MILLIMETER SOURCE 13 S IN R CrA: OBSERVATIONS OF A PROTO-HERBIG Ae SYSTEM CANDIDATE

Let us observe a variety of lines, and as emission signatures from specific physical conditions within the star-forming region vary with transition in addition to the amount of self-absorption, scattering (Fuller 1989), and saturation (Phillips et al. 1979), mean gradients in line width and velocity dispersion may represent systemic shifts in turbulence. The C₂H radical has a ${}^{2}{{\rm{\Sigma }}}^{+}$ electronic ground-state configuration; fine and hyperfine structure result from spin–orbit and electron–nucleus interactions, respectively (Müller et al. 2000). C₂H can probe ultraviolet (UV) irradiated (Fuente et al. 1993) and cold gas (Nakajima et al. 2011). Decreasing optical depth with time suggests use of this species as a "chemical clock" for molecular clouds (Li et al. 2012).

c-C₃H₂ has two equivalent H nuclei whose coupling results in ortho and para spin states. In the hydrocarbon family, sensitivity to UV radiation and turbulent mixing increases significantly from C₂H to C₃H₂ and from C₃H₂ to larger hydrocarbons (Qi et al. 2013). c-C₃H₂ can probe HAe disks (Qi et al. 2013) as well as photodissociation regions (Pety et al. 2005) and planetary nebulae (Tenenbaum et al. 2009), tracing dense and UV-illuminated regions.

Observations and theory suggest a profusion of C₅H and C³⁴S in early stages of dark cloud evolution, where these molecules' ground-state emission originates primarily from a region sheltered from infrared radiation (Leung et al. 1984; Herbst & Leung 1989; Takakuwa et al. 2000; Sakai et al. 2008).

CH₃OH is a principal constituent of grain mantles (Tielens & Allamandola 1987; Allamandola et al. 1992), where it can be produced by hydrogenation reactions of CO (Caselli et al. 1994); energetic processing through UV irradiation may lead to rapid production (Chiar et al. 1996). Methanol abundance is thought to peak early, having formed from C and C⁺ via CH₃⁺, and to decrease significantly later in molecular cloud evolution (Herbst & Leung 1989; Shalabiea & Greenberg 1995; Pratap et al. 1997). CH₃OH has been observed in dense IM cores, IM and massive hot cores (Benedettini et al. 2004; Sánchez-Monge et al. 2010; Fuente et al. 2014), hot core precursor candidates (van der Tak et al. 2000), as well as outflow associated with protobinaries (Parise et al. 2006) and IM protostars (Beltrán et al. 2002).

HC₃N can trace early dark cloud evolution (<10⁵ year) when cores efficiently produce C-chain molecules (Jørgensen et al. 2004; Suzuki et al. 2014), dense cold and warm gas (Meier et al. 2011), filamentary cores (Li & Goldsmith 2012), as well as disks (Chapillon et al. 2012). Higher fractional abundances have been observed in low-mass rather than high-mass cores, indicating destruction by UV radiation (Chung et al. 1991).

High HCN abundances are associated with shock chemistry (Tafalla et al. 2010) and high kinetic temperatures (Harada et al. 2010). The luminosity as traced in HCN, L_HCN, exhibits linear correlations with that in the far-infrared, L_FIR, and SFE (Gao 2009).

H¹³CO⁺ column densities are well correlated with those of DCO⁺, which may originate in denser regions than those probed in traditional dense core tracers such as NH₃ (Butner et al. 1995). H¹³CO⁺ emission is associated with dense outflows as well (Sugitani et al. 2002).

HNC may be destroyed by shocks and at high temperatures through neutral–neutral reactions (Schilke 1992; Schilke et al. 1992), enhancements tracing cold gas. Close correlation is observed between abundances in HNC and HC₃N in low-mass protostellar envelopes (Jørgensen et al. 2004).

N₂H⁺ plays a critical role as it is not readily depleted due to the low binding energy of N₂ to grains (Aikawa et al. 2003). This molecule is a reliable tracer of cold dark cloud cores with densities up to ∼10⁶ cm⁻³ (Daniel et al. 2007), massive dense cores (Pirogov et al. 2003), as well as low-mass (Chen et al. 2007) and IM Class 0 cores (Alonso-Albi et al. 2010).

SO has two unpaired electrons and is excited by near-infrared radiation to the more reactive singlet state. This molecule is found in high velocity outflows (Chernin et al. 1994). Increasing gas-phase abundance with time suggests the use of SO as a "chemical clock" for molecular clouds (Bergin & Langer 1997).

Transitions observed here in C₂H and N₂H⁺, which exhibit a significant non-thermal velocity dispersion (Table 1), have the most similar morphologies and closest peaks of observed species in support of turbulent mixing in the region as these molecules tend to probe UV-enhanced (Fuente et al. 1993; Kastner et al. 2015) and dense environments (Daniel et al. 2005, 2007), respectively (Figure 2). We start by describing the observations and distributions then move to consideration of the proto-HAe system candidate (Figure 1) and wind generation.

Zoom In Zoom Out Reset image size

Table 1.  MMS 13 in R CrA: Observations of a Proto-HAe System Candidate

Line	${\nu }_{0}$	La	${\rm{\Delta }}V$	${\sigma }_{v}$ b	Nc	${M}_{\mathrm{vir}}$ d	M
	(MHz)	(10−2 pc)	( km s−1)	( km s−1)	(1013 cm−2)	( ${M}_{\odot }$)	(${M}_{\odot }$)
C2H 1–0	87316.925	7.1	0.77	0.25	0.3	4.7	0.4
C34S 2–1	96412.961	4.8	0.31	0.24	0.2	0.5	1.7
C5H $\frac{39}{2}$ − $\frac{39}{2}$ f	93094.900	4.0	0.30	0.15	⋯	0.4	⋯
c-C3H2 2–1	85338.906	4.3	0.39	0.19	0.4	0.7	0.07
CH3OH 2–1	96741.377	9.3	0.52	0.33	2.0	2.6	3.1
CS 2–1	97980.953	11.8	1.23	0.56	0.2	18.6	2.7
H13CO+ 1–0	86754.330	8.6	0.93	0.28	0.4	7.9	5.5
HC3N 10–9	90978.989	6.9	1.00	0.36	0.4	7.2	1.7
HCN 1–0	88631.847	9.7	1.74	0.58	6.0	25.9	1.7
HCO+ 1–0	89188.526	12.5	1.43	0.85	19.4	26.8	2.9
HNC 1–0	90663.572	10.0	1.47	0.60	1.0	22.7	3.7
N2H+ 1–0	93173.480	7.1	0.66	0.67	1.0	3.2	3.2
SO 2–1	86093.983	4.1	0.44	0.20	0.3	0.8	0.04
SO 3–2	99299.905	5.9	0.61	0.25	0.4	2.4	0.1

Notes. Species, rest frequency, emission diameter, FWHM line width, velocity dispersion, column density, and virial and abundance-derived mass are listed for each transition.

^aWithin half-peak integrated intensity. ^bAverage second moment values within half-peak contour. ^cSee Section A.1. ^dM_vir ∼ $210R{\rm{\Delta }}{V}^{2}$ ${M}_{\odot }$ with ${\rm{\Delta }}V$ in km s⁻¹ and R = $\sqrt{(\frac{a}{2})(\frac{b}{2}})$ in pc; a, b values are listed in Table 2.

Download table as:  ASCIITypeset image

Maps of integrated intensity are shown in Figures 2 and 3. CS (2–1), HCN (1–0), and HCO⁺ (1–0) exhibit ∼EW extending morphologies with peaks close to IRS 7 as well as MMS 13. H¹³CO⁺ (1–0) and HNC (1–0) are similarly extended yet present more elongated (∼3:1 aspect ratio) 90% distributions, the former peaking ∼0.03 pc SW (at a distance of 130 pc) of IRS 7 within pointing accuracy of the peaks in N₂H⁺ (1–0), C³⁴S (2–1), and C₂H (1–0), the latter peaking ∼0.01 pc further NW toward the "quiescent core" identified by Anderson et al. (1997). Optically thin emission ($\tau \leqslant 0.2$) in H¹³CO⁺ (1–0), C₂H (1–0), c-C₃H₂, C₅H, CH₃OH (2–1), C³⁴S (2–1), and SO (3–2), (2–1) has a center, systemic V_LSR of ∼5.8 km s⁻¹ (e.g., Figure 4), which is also the average velocity of the R CrA core (Harju et al. 1993). The 95% distribution in C³⁴S (2–1) describes a ∼NS filament extending south to the CH₃OH (2–1) peak around which a ring structure in c-C₃H₂ (2–1) and C₅H is observed. N₂H⁺ (1–0) and C₂H (1–0) present similar, NWW-SEE elongated overall morphologies that are more compact in the vicinity of MMS 13 than those in H¹³CO⁺ (1–0) and HNC (1–0), exhibiting a ∼50% more abrupt drop in intensity outside of the ∼80% distribution. HC₃N (10–9) has a distribution intermediate to that in HCO⁺ (1–0) and H¹³CO⁺ (1–0) with maximum brightness at the midpoint between IRS 7 and the N₂H⁺ (1–0) peak within pointing accuracy of MMS 13.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

CH₃OH (2–1) distributions corresponding to wing emission (Figure 4) are observed around the N₂H⁺ (1–0) peak aligned with previously described outflow lobes (Figure 5 of Groppi et al. 2007), IR 1858-37, and several HH objects (Figure 5). SO (3–2) emission lies along a NW–SE ridge with a deficit at IR 1858-37; velocity-extended emission (Figure 5) is aligned ∼EW with previously observed IRS 7 outflow (Figure 5 of Groppi et al. 2007) around an antisymmetry center in HNC (1–0) (Figure 6). SO (2–1) exhibits a peak close to the northern peak in SO (3–2) corresponding to the redshifted lobe (Figure 5). In CH₃OH (2–1), which may probe interaction with outflow in SO (3–2) (Figure 5), northern emission coincides with the compact N₂H⁺ (1–0) and C₂H (1–0) distributions. Emission in elongated (∼3:1 aspect ratio) distributions in C³⁴S (2–1) and CH₃OH (2–1) coincides, tracing gas ∼0.05 pc south of MMS 13 (e.g., Figure 6, bottom left).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Outflow in HCO⁺ (1–0) around IRS 7 is aligned with that in SO (3–2) (Figure 5). The velocity flow at center velocity (hereafter center velocity flow) in H¹³CO⁺ (1–0) and HNC (1–0), whose ${\sigma }_{v}$ is twice supersonic at 20 K, is channeled ∼90° in the vicinity of the peak in N₂H⁺ (1–0) (Figure 7), whose ${\sigma }_{v}$ is similarly turbulent (Table 1), to align with velocity-extended emission (Figure 5); in HCN (1–0), system velocity flow is redirected similarly at the antisymmetry center. N₂H⁺ (1–0) and H¹³CO⁺ (1–0) exhibit a central decay of turbulence (Figure 4) in the region coincident with the flow convergence site and C³⁴S (2–1) filament (Figure 7); toward and around their peaks, which models mark as central to the proto-HAe system candidate (Figure 8, Section 3.2), characteristic infall profiles are observed (Figures 4, 9). Model Gaussian fits to integrated intensities are given in Table 2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 2.  Model Gaussian Fits with IMFIT (Sault et al. 1995)

Line	aa	bb	${\rm{\Theta }}$ c	${\sigma }_{\mathrm{res}}$ d
	('')	('')	(°)	( K km s−1 )
C2H (1–0)	138	92	41.1	0.05
C3H2 (2–1)	75	63	−79.9	0.02
C5H ($\frac{39}{2}-\frac{37}{2}{\rm{f}}$)	82	46	67.2	0.02
CS (2–1)	184	161	77.2	0.15
C34S (2–1)	55	106	−10.0	0.02
CH3OH (2–1)	166	133	−41.2	0.08
HC3N (10–9)	172	70	−79.5	0.08
HCN (1–0)	184	122	89.8	0.15
HCO+ (1–0)	253	156	−77.1	0.27
H13CO+ (1–0)	184	101	−69.4	0.09
HNC (1–0)	230	110	−60.9	0.15
N2H+ (1–0)	135	94	−77.8	0.15
SO (3–2) N	97	89	75.7	0.12
SO (2–1) N	80	49	78.3	0.02

Notes.

^aDeconvolved FWHM major axis. ^bDeconvolved FWHM minor axis. ^cDeconvolved P.A. ^dResidual rms.

Download table as:  ASCIITypeset image

Abundance-derived mass estimates for a cyclindrical distribution, M ∼ $\frac{1}{8}\mu {m}_{H}\pi \frac{N}{X}{L}^{2}$, are listed in Table 1. Abundance- and virial-derived values are closest of the observed species in N₂H⁺ (1–0), CH₃OH (2–1), H¹³CO⁺ (1–0), and C³⁴S (2–1), whose mean M_N is within 10% of that of HNC (1–0), 3.7 ${M}_{\odot }$. The former three species' average, 4.1 ${M}_{\odot }$, is within 5% of the value derived for MMS 13 from millimeter and submillimeter continuua (Chini et al. 2003; Nutter et al. 2005) at 130 pc and a dust temperature of 15 K.

Mass values together with emission in several lines offset from the continuum peak in Figure 1 are consistent with these observations' tracing of depletion and prestellar gas in central MMS 13 (e.g., Tafalla et al. 2002; Nutter et al. 2005). Interestingly, distributions in SO (3–2), CH₃OH (2–1), C³⁴S (2–1), C₂H (1–0), c-C₃H₂ (2–1), and C₅H lie considerably south (∼0.05 pc) of MMS 13, bolstering an additional case together with mass and age estimates for these species' depletion in a core central to the observed peaks in N₂H⁺ (1–0), C₂H (1–0), H¹³CO⁺ (1–0), C³⁴S (2–1), and HNC (1–0) and the MMS 13 S region (see below) as host of a proto-HAe system (in a contraction phase prior to conclusive inner core collapse), shaped through prestellar core interaction³ as well as infall (e.g., Sadavoy et al. 2012). Such interaction would explain naturally (invoking a less severe depletion scenario than that corresponding to all observed emission tracing central MMS 13) (1) systematic distribution and model coincidence in emission tracing the proto-HAe system candidate (∼from S to N: CH₃OH (2–1), C³⁴S (2–1), C₂H (1–0), N₂H⁺ (1–0), H¹³CO⁺ (1–0), and HNC (1–0)) with that tracing MMS 13 (∼from S to N: HC₃N (10–9), HCO⁺ (1–0), HCN (1–0), and CS (2–1)) in a region corresponding to the central decay of turbulence in N₂H⁺ (1–0) and H¹³CO⁺ (1–0) and (2) flow convergence in N₂H⁺ (1–0), H¹³CO⁺ (1–0), and HNC (1–0) in a region corresponding to the central C³⁴S (2–1) filament (Sections 3.3, A.2; Figures 6–8). In this case, mean density in the central system candidate, $\frac{N}{L}$ (in C³⁴S (2–1), N₂H⁺ (1–0), C₂H (1–0), and H¹³CO⁺ (1–0)) is 4.9 × ${10}^{5}$ cm⁻³, in agreement with (less than 20% above) previously derived values in the region (Loren et al. 1983).⁴ Mass calculations together with several kinematic features discussed in Section 3.3 also support this scenario. M_N and M_vir values in CH₃OH (2–1) (which traces dense IM cores and hot core precursors; Section 1.1) are the second closest of observed species after N₂H⁺ (1–0) (which traces IM class 0 cores; Section 1.1), followed by H¹³CO⁺(1–0) as well as C³⁴S (2–1) (which trace dense cores and outflow as well as early-time chemistry, respectively, Section 1.1) whose peaks coincide with that in N₂H⁺ (1–0) (Table 1).

MMS 13 is also a prominent region as observed at submillimeter wavelengths, with an elongated, possibly binary source to the south apparent in 450 μm emission (Figure 3 of Nutter et al. 2005). The proto-HAe system candidate resides at the SW edge of this elongation at a similar intensity level (in 450 μm continuum) as VLA 10 A and 10 B, while IRS 7 lies in a region ∼5σ lower; in 1.2 mm continuum, these sources lie at the same level as the candidate (Figure 1). Temperatures of 11–15 K derived through spectral energy distribution fitting (ibid), the absence of a centimeter source, and age estimates (Section A.2) reinforce these observations' tracing of a youthful (Palla & Stahler 1993) proto-HAe system in MMS 13 S whose central heating is incipient due to turbulent support (in accordance with high non-thermal ${\sigma }_{v}$ in N₂H⁺ (1–0) and turbulent flow convergence with that in HNC (1–0) (Table 1, Figure 7)) and/or early-time chemistry (in accordance with observed distributions in C³⁴S (2–1), C₅H, c-C₃H₂ (2–1), C₂H (1–0), and SO (3–2), (2–1) (Figures 2, 3)) in the region (e.g., Dickens et al. 2001).

Center velocity flow in HNC (1–0) and H¹³CO⁺ (1–0) is channeled (as seen in the 5.8 km s⁻¹ contour being abruptly redirected $90^\circ$, Figure 7) to align with velocity-extended emission in CH₃OH (2–1) and SO (3–2) (Figure 5) which is perpendicular to the 90% integrated intensity in N₂H⁺ (1–0) and C³⁴S (2–1) (Figures 2, 3). Along with the fact that this extended emission is observed around the region corresponding to central turbulence decay in N₂H⁺ (1–0) and H¹³CO⁺ (1–0) (Figure 4), infalling motions (Figures 4, 9), and differential rotation (Figure 6), this is consistent with magnetohydrodynamic wave fluctuation induced wind generation in the proto-HAe system candidate (e.g., Shu et al. 1987; Corcoran & Ray 1998; Markovskii 2001; Isenberg & Vasquez 2011). That extended emission may correspond in part to outflowing motions is in agreement with a reversal of the velocity field gradient over the 5.8 km s⁻¹ contour in HNC (1–0) perpendicular to the rotation axis (e.g., Saul et al. 2011; see Section A.2). Alignment variations in this emission are not anomalous and together with those associated with outflow in other regions of early star formation (Fendt & Zinnecker 2000; Torrelles et al. 2003; Günther et al. 2013) are consistent with X-wind models yielding equatorial streamlines even in collimated flows (Shu et al. 1995; Liseau et al. 2005). Mean velocity dispersion ${\sigma }_{v}$ in species peaking at the proto-HAe system candidate which trace quiescent gas (in C³⁴S (2–1), C₂H (1–0), and H¹³CO⁺ (1–0)) is a factor of ∼3 less than in those peaking near IRS 7 (in CS (2–1), HCN (1–0), and HCO⁺ (1–0)); mean line width in species whose emission extends south of the system (in C³⁴S (2–1) and CH₃OH (2–1)) is a factor of ∼3 less than in that extending north (in H¹³CO⁺ (1–0) and HNC (1–0)), indicative of a similar turbulence shift from quiescent gas in the system to IRS 7 to that within the extended system envelope (e.g., Mannings 1995; Table 1 and see Figures 6, 8). In this scenario, channeling of center velocity flow with turbulence amplification along the proto-HAe system rotation axis shears the velocity field, launching wind (e.g., Parker 1969; Sur et al. 2012; Figures 5, 7).

HNC (1–0) and HCO⁺ (1–0) spectra around the N₂H⁺ (1–0) peak exhibit bulk infall characteristic peak reversal profiles, the blue- or redshifted peaks corresponding to infalling gas approaching or receding along the line of sight (e.g., Myers et al. 1995; Figure 4). HNC (1–0), together with N₂H⁺ (1–0) showing the greatest ${\sigma }_{v}$ of observed species with the exception of HCO⁺ (1–0) (which traces IRS 7 as well as MMS 13), exhibits increasingly blue- and red-skewed profiles toward and away from, respectively, the N₂H⁺ (1–0) peak (Table 1). This trend is similar to that observed in H¹³CO⁺ (1–0), indicative of an inflow boundary where inward (peak N₂H⁺ (1–0) directed) motions are reversed due to mounting winds from the increasingly turbulent proto-HAe system (e.g., Bally 2002) (Section A.2).

Observed intermediate distributions (systematic spatial shift in emission from N to S, in HNC (1–0), H¹³CO⁺ (1–0), N₂H⁺ (1–0), C³⁴S (2–1), and CH₃OH (2–1)) (Figure 6) and a uniform velocity dispersion gradient from IRS 7 to southern portions of the envelope (${\sigma }_{v}$ from N to S ∼ 3:2:1, in HCO⁺ (1–0), HNC (1–0), and CH₃OH (2–1)) (Table 1) combined with central emission features (infall, turbulence decay, channeling of center velocity flow; e.g., Figures 4, 7) is consistent with prestellar core interaction (e.g., merging) in addition to self-gravitational infall driving proto-HAe system formation in the region (e.g., Bonnell et al. 1998; Stahler & Palla 2005; Perets & Murray-Clay 2011). Support for interaction in the system candidate includes (1) 90% and 95% integrated intensities in C³⁴S (2–1) and H¹³CO⁺ (1–0) coincident with CH₃OH (2–1) and HNC (1–0) peaks, respectively (Figures 2, 3, and see Figure 6), (2) a continuous system to global turbulence transition (Section A.2), and (3) the difference in CH₃OH (2–1) and SO (3–2) line peaks (5.67 and 5.94 km s⁻¹) as due to inspiralling gas offset from bulk (systemic) velocity. Other evidence of interaction in CrA is provided by extreme H i to H₂ conversion (Llewellyn et al. 1981) and on a large scale by (a collisional origin for) CrA itself (e.g., Figure 2 in Cambrésy 1999).

In conjunction with mass and age estimates, observation of several physical mechanisms in R CrA implies the presence of a proto-HAe system. The existence of centrally peaking (to the system) turbulent cores in N₂H⁺ (1–0) and HNC (1–0), specifically a ${\sigma }_{v}$ in N₂H⁺ (1–0) greater than that in all observed species except for HCO⁺ (1–0), a ${\rm{\Delta }}V$ and ${\sigma }_{v}$ in HNC (1–0) greater than that in emission closely tracing highly dispersive gas in the vicinity of IRS 7 (HCO⁺ (1–0) and HCN (1–0), respectively, whose ${\sigma }_{v}$ and ${\rm{\Delta }}V$ are the greatest of observed species, respectively (Table 1)), and the absence of central turbulence dissipation in N₂H⁺ (1–0) or HNC (1–0) mean, together with mass values in Section 3.2, it is highly unlikely this source is low-mass, in which case we might expect a decay to near sonic values in central turbulence in N₂H⁺ (1–0) (Nakano 1998) as well as gas in the candidate (e.g., as traced in ${\sigma }_{v}$(N₂H⁺) and ${\sigma }_{v}$(HNC)) to be less turbulent than that in the active IRS 7, X_W region (e.g., as traced in ${\sigma }_{v}$(CS) and ${\sigma }_{v}$(HCN)). Conversely, the presence of differential rotation (evinced in HNC (1–0), Figure 6) implies the candidate is most likely not greater than 5 ${M}_{\odot }$ since disks may not exist around HBe stars (Strom et al. 1993; Natta et al. 2000; Cauley & Johns-Krull 2014), whereas often young and massive (Boissier et al. 2011) disks around HAe stars are observed with 75%–100% frequency (Natta et al. 1997). A more massive, i.e., highly turbulent source would not be affected significantly by less dispersive gas near IRS 7 and neither turbulence amplification along the rotation axis nor channeling of center velocity flow toward IRS 7 (Figure 7) could occur. High rates of mass infall and loss are consistent with accretion driven winds in a proto-HAe system (e.g., Corcoran & Ray 1998; Matt & Pudritz 2005; Section A.2). However, the mechanism of wind acceleration in young HAe/Be systems requires further study (e.g., Dougados et al. 2004; Cranmer 2009). High resolution observations toward the N₂H⁺ (1–0) peak in similar species as presented here could confirm our hypothesis of proto-HAe system wind generation (e.g., Tsinganos et al. 2003; Chyży 2008; Hubrig et al. 2009; Qi et al. 2013) as well as investigate possible episodic infall (e.g., Vorobyov & Basu 2005b; Kim et al. 2011) and a secondary in the region (e.g., Stelzer et al. 2005; Dzib et al. 2010).

Opacities are given by transition intensity ratios,

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{\mathrm{thin}}}{{I}_{\mathrm{thick}}}=\displaystyle \frac{1-\mathrm{exp}({-\tau }_{\mathrm{thin}})}{1-\mathrm{exp}(-{x}_{N}{\tau }_{\mathrm{thin}})},\end{eqnarray} \tag{ 1 }$$

where the abundance ratio,

$$\begin{eqnarray}&&{x}_{N}=\displaystyle \frac{{N}_{\mathrm{thick}}J({T}_{\mathrm{thin}}){\rm{\Delta }}{V}_{\mathrm{thin}}}{{N}_{\mathrm{thin}}J({T}_{\mathrm{thick}}){\rm{\Delta }}{V}_{\mathrm{thick}}}.\end{eqnarray} \tag{ 2 }$$

Similarly, with hyperfine components m, s,

$$\begin{eqnarray*}&&\displaystyle \frac{{I}_{s}}{{I}_{m}}=\displaystyle \frac{1-\mathrm{exp}({-\tau }_{s})}{1-\mathrm{exp}({-\tau }_{m})}.\end{eqnarray*}$$

For single transitions,

$$\begin{eqnarray}&&{\tau }_{{ij}}=\mathrm{ln}\displaystyle \frac{F({T}_{{ij}})-F({T}_{{bg}})}{F({T}_{{ij}})-F({T}_{{bg}})-{T}_{a}^{*}/\eta {\rm{\Phi }}{T}_{0}},\end{eqnarray} \tag{ 3 }$$

where F(T) = $\displaystyle \frac{J(T)}{{T}_{0}}$, J(T) = $\displaystyle \frac{{T}_{0}}{\mathrm{exp}({T}_{0}/T)-1}$, and

$$\begin{eqnarray}&&{T}_{{ij}}={T}_{0}/\mathrm{ln}(1+\displaystyle \frac{{T}_{0}}{J({T}_{{bg}})+\displaystyle \frac{{T}_{a}^{*}}{\eta {\rm{\Phi }}(1-\mathrm{exp}({-\tau }_{{ij}}))}}).\end{eqnarray} \tag{ 4 }$$

From the definition of optical depth,

$$\begin{eqnarray}&&N=\displaystyle \frac{8\pi k}{{{hc}}^{3}}\displaystyle \frac{{\nu }^{2}{Q}_{\mathrm{rot}}}{{A}_{{ij}}{g}_{u}}\mathrm{exp}(\displaystyle \frac{{E}_{i}}{{{kT}}_{{ij}}})\displaystyle \frac{{\tau }_{{ij}}}{1-\mathrm{exp}({-\tau }_{{ij}})}\int {T}_{{mb}}\ {dV},\end{eqnarray} \tag{ 5 }$$

where g_i is the upper level degeneracy which in local thermodynamic equilibrium is governed by the Boltzmann distribution characterized by kinetic temperature T_k ∼ T_ij, and $\int {T}_{{mb}}\ {dV}$ is the observed integrated intensity, for a hyperfine component,

$$\begin{eqnarray}&&\int {T}_{{mb}}\ {dV}\sim [J({T}_{{ij}})-J({T}_{{bg}})]\displaystyle \frac{1-\mathrm{exp}({-\tau }_{{ij}})}{{\tau }_{{ij}}}{\tau }_{{ij}}{\rm{\Delta }}V.\end{eqnarray} \tag{ 6 }$$

N values in Table 1 correspond to T_k ∼ 30 K for HCN (1–0) and CS (2–1), 20 K for HCO⁺ (1–0), SO (3–2), and HNC (1–0), and 10 K for the rest of the observed species except in the case of 15 K for HC₃N (10–9) (supported by a similar elongation to HCO⁺ (1–0) whose peak T_mb ∼ 15 K), consistent with submillimeter continuum observations and a three-phase density regime with a mean log N(H₂) ∼ 22.7 cm⁻² (Figure 3 in Nutter et al. 2005 and Figure 2 in Groppi et al. 2007).

An age estimate is given as the length of velocity-extended emission divided by the corresponding deviation ${\rm{\Delta }}V$ from line center. Assuming constant outflow⁵ velocity at 130 pc, in CH₃OH (2–1) this yields ∼ $80^{\prime\prime} /4.2\;$ km s⁻¹ $\sim \;1.2\times {10}^{4}$ year, in SO (3–2) and H¹³CO⁺ (1–0), $\sim 1.4\times {10}^{4}$ year; in HCO⁺ (1–0) around IRS 7, $\sim 3.6\times {10}^{5}$ year (e.g., Figures 3, 5). These values and a falling ${\rm{\Delta }}{({\sigma }^{2})}_{\mathrm{core}}$ profile from the system candidate to IRS 7 (a ∼50% decrease in ${\rm{\Delta }}({{\sigma }_{v}}^{2})$ from HNC (1–0)/H¹³CO⁺ (1–0) to HCO⁺ (1–0)/CS (2–1) and order of magnitude drop in ${\dot{M}}_{\mathrm{acc}}$ from N₂H⁺ (1–0) or CH₃OH (2–1) to CS (2–1); Saul 2012) in agreement with models finding an order of magnitude decrease in ${\dot{M}}_{\mathrm{acc}}$ from Class 0 to 1 regions (Bontemps et al. 1996; Vorobyov & Basu 2005a) as well as diminishing C³⁴S (1–0)/H¹³CO⁺ (1–0) intensity and width ratios to the NE (Pratap et al. 1997) indicate the proto-HAe system candidate as a young, potential Class 0 object (Nutter et al. 2005; Sicilia-Aguilar et al. 2013).

Using abundance derived mass values, the mechanical luminosity, L ∼ ${{MV}}^{2}/2t$, in CH₃OH (2–1) ∼ $0.2\;{L}_{\odot }$, while the outflow rate, $\dot{M}$ ∼ $M/t$, in SO (3–2) yields $\sim 6.4\times {10}^{-6}\;{M}_{\odot }$ yr⁻¹. With cylinder height H = 10R (Figure 7), the accretion rate $\dot{{M}_{\mathrm{acc}}}$ = $\displaystyle \frac{\pi }{5}{L}^{2}\mu {m}_{{\rm{H}}}{{nV}}_{\mathrm{in}}$, where μ is the mean molecular weight and m_H is the mass of a hydrogen atom; using L(C³⁴S), n ∼ 5.0 × 10⁵ cm⁻³ and a V_in given by mean line width ${\rm{\Delta }}V$ in species peaking at the flow convergence site at an inclination of 60° yields $\dot{{M}_{\mathrm{acc}}}\sim 2.9\times {10}^{-5}\;{M}_{\odot }$ yr⁻¹. Using L(c-C₃H₂) [$\sim L$(C₅H)] and ${\rm{\Delta }}V$(HNC) with the same density gives the same rate. The spherical rate ${\dot{M}}_{\mathrm{acc}}$ = $4\pi {R}^{2}\mu {m}_{{\rm{H}}}{{nV}}_{\mathrm{in}}$, using R = 0.02 pc (∼separation between peaks in N₂H⁺ (1–0) and CH₃OH (2–1) which is similar to that between those in N₂H⁺ (1–0) and HC₃N (10–9), which is $\sim L$(c-C₃H₂)/2) and V_in =0.20 km s⁻¹ (∼inflow boundary velocity ∼rms turbulence ∼c_s in an 11 K molecular gas ∼HNC (1–0) absorption dip deviation from systemic velocity (Figure 4)) yields $\dot{{M}_{\mathrm{acc}}}\sim 3.3\times {10}^{-5}\;{M}_{\odot }$ yr⁻¹). The average value, $3.0\times {10}^{-5}\;{M}_{\odot }$ yr⁻¹, indicates a considerable mass loss rate up to ∼20% that of accretion. Mean ${\rm{\Delta }}V$ in species peaking at the flow convergence site (N₂H⁺ (1–0), C³⁴S (2–1), H¹³CO⁺ (1–0), C₂H (1–0)) is $\sim {\sigma }_{v}$(N₂H⁺), ∼twice that in all observed species except HNC (1–0) and lines tracing IRS 7 (as well as MMS 13), in support of turbulence amplification along the rotation axis driving wind generation within an extended envelope (e.g., Mannings 1995). Turbulent velocity given by composite structure in the Galaxy, $\delta v$ $\sim$ 0.9${{L}_{\mathrm{PCA}}}^{0.56\pm 0.02}$ km s⁻¹ (Heyer & Brunt 2004) with L(N₂H⁺) in pc, is ∼that of the inflow boundary, consistent with a continuous system to global turbulence transition and the system as a source of turbulent energy. Sound speed in the infalling gas c_s ∼ ${(G\dot{{M}_{\mathrm{acc}}})}^{\frac{1}{3}}$ (Shu et al. 1987) is $\sim {V}_{\mathrm{ff}}{(\frac{4{{GM}}_{N}}{L})}^{\frac{1}{2}}$ {with mass and size given by least and most turbulent system components, respectively, in agreement with a quiescent core (e.g., ${\sigma }_{\mathrm{vir}1D}$(C³⁴S) ${(\frac{2{{GM}}_{N}}{5L})}^{\frac{1}{2}}$ > $\delta v$) fueled through turbulent transport (e.g., ${\rm{\Delta }}V$ $(\frac{\mathrm{HNC}}{{C}^{34}S})$ ∼ 5)}, is $\sim {\rm{\Delta }}V$ in CH₃OH (2–1) which has a ${\sigma }_{v}$ similar to that in HC₃N (10–9) despite exhibiting only half its ${\rm{\Delta }}V$, consistent with proto-HAe system candidate—central MMS 13 core interaction. A V_in given by σ(N₂H⁺) yields a spherical infall zone radius of ∼0.011 pc, the width of ${lV}$ indicated channeling in HNC (1–0) (Figure 4). The accretion luminosity, L_acc = ${GM}\dot{{M}_{\mathrm{acc}}}/R$, in H¹³CO⁺ (1–0) gives $\sim 1.7\times {10}^{31}$ erg s⁻¹.