THE AGE, STELLAR CONTENT, AND STAR FORMATION TIMESCALE OF THE B59 DENSE CORE

Following Meyer et al. (1997), we assume that a YSO's observed NIR color (e.g., (J − H)_obs) is due solely to its intrinsic photospheric color (e.g., (J − H)_int), an additional continuum excess from its circumstellar disk (e.g., Δ(J − H), such that (J − H)_CTTS = (J − H)_int + Δ(J − H)), and an independent extinction/reddening term (e.g., E(J − H) = 0.613 × A_H; (J − H)_obs = (J − H)_CTTS +  E(J − H)). Algebraically combining the Meyer et al. (1997) CTTS locus (transformed onto the 2MASS photometric system) with a well-behaved extinction law⁹ then requires a unique combination of reddening and disk excesses/veiling to reconcile a YSO's intrinsic and observed (J − H) and (H − K_s) colors:

$$\begin{eqnarray} &&A_H = 2.512 \times (J-H)_{\rm obs} - 1.527 \times (H-K_s)_{\rm obs} - 1.254,\nonumber \\ \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} &&\Delta (J-H) = (J-H)_{\rm obs} - 0.613 \times A_H - (J-H)_{\rm int},\nonumber \\ \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} &&\Delta (H-K_s) = (H-K_s)_{\rm obs} - 0.354 \times A_H - (H-K_s)_{\rm int}.\nonumber \\ \end{eqnarray} \tag{ 3 }$$

YSOs often demonstrate considerable photometric variability, including in the NIR regime we focus on here (e.g., Carpenter 2001; Morales-Calderón et al. 2009). To estimate each YSO's extinction and NIR excess at the exact epoch that the spectra were obtained, we calculate synthetic NIR photometry from each target's SpeX spectrum following the prescription presented by Covey et al. (2007) in their Section 3.3.1. Using these JHK magnitudes, and assuming intrinsic photospheric colors characteristic of K7/M0 type stars, we can therefore obtain a good initial estimate of each YSO's extinction (A_H) and Δ(J − H) and Δ(H − K_s) color excesses.

Numerous investigators have identified H- and K-band spectral indices sensitive to a star's luminosity class and spectral type (Kleinmann & Hall 1986; Ali et al. 1995; Wallace & Hinkle 1997; Meyer et al. 1998; Aspin 2003; Ivanov et al. 2004; Allers et al. 2007). We present in Table 3 a set of indices well suited for measuring stellar spectral types from moderate resolution (R ∼ 1000–2000) spectra. Each feature's local continuum is measured from a linear fit to the median flux in two nearby regions ("Cont. 1" and "Cont. 2" in Table 3). Integrating the difference between the expected continuum and the actual flux in the line (defined by the "line center" and "line width" columns of Table 3), and dividing by the continuum flux density in the center of the line region, provides an equivalent width (EqW) measure of the strength of each feature. EqW measures are convenient for spectral classification of YSOs: EqWs are relatively insensitive to extinction, which affects both the line and the local continuum equally, and ratios of closely separated lines are relatively robust to excess continuum flux, as both lines will be diluted equally and the sum effect will cancel out.

The strength and shape of water absorption in the H and K bands has also been identified by numerous authors as a useful spectral type and luminosity class indicator (e.g., Wilking et al. 1999; Reid et al. 2001; Geballe et al. 2002; McLean et al. 2003; Slesnick et al. 2004; Allers et al. 2007; Weights et al. 2009), but is less amenable to characterization as an EqW. We defined two indices to characterize water absorption in the H and K bands; these indices are calculated as

$$\begin{equation} \rm {Index} = \frac{\langle Band\, 1\rangle /\langle Band\, 2\rangle }{\langle Band\,2\rangle /\langle Band\,3\rangle }, \end{equation} \tag{ 4 }$$

where 〈X〉 simply denotes the mean flux level within the range of each band as given in Table 4.

To account for any residual sensitivity to extinction or veiling in our spectral indices, we compared our target's index values to those measured from artificially reddened and veiled spectral standards. As described in Section 3.1, synthetic photometry from each SpeX spectrum produces an initial estimate of each target's extinction and (J − H)/(H − K) color excesses assuming the standard K7/M0 spectral type. Adopting the characteristic J-band veiling (r_J=$\frac{F_{\rm ex}}{F_*} = 0.25$) measured by Cieza et al. (2005) for a large sample of CTTSs sets the initial absolute scale for the veiling fluxes implied by each source's Δ(J − H) and Δ(H − K_s) color excesses:

$$\begin{eqnarray} \Delta J &=& 2.5 \times {{\rm log}}(r_J + 1) \nonumber \\ \Delta H &=& \Delta J + \Delta (J-H) \nonumber \\ r_H &=& 10^{\frac{\Delta H}{2.5}}-1. \end{eqnarray} \tag{ 5 }$$

We then iteratively adjusted each target's assumed absolute J-band veiling and spectral type (and thus intrinsic photospheric colors) to identify the self-consistent spectral type/extinction/veiling combination that best replicated the target's measured spectral indices and overall SED shape. Figures 3 and 4 demonstrate our two-dimensional spectral classification of GY 292 and [BHB2007] 5, respectively. GY 292 appears to be moderately veiled (Δ(J − H): 0.22; Δ(H − K_s): 0.35), but [BHB2007] 5 shows no evidence for veiling, so these two stars demonstrate the sensitivity of these spectral indices to the presence of veiling. Veiling has the largest impact on the two water indices shown in the upper left panels of Figures 3 and 4: standards veiled to match GY 292 are significantly compressed compared to the unveiled standards used to type [BHB2007] 5.

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Figure 4 also demonstrates the utility of two-dimensional spectral classification for identifying background giants, as [BHB2007] 5 is clearly identified in each plot as a giant star; lacking significant veiling, or emission lines indicative of mass accretion, this object appears to be a background late K/early M giant star.

Applying our classification algorithm to these spectra identifies two of the B59 candidate YSOs and the majority of the IR excess stars throughout the Pipe as likely giants: we classify [BHB2007] 5, [CLR2010] 3 and 9 as reddened giants or supergiants, [CLR2010] 8 as a giant carbon star, and [CLR2010] 4, 5, 6 and [BHB2007] 17 as OH/IR stars, likely residing in the Galactic bulge. The spectra of these stars are shown in Figure 5 along with spectra of known giants obtained by Lançon & Wood (2000) and Cushing et al. (2005). Our classification of [BHB2007] 5 and 17 as background giants is reinforced by their non-detection at X-ray wavelengths in an XMM pointing containing B59 (Forbrich et al. 2010).

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The spectra of the confirmed B59 YSOs are shown in Figures 6 and 7, with their derived spectral types, extinctions, and JHK veilings presented in Table 5. We tested the accuracy of these results by comparing the parameters we measure for four ρ Oph YSOs to those reported by Luhman & Rieke (1999). We derived spectral types for GY 292 (K5), GY 17 (K5), GY 250 (M1), and GY 93 (M5); Luhman & Rieke (1999) derived spectral types for these objects of K8, K6, M0, and M4, respectively. The types assigned to GY 17, 93, and 250 agree within one subclass, while the type we assign to GY 292 is earlier by two/three subclasses (following Kirkpatrick et al. 1991, our classification scheme omits types K6 and K8). On the basis of this comparison, we adopt a conservative uncertainty of ±2 subclasses in our derived spectral types. Similarly, comparing the extinctions and veilings we derive with those reported by Luhman & Rieke (1999) suggest that we achieve $\sigma _{A_H} \approx$ 0.5 mag and $\sigma _{r_K} \approx$ 0.35.

Two sources, [CLR2010] 1 and 7, present somewhat ambiguous spectra. [CLR2010] 7 possesses a sub-giant/giant-like surface gravity, with prominent Paschen β, Paschen γ, and Brackett γ emission features as seen in some YSOs. [CLR2010] 7 is also located on the edge of a Pipe extinction core, and is on the lower boundary defined by Forbrich et al. (2009) to select candidate Class II sources based on their MIPS spectral index. While these properties are consistent with a YSO classification, Ojha et al. (2007) identify [CLR2010] 7 as a likely high mass-loss asymptotic giant branch (AGB) star in the Galactic bulge in their analysis of detections by the Mid-course Space Experiment. This classification is also consistent with the observed properties of [CLR2010] 7, explaining its strong H i emission as a signature of strong stellar winds. We tentatively classify this source as a giant star, and include its spectrum in Figure 5. [CLR2010] 1 is more ambiguous: this source possesses a low (sub-giant) surface gravity, and has a location in the H-R diagram consistent with that of other B59 members (see Section 3.3 for a discussion of H-R diagram placement). This H-R diagram location implies a rather young age for [CLR2010] 1, however, which is somewhat inconsistent with the source's lack of NIR excess/disk emission or mass accretion sensitive emission lines. Indeed, [CLR2010] 1's NIR photometry is also consistent with that of a reddened background giant/sub-giant. Definitively resolving [CLR2010] 1's status will require additional observations; for now we include it in Table 5 and Figure 6 as a potential Pipe YSO, but exclude it from our population analysis of B59 members.

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One of the IR excess stars located outside of B59, however, is likely a newly identified YSO. [CLR2010] 2 lies in the Stem of the Pipe, within an Alves et al. (2007) extinction core (see Figure 1 for its exact location), and was identified by Forbrich et al. (2009) as a new candidate YSO (source 16 in their object list). While detected as a single source by MIPS, [CLR2010] 2 proved to be a visual binary when observed with SpeX: we obtained spectra of both the NE and SW components, and the spectral indices measured from both sources are consistent with PMS surface gravities. Strong H  i, He  i, and Ca ii emission lines are also visible in the spectrum of [CLR2010] 2 SW, consistent with the source being an actively accreting YSO. This source was also identified as an Hα emission line source by Kohoutek & Wehmeyer (2003), indicating that the H i emission persists over long timescales. These observations suggest that [CLR2010] 2 SW is a bona fide YSO associated with the Pipe Nebula, and [CLR2010] 2 NE is a promising candidate as well. The detection of Hα from [CLR2010] 2, and the low extinction estimates we derive from our SpeX observations, indicates that follow-up optical spectroscopy of the 6707 Å Li line may be a tractable means of definitively resolving each component's PMS status. As with [CLR2010] 1, we include [CLR2010] 2 NE and SW in Table 5 and Figures 6 and 7.

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To compare the properties of B59's YSOs with theoretical models of PMS evolution, we adopted the SpT to T_eff conversion developed by Luhman et al. (1998). The T_eff implied by each source's spectral type is shown in Table 6. In the spectral type range occupied by most B59 members, our ±2 subclass spectral type uncertainty corresponds to an ∼300 K uncertainty in temperature.

With extinction and veiling estimates for each candidate B59 member, we are able to calculate stellar luminosities from their NIR photometry. We followed Hillenbrand (1997) in calculating each YSO's bolometric luminosity as

$$\begin{eqnarray} &&{{\rm log}}(L_{\rm tot}/L_{\odot }) = 0.4 \times \left(4.75- \big (H - A_H - DM + {{\rm BC}}_H \big) \right),\nonumber \\ \end{eqnarray} \tag{ 6 }$$

where DM is the distance modulus to B59 (d = 130 pc, DM = 5.569; Lombardi et al. 2006) and BC_H is the H-band bolometric correction for each star's spectral type as tabulated by Kenyon & Hartmann (1995); the values adopted for each star are included for reference in Table 6.

We also calculate the purely stellar component of each YSOs bolometric luminosity by removing the H-band veiling flux, expressed in magnitudes (see Section 3.2 for the transformation between the veiling flux ratio in a given band (e.g., r_H) and the photometric excess in that band (e.g., ΔH):

$$\begin{eqnarray} &&{{\rm log}}(L_{\rm stel}/L_{\odot }) = 0.4 \times\! \left (4.75- \big (\! H + \Delta H \!-\! A_H - {{\rm DM}} + {{\rm BC}}_H\! \big) \right).\nonumber \\ \end{eqnarray} \tag{ 7 }$$

We adopt the measured 2MASS H-band magnitude for isolated B59 members in this calculation, enabling us to perform an identical analysis of YSOs with known spectral types in other well-studied star-forming regions. Objects with nearby (<4'') companions may be blended in 2MASS due to that survey's relatively large pixels (∼2''); for those sources ([BHB2007] 2, 8 NW and SE, 13 NW, 18 NE and SW; [CLR2010] 2 NE and SW), we adopt the synthetic H-band magnitude measured from our spectra, noting that the SpeXTool reduction pipeline produces spectra with a first-order correction for slit losses derived from the observations of the telluric standard.

Both luminosity estimates (total and stellar only) are listed in Table 6 and shown in Figure 8. Accounting for the uncertainties in each of the input parameters results in a total uncertainty for these luminosity estimates of 0.3 dex. The difference between the total and stellar luminosity estimated for a given YSO is usually less than 0.2 dex, indicating that the veiling correction, while not negligible, does not exceed the overall error in each YSO's location in the H-R diagram.

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We have used the PMS evolutionary models calculated by D'Antona & Mazzitelli (1994) and updated in 1998 (DM98 hereafter), and those calculated by Baraffe et al. (1998), to infer the age and mass of each candidate B59 YSO. These parameters were determined by interpolating between model points with temperatures and luminosities similar to that of each YSO. These theoretical models do not account for accretion luminosity, so for this comparison we adopted the veiling subtracted value of L_stel for each YSO. Table 6 presents masses and ages derived for candidate B59 members with reliable spectroscopic and photometric information.

The stellar ages presented in Table 6 allow us to identify the characteristic timescale over which B59 has been actively forming stars. We calculate this timescale as the median age of all likely B59 members with reliable age estimates (i.e., all YSOs listed in Table 6 except [CLR2010] 2 NE and SW, which may not be linked to B59). We prefer the median to a standard mean because it is more robust to outliers with extreme ages (e.g., [BHB2007] 19). B59's median stellar age, as inferred from DM98 PMS tracks using veiling-corrected luminosity estimates (L_stel), is 2.6 Myr.

Table 6. Inferred Stellar Parameters

Source	Teff	BCH	log $\frac{L_{\rm tot}}{L_{\odot }}$	log $\frac{L_{\rm stel}}{L_{\odot }}$	DM98 Age	DM98 Mass	B98 Age	B98 Mass
					(Myr)	(M☉)	(Myr)	(M☉)
[BHB2007] 1	4060.	2.11	0.02	−0.10	0.79	0.49	4.37	1.14
[BHB2007] 2	3346.	2.37	−0.03	−0.03	≤0.07	0.20	≤1.0	0.60
[BHB2007] 3	2841.	2.58	−1.38	−1.38	2.59	0.09	≤1.0	0.07
[BHB2007] 4	3009.	2.51	−0.75	−0.89	1.04	0.14	≤1.0	0.14
[BHB2007] 6	3514.	2.27	−0.14	−0.14	0.15	0.24	≤1.0	0.62
[BHB2007] 7	4350.	2.02	0.12	−0.22	2.71	0.75	12.02	1.16
[BHB2007] 9	4350.	2.02	−0.37	−0.67	23.4	0.79	50.11	0.77
[BHB2007] 12	3009.	2.51	−1.12	−1.27	2.77	0.14	1.38	0.1
[BHB2007] 13NW	3514.	2.27	0.03	−0.03	0.088	0.23	≤1.0	0.68
[BHB2007] 14	4350.	2.02	0.05	−0.24	3.03	0.77	12.59	1.13
[BHB2007] 15	2841.	2.58	−0.90	−0.91	0.28	0.11	≤1.0	0.12
[BHB2007] 16	4590.	1.98	0.07	−0.09	2.77	0.88	13.18	1.24
[BHB2007] 18NE	3009.	2.51	−0.78	−0.94	1.28	0.14	≤1.0	0.13
[BHB2007] 18SW	3514.	2.27	−0.89	−1.04	6.71	0.34	13.2	0.46
[BHB2007] 19	3346.	2.37	−1.37	−1.47	16.6	0.26	19.1	0.27
[BHB2007] 20	3514.	2.27	−0.44	−0.60	1.37	0.30	3.47	0.50
V359 Oph	4060.	2.11	−0.36	−0.36	2.42	0.61	10.47	1.02
Lk Hα 345	4060.	2.11	−0.19	−0.39	2.83	0.63	10.96	1.00
[CLR2010] 2NE	3346.	2.37	−0.59	−0.72	1.28	0.22	2.19	0.33
[CLR2010] 2SW	3009.	2.51	−0.70	−0.84	0.54	0.13	≤1.0	0.14

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Our confidence in the age estimates we calculate here is reinforced by our ability to independently reproduce the age estimate derived by Luhman & Rieke (1999) for their sample of ρ Oph members. Following Luhman & Rieke (1999) by comparing each star's total (non-veiling corrected) luminosity to the DM98 tracks, and adopting their estimated distance of 166 pc (m − M = 6.1), we measure a median stellar age for ρ Oph of 0.21 Myr, consistent with the ∼0.3 Myr median stellar age Luhman & Rieke (1999) derived.

We also measured median stellar ages for other, well-studied young clusters to provide an indication of B59's relative, rather than absolute, age. These cluster age measurements require YSOs catalogs with measured spectral types and JHK photometry to estimate extinction and veiling-corrected stellar luminosities using the same algorithms we applied to B59's YSOs. Studies by Luhman and collaborators provide such catalogs for YSOs in Taurus, Rho Ophiuchus, and Chameleon (Luhman & Rieke 1999; Luhman et al. 2006; Luhman 2007). We have placed these objects on the H-R diagram using the same routines applied to our B59 data, adopting the following distances to each region: Taurus—140 pc, Oph—126 pc, and Cha—170 pc (Kenyon et al. 2008; Wilking et al. 2008; Luhman 2008). Table 7 presents the median stellar age implied for each cluster by the DM98 and Baraffe et al. (1998) PMS tracks, and Figure 9 shows the locations of each region's YSOs in the H-R diagram.

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Our analysis of the ages of YSOs in other regions, however, lacks the iterative refinement of each YSO's veiling estimate according to the agreement between the strengths of spectral features in the target and artificially veiled standard spectrum. Instead, for YSOs in other regions, we simply adopt the mean CTTS J-band veiling measured by Cieza et al. (2005), which implicitly assumes that CTTSs dominate the population of each star-forming region. This J-band excess is an overestimate of the minimal veiling flux detected from WTTSs, however, such that we will underestimate WTTSs intrinsic stellar luminosity, and thus overestimate their age. Our age estimates for Taurus, ρ Oph, and Chameleon will therefore be slightly biased toward older ages in proportion to the number of WTTSs in the sample: we expect this to be a minimal effect for Taurus and ρ Oph, but potentially of some importance for the age we measure for the Chameleon star-forming region.

Our measurement of B59's median stellar age is subject to a few distinct statistical and systematic uncertainties. These affect the relative and absolute precision of our measurement in different ways, so we discuss them each below.

3.6.1. Random/Statistical Age Uncertainties

3.6.2. Systematic Age Uncertainties: Veiling-corrected Luminosities

3.6.3. Systematic Age Uncertainties: Adopted PMS Tracks

As shown by Hillenbrand et al. (2008), the choice of PMS models from which to infer YSO ages has a significant effect on the absolute age derived for a given cluster. Hillenbrand et al. (2008) found that the PMS models computed by DM98 and Baraffe et al. (1998) predict the youngest and oldest ages, respectively, for a YSO of a given temperature and luminosity. We therefore use these two sets of model tracks to span the full range of B59's potential absolute age. Using the same veiling-corrected luminosities derived above for B59's YSOs, but inferring ages from the α = 1 PMS tracks calculated by Baraffe et al. (1998), results in a median stellar age for B59 of 4.4 Myr, or roughly 70% older than the median stellar age inferred from the DM98 models.

Model-dependent age differences are often attributed to luminosity offsets between equal age isochrones in two sets of PMS tracks. This suggests that, while the absolute ages predicted by two sets of PMS tracks may differ, they should produce similar relative age orderings for a given sample of clusters. Table 7 reveals, however, that this simple expectation is not necessarily borne out in practice: both sets of models indicate that B59 has the oldest median stellar age, but the DM98 models imply that ρ Oph is younger than Taurus and Chameleon, while the Baraffe et al. (1998) models identify ρ Oph as older than Chameleon and Taurus.

These different relative age orderings arise from differences in the stellar population sampled in each cluster, combined with distinct isochrone slopes predicted by the two sets of PMS tracks. The temperature-dependent offset between the 5 Myr DM98 and Baraffe isochrones is shown in the left panel of Figure 10. The Baraffe models imply consistently older ages for a given H-R diagram location, but the age difference increases rapidly toward higher T_eff. This means that the relative age orderings of single stellar populations may not be preserved across models if the YSOs observed sample different temperature ranges. This is precisely the cause of the different relative ages inferred for ρ Oph in the DM98 and Baraffe models: as demonstrated in the right panel of Figure 10, the median temperature of the ρ Oph cluster stars is significantly larger than that of the other clusters analyzed here.

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3.6.4. Systematic Age Uncertainties: Cluster Distances

3.6.5. Total Error Budget for B59's Age Estimate

The prompt star formation paradigm agrees well with the evolutionary timescales expected for dense cores that lack significant internal or external support. Acted on by gravity alone, a core should collapse in roughly one free-fall time, τ_ff = (3π/32Gρ)^1/2. Hydrodynamic models of undriven turbulent molecular clouds predict only slightly longer evolutionary timescales, as the turbulent support dissipates on ∼1–2 free-fall timescales (Klessen et al. 2000). Offner et al. (2008), for example, find that star formation activity ceases after 0.75 τ_ff in their simulations of star formation within undriven turbulent molecular cores.

The uncertainties associated with our measurement of B59's age are sizable, but the most straightforward interpretation of this result is that star formation activity began in B59 nearly 3 Myr ago. The presence of heavily embedded (and presumably young) Class 0/I objects within B59 (Brooke et al. 2007; Riaz et al. 2009) also implies that this star formation activity has persisted to the present day. If the oldest stars in B59 formed from the dense core currently associated with the cluster, these observations would indicate a lower limit of 3 Myr for the core's lifetime. A star formation timescale for B59 comparable to 3 Myr is by no means startling in absolute terms. Indeed, while the stellar content of B59 appears somewhat older than that of the ρ Oph, Taurus, and Chameleon star-forming regions, the inferred star formation timescales agree to within a factor of 2.

Expressing B59's age in units of the core free-fall time and the core's crossing time is also useful for interpreting the core's physical evolution. Adopting the density (n(H₂) = 10⁴ cm⁻³; ρ = 3.5 × 10⁻²⁰ g cm⁻³), radius (R = 0.19 pc = 5.9×10¹² km), and velocity dispersion (σ_v = 0.37 km s⁻¹, calculated from 0.86 km s⁻¹ FWHM) tabulated for the B59 dense core by Rathborne et al. (2009), we calculate τ_ff∼0.35 Myr and τ_cross∼0.5 Myr. These calculations describe B59's current state; if B59 is evolving from a lower density to higher density configuration, these timescales would have been somewhat longer in the past than they are today. Intensive observations of the dense gas within B59, however, have not revealed any kinematic signatures of rapid collapse (Rathborne et al. 2009). If B59 is evolving relatively quiescently, the timescales we derive today are likely comparable to those of B59's recent past.

The uncertainties on B59's age permit that star formation may have begun as recently as the core's last dynamical time, or as long as ∼13 dynamical timescales ago. The maximum likelihood value, however, suggests that B59 has been forming stars for ≈6 crossing or free-fall times. Extinction maps of B59 also indicate that the core is spatially coherent, having not undergone significant fragmentation as it formed stars (Román-Zúñiga et al. 2009). Taken at face value, the maximum likelihood value of B59's star formation timescale suggests that B59 could join a short, but growing, list of dense cores that appear to have resisted global collapse and sustained ongoing star formation for several dynamical times. Swift & Welch (2008) examined the dense gas and stellar population of the L1551 star-forming region, demonstrating that L1551 has been forming stars for ∼5 Myr, or ⩾5 τ_ff; they identify stellar feedback as a likely source of support against collapse within this region. As we find for B59, Swift & Welch (2008) also find that L1551 contains stars over a broad range of evolutionary stages (Class 0–III). Similar results have been reported for the young cluster AGFL961; Williams et al. (2009) conclude that either disk evolution proceeds more rapidly in clustered environments, or that star formation persists in clusters over several dynamical timescales. Finally, Tan et al. (2006) present observationally based calculations that suggest ages of ∼3–4 τ_ff for several rich young clusters that are still forming stars (i.e., ρ Oph, IC 348, ONC, etc.). These measurements suggest that some dense cores can sustain star formation over a few dynamical timescales, including in relatively low-mass cores like B59, which does not appear to host massive stars.

What physical mechanism could be supporting these cores against collapse, extending their lifetimes beyond that expected for cores in free-fall collapse? As noted above, one possibility is stellar outflows: Matzner (2007) calculates that outflows may support clusters against collapse for several crossing times. This mechanism could explain B59's relative stability, particularly given that Onishi et al. (1999) and Riaz et al. (2009) find evidence for an active outflow within the B59 core. A recent ammonia survey of the Pipe, however, finds little evidence for significant non-thermal motions within B59's dense gas, as would be expected if bulk outflow motions are the core's main support against gravitational collapse (Román-Zúñiga et al. 2009; Rathborne et al. 2008). High-resolution observations of the kinematics of B59's dense gas are required to clarify the extent to which it (and, by extension, outflows from previous generations of protostars) could support B59 against collapse.

The collapse of a molecular core may also be strongly affected by radiative feedback from the young protostars it contains. Krumholz et al. (2007) used simulations of massive molecular cores to demonstrate that protostars can contribute significant heating to a collapsing core, thereby suppressing fragmentation. This heating does not, however, appear to slow mass accretion and collapse within the core: much of the radiation "leaks" out of optically thin holes in the core (Krumholz et al. 2009). Offner et al. (2009) extended this investigation into the regime of low-mass star formation, finding a similar reduction in stellar multiplicity due to reduced fragmentation, as well as a significant reduction in the mass accretion rate of the earliest formed protostar. These simulations suggest that radiative feedback could play some role in extending B59's star formation timescale.

Magnetic fields are a final physical mechanism that is often invoked to support cloud cores against collapse. Magnetic fields have been a fundamental component of star formation models for decades (Nakano 1984; Shu et al. 1987; Mouschovias & Ciolek 1999), but observational constraints on the strengths of magnetic fields within molecular clouds are difficult to obtain (e.g., Crutcher et al. 2009). Past measurements suggest magnetic fields may contribute appreciable amounts of support to molecular cores (Troland & Crutcher 2008), and recent polarization measurements in the Pipe Nebula indicate the presence of a ∼17  μG magnetic field within B59 itself (Alves et al. 2008). This suggests that magnetic fields may be providing B59 with some support against collapse, but this is a relatively weak statement: magnetic fields can extend a dense core's lifetime arbitrarily, depending on the field strength adopted.

As the discussion above demonstrates, there are several mechanisms which could plausibly explain B59's maximum likelihood star formation timescale. To provide additional leverage for comparing observations of B59 with predictions of theoretical models of star-forming cores, we now consider B59's SFE in addition to its characteristic timescale.

B59's present-day SFE can be characterized as the mass of the cluster's stellar population divided by the core's initial gas mass. The total mass of all B59 YSOs analyzed here is ∼8 M_☉ according to the DM98 models, and 12 M_☉ according to the Baraffe et al. (1998) models. Brooke et al. (2007) and Riaz et al. (2009) also provide preliminary mass estimates for [BHB2007] 10, 11, and 2M12112255, the B59 YSOs that were too heavily embedded to be observed with SpeX. These embedded YSOs contribute an additional 0.7 M_☉ to B59's total stellar mass, bringing B59's total stellar mass to ∼9–13 M_☉.

B59's initial gas mass can be approximated as the sum of its stellar and gas masses. Extinction maps indicate that B59 contains ∼20 M_☉ of dense gas, implying an initial core mass of ∼29–33 M_☉. This suggests B59's present-day SFE is ∼30%–40%, depending on the choice of models used to infer stellar masses. Combining this SFE with B59's median stellar age produces an estimate of the SFE/τ_ff of the B59 dense core. B59's sizable age uncertainty translates into a large range of allowed SFE/τ_ff values: 3%–40%, though the probability distribution is strongly asymmetric, peaking at a maximum likelihood value of ∼6%.

The SFE/τ_ff values predicted by theoretical models for star-forming cores cover a large range, with slower star formation rates corresponding to models incorporating some additional physical mechanism (driven turbulence, magnetic fields, outflows, etc.) to support cores against collapse. Unsupported models typically produce SFE/τ_ff values ∼ 10%–20%, while models that incorporate additional support often predict proportionally lower SFE/τ_ff values. As one example, the moderately supercritical (i.e., prone to gravitational collapse) magnetic models of Vázquez-Semadeni et al. (2005) produced SFE/τ_ff values ∼5%, whereas earlier non-magnetic models by the same authors produced SFE/τ_ff values ∼15% (Vázquez-Semadeni et al. 2003). The magnetically subcritical models of Nakamura & Li (2008), which also incorporate feedback from stellar outflows, produce SFE/τ_ff values of 1% or less.

The theoretical models calculated by Price & Bate (2009) are arguably the best match to B59's actual physical structure. These models (indicated hereafter as "the PB09 model grid") incorporate both magnetic fields and radiative feedback, and follow the evolution of a cloud core whose mass (50 M_☉) and radius (∼0.2 pc) are reasonably close to the values which likely characterized B59 prior to the onset of active star formation. The PB09 model grid spans magnetic fields of various strengths, but all models were supercritical, with mass-to-flux ratios ranging from 3 to ∞. Though the models were only allowed to evolve over a time span corresponding to 1.5 τ_ff, or 0.35–0.5 τ_ff following the formation of the first star in the core, the implied SFE/τ_ff values range from ∼30% for the model lacking both magnetic fields and radiative feedback, to ∼6% for the model incorporating radiative feedback and the strongest magnetic field (B₀ = 65 μG). In analyzing the range of SFEs produced by their model grid, PB09 note that magnetic fields appear to play a more important role than radiative feedback in quenching star formation.

B59's maximum likelihood SFE/τ_ff value of ∼6% is contained within the range of values predicted by the PB09 models, but B59's observed magnetic field strength (B ∼ 17  μG) is only ∼1/4 that adopted in the least efficient PB09 model (B ∼ 65  μG). The PB09 models and the present-day B59, however, represent significantly different time periods in the evolution of a star-forming core. It would be interesting to see what properties the PB09 models might have if they were allowed to evolve to ∼5 τ_ff: would the magnetic field diffuse out of the core, such that the measured magnetic field strength would better agree with what we observe in B59 today?

It is too early to draw detailed conclusions, but the agreement between B59's observed properties and the predictions of the PB09 model grid are intriguing, and suggest that magnetic support and radiative feedback help support B59 against collapse.

The suggestion that magnetic fields may be important for understanding star formation within the Pipe Nebula is also consistent with the results of the polarization survey conducted by Alves et al. (2008). Alves et al. (2008) measure a significant spatial gradient in the component of the Pipe's magnetic field aligned with the plane of the sky, ranging from ∼17  μG in B59 to ∼65 μG in the Pipe's "Bowl." As Alves et al. (2008) indicate, this gradient correlates with star formation activity: the weakest, most poorly aligned field vectors lie in B59, where the bulk of the Pipe's star formation activity is taking place, while areas with stronger, better aligned magnetic field vectors appear devoid of star formation activity.

In this context, it is interesting to note the location of [CLR2010] 2, the candidate YSO identified by Forbrich et al. (2009) in their MIPS survey of the Pipe, and subsequently confirmed as a likely YSO by our spectroscopic analysis. This candidate YSO lies in the Pipe's "Stem," where the magnetic field appears to be stronger than in B59, but not as strong as in the Bowl. This YSO also displays a rich emission line spectrum, suggesting it is a young, heavily accreting YSO, which would be consistent with a picture in which star formation activity was just beginning in the Neck of the Pipe. We note, however, that [CLR2010] 2 does not appear to be heavily embedded; indeed, [BHB2007] 10 and 11 appear to be in significantly earlier evolutionary stages than [CLR2010] 2, making it difficult to conclude that the onset of star formation activity is simply progressing linearly from B59 towards the Bowl of the Pipe.