Herschel Gould Belt Survey Observations of Dense Cores in the Cepheus Flare Clouds

We present Herschel SPIRE and PACS maps of the Cepheus Flare clouds L1157, L1172, L1228, L1241, and L1251, observed by the Herschel Gould Belt Survey (HGBS) of nearby star-forming molecular clouds. Through modified blackbody fits to the SPIRE and PACS data, we determine typical cloud column densities of 0.5-1.0 $\times$ 10$^{21}$ cm$^{-2}$ and typical cloud temperatures of 14-15 K. Using the getsources identification algorithm, we extract 832 dense cores from the SPIRE and PACS data at 160-500 $\mu$m. From placement in a mass vs. size diagram, we consider 303 to be candidate prestellar cores, and 178 of these to be"robust"prestellar cores. From an independent extraction of sources at 70 $\mu$m, we consider 25 of the 832 dense cores to be protostellar. The distribution of background column densities coincident with candidate prestellar cores peaks at 2-4 $\times$ 10$^{21}$ cm$^{-2}$. About half of the candidate prestellar cores in Cepheus may have formed due to the widespread fragmentation expected to occur within filaments of"transcritical"line mass. The lognormal robust prestellar core mass function (CMF) drawn from all five Cepheus clouds peaks at 0.56 M$_{\odot}$ and has a width of $\sim$0.5 dex, similar to that of Aquila's CMF. Indeed, the width of Cepheus' aggregate CMF is similar to the stellar system Initial Mass Function (IMF). The similarity of CMF widths in different clouds and the system IMF suggests a common, possibly turbulent origin for seeding the fluctuations that evolve into prestellar cores and stars.

. Herschel -derived high-resolution H2 column densities for L1157. Column densities are shown on a logarithmic scale between 2 × 10 21 cm −2 and 2 × 10 23 cm −2 . Ellipses correspond to cores identified in the cloud via getsources. Green, red, and yellow ellipses are cores we identify as "starless cores," "candidate prestellar cores," and "protostellar cores," respectively (see §3.2). The size of an ellipse corresponds to the measured extent of its respective core. The solid black border excludes noisy map edges and delineates the region in the map over which statistics are calculated. based emission or extinction map studies. Moreover, we can provide a census of the starless cores, prestellar cores, and protostellar cores in these five clouds, and corresponding catalogues of their observed and physical properties. Moreover, given the lower column densities previously estimated for these clouds, these observations provide a counterpoint to observations of more active star-forming clouds in the Gould Belt. A recent analysis of other lower column density star-forming clouds in Lupus was recently presented by Benedettini et al. (2018).
This paper is organized as follows: in §2, we describe the observations and data reduction performed on the Herschel data; in §3, we present the results of the data, including column density and temperature maps, and source extractions; in §4, we discuss core formation in the low column density regime of the Cepheus clouds, and discuss the core mass functions of the Cepheus clouds as a whole and separately; in §5, we provide a summary and conclusions. The paper also contains three Appendices: in A, we provide the images of all five clouds at 70 µm, 160 µm, 250 µm, 350 µm and 500 µm; in B, we provide the criteria applied to sources detected by the getsources algorithm for reliability; and in C, we list the information provided in online material, including catalogues of the observed and derived physical properties of all dense cores identified in the Cepheus clouds studied and thumbnail images of each core at 70-500 µm and in H 2 column density.

OBSERVATIONS AND DATA REDUCTION
Each Cepheus field was observed simultaneously with the Herschel Space Observatory's Spectral and Photometric Imaging Receiver (SPIRE) and Photodetector Array Camera and Spectrometer (PACS) instruments in parallel mode, as part of the Herschel Gould Belt Survey (HGBS) Key Program (André et al. 2010) 1 . Further information on Herschel, SPIRE, and PACS can be found in papers by Pilbratt et al. (2010), Griffin et al. (2010), and Poglitsch et al. (2010), respectively. Table 1 summarizes the Herschel observations of the five Cepheus fields, giving the name of each field, the J2000 coordinates of the reference position of each map, the observational date (in UT), and the Observation IDs (OBSIDs), respectively. Each field was observed twice, with scans made in roughly perpendicular position angles, at a scanning speed of 60 s −1 . Fortuitously, L1251 was actually observed four times, i.e., two pairs of orthogonal scans.
The Herschel data were reduced using HIPE (Ott 2011), following the standard HGBS "first generation catalogue" prescriptions. We refer readers to the first HGBS data catalogue paper (Könyves et al. 2015) for details on the data reduction steps. (See also other recent HGBS data catalogue papers by Marsh et al. (2016), Bresnahan et al. (2018), Benedettini et al. (2018), Könyves et al. (2020), and Ladjelate et al. (2020, in press).) We provide a brief sketch of the steps below.
For the PACS data at 70 µm and 160 µm, HIPE version 9.0.3063 was used. After standard steps of masking bad pixels, applying flat-field corrections and non-linear responsivity corrections to the data, deglitching cosmic ray hits, and applying a high-pass filter of scan-leg length, the PACS images were produced with the IDL-based map-maker, Scanamorphos version 20 (Roussel 2013). As in Könyves et al. (2015), the absolute point source flux accuracies in the PACS images are 3% at 70 µm and <5% at 160 µm, with the extended source calibration flux accuracies being uncertain. We also adopt here the more conservative absolute calibration uncertainties of 10% and 20% for integrated source flux densities at 70 µm and 160 µm, respectively.   For the SPIRE data at 250 µm, 350 µm, and 500 µm, HIPE version 10.0.2751 was used. The data were calibrated and appropriate corrections made to account for several issues, including electrical crosstalk, temperature drifts, cosmic ray hits, "cooler burps," and relative gain factors between bolometers. A naïve mapmaker in HIPE was used to produce preliminary images that were destriped. Subsequent iterations of offset fitting and subtraction and destriping were performed until convergence was reached. As in Könyves et al. (2015), the absolute flux accuracy is considered to be <5% for point sources (cf. Bendo et al. 2013) and <10% for extended sources (cf. Griffin et al. 2013) in the three SPIRE bands.
Highly smoothed versions of the Herschel images at each wavelength were compared with images made by extrapolating low-resolution data of the same sky locations obtained with the ESA Planck observatory to the Herschel wavelengths after adopting a dust model (Bernard et al. 2010). This comparison allowed appropriate values of the background emission at each wavelength not included in the Herschel data to be determined.
The intensities in all Herschel PACS/SPIRE maps were converted to MJy sr −1 and reprojected onto a common grid of 3 × 3 pixels. Following extensive tests conducted by Könyves et al. (2015) on the HGBS data of Aquila, we expect the absolute astrometric accuracy to be <3 . The half-power beam width (HPBW) resolutions of the maps are 8. 4, 13. 5, 18. 2, 24. 9, and 36. 2 at 70 µm, 160 µm, 250 µm, 350 µm, and 500 µm, respectively. The pixel sizes of the final images at each wavelength have been set to 3 , 3 , 6 , 10 , and 14 , respectively. The HGBS PACS and SPIRE maps of the Cepheus Flare fields data are publicly available on the HGBS Archive (http://gouldbelt-herschel.cea.fr/archives) in standard FITS format. Note that Planck-derived offsets have not been added to these files. Instead, these offsets can be found in the respective header of each map.

Column Densities and Temperatures
Figures 1-5 show H 2 column density maps of L1157, L1172, L1228, L1241, and L1251, respectively, obtained by fitting the Herschel spectral energy distributions (SEDs) of each pixel (adding Planck offsets at each wavelength) over a wavelength range of 160 µm to 500 µm with a modified blackbody function. The maps were produced at a resolution of 18. 2 following the "high-resolution" method described in Appendix A of Palmeirim et al. (2013) that is standard for HGBS catalogue papers. The modified blackbody used in the SED fitting includes a dust opacity κ ν = 0.144 cm 2 g −1 at 250 µm (incorporating a dust-to-gas ratio of 100) with a power-law dependence with wavelength of index β = 2.0 (Hildebrand 1983). In addition, the same mean molecular weight per H 2 molecule of µ = 2.8 is assumed here (Kauffmann et al. 2008) to convert gas surface density into H 2 column density. (To determine the isothermal sound speed, µ = 2.33 is assumed.) Figure 6 shows the dust temperature maps for each field obtained simultaneously from the fitting of modified blackbodies to the multi-wavelength Herschel data. In Appendix A, we present the actual Herschel images of each field at 70 µm, 160 µm, 250 µm, 350 µm, and 500 µm in their native resolutions and without the Planck offsets added.
The column densities seen in each map are typical of those seen in other HGBS fields of nearby star-forming molecular clouds, e.g., non-zero column densities are found in every pixel. Similarly, each Cepheus cloud field displays a multitude of substructure on many scales, including compact knots amidst longer filaments.  Figure 7 shows histograms of the column densities and temperatures of each field, i.e., their respective probability density functions (PDFs). (Note that the column density PDFs are constructed from all data shown in Figures 1-5 and not only in the last closed contour, as shown recently by Soler (2019).) Table 2 lists the median column density and median temperature of each field shown in Figures 1-6, with associated standard deviations. In terms of column density, L1157, L1172, and L1228 have very similar PDFs, peaking at 6-7 × 10 20 cm −2 and decreasing to smaller and larger column densities at similar rates. Interestingly, L1241 has column densities that peak at a slightly larger value, about twice that of the others, but its PDF falls off faster at smaller and larger column densities than those of L1157, L1172, and L1228 do. Indeed, the width of L1241's column density PDF is about half that observed in other clouds, and no column densities above 10 22 cm −2 are found. In addition, the column densities of L1251 peak at a similar value to that of L1157, L1172, and L1228 but its PDF falls off slightly more slowly at high column densities. In terms of temperature, all five clouds have distributions that peak at around 14 K. The temperature PDFs of L1157, L1228, and L1251 are similar with very few pixels with temperatures above 25 K. L1241 has a temperature PDF that is significantly narrower than the others, with few pixels with values above 20 K. In §3.2 below, we report that no protostellar cores are found in L1241. Such objects would otherwise provide internal heating to the cloud, leading to higher temperatures. In contrast, a long tail to 20-40 K is seen in the temperature PDF of L1172. These high temperatures are found in pixels adjacent to the Herbig Ae star HD 200775 (see Figure 6b), and hence likely arise from the radiative heating of dust by that particularly luminous star. Table 3 lists the estimated masses of each Cepheus cloud given the column densities derived here. L1157, L1172, L1228, and L1251 have similar masses of 1400-1900 M , while L1241 is about double that at 3200 M . Table 3 also gives the area of each cloud in pc 2 given the ∼360 pc distance to the clouds. In addition, Table 3 gives the amount of mass above extinction levels of A V = 1 and 7, where we use the conversion between H 2 column density and extinction of Bohlin et al. (1978). The masses of each cloud at A V > 1 are on average similar (i.e., within 5-40%) to those reported by Yonekura et al. (1997) from 13 CO (1-0) observations after adjustment to a distance of 360 pc. From this comparison, we see that L1241 has the largest amount of material at A V > 1 but curiously also the lowest amount of mass (and lowest fraction of total mass) at A V > 7. L1251, however, has the most amount of mass (and highest fraction) of mass at A V > 7. In total, the Cepheus clouds have ∼500 M at A V > 7, i.e., ∼8% of the mass of all five clouds at A V > 1.

Source Extraction
Compact objects in each Cepheus field were extracted using version 1.140127 of the source identification algorithm getsources (Men'shchikov et al. 2012). For consistency, this approach is the same as that used to produce other HGBS catalogues of dense cores and protostars, e.g., Könyves et al. (2015). The getsources algorithm was specifically developed to identify compact objects within non-uniform emission across many wavelengths and scales, e.g., in Herschel observations of molecular clouds.
The getsources algorithm consists of two distinct "detection" and "measurement" stages. For the first "detection" stage, getsources successively smooths input maps to ever lower resolutions, subtracts maps of adjacent resolutions, and identifies positions of significant emission in the difference maps. Comparing these difference maps over many scales and wavelengths (if available) allows sources to be built up and identified over ranges of scale and wavelength. For the second "measurement" stage, getsources determines fluxes and sizes of sources using the original input images at each wavelength. Overlapping sources are intelligently deblended. Background levels are subtracted after being determined by linear interpolation under the source footprints, taking into consideration the different native angular resolutions at each wavelength. Finally, getsources applies aperture corrections at each wavelength obtained from the PACS and SPIRE Instrument Control Centres (e.g., see (e.g., see Balog et al. 2014;Bendo et al. 2013, respectively).
We ran getsources to extract dense cores and YSOs/protostars separately in the Cepheus fields, using different input maps and parameters. To extract dense cores, we used the Herschel maps at 160 µm, 250 µm, 350 µm, and 500 µm, regridded to pixels in common, as inputs. These four wavelengths bracket the peak of continuum emission from cold (T = 10-20 K) dust in dense cores. We also included the high-resolution column density map (see panel (a) of Figures 1-5) as an additional "wavelength" input to ensure identified objects consist of locally high column density. In addition, for the "detection stage" of this extraction, the native 160 µm maps were substituted with ones corrected for anisotropic temperature gradients. These corrected maps were made by converting the native 160 µm maps to pseudo-column density maps using color temperatures determined from the ratios of the native intensities at 160 µm and 250 µm, at the latter's resolution. To extract YSOs or protostars, we used only the Herschel maps at 70 µm. YSOs and protostars will heat their surrounding dust to temperatures higher than those of cold cores, making them stand out obviously at 70 µm as point-like objects (e.g., see Dunham et al. 2008).
For both sets of extractions, source fluxes and sizes are measured from the native Herschel maps of all five wavelengths, appropriately deblended, background subtracted, and aperture corrected. Source lists were constructed from identified sources deemed reliable following separate standard criteria for each extraction. These criteria are listed in Appendix B. Finally, to reduce potential contamination by background galaxies, source positions were cross-checked with the NASA/IPAC Extragalactic Database (NED) and the SIMBAD database. Herschel sources found within 6 , i.e., approximately half the 13. 5 resolution of Herschel at 160 µm, of a known background galaxy were flagged in the final catalogues. These latter sources are not included as cores in the analysis below.
Finally, each remaining source was visually checked. For inclusion in the final catalogues, a source had to be visible as a peak at its location in the images of at least two Herschel wavelengths and the high-resolution column density map. In total, 115 objects were excluded from the final catalogues as a result of such checks. Table 4 lists the numbers of dense cores obtained from each Cepheus cloud. In total, we identify 832 dense cores from all five clouds observed, and each cloud has ∼150-200 dense cores. Appendix C describes the online material available for this paper, including a catalogue of the observed properties of all Cepheus dense cores extracted from the various maps, such as positions, fluxes, and sizes. Table C1 lists the information provided in this catalogue. The online material also includes thumbnail images of each extracted core at each Herschel wavelength and in the high-resolution column density map. Figures C1 and C2 show example thumbnail images of two cores, HGBS J204306.0+675009 (a robust prestellar core; see §3.3 below) and HGBS J203906.3+680216 (a protostellar core; see §3.3 below). We employed a secondary automated object identification algorithm to provide an independent assessment of the sources extracted from the Herschel images of the Cepheus clouds via getsources. For these assessments, we chose to use the Cardiff Sourcefinding AlgoRithm (CSAR; Kirk et al. 2013), an algorithm that identifies sources in single-wavelength images by following intensities down from maxima in the images until neighboring sources or a noise threshold is met. The CSAR algorithm effectively functions as a conservative variant of the widely used Clumpfind algorithm of Williams et al. (1994) in two dimensions. We used CSAR on the high-resolution column density map only (i.e., Figures 1-5). The catalogue produced by CSAR was checked against that created by getsources, and sources found to be in common (i.e., with peaks located within 6 of each other) are highlighted as such in the getsources catalogues with a flag (see Appendix C and online material). The percentages of objects identified by both algorithms are 54%, 46%, 40%, 60%, and 49% for L1157, L1172, L1228, L1241, and L1251, respectively, values broadly consistent with those obtained in other Gould Belt Clouds studied with Herschel, e.g., 45% in Aquila (Könyves et al. 2015). In general, getsources can identify fainter objects than CSAR because it incorporates information from multiple wavelengths for its assessments.

Dense Core Masses and Sizes
For each dense core extracted from the Herschel maps, an SED was constructed using integrated fluxes corrected for immediate background emission (e.g., from a host filament). As with the determinations of column densities and temperatures across each cloud, the dense core SEDs were fit with a modified blackbody model, assuming the same dependencies on κ ν and β (see §3.1) to determine masses (M core ) and line-of-sight averaged temperatures (T dust ), following Herschel GBS standard procedures (Könyves et al. 2015). If a core has more than three bands in which it is significant (i.e., Sig λ > 5, where Sig λ is the monochromatic significance determined by getsources) and if the 350 µm flux is higher than the 500 µm flux, two SED fits were made. In the first fit, the 70 µm flux was included, the errors used were the "detection error" = total core flux/Sig λ , and the weights of the fitting were 1/(detection error) 2 . In the second fit, the 70 µm flux was neglected, the errors used were the "measurement error" determined by getsources, and the weights of the fitting were 1/(measurement error) 2 . If the mass estimate between both runs varied by less than a factor of two, we used the mass and temperature from the second fit. If the mass estimates differed by more than a factor of two, the mass was calculated from the flux of the longest wavelength of significant flux (i.e., Sig λ > 5), assuming a temperature corresponding to the median core temperature from those cores that passed the fitting test described above. Approximately 45% of cores had mass estimates from the different fits that differed by less than a factor of 2. The median dust temperatures for cores were 11.3 K, 13.6 K, 11.9 K, 11.8 K, and 11.4 K for L1157, L1172, L1228, L1241, and L1251, respectively.
The observed size of each core was determined as the geometrical average of the FWHMs of its major and minor axes in the high-resolution (18. 2) column density map of its host Cepheus cloud (F W HM a NH 2 and F W HM b NH 2 , respectively. This angular size was converted to a physical size (R obs core ) assuming the ∼360 pc distance to the Cepheus Flare clouds (see §1). A deconvolved radius was also determined via R decon core = (R obs core 2 -HP BW N H 2 2 ) 1/2 where HP BW N H 2 is the physical size of the 18. 2 beam, i.e., 0.032 pc at the ∼360 pc distance of the core. We use the determined mass and size of each core to obtain estimates of their peak column densities (N peak H2 ), determined from the peak flux densities at the 36. 3 resolution of the 500 µm data (see Appendix C and online material). In addition, we determine the average column densities of each core before and after deconvolution (N ave H2 and N ave,d H2 , respectively). Next, we determine "peak" (i.e., from the peak column density value; n peak H2 ) and average volume densities before and after deconvolution (n ave H2 and n ave,d H2 , respectively. The "peak" volume density was determined using the peak column density assuming a Gaussian spherical distribution where n • = N • / ( √ 2πσ) and σ is the standard deviation of the Gaussian distribution.
The online material accompanying this paper includes a catalogue of derived physical properties of all Cepheus cores, as described in Appendix C. Table C2 lists the quantities found in this catalogue, including mass, size, column density and volume density estimates. Figure 8 shows the distribution of M core vs. R decon core for the core population of all five Cepheus clouds combined. The cores range in size over ∼0.01-0.2 pc and range in mass over ∼0.02-10 M . There are no significant differences in the ranges of core mass and size between clouds.
Based on the derived mass and deconvolved sizes, we explore the dynamical stability of the Cepheus cores by comparing their physical properties to those of a critical Bonnor-Ebert (BE) sphere (Ebert 1955;Bonnor 1956). For example, the mass of a critical BE sphere is defined as: Figure 8. Mass (Mcore) vs. deconvolved FWHM size (R decon core ) for cores extracted from all five Cepheus clouds. Green, red, and blue dots denote starless cores, candidate prestellar cores, and robust prestellar cores, respectively. Note that robust prestellar cores are a subset of candidate prestellar cores. The critical Bonnor-Ebert mass for isothermal cores with T = 7 K and T = 20 K are shown as black dashed and dotted lines, respectively.
where R BE is the BE radius, c s is the isothermal sound speed, and G is the gravitational constant. Here we neglect any nonthermal contributions to the support of the core, e.g., from turbulence. For each core, we estimated M BE assuming R BE = R decon core from the high-resolution column density map and assumed T = 10 K. We thus define the mass ratio We follow the guidance of Könyves et al. (2015) and use the size-dependent limiting BE mass ratio criterion α BE ≤ 5 × (HP BW NH 2 /F W HM NH 2 ) 0.4 to estimate the dynamical state of a core. Those cores meeting this criterion are deemed "candidate prestellar cores" (i.e., potentially bound by gravity) and those that do not are considered "starless" (i.e., gravitationally unbound). Figures 1-5 show the locations of these types of cores in each Cepheus cloud. By restricting the criterion to α BE ≤ 2, we further define a subset of candidate prestellar cores we call "robust prestellar cores." Those dense cores deemed to be neither prestellar nor protostellar are considered to be "starless cores." Table  4 lists the numbers of starless cores, candidate prestellar cores and robust prestellar cores found in each cloud. In total, this comparison reveals 504 starless cores, 303 candidate prestellar cores, and 178 robust prestellar cores in the Cepheus clouds. (Twenty-five cores are identified as being protostellar; see §3.4 below.) Figure 8 shows the mass vs. size distribution of each starless or prestellar core population in the Cepheus clouds. Figure 8 also shows the expected mass (M core ) vs. size (R decon core ) relationships for critical isothermal BE spheres at temperatures of 7 K and 20 K. All the robust prestellar cores have masses near to or larger than the critical BE mass at a given size and temperature of 7 K. Könyves et al. (2015) conducted extensive completeness tests of the cores extracted from Herschel maps of the Aquila Rift also via the getsources algorithm. They estimated their sample was 90% complete for cores of observed mass of 0.2 M , assuming an Aquila distance of 260 pc. (From other tests, they determined that observed core masses underestimate the true core mass of dense cores by 20-30%.) Given the larger distance of the Cepheus clouds of ∼360 pc, we accordingly estimate our 90% completeness as being 0.4 M . Note, however, that Aquila has a lower Galactic latitude (l ∼ 2-3 • than the Cepheus clouds (l ∼ 13-20 • ), and thus likely includes more background emission from Galactic cirrus. Hence, we consider our adopted value for Cepheus to be a conservative estimate of our observations' true completeness. Indeed, our completeness estimate of 0.4 M is largely consistent with those determined for other Gould Belt clouds via modeling similar to that performed by Könyves et al. (2015), after factoring in distance differences (e.g., Benedettini et al. 2018;Ladjelate et al. 2020, Pezzuto et al. 2020).
To determine the populations of protostellar cores in the Cepheus clouds, we compare the sources detected at 70 µm to the dense cores detected at 160-500 µm. We classify as protostellar those dense cores where a 70 µm source is located within its FWHM ellipse. The catalogues provided in the online material list the observed and derived physical properties of the protostellar cores found in the Cepheus clouds studied here. Only 25 protostellar cores are identified over all five clouds and Figures 1-5 show the locations of the protostellar cores in each cloud. Table 4 lists the numbers of protostellar cores found in each cloud. L1241 has no protostellar cores identified in its midst, consistent with the finding of Kirk et al. (2009) from Spitzer data that L1241 is without YSOs. With 11 protostellar cores, L1251 has the largest number of such cores in the Cepheus clouds, nearly half the identified population, suggesting it is currently the most active star-forming cloud of the five studied here. See §4.2 for discussion of the relative star-forming activity of these clouds.
Given the focus of this paper on the Cepheus clouds' prestellar core population, we do not discuss further the populations of "naked" 70 µm sources or protostellar cores.

Filamentary Substructure
As with all other clouds observed as part of the HGBS, the Herschel data reveal that the five Cepheus clouds have extensive substructure, much of it filamentary in morphology (see Figures 1-5). In particular, L1157, L1228, and L1251 appear to be dominated by filaments. L1172 and L1241 also exhibit filaments but the former is dominated by a high column density clump (NGC 7023) and filaments in the latter appear to be more diffuse.
To quantify the locations of filamentary structure in the Cepheus clouds, we used the "getfilaments" option with standard parameters during our core extractions with getsources (see Men'shchikov 2013). This option provides as output the locations of long contiguous features in input maps that are identified using standard extraction parameters as part of the multi-scale processing of those maps by getsources. Figure 9 shows the locations of filaments identified in each Cepheus cloud from their respective Herschel-derived H 2 column density maps up to spatial scales of 0.125 pc (i.e., 72 at the 358 pc distance to the Cepheus clouds), along with the positions and sizes of associated cores. Figure 9 illustrates how cores in Cepheus are predominantly located on filaments. Figure 10 shows a histogram of the fractions of cores by type that are coincident with filaments in the Cepheus clouds. For this comparison, a core was considered to be "on filament" if its central pixel overlapped with the area of an identified filament, i.e.., the locations identified in Figure 9. Some variation between clouds is seen with L1241 having cores with the least association with filaments (∼40-50%) and L1251 having almost all its cores (∼80-100%) associated with filaments. Excluding L1241, ∼75% of starless cores and ∼80% of candidate prestellar cores are coincident with filaments in Cepheus. The percentages of robust prestellar cores on filaments are similar to those of candidate prestellar cores on filaments. These percentages are roughly equivalent to those obtained for other HGBS clouds, e.g., Aquila (see Figure 14 of Könyves et al. 2015).

Star Formation in Low Column Density Environments
Though the Cepheus clouds show extensive filamentary substructure and their cores are largely associated with that substructure, the clouds have relatively low column densities. For example, the Cepheus clouds have median H 2 Figure 9. Areas of filaments identified from the H2 column density map derived from Herschel data (dark pixels). Spatial scales up to 0.125 pc (i.e., 72 at 358 pc) are shown. In each field, red, blue and yellow ellipses indicate the locations and sizes of candidate prestellar cores, robust prestellar cores, and protostellar cores, respectively. For context, the grey contour denotes the 500 µm intensity level of 94.5 mJy beam −1 . column densities of ∼6-10 × 10 20 cm −2 (see Table 2), corresponding to extinction levels of A V ≈ 0.6-1.0 (Bohlin et al. 1978). For this discussion, we do not subtract foreground/background column densities determined from emission by dust that is arguably unrelated to the cloud. From the histograms of column density in each map shown in Figure 7a, we surmise that the foreground/background column densities for these clouds are likely on the order of ∼1-2 × 10 20 cm −2 or so. Since the filament and cores in which we are interested in each cloud typically have column densities an order of magnitude than this value or more, we do not correct for systematic increases in their total column densities here.
To put the column densities of the Cepheus clouds into perspective, we note that there has been considerable discussion in recent years about a threshold column density for core formation in filaments of A V ≈ 7-8. The physics behind this threshold may be understood from the isothermal infinite cylinder model of Ostriker (1964), which becomes critically stable when its line mass (mass per unit length) M line = 2c 2 s /G ≈ 16 M pc −1 at 10 K. Assuming a common filament width of 0.1 pc (see Arzoumanian et al. 2011Arzoumanian et al. , 2019, this nominal line mass occurs at A V ≈ 7-8 in filaments (André et al. 2014). Indeed, such a threshold appeared evident in the Aquila Rift cloud, where 75% of prestellar cores are associated with filaments with line masses ≥ 16 M pc −1 (Könyves et al. 2015). More recent works than Ostriker (1964), however, have posited that "transcritical" filaments, i.e., with line masses within a factor of ∼2 of this critical value (e.g., 8-32 M pc −1 at 10 K), are actually those susceptible to fragmentation, leading to less of a sharp threshold and more of a smooth transition for core formation with column density in filaments, as has been observed (Inutsuka & Miyama 1997;Fischera & Martin 2012;Arzoumanian et al. 2019;Könyves et al. 2020).
Only 0.02-0.9% of pixels in all five Cepheus clouds have column densities >8 × 10 21 cm −2 , i.e., A V > 8. Nevertheless, modest star formation is indeed occurring in the Cepheus clouds. Such activity is evident by the 303 candidate prestellar cores and 25 protostellar cores identified in the Herschel data alone (Table 4). Moreover, Kirk et al. (2009) using Spitzer data find 93 YSO candidates, mostly Class II objects, in L1172, L1228, and L1251. Notably, they find only one YSO candidate in L1241. As mentioned earlier, L1157 was not included in their study. In terms of core formation activity, the Cepheus clouds appear similar to other low column density environments observed by Herschel, e.g., Lupus I, III, and IV (Benedettini et al. 2015(Benedettini et al. , 2018. In these particular clouds, Benedettini et al. (2015) do find column density PDFs of similar morphology to those of the Cepheus clouds that also peak at 0.5 − 1.0 × 10 21 cm −2 (see §3.1). More recently, Benedettini et al. (2018) identify ∼30% fewer numbers of cores in Lupus than what we find over all five Cepheus clouds, e.g., 532 dense cores of which 102 are candidate prestellar cores. For comparison, the Lupus clouds are ∼160 pc from the Sun , less than half the distance to the Cepheus clouds. As with Cepheus, Benedettini et al. (2018) find that almost all Lupus prestellar cores are associated with filaments, though only a third of the Lupus starless cores are so associated. They also find that 90% of Lupus prestellar cores are located in backgrounds of A V ≥ 2, an extinction level much lower than that seen in other Gould Belt clouds (e.g., Aquila; see Könyves et al. 2015). Benedettini et al. (2015) find the median column densities of filaments in the Lupus I, III, and IV clouds to be 1.2-1.9 × 10 21 cm −2 . Relatedly, they find the median line mass of filaments in the Lupus clouds to be ∼3 M pc −1 (see their Figure 15), somewhat lower than the transcritical range of 8-32 M pc −1 for cylinder stability at 10 K (Arzoumanian et al. 2019). Clearly, filaments remain extremely relevant to core (and star) formation, even in instances like Lupus where their median column densities are lower than that range. Given the large degree of correspondence of cores with filaments in Lupus but lower column densities, Benedettini et al. (2015) and Benedettini et al. (2018) suggest that the condition for overdensity needed for filament fragmentation, i.e., within the transcritical range of column densities, may be only reached locally in Lupus filaments. Indeed, observed filaments are not constant column density structures, and can exhibit significant variations along their lengths (e.g., see Roy et al. 2015). Hence, a low average line mass for an entire filament is not a good parameter for determining whether or not stars will form in that filament. Table 5 lists the median and mean column densities of filaments in the Cepheus clouds (see Figure 9). These values were computed from the column density map using the definitions of filaments shown in Figure 9, and reflect all mass traced within those filaments, including cores. The median filament column densities are 1.8-2.7 × 10 21 cm −2 , about a factor of ∼1.5 higher than the range of those in the Lupus clouds. Adopting an average filamentary width of 0.1 pc (Arzoumanian et al. 2011(Arzoumanian et al. , 2019, the median Cepheus filament column densities translate into median line masses of 4-6 M pc −1 . The mean column densities of the Cepheus filaments, however, are 2.2-4.4 × 10 21 cm −2 , which translate into mean line masses of 5-10 M pc −1 , i.e., 25-66% higher than the median line masses, indicating that the line masses of filaments in these clouds are skewed somewhat above the median, unlike in Lupus. This range of line masses is just below to within the range of transcritical masses at 10 K, i.e., M line = 8-32 M pc −1 . In Figure 11 (left), we show the distribution of background column densities for candidate prestellar cores in the Cepheus clouds. The distribution clearly peaks at a column density of ∼2-4 × 10 21 cm −2 , similar to the mean column densities of the filaments and much lower than the threshold A V ≈ 7 column density. Indeed, ∼80% of candidate prestellar cores in Cepheus are found at background column densities of A V ≤ 7. For comparison, Figure 11 (left) also shows the distribution of background column densities for candidate prestellar cores in the Aquila Rift, where only 20% are found at A V ≤ 7 (Könyves et al. 2015). Note that a significant tail at the higher ends of the distributions are also seen, i.e., up to ∼20 × 10 21 cm −2 in Cepheus. If we assume these background column densities are indicative of the original filament environments in which the respective cores formed, then by number ∼56% of Cepheus candidate prestellar cores formed in filaments with line masses below the transcritical range and ∼44% from filaments with line masses within that range. The original filament line masses of course would be larger if the mass we see now in cores was initially distributed more widely within their host filaments. With that possibility in mind, the split is likely on the order of 50-50.
For further comparison, Figure 11 (right) shows the observed differential core formation efficiencies (CF E obs ) of both the Cepheus clouds and Aquila, where CF E obs (A V ) = ∆M cores (A V ) / ∆M cloud (A V ). Here, ∆M cores (A V ) is the mass of the prestellar cores within a given bin of background A V and ∆M cloud (A V ) is the cloud mass estimated from the column density map in the same A V bin. In Aquila, the CF E obs rises from very low values at low A V and levels off at ∼15% at high A V , with a transition around A V ≈ 7 (Könyves et al. 2015). In Cepheus, however, the CF E obs rises much more quickly with A V , and levels off a similar value of ∼15% at lower A V , with a transition at A V ≈ 3. Given the column densities of filaments in the Cepheus clouds, core formation within them is likely proceeding in a manner that bridges the behaviors identified earlier in Lupus and Aquila. Clearly, the strong association between filaments and prestellar cores throughout Cepheus implicates the role of filaments in the core formation process, as elsewhere. In Cepheus filaments with line masses below the transcritical range though, i.e., M line < 8 M pc −1 , cores are likely forming more sporadically and only where conditions have allowed localized filament fragmentation, as seen in Lupus. In cases with line masses within (but at the low end of) the transcritical range, i.e., M line > 8 M pc −1 , however, cores are likely forming more en masse due to widespread filamentary fragmentation, as seen in Aquila. Following Figure 11 (left), roughly half of the cores in Cepheus may have formed in the former way and half in the latter.
Note that for our column density determinations, we use dust opacity values that are standard for the HGBS, i.e., κ ν = 0.144 cm −2 at 250 µm, which assumes a dust-to-gas ratio of 100 and a power-law dependence with wavelength of index β = 2 (see §3.1). Earlier comparisons of HGBS column densities with extinction maps (Benedettini et al. 2015;Könyves et al. 2020, Pezzuto et al. 2020), however, have indicated such Herschel-based column densities may underestimate the true column densities at lower extinctions, e.g., A V < 4. To explore this possibility for Cepheus, we used near-infrared data from 2MASS (Skrutskie et al. 2006) to determine extinction maps of each cloud at 4 FWHM resolution and compared these extinctions to those expected from Herschel data. Specifically, Figure 12 contains a histogram showing the difference between the extinctions from the two datasets for A V < 4. For this histogram, the 18 FHWM resolution Herschel-based column densities were smoothed to the 4 FWHM resolution of the 2MASS extinction maps, regridded to the same 2 × 2 pixels of the 2MASS extinction maps, and converted to extinctions using the common A V -to-H 2 conversion factor of N(H 2 ) = A V × 0.94 × 10 21 from Bohlin et al. (1978). The comparison clearly shows the Herschel data consistently produce lower extinctions than those expected from 2MASS data by ∼0-2 magnitudes, with a peak difference at ∼1 magnitude. Though the intrinsic resolutions of the datasets differ significantly, Figure 12. Histogram showing the numbers of pixels in all five Cepheus clouds with differences between extinctions based on Herschel data and those based on 2MASS data. The Herschel-based column densities were first smoothed to the 4 FWHM resolution of the 2MASS extinction maps, regridded onto the same 2 × 2 pixels of the 2MASS extinction maps, and converted to AV using the conversion factor of Bohlin et al. (1978).
the Herschel-based column density estimates we use as the basis of our discussion here may be systematically lower by ∼1 × 10 21 cm −2 . Accordingly, the line masses of Cepheus filaments may be systematically larger by ∼2 M pc −1 , somewhat increasing the fraction of such filaments in the transcritical line mass range. See Benedettini et al. (2015) and Könyves et al. (2020) for discussions of possible sources of the disparity between extinctions and Herschel-derived column densities.
Even with a modest increase in local column densities, star formation is occurring in Cepheus in relatively low column density environments. Cores have likely formed in relatively low numbers in Cepheus due to its significant number of lower column density filaments, relative to clouds widely containing filaments at higher (i.e., critical) column densities. Namely, with widespread fragmentation being less available in lower column density filaments, relatively fewer cores would be expected to be produced per filament. Though the range of mean column density in the Cepheus clouds is narrow, it is notable that the numbers of candidate and robust prestellar cores in each cloud roughly track monotonically (though less than linearly) with the mean column density of the filaments in each cloud, with the lowest numbers of prestellar cores found in L1241 and the highest in L1251 (see Tables 4 and 5). In addition, the numbers of Cepheus candidate prestellar cores show that ∼half at present have formed in lower column density filaments (see Figure 11 (left)). The low number of prestellar cores likely has had a concomitant effect on the productivity of star formation in Cepheus, and likely accounts for these clouds' relatively modest protostellar yields. Indeed, the relative unavailability of transcritical filaments widely in lower column density clouds may simply explain why such clouds do not form as many cores and stars as clouds with higher column densities do. Figure 13 shows the number distributions of candidate and robust prestellar core mass in Cepheus. The two core mass functions (CMFs) are virtually the same at the high mass end, i.e., M obs ≥ 1 M . Both CMFs peak at ∼0.7 M , but the robust prestellar CMF falls off more quickly to lower masses than the candidate prestellar CMF does, likely because it is more difficult for lower mass cores to satisfy the requirement that a robust prestellar core have α BE ≤ 2 (see §3.3). Indeed, the cores of the robust prestellar CMF are arguably those most likely to collapse imminently to For comparison, the black solid and dash-dotted lines shows the stellar initial mass functions (IMFs) of Chabrier (2005) and Kroupa (2001), respectively, after scaling by a factor of 10 3 . form a new generation of stars. Notably, we find no robust prestellar cores in Cepheus of mass below 0.1 M , but a few candidate prestellar cores of mass < 0.1 M are seen. These scarcities of low-mass prestellar cores are likely related to our expectation that our source extractions are 90% complete to cores of mass ≈ 0.4 M . Note, however, that the peaks of the prestellar CMFs are well above the 90% completeness limit, indicating that they have not been artificially induced due to incompleteness. As found in other clouds studied in the HGBS, the robust prestellar CMF in Cepheus shows an overall lognormal shape. Indeed, a lognormal fit to that CMF, performed with Levenberg-Marquardt leastsquares minimization over bins at and above the 0.4 M mass limit of 90% completeness, has a peak at 0.56 M ± 0.21 M and a width σ = 0.54 ± 0.06 dex. We note that these errors are likely lower limits since we do not consider uncertainties in the masses of individual cores when fitting these CMFs. Figure 13 also shows the candidate and robust prestellar CMFs for the Aquila Rift, as found by Könyves et al. (2015) using a distance 2 of 260 pc. The robust prestellar CMFs of Cepheus and Aquila show two important similarities and one difference. The first similarity is in the widths of lognormal fits to the two robust prestellar CMFs, e.g., 0.54 ± 0.06 dex for Cepheus vs. 0.48 ± 0.02 dex for Aquila. The second similarity is in the peaks of these CMFs, e.g., 0.56 M ± 0.21 M for Cepheus vs. 0.62 M ± 0.04 M for Aquila. The difference, however, is between the heights of the clouds' CMFs, which can be simply attributed to the fact that Cepheus has ∼60% as many robust prestellar cores than Aquila, e.g., 178 vs. 292, respectively. Nevertheless, this comparison reveals that the lognormal fits to the robust prestellar CMFs in both clouds are very similar. Note the 90% completeness core mass limit for Cepheus (0.4 M ) is roughly twice that of Aquila (0.2 M ).

Core Mass Functions
For further comparison, Figure 13 also shows the stellar initial mass functions (IMFs) determined by Kroupa (2001) for single stars and by Chabrier (2005) for multiple systems. These IMFs have been each scaled by a factor of 10 3 so they can be plotted alongside the CMFs. Both IMFs are also lognormal in character, though they peak at much lower masses than the Cepheus and Aquila CMFs. The 0.54 ± 0.06 dex width of Cepheus' robust prestellar CMF is remarkably similar to the 0.55 dex width of the Chabrier IMF of Galactic disk stellar systems (Chabrier 2005), but is narrower than the Kroupa IMF of single stars. Indeed, comparing the peaks of the Cepheus robust prestellar CMF and the Chabrier IMF, an efficiency factor of ≈ 0.3-0.4 is implicated, similar to the ≈ 0.4 estimated from the Aquila CMF by Könyves et al. (2015). (Of course, this picture assumes the efficiency factor is constant over a wide range of mass.) At their higher mass ends, the slopes of both the Cepheus and Aquila CMFs are also consistent with each other within uncertainties, i.e., -1.31 ± 0.01 and -1.35 ± 0.14, respectively. In turn, these values are themselves consistent with the -1.35 slope of the high-mass end of the IMF determined by Salpeter (1955).  Figure 13 shows the CMF compiled from all five Cepheus clouds, including 178 robust prestellar cores. To explore deeper into the makeup of the lognormal CMF, it is instructive to examine such CMFs drawn from the individual Cepheus clouds. Accordingly, Figure 14 shows the robust prestellar CMFs from each Cepheus cloud, assembled from populations of 14 (L1241) to 53 (L1251) prestellar cores each (see Table 4). (Note that the CMFs in Figure 13 have been shifted vertically by multiples of orders of magnitude so their shapes can be more easily compared.) Some variation between the shapes of the individual cloud CMFs is seen. The CMFs of L1172 and L1251 appear the most lognormal-like, but those of L1228 and L1241 look remarkably flat. With five central bins of similar height, the peak of L1157's CMF is hard to define and so this CMF seems somewhere in between a lognormal and flat distribution. Of course, the smaller numbers of cores per bin in each cloud's CMFs make it hard to tell by eye if the distributions differ significantly.
To provide a quantitative sense of the morphologies of the robust prestellar CMFs of each cloud, we fit lognormals to each CMF at and above 0.4 M , the 90% completeness core mass limit. Table 6 shows the results of the peak mass and width of the lognormal fit to each cloud's robust prestellar CMF with uncertainties. The results for the combined robust prestellar CMF for all five Cepheus clouds are also listed. A lognormal fit is not possible for L1241, especially given the 0.4 M lower limit restricting the sample available to fit. Also, the lognormal fit for L1228 is rather poor, as evidenced by the large uncertainties in peak mass and width listed in Table 6. Meanwhile, the peak masses of the robust prestellar CMFs from the three clouds with reasonable lognormal fits show some possible variation but are largely consistent within errors with 0.6 M , a little higher but within errors of the peak mass of the combined CMF. (The peak mass of the combined CMF is slightly lower than the peak masses of the CMFs of L1157, L1172, and L1251 due to L1228 and L1241 adding mostly lower mass cores to the ensemble.) Furthermore, the widths of the three CMFs vary between 0.41 dex and 0.58 dex, but are largely consistent within 1 σ of the 0.54 dex width of the combined CMF and the 0.55 dex width of the Chabrier system IMF.
A visual comparison of the individual column density and temperature maps of the Cepheus clouds (see Figures  1-5, 6) shows apparent differences between them, with their characters ranging from more diffuse (L1241) to highly filamentary (L1251) to cluster dominated (L1172). To place these differences in context, recall that the Cepheus clouds are distributed quite widely on the sky. Though they share a common name, the Cepheus clouds are more of a loose association rather than a complex. Hence, it is likely that each is at its own stage and ability in producing stars, one related to its total mass, its fraction of dense gas, its immediate physical environment, and time. With these differences, however, it is perhaps not surprising that the individual cloud CMFs shown in Figure 14 differ in appearance, though the small sample sizes make it difficult to be sure. Nevertheless, the Cepheus clouds are broadly similar in terms of their column density and temperature distributions (see Figure 7), which may explain the broad similarity of the lognormal fits to the CMFs of at least three of the clouds. The combination of all five cloud CMFs, however, into a single CMF that is similar in peak mass and width to those seen elsewhere (e.g., in Aquila) is a remarkable demonstration of how the lognormal core mass function arises out of a wide range of initial conditions.
The common peak and width of the robust prestellar CMFs of various nearby clouds may speak to commonalities in how their cores (and stars) formed. Namely, filaments are seen to be central to developing prestellar cores in clouds. Such filaments likely have a turbulent origin, as bulk motions within clouds drive gas together to form sheets and filaments. Indeed, sheets likely fragment very easily into filaments; see André et al. (2014). Given their turbulent origins, the filaments themselves likely retain density perturbations along their lengths consistent with that turbulence. For example, Roy et al. (2015) noted a potential link between the density fluctuations seeded by turbulence in filaments and the CMF. Hence, the similar peaks and widths of robust prestellar CMFs seen in different clouds could be itself an expression of the common influence of turbulence forming filaments and seeding their density fluctuations. As a result, the system IMF arises from molecular clouds where multiple lognormal populations of robust prestellar cores inefficiently produce stars.
More star-forming clouds than just Cepheus and Aquila need to be examined to see if the morphological differences and similarities of CMFs noted here are found elsewhere, e.g., see Fiorellino et al. (2020, submitted). Furthermore, it is important to retain the perspective that the Cepheus clouds (and even Aquila), with relatively modest star formation activity, are relatively minor contributors to the total amount of star formation in the Galaxy. Indeed, the IMF would be set by the much larger engines of star formation in the Galaxy, i.e., Giant Molecular Clouds. Therefore, future detailed examinations of the CMFs in those clouds are also necessary.

SUMMARY AND CONCLUSIONS
In this paper, we examined the SPIRE and PACS observations of five Cepheus Flare clouds, L1157, L1172, L1228, L1241, and L1251, that were obtained as part of the Herschel Gould Belt Survey key project. We summarize our main findings below.
1. The Cepheus clouds are relatively low mass clouds of the Gould Belt. Given the column densities obtained from the Herschel data, we estimate their masses to be 800 M (L1157) to 2300 M (L1241). Like other Gould Belt clouds observed by Herschel, the Cepheus clouds exhibit significant filamentary substructure. The character of the substructure does appear to vary from cloud to cloud, from relatively diffuse (L1241) to more pronounced (L1251) to cluster dominated (L1172).
2. The column density probability density functions (PDFs) obtained from the Herschel observations are generally similar, peaking around 1 × 10 21 cm −2 with a powerlaw-like decline to higher column densities. The column density PDF of L1241, however, is noticeably narrower than the others. The temperature PDFs of all five clouds show similar peaks around 14 K. Those of L1157, L1228, and L1251 have similar widths while those of L1241 and L1172 are narrower and wider, respectively. These differences are likely due to the absence and presence of significant internal heating sources (i.e,. protostars) in these latter clouds, respectively 3. Using the getsources automated source identification algorithm, we identify 832 dense cores in the Herschel 160-500 µm data. Of the dense cores, 504 are classified as starless (i.e., gravitationally unbound) and 303 are classified as prestellar core candidates from their locations in a mass vs. size diagram. A subset of 178 cores from the latter are considered "robust" prestellar cores. The remaining 25 dense cores were found to be coincident with sources extracted independently from the 70 µm data alone, and are classified as protostellar cores.
4. The getsources algorithm also identified filamentary structure in each Cepheus cloud. With some variation between clouds, ∼75% of starless cores and ∼80% of prestellar cores are found to be coincident with filaments. L1251 has the highest percentages of cores coinicident with filaments (80-100%) while L1241 has the lowest (40-60%).
5. The distribution of the background column densities of the population of prestellar cores in the Cepheus clouds peaks at 2-4 × 10 21 cm −2 , but has a small tail leading up to background column densities of ∼20 × 10 21 cm −2 . Approximately half of Cepheus' candidate prestellar cores appear to have formed in filaments with line masses within but at the lower end of the "transcritical" range at T = 10 K, i.e., M line = 8-32 M pc −1 and half in filaments with line masses lower than that range. (Further investigation of the opacity values to use at lower extinctions is needed.) In the former case, greater numbers of cores are expected from widespread filament fragmentation while fewer are expected in the latter due to fragmentation only occurring where localized conditions warrant. As a result, Cepheus is forming fewer cores than higher column density clouds like Aquila.
6. The mass function of robust prestellar cores (CMF) in all five Cepheus clouds combined is lognormal in shape, with a peak mass of 0.56 M and a width of 0.54 dex. In comparison, the Aquila Rift CMF has a lognormal shape as well, with a similar peak mass of 0.62 M and a similar width of 0.48 dex. The Cepheus CMF is consistent with the system IMF of Chabrier (2005), assuming a mass-independent efficiency factor = 0.3-0.4. 7. The robust prestellar CMFs of L1157, L1172, and L1251 can be also fit by lognormals with peak masses consistent within errors with ∼0.6 M and widths broadly consistent with the 0.55 dex width of the system IMF of Chabrier (2005). The flatter CMFs of L1228 and L1241, however, were unable to be reliably fit with lognormals.
Though filamentary substructure is ubiquitous in the Cepheus clouds, this substructure has mean column densities largely below or at the low end of the range of "transcritical" values associated with the radial cylindrical fragmentation mechanism enabling core formation in filaments. Core formation and evolution in Cepheus appears to bridge that observed in lower and higher column density clouds, such as Lupus and Aquila, respectively. As a result, both localized fragmentation where conditions permit and more widespread core fragmentation in transcritical filaments are both occurring, producing cores of seemingly equal number. The CMFs of the individual Cepheus clouds reflect their current core formation potential but in aggregate they reflect a more generalized distribution of prestellar core origins by encompassing a range of environments. Indeed, the common width of the aggregate Cepheus CMF and the Aquila CMF of ∼0.5 dex, hints at a common origin, perhaps due to seeding of the fluctuations that evolve into cores by turbulence. Assuming a mass-independent factor for inefficiently converting core mass into stars, the system IMF may originate from CMFs of similar width from numerous clouds.

ACKNOWLEDGMENTS
We thank the input of an anonymous referee whose comments greatly improved this paper. J.D.  Figures 15 to 19, we provide the Herschel images of L1157, L1172, L1228, L1241, and L1251 at 70 µm, 160 µm, 250 µm, 350 µm, and 500 µm, respectively, at their native resolutions and without the respective Planck offsets added.

B. RELIABILITY CRITERIA FOR GETSOURCES EXTRACTIONS
In this Appendix, we list the criteria applied to the list of sources detected by the getsources algorithm to select reliable extractions. These criteria are the same as those applied by other HGBS teams to extract reliable sources from Herschel data of other nearby molecular clouds (e.g., Könyves et al. 2015).
The criteria applied to the list of dense cores are: • Column density detection significance greater than 5 in the high-resolution column density map (Sig NH 2 > 5); • Global detection significance over all wavelengths greater than 10; • Global goodness > 1, where goodness is an output quality parameter of getsources, combining global SNR and source reliability; • Column density measurement SNR > 1 in the high-resolution column density map; • Monochromatic detection significance greater than 5 (Sig λ > 5) in at least two bands between 160 µm and 500 µm; and • Flux measurement with SNR > 1 in at least one band between 160 µm and 500 µm for which the monochromatic detection significance is simultaneously greater than 5.
The criteria applied to the list of YSOs/protostars are: • Monochromatic detection significance greater than 5 in the 70 µm band (Sig 070 > 5); • Positive peak and integrated flux densities at 70 µm (S peak 070 > 0 and S tot 070 > 0); • Global goodness greater than or equal to 1; • Flux measurement with SNR > 1.5 in the 70 µm band; • FWHM source size at 70 µm smaller than 1.6 times the 70 µm beam size (F W HM 070 < 1.6 × 8. 4 = 13. 44); and • Estimated source elongation < 1.30 at 70 µm, where source elongation is defined as the ratio of the major and minor FWHM sizes (F W HM a 070 / F W HM b 070 < 1.30).

C. CATALOGUES OF OBSERVED AND DERIVED PHYSICAL PROPERTIES OF CEPHEUS DENSE CORES
A catalogue of the observed properties of the Cepheus dense cores can be found in online material. Table C1 describes the entries in this catalogue by column, with associated units and labels following the HGBS definitions provided by Könyves et al. (2015) or comparably used in the online material header. For each dense core, the catalogue includes the host cloud identifier, i.e., its name (Col. 1), the object running number for that cloud (Col. 2), its HGBS source name (3), and its J2000 position (4-9). The HGBS source name is defined with the prefix "HGBS J" directly followed by a tag given by the sexagesimal coordinates of the J2000 position.
For each of the five Herschel wavelengths, the catalogue includes the detection significance (Cols. 10, 20, 30, 40, and 50, respectively). The detection significance is given a special value of 0.0 if the core is not visible in clean single scales. In addition, the catalogue lists for each wavelength the peak intensity and error (Cols. 11 ± 12, 21 ± 22, 31 ± 32, 41 ± 42, and 51 ± 52, respectively). Next, the catalogue lists for each wavelength the contrast over the local background, i.e., the ratio of the background-subtracted peak intensity to the local background intensity (Cols. 13,23,33,43,and 53,respectively). The catalogue then lists the peak flux density at 70 µm, 160 µm, 250 µm, and 350 µm in a 36. 3 beam, i.e., the resolution of the Herschel images at 500 µm (Cols. 14, 24, 34, and 44, respectively) and the total integrated flux and error at each wavelength (Cols. 15 ± 16, 25 ± 26, 35 ± 36, 45 ± 46, and 54 ± 55). The catalogue also lists for each object its major and minor FWHM diameters (Cols. 17 & 18,27 & 28,37 & 38,47 & 48,and 56 & 57,respectively) and the position angle of its major axis east of north (Cols. 19,29,39,49,and 58,respectively), where a value of "-1" indicates that no size measurement was possible. The catalogue also provides for each object its respective detection significance in the high-resolution column density map (Col. 59), the peak H 2 column density at 18. 2 resolution, i.e., the resolution of the Herschel images at 250 µm (60), the column density contrast over the background (61), the peak H 2 column density in a 36. 3 beam, i.e., the resolution of the Herschel images at 500 µm (62), the column density of the local background as determined by getsources (63), the major and minor FWHM diameters and the position angle of the major axis east of north in the high-resolution column density map (64-66), and the number of Herschel bands at which the core has been significantly identified, i.e., Sig λ > 5 (67).
In addition, the catalogue lists (Col. 68) a flag indicating if the core was also identified by CSAR, i.e., "2" if the core has a counterpart also found by CSAR within 6 , "1" if no close CSAR counterpart exists but the peak position of a CSAR source is found within the FHWM contour of the core in the high-resolution column density map, or "0" otherwise. Furthermore, the catalogue lists (Col. 69) the core type, i.e., either starless, (candidate) prestellar, or protostellar. The catalogue also lists the closest SIMBAD, NED, and Spitzer counterparts (see Kirk et al. 2009), if any, within 6 of the Herschel peak position (Cols. 70,71,and 72,respectively). Figures 20 and 21 show example thumbnail images of emission at each wavelength and local column density for a robust prestellar core and a protostellar core, respectively. The full suite of thumbnail images for each dense core is also available as online material. , 500 µm (lower center) and in the high-resolution column density map (lower right). Green ellipses show the extents of the object at each wavelength determined by getsources. Based on its mass and size, this object is estimated to be a robust prestellar core.
A catalogue of the derived physical properties of each Cepheus dense core can be found also in online material. Table C2 describes the entries in this catalogue by column, with associated units and labels again following the HGBS definitions provided by Könyves et al. (2015) or comparably used in the online material header. For each dense core, the catalogue includes its host cloud identifier (Col. 1), its object running number (2), its HGBS source name (3), and its J2000 coordinates (4-9). In addition, the catalogue lists each core's deconvolved and observed core radii, each obtained from the geometrical average of the core's major and minor axis FWHMs, as measured in the high-resolution column density map, after deconvolution from the 18. 2 HPBW of the map and before deconvolution, respectively (10 & 11). As noted by Könyves et al. (2015), these values provide estimates of the outer radius of the core when it can be approximately described by a Gaussian distribution, as is the case for a Bonnor-Ebert spheroid. Next, the catalogue lists for each core its estimated mass and the associated 1 σ uncertainty (12 & 13) and its dust temperature and the associated 1 σ uncertainty (14 & 15), following standard HGBS practices. (Note that the 1 σ uncertainties include statistical errors including calibration uncertainties but not uncertainties in dust opacity.) Next, the catalogue lists for each core its peak column density at 36. 3 resolution, as derived from a greybody SED fit to the core peak flux densities measured at a common 36. 3 resolution at all wavelengths (16). Furthermore, the catalogue lists the average column density measured before and after deconvolution, equal to (M core / πR 2 core )(1/µm H ) where R core is the core radius either before or after deconvolution, respectively, µ = 2.8, and m H is the mass of the hydrogen atom (17 & 18). The catalogue then includes the beam-averaged peak volume density of each core at 36. 3 resolution (19), derived from the peak column density and assuming a Gaussian spherical distribution, i.e., n peak H2 = ( 4 ln2/π)(N peak H2 /F W HM 500 ). In addition, the catalogue lists the average volume density measured before and after deconvolution, equal to (M core /(4/3)πR 3 core )(1/µm H ), where as before R core is the core radius either before or after deconvolution, respectively (20 & 21). Finally, the catalogue lists the Bonnor-Ebert mass ratio α BE = M BE,crit /M core (22), the core type (either starless, (candidate) prestellar, or protostellar; 23), and comments (24). For the latter, if an greybody SED was unable to be fit to the core flux densities, an entry of "no SED fit" is given.    Table C1 is published in its entirety in the electronic edition of the Astrophysical Journal.