The nature of the young and low-mass open clusters Pismis5, vdB80, NGC1931 and BDSB96

We investigate the nature of 4 young and low-mass open clusters (OCs) located in the $2^{nd}$ and $3^{rd}$ quadrants with near-IR 2MASS photometry (errors $<0.1$ mag). After field decontamination, the colour-magnitude diagrams (CMDs) display similar morphologies: a poorly-populated main sequence (MS) and a dominant fraction of pre-MS (PMS) stars somewhat affected by differential reddening. Pismis 5, vdB 80 and BDSB 96 have MS ages within $5\pm4$ Myr, while the MS of NGC 1931 is $10\pm3$ Myr old. However, non-instantaneous star formation is implied by the wider ($\sim20$ Myr) PMS age spread. The cluster masses derived from MS + PMS stars are low, within $\sim60-180 \ms$, with mass functions (MFs) significantly flatter than Salpeter's initial mass function (IMF). Distances from the Sun are within $1.0-2.4$ kpc, and the visual absorptions are in the range $\aV=1.0-2.0$. From the stellar radial density profiles (RDPs), we find that they are small ($\rc\la0.48$ pc, $\rl\la5.8$ pc), especially Pismis 5 with $\rc\approx0.2$ pc and $\rl\approx1.8$ pc. Except for the irregular and cuspy inner regions of NGC 1931 and Pismis 5, the stellar RDPs follow a King-like profile. At $\sim10$ Myr, central cusps - which in old clusters appear to be related to advanced dynamical evolution - are probably associated with a star-formation and/or molecular cloud fragmentation effect. Despite the flat MFs, vdB 80 and BDSB 96 appear to be typical young, low-mass OCs. NGC 1931 and especially Pismis 5, with irregular RDPs, low cluster mass and flat MFs, do not appear to be in dynamical equilibrium. Both may be evolving into OB associations and/or doomed to dissolution in a few $10^7$ yr.


INTRODUCTION
The first few ten Myrs represent the most critical phase in the life of a star cluster, to the point that only about 5% (e.g. Lada & Lada 2003) of the embedded clusters are able to dynamically evolve into bound open clusters (OCs). The rapid gas removal by supernovae and massive star winds associated with this period can produce important changes on the primordial gravitational potential. Obviously, this effect depends essentially on the star-formation efficiency, the actual mass of primordial gas converted into stars and the mass of the more massive stars.
Because of the rather rapidly-reduced potential, a significant fraction of the stars -the low mass ones in particular -moving faster than the scaled-down escape velocity may be driven into the field. Over a time-scale of 10 − 40 Myr, this In some cases, early star cluster dissolution may lead to the formation of low-mass OB associations, the subsequent dispersion of which may be an important source of field stars (e.g. Massey, Johnson & Gioia-Eastwood 1995). Bochum 1, with an irregular and clumpy RDP, can be an example of such an evolving structure. In this context, NGC 2244 appears to be another example of a young OC in the process of dissolving in a few 10 7 yr. Perhaps the difference between objects like Bochum 1 and NGC 2244 and normal young OCs (i.e. with the combined population of MS and PMS stars distributed according to a cluster RDP as in NGC 6611 and NGC 4755) is related to the interplay between environment conditions, star-formation efficiency and stellar mass. Interestingly, the mass stored in the MS+PMS members of Bochum 1 and NGC 2244 is a factor 2-3 lower than those of NGC 6611 and NGC 4755.
In this paper we investigate the nature of the poorly-studied, young and low-mass OCs Pismis 5, vdB 80, NGC 1931 and BDSB 96, by means of their photometric and structural properties. Their location in the Galaxy, in the 2 nd and 3 rd quadrants (Table 1), minimises fieldstar contamination (e.g. Bica, Bonatto & Camargo 2008;Bonatto & Bica 2008b), which is essential when PMS stars are expected to dominate in Colour-Magnitude Diagrams (CMDs). Our main goal is to determine whether such young and low-mass systems can be characterised as typical OCs or if they are on their way to dissolution. In addition, we will derive their fundamental and structural parameters, most of these for the first time.
This paper is organised as follows. In Sect. 2 we recall literature data on the target objects, discuss the 2MASS photometry and build the field-star decontaminated CMDs. In Sect. 3 we derive fundamental cluster parameters. In Sect. 4 we derive structural parameters. In Sect. 5 we esti- mate cluster mass. In Sect. 6 we compare structural parameters and dynamical state with those of a sample of nearby OCs. Concluding remarks are given in Sect. 7.

THE OCS AND THE 2MASS PHOTOMETRY
The optical environments of the objects are shown in 10 ′ × 10 ′ DSS 2 B images ( Fig. 1), in which nebular gas and/or dust emission is present in varying proportions. The embedded clusters show up in the 4 ′ × 4 ′ 2MASS Ks images (Fig. 2).
Discovered in a survey of infrared embedded star clusters and stellar groups carried with 2MASS by Bica et al. (2003), BDSB 96 (in the nebula Cederblad 90, also known as Gum 3, Sh 2-297, RCW 1a, vdB-RN 94 and Ber 134) in Canis Major, was classified as an infrared OC located at about 1.1 kpc from the Sun. Its field contains the single bright star HD 53623 (SIMBAD: α(2000) = 07 h 05 m 16.7 s , δ(2000) = −12 • 19 ′ 34.5 ′′ , V = 8.0, J = 8.0, Ks = 8.0), which is in the MS of BDSB 96 (Fig. 6). Nebular gas and/or dust emission is more conspicuous in its field (Fig. 1, bottom-right panel) than in Pismis 5, vdB 80 and NGC 1931. Table 1 provides parameters found in the literature and derived here. Since accurate spectral types of the bright stars listed above are not available, spectroscopic distances cannot be computed. The central coordinates were recomputed to match the absolute maximum present in the stellar surface densities (Sect. 2.3).

2MASS photometry
The present OCs still retain part of the primordial gas and dust ( Fig. 1), which makes the near-IR the optimal spectral range to probe them. For instance, the number of detected stars at a given radius in NGC 2244 in the optical is significantly lower than in the near-IR, dropping to about 5% for the full field (Bonatto & Bica 2009b). For this purpose we work with the 2MASS 4 near-IR J, H, and Ks photometry, which allows the spatial and photometric uniformity useful for wide extractions that, in turn, provide high star-count statistics. Within this perspective, we have been developing quantitative tools to statistically disentangle cluster evolutionary sequences from field stars in CMDs. Decontaminated CMDs, in turn, have been used to investigate the nature of cluster candidates and derive their astrophysical parameters (e.g. Bica, Bonatto & Camargo 2008). In short, we apply (i) field-star decontamination to uncover the intrinsic CMD morphology, essential for a proper derivation of reddening, age, and distance from the Sun, and (ii) colourmagnitude filters, which are essential for intrinsic stellar RDPs, as well as luminosity and mass functions (MFs). In particular, the use of field-star decontamination in the construction of CMDs has proved to constrain age and distance more than working with raw (observed) photometry, especially for low-latitude OCs (Bonatto et al. 2006a).
2MASS can reach adequate CMD depths for nearby OCs. For instance, our group has studied the young OCs NGC 6611, NGC 4755, NGC 2239 and NGC 2244. Abundant PMS stars were seen in the ≈ 1 Myr old NGC 6611 (which is essentially embedded) and the 1 − 6 Myr old NGC 2244, and a few remaining ones in the ≈ 14 Myr old NGC 4755. As nearby older OCs we cite NGC 2477 (Bonatto & Bica 2005) and M 67 (Bonatto & Bica 2003).
Photometry was extracted in a wide circular field of radius Rext (Table 1) with VizieR 5 . The extraction radii are large enough to allow determination of the background level (Sect. 4) and to statistically characterise the colour and magnitude distribution of the field stars (Sect. 2.2). As photometric quality constraint, only stars with J , H, and Ks errors lower than 0.1 mag were considered 6 . Reddening corrections are based on the relations AJ /AV = 0.276, AH/AV = 0.176, AK S /AV = 0.118, and AJ = 2.76×E(J − H) given by Dutra, Santiago & Bica (2002), with RV = 3.1, considering the extinction curve of Cardelli, Clayton & Mathis (1989).

Field decontamination
Field-star decontamination is a very important step in the identification and characterisation of star clusters, especially the clusters near the Galactic equator. Different approaches are described in Bonatto & Bica (2009b). In this paper we employ the decontamination algorithm detailed in Bonatto & Bica (2007a), Bica, Bonatto & Camargo (2008) and , and briefly described below.  Figure 3. Stellar surface-density σ(stars arcmin −2 ) computed with field-decontaminated photometry to enhance the cluster/background contrast. ∆(α cos(δ)) and ∆δ in arcmin. The algorithm (i) divides the whole range of CMD magnitude and colours into a 3D grid of cells with axes along the J magnitude and the (J − H) and (J − Ks) colours, (ii) estimates the number density of field stars in each cell based on the number of comparison field stars with similar magnitude and colours as those in the cell, and (iii) subtracts the estimated number of field stars from each cell. Typical cell dimensions are ∆J = 1.0 and ∆(J − H) = ∆(J − Ks) = 0.2; the comparison fields are located within R = 30 ′ and the extraction radius. With this setup, the subtraction efficiency, i.e. the difference between the background contamination (which may be fractional) and the number of subtracted stars in each cell (e.g., Bonatto & Bica 2008b), summed over all cells, is higher than 90% in all cases. and field stars) is probably minimised by the field decontamination (Sect. 2.2). Figure 3 shows the spatial distribution of the stellar surfacedensity (σ, in units of stars arcmin −2 ) around the 4 objects, measured with 2MASS photometry. We use field-star decontaminated photometry (Sect. 2.2) to maximise the cluster/background contrast. The surface density is computed in a rectangular mesh with cells 2.5 ′ × 2.5 ′ wide, reaching total offsets of |∆(α cos(δ))| = |∆δ| ≈ 40 ′ with respect to the cluster centre (Table 1). Despite the gas and dust associated with the present low-mass clusters ( Fig. 1), the central excesses are conspicuously detected in the decontaminated surface-density distributions. Besides, the residual surfacedensity around the centre has been reduced to a minimum level.

Decontaminated surface density maps
By design, our decontamination depends essentially on the colour-magnitude distribution of stars located in different spatial regions. The fact that the decontaminated surface-density presents a conspicuous excess only at the assumed cluster position implies significant differences among this region and the comparison field, both in terms of colourmagnitude and star counts within the corresponding colourmagnitude bins. This meets cluster expectations, which can be characterised by a single-stellar population, projected against a Galactic stellar field.
The respective isopleth surface maps are shown in Fig. 4, in which cluster size and geometry can be observed. In all cases, the central region (R < 5 ′ ) appears essentially circular, with elongated external regions, especially NGC 1931.

FUNDAMENTAL PARAMETERS
J × (J − Ks) CMDs built with the raw photometry of the sample objects are shown in the top panels of Figs. 5 and 6. In all cases, the sampled region contains most of the cluster stars (Fig. 10). When qualitatively compared with the CMDs extracted from the equal-area comparison field 7 (middle panels), features typical of very young OCs emerge: a relatively vertical and poorly-populated MS together with a large number of faint and red PMS stars.
The decontaminated CMDs are shown in the bottom panels of Figs. 5 and 6. As expected, essentially all contamination is removed, leaving stellar sequences typical of mildly reddened, young and low-mass OCs, with a developing MS and a significant population of PMS stars.
Colour distributions wider than the spread predicted by PMS models occur in all cases (Fig. 7), which reflects differential reddening. To examine this issue we show in Figs. 5-7 reddening vectors computed with the 2MASS ratios (Sect. 2.1) for visual absorptions AV = 0 to 5. Taking into account the PMS isochrone fit (Fig. 7), the differential reddening appears to be lower than AV = 5.
We base the fundamental parameter derivation on the field-decontaminated CMD morphologies (Fig. 7), using as constraint the combined MS and PMS star distribution. We adopt solar metallicity isochrones because the clusters are young and located not far from the Solar circle (see below),  a region essentially occupied by [F e/H] ≈ 0.0 OCs (Friel 1995).

Decont. Decont
To represent the MS we use Padova isochrones (Girardi et al. 2002) computed with the 2MASS J, H, and Ks filters 8 . The similar decontaminated CMD morphologies, typical of young ages (Fig. 7), indicate similar age-solutions for the present objects.
Sophisticated CMD fit approaches are available, especially for the MS (as summarised in Naylor & Jeffries 2006). However, given the poorly-populated MSs, the 2MASS photometric uncertainties for the lower sequences and the important population of PMS stars, we decided for the direct comparison of isochrones with the decontaminated CMD morphology. Thus, fits are made by eye, taking the combined MS and PMS stellar distributions as constraint, allowing as well for differential reddening and photometric uncertainties. Isochrones of Siess, Dufour & Forestini (2000) with ages in the range 0.2-20 Myr are used to characterise the PMS sequences. The results are shown in Fig. 7 and discussed below.  .04 ± 0.10, respectively, and the distance from the Sun d⊙ = 1.0 ± 0.1 kpc. We adopt R⊙ = 7.2 ± 0.3 kpc ) as the Sun's distance to the Galactic centre to compute Galactocentric distances 9 . For R⊙ = 7.2 kpc, the Galactocentric distance of Pismis 5 is RGC = 7.5 ± 0.1 kpc, which puts it ≈ 0.3 kpc outside the Solar circle. This solution is shown in Fig. 7.
Besides the MS age, the present objects have in common a significant age spread implied by the PMS stars. This indicates a non-instantaneous star formation process, similar to what was found in our previous studies of, e.g. NGC 4755, NGC 6611 and NGC 2244.

Colour-colour diagrams
When transposed to the near-IR colour-colour diagram (J − Ks) × (H − Ks) (Fig. 9), the age and reddening solutions derived for the present objects consistently match their field-star decontaminated photometry. Since they include PMS stars, we use tracks of Siess, Dufour & Forestini (2000) to characterise the age. MS stars lie on the blue side of the diagram. As expected from the CMDs, a significant fraction of the stars appears to be very reddened. Besides, since most stars have (H − Ks) colours close to the isochrone, within the uncertainties, the fraction of stars still bearing circunstellar discs (with excess in H) appears to be low (Bonatto et al. 2006b and references therein).

CLUSTER STRUCTURE
We use the RDPs, defined as the projected stellar number density around the cluster centre (i.e. the maximum of the surface density maps -Sect. 2.3), to derive structural parameters. To minimise noise, we work with colour-magnitude filters (shown in Fig. 7) to exclude stars with colours unlike those of the cluster CMD morphology 10 . This enhances the RDP contrast relative to the background, especially in crowded fields (e.g. Bonatto & Bica 2007a). Examples of the advantage of using colour-magnitude filters can be found in, e.g. Bonatto & Bica (2007b), Bonatto, Bica & Santos Jr. (2008) and Bonatto & Bica (2008b). Rings of increasing width with distance from the cluster centre are used to preserve spatial resolution near the centre and minimise noise at large radii. The set of ring widths used is ∆ R = 0.25, 0.5, 1.0, 2.0, and 5 ′ , respectively for 0 ′ R < 0.5 ′ , 0.5 ′ R < 2 ′ , 2 ′ R < 5 ′ , 5 ′ R < 20 ′ , and R 20 ′ . Because of the low number of stars in the central parts of vdB 80, we used ∆ R = 0.5 for R 1 ′ . The residual background level of each RDP corresponds to the average number-density of field stars. The R coordinate (and uncertainty) of each ring corresponds to the average position and standard deviation of the stars inside the ring. As a caveat we note that the present OCs are not spherical, especially 10 They are wide enough to include cluster MS and PMS stars, together with the photometric uncertainties and binaries (and other multiple systems).
at the outskirts (Fig. 4), which might affect the RDPs for large radii. Because of this, deviations in the central parts of the RDP are not expected to be significant.
Minimisation of the number of non-cluster stars by the colour-magnitude filters yielded RDPs (Fig. 10) highly contrasted relative to the background. For simplicity we fit the RDPs with σ(R) = σ bg + σ0/(1 + (R/Rc) 2 ), where σ bg is the residual background density, σ0 is the central density of stars, and Rc is the core radius. This function, applied to star counts, is similar to that introduced by King (1962) to describe the surface-brightness profiles in the central parts of GCs 11 . To minimise degrees of freedom, σ0 and Rc follow from the fit, while σ bg is measured in the field and kept fixed. The best-fit solutions and uncertainties are shown in Fig. 10, and the parameters in Table 2. We also estimate the cluster radius (RRDP), i.e. the distance from the centre where the cluster RDP and field fluctuations are statistically indistinguishable (e.g. Bonatto & Bica 2005), and the density contrast parameter δc = 1 + σ0/σ bg (Table 2). Interestingly, the density-contrast parameter reaches high values, 7 δc 23, as expected from compact star clusters.
Within uncertainties, the adopted King-like function describes the RDPs of vdB 80 and BDSB 96 along the whole radius range. To a lesser degree, the same applies for Pismis 5 and NGC 1931, in which the innermost bin presents an excess over the fit. In old star clusters, such a cusp has been attributed to a post-core collapse structure, like those detected in some GCs (e.g. Trager, King & Djorgovski 1995). Gyrold OCs, e.g. NGC 3960 ) and LK 10 (Bonatto & Bica 2009a), also display such feature, which is related to dynamical evolution. With respect to very young clusters, the RDPs of NGC 2244 (Bonatto & Bica 2009b) and NGC 6823 (Bica, Bonatto & Dutra 2008) also present a central cusp, similarly to those in Pismis 5 and NGC 1931. Clusters are not expected to dynamically evolve into a postcore collapse on such short time-scales. Consequently, the cusp in young clusters must be related to molecular cloud fragmentation and/or star-forming effects, and may suggest early deviation from dynamical equilibrium (Sect. 6).
Taken at face value, the core radii of the present objects (0.2 Rc(pc) 0.5) fall on the low-Rc tail of the distribution derived for a sample of relatively nearby OCs by Piskunov et al. (2007).
A similar strategy is applied to the PMS stars. We consider the evolutionary tracks for the PMS masses 0.5, 1, 2, 3, 5 and 7 M⊙ (Fig. 8). The number of PMS stars between any 2 tracks is counted for R RRDP and the field, taking into account the reddening vectors. The average mass between two evolutionary tracks is taken as the mass of a respective PMS star. All tracks summed result in the number (nP M S ) and mass (mP M S ) of PMS stars (Table 3).
As anticipated by the CMDs (Fig. 7), the MSs as a rule, are poorly-populated. Pismis  An estimate of the MS and PMS MFs can be made with the approach described above. In Fig. 11 we show the resulting MFs for the PMS and MS stars combined. Since the MSs are very-poorly populated (Table 3), it should be noted that these MFs correspond essentially to the PMS stars; the MSs contribute somewhat to the range m 2 M⊙. Besides, given the simplifying assumptions, the error bars in the MFs are only formal, and should be taken as a lower limit. Bearing this in mind, the MFs can be represented by the function φ(m) = dN dm ∝ m −(1+χ) , with slopes χ (Table 3) significantly flatter than the χ = 1.35 of Salpeter (1955) initial mass function (IMF). Interestingly, these MFs do not appear to present a turnover at the sub-Solar mass range, as suggested by the IMFs of Kroupa (2001) andChabrier (2003). However, given the low number of stars and the simplifying assumptions, we have omitted several possible systematic biases associated with the IMF determination: (i) uncertainties in the low-mass IMF due to differential reddening and possibly crowding (the latter should be minimal, since the objects are intrinsically poorly populated), (ii) missing companion stars (e.g. Maíz Apellániz 2008), (iii) binning (e.g. Maíz Apellániz 2005), and (iv) errors on the mass/luminosity relation of individual stars.     σM0 (M⊙ pc −2 ) 600 (panel e). The exception is NGC 2244, which appears to present too big a core for the total mass.
Finally, when the total (MS+PMS) MF slope is considered (panel c), Pismis 5, vdB 80 and NGC 1931 present MFs significantly flatter than those of similarly young OCs. To a lesser degree, the same applies to the newly formed BDSB 96. Such flat slopes are equivalent to those derived for some very old OCs in the reference sample that, in general, undergo advanced dynamical evolution (e.g. Bonatto & Bica 2005). Given the young age, low mass, irregular RDP and the flat mass function, the OCs NGC 1931 and Pismis 5 may be evolving into OB associations or remnants in a few 10 7 yr. Since both OCs are young, such effects may be related to another mechanism than age-related dynamical evolution. It is probably associated with star formation. vdB 80 and BDSB 96, on the other hand, appear to be typical young and low-mass OCs.

SUMMARY AND CONCLUSIONS
Probably because of the interplay between environmental conditions, star-formation efficiency and stellar mass, only a few percent of the embedded clusters survive the first few tens of Myr. Thus, the derivation of astrophysical parameters of OCs in this phase may shed some light on the roles played by the above process in the dissolution/survival issue. In this context, poorly-populated and massive OCs in different environments are yet to be investigated.
In the present paper we derive astrophysical parameters and investigate the nature of the young and low-mass OCs Pismis 5, vdB 80, NGC 1931 and BDSB 96. The wide-field and near-IR depth provided by 2MASS (with errors lower than 0.1 mag) are employed coupled to field-star decontaminated photometry. This enhances cluster CMD evolutionary sequences and stellar radial density profiles, yielding more constrained fundamental and structural parameters. The OCs are located within 174 • ℓ 260 • and |b| 9 • , thus, the errors potentially induced by the background star subtraction are not critical.
The decontaminated CMDs exhibit similar properties, basically a poorly-populated MS, a dominant fraction of PMS stars together with some differential reddening. MS ages are constrained within 5 ± 4 Myr (Pismis 5, vdB 80, BDSB 96) and 10 ± 3 Myr (NGC 1931). However, the PMS stars suggest a wider age spread (∼ 20 Myr), consistent with a non-instantaneous star formation process. The total (MS+PMS) stellar masses are low, within ∼ 60 − 180 M⊙, with mass functions significantly flatter than Salpeter's IMF.
The present OCs are rather small (Rc 0.48 pc, RRDP 5.8 pc), particularly Pismis 5 with Rc ≈ 0.2 pc and RRDP ≈ 1.8 pc. Structurally, the (MS+PMS) stellar RDPs follow a cluster-like profile for most of the radius range. Exceptions are the inner regions of NGC 1931 and especially Pismis 5, which present a marked stellar-density excess. At ∼ 10 Myr, such a central cusp cannot result from largescale cluster dynamical evolution. Instead, it probably is associated with molecular cloud fragmentation and/or starformation effects.
BDSB 96 and vdB 80 present structural properties of typical young, low-mass OCs, although with flat mass functions. On the other hand, the irregular RDPs -together with the low cluster mass and flat mass functions -of NGC 1931 and especially Pismis 5, suggest that both OCs deviate from dynamical equilibrium. They are possibly evolving to become OB associations or remnants in a few 10 7 yr.