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A&A
Volume 698, May 2025
Article Number A5
Number of page(s) 18
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202453367
Published online 28 May 2025

© The Authors 2025

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

Studies suggest that present-day disc galaxies evolved in a two-phase scenario (e.g. Cook et al. 2010; Oser et al. 2010; Kraljic et al. 2012; Driver et al. 2013). At first, with a high incidence of mergers and interactions in the early Universe, the evolution of galaxies was led by external early events (e.g. Schreiber et al. 2006; Law et al. 2009; Dekel & Ceverino 2009). This is reflected in characteristic turbulent morphologies and built dispersion-dominated structures. Later, with the expansion of the Universe, the rate of interactions and mergers decreased, and at the same time galaxies assembled their masses. With that, they managed to dynamically settle into discs and internal processes took place, which is often referred to as secular evolution (e.g. Kormendy & Kennicutt 2004). It is not clear, however, when discs settled in the Universe and when this transition occurred, a necessary benchmark for cosmological models.

To investigate when discs arose in the history of the Universe, we can analyse the morphology of galaxies at different redshifts. With the inauguration of the ALMA facilities, it became possible to probe the interstellar medium (ISM) at higher redshifts, revealing cold rotationally supported discs up to z≈6 (e.g. Smit et al. 2018; Neeleman et al. 2020; Rizzo et al. 2020; Lelli et al. 2021; Posses et al. 2023). More recently, James Webb Space Telescope (JWST) observations are finding that galaxies with exponential profiles, characteristic of disc galaxies, have existed at least since z≈8, when the Universe was younger than 1 Gyr old (e.g. Ferreira et al. 2022, 2023; Nelson et al. 2022; Jacobs et al. 2023). Nevertheless, Wang et al. (2024) demonstrated that galaxies can be photometrically flat with an exponential light profile and still be supported by random motion. Even though there is mounting evidence of the existence of discs at higher redshifts, the internal dynamics of these discs are still under debate. While some studies find that these discs are usually turbulent and thick (e.g. Elmegreen & Elmegreen 2006; Cresci et al. 2009; Newman et al. 2013), other works find observational evidence for cold discs already at high redshifts (e.g. Rizzo et al. 2020; Lelli et al. 2023). Therefore, despite significant leaps forward over the last few years, the issue of when and how galactic discs settled in the Universe remains one of the most pressing questions in galaxy formation and evolution.

Theoretical works have proposed that bars form when the disc of its host galaxy is dynamically mature, that is, self-gravitating with differential rotation, and rotationally supported with relatively low-velocity dispersion (e.g. Toomre 1963; Hohl 1971; Ostriker & Peebles 1973; Combes & Sanders 1981; Gerin et al. 1990; Combes & Elmegreen 1993; Athanassoula 2002; Kraljic et al. 2012; Fragkoudi et al. 2024). Therefore, the formation of a bar within its host galaxy will, in general, coincide or follow shortly after the formation of its dynamically cold stellar disc. Using cosmological zoom-in simulations, Kraljic et al. (2012) found that the bar formation takes place coincidentally with the disc maturing, specifically when the thin disc forms, at least partially. Additionally, Fragkoudi et al. (2024) find that an important factor for a galaxy to form a bar is when and if it becomes disc-dominated compared to the dark matter halo. Recently, Ghosh et al. (2023) demonstrated that bars can be formed in galaxies with both thin and thick discs. However, in the absence of a thin disc and with the thick disc presenting a large scale length and/or scale height, the bar formation is suppressed. This is in agreement with findings for the Milky Way as well, whose thin disc formed around 8 Gyr ago (e.g. Haywood et al. 2013; Conroy et al. 2022), coincident with the proposed time of bar formation of 7−8 Gyr ago (e.g. Wylie et al. 2022; Sanders et al. 2022; Merrow et al. 2024, but see e.g. Nepal et al. 2024 and references within where young ages for the Milky Way bar are proposed).

Many studies have tried to understand when bars appeared first in the Universe (e.g. Tsukui et al. 2024; Amvrosiadis et al. 2025). Looking back in time, different works measured the fraction of barred galaxies at different redshifts (e.g. Eskridge et al. 2000; Marinova & Jogee 2007; Menéndez-Delmestre et al. 2007; Sheth et al. 2008; Masters et al. 2011; Simmons et al. 2014; Melvin et al. 2014; Le Conte et al. 2024; Guo et al. 2024; Espejo Salcedo et al. 2025). These studies find, for the local Universe, fractions varying between 30%−70%, depending on whether they include weak bars as well. These fractions decrease at higher redshifts, as shown by recent studies using JWST data: Le Conte et al. (2024) found bar fractions of ∼14% at z∼2−3, Guo et al. (2024) found ∼2.4−6.4% at z∼3−4, and Espejo Salcedo et al. (2025) found lower fractions of ∼3% at z∼2−3. However, how much of this decrease is real is still under debate. That is because observational limitations such as spatial resolution, sensitivity, and rest frame wavelength play an important role at higher redshifts. In this context, Le Conte et al. (2024) compared bar fractions based on HST and JWST observations for the same sample, finding a difference factor of ∼2. Additionally, cosmological simulations tend to give differing predictions on the fraction of bars across redshifts, with some simulations finding decreasing bar fractions (e.g. Kraljic et al. 2012; Fragkoudi et al. 2020, 2024), while others find increasing bar fractions at higher redshifts (e.g. Rosas-Guevara et al. 2020).

Another approach to understanding when bars appeared in the Universe is from galactic archaeology (i.e. measuring how old bars are in nearby galaxies). Until recently, however, we lacked a broadly applicable methodology to time bar formation in nearby galaxies, and we mostly had single-galaxy studies. Timing when bars are dynamically formed is not trivial and has been a challenge. This is because bars trap stars from the galactic disc, so the stars that compose the bar can be older than the bar itself. Instead, one can use bar-built nuclear structures, whose oldest stellar population will reflect the time of bar formation (e.g. Gadotti et al. 2015). Theoretical works find that nuclear discs (also known as pseudo-bulges or disc bulges) form shortly after bar formation, at ∼108 yr (e.g. Athanassoula 1992a, b; Lin et al. 2013; Emsellem et al. 2015; Fragkoudi et al. 2016; Seo et al. 2019; Baba & Kawata 2020; Verwilghen et al. 2024). Once the bar forms, it induces shocks in the gas in the host galaxy disc, which thus loses angular momentum and funnels towards the centre of the galaxy, forming the nuclear disc. Therefore, one can use the moment of formation of the nuclear disc to indicate the formation of the bar. In de Sá-Freitas et al. (2023a), we present the first broadly applicable methodology to measure bar ages in the nearby Universe, in a pilot study in which we measure the age of the bar in NGC 1433 as 7 . 5 − 1.1 + 1.6 Gyr $ 7.5^{+1.6}_{-1.1}\,{\textrm {Gyr}} $. For this work, we applied the same methodology to a larger sample of 18 galaxies from the Time Inference with MUSE in Extragalactic Rings (TIMER; Gadotti et al. 2019) project, deriving important insights into bar ageing and secular evolution for the first time from an observational perspective.

This paper is organised as follows. In Sect. 2 we describe the properties of the TIMER sample and the observational data. In Sect. 3 we briefly describe the methodology presented in de Sá-Freitas et al. (2023a) and the modifications adopted in this work. In Sect. 4 we present the derived bar ages. Finally, in Sect. 5 we discuss, for the first time, the implications of our results, on disc settling, the bar fraction over time, bar formation in the downsizing context, multiple-barred systems, and bar-related secular evolution from an observational point of view.

2. Sample and data description

Constraining bar ages for a large sample was not possible until recently with the methodology and pilot case presented in de Sá-Freitas et al. (2023a). To apply the methodology presented in de Sá-Freitas et al. (2023a) to more galaxies, we need high spatial resolution integral-field spectroscopy from the central part of the galaxies, that is, from the region where the bar-built nuclear disc dominates. The TIMER survey (Gadotti et al. 2019) was specially designed with these characteristics and these goals. In this work, we apply our methodology to the TIMER sample to better understand when bars formed in nearby galaxies.

TIMER is a high-quality data survey of the central region of 24 nearby galaxies observed using the MUSE-VLT instrument – from which 21 were observed. The main goals of the survey include i) estimating the cosmic epoch in which disc galaxies settled, hence forming the bar; and ii) test if the downsizing scenario applies to the formation of bars (see discussion in, e.g. Sheth et al. 2012). The sample was selected from the Spitzer Survey of Stellar Structure in Galaxies (S4G – Sheth et al. 2010) considering several morphological and observable characteristics. The TIMER survey focuses on massive galaxies (∼1010−1011 M⊙), with visible bars and inner structures. The sample selection also imposes a limit on the distance (d<40 Mpc) and the inclination of the galaxies (i<60°) to distinguish the different central structures, which also need to be observable from the Paranal Observatory, that is, with Dec. < +25°. Considering these constraints, the TIMER survey consists of 24 galaxies, with distances within 40 Mpc.

The MUSE-VLT instrument is an integral field spectrograph, with a field of view of 1′×1′ and a plate scale of 0.2″/spaxel, which corresponds to approximately 90 000 spectra per pointing. The TIMER observations were carried out during Period 97, 2016, from March to October, for ∼3840 s on average on each source, resulting in a high signal-to-noise ratio (S/N) per pixel (typically above 100 at the centre). The average PSF FWHM is 0.8″−0.9″ and the data was reduced using the MUSE pipeline (version 1.6). For more details on the survey and data reduction analysis, we refer to Gadotti et al. (2019).

For this study, we have selected only those galaxies from TIMER in which a nuclear disc can be identified through a peak in the stellar V/σ radial profile (Gadotti et al. 2020). The radius at which this peak occurs, denoted as Rkin, does not necessarily delimit a sharp end of the nuclear disc, but it can be considered a characteristic dynamical radius. This constraint excludes 3 galaxies from the TIMER sample, which were observed – these are NGC 1291, NGC 1365, and NGC 6902. Additionally, we have included the galaxies from de Sá-Freitas et al. (2023b), NGC 289 and NGC 1566. With that, the final sample considered in this work includes 20 galaxies (see Table 1).

Table 1.

Sample of galaxies used in this work.

Even though the Rkin is dynamically motivated, it is possible to notice star-forming rings placed outside of Rkin in many cases, which are part of the nuclear disc. Because of that, we visually estimated a new nuclear disc size, RND, based on the star formation rate (SFR) and mean stellar age spatial maps. Nevertheless, the correlation between nuclear disc size and bar length discussed in Gadotti et al. (2020) remains strong for the derived nuclear disc sizes in this work (see Fig. 1).

thumbnail Fig. 1.

Nuclear disc sizes visually defined as a function of bar length (see Table 1). We bootstrapped our sample 1000 times to robustly estimate the Pearson correlation coefficient and the p-value, with the associated uncertainties. By different works (e.g. Gadotti et al. 2020), we find a strong correlation (r = 0.750±0.003) between the structures, as expected in a bar-built scenario for nuclear discs.

Lastly, following the analysis in Bittner et al. (2020), we split our sample between two sub-samples: low and high star formation (low-SF and high-SF). We measure the median star formation rate surface density (ΣSFR) in the nuclear disc (as defined in this work – see Table 3), based on the Hα intrinsic luminosity (Kennicutt 1998). Although we consider a sharp limit of 5.2×10−7 M⊙yr−1pc−2 to split our sample into two sub-samples with the same size (10 galaxies each), we find good agreement with the classification of Bittner et al. (2020), in which the authors considered the absolute values and spatial distribution of Hα fluxes.

3. Methodology

As mentioned in the introduction, the ages of the stars in a galaxy's bar are not indicative of its formation epoch, as the bar can form from pre-existing stars in the galaxy's main disc. In de Sá-Freitas et al. (2023a), we presented a methodology to separate the populations of the main disc and the nuclear disc, which we briefly describe below.

3.1. The original method: de Sá-Freitas et al. (2023a)

To study the nuclear disc spectra isolated, one needs to remove the contamination of the old stellar populations already present in the region in which the nuclear disc was formed. In de Sá-Freitas et al. (2023a), we developed a methodology to separate the spectra from the nuclear disc and the main disc. Concisely, the method is based on the assumptions that (1) the populations of the main disc do not change significantly in the regions where the nuclear disc resides, and (2) the brightness of the main disc varies with radius following an exponential law.

We use MUSE datacubes and consider the spectrum of a ring region around the nuclear disc as a proxy for the stellar population of the main disc – which was already present before the formation of the bar. We use this spectrum and the disc scale length of the galaxy (measured in Salo et al. 2015) to model an exponential main disc in the nuclear disc region and subtract it from the observed data. To perform this subtraction between spectra and to avoid creating spectral line artefacts, we shift all the spectra to the rest frame and convolve the lines to the same velocity dispersion, considering the kinematic results from a previous analysis. Additionally, we use the BPT diagram diagnosis (Baldwin et al. 1981) to avoid AGN-dominated spaxels. Once we remove the modelled main disc from the data, we employ the GIST pipeline (Bittner et al. 2019) to derive independent star formation histories (SFHs) on the nuclear and main discs.

For the GIST run, we followed the configuration from previous TIMER papers to guarantee consistency between analyses (e.g. Gadotti et al. 2019; de Lorenzo-Cáceres et al. 2019; Bittner et al. 2020; de Sá-Freitas et al. 2023a, b). We considered a wavelength range of 4800−5800 Å and Voronoi-binned (Cappellari & Copin 2003) the data to a final signal-to-noise ratio of 100. Additionally, we used MILES simple stellar population libraries (SSPs – Vazdekis et al. 2015), with values of [M/H] varying between −1 and 0.04, ages between 0.03 and 14 Gyr, and α-enhancements of 0 and +0.4 – we would like to highlight that for this wavelength range, α measurements are dominated by magnesium (Mg). Firstly, GIST employs an unregularised pPXF (Cappellari & Emsellem 2004; Cappellari 2017) run to derive stellar kinematics. We also include a low-order multiplicative Legendre polynomial to account for mismatches between the observed spectra and the continuum templates. From this step, we derive the stellar velocity, stellar velocity dispersion, h3, and h4. Secondly, GIST employs pyGandALF (Sarzi et al. 2006; Falcón-Barroso et al. 2006) to model and subtract emission lines as Gaussians, resulting in the emission-subtracted spectra. Lastly, GIST employs a regularised pPXF run to the emission-subtracted spectra, fixing the kinematic information from the first step, and fitting different templates of the stellar population from MILES. From the last step, we retrieve the spatial distribution of light-weighted mean stellar population properties – age, [M/H], and [α/Fe]. In addition, the regularised pPXF run results in the weight of each SSP. That is the fraction of the light that each SSP accounts for – for different ages, metallicities, and α-enhancements. Considering the weights for a given age bin and mass-to-light fractions1 (Vazdekis et al. 2015), we can reconstruct the mass-weighted SFH for the nuclear disc and the main disc, independently. We consider the independent SFHs to measure the moment of bar formation.

To test the validity of the described methodology, we reproduced in de Sá-Freitas et al. (2023a) the same approach in simulated galaxies, for which we know the moment the bar has formed. With this test, we also aimed to understand limitations and possible contamination in the nuclear disc clean spectra – and consequently, SFHs. We concluded that a good proxy for timing bar formation is the moment in which the SFH of the nuclear disc surpasses the SFH of the main disc (ND/MD>1) with a positive slope towards younger ages (i.e. when the SFR in the nuclear disc is higher than in the main disc). We would like to stress that this criterion can be a lower limit in some cases. In the scenario in which the SFR of the main disc is still ongoing in the centre when the bar forms, and the gas inflow due to the bar is low – consequently, the SFR in the nuclear disc as well – the criterium of ND/MD>1 might not be sufficient at the moment of bar formation and the bar age we derive would be a lower limit. Nevertheless, we do not expect this to be the case in many galaxies since if the main disc is still forming stars in the centre, the galaxy is most likely gas-rich, and the gas inflow due to the bar is unlikely to be significantly lower. Additionally, studies find that galaxies quench inside-out (e.g. Ellison et al. 2018; Belfiore et al. 2018), so it is expected that the central region of the main disc will present lower SFR than the outer region. We refer to de Sá-Freitas et al. (2023a) for further details and tests.

3.2. This work: complementary approach

The methodology described above was employed in de Sá-Freitas et al. (2023a) for one galaxy and in de Sá-Freitas et al. (2023b) for two galaxies. However, it demands considerable computational time, especially in shifting and convolving the spaxel-by-spaxel spectra. Since our goal is to apply this methodology to a larger sample, we tested a complementary approach to derive bar ages, keeping the same strategy: we use a ring region to model the main disc and subtract it from the original data. The difference lies in the fact that instead of disentangling spectra of different structures – which demands convolving, shifting, and normalising (further details in de Sá-Freitas et al. 2023a) –, we work with the SFHs. We derive the SFHs spaxel-by-spaxel for the original data cube and proceed with disentangling the nuclear disc from the main underlying disc directly on the SFHs, instead of applying this process to the spectra (see Fig. 2). In this work, we derived results from both approaches – spectra vs. star formation histories – for most galaxies, finding agreeable results with differences within 1.0 Gyr, which is comparable to the uncertainties of the original method. The original approach took considerably longer to perform and, since we aim to apply this methodology to larger samples in the near future, we consider a good compromise to use the new approach with larger systematic errors. However, we were not able to derive statistical errors for this sample, which could vary depending on case by case – especially in the case of older bars, in which older stellar populations have higher uncertainties. Considering the systematic errors from de Sá-Freitas et al. (2023a) and the new approach used in this work, we estimate the final average systematic errors of − 1.4 + 1.8 Gyr $ {}^{+1.8}_{-1.4}\,{\textrm {Gyr}} $ – nonetheless, we note that older bars have intrinsic higher uncertainties associated with older stellar populations.

thumbnail Fig. 2.

Bar age measurement method. We illustrate the method described in Sect. 3, analogous to Fig. 2 in de Sá-Freitas et al. (2023a). We show the nuclear disc and representative ring regions, from which we derive the SFH of the original data in the nuclear disc region (red) and the representative region (green). We proceed to subtract the main disc SFH from the original one, and the difference is considered the nuclear disc SFH (blue). We then use the ratio ND/MD to time the moment of bar formation (right plot, orange).

Additionally, considering that some of the galaxies in our sample have ongoing star formation in the nuclear disc region, we decided to mask spaxels with ΣSFR ≥ 2×106 M⊙yr−1pc−2, a typical value we find in star-forming rings in our sample (see for example NGC 1097 in Fig. 3). The only exception is NGC 7552, for which all spaxels in the nuclear disc region have high star formation, and thus, in this case, we masked spaxels with ΣSFR ≥ 5×106 M⊙ yr−1 pc−2, instead. This is because MILES libraries are not well suited for very young stellar populations, and their light can outshine older stellar populations, which is our interest. Nevertheless, we retrieve results both for masking and not masking the star-forming regions, finding differences in the bar age estimates within 0.9 Gyr.

thumbnail Fig. 3.

Star formation rate surface density map of NGC 1097 (ΣSFR in units of M⊙ yr−1 pc−2). We present the limits of the nuclear disc defined in this work (Table 3; solid black contour) and the ring region from which we extract the representative spectrum in dashed black contour (see illustration in Fig. 2). Additionally, we present the ΣSFR = 2×106 mask (solid-white countour). The mask is limited to the star-forming ring. Since we are interested in the oldest stars that belong to the nuclear disc, masking the active star-forming regions will not affect our methodology.

3.3. Multiple nuclear components

Although no large classical bulges with high stellar velocity dispersion have been found in the TIMER sample (Bittner et al. 2020), other structures may be present in the centre of the galaxies, co-existing with the nuclear disc. As demonstrated by Méndez-Abreu et al. (2014), some galaxies can have a small classical bulge, embedded inside the nuclear disc. In this case, the centre of the nuclear disc shows a dispersion-dominated, separate structure. This second structure, if present in our sample, is not accounted for by our methodology when extrapolating the exponential profile of the main disc towards the central region. Furthermore, depending on the formation scenario of this small classical bulge, the stellar populations and SFH may be completely different as compared to the nuclear disc. In this case, there could be contamination on the nuclear disc's “clean” SFH. On the other hand, substructures of the nuclear disc itself, such as nuclear bars (also known as inner or secondary bars) and nuclear spirals, can also increase the velocity-dispersion, although they are expected to be part of the evolution history of the nuclear disc. Due to that, one cannot simply mask regions of higher velocity-dispersion assuming it to be an independent structure, and a detailed stellar population diagnosis should be performed.

In our sample of 20 galaxies, 9 displayed an increase in the velocity dispersion in the central region; they are IC 1438, NGC 1097, NGC 1433, NGC 4371, NGC 4643, NGC 4981, NGC 4984, NGC 5728, and NGC 5850 (see Table 2). Since constructing a detailed diagnosis of substructures is beyond the scope of this work, we decided whether to mask or not these regions, case by case. Amongst these nine galaxies, four have nuclear bars reported; these are IC 1438 (TIMER collaboration, in prep.), NGC 1433 (Erwin 2004; Buta et al. 2015; Bittner et al. 2021), NGC 5728 (e.g. Erwin 2004 – although the presence of the nuclear bar in this case is ambiguous, see de Lorenzo-Cáceres et al. 2019), and NGC 5850 (de Lorenzo-Cáceres et al. 2013). We did not mask the central region of these four galaxies, since the nuclear bar is expected to be part of the nuclear disc evolution and share the same SFH. For the rest, we derive two bar ages: masking the central high-velocity dispersion region [denoted in Table 2 as ‘bar age (masked)’] and not masking it (denoted as ‘bar age’), listed in Table 2. For NGC 4371, NGC 4643, and NGC 4981, we cannot derive bar ages in the configuration where we do not mask the central region, since the criterium of ND/MD>1 is not fulfilled (see Sect. 3). For the remaining two galaxies, NGC 1097 and NGC 4984, the change in bar age is 1.5 and 2.5 Gyr, respectively, where the non-masked results tend to be older. This can be due to two scenarios: (i) the nature of the central velocity dispersion indeed reflects a small classical bulge, which is older and biases our results towards older ages; or (ii) the nuclear disc grows inside-out and the central region formed first (Bittner et al. 2020), so we would be retrieving a lower limit for the bar age by masking this region. Since it is not yet conclusive whether the nuclear disc actually reaches the very centre of the galaxy or has an inner edge, and in the presence of the high-velocity dispersion, we decided to consider the values when masking the central region. In summary, four galaxies have nuclear bars, so we did not mask the very central region with high-velocity dispersion (IC 1438, NGC 1433, NGC 5728, and NGC 5850), and five galaxies have bar ages with the very central region masked (NGC 1097, NGC 4371, NGC 4643, NGC 4981, and NGC 4984).

Table 2.

Objects with multiple nuclear components, with the final ages considered are in boldface.

4. Results

We applied the methodology described in Sect. 3 to all TIMER galaxies with a discernible nuclear disc, listed in Table 1. We successfully derived bar ages for 18 galaxies and added the results from de Sá-Freitas et al. (2023b), resulting in the largest sample of known bar ages, with a total of 20 galaxies (Table 3). In this section we present our main results and the first insights into secular evolution derived from our age-dating of the bars.

Table 3.

Derived bar ages, nuclear disc sizes, and masses.

We find a wide range of bar formation epochs that vary between mass-weighted ages of 1.0−13.0 Gyr (see Fig. 4). The high-SF nuclear discs sub-sample (see Sect. 2) tends to have bars younger than 9 Gyr, whereas the low-SF nuclear disc sub-sample hosts older bars, the majority of them with ages greater than 9 Gyr. The mean bar ages of high- and low-SF nuclear discs are 4.0±2.0 Gyr and 9.3±3.6 Gyr, respectively. The result is not driven by the spaxels with large SFR values, since we mask the ones with values above 2×106 M⊙yr−1pc−2. Three galaxies from the low-SF sub-sample present bar ages of 3.0, 3.5, and 6.0 Gyr; they are NGC 4984, NGC 5248, and NGC 7140, respectively, where the first had the central region masked (see Sect. 3.3) and the last two have ΣSFR close to the sharp limit that defines the sub-samples, which can explain the relatively young ages compared to the rest of the low-SF sub-sample. We show the star formation histories and bar ages derived for each galaxy in Figs. B.1 and B.2.

thumbnail Fig. 4.

Distribution of bar ages derived in this work. We display our main results (total, black line), colour-coded by low- and high-SF sub-samples (yellow and purple, respectively). At the top, we present the median bar age of each sub-sample, together with the standard deviation of each distribution (high-SF: 4.0±2.0 Gyr; low-SF: 9.3±3.6 Gyr). It is clear that low-SF nuclear discs are hosted by older bars (typically older than 9 Gyr), whereas high-SF nuclear discs are hosted by younger bars. Additionally, we derive a large range of bar ages, varying from 1−13 Gyr, illustrating that bars started to form in a young Universe (∼1 Gyr), and that this is an ongoing process in the Local Universe.

In the downsizing scenario of bar formation (see Sheth et al. 2012), it is expected that the most massive galaxies would have achieved the necessary mass to become self-gravitating first, which would suggest that older bars would be hosted by the most massive galaxies. To investigate disc settling in the context of the downsizing picture, we compare the current stellar mass with respect to the bar age in Fig. 5. We use the stellar mass measurements from S4G (Muñoz-Mateos et al. 2013, 2015), from 3.6 μm fluxes. Interestingly, we do not find a correlation between the bar age and stellar mass. This indicates that some massive galaxies are still forming bars – at least for the stellar mass regime of M★≥1010 M⊙ –, in contrast with the downsizing predictions. However, this is in agreement with recent analysis presented in Fragkoudi et al. (2024), where the authors find that, for a sample from Auriga simulations (Grand et al. 2017, 2019) in a similar mass range, that even though the oldest bars are preferentially found in massive galaxies, there is not a correlation between the bar age and the stellar mass. Lastly, we also considered the stellar masses derived in Querejeta et al. (2015) and Leroy et al. (2019) in Appendix A, reaching similar results.

thumbnail Fig. 5.

Stellar masses as a function of bar ages. We consider the stellar masses from the S4G survey, obtained with the 3.6 μm band (Muñoz-Mateos et al. 2015) and the bar ages derived in this work. We bootstrapped our sample 1000 times to robustly estimate the Pearson correlation coefficient and the p-value, with associated uncertainties. Lastly, we display the mean errors in the bar age and stellar mass estimates (black circle). As discussed in Muñoz-Mateos et al. (2015), the main source of error in the galaxy stellar mass comes from errors in distance estimates, which translate to ±0.32 dex error in mass. Contrary to downsizing predictions, we find no correlation between the two properties, with a weak Pearson coefficient of r=−0.180±0.007 – illustrated by the dotted line.

We also investigate how different galaxy properties relate to bar ageing, and how these properties are affected by physical processes connected to bar-driven evolution. In Fig. 6 we show the normalised bar length and strength as a function of the bar age. We consider the bar lengths derived in Herrera-Endoqui et al. (2015), where the authors visually estimate the length of the bar from the distance in between the bar ends, and for bar strength, we consider the values from Díaz-García et al. (2016), as given by the m = 2 Fourier mode of the galaxy surface brightness (A2). Both parameters are normalised to the size of the host galaxy, for which we consider the semi-major axis of the 25.5 mag arcsec−2 isophote, measured on the 3.6 μm band by S4G (Muñoz-Mateos et al. 2015). Throughout this work, we bootstrapped our sample 1000 times to derive robust Pearson's coefficients and p-values. We find a Pearson correlation coefficient of r = 0.654±0.004, with p-value = 0.010±0.001 for the normalised bar length with respect to bar age, and r = 0.480±0.005 with p-value = 0.097±0.005 for normalised strength with respect to bar age.

thumbnail Fig. 6.

Insights into bar ageing. We display the normalised bar lengths (left panel) and normalised bar strengths (A2- right panel) for our sample by galaxy size. We also present the linear regression (dotted black line) for 1000 bootstrap repetitions, the Pearson correlation coefficient r, and the associated null hypothesis p-value. For the two properties, we find trends of correlation. For the bar length, the associated p-value is smaller than 0.05, while for A2 its p-value is ∼1. These results are in agreement with the scenario in which older bars are longer and stronger.

Following the same approach, we investigate the nuclear disc size (given in Table 3) normalised by galaxy size with respect to bar age in Fig. 7, finding a correlation with Pearson coefficient index of r = 0.602±0.004 and p-value = 0.025±0.003. We also compare the nuclear disc size normalised by bar length with bar ages in Fig. 8, where we find a constant size relation of ∼0.12, independent of bar age. This suggests that the nuclear disc is set by the size and growth of the bar. Finally, we compare the relative nuclear disc stellar mass (i.e. normalised by the galaxy total stellar mass) with bar age in Fig. 9, finding a remarkable correlation, with r = 0.850±0.002 and p-value = 2×10−4±0.7×10−5. We derive the stellar masses of the nuclear discs by integrating their SFH (blue dashed curve in Figs B.1 and B.2), following de Sá-Freitas et al. (2023a, b), and present the values in Table 3. Moreover, we colour-code Fig. 9 by the median ΣSFR, where blue and red colours indicate higher and lower values of it, respectively. The mass build-up of the nuclear disc becomes clear, where young bars present less massive nuclear discs with higher star formation and, as the bar ages, the nuclear disc mass increases while star formation decreases. Our findings regarding the nuclear disc evolution with bar ageing are in good agreement with the inside-out scenario, proposed by Bittner et al. (2020), in which nuclear discs are built in rings of star formation that move outwards, growing and building up their mass. From these analyses, one finds that all the mentioned normalised properties are correlated with the bar age, where A2 shows the weakest trend; we note that when we normalise A2 by stellar mass, we find weaker or no correlation. Therefore, for the first time employing directly measured bar ages, we have observational indications that bars and nuclear discs can grow, build up their mass, and strengthen with time.

thumbnail Fig. 7.

Nuclear disc size normalised by galaxy size with respect to bar ages. We present the nuclear disc size normalised by the galaxy size (see Tables 1 and 3) for different bar ages. Additionally, we display the linear regression for 1000 bootstrap repetitions, with the Pearson coefficient value of r = 0.600±0.004 and p-value = 0.029±0.003. From this result, it is clear that older bars tend to host larger nuclear discs, while younger bars have smaller ones. This is consistent with the scenario in which nuclear discs grow with time, following the inside-out evolution context proposed by Bittner et al. (2020).

thumbnail Fig. 8.

Nuclear disc normalised by bar length with respect to bar ages. We present the nuclear disc size normalised by the bar length (see Tables 1 and 3) for different bar ages. It is clear that the size relation between the nuclear disc and the bar does not depend on the bar age, with a constant value close to ∼12%. This demonstrates how the nuclear disc sizes depend on bar properties and resonances, and as the bar evolves, the nuclear disc's absolute size evolves as well.

thumbnail Fig. 9.

Nuclear disc mass build-up. In this plot we present the nuclear disc mass normalised by the galaxy mass for different bar ages. To measure the nuclear disc mass, we integrated the isolated SFH (blue dashed curves in Figs. B.1 and B.2), following the same approach in de Sá-Freitas et al. (2023a, b). Additionally, we color-coded each point according to its ΣSFR, which increases towards blue. It is clear that young nuclear discs are less massive with a higher star formation rate. As the bars age, the nuclear discs gradually present less star formation, while building up their mass. Lastly, we find a correlation coefficient of 0.85±2×10−3, with p-value = 2×10−4±7×10−5.

To address whether or not bars are related to the host galaxy quenching, we compare the main-sequence offset (ΔMS – from Leroy et al. 2019) with bar ages in Fig. 10, available for 18 galaxies in our sample. We find a considerable anti-correlation between ΔMS and bar ageing, with r=−0.699±0.0003 and p-value = 0.007±0.001, suggesting the importance of the bar in suppressing the star formation of the host galaxy. In Figs. 11 and 12, we analyse the median ΣSFR within the nuclear disc and the neutral hydrogen supply of the host galaxy (MHI) with respect to bar ages, investigating secondary consequences of galaxy quenching. For the former, we also find a strong anti-correlation with a Pearson correlation coefficient of r=−0.791±0.003, with p-value = 0.0012±0.0006; while for last, we find a weak trend, with values of r=−0.463±0.007 and p-value ∼ 0.0151±0.007. These results agree with the scenario in which the bar funnels gas inwards and, with the decrease of available gas, the nuclear disc also tends to form fewer stars. However, the bar does not completely exhaust the gas present in the galaxy.

thumbnail Fig. 10.

Galaxy star formation properties with respect to bar ages. We investigate how the bar ageing is related to the star formation of the host galaxy. Left: Main sequence offset (ΔMS – values from Leroy et al. 2019) of the host galaxy with respect to the bar age. Positive values of ΔMS indicate the galaxy is bursting; Negative values indicate quenching. Additionally, we bootstrap our sample 1000 times, in the grey-shaded area, finding a correlation coefficient of r=−0.699±0.003, with p-value = 0.007±0.001. The strong correlation between star formation of the host galaxy and bar ageing is in agreement with the scenario in which bars aid the quenching of the galaxy. Right: Main sequence of galaxies defined in Leroy et al. (2019) (i.e. the sSFR with respect to the galaxy mass). We show their entire sample in a grey density map, while highlighting our sample colour-coded according to bar age, contextualising our results.

thumbnail Fig. 11.

ΣSFR in the nuclear disc with respect to bar ageing. We present the measured median ΣSFR in the nuclear disc region (as defined in this work; see Table 3) for different bar ages, finding a strong anti-correlation (r=−0.791±0.003 and p-value = 0.0011±0.0003). This demonstrates that, as the bar ages, the nuclear discs tend to form fewer stars.

thumbnail Fig. 12.

HI mass of the host galaxy with respect to bar ages. We present the mass of neutral hydrogen from Gadotti et al. (2019), based on the 21 cm line fluxes available from LEDA (see Table 1), finding a weak trend between HI mass and bar age, with r = 0.463±0.007, which is not statistically significant, with p-value = 0.151±0.007. This weaker anti-correlation indicates that even though the bar can aid in the quenching of the host galaxy, the gas of the host galaxy is not completely exhausted, but star formation is less efficient (e.g. Saintonge et al. 2016; Bacchini et al. 2019; Pessa et al. 2022).

5. Discussion

5.1. When do galactic discs settle and bars form?

We derive the bar formation epochs for 18 galaxies in the TIMER survey, forming the largest sample of nearby galaxies with known bar ages. Including the galaxies from de Sá-Freitas et al. (2023b), we find ages between ∼1−13.0 Gyr, which corresponds to redshifts between ∼0−6 (nonetheless, older stellar populations have higher intrinsic uncertainties). Since numerical and theoretical work suggest that galaxies can form a bar once their discs are dynamically mature (at least to a significant extent; e.g. Kraljic et al. 2012 and references therein), our result implies that the necessary conditions to form bars are already in place for some galaxies at those early phases of the evolution of the Universe. This would generally be interpreted as indicating that self-gravitating disc galaxies, baryon-dominated, with relatively low velocity-dispersion – where rotational motions are more significant than pressure-supported motions – exist since z≥2. This is in agreement with recent observational findings from ALMA (e.g, Smit et al. 2018; Neeleman et al. 2020; Rizzo et al. 2020; Lelli et al. 2021; Posses et al. 2023; Lelli et al. 2023) and JWST (e.g. Ferreira et al. 2022, 2023; Nelson et al. 2022; Jacobs et al. 2023). Furthermore, we find galaxies that formed bars relatively recently, with ages below 5 Gyr (z≤0.5), indicating that bar formation is an ongoing process in the Universe. In other words, even though currently bars are understood as old structures – which are robust and long-lived (e.g. Athanassoula 2003, 2005; Gadotti et al. 2015; Pérez et al. 2017; de Lorenzo-Cáceres et al. 2019; Rosas-Guevara et al. 2020; Fragkoudi et al. 2020; de Sá-Freitas et al. 2023a; Fragkoudi et al. 2024; Verwilghen et al. 2024), some bars can still be young and recently formed (see also de Sá-Freitas et al. 2023b; Fragkoudi et al. 2024). Whether or not the young bars in our sample are first-generation or reformed bars is a discussion beyond the scope of this work.

Even though some studies find that high redshift discs are often thick and turbulent (e.g. Elmegreen & Elmegreen 2006; Newman et al. 2013), which indicates that these objects are still under great influence of external processes such as minor mergers, recent works find that this can depend on the choice of gas tracer (e.g. Rizzo et al. 2024). Other studies which investigate galaxy morphology at high redshifts (z≥1.5−4.0) find the presence of well-developed disc galaxies (e.g. Shapiro et al. 2008; Schreiber et al. 2009; Epinat et al. 2012; Wisnioski et al. 2015; Rizzo et al. 2020; Lelli et al. 2021; Posses et al. 2023). More recently, works using JWST data find that disc galaxies, with significant rotational support, can be the majority up to z∼8 (e.g. Ferreira et al. 2022, 2023; Nelson et al. 2022; Jacobs et al. 2023), in agreement with our results that disc galaxies with relatively cold dynamics exist since the Universe was ∼1−2 Gyr old. Even though we present a sample of only 20 galaxies, this work brings a novel and independent benchmark of when internal, secular evolution started to take place in our sample.

Some simulations that investigate how the bar fraction evolves with time find that bars can exist since z>2 (e.g. Kraljic et al. 2012; Rosas-Guevara et al. 2020; Fragkoudi et al. 2020, 2024), which is also in good agreement with our results. More specifically, Rosas-Guevara et al. (2020) find, for an IllustrisTNG sample, that 30% of the galaxies are barred at z≈6 and, while their results have a discrepancy with observational data at intermediate redshifts, they argue that this discrepancy could be a result of observational detection limitations. On the other hand, cosmological zoom-in simulations (e.g. Kraljic et al. 2012; Fragkoudi et al. 2024) tend to find a decreasing bar fraction with redshift, in agreement with our results. On the observational side, Le Conte et al. (2024) derived bar fractions for a sample at 1≤z≤3, based on JWST and HST data separately, finding that the bar fraction is about twice as large with JWST data, as compared to HST data. This illustrates the limitations concerning the detection of bars in previous works at higher redshifts. For the JWST data – better suited for higher redshifts – Le Conte et al. find bar fractions of 14% in bins between 1≤z≤3. In parallel, recent work by Guo et al. (2024) find a bar fraction of 2.4−6.4% at 3≤z≤4.

To understand how our bar age estimates compare to the observed evolution of the bar fraction over time, in Fig. 13 we derive the bar fraction in our sample across cosmic time directly from our derived bar ages, as follows. We compute the cumulative fraction of barred galaxies as a function of lookback time from our bar ages, assuming that once a bar is formed, it is not destroyed. However, since all of our galaxies are barred, we would thus find a bar fraction of 100% in the Local Universe. To rectify this offset from the observed bar fraction a z = 0, we normalise it to the observed bar fraction of 67% (e.g. Eskridge et al. 2000; Menéndez-Delmestre et al. 2007; Marinova & Jogee 2007), and compute the rest of the cumulative distribution accordingly. These extrapolated bar fractions we measure can be considered as a lower limit only due to two main caveats: (i) we only consider galaxies that are barred today, and (ii) we assume that all galaxies in our sample had a clear disc morphology at all redshifts considered. In the case of (i), it is possible that there were more bars in the past that were eventually destroyed (e.g. Rosas-Guevara et al. 2020), which would increase the bar fraction at early epochs. Considering the assumption in (ii), it is possible that some galaxies in our sample hosting younger bars would only develop a clear disc galaxy structure later in time, which would decrease the number of disc galaxies and thus increase the fraction of barred galaxies at earlier times. Additionally, it is expected that disc galaxies can suffer a morphological transformation, and no longer be considered in these fraction measurements, which cannot be accounted for here. Despite these caveats, we find in Fig. 13 a remarkable agreement between our extrapolated bar fractions and the bar fractions at different redshifts – from both observations and zoom-in cosmological simulations –, especially with works that consider both strong and weak bars. We want to emphasise that this is a novel method to investigate bar fractions over time, which is also a completely independent approach to the matter, with a starting point in the derived bar ages in nearby galaxies.

thumbnail Fig. 13.

Extrapolated bar fractions for different redshifts from this work. Based on Fig. 4, we display our cumulative distribution (dashed grey histogram) and normalise it by the observed bar fraction in the Local Universe in studies that consider both weak and strong bars (0.67; e.g. Eskridge et al. 2000; Menéndez-Delmestre et al. 2007; Marinova & Jogee 2007). With this, we derive the extrapolated bar fraction over time in our sample (green dots). Additionally, the shaded green region accounts for the systematic error in our bar age measurements of − 1.4 + 1.8 Gyr $ {}^{+1.8}_{-1.4}\,{\textrm {Gyr}} $. With the grey error bars, we also display the likely ranges in the cumulative distribution considering this systematic error as well. We compare our results with the observed bar fraction from different works, finding a remarkable agreement with works that consider both weak and strong bars.

5.2. Bar formation in the downsizing scenario

When it comes to disc settling and bar formation, the downsizing scenario (e.g. Cowie et al. 1996; Thomas et al. 2010; Sheth et al. 2012) predicts that more massive galaxies would host older bars. In other words, massive galaxies in the Local Universe would have achieved enough mass to dynamically settle their discs first, hence forming their bars first. To test this scenario, we assessed the relation between bar age and the current stellar mass in Fig. 5, finding no correlation in the mass range of our sample, which does not agree with the downsizing scenario predictions. More specifically, we find young bars (∼4 Gyr) with stellar masses ranging between 2≤M★≤18×1010 M⊙, which indicates that even some massive galaxies formed their bars more recently, in agreement with de Sá-Freitas et al. (2023b). However, we cannot yet diagnose if the young bars in massive galaxies are first-generation bars or reformed bars. More recent simulations find that bars formed after z≤2 tend to be robust and long-lived (e.g. Rosas-Guevara et al. 2020; Fragkoudi et al. 2024; Verwilghen et al. 2024; Rosas-Guevara et al. 2024). Rosas-Guevara et al. (2024) demonstrate for a TNG50 sample that bars are mostly stable and, if they are destroyed after z∼1, this is usually due to mergers and the environment. However, only ∼6% of the barred galaxies at z = 1 have a barless disc-like morphology at z = 0. In summary, the destruction of bars usually takes place before z∼1−2, and we do not discard this possibility in the case of our young bars.

Erwin (2018) investigates the bar fraction for different masses in a S4G sample of late-type galaxies (Sheth et al. 2010), finding that the fraction of barred galaxies decreases for galaxies with masses greater than 1010M⊙, which is the TIMER sample regime. Considering bars are robust structures in the context of the downsizing prediction, one would expect that massive galaxies would form bars first and sustain them until z = 0. In other words, the fraction of barred galaxies would increase with mass, which is not observed in Erwin (2018) – although the author does not include lenticular galaxies in his sample. This is consistent with our main results, in which we find that the downsizing scenario might not be sufficient to completely explain bar formation, at least in the mass regime we probe in this work (a sample including lower mass galaxies would be beneficial in this context).

Even though the build-up of stellar mass contributes to the ‘dynamical maturity’ of galaxies, other processes will also play a role in the formation of bars. For example, theoretical studies have shown that when a galaxy is less disc-dominated (i.e. when the dark matter dominates over the stellar disc in the central regions), or if the disc is kinematically hotter, this will contribute to delaying or even suppressing bar formation (e.g. Hohl 1971; Lynden-Bell & Kalnajs 1972; Ostriker & Peebles 1973; Athanassoula & Sellwood 1986; Combes et al. 1990; Berentzen et al. 2007; Bland-Hawthorn et al. 2023; Ghosh et al. 2023; Fragkoudi et al. 2024). Furthermore, studies find that having a gas fraction in the disc above 10% might suppress or delay bar formation (e.g. Athanassoula et al. 2013). Recently, Fragkoudi et al. (2024) showed that, in cosmological simulations, the time of bar formation is well correlated with disc dominance at z = 0, as well as with the time at which the galaxy becomes disc-dominated. While there is a correlation between stellar mass and how disc-dominated (or baryon-dominated) a galaxy is2, the fact that we do not find a clear correlation between mass and bar age neither in cosmological simulations (e.g. Fragkoudi et al. 2024) nor in this work, suggests that stellar mass is not enough to constrain the time of bar formation. Furthermore, interactions may destroy or induce the formation of a bar – even in an otherwise stable disc – depending on the characteristics of the involved galaxies and the orbital properties of the interaction (e.g. Noguchi 1987; Gerin et al. 1990; Gadotti 2009; Li et al. 2009; Méndez-Abreu et al. 2012; Łokas et al. 2014; Méndez-Abreu et al. 2023). This could be the reason for the relatively young bar we find in NGC 1097, the most massive galaxy in our sample. This adds complexities to the downsizing picture, which is not necessarily ruled out by our results.

In addition to the bar formation itself, the expected disc settling moment for different masses is also an open question. Many different works investigate which physical processes are responsible for the disc formation, that is, the transition between a disordered motion supported galaxy to a rotationally supported low-dispersion object (e.g. Fall & Efstathiou 1980; Ryden & Gunn 1987; Okamoto et al. 2005; Brook et al. 2012; Christensen et al. 2016; Stern et al. 2021; Conroy et al. 2022; Hafen et al. 2022; Gurvich et al. 2023; Semenov et al. 2024a, b). Semenov et al. (2024a) demonstrates that the disc formation time can depend on how the halos assembled mass, and if destructive mergers took place late on, which would reset the disc formation process. For example, Fragkoudi et al. (2024) showed that Milky Way mass disc galaxies that host bars tend to assemble their stellar mass earlier on than unbarred disc galaxies. Rosas-Guevara et al. (2020) argue that for an IllustrisTNG Milky-Way-like sample, late disc formation is associated with mass assembly histories with significant mergers taking place later. In summary, the scenario of disc formation and settling is complex and remains an open question, but it does not seem to necessarily relate only to the mass of the galaxy.

5.3. How do bars grow?

For the first time, it is possible to analyse how different properties of galaxies change with the ageing of bars, and how these observational results compare to theoretical work.

When it comes to bar evolution, especially bar growth, many studies reach different conclusions. From an observational viewpoint, Kim et al. (2021) analysed the data from the Cosmic Evolution Survey (COSMOS – Scoville et al. 2007; Koekemoer et al. 2007) and found that the average bar length does not show signs of evolution in the past 7 Gyr – both in normalised and absolute terms. This does not agree with the findings from Rosas-Guevara et al. (2022), where the authors found, for an IllustrisTNG sample (Pillepich et al. 2018; Nelson et al. 2018), that bars do grow in absolute terms. However, the growth takes place at a similar pace as the disc growth, maintaining a fairly constant size relation. In agreement, Zhao et al. (2020) also found for an IllustrisTNG sample that, in the past 6 Gyr, the absolute length of bars increases by a factor of 0.17 dex. Furthermore, Anderson et al. (2022) and Erwin et al. (2023) argue that the presence of “shoulders” – one type of bar profile structure – is evidence of secular bar growth. This is a brief illustration of the lack of agreement between observations and simulations on whether or not bars grow in length as they evolve, both in absolute terms or normalised.

Employing our derived bar ages, we can investigate the normalised bar size evolution as in Fig. 6 and find an indication that younger bars are smaller than older bars when compared to the size of the galaxy. This is consistent with the picture in which the normalised length of bars can increase with their ageing. However, Fragkoudi et al. (2024) showed that the picture is not that simple. For an Auriga simulation sample (Grand et al. 2017, 2019) of galaxies, they retrieved the same relation between normalised bar length with bar age that we find in this work. Still, investigating further the evolution of these bars, they found that not every bar has grown with time. The authors demonstrated that bars which formed at z≥2 already form large and do not grow, while bars that formed at intermediate redshifts (z≤2) do grow with time. In other words, the authors retrieve from their simulations the same relation presented here, but in a scenario in which not all bars have grown.

5.4. Bar-driven galaxy quenching

Several theoretical, numerical, and observational works find that bars, once formed, affect their host galaxy and drive its evolution (e.g. Masters et al. 2012; Schawinski et al. 2014; Haywood et al. 2016; Fragkoudi et al. 2020; Géron et al. 2021; Rosas-Guevara et al. 2022). When comparing a barred sample with a counterpart unbarred sample from the SDSS-IV MANGA survey, Fraser-McKelvie et al. (2020) found that barred galaxies peak their star formation history, quench, and form most of their stellar mass earlier than the unbarred ones. One important process of bar-driven secular evolution is the funnelling of gas towards the central region, forming the nuclear disc and often causing suppression of star formation along most of the bar (e.g. Masters et al. 2012; Schawinski et al. 2014; Géron et al. 2021; Scaloni et al. 2024).

We consider the ΔMS measurements for 18 of the galaxies in our sample (see Figs. 9 and 10), finding a strong anti-correlation with bar age. That is, galaxies with older bars are more ‘quenched’ than galaxies with younger bars, with the SFR in the nuclear disc following the same relation (Fig. 11). Interestingly, when we analyse the availability of neutral gas with bar ages, the trend is weaker and not statistically significant (see Fig. 12). This indicates that, even though the bar can aid in the suppression of star formation in the main disc, it does not exhaust the gas, suggesting the gas is less efficient in forming stars (e.g. Saintonge et al. 2016; Bacchini et al. 2019; Pessa et al. 2022). Further investigation of the star formation efficiency is beyond the scope of this work.

We find interesting correlations between quenching and bar ages in this work. Nevertheless, as illustrated in Fraser-McKelvie et al. (2020), even though the bar can aid in the suppression of star formation in the galaxy, it is not clear what took place first: the quenching of the galaxy or the formation of the bar – since bars tend to form in galaxies with less gas (e.g. Berentzen et al. 2007; Athanassoula et al. 2013). To properly confirm this picture, in the near future, we plan to investigate the gas and star formation rate properties in the entire galaxy in detail and break this degeneracy for the first time.

5.5. Double-barred galaxies are older systems

Studies report that 12−30% of barred galaxies host a second, nuclear bar (e.g. Erwin 2004; Buta et al. 2015), with sizes varying between 0.3−2.5 kpc (de Lorenzo-Cáceres et al. 2020). Historically, mainly two formation scenarios for the nuclear bar have been considered: (i) they are formed from the gas brought inwards from the main bar and/or mergers and interactions, firstly forming a gaseous bar, which forms stars and give place to a fragile stellar bar (e.g. Friedli & Benz 1993; Heller & Shlosman 1994); or, (ii) they are formed dynamically from instabilities in the nuclear disc, similar to the main bar (e.g. Debattista & Shen 2006; Du et al. 2015). In the first scenario, nuclear bars are young and transient structures, being destroyed after just a few hundred Myr. On the other hand, in the second scenario, the nuclear bars share similarities with the main bar (e.g. de Lorenzo-Cáceres et al. 2019; Bittner et al. 2021), being long-lived structures with evidence of buckling in some cases (e.g. Méndez-Abreu et al. 2019). Bittner et al. (2021) argues that double-barred systems behave as “galaxies inside galaxies”. Beyond these two scenarios, Semczuk et al. (2024) proposed that tidal interactions can trigger the formation of the nuclear bar before the outer bar in some cases.

In de Lorenzo-Cáceres et al. (2019), the authors demonstrated that, between the two main scenarios, the second scenario is more likely for NGC 1291 and NGC 5850, measuring the formation epoch of the main bars to be above 6.5 and 4.5 Gyr, respectively – in agreement with the results presented here. Furthermore, other efforts from the TIMER collaboration (e.g. Méndez-Abreu et al. 2019; Bittner et al. 2021) find that nuclear bars are formed through dynamical instabilities in the nuclear discs and that nuclear bars are long-lived systems. These findings suggest that the second scenario for the formation of the nuclear bar is more likely. Nevertheless, using N-body/hydrodynamical simulations, Wozniak (2015) finds that it is also necessary to have a gaseous component with star formation in order to maintain the nuclear bar long-lived and stable.

As discussed in Sect. 3.3, four of the galaxies in our sample have been reported to host an nuclear bar, which are among the oldest bars of our sample. Even though we do not estimate the formation epoch of the nuclear bars, our results agree with the scenario in which nuclear bars form from disc instabilities in the nuclear disc, which require building the mass of the nuclear disc itself, hence longer timescales and older systems – with bar ages >7.5 Gyr. Additionally, studies show that a high gas fraction on the main disc can delay the formation of the main bar (e.g. Berentzen et al. 2007; Athanassoula et al. 2013; Seo et al. 2019). If this is the case also for the nuclear bars, it would be necessary to quench the star formation in the nuclear disc, or at least to consume enough of the gas, to make it possible for the nuclear bar to form. Consistent with that, three of the four doubled-barred systems in our sample belong to the low-SF sub-sample. Lastly, since the investigation of these systems using spatially resolved spectroscopy is very recent, there are few constraints on the timescales for their formation (e.g. de Lorenzo-Cáceres et al. 2019). Overcoming the physical limitations of identifying and studying nuclear bars is a challenge, and further efforts with larger samples are necessary.

6. Summary and conclusions

Studies suggest that, in a simplified picture, disc galaxies evolve in a two-phase scenario: at first, the main drivers of galaxy evolution are external, such as mergers and interactions; later, with the expansion of the Universe and the galaxy assembling enough mass, internal evolutionary processes start to play an important role that is often referred to as secular evolution. The epoch in which this transition happens is a long-standing question. One approach to understanding this transition in individual objects is to time when stellar bars appeared since they can only form once the disc is dynamically mature, at least partially (e.g. Kraljic et al. 2012 and references within).

We summarise this work as follows:

  • We have derived, for the first time, the ages of bars in a sample of 20 galaxies mostly from the TIMER survey (Gadotti et al. 2019), using the methodology presented in de Sá-Freitas et al. (2023a).

  • We find bar ages between 1−13 Gyr (Table 3, Figs. B.1., 4, and B.2), illustrating how settled discs exist in the Universe at least since z>2, and that the dynamical maturing of discs is an ongoing process.

  • We find strong anti-correlations between bar ages and star formation rate surface density in the nuclear disc and main sequence offset ΔMS for the entire galaxy (Fig. 10), in agreement with the scenario in which the presence of the bar aids the suppression of star formation in the galaxy. However, the neutral gas supply is only weakly anti-correlated with bar ages, suggesting less efficient star formation rather than gas exhaustion.

  • Separating our sample according to the star formation rate surface density in the nuclear disc region into low-SF and high-SF nuclear discs, we find that the former are hosted by older bars, while the latter are hosted by younger bars, with mean ages of 9.3±3.6 Gyr and 4.0±2.0 Gyr, respectively. This is in agreement with the scenario in which bars swipe the gas of the disc towards the central region, aiding the suppression of star formation in the main disc.

  • Contrary to predictions from the downsizing picture, we find no correlation between bar age and current galaxy stellar mass (Fig. 5), indicating that, even though having enough mass is necessary to form bars, it is not enough to explain all bar formation. In other words, other factors, such as galaxy interactions and/or gas fractions and disc-dominance, play an important role in determining if and when a bar forms in a given disc galaxy, at least in the mass regime we probe.

  • We find correlations between bar ages and normalised bar length and strength, suggesting the secular evolution of these structures, whereby older bars tend to be larger and stronger (but see also discussion in Sect. 5.3);

  • We find a strong correlation between bar ages and nuclear disc size normalised by galaxy size, whereby older bars host larger nuclear discs. In line with this, we find that the nuclear disc size normalised by bar length does not depend on the bar ageing. Additionally, the nuclear disc stellar mass is tightly correlated with the bar age, where older bars host more massive nuclear discs with less star formation, and young bars host less massive nuclear discs with higher star formation. These findings suggest the co-evolution of the bar and nuclear disc, with the nuclear disc following the inside-out scenario proposed in Bittner et al. (2020), with a dependence on bar properties, such as length.

  • From our bar ages we estimated how the bar fraction evolves over time (Fig. 13), finding remarkable agreement with observed bar fractions in different redshifts with a completely independent and novel approach.

  • We find that systems with double bars tend to be among the oldest in our sample, and have low star formation rate surface density. This is in agreement with the scenario in which the nuclear bar is formed from disc instabilities in the nuclear disc, which is generally on relatively long timescales.

In this work we have provided, for the first time, an observational estimate of the bar ages for a sample of nearby galaxies. This provided us with an independent insight into the cosmic epoch in which disc galaxies started to dynamically mature, and when bar-driven secular evolution processes started to take place in the Universe and shape the properties of disc galaxies. Our results are in agreement with high-redshift observational studies on the bar fraction beyond a redshift of one and up to redshift of four. In addition, we were able the obtain insights into secular evolution directly connected to the measured bar ages, finding evidence regarding the growth of bars and bar-built nuclear discs, and regarding the role of bars in quenching star formation in their host galaxies.

Acknowledgments

We acknowledge the insightful comments of the referee, Dr. H. Wozniak, which improved and clarified the work presented here. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programmes 097.B-0640(A), 095.B-0532(A), and 060.A-9313(A), 096.B-0309, and 0100.B-0116. All raw and reduced data are available in the ESO Science Archive Facility. This work was supported by STFC grants ST/T000244/1 and ST/X001075/1. T.K. acknowledges support from the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2022R1A4A3031306, No. RS-2023-00240212). J.F-B acknowledges support from the PID2022-140869NB-I00 grant from the Spanish Ministry of Science and Innovation. AdLC acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) through RYC2022-035838-I and PID2021-128131NB-I00 (CoBEARD project). PSB acknowledges support from grant PID2022-138855NB-C31, funded by the Spanish Ministry of Science and Innovation, MCIN/AEI/10.13039/501100011033/FEDER, EU. MQ acknowledges support from the Spanish grant PID2022-138560NB-I00, funded by MCIN/AEI/10.13039/501100011033/FEDER, EU. JMA acknowledges the support of the Viera y Clavijo Senior program funded by ACIISI and ULL and the support of the Agencia Estatal de Investigación del Ministerio de Ciencia e Innovación (MCIN/AEI/10.13039/501100011033) under grant nos. PID2021-128131NB-I00 and CNS2022-135482 and the European Regional Development Fund (ERDF) ‘A way of making Europe’ and the ‘NextGenerationEU/PRTR’. PC acknowledges support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grant 310555/2021-3 and from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) process number 2021/08813-7.

2

The stellar fraction peaks around the mass of the Milky Way according to abundance matching relations (e.g. Moster et al. 2013).

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Appendix A: Different mass measurements

To investigate the role of downsizing as a constraint to bar formation, we compare stellar mass with bar ageing, finding no correlation in Fig. 5. To ensure the robustness of our results, we also consider mass measurements from two different works in Fig. A.1: Querejeta et al. (2015) and Leroy et al. (2019). In Querejeta et al. (2015), the authors also consider Spitzer fluxes in the 3.6mμ band but apply a dust correction. On the other hand, Leroy et al. (2019) derive masses from mid-IR fluxes, either from IRAC1 or WISE1. As in Fig. 5, we find no significant correlation between stellar mass and bar age, indicating that the downsizing picture of bar formation cannot completely explain the formation or the absence of bars in disc galaxies.

thumbnail Fig. A.1.

Downsizing and bar formation for different mass measurements. As in Fig. 5, we compare the stellar mass of the host galaxy with respect to bar ages, considering values from Leroy et al. (2019) in the upper panel, and Querejeta et al. (2015) in the bottom panel. For the three different mass measurements we consider in this work, we find no significant correlation between stellar mass and bar ageing.

Appendix B: Individual results

In this work we derived individual bar ages for 18 nearby galaxies from the TIMER sample (Gadotti et al. 2019), applying the methodology described in Sect. 3. In this appendix we display the individual results in Figs. B.1 and B.2, separated by the sub-samples of low- and high-SF, respectively. For each galaxy, we display the SFHs of the original datacube (solid-red curves), the modelled main disc (dot-dashed green curves), and the clean nuclear disc (dashed blue curves). Additionally, we display the ratio between the SFHs of the main disc and the nuclear disc at the bottom of each individual result. We highlight the region in which the criteria for bar age measurement are achieved in orange – that is, ND/MD >1 for the first time towards younger ages. Lastly, we also display the considered systematic errors of − 1.4 + 1.8   Gyr $ {}^{+1.8}_{-1.4}\ {\textrm {Gyr}} $.

thumbnail Fig. B.1.

Individual measurements of bar age of the low-SF sample. Following the de Sá-Freitas et al. (2023a) methodology, we define the bar age as the moment at which the SFH of the nuclear disc (dashed blue line) overcomes the SFH of the main disc (dot-dashed green line). Additionally, based on the tests performed in de Sá-Freitas et al. (2023a) and here, we estimate the systematic measurement error of − 1.4 + 1.8   Gyr $ {}^{+1.8}_{-1.4}\ {\textrm {Gyr}} $.

thumbnail Fig. B.2.

Same as Fig. B.1, but for the high-SF sub-sample.

All Tables

Table 1.

Sample of galaxies used in this work.

In the text
Table 2.

Objects with multiple nuclear components, with the final ages considered are in boldface.

In the text
Table 3.

Derived bar ages, nuclear disc sizes, and masses.

In the text

All Figures

thumbnail Fig. 1.

Nuclear disc sizes visually defined as a function of bar length (see Table 1). We bootstrapped our sample 1000 times to robustly estimate the Pearson correlation coefficient and the p-value, with the associated uncertainties. By different works (e.g. Gadotti et al. 2020), we find a strong correlation (r = 0.750±0.003) between the structures, as expected in a bar-built scenario for nuclear discs.
In the text
thumbnail Fig. 2.

Bar age measurement method. We illustrate the method described in Sect. 3, analogous to Fig. 2 in de Sá-Freitas et al. (2023a). We show the nuclear disc and representative ring regions, from which we derive the SFH of the original data in the nuclear disc region (red) and the representative region (green). We proceed to subtract the main disc SFH from the original one, and the difference is considered the nuclear disc SFH (blue). We then use the ratio ND/MD to time the moment of bar formation (right plot, orange).
In the text
thumbnail Fig. 3.

Star formation rate surface density map of NGC 1097 (ΣSFR in units of M⊙ yr−1 pc−2). We present the limits of the nuclear disc defined in this work (Table 3; solid black contour) and the ring region from which we extract the representative spectrum in dashed black contour (see illustration in Fig. 2). Additionally, we present the ΣSFR = 2×106 mask (solid-white countour). The mask is limited to the star-forming ring. Since we are interested in the oldest stars that belong to the nuclear disc, masking the active star-forming regions will not affect our methodology.
In the text
thumbnail Fig. 4.

Distribution of bar ages derived in this work. We display our main results (total, black line), colour-coded by low- and high-SF sub-samples (yellow and purple, respectively). At the top, we present the median bar age of each sub-sample, together with the standard deviation of each distribution (high-SF: 4.0±2.0 Gyr; low-SF: 9.3±3.6 Gyr). It is clear that low-SF nuclear discs are hosted by older bars (typically older than 9 Gyr), whereas high-SF nuclear discs are hosted by younger bars. Additionally, we derive a large range of bar ages, varying from 1−13 Gyr, illustrating that bars started to form in a young Universe (∼1 Gyr), and that this is an ongoing process in the Local Universe.
In the text
thumbnail Fig. 5.

Stellar masses as a function of bar ages. We consider the stellar masses from the S4G survey, obtained with the 3.6 μm band (Muñoz-Mateos et al. 2015) and the bar ages derived in this work. We bootstrapped our sample 1000 times to robustly estimate the Pearson correlation coefficient and the p-value, with associated uncertainties. Lastly, we display the mean errors in the bar age and stellar mass estimates (black circle). As discussed in Muñoz-Mateos et al. (2015), the main source of error in the galaxy stellar mass comes from errors in distance estimates, which translate to ±0.32 dex error in mass. Contrary to downsizing predictions, we find no correlation between the two properties, with a weak Pearson coefficient of r=−0.180±0.007 – illustrated by the dotted line.
In the text
thumbnail Fig. 6.

Insights into bar ageing. We display the normalised bar lengths (left panel) and normalised bar strengths (A2- right panel) for our sample by galaxy size. We also present the linear regression (dotted black line) for 1000 bootstrap repetitions, the Pearson correlation coefficient r, and the associated null hypothesis p-value. For the two properties, we find trends of correlation. For the bar length, the associated p-value is smaller than 0.05, while for A2 its p-value is ∼1. These results are in agreement with the scenario in which older bars are longer and stronger.
In the text
thumbnail Fig. 7.

Nuclear disc size normalised by galaxy size with respect to bar ages. We present the nuclear disc size normalised by the galaxy size (see Tables 1 and 3) for different bar ages. Additionally, we display the linear regression for 1000 bootstrap repetitions, with the Pearson coefficient value of r = 0.600±0.004 and p-value = 0.029±0.003. From this result, it is clear that older bars tend to host larger nuclear discs, while younger bars have smaller ones. This is consistent with the scenario in which nuclear discs grow with time, following the inside-out evolution context proposed by Bittner et al. (2020).
In the text
thumbnail Fig. 8.

Nuclear disc normalised by bar length with respect to bar ages. We present the nuclear disc size normalised by the bar length (see Tables 1 and 3) for different bar ages. It is clear that the size relation between the nuclear disc and the bar does not depend on the bar age, with a constant value close to ∼12%. This demonstrates how the nuclear disc sizes depend on bar properties and resonances, and as the bar evolves, the nuclear disc's absolute size evolves as well.
In the text
thumbnail Fig. 9.

Nuclear disc mass build-up. In this plot we present the nuclear disc mass normalised by the galaxy mass for different bar ages. To measure the nuclear disc mass, we integrated the isolated SFH (blue dashed curves in Figs. B.1 and B.2), following the same approach in de Sá-Freitas et al. (2023a, b). Additionally, we color-coded each point according to its ΣSFR, which increases towards blue. It is clear that young nuclear discs are less massive with a higher star formation rate. As the bars age, the nuclear discs gradually present less star formation, while building up their mass. Lastly, we find a correlation coefficient of 0.85±2×10−3, with p-value = 2×10−4±7×10−5.
In the text
thumbnail Fig. 10.

Galaxy star formation properties with respect to bar ages. We investigate how the bar ageing is related to the star formation of the host galaxy. Left: Main sequence offset (ΔMS – values from Leroy et al. 2019) of the host galaxy with respect to the bar age. Positive values of ΔMS indicate the galaxy is bursting; Negative values indicate quenching. Additionally, we bootstrap our sample 1000 times, in the grey-shaded area, finding a correlation coefficient of r=−0.699±0.003, with p-value = 0.007±0.001. The strong correlation between star formation of the host galaxy and bar ageing is in agreement with the scenario in which bars aid the quenching of the galaxy. Right: Main sequence of galaxies defined in Leroy et al. (2019) (i.e. the sSFR with respect to the galaxy mass). We show their entire sample in a grey density map, while highlighting our sample colour-coded according to bar age, contextualising our results.
In the text
thumbnail Fig. 11.

ΣSFR in the nuclear disc with respect to bar ageing. We present the measured median ΣSFR in the nuclear disc region (as defined in this work; see Table 3) for different bar ages, finding a strong anti-correlation (r=−0.791±0.003 and p-value = 0.0011±0.0003). This demonstrates that, as the bar ages, the nuclear discs tend to form fewer stars.
In the text
thumbnail Fig. 12.

HI mass of the host galaxy with respect to bar ages. We present the mass of neutral hydrogen from Gadotti et al. (2019), based on the 21 cm line fluxes available from LEDA (see Table 1), finding a weak trend between HI mass and bar age, with r = 0.463±0.007, which is not statistically significant, with p-value = 0.151±0.007. This weaker anti-correlation indicates that even though the bar can aid in the quenching of the host galaxy, the gas of the host galaxy is not completely exhausted, but star formation is less efficient (e.g. Saintonge et al. 2016; Bacchini et al. 2019; Pessa et al. 2022).
In the text
thumbnail Fig. 13.

Extrapolated bar fractions for different redshifts from this work. Based on Fig. 4, we display our cumulative distribution (dashed grey histogram) and normalise it by the observed bar fraction in the Local Universe in studies that consider both weak and strong bars (0.67; e.g. Eskridge et al. 2000; Menéndez-Delmestre et al. 2007; Marinova & Jogee 2007). With this, we derive the extrapolated bar fraction over time in our sample (green dots). Additionally, the shaded green region accounts for the systematic error in our bar age measurements of − 1.4 + 1.8 Gyr $ {}^{+1.8}_{-1.4}\,{\textrm {Gyr}} $. With the grey error bars, we also display the likely ranges in the cumulative distribution considering this systematic error as well. We compare our results with the observed bar fraction from different works, finding a remarkable agreement with works that consider both weak and strong bars.
In the text
thumbnail Fig. A.1.

Downsizing and bar formation for different mass measurements. As in Fig. 5, we compare the stellar mass of the host galaxy with respect to bar ages, considering values from Leroy et al. (2019) in the upper panel, and Querejeta et al. (2015) in the bottom panel. For the three different mass measurements we consider in this work, we find no significant correlation between stellar mass and bar ageing.
In the text
thumbnail Fig. B.1.

Individual measurements of bar age of the low-SF sample. Following the de Sá-Freitas et al. (2023a) methodology, we define the bar age as the moment at which the SFH of the nuclear disc (dashed blue line) overcomes the SFH of the main disc (dot-dashed green line). Additionally, based on the tests performed in de Sá-Freitas et al. (2023a) and here, we estimate the systematic measurement error of − 1.4 + 1.8   Gyr $ {}^{+1.8}_{-1.4}\ {\textrm {Gyr}} $.
In the text
thumbnail Fig. B.2.

Same as Fig. B.1, but for the high-SF sub-sample.
In the text

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