The star formation history of the Sco-Cen association Coherent star formation patterns in space and time

We reconstruct the star formation history of the Sco-Cen OB association using a novel high-resolution age map of the region. We develop an approach to produce robust ages for Sco-Cen’s recently identiﬁed 37 stellar clusters using the SigMA algorithm. The Sco-Cen star formation timeline reveals four periods of enhanced star formation activity, or bursts, remarkably separated by about 5Myr. Of these, the second burst, which occurred about 15 million years ago, is by far the dominant, and most of Sco-Cen’s stars and clusters were in place by the end of this burst. The formation of stars and clusters in Sco-Cen is correlated but not linearly, implying that more stars were formed per cluster during the peak of the star formation rate. Most of the clusters that are large enough to have supernova precursors were formed during the 15Myr period. Star and cluster formation activity has been continuously declining since then. We have clear evidence that Sco-Cen formed from the inside out and contains 100-pc long chains of contiguous clusters exhibiting well-deﬁned age gradients, from massive older clusters to smaller young clusters. These observables suggest an important role for feedback in forming about half of Sco-Cen stars, although follow-up work is needed to quantify this statement. Finally, we conﬁrm that the Upper-Sco age controversy discussed in the literature during the last decades is solved: the nine clusters previously lumped together as Upper-Sco, a benchmark region for planet formation studies, exhibit a wide range of ages from 3 to 19Myr.


Introduction
Reconstructing the star formation history of a star-forming region is essential for gaining insight into the complex and outof-equilibrium process of star formation.A timeline of when and where different sub-populations form offers insights into the underlying physical mechanisms driving star formation.For example, is the star formation rate in a collapsing cloud accelerating until gas consumption?Does star formation leave behind discernible spatio-temporal patterns?Or is it a chaotic process?And if it leaves patterns of progression, are they intrinsic to the process or driven by an external agent?Can variations in the star formation rate directly relate to fundamental properties of the resulting stellar population, for instance, the formation of gravitationally bound clusters as opposed to loose stellar associations?Star formation history encodes much of the information needed to address these questions.It is crucial for developing accurate star formation models and interpreting observations of star-forming regions across the universe.
Unfortunately, recognizing distinct populations in a starforming region is challenging, particularly for loose stellar associations that quickly disperse into the surrounding Galactic field, making them difficult to identify.Moreover, as they are formed from the same molecular cloud complex, the velocities and age differences between different sub-populations are small and, therefore, hard to measure.Despite the growing evidence that sub-populations exist inside the same star formation region (e.g., Alves & Bouy 2012;Jerabkova et al. 2019;Chen et al. 2020;Großschedl et al. 2021;Kerr et al. 2021;Luhman 2022a;Miret-Roig et al. 2022b), there is little evidence so far for largescale star formation patterns (Wright et al. 2022).
Recently, Ratzenböck et al. (2022) presented results from a novel clustering algorithm called Significance Mode Analysis (SigMA), which interprets density peaks separated by dips as significant clusters.Using a graph-based approach, the technique detects peaks and dips directly in the 5D multidimensional phase space.The method can identify co-spatial and co-moving clusters with non-convex shapes and variable densities with a measure of significance.The application of SigMA to Gaia DR3 data (Gaia Collaboration et al. 2022a) of stars in and around the Sco-Cen association led to the discovery of multiple clusters1 , reaching stellar volume densities as low as 0.01 sources/pc 3 and tangential velocity differences of about 0.5 km s −1 between different clusters.This level of accuracy is unprecedented and has unveiled 37 stellar clusters inside Sco-Cen.The SigMA algorithm opens new possibilities for a detailed look at the star formation history of Sco-Cen and other nearby star formation complexes.
The goal of this paper is to derive robust ages for the 37 stellar Sco-Cen clusters identified by Ratzenböck et al. (2022) with the SigMA algorithm (hereafter, Paper I) and reconstruct the Star Formation History of this important region.Given SigMA's ability to disentangle young populations in Sco-Cen, adding robust ages to these clusters should enable the construction of a high-resolution age map of the region.The paper is structured as follows.In Sect.2, we present the data and the quality criteria applied.In Sect. 3 we roughly summarize our methods to determine robust isochronal ages, while we outline the methods in detail in Appendix A. In Sect.4, we present our results, which we then discuss in Sect. 5.In Sect.6, we summarize our conclusions.

Data
In this paper, we determine robust isochronal ages for the 37 SigMA clusters in Sco-Cen, which contain 13,103 candidate Sco-Cen members.A detailed description of the process used to select the cluster sample can be found in Paper I (SigMA algorithm), and an overview of the clusters is presented in Table 1.The clusters are assigned to traditional sub-regions within Sco-Cen, including the classical Blaauw (1946) definition (see details in Paper I and Table 1).However, we point out that these borders were drawn initially in 2D on the plane of the sky and should not be seen as physically meaningful entities.They should instead be used for orientation and comparisons with previous works.
To determine the ages of the Sco-Cen clusters, we utilized two different evolutionary model families: PARSEC v1.2S (Bressan et al. 2012;Chen et al. 2015;Marigo et al. 2017) (hereafter PARSEC) and Baraffe et al. (2015) (hereafter BHAC15).These models are outlined in more detail in Appendix A. We also use two different color-absolute magnitude diagrams (CMDs) based on Gaia photometric systems: (M G versus G BP − G RP ) and (M G versus G − G RP ), which are abbreviated as BPRP and GRP, respectively.The absolute magnitude M G was calculated using the distance modulus using the inverse of the parallax as distance, which is reasonable for sources with Sco-Cen distances and low uncertainties, as discussed in Paper I.
We applied a set of photometric quality criteria to the Gaia DR3 photometry to achieve more reliable isochronal age fitting.The influence of photometric uncertainties is highlighted in Fig. C.1.We use the corrected flux excess factor C * as described in Riello et al. (2021).As noted in Evans et al. (2018), large values of the flux excess factor are the result of issues in the G BP or G RP photometry.Additionally, we cut photometric flux errors G err , G BP,err , and G RP,err , as well as RUWE, which (preferentially) removes unresolved binaries in the sample (Lindegren et al. 2018(Lindegren et al. , 2021)).The parameters used are summarized in Eq. ( 1) and the quality criteria in Eq. ( 2).
Our sample is restricted to sources that satisfy the following photometric quality criteria: We use these criteria for the BPRP CMD, while we exclude the G BP,err condition when using the GRP CMD.We visually confirm that these quality criteria reduce the scatter around isochrones significantly, especially in the low-mass regime (see Fig. C.1).We further constrain the absolute magnitude range of the sample, using different cuts for the two model families.
M G < 10 mag (when using PARSEC models) (3) M G < 12 mag (when using BHAC15 models) (4) These cuts are motivated by our observation of areas in the CMD with varying degrees of overlap between data and model isochrones (see Figs. C.2-C.5).Furthermore, the PARSEC and BHAC15 isochrones start to disagree with each other towards the faint end, while the BHAC15 models tend to agree better with the data fainter than M G 10 mag compared to PARSEC models.Therefore, we cut at M G < 10 mag to reduce systematic age shifts determined with PARSEC.This choice is also supported by the mass coverage of the PARSEC isochrones, which are cut off at 0.09 M , while BHAC15 includes low-mass objects down  3), there are 5,257 (∼40%) sources left in both CMDs for PARSEC-BPRP and PARSEC-GRP.For BHAC15-BPRP and BHAC15-GRP there are 8,514 and 8,521 sources left, respectively (∼65% each), after applying the magnitude cut from Eq. (4).The BHAC15 isochrones do not cover the upper mainsequence, since the models stop around M G ∼ 4 mag (at 1.4 M ).However, this is not an issue for the age fitting method, since the method uses only sources until the maximum brightness of each fitted isochrone.This also reduces the number of sources used for fitting to BHAC15 isochrones, depending on the maximum M G .

Method
Determining an accurate age for each cluster is critical for our goal of distinguishing small age differences between clusters and creating a high-resolution Sco-Cen age map.Our isochrone fitting procedure is summarized here, with a comprehensive description in Appendix A.
Rather than simply minimizing the least sum of squares between data points and isochronal curves, we aim to account for observational trends such as unresolved binaries and extinction.We assume a simple model in which data are generated along isochrones with noise contributions drawn independently from skewed Cauchy distributions with zero means to model nonsymmetric noise sources.The influence of reddening and unresolved binaries on the displacement of sources in the CMD is different for each cluster.Instead of fixing the skewness and scale parameters of the skewed Cauchy distribution, we let them be free parameters of the model, which are obtained during Bayesian inference alongside astrophysical parameters such as cluster age and dust extinction.This age fitting technique is explained in detail in Appendix A.

Results
We present robust isochronal ages for the 37 SigMA clusters in Sco-Cen as selected in Paper I. We provide four different age estimates for the clusters, determined with PARSEC-BPRP, PARSEC-GRP, BHAC15-BPRP, and BHAC15-GRP, as outlined in Sect. 2 and Appendix A. The ages determined in this fashion are listed in Table 1.In Appendix B, we compare our ages in more detail to the cluster sample by Kerr et al. (2021), who found a similar substructure in Sco-Cen, while with lower numbers statistics.The clusters in Kerr et al. (2021) appear to be systematically older compared to our age estimates, while we do not (yet) have a clear explanation for this behavior.
In Appendix C, we provide the CMDs showing the bestfitting isochrone models for each cluster and the four different age-fitting results.Unless otherwise noted, we adopt the PARSEC-BPRP ages in our analysis.These isochrones seem robust within the errors compared to the PARSEC-GRP and BHAC15-GRP ages.Furthermore, the combination of PARSEC-BPRP is often used in the literature, which facilitates comparison to previous work (e.g., Bossini et al. 2019;Dias et al. 2019;Cantat-Gaudin et al. 2020;Kerr et al. 2021).Notes.The ages are given for the four isochronal fitting results using the PARSEC and BHAC15 models for both the BPRP and GRP CMDs.
The lower and upper age limits are given in parenthesis, determined from the 1σ highest density interval from the marginalized posterior PDF.
The differently determined ages are compared in Fig. A.3.The clusters are grouped into traditional subregions for orientation, motivated by the original Blaauw borders, as described in Paper I, while these separations should generally not be treated as physically meaningful entities. (a) The numbers of sources are as follows: All = the number of all stellar member candidates per SigMA cluster.BPRP = after applying the photometric quality criteria for the BPRP CMD.GRP = after applying the photometric quality criteria for the GRP CMD. (b) The three clusters Norma-North, Oph-SE, and Oph-NF are excluded from the analysis of the star formation history in Sco-Cen since they are likely unrelated (see text).
We exclude three clusters from the original SigMA sample of 37 clusters, namely Norma-North (Norma-N), Oph-Southeast (Oph-SE), and Oph-NorthFar (Oph-NF), leaving 34 clusters for further discussion in Sect.5.1.Norma-N is excluded, as it is substantially older (∼40 Myr) than the nominal upper age limit of Sco-Cen, which is about 20 Myr.Moreover, Norma-N, Oph-SE, and Oph-NF appear to be kinematically unrelated as suggested by the trace-backs of the cluster orbits, which is discussed in more detail in a follow-up paper (Großschedl et al. in prep.).
Figure 1 presents the spatial distribution of the surfaces enveloping the 34 clusters, color-coded by cluster ages.This figure can be investigated as an interactive 3D plot 2 , which best illustrates the spatial arrangement of Sco-Cen's clusters.It provides important insight into how the complex was assembled.At first glance, it is easy to see that the center of the association contains the oldest clusters, while the youngest clusters, appearing in blue, tend to be at the outskirts of the association.The existence of patterns of age gradients across contiguously located clusters is also clear.
The age gradients are particularly clear towards two quasivertical, approximately 100-pc long chains of clusters.These contiguous cluster chains connect the older clusters at the (older) center of the association with the younger clusters at the (younger) outskirts.The first one comprises the traditional Blaauw's LCC (from here on, LCC chain), while the second connects CrA to the center of the association (from here on, CrA chain).They are remarkable structures for being a contiguous series of clusters following a coherent age gradient.The LCC chain clusters comprise, from old to young and north to south: σ Cen, Acrux, Musca-foreground, Cham, and η Cham.The member clusters toward the CrA chain are less clear and are tentatively arranged as follows, from old to young: φ Lup, η Lup, (V1062 Sco, µ Sco)3 , Sco-Body, Sco-Sting, CrA-North, and CrA-Main.
Toward the Galactic northeast, the main body of Sco-Cen is connected to USco in a similar manner to the cluster chains (see Fig. 3), forming a third chain of clusters, albeit more complex.Recent attempts to reconstruct the star formation history of the USco region also reveal a more complex substructure compared to the LCC or CrA chains (e.g, Squicciarini et al. 2021;Miret-Roig et al. 2022b;Briceño-Morales & Chanamé 2023).This could possibly be explained by a different original gas distribution and by the number and distribution of massive stars located within USco itself or the older clusters in Sco-Cen (e.g., Diehl et al. 2010;Robitaille et al. 2018;Krause et al. 2018;Neuhäuser et al. 2020;Forbes et al. 2021).The origin of USco warrants a dedicated analysis beyond the scope of this paper, but it seems clear from Fig. 3 that USco is the third chain of clusters.These three chains started to form about 10 Myr ago, and are likely induced or enhanced by the feedback generated by the massive clusters formed about 15 Myr ago.
Figure 2 presents the age distribution within the Sco-Cen complex.In the upper panel, we show the distribution of cluster ages using the selected 34 SigMA clusters.In the lower panel, we display the age distribution for the stellar members by assigning each star the age of the parent cluster.We employ a kernel density estimate (KDE) technique to examine the age distribution of clusters and stars, focusing on uncovering the modality structure of the probability density function (PDF).To account for age uncertainty, we implemented an adaptive KDE in which the kernels' size reflects the determined age variance of the samples (see age uncertainties in Table 1).We have standardized the area under the curves to represent the number of clusters and stars for the respective PDFs.
The distribution of cluster ages in Fig. 2 exhibits a significant multi-modality.When applying the calibrated dip test (Hartigan & Hartigan 1985;Cheng & Hall 1998) to the cluster ages, we find a strong indication (p < 0.05) for multiple modes in the data.To locate the modes, we apply the excess of mass test (Müller & Sawitzki 1991;Cheng & Hall 1998), which finds two modes in the following age ranges: (8.5, 10.2), (14.4,15.9) Myr (see Fig. 2, upper panel).Together they make up the two main modes of star formation in the evolution of Sco-Cen, in which over 60% of stars have been formed.The adaptive KDE in Fig. 2

Discussion
We first examine the spatial-temporal patterns in Sco-Cen revealed by isochrone fitting for the individual clusters (Sect.5.1) and consider potential explanations for the observed age patterns (Sect.5.2).In Sect.5.3, we provide a solution to the Upper-Sco age controversy that has perplexed the literature for decades, clarified by Gaia data.

Spatial-temporal patterns in Sco-Cen
The spatial-temporal arrangement of the clusters in Fig. 1 indicates that star formation in Sco-Cen did not proceed chaotically.
Figure 3 shows groups of clusters associated with the star formation rate peaks from Fig. 2 and Table 2.This figure shows a clear relationship between age and position of Sco-Cen clusters, with the older clusters (age > 15 Myr) towards the association's center and the younger cluster towards the outskirts of the association.This spatial arrangement implies an inside-out star formation scenario for Sco-Cen and evokes a feedback-driven scenario reminiscent of the canonical triggering scenario in Elmegreen & Lada (1977).
Although we could speculate that the oldest clusters in the association's center (e Lup and φ Lup) provided the supernovae (SNe) for the initial trigger, the masses of these clusters suggest that they might have produced only a few SNe, assuming a normal initial mass function (IMF).A dedicated model, like the forward modeling done for the Ophiuchus region by Forbes et al. (2021), is warranted to test this suggestion.Perhaps more impressive is the likely number of SNe provided by the 15 Myr star formation burst, which could be in the tens of SNe when integrating over the massive clusters formed during this high star formation rate period.These SNe, together with stellar winds, Notes.There are two main modes of star formation, including the second and third peak at 15 Myr and 10 Myr ago, which are confirmed as significant by the excess of mass test.We find two smaller peaks at 20 Myr and 5 Myr ago, for which we give the time-frames approximately. (a) We tentatively assign each of the 34 SigMA clusters to one of the peaks, as separately displayed in Fig. 3. (b) CrA-Main is likely closely related to the younger Coronet cluster, which is largely embedded in the head of the CrA molecular cloud.
ionizing radiation, and mass loss events, would have injected substantial energy and momentum into the primeval gas in the Sco-Cen region, likely pushing part of it to collapse.Figure 4 displays the ages as a function of the number of stars per cluster, color-coded by age and scaled by the number of stars per cluster.This visualization facilitates linking individual clusters to peaks in the star formation history of the region.Similarly to Fig. 2, we can see that a peak at around 15 Myr ago contributed the largest numbers of stars and the most massive clusters to the association.Since then, star formation has been declining, although periods of increased star formation rate seem to appear about every ∼ 5 Myr (Fig. 2).Small clusters have formed throughout the entire history of Sco-Cen.
By using the distribution and ages of the SigMA clusters, star formation in Sco-Cen can be described as follows: The first Sco-Cen stars were formed about 20-25 Myr ago in the primordial Sco-Cen giant molecular cloud.At around 15 Myr ago, there was a burst of star and cluster formation where most stars in the association formed.This burst aligns with a scenario presented in Zucker et al. (2022), which suggests that the Local Bubble was triggered by massive stellar feedback originating from Sco-Cen.Zucker et al. (2022) suggest that the first SNe that powered the Local Bubble happened about 14 Myr ago, which is roughly compatible with feedback from the oldest stellar populations in Sco-Cen.Considering that the most massive stars require a few million years to explode as SNe, the likely first Sco-Cen SNe originated in the oldest clusters presented in this work, particularly e Lup and φ Lup.The feedback of possible SNe at that time may have triggered the Sco-Cen 15 Myr burst, which created the most massive clusters in the association.Subsequently, SNe originating from the 15 Myr clusters likely continue feeding the Local Bubble's expansion, with the last SNe taking place about 2 Myr ago (Fuchs et al. 2006;Breitschwerdt et al. 2016;Feige et al. 2017;Krause et al. 2018;Neuhäuser et al. 2020).
While we propose that feedback played a crucial role in the formation of Sco-Cen, it is hard to quantify how crucial it was.At this point, we have no evidence that the formation of the first stars in Sco-Cen was induced by feedback or any external factor to a collapsing molecular cloud.The same can be argued for the origin of the 15 Myr burst.While tempting to invoke e Lup or φ Lup as the potential progenitors of this burst, this is tentative and modeling is required to make a stronger statement.Still, what is clear now is that star formation since the peak of star formation rate about 15 Myr ago formed coherent patterns that are best explained as the direct product of feedback.Clusters younger than 10 Myr are arranged in quasi-linear radial structures with coherent age gradients from old in the center to younger in the outskirts of the association.The observed "chains of clusters" (the LCC, CrA, and the USco chain) are clear examples.

The "Octopus" model
In their study, Krause et al. (2018) proposed a "Surround and Squash" scenario for the formation history of Sco-Cen, suggesting that the region formed from a long connected cloud, shaped as an elongated sheet.They argued that superbubbles continuously broke out of this sheet to surround and squash the denser parts of the cloud (while small cloud fractions initially survive in-between), inducing further star formation and creating several The peaks of star and cluster formation rate seem to be periodically distributed (every ∼ 5 Myr, see also Fig. 2).
shells and superbubbles.The authors also confirmed the existence of a large super-shell around the entire OB association and a nested filamentary super-shell.Krause et al. (2018) suggested that the first SNe occurred at the center of the primordial Sco-Cen cloud, which agrees with our results.They proposed that possible SNe originating from the oldest clusters compressed the surrounding gas, which could have caused the 15 Myr burst.
The "Surround and Squash" model was designed to explain the age ranking of the subgroups, with UCL being the oldest and USco the youngest.The main assumption of this model is that the Sco-Cen population is described by the three main Blaauw subgroups, which we now know is an oversimplified description of the association.Our results instead point to an "Octopus" model, where most stars and clusters are formed at the head of the octopus, and several arms extend radially outward, containing the younger stars and clusters in the association.There is no obvious need for a "Surround and Squash" scenario to explain the observations.Although we do not have sufficient evidence to state the likely role of feedback in the formation of the head, the formation of the arms is very likely a product of the feedback from the massive stellar population in the head.
In conclusion, the star formation patterns described in this work (combined with earlier evidence for massive stellar feedback) suggest an important role for feedback-driven star formation in a manner similar to the classical sequential star formation scenario of Elmegreen & Lada (1977).The observed octopus-like inside-out formation of Sco-Cen provides a simpler explanation compared to the "Surround and Squash" model, while both are feedback driven.Our results for the Sco-Cen OB association suggest a generally significant role for feedback in the formation and evolution of OB associations.Similar evidence can be found in the Orion OB1 association, where also an important role for massive stellar feedback has been found (e.g., Brown et al. 1994Brown et al. , 1995;;Ochsendorf et al. 2015;Großschedl et al. 2021;Swiggum et al. 2021;Foley et al. 2022), as well as in Vela (e.g., Cantat-Gaudin et al. 2019;Armstrong et al. 2022), Cygnus (e.g., Quintana & Wright 2021, 2022), or Cepheus (e.g., Kun et al. 1987;Szilágyi et al. 2023).

Upper-Sco age controversy
There has been a long discussion in the literature about the age of the Upper-Sco Association (USco).Due to its young age, richness, and proximity to Earth, USco is a unique laboratory for early stellar evolution and planet formation studies.Therefore, getting the correct age for USco (or, better said, the ensemble of different coeval clusters that were previously taken as the single population USco) is critical for multiple research fields across astronomical scales.
Traditionally, the stellar populations toward USco were often sub-structured into two parts, ρ Oph (partially embedded young stellar objects in the Ophiuchus cloud), and USco.The age deter-minations for USco in the literature from the last decades (pre-Gaia) fall broadly around two estimates: 5 Myr and 10-12 Myr. de Geus et al. (1989b) used the massive stars in USco to determine an age of about 5 Myr, an estimate confirmed in Preibisch et al. (2002), using the full stellar mass spectrum of USco.Pecaut et al. (2012) on the other hand determined an age of about 10-12 Myr using intermediate to high-mass stars.Sullivan & Kraus (2021) find an age gradient in USco, suggesting that the observed mass-dependent age gradient can be explained by a population of undetected binary stars.They argue their result supports the previously suggested 10 Myr age for USco, with a small intrinsic age spread.
Since the release of Gaia data, several updated cluster catalogs have been published for the USco association, including cluster samples by Squicciarini et al. (2021) 1).
Fang et al. ( 2017) (hereafter F17) discuss a sample of stars in the USco region compiled from several sources in the literature (Preibisch & Zinnecker 1999;Ardila et al. 2000;Slesnick et al. 2006;Preibisch et al. 2002;Luhman & Mamajek 2012;Rizzuto et al. 2015;Pecaut & Mamajek 2016).The sample includes known stellar parameters, such as spectral types, temperatures, and stellar luminosities, allowing for age analysis in the Hertzsprung-Russell diagram (HRD).However, for their discussion, F17 assume that the stars belong to a single population.Treating this sample as a single population generates a large spread in the HRD (see their Fig. 5 and our CMD in Fig. 5), making it impossible to reliably determine the age.For example, isochrones from about 3 to 15 Myr all provide good fits to the data, depending on the spectral type.
The fact that the SigMA clusters4 and the mentioned other recent clustering studies using Gaia data show narrow CMD sequences (hence, better-constrained ages) highlights the high value of the high precision astrometry of the Gaia satellite.We can now revisit the F17 sample cross-matching it with the SigMA clusters5 to investigate the USco age controversy.We find that there are about 500 cross-matches of F17 with SigMA, which are contained in 12 of the SigMA clusters with different ages.Stars from all 12 clusters are projected toward the traditional USco region, while nine out of the 12 clusters have been assigned to the USco clusters and the remaining three clusters have been assigned to the UCL clusters (see Table 1).
Figure 5 shows all stellar members of the 12 clusters in the Gaia BRPR CMD and Fig. C.6 displays the individual clusters separately.In these figures, the blue symbols represent all stellar members from the 12 clusters as selected in Paper I, with additional photometric quality criteria from Eq. ( 2), but excluding the RUWE cut.The red dots represent the sources that are in both samples, Paper I and F17.The isochrones in Figs. 5 & C.6 are PARSEC isochrones for the Gaia DR3 passbands with solar metallicity and no extinction.It becomes now clear that previous USco age estimates have been using a mix of different populations at different evolutionary stages and different locations along the line-of-sight.Such a mixture will naturally broaden the HRD or CMD sequence, as is apparent in Fig. 5.
A possible mixture of populations was already pointed out by F17, while the available data at that time did not allow a clear separation of the stellar clusters, as was achieved with Gaia data.Evidently, separating the F17 sample into coeval clusters, as done by SigMA and other recent studies, solves the age controversy.

Conclusions
In this paper, we reconstruct the star formation history of the closest OB association to Earth, Sco-Cen, by deriving robust isochronal ages for 37 clusters selected with the SigMA algorithm on Gaia DR3 data (Ratzenböck et al. 2022).The ages of the 37 coeval stellar clusters, some previously unrecognized, reveal the complex star formation history of Sco-Cen and are compared with previous work.The main results of this work can be summarized as follows: 1. Sco-Cen's star formation history is dominated by a brief period of intense star and cluster formation rate about 15 Myr ago.This is consistent with previous works.Most of Sco-Cen stars and clusters were in place after this intense formation period.The production of stars and clusters has been slowly declining since this burst.2. We identified four discernible stages during the formation of Sco-Cen associated with elevated star formation activity.
They are, approximately, the 20 Myr, 15 Myr, 10 Myr, and 5 Myr bursts.Remarkably, these elevated star formation activity periods seem periodic, separated by spans of about 5 Myr. 3. The formation of stars and clusters is correlated throughout the entire star formation history of Sco-Cen.Still, after the initial burst 20 Myr ago, the star formation rate more than doubles during the main 15 Myr burst.This implies that the formation of the large majority of clusters with supernova precursors (clusters containing more than about 500 stars) took place during the peak of the star-and cluster-formation rate.4. Sco-Cen was formed inside out, meaning that there is a correlation between the age of a cluster and its distance to the oldest cluster in the association.Older clusters from the 20 Myr and 15 Myr bursts are located in the center of the association, while younger clusters are located toward the outskirts of the association. 5. We find well-defined patterns of star formation progression in space and time.In particular, two 100-pc long chains (LCC and CrA chains) of contiguously located clusters exhibit a well-defined age gradient, from massive older clusters to smaller younger ones.The simplest explanation for these long chains of correlated clusters is feedback acting on a diminishing gas reservoir.These patterns are reminiscent of the classic Elmegreen & Lada (1977) scenario, suggesting an important role for feedback on the formation of the Sco-Cen population.Morphologically, the formation appears to have been "Octopus-like", with most older stars in the head and younger stars in the radial arms, the quasi-linear chains of clusters.6.We confirm the post-Gaia view from recent studies that USco is not a single cluster, which solves the Upper-Sco age controversy.What was taken in the literature of the last decades as the USco stellar population consists instead of up to nine clusters with ages between 3 and 19 Myr, naturally explaining the wide age spread and conflicting results in earlier studies.This realization applies to all Blaauw's subgroups (USco, UCL, and LCC).It directly impacts planet formation studies in Sco-Cen, a benchmark laboratory for planet formation, calling for a revision of disk ages.
Gaia studies of Sco-Cen are revealing a new set of captivating stellar substructures.The classical Blaauw subgroups (USco, UCL, and LCC), originally defined on the plane of the sky in 2D, do not capture the richness of structure and the many stellar populations in Sco-Cen.Separation into three main regions is obsolete and does not encapsulate the more complex, but more revealing star-formation history of this association.Tracebacks of the different Sco-Cen clusters will test the main conclusions of this work, and they will be able to test and characterize the existence of well-defined chains of clusters in OB associations.isochrones found by Bossini et al. (2019) and Dias et al. (2019).
To ensure comparability, we apply the same quality criteria discussed in Sect. 2 and restrict the sample to clusters within 500 pc and to ages < 100 Myr to create similar CMD conditions as Sco-Cen sub-clusters.We assume flat priors between the minimum and maximum of the obtained parameter values.Since different colors have different value ranges, we determine separate scale ranges for G BP − G RP and G − G RP .
We use the Markov Chain Monte Carlo (MCMC) method implemented within the public code emcee (Foreman-Mackey et al. 2013) to generate samples from the posterior PDF in Eq. (A.5).For each parameter, we compute the marginal PDF, its maximum a posteriori (MAP) position, and the 1σ credible interval determined via computing the 68% high-density interval (HDI) to represent the fitting results and uncertainties, respectively.Sun, including the Sco-Cen association.We find a similar extent and clustered substructure in the Sco-Cen region.However, the individual SigMA clusters are significantly larger in size and numbers of stars compared to KRK21 (see Table E.3 in Paper I). Figure B.1 compares the age estimates from KRK21 to ages as determined in this work using the PARSEC-BPRP ages if sufficient overlap between individual clusters is present.KRK21 also uses the PARSEC-BPRP models with solar metallicity, allowing direct comparison.We require that at least 10% of the sources of a matching SigMA cluster need to be part of the corresponding KRK21 cluster and that at least 60% of the sources of one KRK21 cluster need to be part of the same SigMA cluster.The different fractions are chosen since the individual KRK21 clusters are significantly smaller in size compared to SigMA, in particular when considering sub-clusterings which are themselves parts of KRK21's top-level clusterings (TLC) to extract more substructure (sub-clustered by KRK21 with HDBSCAN's EOM or leaf ).
In Figure B.1 there appears to be a trend with growing age in that KRK21 ages are systematically older as a function of our ages, affecting in particular clusters with older ages ( 10 Myr).This trend is puzzling because both studies use the same isochrone models.The imperfect overlap between the two samples could create different outcomes in the age fitting; however, possible imperfect matches of clusters would not create a trend.Another difference is the use of Gaia DR2 in KRK21 versus Gaia DR3 in Paper I. A likely culprit for the age-difference trend seems to be the age correction done in KRK21, which might be biasing their age estimate as a function of age (with their correction procedure, they will necessarily get more field stars for the older clusters) 10 .Moreover, as outlined in the meth-10 They use the selected clusters as "signposts" (training sets) to select additional potential cluster members with HDBSCAN, with similar spa- ods section, selecting an appropriate fitting method is crucial since the scatter of sources in a CMD is not distributed normally around the best fitting isochrone (see the explanations in Appendix A).
The age-difference trend highlights the importance of careful age determination when using isochronal models.It should caution against comparing ages from different works at face value without considering possible biases that the various methods and fitting approaches could introduce.displays the members of all 37 SigMA clusters in the BRPB and GRP CMDs (lightgray dots).After applying the quality criteria from Sect. 2, the scatter of sources in the CMD reduces (colored dots), particularly affecting low-mass sources.There is a trend such that inferior photometry tends to get shifted to the left in the BPRP CMD and to the right in the GRP CMD (see the scatter of the lightgray dots).The reliability of a source's cluster membership, as selected with SigMA, can be estimated via a stability value ranging from 0%-100%, which indicates how often individual sources appear throughout the ensemble of tial and kinematic properties, to reintroduce potentially older members, older than their original age selection of < 50 Myr.clustering solutions per cluster.We color-code the sources by their stability value.It can be seen that sources, which appear on an older age sequence, generally have lower stability and are, therefore, more unreliable members.In this work, we do not remove sources based on a stability cut since our isochrone fitting method is tuned to deal with outliers.

Appendix C: Additional Figures
Figures C.2-C.5 show the Gaia CMDs for each cluster with over-plotted isochrones from the best fitting PARSEC and BHAC15 models, both for BPRP and GRP CMDs.The sources are again color-coded for stability.The maximum stability varies per cluster, while the stellar members of the more massive clusters tend to have higher stability up to 100%, while some smaller scale clusters have a maximum only at around 10%, like Cen-Far or Oph-NF.This does not indicate that such clusters are not real, while their identification in the sea of noise was less pronounced compared to more massive clusters.Therefore, we vary the upper limits of the color scale individually per cluster, using the mean stability per cluster, which is given in the legend of each panel.2) are plotted, with the remaining number of sources given in the legend (Phot-cut).The dots are color-coded for stability with lower limits set to 2.5% (orange) and upper limits (dark) are varied per cluster, as given in the legend (Stab-limit, %).The magenta and blue solid lines show the best-fitting PARSEC (P) and BHAC15 (B) isochrones, respectively, as determined for BPRP, and the dashed lines show the upper and lower age limits (age limits are given in parenthesis in the legend).The horizontal solid and dashed light-gray lines give the magnitude limits at M G > 10 mag and M G > 12 mag for PARSEC and BHAC15, respectively, used to exclude sources from the age fitting.The blue dots are the SigMA members of the respective clusters with additional photometric quality criteria (see Sect. 5.3).The red dots mark the sources that match with the F17 sample.We do not use the RUWE cut for this overview, which reveals some binary sequences.The dashed black line shows the PARSEC isochrone for the cluster age as estimated in this work (see legends).

Fig. 1 .
Fig. 1. 3D distribution of 34 clusters in the Sco-Cen association found by SigMA.The Sun is at (0,0,0) and the Z=0 plane is parallel to the Galactic plane.The surfaces of the cluster volumes are shown, color-coded by age, from dark blue (2 Myr) to dark red (21 Myr).For more details, see the link to the interactive 3D version.

Fig. 3 .e
Fig.3.Star formation progression in Sco-Cen, shown with the same orientation in XYZ and color-scaling as in Fig.1.By separating the clusters in age bins, following the peaks in Fig.2and Table2, one can appreciate a consistent inside-out progression of star formation from older to younger clusters.For more details, see the link to the interactive 3D version.Table2.Overview of the star formation modes/bursts as determined from the age distribution of Sco-Cen clusters (Fig.2).Notation Age (Myr) Description Clusters a 20 Myr peak ∼20-22 Initial onset of star formation in Sco-Cen e Lup, Libra-South, US-foreground

Fig. 4 .
Fig. 4. Timeline of the formation of clusters in Sco-Cen, color-coded by age (same as in Fig.1) and scaled by cluster size.The horizontal lines represent age uncertainties.While Sco-Cen has been forming small clusters (≤ 250 stars) continuously since its formation 20-25 Myr ago, its large clusters ( 1,000 stars) were all formed during the peak of the star formation rate, around 15 Myr ago.Regarding their absolute numbers, most of the stars and clusters we can observe today in the Sco-Cen region were formed around 15 Myr ago.Since then, star formation has been declining.The peaks of star and cluster formation rate seem to be periodically distributed (every ∼ 5 Myr, see also Fig.2).
, Kerr et al. (2021), Miret-Roig et al. (2022b), Briceño-Morales & Chanamé (2023), and the SigMA sample from Paper I. The new view of USco reveals multiple clusters projected on the same region of the sky and the previous ages of 5 or 10 Myr for USco are now superseded.The ages for the overlapping clusters along the same lineof-sight range from 3 to 19 Myr (see Table

Fig. 5 .
Fig. 5. Gaia BPRP CMD displaying members of the 12 stellar clusters that have matches with USco members from F17.The blue dots are all sources in the 12 SigMA clusters that pass additional photometric quality criteria (see text).The red dots indicate sources that are both in SigMA and F17.Two PARSEC isochrones are shown for 5 Myr (solid) and 10 Myr (dashed), marking the earlier assumed nominal ages of USco.The arrow shows an extinction vector with a length of A G = 1 mag.See Fig. C.6 for an overview of the separate CMDs of the individual 12 clusters.
Fig. A.3.Comparison of the cluster ages (in Myr) as determined with different model families (PARSECand BHAC15) and different Gaia CMDs (BPRP and GRP).We observe strong agreement between ages determined with PARSEC BPRP, PARSEC GRP, and BHAC15 GRP isochrones.In contrast, BHAC15 BPRP model fits seem to suggest systematically younger ages.

Fig. B. 1 .
Fig. B.1.Comparison of the cluster ages from this work (using PARSEC-BPRP) to ages from KRK21.Only clusters with sufficient overlap between the two samples are shown (see text for more information).The solid gray line is a one-to-one line, and the black dashed line is a linear fit to the data points, as given in the panel.Individual clusters are marked with different colors and symbols (see legend), including error bars.

Figure C.
Figure C.1 displays the members of all 37 SigMA clusters in the BRPB and GRP CMDs (lightgray dots).After applying the quality criteria from Sect. 2, the scatter of sources in the CMD reduces (colored dots), particularly affecting low-mass sources.There is a trend such that inferior photometry tends to get shifted to the left in the BPRP CMD and to the right in the GRP CMD (see the scatter of the lightgray dots).The reliability of a source's cluster membership, as selected with SigMA, can be estimated via a stability value ranging from 0%-100%, which indicates how often individual sources appear throughout the ensemble of Figure C.1 displays the members of all 37 SigMA clusters in the BRPB and GRP CMDs (lightgray dots).After applying the quality criteria from Sect. 2, the scatter of sources in the CMD reduces (colored dots), particularly affecting low-mass sources.There is a trend such that inferior photometry tends to get shifted to the left in the BPRP CMD and to the right in the GRP CMD (see the scatter of the lightgray dots).The reliability of a source's cluster membership, as selected with SigMA, can be estimated via a stability value ranging from 0%-100%, which indicates how often individual sources appear throughout the ensemble of

Fig
Fig. C.1.Gaia CMDs for the BPRP (left) and GRP (right) colors.The gray sources are all Sco-Cen members from Paper I. Sources that remain after applied quality criteria (see Sect. 2) are color-coded in copper for stability.The scatter of the gray sources compared to the colored sources highlights the influence of photometric uncertainties.PARSEC and BHAC15 isochrones are over-plotted for 5 Myr and 20 Myr.We mark the two magnitude limits at M G > 10 mag and M G > 12 mag in light-purple as used for PARSEC and BHAC15 isochrone fitting, respectively.
Figure C.6 shows the 12 clusters, which have matches with the USco sample from Fang et al. (2017) (see Sect. 5.3), first shown in Fig. 5.The separation of the clusters into individual CMDs highlights the different ages of stellar clusters that are located toward USco, which were often treated as one population in the past.

Fig
Fig. C.2. Gaia BPRP CMDs for the SigMA clusters 1-20.Only cluster members, which pass the photometric quality criteria from Eq. (2) are plotted, with the remaining number of sources given in the legend (Phot-cut).The dots are color-coded for stability with lower limits set to 2.5% (orange) and upper limits (dark) are varied per cluster, as given in the legend (Stab-limit, %).The magenta and blue solid lines show the best-fitting PARSEC (P) and BHAC15 (B) isochrones, respectively, as determined for BPRP, and the dashed lines show the upper and lower age limits (age limits are given in parenthesis in the legend).The horizontal solid and dashed light-gray lines give the magnitude limits at M G > 10 mag and M G > 12 mag for PARSEC and BHAC15, respectively, used to exclude sources from the age fitting.

Fig
Fig. C.4.Similar as Fig. C.2, but showing the GRP CMD for the SigMA clusters 1-20.The best fitting PARSEC isochrone is shown as determined with GRP.

Fig
Fig. C.6.Gaia BPRP CMD showing the 12 SigMA clusters that have matches with sources from F17.Similar to Fig. 5, but now the individual clusters are displayed in separate panels.The sample includes nine clusters from USco and three clusters from UCL (bottom row), as assigned based on traditional borders (see Paper I).The three UCL clusters have only a few matches since they only partially reach into the USco region.The blue dots are the SigMA members of the respective clusters with additional photometric quality criteria (see Sect. 5.3).The red dots mark the sources that match with the F17 sample.We do not use the RUWE cut for this overview, which reveals some binary sequences.The dashed black line shows the PARSEC isochrone for the cluster age as estimated in this work (see legends).
5 (15.0, 16.1) 15.5 (15.1, 15.9)  9.5 ( 8.8, 9.9)14.7 (14.4,15.3) 22 LCC Acrux 394 276 283 11.2 (10.2, 12.2) 10.7 (10.1, 11.5) 7.3 ( 6.9, 7.4) 10.4 (10.1, 10.8) reveals a small third and fourth peak at around 4 Myr and 21 Myr, respectively.The four peaks in star formation rate are summarized in Table 2. Star formation history of Sco-Cen.Top: The age distribution of the 34 clusters in Sco-Cen traces four main star formation events in the history of the association.Bottom: The stellar age distribution in Sco-Cen shows a similar pattern.To study the age distribution of clusters and stars, we used a kernel density estimate with an adaptive bandwidth corresponding to the age uncertainty of each sample.The formation of stars and clusters is correlated, but not linearly, meaning that, when compared to the average in the association, more stars were formed per cluster during the peak of star formation rate, about 15 Myr ago.