.5</td><td>+54 20 55.9</td><td>29.5 ± 4.6</td><td>102 ± 41</td><td><sup>a</sup></td></tr><tr><td>16</td><td>NGC 6946</td><td>20 34 52.2</td><td>+60 09 14.4</td><td>32.3 ± 1.9</td><td>62 ± 3</td><td>...</td></tr><tr><td>17</td><td>NGC 7793</td><td>23 57 49.7</td><td>-32 35 27.9</td><td>52.7 ± 1.0</td><td>100 ± 3</td><td><sup>b</sup>, <sup>c</sup></td></tr></tbody></table>

**Notes.** Summary of the sample galaxy properties. Column (1): index. Column (2): object designation. Columns (3)–(4): central coordinate. Columns (5)–(6): disk inclination *i* and position angle *φ*<sub>PA</sub>. Column (7): note.

<sup>a</sup> The central coordinates from C. Trachternach et al. (2008) and the H I kinematic model from W. J. G. de Blok et al. (2008) are not available. We determine the central coordinate and disk orientation parameters using 3.6 µm images.

<sup>b</sup> CO imaging data from T. T. Helfer et al. (2003) and A. K. Leroy et al. (2009) are not available. We estimate molecular gas distribution by inverting the subkiloparsec Schmidt law (Section 2.4).

<sup>c</sup> A strong disk warp is identified from the H I kinematic model of W. J. G. de Blok et al. (2008).

imaging data from the Spitzer Survey of Stellar Structure in Galaxies (S<sup>4</sup>G; K. Sheth et al. 2010; J. C. Muñoz-Mateos et al. 2013; M. Querejeta et al. 2015; S4G Team 2020; A. E. Watkins et al. 2022),<sup>7</sup> which feature a PSF FWHM of γ<sub>PSF</sub> ≈ (1.7–2.1)" (K. Sheth et al. 2010; H. Salo et al. 2015),<sup>8</sup> and, in these three cases, similar physical resolutions and depths with the SINGS IRAC 1 images.

Masks for unrelated sources and sigma maps, i.e., pixel-wise estimation of flux uncertainty, of S<sup>4</sup>G imaging data are directly adopted from J. C. Muñoz-Mateos et al. (2015) since they have already been optimized for the data. For SINGS images, we generate masks and sigma maps following the procedures outlined in J. C. Muñoz-Mateos et al. (2009) and H. Salo et al. (2015), respectively.<sup>9</sup> To strictly mask out unrelated sources, we also make use of PROFOUND (A. S. G. Robotham 2018; A. S. G. Robotham et al. 2018), which is capable of automatically dilating the mask to contain most flux of the unrelated sources, to generate a second mask and combine it with the previous one. Finally, the 3.6 µm images are converted to the stellar mass surface density following (J. C. Muñoz-Mateos et al. 2013),

$$ \frac{\Sigma_{*}}{M_{\odot} \text{ pc}^{-2}} = 3.7 \times 10^{2} F_{\text{corr}} \cos i \left( \frac{I_{3.6 \mu\text{m}}}{\text{MJy sr}^{-1}} \right), \quad (1) $$

assuming a 3.6 µm mass-to-light ratio γ<sub>3.6 µm</sub> = 0.53 (M. Eskew et al. 2012) and an aperture correction coefficient F<sub>corr</sub> = 0.91.<sup>10</sup>

## 2.3. 21 cm Line Data

We use the natural-weighted 21 cm line data from THINGS (F. Walter et al. 2008), to trace the atomic hydrogen, H I. For our sample galaxies, the 21 cm line data typically feature a synthetic beam FWHM of *b*<sub>FWHM</sub> ≈ 10" or ~400 pc. The typical single-channel noise is ~0.4 mJy beam<sup>-1</sup> or roughly ~0.4 *M*<sub>☉</sub> pc<sup>-2</sup>, assuming a ~20 km s<sup>-1</sup> signal width.

The analyses in the present work implicitly assume that the galaxy disks are flat, which is not necessarily the case, especially for H I disks which might warp (P. C. van der Kruit 2007). Indeed, at least three galaxies (NGC 4736, NGC 5055, and NGC 7793) are identified to show significant H I warps within their disk radius *R*<sub>25.5</sub>, i.e., the radius where the 3.6 µm surface brightness reaches 25.5 mag arcsec<sup>-2</sup>, following the method outlined in G. I. G. Józsa (2007) and J. Wang et al. (2017) using the kinematic information from W. J. G. de Blok et al. (2008). We test and find that removing these three galaxies does not qualitatively alter our major results in Section 4.

## 2.4. Molecular Gas Line Data and Neutral Gas Distribution

We mainly use the CO *J* = 2 → 1 *ν* = 230 GHz emission line data from the Heterodyne Receiver Array C. Line Extragalactic Survey (HERACLES; A. K. Leroy et al. 2009) to trace the

<footnote n="7"><sup>7</sup> https://irsa.ipac.caltech.edu/data/SPITZER/S4G</footnote>

<footnote n="8"><sup>8</sup> The PSF properties for the Spitzer post-cryogenic mission are quoted, as the bulk of the S<sup>4</sup>G imaging data has been obtained over this period.</footnote>

<footnote n="9"><sup>9</sup> Note that for SINGS images, the background subtracted by the SINGS pipeline should also be added back in Equation (8) of H. Salo et al. (2015).</footnote>

<footnote n="10"><sup>10</sup> This so-termed “maximum scaling factor” aperture correction coefficient in principle applies to surface brightness measurements of very extended sources. See Section 8.2 of IRAC Instrument & Instrument Support Teams (2021).</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Showcasing torque force field evaluation for barred spiral galaxy NGC 2903 (top row) and nonbarred spiral galaxy NGC 628 (bottom row). (a), (d) Deprojected stellar mass surface density in $M_{\odot} pc^{-2}$. (b), (e) Evaluated torque force field $Q_T$, sign being arbitrary. (c), (f) Radial profile of $Q_T$. The hatched region shows 3 times the PSF FWHM.</figcaption></figure>

molecular gas. For NGC 3351, we use the CO $J=1 \rightarrow 0$ $\nu=115$ GHz emission line data from the BIMA Survey of Nearby Galaxies (BIMA SONG; T. T. Helfer et al. 2003). These molecular line data typically feature a beam FWHM of $b_{FWHM} \approx 13''$ or $\sim 560$ pc and reach a depth of $\sim 0.10 M_{\odot} pc^{-2}$ assuming a $\sim 20$ km s$^{-1}$ signal width. Neither data are available for NGC 3621, NGC 5236, and NGC 7793, and we thus estimate the molecular gas distribution by inverting the subkiloparsec Schmidt law (F. Bigiel et al. 2008), with the star formation rate distribution evaluated using the $15''$ resolution (for these three galaxies, $\sim 360$ pc) WISE4 and far-UV images retrieved from the $z=0$ Multiwavelength Galaxy Synthesis database (A. K. Leroy et al. 2019; K. Sandstrom 2019).<fnref n="11" />

We match the beam size and combine the H I and molecular gas distribution for each galaxy, which is then converted into mass surface density units following the appendix of A. K. Leroy et al. (2008). Following A. K. Leroy et al. (2008), we adopt a uniform working threshold of $\Sigma_{\text{neutral,thresh}} = 1 M_{\odot} pc^{-2}$ in the present work.

### 3. Method

We now describe how we characterize the nonaxisymmetric structures as well as the neutral gas distribution within the galactic disk. In the present work specifically, we employ optimal bulge stretching correction to improve the accuracy of the torque force field evaluation and also consider the stabilizing effects of the dark matter halo in addition to the bulge and the symmetric part of the disk (detailed in Sections 3.2 and 3.3, respectively).

#### 3.1. Estimating the Torque Forces

To quantify the strength of nonaxisymmetric structures in terms of perturbing the motion of disk material, we evaluate the tangential force specifically due to the nonaxisymmetric structures (F. Combes & R. H. Sanders 1981; A. C. Quillen et al. 1994), $f_t$, and the radial force that counters its action, $f_r$. The ratio

$$Q_T = |f_t|/|f_r|, \qquad (2)$$

thus, quantifies the impact of the nonaxisymmetric structures at each point within the galactic disk (e.g., H. Salo et al. 1999; E. Laurikainen & H. Salo 2002; S. Díaz-García et al. 2016b).

Typical distributions of the torque force amplitude $Q_T$ are showcased in Figure 1 for barred galaxy NGC 2903 and nonbarred galaxy NGC 628, respectively. From Figure 1, one identifies the symbolic four-quadrant, or “butterfly” bar perturbation pattern (e.g., inside the bar-dominated region of NGC 2903; R. Buta & D. L. Block 2001; E. Laurikainen & H. Salo 2002). One also sees that spiral arms might also induce significant perturbation beyond the bar-dominated region or in nonbarred galaxies, which appears more twisted and less regular. Figure 1 also shows the radial profiles of $Q_T$ by taking the azimuthal median at each radius. The multiple peaks in NGC 2903 correspond to the bar and the spiral arms, respectively, while those in NGC 628 are exclusively due to spiral arms. In these nearby galaxies, the torque forces are mainly due to the stellar nonaxisymmetric structures (blue curves in Figures 1(c), (f)), which are quantified by $Q_T$ in the present work. We also calculate the torque force field with the gas self-gravity combined along with the stellar forces, which is denoted as $Q_{T,+gas}$. Comparison suggests that perturbation due to gaseous features (S. E. Meidt et al. 2021;

<footnote n="11">¹¹ https://irsa.ipac.caltech.edu/data/WISE/z0MGS/overview.html</footnote>
S. K. Stuber et al. 2023) seems to contribute in a subdominant manner (see Appendix A.2 in the Appendix for further discussion), and seems to be less closely related to the neutral gas concentration (Section 4.1).

In the present work, torque force fields like those shown in Figure 1 are calculated largely following the “polar” method (e.g., H. Salo et al. 1999; E. Athanassoula & A. Misiriotis 2002; E. Laurikainen & H. Salo 2002; R. Buta et al. 2003; S. Díaz-García et al. 2016b). This method integrates the stellar and gas mass surface density field reconstructed from Fourier decomposition

$$ \Sigma_{*}(r, \phi) = \Sigma_{*,0}(r) \left\{ 1 + \sum_{m \in M} A_{m}(r) \cos[m\phi - \phi_{m}(r)] \right\}. \quad (3) $$

Here, $A_m(r)$ is the normalized mth-order Fourier amplitude and $\phi_m(r)$ is the corresponding phase angle. In particular, we choose to consider in Equation (3) $m \in M = \{0, 1, 2, 3, 4, 6, 8\}$ to account for perturbation due to bars (K. Ohta et al. 1990; E. Athanassoula & A. Misiriotis 2002; E. Laurikainen & H. Salo 2002), various types of spiral arms (S. Considere & E. Athanassoula 1988; A. Durbala et al. 2009; S.-Y. Yu et al. 2018), and disk lopsidedness (F. Bournaud et al. 2005; J. van Eymeren et al. 2011). To ensure robust evaluation, we choose not to incorporate higher-order Fourier modes, which are in most cases subdominant but might be locally biased by, e.g., a low signal-to-noise ratio or contaminant emission (see Appendix A; E. Laurikainen & H. Salo 2002; S. Díaz-García et al. 2016a). We assume a scale height as a function of the morphological type T from R. de Grijs (1998) in our evaluation.

The uncertainty of $Q_T$ is mostly propagated from the central position, the disk inclination and position angle, and the uncertain disk scale height. The interested reader is kindly referred to Appendix A for a detailed discussion of uncertainty analyses.

We summarize our evaluated torque force field in Appendix C for each of the individual galaxies.

## 3.2. Improved Bulge Stretching Correction with Optimal Multicomponent Decomposition

Torque force evaluation frequently relies on multicomponent decomposition to properly consider the stabilizing effects of the bulge and avoid artificial “stretching” in deprojection (E. Laurikainen et al. 2004; S. Díaz-García et al. 2016b). Yet, an oversimplified decomposition strategy might lead to inaccurate bulge measurement (D. A. Gadotti 2009; H. Gao & L. C. Ho 2017); thus inaccurate bulge stretching correction is to be applied. An optimal bulge decomposition strategy is therefore crucial in yielding robust torque force evaluation, especially in the inner part of the disk.

We therefore follow the strategy of H. Gao & L. C. Ho (2017) to measure bulges in the sample galaxies. H. Gao & L. C. Ho (2017) have demonstrated that properly modeling secondary morphological features (such as bars, nuclear bars, nuclear/inner rings, nuclear/inner lenses, and disk breaks) is crucial for accurate bulge measurement. We thus choose to construct models including bars, nuclear features, various types of rings, and disk breaks, with initial guesses consulting literature dedicated to morphology (M. Herrera-Endoqui et al. 2015), or from visual inspection.

Figure 2 compares our results with H. Salo et al. (2015), who have performed multicomponent decomposition, yet with a preselected, limited number (no more than four) of components. In comparison, our decomposition does not set a constraint for the number of components and considers up to seven components for cases with complex morphology. Indeed, one sees cases with significantly different effective radii $r_{e,b}$, ellipticities $\epsilon_b$, bulge-to-total ratios $B/T$, and Sérsic indices $n_b$, in Figure 2. A further detailed inspection suggests that the differences for the labeled extreme cases could largely be attributed to the difference made by our more dedicated models. We thus consider elaborate multicomponent decomposition to be necessary for robust and accurate evaluation of the torque field. The interested reader is referred to Appendix A.3 for this closer inspection.

We follow the formulae in E. Vitral & G. A. Mamon (2020) to estimate the radial force from the bulge measurements returned by our optimal multicomponent decomposition. Note that E. Vitral & G. A. Mamon (2020) assumes spherical geometry, which is presumably not a good approximation for disk-like pseudobulges (J. Kormendy & R. C. Kennicutt 2004; E. Athanassoula 2005; D. A. Gadotti et al. 2020). We test and find that the uncertainty introduced by the assumed geometry is subdominant compared to what would have been introduced by the bulge stretching effects, mitigating the concern to some extent (Appendix A).

## 3.3. Improved Estimation for Total Radial Force

Alongside the bulge and the symmetric part of the disk, the dark matter halo arguably also stabilizes the disk and counters the action of the nonaxisymmetric structures, especially at large radii (W. J. G. de Blok et al. 2008). It is possible to globally account for these effects, e.g., using the H I line width (S. Díaz-García et al. 2016b). One might also wish to use the H I rotation curve to construct a more detailed estimation for the radial force at each radius; yet accurately measuring the rotation curve is itself challenging if there are strong nonaxisymmetric structures and thus strong streaming motion (I. Dicaire et al. 2008; T. H. Randriamampandry et al. 2015, 2018). Most importantly, both methods are impractical for galaxies with low inclination, which are the most ideal targets for characterizing the nonaxisymmetric structures and yet difficult cases to extract reliable kinematic information.

In the present work, alternatively, we make use of the radial acceleration relation to account for the stabilizing effects of the dark matter halo. The radial acceleration relation (RAR; F. Lelli et al. 2017a, 2017b) is an observational empirical relation between the radial force solely due to baryonic matter (i.e., stars and gas), and that due to dark matter. RAR is remarkably tight with a scatter of a mere (0.13–0.15) dex (F. Lelli et al. 2017b), making it a powerful tool for estimating the total radial force at each location within the disk. The RAR parameters from F. Lelli et al. (2017b) are adopted. When the H I rotation curve is available from W. J. G. de Blok et al. (2008), we scale the estimated total radial force to match the measured H I rotation curve (technically, by fitting for a free $\hat{y}$ in Equation (9) of F. Lelli et al. 2017b) to further improve the accuracy slightly.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Comparison between the best-fit (a) effective radii $r_{e,b}$, (b) ellipticities $\epsilon_b$, (c) bulge-to-total ratios $B/T$, and (d) Sérsic indices $n_b$, of the bulge components, evaluated from the multicomponent decomposition performed in the present work and that presented by H. Salo et al. (2015). Symbols are differentiated by the quality flags assessed by H. Salo et al. (2015), where Quality 5 (blue circle) represents the most reliable cases and Quality 4 (red square) represents the less reliable cases. The dashed line and the dotted lines indicate $y = x$ and offsets of $\pm 0.3$ dex, respectively. Pearson's correlation coefficients are also quoted in the lower right-hand corner of each panel.</figcaption></figure>

## 4. Results

We are now in a position to investigate how the neutral gas distribution is linked to the strength of nonaxisymmetric structures, quantitatively measured as the torque forces they exert.

### 4.1. Neutral Gas Concentration and Average Torque Forces

We begin by investigating how the neutral gas radial distribution might be related to the torque field exerted by the nonaxisymmetric structures.

Figure 13 serves as a quick-look table for neutral gas radial profiles of all galaxies sorted by the radially average torque forces within the disk exerted by the stellar nonaxisymmetric structures,

$$ \bar{Q}_{\mathrm{T}} = \mathrm{average}\{Q_{\mathrm{T}}(r)\}, \quad 3\gamma'_{\mathrm{PSF}} < r < R_{25.5}. \quad (4) $$

Here, the $\gamma'_{\mathrm{PSF}}$ refers to the PSF FWHM projected onto the galaxy disk plane. We define the inner neutral gas

concentration parameter

$$ C_{\mathrm{neutral}} = \log_{10} \left[ \frac{M_{\mathrm{neutral}}(0.5R_{25.5})}{M_{\mathrm{neutral}}(R_{25.5})} \right] + \mathrm{constant}, \quad (5) $$

to capture the disk-scale concentration of neutral gas. Though this definition of $C_{\mathrm{neutral}}$ appears similar to those proposed by N. Kuno et al. (2007) and S.-Y. Yu et al. (2022b), we emphasize that the concentration parameters defined by these authors, comparatively, highlight the central 1 kpc region instead of the disk scale.

Figure 3 shows that there is a positive correlation between $\bar{Q}_{\mathrm{T}}$ and $C_{\mathrm{neutral}}$, despite the small size of the sample. Furthermore, one sees that barred galaxies (square) and nonbarred galaxies (circle) form a continuous sequence together in this $\bar{Q}_{\mathrm{T}}-C_{\mathrm{neutral}}$ parameter space. To our knowledge, this continuous sequence in $\bar{Q}_{\mathrm{T}}$ and $C_{\mathrm{neutral}}$ has remained elusive in previous works, both in the sense that the torque forces $\bar{Q}_{\mathrm{T}}$ directly quantify the physical effects of
<table><caption>**Table 2**
Summary of Correlation Coefficients</caption><thead><tr><th rowspan="2">Index<br>(1)</th><th rowspan="2">x<br>(2)</th><th rowspan="2">Spearman's Correlation Coefficient<br>(3)</th><th colspan="2">Partial Spearman's Correlation Coefficient<br>(4)</th><th rowspan="2">Note<br>(6)</th></tr><tr><th>log<sub>10</sub>(Σ<sub>*</sub>/M<sub>☉</sub> pc<sup>-2</sup>)</th><th>Neutral Gas Fraction<br>(5)</th></tr></thead><tbody><tr><td colspan="6" style="text-align: center; font-weight: bold;">Correlations with C<sub>neutral</sub></td></tr><tr><td>1</td><td>log<sub>10</sub>Q&#773;<sub>T</sub></td><td><b>0.56</b><sup>+0.16</sup><sub>-0.21</sub> (<b>0.02</b><sup>+0.15</sup><sub>-0.02</sub>)</td><td><b>0.61</b><sup>+0.14</sup><sub>-0.28</sub> (<b>0.01</b><sup>+0.18</sup><sub>-0.01</sub>)</td><td><b>0.54</b><sup>+0.17</sup><sub>-0.41</sub> (<b>0.03</b><sup>+0.48</sup><sub>-0.03</sub>)</td><td>...</td></tr><tr><td>2</td><td>log<sub>10</sub>Q&#773;<sub>T,+gas</sub></td><td>0.39<sup>+0.23</sup><sub>-0.25</sub> (0.12<sup>+0.41</sup><sub>-0.11</sub>)</td><td><b>0.51</b><sup>+0.18</sup><sub>-0.29</sub> (<b>0.04</b><sup>+0.27</sup><sub>-0.04</sub>)</td><td>0.42<sup>+0.21</sup><sub>-0.40</sub> (0.11<sup>+0.49</sup><sub>-0.10</sub>)</td><td>a</td></tr><tr><td>3</td><td>2 + log<sub>10</sub>s<sub>disk</sub></td><td>0.45<sup>+0.20</sup><sub>-0.22</sub> (0.07<sup>+0.31</sup><sub>-0.07</sub>)</td><td>0.47<sup>+0.17</sup><sub>-0.24</sub> (0.07<sup>+0.31</sup><sub>-0.06</sub>)</td><td>0.43<sup>+0.18</sup><sub>-0.29</sub> (0.09<sup>+0.39</sup><sub>-0.08</sub>)</td><td>...</td></tr><tr><td>4</td><td>log<sub>10</sub>Q<sub>g</sub></td><td><b>0.76</b><sup>+0.11</sup><sub>-0.18</sub> (<b>0.00</b><sup>+0.02</sup><sub>-0.00</sub>)</td><td><b>0.72</b><sup>+0.13</sup><sub>-0.38</sub> (<b>0.00</b><sup>+0.22</sup><sub>-0.00</sub>)</td><td><b>0.68</b><sup>+0.16</sup><sub>-0.63</sub> (<b>0.01</b><sup>+0.48</sup><sub>-0.01</sub>)</td><td>b</td></tr><tr><td>5</td><td>log<sub>10</sub>Q<sub>g,+gas</sub></td><td><b>0.61</b><sup>+0.16</sup><sub>-0.24</sub> (<b>0.01</b><sup>+0.16</sup><sub>-0.01</sub>)</td><td><b>0.64</b><sup>+0.15</sup><sub>-0.35</sub> (<b>0.01</b><sup>+0.28</sup><sub>-0.01</sub>)</td><td><b>0.54</b><sup>+0.27</sup><sub>-0.51</sub> (<b>0.05</b><sup>+0.56</sup><sub>-0.04</sub>)</td><td>a, b</td></tr><tr><td>6</td><td>log<sub>10</sub>R&#773;</td><td>0.33<sup>+0.23</sup><sub>-0.24</sub> (0.20<sup>+0.43</sup><sub>-0.18</sub>)</td><td><b>0.50</b><sup>+0.16</sup><sub>-0.25</sub> (<b>0.05</b><sup>+0.28</sup><sub>-0.04</sub>)</td><td>0.40<sup>+0.19</sup><sub>-0.40</sub> (0.13<sup>+0.49</sup><sub>-0.11</sub>)</td><td>...</td></tr><tr><td>7</td><td>log<sub>10</sub>R&#773;<sub>gas</sub></td><td>0.15<sup>+0.27</sup><sub>-0.27</sub> (0.56<sup>+0.24</sup><sub>-0.48</sub>)</td><td>0.41<sup>+0.16</sup><sub>-0.25</sub> (0.12<sup>+0.35</sup><sub>-0.10</sub>)</td><td>0.33<sup>+0.18</sup><sub>-0.33</sub> (0.21<sup>+0.47</sup><sub>-0.17</sub>)</td><td>a</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">Correlations with C<sub>CO</sub></td></tr><tr><td>8</td><td>log<sub>10</sub>Q&#773;<sub>T</sub></td><td><b>0.51</b><sup>+0.26</sup><sub>-0.28</sub> (<b>0.04</b><sup>+0.32</sup><sub>-0.04</sub>)</td><td><b>0.50</b><sup>+0.26</sup><sub>-0.33</sub> (<b>0.05</b><sup>+0.40</sup><sub>-0.05</sub>)</td><td><b>0.51</b><sup>+0.26</sup><sub>-0.30</sub> (<b>0.04</b><sup>+0.36</sup><sub>-0.04</sub>)</td><td>...</td></tr><tr><td>9</td><td>log<sub>10</sub>Q&#773;<sub>T,+gas</sub></td><td>0.42<sup>+0.25</sup><sub>-0.28</sub> (0.09<sup>+0.43</sup><sub>-0.09</sub>)</td><td>0.45<sup>+0.23</sup><sub>-0.33</sub> (0.08<sup>+0.45</sup><sub>-0.08</sub>)</td><td>0.43<sup>+0.25</sup><sub>-0.31</sub> (0.10<sup>+0.45</sup><sub>-0.10</sub>)</td><td>a</td></tr><tr><td>10</td><td>2 + log<sub>10</sub>s<sub>disk</sub></td><td>0.42<sup>+0.24</sup><sub>-0.26</sub> (0.09<sup>+0.39</sup><sub>-0.09</sub>)</td><td>0.41<sup>+0.24</sup><sub>-0.31</sub> (0.11<sup>+0.46</sup><sub>-0.11</sub>)</td><td>0.43<sup>+0.23</sup><sub>-0.29</sub> (0.10<sup>+0.43</sup><sub>-0.09</sub>)</td><td>...</td></tr></tbody></table>

**Notes.** Summary of correlation coefficients. Bracketed values are the corresponding *p*-values. Uncertainties are quoted as 16% and 84% percentiles evaluated from the bootstrap sampling method. Statistically significant correlations (with *p* < 0.05 at face values) are highlighted in bold typeface. Column (1): index. Column (2): abscissa *x*. Column (3): Spearman's correlation coefficient. Column (4): partial Spearman's correlation coefficient, controlling for the average stellar mass surface density log<sub>10</sub>(Σ<sub>*</sub>/M<sub>☉</sub> pc<sup>-2</sup>). Column (5): partial Spearman's correlation coefficient, controlling for the neutral gas fraction within the corresponding radial range. For correlations with C<sub>neutral</sub>, this is f<sub>neutral</sub>(R<sub>25.5</sub>); for correlations with C<sub>CO</sub>, this is f<sub>neutral</sub>(r<sub>50</sub>). Column (6): note.

a Gas self-gravity is considered in evaluating the torque field, and the relevant parameters.

b Only galaxies with Q<sub>g</sub> and Q<sub>g,+gas</sub> reliably determined from the torque forces radial profiles are considered (Section 4.4).

nonaxisymmetric structures, and that C<sub>neutral</sub> refers to neutral gas distribution in a relatively wide disk radial range.

All sample galaxies taken together, we find a Spearman's correlation coefficient of $\rho = 0.56^{+0.16}_{-0.21}$, with a corresponding *p*-value $p = 0.02^{+0.15}_{-0.02}$ between Q&#773;<sub>T</sub> and C<sub>neutral</sub>, indicating relatively strong, statistically significant correlation, though a rigorous conclusion is precluded due to the small sample size. Interestingly, when gas self-gravity is considered in evaluating the torque forces, the correlation between Q&#773;<sub>T,+gas</sub> and C<sub>neutral</sub> is seen to be weaker and statistically insignificant (see Table 2 for a summary of statistics). This seems to suggest that the torque forces exerted by stars are more closely related to the neutral gas distribution within the galactic disk, while gas self-gravity does not contribute significantly (T. A. Davis et al. 2022). Another possibility is that the nonaxisymmetric part of the self-gravity forces might be significantly contributed by shock fronts, shells, bubbles and holes of sizes up to ~1 kpc, driven by spiral arm dynamics and stellar feedback, and further stretched and elongated by the shearing motion (e.g., J. Palous et al. 1990; D. R. Weisz et al. 2009; W.-Y. Seo et al. 2019; A. T. Barnes et al. 2023; E. J. Watkins et al. 2023). While playing an important role in shaping the overall disk cold gas structures, some of these features could be transient (e.g., typical lifetimes of shell-like features ~10 Myr; E. J. Watkins et al. 2023), and might thus be difficult to have a coherent impact on the radial distribution of disk neutral gas, which is expected on timescales of the disk dynamical timescale (~100 Myr). Here and in what follows, the uncertainties of statistics are evaluated by bootstrapping the sample to account for the dominant impact of the small sample size and are quoted as the 16% and the 84% percentiles, respectively.

It seems most likely that the correlation seen in Figure 3 is reflecting gas concentration on the disk scale, instead of simply because the gas in the central 1 kpc is enhanced (e.g.,

<figure><img src="image_6.png" /></figure>

**Figure 3.** Correlations between the average torque forces Q&#773;<sub>T</sub> and the inner neutral gas concentration parameter C<sub>neutral</sub>. Symbols are color coded by the average stellar surface density, Σ<sub>*</sub>, and are distinguished for barred (square) and nonbarred (circle) galaxies. Open symbols represent results for Q&#773;<sub>T,+gas</sub>, i.e., when gas self-gravity is combined in evaluating the torque forces. Spearman's and partial Spearman's correlation coefficients (controlling for Σ<sub>*</sub>, bracketed) are quoted at the upper left-hand corner of the figure for Q&#773;<sub>T</sub> (first row) and Q&#773;<sub>T,+gas</sub> (second row), respectively. Statistically significant (*p* < 0.05) correlations are highlighted in bold typeface.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Neutral and molecular gas concentrations and nonaxisymmetric structure strength, quantified by different measures. Symbol style and color are the same as in Figure 3. Spearman's and partial correlation coefficients (controlling for $\bar{\Sigma}_*$, bracketed) are quoted at the corner of each panel. In panels (a) and (d), correlation coefficients for torque forces evaluated without (first row) and with gas self-gravity considered (second row) are quoted, respectively. Statistically significant (*p* < 0.05) correlations are highlighted in bold typeface. (a) Radially average torque forces $\bar{Q}_T$ and central 1 kpc scale molecular gas concentration index $C_{CO}$. (b) Average nonaxisymmetric surface density Fourier amplitudes $2 + \log_{10} s_{disk}$ and inner neutral gas concentration parameter $C_{neutral}$. (c) $2 + \log_{10} s_{disk}$ and $C_{CO}$. Measurements (smaller symbols) and linear regression (gray line) from S.-Y. Yu et al. (2022b) are also shown. (d) Maximal torque forces $Q_g$ and $C_{neutral}$. Marginally strong and significant (*p* < 0.05) correlations could be seen in (a) for stellar $\bar{Q}_T$, no strong and statistically significant correlation is seen in (b), (c) for our sample, while strong and statistically significant correlations are seen in (d).</figcaption></figure>

K. Sakamoto et al. 1999; K. Sheth et al. 2005; N. Kuno et al. 2007; J. Wang et al. 2012; R. Chown et al. 2019). For a comparison, we present the average torque forces $\bar{Q}_T$ and the central-kiloparsec molecular gas concentration index $C_{CO}$ (defined in S.-Y. Yu et al. 2022b) in Figure 4(a). The correlation between $\bar{Q}_T$ and $C_{CO}$ is almost as strong as that between $\bar{Q}_T$ and $C_{neutral}$ but becomes weaker than the latter when we consider partial correlations in the next subsection. Furthermore, although we do not show explicitly, if we mimic the definition of $C_{CO}$ (S.-Y. Yu et al. 2022b), to define a

“central-kiloparsec neutral gas concentration index” considering both molecular and atomic gas in the central-kiloparsec regions, then the correlation becomes even weaker and less statistically significant. It implies that processes other than neutral gas radial transportation might also be at play, like the conversion of H I to the molecular gas, to display the $\bar{Q}_T-C_{CO}$ relation. The relatively safe conclusion here is that, the disk-scale $\bar{Q}_T-C_{neutral}$ relation is unlikely caused by the 1 kpc scale $\bar{Q}_T-C_{CO}$ one, as otherwise the former should be weaker than the latter. Instead, the $\bar{Q}_T-C_{neutral}$ relation is marginally
stronger (with ~0.2σ significance in difference of Spearman's ρ), which is physically reasonable as nonaxisymmetric structures spread disk-wide and $\bar{Q}_T$ is a disk-scale measure.

## 4.2. Partial Correlations

We investigate whether the correlation discussed above holds if we take the covariant into consideration (i.e., control for the mutually dependent parameter), most relevantly the neutral gas fraction within the corresponding radial range and the average stellar mass surface density. This is important as part of our conclusions since it has been known that there is a complex interplay between the gas concentration, the nonaxisymmetric structures, and the aforementioned factors. The gas content affects the gas concentration (e.g., regulation of H I as revealed by the size-mass relation; J. Wang et al. 2016, 2020b) and the strengths of the nonaxisymmetric structures (K. L. Masters et al. 2012; S.-Y. Yu et al. 2021), simultaneously. Likewise, the stellar mass surface density might also affect the strengths of the nonaxisymmetric structures (A. Bittner et al. 2017), and the transition between H I and molecular gas to affects the regulation of gas (A. K. Leroy et al. 2009; E. C. Ostriker et al. 2010; C. d. P. Lagos et al. 2011). This complex interplay incompletely outlined above entails an inspection of partial correlations before one infers causality.

We find that our correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$ is unlikely due to the aforementioned mutual dependence on the stellar mass surface density or the neutral gas fraction. Instead, controlling for the mutually dependent parameters might enhance the correlation. In Figure 3, symbols are color coded by the average stellar mass surface density

$$ \bar{\Sigma}_{\star} = \frac{0.5M_{\star}}{\pi r_{50}^2}. \qquad (6) $$

Comparison of Spearman's correlation coefficients and the corresponding p-values suggests that the correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$ is unlikely originated from neutral gas distribution and nonaxisymmetric structures being simultaneously affected by $\bar{\Sigma}_{\star}$. Instead, it is interesting to see that the extreme $\bar{\Sigma}_{\star}$ seems to explain the two sample galaxies that show the largest offsets from the linear regression presented in Figure 3, seemingly reflecting the interplay between stellar mass surface density and gas (A. K. Leroy et al. 2009; E. C. Ostriker et al. 2010; C. d. P. Lagos et al. 2011), in these extreme cases. As a result, statistics suggest that the correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$ seems to become stronger as $\bar{\Sigma}_{\star}$ is controlled for. The partial correlation between $\bar{Q}_{T,+\text{gas}}$ and $C_{\text{neutral}}$ also becomes statistically significant when controlling for $\bar{\Sigma}_{\star}$; yet the correlation is comparatively weaker than the one not including the gas self-gravity, again suggesting the important role of torque forces induced by stars rather than the neutral gas self-gravity. The correlation seems to be less dependent on the gas fraction, here defined as

$$ f_{\text{neutral}}(R_{25.5}) = \frac{M_{\text{neutral}}(R_{25.5})}{M_{\star}(R_{25.5})}; \qquad (7) $$

yet the partial correlation controlling for $f_{\text{neutral}}(R_{25.5})$ remains statistically significant. See Appendix B for figures color coded by the gas fraction in the corresponding radial range instead.

In contrast, the partial correlations between $\bar{Q}_T$ and $C_{\text{CO}}$ are consistently weaker and marginally significant at best. No statistically significant correlation between $\bar{Q}_{T,+\text{gas}}$ and $C_{\text{CO}}$

could be seen. These results further strengthen our confidence that the correlation seen in Figure 3 is not likely simply due to the enhanced molecular gas content in the central-kiloparsec regions.

## 4.3. Nonaxisymmetric Structures Torque Forces versus Surface Density Fourier Amplitudes

S.-Y. Yu et al. (2022b) have quantified the strength of nonaxisymmetric structures by the surface density Fourier amplitudes $2 + \log_{10} s_{\text{disk}}$, where

$$ s_{\text{disk}} = \text{average}\{\sqrt{A_2^2(r) + A_3^2(r) + A_4^2(r)}\}, \qquad (8) $$

with $A_m$ defined in Equation (3) evaluated within the disk-dominated regions (for detailed definition see S.-Y. Yu et al. 2018, 2022b). These authors have shown that $C_{\text{CO}}$ correlates with $2 + \log_{10} s_{\text{disk}}$ for both barred and nonbarred galaxies. We make the comparison to understand which measure better quantifies the efficiency of nonaxisymmetric structures in affecting the neutral gas distribution.

Figure 4(b) suggests that there is no statistically significant correlation between $2 + \log_{10} s_{\text{disk}}$ and $C_{\text{neutral}}$ for our sample. Although a positive trend could be vaguely seen, Spearman's statistics suggest that our small sample does not support a strong and statistically significant correlation between $s_{\text{disk}}$ and $C_{\text{neutral}}$ (Table 2). Controlling for $\bar{\Sigma}_{\star}$ or $f_{\text{neutral}}(R_{25.5})$, the partial correlation strength between $2 + \log_{10} s_{\text{disk}}$ and $C_{\text{neutral}}$ and the statistical significance remain largely unchanged. It therefore seems that the correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$ is more intrinsic.

In Figure 4(c), we show $2 + \log_{10} s_{\text{disk}}$ and the central-kiloparsec molecular gas concentration index $C_{\text{CO}}$. We reach similar conclusions as in Figure 4(b). It is to be noted that our sample majorly consists of galaxies with intermediate strength of nonaxisymmetric structures, in contrast with that of S.-Y. Yu et al. (2022b; underlain in Figure 4(c)). Our point is that the radially average torque forces parameter $\bar{Q}_T$ seems to sensitively quantify the effect of neutral gas distribution being regulated by the nonaxisymmetric structures, even when the $s_{\text{disk}}$ dynamical range is limited.

## 4.4. Neutral Gas Distribution and Maximal Torque Forces

We further investigate how the neutral gas distribution might be correlated with the maximal torque forces (e.g., E. Laurikainen & H. Salo 2002; R. Buta et al. 2004; R. D. Grouchy et al. 2010)

$$ Q_g = \max\{Q_T(r)\}, \quad 3\gamma'_{\text{PSF}} < r < R_{25.5}, \qquad (9) $$

and similarly also $Q_{g,+\text{gas}}$, within the galaxy disk. Compared to the average counterpart, these maximal torque forces arguably highlight more specifically the contribution from the strongest component, and measure the utmost extent to which the motion of neutral gas could be affected. In this regard, it would also be interesting to examine whether the maximal torque forces correlate with the neutral gas concentration as well as neutral gas overdensities at smaller scales.

Before we move on to show the results, it is to be noted that $Q_g$ and $Q_{g,+\text{gas}}$ could not always be precisely measured, especially in cases of late-type galaxies. In our sample, for NGC 925 and NGC 3621, in particular, we observe torque forces decreasing almost monotonically with the radius; thus a maximal torque force would occur at $r \to 0$. This is neither physical nor reliable since the central pixels are inevitably
<figure><img src="image_8.png" /><figcaption>**Figure 5.** (a) Radius of maximal torque forces $Q_g$ plotted against the radius of the nearest kiloparsec-scale neutral gas overdensity. Symbols are colored by the corresponding $Q_g(Q_{g,+gas})$, and are distinguished for barred (square) and nonbarred (circle) galaxies. Open symbols show the results if we consider the gas self-gravity in evaluating the maximal torque forces $Q_{g,+gas}$. (b) Radius of maximal $m = 2$ surface density amplitude max {$A_2$} and radius of the nearest gas overdensity, with symbols colored by the corresponding max {$A_2$}. It seems that the kiloparsec-scale gas overdensity tends to occur in the vicinity of the maximal torque forces, especially when the torque forces are comparatively strong ($Q_g \gtrsim 0.05$), but less likely for max {$A_2$}.</figcaption></figure>

affected by the (intrinsically asymmetric and artificially elongated in deprojection) shape of the PSF. We therefore refrain from determining the maximal torque forces for these two galaxies and omit them in the analyses below in this section. See Appendix C for torque forces $Q_T(r)$ measured for each individual galaxy.

### 4.4.1. The Disk-scale Neutral Gas Concentration

With this caveat in mind, we see in Figure 4(d) that there is also a positive correlation between the maximal torque forces $Q_g$ and the inner neutral gas concentration parameter $C_{neutral}$. With a reduced subsample, it seems that this correlation is strong and statistically significant despite the small sample size. The partial correlations controlling for $\bar{\Sigma}_*$ or $f_{neutral}(R_{25.5})$ are also seen to be strong and statistically significant. A positive correlation between $Q_{g,+gas}$ and $C_{neutral}$ could also be seen, though the statistical significance is marginal when controlling for $f_{neutral}(R_{25.5})$ (Table 2).

It would thus be interesting to examine which of the correlations, i.e., whether it is the $\bar{Q}_T-C_{neutral}$ correlation (Figure 3) or the $Q_g-C_{neutral}$ correlation (Figure 4(d)), is more intrinsic to provide constraints on the detailed underlying physics. However, although the correlation coefficients and the p-values appear to hint toward stronger correlations with the latter, the statistics are derived over the reduced subsample for the $Q_g-C_{neutral}$ correlation, and when we force the sample to be the same, the Spearman's correlation coefficients and the corresponding p-values become quite close. Considering the statistical uncertainties, we therefore refrain from reaching a solid conclusion and leave this comparison to further investigations where larger samples are accessible.

### 4.4.2. Localized Neutral Gas Overdensities

Lastly, we divert our attention to the kiloparsec-scale neutral gas overdensities readily seen from the radial profiles. The find_peak function in `SCIPY.SIGNAL` module is used to extract these overdensities as local peaks from the neutral gas radial profiles within $R_{25.5}$. It turns out that the width of these

peaks is typically ~1 kpc, hence the terminology. NGC 2903, NGC 5055, NGC 6946, and NGC 7793 feature generally smooth neutral gas radial profiles from which no local peak could be identified, and are thus omitted from the analyses below in this section. A usual prediction from theories and simulations is that dissipative processes could be responsible for accumulating the gas at the shock front (e.g., E. Athanassoula 1992; Y. Kim & W.-T. Kim 2014). In line with these predictions, since gas motion is perturbed most strongly near the location of maximal torque force, it is natural for us to conjecture that there is a connection between the maximal torque force and the kiloparsec-scale gas overdensities. Below, we look into this conjecture with our measurements.

In Figure 5(a) we show the radii corresponding to the measured $Q_g$ and the radii of the kiloparsec-scale gas overdensities. Since on average ~2 gas peaks could be identified for each radial profile, we choose the nearest one to the maximal torque force. Figure 5(a) suggests that the radial offset between $Q_g(Q_{g,+gas})$ and the gas overdensity is minimal, especially when we focus on galaxies with strong torque forces (barred and nonbarred galaxies with $Q_g \gtrsim 0.05$), suggesting gas overdensity occurring close to $Q_g$. The median radial offset from $Q_g$ to the nearest gas overdensities is ~0.07$R_{25.5}$ (~0.08$R_{25.5}$ for $Q_{g,+gas}$). This is to be compared with the median complying with the null hypothesis, which is ~0.16$R_{25.5}$, assuming that $Q_g$ and the two gas overdensities occur randomly within $R_{25.5}$. All galaxies with $Q_g \gtrsim 0.05$ have radial offsets smaller than this median complying with the null hypothesis. This suggests that the observed proximity between the maximal torque forces and the kiloparsec-scale gas overdensities does not seem to be a coincidence.

In comparison, Figure 5(b) suggests that the maximal $m = 2$ surface density Fourier amplitude max {$A_2$} radius and the (corresponding nearest) gas peak radius show a distribution that complies more with randomness. Data points with stronger max {$A_2$} do not seem to show smaller radial offsets. The median radial offset of ~0.12$R_{25.5}$ is close to the expectation for no connection.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Dynamical torque term $\bar{\Gamma}$ and the inner neutral gas concentration parameter $C_{\text{neutral}}$. Symbol color, style, and annotations are the same as in Figure 3. A positive trend might be seen, albeit with a significantly larger scatter, and only of marginal statistical significance at best.</figcaption></figure>

Our results are thus consistent with the scenario where sufficiently strong nonaxisymmetric structures, especially when satisfying $Q_g \gtrsim 0.05$, might directly induce kiloparsec-scale neutral gas overdensities in their vicinity. As has been mentioned, a likely mechanism is the induced shock processes, which compress the gas along the leading edges of the bar (e.g., E. Athanassoula 1992; F. Renaud et al. 2015), as gas enters the spiral gravitational potential (e.g., Y. Kim & W.-T. Kim 2014), or where gas orbits intersect or autosect (M. W. Regan & P. Teuben 2003; M. W. Regan & P. J. Teuben 2004). It is to be noted that, in addition to the shock-related processes, several other mechanisms have also been proposed to lead to small-scale gas overdensities, such as dynamical resonances (B. G. Piner et al. 1995; P. Rautiainen & H. Salo 2000), accumulation of inflowing gas where the centrifugal force balances gravity (W.-T. Kim et al. 2012a), or where the shear reduces (M. R. Krumholz & J. M. D. Kruijssen 2012b). These mechanisms might provide an explanation for gas overdensities that occur far from the maximal torque force radius.

# 5. Discussion

## 5.1. The Advantage of $Q_T$ in Characterizing the Driven Gas Inflow

As has been discussed in Section 1, nonaxisymmetric structures (bars and spiral arms) share a uniformity in their role to interact with the neutral gas and drive the gas inward. Stronger disk nonaxisymmetric structures could arguably perturb the gas motion and drive gas inflow in a more efficient manner (e.g., E. Athanassoula 1992; W.-T. Kim et al. 2012a; Y. Kim & W.-T. Kim 2014).

Our finding suggests that nonaxisymmetric structures are able to affect neutral gas concentration on the disk scale (in the present work, the scale of $0.5R_{25.5}$). This is roughly ~2 times the optical half-light radius for typical star-forming galaxies, and on average corresponds to a physical diameter of ~13.5 kpc in our sample. This complements previous works demonstrating enhanced central-kiloparsec molecular gas content and star formation in barred galaxies (e.g., K. Sakamoto et al. 1999; K. Sheth et al. 2005; N. Kuno et al. 2007; J. Wang et al. 2012; L. Lin et al. 2017; R. Chown et al. 2019) or galaxies with strong spiral arms (S.-Y. Yu et al. 2022b), which presumably leads to the growth of pseudobulges (J. Kormendy & R. C. Kennicutt 2004; E. Athanassoula 2005; S.-Y. Yu et al. 2022a).

The efficiency of nonaxisymmetric structures in driving this neutral gas concentration is seen to depend on their strength to perturb the gas motion. The radially average torque forces $\bar{Q}_T$ seem to be more intrinsic in quantifying this strength, compared with the more conventional method based on the Fourier amplitudes of stellar mass surface density (e.g., S.-Y. Yu et al. 2022b). In this regard, we highlight that these two methods of characterizing the nonaxisymmetric structures have different focuses and are arguably complementary. The more conventional characterization based on the stellar mass surface density measures the morphological strength of nonaxisymmetric structures in an absolute sense and is helpful in understanding the formation and temporal evolution of nonaxisymmetric structures (e.g., E. Athanassoula & A. Misiriotis 2002; E. Athanassoula 2003; E. Athanassoula et al. 2013) and the dependence upon galaxy properties (e.g., S. Díaz-García et al. 2016b; S.-Y. Yu et al. 2021). In contrast, $\bar{Q}_T$ quantifies not only the tangential force due to nonaxisymmetric structures but also considers factors such as stabilization due to bulge and dark matter halo (E. Laurikainen et al. 2004; S. Díaz-García et al. 2016b), which counter their actions. The $\bar{Q}_T$ parameter thus better highlights the dynamical strength of nonaxisymmetric structures, which is more directly related to the gas motion and the gas redistribution (S. García-Burillo et al. 2005; S. Haan et al. 2009; J. C. Muñoz-Mateos et al. 2013; M. K. Seidel et al. 2015). In this sense, the findings of the present work further provide a physical aspect of how the gas inflow leading up to the observed inner gas concentration is happening.

## 5.2. The Nontrivial Gas Inflow

An interesting finding of the present work is that both the average torque forces and the maximal torque forces correlate with the inner neutral gas concentration parameter. It would thus be interesting to distinguish which of the two correlations is more statistically significant and thus likely more intrinsic. If the correlation between the gas distribution and the average value is more intrinsic, then it is preferable to conjecture that nonaxisymmetric structures likely work together or in relay to transport the gas across the disk (e.g., I. Minchev et al. 2012; J. Wang et al. 2012, 2020a). Otherwise, the strongest and the most dominant component likely dominates or controls the processes. Indirect arguments from the literature exist. For example, W.-Y. Seo & W.-T. Kim (2013) have noted that in their simulations, without fueling, e.g., from the spiral arms (Y. Kim & W.-T. Kim 2014), the starbursts in the nuclear ring
of barred galaxy dwindle quickly (often in ~0.1 Gyr), which we note are inconsistent with observations demonstrating more persistent star formation enhancements (≥1 Gyr though possibly episodic; T. P. R. van der Laan et al. 2013; L. Lin et al. 2017, 2020). Observationally, J. Wang et al. (2020a) have demonstrated that barred galaxies with central star formation enhancement/suppression preferentially have stronger/weaker spiral arms. These authors have proposed a possible scenario in which various disk morphological features have different pattern speeds Ωp (as has been expected by theories such as I. Minchev et al. (2012) and indeed been found in observations such as R. J. Buta & X. Zhang (2009)) such that they could each transport gas inward within the respective corotation resonance (M. Tagger et al. 1987; J. Kormendy & R. C. Kennicutt 2004), thus forming concentrated gas distribution more effectively. Sadly, a meticulous comparison between the average and the maximal torque forces is hindered by the small sample size of the present work, and we leave this as an open issue for future investigations.

While we highlight the use of the “torque forces parameter” $\bar{Q}_T$ to characterize the nonaxisymmetric structures, we do not intend to claim that the dynamical torque is the only or the dominant mechanism in the inward transportation of the neutral gas. In Figure 6, we show the dynamical torque term defined as

$$ \bar{\Gamma} = \text{average} \left\{ \frac{r}{R_{25.5}} \cdot \frac{f_T}{f_r} \right\}, \quad 3\gamma'_{\text{PSF}} < r < R_{25.5}, \quad (10) $$

mimicking the textbook definition of gravitational torque, $\Gamma = r \times f$, and the inner neutral gas concentration $C_{\text{neutral}}$. A correlation between $\bar{\Gamma}$ and $C_{\text{neutral}}$ is expected if we envision a situation in which the gas hardly dissipates, being collected and funneled inward only passively with the dynamical torque being the sole channel for the gas to lose angular momentum. However, Figure 6 suggests that this does not seem to be the case, since a larger scatter compared to the correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$ (Figure 3) seems to be seen, with the correlation appearing to be only marginally statistically significant at best, seen from Spearman’s statistics. In this regard, Y. Kim & W.-T. Kim (2014) have demonstrated in their simulations that, in principle, three mechanisms might be at work in transporting the gas inward, i.e., (i) gravitational torque due to stellar nonaxisymmetric structures, (ii) due to the gas self-gravity, and (iii) dissipative processes, e.g., shocks. These authors have estimated that these three mechanisms each contribute ~40%, ~10%, and ~50%, respectively, to the mass inflow rate averaged between the inner Lindblad and the corotation resonances. In this regard, gas dissipation is arguably a more important mechanism (e.g., E. Athanassoula 1992; W.-T. Kim et al. 2012a; Y. Kim & W.-T. Kim 2014), and our $\bar{Q}_T$ measures more intrinsically the efficiency of nonaxisymmetric structures in perturbing the gas motion, and inducing these dissipative processes. Future observations directly comparing gas kinematics (e.g., T. M. Schmidt et al. 2016; E. M. Di Teodoro & J. E. G. Peek 2021; C. López-Cobá et al. 2022) and gravitational force and torque estimation (e.g., S. García-Burillo et al. 2005; S. Haan et al. 2009; M. Querejeta et al. 2016; P. da Silva & F. Combes 2024) might be needed to constrain the contribution of each mechanisms in the real Universe.

To summarize, we emphasize that, these complexities of gas inflow driven by nonaxisymmetric structures do emerge only when the physically motivated radially average torque forces $\bar{Q}_T$ parameter is used to quantify the effects related to the nonaxisymmetric structures.

### 5.3. Other Processes Affecting the Neutral Gas Distribution

Apart from the nonaxisymmetric structures, several other mechanisms or processes might also affect the neutral gas distribution, which we briefly discuss here for the purpose of completeness. Viscosity (D. Lynden-Bell & J. E. Pringle 1974; G. T. Bath & J. E. Pringle 1981) affects gas motion significantly at a ~100–200 pc scale; yet it should be rather inefficient at the kiloparsec scale (for an estimation of the viscous timescale as a function of the galactocentric radius, see S. García-Burillo et al. 2005). Galactic fountain (C. B. Brook et al. 2012; R. J. J. Grand et al. 2019) might enhance the accretion of gas with lower angular momentum, raising the concentration in roughly a few Gyr (B. G. Elmegreen et al. 2014); yet it should be universal and thus is irrelevant to the observed correlations between gas distribution and the torque parameter.

Environmental effects are arguably more intricate mechanisms, which affect both the neutral gas distribution (e.g., R. Chown et al. 2019; J. Wang et al. 2021; S. Wang et al. 2022; X. Lin et al. 2023), and induce or enhance the nonaxisymmetric structures (J. E. Barnes & L. E. Hernquist 1991; E. L. Łokas et al. 2014; N. Peschken & E. L. Łokas 2019), which might be long-lived (up to ~10 Gyr; E. L. Łokas et al. 2014, 2016). For a vivid example, while dynamical modeling has suggested that the grand-design spiral arms of M51a (NGC 5194) are of tidal origin (C. L. Dobbs et al. 2010), there is observational evidence for gas inflow purely due to the spiral gravitational torque (M. Querejeta et al. 2016). Disentangling these effects is beyond the scope of the present work, which makes use of a small sample.

### 5.4. Implications of Galaxy Evolution Driven by Nonaxisymmetric Structures

Recent investigations with JWST and the Atacama Large Millimeter/submillimeter Array have found that galactic disks (L. Ferreira et al. 2022; K. A. Hamilton-Campos et al. 2023; J. S. Kartaltepe et al. 2023; E. J. Nelson et al. 2023; Y. Wu et al. 2023; J. Lian & L. Luo 2024; W. Sun et al. 2024), some of which are dynamically cold (F. Fraternali et al. 2021; L. E. Rowland et al. 2024; Y. Xu et al. 2024), as well as bars and spiral arms therein (Y. Guo et al. 2023; S. Huang et al. 2023; B. E. Robertson et al. 2023; V. Kuhn et al. 2024; Z. A. Le Conte et al. 2024) seem to develop early in the cosmic time. These exciting findings hint at a possible revision to the secularly versus merger-built bulge-like structures in the Universe. Since the Hubble Space Telescope campaigns on several deep galaxy fields, it has been conventional conduct to count fraction of galaxies hosting bars or spiral arms as a function of the redshift, to evaluate the formation, growth, and weakening of these structures, as well as their impact on secular evolution in the galaxy lifetime (K. Sheth et al. 2008; D. M. Elmegreen & B. G. Elmegreen 2014; T. Melvin et al. 2014; B. D. Simmons et al. 2014). Our results suggest that specific studies on the impact of single, particular
morphological features on the buildup of galaxy central stellar mass concentration could be unified within the same physical framework of nonaxisymmetric structures. Such a unified view is important considering the fact that the nonaxisymmetric structures are more complex than just bars and spiral arms and that these structures might not be highly independent of each other. For example, *m* = 1 nonaxisymmetric structures induced by tidal interactions or gas accretion are more common at high *z* (B. S. Kalita et al. 2022; A. Le Bail et al. 2024); kiloparsec-scale clumps produced in turbulent disks at high *z* could be much more significant nonaxisymmetric structures than those seen at low *z* in the appearance of bars and spiral arms (B. G. Elmegreen et al. 2008; B. S. Kalita et al. 2024); bars and spiral arms are often triggered by the same perturbation that produces *m* = 1 structures (e.g., tidal interactions, E. L. Łokas et al. 2014); bars and spiral arms could be coupled with one another (I. Minchev & B. Famaey 2010; H. Salo et al. 2010); and bars could dissolve into lenses, which might still be significantly nonaxisymmetric (J. Kormendy & R. C. Kennicutt 2004).

These relevant effects should be reevaluated not only in terms of observations but also in terms of simulations. The predictions from state-of-the-art cosmological hydrodynamical simulations still deviate significantly from the observational trend in the size-mass relation of relatively passive, thus more bulge-dominated, galaxies while the disks produced in these simulations are often too hot and too thick (see R. A. Crain & F. van de Voort 2023, and references therein). A cold dynamical state of the stellar disks is necessary for the formation of nonaxisymmetric structures (K. Kraljic et al. 2012; K. Sheth et al. 2012; E. Athanassoula et al. 2013; W.-Y. Seo et al. 2019), while the gas inflow driven by these structures is important in fueling inner disk star formation and pseudobulge formation (J. Kormendy & R. C. Kennicutt 2004). It is therefore reasonable to speculate that future simulations must first reproduce realistic nonaxisymmetric structures, including bars and spiral arms, simultaneously, before they could physically solve the size-mass relation problem.

The torque forces evaluated in the present work provide a physically motivated simple tool to avoid biased focuses on a single particular morphological feature to link the related processes and aspects of nonaxisymmetric and axisymmetric structure formation, as well as to bridge the gap between simulations and observations. Such quantification on the observational side would be feasible for large samples with the upcoming wide-field, high-quality imaging surveys, including the High Latitude Wide Area Survey (D. Spergel et al. 2015; R. Akeson et al. 2019) with the Nancy Grace Roman Space Telescope, the Euclid Wide Survey (Euclid Collaboration et al. 2022 with the Euclid Space Telescope, the Legacy Survey of Space and Time (Ž. Ivezić et al. 2019) with the Vera C. Rubin Observatory and the Chinese Space Station Optical Survey (H. Zhan 2011, 2018; Y. Cao et al. 2018; Y. Gong et al. 2019) with the Chinese Space Station Telescope.

## 5.5. Limitations and Caveats

Before bringing our discussion to an end, it is important to reiterate that the results of the present work are based on a sample limited in size. The limitation stems from the need for a set of uniform and high-resolution neutral gas imaging data capable of resolving the disk. We acknowledge that the sample size has inevitably limited the statistical significance of our

work. The goal of this work is thus to establish the existence of potential correlations between observables, and future observations of larger sample sizes are needed to further investigate the statistical significance of these correlations.

Due to the small sample size, we are not able to take into account the potential impact of environmental effects on galaxy evolution (Section 5.3). Future studies that probe a significant cosmic volume will further deepen our understanding of the complicated interplay between different processes in galaxy evolution.

# 6. Summary and Conclusion

In the present work, we demonstrate the existence of a potential correlation between the strength of nonaxisymmetric structures, quantified by the exerted torque forces, and the distribution of the total neutral (i.e., atomic and molecular) gas in disk galaxies. With 17 galaxies selected from the THINGS sample, we estimate the torque field $Q_T$ using the 3.6 µm images (Section 2). Recognizing the importance of properly calculating the forces due to the bulge component and the dark matter halo, we improve the bulge stretching correction with optimal decomposition strategy and take the stabilizing effects of the dark matter halo into consideration (Section 3). The evaluated $Q_T$, which we believe is a physically motivated estimation for the strength of the nonaxisymmetric structures, is then used to examine the correlations with the disk-scale neutral gas distribution (Section 4). We summarize our major results as follows.

i. Galaxies with stronger average torque forces $\bar{Q}_T$ due to nonaxisymmetric structures tend to have a more concentrated disk-scale neutral gas distribution within the inner disk (quantified by $C_{\text{neutral}}$; Figure 3). The enhanced inner neutral gas concentration seems unlikely to be explained fully by the enhanced molecular gas content in the central-kiloparsec regions (quantified by $C_{\text{CO}}$) as is known in the literature (Figure 4(a)).

ii. Controlling for either the disk gas fraction $f_{\text{neutral}}$ ($R_{25.5}$) or the average stellar mass surface density $\Sigma_*$ does not significantly affect the correlation between $\bar{Q}_T$ and $C_{\text{neutral}}$, suggesting that the complex gas regulation cannot fully explain the observed trend (Section 4.2).

iii. We do not observe a significant correlation of $2 + \log_{10} s_{\text{disk}}$ with $C_{\text{neutral}}$ or $C_{\text{CO}}$, likely suggesting that torque forces are a more intrinsic observable quantifying the dynamical strength of disk nonaxisymmetric structures (Figures 4(b), (c)).

iv. Inner neutral gas concentration $C_{\text{neutral}}$ correlates with the maximal torque forces $Q_g$ as well (Figure 4(d)), raising the problem of which of the two correlations ($\bar{Q}_T-C_{\text{neutral}}$ or $Q_g-C_{\text{neutral}}$) might be more intrinsic.

v. Provided that the torque forces are locally sufficiently strong ($Q_g \gtrsim 0.05$), the kiloparsec-scale neutral gas overdensities preferentially occur close to the maximal torque forces radius, suggesting a connection. When the gravitational perturbation is less strong ($Q_g \lesssim 0.05$), there does not seem to be such a connection (Figure 5).

Our results are consistent with the secular evolution scenario in which the nonaxisymmetric structures perturb the motion of the gas, trigger shock processes, and funnel the gas inward within the galactic disk. Nonaxisymmetric structures share a uniform role in this process, with the effectiveness dependent upon the
strength to dynamically perturb the gas motion, quantifiable by the torque forces parameter $\bar{Q}_T$ (Section 5).

The limitations of the present work mainly concern the small sample size (Section 5.5). Future studies extending the methodology to larger samples would be needed to reexamine the generality of conclusions in the present work, as well as to revisit the role of nonaxisymmetric structures in galaxy secular evolution.

## Acknowledgments

We are extremely grateful to the anonymous referee for constructive comments and practical suggestions that greatly improved this work. J.W. is grateful for the support of research grants from Ministry of Science and Technology of the People's Republic of China (NO. 2022YFA1602902), National Science Foundation of China (NO. 12073002, 12233001, 8200906879), and the China Manned Space Project. L.C.H. was supported by the National Science Foundation of China (11991052, 12011540375, 12233001), the National Key R&D Program of China (2022YFF0503401), and the China Manned Space Project (CMS-CSST-2021-A04, CMS-CSST-2021-A06). This work made use of THINGS, “The H1 Nearby Galaxy Survey” (F. Walter et al. 2008). This work made use of HERACLES, “The HERA C. Line Extragalactic Survey” (A. K. Leroy et al. 2009). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr; D. Makarov et al. 2014). This work made use of ASTROPY:<fnref n="12" /> a community-developed core Python package and an ecosystem of tools and resources for astronomy (Astropy Collaboration et al. 2013, 2018, 2022). This research made use of PHOTUTILS, an ASTROPY package for the detection and photometry of astronomical sources (L. Bradley et al. 2022).

**Facilities:** Spitzer, VLA (NRAO), BIMA, IRAM:30m, WISE, GALEX.

**Software:** ASTROPY (Astropy Collaboration et al. 2013, 2018, 2022), IMFIT (P. Erwin 2014, 2015), MATPLOTLIB (J. D. Hunter 2007), NUMPY (C. R. Harris et al. 2020), PHOTUTILS (L. Bradley et al. 2022), PINGOUIN (R. Vallat 2018), PROFOUND (A. S. G. Robotham et al. 2018; A. S. G. Robotham 2018), PYRAF (M. D. de La Peña et al. 2001; Science Software Branch at STScI 2012), REPROJECT (T. Robitaille 2018), SCIPY (P. Virtanen et al. 2020), SOURCE-EXTRACTOR (E. Bertin & S. Arnouts 1996).

## Appendix A
Uncertainty in Torque Evaluation

Apparently, the evaluation of the torque field outlined in Section 3 depends upon the multicomponent decomposition (Section 3.2), the selection of the Fourier components, and the adopted disk scale height, inclination, and position angle. We run tests evaluating the torque field with alternation in inputs to estimate the uncertainties associated with the torque field evaluation for each of our sample galaxies, propagated from the aforementioned sources. The results are summarized in Table 3, and as follows.

<table><caption>**Table 3**
Uncertainty Analysis for $\bar{Q}_T$</caption><thead><tr><th rowspan="2">Index<br>(1)</th><th rowspan="2">Item<br>(2)</th><th colspan="2">Uncertainty</th><th rowspan="2">Note<br>(5)</th></tr><tr><th>Absolute<br>(3)</th><th>Relative<br>(4)</th></tr></thead><tbody><tr><td>1</td><td>Bulge correction omitted</td><td>~0.003</td><td>~13%</td><td><sup>a</sup></td></tr><tr><td>2</td><td>Bulge shape</td><td>~0.0003</td><td>~1.2%</td><td><sup>a</sup></td></tr><tr><td>3</td><td>Decomposition statistical error</td><td>~0.0003</td><td>~0.9%</td><td><sup>a</sup></td></tr><tr><td>4</td><td>Disk scale height</td><td>~0.0017</td><td>~5%</td><td>...</td></tr><tr><td>5</td><td>Integration boundary</td><td>~0.000006</td><td>~0.025%</td><td>...</td></tr><tr><td>6</td><td>Set inner harmonics to zero</td><td>~0.00030</td><td>~0.9%</td><td>...</td></tr><tr><td>7</td><td>Higher even-order harmonics</td><td>~0.0013</td><td>~4%</td><td><sup>b</sup></td></tr><tr><td>8</td><td>Higher odd-order harmonics</td><td>~0.0022</td><td>~7%</td><td><sup>c</sup></td></tr><tr><td>9</td><td>Inclination <i>i</i></td><td>~0.004</td><td>~18%</td><td>...</td></tr><tr><td>10</td><td>Position angle <i>φ</i><sub>PA</sub></td><td>~0.004</td><td>~15%</td><td>...</td></tr><tr><td>11</td><td>Center</td><td>~0.0020</td><td>~6%</td><td>...</td></tr><tr><td>12</td><td>All</td><td>~0.013</td><td>~48%</td><td><sup>d</sup></td></tr><tr><td>13</td><td>Dust emission correction</td><td>≤0.010</td><td>≤39%</td><td><sup>e</sup></td></tr><tr><td>14</td><td>Neutral gas self-gravity</td><td>~0.0027</td><td>~10%</td><td>...</td></tr></tbody></table>

**Notes.** Uncertainty estimation for the average torque forces $\bar{Q}_T$. Column (1): index. Column (2): item considered. Column (3): absolute uncertainty propagating to $\bar{Q}_T$. Column (4): relative uncertainty propagating to $\bar{Q}_T$. Column (5): note.

<sup>a</sup> Bulgeless galaxies are omitted from consideration.

<sup>b</sup> Azimuthal Fourier harmonics $m = 10, 12, 14, \dots, 20$ are included in the evaluation in addition to the default $m = 0, 1, 2, 3, 4, 6, 8$, to evaluate the contribution of higher even-order harmonics.

<sup>c</sup> Azimuthal Fourier harmonics $m = 5, 7, 9$ are included in the evaluation in addition to the default to evaluate the contribution of higher odd-order harmonics.

<sup>d</sup> The total uncertainty is estimated by summing all terms listed above in quadrature.

<sup>e</sup> Only galaxies with the ICA stellar mass (s1) maps available from M. Querejeta et al. (2015) are considered. Some galaxies with low dust emission are thus excluded by this selection.

Overall, our estimation suggests that the most significant contributors of uncertainties in $\bar{Q}_T$ include (i) disk inclination (contributing to an absolute uncertainty in $\bar{Q}_T$ of order ~0.004, or a relative uncertainty of ~18%, corresponding to errors reported in Table 1), (ii) disk position angle (~0.004, or ~15%, corresponding to errors reported in Table 1), (iii) bulge stretching correction (~0.003, or ~13%, if completely omitted). It could be seen that the uncertainties associated with the bulge stretching correction increase with decreasing radius, while those propagated from inclination and position angle are significant throughout all radial ranges. The result agrees with the literature suggesting that the disk inclination and position angle could be a major source of uncertainty, in that any errors in the disk orientation would lead to an artificially distorted disk in deprojection (E. Laurikainen et al. 2004; S. Haan et al. 2009; M. Querejeta et al. 2016). The large uncertainty associated with the bulge projection underscores the importance of bulge stretching correction (E. Laurikainen et al. 2004) and necessitates the employment of optimal multicomponent decomposition to further prevent the potentially dramatic error in the decomposition itself (H. Salo et al. 2015; H. Gao & L. C. Ho 2017).

Within the inner disk, the uncertainties introduced by (iv) the central coordinate (overall, ~0.0020, or ~6%, assuming precise to $\gamma_{PSF}$) and (v) the assumed disk scale height (overall,

<footnote n="12">¹² http://www.astropy.org</footnote>
~0.0017, or ~5%, corresponding to scatter reported in R. de Grijs 1998) could also be significant sources of uncertainties. Though they contribute minimally to the overall uncertainty of $\bar{Q}_T$ (averaged within $R_{25.5}$), their contribution to the local estimation $Q_T$ could be greater than $\ge$0.003, or $\ge$10% within ~ (0.1–0.2)$R_{25.5}$, roughly the typical bar radius (S. Díaz-García et al. 2016b). Investigation focusing on the inner disk or the inner nonaxisymmetric structures (e.g., bars) might therefore find it necessary to consider these uncertainties (e.g., as in E. Laurikainen & H. Salo 2002; E. Laurikainen et al. 2004; S. Díaz-García et al. 2016b).

Some uncertainties arise from the assumption of the bulge shape and the harmonics included in the integration; yet they are of limited magnitude and should be sound to omit in simplified analyses. Assuming a symmetric yet disk-like bulge (E. Athanassoula 2005), leads to differences of order ~0.0003, or ~1.2% compared to the default assumption adopted in the present work (i.e., symmetric and spherical), with the uncertainty increases with decreasing radius. Compared with the uncertainty that would have been introduced by omitting the bulge stretching correction, the uncertainty associated with the bulge shape would be practically negligible. Including higher even-order and odd-order harmonics leads to differences of order ~0.0013 and order ~0.0022, or ~4% and ~7%, respectively, across all the radial ranges. Despite so, as has been argued in Section 3, including the higher-order harmonics risks biases by sharp features due to, e.g., low signal-to-noise ratio or contaminant emission (E. Laurikainen & H. Salo 2002; S. Díaz-García et al. 2016a), which would be undesirable for robust estimation.

In comparison, statistical uncertainties associated with the optimal multicomponent decomposition (estimated following the method outlined in H. Salo et al. 2015)<fnref n="13" /> propagate minimally to the uncertainty in $\bar{Q}_T$. Setting nonaxisymmetric harmonics inside the bulge-dominated region to zero also introduces negligible difference suggesting little impact of nuclear axisymmetric structures (I. Shlosman et al. 1989; P. Englmaier & I. Shlosman 2004), on the global dynamics, justifying the omission of nuclear morphological features in multicomponent decomposition of a large sample (H. Gao et al. 2019). Neglecting the inner nonaxisymmetric harmonics would also suppress the sometimes large residual resulting from the multicomponent decomposition. In terms of convergence, an outer integration boundary beyond $\ge R_{25.5}$ is seen to be largely sound if one wishes to evaluate the torque field within this radius.

By summation in quadrature, one could estimate a total uncertainty typically of level ~0.013, or ~48%, in the evaluated $\bar{Q}_T$. See also E. Laurikainen & H. Salo (2002) and S. Díaz-García et al. (2016b) for further arguments on how the further detailed assumptions on the disk vertical structures (the vertical profile and the radial gradient of the scale height) influence the torque field evaluation in a practically negligible manner.

There are also uncertainties that are difficult to estimate strictly in the scope of the present work, including (i) the mass-to-light ratio $\Upsilon_{3.6\mu m}$, whose scatter is typically ~30% (M. Eskew et al. 2012), (ii) the scatter associated with the

radial acceleration relation (F. Lelli et al. 2016, 2017b). F. Lelli et al. (2017b) have reported scatters of typically (0.13–0.15) dex, respectively, and eventually (iii) the photo-metric calibration of IRAC imaging data and the aperture correction factors, which should each be accurate to ~3% and ~10%,<fnref n="14" /> respectively. One would therefore expect the actual uncertainty associated with the torque parameter $Q_T$ to be slightly larger than that estimated in Table 3.

### A.1. Dust Emission

Mid-infrared imaging data at 3.6 µm capture emission due to hot dust, polycyclic aromatic hydrocarbon (PAH), as well as intermediate-age stars in addition to the light from the underlying old stellar populations (S. E. Meidt et al. 2012). We test whether this former emission component could significantly affect the evaluation of the torque force $\bar{Q}_T$. M. Querejeta et al. (2015) have provided an estimation of the ratio between these two emission components based on the independent-component analysis (ICA) technique with the $S^4G$ 3.6 µm/4.5 µm images (S. E. Meidt et al. 2012; M. Querejeta et al. 2015). The derived ICA s1 (stellar mass) maps from M. Querejeta et al. (2015) are available for 10 out of our 17 sample galaxies, which excludes NGC 3031, NGC 5055 ([3.6 µm] – [4.5 µm] color suggests dominance of old stellar population emission), NGC 5457 (low signal-to-noise ratio), NGC 925, NGC 2403, NGC 3621, and NGC 6946 (not included in the $S^4G$ sample; K. Sheth et al. 2010). We do not consider NGC 5194 in the test either, for the presence of NGC 5195 in the field of view. These galaxies are thus omitted from the test.

Figure 7 compares the average torque force $\bar{Q}_T$ evaluated from the 3.6 µm images and from the ICA s1 (stellar mass) maps derived by M. Querejeta et al. (2015) that effectively trace the underlying old stellar populations. Note that we have not performed multicomponent decomposition on the ICA s1 (stellar mass) map, since we consider it difficult to evaluate the corresponding pixel-wise uncertainty strictly. We thus expect some overestimation due to the bulge projection, which is indeed seen in Figure 7 in which data points tend to lie above the diagonal line. Beyond the bulge-dominated region, slight reduction is sometimes seen with the $Q_T(r)$ profiles evaluated with the ICA s1 (stellar mass) maps; yet they generally agree with those evaluated with the 3.6 µm images within uncertainty. The considerably large underestimation seen for NGC 3627 might be attributed to over-subtraction of the ICA technique preferentially along spiral arms, which, in the most extreme case, leads to zero flux along the prominent spiral arms. M. Querejeta et al. (2015) have also considered that the ICA result for this galaxy is less reliable (by assigning a quality flag 2).

For the nine sample galaxies shown in Figure 7, we estimate the differences between $\bar{Q}_T$ evaluated with the 3.6 µm images and with the ICA s1 (stellar mass) maps to be of order $\le 0.010$, or $\le 39\%$. Note that we regard this estimation as an upper limit here, as a subsample of galaxies overlapped with that of M. Querejeta et al. (2015) is considered, and some galaxies with low dust emission are excluded by this selection. It thus seems that the contaminant emission does affect the evaluation of the torque field, but only in a limited manner compared to

<footnote n="13">¹³ In the present work, the differences between the cryogenic and the post-cryogenic PSF are additionally considered together with the uncertainties associated with the sigma map, background subtraction, and the asymmetry of PSF considered in H. Salo et al. (2015).</footnote>

<footnote n="14">¹⁴ See Sections 4.3 and 8 of IRAC Instrument & Instrument Support Teams (2021).</footnote>
<figure><img src="image_10.png" /></figure>

**Figure 7.** Comparison between the default $Q_T$ evaluation (based on 3.6 µm images), and that based on the ICA stellar mass (s1) maps derived by M. Querejeta et al. (2015), for nine sample galaxies. Symbols are color coded according to the s1-to-total flux ratio $f_{s1}$ and are distinguished for barred (square) and nonbarred (circle) galaxies. Filled symbols show cases with the most reliable ICA results, and open symbols show those that have been considered less reliable (quality flag of 1 or 2, 3, respectively; M. Querejeta et al. 2015). The dashed line represents $y = x$. General agreement is seen.

the uncertainties of other sources (see also comparisons in S. Díaz-García et al. 2016b).

## A.2. Neutral Gas Self-gravity

We also evaluate the torque force field associated with the distribution of the neutral gas to understand its contribution. Neutral gas in disk could display rich structures due to various mechanisms including fragmentation, shocks, feedback, and hydrodynamical instability (e.g., E. Athanassoula 1992; Y. Kim & W.-T. Kim 2014; W.-T. Kim et al. 2014b; S. E. Meidt et al. 2021; A. T. Barnes et al. 2023; S. E. Meidt et al. 2023), some of which (e.g., feedback-driven shells, bubbles, and holes, stretched and elongated by shearing motion; D. R. Weisz et al. 2009; W.-Y. Seo et al. 2019; A. T. Barnes et al. 2023; E. J. Watkins et al. 2023) are considered to be transient compared to the disk dynamical timescale. We thus choose to convolve the gas distribution to a physical resolution of ~1.5 kpc and omit the gas structures under this scale, which we believe to be less coherent in affecting the motion of the gas. Even so, these feedback-driven features might still contribute to the nonaxisymmetric part of the neutral gas self-gravity forces, since they could feature sizes up to ~1 kpc (A. T. Barnes et al. 2023). We assume an infinitesimally thin gaseous disk and omit the gas beyond the warp onset radius for NGC 4736, NGC 5055, and NGC 7793 in this evaluation. We denote the average torque forces evaluated with the neutral gas self-gravity combined as $\bar{Q}_{T,+\text{gas}}$.

From Figure 8, one sees that the inclusion of the gas self-gravity leads to an increase in the evaluated average torque

<figure><img src="image_11.png" /></figure>

**Figure 8.** Comparison between the default $\bar{Q}_T$ evaluation (torque forces solely due to stars), and $\bar{Q}_{T,+\text{gas}}$ that involves the gas self-gravity. Symbols are color coded according to the neutral gas fraction $f_{\text{neutral}}$ (R25.5), and are distinguished for barred (square) and nonbarred (circle) galaxies. The dashed line represents $y = x$. An increase dependent upon gas fraction is seen when gas self-gravity is considered, though of limited amplitude.

forces (i.e., $\bar{Q}_{T,+\text{gas}} > \bar{Q}_T$ in general). Galaxies with more notable increases are seen to be comparatively richer in gas. Yet, the increase is in general limited in amplitude, with a typical difference of ~0.0027, or ~10%. This suggests that the neutral gas self-gravity contributes but to a limited extent to the overall torque force field. Furthermore, it seems that the nonaxisymmetric part of the self-gravity forces is less closely related to the disk-scale neutral gas concentration (Section 4.1).

## A.3. Optimal Multicomponent Decomposition

Figure 2 suggests that including secondary morphological features (nuclei, rings, lenses, disk breaks, etc.) could occasionally lead to significant differences in the multi-component decomposition when compared to more simplified treatments. Figures 9–10 display some of the most extreme cases corresponding to the objects specifically labeled in Figure 2, for which differences exceeding ~0.3 dex are seen in at least one bulge parameter.

In Figures 9–10, 2D profiles corresponding to optimal multicomponent decomposition models constructed in the present work are compared to those presented by H. Salo et al. (2015). In general, it could be seen from Figures 9–10 that including components such as nuclear rings (NGC 2903, NGC 3351, and NGC 5236) and bar lenses (NGC 3351; E. Athanassoula et al. 2015; M. Herrera-Endoqui et al. 2015) improves the fitting, such that the consequent best-fit models are seen to agree with the data in a more detailed manner. The improvement is seen not only in terms of the surface brightness but also in terms of the corresponding scatter at a given sky-projected distance, especially in the central regions.
<figure><img src="image_12.png" /><figcaption>**Figure 9.** 2D profiles constructed from the best-fit models presented by H. Salo et al. (2015) and those constructed in the present work. The surface brightness of each individual component is shown on top of the background data (white) and the best-fit model as a whole (magenta) and as a function of the sky-projected distance $R_{sky}$. The left column shows the results from H. Salo et al. (2015), which are to be compared with those from the present work shown in the right column. (a), (b) NGC 2903, (c), (d) NGC 3184, (e), (f) NGC 3351, (g), (h) NGC 5055.</figcaption></figure>

Two objects in our sample, i.e., NGC 5055 (Figures 9(g), (h)) and NGC 7793 (Figures 10(c), (d)), are considered by H. Salo et al. (2015) not to have a resolved bulge component but are modeled with a bulge component included in the present work. Figures 9–10 suggest that the best-fit models with bulge are favored for their better agreement with the data, especially at $r \approx (10-20)''$.

Combined with the fact that the bulge stretching correction could be a major source of uncertainty (Table 3), it seems that an elaborate, detailed multicomponent decomposition could be

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Figure 9 continued. (a), (b) NGC 5236, (c), (d) NGC 7793.</figcaption></figure>

crucial to improve the robustness and accuracy of torque field evaluation.

### A.4. Comparison with S. Díaz-García et al. (2016b)

For a final check for robustness, we compare our evaluation of the torque force field to that of S. Díaz-García et al. (2016b), who have evaluated torque force fields for a sample of ~600 S\*G galaxies to characterize the stellar bars. Note that S. Díaz-García et al. (2016b) have not applied dark matter halo correction to all their sample galaxies. Also note that S. Díaz-García et al. (2016b) adopted azimuthal maximum instead of median to extract the $Q_T(r)$ profiles. In these two aspects, we adjust our measurements to comply with their methodology for the purpose of fair comparison in this section.

Figure 11 compares the average torque force $\tilde{Q}_T$ measured in the present work, to that derived from the $Q_T(r)$ profiles evaluated by S. Díaz-García et al. (2016b). Differences beyond the estimated uncertainty are only occasionally seen with several data points and could be attributed to differences in (i) the considered Fourier harmonics. We consider lower odd-order harmonics in addition to even-order harmonics, which explains the slightly larger $\tilde{Q}_T$ compared to S. Díaz-García et al. (2016b) for NGC 2903 (specifically for $r \gtrsim 100''$) and NGC 3184 ($r \gtrsim 50''$) since both are multiarmed and a significant contribution from odd-order Fourier harmonics could thus be expected (R. J. Buta et al. 2015; S.-Y. Yu et al. 2018); (ii) the disk orientation. For NGC 5055, S. Díaz-García et al. (2016b) have adopted the disk inclination estimated from outer isophotes (H. Salo et al. 2015), while we adopt an inclination derived from the H I kinematic model (W. J. G. de Blok et al. 2008).

Despite these detailed differences, general agreement within uncertainty is seen between the two measurements shown in Figure 11, suggesting that our measurements are largely robust.
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Comparison between the average torque forces $\bar{Q}_T$ evaluated in the present work, and that evaluated by S. Díaz-García et al. (2016b). Symbols are for barred (square) and nonbarred (circle) galaxies, and according to whether or not halo correction is applied (red and blue, respectively). The dashed line represents $y = x$. General agreement is seen.</figcaption></figure>

# Appendix B

## Partial Correlations Controlling for Neutral Gas Fraction as Covariant

Figure 12 shows alternative versions of Figures 3–4, as well as Figure 6, in which the symbols are color coded by the

neutral gas fraction $f_{\text{neutral}}(R_{25.5})$ (within $R_{25.5}$) or $f_{\text{neutral}}(r_{50})$ (within $r_{50}$). Spearman’s and partial correlation coefficients controlling for neutral gas fraction within the corresponding radial range are quoted in Figure 12.
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Correlations discussed in Sections 4–5, color coded instead by the neutral gas fraction $f_{\text{neutral}}(R_{25.5})$ (within $R_{25.5}$) or $f_{\text{neutral}}(r_{50})$ (within $r_{50}$). Spearman's and partial correlation coefficients (controlling for the neutral gas fraction within the corresponding radial range, bracketed) are quoted at the corner of each panel. In panels (a), (b), (c), and (f), correlation coefficients for torque forces evaluated without (first row) and with gas self-gravity considered (second row) are quoted, respectively. Statistically significant ($p < 0.05$) correlations are highlighted in bold typeface.</figcaption></figure>

## Appendix C
### Measurements for Individual Galaxies

We show the neutral gas profiles for each individual sample galaxies in Figure 13. For convenience of comparison, panels

in Figure 13 are ordered by the increasing average torque forces $\bar{Q}_T$. We summarize the measured physical quantities in Table 4, and show the measured torque field distribution and neutral gas distribution in Figure 14, for each of the individual galaxies.
<figure><img src="image_16.png" /><figcaption>**Figure 13.** Neutral gas surface density profiles (blue solid curve) for the sample galaxies, as well as the corresponding H I (orange dashed curve) and molecular gas (green dotted curve) profiles. For galaxies whose designations are shown with asterisks, molecular gas distributions are derived by inverting the subkiloparsec-scale Schmidt law (F. Bigiel et al. 2008). Hatched regions correspond to H I disk warps. In this figure, panels are sorted by the increasing average torque forces $\bar{Q}_T$, labeled at the top right-hand corner. Moving from top to bottom, the average torque forces $\bar{Q}_T$ increase, while the neutral gas distribution appears to be more concentrated at the ~0.5$R_{25.5}$ scale.</figcaption></figure>
<table><caption>**Table 4**
Summary of Measurements</caption><thead><tr><th rowspan="2">Index<br>(1)</th><th rowspan="2">Object<br>(2)</th><th colspan="2">Average Torque Forces</th><th colspan="6">Maximal Torque Forces</th><th colspan="2">Average Torques</th></tr><tr><th>Q&#773;<sub>T</sub><br>(3)</th><th>Q&#773;<sub>T,+gas</sub><br>(4)</th><th>Q<sub>g</sub><br>(5)</th><th>r<sub>Qg</sub><br>(arcsec)<br>(6)</th><th>Gas peak<br>(arcsec)<br>(7)</th><th>Q<sub>g,+gas</sub><br>(8)</th><th>r<sub>Qg,+gas</sub><br>(arcsec)<br>(9)</th><th>Gas peak<br>(arcsec)<br>(10)</th><th>r&#773;<br>(11)</th><th>r&#773;<sub>+gas</sub><br>(12)</th></tr></thead><tbody><tr><td>1</td><td>NGC 628</td><td>0.022 ± 0.010</td><td>0.024</td><td>0.04 ± 0.01</td><td>128 ± 16</td><td>77 ± 16</td><td>0.04</td><td>111</td><td>77 ± 16</td><td>0.010 ± 0.004</td><td>0.011</td></tr><tr><td>2</td><td>NGC 925</td><td>0.040 ± 0.013</td><td>0.047</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.018 ± 0.005</td><td>0.022</td></tr><tr><td>3</td><td>NGC 2403</td><td>0.026 ± 0.012</td><td>0.028</td><td>0.04 ± 0.01</td><td>168 ± 41</td><td>217 ± 6</td><td>0.05</td><td>168</td><td>217 ± 6</td><td>0.010 ± 0.003</td><td>0.012</td></tr><tr><td>4</td><td>NGC 2903</td><td>0.050 ± 0.019</td><td>0.059</td><td>0.08 ± 0.02</td><td>156 ± 46</td><td>...</td><td>0.10</td><td>55</td><td>...</td><td>0.022 ± 0.008</td><td>0.025</td></tr><tr><td>5</td><td>NGC 2976</td><td>0.077 ± 0.053</td><td>0.083</td><td>0.16 ± 0.08</td><td>65 ± 11</td><td>77 ± 4</td><td>0.18</td><td>58</td><td>77 ± 4</td><td>0.029 ± 0.023</td><td>0.032</td></tr><tr><td>6</td><td>NGC 3031</td><td>0.009 ± 0.013</td><td>0.011</td><td>0.02 ± 0.01</td><td>280 ± 268</td><td>605 ± 210</td><td>0.02</td><td>293</td><td>605 ± 210</td><td>0.004 ± 0.003</td><td>0.006</td></tr><tr><td>7</td><td>NGC 3184</td><td>0.027 ± 0.013</td><td>0.032</td><td>0.06 ± 0.01</td><td>82 ± 25</td><td>98 ± 9</td><td>0.09</td><td>75</td><td>98 ± 9</td><td>0.012 ± 0.006</td><td>0.013</td></tr><tr><td>8</td><td>NGC 3351</td><td>0.040 ± 0.010</td><td>0.041</td><td>0.10 ± 0.01</td><td>47 ± 4</td><td>70 ± 0</td><td>0.10</td><td>51</td><td>70 ± 0</td><td>0.013 ± 0.004</td><td>0.013</td></tr><tr><td>9</td><td>NGC 3621</td><td>0.027 ± 0.014</td><td>0.034</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.010 ± 0.005</td><td>0.013</td></tr><tr><td>10</td><td>NGC 3627</td><td>0.043 ± 0.017</td><td>0.042</td><td>0.14 ± 0.03</td><td>50 ± 12</td><td>70 ± 13</td><td>0.15</td><td>48</td><td>70 ± 13</td><td>0.013 ± 0.006</td><td>0.013</td></tr><tr><td>11</td><td>NGC 4736</td><td>0.026 ± 0.011</td><td>0.027</td><td>0.11 ± 0.02</td><td>8 ± 2</td><td>42 ± 0</td><td>0.08</td><td>15</td><td>42 ± 0</td><td>0.009 ± 0.002</td><td>0.010</td></tr><tr><td>12</td><td>NGC 5055</td><td>0.030 ± 0.021</td><td>0.032</td><td>0.06 ± 0.02</td><td>79 ± 11</td><td>...</td><td>0.08</td><td>82</td><td>...</td><td>0.012 ± 0.006</td><td>0.013</td></tr><tr><td>13</td><td>NGC 5194</td><td>0.036 ± 0.018</td><td>0.037</td><td>0.06 ± 0.02</td><td>79 ± 16</td><td>21 ± 9</td><td>0.06</td><td>70</td><td>21 ± 9</td><td>0.017 ± 0.004</td><td>0.018</td></tr><tr><td>14</td><td>NGC 5236</td><td>0.044 ± 0.011</td><td>0.041</td><td>0.16 ± 0.01</td><td>99 ± 10</td><td>112 ± 0</td><td>0.14</td><td>78</td><td>112 ± 0</td><td>0.011 ± 0.002</td><td>0.011</td></tr><tr><td>15</td><td>NGC 5457</td><td>0.030 ± 0.015</td><td>0.039</td><td>0.06 ± 0.02</td><td>254 ± 34</td><td>266 ± 31</td><td>0.08</td><td>127</td><td>126 ± 20</td><td>0.012 ± 0.005</td><td>0.017</td></tr><tr><td>16</td><td>NGC 6946</td><td>0.034 ± 0.009</td><td>0.037</td><td>0.07 ± 0.02</td><td>51 ± 8</td><td>...</td><td>0.08</td><td>150</td><td>...</td><td>0.012 ± 0.003</td><td>0.014</td></tr><tr><td>17</td><td>NGC 7793</td><td>0.017 ± 0.014</td><td>0.019</td><td>0.03 ± 0.06</td><td>49 ± 22</td><td>...</td><td>0.04</td><td>144</td><td>...</td><td>0.007 ± 0.004</td><td>0.008</td></tr></tbody></table><table><thead><tr><th colspan="3">Normalized Fourier Amplitudes</th><th rowspan="2">s<sub>disk</sub><br>(16)</th><th colspan="2">Gas Concentration Indices</th><th colspan="2">Neutral Gas Fractions</th><th rowspan="2">Σ<sub>*</sub><br>(M<sub>☉</sub> pc<sup>-2</sup>)<br>(21)</th><th rowspan="2">Note<br>(22)</th></tr><tr><th>max {A<sub>2</sub><br>(13)</th><th>r<sub>max {A<sub>2</sub><br>(14)</sub></th><th>Gas peak<br>(arcsec)<br>(15)</th><th>C<sub>neutral</sub><br>(17)</th><th>C<sub>CO</sub><br>(18)</th><th>f<sub>neutral</sub> (R<sub>25.5</sub>)<br>(19)</th><th>f<sub>neutral</sub> (r<sub>50</sub>)<br>(20)</th></tr></thead><tbody><tr><td>0.51 ± 0.29</td><td>298 ± 21</td><td>77 ± 16</td><td>0.28 ± 0.08</td><td>0.18 ± 0.05</td><td>0.36 ± 0.07</td><td>0.27 ± 0.02</td><td>0.10 ± 0.01</td><td>89 ± 4</td><td>...</td></tr><tr><td>0.48 ± 0.05</td><td>270 ± 9</td><td>...</td><td>0.38 ± 0.04</td><td>0.03 ± 0.06</td><td>0.63 ± 0.10</td><td>0.53 ± 0.05</td><td>0.22 ± 0.02</td><td>20 ± 1</td><td><sup>a</sup></td></tr><tr><td>0.45 ± 0.03</td><td>196 ± 8</td><td>217 ± 6</td><td>0.30 ± 0.06</td><td>0.13 ± 0.06</td><td>0.42 ± 0.10</td><td>0.29 ± 0.03</td><td>0.10 ± 0.01</td><td>60 ± 3</td><td>...</td></tr><tr><td>0.78 ± 0.14</td><td>178 ± 16</td><td>...</td><td>0.52 ± 0.12</td><td>0.39 ± 0.06</td><td>0.67 ± 0.10</td><td>0.13 ± 0.01</td><td>0.09 ± 0.01</td><td>239 ± 23</td><td><sup>b</sup></td></tr><tr><td>0.75 ± 0.38</td><td>96 ± 19</td><td>77 ± 4</td><td>0.49 ± 0.25</td><td>0.49 ± 0.06</td><td>0.26 ± 0.14</td><td>0.12 ± 0.01</td><td>0.10 ± 0.02</td><td>72 ± 11</td><td>...</td></tr><tr><td>0.47 ± 0.10</td><td>615 ± 30</td><td>605 ± 210</td><td>0.24 ± 0.07</td><td>-0.04 ± 0.08</td><td>0.03 ± 0.15</td><td>0.07 ± 0.01</td><td>0.00 ± 0.00</td><td>418 ± 30</td><td>...</td></tr><tr><td>0.51 ± 0.15</td><td>213 ± 37</td><td>98 ± 9</td><td>0.32 ± 0.06</td><td>0.23 ± 0.06</td><td>0.45 ± 0.08</td><td>0.23 ± 0.02</td><td>0.13 ± 0.01</td><td>61 ± 4</td><td>...</td></tr><tr><td>0.52 ± 0.02</td><td>39 ± 4</td><td>70 ± 0</td><td>0.32 ± 0.05</td><td>0.27 ± 0.06</td><td>1.10 ± 0.09</td><td>0.09 ± 0.01</td><td>0.04 ± 0.00</td><td>217 ± 13</td><td>...</td></tr><tr><td>0.25 ± 0.14</td><td>226 ± 9</td><td>...</td><td>0.22 ± 0.06</td><td>0.26 ± 0.15</td><td>0.26 ± 0.34</td><td>0.24 ± 0.05</td><td>0.10 ± 0.04</td><td>139 ± 7</td><td><sup>a, c</sup></td></tr><tr><td>0.58 ± 0.12</td><td>141 ± 16</td><td>70 ± 13</td><td>0.38 ± 0.12</td><td>0.57 ± 0.06</td><td>0.53 ± 0.10</td><td>0.07 ± 0.01</td><td>0.07 ± 0.01</td><td>244 ± 34</td><td>...</td></tr><tr><td>0.59 ± 0.08</td><td>201 ± 4</td><td>315 ± 6</td><td>0.36 ± 0.05</td><td>0.50 ± 0.05</td><td>0.59 ± 0.08</td><td>0.04 ± 0.00</td><td>0.02 ± 0.00</td><td>2021 ± 57</td><td>...</td></tr><tr><td>0.58 ± 0.08</td><td>493 ± 3</td><td>...</td><td>0.32 ± 0.12</td><td>0.45 ± 0.05</td><td>0.64 ± 0.08</td><td>0.14 ± 0.01</td><td>0.08 ± 0.01</td><td>195 ± 13</td><td><sup>b</sup></td></tr><tr><td>0.94 ± 0.08</td><td>317 ± 8</td><td>21 ± 9</td><td>0.56 ± 0.10</td><td>0.50 ± 0.06</td><td>0.58 ± 0.09</td><td>0.16 ± 0.01</td><td>0.13 ± 0.02</td><td>235 ± 21</td><td>...</td></tr><tr><td>0.47 ± 0.01</td><td>115 ± 12</td><td>112 ± 0</td><td>0.33 ± 0.03</td><td>0.50 ± 0.26</td><td>0.83 ± 0.36</td><td>0.11 ± 0.04</td><td>0.10 ± 0.05</td><td>339 ± 6</td><td><sup>c</sup></td></tr><tr><td>0.68 ± 0.35</td><td>511 ± 32</td><td>490 ± 47</td><td>0.40 ± 0.14</td><td>0.15 ± 0.06</td><td>0.49 ± 0.08</td><td>0.32 ± 0.04</td><td>0.12 ± 0.02</td><td>59 ± 6</td><td>...</td></tr><tr><td>0.70 ± 0.03</td><td>464 ± 5</td><td>...</td><td>0.37 ± 0.03</td><td>0.41 ± 0.05</td><td>0.91 ± 0.07</td><td>0.22 ± 0.02</td><td>0.17 ± 0.02</td><td>195 ± 6</td><td><sup>b</sup></td></tr><tr><td>0.21 ± 0.02</td><td>152 ± 10</td><td>...</td><td>0.14 ± 0.03</td><td>0.21 ± 0.13</td><td>0.36 ± 0.34</td><td>0.33 ± 0.06</td><td>0.17 ± 0.05</td><td>60 ± 1</td><td><sup>b, c</sup></td></tr></tbody></table>

Notes. Summary of measurements. Column (1): index. Column (2): object designation. Column (3): average torque forces $\bar{Q}_T$. Column (4): average torque forces $\bar{Q}_{T,+gas}$, with the neutral gas self-gravity combined in evaluating the torque forces. Column (5): maximal torque forces $Q_g$. Column (6): radius $r_{Qg}$ corresponding to $Q_g$. Column (7): radius of kiloparsec-scale neutral gas overdensity proximate to $r_{Qg}$. Columns (8)–(10): same as columns (5)–(7), with the neutral gas self-gravity combined in evaluating the torque forces. Column (11): average dynamical torque term $\bar{\Gamma}$. Column (12): average dynamical torque term $\bar{\Gamma}_{+gas}$, with the neutral gas self-gravity combined in evaluating the torque. Column (13): maximal $m = 2$ Fourier amplitude of the stellar mass surface density $\max\{A_2\}$. Column (14): Radius $r_{max\{A_2\}}$ corresponding to $\max\{A_2\}$. Column (15): radius of kiloparsec-scale neutral gas overdensity proximate to $r_{max\{A_2\}}$. Column (16): average stellar mass surface density. Column (17): inner neutral gas concentration parameter $C_{\text{neutral}}$. Column (18): central molecular gas concentration index $C_{\text{CO}}$. Column (19): neutral gas fraction $f_{\text{neutral}}(R_{25.5})$ within $R_{25.5}$. Column (20): neutral gas fraction $f_{\text{neutral}}(r_{50})$ within $r_{50}$. Column (21): average stellar mass surface density $\bar{\Sigma}_*$. Column (22): note.

<sup>a</sup> Maximal torque forces are not determined given the overall monotonically decreasing $Q_T(r)$ [$Q_{T,+gas}(r)$] as a function of the radius.

<sup>b</sup> Kiloparsec-scale neutral gas overdensity cannot be determined from the generally smooth neutral gas radial profile.

<sup>c</sup> Molecular gas distribution is inferred from the star formation rate distribution by inverting the subkiloparsec Schmidt law (F. Bigiel et al. 2008).
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Summary of measurements for NGC 628. The left column shows (a) the deprojected stellar mass surface density $\Sigma_*$ with (c) the nonaxisymmetric structures highlighted, (e) the evaluated torque force field $Q_T$, and (g) the neutral gas distribution. Red circles indicate $R_{25.5}$. The right column shows (b) the corresponding rotational velocity, (d) Fourier amplitudes, (f) torque forces, and (h) neutral gas surface density as functions of the radius. In panel (b), the rotational velocity solely due to the stellar mass (red dashed curve) and more specifically due to the stellar bulge (red dotted curve) are shown along the estimated rotation curve $v_c$ (blue solid curve). In panel (d), the Fourier amplitudes $A_2$ (blue), $A_3$ (red), and $A_4$ (green) are shown, with the max $\{A_2\}$ highlighted with the blue symbol. In panel (f), the torque force due to stars $Q_T$ (blue solid curve), and that evaluated with the neutral gas self-gravity combined $Q_{T,+\text{gas}}$ (blue dashed curve) are shown, with the maximal value $Q_g$ ($Q_{g,+\text{gas}}$) highlighted by the filled (empty) symbol, respectively. In panel (h), the neutral gas mass surface density $\Sigma_{\text{neutral}}$ (blue solid curve), the H I mass surface density $\Sigma_{\text{H I}}$ (red dashed curve), and the molecular gas mass surface density $\Sigma_{\text{H}_2}$ (green dotted curve) are shown, with kiloparsec-scale neutral gas overdensities highlighted by the blue symbols.</figcaption></figure>

(The complete figure set (16 images) is available in the online article.)
ORCID iDs

Ze-Zhong Liang https://orcid.org/0009-0007-9363-2582

Jing Wang https://orcid.org/0000-0002-6593-8820

Hua Gao https://orcid.org/0000-0003-1015-5367

Luis C. Ho https://orcid.org/0000-0001-6947-5846

E. Athanassoula https://orcid.org/0000-0001-6079-1332

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