THE KINEMATIC AND CHEMICAL PROPERTIES OF A POTENTIAL CORE-FORMING CLUMP: PERSEUS B1-E

The Perseus molecular cloud was observed by Herschel as part of the Herschel Gould Belt Survey⁷ (HGBS; André et al. 2010), with the western field mapped in 2010 February and the eastern field mapped in 2011 February. Both Perseus fields were observed using the PACS/SPIRE parallel mode scanning technique with a 60 arcsec s⁻¹ scan rate (Pezzuto et al. 2012, S. Pezzuto et al. 2015, in preparation; Sadavoy et al. 2012). The data were reduced using HIPE version 7 and modified standard reduction scripts by M. Sauvage (PACS) and P. Panuzzo (SPIRE) in the same manner as Sadavoy et al. (2014). We used scanamorphos 11 (Roussel 2013) to produce the final maps.

We corrected the zero-point offset at each wavelength for both the eastern and western fields using Planck observations following Bernard et al. (2010). Since both fields maps overlapped toward B1-E, we mosaicked the two fields using the Starlink task wcsmosaic and bilinear interpoloation. For the 160–500 μm data, the two fields had excellent agreement in their mosaics. Finally, we convolved the mosaics to a common resolution of 363 (the 500 μm beam) and a common grid of 14'' pixels.

We observed the B1-E clump with the Heterodyne Array Receiver Programme (HARP) detector at the James Clerk Maxwell Telescope (JCMT) in the same manner as the JCMT Gould Belt Survey (Buckle et al. 2009). The HARP detector was tuned to map B1-E simultaneously in $^{13}{\rm CO}$ (3–2) and ${{{\rm C}}^{18}}{\rm O}$ (3–2) line emission at 330.58796 and 329.330545 GHz, respectively. Observations were taken using position-switching, orthogonal raster scans with 1/4 array spacing over a $25^{\prime} \;\times \;14^{\prime}$ region. The backend was configured to 4096 channels over 250 MHz, resulting in ∼0.055 ${\rm km}\;{{{\rm s}}^{-1}}$ velocity resolution. B1-E was observed on 2011 July 13 and 2012 January 12 for ∼2.2 hr of observing time (∼20% of the total project time). We selected the coordinates 03:35:47.7, 31:45:30.5 (J2000.0) for our off-position.

The HARP data were processed using the Auto-Correlation Spectral Imaging System (ACSIS; Jenness et al. 2008) and reduced using the ACSIS pipeline (Cavanagh et al. 2008) in a similar manner as described in Currie & Friedel (2013) and Sadavoy et al. (2013). In brief, the HARP data were reduced using a two-stage, fully automated methodology. First, we conducted a quality assurance, which mostly removed those spectra degraded by a variety of instrumental effects. Second, we performed an iterative procedure that used spectral cubes to estimate linear baselines and to identify emission features to be masked for a more refined baseline subtraction. For the B1-E data, one iteration was sufficient to characterize the baselines. Detailed descriptions of the methods used can be found in Jenness et al. (2015).

Finally, we used a main-beam efficiency of ${{\eta }_{{\rm MB}}}=0.61$ for our reduced spectra. The effective beam of these data is 173, which we convolved with a 319 beam to get our data at an equivalent resolution of 363, or the resolution of our 500 μm Herschel observations. The 1σ line sensitivities at this spatial resolution are ∼0.2 and ∼0.3 K for the $^{13}{\rm CO}$ (3–2) and ${{{\rm C}}^{18}}{\rm O}$ (3–2) data, respectively.

The B1-E clump was mapped using the 10 m of the Arizona Radio Observatory (ARO) Submillimeter Telescope (SMT) in dual polarization, 4-IF mode over ∼35 hr in 2012 March. We used the 1 mm ALMA prototype receivers to make position-switching on-the-fly (OTF) maps with the upper sideband tuned to $^{12}{\rm CO}$ (2–1) at 230.538 GHz and the lower sideband tuned to $^{13}{\rm CO}$ (2–1) at 220.3987 GHz with a ∼5.0 GHz IF. With the 250 kHz filterbank backends, the velocity resolution is ∼0.34 ${\rm km}\;{{{\rm s}}^{-1}}$ and the spatial resolution is ∼337 at 220 GHz. At this time, we only discuss the $^{13}{\rm CO}$ (2–1) data.

Point and focus observations were made on Venus or Jupiter. Line calibrations to measure the sideband spillover were made using the standard SMT line calibrator in Orion A (J2000.0: 05:35:14.48, −05:22:27.6). The beam efficiency ($\eta \approx 0.62$) was measured using the average efficiency from observations of Venus and Jupiter. The beam efficiency was stable (within 5%) throughout the observations.

To avoid artifacts introduced by long scans, we divided B1-E into smaller subregions, mapping each block separately. We used four overlapping subregions, where each subregion was $9^{\prime} \;\times \;7^{\prime}$, with a 2' overlap, for a total map area of ∼190 arcmin². We initially used an OTF scanning rate of 10'' s⁻¹, but switched to 20'' s⁻¹ to speed up the mapping. Each region was observed in orthogonal scans (along R.A. or decl.) with 10'' spacings at least once at 10'' s⁻¹ or twice at 20'' s⁻¹ along each direction. We selected the coordinates 03:35:31.0, 31:45:31.0 (J2000.0) for our off-position.

The observations were reduced using the gildas reduction software, class. We reduced the horizontal and vertical polarizations separately using an initial single-order baseline fit. The telescope was fairly stable over the observations, and we rejected only two scans in one subregion due to unusual spectral signatures. The spectral line data were combined onto a evenly spaced grid and smoothed to 36 3 resolution, the resolution at the 500 μm beam. Several rows of spectra had curved baselines. To improve these baselines, we subtracted an additional quadratic function using a wide velocity range (−11–28 ${\rm km}\;{{{\rm s}}^{-1}}$). The final 1σ rms of the smoothed maps is ∼0.05 K toward the center (highest sampling) and ∼0.15 K toward the corners of the map.

We also fully mapped B1-E with the IRAM 30 m telescope in 2012 August using the EMIR receiver and VESPA backend to observe simultaneously $^{13}{\rm CO}$ (1-0) at 110.2014 GHz, ${{{\rm C}}^{18}}{\rm O}$ (1-0) at 109.7822 GHz, and ${{{\rm C}}^{18}}{\rm O}$ (2-1) at 219.5604 GHz. We made frequency-switching OTF maps with a throw of 3.9 MHz in the 90 GHz band and 11.7 MHz in the 230 GHz band. The respective velocity resolutions are ∼0.106 and ∼0.053 ${\rm km}\;{{{\rm s}}^{-1}}$ and the respective spatial resolutions are ∼24'' and ∼12'' at 110 and 220 GHz.

Like our SMT observations, we mapped B1-E with orthogonal scans in four smaller, overlapping subregions for a total coverage of ∼190 arcmin² in all three tracers (see Section 2.3) with a step size between scans of 5'' and a scan rate of 7 5 s⁻¹. Point and focus observations were done using Uranus after full scans of each subregion. Line calibrators were observed while B1-E was in transit. We adopted beam efficiencies and forward efficiencies of ${{\eta }_{{\rm beam}}}=0.78$ and ${{F}_{{\rm eff}}}=0.94$ at 110 GHz and ${{\eta }_{{\rm beam}}}=0.61$ and ${{F}_{{\rm eff}}}=0.93$ at 220 GHz. The total on sky time was ∼13 hr.

The IRAM 30 m observations were reduced using class. We removed an initial single-order baseline from all spectra before folding the spectra. For the ${{{\rm C}}^{18}}{\rm O}$ (1–0) and ${{{\rm C}}^{18}}{\rm O}$ (2–1) observations, we subtracted additional single-order or second-order baselines to remove large-scale ripples after the spectra were folded. As with the previous line data, we smoothed the data to a similar grid as our the 500 μm Herschel data. The final 1σ rms of the smoothed maps range from ∼0.03–0.1 K for $^{13}{\rm CO}$ (1–0), ∼0.03–0.1 K for ${{{\rm C}}^{18}}{\rm O}$ (1–0), and ∼0.1–0.2 K for ${{{\rm C}}^{18}}{\rm O}$ (2–1) between the center of the map (highest sampling) and the corners (lowest sampling).

Figure 2 shows three sample IRAM $^{13}{\rm CO}$ (1–0) and ${{{\rm C}}^{18}}{\rm O}$ (1–0) spectra for the sample pixels toward the northwest (NW) corner, center (C), and southeast (SE) corner of the B1-E clump (see Figure 1). The IRAM $^{13}{\rm CO}$ (1–0) line emission has a main velocity component at ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ with less prominent emission at ∼3 ${\rm km}\;{{{\rm s}}^{-1}}$. The integrated intensity associated with the ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ component dominates over the ∼3 ${\rm km}\;{{{\rm s}}^{-1}}$ component by a factor of ∼5 on average. The ${{{\rm C}}^{18}}{\rm O}$ (1–0) observations barely show any emission at ∼3 ${\rm km}\;{{{\rm s}}^{-1}}$, indicating that the gas associated with the ∼3 ${\rm km}\;{{{\rm s}}^{-1}}$ component is more diffuse than the gas found at the ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ (see also, Sadavoy et al. 2012). Hereafter, we will only discuss the 7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ velocity component, unless stated otherwise.

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The IRAM $^{13}{\rm CO}$ (1–0) and IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) spectra at ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ reveal very complicated, non-Gaussian profiles indicative of several sub-components at very similar, overlapping velocities. The best-fit velocity profiles in Figure 2 show single Gaussian fits for each of the 3 and 7.5 ${\rm km}\;{{{\rm s}}^{-1}}$ components, whereas many IRAM $^{13}{\rm CO}$ (1–0) spectra require five unique velocity subcomponents to fit well the observed velocity profiles at ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$, and similarly, the IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) spectra need three components at ∼7.5 ${\rm km}\;{{{\rm s}}^{-1}}$. The SMT $^{13}{\rm CO}$ (2–1), JCMT $^{13}{\rm CO}$ (3–2), and IRAM ${{{\rm C}}^{18}}{\rm O}$ (2–1) line emission also show complex line profiles.

Figures 3 and 4 show, respectively, the integrated intensity maps for all the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ transitions across the main velocity structure over 5–9 ${\rm km}\;{{{\rm s}}^{-1}}$. Both Figures include ${\rm N}({{{\rm H}}_{2}})$ contours to highlight the regions with higher column densities of dust. We find that the $^{13}{\rm CO}$ observations show some agreement with the dust, whereas the IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) and (2–1) integrated intensities show excellent correspondence with the dust-derived column densities. Although the right panel of Figure 4 hints at possible JCMT ${{{\rm C}}^{18}}{\rm O}$ (3–2) emission, particularly toward the B1-E1 region (see Figure 1), any detections are very weak (i.e., $\lesssim 3\sigma$). We do not use the JCMT ${{{\rm C}}^{18}}{\rm O}$ (3–2) data in our subsequent analyzes.

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The IRAM $^{13}{\rm CO}$ (1–0) and IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) spectra show a radial velocity gradient, where the centroid velocities increase from the NW to the SE (see Figure 2). Figure 5 shows position–velocity diagrams for the IRAM $^{13}{\rm CO}$ (1–0) and IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) line transitions. We find consistent flux-weighted gradients for both line transitions of 0.94 ${\rm km}\;{{{\rm s}}^{-1}}$ pc⁻¹ from the IRAM $^{13}{\rm CO}$ (1–0) observations and 1.0 ${\rm km}\;{{{\rm s}}^{-1}}$ pc⁻¹ for the IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) observations at an angle of ∼20°–30° north-to-west. This gradient of ∼1 ${\rm km}\;{{{\rm s}}^{-1}}\;{\rm p}{{{\rm c}}^{-1}}$ is consistent with the results of Kirk et al. (2010) for the B1-E clump. We also find a similar gradient and angle with the 3 ${\rm km}\;{{{\rm s}}^{-1}}$ component.

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On much larger scales, a steep velocity gradient across the Perseus cloud has been well identified in previous studies (e.g., Ridge et al. 2006; Sun et al. 2006). Figure 6 compares the channel maps of B1-E to those of L1455 (clump west of B1-E) and IC348 (clump east of B1-E) using data from the COMPLETE survey (Ridge et al. 2006). The line-of-sight velocities in Perseus typically increase from the southwest (SW) to the northeast (NE), as illustrated by the channel maps of L1455 and IC348, as well as their centroid velocities. Moreover, the COMPLETE $^{13}{\rm CO}$ (1–0) and $^{12}{\rm CO}$ (1–0) data give very similar gradients.

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To characterize better the velocity gradients elsewhere in Perseus, we used the $^{12}{\rm CO}$ (1–0) observations from the COMPLETE survey (Ridge et al. 2006) in a similar manner as our IRAM observations of B1-E. We broke up the Perseus cloud into rectangular regions identified by-eye to enclose B5, IC348, B1-E, B1, L1455, and L1448 (e.g., see Sadavoy et al. 2014), as well as additional regions encompassing the "bridge" material between IC348 and B1-E (see Bally et al. 2008). We excluded NGC 1333 due to its large sample of outflows (Hatchell et al. 2007; Arce et al. 2010). Note that we generally selected more material than Kirk et al. (2010) in measuring the gradients. Figure 7 shows the radial velocity gradient orientations across Perseus using the same technique outlined in Figure 5. Most regions have gradients of ∼0.3–0.6 ${\rm km}\;{{{\rm s}}^{-1}}$ pc⁻¹, where the centroid velocities increase from the SW to the NE at position angles of ∼30°–50° north-to-east. Thus, the velocity gradients toward B1-E and the nearby "bridge" region stand out significantly for increasing instead in directions perpendicular to the velocity gradients found in the other Perseus clumps.

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To quantify the level of turbulent motion in B1-E, we measured the non-thermal velocity dispersion for both IRAM $^{13}{\rm CO}$ (1–0) and IRAM ${{{\rm C}}^{18}}{\rm O}$ (1–0) line emission using two methods; (1) we adopted the median velocity dispersion from the single-Gaussian fits (see Section 3.1); (2) we summed all the spectra, where each spectrum was re-centered prior to stacking them (to correct for the observed velocity gradient; see previous section). Table 2 gives the velocity dispersions associated with each method and each molecule. For both molecular tracers, the velocity dispersion is slightly higher when using the stacked spectra compared to the median velocity dispersion of all spectra, though both methods agree within uncertainties. Additionally, our line widths for B1-E agree well with those found in other (more active) clumps of Perseus (e.g., Hatchell et al. 2005; Kirk et al. 2010).

Table 2.  Turbulent Velocity Dispersions Across B1-E

Line	Mediana	Stacked Spectrumb
$^{13}{\rm CO}$ (1–0)	0.7 ${\rm km}\;{{{\rm s}}^{-1}}$	0.8 ${\rm km}\;{{{\rm s}}^{-1}}$
${{{\rm C}}^{18}}{\rm O}$ (1–0)	0.4 ${\rm km}\;{{{\rm s}}^{-1}}$	0.5 ${\rm km}\;{{{\rm s}}^{-1}}$

^aThe distribution of velocity dispersions across B1-E are non-Gaussian. For the $^{13}{\rm CO}$ (1–0) and ${{{\rm C}}^{18}}{\rm O}$ (1–0) data at ${\rm N}({{{\rm H}}_{2}})\ \geqslant 5.0\times {{10}^{21}}\;{\rm c}{{{\rm m}}^{-2}}$ , ∼75% of spectra have velocity dispersions within 0.13 and 0.15 ${\rm km}\;{{{\rm s}}^{-1}}$ of the respective median velocity dispersion. ^bSingle Gaussian fits yield robust velocity dispersions with uncertainties better than 1%.

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We estimated the thermal and non-thermal line contributions using the median dust temperature of ∼14 K, as determined from modified blackbody fitting to the Herschel spectral energy distributions (SEDs; see also the Appendix), as a proxy for the gas kinetic temperature. Assuming an equivalent gas kinetic temperature of 14 K, the thermal line widths of $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ are ∼0.06 ${\rm km}\;{{{\rm s}}^{-1}}$, whereas the observed velocity dispersions are $\sigma \gtrsim 0.3\;{\rm km}\;{{{\rm s}}^{-1}}$. Although the gas and dust are likely decoupled at the densities the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ line emission trace, these temperatures should agree within a factor of two (e.g., Young et al. 2004; Ceccarelli et al. 2007). Thus, the expected thermal velocities will be $\lt 0.1\;{\rm km}\;{{{\rm s}}^{-1}}$ (e.g., for ${{T}_{K}}\lt 2{{T}_{{\rm dust}}}$) and the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ spectra cannot be explained by thermal broadening alone. Rather, we assume the observed line widths represent the turbulent (non-thermal) velocity dispersion.

Sadavoy et al. (2012) identified nine substructures in B1-E (see also, Figure 1) and characterized them with ${\rm N}{{{\rm H}}_{3}}$ (1,1) emission. Figures 8 and 9 compare the (1–0) and (2–1) spectra of both $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$, respectively, with the ${\rm N}{{{\rm H}}_{3}}$ (1,1) centroid velocities (dashed line) of these nine objects. The ${\rm N}{{{\rm H}}_{3}}$ (1,1) data trace the denser central material of each substructure, whereas the ${{{\rm C}}^{18}}{\rm O}$ and $^{13}{\rm CO}$ data trace better the source envelopes and more diffuse clump, respectively. In general, most substructures show a good agreement between the ${\rm N}{{{\rm H}}_{3}}$ (1,1) centroid velocities and the ${{{\rm C}}^{18}}{\rm O}$ velocity peaks, in agreement with previous studies (e.g., Walsh et al. 2004; André et al. 2007; Kirk et al. 2007, 2010). This similarity supports the notion that the dense material within cores forms quiescently within their envelopes (see also, Offner et al. 2008). The $^{13}{\rm CO}$ spectra show more deviations in centroid velocity (and higher line widths), which is unsurprising as $^{13}{\rm CO}$ is a better tracer of lower density ($\sim {{10}^{3}}\;{\rm c}{{{\rm m}}^{-3}}$) gas.

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The B1-E1 and B1-E4 substructures are the only objects with significant ($\gt 3\sigma$) deviations between the peak-line velocities of ${{{\rm C}}^{18}}{\rm O}$ and ${\rm N}{{{\rm H}}_{3}}$ (Figures 8 and 9). In particular, these objects have asymmetric ${{{\rm C}}^{18}}{\rm O}$ profiles with a narrow Gaussian-like peak and a broad blueshifted "knee," where the ${\rm N}{{{\rm H}}_{3}}$ emission peaks between the Gaussian-peak and the "knee." In addition to these, the B1-E6 source has a double peaked ${{{\rm C}}^{18}}{\rm O}$ spectrum (a feature seen in both transitions) with single-Gaussian ${\rm N}{{{\rm H}}_{3}}$ (1,1) emission at velocities directly between the two ${{{\rm C}}^{18}}{\rm O}$ peaks. Normally, a double-peaked spectrum with brighter emission toward the bluer side would suggest self-absorption and perhaps infall. Nevertheless, ${{{\rm C}}^{18}}{\rm O}$ emission is generally optically thin (see Section 4) and as such, will not produce such a feature. Moreover, the $^{13}{\rm CO}$ spectra, which should be more optically thick, do not show this double-peaked profile. Thus, the B1-E6 spectra may correspond to multiple velocity subcomponents along the line of sight. For example, the bluer ${{{\rm C}}^{18}}{\rm O}$ velocity peak matches the centroid velocity of the nearby B1-E7 source, whereas the redder peak appears associated with a separate velocity structure east of the B1-E6 and B1-E7 ridge. We discuss the possibility of multiple subcomponents in Section 5.

In addition to similar core-envelope velocities, several studies have compared the core-to-core centroid velocity dispersion with the turbulence in their surrounding environment. From Sadavoy et al. (2012), the substructures have an ${\rm N}{{{\rm H}}_{3}}$-derived core-to-core relative motion of ${{\sigma }_{{\rm sys}}}\sim 0.24\;{\rm km}\;{{{\rm s}}^{-1}}$. This core-to-core centroid velocity dispersion matches well the dispersion of the ${{{\rm C}}^{18}}{\rm O}$ (1–0) peak velocities (∼0.29 ${\rm km}\;{{{\rm s}}^{-1}}$), but is factors of two to three lower than the typical velocity dispersions observed across the entire clump (see Table 2). Kirk et al. (2010) similarly found that the starless (and protostellar) cores in other regions of Perseus systematically had much lower relative motions than the turbulence detected in the more diffuse, ambient clump material (see also Kirk et al. 2009). Therefore, these core precursors do not appear to move in a manner similar to the B1-E clump as a whole, but rather, they have more homogenous velocities like those seen in more evolved dense cores. We also find that the ${\rm N}{{{\rm H}}_{3}}$ detections show no indication of a velocity gradient, whereas the ${{{\rm C}}^{18}}{\rm O}$ data clearly show a ∼1 ${\rm km}\;{{{\rm s}}^{-1}}$ pc⁻¹ radial velocity gradient across B1-E. Thus, the B1-E substructures appear to be decoupled (i.e., following a distinctly different velocity distribution) from the moderately dense gas as traced by the ${{{\rm C}}^{18}}{\rm O}$ emission, suggesting that the systemic motions of dense cores somehow homogenize very quickly in their evolution (see also, Section 5.2.2).

The B1-E substructures have very broad ${\rm N}{{{\rm H}}_{3}}$ emission compared to typical observations of dense gas in prestellar cores. For example, Rosolowsky et al. (2008) conducted a targeted ${\rm N}{{{\rm H}}_{3}}$ survey of Perseus, and from their results, the prestellar cores have ${\rm N}{{{\rm H}}_{3}}$ velocity dispersions $\sigma \;\lt 0.25\;{\rm km}\;{{{\rm s}}^{-1}}$, with an median value of $\sigma \sim 0.15\;{\rm km}\;{{{\rm s}}^{-1}}$. In comparison, most of the B1-E substructures have much broader ${\rm N}{{{\rm H}}_{3}}$ velocity dispersions of $\sigma \gtrsim 0.3\;{\rm km}\;{{{\rm s}}^{-1}}$ (Sadavoy et al. 2012). The most line-broadened substructures have similar velocity dispersions (∼0.4 ${\rm km}\;{{{\rm s}}^{-1}}$) as the larger-scale ${{{\rm C}}^{18}}{\rm O}$ gas. If these broad line widths represent the turbulent motions within these objects, the B1-E substructures have significant internal pressures. Assuming a typical substructure density of 10⁴ ${\rm c}{{{\rm m}}^{-3}}$ (see Sadavoy et al. 2012), the substructures have internal pressures of ${{P}_{{\rm sub}}}/k=\rho {{\sigma }^{2}}=(0.3-6)\;\times \;{{10}^{5}}{\rm K}\;{\rm c}{{{\rm m}}^{-3}}$. In comparison, the volume-averaged gravitational pressure of the B1-E clump can be estimated from Bertoldi & McKee (1992) as

$$\begin{eqnarray}&&\frac{{\bar{P}}}{k}=1.01\ {{a}_{1}}\left\langle {{\phi }_{G}} \right\rangle {{\left( \frac{M}{{{M}_{\odot }}} \right)}^{2}}{{\left( \frac{R}{1\;{\rm pc}} \right)}^{-4}}{\rm K}\;{\rm c}{{{\rm m}}^{-3}},\end{eqnarray} \tag{ 1 }$$

where M is the clump mass, R is the observed clump size, a₁ is a scaling factor corresponding to a nonuniform density distribution, and $\left\langle {{\phi }_{G}} \right\rangle$ is a scaling factor corresponding to the cloud geometry (${{\phi }_{G}}=1$ for a perfect sphere). Following Lada et al. (2008), we assume a₁ = 1.3, appropriate for a self-gravitating cloud. We also adopt $\left\langle {{\phi }_{G}} \right\rangle \sim 1.01$, since B1-E is fairly circular (∼1.2 aspect ratio; see Bertoldi & McKee 1992). Thus, the B1-E volume-average gravitational pressure is $\sim 3\times {{10}^{5}}\;{\rm K}\;{\rm c}{{{\rm m}}^{-3}}$, which is very similar to the internal pressures for the B1-E substructures. Moreover, if the substructures are centrally concentrated, their surface pressures may be much lower than their average internal pressures (Lada et al. 2008), suggesting that the external pressure of the clump is sufficient to keep the B1-E substructures confined. Such pressure-confined structures have been seen more recently in different environments, including Taurus (Seo et al. 2015) and Ophiuchus (Pattle et al. 2015).

The formation mechanism for the B1-E substructures must explain why the B1-E clump is only condensing to form cores now, whereas the other clumps in Perseus have formed populations of dense cores and YSOs (e.g., Kirk et al. 2006; Evans et al. 2009). One simple explanation could be that the condensation of the B1-E clump itself was triggered only recently. B1-E has a radial velocity gradient nearly perpendicular (in the plane of the sky) to the typical velocity gradient associated with the main Perseus cloud (see Section 3.2). Thus, this clump may be impacted by large-scale processes such as shearing flows or collisions that have only occurred recently. Indeed, we see unusual, non-Gaussian ${{{\rm C}}^{18}}{\rm O}$ spectra toward B1-E1 and B1-E4 that match well the spectra associated with colliding clouds modeled by Keto & Lattanzio (1989). Since these two sources are located along the western-edge of B1-E at the junction between the B1-E velocity gradient and the Perseus overall gradient, they are most likely to be affected by the interaction of these gas flows (see Section 3.4). Nevertheless, large-scale flows are generally associated with subsonic motions and filamentary morphologies (e.g., Klessen et al. 2000, 2005; Bate et al. 2003; Li & Nakamura 2004; Clark & Bonnell 2005; Basu et al. 2009a), and the B1-E clump and its substructures shows no evidence of these properties.

The relationship between the B1-E velocity gradient and that of the Perseus cloud remains unclear. For example, perpendicular velocity gradients may arise from (1) independent clouds along the line of sight, (2) material flowing into or out of the system, (3) dynamic turbulence on small scales (e.g., Smith et al. 2012), or (4) strong magnetic fields. At this time, we cannot distinguish between these possibilities to explain the perpendicular velocity gradient between B1-E and the Perseus cloud. Specific predictive simulations of clump fragmentation triggered by low-velocity shearing (or colliding) flows are needed to determine the origin and impact of the perpendicular velocity gradient in B1-E.

If the condensation of the B1-E clump was not triggered by an external process, its star formation could be delayed compared to the other Perseus clumps. Sadavoy et al. (2012) suggested that B1-E may be under the influence of a strong, localized magnetic field. B1-E has uniquely strong R-band polarization vectors (Goodman et al. 1990), and a strong magnetic field has been shown to both delay star formation and to form objects in a loose configuration without filaments as seen in B1-E (e.g., Li & Nakamura 2004; Basu et al. 2009a). Alternatively, B1-E and its substructures may be influenced by significant turbulent processes (see Sections 3.1 and 3.4). Indeed, Pon et al. (2014) found excess emission in high-J $^{12}{\rm CO}$ lines toward the B1-E5 substructure, which they interpreted as evidence of low-velocity shocked gas. Such small-scale turbulent shocks are expected to form few sources in isolated morphologies on longer time scales than large-scale, high velocity processes (e.g., Klessen et al. 2000). Thus, the loose configuration of the B1-E substructures and their delayed formation with respect to the other Perseus clumps may indicate that this region is dominated by small-scale turbulent shocks or magnetic fields.

5.2.1. Comparisons with More Evolved Perseus Clumps

5.2.2. Comparisons with Simulations

5.2.3. Connecting Dynamics and Chemistry

In Section 4, we used the radiative transfer code, RADEX, to model the multi-J $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ observations using the Herschel-derived dust temperature as a proxy for the kinetic gas temperature. Since the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ line emission mainly trace material at $n\lesssim {{10}^{4}}\;{\rm c}{{{\rm m}}^{-3}}$, the gas and dust may be decoupled such that the kinetic gas temperatures (at the densities traced by $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$) are warmer than the dust temperatures (e.g., Goldreich & Kwan 1974; Goldsmith 2001; Ceccarelli et al. 2007; Di Francesco et al. 2007). Morevoer, the best-fit radiative transfer models had different excitation temperatures for each J-line, suggesting the molecules whose emission we observe are not in thermal equilibrium with the unknown kinetic gas temperature.

We estimated the kinetic gas temperature using the COMPLETE survey (Ridge et al. 2006), which mapped the entire Perseus molecular cloud in $^{12}{\rm CO}$ (1–0) and $^{13}{\rm CO}$ (1–0) at ∼45'' resolution. Using these data, Pineda et al. (2008) determined the excitation temperature, T_ex, from the $^{12}{\rm CO}$ (1–0) data assuming optically thick emission, following;

$$\begin{eqnarray}&&{\Delta }{{T}_{{\rm MB}}}=(1-{{e}^{-\tau }})\frac{h\nu }{k}\left[ f({{T}_{{\rm ex}}})-f({{T}_{{\rm CMB}}}) \right],\end{eqnarray} \tag{ 2 }$$

where ${\Delta }{{T}_{{\rm MB}}}$ is the main beam brightness of the line, τ is the optical depth, h is the Planck constant, k, is the Boltzmann constant, and f(T) corresponds to,

$$\begin{eqnarray}&&f(T)={{\left[ {\rm exp} \left( \frac{h\nu }{kT} \right)-1 \right]}^{-1}}\end{eqnarray} \tag{ 3 }$$

and f(T) is measured for the excitation temperature (T_ex) and the background temperature, given by the cosmic microwave background (CMB). Assuming a CMB temperature of 2.73 K, T_ex is measured as,

$$\begin{eqnarray}&&{{T}_{{\rm ex}}}=\frac{5.53{\rm K}}{{\rm ln} \left( 1+\frac{5.53{\rm K}}{{\Delta }{{T}_{{\rm MB}}}+0.84{\rm K}} \right)}.\end{eqnarray} \tag{ 4 }$$

Pineda et al. (2008) reported typical T_ex values of T_ex ∼ 11 K in different regions of Perseus at 5' resolution (to match the resolution of their extinction data). We followed the same procedure to characterize T_ex on a pixel-by-pixel basis at the native resolution of the COMPLETE data (∼45''). We used single Gaussian fits to measure the peak line brightness (T_MB) at each pixel, assuming a beam correction factor of ∼0.45 to convert from $T_{A}^{\star }$ to T_MB. We also assumed the emission filling fraction is unity.

Figure 12 shows the excitation temperature across B1-E determined from Equation (4) with the integrated intensity map of the $^{12}{\rm CO}$ (1–0) observations from COMPLETE. For comparison, we also show the Herschel-derived dust temperature (T_dust) map from SED fitting (see Section 2 and Sadavoy et al. 2014 for details) and the ratio of T_dust and T_ex. Both temperature maps show very different structures. The $^{12}{\rm CO}$-derived T_ex measurements range over 10–22 K, with the highest values toward the center of the field, and no correlation is found between T_ex and column density (contours). Since the $^{12}{\rm CO}$ (1–0) line emission is optically thick, it will not trace the dust emission (e.g., see the $^{12}{\rm CO}$ integrated intensity map in Figure 12). In contrast, the Herschel-derived dust temperatures range over 12–16 K, with a strong correlation between T_dust and column density such that the lowest temperature values are toward the densest regions of B1-E. Similarly, the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ integrated intensity maps also trace the dust emission well (see Figures 3 and 4). Therefore, T_dust is likely a better representation of the kinetic gas temperature associated with the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ gases than the $^{12}{\rm CO}$-derived T_ex values.

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Although the gas and dust are likely not coupled toward most of B1-E, the kinetic gas temperature and the dust temperature are expected to vary by only a few Kelvin at densities of $n\sim {{10}^{3-4}}\;{\rm c}{{{\rm m}}^{-3}}$ (e.g., Young et al. 2004; Ceccarelli et al. 2007), which represent the bulk densities of B1-E (see Sadavoy et al. 2012). Therefore, we re-ran the RADEX models for a randomly selected sample of test pixels assuming the CO gas kinetic temperature is warmer than the dust temperature by 2 K. We found that the $^{13}{\rm CO}$ column densities were generally lower by ≲20%, whereas the ${{{\rm C}}^{18}}{\rm O}$ column densities were lower by $\lt 10$%. These uncertainties are relatively minor, considering the complex spectra of the $^{13}{\rm CO}$ and ${{{\rm C}}^{18}}{\rm O}$ gases and the simple geometric assumptions in the RADEX routine. As such, in the absence of proper gas kinetic temperatures, the Herschel-derived dust temperatures give a good first-order estimate for abundances from RADEX.