DEEP NEAR-INFRARED SURVEY OF THE PIPE NEBULA. II. DATA, METHODS, AND DUST EXTINCTION MAPS

The main observations of the survey were made with the ISAAC and the Son of ISAAC (SOFI) near-infrared imagers, mounted, respectively, at the UT3 8.2 m unit of the VLT array at Cerro Paranal and the 3.5 m NTT at La Silla, both parts of the ESO in Chile. The two observing runs were completed with uniformly good weather in the summer months of 2001 and 2002. Two fields, FeSt 1-457 and B68, were observed previously in 2000 under similar conditions and requirements. All the data are currently available at the ESO archives. The imager SOFI at the NTT 3.5 m telescope presents a field of view (FOV) of 5' × 5' with plate scale of 0.288 arcsecpixel⁻¹, almost seven times the angular resolution of 2MASS, and higher sensitivity: achieved limits are estimated to be about 4–5 mag deeper than 2MASS in each band. Such characteristics are enough to resolve the densely crowded Galactic Bulge field in the background of the Pipe Nebula and to penetrate in regions with up to about 50 mag of visual extinction. The FOV of SOFI is ample enough to allow to completely contain some of the larger dense regions in the Pipe Nebula (R ∼ 0.1–0.15 pc), with the exception of the central core in Barnard 59, which nearly doubles the size of the FOV. A total of 55 fields in the cloud were successfully observed in H and K_s, with a few also observed in J. In addition, a control field located approximately 1° west of Barnard 59 was observed with similar conditions in order to determine the intrinsic background field colors, essential to determine absolute dust extinction values. The ISAAC observations were intended to fully resolve the centers of the most dense and obscured regions. A total of seven fields were observed with ISAAC during the same observing seasons in H and K_s at a resolution of 0.144 arcsecpixel⁻¹ with an FOV a quarter of the size of that of SOFI. Interestingly, the ISAAC fields observed in the center of Barnard 59 were capable of detecting only a handful of the individual sources in and behind the core. This shows that extinction values above A_V = 60 mag are close to the limit of the penetrating power in the near-infrared even for an 8 m class telescope. As mentioned before, space-based mid-infrared observations were required to resolve more of the highly obscured background sources in B59 (Brooke et al. 2007; Román-Zúñiga et al. 2007; Paper I).

The Centro Astronómico Hispano Alemán (CAHA) 3.5 m observations were done with the OMEGA 2000 camera, which has a wide FOV of 15'. A total of 21 fields, complementary to the ESO survey, were observed during 2007 June and 2008 June with acceptable weather. The fields observed with the CAHA 3.5 m telescope were selected to cover the surrounding areas in the densest region near the "Pipe Molecular Ring" (Muench et al. 2007) in the central part of the cloud, and also to obtain fresh data in a number of fields at the westernmost regions of the cloud (see Figure 1). The resolution of OMEGA 2000 at the 3.5 m telescope is 0.45 arcsecpixel⁻¹ and the sensitivity is expected to be equivalent to that of SOFI. However, even with excellent weather and instrumental conditions at Calar Alto, the low inclination of the Pipe Nebula at the latitude of the observatory resulted in large seeing values (16 ±  02 on average) and some internal reflection effects that affected the colors of sources near the edges of the detector. See also Section 3.1.

Data from the three survey groups were reduced with modified versions of the FLAMINGOS near-infrared reduction and photometry/astrometry pipelines, which are built in the standard IRAF Command Language environment.

One pipeline (see Román-Zúñiga 2006) processes all raw frames by subtracting darks and dividing by flat fields, improving signal-to-noise ratios by means of a two pass sky subtraction method, and combining reduced frames with an optimized centroid offset calculation.

For the ESO survey data, slight modifications were implemented to the reduction pipeline in order to account for some—well-documented—instrumental biases: for the SOFI-NTT data, we took into account corrections for instrumental crosstalk using the IRAF task provided in the ESO SOFI Web sites. Nonlinearity corrections were applied by using the coefficients listed by Tinney et al. (2003). Finally, we used the dome flats and illumination correction field sets provided by ESO to avoid well-known "shade" effects often encountered with sky and super-sky flat fields. In the case of the ISAAC-NTT fields, master darks, twilight flats, and illumination field frames were created with the aid of the ISAAC pipelines provided in the ESO Web sites, previous to the batch reduction with our pipelines. For the Calar Alto data, the reduction was performed using our pipeline in standard mode. We used dark frames and dome flats obtained within 48 hr of each observation. No other specific instrumental corrections were applied.

The final combined product images were then analyzed by a second pipeline (see Levine 2006), which identifies all possible sources from a given field using the SExtractor algorithm (Bertin & Arnouts 1996), applies PSF photometry, calibrates observed magnitudes to a constant zero point, and finds an accurate astrometric solution. Both photometry and astrometry of SOFI and OMEGA 2000 data products were calibrated with respect to 2MASS catalogs retrieved from the All Sky Data Release databases. ISAAC calibrations were obtained by bootstrapping to the calibrated SOFI data. The final photometry catalogs, containing either J, H, and K_s, or H and K_s photometry were prepared by a routine that makes use of the routine CCXYMATCH. In the case of overlapping fields and fields with observations done in more than one instrument, the catalogs were put together with our own matching routines, designed to list preferentially a higher quality observation (e.g., ISAAC) over a lower quality one in the overlapping areas. We prepared joint catalogs to construct multiple-field extinction maps for a limited number of cases. In the cases of FeSt 1-457, and SOFI fields 29, 31, and 45, we used hybrid SOFI+ISAAC catalogs.

The maps were constructed with the Near-infrared Color Excess Revised (NICER) technique (Lombardi & Alves 2001). NICER is an optimized multi-band technique to estimate extinction from the infrared excess calculated from observations at three different bands—in our case J, H, and K_s, which allow to use two independent colors. Choosing J − H and H − K_s, the estimator of the extinction, A_V is of the form

$$\begin{equation} A_V(s) = a+ b_1[E(J-H)]+b_2[E(H-K_s)], \end{equation} \tag{ 1 }$$

where the coefficients, a, b₁, and b₂ can be determined by assuming that A_V is an unbiased estimator and that it has minimum variance. The first condition is expressed as b1/C₁ + b2/C₂ = 1, where, in our case, the coefficients C₁ = 9.35 and C₂ = 16.23 are from the reddening law of Román-Zúñiga et al. (2007). The second condition is expressed as a + b₁(J − H)₀ + b₂(H − K_s)₀ = 0, where (J − H)₀ and (H − K)₀ are the intrinsic values of the colors, estimated from an off-cloud control field with negligible extinction (see Figure 1 and Table 1). The second condition is granted through the minimization of the variance of A_V, expressed in terms of the scatter of the intrinsic colors and the photometric errors (please see LA01 for details). We estimated the intrinsic values of background sources in the control field as the median value along a fiducial line represented by the average colors in bins of equal size in K_s, for K_s < 17.0 mag. The intrinsic colors are practically constant across the control field area, with scatter comparable to or smaller than the typical color photometric uncertainty. This is expected, because the field population toward the Galactic Bulge is mostly composed of red giant stars, which have a very small intrinsic color dispersion in the near-infrared. However, the source catalogs also have to be restricted to reject any stars with intrinsic color excess, like in the case of OH IR stars, as discussed by LAL06. We selected infrared excess stars in two ways: for sources having J, H, and K photometry we selected out those falling to the right of the line H − K_s = 1.692(J − H). For sources not having a J-band observation we cannot guarantee that they will not have an intrinsic excess, especially if H − K_s > 1. However those cases should be rare in background giant sources. For this reason, we limited our catalogs to stars with K_s > 10.0; this restriction removes contamination from foreground stars and most contamination from OH-IR stars (see LAL06).

To make a map, the extinction measurements for individual sources have to be spatially smoothed. In our case, we used a Gaussian filter and Nyquist sampling. At each position (line of sight) in the map, each star falling within the beam is given a weight calculated from a Gaussian function, and the inverse of the variance squared. Then, the value of A_V at the map position is calculated as the weighted median of all possible values (please see LA01, Section 3.2 for details). The uncertainty in the measurement, $\sigma _{A_V}$, which determines the noise per pixel, was calculated as $\sqrt{\sigma ^2(A_V)/N}$.

We do not have ESO J-band observations available for a majority of the ESO fields. Therefore, for many ESO sources, extinction was determined from only one color, H − K_s, just as in the original color excess technique (NICE; Lada et al. 1994). The difference is that using the NICER method we are able to use the error associated with a measurement to keep track of its corresponding weight. For example, by setting the photometric uncertainty of stars with no J measurement at a very large value (99.999) in that band, NICER automatically discards that J − H measurement and either accepts or rejects a value of A_V for a star given the weight associated with the value of its H − K_s color alone.

The maps we present in this paper are constructed with a Gaussian filter with an FWHM of 20'' and Nyquist sampling (i.e., pixels on the map have a width of 10''). This represents a resolution three times higher than the one achieved in the large-scale map of LAL06. This is approximately equal to 1/10 of the median Jeans length across the cloud (0.2 pc; RLA09).

In the case of the CAHA observations we had three bands available, H, J, and K_s, thus two colors c₁ = H − K_s, c₂ = J − K_s, and a pixel sampling not too different from SOFI. However, the Pipe Nebula is a target that does not reach a very high elevation at Calar Alto, and the inclination of the telescope was large enough to cause internal reflections in the camera. These reflections affected the colors of stars near the corners of the frames. We decided to mask out the frame corners by using sources within a circular area with a radius smaller to the diagonal length of the field. However, because each OMEGA 2000 field contained an average of 3.5 × 10⁴ detected sources, we were still able to obtain uniformly covered maps with a very acceptable number of 15–60 sources per pixel and an average completeness limit of K_s = 16.75 after applying the restrictions, which was enough to resolve structures in all regions of the Pipe (with the exception of B59) at the nominal resolution of 20''.

We constructed individual dust extinction maps for each of the SOFI and CAHA fields observed. In the case of the few deep ISAAC fields observed, we merged the catalogs with the corresponding ones from SOFI before proceeding to the map construction following the procedure described below. The individual ESO and CAHA maps constitute a high-resolution dust extinction map atlas of the Pipe Nebula which we present as a separate document, accessible in the electronic (online) version of the paper. The dynamical range of the new maps covers column densities between 10²¹ and 10²³ cm⁻².

We merged overlapping ISAAC, SOFI, and CAHA catalogs to form larger pieces which were subsequently merged onto five large "bed" catalogs that defined the main regions of the cloud. This way, we constructed five large-scale maps comprising the main regions of the Pipe—namely "Barnard 59," "The Stem," "The Shank," "The Bowl," and "The Smoke." A diagram showing the extent of each region is presented in Figure 2. The five large-scale extinction maps are shown in Figures 3–7. In Table 1, we list the limits defining the five areas, the fields included in each one of the maps. The hybrid catalogs were constructed by joining the photometry lists from the various surveys in a progressive sequence: ISAAC catalogs were merged with the corresponding SOFI catalogs by using a matching algorithm that preferentially listed ISAAC over SOFI detections. For those matches with a SOFI J-band detection, we used that value to replace the null J-band value from ISAAC (e.g., FeSt 1-457 field); this resulted in a small but useful reduction of the scatter as a function of extinction ($\sigma _{A_V}$ versus A_V). Positional matching between NTT and VLT observations was calculated within a tolerance radius of 024, i.e., twice the average positional uncertainty of the NTT astrometric solutions. Then, when possible, we merged coincident ESO and CAHA fields using a slightly larger tolerance radius of 03 (to compensate for the slightly lower resolution of the OMEGA 2000 respect to SOFI). A final "high resolution" catalog was constructed by putting together all ESO-CAHA merges, and merging it to a 2MASS "bed" catalog obtained from the All Sky Data Release. The 2MASS "bed" catalogs define the extent of each map, and excluded sources with photometric flags "U" and "X" which indicate upper limits and defective observations, respectively. Positional matching between the ESO-CAHA catalogs and the 2MASS bed catalogs was determined using a tolerance radius of 036 (three times the average uncertainty of the ESO-NTT astrometric solutions), and we rejected the 2MASS matching sources except in the cases where an ESO or CAHA source was saturated. The infrared excess restriction applied to the 2MASS sources is the same as the one described in Section 3.1.

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We determined that a small color correction had to be applied to correct for the differences between the SOFI/ISAAC, OMEGA-2000, and 2MASS passbands. This correction was determined by plotting the differences Δ(H − K_s) = (H − K_s) − (H − K_s)_2MASS for ESO or CAHA versus (J − H)_2MASS and applying a linear least-squares fit. The slopes did not vary much between ESO and CAHA fields. We estimated an average correction of Δ(H − K_s) = −0.08 + 0.07(J − H)_2MASS and applied it directly to the individual H − K_s colors of sources entering the NICER calculations.

The maps of Figures 3–7 show that there is abundant low density material between A_V = 2 ± 1 and A_V = 6 ± 1 mag with a rough filamentary morphology. This is probably tracing a more diffuse medium, as most significant extinction peaks appear to be embedded in these relatively large, low density structures. The correct detection and delimitation of individual features is complicated by this aspect, because we need to be careful at defining clearly the boundary of a feature projected against an extended emission structure. In some cases, two or more peaks are located close to each other and are projected toward the same filament or wisp of the cloud, making it difficult to determine their individual boundaries. Because we estimate sizes and masses of features from those boundaries, crowding and overlapping may ultimately play a crucial role in the correct determination of a dense core mass function for the cloud, although in the Pipe Nebula, crowding is a relatively small effect (Kainulainen et al. 2009) due to the proximity and particular layout the cloud. In the previous studies of extinction maps of the Pipe Nebula, the detection of individual extinction peaks was optimized in two steps: (1) filtering the local background structures and (2) extracting individual features by means of a two-dimensional peak finding algorithm. We also follow these steps in our analysis, as described below.

4.1.1. Filtering and Detection

4.1.2. Properties of Extinction Peaks

For each of the extinction peaks identified, CLF2D defines an optimized boundary. The size of a feature is defined as the equivalent radius of the area within the boundary. Mass was estimated by summing the background corrected total extinction in pixels within the boundary. The conversion to mass, assuming a standard value for the gas to dust ratio N_H/A_V = 2.0 × 10²¹ cm⁻², is given as

$$\begin{equation} \frac{M_{\rm peak}}{(M_\odot)} = 1.28\times 10^{-10}\left(\frac{\theta }{\mbox{$^{\prime \prime }$}}\right)^2 \left(\frac{D_{\rm cloud}}{\mathrm{pc}}\right)^2 \sum _{i=1}^{N}{(A_V)_i}\ M_\odot, \end{equation} \tag{ 2 }$$

where ∑^N_{i = 1}(A_V)_i adds the contribution of N pixels within the feature boundary in the wavelet-filtered map, θ is the beam size, and D_cloud is the distance to the cloud. In our case, D = 130 pc and θ = 20''. Using the values for mass and equivalent radii, we made estimates of the average density of the peaks, $\bar{n}=3M/4\pi \mu m_{\rm H}R^3$. Uncertainties were calculated by adding random noise to the each of the five wavelet-filtered maps (this was done following the $\sigma _{A_V}\mbox{ versus }A_V$ behavior described in Section 4.1.1), and then running CLF2D, to register the differences in mass and radius for all peaks that had a matched detection with the original map. We repeated this process 25 times, and then we calculated the mean deviation from the original values. The resultant uncertainties are 11.7%, 12.5%, and 23.2% in mass, radius, and density, respectively.

Assuming a gas temperature of 10 K (consistent with estimates of T_K from pointed observations of ammonia emission by RLA09) we calculated the local Jeans length, L_J for each feature as

$$\begin{equation} \frac{L_J}{\mathrm{\ (pc)}} = 0.2\left(\frac{T}{10 \ \mathrm{K}}\right)^{1/2} \left(\frac{\bar{n}}{10^4\mathrm{\ cm}^{-3}}\right)^{-1/2}. \end{equation} \tag{ 3 }$$

4.1.3. Resolving Higher Column Density Structures

The depth and resolution of the 2MASS survey allowed LAL06 to produce a map with reliable column density measurements up to a limit of A_V ≈ 25 mag. One of the main goals of our high-resolution survey is to improve on this limit. Our high-resolution maps now resolve the densest parts of the cloud and increase the previous peak values by a factor of up to four. It is important to assess how significant are these changes for the physical characterization of the prestellar structure.

In order to assess this effect, we applied a simple unsharp masking test to the large-scale maps. This technique is frequently used in astronomical imaging to enhance or to determine the significance of detected features (e.g., Fabian et al. 2006; Moriarty-Schieven et al. 2006). For our maps, the masking is done in the following manner: first, we convolved the maps with a 60'' Gaussian beam, i.e., three times larger than the nominal resolution. These smoothed images are taken as being local equivalents to the map of LAL06. Then we subtracted these smoothed from the original images, resulting in frames with values fluctuating mostly around zero (with both positive and negative values), except on the centers of the denser peaks, where the residuals are relatively large and positive. We determined the mass of the residual and of the core in the 60'' convolved maps using the formulation described in Section 4.1.2. The results are summarized in Figure 8, where we plot the ratio of the masses for positionally coincident features in the residual and the low-resolution image. The ratios of the masses show clearly how the residual pixels only account, in most cases for a 5%–30% of the total mass of the feature, with the larger differences being for the less massive peaks. Thus, it is unlikely that masses of peaks in the 2MASS map of Alves et al. were underestimated significantly because only the centers of the densest peaks were not resolved completely. Likewise, we should not expect to find a significant number of new high extinction peaks on the high-resolution maps, as the low extinction parts of these peaks should have been easily detected in the 2MASS map.

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A total of 90 individual extinction peaks in our list would fall below RLA09 detection threshold. This is equivalent to saying that about 37% of the substructure we found in the new maps is below the minimum area threshold used by RLA09 in their analysis of the 2MASS map. This represents a significant increase in the detection of small-scale structures. We compared the diameters and separations for our list of extinction peaks. The comparison is summarized in Figure 9, where we used astronomical units as well as pixel width (10'') as units of measurement. The peak-to-peak separations and peak diameters have median values equivalent to 1.6and2.3 × 10⁴ AU (0.08 pc and 0.11 pc), respectively, which are near half of the median Jeans length at T = 10 K (3.7 × 10⁴ AU or 0.18 ± 0.05 pc). Note that the distribution of peak separations decreases sharply below the median value, indicating that we do not detect a significant number of extinction peaks below that limit. We come to this point later in Sections 5.2 and 6. The distribution of peak diameters shows that a majority of the extinction peaks appear to have sub-Jeans sizes, but it also shows that in most cases they are significant with respect to the minimum detection diameter of 8.3 × 10³ AU (0.04 pc). This confirms that at the resolution of our maps, we are measuring structures that have dimensions below the typical scale of thermal fragmentation for a significant number of cases. Moreover, in Figure 9 we also show, for comparison, the detection threshold for the analysis of the 2MASS map, showing that the high resolution of our maps resulted in an effective increase in the detection of small-scale structure, which was not resolved before.

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In Figure 10, we present the mass distribution for the extinction peaks. The light colored solid curve is the probability density function constructed with a Gaussian kernel with a width of 0.2 in the log mass scale. The broken, dark colored line is the best fit for the trapezium IMF of Muench et al. (2002) scaled by a constant (horizontal) factor in mass. The shape of the mass distribution shows a clear departure from a single power law at high mass. This break is above the mass completeness limit of 0.2 M_☉ (see Appendix B). Provided that each extinction peak would end up forming one star (an unlikely scenario, see Sections 5.3 and 6), the mass scaling factor with respect to the Trapezium IMF is 1.6 ± 0.1, which, following the reasoning of Alves et al. (2007), translates into a star-forming efficiency of 0.63 ± 0.04.

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In the top panel of Figure 11, we show the mass versus radius relationship considering all extinction peaks detected. The least-squares fit to the data points shows that we agree well with the power-law exponent of 2.6 found by Lada et al. (2008). The bottom panel shows the distribution of mean densities; the mean value for the extinction peaks is 1.1 × 10⁴ cm⁻³, in good agreement with Lada et al. (2008).

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We calculated the mean surface density of companions (MSDC), Σ_θ, for extinction peaks. The MSDC have been used extensively to discuss the spatial distribution of young stars in a number of regions, particularly in Taurus (Gómez et al. 1993; Larson 1995; Simon 1997; Hartmann 2002; Kraus & Hillenbrand 2008). Following Simon (1997), we determined, for a list of N_peaks peaks, the projected distances or separations, θ, from each to every other feature. Then we organized them in bins (annuli) of 0.2 dex in the range −2.0 < log θ ° < 2.0. Then Σ_θ was calculated by dividing the number of separations in each bin, N_p(θ), by the area of each annulus, and then normalizing by the total number of features. Another way to calculate Σ_θ is to use the two-point correlation function (TPCF), W(θ) (Peebles 1973; Hewett 1982), which compares the measured Σ_θ with that for a random, uniform distribution of points in the plane. We calculated

$$\begin{equation} W(\theta)=\frac{N_p(\theta)}{N_r(\theta)} - 1, \end{equation} \tag{ 4 }$$

where N_r(θ) is the number of separations per bin for a collection of points distributed at random positions over the same area as the survey, A_map. In our case, A_map was chosen as a rectangle of 8 × 6(°)² which encloses all the regions in our maps in the R.A.–decl. plane. We evaluated N_r from the average of 5000 drawings made with a Monte Carlo routine. This way

$$\begin{equation} \Sigma _\theta ({\rm TPCF})=\bigg (\frac{N_{\rm peaks}}{A_{\rm map}}\bigg)(1+W(\theta)), \end{equation} \tag{ 5 }$$

which can be compared with the MSDC estimated from direct counting. The results are shown in Figure 12. We see that Σ_θ is anti-correlated to θ, and that both estimates (MSDC and TPFC, white triangles and black squares, respectively) are consistent with each other in the range −1.8 < log θ < 0.4 (0.04–5.7 pc). The data points show that Σ_θ has a maximum near log θ° = −1.5 ≈ log θpc = −1.1, and then it flattens out. This break is below the median value of the local Jeans length but above our minimum detectable size scale. This suggests that peaks are genuine substructures extending below the thermal fragmentation length. Moreover, this maximum is equivalent to 1.45 × 10⁴AU or 0.07 pc and it is not far from the median of distribution of peak-to-peak separations (16500 AU or 0.08 pc) in Figure 9. This indicates that we detect a significant decrease in structure of the cloud at (1.45 ± 0.2) × 10⁴ AU, setting an observed limit of fragmentation in the Pipe Nebula.

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For large values of θ (log θ = 0.4 and above), the values of Σ_θ derived from the MSDC and the TPCF lose consistency because the separations start to be comparable to the angular size of the map itself and we lose information. The large "bump" near log θ = 0.5 (∼3°, about 6.8 pc) in the large-scale end of the TPCF is likely a signal (somewhat diluted) from the cloud itself, which at the largest separation scales is comparable to the size of the map. While the largest values of θ for the measured peaks are distributed around the median length of the cloud, the random placed peaks used to calculate the TPCF are distributed within the whole 8 × 6(°)² rectangle. We made a linear fit to the data points in the range −1.5 < log θ < 0.4. The resultant slope is −0.91 ± 0.04, with a correlation (Pearson) coefficient close to 1.0. This near linear fit is indicative of a well-defined power-law behavior of the MSDC for prestellar condensations across the cloud within two orders of magnitude. The linear fit and the slope near −1 are similar to values obtained by Hartmann (2002) and Kraus & Hillenbrand (2008) for the MSDC of single stars in Taurus over a similar range of scales.

5.2.1. Clustering of Peaks?

We constructed a simple map of the surface density of extinction peaks as number of peaks per square degree, using a Nyquist sampled square grid with spatial resolution of 05. The resultant map is shown in Figure 13. From the map, we see that the Bowl is the region with the largest density of peaks per unit area, followed by B59. The Stem and the Shank regions have lower but similar total surface densities, closer to the cloud average. The Smoke region appears to be a moderately dense region in the Pipe Nebula, despite its peaks being less embedded. The map also shows that the surface density of extinction peaks is not uniform across the cloud but displays instead distinct groupings of peaks. We calculated the nearest neighbor distance between local surface density maxima and found a very narrow distribution, with a median value of 0.84 ± 014, or 1.90 ± 0.32 pc. The distribution is shown in Figure 14. This median distance is very close to the expected Jeans length (2.0 pc) for a mean density of 10² cm⁻³ and T_K = 10 K. Such values may be typical of the more diffuse medium traced by ¹²CO.

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In the analysis of the 2MASS map by RLA09, they found that about 45% of the extinction peaks they detected were separated by less than a Jeans length. They reasoned that unless large gas motions occur in the plane of the sky, closely separated peaks with similar values of radial velocity must represent sub-structure belonging to the same physical entity, a cloud core. Consequently, they merged those extinction peaks (about 20% of the total) which were separated by less than a Jeans length and had radial velocity differences smaller than the one-dimensional projected sound speed in a 10 K gas (δv < 0.12 km s⁻¹). This way they obtained a final list of 134 cores out of 158 extinction peaks. Although empirical, the prescription of RLA09 is consistent with defining a core as a bounded Jeans sized region with coherent velocity (Goodman et al. 1998; Bergin & Tafalla 2007). The use of such a prescription to define a core based on a Jeans length scale is in part justified by the fact that the global properties of these cores suggest that they are a collection of thermally supported structures (Lada et al. 2008). In most cases the cores have thermally dominated gas motions, as deduced from their narrow line widths (RLA09; Paper I).

In our analysis, we find that 163 out of 237 peaks are separated by their nearest neighboring peak by less than the median Jeans length. Based on RLA09 we know that at least a fraction of them could be grouped into multiple peaked cores (for example, we used this information to merge some of the peaks of B59 in Paper I). The main result of such merging is that the mass distribution function of peaks is different from the mass distribution function of cores. Unfortunately, we do not have radial velocity information for all of the peaks we detected in our maps, so we cannot know the total fraction of peaks that could be merged into multiple peaked cores. For instance, in the study of RLA09 about half of sub-Jeans peaks were not close enough in radial velocity to belong to the same core, so we could expect this to occur for a significant number of our detections. In Table 2, we used the numbering in the list of RLA09 to name those peaks separated from one of their listed positions by less than one Jeans length, using an alphabetic subindex to identify them from the most to the less massive. We compared this list against the list of RLA09 and found 93 peaks matching in position, and thus having velocity information. In most cases, the C¹⁸O pointing coincided with the most massive peak in a group. Only in a handful of cases a second peak in a group was also observed in C¹⁸O and we were able to tell if those two peaks in the group were also close in velocity (we marked these cases with an asterisk). However, this information is still insufficient for the majority of our peaks and we cannot make a complete list of merged cores as in RLA09.

As a cloud evolves toward star formation, an increasing fraction of material will be above a given threshold extinction, at which the cloud is likely to reach the critical densities for gravitational dominance. By comparing the cumulative mass distribution for different clouds with expected different levels of activity, Lombardi et al. (2008) and Lada et al. (2009) showed that clouds with higher levels of high formation activity (e.g., Ophiuchus versus the Pipe Nebula and Orion versus the California Nebula) also have a significantly larger fraction of material with high column densities. While the Pipe Nebula is known to have one of the lowest levels of star-forming activity, our maps give us a good opportunity to compare the cumulative mass distribution of the five different regions of the cloud we mapped.

In Figure 15, we plot the cumulative mass fraction as a function of extinction for each of the large-scale maps. The curves were constructed by counting the mass of the cloud above A_V = 2.0 mag. The resultant profiles for the five regions of the cloud we mapped are, indeed, very different from each other. The fraction of the mass located at high extinction varies dramatically from the outer layers in the Smoke to the cluster-forming region in B59. For example, the fraction of pixels with values above A_V = 10 mag is only over half percent in the Smoke, the Stem, and the Shank regions, but although extinction rises as high as A_V ≈ 30 mag in the Smoke (toward B68), it never reaches a level of 20 mag in the Stem–Shank transition region. At the Bowl region the fraction of pixels with A_V > 10 mag is already over 5% and then it is three times higher at B59. Therefore, in the Pipe Nebula the fraction of high density material appears to be directly related to the condensation of the material toward star formation. Our data show that a significant increase in the fraction of high extinction material as star formation is onset, is not only noticeable from cloud to cloud, but within regions in the same cloud. Moreover, the cumulative mass fraction in the Pipe Nebula appears to vary significantly even though its global star formation rate is low.

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We performed a series of Monte Carlo experiments to determine the completeness of our peak mass sample. For each experiment we simulated a stellar field of 5' × 5' (equal to the SOFI FOV), with a brightness distribution and stellar surface density similar to those observed in the bulge field behind the Pipe (8 < K < 21.0 and 450 stars arcmin⁻², respectively, as observed in the control field) and ran NICER over the field. Each star was then reddened according to a predetermined two-dimensional column density distribution to simulate the peak. The mass of each peak, distributed accordingly over the column density profile, was pre-determined from the mass–size relationship. Then we added the resulting A_V distribution at a random position on the background frame (original minus wavelet filtered) of the Shank region to form an embedded extinction feature. We processed the image with the wavelet filter and ran CLF2D. The completeness of the sample was then determined by counting how many peaks were recovered with a CLFD2D mass value falling within a 20% tolerance range from the input value. We estimate that our method detects and measures correctly extinction peak masses for over 90% ± 5% of peaks with masses above 0.2 M_☉. below this limit, the detection rates drop to 80% and then to 55%, as shown in Figure B1. This means that the last three bins in the histogram of Figure 10 would be off by a factor of less than two. However, this also is a significant improvement over the detection rates in the map of Lombardi et al. for which the completeness limit is estimated to be 3–5 times larger.

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