PROTOPLANETARY DISK EVOLUTION AROUND THE TRIGGERED STAR-FORMING REGION CEPHEUS B

The X-ray observations of the Cep B/OB3b and their data analysis are described in detail by Getman et al. (2006). The 30 ks exposure was obtained on 2003 March 11.51–11.88 with the Advanced CCD Imaging Spectrometer (ACIS) detector (Garmire et al. 2003) on board NASA's Chandra X-ray Observatory (Weisskopf et al. 2002) as part of the ACIS Instrument Team's Guaranteed Time Observations (ObsId No. 3502, P.I.: G. Garmire). The imaging array (ACIS-I) consists of four abutted 1024 × 1024 pixel front-side illuminated charge-coupled devices (CCDs) covering about 17' × 17' on the sky. Following data reduction based on the ACIS Extract IDL script, Getman et al. (2006) obtained an X-ray catalog of 431 sources, most with <05 positional accuracy (Figure 2). Using Two Micron All Sky Survey (2MASS) counterparts, 89% of the X-ray sources are confidently associated with cluster PMS members of the region. The remaining X-ray sources are mostly extragalactic active galactic nuclei.

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The mid-IR observation of Cep B and Cep OB3b was obtained on 2007 February 18 with the IRAC detector (Fazio et al. 2004) on NASA's Spitzer Space Telescope in the 3.6, 4.5, 5.8, and 8.0 μm channels. This is a General Observer project (program identification No. 30361; P.I.: J. Wang). Two adjacent fields subtending ∼20' × 15' in channel pairs 3.6/5.8 μm and 4.5/8.0 μm were centered, respectively, on α = 22^h57^m097, δ = +62°37'523 (J2000) and α = 22^h56^m203, δ = +62°41'430 (J2000). The orientation of the fields long axis is P.A. = 363. These fields were imaged with a 3 × 4 mosaic of adjacent positions separated by 290'', and images were taken at 12 dithered positions for each of the 12 cells of the mosaic. The images were taken in the high dynamic-range mode with long effective exposures of 96.8 s in 3.6, 4.5, 5.8 μm channels, and two 46.8 s exposures in the 8.0 μm channel, as well as short effective exposures of 0.4 s in all four channels. Full coverage in all four channels is obtained for a ∼13' × 15' area, which in turn covers ∼65% of the 17' × 17' Chandra's ACIS-I field, as shown in Figures 1 and 2.

Basic Calibrated Data (BCD) products from the Spitzer Science Center's IRAC pipeline version S15.3.0 were automatically treated with the WCSmosaic IDL package developed by R. Gutermuth for the IRAC instrumental team. Starting with BCD data products, the package mosaics individual exposures while treating bright source artifacts, cosmic ray rejection, distortion correction, subpixel offsetting, and background matching (Gutermuth et al. 2008). We selected a plate scale of 086 for the reduced IRAC mosaics, which is the native scale divided by $\sqrt{2}$.

Aperture photometry of IRAC sources was obtained using the IRAF task PHOT. For most of the X-ray and non-X-ray (Section 4) selected sources, an aperture radius of 4 pixels (344) was used with an adjoining sky annulus width of 1 and 6 pixels (086 and 516) for the 3.6/4.5 and 5.8/8.0 μm bands, respectively. For the crowded sources, aperture radii of 2 or 3 pixels (172 and 258) and adjoining sky annulus width of 1 pixel (086) in all four bands were used. We adopted zero-point magnitudes (ZP) of 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 μm bands, where M = −2.5log(DN/sec) + ZP (Reach et al. 2005). The total aperture corrections applied to our measurements are: 0.185, 0.175, 0.165, 0.250 in the case of 4 pixel aperture; 0.275, 0.305, 0.515, 0.735 in the case of 3 pixel aperture; and 0.655, 0.735, 1.005, 1.010 in the case of 2 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 μm bands, respectively. The reported photometric errors include Poisson errors in the source and background emission plus a 2% uncertainty in the calibration of IRAC (Reach et al. 2005).

The initial list of point sources in these images was produced by running IRAF task STARFIND with a low detection threshold in order to identify as many sources as possible, permitting false detections in this stage of the analysis. An automated cross-correlation between the Chandra source positions of Getman et al. (2006) and IRAC candidate source positions was made using a search radius of 2'' within ∼6' of the ACIS field center, and a search radius of 35 in the outer regions of the ACIS field where X-ray source positions are more uncertain due to the deterioration of the Chandra telescope point-spread function (Figure 2). This was followed by a careful visual examination of each source in both bands to remove dubious sources and associations.

Of the 431 X-ray sources within the 17' × 17' Chandra ACIS-I field (Getman et al. 2006), 396 (92%) lie within the 3.6/5.8 μm IRAC coverage and 412 (96%) lie within the 4.5/8.0 μm IRAC coverage. Out of [396, 412, 396, 412] X-ray sources in the [3.6, 4.5, 5.8, 8.0 μm] channels, [384, 399, 369, 385] are identified with IRAC sources. The IRAC detection rate of X-ray sources is thus ∼97% for 3.6 and 4.5 μm channels and ∼93% for 5.8 and 8.0 μm channels.

2MASS associations are obtained as described in Getman et al. (2006). Optical counterparts were identified from the VI_c photometric catalog of Mayne et al. (2007).⁵ Unlike the search for the IR counterparts, we lacked the ability to visually examine the Chandra-optical matches. We therefore compared the Chandra-optical offset (Off₁ in Table 1) with the Chandra-2MASS and Chandra-IRAC positional offsets (Off₂ and Off₃). Accepted optical matches typically have |Off₁ − Off_2,3| ≲ 02. Out of the total of 431 Chandra X-ray sources, 368 are in the field of view of the optical survey and 321 of them have optical counterparts. The detection rate of the X-ray sources in the optical survey is thus ∼87%.

There are [12, 13, 27, 27] X-ray sources in the [3.6, 4.5, 5.8, 8.0 μm] channels lacking mid-IR counterparts. Roughly half of these lie in the interface region between the Cep B molecular cloud and S 155 H ii region where the IRAC point source sensitivity is reduced by the high background nebular emission from heated dust (Figure 1). These are probably true cluster members, but are omitted from the science analysis below. The other half of these unidentified X-ray sources is uniformly distributed outside of the Cep B cloud with weak X-ray fluxes and high X-ray median energies consistent with extragalactic background sources. Most of these are listed in Table 4 of Getman et al. (2006) as likely extragalactic contaminants.

The results of this search for stellar counterparts of the Chandra sources are presented in Table 1. Listed by Chandra sequence number, the table gives offsets between the optical/IR stars and the X-ray sources, VI_c JHK_s and IRAC photometry, and photometric flags. The final column gives the aperture used in the photometry for each IRAC band; a "9" value indicates that the X-ray source lies outside the IRAC coverage in that band or the IRAC source is too weak or strongly contaminated with no reliable photometry.

First, a rough estimate of individual stellar masses of the Cepheus PMS stars is made by dereddening star positions in the J versus J−H color–magnitude diagram to the 3 Myr and 2 Myr theoretical isochrones for the Cep OB3b/S 155 and Cep B subregions, respectively, based on the models of Siess et al. (2000) and Baraffe et al. (1998; see Appendix A). These individual stellar photometric mass and extinction estimates are listed in Table 2. Although individual mass estimates may be subject to significant uncertainties and may not be always compatible with masses obtained by more accurate methods such as optical spectroscopy, this approach should be adequate to assign an IC 348 SED template (Table 4 of Lada et al. 2006) to individual Cepheus PMS stars.

Second, it is important to note that the IC 348 template SEDs are observed (not dereddened) and exhibit an extinction of A_V ∼ 2–2.5 mag (Lada et al. 2006). Thus for each of the Cepheus stars, an IC 348 template SED at the corresponding spectral subclass is first reddened and dereddened within the wide but finite range of extinctions using reddening relationships described in Appendix A for JHK_s and Flaherty et al. (2007) for IRAC bands. The (de)reddened IC 348 template which, after normalization to an observed J-band Cepheus SED point, is the closest to an observed H-band Cepheus point (both J and H-band points are considered to be indicators of a pure photospheric emission) is recognized here as the best-fit to Cepheus data. Third, the best-fit IC 348 (de)reddened median template is visually matched to the observed Cepheus SED, allowing classification of the Cepheus stars.

Out of the total of 431 X-ray Cepheus sources, our classification procedure yields 215 diskless Class III systems (labeled "NoD" in Table 2) and 139 Class II or I disk-bearing systems ("DSK"). Based on the membership analysis of Getman et al. (2006), 24 X-ray sources without IR counterparts are possible extragalactic contaminants ("EXG") and 13 are foreground candidates ("FRG"). Forty Chandra sources with IR detections that are unreliable or insufficient for classification have an uncertain classification ("UNC"). We further subjectively classify 20 stars as Class II/III transition disks (labeled as "TD" and "DSK"); these follow the photospheric SED at wavelengths shorter than at least ∼3.6 μm. Four Chandra sources (Nos. 314, 322, 328, and 390) embedded in the Cep B core have extreme SED excesses with α>0 and are classified as Class I stars.

Examples of disk-free, disk-bearing, and transition SEDs are shown in Figures 3–5. The complete set of SEDs for 354 X-ray emitting Cepheus PMS stars classified here is available online as a figure set. The online atlas contains 161 disk-free stars of the Cep OB3b region (labeled as "NoD" and "CepOB3b" in Table 2); 75 disk-bearing stars of the Cep OB3b ("DSK" and "CepOB3b"); 36 disk-free stars of the S 155 region ("NoD" and "S 155"); 26 disk-bearing stars of the S 155 region ("DSK" and "S155"); 18 disk-free stars in the Cep B region ("NoD" and "CepB"); and 38 disk-bearing stars in the Cep B region ("DSK" and "CepB"). Quantitative information derived from the fitting process is given in Table 2 including the masses and absorptions estimated from the J − (J − H) color–magnitude diagram (Columns 4 and 5) and the SED classification obtained by comparison with IC 348 templates (Columns 6 and 7).

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View figure set (61 panels)

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We performed least-squares linear fits to the log(λF_λ) values in the four IRAC wavelength band to obtain the observed (not dereddened) SED spectral index, α₀. These are tabulated in Column 2 of Table 2. Figure 6 shows the histogram of 354 α₀ values for the X-ray-selected Cepheus PMS stars compared to 299 IC 348 PMS stars from Lada et al. (2006).

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Two important features are noted. First, the Cepheus histogram shows a bimodal distribution with peaks at α₀ ∼ −1.3 and −2.7 corresponding to disk-bearing and diskless star samples, respectively. The IC 348 histogram has the same peaks, and similar bimodality is seen in the PMS populations of the Cha I cloud (Luhman et al. 2008b) and σ Ori cluster (Hernández et al. 2007). Second, in contrast to the IC 348 population, the Cepheus region does not produce a rich TD population in the interval −2.6 < α₀ < −1.8. The X-ray-selected Cepheus population has 20/139 (14%) TDs among disk-bearing stars compared to 70/163 (43%) in IC 348. This apparent difference in TD frequency is discussed in Section 6.3.

Comparison of Spitzer-IRAC source positions in the [3.6] − [4.5] versus [5.8] − [8.0] diagram with the results of models of stars with dusty disks and envelopes led Allen et al. (2004) and Megeath et al. (2004) to propose this diagram as an excellent tool for PMS classification. Hartmann et al. (2005) show that similarly successful PMS classification schemes can be obtained at shorter wavelengths using the [3.6] − [4.5] versus [4.5] − [5.8] and K_s − [3.6] versus [3.6] − [4.5] diagrams. In Figure 7, we compare the SED-based classifications of Cepheus X-ray stars derived in Section 3.1 with the expected loci of PMS stars in IRAC color–color diagrams. Here, we also begin comparison of the disk characteristics in three spatial subregions: the unobscured Cep OB3b cluster, the optically bright S 155 nebula, and the Cep B molecular cloud core. The regions are measured radially from the location of the hot molecular core at α = 22^h57^m152, δ = +62°37'111 (J2000).

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Figure 7 shows the three IRAC color–color diagrams for the sources in the three subregions. Seventy-seven Cep OB3b sources are missing from the plots due to inadequate photometry, often due to location outside of the full four-band coverage. Sources are also omitted from the S 155 and Cep B areas when photometry at the longer 5.8 μm and 8.0 μm bands are absent or inaccurate due to bright nebular emission. The positions of stars in the color–color diagrams generally agree with our previous classification of stars as disk-bearing and diskless PMS stars based on comparison with IC 348 stars (Section 3.1), shown as blue and red symbols in Figure 7. The F₂ flag of Table 2 indicates sources with their disk classification from Section 3.1 inconsistent with the simple color criterion that diskless stars have [3.6] − [4.5] ≲ 0.2, [4.5] − [5.8] ≲ 0.2, or [5.8] − [8.0] ≲ 0.2. Several sources with such "discrepant" locations on color–color diagrams may represent additional cases of transitional disks.

Growing evidence has emerged from IRAC young cluster studies that more massive PMS stars have shorter disk lifetimes. Luhman et al. (2008a, 2008b) find that disk fractions in the 2–3 Myr old IC 348 and σ Ori clusters decrease from ∼50%–60% in brown dwarfs to ∼30%–40% in stars with M ≳ 1 M_☉. In the older 5 Myr old Upper Sco and NGC 2362 clusters, the disk fraction decreases from 10%–20% in 0.1–1 M_☉ stars to ≲1% in higher mass stars (Carpenter et al. 2006; Dahm & Hillenbrand 2007). The trend may not be universal: the disk fraction of M ≳ 1 M_☉ stars in the 2 Myr old Cha I cluster is >60% (Luhman et al. 2008b), much higher than that found in IC 348 and σ Ori at similar ages.

Figure 10 compares the mass-dependent disk fractions of Cep OB3b and the other three regions examined by Luhman et al. (2008a). Our sample here is the combined 215 Chandra (classified as "DSK" or "NoD" in Table 2) and 142 disk-bearing non-Chandra (Table 3) Cep OB3b sources within the overlap area of four IRAC band and Chandra fields, omitting the most massive young star in the region, O7Vn star (Chandra No. 240) with M_J < 0 mag, and 37 non-Chandra IR-excess possible members of Cep OB3b with inferred masses below 0.1 M_☉. Appendix B shows that the relatively short Chandra observation is only sensitive to stars down to 0.2 M_☉, so we have no Cep OB3b coverage for very low mass Class III stars and brown dwarfs. Cep OB3b stars have average ages around 2–3 Myr old (Appendix A) similar to the ages in Cha I, IC 348, and σ Ori; possibly younger stars in the S 155 and Cep B region are omitted here. Following Luhman et al., the absolute J-band magnitude M_J serves as a proxy of mass. Our M_J values are obtained using individual A_J extinctions from Tables 2 and 3, which in turn were derived through the evolutionary model-dependent procedure assuming the distance of 725 pc and the age of 3 Myr. Individual magnitude accuracies should be sufficient to reliably assign individual sources to the coarse, 2 mag wide M_J bins. Errors on disk fractions have been estimated using binomial distribution statistics as described by Burgasser et al. (2003). For the Cep OB3b stars, M_J bins have been systematically shifted by +0.3 mag from those of other regions in order to include in the second M_J bin the ∼0.5 M_☉ mass stars, stars for which the combined Chandra and non-Chandra Cep OB3b sample is complete (Section 5).

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Figure 10 shows that the disk fraction of the Cep OB3b stars (circles) for the two highest mass bins is around 45% and agrees with the fractions seen in IC 348, but appears higher than the comparison clusters for the lowest <0.5 M_☉ mass bin. The most plausible explanation for the reduced disk fraction in the <0.5 M_☉ bin is incompleteness of the Cep OB3b sample at low masses (Section 5). Here, our short Chandra observation is not sensitive to many low-mass Class III stars and the observational bias toward non-Chandra disk-bearing stars affects the sample selection.

We thus find no significant dependence of disk fraction on mass in the Cep OB3b Chandra plus non-Chandra-selected sample above 0.5 M_☉.⁶ This agrees with the lack of mass dependence seen in IC 348 and σ Ori in the >0.2 M_☉ regime. The increased fractions reported in these clusters were found in the <0.2 M_☉ regime which is not covered by our Cep OB3b-selected sample. However, we do not support studies in other clusters that report a rapid loss of IRAC-band disk emission in intermediate-mass stars. These studies might consider possible sample incompleteness effects, such as an undersampling of disk-free Class III low-mass members. Our inclusion of the X-ray-selected sample is specifically designed to be nearly free of this bias.

We now consider spatial distribution of the disks around the mass-complete Chandra plus non-Chandra PMS samples over the area covered by the four IRAC mosaics and the Chandra field. Figure 11 shows the spatial distribution, and Table 4 provides quantitative details for two mass strata, two azimuthal zones (northeast (NE) and southwest (SW)), three radial subregions (Cep OB3b, S 155, and Cep B), and three radial layers discussed below (inner, intermediate, and outer). The azimuthal zones are separated by the line that roughly bisects the optically bright (Figure 1) and IR-bright nebular emission. Radial distances are measured from the hot core of the molecular cloud (α = 22^h57^m152, δ = +62°37'111 (J2000)). Below we consider the Cepheus sample of 220 Chandra plus non-Chandra PMS stars with stellar masses above 0.5 M_☉, the mass completeness limit for Cep OB3b/S 155 stars (Section 5), as well as its mass-stratified subsamples. The observed stellar population of the embedded Cep B cluster may be complete somewhere above 1 M_☉ (Section 5) and thus the analysis of the >1 M_☉ stellar subsample may provide more realistic disk fraction estimates for this subregion.

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Examining first azimuthal dependence, we find that the NE zone of the region has ∼1.5–1.7 times higher stellar surface density than the SW zone. There is also an indication for possible slight increase in disk fraction from NE to SW zones of the Cep OB3b/S 155 region, although the effect is not statistically significant (Table 4).

Examining next the radial dependence, a dramatic trend is seen: the disk fraction increases from 40%–50% in the Cep OB3b subregion to 50%–60% in the S 155 subregion to 70%–80% in Cep B (Table 4). This trend is elucidated in more detail in Figure 12 as a running average disk fraction. Here, the running disk fraction for the >0.5 M_☉ mass stratum (red) is evaluated within a 2' wide sliding window at 1' intervals, while the 0.5 M_☉ < M < 1 M_☉ (black) and M>1 M_☉ (blue) mass strata are evaluated within a 4' wide sliding window at 2' intervals. Note these values are not independent because a given star is included in two adjacent values. The effect could either be viewed as a smooth trend in disk fractions, or a step function at 30% (outer layer), 60% (intermediate layer), and 70%–80% (inner layer) disk fractions in 0.6–0.8 pc radial bins (gray bars). It is important to note that the outer edge of the second bin (intermediate layer) is coincident with the projected position of the ionizing source of the region, O7V star HD 217086.

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If one adopt the simple relation between stellar age and disk fraction derived by Hernández et al. (2007, see their Figure 14), the Cepheus disk fraction gradient corresponds to an age gradient from 3 to 5 Myr in the outer layer (part of Cep OB3b subregion), 2 to 3 Myr in the intermediate layer (part of Cep OB3b/S 155 region), and ∼1 Myr in the inner layer (embedded Cep B subregion). This inferred age gradient agrees with that estimated from stellar (versus disk) properties in Appendix A.

As noted earlier in Section 3.2, the Cepheus OB3b population appears deficient in transition disks compared to the 2–3 Myr old cluster IC 348. We investigate this further here, including comparison to the low-mass 1 Myr old Coronet cluster (Sicilia-Aguilar et al. 2008) and the 4 Myr old Tr 37 cluster (Sicilia-Aguilar et al. 2006). Tr 37, like our Cep OB3b field, harbors an O7-type star.

It is important to recall that different studies of different star-forming regions use different criteria for identifying TDs. In the Tr 37 and the Coronet cluster studies, TDs are identified with a photometric excess longward of ∼6 μm. In the study of IC 348, small excesses around 2 μm define "anemic disks" systems (Lada et al. 2006). Our classification of Cepheus stars here (Section 3) relies on an intermediate criterion of excess longward of ∼3.6 μm. Thus, if the fraction of transition disks were intrinsically the same in all clusters, we expect the reported fractions to be largest in IC 348, intermediate in our sample, smallest in Tr 37 and the Coronet. Furthermore, intercluster comparison of TD fractions should also consider similar mass strata, as lower mass PMS stars may have flatter disks with more frequent inner holes than more massive PMS stars (e.g., Hartmann et al. 2006; Sicilia-Aguilar et al. 2008). From Table 2 of Lada et al. (2006), a TD fraction among disk-bearing stars in IC 348 decreases from 0.45 ± 0.04 (64/142) for M-type stars to 0.31^+0.15_−0.09 (4/13) for G-K-type stars, although this decrease is not statistically significant. The Tr 37 study combined stars from late G to M2-type (∼0.4–2 M_☉) and reported a 0.10^+0.03_−0.02 (11–14 out of 140–150) TD fraction among disk-bearing stars. The Coronet cluster study included only M0–M8 objects and reported a 0.50^+0.13_−0.12 (7/14) TD fraction.

Our classification of X-ray-selected PMS stars in the Cep B/Cep OB3b obtained 20 TDs out of 139 disk-bearing stars giving a TD fraction of 0.14^+0.03_−0.02. Most of these (13 out of 20) are in the unobscured Cep OB3b subregion and none are present close to the Cep B hot core. To perform a mass-stratified analysis, we consider here only the most rich star sample, Cep OB3b. From Table 2, we find the Cep OB3b TD fraction may be mass-dependent with 0.29^+0.1_−0.07 (8 out of 28) among M ≲ 0.5 M_☉ (M-type) disk-bearing stars and 0.11^+0.06_−0.03 (five out of 47) around more massive stars.

These results are roughly consistent with the previous studies, once the TD definitions and mass ranges are taken into account. Our overall ∼14% TD fraction is intermediate between the ∼40% reported for IC 348 and ∼10% reported for Tr 37, as expected for an intrinsically constant TD fraction. Our finding that M stars have a higher TD fraction than more massive stars agrees with the indication for trend seen in IC 348 and the high fraction found in Coronet M stars. We thus conclude that the fraction of Cep OB3b TDs agrees with that of other clusters despite the apparent deficit noted earlier in Figure 6.

The observed picture of the Cep B region is in many respects reminiscent, on a larger scale of several parsecs, of those of smaller bright-rimmed clouds (BRCs) and cometary globules (CGs) found on the edges of giant H ii regions (Sugitani et al. 1991). BRCs are isolated clouds surrounded by ionized rims facing the exciting star(s) with their dense cores close to the rims. BRCs are modeled as externally illuminated, photoevaporated and ablated into elongated head–tail morphologies by ultraviolet radiation of OB stars (Reipurth 1983). It is likely that pressure from the ionization shock front at the surface propagates through a globule and overcomes the magnetic, turbulent and thermal pressure that supports it against collapse, thereby triggering localized star formation. This astrophysics of RDI in molecular globules has been extensively studied (e.g., Bertoldi 1989; Lefloch & Lazareff 1994; Miao et al. 2009). RDI models typically consider the triggering of a single star formation episode in a small (<1 pc) cloud with tens of M_☉ of molecular gas. The characteristic timescale for producing cometary morphologies and inducing gravitational collapse varies with initial conditions from 0.1 to ∼1 Myr.

In most cases, molecular, IR, Hα surveys of BRCs trace only the most recently formed stars (e.g., Sugitani et al. 1995; Ogura et al. 2002; Thompson et al. 2004; Urquhart et al. 2006). In a few cases, Chandra observations have added the disk-free PMS populations (Getman et al. 2007, 2008c; Sanchawala et al. 2007; Wang et al. 2009). Triggered BRCs often show a few embedded mid-IR sources denoting protostars, while Hα, JHK, and X-ray surveys reveal small clusters of disk-bearing PMS stars within and in front of the bright rim. In a few cases, spatial-age gradients in the stellar population are seen where the youngest stars are embedded and older stars are aligned toward the ionizing sources (Matsuyanagi et al. 2006; Ogura et al. 2007; Getman et al. 2007). This directly supports the RDI mechanism and implies that the existing clouds have been actively forming stars for several million years.

The Cepheus region possesses all of the observational features of an RDI triggered star formation region.

• 1.  
  The presence of exciting star(s) and a molecular cloud surrounded by an ionized rim facing the exciting stars shown in Figures 1 and 2 (Minchin et al. 1992; Beuther et al. 2000).
• 2.  
  The presence of a dense molecular core close to the rim (Yu et al. 1996; Beuther et al. 2000).
• 3.  
  The spatio-temporal gradient of young stars oriented toward the exciting star(s) shown in Figures 11 and 12.

The major difference of the Cepheus region from other BRCs is its larger scale: its extent is ∼4 pc linear size, its molecular mass is ∼200 M_☉, its observed PMS X-ray stellar population is >60 embedded and up to ∼300 older unobscured members, as well as estimated intrinsic population of ∼1000 unobscured and possibly a few hundred embedded stars (Section 5). The large-scale morphology is also different from most other BRCs. Rather than lying on the edge of a circular H ii region surrounding a concentrated OB association, it is an extension of a giant molecular cloud protruding into a large evacuated region produced by a partially dispersed OB association. Another unusual case of a very large BRC with star formation triggered over several million years is the high-latitude cometary globule CG 12 (Getman et al. 2008c).

Based on the RDI triggered star formation concept, we can propose some new insights into the star formation process of the Cepheus region and make some simple model-independent estimates for a shock propagation velocity and a star formation efficiency (SFE) of the RDI process. In Section 6.2 and Appendix A, we establish the spatio-temporal gradient of Cepheus PMS stars from the center of the cloud toward the HD 217086 O7Vn star. Assuming a distance around 725 pc, the innermost 0.6–0.8 pc adjoining the hot core of the cloud has the youngest (<1–2 Myr) stars with the highest seen disk fraction (70%–80%). The intermediate 0.6–1 pc layer around S 155 has older (2–3 Myr) stars with an intermediate disk fraction (∼60%; Figure 12). The outer layer of mostly diskless stars in the unobscured Cep OB3b cluster has the lowest disk fraction (∼30%).⁷

We consider two scenarios for RDI-induced star formation in this region. First, a relatively slow shock with speed ≲0.5 km s⁻¹ may have passed through the molecular cloud, triggering star formation in the outer layers around 2–3 Myr ago and continuing to trigger star formation close to the Cep B hot core today. This slow shock speed is consistent with the 0.6 km s⁻¹ propagation rate inferred from the age gradient of the PMS stars in the globule IC 1396N, located ∼11 pc projected distance of its ionizing O6e type star (Getman et al. 2007). In this scenario, stellar kinematic drift from their birthplaces plays an important role in relocating PMS stars. The O7Vn star HD 217086 star is probably the principal ionization source but other OB stars (Figure 1), including the B1Vn star HD 217061 currently located within the SW zone of the S 155 subregion, probably also play a role. If the original cloud were only slightly larger than the size observed today, the RDI shock would have slowly propagated through ∼1 pc of the Cep B molecular cloud over ∼2–3 Myr years, implying a shock velocity around ≲0.5 km s⁻¹. The stars formed early in this process would have drifted 2'–10' (0.4–2 pc) in all directions, populating much of the Chandra field of view with triggered stars. Such star drifting would require a stellar velocity dispersion around 1 km s⁻¹. This is expected from the turbulent velocities within a cloud several parsecs in extent (Efremov & Elmegreen 1998), which can be supplemented by dynamical interactions between protostars during star formation (Bate 2009; Fűrész et al. 2008).

A second scenario involves the passage of a faster shock propagating at ∼1 km s⁻¹ through a cloud that was originally much larger than the Cep B cloud we see today. In this model, most of the original cloud material has ablated and most of the stars in the Chandra field formed in the cloud during the past ∼2–3 Myr. Present locations of the intermediate layer around S 155 and the inner layer around the molecular core (separated by 0.8–1 pc, Figure 12) may be directly associated with the passage of the RDI shock ∼2–3 and ≲1–2 Myr ago, respectively. Star drift plays a less important role here. A similar fast shock speed is observed in the triggered star formation in the molecular pillars of the Eagle Nebula (M 16) and other bright rimmed clouds (Fukuda et al. 2002; Thompson et al. 2004), and is consistent with the theoretical models of Motoyama et al. (2007).

A critical discriminant between these scenarios is the SFE of the cloud. Integrating the stellar masses in Figure 9, the total stellar mass of the Cep OB3b disk-bearing population assuming a standard Galactic field IMF is ∼130 M_☉ in our observed field. With the average disk fraction of 45% (Section 6.1, Table 4), we add ∼160 M_☉ of disk-free stars and ∼20 M_☉ from HD 217086 to give a total mass of the Cep OB3b population around 310 M_☉. A similar estimate for the S 155 population from information in Figure 9 and Table 4 gives a total stellar mass around 80 M_☉. Assuming that the observed Cep B embedded population is complete only somewhere above 1 M_☉ (Section 5) and follows a standard Galactic field IMF as well, we use star count and disk fraction information for the highest mass bin from Figure 9 and Table 4 to obtain an estimated total mass of the Cep B population of 120–250 M_☉. The mass of the observed molecular gas in the Cep B molecular portion of the Cepheus molecular cloud is only ∼200 M_☉ (Yu et al. 1996; Beuther et al. 2000).

The inferred SFE for the embedded Cep B population alone is thus around 35%–55%, at the top of typical SFE range of 10%–40% measured in other active star-forming regions (Elmegreen et al. 2000, and references therein). This is far above the SFE found in smaller molecular globules triggered by UV shocks (e.g., Getman et al. 2007). For the total Cepheus stellar population within the Chandra field, the apparent SFE is extremely high around ≳70%. This is unrealistically high and indicates that most of the Cep OB3b stars were not formed from the presently seen cloud material but arose from an earlier generation of star formation from gas that is no longer present. This supports the second scenario involving a fast shock passing through a much larger and more massive original cloud.

Two other aspects of RDI triggered star formation can be discussed. First, Sugitani et al. (1991) provided observational evidence for a nonstandard IMF where intermediate-mass stars are preferentially formed over lower mass stars in BRCs. In the case of the embedded triggered PMS population of IC 1396N, Getman et al. (2007) also found indications for a nonstandard IMF biased toward higher mass stars, but cautioned about possible observation selection effects. A similar situation arises here in the case of the embedded Cep B population (Section 5). While the shape of the Cep B stellar mass distribution is not definite yet, the stellar mass distribution of likely RDI triggered stellar population of the Cep OB3b/S 155 region agrees well with a standard Galactic IMF, at least down to ∼0.2–0.5 M_☉ (Section 5).

Second, most theoretical calculations of RDI triggering involve small globules and a single episode of triggering. The 2–3 Myr range of stellar ages found in the Cep B/Cep OB3b region, and an even wider age spread found in CG 12 (Getman et al. 2008c), implies repeated or continuing star formation over millions of years when the RDI mechanism occurs in a larger molecular cloud.