The effects of bar strength and kinematics on galaxy evolution:
slow strong bars affect their hosts the most

We generate radial profiles for EW[H$\alpha$] and D_n4000 obtained from MaNGA in order to probe the effect that a bar has on different regions of a galaxy. These radial profiles are constructed for all the galaxies in the GZ DESI-MaNGA sample. Figure 3 shows the radial profiles of the Gaussian-fitted equivalent width measurement of H$\alpha$ (EW[H$\alpha$]) for each bar type: strong, weak, and unbarred. The galaxies are categorised as SF or quenching based on Equation 2.5 shown in Section 2.5. The top row shows the profiles for SF galaxies, while the bottom row shows the profiles for quenching galaxies. The profiles are shown in terms of distance to the centre of the galaxy (in kpc, left column) and relative to the bar radius (right column). However, it is important to realise that a distance of e.g. $2R_{\textrm{bar}}$ is farther out in the disc of the galaxy for a strong bar than for a weak bar, as strong bars are typically longer than weak bars (de Vaucouleurs, 1959, 1963; Géron et al., 2021). The top part of each panel shows the number of galaxies that have spaxels in each radial bin. The bottom part of every panel shows the difference between the radial profiles of any two samples. The significance of the difference in every bin is shown by the size of the point, with the largest sizes representing a significant difference greater than 3$\sigma$ after comparing the two populations with an Anderson-Darling test. Conversely, the smallest sizes represent $<$1$\sigma$. Bins with a significant difference exceeding 3$\sigma$ are additionally outlined in black.

The EW[H$\alpha$] radial profile of strongly barred SF galaxies (orange, top row of Figure 3) peaks in the central bins, after which it reaches a minimum in the arms of the bar. Interestingly, the profile rises again, reaching another peak beyond the bar-end region (at $R\approx 1.2-1.5R_{\textrm{bar}}$), before decreasing again at higher radii. This profile suggests a higher SFR in the centre and beyond the bar-end, as EW[H$\alpha$] serves as a proxy for sSFR, while it is suppressed in the arms of the bar. The EW[H$\alpha$] profiles of weakly barred SF galaxies and unbarred SF galaxies closely resemble each other. Both profiles are flat in the outskirts (at R $\gtrsim$ 5 kpc or $\gtrsim$ 1.5 $R_{\textrm{bar}}$) and have lower median values for EW[H$\alpha$] closer to the centre. Additionally, it is interesting to note that the EW[H$\alpha$] is lower for strongly barred SF galaxies compared to weakly barred and unbarred SF galaxies in the outskirts of the galaxy.

The bottom half of Figure 3 shows the radial profiles for quenching galaxies with strong bars, weak bars, and no bars. Strongly barred quenching galaxies have consistently lower values for EW[H$\alpha$], while weakly and unbarred galaxies have relatively similar values to each other. All profiles have higher values for EW[H$\alpha$] in the outskirts of the galaxy, which decrease towards the centre, which is the opposite trend to what we saw for strongly barred SF galaxies. Interestingly, for both weak and strong bars, this decrease starts around the bar-end ($R\approx 1.0-1.2R_{\textrm{bar}}$), although it is more distinct for strong bars. This decrease at the bar-end region is not found in the profiles of the unbarred galaxies normalised to the bar radius. However, it is important to keep in mind that the profiles normalised to the bar radius for unbarred galaxies are not physical. They are constructed by assigning a random bar radius to every unbarred galaxy, which is drawn from a log-normal distribution fitted to all the barred galaxies in the same stellar mass bin to the unbarred galaxy (see Section 2.4 for more details).

Figure 4 shows the radial profiles for D_n4000. The average profile for strongly barred SF galaxies is low in the centre of the galaxy, reaches a maximum in the middle of the arms of the bar ($R\approx 0.5R_{\textrm{bar}}$), followed by a decline and flatting beyond the bar-end region ($R\approx 1.2-1.5R_{\textrm{bar}}$). This profile is in contrast from the profiles observed in weakly barred and unbarred galaxies. Here, D_n4000 is highest in the centre and decreases monotonically with radius. On average, strongly barred galaxies have the highest values for D_n4000, followed by weakly barred and unbarred SF galaxies, which have very similar values to each other. These results suggest that the stellar population is oldest in the arms of the bar of strongly barred SF galaxies and that they have younger stellar populations in the centre and beyond the bar-end. These results are consistent with the results obtained from the EW[H$\alpha$] radial profiles. These results confirm that strong bars can impact stellar populations, implying that strong bars are a long-lived phenomena. This is not the case for weakly barred galaxies, whose D_n4000 profiles closely resemble those of unbarred galaxies. These results are discussed in more detail in Section 4.1.2.

Among quenching galaxies (bottom row of Figure 4), the profiles of the three samples exhibit similar trends: highest in the centre and decreasing monotonically with radius. However, for strongly barred galaxies, this decrease happens around the bar-end region, whereas it is much more gradual for weakly barred and unbarred galaxies. In the outskirts of the galaxy, the value for D_n4000 is comparable for all three samples. Strongly barred quenching galaxies have higher values for D_n4000 overall, while weakly and unbarred galaxies have similar values to each other.

To summarise: strongly barred SF galaxies have increased star formation in the centre and bar-end region, while suppressing star formation in the arms of the bar. In contrast, the profiles of weakly barred and unbarred galaxies are very similar to each other. Weakly and unbarred galaxies have lower star formation in the centre, which increases with radius. These results are further discussed in greater detail and compared to the literature in Section 4.1.1.

Unbarred, weakly barred and strongly barred galaxies typically have different stellar masses (Géron et al., 2021). To investigate how stellar mass impacts the results of this paper, we also generated the radial profiles for all SF galaxies across three different mass bins: low mass ($M_{*}<10^{10.2}M_{\odot}$), intermediate mass ($10^{10.2}M_{\odot}<M_{*}<10^{10.6}M_{\odot}$) and high mass ($M_{*}>10^{10.6}M_{\odot}$). These thresholds were selected so that an equal number of galaxies are in each bin (471 galaxies in each).

The left column of Figure 5 shows the radial profiles of EW[H$\alpha$] for the three mass bins. The central peak of EW[H$\alpha$] for strongly barred galaxies is found in all mass bins. However, the suppression of EW[H$\alpha$] and the subsequent second peak beyond the bar-end region ($R\approx 1.2-1.5R_{\textrm{bar}}$) among strongly barred SF galaxies are only observed in the intermediate and high mass bins, not in the low mass bin. Interestingly, the EW[H$\alpha$] of the weakly barred galaxies also increases around the bar-end in the high mass bin. A similar result is shown in in right column of Figure 5, where the radial profiles of D_n4000 for SF galaxies in the different mass bins are shown. The increase of D_n4000 in the arms of strong bars is much more prominent in the intermediate mass and high mass bins, compared to the low mass bin. The profiles of the weakly barred SF galaxies and unbarred SF galaxies are similar across all mass bins in both the EW[H$\alpha$] and D_n4000 radial profiles.

These results show that the conclusions drawn in this paper regarding bar strength hold true for intermediate mass and high mass galaxies, but not for low mass galaxies. This is in agreement with the results found in Géron et al. (2021), who showed that strong bars are most efficient at facilitating quenching at higher stellar masses. Other studies have found that more massive galaxies have longer and stronger bars (Aguerri et al., 2009; Erwin, 2019; Fraser-McKelvie et al., 2020b; Kim et al., 2021). This implies that the strongest bars, which have the most effect on their host, are predominantly found in the highest mass bin.

The bar-end region is of particular interest. A local peak of EW[H$\alpha$] is found here for strongly barred SF galaxies, but not for weakly barred SF galaxies. Moreover, the bar-end region appears to be a turn-over point in the EW[H$\alpha$] and D_n4000 profiles for strongly barred galaxies. To study this region in more detail and compare it to corresponding off-bar regions, we construct radial profiles with the aperture placed parallel and perpendicular to the bar (the rest of the procedure remains identical, see Section 2.4 for more details). The profiles created with the aperture placed parallel to the bar (as shown in Figures 3, 4 and 5) provide information specifically about the barred region, such as the bar-end. In contrast, profiles created with the aperture placed perpendicular to the bar probe the off-bar regions. Comparing the profiles generated with these two apertures will show what the impact of the bar is (e.g. in the bar-end region) with respect to the rest of the galaxy. However, do note that the central region of the profiles should be similar, given that the parallel and perpendicular apertures overlap in the 3 arcsec centre.

This is done in Figure 6 for all strongly barred SF galaxies (top row) and weakly barred SF galaxies (bottom row) for both EW[H$\alpha$] (left column) and D_n4000 (right column). The median difference in EW[H$\alpha$] beyond the bar-end region ($R\approx 1.2-1.5R_{\textrm{bar}}$) is $\sim$10 Å for strongly barred SF galaxies, while this is only $\sim$4 Å for weakly barred SF galaxies, though it is $>$3$\sigma$ significantly different for both strongly and weakly barred SF galaxies. Additionally, the profile with the aperture aligned with the bar clearly shows the peak beyond the bar-end region, which this is not observed in the profile with the aperture placed perpendicular to the bar. The difference in D_n4000 at the bar-end region for strongly barred SF galaxies is $\sim$0.05 and it is $>$3$\sigma$ significant. Meanwhile, the difference in D_n4000 is only $\sim$0.01 for weakly barred SF galaxies and this difference not significant ($<$2$\sigma$) in any bin.

Thus, the difference in EW[H$\alpha$] and D_n4000 around the bar-end region is significantly higher for strongly barred SF galaxies compared to weakly barred SF galaxies. This suggests that there is more star formation in the bar-end region of strongly barred SF galaxies compared to the bar-end region of weakly barred SF galaxies.

The radial profiles of EW[H$\alpha$] for fast and slow bars in SF and quenching galaxies are shown in Figure 7, which is constructed similarly as before. The top-left panel clearly shows that slow bars have higher EW[H$\alpha$] than fast bars in SF galaxies, especially in the intermediate radius range of the galaxy ($\sim$2-4 kpc). The top-right panel shows that the median profile is slightly higher for slow bars than for fast bars in SF galaxies when expressing distance normalised to the bar radius, although the difference remains less than 3$\sigma$. Both slow and fast bars have higher EW[H$\alpha$] in the centre and bar-end compared to the arms of the bar. The profiles for quenching galaxies are relatively similar between slow and fast bars, except around the bar-end, where the EW[H$\alpha$] profile is steeper for fast bars and fast bars have significantly ($>$3$\sigma$) higher values for EW[H$\alpha$]. The rest of the EW[H$\alpha$] profile rises slowly with increasing distance from the galaxy.

Similar conclusions are drawn for the D_n4000 profiles, which are shown in Figure 8. Slow bars in SF galaxies have significantly lower values for D_n4000 in the intermediate radius range of the galaxy ($\sim$3-5 kpc) than fast bars. The average profile for slow bars in SF galaxies decreases monotonically with radius, while the profile for fast bars has a bump in the arms of the bar. Again, the profiles of slow and fast bars in quenching galaxies are relatively similar, except at the bar-end region.

These results suggest that there is more star formation along slow bars compared to fast bars in SF galaxies, as we find higher values for EW[H$\alpha$] and lower values for D_n4000 in slow bars than in fast bars.

The results presented in Section 3.2.1 suggest that there is more star formation along slow bars compared to fast bars in SF galaxies. At the same time, we showed in Section 3.1 that there is more star formation in strongly barred galaxies than in weakly barred galaxies. In this section, we will address whether there is a combined effect between these two independent results.

The effect of bar strength on the profiles of fast and slow bars is studied in Figure 9, which shows the radial profiles for EW[H$\alpha$] (left column) and D_n4000 (right column) for strongly barred SF galaxies (top row) and weakly barred SF galaxies (bottom row). The median profile of EW[H$\alpha$] for slow strong bars is always higher than that of fast strong bars, as shown in the top-left panel of Figure 9, although the significance of the difference is always $<$3$\sigma$. These profiles are reminiscent of the profiles previously shown in Figure 3 for strong bars: high EW[H$\alpha$] in the centre, lower values in the arm of the bar and a second peak beyond the bar-end. However, the increase of EW[H$\alpha$] beyond the bar-end region is more pronounced in slow strong bars than in fast strong bars. The median EW[H$\alpha$] is also higher in the arms of slow strong bars than in the arms of fast strong bars. The EW[H$\alpha$] profiles for slow weak bars and fast weak bars, shown in the bottom-left panel, are similar to each other ($<$1$\sigma$ at all radii smaller than 2$R_{\rm bar}$).

The top-right panel shows that the median values for D_n4000 are always lower for slow strong bars than for fast strong bars, which is consistent with the EW[H$\alpha$] profiles. Fast strong bars have a very distinct peak of D_n4000 in the arms of the bar, which is not as apparent in slow strong bars. This suggests that galaxies with slow strong bars might have younger stellar populations in the arms of the bar due to more recent star formation, presumably triggered by the presence of the slow strong bar. However, these differences are again not significantly different ($<$3$\sigma$), possibly due to the very low sample size. The bottom-right panel shows that the D_n4000 profiles for fast weak and slow weak bars are very similar to each other ($<$1$\sigma$ at all radii smaller than 2$R_{\rm bar}$).

Despite the limited sample sizes used in this analysis, bars strength seems to have an effect on the profiles of fast and slow bars. While not statistically significant ($<$3$\sigma$), these results suggest that there is more star formation at all radii in slow strong bars, compared to fast strong bars. In contrast, the profiles of fast and slow weak bars are very similar to each other. Increasing the sample size in future studies will be crucial to clarify these issues, as discussed in more detail in Section 4.2.2. The physical interpretation of this observation will be addressed in the following two subsections.

We have shown that slow bars have higher EW[H$\alpha$] than fast bars in SF galaxies, which implies more star formation in slow bars than fast bars. Interestingly, Figure 10 shows that the global SFR (obtained from Pipe3D, Sánchez et al., 2016a, b, 2018) is not significantly different between SF galaxies with fast and slow bars (the p-value of an Anderson-Darling test between the SFRs of fast and slow bars is $>$0.25). These observations initially seem contradictory to each other. However, the radial profiles are constructed using a aperture with a width of 3 arcsec oriented along the position angle (PA) of the bar. This means that these results suggest that the increase in EW[H$\alpha$] observed in slow bars only affects the bar region locally, without a significant impact on the global star formation of the galaxy. In other words, a slow bar seems to concentrate its SF along the bar, without increasing the global star formation.

This hypothesis can be tested by constructing radial profiles of EW[H$\alpha$] with apertures parallel and perpendicular to the bar and comparing the differences. This is done for all SF galaxies in Figure 11. The barred galaxies are divided into four subsamples: galaxies with slow strong bars, fast strong bars, slow weak bars and fast weak bars. The biggest difference between the parallel and perpendicular apertures was observed among slow strong bars, where the parallel aperture has significantly ($>$3$\sigma$) higher values for EW[H$\alpha$] between $\sim$1.2 - 1.8 $R_{\rm bar}$ compared to the perpendicular aperture. No significant difference ($>$3$\sigma$) between the parallel and perpendicular apertures is observed for fast strong bars, fast weak or slow weak bars.

This confirms that a slow bar will increase star formation along the position angle of the bar, but not in the entire galaxy. This was only observed for slow strong bars, which suggests that a slow bar will have more of an effect on its host if it is also a strong bar. This result is further discussed in Section 4.2.3.

The results presented in the last few sections suggest that slow bars induce more star formation along the bar compared to fast bars in SF galaxies. However, the underlying physical cause of this increased star formation remains unclear. As mentioned above, the classification of bars into fast and slow depends on $\mathcal{R}$, which is based on the kinematics of the bar and galaxy. Fast bars typically end near the corotation radius, whereas slow bars have bar radii shorter than the corotation radius, given that $\mathcal{R}=R_{\rm CR}/R_{\rm bar}$. The corotation radius is the radius at which the stars in the disc rotate with a speed equal to the rotation of the bar. This means that the bar-end region of fast bars typically rotates with a velocity similar to stars in the disc, whereas the bar-ends of slow bars should rotate much slower. This is illustrated in the left panel of Figure 12, where the difference in the velocity of the stars ($V_{*}$) at $R_{\rm bar}$, based on the stellar rotation curve, and the velocity of the bar-end ($V_{\rm bar-end}$) is measured for all SF galaxies. Bars with $\mathcal{R}>1$ will have $V_{*}>V_{\rm bar-end}$, while bars with $\mathcal{R}<1$ (i.e. ultrafast bars) will have $V_{*}<V_{\rm bar-end}$. For bars with $\mathcal{R}=1$, the velocities will be equal to each other, as $R_{\rm CR}=R_{\rm bar}$ for these bars. The difference in velocity is clearly bigger for slow bars in SF galaxies compared to fast bars in SF galaxies, as indicated by an Anderson-Darling test (p-value $<$ 0.001; $>$3.3$\sigma_{\rm AD}$). The median difference in velocity is 4.2 km s^-1 for fast bars and 49.6 km s^-1 for slow bars.

Note that these differences in velocity are a direct consequence of the definitions of fast and slow bars based on $\mathcal{R}$, so this is what we expect to find. Nevertheless, quantifying this difference highlights how significant it is. Additionally, $\mathcal{R}$ was calculated based on the stellar kinematics of the galaxy. However, we also see a difference between the velocity of the gas ($V_{\rm gas}$) at $R_{\rm bar}$, based on the gas rotation curve, and the velocity of the bar-end ($V_{\rm bar-end}$), which is shown in the right panel of Figure 12. The gas rotation curves are constructed similarly to the stellar rotation curves (see Section 2.3). However, instead of using the stellar velocity maps from MaNGA, the gas rotation curve is derived from a Gaussian fit to the H$\alpha$ emission line. The difference between $V_{\rm gas}$ and $V_{\rm bar-end}$ is significantly higher for slow bars in SF galaxies (the median value is 59.0 km s^-1) than for fast bars (12.7 km s^-1) in SF galaxies.

These results confirm that slow bars have a large difference in velocity compared to the stars and gas in the disc in the bar-end region. This is not observed for fast bars. These differences in velocity at the bar-end between slow and fast bars suggest that slow bars come into contact and interact with a more significant amount gas than fast bars, which could explain the observed differences in local star formation. The implications of this are discussed in more detail in Section 4.2.4.

Géron et al. (2021) found that strong bars in SF galaxies increase the central star formation of their hosts, while weak bars do not. However, the impact of strong bars in other regions, and whether weak bars behave similarly in these other regions, remained unclear. This was studied in Figures 3 and 4 using EW[H$\alpha$] and D_n4000, respectively. These figures show that strongly barred SF galaxies have higher star formation in the centre of their galaxy, compared to weakly barred and unbarred SF galaxies, in agreement with the results from Géron et al. (2021). There are many other examples in the literature of barred galaxies increasing the SFR in their host (Alonso-Herrero & Knapen, 2001; Hunt et al., 2008; Ellison et al., 2011; Coelho & Gadotti, 2011; Hirota et al., 2014; Janowiecki et al., 2020; Magaña-Serrano et al., 2020; Lin et al., 2020). The increase in central star formation in strongly barred galaxies can be attributed to the gas inflow from the outskirts to the centre induced by the bar (Athanassoula, 1992a; Athanassoula et al., 2013; Villa-Vargas et al., 2010), where the gas is available to increase star formation. However, this is only found here for strongly barred SF galaxies and is not observed in weakly barred SF galaxies or all quenching galaxies.

Figures 3 and 4 also show that, on average, the arms of a strong bar on suppress star formation, as suggested by low values for EW[H$\alpha$] and high values for D_n4000 around $R\approx 0.5R_{\textrm{bar}}$. This is consistent with other studies that have found evidence for lower SFR and star formation efficiency (SFE) in the arms of the bar (Reynaud & Downes, 1998; Sheth et al., 2000; Watanabe et al., 2011; Khoperskov et al., 2018). This is typically attributed to high velocity dispersion or shear caused by the bar potential (Athanassoula, 1992a; Reynaud & Downes, 1998; Sheth et al., 2000; Zurita et al., 2004; Haywood et al., 2016; Khoperskov et al., 2018) or by fast cloud-cloud collisions (Fujimoto et al., 2014; Maeda et al., 2018; Fujimoto et al., 2020; Maeda et al., 2021). Regardless of the specific physical process, these findings imply substantial gas flows along the arms of a strong bar. These results are also consistent with the ‘star formation desert’ described by James & Percival (2018) as well as the gas-depleted regions observed in barred galaxies in George et al. (2019) and Newnham et al. (2020). The EW[H$\alpha$] and D_n4000 profiles of weakly barred galaxies are very similar to the profiles of unbarred galaxies in the arms of the bar of SF galaxies. This implies that the suppression of star formation and evidence for gas flows are not found for weak bars in SF galaxies and that weak bars are not as efficient in transporting gas to the centre of the galaxy. This is also in agreement with the previous result that lower rates of star formation are found in the centre of weakly barred galaxies. Interestingly, the EW[H$\alpha$] profile of weakly barred quenching galaxies also drops at $R\approx 1R_{\textrm{bar}}$, although not as abruptly as in strongly barred quenching galaxies. This suggests that the arms of a weak bar in a quenching galaxy can still suppress some star formation, possibly due to increased velocity dispersion in the barred region of galaxies with lower gas concentrations.

There is a second peak of EW[H$\alpha$] found just beyond the bar-end ($R\approx 1.2-1.5R_{\textrm{bar}}$) in strongly barred SF galaxies, shown in Figure 3. This was studied in more detail in Figure 6, where we found that the difference in EW[H$\alpha$] and D_n4000 between slits placed parallel and perpendicular to the bar around the bar-end region was larger for strongly barred SF galaxies compared to weakly barred SF galaxies, which illustrates the importance of the bar-end region for strong bar. This is in agreement with other studies that have found increased star formation in the bar-end region (Reynaud & Downes, 1998; Verley et al., 2007; Emsellem et al., 2015; D´ıaz-Garc´ıa et al., 2020). For example, Maeda et al. (2020) found higher SFEs in the bar-end region than in the arms of the bar. Fraser-McKelvie et al. (2020b) also found increased H$\alpha$ in the bar-ends of 18% of barred galaxies, most of which have high stellar masses ($M_{*}>10^{10}M_{\odot}$). They also found increased H$\alpha$ in a ring around the bar, including at the bar-end in an additional 21% of their sample. This brings the total to 38% of galaxies in Fraser-McKelvie et al. (2020b) with elevated H$\alpha$ emission in the bar-end region. However, we only observe increased H$\alpha$ emission specifically in SF galaxies, while Fraser-McKelvie et al. (2020b) did not differentiate between SF and quenching galaxies. This implies that the fraction of galaxies with increased H$\alpha$ emission in the bar-end region in Fraser-McKelvie et al. (2020b) would likely be even higher if only SF galaxies were considered. This beyond the bar-end region might correspond to the “bar shoulders” found in the simulations of Anderson et al. (2022) and Beraldo e Silva et al. (2023). They show that these shoulders form due to looped x₁ orbits and appear in growing bars. Erwin et al. (2023) also found these shoulders in the surface brightness profiles of nearby barred galaxies. Interestingly, they noted that the shoulders were preferentially found in stronger bars, though they mention that this trend could mostly be explained by accounting for stellar mass. This is consistent with our results, as the increase in EW[H$\alpha$] beyond the bar-end is highest for the galaxies with higher mass (see Figure 5). These increases in star formation at the bar-end can be attributed to an increased probability of cloud-cloud collisions due to orbital crowding and high gas density, and low amounts of shear in the bar-end region (Renaud et al., 2015; Emsellem et al., 2015; Fraser-McKelvie et al., 2020b). However, an increase in star formation in the bar-end is more pronounced in this work for strongly barred SF galaxies, compared to weakly barred SF galaxies. This suggests that a weak bar less capable of inducing or supporting the effects described above.

The profiles in Figures 3 and 4 show that strongly barred SF galaxies have significantly lower EW[H$\alpha$] and higher D_n4000, implying lower star formation, in the outskirts of the galaxy, compared to weakly barred and unbarred SF galaxies. This is consistent with the hypothesis that strong bars induce gas inflow from the outskirts to the centre of the galaxy, where it is available to increase star formation (Athanassoula, 1992a; Athanassoula et al., 2013). However, this result is more prominent in the radial profiles expressed in absolute units and less in the ones normalised to the length of the bar. This can be explained by the normalisation that is used: a distance of $2R_{\textrm{bar}}$ extends much farther out into in the disc of the galaxy for a strong bar than for a weak bar, as strong bars are longer than weak bars.

These results show that strong bars have more star formation in their centre and beyond the bar-end, while suppressing star formation in the arms of the bar. These findings are consistent with much of the literature. This suggests heavy gas flows along the arms of a strong bar to the centre and confirms that strong bars have a significant influence on their host. Additionally, these results show that strong bars can facilitate the quenching process, which is in agreement with the results from Géron et al. (2021). However, these observations are not found for weakly barred galaxies, which suggest that they do not affect their host in a significant way. This highlights the importance of bar strength on galaxy evolution and quenching.

The shape of the D_n4000 profiles of strongly barred galaxies are very different to those of weakly and unbarred galaxies, as shown in Figures 4 and 6. This implies that strong bars are long-lived structures, as they have been able to able to influence the average age of the stellar populations. This is particularly evident in the arms of the bar. The median value of D_n4000 for strongly barred SF galaxies in the arms of the bar is $\sim$1.4. This suggests that the mean age of the stellar population in the arms of the bar is $\sim$1 Gyr (Kauffmann et al., 2003; Paulino-Afonso et al., 2020), which is consistent with the results presented in Géron et al. (2023) as well as other studies that show that bars are robust and have a long lifetime (Jogee et al., 2004; Shen & Sellwood, 2004; Debattista et al., 2006; Kraljic et al., 2012; Athanassoula et al., 2013).

However, this was not observed for weakly barred galaxies, whose D_n4000 profiles closely resemble those of unbarred galaxies. This could mean that weak bars are transient and short-lived structures that do not have the time to affect the stellar populations of their host. The simulations of Bournaud & Combes (2002) and Bournaud et al. (2005) found that bars are short-lived and significantly weaken before they are destroyed. The results presented in this paper suggest that this may be applicable to weak bars, but not to strong bars. Alternatively, weak bars might be simply recently formed structures or they lack the ability influence the stellar population of their host in a significant way, even if they were long-lived.

The bar continuum was introduced in Géron et al. (2021), which showed that weak and strong bars are part of a continuum of bar types and that differences between weak and strong bars disappeared when correcting for bar length. The bar continuum suggests that the radial profile of a weak bar should gradually change to that of a strong bar when considering bars of increasing bar strength along this continuum. For example, as the bar becomes stronger, the increase of EW[H$\alpha$] in the centre and the suppression of EW[H$\alpha$] in the arms of the bar should become increasingly more pronounced. This suggests that there are many intermediate radial profiles between the typical weak and strong profiles. This is indeed what is found (see Figures 3 and 4 in particular), as the shaded regions in the radial profiles indicate that there is substantial variability and scatter in these profiles. An alternative possibility is that the probability of observing these features (i.e. the peak of EW[H$\alpha$] in the centre) increases with bar strength. Either scenario can be tested in future work by characterising the diversity of the radial profiles of galaxies of different bar types in more detail.

We investigated the impact of bar kinematics on their host galaxies in terms of star formation in Section 3.2 using EW[H$\alpha$] and D_n4000. Figure 7 shows that slow bars in SF galaxies have significantly higher values of EW[H$\alpha$] in the intermediate radius range of the galaxy ($\sim$2-4 kpc) compared to fast bars in SF galaxies.

This is consistent with the results found in Figure 8, where significantly lower values for D_n4000 were found in the intermediate radius range of SF galaxies with slow bars, compared to fast bars in SF galaxies. This suggests the presence of younger stellar populations due to more recent star formation and implies that slow bars in SF galaxies have significantly more star formation compared to fast bars along the PA of the bar.

This effect is only observed for SF galaxies and not for quenching galaxies. The radial profiles for fast and slow bars in quenching galaxies have similar trends: EW[H$\alpha$] increases with radius, while D_n4000 decreases monotonically with radius. A similar result was found in Géron et al. (2021), who showed that strong bars increase the central star formation for SF galaxies, but not for quenching galaxies. This is presumably because the underlying physical processes that cause the observed differences in star formation are related to the gas distribution of the galaxy. If a feature (e.g. a slow bar) influences the gas distribution in a galaxy, and SF galaxies have more gas than quenching galaxies (Baldry et al., 2006; Dekel & Birnboim, 2006), it is expected that this feature affects SF galaxies more than quenching galaxies.

The impact of bar strength on the results presented above was studied in Figure 9 in SF galaxies using EW[H$\alpha$] and D_n4000. The median value for EW[H$\alpha$] was always higher in slow strong bars than in fast strong bars. The increase of EW[H$\alpha$] beyond the bar-end region, which is characteristic for strong bars, was much more pronounced in slow strong bars compared to fast strong bars, implying that the latter have more star formation there than the former. Additionally, the median EW[H$\alpha$] in the arms of a slow strong bar was also higher than in the arms of a fast strong bar.

The median value for D_n4000 was also consistently lower along slow strong bars compared to fast strong bars. The value for D_n4000 was especially high in the arms of fast strong bars, suggesting that the arms of fast strong bars are more efficient in suppressing star formation than the arms of slow strong bars. However, an Anderson-Darling test reveals that these profiles are not significantly different. The profiles for fast weak and slow weak bars are very similar to each other and are not significantly different.

The biggest limiting factor of this analysis is the sample size. These results hint that a slow bar will increase star formation more if it is also a strong bar. In contrast, the profiles of fast weak and slow weak bars are difficult to distinguish from each other. However, a bigger sample size is needed to verify whether these effects are statistically significant. The sample size is relatively modest due to the need for very robust data to perform the TW method. Although this is the largest sample the TW method has been applied to so far, it only contains 210 galaxies with reliable measurements of $\mathcal{R}$ (see Géron et al. (2023) for more details). Subsequently dividing the sample into different subsamples (SF or quenching, weak or strong, fast or slow) further reduces the sample size in the final comparisons. Increasing the total sample size, by including data from past and future IFU surveys, would greatly help to clarify the impact that bar strength has on the profiles of fast and slow bars.

Even though we have shown that slow bars in SF galaxies have higher EW[H$\alpha$] along the PA of the bar, Figure 10 shows that the global SFR is not significantly different between SF galaxies with slow or fast bars. This apparent contradiction is explained in Figure 11, where we constructed radial profiles with apertures placed parallel and perpendicular to the PA of the bar. The EW[H$\alpha$] between the parallel and perpendicular profiles was only significantly different for slow strong bars in SF galaxies, particularly in the region beyond the bar-end (1.2-1.5 $R_{\rm bar}$). This is also the region where the second peak of EW[H$\alpha$] was typically found in strongly barred SF galaxies in Figure 3, implying that this peak is most prevalent among strong bars in SF galaxies that are also slow. Although not significantly different, the median value of EW[H$\alpha$] for the profile with the parallel aperture is higher than the profile with the perpendicular aperture in the region beyond the bar-end of fast strong and fast weak bars as well. The profiles for the parallel and perpendicular apertures for weak strong bars in SF galaxies were also not significantly different. This implies that the distribution of star formation along the PA of the bar is shaped by whether the bar is fast or slow, despite both fast and slow bars having similar effects on their host in terms of global SFR. This suggests that star formation is more concentrated along the bar for slow bars compared to fast bars. However, as the global SFR remains the same, this also suggests that a slow bar does not change the overall rate of gas consumption of its host. Instead, a slow bar influences its host by changing where gas consumption and star formation take place. As a side note, these results also highlight the importance of using IFUs to study galaxy evolution. The crucial kinematic distinction between fast and slow bars could not have been found using only global properties and photometry.

The results from the previous section suggest that slow bars have more star formation along their bars. But we have not yet looked into a possible physical explanation for this observation. A bar is classified as slow or fast based on its kinematics. Slow bars are shorter than their corotation radius, whereas fast bars end near the corotation radius. As the corotation radius is the radius where the stars in the disc rotate with the same speed as the bar, this implies that the bar-end of fast bars should move with a similar velocity as the stars in the disc. Conversely, the stars in the disc should rotate faster than the bar-end region of slow bars. This is confirmed in the left panel of Figure 12, while the right panel shows that this is also the case for the gas in the disc: the difference in velocity between the bar-end and gas in the disc is much higher for slow bars than for fast bars.

Figure 13 shows a possible interpretation of how these differences in velocity cause changes to the radial profiles of slow bars (left panel) and fast bars (right panel). Because of the greater difference in velocity between the bar-end and disc, a rotating slow bar will come into contact with much more of the gas of its host, compared to a fast bar. This suggests that slow bars possibly trap and concentrate more gas along the bar than fast bars. This increased concentration of gas will increase the observed values of EW[H$\alpha$] along the bar for slow bars. Conversely, the bar-ends of fast bars rotate with a similar velocity to the stars and gas in the disc and will not concentrate as much gas along the bar. This results in lower observed values of EW[H$\alpha$] along the bar for fast bars. We stress that this is one possible interpretation of the results presented in this paper and that more detailed observations of the effect of bar kinematics on the distribution of gas will help to clarify any remaining questions.

This interpretation suggests that slow bars are possibly more efficient at sweeping up gas and creating gas-depleted regions, such as the ones observed by Gavazzi et al. (2015); James & Percival (2018); George et al. (2019); Newnham et al. (2020). Simulations also find such gas-depleted regions. For example, the high-resolution cosmological ‘zoom-in’ simulation of Spinoso et al. (2017) finds a very clear gas-depleted region in a barred galaxy. The bar has a radius of $\sim$1.5 kpc at z = 0.02, at which point the corotation radius is $\sim$3.5 kpc, so that $\mathcal{R}$ $\approx$ 2.3. Therefore, the bar that created the obvious gas-depleted region is a slow bar. Similarly, the self-consistent simulations of Milky Way-sized isolated disc galaxies in Seo et al. (2019) also show clear gas-depleted region in barred galaxies. The bars all start out as fast, but quickly become slow. However, as explained in Géron et al. (2023), simulations tend to overestimate the observed values for $\mathcal{R}$, which implies that studying the effect that slow and fast bars have on the gas-depleted regions using simulations might not be robust. It would be better to study this observationally instead. This could be done with resolved gas observations of multiple slow and fast bars in galaxies, verifying whether the gas-depleted region is more pronounced in slow bars than in fast bars.

However, as noted in the previous section and shown in Figures 10 and 11, slow and fast bars have similar global SFRs, despite the differences observed along the bar. This suggests that the total star formation efficiency of the galaxies remains the same. Even though a slow bar is likely to be more efficient at sweeping up and concentrating gas in the bar region compared to a fast bar, an additional element must be acting to counteract the expected increase in star formation efficiency that a higher gas concentration implies. A likely candidate is the increased velocity dispersion or shear that is commonly associated with strong gas flows in the arms of the bar (Athanassoula, 1992a; Reynaud & Downes, 1998; Sheth et al., 2000; Zurita et al., 2004; Haywood et al., 2016; Khoperskov et al., 2018). As Figure 9 shows, the arms of the bar are where the most significant differences are observed between fast and slow bars, especially if the bar is strong as well. Thus, while slow bars increase the concentration of gas in the bar, the global SFR does not increase due to the high amounts of shear in the arms of the bar. These opposing effects result in a global SFR in slow bars that is similar to that of fast bars. In other words, because of these effects, the kinematics of the bar do not affect global SFR, but dictate where star formation occurs.

The idea of fast and slow bars works conceptually well with the continuous nature of bar types, given that $\mathcal{R}$, which is used to classify bars into slow or fast, is a continuous variable. Futhermore, $\mathcal{R}$ is defined as the ratio of the corotation radius to the bar radius, both of which are known to change over time. This implies that $\mathcal{R}$ can vary over time as well and that bars can become ‘slower’ or ‘faster’. This is similar to the classification of bars into strong and weak, based on $p_{\rm strong}$. This parameter can also change over time, so that bars can become stronger or weaker. However, the classification of bars into weak or strong, and the bar continuum presented in Géron et al. (2021), are based on visual morphology. In contrast, the classification of bars as fast and slow is based on the kinematics of the bar. This suggests that a potential second - kinematic - axis should be added to the bar continuum, which would accurately reflect that the kinematics of the bar has an important role in galaxy evolution as well.

A visualisation of the distribution of galaxies in the TW sample on such a two-dimensional plane is shown in Figure 14, where $\mathcal{R}$ is plotted against the normalised strong bar vote fraction ($\tilde{p}_{\textrm{strong bar}}$) from GZ DESI. The normalised strong bar vote fraction is defined as follows:

where $p_{\textrm{strong bar}}$ is the strong bar vote fraction from GZ DESI and $p_{\textrm{weak bar}}$ the weak bar fraction fraction from GZ DESI (see Section 2.1 for more detailed information about Galaxy Zoo). This is done to eliminate the dependence of the unbarred vote fraction ($p_{\textrm{no bar}}$) and implies that all strong bars have $\tilde{p}_{\textrm{strong bar}}>0.5$ and all weak bars have $\tilde{p}_{\textrm{strong bar}}<0.5$.

This plane has four separate quadrants: one for galaxies with slow weak bars, fast weak bars, fast strong bars and slow strong bars. The characteristic radial profile of EW[H$\alpha$] of SF galaxies in each quadrant (as calculated in Figure 9) is shown in the corresponding insets. It is clear from this figure that there are barred galaxies in every quadrant. This means that a classification based on bar strength does not preclude any classification based on kinematics. In order words, a strong bar can still be either fast or slow. This also suggests that both the kinematic and photometric information are needed in order to fully characterise a barred galaxy.

The results in this paper suggest that barred galaxies on the right side of the plot (strong bars, $\tilde{p}_{\textrm{strong bar}}>0.5$) will increase the star formation in the centre of the bar and beyond the bar-end, while suppressing star formation along the arms of the bar. This is in contrast to barred galaxies on the left side of the plot (weak bars, $\tilde{p}_{\textrm{strong bar}}<0.5$), which do not seem to significantly influence star formation in their hosts. Additionally, barred galaxies in the upper half of the plot (slow bars, $\mathcal{R}>1.4$) will concentrate their star formation more along their barred regions and sweep up gas more efficiently, compared to barred galaxies in the bottom half of this plot (fast bars, $\mathcal{R}<1.4$). Therefore, bars in the upper-right quadrant of Figure 14, i.e. slow strong bars, will affect their hosts the most.