SPITZER IMAGING OF THE NEARBY RICH YOUNG CLUSTER, Cep OB3b

Mid-infrared (MIR) observations were obtained with the Spitzer IRAC (Fazio et al. 2004) and the MIPS (Rieke et al. 2004) as part of a Spitzer Cycle-2 GO survey (PID 20403) of the entire Cepheus OB3 molecular cloud. The molecular cloud was mapped by IRAC at two different epochs: the first on 2005 December 25 and the second 2006 August 8. The map was further extended in two epochs (2007 August 17 and 2008 January 31) to cover the entire Cep OB3b cluster as part of the Spitzer program PID 40147. Each field was observed four times in 12 s high dynamic range mode. A total integration time of 41.6 s was obtained at each wavelength for each field.

The Spitzer/MIPS 24 μm images were obtained on 2007 February 25–26 and 2007 October 27 as part of the programs described above (PID 20403 and 40147), using scan maps at a medium scan rate with an offset of 302'' between scan legs. Complete coverage was obtained only for the 24 μm band; consequently, we only present results from this MIPS band. This paper focuses on a 49' × 33' region on the northwest edge of the large Cep OB3 molecular cloud which encompasses Cep OB3b.

Mosaics of the IRAC data were constructed from the basic calibrated data (BCD) products provided by the Spitzer Science Center using their standard data processing pipeline versions S18.5 and 18.7. Post-BCD reduction of the Spitzer/IRAC data was executed using a software package called "Cluster Grinder" (see Gutermuth et al. 2009), developed specifically to work on young clusters. The package includes modules for bright source artifact correction, cosmic-ray removal, mosaicking, and the visualization and photometry tool "Photvis" (Gutermuth et al. 2008) for point-source extraction and aperture photometry. Radii of 24, 24, and 72 were used for the aperture, inner, and outer sky annular limits, respectively (choices of aperture and annuli are justified in Allen et al. 2008 and Gutermuth et al. 2008).

The instrumental magnitudes were derived directly from the BCD frames converted into units of DN. For the 10.4 s frames, the adopted zero-magnitudes were 22.00, 21.24, 19.04, and 19.43 mag for the 3.6, 4.5, 5.8, and 8 μm bands, respectively (Reach et al. 2005). These included aperture corrections from a 2 pixel to 10 pixel aperture of 1.21, 1.23, 1.58, and 1.58, respectively, as tabulated in the IRAC Data Handbook. The Spitzer band magnitude labels are denoted by (wavelength in microns): for example, [3.6] = 15.16 means that the 3.6 μm magnitude is 15.16. Ninety percent differential completeness limits of the final mosaics are approximately [3.6] = 15.16, [4.5] = 15.18, [5.8] = 13.71, and [8.0] = 11.72 (see Gutermuth et al. 2005 for the estimation technique).

PID 20403 MIPS data were processed by the MIPS instrument teams' Data Analysis Tool (Gordon et al. 2005), which calibrates the data, corrects distortions, and rejects cosmic rays during the co-adding and mosaicking of individual frames. The MIPS 24 μm mosaic created from the four scan maps has a pixel size of 1245 and units of DN s⁻¹ pixel⁻¹. The MIPS field was extended in the PID 40147. For this second observation, MIPS BCD data from the S16.1 pipeline were mosaicked using the "Cluster Grinder" package. A pixel size of 2547 was used for this mosaic. Point sources were identified in the Spitzer/MIPS data using Photvis; aperture photometry was then obtained using 74, 147, and 245 for the aperture, inner, and outer sky annular limits. These magnitudes were then used as the initial guesses for point-spread function (PSF) fitting photometry of the identified sources using the IDL implementation of DAOPHOT (Landsman 1995); this version of DAOPHOT was modified to mask out saturated pixels in partially saturated PSFs (Kryukova et al. 2012). Two PSFs, one to fit unsaturated sources and a larger one to be used to fit partially saturated sources, were created from 15 sample stars located across the MIPS field. The PSF generated for the unsaturated sources had a size of 62'' × 62'', while the PSF generated for the saturated sources was 87'' × 87'' in size. The fitting radii were 25 and 1245 for the unsaturated and saturated PSFs, respectively. The large fitting radius for the saturated PSF was needed to fit the wings of the PSF after the central, saturated pixels were excluded from the fit. The MIPS photometry were calibrated using a zero-point flux density of 7.17 Jy, referenced to Vega (Engelbracht et al. 2007). The 90% differential completeness limit is [24] = 7.68. A three-color rendering of the Spitzer data can be seen in the top panel of Figure 1.

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X-ray data were obtained with the ACIS instrument aboard the Chandra X-ray Observatory. Two 17' × 17' fields were imaged covering both sub-clusters. Three images of the field covering part of the eastern sub-cluster were obtained with an aim point of 22:55:47.5, +62:38:10.3 (PIDs 9920, 10809, and 10810, with roll angles of 48°, 35°, and 72°, respectively), and three images of the field covering the western sub-cluster were obtained with an aim point of 22:53:31.7, +62:35:33.4 (PIDs 9919, 10811, and 10812, with roll angles of 68°, 63°, and 63°, respectively). Each image has an integration time of 28 ks. The remainder of the eastern sub-cluster was previously imaged with Chandra by Getman et al. (2006; PID 3502, aim point of 22:56:49.4, +62:39:55.6 and roll angle of 79). The fields are outlined in the bottom panel of Figure 1.

These data have all been reduced in a similar manner using the Chandra Interactive Analysis of Observations (CIAO) software tools. The data were processed through the standard CIAO pipeline at the Chandra X-ray Center, using their software version DS7.6. This version of the pipeline automatically incorporated a noise correction for low energy events. This filter can remove good events from the cores of bright point sources, resulting in an underestimation of the X-ray flux. In this case, the count rate did not exceed 0.02 counts per second for any source thus, event loss was not a concern. Background was nominal and non-variable.

As the goal of the observations was the correlation of X-ray and infrared sources, point-source detection was aggressive. First the CIAO script flux image was used. The flux image script creates exposure-corrected images of ACIS observations as well as the corresponding aspect and instrument maps which prepare the data for point-source detection. The script is especially efficient in cases in which multiple observations are used. Sources were detected using the Wavdetect routine. Wavdetect correlates the image with PSFs (wavelets) of different scales and then searches the results for significant correlations. In this case, scales of 1–16 pixels were searched on with logarithmic spacing. Significances as low as 1σ were returned. To ensure detection, we require a corresponding detection in the infrared to confirm the X-ray nature of the source. As discussed in Section 3.2, the vast majority of X-ray sources with visible and infrared counterparts are found toward the Cep OB3b isochrone. This shows that there are few spurious X-ray sources in our sample.

Sources detected by Spitzer and Chandra were matched with counterparts from the 2MASS Point Source Catalog (PSC) and the BVI band catalog of Mayne et al. (2007). A matching radius of 2'' was used in all cases. The addition of these catalogs extends the wavelength coverage for these objects into the near-infrared (∼1 μm) and the visible (∼0.5 μm). A catalog combining the Spitzer, 2MASS, and Chandra data will be called the X-ray sample and a catalog combing the Spitzer, 2MASS, and VBI data will be called the visible sample.

Gutermuth et al. (2009) presented a new empirical three-phase scheme to identify young stellar objects (YSOs) with infrared excess (i.e., protostars with dusty infalling envelopes and young PMS stars with dusty disks) which we adopt here. Those classifications are illustrated in the IRAC/MIPS color–color and color–magnitude diagrams shown in Figure 2.

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In phase 1, all four IRAC bands with photometric uncertainties σ < 0.2 mag are used to separate sources with infrared excesses due to disks and infalling envelopes (Class II and Class 0/I, respectively) from pure photospheres (Class III/field stars) based on [3.6] − [5.8] and [4.5] − [8] colors. Various non-stellar contaminating sources (e.g., polycyclic aromatic hydrocarbon (PAH) and active galactic nucleus (AGN) extra-galactic sources) also show infrared excesses; they must be eliminated by several criteria described in detail by Gutermuth et al. (2008,Appendix A). Galaxies with strong PAH emission are eliminated by their colors. AGNs mimic the colors of YSOs and must be eliminated by their faintness, as determined by their location in the [4.5] versus [4.5] − [8] color–magnitude diagram (these cuts are shown in Figure 2). Unresolved shocked emission blobs arising in YSO outflows are identified by their strong 4.5 μm emission. All sources classified as contaminants were re-examined in the third phase of our identification process for excess emission at 24 μm since some protostars might be masquerading as contaminants. The remaining infrared excess sources which are not removed as contaminants can be classified by [4.5] − [5.8] color as Class 0/I objects (protostars) or Class II objects (PMS star with disk). The sources that do not show IR-excesses are consistent with pure photospheric emission between 1 and 8 μm. These include Class III (diskless PMS star), field stars, as well as transition disk objects (stars with disks exhibiting AU-scale inner holes) which will be identified in later phases. The distinct mid-IR colors of Class 0/I objects, Class II objects, and pure photospheres are clearly evident in Figure 2.

Phase 2 is applied to those sources which lack IRAC detections at 5.8 or 8.0 μm, but which have high-quality 2MASS detections (σ < 0.1) in at least H and K_s bands. Line-of-sight extinction to each of these sources is estimated using 2MASS colors (if J, H, K_s detections are all available) by de-reddening the sources that lie above the classical T-Tauri star (CTTS) locus of Meyer et al. (1997) or an adopted standard dwarf-star color ((J − H)₀ = 0.6; Bessel & Brett 1988) in J − H and H − K_s color space. The sources that lie on or below these fiducial values are assumed to have no measurable reddening. If high-quality J detections are unavailable, the line-of-sight extinction is estimated by de-reddening the source to the CTTS locus in H − K_s and [3.6] − [4.5] color space (see Allen et al. 2008) and using the reddening law of Flaherty et al. (2007); this law was derived for star-forming regions similar to Cep OB3b. Sources are then classified as either Class III/field objects, Class II objects, or Class 0/I objects based on their position in de-reddened (K − [3.6])₀ and ([3.6] − [4.5])₀ color space (Allen et al. 2008). It must be noted that this phase applies primarily to lower-mass objects with disks, which are not detected at the longer IRAC wavelengths due to the increased background levels at those wavelengths. Due to the rising spectral energy distribution of the protostars with envelopes, we expect most of them to be detected at the longer IRAC wavelengths and thus, we expect this phase to only add a few, if any, protostars to our catalog. As expected, all the protostars in our catalog are classified during phase 1.

In addition, there are a handful of objects with Near-IR+IRAC colors of Class IIIs, but which exhibit a 24 μm excess (e.g., ([5.8] − [24]) > 1.5 and ([8] − [24]) > 1.5). These objects are classified as transition disk objects, PMS stars surrounded by disks that contain AU-scale inner holes (Muzerolle et al. 2010). Due to the inner hole, these disks typically emit weakly at wavelengths ⩽8 μm.

Phase 3 is applied to all sources classified in phase 1 with MIPS 24 μm detections with σ < 0.2 mag. This phase re-examines all sources including contaminants and identifies Class 0/I objects and transition disk objects on the basis of their 24 μm photometry. In this phase, Class 0/I objects are defined as sources with [5.8] − [24]) > 4. The [3.6] − [4.5] versus [4.5] − [24] color–color diagram (Figure 2) clearly shows the distinct colors of our identified Class 0/I and Class II sources.

In total, there are 1135 objects in the Near-IR + IRAC data set with evidence for dusty envelopes or disks: these objects will be used in the following analysis. Of these, 56 are classified as protostars (Class 0/I), 1014 as PMS stars with disks (Class II), and 65 are transition disk objects with AU-scale disk holes. Tables 1, 2, 3 and 4 list the sources identified as Class 0/I, Class II, transition disk, and Class III, respectively. A full source list is included with the electronic version of this paper.

An estimate of the total number of young stars both with and without disks requires a method for identifying and counting diskless Class III objects. These pure photospheric sources cannot be distinguished from background field stars by their near-to-mid-IR colors. In the following sub-sections, we use two separate methods to quantify the number of diskless Class III objects. The first method directly identifies potential Class III objects from their X-ray flux density and the second method distinguishes potential Class III objects using their visible magnitudes and colors.

Young stars have enhanced X-ray luminosities by orders of magnitude with respect to the main sequence (MS) in large part due to increased chromospheric activity (Feigelson et al. 2007). By selecting objects that have both photospheric colors in the infrared as well as X-ray emission, we can identify diskless young members of the cluster. To make this selection, we only need the spatial positions of the X-ray sources. The analysis of the flux densities and other X-ray properties of these sources will be discussed in a future paper.

We identify as X-ray members of Cep OB3b all sources that have a Chandra X-ray detection and have been classified as a Class 0/I/II/photospheric source using the Spitzer and 2MASS three-phase classification scheme. However, it is possible that coronal activity from another type of X-ray active field star, such as a flaring dMe star (the X-ray luminosity of dMe stars can reach up to log L_x ∼ 30 erg s⁻¹; Marino et al. 1998) could lead to a misidentification of a field star as a young star. In comparison, the typical young star has an X-ray luminosity in the range of 28 < log L_x < 32 erg s⁻¹; Feigelson et al. 2007). Thus, the X-ray active field stars may contaminate the Chandra sample and be misclassified as a Class III source. To estimate the potential magnitude of the background contamination, we examine the location of the X-ray sources in V and V − I color–magnitude space (right panel in Figure 3). We consider the sub-set of sources that have detections in all three data sets Spitzer, Chandra, and BVI. This sample contains 0 Class 0/I, 136 Class II, 9 transition disk, and 329 Class III sources. We assume that the potential Class III sources that lie below the zero-age main sequence (ZAMS) in Figure 3 are all background contaminants (there are only two Class II sources in that region, they are the sources with V − I < 2). Furthermore Getman et al. (2006) estimate that 13 sources in their 17' × 17' of Cep B are foreground stellar sources. If we apply this number to out full Chandra field of view, which is 729 arcmin², we estimate that there will be 33 additional contaminants. Combining these two estimates yield 11% (53/499) of the sources as contaminants. Considering the full Chandra field of view of 729 arcmin², we have an X-ray contamination rate of 0.07 stars arcm².

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The X-ray sample includes 5 Class 0/I, 233 Class II, 16 transition disk, and 499 Class III sources, of which 53 may be contaminating X-ray active field stars. For reference, within the region imaged by Chandra there are 36 Class 0/I, 810 Class II, 29 transition disk, and 3213 photospheric sources (Class III or field stars) as classified via Spitzer and 2MASS colors alone. Thus, we are detecting 29%(233/801) of the Class II sources and 55%(16/29) of the transition disk sources with Chandra.

We can also search for diskless young stars by utilizing the intrinsic magnitudes and colors of young stars to separate them from field stars in V versus V − I space (Figure 3). Young stars are still contracting to the MS, and thus for a given temperature, young stars have a greater luminosity than field stars at an equal or a greater distance. The young stars occupy an isochrone (or bands of isochrones) that lies above the MS, and the extinction vector is approximately parallel to this isochrone. Using the V- and I-band data of Mayne et al. (2007) for stars with V and V − I photometric errors less than 0.1 mag, we empirically determine the YSO locus in V and V − I space. To determine the isochrone of young stars in the cluster, the locations of members identified by Spitzer and Chandra are plotted in V and V − I space (Figure 3). The young stars are then divided into 0.75 mag bins between V magnitudes of 15 and 24, and a two-step iterative process is used to determine the median V − I color of the known YSO population in each bin. First, the median color of the bin is calculated using all sources in the bin. Next outliers greater than 3σ from the median are rejected and a new median and standard deviation are calculated. The width of the YSO isochrone in color space is then taken to be between −1.25σ and 2σ around the median color of the bin. The median color of the YSO isochrone is fit with a third-order polynomial, as are the outer bounds of the YSO isochrone; all stars between the two outer bounds are considered to be likely members. The lower bound of the isochrone is cropped closer to the median value because the density of sources quickly increases in the direction perpendicular to the isochrone in the direction toward the ZAMS. In particular, foreground dwarfs and background giants may masquerade as YSOs by appearing more luminous for a given color. The outer bounds are shown in Figure 3. Hereafter, this selection of sources will be denoted by the visible sample.

We can estimate an upper bound to the possible non-member stellar contamination (both foreground and background) by considering the V and I photometry from field 3a from Pozzo et al. (2003), hereafter called the Pozzo field. This is a 12' × 12' field centered on R.A.: 22:50:21.14 and decl.: 62:46:44.88, on the northwest of the molecular clump Cep F. We choose this region due to its location off the cluster and because it has the least number of Spitzer identified excess sources; only four. If we assume that these four sources are the only sources in this field that are members of Cep OB3b, then we can apply the same V and V − I selection criteria and consider all remaining sources that occupy the YSO dominated region of color–magnitude space as contaminants. There are 98 sources that fit this criteria (102 sources in the YSO dominated region, minus the 4 known excess sources), for a contamination rate of 0.6 stars arcmin⁻².

Another way to estimate the number of non-member stellar contaminants in the V and V − I space is to extrapolate from the number of sources in the region of V and V − I space below the YSO isochrone into the YSO isochrone. Assuming that there is a constant stellar density along the line of sight, then the number of stars of a given magnitude, m, is approximately 10^0.6m (Binney & Merrifeld 1998). We approximate the YSO isochrone with a linear strip in V and V − I space that is 2 mag wide (bounded by the lines V = 2.9(V − I) + 9.4 and V = 2.9(V − I) + 11.4), and consider the sources found in the 1 mag linear strip below the YSO isochrone, bounded by the lines V = 2.9(V − I) + 11.4, V = 2.9(V − I) + 12.4, V = 14.5, and V = 22.5 to be non-member field stars. Then the ratio of non-member field stars along the line of sight within the YSO isochrone to the number of stars within the field star isochrone is just

$$\begin{equation} \frac{N_{\mathrm{contaminants}}}{N_{\mathrm{field}}} = \frac{\int _{0}^{2} 10^{0.6m} {d}m}{\int _{2}^{3} 10^{0.6m} {d}m} = 0.314. \end{equation} \tag{ 1 }$$

Since there are 1211 sources in the 1 mag field star strip, we estimate 381 contaminants in the YSO isochrone. Dividing by the area covered by the visible data (4 × 11' × 22') leads to a contamination rate of 0.4 stars arcmin⁻². This figure is similar to, but slightly lower than, the density of contamination derived from the Pozzo field. Because the Pozzo field may contain some young sources due to its proximity to the molecular cloud, we adopt 0.4 stars arcmin⁻² as the visible selection contamination rate.

The visible sample includes 402 Class II, 23 transition disk, and 1270 Class III sources, of which 381 may be contaminants. If we restrict the sample to only the sources that lie within the region with a field of view in common with the Chandra images (we will call this region the overlap region), we find 372 Class II, 17 transition disk, and 914 Class III sources, with an estimated 232 contaminants.

To estimate the disk fraction we require a census of the cluster members with and without disks. While the number of members with disks is reliably determined from our sample of IR-excess sources, to determine the number of diskless members we require a method to distinguish between diskless Class III and field stars seen in projection toward the cluster. This has often been done by using measurements of the source density in off-cluster regions to estimate the number of field stars (see, for instance, Carpenter 2000 and Allen et al. 2007). However, these methods require assumptions about the homogeneity of the background distribution of stars and line-of-sight extinction that may not hold in a large, complex OB association with multiple epochs of star formation. Thus, we use the direct identification of Class III members using either their X-ray flux or their position on the V versus V − I diagram, as described in Section 3.3.

Since disk sources are selected because of their increased flux in the infrared, sources with disks can be detected to fainter magnitudes, and higher extinctions, than purely photospheric sources. To reduce the impact of this bias, we apply a near-IR magnitude and color requirement based on the position of the source on the J versus J − H color–magnitude diagram (Figure 5). The sources that remain are those that are brighter than a de-reddened J-band magnitude of 14.75. This magnitude and reddening vector correspond to a 0.2 M_☉ star at a distance of 700 pc using the models of Baraffe et al. (1998). Further, these sources must have colors that indicate an extinction of less than 6A_V. These limits were set based on a visual inspection of the positions of the sources in Figure 5.

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After applying these magnitude and extinction cuts, we are left with 51 Class 0/I, 727 Class II, and 56 transition disk sources from the Spitzer and 2MASS sample. For the X-ray sample 2 Class 0/I, 207 Class II, 16 transition disk, and 451 Class III sources remain, and for the visible sample 345 Class II, 22 transition disk, and 1139 Class III sources remain.

We calculate the disk fraction for the entire cluster and for two 5' radius regions centered on the eastern (R.A.: 22:56:49.44, decl.: 62:39:55.54) and western (R.A.: 22:53:50.83, decl.: 62:35:36.37) sub-clusters, shown as red circles in Figure 4(a). The disk fraction for the entire X-ray sample is 33% ± 2% (207 Class II, 16 transition disk, and 451 Class III). The eastern sub-cluster has a disk fraction of 32% ± 4% (62 Class II, 2 transition disk, and 137 Class III), while for the western sub-cluster, the disk fraction is 50%  ±  6% (64 Class II, 7 transition disk, and 71 Class III). The disk fraction for the visible sample is 24% ± 1% (345 Class II, 22 transition disk, and 1139 Class III). This is significantly lower that the disk fraction estimated using the X-ray sample. The visible data used in this analysis, however, extend to the north of the region imaged by Chandra. If we restrict our estimate to only those sources in the visible sample located in the region imaged by Chandra, the disk fraction is 29% ± 2% (321 Class II, 17 transition disk, and 811 Class III). This is consistent with the disk fraction estimated with the X-ray sample. Further, we find disk fractions of 34% ± 3% (i.e., 103 Class II, 0 transition disk, and 199 Class III) in the eastern sub-cluster and 44% ± 5% (i.e., 71 Class II, 4 transition disk, and 96 Class III) in the western sub-cluster. Note that the fraction of sources with disks is similar regardless of the method used to identify the diskless Class III sources. These results are summarized in Table 5, where we tabulate the disk fractions with and without the J versus J − H cuts.

Although we have minimized the contamination of the Class III sample by requiring either an X-ray detection or V versus V − I colors coincident with the Cep OB3b isochrone, the residual contamination is the primary systematic uncertainty in our disk fraction measurement. In Table 5, we correct for the background contamination using the 0.4 arcmin⁻² contamination rate from Section 3. Since we do not know the J- and H-band magnitudes of the contamination, we do not apply the J versus J − H cut and background subtraction simultaneously. The correction for contamination raises the disk fraction because the background subtraction is only applied to the Class III objects. For example, the background-subtracted disk fractions for the overlap region increases to 36% ± 2% for both the X-ray and visible sample. Although the sub-clusters subtend a smaller region of the sky and hence have smaller rates of contamination; the subtraction of contamination can accentuate the difference in the disk fractions. In particular, if we consider the visible selection contamination rate of 0.4 stars arcmin², this is equivalent to 31 contaminants in each sub-cluster. After subtracting these from the Class III count, the disk fractions increase to 39%  ±  4% (i.e., 121 Class II, 0 transition disk, and 191 Class III in the eastern sub-cluster and 53% ± 6% (i.e., 83 Class II, 4 transition disk, and 75 Class III in the western sub-cluster. If we subtract out the potential contamination in the X-ray data (0.07 arcmin⁻²) then this corresponds to a contamination rate of six contaminating sources in each sub-cluster, resulting in disk fractions of 34% ± 4% in the eastern sub-cluster (72 class II, 2 transition disk, and 145 class III) and 52% ± 6% in the western sub-cluster (73 class II, 7 transition disk, and 73 class III), see Table 5.

We place the disk fraction estimates for Cep OB3b and its two sub-clusters within the context of other star-forming regions by placing them on a plot similar to Figure 14 from Hernandez et al. (2008), as seen in Figure 6. We adopt the disk fractions for the X-ray sample with the J versus J − H cut (32% ± 4% in the eastern sub-cluster and 50% ± 6% in the western sub-cluster); the systematic uncertainties due to Class III selection and contamination are similar to the formal uncertainties displayed in the figure. The age is assumed to be between 3 and 5 Myr, represented by the horizontal uncertainty bars on the plot.

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Spitzer observations of young stellar clusters suggest that the disk fraction may be mass dependent, with the gas-rich disks around more the massive stars disappearing first (Lada et al. 2006; Hernandez et al. 2007, 2009). To search for a similar trend in our data, we use the de-reddened V − I color as a proxy for the mass, where sources are de-reddened with the line-of-sight extinction estimated using the method described in Section 3.1. To directly compare the visible and X-ray samples, we consider those members detected in the V and I bands in the field of view common to both the visible and X-ray samples. We bin the sources into three bins of blue, intermediate, and red colors, with roughly 380 sources in each bin. The de-reddened V − I bounds for these three bins are −0.5 to 1.05 mag, 1.05–1.72 mag, and 1.72–4.35 mag, respectively. We use the blue, intermediate, and red bins as proxies for high-, intermediate-, and low-mass young stars. To roughly estimate the corresponding mass ranges for to these color bins, we compare these de-reddened colors to Table 5 in Kenyon & Hartmann (1995). These colors correspond to spectral-type ranges of greater than K3, K3 to M0, and M0 to M6, respectively. Using the tracks of Siess et al. (2000) and an age of 3 Myr, these correspond to masses of greater than 1.7 M_☉, 1.7–0.6 M_☉, and 0.6–0.2 M_☉. Table 6 shows the results for the field of view common to the X-ray and visible light observations and for the sub-clusters, respectively.

We would also like to estimate the potential number of non-member stellar contaminants in each of these color bins. To do so we consider the same field star reference strip as defined in Section 3.3. However, to determine the color bins above, we depend on the line-of-sight extinction estimates to each of the sources. We do not know what these will be for the potential contaminants. Instead we re-redden the bounds for the color bins using the median A_V of all the sources considered to create the color bins. The median A_V of these sources is 3.3 mag, and the resulting V − I color bounds are 1.22–2.77 mag, 2.77–3.44 mag, and 3.44–6.07 mag for the blue, intermediate, and red bins, respectively. Since there are 739, 340, and 115 sources in the blue, intermediate, and red sections of the field star strip, we estimate 232, 107, and 36 contaminants using Equation (1), and a contamination rate of 0.24, 0.11, and 0.04 stars arcmin⁻², respectively.

Table 6 shows the disk fraction as a function of de-reddened V − I color bin. For the common field of view, the disk fraction is the same for all three bins of the X-ray sample, roughly 30% ± 5%, whereas for the visible sample, the intermediate bin (31% ± 3% for 1.7–0.6 M_☉) has a slightly lower disk fraction than the reddest bin (38% ± 3% for 0.6–0.2 M_☉), and the blue bin (19% ± 2% for >1.7 M_☉) shows a substantially lower disk fraction than the intermediate bin. Note that if we subtract the potential contaminants from the visible sample, the large discrepancy between the visible sample disk fraction (30% ± 4%) and the X-ray sample disk (30% ± 5%) in the blue bin disappears, while for the red bin the disk fractions differ by about 1.7σ (41% ± 3% for the visible sample and 31% ± 5% for the X-ray sample). Examination of the right panel of Figure 3 shows that the discrepancy in the red bin could be due to a lack of X-ray sensitivity to the reddest, lowest mass members.

Looking at the sub-clusters in Table 6, we find that the disk fraction does not vary greatly between the three bins for the western sub-cluster. In contrast, the disk fraction in the blue bin (19% ± 4% > 1.7 M_☉) for the eastern sub-cluster is half that of the disk fraction in the intermediate bin (40% ± 6% 1.7 to 0.6 M_☉). If we examine the difference in the disk fraction between the two sub-clusters, this difference is greater that 2σ for both the visible sample and the X-ray sample in the blue bin (>1.7 M_☉). The disk fraction can be found in Table 6. In contrast, for the intermediate bin (1.7–0.6 M_☉) the disk fractions of the two sub-clusters are within 1σ for the visible sample and 1.2σ for the X-ray sample. For reddest bin (0.6–0.2 M_☉), the difference in disk fractions is about 1.3σ for the X-ray sample and 1.2σ for the visible sample. Subtracting the potential contaminants from the visible sample increases the difference in the disk fraction between the two sub-clusters in the bluest bin. The intermediate bin still has no difference, and the red bin has a difference of 1.1σ. Thus, the lowest disk fractions and the largest difference in the disk fraction between the sub-clusters are in the bluest V − I bin with the highest mass stars. As we will discuss in Section 6.3, the observed difference for the bluest stars may be due to a systematically older age in the eastern sub-cluster.

Broadband magnitude and color determinations of stellar mass are highly uncertain due to the number of non-mass-related factors that could affect the magnitude, and color, of a young source, such as age, accretion, etc. It is therefore prudent to base mass estimates of young stars from more robust measurements such as their spectral type, which will be done in a future paper. We defer further investigations of the stellar mass dependence of the disk fraction until that paper.

The different disk fractions found in the two sub-clusters motivate an examination of the spatial dependence of the disk fraction. We use two methods for visualizing the spatial variation of the disk fraction in Cep OB3b. First, we create maps of the disk fraction throughout the cluster. We created two disk fraction maps utilizing the X-ray sample and the visible sample. To make these maps we first created a grid covering the entire region with nodes spaced every ∼50''. The disk fraction at each node was then determined using all classified sources within a 2' radius of that node. A map was then created using the disk fraction at a given node as the value for the respective "pixel" on the map. Figure 7 shows the results of this process for both samples, and Figure 8 shows a "pixel-by-pixel" comparison of the two maps. Second, we consider the disk fraction in annular regions in the eastern sub-cluster centered on the O7V star HD271086 or the western sub-cluster centered on the B1V star V454 Cep, as seen in Figure 9 for the X-ray-selected set and Figure 10 for the visible-selected set. Note that since the background contamination may be spatially variable due to spatially varying extinction, we do not correct for contamination. Correcting the Class III sample for contamination would systematically increase the disk fraction and the amplitude of the observed variations.

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Both methods of visualizing the spatial variation in the disk fraction show the same general morphology. The eastern sub-cluster is characterized by a broad area of fairly homogenous disk fraction, and as shown in a recent paper by Getman et al. (2009), the disk fraction increases from about 30% to over 50% as one traces a path from the O star, to the Cep B molecular clump and its embedded population (Figure 7). The western sub-cluster, however, is characterized by a high disk fraction in the center of the sub-cluster that drops-off radially outward. Note that the visible sample is biased toward the less embedded sources, and the map derived with this sample does not find some of the smaller clumps of stars with high disk fractions apparent in the X-ray map.

One question we must ask is whether the observed variation in the disk fraction is consistent with random fluctuations. To address this question, we focus on the different disk fractions observed toward the two sub-clusters. To consider the range of disk fraction ratios we would expect due to statistical fluctuations, we perform a Monte Carlo simulation. We assume that each member of the cluster has a probability of harboring a disk to be equal to the disk fraction of the entire region. For each source in a given sub-cluster, we draw a random number from a uniform distribution between zero and one using the IDL routine RANDOMU. If the random value associated with a given source has a value less than or equal to the disk fraction for the entire sample it is considered to be a disk source, otherwise it is considered to be a non-disk source. Once this is done for each source, the disk fractions for the sub-clusters are calculated, and their ratio is determined for this particular realization. This is then computed for 10,000 realizations. Figure 11 shows the distribution of ratios derived using the visible sample, in the right panel, and the X-ray sample, in the left panel. The actual ratio is given by the red line. This exercise shows that the disk fractions in the two sub-cluster are different with a 95% confidence.

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We can use the disk fractions measured in the sub-clusters to estimate the total number of cluster members from the number of IR-excess sources. The Spitzer data show 1135 infrared excess sources, the vast majority of which are young stars with disks. From Figure 5, we ascertain that most of the sources above 0.2 M_☉ are detected (adopting the Baraffe et al. 1998 tracks for a 3 Myr stars). Using the average disk fraction determined from the X-ray sample, 33% ± 2%, we then estimate that there are about 3000 total members in the Cep OB3b cluster down to the approximate mass limit of our survey.

Our estimated membership of Cep OB3b of 3000 primarily low-mass stars shows that Cep OB3b is comparable in size and membership to the ONC (Allen et al. 2007; Carpenter 2000, ∼1000 stars in a 10 pc × 5 pc region), although the peak surface densities are considerably less dense than the peak densities in the ONC (Hillenbrand & Hartmann 1998; S. T. Megeath et al., in preparation). The content of massive stars in Cep OB3b is only slightly lower than that of the ONC: one O7 star in Cep OB3b compared to an O6 and an O9.5 in the ONC; Muench et al. (2008). These results suggest that Cep OB3b is the second nearest, large, (>1000 star) young (<5 Myr) stellar cluster to the Sun. Furthermore, the published isochrones and the relatively low extinction toward the region suggest that Cep OB3b is older and more evolved than the ONC. The older ages and lower stellar ages suggest that this cluster has expanded since it dispersed its parental gas.

Other than the ONC, there are no known clusters within 1 kpc that are comparable to Cep OB3b in age, size, and average density. The largest known young cluster next to the ONC and CepOB3b within 1 kpc is in the NGC 2264 region at 760 pc, part of the Mon OB1 molecular cloud. This cluster contains ∼450 young stars with disks, less than half as many as CepO3b (Sung et al. 2009). The next largest known young clusters within 1 kpc, ranked by number of known disk sources, are IC 348, ∼400 (Muench et al. 2007); Sigma Ori, 336 (Hernandez et al. 2007); TR 37, ∼200 (Sicilia-Aguilar et al. 2006); Mon R2, 235 (Gutermuth et al. 2009); IRAS 20050, 177 (Gutermuth et al. 2009); AFGL 490, 161 (Gutermuth et al. 2009); and IC5146, 149 (Gutermuth et al. 2009). A major uncertainty in comparing the sizes of clusters is the number of diskless PMS stars. Since the membership counts listed in this section are primarily from Spitzer counts of disk sources, they are lower limits to the actual membership counts. Nevertheless, the number of known disk sources in these other clusters are much less than the number of known disk sources in Cep OB3b.

It has been known for over a decade that UV radiation from O stars can ablate the outer regions of disks, a process that has been directly observed in the ONC (Bally et al. 1998). The IR-excesses detected by Spitzer originate from the warm inner disk, while photoevaporation primarily truncates the outer disk (Adams et al. 2004). However, disks may be rapidly destroyed by a combination of photoevaporation and viscous accretion (Matsuyama et al. 2003). Evidence for the destruction of inner and outer disks has been found in previous Spitzer observations of young clusters. In NGC 2244, the Rosette Nebula, at a distance of 1.6 kpc, Balog et al. (2006) find outer disks being ablated near a massive O star. Balog et al. (2007) also find evidence that the fraction of young stars with disks drops near the massive O stars, evidence for the destruction of disks by the O stars. Similarly, Sung et al. (2009) examine the young cluster NGC 2264 and find that the disk fraction tends to increase radially away from the O7V star S Mon.

The only known O star within the Cep OB3b cluster is the O7Vn star HD 217086 (Herrero et al. 1992), which is the primary ionizing source for the H ii region Sh 155, and is illuminating and photoevaporating the surface of the nearby cloud as delineated by bright nebulosity in the IRAC and MIPS bands. HD 217086 is also situated close to the highest projected surface density of YSOs in the eastern sub-cluster (Figure 4(b)). A B1V star is also coincident with this sub-cluster. In contrast, a B0V and three B1V stars are found in the western sub-cluster. The Lyman continuum production rate of the O7 star is nine times higher than that of a B0V star (Vacca et al. 1996), thus we must ask if the difference in the observed disk fractions in the two sub-clusters is due to a much higher incident EUV flux in the eastern sub-cluster (Adams et al. 2004).

A signature of disk photoevaporation would be a decrease in the disk fraction radially toward the O star. Figure 9 shows the disk fraction as a function of radial distance away from a massive star in each sub-cluster, using the X-ray sample. The top panel is centered on the O7V star HD 217086 in the eastern sub-cluster. Each annulus centered on this star has a width of 2' within which the disk fraction is estimated by counting the number of sources with and without a Spitzer excess. The bottom panel is centered on the B1V star HD 216711 (V 454 Cep), in the western sub-cluster, and the disk fraction is estimated in the same manner as the top panel. The disk fraction is fairly constant as a function of radial distance from the O7V star in the eastern sub-cluster, while it increases significantly toward the B1V star in the western sub-cluster. Figure 10 shows the same radial disk fraction distribution if the visible sample is used to select sources. We find no evidence for disk photoevaporation in these plots.

To consider whether mixing could influence the radial disk fraction distribution, i.e., if stars move into and away from the harsh radiation environment near the O7V star on timescales short enough to erase any disk fraction differences due to photoevaporation, we use the virial theorem to estimate the velocity of a typical star in the innermost 2' radius region of each sub-cluster. We assume that each star has the same mass (0.5 M_☉), an isotropic velocity distribution, and experiences the same gravitational potential. We assume the cluster is fully exposed, so that the mass of each sub-cluster is just the number of sources times the assumed average mass and is estimated to be 46 × 0.5 M_☉ = 23 M_☉ for the western sub-cluster and 75 × 0.5 M_☉ = 37.5 M_☉ for the eastern sub-cluster. Note that here we consider all sources and do not apply the magnitude and color cuts of Section 5. The typical velocity then would be 0.27 km s⁻¹ in the western sub-cluster and 0.22 km s⁻¹ in the eastern sub-cluster. These correspond to a time of roughly 2 Myr to move 2' in projection through the sub-clusters. This time is less than the lower end of the estimated age range of 3–5 Myr. Therefore, even though the radial disk fraction distribution near the O7V star does not indicate that photoevaporatation is the cause of the disk fraction difference between the two sub-clusters, the photoevaporation of disks in the eastern sub-cluster cannot be ruled out based on the radial disk fraction distribution alone.

Finally, if disk photoevaporation is responsible for the different disk fractions in the two sub-clusters, we would expect the lowest mass stars to be affected the most due to their lower gravitational binding energy (Adams et al. 2004). Instead, in Table 6, we find the stars with the bluest V − I colors, and hence highest masses, have the largest discrepancy in their disk fractions. This is evidence against disk photoevaporation.

Variations in the observed disk fraction may also be due to variations in the ages of the members. For instance, Hernandez et al. (2008) show that the disk fraction decreases from 80% to 30% as a stellar cluster/association's age increases from 1 to 5 Myr (see Figure 6). An age variation due to an evolutionary gradient was proposed in Getman et al. (2009). Using deep IRAC observations of the eastern sub-cluster to supplement their earlier X-ray observations, they have evaluated disk fractions as a function of radius from the hot molecular core Cep B, which is in the molecular clump at the edge of the eastern sub-cluster (Beuther et al. 2000). They find disk fractions of ∼75% within 3' from Cep B, ∼55% within an annulus 3'–7' from Cep B, and ∼20% within an annulus 9'–12' from Cep B. They interpret this spatial gradient as temporal, with young stars dominant in the hot molecular core and progressively older stars with increasing distance from the core. The temporal gradient results from a sequence of star formation triggered by compression driven by the UV radiation from the O7V star. Our eastern sub-cluster includes most of the stars in these annuli, and we examined the disk fraction for the X-ray sample of young stars in two sections within the 5' region centered on the eastern sub-cluster. The first section is toward the high-extinction region of the cloud and the second section is toward the lower extinction of the S155 H ii region and HD 217086. We confirm that there is a higher disk fraction toward the cloud than toward HD 217086, see Section 5.3 and Figures 4 and 7.

To examine the possibility that an age difference could explain the difference in disk fraction between the two sub-clusters, we use the V and I data from Mayne et al. (2007) of the Spitzer- and Chandra-selected young sample. We divide the sample into two sets, one for each of the two 5' radius sub-cluster regions defined above. Figure 12(a) shows the location of these sources in V versus V − I color–magnitude space. Note that the reddening vector in V versus V − I space is approximately parallel to the YSO locus, thus any extinction difference between the sub-clusters cannot masquerade as an age difference.

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By binning the V − I axis into half-magnitude bins between V − I colors of 2 and 4.5, we find the median V magnitude of all the young sources in each bin. We then examine the offset of the V-magnitude distribution for each sub-cluster from the median V magnitude by subtracting the median V magnitude of a given color bin from the V magnitude for each source in the same color bin. Next, we plot the normalized histogram of the distribution of the offsets for each sub-cluster. Due to the larger luminosity of younger stars of a given mass, we would expect a younger sub-set of stars to have a negative offset from the overall median. Conversely, an older sub-set would have a positive offset. An examination of Figure 12 shows that the sub-sample of sources from the western sub-cluster has a median offset that is slightly negative (−0.2 mag), while the eastern sub-cluster has an offset consistent with zero. If we consider the 4 Myr isochrone from the model of Baraffe et al. (1998) and shift it by an amount 0.2 mag along the V-magnitude axis in V versus V − I color–magnitude space, this shift corresponds to an age difference of 1 Myr for stars within the 0.2 M_☉–1.0 M_☉ mass range.

The FWHM of the distributions of offsets in Figure 12 is about 1 mag for both sub-clusters. If we interpret this as a proxy for an age spread, then the age spreads for the sub-clusters are roughly 6 Myr, using the same assumptions as above. An age spread in the cluster is expected: we find both regions of the cluster that have dispersed their gas and have low disk fractions as well as regions of ongoing star formation. However, there are various sources of scatter in the luminosities of YSOs that could be mistaken for an age spread. Potential sources of scatter are discussed in recent papers by Jeffries (2011) and Reggiani et al. (2011). If this scatter is accounted for, we would expect the age spread to be much smaller. We will examine the observed scatter in a future paper.

An examination of the disk fraction as a function of age curve from Hernandez et al. (2008; see Figure 6) shows a roughly 13% Myr⁻¹ drop in the disk fraction between the ages of 2 and 6 Myr. If we assume a 1 Myr age difference between the sub-clusters, then we find a 18% Myr⁻¹ drop in the disk fraction using the X-ray sample and a 10% Myr⁻¹ drop in the disk fraction using the visible sample. This is roughly consistent with the disk fraction curve from Hernandez et al. (2008). Interestingly, if we assume that there is an age difference of 1 Myr, then the large disk fraction difference seen in the blue bin in Table 6 could imply that disk dissipation is more rapid in the higher mass stars. This would be consistent with the observations of Lada et al. (2006) and Hernandez et al. (2009).