WiNDS: An H_α Kinematics Survey of Nearby Spiral Galaxies—Vertical Perturbations in Nearby Disk-type Galaxies

Over the last ten years, oscillatory perturbations toward the outskirts of the solar neighborhood in the Galactic disk have been reported several times (e.g., López-Corredoira et al. 2002; Momany et al. 2006; Widrow et al. 2012; Slater et al. 2014; Price-Whelan et al. 2015; Xu et al. 2015; Antoja et al. 2018; Collaboration et al. 2021). In particular, using 11k main-sequence stars from the Sloan Digital Sky Survey (SDSS; York et al. 2000) Widrow et al. (2012) detected asymmetries in both, (i) the bulk velocity of solar neighborhood stars associated with a breathing pattern, i.e., compression and rarefaction motions; and (ii) in the vertical stellar number density distribution. The latter was related to a bending pattern, i.e., local displacements of the disk from the midplane (Widrow et al. 2014). This study was followed up by Xu et al. (2015), who analyzed measurements of stellar number counts of main-sequence stars located at Galactic latitudes 110° < l < 229°, as a function of Galactocentric radius. They showed that the amplitude of the perturbations in the vertical stellar number counts, i.e., the displacement of the disk with respect to its midplane, increases toward the outskirts of the Galaxy. This type of oscillatory perturbation on the stellar and/or gaseous component of the disk is known as a corrugation pattern. Thanks to the analysis of the full 6D phase-space information for more than six million stars from Gaia Collaboration et al. (2018), Antoja et al. (2018) showed that, indeed, our own Galactic disk is undergoing phase mixing of a nonequilibrium configuration, a perturbation likely associated with the interaction of the Milky Way with the Sagittarius dwarf galaxy in the past (e.g., Gómez et al. 2013; Laporte et al. 2018b, 2019, 2020, Bland-Hawthorn et al. 2019, Bland-Hawthorn & Tepper-García 2021). More recently, Gaia Collaboration et al. (2021) confirmed that the Milky Way disk has very complex dynamics, with vertical velocity perturbations that can be partially described as a bending wave.

Interestingly, evidence of such complex vertical oscillatory patterns on external galaxies, such as those observed in the Milky Way, is still extremely limited. Vertically perturbed disks have been extensively observed, especially in edge-on galaxies. Studies of 21 cm neutral hydrogen line observations show that most galaxies that have extended HI disks, with respect to the optical, are warped. Using a sample of 26 edge-on galaxies located in different environments with inclinations i > 75° and blue diameters larger than 15, from the Westerbork HI Survey of Spiral and Irregular Galaxies (WHISP; van der Hulst et al. 2001), García-Ruiz et al. (2002) showed that all galaxies in their sample with an extended HI disk (∼76%) are warped with respect to the optical disk. They also found that warped disk galaxies are more often found in less dense environments, indicating that tidal interactions are not the only mechanism producing galactic warps. However, in denser environments, the disk vertical perturbations typically show larger amplitudes than those in less dense environments. This is likely due to the fact that, in denser environments, galaxies are more likely to undergo violent tidal interactions with companion galaxies.

For observations in optical bands, Ann & Park (2006) analyzed a sample of 325 galaxies from the SDSS, which consists of a majority of late-type spiral galaxies with inclinations i > 84° and isophotal major axis length ${D}_{25}\gt 1^{\prime}$ at ${\mu }_{B}=25\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}$. The study showed that 73% of the sample contained a warped disk: 51% corresponds to S-shaped and 22% to U-shaped perturbations. For the analysis of the environment dependence on the frequency of warps, Ann & Park (2006) analyzed 75 galaxies with redshift data from the SDSS DR3, of which 56 have companion galaxies. For the subset of galaxies that have companions, 64% show warped disks. For galaxies without companions, 81% show warped disks. This result is consistent with that presented in García-Ruiz et al. (2002), i.e., in poor environments, a higher frequency of warped disks is found than in rich environments. Vertical perturbations have also been studied in edge-on galaxies using dust lines. Narayan et al. (2020) analyzed a sample of five nearby objects with inclinations i > 80° and also showed that such perturbations are common.

S-shaped warps are expected to be a very common feature of both interacting and isolated late-type galaxies. Gómez et al. (2016, 2017) studied in detail the origin and evolution of vertical perturbation in the disk of late-type galaxies using high-resolution cosmological magnetohydrodynamical simulations of the Auriga Project (Grand et al. 2017). By means of the construction of mass-weighted mean height, 〈Z〉, and mean vertical velocities maps, 〈V_Z〉, for both the stellar and cold gas components, these studies found that 70% of the Milky Way-like models showed strongly vertically perturbed disks. Interestingly, while only half of the vertically perturbed disks showed integral-sign (S-shaped) warps, the remaining half showed a more complex vertical structure, i.e., corrugation patterns, indicating that such structures are expected to be common.

A possible reason behind the lack of detected vertical patterns relates to the complexity behind their observation. On edge-on galaxies, such a pattern can be easily confused with S-shaped warps due to projection effects. However, as discussed in Gómez et al. (2017), such a corrugation pattern should be detectable along the line-of-sight velocity (V_los) of nearly face-on galaxies. Due to the oscillating nature of a corrugation, global patterns on the (V_los) field can be directly linked to global patterns in a 〈Z〉 map. Until recently, previous efforts to detect corrugations in the cold gas disk component of nearby galaxies were based on H_α emission through long-slit spectroscopy. Alfaro et al. (2001) analyzed NGC 5427, a galaxy with an inclination angle of 30°, and found wavy-like variations in the velocity profile of the ionized gas. Sánchez-Gil et al. (2015) analyzed a sample of four spiral galaxies and showed that two presented corrugation patterns. However, due to the limited coverage associated with the long-lit spectroscopic observations, such patterns could be confused with the effects of local perturbations such as fountain flows. In a recent work, Gómez et al. (2021) presented a full 2D velocity map of the low-inclination galaxy, VV304a. Their study was based on Fabry–Perot (FP) interferometer H_α observations. This technique has the great advantage of providing high spectral resolution in a narrow frequency range, along with good spatial resolution (in this work ∼2''). As such, it allows resolving local velocity perturbations with amplitudes of the order of 10 km s⁻¹. The study showed, for the first time, that VV304a presents global and coherent velocity perturbations that are consistent with a corrugation pattern. They also showed that these velocity perturbations cannot be described by the effects associated with the presence of axisymmetric features on its disk, such as the bar and spiral structure. Thus, they conclude that these perturbations are a direct consequence of the gravitational interaction with its similar mass companion galaxy, VV304b.

The characterization of vertical perturbations in nearby disk galaxies can provide very valuable information about their recent interaction with their environment. Several mechanisms could be behind the formation of warps and corrugation patterns (Sellwood 2013; Gómez et al. 2016, 2017). One of them is the tidal distortion of a pre-existing disk by an external perturber, such as the case of our own Milky Way (Antoja et al. 2018; Laporte et al. 2019) and VV304a (Gómez et al. 2021). The strong tidal torques being exerted on a pre-existing disk as relatively massive satellites fly by or merge can induce strong vertical perturbations (Ostriker & Binney 1989; Quinn et al. 1993; Velazquez & White 1999; Bailin 2003; Kazantzidis et al. 2009; Gómez et al. 2013; D'Onghia et al. 2016; Gómez et al. 2017; Laporte et al. 2018a, 2018b). In addition, the torques associated with a non-spherical mass distribution of dark matter can also trigger the formation of vertical patterns (Debattista & Sellwood 1999; Jiang & Binney 1999; Shen & Sellwood 2006; DeBuhr et al. 2012; Yurin & Springel 2015; Gómez et al. 2016; Laporte et al. 2018a). Other possibilities may include misaligned accretion of cold gas due to the cooling of hot gas halo, infalling from the cosmic web, or being left by gas-rich host-satellite interactions (Jiang & Binney 1999; Sancisi et al. 2008; Roškar et al. 2010; Aumer et al. 2013; Radburn-Smith et al. 2014; Gómez et al. 2017) and ram pressure of the surrounding intergalactic material (Haan & Braun 2014). The objective of this work is to search for velocity perturbations in the disks of nearby late-type galaxies. To achieve this goal we use high-resolution observations of near face-on galaxies obtained with an FP interferometer. For this purpose, we present the Waves in Nearby Disk galaxies Survey (WiNDS), which consists of a data set with high spectral resolving power (R ∼10000) and large spatial coverage, making them ideal for investigating the kinematics of the ionized gas in galactic disks. This study is the first step in an effort that aims to characterize the history of interactions of nearby galaxies, and estimate the frequency with which vertical disturbances such as those observed in the Milky Way arise in the local universe.

This paper is organized as follows. In Section 2, we introduce the WiNDS data sample and describe our new observations. In Section 3, we discuss the data reduction procedure. Sections 4 and 5 describe the data analysis and selection and quantification criteria of bending modes. Finally, we present our results in Section 6 and in Section 7 we provide a discussion and our conclusions. In Appendix A, the comments for each individual galaxy and maps of the new observations made in this work are given. The residual velocity maps are shown in Appendix B.1. The rotation curves are displayed in Appendix C.1. In Appendix D.1, the image processing method is described.

In this section, we present our WiNDS survey, an ongoing observational campaign currently comprising 40 nearby nearly face-on spiral galaxies. WiNDS consists of 12 new observational data and we complement it with additional archival data of 28 late-type galaxies from different surveys. The entire data sample contains 3D data cubes obtained using an FP interferometer with a resolving power at the H_α rest wavelength of R ≈ 10000. The galaxies in the WiNDS sample were selected according to three main criteria:

• 1.  
  Distance: Nearby spiral galaxies were selected to have systemic velocities v ≤ 3000 km s⁻¹, corresponding to less than 45 Mpc.
• 2.  
  Inclination: All galaxies have previously estimated low-inclination angles i ≤ 40°. Both morphologically and kinematically estimated inclination were considered in this step.
• 3.  
  Size: All galaxies have projected diameters, a_p , between $2^{\prime} \leqslant {a}_{p}\leqslant 4^{\prime}$.

The goal of this selection criteria is to allow us to resolve velocity perturbations in the observed disks with amplitudes as small as 10 km s⁻¹. In what follows we discuss WiNDS new observations in detail. We also briefly describe the additional surveys utilized to complement WiNDS. In Table 1, we list some of the main properties of the WiNDS sample. The blue histograms in Figure 1 show the distribution of the most relevant parameters for the final WINDS sample. The solid curves depict the smooth continuous approximation of the underlying histograms. These smooth histograms were obtained using a Gaussian Kernel Density Estimator. The green histograms in the same figure show the parameter distribution of the vertically perturbed galaxy candidates within the WiNDS sample (see Section 5). Although the WiNDS sample is not complete in terms of, e.g., mass and magnitude, it allows performing a first systematic search of vertically perturbed disks in the nearby universe. The 40 selected galaxies span different environments such as clusters, groups, and field galaxies, and a wide variety of morphologies (Sa to Sc). Note, however, that this is an evolving project, and more objects will be added in the future to complement the available sample. Figure 2 shows the optical images of the WiNDS sample, obtained from SDSS DR9 using the g, r, and z bands.

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Table 1. WiNDS Galaxy Targets and Data Archive Parameters

NGC	Morph	tmorph	Ropt	vsys	d	MB	${v}_{\mathrm{rot}}^{\max }$	log(Mstar)	log(MH i )	log	i	PA
	(Type)		(kpc)	(km s−1)	(Mpc)	(mag)	(km s−1)	(M⊙)	(M⊙)	(SFR)	(°)	(°)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
New observations
628	SAc	5.2	16.4	657.2	10.8	−20.7 ± 0.3	64	10.3a	9.7b	...	7m	252
1058	SAc	5.1	4.3	518.0	9.7	−18.9 ± 0.4	13	...	8.8d	...	6m	152
2500	SBd	7.0	4.5	503.9	10.5	−17.9 ± 1.7	131	9.4a	9.0c	...	40k	86
2763 (SAM-FP)	SBcd	9.9	10.0	1891.6	29.6	−19.8 ± 0.3	117	...	...	...	30k	50
3147	SAbc	3.9	26.1	2801.9	46.1	−21.9 ± 0.2	335	11.4a	...	...	32m	147
3184	SABcd	5.9	11.4	592.1	10.9	−19.1 ± 0.4	208	10.4a	9.3c	...	16k	1
3423	SAcd	6.0	8.5	1004.0	15.2	−20.0 ± 0.2	128	9.7a	9.1b	...	19k	45
3485	SBb	3.2	9.4	1436.0	28.2	−19.1 ± 0.8	188	9.9a	9.3b	0.6e	20k	116
3642	SAbc	4.0	23.3	1588.0	30.0	−20.6 ± 0.6	48	10.4a	...	...	25k	123
4136	SABc	5.2	4.2	608.9	7.2	−18.5 ± 1.5	102	9.5a	8.9b	...	22k	72
4900	SBc	5.1	3.2	959.6	9.8	−19.2 ± 1.1	112	10.4a	9.1b	...	5k	0
5194	SAbc	4.0	15.8	462.9	9.8	−21.3 ± 0.3	134	10.9a	9.3c	...	20k	13
Data archive
864 (G)	SABc	5.1	15.3	1561.9	22.6	−19.9 ± 0.4	134	10.2a	9.6b	...	35k	27
2775 (G)	SAab	1.6	14.3	1350.0	23.0	−20.6 ± 0.8	296	10.9a	8.6b	...	38k	157
3344 (G)	SABbc	4.0	7.7	580.1	7.4	−19.6 ± 0.3	217	9.7a	9.6b	...	18k	156
3346 (G)	SBcd	5.9	10.3	1274.1	24.5	−19.1 ± 0.9	126	10.2a	9.1b	0.6e	34m	113
3351 (S)	SBb	3.1	10.5	777.9	9.7	−19.8 ± 0.1	151	10.5a	9.0b	...	40k	11
3504 (G)	SABab	2.1	11.7	1525.0	29.8	−20.5 ± 0.7	194	10.4a	8.8b	3.6e	39k	164
3596 (G)	SABc	5.2	14.0	1192.9	24.2	−19.7 ± 0.9	157	10.0a	9.0b	...	17k	77
3631 (H)	SAc	5.1	17.3	1155.9	23.8	−21.0 ± 0.8	79	10.2a	...	2.7e	24k	171
3938 (S)	SAc	5.1	12.9	809.1	16.6	−20.1 ± 1.1	128	10.5a	9.3d	...	8k	17
4037 (H)	SBb	3.3	5.5	932.1	15.1	−18.0 ± 0.1	101	9.7a	8.5b	0.2e	32k	151
4189 (V)	SABcd	5.9	5.3	2115.0	15.1	−19.7 ± 0.5	196	10.5a	9.4b	...	31k	70
4321 (V)	SABbc	4.0	16.3	1570.9	15.1	−21.2 ± 0.1	279	10.9a	9.4b	6.2e	38k	149
4411B (H)	SABcd	6.2	5.5	1272.0	14.9	−19.4 ± 0.2	76	9.5a	9.0b	...	18k	52
4430 (H)	SBb	3.5	4.9	1451.0	14.7	−20.3 ± 0.5	87	9.8a	8.6b	0.7e	28m	60
4519 (V)	SBd	6.9	6.9	1218.1	14.8	−19.3 ± 0.2	117	10.2a	9.5b	0.9e	40k	180
4625 (S)	SABm	8.7	3.6	620.9	11.3	−17.9 ± 1.3	39	9.1a	8.5c	...	36k	126
4725 (S)	SABab	2.2	45.0	1206.1	28.8	−20.7 ± 0.2	257	10.9a	9.6b	1.6e	30m	28
4736 (S)	SAab	2.3	8.4	307.9	5.2	−19.7 ± 0.3	182	10.5a	8.3c	...	36k	118
5204 (G)	SAm	8.9	4.4	200.9	5.9	−17.0 ± 0.1	56	8.7a	8.6c	...	40k	17
5334 (H)	SBc	5.3	15.9	1385.9	26.1	−19.1 ± 1.1	133	10.4a	9.1c	0.5e	38k	6
5430 (G)	SBb	3.1	16.1	2961.1	50.5	−20.8 ± 0.4	188	10.7a	...	...	32k	8
5585 (G)	SABd	6.9	7.1	292.9	8.2	−18.7 ± 0.2	79	9.3a	8.8c	...	36k	50
5668 (G)	SAd	6.9	14.3	218.4	29.7	−20.1 ± 0.6	73	10.2a	9.9b	1.6e	18k	146
5669 (H)	SABcd	6.0	15.8	1367.9	27.3	−18.6 ± 0.7	102	10.2a	9.3b	1.0e	36m	71
5713 (S)	SABbc	4.0	13.5	1898.9	33.8	−21.2 ± 0.5	108	10.6a	...	...	33k	23
6217 (G)	SBbc	4.0	11.4	1362.0	26.1	−20.5 ± 0.7	113	10.5a	9.6c	...	34k	105
6946 (G)	SABcd	5.9	10.0	39.9	5.9	−20.9 ± 0.2	315	...	9.9c	...	17m	61
UGC 3685 (G)	SBb	3.0	14.6	1797.0	30.3	−19.9 ± 0.6	41	...	9.8c	...	12k	134

Note. (1) Galaxy name in the NGC catalog, except for UGC 3685, which does not have an NGC name; the letter in parenthesis corresponds to the survey name: (G) for GHASP (Epinat et al. 2008a, 2008b), (S) for SINGS (Daigle et al. 2006a; Dicaire et al. 2008), (V) for Virgo (Chemin et al. 2006), and (H) for HRS (Gómez-López et al. 2019); (2) and (3) morphological type found in the HyperLeda database; (4) optical radius considering the isophotal radius at the limiting surface brightness of 25 B mag arcsec⁻² from the Third Reference Catalog of Bright Galaxies (RC3; de Vaucouleurs et al. 1991) corrected for the Virgo and Great Attractor (GA) infall, assuming H₀ = 67.8 km s⁻¹ Mpc⁻¹; (5) systemic velocity from NED; (6) distance in megaparsec from NED, corrected for the Virgo and GA infall, assuming H₀ = 67.8 km s⁻¹ Mpc⁻¹; (7) absolute B-band magnitude (HyperLeda); (8) maximum rotation velocity corrected for inclination from HyperLeda; (9) stellar mass a from Sheth et al. (2010); (10) H i mass b from Haynes et al. (2018), c from Karachentsev et al. (2013), d from the radio survey Westerbork survey of H i in SPirals (WHISP) galaxies https://www.astro.rug.nl/~whisp/; (11) star formation rate. e from Boselli et al. (2015); (12) inclinations k correspond to kinematic values and m correspond to morphological values from the literature; and (13) PA.

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2.1. WiNDS: New Data Cubes

2.2. Additional Data Archive

The WiNDS data sample was reduced using the pipeline-based program computeeverything ⁹ and the reducWizard ¹⁰ interface, following the steps described in Daigle et al. (2006b) and Epinat et al. (2008b).

The data reduction process includes (a) the wavelength calibration, (b) the night-sky lines subtraction, (c) the astrometry process, (d) the adaptive spatial binning using the 2D Voronoi tessellation, whose implementation finally produces a smoothing specially adapted to a given signal-to-noise ratio (S/N), (e) the generation of the 2D momentum maps, (f) a semiautomatic cleaning of the velocity fields, and (g) velocity dispersion correction. In the following we briefly describe these processes:

• (a)  
  The calibration process consists of applying a phase map to provide the same wavelength/velocity origin to each profile, for each pixel of the observation datacube. The 2D phase map is computed from the two calibration datacubes. During the phase correction process, the individual exposures are recentered with respect to each other, using field stars, to minimize telescope drifts and instrument bend.
• (b)  
  The OH emission lines are the main foreground sky contamination. The sky subtraction is done by dividing the collapsed datacube into a galaxy-dominant and a sky-dominant region. The night-sky emission is interpolated from this galaxy-free region using a two-degree polynomial, and subsequently removed from the whole datacube.
• (c)  
  The next step is astrometry, which is done through the KOORDS task in the KARMA ¹¹ package (Gooch 1996), comparing star fields between XDSS ¹² R-band images and our continuum images of each galaxy.
• (d)  
  For the estimation of the S/N, which is related to the flux in the line, to the spectral resolution and the rms in the continuum, we use adapted spatial binning through Voronoi tessellation, as described in Daigle et al. (2006b). This allows us to obtain the highest spatial resolution for a given S/N, which is the main advantage of this binning technique. The Voronoi bins are constructed iteratively from a given pixel, by accreting adjacent pixels until the resulting spectrum reaches the desired S/N. Pixels where the S/N is greater than the chosen threshold value will not be affected by the binning process, while regions of low S/N will emerge from noise without being contaminated by adjacent regions of higher S/N. For the WiNDS sample, the objective is to obtain an S/N ≥ 7 per spatial bin, where S/N is considered as the square root of the flux in the line. We implemented a Hanning smoothing of a one-spectral element of the spectrum, which preserves the flux.
• (e)  
  From this Voronoi binned datacube, the different momentum maps are computed as explained in Daigle et al. (2006b): after identifying the H_α line boundaries, the continuum emission around the line is estimated and subtracted from the spectrum. The moments of the line are then estimated. Namely, the line or monochromatic flux is the zeroth-order moment (intensity integrated within the line boundaries), the line-of-sight velocity (V_los) is the first-order moment (intensity-weighted velocity sum within the line boundary), and the line-of-sight velocity squared velocity dispersion (variance) as the second-order moment (difference between the intensity-weighted squared velocity and squared intensity-weighted velocity within the line boundaries).
• (f)  
  In some cases, the lowest S/N regions are strongly affected by night-sky line contamination. Thus, a semiautomatic cleaning is performed. Indeed, to achieve the desired S/N in the outermost galactic regions very large Voronoi bins are produced. These are mainly associated with sky subtraction residuals and background emission. Those bins are first semiautomatically erased and then manually deleted when the semiautomatic process is not sufficient.
• (g)  
  Finally, velocity dispersion maps were corrected by instrumental width. This correction was done by subtracting the mean dispersion of the instrument contribution to the observed velocity dispersion map, as follows:

  $$\begin{eqnarray}&&{\sigma }_{\mathrm{corr}}=\sqrt{{\sigma }_{\mathrm{obs}}^{2}-{\sigma }_{\mathrm{inst}}^{2}},\end{eqnarray} \tag{ 1 }$$

  where σ_obs corresponds to the observed velocity dispersion and σ_inst is the mean dispersion of the instrument contribution. Moreover, σ_inst is a function of the FSR, the interference order p, and the resolving power R:

  $$\begin{eqnarray}&&{\sigma }_{\mathrm{inst}}=\displaystyle \frac{\mathrm{FSR}\ p}{R}.\end{eqnarray} \tag{ 2 }$$

The results of the data reduction process are presented below for a WINDS subsample where panels (a)–(c) show the XDSS B-band image, the H_α line-of-sight velocity map, and the H_α velocity dispersion map, respectively. In addition, the results of the data reduction for the remaining new observations made in this work, where the XDSS blue image (top left panel), the H_α monochromatic image (top right panel), H_α velocity field (bottom left panel), and the H_α residual velocity field (bottom right panel) are shown in Appendix A.2.

Our goal is to analyze the previously derived line-of-sight velocity map, V_los, to search for evidence of large, global, and, coherent kinematic perturbations on our sample of late-type, low-inclination galaxies. In particular, we seek perturbations that are consistent with bending modes produced by warps and corrugation patterns. In this section, we discuss the procedure followed to analyze our resolved velocity fields.

As discussed in Gómez et al. (2021), the observed V_los field of each galaxy is bound to contain contributions from three different velocity components: the distributions within the disk plane, radial V_R and rotational, V_rot, and the perpendicular velocity to the disk plane, V_Z. More precisely, each V_los can be described as

$$\begin{eqnarray}\begin{array}{rcl}{V}_{\mathrm{los}} & = & {V}_{\mathrm{sys}}(r)+{V}_{\mathrm{rot}}(r)\cos \theta \sin i\\ & & +\ {V}_{{\rm{R}}}(r)\sin \theta \sin i\\ & & +\ {V}_{{\rm{z}}}(r)\cos i,\end{array}\end{eqnarray} \tag{ 3 }$$

where V_sys is the systemic velocity of the galaxy and it is considered a fixed value. The polar coordinates (r, θ) in the plane of the galaxy are measured from the position angle (PA), inclination (i), and sky position (α, δ) of the rotation center. The first step in identifying global perturbations in the data is to subtract from the V_los map an axisymmetric model of V_rot. To obtain such an axisymmetric velocity model we assume that, at first order, the contributions from the radial and the vertical velocities to V_los are negligible. Therefore, the observed velocity Equation (3) reduces to

$$\begin{eqnarray}&&{V}_{\mathrm{los}}={V}_{\mathrm{sys}}(r)+{V}_{\mathrm{rot}}(r)\cos \theta \sin i.\end{eqnarray} \tag{ 4 }$$

To obtain V_rot(R), we use the tilted-ring method (Begeman 1987), which assumes that the galaxy can be analyzed using concentric rings along the major axis, which are described by the parameters V ${}_{\mathrm{rot}}^{r},{i}^{r},{{\rm{PA}}}^{r}$. Here, the supra index r indicates that we are referring to the rings. In this work, we use an improved tilted-ring method, described in detail in Epinat et al. (2008b), and derive V_rot(R) for each galaxy bin modeled using the modified Zhao function (Epinat et al. 2008b),

$$\begin{eqnarray}&&{V}_{\mathrm{rot}}(r)={v}_{{\rm{t}}}\displaystyle \frac{{\left(r/{r}_{{\rm{t}}}\right)}^{g}}{1+{\left(r/{r}_{{\rm{t}}}\right)}^{a}}.\end{eqnarray} \tag{ 5 }$$

This four-parameter model was especially chosen for its versatility to adjust to a very diverse set of different rotation curve shapes. The four parameters involved in the V_rot model are v_t and r_t, which correspond to the velocity and radius when the rotation curve changes from an increasing velocity to a flat regime, respectively; a and g, which are related to the sharpness of the turnover. As discussed in Epinat et al. (2008b), for each galaxy the fitting procedure requires a set of initial values for the Zhao function parameters as well as for (α, δ), i, and PA. In our work, the values of (α, δ) are set to the peak of the emission in the continuum image and set as fixed values. For the systemic velocity, PA, and i, initial values were extracted from the literature. The resulting values of i and PA, obtained as a result of the fitting procedure, are referred to as kinematically inferred values. Note that, in those cases where disks are projected nearly perfectly face-on (i < 10°), the value of i is not allowed to vary, and thus, is kept fixed to their estimated morphological value. Instead, the v_t, r_t, a, and g parameters are always allowed to vary. Finally, V_rot for each Voronoi binning is estimated through the minimization of χ² based on the Levenberg–Marquardt method (Press et al. 1992), computing an iterative 3.5σ clipping on the observed bin-centroid velocity field. All kinematical parameters (i_k , PA_k , and V_sys) estimated for the WiNDS galaxies are listed in Table 4. The estimation of errors in the determination of kinematic parameters for the WiNDS sample was calculated using the power spectrum of the residual velocity field and the application of a Monte Carlo method, as described in more detail in Epinat et al. (2008b). It is worth noting that the degeneracy between ${V}_{\max }$ and i when fitting our models (Begeman 1989), is especially for very low-inclination disks, does not affect our results as we are focusing our analysis on the residual velocity fields, ${V}_{\mathrm{res}}$. The H_α ${V}_{\max }$ values derived in this work are listed in Table 4.

Table 4. Model Parameters

ID	ik	PAk	Vsys	${v}_{\mathrm{rot}}^{\max }$
	(°)	(°)	(km s−1)	(km s−1)
(1)	(2)	(3)	(4)	(5)
New observations
NGC 628	7*	155 ± 2	658 ± 1	147
NGC 1058	6*	34 ± 2	521 ± 0	140
NGC 2500	41 ± 11	85 ± 2	512 ± 1	49
NGC 2763	30 ± 8	47 ± 1	1884 ± 1	123
NGC 3147	32 ± 20	37 ± 8	2894 ± 3	164
NGC 3184	16 ± 9	5 ± 1	592 ± 0	155
NGC 3423	40 ± 8	134 ± 1	1007 ± 1	76
NGC 3485	30 ± 7	156 ± 2	1428 ± 1	146
NGC 3642	36 ± 8	70 ± 8	1581 ± 1	72
NGC 4136	20 ± 6	108 ± 1	606 ± 1	82
NGC 4900	5*	80 ± 2	959 ± 1	297
NGC 5194	20 ± 11	13 ± 2	464 ± 2	189
Data archive
NGC 864 (G)	35 ± 18	30 ± 3	1525 ± 3	52
NGC 2775 (G)	38 ± 3	157 ± 0	1350 ± 1	262
NGC 3344 (G)	15 ± 11	153 ± 2	580 ± 1	262
NGC 3346 (G)	29 ± 8	113 ± 2	1245 ± 1	95
NGC 3351 (S)	21 ± 5	169 ± 1	781 ± 1	289
NGC 3504 (G)	39 ± 13	160 ± 3	1523 ± 2	100
NGC 3596 (G)	17 ± 12	78 ± 2	1190 ± 2	87
NGC 3631 (H)	24 ± 14	151 ± 2	1150 ± 2	59
NGC 3938 (S)	14 ± 8	164 ± 1	809 ± 0	143
NGC 4037 (H)	32 ± 20	151 ± 3	924 ± 1	50
NGC 4189 (V)	31 ± 11	169 ± 1	2102 ± 1	128
NGC 4321 (V)	25 ± 9	29 ± 1	172 ± 1	190
NGC 4411B (H)	18 ± 15	49 ± 3	1267 ± 1	37
NGC 4430 (H)	28 ± 13	75 ± 2	1424 ± 1	180
NGC 4519 (V)	40 ± 16	180 ± 4	1216 ± 2	124
NGC 4625 (S)	8 ± 12	124 ± 3	626 ± 1	105
NGC 4725 (S)	43 ± 4	156 ± 1	1198 ± 2	227
NGC 4736 (S)	25 ± 7	122 ± 1	318 ± 1	245
NGC 5204 (G)	40 ± 11	166 ± 1	186 ± 1	87
NGC 5334 (H)	38 ± 4	6 ± 1	1402 ± 7	105
NGC 5430 (G)	32 ± 8	2 ± 1	2963 ± 3	255
NGC 5585 (G)	36 ± 20	53 ± 3	298 ± 2	59
NGC 5668 (G)	18 ± 14	146 ± 2	1575 ± 1	94
NGC 5669 (H)	36 ± 9	65 ± 1	1377 ± 1	116
NGC 5713 (S)	12 ± 12	154 ± 3	1896 ± 1	84
NGC 6217 (G)	18 ± 10	104 ± 1	1356 ± 1	207
NGC 6946 (G)	17 ± 14	61 ± 2	38 ± 2	185
UGC 3685 (G)	12 ± 19	118 ± 10	1815 ± 3	25

Note. (1) Galaxy name, the letter corresponds to the survey name; (2) kinematic inclination, those marked with an asterisk (*) have been fixed equal to morphological value, (3) kinematic PA, (4) systemic velocity, and (5) maximum rotation H_α velocity corrected for inclination derived in this work.

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Once an unperturbed axisymmetric model of V_los is obtained for each galaxy, we generate their corresponding ${V}_{\mathrm{res}}$ fields. This is done by subtracting the properly V_los model from the observed V_los maps. It is worth recalling that global and coherent features in a ${V}_{\mathrm{res}}$ field of a late-type galaxy could be the result of kinematic perturbations induced by features such as a bar or spiral structures, but also from improper model parameters (such as center, systemic velocity, PA of the major axis, inclination, or rotation curve model). The multipolar signatures expected for ill-defined parameters (Warner et al. 1973) are not observed in our data.

It is also worth noting that small variations in the magnitude of ${V}_{\mathrm{res}}$ could be attributed to uncertainties in the determination of the kinematic parameters (PA and center). In order to verify the sensitivity of the method used to the initially chosen and fixed inclination value, the model is rerun considering the extreme values of the inclination that are within the error range shown in Table 4.

The contributions from in-plane flows are expected to be small in low-inclination galaxies such as those studied in this work. Using a suite of numerical simulations, Gómez et al. (2021) characterized the contribution from in-plane flows to the V_los driven by non-axisymmetric structures. Their models consisted of a disk galaxy, projected into an inclination of 35°, considering a bar with similar characteristics to that of the Milky Way and spiral overdensities that ranged from 100%–1000% density contrast (Δρ/ρ) with respect to the disk background density. Even for Δρ/ρ = 1000 the resulting velocity perturbations in the corresponding ${V}_{\mathrm{res}}$ field were ≲10 km s⁻¹.

In this section, we describe the selection criteria applied to select those galaxies within the WiNDS sample that show velocity perturbations consistent with a bending mode, such as a warp or corrugation pattern. To avoid selecting discrete and local vertical perturbations, such as those associated with, e.g., fountain flows, we have established the main criteria to select strong candidates as follows:

• 1.  
  We focus on galaxies that present an extended H_α coverage, extending for at least 0.7 R_opt. This criterion allows us to globally explore the kinematics of the disks, especially in the outer regions where bending modes typically show their stronger amplitudes.
• 2.  
  We focus on galaxies where global perturbations show amplitudes that are >10 km s⁻¹. This enhances the chances that the observed perturbations in this low-inclination sample of disks are not mainly driven by the axisymmetric components of the galaxies.
• 3.  
  We applied a Gaussian low-pass filter to the V_res images in Fourier space with a cutoff frequency equivalent to a spatial distance of ≈500 pc to highlight relevant and large perturbations (see Appendix D.1). This allows us to smooth out local and discrete perturbations, and focus on large-scale and coherent features. Based on these images, using a circular grid centered at the center of the galaxy, evenly spaced by 0.3 R_opt, as shown in Figure 3, we select as potential candidates all those galaxies where the perturbations cover at least an azimuthal extension of 60°. We consider perturbations that at a given azimuthal angle cover a radial extension ≲0.3 R_opt as corrugation patterns, whereas the remaining as typical warps.

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Examples of the resulting filtered images are shown in Figure 3. The upper panel shows an example of well-defined global and coherent velocity perturbations. The bottom panel shows the case where the map was consistent with an unperturbed velocity field. According to these criteria, eight galaxies show V_res maps consistent with a vertical perturbed disk.

We note that previous studies have analyzed velocity dispersion maps, V_disp, to identify vertically perturbed disk galaxies. For example, Jiménez-Vicente & Battaner (2000) used V_disp to detect plausible shells or chimneys in the galactic disk of NGC 5668. This was done by comparing the geometry of the ${V}_{\mathrm{res}}$ and V_disp maps and associating local perturbations in both maps to vertical motions in the galaxy. In our work, V_disp maps are obtained as a subproduct of the data reduction process (see Section 3), and thus, we present them together with the ${V}_{\mathrm{res}}$ maps. However, as opposed to Jiménez-Vicente & Battaner (2000), our goal here is to identify global rather than localized and discrete velocity perturbations. As a result, V_disp maps were not explored in detail. We will further analyze these maps in follow-up work.

We emphasize that our selection criteria cannot confirm or rule out the presence of vertical perturbations in our disks. Although the objective is to detect global and coherent perturbations, it should be noted that our method does not exclude the presence of fountain flows, which are shown as local and discrete perturbations, but rather, both types of perturbations could coexist. Nonetheless, note that we have carefully checked the H_α intensity profiles in all galaxies that were selected as potential vertically perturbed objects. We found that all candidates within the WiNDS sample show, in general, well-behaved Gaussian profiles. That is, there is no presence of strong and intense multiple components in the H_α profiles due to the presence of other velocity components (such as those observed in merging systems such as HCG 31, for example, Amram et al. 2007).

In this section, we analyze and discuss the resulting V_res fields of the eight WiNDS galaxies that fulfilled our quantification criteria described in Section 5. However, we discuss the remaining newly observed galaxies in Appendix A.1 and in Appendix B.1 we present the V_res maps of galaxies that do not accomplish the criteria described in Section 5.

In Figure 4, we show the results obtained for the galaxy NGC 3344. This galaxy has a very low morphological inclination angle (i ∼ 18°, Paturel et al. 1997), and thus, represents an ideal candidate to search for vertical perturbations on its galactic disk. In panel (a) we show a B-band image of the galaxy, obtained from the XDSS (see footnote 3). The galaxy shows a well-defined flocculent spiral structure and a weak bar inside the inner ring (Verdes-Montenegro et al. 2000). It has an optical radius, R_opt, of 7.7 kpc (RC3; de Vaucouleurs et al. 1991), i.e., approximately half the size of the Milky Way. In panel (b) we show the resulting V_los map, obtained following the procedure outlined in Section 3. The map shows good H_α coverage of the overall disk (1 R_opt), despite being limited by the FoV of the GHASP instrument. The amplitude of V_los reaches ≈100 km s⁻¹. Panel (c) shows the H_α velocity dispersion map, normalized to σ_95th = 44.2 km s^{−1 13}

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Panel (d) shows the residual velocity field, ${V}_{\mathrm{res}}$, obtained after subtracting the axisymmetric rotational velocity model from V_los. Interestingly, the ${V}_{\mathrm{res}}$ map reveals a global, strong, and coherent oscillating-like pattern throughout the entire disk of the galaxy, with an amplitude of the order of ±30 km s⁻¹. To compare the disk morphology to the structure observed on its residual velocity field, in panel (e) we show the galaxy B-band image with the contours obtained from the ${V}_{\mathrm{res}}$ field. Notice that no clear correlation between axisymmetric patterns and velocity perturbations can be observed. The extended black box or slit, placed across the disk in panel (e), highlights the multiple transitions from positive to negative values experienced by ${V}_{\mathrm{res}}$ as a function of galactocentric distance. This is better shown in panel (g) where we highlight the behavior of ${V}_{\mathrm{res}}$ across this particular slit (black crosses). Here, the black line represents the corresponding smoothed data using a moving average function with a seven data point window, while the dashed vertical line indicates the galaxy center. The direction of the slit was chosen to highlight transitions of the residual velocity values. NGC 3344 is a galaxy that is cataloged as isolated, with no nearby galaxies within a projected radial distance of 150 kpc and radial velocity difference Δ ≤ 500 km s⁻¹. We recall that NGC 3344 has a very mildly inclined disk, i ∼ 18°. Thus, the contribution from in-plane flows to the resulting ${V}_{\mathrm{res}}$, associated with, e.g., bars and/or spiral structure, is expected to be small. As previously discussed, a plausible interpretation of these ${V}_{\mathrm{res}}$ perturbations is associated with the contribution from a vertical corrugation pattern. Such corrugation pattern could be the result of several mechanisms, such as close interactions with satellites (Jiang & Binney 1999; Sancisi et al. 2008; Roškar et al. 2010; Aumer et al. 2013; Radburn-Smith et al. 2014; Gómez et al. 2017), torques associated with either misaligned triaxial DM halos or even DM overdensity wakes (Ostriker & Binney 1989; Quinn et al. 1993; Velazquez & White 1999; Bailin 2003; Kazantzidis et al. 2009; Gómez et al. 2013; D'Onghia et al. 2016). Vertical perturbations on this galaxy have previously been reported by other authors. Indeed, Briggs (1990) reports the presence of a warp in the outer regions of NGC 3344 after analyzing observations of the HI 21 cm line. Verdes-Montenegro et al. (2000) presented a detailed study of this galaxy, also using HI 21 cm lines. The authors suggest a possible relationship between the inner and outer star-forming rings with a strong spiral structure and the warp in the HI layer. However, they were not able to clearly link the warp structure with the perturbation in the more internal regions. Our analysis of NGC 3344, with a spectral resolution ∼10 km s⁻¹, reveals a very complex structure of NGC 3344. NGC 3344 is a very interesting candidate of the vertically perturbed galaxy that will be analyzed in greater detail in a follow-up study.

In Figure 5, we now show the results obtained for NGC 628 (M74). This is a nearly face-on galaxy with an inclination angle of 65, and thus, an ideal candidate to search for possible vertical perturbations. In panel (a), we display a B-band image of the galaxy, obtained from XDSS. NGC 628 is a non-barred galaxy with two main spiral arms emerging from its bulge. The H_α observation coverage of NGC 628 corresponds to a mean radius of 12.5 kpc, which represents 0.8 R_opt. The H_α velocity map (panel (b)) shows an amplitude of ∼60 km s⁻¹, as expected from a low-inclination galaxy. For comparison, we also show in panel (f) the HI velocity map from The HI Nearby Galaxy Survey (THINGS; Walter et al. 2008) observed with the Very Large Array (VLA), which is consistent with the H_α velocity map. Interestingly, studies based on neutral hydrogen (Kamphuis & Briggs 1992) have detected the presence of an elongated warp structure at around a 12' projected distance from the nucleus. In panel (c), we show the derived H_α velocity dispersion map, normalized to σ_95th =14 km s⁻¹. The ${V}_{\mathrm{res}}$ field of NGC 628 is shown in panel (d). Interestingly, global and coherent velocity perturbations, of the order of 20 km s⁻¹, can be clearly observed. Panel (e) allows us to correlate NGC 628-disk morphology with its residual velocity map. The velocity perturbations on this galaxy are more clearly highlighted in panel (g) where we follow the mean ${V}_{\mathrm{res}}$ along the highlighted slit, suggesting a warp-like structure.

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As shown in its B-band image (panel (a)), an extended tail is observed in the southwest direction of the disk. This substructure has previously been reported in Kamphuis & Briggs (1992). Although NGC 628 currently has no close companions, a dwarf galaxy system (UGC 1176 and UGC 1171) is located at 140 kpc. The overall mass of the satellite system has been reported to lie on the order of magnitude of the total NGC 628 mass (Michałowski et al. 2020). This system may have played an important role in the evolution of NGC 628. As discussed by Briggs (1986), if the dwarf system is at rest at its current location concerning NGC 628, it would fall into its host in about 1–2 Gyr. However, a more recent study by Michałowski et al. (2020) suggests that a tidal origin for the asymmetric HIH i tail located on the southwestern outskirt is an unlikely scenario. They argue that the tail does not resemble recent tidal features, whereas an older feature would wind almost symmetrically around the galaxy. In addition, recently induced tidal tails typically show m = 2 patterns, with two nearly symmetrical arms. Instead, NGC 628 shows a strong m = 1-like spiral structure. Nonetheless, they do not rule out a possible previous interaction with the neighboring dwarf pair. It is interesting to compare with the results presented in Gómez et al. (2017), based on fully cosmological simulations. In particular, their model S13 shows morphology similar to that of NGC 628, with a strong m = 1 arm extending from the inner galactic regions. This model displays a vertically perturbed stellar and cold gas disk, but no recent interaction with massive satellites (M_sat/M_host > 0.03). Instead, S13 experienced a massive gas-rich merger 5 Gyr ago. As a result, its preexisting disk was destroyed but a new thin disk quickly formed thereafter due to the re-accretion of misaligned gas. This gas accretion gives rise to both the vertical perturbations observed in this modeled galaxy and its strong m = 1 morphology. This suggests that the velocity perturbations observed in NGC 628, as well as its m = 1 spiral morphology, could be linked to the recent accretion of misaligned cold gas.

In Figure 6, we focus on NGC 6946. This is a spiral galaxy classified as SABcd with a kinematical inclination of i ∼ 17°, an optical radius of ≈10 kpc, and an estimated total mass of 1.2 × 10¹¹ M_⊙ (Pisano & Wilcots 2000). Optical and neutral hydrogen observations of NGC 6946 have revealed its strong spiral arms, a particularly high star formation rate, a nuclear starburst, and a weak bar (Pisano & Wilcots 2000; Schinnerer et al. 2006). Panel (a) shows its XDSS B-band image, where we can clearly see its spiral nature. NGC 6946 is considered to be isolated (Tully 1988). Using HI observations, previous studies have detected a dozen low mass irregular dwarf galaxies companions (Karachentsev et al. 2000; Pisano & Wilcots 2000; Karachentsev et al. 2005). However, at the present day, NGC 6946 does not show any signs of undergoing strong direct gravitational interactions with its satellite population. Its two most massive companions, UGC 11583 and L149, have estimated total masses of 1.5 × 10⁹ and 3.0 × 10⁸ M_⊙ and projected distances of 83 and 75 kpc, respectively (Pisano & Wilcots 2000). The H_α V_los map of NGC 6946, shown in panel (b), has an amplitude of ∼ 150 km s⁻¹. Following our selection criteria, the map reveals significant H_α coverage, reaching at least a radius of 7 kpc, corresponding to 0.7 R_opt. As in the case of NGC 3344, the coverage for NGC 6946 is limited by the FoV of the GHASP instrument. For comparison, we show (in panel (f)) the HI velocity map extracted from Walter et al. (2008). Both maps are consistent, even though they consider different components of the interstellar medium (ISM) and come from different instruments and techniques. Note, however, that our observations have a better spatial resolution of 3'' against the 6''–12'' resolution in the observations. The H_α velocity dispersion map is shown in panel (c), normalized to σ_95th = 55.2 km s⁻¹. In panels (d) and (e), we show the galaxy ${V}_{\mathrm{res}}$ map, which reveals global and coherent perturbations, reaching amplitudes ≲35 km s⁻¹. The ${V}_{\mathrm{res}}$ velocity contours, overlaid on the B-band image (panel (e)), allow us to directly contrast this velocity structure with the morphology of NGC 6946. The oscillating nature of this velocity field is better highlighted in panel (g), where we show the mean ${V}_{\mathrm{res}}$ along the highlighted slit in panel (e). It is worth recalling the spiral nature of NGC 6946, and its low but not negligible inclination. As a result, a contribution from in-plane flow to the ${V}_{\mathrm{res}}$ field can be expected. However, as shown by Gómez et al. (2021), for disks as inclined as NGC 6946 (i ∼ 40°), even a spiral structure 1000 times denser than its mean background disk density cannot generate velocity perturbations with amplitudes ≳10 km s⁻¹. This indicates that the observed global velocity perturbation could be partially linked to vertical velocity flows.

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It is interesting to consider what mechanisms could be driving the perturbations in this galaxy. As previously discussed, NGC 6946 does not have nearby massive satellites that could be directly tidally interacting with its disk. However, even low mass satellites at relatively large galactocentric distances could significantly perturb an embedded disk through the excitation of dark matter overdensity wakes (Weinberg 1998; Vesperini & Weinberg 2000). For example, using cosmological simulations of Milky Way-mass galaxies, Gómez et al. (2016) studied the onset and evolution of a strong vertical pattern in the disk. The vertical pattern in this model, with an amplitude of ∼50 km s⁻¹, is the result of a satellite-host halo-disk interaction. Interestingly, the satellite had a total mass of ∼5% of the host and a pericenter distance of 80 kpc. The satellite was not massive enough to directly perturb the galactic disk but the density field of the host dark matter halo responded to the satellite passage and strongly amplified its perturbative effects. A similar scenario could be taking place in the case of NGC 6946, considering its low mass companions at a relatively large projected galactocentric distance. Other possible mechanisms, in addition to the previously discussed contribution from in-plane flows, could be related to the smooth accretion of misaligned cold gas.

In Figure 7, we show NGC 4321 (M100), a grand-design nearby spiral galaxy belonging to the Virgo Cluster, classified as SABbc (RC3). The galaxy has a small bulge and two well-defined, prominent, and symmetric spiral arms, as shown in its B-band image (panel (a)). The nucleus of the galaxy is compact and bright. NGC 4321 is a very low-inclination galaxy, with a kinematical inclination of i ≈ 25° and an optical radius of R_opt = 16.3 kpc from RC3. Panel (b) shows that the coverage of the V_los distribution, obtained from the H_α observations, is extensive and nearly reaches nearly its optical radius, i.e., 13 kpc ∼ 0.8R_opt. The V_los map shows an amplitude of ≈150 km s⁻¹. For completeness, we show in panel (c) the H_α velocity dispersion map, normalized to σ_95th = 33.1 km s⁻¹.

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The derived residual velocity map, obtained after subtracting the axisymmetric velocity model is shown in panels (d) and (e). As in previous examples, this map reveals global and coherent velocity flows with amplitudes that can reach ∼ 30 km s⁻¹. Panel (f) more clearly shows the radial variations of the residual velocity along the highlighted slit in panel (e). Note the oscillatory behavior of ${V}_{\mathrm{res}}$ across the disk. These perturbations, observed in the ionized gas of NGC 4321, could be the result of a recent interaction with one of its satellite galaxies. Indeed, NGC 4321 has two dwarf companion galaxies, NGC 4328 and NGC 4323, located at projected distances of 24 and 28 kpc from their host, respectively (Hernandez et al. 2005). Knapen et al. (1993) showed that the HI component of NGC 4321 is mostly contained within the optical disk. However, they also identify a large HI extension that could be the result of the tidal interaction with NGC 4323. Indeed, Knapen et al. (1993) find important differences in the behavior of its rotation between the approaching and the receding sides. They suggest these differences could be caused by deviations from circular motions in the outer disk probably due to a close passage of its companion galaxy. They also suggest this interaction could be the cause of the observed asymmetry in the total HI distribution. NGC 4321 also shows diffuse stellar extension in two directions, one of them toward NGC 4323, likely the result of ongoing interaction with this satellite (Hernandez et al. 2005).

NGC 5194 (M51a) is a well-known nearby grand-design spiral galaxy classified as non-barred by RC3, with a very low-inclination angle i = 20°. NGC 5194 is tidally interacting with its companion NGC 5195 (M51b), an early-type SB0 galaxy. NGC 5194 shows an intense star formation activity at its center and along its spiral arms. Panel (a) in Figure 8 clearly shows its strong spiral structure with signs of being lopsided, likely due to the interaction with its companion. Panel (b) shows that the H_α observations provide wide coverage of the disk, which allows us to obtain its velocity field up to distances of 12 kpc ∼ 0.8 R_opt. The resulting V_los map shows a velocity range of ≈ 150 km s⁻¹. It is interesting to compare our H_α velocity map with the one derived from HI observations, obtained from THINGS using VLA (Walter et al. 2008), shown in panel (f). As seen in NGC 628 and NGC 6946, the HI velocity map of NGC 5194, constrained to the same FoV as the H_α data, shows a very good agreement with the ionized gas velocity map, despite differences in both the spatial and spectral resolutions. In panel (c), we show the velocity dispersion map normalized to σ_95th = 15 km s⁻¹.

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The residual velocity map is shown in panels (d) and (e). It is interesting to note the large velocity perturbations throughout the disk, reaching amplitudes of 40 km s⁻¹. We recall the very low-inclination angle of this galaxy, thus rendering it unlikely that these velocity perturbations are mainly due to in-plane velocity flow. Panel (e) allows comparing the substructure of the ${V}_{\mathrm{res}}$ map with the galaxy morphology as seen in the B-band image. In panel (g), we follow the smoothed residual velocity profile along the highlighted slit. As before, this allows appreciating the radial oscillatory behavior of ${V}_{\mathrm{res}}$, consistent with what is expected for a corrugated disk. Shetty et al. (2007) presented a deep kinematic study of NGC 5194 using full 2D velocity distributions from interferometric CO and FP H_α observations. They report a complex velocity field, with variations of the disk's PA and inclination along the galactic radius that strongly suggest a vertically perturbed disk and very significant out-of-plane motions. An HIH i warp has also been previously reported in NGC 5194 (Rots et al. 1990; Haan & Braun 2014; Oikawa & Sofue 2014), which has been attributed to the tidal interaction with NGC 5195. The presence of vertical velocity flows in this very interesting galaxy will be further analyzed in a follow-up study, following the procedure described in Gómez et al. (2021).

In Figure 9, we present NGC 5668, a nearly face-on late-type spiral galaxy with an estimated inclination angle of 18° (Schulman et al. 1996) and R_opt of ∼14.3 kpc, located at 27.6 Mpc. The galaxy is classified as a SA(s)d by RC3, and on its optical image (panel a), it shows a weak bar or oval structure in its inner 12'' region. Observations of NGC 5668 were extracted from the GHASP sample (Epinat et al. 2008b). The H_α coverage reaches out to 20 kpc corresponding to ∼1.4 R_opt. In panel (b), we show the resulting V_los field, with a velocity amplitude reaching ≈ 70 km s⁻¹. The velocity dispersion map, normalized to σ_95th = 57.5 km s⁻¹, is shown in panel (c).

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The ${V}_{\mathrm{res}}$ map, shown in panel (d), reveals global perturbations with amplitudes >20 km s⁻¹ km s⁻¹, which are also consistent with a warped H_α disk. In panel (e), we present the optical image with the overlay of the residual velocity map. The warp is better shown in panel (f), where we can see the mean velocity profile along the highlighted slit in panel (e). Note the large amplitude of this kinematical perturbation reaching velocities >20 km s⁻¹ at the disk outskirts. High-resolution observations in the 21 cm line of the neutral hydrogen velocity field, from VLA, have detected a kinematic warp that begins, at least, at the end of the optical radius (Schulman et al. 1996). Note that the H_α warp is very well aligned with the previously reported HI warp, indicating that the perturbation extends even within the optical radius of the galaxy. In addition to the HI kinematic warp, Schulman et al. (1996) detected high-velocity wings beyond the double-horned 21 cm profile, related to high-velocity clouds (HVCs) in the disk and halo of the galaxy. As discussed by Schulman et al. (1996), the high-velocity wings located outside the optical disk may be the result of infalling material, comparable to the Magellanic Stream observed in the Milky Way.

The origin of the kinematic warp, and the infalling material, could be related to a past interaction with its neighbor galaxy UGC 9380, currently located at a projected distance of ∼200 kpc of NGC 5668. It is worth mentioning that Jiménez-Vicente & Battaner (2000) also analyzed the 2D velocity field of this galaxy through its H_α emission using an FP interferometer. However, they did not cover the region where we detect the kinematic warp. Instead, they reported the detection of HVCs and localized high residual velocity dispersion regions, associating them with shell/chimney regions. Even though we present a velocity dispersion map in panel (c), in this work we have not attempted to recover these regions, typically associated with vertical motions of ionized gas due to star-forming processes.

In Figure 10, we show NGC 2763. This low-inclination disk galaxy (i ≈ 295) is the only object in WiNDS observed in the Southern Hemisphere, and one of the first galaxies observed with the SAM-FP instrument (Mendes de Oliveira et al. 2017). The B-band image in panel (a) reveals two main spiral arms, each with multiple sub-arms and a small bar. In addition, it shows a significantly lopsided structure. The galaxy shows an extended H_α emission across the disk, reaching up to 0.9 R_opt, with R_opt ≈ 9.9 kpc. Panel (b) shows its V_los maps, with an amplitude of ≈ 100 km s⁻¹. The velocity dispersion map, normalized to σ_95th = 37.2 km s⁻¹, is shown in panel (c).

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The resulting ${V}_{\mathrm{res}}$ maps, shown in panel (d), reveal a very complex structure with global residual velocity flows reaching amplitudes ≳20 km s⁻¹. In panel (e), we can observe the B-band image of NGC 2763 with the residual velocity map overlapped, highlighting the region where complex residual velocity perturbations are observed. Interestingly, no detailed kinematical studies of NGC 2763 velocity field, nor companion galaxies within 150 kpc, have been reported. We have confirmed the lack of massive nearby companions by performing a systematic search within a radial projected distance of 250 kpc and radial velocity difference Δ ≤ 1000 km s⁻¹ using the NASA/IPAC Extragalactic Database. Thus, NGC 2763 is considered an isolated galaxy. As such, it is not clear whether its significantly perturbed morphology and kinematics are the results of a previous minor merger event or due to significantly misaligned smooth gas accretion.

NGC 5713 is oriented nearly face-on, with an inclination i ≈ 10°, and shows a significantly lopsided morphology. This can be seen in panel (a) of Figure 11, where we show its XDSS B-band image. NGC 5713 has an R_opt ∼ 13.5 kpc, it is a barred and multiple arm spiral galaxy (SABb type; de Vaucouleurs et al. 1991), and is located at 33.4 Mpc. The H_α V_los map, shown in panel (b), covers a region of ∼ 0.9 R_opt, and shows an amplitude of ∼ 100 km s⁻¹. The velocity dispersion map, normalized to σ_95th = 54.2 km s⁻¹, is shown in panel (c).

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The ${V}_{\mathrm{res}}$ (panel (d)) reveals a very peculiar structure, with several global and coherent perturbations reaching peak velocities ≥30 km s⁻¹. The galaxy is currently undergoing a very strong tidal interaction with its similar mass Sab-type companion, NGC 5719 (Vergani et al. 2007), and shows two H i tidal tails. Both galaxies (NGC 5713 and NGC 5719) show an optical radius at a similar galactocentric distance and are connected by two HI tidal bridges. The projected distance between these two galaxies is ∼77 kpc. NGC 5719 shows an ionized gas disk that counter-rotates with respect to its neutral gas counterpart. According to Vergani et al. (2007), this counter-rotating disk is the result of the accretion of NGC 5713 material onto NGC 5719 during their closest approach. Interestingly NGC 5719 shows a nearly edge-on configuration with a clearly visible warped disk. In addition, NGC 5713 is interacting with the Sm-type dwarf galaxy, PGC 135857, which is located at a projected distance of ∼64 kpc (Vergani et al. 2007). These interactions are likely behind the observed NGC 5713 strongly perturbed velocity field. The interacting system will be compared against numerical models in a follow-up study.

In this study, we have presented WiNDS, which currently consists of 40 nearby low-inclination spiral galaxies, including objects with diverse morphological features. The WiNDS sample contains galaxies within a distance limit of 45 Mpc and absolute B magnitude between −17.0 and −21.9 mag, all observed in H_α with an FP interferometer. These observations allow us to obtain very detailed velocity maps of the ionized gas distribution, with velocity sampling precision as low as 3 km s⁻¹, which translates into a resolution of 6 km s⁻¹. Our sample was selected such that galaxies have an inclination angle i ≲ 40°. WiNDS consists of 12 new data observed, and includes archival data for 28 low-inclination late-type galaxies, extracted from the GHASP, SINGS-H_α , VIRGO-H_α , and HRS-H_α surveys. For each galaxy in the final sample, we derived their line-of-sight velocity field, an unperturbed axisymmetric velocity model, kinematical parameters, the corresponding residual velocity fields. The results of the reduction are presented in Figures 13–15 and Appendix A.2, A.3 and B.1, respectively. Finally, the rotation curves are displayed in Figure 16 and Appendix C.1.

Our main goal in this work was to examine the resulting V_res fields to search for evidence of large, global, and coherent kinematic perturbations in our sample of low-inclination late-type galaxies. In particular, we seek perturbations that are consistent with those produced by warps and corrugation patterns. Through three criteria we identify clear signatures of perturbations. First, we are interested in objects that present a wide H_α coverage (≥0.7 R_opt) so that the kinematics of the disks could be globally explored. Second, we focused on galaxies with V_res amplitude that are >10 km s⁻¹, which allows us to be more confident in observing perturbations in the low-inclination disks that are not the result of the axisymmetric components of the galaxies. Finally, we also searched for perturbations in the V_res fields that show global and coherent velocity flows, avoiding local and discrete perturbations that could be linked to, e.g., fountain flows.

We emphasize that our selection criteria cannot confirm nor rule out the presence of vertical perturbations in our disks. Instead, our goal is to select potentially strong candidates for follow-up studies. Note, however, that as shown by Monari et al. (2016) and Gómez et al. (2021), the amplitude of the observed velocity flows in these low-inclination disks are, typically, much too large to be driven either by spiral structure or by a bar. Within the subset of galaxies with vertical perturbations considered as candidates, those displaying discrete and local perturbations that could be associated with fountain flows are not excluded since such signatures can coexist with the global and coherent perturbations that we aim at detecting in this study.

A vertical perturbation such as a warp or a corrugation pattern is manifested by an extended and oscillatory vertical displacement of the disk with respect to the overall midplane. Its characterization can allow us to constrain the recent interaction history of a galaxy. Previous studies based on cosmological simulations (e.g., Gómez et al. 2017) have identified four main mechanisms behind such perturbations: distant fly-by massive companions, close satellite encounters, re-accretion of cold gas from progenitors of a gas-rich major merger, and accretion of misaligned cold gas. Out of 40 observed low-inclination galaxies, we find that approximately 20% of the sample shows clear signatures of global and coherent perturbations. Adding to this statistic to the results of our pilot study based on VV304a (Gómez et al. 2021) brings this number to 22%. We note however that, as further discussed below, some of our observations were either not sufficient or not adequate to identify velocity perturbation on the disk outskirts, and thus, this percentage could be higher. In fact, out of the 40 galaxies in the WiNDS sample, only 70% show good H_α coverage. If we only consider this subset, the fraction of vertically perturbed galaxy candidates rises to 32%.

From the galaxies that show signs of potential vertical perturbation, six of them are interacting with a satellite galaxy and/or belong to a group. Thus, the observed kinematic perturbations are likely directly linked with recent environmental interactions. The rest of the perturbed subsample of galaxies are considered to be isolated. Therefore, their perturbations could be the result of previous minor mergers or misaligned cold gas accretion. A deeper and more detailed study must be performed for each galaxy to constrain the origin of their perturbed velocity field. As shown in Figure 1, the vertically perturbed candidates within the WiNDS sample (green distribution) show no preferential distribution of the main parameters with respect to the overall WiNDS sample.

Previous studies, either in HI (García-Ruiz et al. 2002) or in the optical (Reshetnikov & Combes 1998; Ann & Park 2006, for the edge-on galaxies) that have characterized the frequency that vertically perturbed disks arise in the local universe, have found that approximately 70% of them present a warped disk, typically displaying an S-shaped configuration. However, evidence for more complex corrugation patterns in external galaxies, such as those hinted at in this work, has been extremely scarce. Indeed, only a handful of previous studies have previously reported corrugations on external galaxies (e.g., Sánchez-Gil et al. 2015; Narayan et al. 2020; Gómez et al. 2021). In agreement with observations, cosmological simulations of high-resolution late-type galaxies within Milky Way-sized halos, Gómez et al. (2016, 2017) estimated that 70% should show strongly vertically perturbed disks, and 35% should present a corrugated structure. The scarcity in the detection of corrugation patterns on external galaxies so far was not that surprising since most studies attempting to characterize stellar disk vertical structures have been focused on edge-on systems in which corrugation is difficult to detect due to projection effects. Our study shows that high-resolution velocity maps, obtained with techniques such as an FP interferometer, allow us to reveal much more complex velocity structures on external galactic disks. Furthermore, due to the low-inclination angles of the disks in our sample, these are likely linked with vertical flows and consistent with corrugation patterns. Eight galaxies from WiNDS show potential vertical patterns, of which 25% are in a close interaction with a massive companion, 50% show nearby dwarf satellite galaxies, and 25% can be regarded as isolated.

However, the fraction of low-inclination galaxies with detected velocity flow, i.e., ≈ 20%, is currently significantly lower than the expected fraction of vertically perturbed disks. Several factors could be playing a role here. The first and most obvious reason is that a fraction of ≈30% of the galaxies in our sample did not show a wide H_α coverage. Such cases either presented a patchy and poor H_α emission distribution, or it was concentrated within the inner ∼0.5 R_opt. As a result, we were not able to globally explore the kinematics of their disks, especially on the outer disk regions where warps and vertical perturbations are expected to be stronger. Second, the weather conditions in ≈12.5% of our observations were not ideal. As a result, the observations were not sufficient to generate kinematic maps accurate enough to properly resolve their velocity fields. Considering these caveats, it is not surprising that we have been able to detect kinematic perturbation, consistent with a vertical perturbed disk, in a smaller fraction of galaxies than previously reported.

In a follow-up study, deeper and better observations will be presented. Following Gómez et al. (2021) we will compare our observations against detailed analytic kinematic models that account for the axisymmetric perturbations measured on each galaxy and thus constrain the origin of their velocity perturbations.

F.A.G. and C.U-M. acknowledge financial support from FONDECYT Regular 1211370. F.A.G., A.M., and C.U-M. gratefully acknowledge support by the ANID BASAL project FB210003 and funding from the Max Planck Society through a Partner Group grant. A.M. acknowledges financial support from FONDECYT Regular 1212046. F.M. acknowledges support through the Program "Rita Levi Montalcini" of the Italian MIUR. C.U-M also acknowledges financial support through the fellowship "Becas Doctorales Institucionales ULS", granted by the Vicerrectoría de Investigación y Postgrado de la Universidad de La Serena. The WiNDS survey is based on observations taken at the Observatoire de Haute Provence (OHP, France), operated by the French CNRS. The authors warmly thank the OHP team for their technical assistance before and during the observations, namely, the night team: Jean Balcaen, Stéphane Favard, Jean-Pierre Troncin, Didier Gravallon, and the day team led by François Moreau as well as Dr. Auguste Le Van Suu. We are grateful to the whole SAM/SOAR team, who assisted us in the preparation and execution of the observations. This work was supported by the Programme National Cosmology et Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, cofunded by CEA and CNES. C.U-M. also acknowledges all the help and insights from Jesús Gómez-López and Gustavo Morales during the writing and data processing steps. The author also acknowledges Diego Pallero, Ciria Lima-Dias, and Daniel Hernández for their valuable discussions and comments.

A.1. Comments for Individual Galaxies

NGC 1058 is a nearly normal Sc face-on spiral galaxy with an inclination angle of 6°. NGC 1058 does not present well-defined arms in H_α emission and reveals a weaker emission in the innermost than in the outer regions. The galaxy is located at a distance of 9.93 Mpc, the most recent work distance value is considered. It has an angular diameter of 3' with an apparent magnitude in the B band of about 12 mag. NGC 1058 belongs to the group NGC 1023 being the least bright member. This galaxy was observed in the H_α line (Sánchez-Gil et al. 2015) to analyze if it presents vertical flows using the long-slit technique using different PAs and finding that velocity peaks are associated with star-forming regions. Two supernovae 1961V and 1969L have been reported in the outer disk.

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NGC 2500 is a nearby spiral galaxy with a short bar aligned with its minor kinematical axis, classified as SB(rs)d, located at 9.79 kpc at an inclination angle of 40°. This galaxy was observed using an H_α filter by Epinat et al. (2008a), who find diffuse emission in their observed H_α maps. NGC 2500's corrugated velocity patterns were studied using the long slits with H_α observations in Sánchez-Gil et al. (2015), where the vertical displacements do not seem to be related to an H_α emission peak. Like NGC 1058, this galaxy is part of the sample by Sánchez-Gil et al. (2015) but unlike in NGC 1058 where they find speed peaks, in NGC 2500 it was not conclusive.

NGC 3147 is a non-barred galaxy and it is classified as SA(rs)bc. It is considered the best type 2 Seyfert candidate using optical and X-ray observations, simultaneously (Bianchi et al. 2012).

NGC 3184 is a nearby grand-design spiral SABc type. Located at a distance of 10.05 Mpc, it has a nearly face-on orientation with inclination angles 167 and 1845 deviated in this article using the methodology described previously. This galaxy belongs to the group NGC 3184 being the brightest with 9.7 mag. Other members are NGC 3198, NGC 3432, and NGC 3319.

NGC 3423 is a nearby spiral galaxy Sc type with an absolute B-band magnitude of 12 mag and angular size 356 and is located at 15 Mp. There are no previous analysis studies in particular of this galaxy.

NGC 3485 is a nearby spiral galaxy located at 28.17 Mpc with an absolute B-band magnitude of 12.7 mag. The kinematical inclination derived in this work is 26°. There are no individual works for this galaxy previously. In this work, the H_α emission is faint and is located in the galaxy arm.

NGC 3642 is a non-barred galaxy with three rings and dusty spiral arms classified as an SAbc type. The galaxy shows a warped outer disk in the HI line (Verdes-Montenegro et al. 2002). NGC 3642 belongs to a group composed of five galaxies. NGC 3642 is the brightest member with elliptical galaxies NGC 3610 and NGC 3613 with similar magnitude. Another member is NGC 674, and NGC 3683 is fainter by more than 2 mag. It is an extended galaxy and shows around an internal disk from which a spinal arm appears that forms an external disk.

NGC 4136 is a nearby face-on galaxy with a bar and a ring as well as a well-developed spiral structure in its outer disk with low luminosity, and is classified as an SBc type (Gusev et al. 2003).

NGC 4900 is a spiral barred galaxy, classified as SB(rs)c located in the Virgo cluster at a distance of 13.3 Mpc and at about 12° southeast of M87. NGC 4900 presents an HII nucleus obtained with CO observations (Lee et al. 1998).

A.2. Presentation of the H_α Maps of the New Observation Data

A.3. Presentation of the H_α Monochromatic Maps of the Candidates of Vertically Perturbed Disks

The set of H_α monochromatic maps of the candidates of vertically perturbed disks is available in the online journal.

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B.1. Residual Maps without Signs of Vertical Perturbations

The set of residual velocity maps without signs of vertical perturbations is available in the online journal.

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C.1. Presentation of the Rotation Curves of WiNDS

The set of WiNDS rotation curves is available in the online journal.

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D.1. Imaging Process for the Quantification of Vertical Perturbations on the ${V}_{\mathrm{res}}$ Field (Figure 12)

To highlight the larger velocity amplitudes in the ${V}_{\mathrm{res}}$ map, we use a filter on the residual field through Fourier transform and a Gaussian low-pass filter. The image filtering process is carried out following the process described in Figure 12.

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A spatial image f(x,y) with dimension N × N in the Discrete Fourier Transform (DFT) of f called F(u,v) is defined as

$$\begin{eqnarray}&&F(u,v)=\displaystyle \frac{1}{N}\sum _{x=0}^{N-1}\sum _{y=0}^{N-1}f(x,y){e}^{-2\pi i({ux}+{vy})/N}\end{eqnarray} \tag{ A1 }$$

with u = 0, 1, 2,...,N − 1 − 1, and v = 0, 1, 2,...,N − 1, coordinates in Fourier space.

The inverse DFT is defined as

$$\begin{eqnarray}&&f(x,y)=\displaystyle \frac{1}{N}\sum _{x=0}^{N-1}\sum _{y=0}^{N-1}F(u,v){e}^{2\pi i({ux}+{vy})/N}.\end{eqnarray} \tag{ A2 }$$

To remove or attenuate high frequencies in the Fourier domain, related to image noise, the Gaussian low-pass filter is used.

$$\begin{eqnarray}&&H(u,v)={e}^{-{D}^{2}(u,v)/2{D}_{0}^{2}},\end{eqnarray} \tag{ A3 }$$

where D(u,v) corresponds to the Euclidean distance from (u,v) to the origin of the frequency plane and D₀ is the cutoff frequency in pixels in Fourier space.