Differences in star formation activity between tidally triggered and isolated bars: a case study of NGC 4303 and NGC 3627

We first present the general morphological features of our two models for bar formation. Figure 2 shows a face-on view of the stellar and gas populations with the disc plane set onto the $xy$-plane for both the IsoB and TideB cases. The colour weighting is held constant over both cases. In this figure, the top row of each case corresponds to the stellar component and the second row to the gas component. The columns correspond to steps of 100 Myr, commencing one period immediately preceding a clearly identifiable bar forming. Both cases produce an essentially two-armed structure with a central bar, although there are obvious visual differences within this general morphology.

The IsoB case, which formed a bar through some initial disc instability, seems to evolve from a more flocculent type galaxy into a two-armed structure as the bar grows. Conversely, the TideB case is strongly affected by the interaction occurring at approximately 100 Myr (closest approach $\sim 94$ Myr), producing clear, crisp two-arm features. These features however, are significantly impacted by gravitational effects, both from the inner disc and the external companion, constantly strengthening and decoupling over the period of interest. As the simulation evolves, the bar forms and the disc stabilises. Due to the decoupling of the arms in the tidally driven case the bar length intermittently appears to extend. This may also affect an assessment of bar orientation.

Additionally, it is possible to see that the tidally driven case produces a pronounced bar feature significantly faster than the isolated disc. For convenience, we present all subsequent results in terms of a shifted time scale ($t^{\prime}$), relative to the bar formation time (rounded to the nearest 100 Myr) such that $t^{\prime}=0$ at the approximate period of distinct bar formation. This revised time of $t^{\prime}=0$ corresponds to the $t=400$ Myr snapshot of IsoB and the $t=200$ Myr snapshot for TideB which can be seen in Figure 2. At a given evolutionary period (within each column of Figure 2) when the bar is well developed, the large-scale structural features of each case do not appear substantially different. The bar lengths and strength appear visually similar within each disc. The number and prominence of the arms, as well as their pitch angles, are also similar.

Figure 3 shows the stellar surface density profile for each case, both along the bar (major axis) and perpendicular to it (minor axis). Each model exhibits very similar profiles both parallel and perpendicular to the bar orientation. Stellar surface densities within the central region clearly decrease exponentially and in a manner which is noticeably steeper than the surrounding regions that are solely composed of the non-barred portion of the disc. This sharply exponential shape is noticeably prevalent in a much narrower section of the bar minor axis as would be expected from the elliptical shape of the bar morphology that can be seen in Figure 2.

Both cases can be categorically described as hosting very similar bars of exponential (late) type, rather than the alternative flat (early) type (Elmegreen & Elmegreen, 1985). Both NGC 4303 and NGC 3627 have been determined to have later type Hubble classifications (de Vaucouleurs et al., 1991). Hence, this is in line with expectations for the target galaxies as well as the exponential disc profile used to produce the initial simulation conditions. It may thus be naively expected that these two bars should generally impact the disc structure in a similar manner.

Non-axisymmetric morphological features are known to act as perturbations to the galactic velocity field (e.g. de Blok et al. 2008). The two target systems in particular are known to show clear non-circular motions, both from moment maps and undulations in the rotation curves (Law et al., 2018; Schinnerer et al., 2002).

As a first order metric of the non-circular velocities in these discs, we show the azimuthal and radial streaming motions of the gas component in a face-on projection in Figure 4 (also see Appendix A for the evolution of the rotation curves). The top two rows show the IsoB disc velocity features evolving with time, and the bottom two rows show the TideB disc. A significant difference between the two cases is immediately obvious. It is clear that the tidal forces in the interacting case increase the overall degree of non-axisymmetric motion in the TideB disc. Both velocity components show clear asymmetries that are strongest during closest approach ($t^{\prime}=-100$ Myr) which are especially clear in the outer disc whereas the isolated case is relatively unperturbed outside the bar region. These asymmetries correspond with a migration of the system centre of mass, which has been corrected for in Figure 4. While these strong outer asymmetries in TideB do decay over time as the companion moves away, they remain many times larger than those in the isolated disc. The azimuthal response between the two arms of TideB is also asymmetric, with the northern (southern) arm appearing to rotate somewhat faster (slower) than the disc average, which will result in asysmmetries in galactic shear experienced by gas in each arm region. Only the central regions of the IsoB case seem to show similarly high non-circular velocities which are comparable to the values that fill the entire disc regions of the post-interaction TideB results.

A clear central quadrupole velocity signature is evident in the central region of the radial velocity plots for both discs beyond $t^{\prime}\geq 0$ Myr. This feature is indicative of a bar being present in the inner disc, as material streams radially to follow elliptical orbits aligned with the bar (e.g. Bovy et al. 2019). The bar kinematics appear strikingly similar between the two models, also showing clear similarities in the azimuthal motion (lower $V_{t}$ along the bar axis, with two “lobes" of high $V_{t}$ perpendicular to the bar axis in the galactic centre, see also Renaud et al. 2015). The extent of the quadrupole-like region acts a good visual approximation of the bar extent. It can be seen that the radial size of the bar remains relatively constant once it forms. By qualitatively defining the bar region (as outlined in Section 4.2), it was determined that this approximation of the bar extent from the velocity quadrupole was consistent with the values determined from a Fourier method and that the bar extent does indeed remain generally constant once it stabilises over the period of $t^{\prime}=200$ Myr, although the expected bar shortening does become more significant over much longer time-scales. This is also consistent with the assumptions drawn from Figure 2, despite the clearly strong differences in the magnitude of non-axisymmetric velocities between the two cases.

One particular point of comparison between the two models is how the velocity features propagate radially. In the IsoB case the positive or negative radial motion traces a single feature from the galactic centre to the outer disc, following from the quadrupole to along the arms and outwards. In the TideB case the feature is not so continuous, with the quadrupole radial velocity features being engulfed by the strong radial motions exhibited by the tidal arms. Such a signature is evidence of the rapid decoupling between the tidal arms and inner bar of the TideB model. Bar and spiral decoupling is a known phenomena in isolated discs (e.g. Sellwood & Sparke 1988; Baba 2015) but has not been discussed in the context of tidal interactions where arms are driven by an external agent. We will revisit this topic in Section 5.

We begin by formally constraining the morphology of active star forming regions in the two cases as a measure of the number of new stars formed in a given time period ($\Delta t_{\rm SF}$):

Here, star formation rate (SFR) can be calculated at the current time ($t_{i}$) by summing new stellar mass ($M_{*}$) in the star forming period ($\Delta t_{\rm SF}$).This rate is then converted to a surface star formation rate ($\Sigma_{\rm SFR}$) in order to be more comparable to the quantities measured in observations by binning over a 0.1 $\times$ 0.1 kpc grid. The look-back time for star formation is the age range $\Delta t_{\rm SF}=10$ Myr which is comparable to the star forming time-scale determined observationally for NGC 4303 (Koda & Sofue, 2006; Egusa et al., 2009). A projection of this $\Sigma_{\rm SFR}$ is shown in Figure 5. This figure is similarly set into the $xy$- disc plane with columns advancing in time for the same time period as the previous projections of the stellar, gas and velocity features (see Figures 2, 4).

From Figure 5 it is possible to assess the location of current (or very recent) star formation, as well as the intensity of such formation. For example, the centre-most region in all the barred snapshots ($t^{\prime}\geq 0$ Myr) for both cases is dominated by an almost circular, bulge-centred region with the highest star formation rate. This circular region expands as the bar evolves in both cases, a likely by-product of gas inflow to this central circumnuclear disc. However, while it is approximately the same size in both cases in the $t^{\prime}=100$ Myr snapshot, by $t^{\prime}=200$ Myr the circular region in the TideB case has become significantly larger than the IsoB case, showing the TideB case has a less concentrated but no less intense region of star formation at the centre. This central nuclear disc of star formation is commonly seen in barred systems, where it is fueled by the inflow of gas from the torques present in the bar region (Athanassoula, 1992; Wang et al., 2012; Cole et al., 2014; Baba & Kawata, 2020). Interactions are also known to be drivers of enhanced star formation (e.g. Patton et al. 2013; Pan et al. 2019), with the interaction event itself driving inflows that help fuel central star formation (Torrey et al., 2012; Pettitt et al., 2016). As such, the combined effect of the bar evolution and the interaction provides an increase in fueling of the central nuclear disc in TideB, and the larger central star forming region.

The bar is also a clear feature in these SFE maps, with pockets of intense star formation flaring along the bar and in clumps along the spiral arms. However, star formation for the tidally driven bar appears to be predominantly contained within the bar and arm features in all barred time periods ($t^{\prime}>0$). In contrast, each of the IsoB maps in Figure 5 show wide areas of strong star formation throughout the disc which cannot be clearly associated with either the bar or any obvious arm feature. This seems to indicate the isolated IsoB case has a greater amount of inter-arm star formation, whereas the tidally driven case concentrates gas more strongly into the arms and core, limiting star formation outside of these areas.

Considering time dependent features, the shape of the SFR projection in the bar region changes in both cases dramatically over a relatively short time-scale ($\Delta t^{\prime}\approx 200$ Myr). Figure 5 shows distinctly different star forming structures within the bar region, and that the evolution process of this structure can be seen to differ between the two cases. For example, in the $t^{\prime}=200$ Myr snapshot of the IsoB case, very clear arms comprised of star forming regions can be seen to be somewhat disconnected from a dense, almost triangular central region within the bar. Comparatively, in the same snapshot for the TideB case, the central region is also clumpy but is mostly connected to the arms along a straight central axis of star formation that spans the full bar length. This axis is accompanied by a curved envelope of similarly intense star formation encasing the central axis from both above and below, which seemingly connects each arm to the other. Additionally, the bar in the TideB model at $t^{\prime}=100$ Myr shows a wide, long clump along the bar axis in the centre which tapers off toward the middle of the bar, before once again intensifying into a thicker bar at the end just before the arms connect. This is dissimilar to any of the other snapshots for either case. These star forming structures vary broadly, even between evolutionary periods in a single simulated case which make it difficult to produce any sweeping, general statements to describe definitive features. However, this difficulty itself supports the range of observations that indicate star formation within galaxies seems to be consistently inconsistent.

To consider more specifically the time evolution of star formation in the simulations, we take the disc-averaged star formation history for the two simulations up to $t^{\prime}=200$ Myr and present Figure 6. The axis in this figure is set in the original simulation time, and for each case a vertical line denotes $t^{\prime}=0$. The solid blue line is the star formation history for the isolated IsoB case, whereas the orange dotted line indicates the history of the tidally driven case. The time of closest approach for the companion in this case is at approximately 94 Myr.

It is apparent that both cases seem to show relatively similar star formation rates. There are also some similarities in the shape of the star formation profile as it evolves. For example, there is evidence of an extended rise in star formation at around the time the bar forms in both cases (indicated by the vertical dotted lines). The relative shape (height and duration) of this increase in both cases appears to be similar: IsoB $\sim\Delta\mbox{\rm SFR}=3.08$ M_⊙ yr^-1, $\Delta t=145$ Myr; TideB $\sim\Delta\mbox{\rm SFR}=3.79$ M_⊙ yr^-1, $\Delta t=127$ Myr. The first obvious difference between the two cases is in the earlier stages of evolution (pre-bar formation $t^{\prime}\leq 0$ Myr). While the IsoB case seems to have a relatively constant level of star formation before the bar forms (after the initial boost on start-up), the TideB case has an additional, earlier period with an extended rise and fall of star formation intensity which is similar to the boost feature previously linked to the bar formation. This occurs just after the closest approach of the companion. Although this early boost is smaller in amplitude than the bar effect, it appears to last for a similar duration before returning to what seems to be the original baseline rate just before the advent of the bar formation, where it steeply rises again. This can be considered to be a double peaked trend of star formation history and is likely attributable to a starburst triggered by the interaction. As the bar has not yet formed and the density and SFR projections both show the two arm features are dominant in that period, a logical assumption would be for this boost to be mostly limited to increased star formation in the strong tidally induced arms, rather than within the central region which later becomes the bar. The magnitude of the bar-triggered boost in SFR is similar for both the isolated and perturbed disc (79% and 66% respectively), while the interaction triggered burst is milder at 31%.

To study the morphological dependence of these star formation features in more depth, three key morphological regions are defined to be the bar, arm and inter-arm components. Using Fourier decomposition, it was possible to identify analytically relevant traits of the bar and arm components. The inter-arm region could then be defined as neither bar nor arm within a certain radius of interest. The extent of the bar region was determined from the amplitude of the Fourier $|A_{2}|$ mode. Identifying the radial extent of features in this mode allowed for the bar component to be defined with a simple radial criterion to form a central circular region encasing the full bar length.

As mentioned previously, it was found that the bar extent was relatively constant throughout the considered duration, decreasing only a small fraction by $t^{\prime}=200$ Myr. Hence, a single value was adopted for the bar extent for the following analysis (IsoB: $R_{\rm bar}=2.10$ kpc; TideB: $R_{\rm bar}=3.12$ kpc). From the population outside of this $R_{\rm bar}$, the arm component was defined by fitting a log spiral of the form $r=a\exp{b\theta}$ with a standard width of $\pm 1$ kpc to the peaks of the polar angle $\theta$ set to lie in the disc plane at a given radius. The inter-arm region was correspondingly defined as the remainder within a set radius of 10 kpc determined to contain the majority of significant disc features for both cases.

In Figure 7, a similar star formation history is plotted to Figure 6, however, this is a measure of the fractional contribution from each region (bar, arm and inter-arm) to the total number of young stars produced, shown over the simulation time. These specific regions were defined and analysed at every 10 Myr, with a look-back time consistent with the previous star formation analysis ($\Delta t_{\rm SF}=10$ Myr). The blue line with crosses at each calculation point denotes the contribution from the defined bar region; the filled-in red circles indicate the contribution from within the arm regions; and finally, the open circles in magenta show the inter-arm contribution. The axis is set in the $t^{\prime}$ scheme with a vertical line at $t^{\prime}=0$ to indicate the approximate time of bar formation.

In both cases, it is possible to see how star formation in the bar region climbs steadily as the bar is formed and that the inter-arm region contributes the least for the majority of times analysed. For the IsoB case, this inter-arm contribution is consistently $\sim 10\%$ of the total stellar mass formed and the fraction is even lower in the TideB case ($\sim 5\%$ or less once the bar has formed). This is also a representation of the way that the star formation seems to be more cleanly located in the apparent bar and arm features in the TideB case, particularly as seen in Figure 5. Considering the contributions from both bar and arm components however, there are a number of very noticeable differences between the two cases. For example, for times when $t^{\prime}\leq 0$ Myr, it can be seen that the arms in the TideB case show a very different development of the fraction of stars produced. In the IsoB case, the fraction of star formation over the disc features seems to be initially similar for the first $\sim 50$ Myr ($t^{\prime}\leq-50$ Myr), before becoming increasingly centrally dominated as the bar forms ($\sim t^{\prime}=0$ Myr). Contrastingly, the highest period of intensity for star formation in the TideB arms is very noticeably within $\pm\,50$ Myr either side of the bar formation time ($-50\leq t^{\prime}\leq 50$ Myr). This corresponds to the time in Figure 6 where the smaller peak of star formation can be seen after closest approach and before the bar has completely formed. Compared to the IsoB case, which has a steady baseline level of star formation at that time, the interaction has clearly driven a burst of star formation which is predominantly located in the arms. At later times in Figure 7 ($\sim t^{\prime}>50$ Myr), a potential periodicity also appears in the contribution from the bar region of the IsoB case which is not reflected in the bar of the TideB case. The TideB case at this time shows a much smoother profile. While overall star formation history may appear relatively indistinguishable once the bar has formed, a number of significant differences seem to exist when considering instead the contribution to the overall SFR from region to region.

The radial dependence of SFE across the disc of each case is shown in Figure 10. Each radial bin is defined with a width of $\Delta R=1$ kpc and the SFR and gas mass averaged over each annuli to calculate the SFE value in each bin. This is determined every 10 Myr for each case over the barred period ($t^{\prime}>0$ Myr) with consistent star formation look-back time ($\Delta t_{\rm SF}=10$ Myr). Saturation indicates time evolution with colour from dark to light corresponding to increasing $t^{\prime}$. Additionally, the bin which would coincide with the bar end is shaded in grey.

Naturally, the centre-most bin shows the highest result at all times for both cases of bar formation. This is in line with the noticeably high star forming central region, or nucleus, which was identified in previous sections (see Figure 5, 8, 9). Within each bin, there does not appear to be any immediately obvious or consistent trend as the SFE varies with time in either case. It neither continuously grows, declines, nor oscillates in any discernible pattern. In considering the broader trend as SFE changes with radius across all bins, there does appear to be a certain difference between the two cases. Outside of the central bin, the average level of SFE in the disc appears to be mostly constant in the IsoB case, whereas the TideB case shows more of an increasing or sinusoidal shape with radius; showing lower SFE towards the centre ($\sim R_{\rm bar}\pm 2$ kpc) and higher SFE towards the outer edge. This may be evidence that the interaction has caused the inner regions to suffer a depletion of gas compared to the relatively more stable conditions in outer disc. However, these broad trends are not necessarily true at all times, as the inner deficit is clearly not prevalent in the first 3-4 periods ($\sim t^{\prime}<80$ Myr).

To further understand any trends in this evolution of the radial dependence of star formation efficiency, we consider the change of the gradient in Figure 10 with time for each case. To determine this gradient a linear least-squares fit was applied for all histogram bins excluding the centre-most bin defining $R<1$ kpc. The resulting first coefficient of this fit is plotted in Figure 11 showing the gradient change with time. A positive result indicates the SFE increases overall with radius and, conversely, a negative result shows a decreasing SFE with radius. In this figure blue squares correspond to the calculated IsoB gradients, whereas TideB is denoted by orange triangles. It is clear that there is significant variation in the SFE dependence with radius over the evolution time for both cases. During the first 50-100 Myr after bar formation, the trend for each case appears similar: a steep negative gradient steadily begins to flatten and oscillate around zero, indicating average SFE across the disc is generally constant at that time. However, while the isolated case seems to remain mostly within $\pm 1$ Myr^-1kpc^-1 of zero, the TideB results continue to climb, transitioning through zero to develop a clearly positive gradient for the duration of the second 100 Myr and thus a decreasing depletion time increasing with radius. In the last 50 Myr of the period considered, the TideB gradient does reduce to values possibly comparable to the steepest positive extent of the isolated case.There is one period of the IsoB case in later times which seems noticeably inconsistent with the other values. At $t^{\prime}=160$ Myr the gradient is almost the steepest negative result of both cases after bar formation. It is unclear from this analysis what kind of event caused such a strongly declining profile of SFE just for this brief time. However, it can be seen clearly in Figure 13 that there is a uncommonly high value of SFE across the length of the bar for this particular time period ($t^{\prime}=160$ Myr). Although, this is simply an illustration of the mathematical cause for such a strongly declining trend and does not necessarily explain the physical origin. More discussion of the spatial and temporal variations of bar SFE is included in the following section.

In the context of observational studies, the results in Figure 10 and Figure 11 are generally consistent with observed SFE trends in galaxies, however the TideB response is somewhat significant. Leroy et al. (2008) measure the radial changes of SFE in the THINGS dataset (Walter et al., 2008) and observe that most systems show that SFE in most galaxies tends to either maintain a constant value or decay with increasing radius. Some systems however, such as NGC 5194 (M51) and NGC3627 (the observational target for TideB), do conversely display localised regions with increasing SFE with radius in the disc (Leroy et al., 2008). This result is confirmed by Muraoka et al. (2019) with the COMING (Sorai et al., 2019) observational survey data showing that, while NGC3627 appears to have a generally constant SFE across the radii measured, there is clearly a slightly increasing trend at outer radii. M51 was not included in Muraoka et al. (2019) but the isolated target (NGC4303) was. Comparatively, NGC4303 shows a more consistently flat profile with smaller scale radial fluctuations in SFE across the disc (Muraoka et al., 2019). This observed SFE behaviour for NGC4303 is indeed similar to the IsoB result reflected in Figure 11 which is primarily constant with only slight variation in both directions over time. M51 is a clearly interacting galaxy (Leroy et al., 2008; Buta, 2019; Colbert et al., 2004; Karachentsev et al., 2013); NGC3627 was specifically chosen for this study due to the possibility of an interaction rich history; and, the TideB response can also be seen to decay on a time-scale similar to the interaction time-scale. This may suggest that the characteristic of a positive SFE gradient toward outer radii is indicative of an ongoing, or at least recent, interaction. If this is the case, it would mean that an increasing SFE with radius may be used as a possible metric of tidally driven disc features. The relatively constant or negative gradients—which dominate the IsoB result and other times of TideB—can then also be considered compatible with more commonly observed trends, as instances where this may be observed for either IsoB or TideB over the duration of the simulation would indeed make it most common.

To specifically highlight changes within the bar, Figure 12 shows a similar histogram representation of SFE to Figure 10 this time binned along the bar axis. Many studies have shown that SFE in barred-spiral galaxies is lower in the bar than the associated arm features (Momose et al., 2010; Hirota et al., 2014; Yajima et al., 2019), and in some cases that SFE even varies across the length of the bar (Downes et al., 1996; Sheth et al., 2002; Muraoka et al., 2019). For the target galaxy NGC 3627 specifically, it appears that there is unexpectedly higher SFE at the bar ends and centre than elsewhere (Watanabe et al., 2011; Law et al., 2018). Additionally, this work has shown in the previous sections that there are discernible differences in the shape of features within the bar region which can be seen in projections $\Sigma_{\rm SFR}$ across the disc (see Figure 5).

We define a bar axis and calculate the specific SFE in a polygon cut-out running parallel to this axis with a width of 2 kpc. We consider the bar to be a solid body rotating about the major axis, as bar slow-down tends to occur on much longer time-scales than investigated here (Miwa & Noguchi, 1998; Debattista & Sellwood, 2000; Kormendy, 2013). The bar orientation is determined by identifying density peaks in the stellar population within the bar radius. The orientation of the bar axis is then used to transform all the simulated positional information to a co-rotating co-ordinate system wherein the bar lies along the $x-$axis. Additionally, the bar length varies between the two cases so, in order to produce comparable bin limits, the total bar length was divided into a set number of bins which would correspond to a fraction of the whole bar. These are labelled as dimensionless fractional bar elements ($\delta_{b}$) and numbered outwards from the centre-most bin to the calculated bar extent, plus two extra bins to encompass the bar end regions. While this indicates that the physical size of bins is different for each result, this difference is sufficiently negligible to the effect of scale on SFE results in this case. As in Figure 10, the star formation time is $\Delta t_{\rm SF}=10$ Myr and the time evolution is mapped by coloured bars corresponding to time steps of 20 Myr evolving from dark to light. Similarly, the bin coinciding with the bar end is shaded in grey.

Along the bar, we are looking to assess two key features: symmetry about $x=0$ to consider whether star formation is symmetrical along the bar; and whether there is any noticeable trend in the SFE($x$) profile such as significant peaks or troughs in SFE at key regions (i.e. at the bar ends). Interestingly, in both cases the SFE profile along the bar does not seem particularly symmetrical at any of the time periods shown in Figure 12. However, neither does it seem consistently asymmetric or skewed to one particular direction at all times for either case.

Within each bin, there is also no standard trend of SFE changing with time, similar to the radial dependence. There is, however, noticeable evolution in the shape of the bar-wide trends in both cases. In the case of IsoB, at earlier times the SFE seems to decrease steeply toward the bar ends ($t^{\prime}<100$ Myr). In the period after $t^{\prime}=100$ Myr, the SFE values for each bin appear variable along the bar axis in the small scale but are generally constant on average. Comparatively, the TideB result also seems to predominantly show SFE decreasing steeply towards the bar end for the earliest times. After $t^{\prime}\sim 60$ Myr, however, the SFE appears to drop in the middle bar ($2\delta_{\mathrm{b}}\lesssim|x|\lesssim 5\delta_{\mathrm{b}}$) before rising again towards the bar edges. This is consistent with the previous section where a significant change in the SFE gradient with radius of the TideB case was observed at almost exactly this time period, showing lower SFE in the inner region of the disc compared to outer radii.

To further quantify this variation of SFE along the bar, we re-orient Figure 12 as a heat-map of the SFE along the bar axis in Figure 13. In this figure, the SFE values for each time are smoothed by fitting a spline interpolant and then plotted along a strip of bar axis values in kpc for each case. Time evolution is defined as downward along the $y$-axis and the calculated result for each 10 Myr. While no obvious trend appears outside the peak of the centre-most nucleus in the IsoB case, the bar in the TideB case quickly evolves to show strong SFE at the bar ends (delineated by white vertical dashed lines) and low SFE at approximately half the bar radius, alongside the expected high peak in the central region. The IsoB case does show a similar SFE deficiency at some time periods but this appears more serendipitous as a part of random variation which fluctuates along the entire length of the bar. From this figure, it is also evident that there is some variation in the intensity of SFE in the central region with time. This trend is similar between the two cases, appearing suddenly and showing brightest in the early period of the bar before decreasing slightly but steadily as the bars evolve.