The spatial distribution of star formation in the solar neighbourhood: do all stars form in dense clusters?

Abstract

We present a global study of low-mass, young stellar object (YSO) surface densities (Σ) in nearby (<500 pc) star-forming regions based on a comprehensive collection of Spitzer Space Telescope surveys. We show that the distribution of YSO surface densities in the solar neighbourhood is a smooth distribution, being adequately described by a lognormal function from a few to 10³ YSOs pc⁻², with a peak at ∼22 stars pc⁻² and a dispersion of . We do not find evidence for multiple discrete modes of star formation (e.g. clustered and distributed). Comparing the observed surface density distribution to previously reported surface density threshold definitions of clusters, we find that the fraction of stars in clusters is crucially dependent on the adopted definitions, ranging from 40 to 90 per cent. However, we find that only a low fraction (<26 per cent) of stars are formed in dense environments where their formation/evolution (along with their circumstellar discs and/or planets) may be affected by the close proximity of their low-mass neighbours.

stars: formation, stars: protostars, open clusters and associations: general, infrared: stars

1 Introduction

It is often stated that most if not all stars form in stellar clusters. This view is based largely on near-infrared (NIR) studies of star-forming (SF) regions within several hundred parsecs of the Sun (Lada & Lada 2003; Porras et al. 2003). However, adding high-resolution mid-infrared (MIR) data to the NIR makes young stellar object (YSO) identification more robust and less likely to be contaminated by field stars, which leads to better tracing of YSO surface densities. This means that with the NIR alone, there were large uncertainties in the number of stars at low values of YSO surface densities (Σ_YSO) (Carpenter 2000).

The spatial distribution of forming stars, i.e. do they form in clusters, is important for two main reasons. The first is that dense environments can affect the evolution of the young stars as well as alter their disc and planet formation/evolution (Allen et al. 2007). The second is to locate the progenitor population of open clusters and to determine why such a low fraction of the Galactic stellar population is observed in clusters. Are there multiple discrete modes, such as clustered and distributed, in the star formation process that manifest themselves as peaks in a surface density distribution (e.g. Strom, Strom & Merrill 1993; Carpenter 2000; Weidner, Kroupa & Larsen 2004; Wang et al. 2009)?

With the launch of the Spitzer Space Telescope (Werner et al. 2004) we are now able to differentiate YSOs and contaminating sources based on colour information, and hence can study the distribution of YSOs independently of the surface densities. Large field-of-view (FOV) Spitzer observations of SF regions (Allen et al. 2007; Evans et al. 2009) found that YSOs extend well beyond the densest groups in their environment and continue throughout. We combine several Spitzer surveys that cover nearly all the SF regions within 500 pc of the Sun. A list of the regions and their properties is given in Table 1. Note that with only the local SF environments being considered, we are not sampling massive SF regions that are found beyond 500 pc.

Table 1

The Spitzer surveys used in the present work includes 12 SF regions with 3857 YSOs. The numbers in brackets refer to the total number of sources in the catalogues for each region, while the number before the brackets is the number used in the present analysis. The difference is due to the application of the absolute magnitude cuts as well as the elimination of Class III YSOs from the sample. The sources for these SF regions are the (1) GB survey, (2) c2d survey, (3) Orion survey and (4) Taurus survey.

Using the comprehensive collection of Σ_YSO, we investigate what fraction of YSOs are found in dense clusters. We define dense clusters as regions where YSOs are affected by their neighbours in sufficiently short time-scales of <10⁵ yr, such that its surface densities exceed ∼200 YSO pc⁻² (see Gutermuth et al. 2005). We also review what surface densities are required to identify ‘clusters’ according to definitions provided by Carpenter (2000), Lada & Lada (2003), Allen et al. (2007), Jørgensen et al. (2008) and Gutermuth et al. (2009) in Section 5. In this Letter, we will investigate (1) whether there is evidence for multi-modality in the surface densities of YSOs, (2) what fraction of stars form in dense clusters in the local neighbourhood and (3) how relevant the various cluster definitions are.

2 Observations and Data

Multiple Spitzer surveys were used to generate a comprehensive and statistically significant data set to investigate the spatial surface density properties of forming stars in the solar neighbourhood. The surveys are the Gould's Belt (GB) survey (Allen et al., in preparation), Orion survey (Megeath et al., in preparation), Cores to Discs (c2d) survey (Evans et al. 2003) and the Taurus survey (Rebull et al. 2010). The GB and Orion catalogues have not been publicly released yet. We have more than 7000 YSO detections in the combined catalogues at distances between 100 to 500 pc.

Spitzer data are necessary for this study as low Σ_YSO can be differentiated from field star populations, unlike NIR observations where field star contamination can be problematic. The YSO population that we have collected represents a global view of the low-mass SF region in the local neighbourhood from low to high surface densities. These Spitzer surveys combined represent the most complete census of star formation within 500 pc of the Sun available to date.

In order to homogenize the data from the surveys, we accounted for distance effects on photometry, namely we limit the absolute magnitude range used for individual sources to that of the faintest YSO detectable in the furthest SF region and the brightest in the nearest SF region. The absolute magnitude limit used for the 500 pc data collection is 0 ≤M_{3.6 μm}≤ 5.91, based on Orion at a distance of 414 pc (Menten et al. 2007; Mayne & Naylor 2008) for the faint sources and Ophiuchus at 125 pc for the bright sources. This reduces the number of YSOs we can use, but it mitigates detection biases introduced for SF regions at different distances.

The GB and c2d surveys classify YSOs using spectral indices (Lada 1987; Greene et al. 1994). The Taurus and Orion YSOs are classified by using colour–colour diagrams (Allen et al. 2004; Megeath et al. 2004; Gutermuth et al. 2005, 2009). What fraction of the YSOs are discless, generally classified as Class III, and hence not identifiable in the IR? Based on Hernandez et al. (2007) we assume that 65 per cent of the YSOs have discs. We corrected the stellar surface densities of the data for the missing fraction of 35 per cent.

Orion, which offers the largest range of stellar surface densities and hosts the most massive stars of the SF regions considered in this Letter, had to be treated separately from the other surveys. The ONC, in particular the Trapezium region, has two Spitzer based issues: stellar surface densities that exceed Spitzer's spatial resolution and the extremely bright nebulosity that diminishes effective sensitivity considerably. The bright nebulosity introduces errors for YSO identification since the PAH emission outshines lower mass YSOs and introduces large errors in the photometry. To compensate for the complex incompleteness, we removed all YSOs centred on Θ1 Orionis within a radius of 0.56 pc (4.7 arcmin). To correct for missing YSOs from the removed region, we estimated that the mass removed was ∼25 per cent of the total Orion complex (Getman et al. 2005). Excluding the ONC from our analysis does not significantly change the presented cumulative distribution of surface densities presented in this Letter. If we were able to observe all the members in the ONC based on the ∼25 per cent of mass we estimated to be missing, the average Σ_ONC≤ 1000 YSOs pc⁻². This surface density regime goes beyond the scope of values we are presently considering. Hence we are not sensitive to the extreme high Σ tail end of the ONC distribution.

Spitzer is not completely free of contamination when identifying YSOs, i.e. AGBs/Be stars (Robitaille et al. 2008; Cieza et al. 2010) and galaxies (Gutermuth et al. 2008; Evans et al. 2009). Oliveira et al. (2009) found that ∼25 per cent of the identified YSOs in the c2d Serpens catalogue are AGBs, which is likely an isolated worst case scenario as Serpens is the field closest to the Galactic plane in our compilation of SF regions. Two of the 20 contaminants Oliveira et al. (2009) identified are Class II objects and the rest of the contaminants are Class III objects. We only consider Class I/II objects, where the AGB contamination is <10 per cent, and remove all Class III objects. The flat spectrum sources are grouped with Class I objects. Between the methods used to identify YSOs in the c2d, GB, Taurus and Orion data, which are the c2d (Evans et al. 2009) and Gutermuth et al. (2008, 2009) methods, the selection discrepancy is ≤5 per cent (Rebull et al. 2010). By selection discrepancy we mean the agreement that an object is or is not a YSO (Class I/II).

Extragalactic background contamination for YSO MIR identification is well studied. For the c2d and GB catalogues, which use the same data-reduction pipeline, Evans et al. (2009) found that background galaxies contaminate ≤5 per cent of the YSOs. Similarly, YSOs identified via the Gutermuth et al. (2009) method for Orion is <1 per cent. For Taurus the expected contamination rate is ≤5 per cent (Rebull et al. 2010).

3 Σ_YSO Distributions

Our primary tool for analysing the surface densities is computing the local observed surface density of YSOs centred on each YSO's position, where Σ_YSO= (N− 1)/(πD²_N) and N is the Nth nearest neighbour, and D_N is the projected distance to that neighbour (see Casertano & Hut 1985). Throughout this work, we will adopt N= 7, although we note that all results have been tested for N= 4–22 and no significant differences were found.

Fig. 1 shows the surface density distribution of all YSOs in our sample, corrected for the discless fraction. Additionally, we show a lognormal fit to the data as a dashed red line (see Section 4). The overprediction of the lognormal at high Σ_YSO compared to the observations is most likely due to the exclusion of the ONC and surrounding area (see Section 2). The bottom panel of Fig. 1 shows the surface density distribution for each of the three surveys separately.

Figure 1

Top panel: the surface density distribution of the total sample of YSOs in the solar neighbourhood used in this work (black). A lognormal function with a peak at ∼22 YSOs pc⁻² and a dispersion is shown as a dashed (red) line. Bottom panel: the same as the top panel but now broken into the three respective surveys. Note that Orion dominates the number statistics.

In order to see the fraction of YSOs above a given Σ threshold, we show the combined Σ_YSO distribution (shown as a cumulative fraction normalized to the number in each combined survey) for the three surveys used in this study in Fig. 2(a). Note that the GB/Taurus distribution lies to the left of the c2d survey. This is simply due to the GB/Taurus focussing on lower density regions than c2d. The cumulative distribution for the Orion survey only reaches 0.73 in Fig. 2(a) and 0.81 in Fig. 2(c), where all the surveys have been combined, due to the exclusion of the ONC. In Fig. 2(c), we show the cumulative distribution of all YSOs included in our survey, while in Fig. 2(b) we split the survey into Class I and Class II objects.

Figure 2

(a) The cumulative fraction of surface densities for the GB+Taurus, c2d and Orion surveys. Each SF region included in the distributions has N(YSOs) ≥10 and a sufficient FOV to properly calculate stellar surface densities. The Orion survey stops at 80 per cent for the cumulative fraction since the ONC is excluded. We adopt a 65 per cent disc fraction for all of the SF regions. We normalized each curve by the number of YSOs in each survey. (b) With the GB+Taurus, c2d and Orion surveys combined we see Class I & II distributions having similar profiles with a small offset in density, showing that we are likely seeing the primordial distribution of the YSOs. (c) With all of the Spitzer surveys combined we compare several cluster definitions. The vertical grey lines from left to right are Lada & Lada (2003), Megeath et al. (in preparation), Jørgensen et al. (2008), Carpenter (2000) and Gutermuth et al. (2009) stellar density requirements for clusters. These values correspond to 3, 10, 20, 32 and 60 YSOs pc⁻² and intersect the corrected cumulative distribution profile, implying that 87, 73, 62, 55 and 43 per cent of stars form in clusters, respectively. The percentages correlate to what fraction of stars form in ‘clusters’ based on the various definitions. The black vertical line is for a dense cluster where Σ≥ 200 YSOs pc⁻². The fraction of YSOs in a dense cluster is <26 per cent.

4 Results

It has been long assumed that two distinct modes of star formation exist for YSOs, ‘clustered’ and ‘distributed’ (e.g. Gomez et al. 1993; Carpenter 2000; Lada & Lada 2003), but the notion has been questioned after Spitzer results hinted otherwise (Allen et al. 2007). If there are indeed two modes, then we would expect to see a bi- or multi-modal profile in cumulative surface density distribution plots such as Figs 1, 2(a) and (c). Instead we see smooth and featureless distributions from the low to high stellar surface densities for the c2d, GB, Taurus and Orion surveys. We find that the Σ_YSO distribution of low-mass stars in the solar neighbourhood can be well described by a lognormal function, as seen in Fig. 1, with a peak at ∼22 YSOs pc⁻² and a dispersion .

The spatial distribution of the YSOs in these SF regions is expected to be close to primordial since their YSOs, in particular Class I and Class II objects, are ≤2 Myr old (Haisch, Lada & Lada 2001; Hernandez et al. 2007). In order to place stricter constraints on this, we now split the complete sample into Class I and II objects, which can be roughly attributed to an age sequence. The cumulative Σ distributions of Class I and II YSOs are shown in Fig. 2(b). We see that the two distributions have similar smooth density spectra, however they are slightly offset. The Σ of the Class I/II objects are calculated by finding a YSO's Nth nearest YSO. Once this is done for the YSOs we separate the Class I/II objects. Σ is calculated this way since Class I and Class II objects are not always spatially distinct from one another (Gutermuth et al. 2009). Class II objects are known to be slightly more dispersed than Class I objects in high-density regions (Gutermuth et al. 2009), reflecting early dynamical evolution. However, the similar distribution between these classes leads us to conclude that the distribution of observed Σ is mainly primordial in nature.

5 Cluster Identification

The definitions of what defines a cluster vary widely as we have limited knowledge about YSO membership other than their projected two-dimensional spatial distributions. Some definitions have a physical motivation (e.g. Lada & Lada 2003), while the others are generally empirically derived from the data being considered (Allen et al. 2007). When applied to a uniform data set like ours, differing choices of a surface density threshold returned different ‘clustered fractions’, as summarized below.

Carpenter (2000): clusters in SF regions are identified by using stellar density maps in the K_s band. The density maps are field-star background-subtracted (galactic coordinate dependent) based on semi-empirical models. Clusters are identified as 2σ overdensities and defined as regions with 6σ overdensities (with total number of members taken as the number of sources above the 4σ threshold) with respect to the local background. Carpenter's cluster Σ_YSO ranged from 20 to 67 YSOs pc⁻² with a median of 32 YSOs pc⁻². Considering the median, 55 per cent of the YSOs are contained in clusters.

Lada & Lada (2003): a physically related group of stars, called an embedded cluster, that (1) is partially or fully enshrouded in interstellar gas and dust, (2) has ≥35 YSOs and (3) has a stellar-mass volume density of 1.0 M_⊙ pc⁻³ or greater such that its evaporation time exceeds 10⁸ yr. In surface density, rather than volume density, the number of YSOs pc⁻² necessary for ‘cluster’ is ∼ 3 (see, Jørgensen et al. 2008). The authors estimated that 80–90 per cent of the YSOs are in embedded clusters, which is found to be in agreement with our Spitzer data.

Gutermuth et al. (2009): building upon the Lada & Lada (2003) definition of an embedded cluster, Jørgensen et al. define a cluster as being ‘loose’, which is the same as an embedded cluster, and a ‘tight’ cluster. A tight cluster requires a stellar-mass volume density of ≥ 25 M_⊙ pc⁻³ and > 35 YSOs, which implies that 62 per cent of the YSOs from our data are contained in such clusters. This finding is close to 54 per cent as found in Evans et al. (2009).

Jørgensen et al. (2008): this method employs the minimal spanning tree (MST) algorithm to define cluster cores by isolating the densest parts of larger scale overdensities. The MST is a network of lines that connects a set of points, has no closed loops and the set of edges add up to the shortest total length possible between all points. After determining a cut-off length for the MST collection, YSOs can be separated into two populations: clustered and distributed. The authors found that the clusters from this analysis range between 0.64 and 78 YSOs pc⁻² with a median of 60 YSOs pc⁻². Roughly 43 per cent of the YSOs are found in a median core clusters.

Megeath et al. (in preparation): a cluster is a set of contiguous objects which have nearest neighbour densities ≥10 YSO pc⁻². The 10 YSOs pc⁻² is similar to the cluster definition given in Allen et al. (2007) and motivated by a comparison of the Orion (Megeath et al., in preparation) and the Taurus molecular clouds. The Taurus and other similar dark clouds, i.e. Chameleon and Lupus, have most of their objects at densities below 10 pc⁻², while Orion and other clouds with clusters have 70–80 per cent above this threshold. Applying the 10 YSOs pc⁻² definition to our data set results in 73 per cent of YSOs being in clusters.

In Fig. 2(c) we show five vertical grey lines that refer to the defined densities required for a collection of YSOs to be considered ‘clustered’ (Carpenter 2000; Lada & Lada 2003; Jørgensen et al. 2008; Gutermuth et al. 2009; Megeath et al., in preparation). The vertical lines fall on the same featureless slope and do not correspond to any preferred density. The black vertical line, which corresponds to dense clusters (as defined in Gutermuth et al. 2005), shows that <26 per cent of YSOs are formed in environments where they (along with their discs and planets) are likely to interact with their neighbours.

6 Discussion and Conclusions

We have compared our global surface density distribution with previously reported definitions of clusters (discussed in Section 5), and find that the fraction of stars in the solar neighbourhood forming in clusters is crucially dependent on the adopted definitions (ranging from ∼45 to 90 per cent). Lada & Lada (2003) used a physically motivated definition of clusters, and their adopted low surface density of ∼ 3 YSO pc⁻² encompasses nearly all star formation in the solar neighbourhood. However, only a small fraction (<26 per cent) of stars form in dense clusters where their formation and/or evolution is expected to be influenced by their surroundings.

We conclude that stars form in a broad and smooth spectrum of surface densities and do not find evidence for discrete modes of star formation in the Σ of low-mass YSOs forming in the solar neighbourhood. Only a small fraction of YSOs form in dense clusters where nearby YSO members affect its disc/planets evolution. The observed lognormal surface density distribution is consistent with predictions of hierarchically structured star formation, where the structure comes from the MC hierarchical structure (Elmegreen 2002, 2008). By hierarchical structure we mean a smoothly varying non-uniform distribution of densities, where denser sub-areas are nested within larger, less dense areas (Scalo 1985; Elmegreen et al. 2006; Bastian et al. 2007). SF environments provide the initial conditions from which star clusters may eventually form, albeit rarely. Since the probability density function of molecular gas varies with environment, as does the tidal field experienced by the SF region, it is likely that the fraction of YSOs ending up in bound star clusters varies with environment (Elmegreen 2008) and the observed Σ_YSO is not universal. Hence, in a future study we will extend this work out to 2 kpc, which includes high-mass SF regions and more extreme environments that may show different results than what we see for the solar neighbourhood.

Acknowledgments

We would like to thank Mark Gieles, Michael Meyer, August Muench, Dawn Peterson, Thomas Robitaille and Scott Schnee for their thoughtful feedback on the research. EB gratefully thanks the Royal Astronomical Society for their generous travel support. NB is supported by an STFC advanced fellowship. TPR would like to thank Science Foundation Ireland for support under grant 07/RFP/PHYF790. Support for this work, part of the Spitzer Legacy Science Program, was provided by NASA through contract 1224608 and 1288664 issued by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407. NJE acknowledges support by NSF Grant AST-0607793