Dynamical timescale of precollapse evolution inferred from chemical distribution in the Taurus Molecular Cloud-1 (TMC-1) filament

TL;DR

This study investigates the chemical distribution and dynamical evolution of the TMC-1 filament in Taurus, revealing how different chemical depletion patterns relate to the region's collapse timescales and star formation activity.

Contribution

It provides new insights into the relationship between chemical distributions and dynamical timescales in a star-forming filament through combined observations and chemical modeling.

Findings

CO depletion is more significant in the ammonia peak than in the cyanopolyyne peak.

N2H+ shows little depletion in either peak.

Chemical distribution differences are explained by varying dynamical timescales.

Abstract

We present observations and analysis of the low-mass star-forming region, Taurus Molecular Cloud-1 (TMC-1). CS ($J$=2-1)/N$_2$H$^+$ ($J$=1-0) and C$^{17}$O ($J$=2-1)/C$^{18}$O ($J$=2-1) were observed with FCRAO (Five College Radio Astronomy Observatory) and SRAO (Seoul Radio Astronomy Observatory), respectively. In addition, Spitzer infrared data and 1.2 mm continuum data observed with MAMBO (Max-Planck Millimetre Bolometer) are used. We also perform chemical modeling to investigate the relative molecular distributions of the TMC-1 filament. Based on Spitzer observations, there is no young stellar object along the TMC-1 filament, while five Class II and one Class I young stellar objects are identified outside the filament. The comparison between column densities calculated from dust continuum and C$^{17}$O 2-1 line emission shows that CO is depleted much more significantly in the ammonia peak than in the cyanopolyyne peak, while the column densities calculated from the dust continuum are similar at the two peaks. N$_2$H$^+$ is not depleted much in either peak. According to our chemical calculation, the differential chemical distribution in the two peaks can be explained by different timescales required to reach the same density, i.e., by different dynamical processes.

Tables

Table 1. Table 1: List of Observed Lines.

Molecule	Transition	Telescope	$\nu$	$\delta v$	${\theta }_{\mathrm{mb}}$	${\eta }_{\mathrm{mb}}$	rms	Observing Date
			(GHz)	(km s-1)	(arcsec)		(K)
N2H+	$J$=1–0	FCRAO 14 m	93.174	0.08	58	0.5	0.1	2003 Jan.
CS	$J$=2–1	FCRAO 14 m	97.981	0.07	55	0.5	0.1	2003 Jan.
C18O	$J$=2–1	SRAO 6 m	219.560	0.13	48	0.57	0.04	2009 Feb.
C17O	$J$=2–1	SRAO 6 m	224.714	0.13	48	0.57	0.04	2009 Feb.

Table 2. Table 2: Fluxes of Young Stellar Object Candidates in TMC-1.

				Fluxes from 2MASS (mJy)				Fluxes from Spitzer (mJy)
SourceaaThe numbers refer to the marked YSOs in Fig. 1.	c2d ID	R.A. (J2000)	Dec. (J2000)	J	H	Ks		IRAC1	IRAC2	IRAC3	IRAC4	MIPS1	MIPS2
		(h m s)	($°$ $\prime$ $″$)	(1.235 $\mathrm{\mu m}$)	(1.662 $\mathrm{\mu m}$)	(2.159 $\mathrm{\mu m}$)		(3.6 $\mathrm{\mu m}$)	(4.5 $\mathrm{\mu m}$)	(5.8 $\mathrm{\mu m}$)	(8.0 $\mathrm{\mu m}$)	(24 $\mathrm{\mu m}$)	(70 $\mathrm{\mu m}$)
YSO 1	SSTc2d J044049.5+255119	04 40 49.5	25 51 19.1	7.99E+01	1.10E+02	1.06E+02		6.69E+01	6.42E+01	5.54E+01	5.43E+01	5.58E+01
YSO 2	SSTc2d J044108.2+255607	04 41 08.2	25 56 07.4	5.11E+00	1.42E+01	2.45E+01		3.71E+01	4.11E+01	4.46E+01	5.19E+01	8.64E+01
YSO 3	SSTc2d J044110.8+255512	04 41 10.8	25 55 11.6	8.42E+00	1.45E+01	1.76E+01		1.32E+01	1.36E+01	1.37E+01	1.59E+01	1.80E+01
IRAS sourcebbIRAS 04381+2540.	SSTc2d J044112.6+254635	04 41 12.6	25 46 35.4	2.20E-01	2.27E+00	1.61E+01			1.39E+02		3.46E+02	1.72E+03	6.74E+03
YSO 4	SSTc2d J044124.6+254353	04 41 24.6	25 43 53.0	3.30E-01	3.95E+00	1.33E+01		1.95E+01	2.05E+01	2.09E+01	1.94E+01	4.31E+01
YSO 5	SSTc2d J044138.8+255627	04 41 38.8	25 56 26.8	2.90E+01	9.14E+01	1.39E+02		1.16E+02	1.59E+02	2.48E+02	4.22E+02	1.27E+03	2.11E+03

Table 3. Table 3: Comparison with Previous Studies.

SourceaaThe numbers refer to the marked YSOs in Fig. 1.	c2d ID	Gutermuth CategorybbGutermuth et al. (2008, 2009)	Rebull CategoryccRebull et al. (2010)	This Study	IdentificationddReference for the first identification of each source: JH 223 - Jones & Herbig (1979); ITG 33A, ITG 34 - Itoh et al. (1999); IRAS 04381+2540 - Beichman et al. (1986); GKH 32 - Gomez et al. (1994); Haro 6-33 - Haro et al. (1953).
YSO 1	SSTc2d J044049.5+255119	Class II	Class II	II	JH 223
YSO 2	SSTc2d J044108.2+255607	Class II	Flat	II	ITG 33A
YSO 3	SSTc2d J044110.8+255512	Class II	Class II	II	ITG 34
IRAS source	SSTc2d J044112.6+254635	Embedded	Class I	0/I	IRAS 04381+2540
YSO 4	SSTc2d J044124.6+254353	Class II	Flat	II	GKH 32
YSO 5	SSTc2d J044138.8+255627	Class II	Flat	II	Haro 6-33

Table 4. Table 4: Results of Bolometric Luminosity and Temperature of 6 YSO Candidates in TMC-1.

SourceaaThe numbers refer to the marked YSOs in Fig. 1.	c2d ID	$L_{\mathrm{bol}}$ ($L_{☉}$)		$T_{\mathrm{bol}}$ (K)	CLASS
YSO 1	SSTc2d J044049.5+255119	0.12		1722	II
YSO 2	SSTc2d J044108.2+255607	0.04		991	II
YSO 3	SSTc2d J044110.8+255512	0.02		1460	II
IRAS sourcebbIRAS 04381+2540.	SSTc2d J044112.6+254635	0.54		214	I
YSO 4	SSTc2d J044124.6+254353	0.02		922	II
YSO 5	SSTc2d J044138.8+255627	0.33		758	II

Table 5. Table 5: Results of Gaussian fits to CS ( J 𝐽 J =2–1) and C 18 O ( J 𝐽 J =2–1) Lines.

	Cyanopolyyne Peak					Ammonia Peak
Line	$V_{\mathrm{LSR}}$	$\Delta V$	$T_A$	$\int T_A𝑑V$		$V_{\mathrm{LSR}}$	$\Delta V$	$T_A$	$\int T_A𝑑V$
	(km s-1)	(km s-1)	(K)	(K km s-1)		(km s-1)	(km s-1)	(K)	(K km s-1)
CS ($J$=2–1)	5.91	0.63	0.60	0.40		5.78	0.70	1.16	0.86
	(0.01)	(0.03)		(0.01)		(0.01)	(0.02)		(0.02)
C18O ($J$=2–1)	5.61	0.76	1.08	0.87		5.42	0.94	0.80	0.80
	(0.01)	(0.02)		(0.01)		(0.02)	(0.05)		(0.03)

Table 6. Table 6: Results of Hyperfine structure to N 2 H + ( J 𝐽 J =1–0) and C 17 O ( J 𝐽 J =2–1) Lines.

	Cyanopolyyne Peak				Ammonia Peak
Line	$V_{\mathrm{LSR}}$	$\Delta V$	$\tau$aa$\tau$ is the sum of the optical depths of all hyperfine components.		$V_{\mathrm{LSR}}$	$\Delta V$	$\tau$aa$\tau$ is the sum of the optical depths of all hyperfine components.
	(km s-1)	(km s-1)			(km s-1)	(km s-1)
N2H+ ($J$=1–0)	5.60	0.44	7.64		5.75	0.41	6.77
	(0.01)	(0.03)	(2.11)		(0.01)	(0.02)	(1.63)
C17O ($J$=2–1)	5.65	0.68	1.71		5.53	1.01	0.10
	(0.02)	(0.05)	(0.66)		(0.02)	(0.04)	(0.16)

Table 7. Table 7: LSR Velocity in the TMC-1 filament.

Position	R.A. (J2000)	Dec. (J2000)	LSR Velocity
	(h m s)	($°$ $\prime$ $″$)	(km s-1)
The direction along the TMC-1 filament
P1	04 41 13.8	25 49 49.5	5.82 (0.01)
P2aaAmmonia peak.	04 41 20.9	25 48 07.2	5.75 (0.01)
P3	04 41 37.2	25 43 38.5	5.66 (0.01)
P4bbCynaopolyyne peak.	04 41 42.5	25 41 27.0	5.60 (0.01)
P5	04 41 51.9	25 38 09.5	5.42 (0.01)
IRASccIRAS 04381+2540.	04 41 12.8	25 46 33.5	5.20 (0.01)

Table 8. Table 8: Parameters for Molecules.

Line	Rotational Constant B	Dipole Moment $\mu$
	(MHz)	(DaaThe Debye (D) is a unit of the electric dipole moment, 1 D = 10-18 g1/2 cm5/2 s.)
N2H+ 1–0	46586.87	3.40
C17O 2–1	56179.99	0.11

Table 9. Table 9: Column Densities and Abundances for Molecular Lines.

	Cyanopolyyne Peak			Ammonia Peak
Line	Column Density	Abundance		Column Density	Abundance
	($\times$1013 cm-2)	($\times$10-9)		($\times$1013 cm-2)	(   $\times$10-9)
N2H+ 1–0	0.5 (0.2)	0.3 (0.1)		0.6 (0.2)	0.3 (0.1)
C17O 2–1	66.5 (26.7)	33.4 (13.9)		25.1 (3.1)	13.4 (2.0)

Table 10. Table 10: Depletion Factors of CO and N 2 H + .

	Depletion Factors ($X_{\mathrm{canonical}}$/$X_{\mathrm{measured}}$)
	Cyanopolyyne Peak	Ammonia Peak
C17O	4.5 (1.9)	11.9 (1.9)
N2H+	1.8 (0.7)	1.6 (0.6)

Table 11. Table 11: Timescale of Density Evolution for Chemical Modeling.

	TimescaleaaTimescale spent from a given density to the next density. The final density is 105 cm-3. (yrs)
Gas DensitybbGas density with the mean molecular weight of $\mu =2.3$. (cm-3)	Cyanopolyyne Peak Model	Ammonia Peak Model
103	1.0$\times$106	1.5$\times$106
104	1.0$\times$105	6.0$\times$105
3$\times$104	4.0$\times$104	4.0$\times$104

Table 12. Table 12: Abundances of CO and N 2 H + at n ​ ( H 2 ) = 10 5 𝑛 subscript H 2 superscript 10 5 n(\rm H_{2})=10^{5}  cm -3 in the Chemical Calculation.

	Abundance
Molecule	Cyanopolyyne Peak Model	Ammonia Peak Model
COaaThe maximum CO abundance is 1.2$\times$10-4 in both models.	6.50$\times$10-5	2.17$\times$10-5
N2H+bbThe maximum abundance of N2H+ is different in the two models (5$\times$10-10 in the cyanopolyyne peak model and 6.5$\times$10-10 in the ammonia peak model).	1.06$\times$10-10	1.03$\times$10-10

Equations

$$L_{\mathrm{bol}}=4\pi d^2{\int }_0^{\infty }{S}_{\nu }d\nu ,$$

$$T_{\mathrm{bol}}=1.25\times 10^{-11}\frac{{\int }_0^{\infty }\nu S_{\nu }d\nu }{{\int }_0^{\infty }{S}_{\nu }d\nu }\mathrm{K}.$$

$$N({\mathrm{H}}_2)=\frac{F_{\nu }^{\mathrm{beam}}}{{\Omega }_{\mathrm{A}}{\mu }_{{\mathrm{H}}_2}{m}_{\mathrm{H}}{\kappa }_{\nu }{B}_{\nu }(T)}$$

$$N(x)=\frac{3kQ{e}^{E_J/k{T}_{\mathrm{ex}}}}{8{\pi }^3\nu {\mu }^{2}J}\int T_{R}dv$$

$$N_{\mathrm{thick}}=N_{\mathrm{thin}}\frac{{\tau }_{\nu }}{1-e^{-{\tau }_{\nu }}}$$

$$X(x)=\frac{N(x)}{N({\mathrm{H}}_2{)}_{\mathrm{Dust}}}$$

Full text

astrochemistry — ISM: individual objects (TMC-1) — ISM: molecules — ISM: abundances

1 Introduction

Gravitationally bound starless cores, that is, prestellar cores, are cold ($T_{\rm k}\sim 10$ K), dense ($n>10^{4}$ cm*-3*) condensations of gas with no sign of a central protostellar object, implying that they are the earliest identifiable stage of star formation (e.g., Shu et al., 1987; Lee & Myers, 1999; Crapsi et al., 2005; Ward-Thompson et al., 2007). Therefore, prestellar cores are the places that we can study the initial conditions of star formation such as the distribution of density, temperature, and velocity (Benson & Myers, 1989; Ward-Thompson et al., 1994). Prestellar cores have a constant density in the inner part and a decreasing density at larger radii (Ward-Thompson et al., 1994, 1999, 2000; Andre et al., 1996), which can be well described with a Bonnor-Ebert sphere density profile (Evans et al., 2001). Dust grain temperatures decrease toward the center of prestellar cores (Evans et al., 2001; Zucconi et al., 2001; Ward-Thompson et al., 2002; Crapsi et al., 2007; Harju et al., 2008; Nielbock et al., 2012) since the interstellar radiative field (ISRF) is the only heating sources of prestellar cores.

Although there are several model scenarios to explain core formation, they can be divided into two extreme paradigms: slow quasistatic contraction and dynamic turbulent processes. In the former process, a core gradually becomes condensed toward the center through ambipolar diffusion, increasing the ratio of core mass to magnetic flux. As a core switches from magnetically subcritical to a supercritical condition, the core can collapse gravitationally (Mouschovias, 1991; Mouschovias & Ciolek, 1999; Shu et al., 1987). If compressible turbulence dominates in a prestellar core, the turbulence will decline in a short time (e.g., Mac Low et al., 1998) and collapse will happen. This means that the prestellar core disappears quickly or rapidly collapses. The detailed modeling results of this process suggest that the cores live for only one or two free-fall times (e.g., Ballesteros-Paredes et al., 2003; Vázquez-Semadeni et al., 2005). Demographic studies indicate lifetimes that decline with increasing density from near 10 free-fall times at $10^{3}$ cm*-3* to a few free-fall times, or about 0.5 Myr, once the mean density rises above $2\times 10^{4}$ cm*-3*, and one free-fall time once the mean density is above $10^{6}$ cm*-3* (Ward-Thompson et al., 2007; Enoch et al., 2008; André et al., 2014).

Studies show that the chemical compositions of dark cloud cores can be a useful tracer of their evolutionary status in a given dynamical process, as the chemistry is time dependent. The dynamical evolutionary stage can be inferred by the density structure of a core, which can be obtained through the dust continuum emission. However, one of the important properties of dynamical processes is the velocity distribution, which is traced only by line profiles within the core. Molecular line profiles are affected by not only density and temperature profiles but also the abundance structure in the core. Therefore, it is necessary to understand the chemical distribution within cores (e.g., Mizuno et al., 1990; Zhou et al., 1993; Choi et al., 1995; Bergin et al., 1995; Gregersen et al., 1997; Gregersen & Evans, 2000; Mardones et al., 1997; Aikawa et al., 2001; Lee et al., 2003, 2004; Di Francesco et al., 2001; Belloche et al., 2002).

Taurus Molecular Cloud-1 (TMC-1) is an interesting source for exploring the chemistry of dark clouds. It is a cold and dense cloud with a narrow filamentary structure (5$\arcmin\times 15\arcmin$) in the Taurus dark-cloud complex at a distance of $\sim$140 pc (Elias, 1978; Kenyon et al., 1994; Torres et al., 2012) extending from the southeast to northwest direction, with an infrared source (IRAS 04381+2540) located outside the northwest part. The TMC-1 filament has been observed in many molecular lines. According to those molecular observations, carbon-chain molecules such as CCS, C4H, and HC3N are abundant in the southeast part (cyanopolyyne peak) of the TMC-1 filament, and NH3 are N2H+ are abundant in its northwest part (ammonia peak). This peculiar chemical feature of TMC-1 has been an interesting problem, so there have been many studies attempting to understand the chemical distributions in TMC-1 (e.g., Churchwell et al., 1978; Little et al., 1979; Wootten et al., 1980; Toelle et al., 1981; Guelin et al., 1982; Snell et al., 1982; Schloerb et al., 1983; Olano et al., 1988; Hirahara et al., 1992; Suzuki et al., 1992; Pratap et al., 1997; Hirota et al., 1998; Markwick et al., 2000, 2001; Saito et al., 2002; Hirota et al., 2003; Suutarinen et al., 2011).

Many studies have concluded that the cyanopolyyne peak is at an earlier evolutionary stage than the ammonia peak, and thus the cyanopolyyne peak (southeast part) is less chemically evolved than the northwest part based on the chemical models and molecular line observations such as CCS, HC5N, C34S, NH3, C34S, DCO+, H13CO+, and CH. The estimated chemical evolutionary age difference between the two peaks is more than 105 yr (e.g., Suzuki et al., 1992; Hirahara et al., 1992; Hanawa et al., 1994; Howe et al., 1996; Pratap et al., 1997; Saito et al., 2002; Suutarinen et al., 2011).

Hirahara et al. (1992) showed that the H2 density of the southeast part was lower than that of northwest part by a factor of 10 using C34S. They suggested that the cyanopolyyne peak was in an earlier stage of chemical evolution than the ammonia peak because of the higher density at the ammonia peak. Pratap et al. (1997) observed several molecular species and suggested two possibilities for the chemical difference along the TMC-1 filament. One was a small variation in the C/O ratio from 0.4 to 0.5. Another was that differences in density, which varies by a factor of 2 along the filament, could explain the difference of chemical distribution in the TMC-1 filament. The latter was consistent with the result by Hirahara et al. (1992) because the higher density could drive chemical processes more rapidly. Recently, Suutarinen et al. (2011) presented a CH abundance gradient in TMC-1, from $\sim$1.0$\times$10*-8* in the northwestern part to $\sim$2.0$\times$10*-8* in the southeastern part of TMC-1, and they noted that the CH column density peaks close to the cyanopolyyne peak. They suggested that the southeastern part in the vicinity of the cyanopolyyne peak had an extensive low-density envelope based on the comparison of the dust continuum maps from SCUBA 850 and 450 $\micron$ (Nutter et al., 2008) and the modelling of molecular lines (Hirahara et al., 1992; Pratap et al., 1997), implying that the cyanopolyyne peak was in the early stage of dynamical evolution and this peak was also chemically less evolved than the ammonia peak because of the lower density.

Markwick et al. (2000, 2001) proposed another explanation for molecular abundance differences along the TMC-1 filament. They investigated the possibility that the gradients were produced by spontaneous explosive desorption of UV-photolyzed ice mantles, triggered by the heating of dust grains and their ices, through grain-grain collisions induced by MHD waves from IRAS 04381+2540 near the ammonia peak. The chemical processes occurred first in the ammonia peak and later in the cyanopolyyne peak, which induced the gradient of molecular abundances along the TMC-1 filament. According to their chemical models, the ammonia peak is 1.5$\times$105 yr older than the cyanopolyyne peak, assuming the speed of the MHD wave of 2 km s*-1*.

A very different explanation for the chemical distribution along the TMC-1 filament might be possible. According to gas-phase chemical models, carbon-chain species such as CCS form before atomic carbon mainly reacts with atomic oxygen, which drives all carbon-bearing species into CO. When the depletion of CO (and even N2H+) is very significant, abundances of carbon-chain species increase again, which is called a late-time secondary abundance peak of carbon-chain species (Ruffle et al., 1997, 1999; Li et al., 2002; Lee et al., 2003). In this case, the cyanopolyyne peak might be chemically older than the ammonia peak, unlike the conclusion from the rest of the studies. Therefore, we need to calculate accurate depletion factors of N2H+ and CO in the two peaks using accurate H2 column densities.

In this study, we present new data from the FCRAO (Five College Radio Astronomy Observatory) 14-m Telescope and the SRAO (Seoul Radio Astronomy Observatory) 6-m Telescope, along with data from the Spitzer Space Telescope and MAMBO (Max-Planck Millimetre Bolometer) at the IRAM 30-m Telescope. We combine these data sets to study the reason for the chemical differentiation along the filament. We determine the degree of molecular depletion by comparing column densities calculated from dust continuum emission and molecular line emission, since the dust continuum at (sub)millimeter traces the total material along the line of sight very well. We also carry out chemical calculations to study the abundance evolution of CO and N2H+ with different assumptions about the evolution of the core densities.

Observations of TMC-1 are summarized in Section 2. In Section 3 we show the observational results and simple analysis. Section 4 presents the column densities using several molecules and dust continuum emission. Section 5 describes the chemical modeling sequence and results. Finally, we discuss our results in Section 6.

2 Observations

2.1 Five College Radio Astronomy Observatory (FCRAO) Observations

Maps of CS ($J$=2–1) and N2H+ ($J$=1–0) toward TMC-1 were made in 2003 January with the 14-m telescope of the Five College Radio Astronomy Observatory (FCRAO). The 32-element heterodyne receiver SEQUOIA was used with the auto-correlator configured with a band width of 25 MHz over 1024 channels. The total mapping times were 237 hours and 130 hours for CS ($J$=2–1) and N2H+ ($J$=1–0), respectively. The reference center of maps was ($\alpha$, $\delta$)=(4h41m44.0s, +25$\arcdeg$42$\arcmin$22.0$\arcsec$).

2.2 Seoul Radio Astronomy Observatory (SRAO) Observations

We observed TMC-1 in C17O ($J$=2–1) and C18O ($J$=2–1) with the 6-m telescope of Seoul Radio Astronomy Observatory (SRAO) in 2009 February. The autocorrelator was configured with a band width of 100 MHz over 2048 channels. The pointing uncertainty was less than 10$\arcsec$ in both azimuth and elevation. We observed the positions of the cyanopolyyne peak and the ammonia peak in the TMC-1 filament. The total integration time for each position was 30 minutes.

Table 1 summarizes basic observational parameters of the FCRAO and SRAO data, including the frequency ($\nu$), velocity resolution ($\delta v$), the FWHM beam size ($\theta_{\rm mb}$), the main beam efficiency ($\eta_{\rm mb}$), rms noise level at the given velocity resolution, and the observing date.

2.3 The Spitzer Space Telescope Observations

The Spitzer Legacy Program “From Molecular Cores to Planet Forming Disks” (c2d; Evans et al., 2003) observed TMC-1 at 3.6, 4.5, 5.8, and 8.0 $\micron$ with the Infrared Array Camera (IRAC; Fazio et al., 2004) on 2004 October 8 and at 24 and 70 $\micron$ with the Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al., 2004) on 2004 September 25. The pixel sizes are 1$\arcsec$.2 for all IRAC bands and 2$\arcsec$.45 at MIPS 24 $\micron$. These images were centered at ($\alpha$, $\delta$)= (4h41m14s, +25$\arcdeg$59$\arcmin$31$\arcsec$) for the 3.6 and 5.8 $\micron$ bands and (4h41m19s, +25$\arcdeg$52$\arcmin$49$\arcsec$) for the 4.5 and 8.0 $\micron$ bands. MIPS image was centered at ($\alpha$, $\delta$)=(4h41m21s, +25$\arcdeg$55$\arcmin$46$\arcsec$). For detailed descriptions of data reduction refer to Evans et al. (2007).

2.4 Max-Planck Millimetre Bolometer (MAMBO) Observations

The observations of the 1.2 mm thermal dust continuum emission toward TMC-1 were performed with the IRAM 30-m-telescope on Pico Veleta (Spain) using the 117-receiver MAMBO-2 (240$\arcsec$ diameter) camera (Kreysa et al., 1999). The beam size on the sky was 11$\arcsec$, and the effective frequency is 250 GHz with half sensitivity limits at 210 GHz and 290 GHz. TMC-1 was observed between the summer of 2002 and the winter of 2003/2004. The detailed process of the data reduction of MAMBO observations was explained in Kauffmann et al. (2008), where these data were first presented.

3 Observational Results & Basic Analysis

We present the relevant data sets in this section, starting with the infrared and submillimeter continuum data, which establish the environmental context for the molecular line observations.

3.1 Infrared Observations

Figure 1 shows 1.2 mm dust continuum emission (contours) on top of the Spitzer three-color image (4.5, 8.0, and 24 $\micron$ for blue, green, and red, respectively). The 1.2 mm dust continuum emission shows that the contours around the cyanopolyyne peak are complex compared to those around the ammonia peak. The IRAS source (IRAS 04381+2540) marked with a large box, is located in the northwest part of TMC-1. The small boxes represent YSO candidates that are classified in the c2d source catalogs (Evans et al., 2007). The source identification numbers are assigned with increasing right ascension. With the Spitzer observations, we confirm that there are no YSO candidates along the densest part of the TMC-1 filament although 6 YSO candidates (including the IRAS source) are identified outside or at boundary of the TMC-1 filament. There is a gradient in the 4.5 and 8 $\micron$ emission from northwest to southeast direction probably due to IRAS 04380+2553, which is a late B-type star, HD 29647, behind TMC-1 (Whittet et al., 2004; Mooley et al., 2013). The 4.5 and 8 $\micron$ radiation from HD 29747 is scattered by dust grains in low densities. Therefore, the gradient of the scattered light emission might imply that the TMC-1 filament is inclined toward HD 29647. As a result, the surface of its northwest part is more illuminated by the B star.

To check the evolutionary stages of the 6 YSO candidates we use the same color-color and color-magnitude diagrams (Fig. 2) as used in Lee et al. (2006). The diagrams use the photometric data from the 2MASS (Two Micron All Sky Survey; Skrutskie et al., 2006), IRAC, and MIPS bands. IRAS 04381+2540 is not included in the color-color diagram since it is not covered by the observations at 3.6 and 5.8 $\micron$. The coordinates and fluxes from the 2MASS and Spitzer observations of these YSO candidates are listed in Table 2. As seen in Fig. 2, the IRAS source is a Class 0/I candidate, and 5 YSO candidates are classified as Class II. We compare our classification to previous results in the literature. 6 YSOs including the IRAS source are in good agreement with previously identified objects in the catalogs of Gutermuth et al. (2008, 2009) and Rebull et al. (2010). Table 3 lists previous studies, our classification, and identifications for 6 YSOs.

We also calculate the bolometric luminosity ($L_{\rm bol}$) and bolometric temperature ($T_{\rm bol}$) for these 6 YSO candidates using the observed fluxes (see Table 2). The bolometric luminosity ($L_{\rm bol}$) is calculated by integrating the spectral energy distributions (SEDs), including far-infrared and sub-millimeter wavelengths by extrapolation.

[TABLE]

where $d$ is the distance to the source and $S_{\nu}$ is the flux as a function of frequency of the source. The bolometric temperature ($T_{\rm bol}$) is described as the temperature of a blackbody with the same flux-weighted mean frequency as the observed SED and it is calculated using the following equation (Myers & Ladd, 1993):

[TABLE]

Table 4 shows that the evolutionary stage of each source based on the bolometric temperature (Class I : 70 K $\leq$ $T_{\rm bol}$ $\leq$ 650 K, Class II : 650 K $<$ $T_{\rm bol}$ $\leq$ 2880 K; Chen et al., 1995) is consistent with the result found using the color-color and color-magnitude diagrams. Furthermore, Dunham et al. (2008) calculated the bolometric luminosity and temperature of $\sim$0.73 L☉ and $\sim$165 K for the IRAS source, which is also classified as a Class I object.

3.2 Molecular Line Observations

Figures 3 and 4 present four spectra observed at the cyanopolyyne and ammonia peaks. The Gaussian fitting results of CS 2$-$1 and C18O 2–1 are obtained using the GILDAS/CLASS package111http://www.iram.fr/IRAMFR/GILDAS/ and they are summarized in Table 5. N2H+ 1–0 and C17O 2–1 have hyperfine structures and they are fitted using the method in the program CLASS (METHOD HFS), which fits the relative intensities of the hyperfine structure lines of a molecular rotational transition to derive the optical depth of the line. The hyperfine fitting results are listed in Table 6. CS 2–1, C18O 2–1, and the isolated component of N2H+ 1–0, especially at the cyanopolyyne peak, show double peaks. This double peak feature could be caused either by optical depth or by two velocity components. Here, we assume that the line shape is caused by optical depth, rather than two velocity components, and fit the data with a single Gaussian.

Figures 5 and 6 present the integrated intensity maps of CS 2–1 (green line) and N2H+ 1–0 (yellow line) obtained at the FCRAO. In the figure, line emissions (contours) are overlaid on the 1.2 mm dust continuum emission map (grey image), and the locations of the cyanopolyyne peak and the ammonia peak are denoted by red and blue triangles, respectively. This 1.2 mm dust continuum emission map, the best tracer of column density, is the first 1.2 mm dust continuum emission map of its type for the whole TMC-1 region (Kauffmann et al., 2008). The CS 2–1 intensity does not peak at the cyanopolyyne peak, while it peaks close to the ammonia peak. However, the N2H+ 1–0 intensity peaks around both cyanopolyyne and ammonia peaks although the intensity close to the cyanopolyyne peak is weaker than that around the ammonia peak. The differences of the molecular line intensities at the two peaks can be caused by differences in (1) density, (2) temperature, (3) abundance, or any combinations of these properties.

We use the N2H+ 1–0 line to study the velocity field because that line has the lowest optical depth. Figure 7 presents the first moment map. We found three velocity components; the northern part (red to yellow), the southern part (green), and the northwestern part (sky blue). In the northern part (P1) of the TMC-1 filament, the velocity is $\sim$5.8 km s*-1* and it drops to about 5.4 km s*-1* in the the southern part (P5). On the other hand, the source velocity in the northwestern part (IRAS 04381+2540, $V_{\rm LSR}\sim$5.2 km s*-1*) is lower than the typical velocity along the TMC-1 filament ($V_{\rm LSR}\sim$5.6 km s*-1*), suggesting that this region may be separated from the TMC-1 filament along the line of sight (Toelle et al., 1981; Snell et al., 1982; Kolotovkina et al., 1986; Olano et al., 1988; Fehér et al., 2016).

Table 7 summarizes the source velocities of five positions (P1, P2, P3, P4, and P5) along the TMC-1 filament, consistent with the MAMBO dust continuum peaks (Kauffmann et al., 2008), and the IRAS source (IRAS 04381+2540).

4 Column Density Calculations

4.1 H2 Column Density from Dust Continuum Emission

We compare H2 column densities calculated from molecular line emission and dust continuum emission to calculate the degree of depletion of molecules.

If the dust continuum emission is optically thin, the observed flux ${F}^{\rm beam}_{\nu}$ can be related to the column density of gas. Therefore, we calculate the H2 column density with the MAMBO flux as given by this equation (Hildebrand, 1983).

[TABLE]

where ${F}^{\rm beam}_{\nu}$ is the observed flux per beam, $\mu_{\rm{H_{2}}}$ (= 2.3) is the molecular weight per hydrogen molecule, $m_{\rm H}$ is the atomic mass unit, $\kappa_{\nu}$ (= 0.0102 cm2g*-1*) is the mass opacity of dust per gram of gas at 1.2 mm (Kauffmann et al., 2008), $B_{\nu}(T)$ is the Planck function, and $\Omega_{\rm A}$ is the beam solid angle; $\Omega_{\rm A}=(\pi\theta^{2}_{\rm HPBW})/(4\rm{ln}2)$ for a Gaussian function (Lee et al., 2003; Kauffmann et al., 2008). The MAMBO map is convolved with a Gaussian profile with the FWHM of the beam of molecular observations. As a result, the H2 column density calculated from dust continuum emission at the cyanopolyyne and the ammonia peak is (1.99$\pm$0.20)$\times$1022 cm*-2* and (1.87$\pm$0.19)$\times$1022 cm*-2*, respectively. The H2 column densities calculated from the dust continuum emission, the best tracer of the column density along the line of sight, is essentially identical at the two peaks.

Two other recent studies also concluded that the column densities in the ammonia and cyanopolyyne peaks are comparable. Suutarinen et al. (2011) estimated the total H2 column density in the TMC-1 region using the SCUBA 850 and 450 $\micron$ data from Nutter et al. (2008). The derived $N$(H2) are $\sim 1.3\times 10^{22}$ cm*-2* and $\sim 1.6\times 10^{22}$ cm*-2* at the ammonia peak and the cyanopolyyne peak, respectively. In addition, Fehér et al. (2016) used the Herschel/SPIRE images to derive the column densities of $3.3\times 10^{22}$ cm*-2* at the ammonia peak and $2.7\times 10^{22}$ cm*-2* at the cyanopolyyne peak. These absolute values are different from ours probably because of different beam sizes. However, the very important point of these calculations including ours is that the column densities at the ammonia and cyanopolyyne peaks are similar, contrary to suggestions by some previous studies (see Section 1).

4.2 Column Density and Abundance for Molecular Line Emission

Chemical models predict that CO and N2H+ will be anti-correlated because CO destroys N2H+ in the gas phase. Previous observations of pre- and protostellar regions (Bergin et al., 2001; Tafalla et al., 2002; Lee et al., 2003; Di Francesco et al., 2004; Jørgensen et al., 2004; Pagani et al., 2005) confirmed that N2H+ becomes abundant as CO is frozen onto grain surfaces. Therefore, these two molecules together can trace different chemical evolutionary stages of molecular cores. We use the N2H+ and C17O lines to calculate column densities more accurately because these lines have hyperfine structures. In this calculation, we assume that (1) the dust continuum emission traces all material along a line of sight; (2) dust and gas are well coupled thermally ($T_{\rm d}$ = $T_{\rm k}$ = 10 K, Pratap et al., 1997); (3) molecular abundances are constant along the line of sight; and (4) all levels are in LTE, following Lee et al. (2003).

For line emission, if a line is optically thin ($\tau$ $<$ 0) for the transition $J=J\rightarrow J-1$ in a linear molecule, the relation between the column density $N(x)$ of molecule $x$ and the integrated intensity of the line is

[TABLE]

where $T_{\rm ex}$ is the excitation temperature above the ground state, and $\mu$ is the dipole moment. The frequency ($\nu$), energy above ground ($E_{J}$), and the partition function ($Q$) can be computed from $B$, the rotational constant.

However, if the optical depth is not negligible, the optical depth effect is corrected for with the equation :

[TABLE]

Additionally, we calculate the abundance of molecule, $X(x)$, using the H2 column density calculated from the dust continuum emission.

[TABLE]

Table 8 summarizes the parameters (the rotational constant $B$ and the dipole moment $\mu$) used for the calculation of the column densities. The optical depths of the N2H+ 1–0 and C17O 2–1 lines are obtained by the hyperfine fitting method in the CLASS package (see Table 6). We find that C17O 2–1 is optically thick at the cyanopolyyne peak, but optically thin at the ammonia peak. On the other hand, the total optical depth of N2H+ is too large at both peaks to adopt the Eq. 5. Therefore, we use the isolated component (see Fig. 3 and 4) to derived the column density of N2H+ by assuming that the optical depth of each component is proportional to its LTE intensity ratio. The optical depth of the isolated component is 10% of the total optical depth.

The column densities and abundances for molecular lines are listed in Table 9. The column density from C17O 2–1 is a factor of 2 larger at the cyanopolyyne peak than at the ammonia peak. However, there is no significant difference in the column densities of N2H+ 1–0 between the cyanopolyyne and the ammonia peaks when the error is considered.

Table 10 represents the depletion factors of C17O and N2H+ when we compare the calculated abundances with the canonical abundances, $X(\rm{C^{17}O})=1.5\times 10^{-7}$ and $X(\rm{N_{2}H^{+}})=5.0\times 10^{-10}$. This canonical abundance of C17O is obtained by assuming 16O/18O of 540, 18O/17O of 3.65 (Wilson & Rood, 1994; Penzias, 1981), and CO/H2 of 2.7$\times$10*-4* (Lacy et al., 1994). The canonical abundance of N2H+ is adopted from Johnstone et al. (2010). We find that the depletion of CO is more significant in the ammonia peak (CO depletion factor = 11.9) compared to the cyanopolyyne peak (CO depletion factor = 4.5). This suggests that the ammonia peak is more chemically evolved than the cyanopolyyne peak. On the other hand, the depletion of N2H+ is almost identical in the two peaks if errors are considered.

5 Chemical Modeling

We calculate the evolution of chemical abundances of CO and N2H+ molecules to explain the differential chemical distribution along the TMC-1 filament. According to our analysis in the previous section, the cyanopolyyne and ammonia peaks have similar column densities calculated from the dust continuum emission while CO is depleted more significantly at the ammonia peak than at the cyanopolyyne peak. This trend implies that longer timescales at lower densities are necessary at the ammonia peak during the density evolution since in that condition, N2 forms more in the gas and CO is frozen-out more onto grain surfaces, resulting in a high abundance of N2H+ with a significant depletion of CO. Therefore, we calculate the chemical evolution by varying the timescales over which density evolves to account for the observational results.

We adopt the chemical network used in Lee et al. (2004) and the updated N2 binding energy used in Chen et al. (2009). In the chemical network, the interactions between gas and dust grains (i.e., freeze-out and evaporation of molecules on and off grain surfaces) are included as well as the pure gas chemistry. We assume that the grain surface is coated by water ice and use the same initial elemental abundances as presented in Table 3 of Lee et al. (2004). According to previous studies (Hirota et al., 1998, 2003), the two peaks have a current density of $\sim$105 cm*-3*. We therefore consider that the densities of the two peaks evolve from 103 cm*-3* to 105 cm*-3* and assume that a core is formed when a density condensation is larger than 103 cm*-3*, which is the lowest density at which prestellar cores can be identified (Ward-Thompson et al., 2007). Table 11 lists the timescale of density evolution, i.e., the amount of time spent from each density to the next density until the density of the two peaks reaches 105 cm*-3* in the models, which fit the observations the best. The densities in the two models gradually increase as time goes by (see Fig. 8). The timescale spent at low densities (until the density reaches 3$\times$104 cm*-3*) is shorter in the cyanopolyyne peak model (1.1$\times$106 yrs) than in the ammonia peak model (2.1$\times$106 yrs); the density evolves faster in the cyanopolyyne peak model than the ammonia peak model until the density reaches 3$\times$104 cm*-3*.

Figure 8 presents the abundance evolution of CO and N2H+ in the best-fit models for the cyanopolyyne peak and the ammonia peak, and the abundances of the two molecules at $n(\rm H_{2})$=105 cm*-3* in the two models are listed in Table 12. During the density evolution, the CO freeze-out occurs in the two models, but it is more significant in the ammonia peak model than the cyanopolyyne peak model, as seen in the observations (see Table 10). The abundance of CO in the cyanopolyyne peak model is higher than that of CO in the ammonia peak model by a factor of $\sim$3 at $n(\rm H_{2})$=105 cm*-3*. On the other hand, the N2H+ abundances in the two models are similar at $n(\rm H_{2})$=105 cm*-3*; the N2H+ abundance decreases quickly at $n(\rm H_{2})$=104 cm*-3* in the cyanopolyyne peak model because of its destruction via abundant CO, while the N2H+ abundance declines slowly in the ammonia peak model because its destroyer, CO, is already depleted at the low density. In the cyanopolyyne peak model, the maximum abundance of N2H+ is lower than that in the ammonia peak model because its destruction by CO is more efficient in the cyanopolyyne peak model.

According to our modeling, the timescale difference of 1$\times$106 yrs in density evolution is needed in order to explain the chemical differentiation between the cyanopolyyne and ammonia peaks; the cyanopolyyne peak has a shorter timescale than the ammonia peak. This implies that the core at the ammonia peak forms earlier than the core at the cyanopolyyne peak, which is consistent with the suggestion by previous studies; core formation propagated from the ammonia peak to the cyanopolyyne peak (Hanawa et al., 1994; Howe et al., 1996; Markwick et al., 2000, 2001; Saito et al., 2002). However, the current densities of the two peaks are similar. Therefore, once the core at the ammonia peak forms, it might evolve very slowly until the core at the cyanopolyyne peak forms and catches up in its density evolution. According to our chemical models combined with the density evolution of cores, the more evolved chemistry at the ammonia peak can be attributed to the longer timescale of density evolution at the peak.

Lee et al. (2003) suggested that the chemical evolution of a core depends on its dynamical timescale as well as its density structure by comparing the chemical distributions in three isolated prestellar cores (L1512, L1544, and L1689B). According to Lee et al. (2003), L1544 and L1689B have the same density distribution, but L1689B is chemically much younger than L1544. In conclusion, L1689B might experience a free-fall like dynamical process, while L1544 might undergo an ambipolar diffusion process for the dynamical evolution. In the TMC-1 filament, the core associated with the ammonia peak requires a longer evolutionary timescale, so it would have formed via ambipolar diffusion. On the other hand, the core associated with the cyanopolyyne peak might have formed by a more violent dynamical process. Some evidence for the dynamical process on a short timescale is present in our observations. First, the 1.2 mm dust continuum emission, which traces the total amount of material the best, shows a complex structure around the cyanopolyyne peak (see Fig. 1). Second, the central velocity of the N2H+ line changes sharply around the cyanopolyyne peak (see Fig. 7). Finally, the molecular line profiles, especially the isolated component of N2H+ $J$=1–0, show a double peak feature (see Fig. 3), indicative of two velocity components. (CS 2–1 and C18O 2–1 are also affected by optical depths.) From this evidence, we could consider that two molecular clouds are colliding around the cyanopolyyne peak to induce a fast core formation.

6 Summary

We study a possible interpretation of the differentiated chemical distribution in the TMC-1 region using various observational data and chemical modeling.

From $Spitzer$ infrared observations, we confirm that there is no YSO candidates along the TMC-1 filament although there are 6 YSO candidates located outside or at boundary of the TMC-1 filament; five classified YSO candidates objects are classified as Class II sources, and IRAS source (IRAS 04381+2540) is a Class I object, which agree with previous classifications (Dunham et al., 2008; Gutermuth et al., 2008, 2009; Rebull et al., 2010).

The CS 2–1 and N2H+ 1–0 lines are stronger at the ammonia peak than at the cyanopolyyne peak. On the other hand, C17O 2–1 and C18O 2–1 lines are stronger at the cyanopolyyne peak than at the ammonia peak.

Using the C17O and N2H+ lines, which have hyperfine structures, we calculate the H2 column density to compare with the column density calculated from the dust continuum emission, which traces the material the best along the line of sight. The column densities calculated from the dust continuum emission and from the N2H+ 1–0 line are similar at the cyanopolyyne and ammonia peaks, while the column density calculated from C17O 2–1 is much greater at the cyanopolyyne peak than at the ammonia peak.

Comparing the depletion factors of CO and N2H+ (see Table 10), we find that the CO molecule is much less depleted at the cyanopolyyne peak than at the ammonia peak, while the N2H+ abundance is similar at both peaks, ruling out the possibility of a late-time secondary abundance peak of carbon-chain molecules (Ruffle et al., 1997, 1999; Li et al., 2002; Lee et al., 2003) because both CO and N2H+ are significantly depleted in the late stage of chemical evolution. Therefore, the relative depletion factors of CO and N2H+ imply that the cyanopolyyne peak is chemically younger (see Section 1).

According to our chemical modeling, the ammonia peak stays for a longer time at low density (103–105 cm*-3*) than the cyanopolyyne peak to explain the chemical difference between the two peaks, indicating that the dynamical evolution can affect the chemical evolution, resulting in different chemical states even at the same final density. As a result, we suggest that the chemical differentiation along the TMC-1 filament can be induced by different dynamical processes of core formation; the ambipolar diffusion for the ammonia peak and a free-fall like process for the cyanopolyyne peak. Some evidence, such as the complex distribution of the 1.2 mm continuum emission (see Fig. 1), the sharp shift of the central velocity of N2H+ 1–0 (see Fig. 7), and the double peak feature of molecular line profiles around the cyanopolyyne peak (see Fig. 3) suggest that two molecular clouds are colliding around the cyanopolyyne peak to induce a fast core formation.

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) (grant No. NRF-2015R1A2A2A01004769) and the Korea Astronomy and Space Science Institute under the R&D program (Project No. 2015-1-320-18) supervised by the Ministry of Science, ICT and Future Planning.