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SPITZER: Accretion in Low Mass Stars and Brown Dwarfs in the Lambda Orionis Cluster

We present multi-wavelength optical and infrared photometry of 170 previously known low mass stars and brown dwarfs of the 5 Myr Collinder 69 cluster (Lambda Orionis). The new photometry supports cluster membership for most of them, with less than 15% of the previous candidates identified as probable non-members. The near infrared photometry allows us to identify stars with IR excesses, and we find that the Class II population is very large, around 25% for stars (in the spectral range M0 - M6.5) and 40% for brown dwarfs, down to 0.04 Msun, despite the fact that the H(alpha) equivalent width is low for a significant fraction of them. In addition, there are a number of substellar objects, classified as Class III, that have optically thin disks. The Class II members are distributed in an inhomogeneous way, lying preferentially in a filament running toward the south-east. The IR excesses for the Collinder 69 members range from pure Class II (flat or nearly flat spectra longward of 1 micron), to transition disks with no near-IR excess but excesses beginning within the IRAC wavelength range, to two stars with excess only detected at 24 micron. Collinder 69 thus appears to be at an age where it provides a natural laboratory for the study of primordial disks and their dissipation.


Introduction
The star-formation process appears to operate successfully over a wide range of initial conditions. In regions like Taurus, groups of a few stars to a few tens of stars are the norm. The molecular gas in Taurus is arranged in a number of nearly parallel filaments, possibly aligned with the local magnetic field, and with the small stellar groups sited near end-points of the filaments (Hartmann 2004). No high mass stars have been formed in the Taurus groups, and the Initial Mass Function (hereafter, IMF) also appears to be relatively deficient in brown dwarfs Luhman 2004) -but see also (Guieu et al. 2006) for an alternate view. The Taurus groups are not gravitationally bound, and will disperse into the field on short timescales. At the other end of the mass spectrum, regions like the Trapezium cluster and its surrounding Orion Nebula cluster (ONC) have produced hundreds of stars. The ONC includes several O stars, with the earliest having spectral type O6 and an estimated mass of order 35 M ⊙ . The very high stellar density in the ONC (10,000 stars/pc 3 at its center (McCaughrean & Stauffer 1994)) suggests that star-formation in the ONC was gravity dominated rather than magnetic field dominated. It is uncertain whether the ONC is currently gravitationally bound or not, but it is presumably at least regions like the ONC that are the progenitors of long-lived open clusters like the Pleiades. UV photoionization and ablation from O star winds likely acts to truncate the circumstellar disks of low mass stars in the ONC, with potential consequences for giant planet formation.
An interesting intermediate scale of starformation is represented by the Lambda Ori association. The central cluster in the association -normally designated as Collinder 69 or the Lambda Orionis cluster-includes at least one O star, the eponymous λ Ori, with spectral type O8III. However, a number of lines of evidence suggests that one of the Coll 69 1 Based on observations collected Spitzer Space Telescope; at the German-Spanish Astronomical Center of Calar Alto jointly operated by the Max-Planck-Institut für Astronomie Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC); and at the WHT operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofsica de Canarias stars has already passed through its post-main sequence evolution and become a supernova, and hence indicating it was more massive than Lambda Ori (see the complete Initial Mass Function in Barrado y Navascués, Stauffer, & Bouvier (2005)). A census of the stars in Coll 69 by Dolan & Mathieu (2001) -hereafter, DM-indicates that the cluster is now strongly unbound. DM argue that this is due to rapid removal of molecular gas from the region that occurred about 1 Myr ago when the supernova exploded. They interpreted the color-magnitude diagram of Coll 69 as indicating a significant age spread with a maximum age of order 6 Myr; an alternative interpretation is that the cluster has negligible age spread (with age ∼6 Myr) and a significant number of binary stars. While DM identified a large population of low mass stars in Coll 69, only four of 72 for which they obtained spectra are classical T Tauri stars (based on their Hα emission equivalent widths). Much younger stars, including classical T Tauri stars, are present elsewhere in the Lambda Ori SFR, which DM attribute to star-formation triggered by the supernova remnant shock wave impacting pre-existing molecular cores in the region (the Barnard 30 and Barnard 35 dark clouds, in particular).
We have obtained Spitzer space telescope IRAC and MIPS imaging of a ∼one square degree region centered on the star λ Ori in order to (a) search for circumstellar disks of members of the Coll 69 cluster and (b) attempt to identify new, very low mass members of the cluster in order to determine better the cluster IMF (in a forthcoming paper). In §2, we describe the new observations we have obtained; and in §3 we use those data to reconsider cluster membership. In §4 we use the new candidate member list and the IR photometry to determine the fraction of cluster members with circumstellar disks in both the stellar and substellar domain, and we sort the stars with disks according to their spectral slope from 1 to 24 µm.

Optical and Near Infrared photometry
The optical and the near IR data for the bright candidate members come from Barrado y Navascués et al. (2004) -hereafter, Paper I. The RI -Cousins system-data were collected with the CFHT in 1999, whereas the JHKs come from the 2MASS All Sky Survey (Cutri et al. 2003). For cluster members, the completeness limit is located at I(complete,cluster) ∼ 20.2 mag, whereas 2MASS provides near infrared data down to a limiting magnitude of J=16.8, H=16.5, and Ks=15.7 mag. In some cases, low resolution spectroscopy in the optical, which provides spectral types and Hα equivalent widths, is also available. Twentyfive objects out of the 170 CFHT1999 candidate members are in common with Dolan & Mathieu (1999, 2001. Those 25 stars also have Hα and lithium equivalent widths, and radial velocities.

New deep Near Infrared photometry
For the objects with large error in 2MASS JHKs, or without this type of data due to their intrinsic faintness, we have obtained additional measurements with the WHT (La Palma Observatory, Spain) and INGRID (4.1×4.1 arcmin FOV) in November 2002 and February 2003, and with the Calar Alto 3.5m telescope (Almeria, Spain) and Omega2000 in October 2005 (15.36×15.36 arcmin FOV). In all cases, for each position, we took five individual exposures of 60 seconds each, with small offsets of a few arcseconds, thus totalling 5 minutes. In the case of the campaigns with IN-GRID, we observed the area around the star λ Orionis creating a grid. Essentially, we have observed about 2/3 of the CFHT 1999 optical survey region in J (in the area around the star and west of it), with some coverage in H and K. On the other hand, the Omega2000 observations, taken under a Director's Discretionary Time program, were focused on the faint candidate members. Except for one object (LOri154), we collected observations in the J, H and Ks filters. The conditions of the first observing run with INGRID were photometric, and we calibrated the data using standard stars from Hunt et al. (1998) observed throughout the nights of the run. The average seeing was 0.9 arcsec. We had cloud cover during the second run with INGRID, and the data were calibrated using the 2MASS catalog and the stars present in each individual image. The dispersion of this calibration is σ=0.05 magnitudes in each filter, with a seeing of about 1.0 arcsec. Finally, no standard stars were observed during the DDT observations at Calar Alto. The seeing in this case was 1.2 arc-sec. The faint Lambda Orionis candidate members were calibrated using also 2MASS data. In this last case, the dispersion is somewhat higher, probably due to the worse seeing and the larger angular pixel scale of the detector, with σ=0.1 mag. Note that this is dispersion not the error in the calibration. These values correspond to the FWHM of the gaussian distribution of the values zeropoint(i)=mag raw (i)-mag 2MASS (i), for any star i, which also includes the photometric errors in the 2MASS photometry and any contribution due to the cluster stars being photometrically variable. Since there is a large number of stars per field (up to 1,000 in the Omega2000 images), the peak of this distribution can be easily identified and the zero points derived. A better estimate of the error in the calibration is based on the distance between mean, median and mode values, which are smaller than half of the FWHM (in the case of the mean and the median, almost identical to the hundredth of magnitude). Therefore, the errors in the calibration can be estimated as 0.025 and 0.05 magnitudes for the INGRID and the Omega2000 datasets, respectively.
All the data were processed and analyzed with IRAF 2 , using aperture photometry. These measurements, for 166 candidate members, are listed in Table 1 (WHT/INGRID) and Table 3 (CAHA/Omega2000). Note that the errors listed in the table correspond to the values produced by the phot task with the digi.apphot package and does not include the errors in the calibrations.

Spitzer imaging
Our Spitzer data were collected during March 15 (MIPS) and October 11 (IRAC), 2004, as part of a GTO program. The InfraRed Array Camera (IRAC, Fazio et al. (2004)) is a four channel camera which takes images at 3.6, 4.5, 5.8, and 8.0 µm with a field of view that covers ∼5.2×5.2 arcmin. IRAC imaging was performed in mapping mode with individual exposures of 12 seconds "frametime" (corresponding to 10.4 second exposure times) and three dithers at each map step. In order to keep the total observation time for a given map under three hours, the Lambda Ori map was broken into two segments, each of size 28.75×61.5 arcmin -one offset west of the star λ Ori and the other offset to the east, with the combined image covering an area of 57×61.5 arcmin, leaving the star λ Orionis approximately at the center. Each of the IRAC images from the Spitzer Science Center pipeline were corrected for instrumental artifacts using an IDL routine developed by S. Carey and then combined into the mosaics at each of the four bandpasses using the MOPEX package (Makovoz & Khan 2005). Note that the IRAC images do not cover exactly the same FOV in all bands, providing a slice north of the star with data at 3.6 and 5.8 micron, and another slice south of it with photometry at 4.5 and 8.0 microns. The size of these strips are about 57×6.7 arcmin in both cases. The Multiband Imaging Photometer for Spitzer (MIPS, Rieke et al. (2004)) was used to map the cluster with a medium rate scan mode and 12 legs separated by 302 arcsec in the cross scan direction. The total effective integration time per point on the sky at 24 µm for most points in the map was 40 seconds, and the mosaic covered an area of 60.5×98.75 arcmin centered around the star λ Orionis. Since there were no visible artifacts in the pipeline mosaics for MIPS 24 µm we used them as our starting point to extract the photometry. We obtained MIPS 70 µm and 160 µm imaging of the λ Ori region, but very few point sources were detected and we do not report those data in this paper.
The analysis of the data was done with IRAF. First, we detected objects in each image using the "starfind" command. Since the images in the [3.6] and [4.5] bands are deeper than those in the [5.8] and [8.0] bands, and since the fluxes of most objects are brighter at those wavelengths, the number of detections are much larger at the IRAC short wavelengths than at the longer ones. Only a relatively few objects have been detected at 24 µm with MIPS. As a summary, 164 objects were detected at at 3.6 and 4.5 micron, 145 at 5.8 micron, 139 at 8.0 micron and 13 at 24 micron.
We have performed aperture photometry to derive fluxes for C69 cluster members. For the IRAC mosaics we used an aperture of 4 pixels radius, and the sky was computed using a circular annulus 4 pixels wide, starting at a radius 4 pixels away from the center. It is necessary to apply an aper-ture correction to our 4-pixel aperture photometry in order to estimate the flux for a 10-pixel aperture, because the latter is the aperture size used to determine the IRAC flux calibration. In some cases, due to the presence of nearby stars, hot pixels, or because of their faintness, a 2 pixel aperture and the appropriate aperture correction were used (see notes to Table 3). For the MIPS photometry at 24 µm, we used a 5.31 pixels (13 arcsec) aperture and a sky annulus from 8.16 pixels (20 arcsec) to 13.06 pixels (32 arcsec). An aperture correction was also applied. Table 2 provides the zero points, aperture corrections and conversion factors between magnitudes and Jansky, as provided by the Spitzer Science Center website.

Data cross-correlation
The coverage on the sky of our Spitzer/IRAC data is an approximate square of about 1 sq.deg, centered on the star λ Orionis. The optical data taken with the CFHT in 1999 covers an area of 42×28 arcmin, again leaving the star in the center of this rectangle. Therefore, the optical survey is completely included in the Spitzer mapping, and we have been able to look for the counterpart of the cluster candidates presented in Paper I. The analysis of the area covered by Spitzer but without optical imaging in the CFHT1999 survey will be discussed in a forthcoming paper. We have not been able to obtain reliable Spitzer photometry for some candidate members from Paper I, especially at the faint end of the cluster sequence. The faintest detected object, LOri167, depending on the isochrone and the model, would have a mass of ∼0.017 M ⊙ , if it is a member (Barrado y Navascués, Huélamo, & Morales Calderón (2005)).
The results are listed in Table 3, where nonmembers and members are included, respectively (see next section for the discussion about the membership). In both cases, we include data corresponding to the bands R and I -from CFHT-, J, H and Ks -from 2MASS and CAHA-, [3.6], [4.5], [5.8], and [8.0] -from IRAC-and [24] -from MIPS. Additional near IR photometry from WHT can be found in Table 1.

Color-Color and Color-Magnitude Diagrams and new membership assignment
Before discussing membership of the Paper I stars based on all of the new optical and IR data, we have made an initial selection based on the IRAC colors. Figure 1 (see further discussion in the next section) displays a Color-Color Diagram with the four IRAC bands. We have found that 31 objects fall in the area defined by Allen et al. (2004) and Megeath et al. (2004) as Class II objects (ie, TTauri stars). Another two candidate members are located in the region corresponding to Class I/II objects. We consider all these 33 objects as bona-fide members of the C69 cluster. Harvey et al. (2006) have discussed the confusion by extragalactic and other sources when analysing Spitzer data (in their case, they used Serpens, a cloud having a large extinction). We believe that this contribution is negligible for our Lambda Ori data, since those Class II objects detected at 24 micron are in the TTauri area defined by Sicilia-Aguilar et al. (2005), as displayed in her figure 5. There can be a higher level of contamination among the objects classiefied as Class III. All of the objects in Figure 1 had previously been identified as cluster candidate members based on optical CMDs -it is unlikely that a significant number of AGN would have passed both our optical and our IR criteria (and also have been unresolved in our optical CFHT images). Moreover, prior to our Spitzer data, only 25% candidate members which had optical, near-IR data and optical low-resolution spectroscopy turned out to be non-members (Paper I). After adding the Spitzer photometry, we are quite confident in the membership of the selection. Figure 2 and Figure 3 display several colormagnitude diagrams (CMD) using the data listed in Tables 1 and 3. In the case of the panels of the first figure, we present optical and IR, including Spitzer/IRAC data; whereas in the second set of figures only IR data are plotted. For the sake of simplicity, we have also removed the non-members from Figure 3.
Based on these diagrams and on the spectroscopic information included in Paper I, we have reclassified the candidate members as belonging or not to the cluster. In color-magnitude diagrams, C69 members lie in a fairly well-defined locus, with a lower bound that coincides approximately with the 20 Myr isochrone in this particular set of theoretical models (Baraffe et al. 1998). Stars that fall well below (or blueward) of that locus are likely non-members; stars that fall above or redward of that locus are retained because they could have IR excesses or above average reddening. We combine the "votes" from several CMD's to yield a qualitative membership determination, essentially yes, no or maybe. In total, out of 170 candidates, 19 are probable non-members, four have dubious membership and the rest (147 objects) seem to be bona-fide members of the cluster. Therefore, the ratio of non-members to initial candidate members is 13.5 %. In any case, only additional spectroscopy (particularly medium and high resolution) can be used to establish the real status. Proper motion might be helpful, but as shown by Bouy et al. (2007), some bona-fide member can appear to have discrepant proper motions when compared with the average values of the association. Table 4 shows the results for each candidate in the different tests used to determine its membership, the membership as in Paper I, and the final membership based on the new photometry. The second and last columns show the spectroscopic information. Note that the degree of confidence in the new membership classification varies depending on the available information and in any event it is always a matter of probability.
As Table 3 shows, the Spitzer/IRAC data does not match completely the limiting magnitudes of either our optical survey with CFHT or the 2MASS JHKs data. In the case of the band [3.6], essentially all the Lambda Orionis candidate members should have been detected (except perhaps the faintest ones, at about I=22 mag). Some objects in the faint end have 3.6 micron data, but lack 2MASS NIR, although in most cases we have supplied it with our own deep NIR survey. In the case of the Spitzer data at 4.5 micron, some additional candidate members fainter than I=20.9 mag were not found, due to the limiting magnitude of about [4.5] lim =16.3 mag. The data at 8.0 micron only reach [8.0] lim =14.0 mag, which means that only cluster members with about I=18.6 mag -or Ks=14.9-can be detected at that wavelength. This is important when discussing both the membership status based on color-magnitude diagrams and the presence of infrared excesses by examin-5 ing color-color diagrams. Note, however, that objects with IR excesses have fainter optical/near-IR counterparts than predicted in the table. Figure 4 presents another CMD with the optical magnitudes from the CFHT survey (R and I), where we display the 170 candidate members using different symbols to distinguish their actual membership status. Small dots correspond to non-members based on the previous discussion, whereas plus symbols, crosses and circles denote probable members. In the first case -in most cases due to their faintness-they do not have a complete set of IRAC magnitudes, although they can have either a measurement at 3.6 and 4.5, or even at 5.8 microns. In the case of the objects represented by crosses, they have been classified as Class III objects (Weak-line TTauri stars and substellar analogs if they indeed belong to the cluster) based on an IRAC color-color diagram (see next section and Figure 1). Finally, big circles correspond to Class II sources. The pollution rate seems to be negligible in the magnitude range I=12-16 (1.2-0.17 M ⊙ approx, equivalent to M0 and M5, respectively), where our initial selection based on the optical and the near infrared (2MASS data) has worked nicely. However, for fainter candidates, the number of spurious members is very large and the pollution rate amounts to about 15% for objects with 16 < I < 19, and about 45% for I≥19 (approximately the magnitude beyond the reach of the 2MASS survey).
At a distance of 400 pc and for an age of 5 Myr, and according to the models by Baraffe et al. (1998), the substellar borderline is located at about I=17.5 mag. Table 5 lists other values for different ages, as well other bands -J, Ks and L ′ -discussed in this paper. Among our 170 CFHT candidate members, there are 25 objects fainter than that magnitude, and which pass all of our membership criteria which are probable brown dwarfs. Out of these 25 objects, 12 have low-resolution spectroscopy and seem to be bonafide members and, therefore, brown dwarfs. The other 13 objects are waiting for spectral confirmation of their status. Assuming an age of 3 or 8 Myr would increase or decrease the number of brown dwarf by seven in each case. In the first case (3 Myr), five out of the seven possible BDs have spectroscopic membership, whereas in the second case only three were observed in Paper I.
As a summary, we have found between 18 and 32 good brown dwarfs candidates (depending on the final age) in the Lambda Orionis cluster, and between 17 and 9 have their nature confirmed via low-resolution spectroscopy. Note that even this technique does not preclude the possibility that a few among them would actually be non-members.

The Color-Color diagrams, the diagnostic of IR excess and the disk ratio
The Spitzer/IRAC colors are a powerful tool to reveal the dust and, therefore, the population of Class I and II sources in a stellar association.  Megeath et al. (2004)) displays the colors derived from the measurements at 3.6 minus 4.5 microns, versus those obtained at 5.8 minus 8.0 microns. This diagram produces an excellent diagnostic, allowing an easy discrimination between objects with and without disks. Note that due to the limiting magnitudes of the IRAC bands (see the discussion in previous section), objects fainter than about I=18.6 mag cannot have a complete set of IRAC colors and therefore cannot be plotted in the diagram. This fact imposes a limit on our ability to discover mid-IR excesses at the faint end of the cluster sequence. For Lambda Orionis cluster members, assuming a distance of 400 pc and an age of 5 Myr (and according to the models by Baraffe et al. (1998)), this limit is located at 0.040 M ⊙ . Figure 1 contains a substantial number of objects in the region corresponding to the Class II sources. In total, there are 31 objects located within the solid rectangle out of 134 Lambda Orionis members with data in the four IRAC bands. Among them, three (LOri045, LOri082 and LOri092) possibly have relatively large photometric errors in their 5.8 µm flux, because inspection of their SEDs indicates they are likely diskless. Two additional objects, LOri038 and LOri063, have IRAC colors indicating Class I/II (actually, LOri038 is very close to the Class II region). The SED (see below) in-dicates that both are Class II stars. Therefore, the fraction of cluster members that are Class II PMS stars based on their IR excesses is ∼22-25%, for the spectral range M0-M6.5. This is different from what was inferred by Dolan & Mathieu (1999, 2001) and by us (Paper I), based on the distribution of the Hα emission and near-infrared color-color diagrams. The Spitzer/IRAC data clearly demonstrate that Lambda Orionis cluster does contain a significant number of stars with dusty circumstellar disks. No embedded objects (Class I) seem to be present, in agreement with the age range for the association (3-8 Myr or even slightly larger). Note that our different IR excess frequency compared to Dolan & Mathieu may result from their sample being primarily of higher mass stars than ours. Figure 5 is a blow-up of the region in Figure 1 corresponding to the Class II sources. We have also added big minus and plus symbols, and large squares, to indicate those objects with measured Hα equivalent widths (in low-and mediumresolution spectrum). We have used the saturation criterion by Barrado y Navascués & Martín (2003) to distinguish between objects with high W(Hα) -plus symbols-and normal W(Hα)minus symbols. In principal, an object with a W(Hα) value above the saturation criterion is either accreting or is undergoing a flare episode. There are two low mass stars (LOri050 and LOri063) with an Hα line broader than 200 km/s (Muzerolle et al. 2003), another independent indication of accretion (based on Natta et al. (2004), they should have very large accretion rates ∼10 −9 M ⊙ /yr). The theoretical disk models used to interpret IRAC Color-Color Diagram by Allen et al. (2004) suggest that the accretion rates increase from the bottom-left to the top-right of the figure. This is in agreement with our results, since most of the accreting objects (assuming that strong Hα is a good indicator of accretion) lie in the area of the figure with the larger excesses (top-right). A couple of objects with very low Hα emission are located near the edge of the Class II area (bottom-left), a fact that suggest that they may have a relatively thin disk, with small or negligible accretion. Actually these objects are surrounded by thin disks instead of thick primordial disks (see next section).
Regarding the brown dwarfs in the cluster, several probable members (LOri126, LOri129, LOri131, LOri132, LOri139 and LOri140) are located within the precinct of Classical TTauri stars.
They are just at the border between stars and substellar objects, with magnitudes in the range I=17.52-18.21 and J=15.38-16.16 (the boundary is located at I=17.55 and J=15.36 for 5 Myr, see Table 5). In Paper I we presented low-resolution spectroscopy of LOri126, LOri139 and LOri140, which suggests they are cluster members (the spectral types are M6.5, M6.0 and M7.0 with a Hα equivalent width of 26.2, 19.7 and 72.8Å, respectively). In addition we have confirmed the membership of LOri129 via medium-resolution spectroscopy (spectral type, M6.0 with a Hα equivalent width of 12.1Å).
In total, there are 15 brown dwarf candidates with a complete set of IRAC colors, six of which fall in the Class II region, thus making the fraction of brown dwarfs with IR colors indicative of circumstellar disks close to 40% (down to 0.04 M ⊙ ), similar to the 50% obtained by (Bouy et al. 2007) in Upper Sco brown dwarfs, using mid-IR photometry or the 50% derived by Guieu et al. (2006) in Taurus brown dwarfs with Spitzer.

The Spectral Energy Distribution
We have plotted the SEDs of our Lambda Orionis candidate members in Figures 6-8. There is clearly a range from approximately flat spectrum, to black-body in the near-IR but starting to show excesses at IRAC wavelengths, to only showing excess at 24 micron. A way to study the presence of a circumstellar disk around an object is to analyze the shape of the SED. After Lada et al. (2006) we have used the 3.6-8.0 µm slope for each source detected in at least three IRAC bands to distinguish between objects with optically thick, primordial disks, objects surrounded by optically thin or anemic disks and objects without disks. The results of this test are presented in Table 4. In Figures 6-8 the SEDs are sorted in agreement with their IRAC slope classification: diskless objects (slope index or α<−2.56) in Figure 6, thick disks (α>−1.8) in Figure 7, and objects surrounded by thin disks (−1.8<α<−2.56) in Figure 8. In this last figure we also include two low mass stars which present an excess only at 24 micron, due to a transition disk (see below). According to the IRAC slope the fraction of cluster members detected in at least three of the IRAC bands with optically thick disks is 14%, while the total disk fraction is found to be 31% (similar to the 25% derived with the IRAC CCD). This fraction is lower than the 50% found by Lada et al. (2006) in IC348 (1-3 Myr) as expected due to the different age of the clusters. Figure 9 illustrates the evolution of the disk fraction with the age for several stellar associations (assuming that the infrared excess serves as a proxy of the presence of a circumstellar disk). The ratios for the different associations come from IRAC data Lada et al. 2006;Sicilia-Aguilar et al. 2006) in order to avoid different results depending on the technique used (Bouy et al. 2007). The ratio for the Lambda Orionis cluster (Collinder 69) is about 30% and, as stated before, for the objects below the substellar borderline, the fraction of Classical TTauri objects seems to be larger. According to its older age, the thick disk fraction in Collinder 69 is lower than that of IC348 (this fraction is represented by open squares in Figure 9).
Among the objects classified as Class III sources from Figure 1, only two (LOri043 and LOri065) have a measurement at [24] with an unambiguous detection. These two stars do not have excesses at 3.6 or 4.5 micron. Therefore, they can be classified as transition objects, the evolutionary link between the primordial disks and debris disks. A third of the Class II sources (11 out of 33) have measurements in the [24] band, all of them with clear excess, as expected from their Class II status. The lack of IR excesses at shorter wavelengths for LOri043 and LOri065 probably stems from an inner disk hole or at least less inner dust than for the Class II sources. Models of similar 24 µm-only excess sources and a discussion of their disk-evolutionary significance can be found in Sicilia-Aguilar et al. (2006); Muzerolle et al. (2006);D'Alessio et al. (2006). Figure 10 shows the same diagram as in Figure 1 but the MIPS 24 µm information is included as dashed squares. The small circles stand for objects having optically thin (dashed) or optically thick (solid) disks based on their IRAC slope. The diagram shows a smooth transition between the three types of objects: diskless, thin, and primordial disks. LOri103 has a thin disk based on its 3.6-5.8 µm slope. It has been classified as Class III due to its magnitude at 8.0 µm but we believe that it is actually a Class II source and the faint magnitude at this bandpass is probably due to the presence of a nebulosity.
There are some objects classified as Class III sources by the IRAC CCD (they are outside, but close to the Class II area in the diagram), but have disks based on their IRAC slope. All these objects are brown dwarfs according to the models by Baraffe et al. (1998) (5 Myr) which pass all our membership criteria and thus the ratio of substellar objects bearing disks increases to 50 % (note that we need detections in at least three IRAC bands to calculate the IRAC slope).
None of our brown dwarf candidates have been detected at 24 micron. This is probably due to the detection limits for this band.
As a summary, of the 170 objects presented in Paper I, 167 are discussed here (the other three are spurious detections or the Spitzer photometry is not reliable). Excluding the sources classified as non-members, there are 22 which cannot be classified due to the incompleteness of the IRAC data, 95 have been classified as diskless, another two have transition disks, 25 thin disks and 20 thick disks. All this information has been listed in Table 4. Note that there are nine objects classified as Class III from color-color diagrams but which have thin disks according to the SED slopes, and another one (LOri156, a very low mass brown dwarf candidate with a very intense Hα) which has a thick disk based on the slope of the IRAC data.

The Spatial distribution of the members
We have plotted the spatial distribution of our good candidate members in Figure 11. Four-point stars represent B stars and λ Orionis (O8III). The Class III members (crosses) are approximately randomly distributed across the survey region. Both the Class II sources and the B stars give the impression of being concentrated into linear grouping -with most of the B stars being aligned vertically near RA = 83.8, and a large number of the Class II sources being aligned in the East-Southeast direction (plus some less well-organized alignments running more or less north-south). It is possible the spatial distributions are reflective of the birth processes in C69 -with the youngest objects (the Class II sources and B stars) tracing the (former?) presence of dense molecular gas, whereas the Class III sources have had time to mix dynamically and they are no longer near the locations where they were born. Figure 12 shows three different views of the central portion of the Spitzer mosaic at 3.6 microns for the C69 region. Figures 12a and 12b (with 12b being a blow-up of the center of 12a) emphasize the distribution of Class II sources relative to the cluster center; Figure 12c shows the distribution of our brown dwarf candidates. The star λ Orionis is at the center of each of these figures. The object located south of the star λ Orionis is BD+09 879 C (or HD36861 C, a F8 V star), with an angular distance of about 30 arcsec from the close binary λ Orionis AB (the projected distance, if BD+09 879 C is a cluster member, would be 12,000 AU from the AB pair). The apparent relative lack of cluster candidate members within about 75 arcsec from the star λ Orionis may be illusory, as this region was "burned out" in the optical images of the CFHT1999 survey and is also adversely affected in our IRAC images. There are a number of Class II sources at about 75-90 arcsec from λ Ori, corresponding to a projected separation of order 30,000 AU, so at least at that distance circumstellar disks can survive despite the presence of a nearby O star.
Regarding the distribution of brown dwarfs, a significant number of them (30 %) are within the the inner circle with a diameter of 9 arcmin (our original optical survey covered an area of 42×28 arcmin). However, there are substellar members at any distance from the star λ Ori (Figure 12c), and there is no substantial evidence that the cluster brown dwarfs tend to be close to the massive central star.
We have estimated the correlation in spatial distribution of different sets of data: Class II vs. Class III candidates, objects with any kind of disk (thin, thick and transition) vs. diskless objects, and stellar vs. substellar objects (following the substellar frontier given in Table 5 for different ages and bands). We have computed the two-sided Kuiper statistic (invariant Kolmogorov-Smirnov test), and its associated probability that any of the previously mentioned pairs of stellar groups were drawn from the same distribution. We have calculated the two dimensional density function of each sample considering a 4.5×3 arcmin grid-binning in a 45×30 arcmin region centered at 05:35:08.31, +09:56:03.6 (the star Lambda Orionis). The test reveals that in the first case, the cumulative distribution function of Class II candidates is significantly different from that of Class III candidates, with a probability for these data sets being drawn from the same distribution of ∼ 1%. This situation changes when comparing the set of objects harbouring any kind of disk with that of diskless objects, finding a probability of ∼ 50% in this case (and hence no conclusion can be drawn, other than that there is no strong correlation). On the other hand, regarding a correlation with age, the test points out a trend in the relationship between the spatial distribution of stellar and substellar objects depending on the assumed age. The value of the probability of these two populations sharing a common spatial distribution decreases from a ∼ 30% when assuming an age of 3 Myr, to ∼ 0.001% for an age of 8 Myr. The value assuming an age of 5 Myr is ∼ 1%.
The spatial distribution of objects detected at 24 micron can be seen in Figure 13. The nebulosity immediately south of the star λ Orionis (close to BD +09 879 C) corresponds to the HII region LBN 194.69-12.42 (see the detail in Figure 12b in the band [3.6]). Most of the detected members are located within the inner 9 arcmin circle, with an apparent concentration in a "filament" running approximately north-south (i.e. aligned with the B stars as illustrated in Figure 11b). Out of the cluster members discovered by Dolan & Mathieu,11 are within the MIPS [24] image (see Figure 13) and have fluxes above the detection level. The closest member to λ Orionis is D&M#33 (LOri034), about 2 arcmin east from the central star.
The MIPS image at 24 micron suggest that there are two bubbles centered around the λ Orionis multiple star (actually, the center might be the C component or the HII region ). The first one is about 25 arcmin away, and it is located along the North-East/South-West axis. More conspicuous is the smaller front located at a distance of 10.75 arcmin, again centered on the HII region and not in λ Orionis AB. In this case, it is most visible located in the direction West/North-West, opposite to the alignment of Class II objects and low mass members with excess at 24 micron. Similar structures can be found at larger scales in the IRAS images of this region, at 110 and 190 arcmin.
The star 37 Ori, a B0III, is located at the center of the cocoon at the bottom of the image. The source IRAS 05320+0927 is very close and it is probably the same.
Note that while BD +09 879 C would appear to be the source of a strong stellar wind and/or large UV photon flux, it is not obvious that the visible star is the UV emitter because the spectral type for BD +09 879 C is given as F8V (Lindroos 1985). It would be useful to examine this star more closely in order to try to resolve this mystery.

Conclusions
We have obtained Spitzer IRAC and MIPS data of an area about one sq.deg around the star λ Orionis, the central star of the 5 Myr Lambda Orionis open cluster (Collinder 69). These data were combined with our previous optical and near infrared photometry (from 2MASS). In addition, we have obtained deep near infrared imaging. The samples have been used to assess the membership of the 170 candidate members, selected from Barrado y Navascués et al. (2004).
By using the Spitzer/IRAC data and the criteria developed by Allen et al. (2004) and Hartmann et al. (2005), we have found 33 objects which can be classified as Classical TTauri stars and substellar analogs (Class II objects). This means that the fraction of members with disks is 25% and 40%, for the stellar (in the spectral range M0 -M6.5) and substellar population (down to 0.04 M ⊙ ). However, by combining this information with Hα emission (only a fraction of them have spectroscopy), we find that some do not seem to be accreting.
Moreover, as expected from models, we see a correlation in the [3.6] -[4.5] vs. [5.8] -[8.0] diagram for objects with redder colors (more IR excess) to have stronger Hα emission. In addition, following Lada et al. (2006) and the classification based on the slope of the IRAC data, we found that the ratio of substellar members bearing disks (optically thin or thick) is ∼ 50%, whereas is about 31% for the complete sample (14% with thick disks). This result suggests that the timescale for primordial disks to dissipate is longer for lower mass stars, as suggested in Barrado y Navascués & Martín (2003).
We have also found that the distribution of Collinder members is very inhomogeneous, specif-ically for the Class II objects. Most of them are located in a filament which goes from the central star λ Orionis to the south-east, more or less towards the dark cloud Barnard 35. In addition, there are several Class II stars close to the central stars. If the (previously) highest mass member of C69 has already evolved off the main sequence and become a supernova, either the disks of these Class II stars survived that episode or they formed subsequent to the supernova.
We have also derived the fluxes at 24 micron from Spitzer/MIPS imaging. Only a handful -13-of the low mass stars were detected (no brown dwarfs). Most of them are Class II objects. In the case of the two Class III members with 24 micron excess, it seems that they correspond to transitions disks, already evolving toward the protoplanetary phase.
2 Membership as in Paper I.  Lada et al. (2006) classified the objects according to their IRAC slope: α <-2.56 for a diskless object, -2.56< α <-1.80 for a transition object, and α >-1.80 for objects bearing optically thick disks 6 Ha+ = W(Halpha) above the saturation criterion. Ha-= W(Halpha) below the saturation criterion. 200km = width of Halpha equal or larger than this value. WHa(DM) = from Dolan & Mathieu 7 Probably diskless objects. The different results on IRAC CCD and IRAC slope are probably due to an uncertain measure at 5.8 µm. Table 5 Location of the substellar frontier, using models by Baraffe et al. (1998)   Non-members appear as dots. Class II sources (Classical TTauri stars and substellar analogs) have been included as big (red) circles, whereas Class III (Weak-line TTauri) objects appear as crosses, and other Lambda Orionis members lacking the complete set of IRAC photometry are displayed with the plus symbol. The figure includes 1, 3, 5, 10, 20, 50, and 100 Myr isocrones from Baraffe et al. (1998) as solid lines, as well as 5 Myr isochrones corresponding to dusty and COND models (Chabrier et al. 2000; Baraffe et al. 2002), as dotted and dashed lines.    Class II sources (Classical TTauri stars and substellar analogs) have been included as big (red) circles, whereas Class III (Weak-line TTauri) objects appear as crosses, and other Lambda Orionis members lacking the complete set of IRAC photometry are displayed with the plus symbol. b) Spatial distribution of the low mass stars from Dolan & Mathieu (1999, 2001. OB stars appear as four-point (blue) stars, with size related to magnitude (the bigger, the brighter). The overplotted thick triangles indicates those stars whose Hα equivalent width is larger than the saturation criterion defined by Barrado y Navascués & Martín (2003), thus suggesting the presence of active accretion. Based on Hα alone, the fraction of accreting stars would be 11%.
30 Fig. 12.-Spitzer/IRAC image at 3.6 micron centered around the star λ Orionis. a) The size is about 9×9 arcmin, equivalent to 192,000 AU. The double circle indicates the presence of a Class II object, whereas squares indicate the location of cluster members from Dolan & Mathieu (1999;2001). The intensity of the image is in logarithmic scale. b) Detail around the star λ Orionis. The size is about 3.3×3.3 arcmin, equivalent to 80,000 AU. c) Distribution of bona-fide brown dwarfs. The size of the image is 45×30 arcmin. North is up, East is left. Fig. 13.-Spitzer/MIPS image at 24 microns which includes the members of the Lambda Orionis cluster visible at this wavelength, including those cluster members by Dolan & Mathieu (1999, 2001 as big circles and CFHT member as small circles detected at this wavelength. The size is about 60.5×60.5 arcmin. North is up, East is left. The figure is centered on the star λ Ori AB.