PRE-MAIN-SEQUENCE TURN-ON AS A CHRONOMETER FOR YOUNG CLUSTERS: NGC 346 AS A BENCHMARK^*

The main-sequence (MS) turnoff is the most reliable feature for age-dating a star cluster. Nevertheless for very young clusters, with ages of tenths to a few Myr, the identification of the turnoff is usually hampered by the paucity of massive stars.

We propose to take a different point of view, focusing on the Turn-On (TOn), the color-magnitude diagram (CMD) locus where the pre-main sequence (PMS) joins the MS. Although the importance of the TOn has already been emphasized in several papers (e.g., Stauffer 1980; Belikov et al. 1998; Baume et al. 2003; Naylor et al. 2009), its application to dating extragalactic star-forming regions is a new proposition.

In analogy with the turnoff, the TOn properties are directly related to the age of the stellar population, but with evolutionary times much shorter than the corresponding MS times. In fact, from simple stellar evolution arguments, the age of a cluster is equal to the time spent in the PMS phase by its most massive star still in the PMS phase. By definition, this star is at the TOn. Hence, when the intrinsic luminosity of the TOn is detected, it is straightforward to associate it with the age of the cluster.

In the first part of this Letter, we describe how the intrinsic properties of the TOn can be used as a clock. In the second part, we present a new method for applying TOn-related properties to date extragalactic systems. Finally, we apply this method to the largest extragalactic star-forming region, NGC 346, in the Small Magellanic Cloud (SMC).

The potential strength of the TOn is apparent from the morphology of isochrones taking both the PMS and MS phases into account. Figure 1(a) shows five isochrones with metallicity Z = 0.004, obtained combining the Pisa PMS tracks (Cignoni et al. 2009) with the Padua evolutionary tracks (Fagotto et al. 1994) to cover the entire mass range 0.45–120 M_☉. For all ages younger than 15 Myr, the isochrone portion just before the zero-age main sequence (ZAMS) has a hook and then is significantly flatter than the ZAMS. The TOn is at the vertex of the hook, quite easy to recognize.

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To test if/how the TOn can be useful as a cosmo-chronometer, we simulated synthetic simple stellar populations (SSPs), using the tracks quoted above. As an example, we describe the case with metallicity Z = 0.004, burst duration 1 Myr, Salpeter's initial mass function (IMF), and no binaries. To guarantee statistically significant tests, extensive theoretical simulations have been performed with a number of synthetic stars up to 1 × 10⁶.

Panels (b)–(f) in Figure 1 show the luminosity functions (LFs), binned in 0.2 magnitude bins and scaled to the total number of stars, of synthetic SSPs (open histograms) corresponding to the isochrones of panel (a). A reference synthetic zero-age population, which is artificially built without⁸ PMS stars (gray filled histogram), is also shown. In the LF without PMS, the only valuable feature is a mild peak around M_V ≈ 2, consequence of an inflection in the derivative of the mass–M_V relation in MS stellar models around m = 2 M_☉. By contrast, when the evolution starts from the PMS phase, the corresponding LFs develop an additional strong peak followed by a dip. Peak and dip reflect respectively the steep dependence of stellar mass on M_V near the TOn (see also the discussion in Piskunov et al. 2004) and the following flattening below the TOn (caused by the short evolutionary timescale of the PMS phase compared to the MS). After the dip, the shape of the LF mimics the IMF.

The LFs in Figure 1 indicate the importance of both features, peak and dip, to infer the cluster age: the older the age, the fainter the LF TOn peak and the corresponding dip. On the other hand, for the explored range of ages the magnitude of the MS peak is fairly constant (M_V ≈ 2), being locked to the (much longer) MS evolutionary times. Through a polynomial fit to the models, theory provides a useful relation between age (τ) of the SSP and the magnitude M_V of the TOn in the range 2–100 Myr:

$$\begin{eqnarray} \displaystyle \tau ({\rm Myr})=&\sum _{j=0,5} a_{j}\times (M_{V})^j&. \end{eqnarray} \tag{ 1 }$$

In turn:

$$\begin{eqnarray} \displaystyle M_{V}=&\sum _{j=0,5} b_{j}\times \lbrace \log [\tau ({\rm Myr})]\rbrace ^j&. \end{eqnarray} \tag{ 2 }$$

Once the bin width of the LF is chosen, Equation (1) (whose coefficients are given in Table 1) gives also the intrinsic uncertainty on the age. Assuming 0.2 mag wide bins, the minimum uncertainty is about 0.6 Myr at 3 Myr, 1.3 Myr at 20 Myr, 2.5 Myr at 30 Myr, and 6 Myr at 50 Myr. The TOn formula is deliberately limited to populations older than 2 Myr, since for younger ages the current PMS models are still extremely uncertain (see Baraffe et al. 2002, for a discussion).

Although attractive, the TOn dating method should be used with caution. When we compare the observed and theoretical LFs, it is important to evaluate the following uncertainties.

Incompleteness and photometric errors. To test real conditions, the synthetic SSPs have been degraded assuming reddening and distance of the SMC, E(B − V) = 0.08 and (m − M)₀ = 18.9, and photometric errors and incompleteness as derived by Sabbi et al. (2007) from Hubble Space Telescope (HST) images of NGC 346. Figure 2(a) shows the degraded LF for populations of 5, 30, 40, 50 Myr: at the distance of SMC the excellent quality of the HST/Advanced Camera for Surveys (ACS) photometry guarantees perfect detectability of the peak/dip feature up to about 50 Myr. Beyond this age, the TOn becomes too faint to be detected.

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Poisson fluctuations. In order to check how many stars are necessary to safely identify the TOn, we progressively reduced the number of synthetic stars belonging to the 5 Myr population, until the TOn peak was hidden by the Poisson fluctuations. This experiment indicates that about 50 stars brighter than M_V ≈ 5 (corresponding to a cluster total mass of ≈500 M_☉) are sufficient to identify the TOn with a significance of 2σ.

IMF, binaries, star formation duration. In Figure 2(b), the synthetic 5 Myr SSP has been modeled changing the binary fraction (50% of simulated stars have now an unresolved companion, randomly extracted from the same IMF as the primary) and the IMF exponent (1.5–3). None of these changes alters significantly the TOn position: the case with binaries is almost identical to the reference case, while the adoption of different IMFs modifies only the shape of the LF before and after the TOn peak.

In Figure 2(c) we have simulated a 10 Myr old cluster with a star formation activity that lasts 1, 3, and 5 Myr (see, e.g., Palla & Stahler 2000). As expected, with a prolonged star formation activity the LF peak grows brighter and broader. In this case, the peak magnitude provides information on the average age of the population.

Reddening. Typical of star-forming regions, the presence of highly obscuring material (foreground as well as local) can significantly dim and blur a TOn. Thus, reliable reddening estimates are fundamental to obtain unbiased ages. On the other hand, there are several regions with affordable foreground and intrinsic extinction. NGC 346 is one of them with foreground E(B − V) ∼ 0.08 and internal ≲0.1 mag (as deduced from the upper MS), which contributes to the final uncertainty by ≈1–2 Myr.

Our goal is to study how star formation develops in extragalactic star-forming regions. In the CMD of these regions, the MS is often contaminated by young fore/background stars, and membership information is available for a safe decontamination only in a few cases. The presence of the field MS partially fills the LF dip and sensibly lowers the significance of the TOn in the LF.

To get around the problem of contamination, we propose to combine the fact that, by definition, no sub-cluster member on the MS can be fainter than the TOn, together with a careful analysis of the spatial distribution of the stars in the region. The procedure we suggest has three main steps. (1) Selection of bona fide MS stars (both members and non-members of the clusters) of all magnitudes. In order to take into account photometric errors and reddening, we consider all the stars bluer than a ridge line appropriately redder than the theoretical ZAMS. (2) Division of the selected MS stars into bins of progressively fainter magnitude. For each bin of a given magnitude, the spatial distribution of stars is examined to assess whether the sub-clusters are still visible. When a sub-cluster is clearly identified up to a given magnitude, but it disappears in the fainter maps, we identify the magnitude of its TOn. This is because we have reached the magnitude where the sub-cluster members have not yet reached the MS, and MS stars fainter than this limit do not belong to that sub-cluster. In order to evaluate the statistical significance of the sub-cluster disappearance from the maps, for each of the three sub-clusters we built a stellar density radial profile and we evaluated the contribution from different magnitude bins. For field stars, we expect a flat stellar density profile, while a decrease in stellar density is the typical signature of a sub-cluster. The range of magnitudes where the transition between the two profiles occurs identifies the apparent magnitude of the TOn. (3) Age determination of the sub-clusters. After applying reddening and distance modulus corrections, we use Equation (1) to translate the sub-cluster TOn magnitude into an age. The final uncertainty is fixed by the bin width, which is, in turn, chosen to obtain an acceptable number of counts per bin.

To test the strength of our method, we applied it to the star-forming region NGC 346 in the SMC, whose images acquired by the HST ACS have revealed a wealth of young sub-clusters containing several PMSs (Sabbi et al. 2007). This region provides excellent conditions in which to test our method because its recent strong activity supplies an outstanding sample of PMS stars (Nota et al. 2006). The complexity of its structure, with several non-coeval sub-clusters, requires a method able to trace the temporal sequence of events leading to the present configuration. In this Letter, we focus on three of the richest sub-clusters, SC-1, SC-13, and SC-16, as defined by Sabbi et al. (2007). Their location in the region can be seen in their Figure 8.

Figure 3 summarizes our analysis of NGC 346. To select only MS stars, we used a ridge line 0.05 mag redder than the theoretical Z = 0.004 ZAMS. We considered all the stars bluer than this line as bona fide MS stars and divided them into six bins of different sizes. Bona fide MS stars are drawn in black in the top-left panel of Figure 3, where all the other stars are marked in gray. The other five panels show the spatial distribution of the bona fide MS stars for progressively fainter bins of magnitude. Analyzing these maps, we find that the central sub-cluster SC-1 is well visible down to V = 21, while no obvious spatial structure resembling SC-1 is observable in the fainter maps. The sub-cluster SC-16, on the contrary, is still clearly visible down to V = 23. Beyond this limit, also SC-16 vanishes. The small sub-cluster SC-13 is recognizable at least to V = 21. Note that the stellar agglomeration appearing at V = 22 corresponds to the 4–5 Gyr turnoff stars of the older cluster BS90 (see, e.g., Sabbi et al. 2007) in the foreground of NGC 346.

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In order to test the significance of the sub-clusters, we examined the radial density profile of the three sub-clusters as a function of magnitude (Figure 4, left panels). The profiles are calculated using annuli of equal area centered on the highest density peak. The inner radius is fixed at 150 pixels. To exclude any completeness issue in these crowded regions, we also show in the middle panels of Figure 4 the completeness factors obtained from the extensive artificial star tests performed by Sabbi et al. (2007), for all stars within 100 pixels from the centers of SC-16, SC-1, and SC-13. To further test the final ages, theoretical isochrones are over-imposed on the CMDs (right panels of Figure 4).

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3.1. SC-16

3.2. SC-1

3.3. SC-13

The evolution of young star-forming regions in their earliest stages is still quite unknown. For very young clusters, with ages of tenths to a few Myr, the identification of the turnoff is usually hampered by the paucity of massive stars. However, when a cluster is sufficiently young to harbor PMS stars, the luminosity of its TOn provides a robust indication of its age. Furthermore, while the PMS evolutionary models still suffer several limitations, the simple comparison of TOn luminosities is a reliable measure of relative ages.

In the LF, the TOn is a narrow peak followed by a dip. The TOn is very sensitive to age: for a ∼30 Myr old stellar population the luminosity of the TOn changes by ∼0.08 mag Myr⁻¹, but at ∼20 Myr it already changes by ∼0.15 mag Myr⁻¹, and by ∼0.33 mag Myr⁻¹ at 3 Myr.

To guarantee a safe TOn identification, it is important to select targets with low or well-known reddening. In the visual, this currently excludes Galactic clusters like Westerlund 1–2, NGC 3603, Arches and Quintuplet, but good targets can be found in the solar vicinity and in some nearby irregular galaxies like the Magellanic Clouds and IC1613.

In this Letter, we have presented a new method for investigating how star formation develops in complex extragalactic young clusters such as NGC 346 in the SMC.

Our method combines the analysis of the star clusters' stellar densities profiles with the notion that in a cluster no star on the MS can be fainter than the cluster TOn. This approach has the advantage of strongly reducing the uncertainties introduced by the contamination to the CMD by young stars that do not belong to the cluster, ultimately affecting the TOn detectability in both CMD and LF.

Clearly, there are limitations to the applicability of the method. The bona fide MS selection may include intruders like PMS and stars evolved off the MS, reducing the TOn visibility. The issue is particularly thorny at ages larger than about 30 Myr, because the PMS isochrones are close to the ZAMS (see Figure 1(a)). The method relies on the assumption that the formation sites are agglomerations of stars: if for some reason the newborn stars formed in isolation or, drifting apart, were too diluted to be detected as aggregates, the method would not be applicable. In this respect, the study by Pfalzner (2009), exploiting the density–radius relation to date nearby clusters younger than 20 Myr is interesting and reassuring.

We applied the TOn method to NGC 346 in SMC, and we found that the onset of the star formation in the sub-cluster SC-1 was between 3.5and6.5 Myr, in the sub-cluster SC-13 3 Myr ago or less and in SC-16 between 12.5and18 Myr ago, in good agreement with the results from the literature.

Having established the effectiveness of our method, the next steps will be to (1) incorporate near-infrared photometry and use it to study extinguished regions, where measurements of the upper MS are difficult to carry out and (2) undertake comparative studies of the duration and spatial patterns of star formation in Magellanic Cloud regions ranging from the giant 30 Dor complex to the comparatively isolated NGC 602 cluster.

We thank A. Bragaglia and S. N. Shore for useful suggestions. M.C. and M.T. acknowledge financial support through contracts ASI-INAF-I/016/07/0 and PRIN-MIUR-2007JJC53X-001. Partial support for US research in program GO10248 was provided by NASA through a grant from the STScI, which is operated by the AURA, Inc., under NASA contract NAS5-26555.