2. Data and methods

In this section we will discuss the criteria applied for the sample selection, give details of the observations, list the steps followed in the data reduction process and discuss the source finding and characterisation. We will also describe the kinematic modelling for the sample galaxies which is necessary to derive their rotation curves.

2.1. Sample selection

We use the Catalogue of Southern Ringed Galaxies (CSRG, Buta Reference Buta2001), obtained through the Vizier catalogue access tool (Ochsenbein, Bauer, & Marcout Reference Ochsenbein, Bauer and Marcout2000) to select our sample of ring galaxies. The CSRG was originally published by Buta (Reference Buta1995), presenting properties of outer and inner rings, pseudo-rings and lenses of 3692 galaxies south of −17 $^\circ$ in declination.

Our selection criteria was based on galaxy size, position, visual inspection of each galaxy from CSRG, and a cross-check as to whether the galaxies were detected in the Hi All Sky Survey (HIPASS, Barnes et al. Reference Barnes2001; Meyer et al. Reference Meyer2004):

• • Our primary selection criteria was galaxy size, selecting galaxies with large angular size, sufficient to resolve the Hi in the rings, to be able create reliable kinematic models. We selected galaxies with D $_{\textrm{25}}$ $\geq$ 180 $^{\prime\prime}$ , where D $_{\textrm{25}}$ is the B-band 25 mag arcsec $^{-2}$ isophotal diameter, from ESO-LV ‘Quick Blue’ IIa-O (Lauberts & Valentijn Reference Lauberts and Valentijn1989).

• • The secondary constraint was declination of the galaxy, selecting galaxies south of −25 $^\circ$ in declination. This criteria ensures good observability with the ATCA, avoiding an elongated synthesised beam.

• • Using Astroquery SkyView cutout service (Ginsburg et al. 2019), we obtained DSS images of all $\sim$ 3692 galaxies from the CSRG and visually inspected them. This step was necessary to validate the galaxy selection process and it was done before and after size/declination restrictions to the catalogue. Next, with visual inspection of 101 ring galaxies—obtained after the declination and size restrictions—we removed highly edge-on galaxies and galaxies with no clear rings and/or inner (pseudo)rings. Galaxies with unclear/faint images were re-checked in NED database. Additionally, two ring galaxies—ESO 215-31 and ESO 179-IG-013, were added to our sample through visual inspection.

• • As a final check, we inspected the HIPASS data to see if the selected galaxies have an Hi detection. This step was necessary to minimise risk of not detecting Hi through our new ATCA observations. With this check five galaxies were removed due to Hi non-detection in HIPASS.

The above criteria left us with a sample of 27 ring galaxies of the $\sim$ 3692 from the original CSRG sample, as the majority of galaxies have an angular size too small to be sufficiently resolved with the ATCA. Out of the 27, 12 galaxies were found to have archival ATCA data (in the 1.5 km, 750 m and 352/375 m configurations). We have observed 15 ring galaxies with our ATCA proposal (C3385). Ultimately, due to calibration issues and/or not being able to derive reliable kinematic models, 3 of the 12 galaxies from the archive were rejected, leaving us with a final sample size of 24 ring galaxies. Figure 1 shows the spatial and velocity distribution of our sample of ring galaxies.

Figure 1. Spatial and velocity distribution of galaxies in the Hi in Ring Galaxies Survey (Hi-RINGS). The grey points show all the ring galaxies from the (Buta Reference Buta1995) catalogue, the stars show our sample of ring galaxies where colour denotes their Heliocentric velocity.

2.2. Observations

The 15 galaxies in our sample, for which no archival data are available, were observed with the ATCA in one of the default 750 m and 1.5 km array configurations. These observations were carried out through the ATCA project C3385 in 2020OCTS and 2021APRS semesters with a total observation time of 307.5 h, and an average on-source time of $\sim$ 11 h per array configuration. Combining the data from these two configurations will result in increasing both sensitivity and spatial resolution of the synthesised data, which is key to accurately modelling the kinematics of the sample galaxies (see Section 2.7). The ATCA, which is equipped with the Compact Array Broad-band Backend (CABB, Wilson et al. Reference Wilson2011), allows us to observe the galaxies in both continuum and spectral-line mode. The total bandwidth in the continuum band is 2048 MHz with a frequency resolution of 1 MHz, centred at 2.1 GHz. The spectral line observations have a total bandwidth of 8.5 MHz with a channel resolution of $0.5$ kHz, which corresponds to a velocity resolution of $\sim$ 1 $\textrm{km s}^{-1}$ . We employed the following strategy for the observations—55 min on source followed by 5 min on the phase calibrator each hour. The primary calibrators used are PKS 1934-638 and PKS 0823-500 depending on the time of observations. The primary calibrator was observed for 10 min at the start and end of the observing run. Other details of the observations for the sample are listed in Table 1.

Table 1. Details of the observations. Col (1): Common name; (2) ATCA baseline observation configuration; Col (3): The central frequency of the observation; Col (4): Primary flux calibrator used; Col (5): Phase calibrator used; Col (6): rms in the image cubes; Col (7): Synthesised beam size major and minor axis, respectively; Col (8): Notes about observations: This survey—ATCA project C3385; NGC 1433 data is from C305 (Ryder et al. Reference Ryder1996); NGC 7531 data is from C2196 (Koribalski et al. Reference Koribalski, Ryder, Lopez-Sanchez and Karachentsev2009); NGC 1808 data is from C585 (Dahlem, Ehle, & Ryder Reference Dahlem, Ehle and Ryder2001); NGC1533 data is from C934 and C1003 (Ryan-Weber, Webster, & Staveley-Smith Reference Ryan-Weber, Webster and Staveley-Smith2003); NGC 7098 data is from C744 (Pisano, Wilcots, & Liu Reference Pisano, Wilcots and Liu2002).

4. Bar-driven resonance rings

In this section, we study the effects of bars in driving the ring structure among the secularly evolving ring galaxies in our sample. There is a lot of evidence from both observations and models that suggest that bars can lead to the formation of resonance rings (Schwarz Reference Schwarz1981; Buta Reference Buta1986; Buta & Crocker Reference Buta and Crocker1991; Sellwood & Wilkinson Reference Sellwood and Wilkinson1993). The non-axisymmetric gravitational potential of a bar can trigger density waves that leads to orbital resonances where gas and stars can accumulate to form ring-like structures. The location of these orbital resonances (also called Lindblad resonances) depend primarily on the bar patter speed ( $\Omega_{\textrm{bar}}$ ), the angular velocity ( $\Omega$ ) and the radial epicyclic frequency ( $\kappa$ ) of the gas and stars orbiting the galaxy (Lindblad Reference Lindblad1964; Buta Reference Buta1999). The resonances occur at the radius where the following condition is met:

\begin{align*}\Omega_{\textrm{bar}} = \Omega \pm \kappa/m\end{align*}

where m is an integer. The most commonly observed resonances in galaxies are the Outer Lindblad Resonance (OLR), with $\Omega_{\textrm{bar}} = \Omega + \kappa/2$ , the Inner Lindblad Resonance (ILR), where $ \Omega_{\textrm{bar}} = \Omega - \kappa/2$ , the inner Ultra-harmonic Resonance (iUHR) $ \Omega_{\textrm{bar}} = \Omega - \kappa/4$ and the outer Ultra-harmonic Resonance (oUHR), where $\Omega_{\textrm{bar}} = \Omega + \kappa/4$ .

We measure the location of the various resonance radii based on the semi-major axis radius ( $a_{\textrm{bar}}$ ) and the angular pattern speed of the bar ( $\Omega_{\textrm{bar}}$ ). Various methods have been proposed in the literature to measure the length of bars in galaxies including visual methods based on where the isophotes diverge from the typical boxy shape of the bar (e.g., Garcia-Barreto & Momjian Reference Garcia-Barreto and Momjian2022); bar radius defined as the radius at which the intensity along the major axis of the bar drops to half the intensity of the peak (Salo et al. Reference Salo2015); as well as based on Fourier analysis (Laurikainen & Salo Reference Laurikainen and Salo2002; Buta et al. Reference Buta, Laurikainen, Salo, Block and Knapen2006).

We measure the bar size visually following the methods described in Garcia-Barreto & Momjian (Reference Garcia-Barreto and Momjian2022). As the stellar population of the bar is mostly dominated by older stars which are better represented in the IR (see for example Buta Reference Buta1999; Eskridge et al. Reference Eskridge2000; Herrera-Endoqui et al. Reference Herrera-Endoqui, Díaz-García, Laurikainen and Salo2015 and references therein), we make use of the DSS IR-band image to visually determine the radius of the bar ( $a_{\textrm{bar}}$ ) for our sample of barred ring galaxies. This involves plotting isophotal contours on the DSS IR image and defining the bar radius as the distance from the centre of the galaxy to the last isophote that follows a boxy contour (see Figure 4). We measure the length of the semi-major axis radius of the bar from the centre to each ends of the isophote along the major axis of the bar and take the bar radius to be the average of the two, we term this value $a_{\textrm{bar}}^{\textrm{uncorr}}$ . We compute the standard error on the average value of $a_{\textrm{bar}}^{\textrm{uncorr}}$ and propagate this error when computing the de-projected bar radius $a_{\textrm{bar}}$ .

The measured average uncorrected bar radius ( $a_{\textrm{bar}}^{\textrm{uncorr}}$ ) is then de-projected to the kinematical major axis of the galaxy, to obtain the corrected bar radius ( $a_{\textrm{bar}}$ ). Again, this is done following the method described in Garcia-Barreto & Momjian (Reference Garcia-Barreto and Momjian2022) as:

\begin{align*}a_{\textrm{bar}} = a_{\textrm{bar}}^{\textrm{uncorr}} \sqrt{\cos ^2\!(\phi)+\left(\sin ^2\!(\phi) / \sin ^2\!(i)\right)}.\end{align*}

Here $\phi$ is the absolute difference between the median kinematic position angle (P.A) of the disk of the galaxy and the position angle of the bar and i is the inclination angle of the optical disc of the galaxy as described in Section 2.7. $a_{\textrm{bar}}$ is then converted to a physical size in units of kpc using the distance (D) to the source. We propagate the errors associated with $a_{\textrm{bar}}^{\textrm{uncorr}}$ , $\phi$ and assume a nominal 10% error on the distance measurements to compute the errors on $a_{\textrm{bar}}$ . We list the $a_{\textrm{bar}}$ values in Table 4.

Table 4. Properties of the bar and Lindblad resonances. Col (1): Common name; Col (2): Average length of the semi-major axis of the bar in kpc; Col (3): Bar patter speed in units of $\textrm{km s}^{-1}$ kpc $^{-1}$ ; Cols (4)–(7): measured radius of the inner Lindblad resonance (ILR), inner Ultra-harmonic resonance (iUHR), outer Ultra-harmonic resonance (oUHR) and outer Lindblad resonance (OLR) respectively in units of kpc.

Figure 4. DSS IR-band image of the zoomed-in central region of the ring galaxy NGC 5101, showing the bar. The yellow curves are the IR-band isophotal contours overlaid on the image. The red cross denotes the centre of the galaxy and the orange arrows represent the length of bar semi-major axis radius towards each end of the bar along the major axis of the bar.

Once we determine the corrected/de-projected bar radius, we assume the ratio of co-rotation radius of the bar and bar radius, $R \equiv R_{\textrm{CR}}/a_{\textrm{bar}} = 1$ , so that $R_{\textrm{CR}} = a_{\textrm{bar}}$ . A number of previous works have shown that the value of R ranges from 1 to 1.6 (e.g., Debattista & Sellwood Reference Debattista and Sellwood2000; Guo et al. Reference Guo2019; Schmidt et al. Reference Schmidt2019). While other works have shown that $\sim$ 90% of the barred galaxies have $1.0 \leq R \leq 1.4$ (Athanassoula Reference Athanassoula1992; Debattista & Sellwood Reference Debattista and Sellwood2000; Starkman et al. Reference Starkman, Lelli, McGaugh and Schombert2018). Therefore, setting $R = 1$ is a reasonable approximation to make for our analysis. Indeed, we find that setting $R = 1.2$ , which is the average of the range of reported values does not significantly affect our results.

Next, we derive the angular velocity profile ( $\Omega$ Hi) from the Hi gas for our sample galaxies using the Hi rotation curve ( $v_{\textrm{rot}}(r)$ ) extracted from 3DBarolo (see Section 2.7). The observed rotation curve is fit with a simple analytic function introduced in previous works (e.g., Boissier et al. Reference Boissier, Prantzos, Boselli and Gavazzi2003; Obreschkow et al. Reference Obreschkow2016) and of the form,

\begin{align*}v_{\textrm{rot}}(r) = v_{\max}\left(1-e^{-r / r_{\text{max}}}\right)\end{align*}

where $v_{\max}$ is the maximum rotation velocity corresponding to the flat part of the rotation curve and $r_{\text{max}}$ is the radius where the rotation curve transitions to the flat part. Both $v_{\max}$ and $r_{\text{max}}$ are left as free parameters during the fit. We use the best fitting function describing the rotation curve to then derive the angular velocity profile of the Hi gas, $\Omega$ Hi $= v_{\textrm{rot}}(r)/r$ , where $v_{\textrm{rot}}(r)$ is the circular rotation velocity in $\textrm{km s}^{-1}$ and r is the radius in kpc. We note that the choice of the analytic function used to fit the rotation curves was motivated on the basis of its simplicity as well as the fact that we were able to obtain reasonably good fits for our sample. Following this we measure the bar pattern speed, $\Omega_{\textrm{bar}}$ . $\Omega_{\textrm{bar}}$ is the angular velocity corresponding to the bar co-rotation radius $R_{\textrm{CR}}$ (see panel (c) in Figure 5). To determine the various Lindblad resonance radii, we first need to derive the epicyclic frequency ( $\kappa$ ), which can be approximated as follows:

Panel (c) of Figure 5 shows a plot of the angular velocity profile $\Omega$ _Hi as well as the Lindblad curves, $\Omega$ _Hi $\,-\,\kappa/2$ , $\Omega$ _Hi $\,-\,\kappa/4$ , $\Omega$ _Hi $\,+\,\kappa/4$ and $\Omega$ _Hi $\,+\,\kappa/2$ for the galaxy NGC 7098 (black, blue, green, pink and orange curves respectively). The location of the co-rotation radius ( $R_{\textrm{CR}}$ ) of the bar is represented by the black dashed vertical line in panel (c) of Figure 5. The bar pattern speed ( $\Omega_{\textrm{bar}}$ ) is represented by the horizontal black dotted line. The ILR, iUHR, oUHR and OLR radii are determined as the radius at which $\Omega_{\textrm{bar}}$ intersects the $\Omega$ _Hi $\,-\,\kappa/2$ , $\Omega$ _Hi $\,-\,\kappa/4$ , $\Omega$ _Hi $\,+\,\kappa/4$ and $\Omega$ _Hi $\,+\,\kappa/2$ curves respectively. The position angle of the inner rings (ILR and iUHR) is set to be equal to that of the bar position angle, as many previous studies have shown that the inner rings are typically aligned parallel to the major axis of the bar (e.g., Buta & Combes Reference Buta and Combes1996). The position angle of the outer rings (oUHR and OLR) are set equal to the median kinematic P.A of the galaxy.

Figure 5. (a) Hi moment 0 intensity map of NGC 7098. The synthesised beam is shown in the left bottom corner. (b) DSS composite optical image of NGC 7098. The blue, green, pink and orange ellipses represent the location of the ILR, iUHR, oUHR and OLR, respectively. (c) The plot shows the angular velocity ( $\Omega$ Hi; black line) derived from the rotation velocity of the Hi gas as a function of radius for the galaxy NGC 7098. The blue, green, pink and orange profiles represent the ILR, iUHR, oUHR and OLR Lindblad resonance curves respectively. The vertical black dashed line represents the measured bar co-rotation radius (R $_c$ ), the horizontal black dotted line represents the bar pattern speed ( $\Omega_{\textrm{bar}}$ ). The blue, green, pink and orange vertical dashed lines denote the location of the ILR, iUHR, oUHR and OLR resonance radii respectively. (d) Top panel: Radial profile of the Hi surface density of the galaxy NGC 7098. Bottom panel: Radial profile of the SFR surface density.

Panels (a) and (b) in Figure 5 show the Hi moment 0 map and the optical DSS image respectively of NGC 7098 with the ILR, iUHR, oUHR and OLR ring locations indicated by the blue, green, pink and orange ellipses. NGC 7098 is observed to posses an inner ring as well as an outer ring (see DSS optical image in panel (b) of Figure 5) and we find that the predicted location of the oUHR (pink ellipse) coincides nicely with the observed inner ring and the predicted OLR (orange ellipse) traces the outer ring in very good agreement. Additionally, we also observe an Hi ring located at the OLR radius.

In addition, we derive the star formation rate (SFR) surface density profiles for our sample to examine if the SFR is enhanced at the locations of the resonance rings. A number of previous works have highlighted that star formation is triggered at the resonance locations in the disc where the Hi gas accumulates. We derive the SFR surface density profiles for the galaxies in our sample using their WISE $W_3$ and $W_1$ images procured from the NASA/IPAC IRSAFootnote ^c image cutout service. The $W_3$ flux is shown to be a good tracer of the SFR in galaxies, however, this flux is also contaminated by the contribution from older stellar population (Jarrett et al. Reference Jarrett2011; Cluver et al. Reference Cluver2017). We correct for this following the methods described in Cluver et al. (Reference Cluver2017) and subtract $\sim$ $15.8\%$ of the $W_1$ -band flux from the $W_3$ flux.

We first process both the $W_3$ and $W_1$ images to remove foreground stars. We run the source finding code SExtractor (Bertin & Arnouts Reference Bertin and Arnouts1996) to identify point-like sources in the images, following this we use the IRAF (Tody Reference Tody and Crawford1986) task imedit to replace the bad pixels of the star with random pixels surrounding the star. In the next step we place an annulus around each galaxy and measure the median local sky background values from both the $W_3$ and $W_1$ images, before subtracting this from the respective images. Next, we measure both the $W_3$ and $W_1$ flux within concentric ellipses, with position angle set to the median kinematic position angle of the galaxy, and convert the corrected $W_3$ flux to SFR following the methods described in Cluver et al. (Reference Cluver2017).

In Panel (d) of Figure 5 we plot both the azimuthally averaged Hi surface density ( ) and the SFR surface density profile ( $\Sigma_{\textrm{SFR}}$ ) for NGC 7098. The inner region (<10 kpc) of this galaxy is observed to have a dip in Hi surface density ( ), while showing a peak in SFR surface density. At the location of the resonance radii, there is an enhancement in and $\Sigma_{\textrm{SFR}}$ . This is also observed in most of the barred galaxies in our sample (see Appendix B for more details) and is consistent with the theory that bars drive resonances, where the disk stars and Hi gas accumulate, and the gas eventually collapses to form new stars, thereby resulting in increased SFR at the resonance ring locations (Buta & Combes Reference Buta and Combes1996). Such ring-like structures are likely to remain in equilibrium for a few Gyrs as the resonant locations are regions in the galactic disc where the net torque is zero (e.g., Buta Reference Buta1999; Bournaud, Combes, & Semelin Reference Bournaud, Combes and Semelin2005).

We perform the above resonance model analysis for the rest of the barred galaxies in our sample to see if we are able to predict the location of the resonance rings consistently. We report that there is good agreement between the predicted locations of the resonances and the presence of actual ring-like structures (in Hi and/or in the optical) for the majority of the galaxies. We note that depending on the angular velocity profiles, bar radius and pattern speed of the individual galaxies, we are unable to always measure all four resonances. We list the measured bar radius ( $a_{\textrm{bar}}$ ), pattern speed ( $\Omega_{\textrm{bar}}$ ) and various resonance radii for the sample in Table 4. Figures B.5–B.9 in Appendix B show the outcomes of the resonance model analysis for the other barred galaxies in our sample.

The measured values of the bar pattern speed ( $\Omega_{\textrm{bar}}$ ) for our sample range from $\sim$ 10–90 $\textrm{km s}^{-1}$ kpc $^{-1}$ , with a median value of $\sim$ 44 $\textrm{km s}^{-1}$ kpc $^{-1}$ . This range is consistent with previous works that have measured $\Omega_{\textrm{bar}}$ values in galaxies (e.g., Corsini Reference Corsini2011; Williams et al. Reference Williams2021). In addition, we found a few galaxies in our sample for which the $\Omega_{\textrm{bar}}$ measurements were available in the literature and find that overall the values are in good agreement. For example, Moore & Gottesman (Reference Moore and Gottesman1995) use VLA Hi observations to determine $\Omega_{\textrm{bar}}$ of NGC 1398 and estimate a value $\sim$ 46 $\textrm{km s}^{-1}$ kpc $^{-1}$ , which is in very good agreement with our measured value of $47\pm3$ $\textrm{km s}^{-1}$ kpc $^{-1}$ . Garcia-Barreto et al. (Reference Garcia-Barreto, Dettmar, Combes, Gerin and Koribalski1991) measure a pattern speed value of $\sim$ 60 $\textrm{km s}^{-1}$ kpc $^{-1}$ for NGC 1326, while we measure a pattern speed of $52\pm5$ $\textrm{km s}^{-1}$ kpc $^{-1}$ . We measure $\Omega_{\textrm{bar}}$ $90\pm13$ $\textrm{km s}^{-1}$ kpc $^{-1}$ for NGC 6300, which is in disagreement with the value measured by Ryder et al. (Reference Ryder1996), who estimate a bar pattern speed of $27 \pm 8$ $\textrm{km s}^{-1}$ kpc $^{-1}$ . However, we emphasise that the higher $\Omega_{\textrm{bar}}$ value we measure predicts the existence of an OLR at a radius of $\sim$ $3.57$ kpc, which coincides with the location of both an Hi and stellar ring in NGC 6300 (see Figure B.7 in Appendix B). While Ryder et al. (Reference Ryder1996) report that assuming the lower bar pattern speed of $\sim$ 27 $\textrm{km s}^{-1}$ kpc $^{-1}$ would result in the location of an OLR at radius between 8–15 kpc, where they find no Hi or stellar ring. The fact that our $\Omega_{\textrm{bar}}$ measurement for NGC 6300 better matches the resonance model instils confidence in our analysis.

Overall, from our analysis, we find that the bar driven resonance theory explains the location of the inner and outer rings that we observe among galaxies in our sample. It is indeed promising to note that we are able to reliably measure the location of the various Lindblad resonances using just the Hi rotation curve and a visual measurement of the size of the bar. These results come in support of the important role played by the bar in not only funnelling gas to the centres of galaxies but also in driving resonances and redistributing the angular momentum in galactic discs. As noted in Section 3.2, where we observed strongly barred galaxies in our sample to be in general more Hi-deficient compared to the weak and non-barred galaxies, it seems evident that bars accelerate the evolution of galaxies via their ability to both use-up large reserves of the Hi gas as well as making gas in the outskirts unavailable for star formation due to a kick in angular momentum, thus driving quenching in galaxies.

5. Summary and future

We have introduced the new Hi in Ring Galaxies Survey (Hi-RINGS), comprising of 24 ring galaxies for which we have obtained high-resolution Hi observations using the Australia Telescope Compact Array. The ring galaxies were selected on the basis of their large angular size, their declination range and a detection in the HIPASS catalogue. Our sample consists of a variety of ring galaxies including what have been regarded in the literature as resonance, collisional and interaction rings. We presented an overview of the sample, including their Hi, stellar and star formation properties. In addition, we also highlighted their Hi morphology and kinematics.

We segregated our sample of ring galaxies into two groups—those with a strong bar and those with a weak or no bar. We find that in general the strongly barred galaxies are more Hi-deficient compared to the weakly barred or unbarred galaxies in our sample. We also probed the local environment densities of our sample galaxies in addition to looking at their optical and Hi maps to examine if the environment is playing a prominent role in driving the Hi deficiency in the galaxies, but find no strong evidence for the same. We therefore hypothesise as suggested by previous works (e.g., Masters et al. Reference Masters2012) that the bars are potentially driving the observed Hi deficiency, via their ability to funnel copious amounts of Hi gas within the co-rotation radius of the bar to the centres of galaxies. In addition, the bars also transport angular momentum to the outer parts of the disc making the Hi gas in the outskirts of galaxies gain a kick in angular momentum and remain stable against collapsing to form stars. This combined effect potentially leads to bar quenching in galaxies as noted in other works.

We also employed Lindblad’s resonance theory to test if we are able to predict the radius of the major resonances for a sub-sample of barred galaxies. To determine the resonance radii, we measured the bar radius based on a visual method and combined with the derived rotation curves of the galaxies, we measure the bar pattern speed ( $\Omega_{\textrm{bar}}$ ) before computing the location of the ILR, iUHR, oUHR and OLR radius. The measured $\Omega_{\textrm{bar}}$ values range from 10–90 $\textrm{km s}^{-1}$ kpc $^{-1}$ in good agreement with previous works. We find that the predicted location of the resonance radii are in good agreement with the observed physical locations of the Hi/optical inner and/or outer rings in our galaxies. Furthermore, we derived the azimuthally averaged Hi ( ) and SFR surface ( $\Sigma_{\textrm{SFR}}$ ) density profiles for these galaxies and found that there is an enhancement in either , $\Sigma_{\textrm{SFR}}$ or both corresponding to one or more of the resonances.

In forthcoming papers, we aim to study the global and resolved scaling relations for our sample of ring galaxies to see how the different types of ring galaxies behave in the various scaling relations. In addition, we also aim to examine the properties of the collisional and interaction galaxies in our sample. These are interesting systems as the ring structure is believed to be driven by external perturbations. Specifically, as part of the Hi-RINGS survey, we have high-resolution Hi observations for a recently discovered collisional ring galaxy ESO179-IG013, also called ‘Kathryn’s Wheel’ (Parker et al. Reference Parker2015), which is touted to be the nearest collisional ring galaxy and as such offers a great opportunity to probe its Hi and star formation properties. In the near future we aim to address most of the questions posed in the introduction pertaining to the evolution of ring galaxies.