THE SUBSTELLAR POPULATION OF σ ORIONIS: A DEEP WIDE SURVEY

We obtained IZ images with the Wide Field Camera (WFC) mounted on the Cassegrain focus of the Isaac Newton Telescope (INT) on 1998 November 12 and 13. The camera consists of a mosaic of four 2 k × 4 k Loral CCD detectors, providing a pixel projection of 0.33 and covering an effective area of 1012 arcmin² in each exposure. We observed four different fields with tiny overlapping between neighboring pointings, covering a total area of 1.12 deg². The central coordinates of these pointings are indicated in Table 1. A representation of the survey can be seen in Figure 1. We performed three individual exposures of 1200 s in each pointing, resulting in a total exposure time of 1 hr in each field and filter.

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Raw frames were reduced within the IRAF⁹ environment, using the CCDRED package. Images were bias subtracted, trimmed, and flat field corrected. We suitably combined our own long exposure scientific images to obtain flat fields. These flat images, usually called superflats, are very useful for correcting fringing patterns not present in sky or dome flats. The photometric analysis was performed using routines within DAOPHOT, which include the selection of objects with stellar point spread function (PSF) using the DAOFIND task (extended objects were mostly avoided) and aperture and PSF photometry. The average seeing on both nights varied from 1.0 to 1.2 arcsec. Nights were not photometric and instrumental magnitudes were transformed into the real magnitudes in the Cousins I system using observations of common stars obtained with the same instrumentation on a photometric night on 2003 January 8. This night was calibrated using photometric standard stars from Landolt (Landolt 1992), observed throughout the night and in each of the four detectors. We found a difference in the zero points of the detectors, and hence, we calibrated each of them independently. Basically, detector 4 (the one in the center) systematically has a zero point ∼0.4 mag fainter, while the rest of them are similar within 0.1 mag. The calibration of these data in BMZO was done assuming that the sensitivity of all the detectors were similar and this explains why the I-band photometry of some of the objects presented here is different from that presented in BMZO and Zapatero Osorio et al. (2000). Instrumental magnitudes of the Z filter were pseudo-transformed into apparent magnitudes assuming that the distribution of the number of stars per interval of magnitude I − Z is similar to that of the Pleiades cluster (Zapatero Osorio et al. 1999b) and has a maximum around I − Z ∼ 0.4 mag. The absolute calibration of this filter is not strictly necessary for the selection of our candidates, since this task is carried out in relative terms: for a given I-band magnitude, candidates must have I − Z colors redder than field sources and overlap and extrapolate the expected photometric sequence of the cluster defined by known members. We always refer to the calibrated I band to estimate masses for our objects. The survey completeness magnitudes are I = 22.0, Z = 21.5 mag and the limiting magnitudes are I = 23.8, Z = 23.0 mag. We adopted as the completeness magnitude the value at which the histogram of detections as a function of magnitude reaches a maximum (∼10σ detection), and as limiting magnitude the value at which 50% of the objects at the maximum of the histogram are detected (∼3σ detection limit).

Table 2 contains the optical photometry and coordinates of selected objects (see Section 3). The error bars account for both the instrumental magnitude errors and the uncertainties in the photometric calibrations, which are typically 0.03–0.04 mag. Astrometry was derived from the UKIDSS Galactic Cluster Survey (GCS) catalog for those objects present in Data Release 6 (a correlation radius of 5 arcsec were used to cross-match the list of targets). The astrometry of fainter candidates not detected in UKIDSS was obtained from the plate solution of each detector derived using the UKIDSS astrometry of bright objects in common and the CCMAP routine. Typical root mean squares of 0.1–0.4 arcsec were found in the astrometric solution for different detectors.

We obtained J-band photometry with the CAIN infrared camera on the Telescopio Carlos Sánchez (TCS) at Observatorio del Teide, on 1998 September 18, 1999 January 23, 24, February 24, August 22, 23, 24, November 26, 27, December 28, 29, and 2000 January 27, and February 11, 12, and with the MAGIC instrument mounted on the 2.2 m telescope at the Calar Alto Observatory on 1998 December 6. The CAIN camera consists of a 256 × 256 pixel NICMOS3 infrared array, providing a pixel projection of 1.00 arcsec and covering a total area of 4.3 × 4.3 arcmin² in each exposure. The MAGIC instrument has also a 256 × 256 pixel NICMOS3 infrared array, providing a pixel projection of 0.64 arcsec and covering an area of 2.7 × 2.7 arcmin². Exposure times ranged from 60 to 1000 s (CAIN) and from 405 to 900 s (MAGIC). Average seeing varied from 1.5 to 4.0 arcsec during the TCS observations and from 1.0 to 2.0 arcsec during the Calar Alto run. We also obtained J-band photometry for the complete area of the BZOR survey on the 3.5 m Calar Alto telescope in 1998 October, using the Omega-Prime instrument, which was cross-matched with our optical photometry. See Zapatero Osorio et al. (2000) and BMZO for more details about these J-band data. The raw CAIN and MAGIC data were processed within the IRAF environment, including sky subtraction and flat-field correction. Final individual images were properly aligned and combined. Aperture photometry was performed using the DAOPHOT routines. Instrumental magnitudes were transformed into apparent magnitudes in the UKIRT system using several photometric field standards obtained for each night (Hunt et al. 1998). For some of our objects observed in non-photometric conditions, the CAIN photometry was calibrated using the 2MASS photometry of objects in common in the same field of view. For a few objects for which the CAIN photometry has large uncertainties (>0.2 mag) or there are no available data, we have adopted the photometry from UKIDSS (described below). All the available J-band data for our candidates are provided in Table 2. Error bars account for the instrumental magnitude errors and the uncertainties in the photometric calibrations, which are typically 0.02–0.13 mag for the CAIN and MAGIC data and 0.05 mag for Omega-Prime.

2.2.1. 2MASS and UKIDSS Near-infrared Photometry

2.2.2. IRAC/Spitzer Mid-infrared Photometry

The first question that arises in our study is whether there is clear evidence of the existence of a clustering of substellar objects around the multiple star σ Orionis. The representation of the spatial distribution in Figure 1 shows that there is a concentration of substellar objects around σ Orionis. To test this we have calculated the distributions of the object density per arcmin² in the present survey along the α and δ axes centered on the σ Orionis AB coordinates. A representation of these distributions can be seen in the top and bottom panels of Figure 4. It can be seen that the distribution decreases from the central star in both the α and δ axes, indicating the existence of a greater concentration of objects around σ Orionis. It is interesting to note that from both figures we can see that there is also an increase in the last bins (at separations larger than 30 arcmin) to the north and west of σ Orionis. Some of these objects are located at distances closer to the star ζ Orionis and could be related to the existence of a substellar population around this star. The rest of these objects are located closer to σ Orionis than to any other OB star, but this population can be related to the sparse, wide clustering around the Orionis cluster (Sherry 2003; Briceño et al. 2005; Caballero & Solano 2008). It might be that the population identified by Jeffries et al. (2006), which is kinematically different from the σ Orionis cluster and seem to be concentrated to the northwest of the star, is also related with the excess of sources observed. Objects in this region are identified in the last column of Table 2. After discarding this population of possible Orion background objects a total of 102 bona fide member candidates remains concentrated around the σ Orionis star. We determine that the central coordinates of the cluster, according to the substellar distribution, are within the central bins of 5 arcmin around the massive star. This estimate is not very precise because of the limits imposed by the geometry of our survey and the radial dependence of the object density in a cluster. The center of mass of the multiple star σ Orionis is located a few arcseconds from the central star σ Orionis AB (see Caballero 2007, 2008b). We can estimate the center of mass of the substellar population of the cluster and find that this is located within 2 arcmin of the more massive stars; considering the uncertainties, we can argue that they are the same. In the remaining discussion of the spatial distribution we consider the coordinates of σ Orionis AB as the central coordinates of the cluster.

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The next objective in our study is to characterize the radial distribution of the surface density of the substellar objects in the cluster. In order to calculate this we have estimated the surface density of the number of objects in concentric coronas at different distances to the center of the cluster. This is a decreasing function with distance to the center and is shown in Figure 5. The increase in this distribution at distances larger than 30 arcmin can be explained by the presence of other population of Orion (see previous subsection). We can try to adjust this distribution with different empirical functions obtained for star clusters such as an exponential (Van den Bergh & Sher 1960) or a King distribution (King 1962). In the case of the σ Orionis cluster, due to the sharpness of the decay and the contamination of a background population at large distances, the former seems to be more suitable. In addition, the King function was developed to reproduce dynamically relaxed clusters, and, given the very young age of σ Orionis, we do not expect that dynamical evolution is yet important. We have adjusted the surface density to an exponential law, $\sigma = \sigma _{0} e^{-r/r_{0}}$, where r₀ is the characteristic radius of a cluster, defined as the radius at which the density has diminished by a factor e, and σ₀ is the central density. The best-fit values obtained for these variables in the distance range between 5 and 25 arcmin from the center are r₀ = 9.5 ± 0.7 arcmin (∼1 pc at the distance of σ Orionis) and σ₀ = 0.23 ± 0.03 object arcmin⁻². Similar results are found for brighter candidates (I <18 mag) and fainter ones (I >18 mag), indicating that there is no significant mass segregation between more and less massive brown dwarfs in the cluster. The dashed line in Figure 5 shows the surface density of the 102 σ Orionis member candidates after subtracting the possible background population located at projected distances larger than 30 arcmin to the north and west of the cluster. We can see that the estimated exponential law extrapolates reasonably well this surface density to distances up to 40 arcmin, although we can see that the real numbers could be slightly larger. This could indicate a lower decrease in the surface density at these distances as pointed out by Caballero (2008b), who argued that an extended halo of low-mass stars is present in the cluster at distances larger than 20 arcmin.

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Although comparison with previous studies of spatial distribution of the low-mass population of the cluster is difficult due to the different functions adopted to fit the surface density, we can say that the radial distributions of substellar objects found in this paper is similar to that of the low-mass stars of the cluster (Sherry et al. 2004; Caballero 2008b). These two studies used a King model to adjust radial surface density and found a core radius r_c of 10–12 arcmin (r₀ ∼ 1.36r_c). In addition, Caballero (2008b) also studied an exponential and a potential law and found a characteristic radius between 12 and 18 arcmin (see their Figure 3) and find that the best fit for the radial surface density is obtained for an r⁻¹ function. Another study that has investigated the spatial distribution of low-mass stars and brown dwarfs in the σ Orionis cluster is that by Lodieu et al. (2009). In this case they did not adjust any function to the radial distribution, but they found that cluster members are clearly concentrated within the central 30 arcmin; they also found a deficit of brown dwarfs in the central 5 arcmin with respect to the stars. A similar result was also previously reported for very low mass stars and brown dwarfs by Caballero (2008b). Our present survey does not cover this region and hence we cannot address this question. Preliminary results of the spatial distribution of brown dwarfs using the same optical data as those studied here were also presented in Béjar et al. (2004a). They found similar results of the central density and characteristic radius within 1σ–2σ the quoted uncertainties.

To investigate whether the location of brown dwarfs in the σ Orionis cluster can be affected by the presence of other substellar objects, which could be a residual phenomenon of a common process of formation, we have investigated whether the distribution of the substellar population is Poissonian at each radial distance to the center of the cluster. In order to do that, we have investigated the distance to the nearest neighbor. We have compared the results obtained in our sample of substellar objects with theoretical predictions for a Poissonian distribution and with the results for Monte Carlo simulations of clusters in the same conditions as ours. We computed 10,000 simulated clusters with the same radial surface density of substellar objects obtained in Section 4.2 for separations to the center between 0 and 50 arcmin and with a total number of 130 objects, given by the integration of this exponential distribution between both radii. An increase in the number of simulated clusters does not improve the statistical uncertainties in our computations because these are dominated by the small number of objects (between 10 and 20) in the radial bins of the distribution.

The solid histogram of Figure 6 shows the average value of the nearest neighbor distance of the σ Orionis member candidates as a function of the separation from the cluster center. For comparison purposes, we also show the expected value for a Poissonian distribution and the nearest neighbor distances derived from Monte Carlo simulations. In this case we have only taken into account those objects in the simulated clusters that are located within the surveyed area of the real observations. The reason is to eliminate border effects due to the particular geometry of our study that might affect the nearest neighbor distance estimator. From this figure we can see that this distance is similar in our sample to that estimated for the Monte Carlo simulations, and that at close separations to the center it is similar to that expected from a theoretical Poissonian distribution. Between 5 and 15 arcmin both the nearest neighbor distance of the sample and simulations are slightly larger than the Poissonian homogeneous distribution due to boundary problems caused by the incompleteness of our survey at these distances. This effect is not a consequence of the existence of sub-clustering as shown by the simulations because, if this happened, we would expect lower separations. At separations larger than 30 arcmin we are dominated by the incompleteness of our survey and separations are lower than expected for a Poissonian homogeneous distribution. As an example, the solid histogram of Figure 7 show the nearest neighbor distances of the candidates located between 10 and 15 arcmin from the cluster center. For comparison, we also show the histogram of the values of simulated clusters and the expected Poissonian distribution with the mean surface density of the cluster at these distances. We can say that all these distributions are consistent among themselves, considering the uncertainties due to the low number of objects per bin. These results indicate that the distribution of substellar objects at the same radial distance to the center of the cluster is almost Poissonian and, hence, that this is not dominated by the presence of aggregations or sub-clustering of these objects.

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We have used the available JHK_s photometry from the UKIDSS catalog of those reliable cluster member candidates with errors smaller than 0.10 mag to study the presence of near-infrared excesses. A total of 98 objects have available photometry within this requirement, which includes the majority of our candidates within the completeness of the survey. According to theoretical evolutionary models, these cluster member candidates have masses in the interval 0.11–0.013 M_☉. We have built the H − K_s, J − K_s and I − J, J − K_s color–color diagrams shown in Figure 8. From these representations we can see that 5 objects present near-infrared H − K_s and J − K_s colors deviating from the expected sequence of non reddened cluster members by more than 2σ. All except one and another four of the candidates show a redder J − K_s color than expected for their I − J color by more than 2σ. These objects are marked in the last column of Table 3. This indicates that five to nine of the 98 σ Orionis cluster member candidates with accurate UKIDSS photometry(∼ 5%–9%) could have near-infrared excesses. Three of these objects (S Ori J053849.29–022357.6, S Ori J053907.56–021214.6, and S Ori J053940.58–023912.4) also show near-infrared excesses using the photometry from 2MASS, while the rest of them are very faint or have large error bars in this catalog.

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Using the same criteria as above, we have found that 2 or 3 out of the 17 objects (12%–18%) of the Orion background population also have these excesses, which indicates a similar fraction to that of the cluster member candidates. Curiously, two to three out of the nine objects (22%–33%) considered as non-members present near-infrared excesses. As explained before, we estimated that most of the non-member contaminants of our survey are formed by field M dwarfs; hence, it is not expected that they still have a disk and have such a large fraction of infrared excesses. These three objects (S Ori J053945.35–025409.0, S Ori J053840.38–030403.2, and S Ori J053936.08–023627.3) lie quite close to the photometric sequence of the cluster and hence might be members. In these cases, variability and photometric errors can likely explain their location in the I, I − J color–magnitude diagram. Because they show infrared excesses, they could also be members partially occulted by the presence of their disks. Another possibility is that these three objects could be unresolved galaxies; some of these galaxies show very red near and mid-infrared colors but not so red I − J colors (see, for example, Caballero et al. 2008b). Additional photometry and spectroscopy is required to determine the true nature of these objects. If they are really bona fide members of the cluster, the fraction of substellar objects with near-infrared excesses could be increased by up to 7%–12%. We will not consider these objects as cluster members for our estimation of the substellar mass function in the next section. Following these considerations, we have estimated that about 2%–3% of the cluster members could be lost with our selection criteria.

In summary, we have found that ∼5%–9% of the very low mass stars and brown dwarf candidates in the σ Orionis cluster have near-infrared excesses at 2.2 μm that could be related to the presence of disks. Other studies have found similar results with a fraction of near-infrared excesses between 5% and 12% in cluster member candidates (Oliveira et al. 2002; Barrado y Navascués et al. 2003; Béjar et al. 2004b; Caballero 2008a).

In order to identify the population of substellar objects with mid-infrared excesses in the σ Orionis cluster, we have used the available 3.6, 4.5, 5.8, and 8.0 μm photometry from the IRAC/Spitzer data. Following a similar procedure as in Caballero et al. (2007), we have built [3.6] − [5.8], I − J and [3.6] − [8.0], I − J color–color diagrams, shown in Figure 9. A total of 67 good cluster member candidates have I, J, [3.6], [5.8] or I, J, [3.6], [8.0] photometry. Of the 67 objects, 19 (28% ± 7%) show [5.8] − [3.6] ⩾ 0.4 mag and 18 of the 58 (31% ± 7%) show [3.6] − [8.0] ⩾ 0.8 mag. We have used these color criteria to identify mid-infrared flux excesses, which are based on the separation between objects with and without disks adopted in Caballero et al. (2007), Zapatero Osorio et al. (2007), and references therein. The presence of mid-infrared excesses is also indicated in the last column of Table 3. All the candidates that show infrared excess in the [5.8] band and have available photometry in [8.0] also present infrared excess in this band. In addition, all except one of the objects that show infrared excess in [8.0] also show it in [5.8]. By considering both the excesses at [5.8] and [8.0], we have found that 20 of the 67 candidates (30% ± 7%) show a larger emission at wavelengths longer than 5.8 μm. In any case all these results are lower limits, since some of the candidates can be field dwarf contaminants. Adopting the maximum number of contaminants previously estimated, this fraction could be increased up to 40% ± 9%. Six of the nine cluster member candidates with near-infrared excesses have available IRAC/Spitzer photometry in [3.6] and [5.8] or [8.0]. Two of them also have a larger emission in the mid-infrared, while the other four have not. All except two (18) of the candidates presenting mid-infrared excesses have available accurate UKIDSS photometry. Only the two objects mentioned above also show a larger emission in the K band, while the rest of them (16) only present excesses at wavelength longer than 5.8 μm.

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In summary, we have found that about 30% ± 7% of the substellar cluster member candidates show mid-infrared excesses that are probably associated with the presence of disks. A similar result has also been found in other studies of the cluster, both in low-mass stars, brown dwarfs and planetary-mass domain (Jayawardhana et al. 2003; Oliveira et al. 2004, 2006; Hernández et al. 2007; Caballero et al. 2007; Zapatero Osorio et al. 2007; Scholz & Jayawardhana 2008; Luhman et al. 2008). Given that the fraction of candidates with excesses at wavelengths longer than 5.8 μm are notably larger than at 2.2 μm, most of the disks around these objects seem to be "transition disks," which are characterized for the weak or absent near-infrared emission and the presence of mid- and far-infrared excesses (Strom et al. 1989; Sicilia-Aguilar et al. 2006). This is explained by a process of clearing in the inner part of the disk, probably due to the formation of planetesimals, leading to a transition from optically thick to optically thin inner disks.