TMC-1C: an accreting starless core
S. Schnee, P. Caselli, A. Goodman, H. G. Arce, J. Ballesteros-Paredes, K. Kuchibhotla
aa r X i v : . [ a s t r o - ph ] J un Draft version October 28, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
TMC-1C: AN ACCRETING STARLESS CORE
S. Schnee , P. Caselli , A. Goodman , H. G. Arce , J. Ballesteros-Paredes , & K. Kuchibhotla Draft version October 28, 2018
ABSTRACTWe have mapped the starless core TMC-1C in a variety of molecular lines with the IRAM 30mtelescope. High density tracers show clear signs of self-absorption and sub-sonic infall asymmetriesare present in N H + (1–0) and DCO + (2–1) lines. The inward velocity profile in N H + (1–0) is extendedover a region of about 7,000 AU in radius around the dust continuum peak, which is the most extended“infalling” region observed in a starless core with this tracer. The kinetic temperature ( ∼
12 K)measured from C O and C O suggests that their emission comes from a shell outside the colderinterior traced by the mm continuum dust. The C O(2–1) excitation temperature drops from 12 Kto ≃
10 K away from the center. This is consistent with a volume density drop of the gas traced by theC O lines, from ≃ × cm − towards the dust peak to ≃ × cm − at a projected distance fromthe dust peak of 80 ′′ (or 11,000 AU). The column density implied by the gas and dust show similarN H + and CO depletion factors ( f D ≤ n (H ) ≃ cm − ), where COis mostly in the gas phase and the N H + abundance had time to reach equilibrium values; (ii) thesurrounding material (rich in CO and N H + ) is accreting onto the dense core nucleus; (iii) TMC-1C isolder than 3 × yr, to account for the observed abundance of N H + across the core ( ≃ − w.r.t.H ); and (iv) the core nucleus is either much younger ( ≃ yr) or “undepleted” material from thesurrounding envelope has fallen towards it in the past 10,000 yr. Subject headings: stars: formation — dust, extinction — submillimeter, molecules INTRODUCTION
Dense starless cores in nearby low-mass star-formingregions such as Taurus represent the simplest areas inwhich to study the initial conditions of star formation.The dominant component of starless cores, H , is largelyinvisible in the quiescent interstellar medium, so as-tronomers typically rely on spectral line maps of tracemolecules and continuum observations of the thermalemission from dust to derive their kinematics and phys-ical state. However, it is now well established thatdifferent species and transitions trace different regionsof dense cores, so that a comprehensive multi–line ob-servations, together with detailed millimeter and sub–millimeter continuum mapping are required to under-stand the structure and the evolutionary status of anobject which will eventually form a protostar and a pro-toplanetary system.Previous studies of starless cores in Taurus, as wellas other nearby star-forming regions, have shown thatthe relative abundance of many molecules varies signifi-cantly between the warmer, less dense envelopes and thecolder, denser interiors (see Ceccarelli et al. 2006 and Electronic address: [email protected] Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138 Department of Astronomy, California Institute of Technology,MC 105-24 Pasadena, CA 91125 INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5,50125 Firenze, Italy Department of Astrophysics, American Museum of NaturalHistory, New York, NY 10024 Centro de Radioastronom´ıa y Astrof´ısica, UNAM. Apdo.Postal 72-3 (Xangari), Morelia, Michoc´an 58089, M´exico Harvard Medical School, 25 Shattuck Street, Boston, MA02115
Di Francesco et al. 2006 for detailed reviews on thistopic). For instance, Caselli et al. (1999), Bergin et al.(2002) and Tafalla et al. (2004) have shown that carbon-bearing species such as C O, C O, C S, and CS arelargely absent from the cores L1544, L1498 and L1517Bat densities larger than a few 10 cm − , while nitrogen-bearing species such as N H + and ammonia are prefer-entially seen at high densities. The chemical variationswithin a starless core are likely the result of molecu-lar freeze–out onto the surfaces of dust grains at highdensities and low temperatures, followed by gas phasechemical processes, which are profoundly affected by theabundance drop of important species, in particular CO(see e.g. Dalgarno & Lepp 1984; Bergin & Langer 1997;Taylor et al. 1998; Aikawa et al. 2005).In the past few years it has also been found that not allstarless cores show a similar pattern of molecular abun-dances and physical structure. Indeed, there is a sub-sample of starless cores (often called pre-stellar cores),which are particularly centrally concentrated, that showskinematic and chemical features typical of evolved ob-jects on the verge of star formation. These features in-clude large values of CO depletion and deuterium frac-tionation, and evidence of “central” infall, i.e. pres-ence of infall asymmetry in high density tracers in a re-stricted region surrounding the mm continuum dust peak(Williams et al. 1999; Caselli et al. 2002a; Redman et al.2002; Crapsi et al. 2005; Williams et al. 2006). It is in-teresting that not all physically evolved cores show chem-ically evolved compositions, as shown by Lee et al. (2003)and Tafalla & Santiago (2004b). It is thus important tostudy in detail a larger number of cores to understandwhat is causing the chemical differentiation in objectswith apparently similar physical ages. This is why we Schnee, S. et al.decided to focus our attention on TMC–1C, a dense corein Taurus, with physical properties quite similar to theprototypical pre–stellar core L1544 (also in Taurus), tostudy possible differences and try to understand theirnature.TMC–1C is a starless core in the Taurus molecularcloud, with a distance estimated at 140 pc (Kenyon et al.1994). In a previous study, we have shown that TMC–1C has a mass of 6 M ⊙ within a radius of 0.06 pc fromthe column density peak, which is a factor of two largerthan the virial mass derived from the N H + (1–0) linewidth, and we have shown that there is evidence for sub-sonic inward motions (Schnee & Goodman 2005) as wellas a velocity gradient consistent with solid body rota-tion at a rate of 0.3 km s − pc − (Goodman et al. 1993).TMC–1C is a coherent core with a roughly constant ve-locity dispersion, slightly higher than the sound speed,over a radius of 0.1 pc (Barranco & Goodman 1998;Goodman et al. 1998). Using SCUBA and MAMBObolometer maps of TMC-1C at 450, 850 and 1200 µ m,we have mapped the dust temperature and column den-sity and shown that the dust temperature at the centerof the core is very low ( ∼ OBSERVATIONS
Continuum
To map the density and temperature structure ofTMC–1C, we have observed thermal dust emission at450 and 850 µ m with SCUBA and at 1200 µ m withMAMBO–2. SCUBA
We observed a 10 ′ × ′ region around TMC-1C us-ing SCUBA (Holland et al. 1999) on the JCMT at 450and 850 µ m. We used the standard scan-mappingmode, recording 450 and 850 µ m data simultaneously(Pierce-Price et al. 2000; Bianchi et al. 2000). Chopthrows of 30 ′′ , 44 ′′ and 68 ′′ were used in both the rightascension and declination directions. The resolution at450 and 850 µ m is 7.5 ′′ and 14 ′′ respectively. The ab-solute flux calibration is ∼
12% at 450 µ m and ∼
4% at850 µ m. The noise in the 450 and 850 µ m maps are 13and 9 mJy/beam, respectively. The data reduction isdescribed in detail in Schnee et al. (2007). MAMBO-2
Kauffmann et al. (in prep.) used the MAMBO-2 array(Kreysa et al. 1999) on the IRAM 30–meter telescope onPico Veleta (Spain) to map TMC–1C at 1200 µ m. The MAMBO beam size is 10 . ′′
7. The source was mapped on-the-fly, chopping in azimuth by 60 ′′ to 70 ′′ at a rate of 2Hz. The absolute flux calibration is uncertain to ∼ µ m map is 3 mJy/beam. Thedata reduction is described in detail in Kauffmann et al.(in prep.). Spectral Line
We have used the IRAM 30-m telescope to map outemission from several spectral lines in order to under-stand the kinematic and spectral structure of TMC–1C.In November 1998, we mapped the spectral line mapsof the C O(1–0), C O(2–1), C O(2–1), C S(2–1),DCO + (2–1), DCO + (3–2), N H + (1–0) transitions. Theinner 2 ′ of TMC-1C were observed with 20 ′′ spacing infrequency-switching mode, and outside of this radius thedata were collected with 40 ′′ sampling. The data werereduced using the CLASS package, with second-orderpolynomial baselines subtracted from the spectra. Thesystem temperatures, velocity resolution, beam size andbeam efficiencies are listed in Table 1. RESULTS
Spectra
The spectra taken at the peak of the dust column den-sity map are shown in Figure 1. The integrated intensity,velocity, line width and RMS noise for each transition isgiven in Table 2. From the figure it is evident that self–absorption is present everywhere, except in C O andC O lines. Clear signatures of inward motions (brighterblue peak; e.g. Myers et al. 1997, see also Sect. 4.3)are only present in the high density tracers N H + andDCO + , which typically probe the inner portion of densecores (e.g. Caselli et al. 2002b; Lee et al. 2004). TheC S(2–1) line appears to be self–absorbed at the cloudvelocity, but the spectrum is too noisy to confirm this.To highlight the extent of the “infall” asymmetry inN H + (1–0), Fig. 2 shows the profile of the main hyper-fine component of the N H + (1–0) transition (F ,F = 2,3 → Maps
From Fig. 1 and 2, it is clear that the main N H + (1–0)hyperfine components are self-absorbed around the dustpeak position. Therefore, a map of the N H + (1–0) in-tensity integrated under the seven components will notreflect the N H + column density distribution. However,the weakest component (F F = 10 →
11) is not af-fected by self-absorption, as shown in Fig. 3, where theweakest and the main (F F = 23 →
12) componentstoward the dust peak position (the most affected by self-absorption) are plotted together for comparison. The twohyperfines in Fig. 3 have very different profiles: the maincomponent is blue-shifted, suggestive of inward motions(see Sect. 4.3), whereas the weak component is symmet-ric and its velocity centroid is red shifted compared tothe main component, indicating optically thin emission.Given that the self-absorption is more pronounced at theMC-1C: an accreting starless core 3position of the dust peak, where the N H + (1–0) opticaldepth is largest, we conclude that the weak componentis likely to be optically thin across the whole TMC–1Ccore.Thus, in the case of N H + (1–0) self–absorption, weused the weak hyperfine component, divided by 1/27(its relative intensity compared to the sum, normal-ized to unity, of the seven hyperfines), to determinethe N H + (1–0) integrated intensity, line width, and, asshown in Sec. 5, the N H + column density. In this anal-ysis, only spectra with signal to noise (S/N) for the weakcomponent > H + (1–0) did not show signs of self–absorption and anormal integration below the 7 hyperfines has been per-formed.Based on hyperfine fits to the C O(1–0) transition anda comparison of the relative strengths of the three com-ponents, we see that the C O(1–0) emission is opticallythin throughout TMC–1C. Although the noise is gener-ally too high in the C O(2–1) data to make indisputablehyperfine fits, the results of such an attempt suggest thatthe C O(2–1) lines are also optically thin, which is ex-pected for thin C O(1–0) emission and temperatures of ∼
10 K. Thus, the integrated intensity maps of C O lineswill reflect the C O column density distribution.In order to estimate the optical depth of the C O(2–1)lines, we compare the integrated intensity of C O(2–1)to that of C O(2–1). If both lines are thin, then theobserved ratio should be equal to the cosmic abundanceratio, R , ≡ [ O]/[ O] = 3.65 (Wilson & Rood 1994;Penzias 1981). We observe that the ratio of the inte-grated intensities R , = 2 . ± .
9, which correspondsto an optical depth of the C O(2–1) line of τ ≃ . O(1–0), C O(2–1),C O(2–1), DCO + (2–1) and N H + (1–0) are shown inFig. 4. Note that the N H + integrated intensity mappeaks right around the position of the dust column peaks,which is not true for C O and C O. We do not presentintegrated intensity maps of C S(2–1) or DCO + (3–2),which have lower signal to noise. ANALYSIS. I. KINEMATICS
Line Widths
Ammonia observations have shown that TMC–1C is acoherent core, having a constant line width across thecore at a value slightly higher than the thermal width,and increasing outside the “coherent” radius, ∼ H + observationsof TMC–1C show that the line width remains constant,at a value ∼ H + line width is very large. This re-sult is in agreement with the NH observations of TMC–1C, and is not consistent with the decreasing N H + andN D + linewidths at larger radii seen in L1544 and L694-2, which in other important ways (density and temper-ature structure, velocity asymmetry seen in N H + (1–0))closely resemble TMC–1C. To make sure that the lackof correlation of the N H + (1–0) line width is not dueto geometric effects, considering the elongated structureof TMC–1C, we also plotted the N H + (1–0) line widthas a function of antenna temperature, and found similar results.This behavior may be due to the coherence of the cen-tral portion of the core, which has nearly constant lengthalong the line of sight, and thus the velocity dispersioncomes from regions of the core that have similar scales(see Fig. 4 in Goodman et al. 1998). Cores formedby compressions in a supersonic turbulent flow naturallydevelop these regions of constant length at their centers(Klessen et al. 2005). Another reason that the N H + line widths appear constant across the cloud could bethe different “infall” velocity profile, with the velocitypeaking farther away from the dust peak than in L1544and L694-2 (though the projected velocity would stillbe at its maximum at the dust peak). In the case ofL1544, Caselli et al. (2002a) showed that the N H + (1–0)line profile is consistent with the Ciolek & Basu (2000)model at a certain time in the cloud evolution, where the“infall” velocity profile peaks at a radius of about 3,000AU (see also Myers 2005 for alternative models with sim-ilar radial velocities). Indeed, in Sec. 4.3 we show thatthe extent of the asymmetry seen in N H + (1–0) suggeststhat the peak of the inward motions is at about 7,000 AU,so that one does not expect to see broader line widthswithin this radius. In fact, the binned data in Fig. 5 showa hint of a peak at about 50 ′′ (7000 AU at the distanceof Taurus).In order to compare the thermal and non-thermal linewidths in TMC-1C, we assume that the gas temperatureis equal to 10 K and use the formulae:∆ v T = s(cid:18) kT g µm H (cid:19) (1)∆ v NT = p (∆ v obs ) − (∆ v T ) (2)where µ is the molecular weight of the species and m H is the mass of hydrogen.Figure 6 shows the non-thermal line width plottedagainst the thermal line width at the position of the dustcolumn density peak. To allow a fair comparison, allthe data in the figure have been first spatially smoothedat the same resolution of the NH map (1 ′ ). AlthoughC O, C O, DCO + and N H + all have similar molec-ular weights, they have significantly different values fortheir non-thermal line widths. The thermal line widthis much smaller than the non-thermal line width for themolecules C O and C O, while the ratio is closer tounity for DCO + and N H + . This suggests that the iso-topologues of CO are tracing material at larger distancesfrom the center, with a larger turbulent line width, thanare DCO + and N H + , which presumably are tracing thehigher density material closer to the center of TMC-1C.The C O(2–1) line is slightly thick, and this is probablythe reason of its slightly larger line width when comparedto the thin C O(2–1) line, as shown in Figure 6. Foreach transition observed, we see no clear correlation be-tween the observed line width and the thermal line width(and therefore with temperature, column density and dis-tance from the peak column density, see Section 5.2). Asin the study of depletion, the lower signal to noise inC S(2–1), DCO + (2–1) and DCO + (3–2) make any pos-sible trends between ∆ v and ∆ v thermal more difficult todetermine. From Fig. 6 we note that NH and N H + Schnee, S. et al.have similar non-thermal line widths, which makes sensegiven that N H + and NH are expected to trace similarmaterial (e.g. Benson et al. 1998). However, this resultis in contrast with the findings of Tafalla et al. (2004)who found narrower NH line widths towards L1498 andL1517B.We finally note that the line widths that we measurein C O and C O are larger than the N H + linewidthsthroughout TMC–1C, which contrasts with the resultsseen in C O and N H + in B68 (Lada et al. 2003). Thisis consistent with the fact that TMC–1C, unlike B68,is embedded in a molecular cloud complex and it is notan isolated core. Thus, CO lines in TMC–1C also tracethe (lower density and more extended) molecular mate-rial, part of the Taurus complex, where larger ranges ofvelocities are present along the line of sight. Velocity Gradients
In order to study the velocity field of TMC-1C, we de-termine the centroid velocities for C O(2–1), C O(2–1), C S(2–1), DCO + (2–1) and DCO + (3–2) with Gaus-sian fits. The centroid velocities of the C O(1—0) andN H + (1–0) lines are determined by hyperfine spectralfits. For those N H + spectra that show evidence of self-absorption, the velocity is derived from a Gaussian fit tothe thinnest component. The velocity gradient at eachposition is calculated by fitting the velocity field with thefunction: v lsr = v o + dvds ∆ α cos θ + dvds ∆ δ sin θ (3)where v o is the bulk motion along the line of sight, ∆ α and ∆ δ are RA and DEC offsets from the position ofthe central pixel, dv/ds is the magnitude of the velocitygradient in the plane of the sky, and θ is direction ofthe velocity gradient. The fit to the velocity gradient isbased on fitting a plane through the position–position ve-locity cube as in Goodman et al. (1993) (for the “total”gradient across the cloud) and in Caselli et al. (2002b)(for the “local” gradient at each position). The fit forthe “total” velocity gradient gives a single direction andmagnitude for the entire velocity field analyzed. The“local” velocity gradient is calculated at each position inthe spectral line maps based on the centroid velocities ofthe center position and its nearest neighbors, with theweight given to the neighbors decreasing exponentiallywith their distance from the central position.Analysis of ammonia observations with ∼ ′′ reso-lution of TMC–1C indicate an overall velocity gradi-ent of 0.3 km s − pc − directed 129 degrees East ofNorth (Goodman et al. 1993). The velocity field thatwe measure in TMC–1C has spatial resolution threetimes greater ( ∼ ′′ ) than the ammonia study, and re-veals a pattern more complicated than that of solid bodyor differential rotation. The velocity fields measuredby C O(1–0), C O(2–1) and C O(2–1) are shown inFig. 7. Although there is a region that closely resemblesthe velocity field expected from rotation (gradient arrowsof approximately equal length pointing in the same di-rection), the measured velocities vary from blue to redto blue along a NW - SE axis. The N H + (1–0) veloc-ity fields (shown in Fig. 7) also follow the same blue tored to blue pattern along the NW - SE axis, but the ob- servations cover a somewhat different area than the COobservations, which complicates making a direct compar-ison. Taken as a whole, it is clear that there is an orderedvelocity field in portions of the TMC-1C core, and thatthe lower density CO tracers “see” a velocity field similarto that probed by N H + lines, which trace higher densitymaterial. In any case, the velocity field that looks likerotation reported in Goodman et al. (1993) turns out tobe more complicated when seen over a larger area withfiner resolution. The direction and magnitude of the ve-locity gradient in the region that resembles solid bodyrotation is shown in Fig. 8 for each transition. Inward Motions
To quantify the velocity of the inward motion fromthe N H + (1–0) line across the TMC–1C cloud, we usea simple two–layer model, similar to that described byMyers et al. (1996). This model assumes that the cloudcan be divided in two parts with uniform excitation tem-perature ( T ex , gradients in T ex between the two layers asin De Vries & Myers 2005, are not considered here), linewidth (∆ v ), optical depth ( τ ) and LSR velocity ( V LSR )and that the foreground layer has a lower excitation tem-perature. For simplicity, we also assume that the sevenhyperfines have the same T ex , which is a very rough as-sumption in regions of large optical depth, as recentlyfound by Daniel et al. (2006). Despite of the simplicityof the model, we find good fits to the seven hyperfinelines and determine the value of the velocity differencebetween the two layers, which can be related to the “in-fall” velocity.In Fig. 9 we present five spectra which represent a cutacross the major axis of the core, passing through thedust peak. For display purposes, the spectra have beencentered to 0 velocity, subtracting the LSR velocity ob-tained from a Gaussian fit to the weak hyperfine compo-nent (for offsets [-40,60], [-20,40], [0,20], where the self-absorption in present) or hfs fits in CLASS (for offsets[20,0] and [40,-20]). The V LSR velocity is shown in the topright of each panel. The cut is from South-East (offset[40,-20], see Fig. 2) to North-West (offset [-40,60]). Thefirst thing to note in the figure is that clear signs of self-absorption and asymmetry are present toward the dustpeak and in the North-West, but not in the two Southernpositions. This trend can also be seen as a general fea-ture in Fig. 2, where it is evident that asymmetric linesare more numerous North–West of the dust peak.The excitation temperature, total optical depth, linewidth and the velocity ( V − V LSR , see Fig. 9) of the fore-ground (F) and background (B) layers are reported in Ta-ble 3. To find the best fit parameters, we first performedan hfs fit to the [20,0] spectrum, which is the closest spec-trum to the dust peak not showing self-absorption. Thevalues of τ TOT , T ex and line width obtained from this fithave been adopted for the background emission at thedust peak position and the best fit has been found byadding the foreground layer and minimising the residu-als. For the two spectra North–West of the [0,20] po-sition, adjustment to the parameters of the backgroundlayer were necessary to obtain a good fit. We point out MC-1C: an accreting starless core 5that the five spectra we chose for this analysis are rep-resentative of the whole area surrounding the TMC–1Cdust peak, where a mixture of symmetric, blue–shiftedand red–shifted spectra are present. As already stated,the majority of the asymmetric spectra show inward mo-tions and extend over a region with radius ∼ T ex ≃ τ TOT ≃ v ≃ − ) havebeen used as input parameters in a Large Velocity Gra-dient (LVG) code for a uniform medium and found to beconsistent with the N H + (1–0) tracing gas at a density n (H ) ≃ × cm − , kinetic temperature T kin ≃
10 Kand with column density N (N H + ) ≃ × cm − , val-ues comparable to those found for the background layer(see Table 5 and Sec. 5.1).It is interesting that the maximum of the line-of-sight component of the inward velocity ( ∼ − )is found toward the dust peak, whereas one pixel awayfrom it, the inward velocity drops to 0.05 km s − . Thisis suggestive of a geometric effect, in which the inwardvelocity vector is directed toward the dust peak, so thatonly a fraction cos ( θ ) (with θ the angle between the l.o.s.and the infall velocity direction) of the total velocity isdirected along the line of sight in those positions awayfrom the dust peak. Of course, our simplistic model pre-vents us to go further than this, i.e. the uncertaintiesare too large to build a 3D model of the velocity profilewithin the cloud.As shown in Fig. 2, in the North–West end of theTMC–1C core (around offset [-250,150]), there are othersignatures of inward motions, which may indicate thepresence of another gravitational potential well. Thissuggestion is indeed reinforced by Fig. 8 of Schnee et al.(2007), which shows high extinction and low tempera-tures in the same direction. Unfortunately, the contin-uum coverage is not good enough to attempt a detailedanalysis, but it appears evident that the extension to-ward the North–West is another dense core connected tothe main TMC–1C condensation with lower density andwarmer gas and dust. ANALYSIS. II. COLUMN DENSITY AND TEMPERATURE
Gas Column Density
To derive the column density of gas from eachmolecule, we assume that all rotation levels are char-acterized by the same excitation temperature T ex (theCTEX method, described in Caselli et al. 2002b). Incase of optically thin emission, N tot = 8 πWλ A g l g u J ν ( T ex ) − J ν ( T bg ) 11 − exp( − hν/kT ex ) Q rot g l exp( − E l /kT ex )(4)where λ and ν are the wavelength and frequency of thetransition, k is the Boltzmann constant, h is the Planckconstant, A is the Einstein coefficient, g l and g u are thestatistical weights of the lower and upper levels, J ν ( T ex )and J ν ( T bg ) are the equivalent Rayleigh-Jeans excitationand background temperatures, W is the integrated in-tensity of the line. The partition function ( Q rot ) andthe energy of the lower level ( E l ) for linear molecules are ∼ moldata/radex.php given by: Q rot = ∞ X J =0 (2 J + 1) exp( − E J /kT ) (5)and E J = J ( J + 1) hB (6)and B is the rotational constant (see Table 4 for thevalues of the constants).The C O(1–0) and (2–1) lines have hyperfine struc-ture, enabling the measurement of the optical depth. Wefind that the lines are optically thin throughout the core.To determine the column density, we assume an excita-tion temperature of 11 K, which is the average value of T ex found from our C O data around the dust peak po-sition, as explained in Sect. 5.3. In the case of C O(2–1)lines, we correct for optical depth before determining thecolumn density, using the correction factor: C τ = τ − e − τ (7)As explained in Sect. 3.1, N H + (1–0) lines show clearsigns of self–absorption in an extended area around thedust peak. To determine the column density across thecore, first we select spectra without self–absorption, andthose with high S/N (i.e. with W/σ W >
20, with W ≡ integrated intensity; see Caselli et al. 2002b) have beenfitted in CLASS to find T ex and τ . The mean value of T ex found with this analysis (4.4 ± T ex was not possible (i.e. for self-absorbed or thin lines). Foroptically thin N H + (1–0) transitions, the intensity wasintegrated below the seven hyperfine and the expression(4) used to determine the total column density.In cases of self-absorbed spectra, the N H + columndensity has been estimated from the integrated intensityof the weakest (and lowest frequency) hyperfine compo-nent ( F F = 1 0 → T ex =4.4 K)and multiplying by 27 (the inverse of the hyperfine rel-ative intensity). The weakest component is not affectedby self–absorption, as shown in Fig. 3, suggesting that itsoptical depth is low. We have checked that these two dif-ferent methods approximately give the same results bymeasuring the N H + column density with both proce-dures in those cases where self-absorption is not presentand where the weakest hyperfine component has a S/Nratio of at least 4. We found that the two column densityvalues agree to within 10%.DCO + (2–1) and DCO + (3–2) lines are clearly self–absorbed and the column density determination is veryuncertain (given that there are no clues about their op-tical depth and excitation temperature). The estimateslisted in Table 5 should be considered lower limits. T ex = 4.4 K has beed assumed, based on the fact that theDCO + lines are expected to trace similar conditions thanN H + . C S(2–1) spectra have low sensitivity, and thelines are affected by self–absorption (see Fig. 1), so thederived C S column density is highly uncertain.The N H + abundance, X (N H + ) ( ≡ N (N H + ) /N (H )), toward the dust peak is 1.6 × − ,identical (within the errors) to that derived towardthe L1544 dust peak (Crapsi et al. 2005, e.g.). Thisis interesting considering that N (H ) in TMC–1C is Schnee, S. et al.1.6 times lower than in L1544, in which N H + closelyfollows the dust column (as already found in previ-ous work). However, unlike L1544, where the N H + abundance appears constant with impact parameters(e.g. Tafalla et al. 2002 and Vastel et al. 2006), inTMC–1C the N H + abundance increases away fromthe dust peak by a factor of about two within 50 ′′ , asshown in Fig. 10 (see also Fig. 14 in Sect. 6.1). Fig. 10displays A V (see Sect. 5.2), N (N H + ) and X (N H + ),normalized to the corresponding maximum values (63.2mag, 1.1 × cm − , and 4.8 × − , respectively) intwo cuts (one in right ascension and one in declination)passing through the dust peak. One point to note isthat the abundance derived at the dust peak (marked bythe black dotted line) is the minimum value observed,indicating moderate (factor of ∼
2) depletion.
Dust Column Density
In Schnee et al. (2007) we used SCUBA and MAMBOmaps at 450, 850 and 1200 µ m to create column den-sity and dust temperature maps of TMC–1C. In this pa-per we smooth the dust continuum emission maps to the20 ′′ spacing of the IRAM maps and then derive A V and T d to facilitate a direct comparison of the gas and dustproperties. At each position, we make a non-linear leastsquares fit for the dust temperature and column densitysuch that the difference between the predicted and ob-served 450, 850 and 1200 µ m observations is minimized.The errors associated with such a fitting procedure aredescribed in Schnee et al. (2007). Dust column densityand temperature maps of TMC–1C are shown in Fig. 8of Schnee et al. (2007).From Fig. 8 in Schnee et al. (2007), it is clear thatthere is an anti-correlation between extinction and dusttemperature (as also predicted by theory, e.g. Evans etal. 2001, Zucconi et al. 2001, Galli et al. 2002). To bet-ter show this, the two quantities are plotted in Fig. 11.The data in Fig. 11 are not smoothed to the IRAM 30mbeam at 3 mm, since this is only a dust property in-tercomparison and does not refer to the gas properties.Higher A V (60 < A V ≤
90 mag) and lower dust temper-atures (5 ≤ T dust < T d − A V relationship seenin TMC–1C with that predicted by Zucconi et al. (2001)for an externally heated pre-protostellar core (the solidred line in Fig. 11). We find that at high column density( A V >
30) the observed dust temperature in TMC–1C islower than that of the model core, while at low columndensity (10 < A V <
20) the observed dust temperatureis higher than the model predicts. However, given thatthe model predicts the dust temperature at the center ofa spherical cloud, and that the geometry of TMC–1C iscertainly not spherical, only a rough agreement betweenthe model and observations should be expected.
Gas Temperature
Because of its low dipole moment, CO is a good gasthermometer, given that it is easily thermalized at typ-ical core densities. However, it is now well establishedthat CO is significantly frozen onto dust grains at densi-ties ≥ cm − (one exception being L1521E; Tafalla &Santiago, 2004b) and this is also the case in TMC–1C.Therefore, at the dust peak we do not expect to mea-sure a gas temperature from CO of ∼ O(1–0), C O(2–1), and C O(2–1). TheC O(2–1)/C O(2–1) brightness temperature ratio hasbeen used to derive the excitation temperature of theC O line, which is coincident with the kinetic temper-ature if the line is thermalized. To test the hyposthe-sis of thermalization we use an LVG (Large-Velocity-Gradient) program to determine at which volume den-sity and kinetic temperature the observed C O(1–0)and C ∼ moldata/radex.html. C O(2-1) and C O(2-1) as a measure of T kin These two lines have similar frequencies, so the corre-sponding angular resolution is almost identical and noconvolution is needed. Following a similar analysis donewith the J=1–0 transition of the two CO isotopologues(Myers et al. 1983), the optical depth of the C O(2–1)line ( τ ) can be found from: T mb [C O(2 − T mb [C O(2 − . × − e − τ τ , (8)where T mb [ i ] is the main beam brightness temperatureof transition i (assuming a unity filling factor). The lastterm in the right hand side is the optical depth correc-tion which is used to determine the total column densityof C O in a plane parallel geometry, which most likelyapplies to CO emitting regions, i.e. the external corelayers.Once τ is measured, the excitation temperature ( T ex )of the corresponding transition (thus the gas kinetic tem-perature, if the line is in local thermodynamic equilib-rium) can be estimated from the radiative transfer equa-tion: T mb = [ J ν ( T ex ) − J ν ( T bg )](1 − e − τ ) , (9)where J ν ( T ex ) and J ν ( T bg ) are the equivalent Reyleigh–Jeans temperatures, with J ν ( T ) = T exp( T /T ) − , (10) T = hν/k B , and ν the frequency of the C O(2–1) line(see Table 1).Figure 12 (left panel) shows the results of this analysis.The set of data points in Fig. 12 is limited to only thosespectra with T mb [C O(2 −− /T rms ≥
10, to avoid scat-ter due to noise. The error associated with the gas tem-perature has been calculated by propagating the errorson τ and T mb [C O(2–1)] into Eq. 9 and its expressionis given in the appendix.It is interesting to note that the C O(2–1) excitationtemperature appears to decrease away from the center,and, if this line is thermalized, it suggests that the kinetictemperature also drops away from the center, in contrastwith the dust temperature. Indeed, the two quantitiesare completely uncorrelated in the 12 common positionswith large S/N C O(2–1) spectra (not shown). T ex isclose to 12 K at the core center, whereas it drops to 9–10 K one arcmin away from the dust peak. Is this dropMC-1C: an accreting starless core 7due to a decreasing gas temperature, as recently foundby Bergin et al. (2006) in the Bok Globule B68? Un-like B68, we believe that our result is due to the volumedensity decrease. Indeed, the critical densities of the J= 2–1 lines of C O and C O are a few × cm − ,so that only if the volume density traced by one of thetwo isotopologues is larger than, say, 5 × cm − canthe J = 2–1 lines be considered good gas thermometers.In the next subsection, we investigate this point morequantitatively. C O(1–0) and C O(2–1) to measure T ex [ C O (2–1)] In Fig. 12 (right panel), the brightness temperatureratio of the C O(1–0) and C O(2–1) lines is plottedas a function of distance from the dust peak. Becauseof the different angular resolutions at the 2–1 and 1–0frequencies, the 1 mm data have been smoothed to the3 mm resolution and both data cubes have then beenregridded, to allow a proper comparison. The ratio is in-deed increasing towards the edge of the cloud, consistentwith our previous finding of a T ex [C O(2–1)] drop in thesame direction (see left panel).Both C O(1–0) and (2–1) lines possess hyperfinestructure, which provides a direct estimate of the lineoptical depth. Using the hfs fit procedure available inCLASS, we found that all over the TMC–1C cloud, bothlines are optically thin. This means that it is not possibleto derive the excitation temperature in an analytic way,so we use the LVG code introduced in Sect. 5.3. Thiscode assumes homogeneous conditions, which is likely tobe a good approximation for the region traced by CO iso-topologues. In fact, because of freeze-out, CO does nottrace the regions with densities larger than about 10 cm − (see below and Sect. 6.1), so that the physical con-ditions traced by CO around the dust peak are likely tobe close to uniform (n(H ) ∼ a few times 10 and aboutconstant temperature). This is also supported by the in-tegrated intensity CO maps, which appear extended anduniform around the dust peak (see Fig. 4).To better understand this result, the LVG code hasbeen run to see how changes in volume density andgas temperature affect the line ratio. This is shown inFig. 13, where the top panel shows the T mb ratio asa function of T kin for a fixed value of the volume den-sity ( n (H ) = 2 × cm − ), a C O column density of10 cm − (as found in Section 5.1), and a line width of0.4km s − , as observed. The horizontal dashed lines en-close the range of T mb ratios observed in TMC–1C andreported in Fig. 12. Thus, the observed T mb range (atthis volume density) corresponds to a range of gas tem-perature between 11 K toward the dust peak and ∼ O(2–1) excitation temperature away fromthe dust peak.In the bottom panel of Fig. 13, the same brightnesstemperature ratio is plotted as a function of n (H ), fora fixed kinetic temperature ( T kin =11 K), N (C O) =10 cm − and ∆ v =0.4 km s − , as before. The blackcurve shows this variation and, not surprisingly, the ob-served range of T mb ratios can also be explained if thevolume density (traced by the C O lines) decreases from ≃ × cm − toward the dust peak to ≃ × cm − away from it (the point farthest away being at a pro-jected distance of 80 ′′ , or 11,000 AU, see Fig. 12). Notethat the volume density traced by the C O line towardsthe dust peak is significantly lower than the central den-sity of TMC-1C ( ≃ × cm − ; see Schnee et al. 2007),once again demonstrating that CO is not a good tracerof dense cores. The bottom panel of Fig. 12 is consis-tent with a volume density decrease away from the dustpeak, or, more precisely, a lower fraction of (relatively)dense gas intercepted by the C O lines along the lineof sights. In the same plot, the red curves show the ex-citation temperatures of the C O(1–0) and (2–1) linesvs. n (H ). Note that T ex [C O(2–1)] = T kin only whenthe density becomes larger than ∼ cm − . Thus, theC O(2–1) line is sub-thermally excited in TMC–1C.In summary, the rise in the C O(1–0)/(2–1) brigth-ness temperature ratio away from the dust peak ratiocan be caused by either a gas temperature decrease or avolume density decrease (or both). Considering that thedust (and likely the gas; see the recent paper by Crapsiet al. 2007) temperature is clearly increasing away fromthe dust peak, we believe that the drop in T ex observedboth using the C O and C O lines is more likely dueto a drop in the volume density traced by these species.This is reasonable in the case of a core embedded in amolecular cloud complex, such as TMC–1C, where thefraction of low density material intercepted along the lineof sight by C O and C O observations is significantlylarger than in isolated Bok Globules such as B68 (seeBergin et al. 2006). In any case, a detailed study ofthe volume density structure of the outer layers of densecores will definitely help in assessing this point. ANALYSIS. III. CHEMICAL PROCESSES
Molecular Depletion
By comparing the integrated intensity maps of COisotopologues and N H + (1–0) (Fig. 4) in TMC-1C withthe column density implied by dust emission (Fig. 8 inSchnee et al. (2007)), we see that at the location of thedust column density peak the CO emission is not peakedat all. The N H + (1–0) emission peaks in a ridge aroundthe dust column density maximum, not at the peak, butin general N H + traces the dust better than the C Oemission does. Below, we measure the depletion of eachobserved molecule and compare our results to similarcores.Previous molecular line observations of starless coressuch as L1512, L1544, L1498 and L1517B, consistentlyshow that CO and its isotopologues are significantly de-pleted, e.g. (Lee et al. 2003; Tafalla et al. 2004). How-ever, other molecules such as DCO + and N H + are typ-ically found to trace the dust emission well, (e.g. Caselliet al. 2002b; Tafalla et al. 2002, 2004), although there issome evidence of their depletion in the center of chem-ically evolved cores, such as B68 (Bergin et al. 2002),L1544 (Caselli et al. 2002b) and L1512 (Lee et al. 2003).In order to measure the depletion in TMC-1C, we definethe depletion factor of species i : f D ( i ) = X can ( i ) N ( H ) dust N ( i ) (11)where X can is the “canonical” (or undepleted) fractionabundance of species i with respect to H (see Table 4), Schnee, S. et al. N ( H ) dust is the column density of molecular hydrogenas derived from dust emission, and N ( i ) is the columndensity of the molecular species as derived in Section 5.1.The derived depletion factors for each molecule (exceptfor DCO + and C S, where the column density determi-nation is quite uncertain, as explained in Sec. 5.1) ineach position with signal to noise > ∼ O and C O de-pletion and dust-derived column density, which has alsobeen seen in C O by Crapsi et al. (2004) in the coreL1521F, which contains a Very Low Luminosity Object(Bourke et al. 2006). To check the impact of resolu-tion on the derived depletion, we compare the C O(2–1) depletion when smoothed to 20 ′′ (the resolution ofthe C O(1–0) data) with that derived from smoothingC O(2–1) to 14 ′′ (the resolution of the bolometer data).We find no systematic difference between the two calcu-lations of the depletion, and a 13% standard deviation inthe ratio of the derived depletions.The depletion factor and column density at the posi-tion of the dust peak is listed in Table 5 for each tracer.The depletion factor measured in N H + clearly follows adifferent trend compared to the CO isotopologues. Firstof all, in Fig. 14 the N H + depletion factor is allowed tohave values below 1, because of our (arbitrary) choice forthe “canonical” abundance of N H + assumed here to beequal to 1.4 × − , the average value across TMC–1C.We point out that a “canonical” abundance for N H + ismuch harder to derive than for CO, because N H + linesare much harder to excite (and thus detect) in low den-sity regions where depletion is negligible. Nevertheless,Fig. 20 shows that the N H + depletion factor monotoni-cally increases (as in the case of CO) for N(H ) ≥ × cm − (or A V ≥
30 mag).
This is clear evidence of N H + depletion in the core nuclei, in a central region with ra-dius ∼ V ≥ mag (see also Fig. 10).The dispersion in the N H + depletion factor vs. N(H )relation is very large with no obvious trend at lowerA V values (N(H ) < × cm − ), which we believeis due to our choice of excitation temperature wherethe N H + (1–0) line is optically thin. As explained inSect. 5.1, in the case of optically thin lines, T ex has beenassumed equal to 4.4 K, the mean value derived from theoptically thick spectra which do not show self-absorption(and which trace regions with A V ≥
20 mag). There-fore, in all positions with N(H ) below 2 × cm − ,where the volume density is also likely to be low, theassumed N H + (1–0) excitation temperature is likely tobe an overestimate of the real T ex . To see if this canindeed be the cause of the observed scatter, consider acloud with kinetic temperature of 10 K, volume densityof 3 × cm − , line width of 0.3 km s − and an excita- tion temperature of 4.4 K for the N H + (1–0) line. Usingthe RADEX LVG program, this corresponds to a N H + column density of 10 cm − . If the density drops bya factor of two (whereas all the other parameters arefixed), the N H + (1–0) excitation temperature drops to3.6 K. In these conditions, using T ex = 4.4 K instead of3.6 K, in our analytic column density determination (seeSect. 5.1), implies underestimating N(N H + ) by 50%.Therefore, our assumption of constant T ex can be themain cause of the observed f D scatter at low extinctions.Because of the anti-correlation between dust temper-ature and column density (see Fig. 11), we expect thatthere will also be an anti-correlation between the deple-tion factor, f D , and dust temperature. Figure 14 (rightpanels) shows the depletion factor for each molecule plot-ted against the line-of-sight averaged dust temperature.As expected, the depletion is highest in the low temper-ature regions though the lower signal to noise in C Sand DCO + make this somewhat harder to see. The anti-correlation between the depletion factor and dust tem-perature has also been seen by Kramer et al. (1999) inIC5146 in C O, though in TMC-1C the temperaturesare somewhat lower.Our data clearly suggest that there is an increasingdepletion of N H + with increasing H column (and vol-ume) density. In previous work (e.g. Tafalla et al. 2002,2004; Vastel et al. 2006), the observed N H + abundanceappears constant across the core, although the data arealso consistent with chemical models in which the N H + abundance decreases by factors of a few (Caselli et al.2002b). Bergin et al. (2002) also deduce small depletionfactors for N H + when comparing data to models andPagani et al. (2005) found clear signs of N H + deple-tions at densities above ∼ cm − . There is also ev-idence of N H + depletion towards the Class 0 protostarIRAM 04191+1522 (Belloche & Andr´e 2004) in Taurus.The average N H + abundance that we find in TMC-1C,relative to H , is 1.4 × − .What appears to be different from previous work isthat the CO depletion factor towards the dust peakis relatively low (compared to, e.g., L1544), and, atthe same time , N H + (1–0) lines are bright over anextended region. If TMC–1C were chemically young(such as L1521E; Tafalla & Santiago 2004, Hirota etal. 2002), then there would be negligible CO freeze–out and low abundances of N H + , given that N H + is a“late-type” molecule (i.e. its formation requires signifi-cantly longer times (factors >
10) than CO and other C–bearing species). In TMC–1C we observe moderate CO and N H + depletions, as well as extended N H + emissionwith derived fractional abundances around 10 − . Toderive an approximate value of the average gas numberdensity of the region where N H + emission is present, wefirst sum all the observed N H + (1–0) spectra (over thewhole mapped area, with size ≃ ′′ × ′′ , correspond-ing to a linear geometric mean of about 40,000 AU; seeFig. 7) and then perform an hfs fit in CLASS to derive theexcitation temperature. We find T ex = 3.6 ± N (N H + ) = 4.84 ± × cm − , which can be repro-duced with the LVG code if n (H ) = 5 × cm − and T kin = 11 K, as found in previous sections (see Sect. 4.3and 5.3). The average value of the extinction across thewhole TMC–1C core is 23 mag, so that the correspondingMC-1C: an accreting starless core 9N H + abundance is 2 × − , close to the average valuefound before. How long does it take to form N H + withfractional abundances of ∼ − in regions with volumedensities ∼ × cm − ? Roberts et al. (2004) derivetimes ≥ × yr at n(H ) = 10 cm − , so that this canbe considered a lower limit to the age of the TMC–1Ccore .In summary, all the above observational evidence sug-gests that the majority of the gas observed towardsTMC–1C has been at densities ∼ cm − for at least afew times 10 yr and that material is accreting towardthe region marked by the mm dust emission peak. We fi-nally note that the density profile of the region centeredat the dust peak position is steeper (consistent with apower law; see Fig. 13 of Schnee & Goodman 2005) thanfound in other cores, so that Bonnor-Ebert spheres maynot be the unique structure of dense cores in their earlystages of evolution. Chemical Model
Although TMC–1C is more massive than L1544 bya factor of about two, the physical structures of thetwo cores are similar: the central density of TMC–1Cis ∼ × cm − (factor of ∼ ∼ H + column density at the dust peak is twotimes lower and the C O column density is 1.7 timeslarger than in L1544 (Caselli et al. 2002b). All this isconsistent with a younger chemical (and dynamical) age(Shematovich et al. 2003; Aikawa et al. 2005).To understand this chemical differentiation in objectsin apparently similar dynamical phases, we used the sim-ple chemical model originally described in Caselli et al.(2002b) and more recently updated by Vastel et al.(2006). The model consists of a spherical cloud withdensity and temperature gradients as determined bySchnee et al. (2007). The model starts with H , N , COand O in the gas phase, a gas–to–dust mass ratio of 100,and a Mathis, Rumpl & Nordsiek (1977; MRN) grain sizedistribution. Molecules and atoms are allowed to freeze–out onto dust grains and desorb via cosmic–ray impulsiveheating (Caselli et al. 2002b; Hasegawa & Herbst 1993).The adopted binding energies of CO and N are 1100 Kand 982.3 K, respectively. The CO binding energy is in-termediate between the one measured for CO onto (i) icymantles (1180 K; Collings et al. 2003 and Fraser et al.2004) and (ii) CO mantles (885 K; ¨Oberg et al. 2005).The adopted value (1100 K) is the weighted mean of thetwo measured values, assuming that water is about fourtimes more abundant than CO in the Taurus molecu-lar cloud (see Table 2 of Ehrenfreund & Charnley 2000and references therein). See ¨Oberg et al. (2005) for ad-sorption onto icy mantles. For the atomic oxygen bind- ing energy we used 750 K, as in Vastel et al. (2006).The following parameters have also been assumed fromVastel et al. (2006): (i) the cosmic ray ionization rate(1.3 × − s − ); (ii) the minimum size of dust grains( a min = 5 × − cm); (iii) the “canonical” abundance ofCO (9.5 × − , from Frerking et al. (1982); (iv) the stick-ing coefficient ( S =1, as recently found by Bisschop et al.(2006) for CO and N ); (v) the initial abundance ofN equal to 4 × − , i.e. about 50% the total abun-dance of nitrogen observed in the interstellar medium(Meyer et al. 1997); (vi) the initial abundance of “met-als” (M + , in Fig. 15) of 10 − (from McKee (1989)); and(vii) the initial abundance of Oxygen, fixed at a half thecanonical abundance of CO (i.e. 13 times lower than thecosmic abundance; Meyer et al. 1998).The model is run until the C O column density to-ward the center of the cloud reaches the observed value( t = 8 × yr). During this time, the abundance ofmolecular ions is calculated within the cloud using steadystate chemical equations with the instantaneous abun-dances of the neutral species. To determine x ( e ), the re-action scheme of Umebayashi & Nakano (1990) is used,where the abundance of the generic molecular ion “mH + ”(essentially the sum of HCO + , N H + , H O + and theirdeuterated forms) is calculated (see Caselli et al. (2002b)for more details). The calculated abundance profiles ofthe various species have then been convolved with theHPBWs of the 30m antenna at the corresponding fre-quencies and the derived column densities are in verygood agreement with the observed quantities (within fac-tors of 2 for N H + , N D + and, of course, CO isotopo-logues), which is very encouraging, considering the sim-plicity of the model.The best-fit chemical structure of TMC–1C, reachedafter 10,000 yr, is shown in the left panel of Fig. 15.Note that despite the similar binding energies of CO andN , the HCO + and DCO + drops are steeper than thoseof N H + and N D + , which is due to the fact that theCO freeze–out (although lower than in L1544) enhancesthe N H + production rate, as pointed out by previouschemical models (Aikawa et al. 2001). Finally, we notethat the CO depletion factor within the cloud, F D (CO) ,is significantly lower than in L1544 at radii < ∼ × cm − (as found in L1544, L1498 andL1517B; Caselli et al. 2002, Tafalla et al. 2002, 2004).Indeed, the case of L1521E, a Taurus starless core, wherethe central density is 10 cm − but no CO freeze–out isobserved (Tafalla & Santiago 2004b), suggests that cloudcores in similar dynamical stages can have different chem-ical compositions. This point has been further discussedby Lee et al. (2003), who underline the importance of theenvironment in setting the chemical/dynamical stage of The symbol F D (CO), used here to indicate the CO deple-tion within the cloud, should not be confused with f D (CO), the observed (or integrated-along-the-line-of-site) CO depletion factor( f D = R F D ( l ) dl ; see also Crapsi et al. 2004). H + had time to freeze–out (as found by Bergin et al.(2002)).The present detailed study of TMC–1C adds a newpiece to the puzzle: cores which are currently accretingmaterial from the surrounding cloud appear chemicallyyounger, with lower CO depletion factors. If the accret-ing cloud material, at densities < ∼ cm − , is old enough( > ∼ × yr) to have formed observable abundances ofN H + (as in TMC–1C), then N H + lines toward the dustpeak will be bright. On the other hand, the chemicalstructure of cores such as L1521E (rich in CO, but poorin N–bearing species such as N H + and NH ) may beunderstood as young condensations which are accretingeither lower density material (where the chemical timesscales for N H + formation are significantly longer) ormaterial which spent only a small fraction of 10 yr atrelatively high densities ( ∼ cm − ). The former hy-pothesis may be valid in environments less massive thanthose associated with TMC–1C (and it does not requirelarge contraction speeds), whereas the latter hypothe-sis needs dynamical time scales shorter than or at mostcomparable to chemical time scales (which are about 10 yr at densities of ∼ cm − , as can be found from thefreeze–out time scale of species such as CO).In summary, TMC-1C, being more massive than L1544and other typical low-mass cores, has a larger reservoir ofundepleted material at densities close to 10 cm − , whereboth CO and N H + are abundant. Detailed chemicalmodels suggest that TMC–1C must be at least 3 × yrold, to reproduce the observed N H + abundances acrossthe cloud. Our simple chemical code tell us that theobserved CO depletion factors can be reached in only10,000 yr. Therefore, the core nucleus is either signifi-cantly younger than the surrounding material or the sur-rounding (undepleted) material has accreted toward thecore nucleus in the past 10,000 yr. In either case, this isevidence that the densest part of TMC–1C has recentlyaccreted material .From the velocity gradients presented in Section 4.2 itis hard to see a clear pattern of flowing material towardsthe dust peak, but the “chaotic” pattern is reminiscentof a turbulent flow that may be funnelling towards thedensest region, aided by gravity. In any case, the ex-tended inward motions deduced from N H + observations(see Sect. 4.3) is consistent with material at about (5–10) × cm − currently accreting toward the dust peakposition at velocities around 0.1 km s − . It will be ex-tremely important to compare this velocity field withthose predicted by turbulent simulations of molecularcloud evolution, especially considering the possibility ofcompetitive accretion (Bonnell & Bate 2006). Observa-tion of CS will also be important to check our predictionof a larger “extended infall” velocity, when compared toL1544. SUMMARY
A detailed observational study of the starless coreTMC–1C, embedded in the Taurus molecular cloud, hasbeen carried out with the IRAM 30m antenna. We havedetermined that TMC-1C is a relatively young core (t > ∼ × yr), with evidence of material accreting towardthe core nucleus (located at the dust emission peak). Thecore material at densities > ∼ cm − is embedded in acloud condensation with total mass of about 14 M ⊙ andaverage density of ≃ cm − , where CO is mostly inthe gas phase and N H + had the time to reach the ob-served abundances of ≃ − . The overall structure issuggestive of ongoing inflow of material toward the cen-tral condensation. In addition, we have found that:1. N H + (1–0) lines show signs of inward asymmetry overa region of about 7,000 AU in radius. This is the most ex-tended inward asymmetry observed in N H + so far. Thedata are consistent with simple two–layer models, wherethe line-of-sight component of the relative (infall) veloc-ities range from ∼ − (toward the dust peak) to ∼ − (at a distance from the dust peak of about7,000 AU).2. CO isotopologues and N H + show increasing deple-tion as A V increases and T d decreases. The amount ofCO depletion that we observe is a factor of ∼ H + column densities are onlya factor of two lower. Also, N H + show clear signs ofmoderate depletion toward the dust peak position.3. The gas temperature determined from C O(2–1) is12 K at the dust peak, indicating that CO is not trac-ing the dense ( n (H ) > × cm − ) and cold ( T kin <
10 K) regions of dense cores. The C O(2–1) excita-tion temperature drops outside the dust peak, and thisis consistent with a roughly constant kinetic tempera-ture and a dropping volume density ( traced by CO iso-topologues ) from ∼ × cm − toward the dust peakto ≃ × cm − at a projected distance from the dustpeak of about 11,000 AU (no high S/N data are availableto probe larger size scales).4. N H + (1-0) line widths are constant across the core,which is consistent with previous NH measurements(Barranco & Goodman 1998), but different from whathas been found with N H + and N D + observationsof L1544 and L1521F (Crapsi et al. 2005), where linewidths are increasing toward the core center. The in-crease in line width with radius seen in C O and N H + in B68 (Lada et al. 2003) is not seen in TMC–1C, andunlike B68, the C O line width is significantly largerthan the N H + line width throughout TMC-1C. This isconsistent with the fact that TMC–1C, unlike B68, is em-bedded in a molecular cloud complex, so that CO linestrace more material along the line of sight of TMC–1C.5. The velocity field that we see in TMC–1C does notshow the global signs of rotation that were seen in NH observations over a somewhat different area at arcminuteresolution in Goodman et al. (1993). Nevertheless, oneportion of TMC–1C encompassing the dust peak posi-tion does have a more coherent velocity field, suggestiveof solid body rotation with magnitude ≃ − pc − ,in the tracers C O(1-0), C O(2-1), C O(2-1) andN H + (1-0).6. The observed chemical structure of the TMC–1C corecan be reproduced with a simple chemical model, adopt-MC-1C: an accreting starless core 11ing the CO and N binding energies recently measuredin the laboratory. We argue here that “chemically youngand physically evolved” cores like L1521E and L1698B(those with low CO depletion, faint N H + lines, cen-tral densities above 10 cm − and centrally concentratedstructure) have lower density envelopes than TMC–1Cin which the N H + abundance did not have the time toreach equilibrium values. On the other hand, “chem-ically and physically evolved cores” like L1544, L694-2 and L183 (those with high CO depletion and brightN H + lines) are likely to have lower rates of accretion ofmaterial from the envelope to the nucleus than in TMC–1C (or it has ended), and with a core nucleus undergoingcontraction. Finally, “chemically evolved” but less cen-trally concentrated cores (e.g. L1498, L1512, B68), canjust be older objects (age > ∼ yr), close to equilibrium,as suggested by Lada et al. (2003). In the case of TMC–1C, there is evidence that the core is at least 3 × yr old and has recently accreted less chemically evolvedmaterial.More comprehensive chemical models, taking into ac- count the accretion of chemically young material, as wellas a comparison between the observed velocity patternsand turbulent models of cloud core formation are sorelyneeded to test our conclusions.Our anonymous referee has provided valuable com-ments and suggestions which have improved the contentand clarity of this paper. We would like to thank PhilMyers, Ramesh Narayan, David Wilner and Doug John-stone for their suggestions, assistance, and insights. TheJames Clerk Maxwell Telescope is operated by The JointAstronomy Centre on behalf of the Particle Physics andAstronomy Research Council of the United Kingdom, theNetherlands Organisation for Scientific Research, and theNational Research Council of Canada. IRAM is sup-ported by INSU/CNRS (France), MPG (Germany), andIGN (Spain). This material is based upon work sup-ported under a National Science Foundation GraduateResearch Fellowship. APPENDIX
ERROR ESTIMATES ON T EX From the equation of radiative transfer (see eq. 9), once T mb , τ and the corresponding errors are known, the erroron T ex ( σ T ex ) can be determined following the rules of error propagation: σ T ex = (cid:18) ∂T ex ∂T mb σ T mb (cid:19) + (cid:18) ∂T ex ∂τ σ τ (cid:19) , (A1)where σ T mb and σ τ are the errors associated with T mb and τ , respectively.The expression of T ex is found by inverting eq. 9: T ex = T ln[ T /A + 1] , where (A2) A = T mb − e − τ + J ν ( T bg ) . Thus, the partial derivatives in eq. A1 are: ∂T ex ∂T mb = a b ( bc + T mb )( ab + cb + T mb ) ln (cid:16) abbc + T mb + 1 (cid:17) (A3) ∂T ex ∂τ = − a ln (cid:20) ac − T mb /b + 1 (cid:21) × aT mb e τ ( e τ T mb − bc )( e τ T mb − ab − bc ) (A4)where, a ≡ T (A5) b ≡ − e − τ (A6) c ≡ J ν ( T bg ) . (A7) REFERENCESAikawa, Y., Herbst, E., Roberts, H., & Caselli, P. 2005, ApJ, 620,330Aikawa, Y., Ohashi, N., Inutsuka, S.-i., Herbst, E., & Takakuwa,S. 2001, ApJ, 552, 639Barranco, J. A., & Goodman, A. A. 1998, ApJ, 504, 207Belloche, A., & Andr´e, P. 2004, A&A, 419, L35Benson, P. J., Caselli, P., & Myers, P. C. 1998, ApJ, 506, 743Bergin, E. A., Maret, S., van der Tak, F. F. S., Alves, J.,Carmody, S. M., & Lada, C. J. 2006, ApJ, 645, 369 Bergin, E. A., Alves, J., Huard, T., & Lada, C. J. 2002, ApJ, 570,L101Bergin, E. A., & Langer, W. D. 1997, ApJ, 486, 316Bianchi, S., Davies, J. I., Alton, P. B., Gerin, M., & Casoli, F.2000, A&A, 353, L13Bisschop, S. E., Fraser, H. J., ¨Oberg, K. I., van Dishoeck, E. F.,& Schlemmer, S. 2006, A&A, 449, 1297Bonnell, I. A., & Bate, M. R. 2006, MNRAS, 370, 488Bourke, T. L., et al. 2006, ApJ, 649, L37
Caselli, P., Walmsley, C. M., Tafalla, M., Dore, L., & Myers, P. C.1999, ApJ, 523, L165Caselli, P., Walmsley, C. M., Zucconi, A., Tafalla, M., Dore, L., &Myers, P. C. 2002, ApJ, 565, 331Caselli, P., Walmsley, C. M., Zucconi, A., Tafalla, M., Dore, L., &Myers, P. C. 2002, ApJ, 565, 344 5ACeccarelli, C., Caselli, P., Herbst, E., Tielens, X., & Caux, E.2006, in Protostars & Planets V, in press (astro-ph/0603018)Ciolek, G. E., & Basu, S. 2000, ApJ, 529, 925Collings, M. P., Dever, J. W., Fraser, H. J., McCoustra, M. R. S.,& Williams, D. A. 2003, ApJ, 583, 1058Crapsi, A., Caselli, P., Walmsley, C. M., Tafalla, M. 2005, A&A,in press (astro-ph/0705.0471)Crapsi, A., Caselli, P., Walmsley, C. M., Myers, P. C., Tafalla,M., Lee, C. W., & Bourke, T. L. 2005, ApJ, 619, 379Crapsi, A., Caselli, P., Walmsley, C. M., Tafalla, M., Lee, C. W.,Bourke, T. L., & Myers, P. C. 2004, A&A, 420, 957Dalgarno, A., & Lepp, S. 1984, ApJ, 287, L47Daniel, F., Cernicharo, J., & Dubernet, M.-L. 2006, ApJ, 648, 461De Vries, C. H., & Myers, P. C. 2005, ApJ, 620, 800Di Francesco, J., Evans, N. J., II, Caselli, P., Myers, P. C.,Shirley, Y., Aikawa, A., & Tafalla, M. 2006, in Protostars &Planets V, astro-ph/0602379Dore, L., Caselli, P., Beninati, S., Bourke, T., Myers, P. C., &Cazzoli, G. 2004, A&A, 413, 1177Ehrenfreund, P., & Charnley, S. B. 2000, ARA&A, 38, 427Evans, N. J., II, Rawlings, J. M. C., Shirley, Y. L., & Mundy,L. G. 2001, ApJ, 557, 193Frerking, M. A., Langer, W. D., & Wilson, R. W. 1982, ApJ, 262,590Galli, D., Walmsley, M., & Gon¸calves, J. 2002, A&A, 394, 275Goldsmith, P. F., Bergin, E. A., & Lis, D. C. 1997, ApJ, 491, 615Goodman, A. A., Barranco, J. A., Wilner, D. J., & Heyer, M. H.1998, ApJ, 504, 223Goodman, A. A., Benson, P. J., Fuller, G. A., & Myers, P. C.1993, ApJ, 406, 528Gottlieb, C. A., Myers, P. C., & Thaddeus, P. 2003, ApJ, 588, 655Hasegawa, T. I., & Herbst, E. 1993, MNRAS, 263, 589Hirota, T., Ito, T., & Yamamoto, S. 2002, ApJ, 565, 359Holland, W. S., et al. 1999, MNRAS, 303, 659Kenyon, S. J., Dobrzycka, D., & Hartmann, L. 1994, AJ, 108,1872Klessen, R. S., Ballesteros-Paredes, J., V´azquez-Semadeni, E., &Dur´an-Rojas, C. 2005, ApJ, 620, 786Kramer, C., Alves, J., Lada, C. J., Lada, E. A., Sievers, A.,Ungerechts, H., & Walmsley, C. M. 1999, A&A, 342, 257Kreysa, E., Gem¨und, H.-P., Gromke, J. 1999 Infrared Phys.Techn. 40, 191Lada, C. J., Bergin, E. A., Alves, J. F., & Huard, T. L. 2003,ApJ, 586, 286 Lee, C. W., Myers, P. C., & Plume, R. 2004, ApJS, 153, 523Lee, J.-E., Evans, N. J., II, Shirley, Y. L., & Tatematsu, K. 2003,ApJ, 583, 789Lee, H.-H., Bettens, R. P. A., & Herbst, E. 1996, A&AS, 119, 111Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425McKee, C. F. 1989, ApJ, 345, 782Meyer, D. M., Jura, M., & Cardelli, J. A. 1998, ApJ, 493, 222Meyer, D. M., Cardelli, J. A., & Sofia, U. J. 1997, ApJ, 490, L103Myers, P. C. 2005, ApJ, 623, 280Myers, P. C., Mardones, D., Tafalla, M., Williams, J. P., &Wilner, D. J. 1996, ApJ, 465, L133¨Oberg, K. I., van Broekhuizen, F., Fraser, H. J., Bisschop, S. E.,van Dishoeck, E. F., & Schlemmer, S. 2005, ApJ, 621, L33Ossenkopf, V., & Henning, T. 1994, A&A, 291, 943Pagani, L., Pardo, J.-R., Apponi, A. J., Bacmann, A., & Cabrit,S. 2005, A&A, 429, 181Penzias, A. A. 1981, ApJ, 249, 518Pierce-Price, D., et al. 2000, ApJ, 545, L121Redman, M. P. Rawlings, J. M. C., Nutter, D. J.,Ward-Thompson, D., & Williams, D. A. 2002, MNRAS, 337,L17Roberts, H., Herbst, E., & Millar, T. J. 2004, A&A, 424, 905Schnee, S., & Goodman, A. 2005, ApJ, 624, 254Schnee, S., Kauffman, J., Goodman, A. & Bertoldi, F. 2007, ApJ,in press.Sch¨oier, F. L., van der Tak, F. F. S., van Dishoeck, E. F., &Black, J. H. 2005, A&A, 432, 369Shematovich, V. I., Wiebe, D. S., Shustov, B. M., & Li, Z.-Y.2003, ApJ, 588, 894Tafalla, M., Myers, P. C., Caselli, P., & Walmsley, C. M. 2004,Ap&SS, 292, 347Tafalla, M., & Santiago, J. 2004, A&A, 414, L53Tafalla, M., Myers, P. C., Caselli, P., Walmsley, C. M., & Comito,C. 2002, ApJ, 569, 815Tafalla, M., Mardones, D., Myers, P. C., Caselli, P., Bachiller, R.,& Benson, P. J. 1998, ApJ, 504, 900Taylor, S. D., Morata, O., & Williams, D. A. 1998, A&A, 336, 309Umebayashi, T., & Nakano, T. 1990, MNRAS, 243, 103van der Tak, F. F. S., Black, J. H., Sch¨oier, F. L., Jansen, D. J.,& van Dishoeck, E. F. 2007, A&A, 468, 627Vastel, C., Caselli, P., Ceccarelli, C., Phillips, T., Wiedner, M. C.,Peng, R., Houde, M., & Dominik, C. 2006, ApJ, 645, 1198Williams, J. P., Lee, C. W., & Myers, P. C. 2006, ApJ, 636, 952Williams, J. P., Myers, P. C., Wilner, D. J., & di Francesco, J.1999, ApJ, 513, L61Wilson, T. L., & Rood, R. 1994, ARA&A, 32, 191Zucconi, A., Walmsley, C. M., & Galli, D. 2001, A&A, 376, 650
MC-1C: an accreting starless core 13
TABLE 1Observing Parameters of IRAM Spectra
Transition T sys Spectral Resolution FWHM B eff Frequency VLSRKelvin km s − arcseconds GHz km s − C O(1-0) 353 0.052 18.4 0.66 112.3592837 a O(2-1) 1893 0.052 9.2 0.40 224.7143850 a O(2-1) 1050 0.053 9.4 0.41 219.5603541 a S(2-1) 202 0.061 21.4 0.72 96.4129495 a + (2-1) 479 0.041 14.3 0.54 144.0773190 a + (3-2) 622 0.054 9.5 0.42 216.1126045 a H + (1-0) 185 0.031 22.1 0.73 93.1737725 b a Frequency taken from the Leiden Atomic and Molecular Database (Sch¨oier et al. 2005) b Frequency taken from Dore et al. (2004)
TABLE 2Fit Line Parameters at Dust Peak
Transition VLSR R Tdv a FWHM rmskm s − K km s − km s − KC O(1-0) 5.33 ± ± ± O(2-1) 5.49 ± ± ± O(2-1) 5.20 ± ± ± S(2-1) 5.26 ± ± ± + (2-1) 5.14 ± ± ± + (3-2) 5.25 ± ± ± H + (1-0) 5.20 ± ± ± a Integrated intensity over entire spectrum (all hyperfine compo-nents included in the case of C O and N H + ). TABLE 3Fit results for the five spectra in Fig. 9
Offset T ex τ TOT ∆ v V f − V b (arcsec) K km s − km s − -40,60 B a b ± ± ± ± ± ± a B ≡ background layer b F ≡ foreground layer TABLE 4Molecular Transition Constants and Assumed Abundances
Transition A a B b,c g l g u X can d s − GHz n/n H C O(1-0) 6.697E-8 56.179990 1 3 4 . × − C O(2-1) 6.425E-7 56.179990 3 5 4 . × − C O(2-1) 6.011E-7 54.891420 3 5 1 . × − C S(2-1) 1.600E-5 24.103548 3 5 1 . × − DCO + (2-1) 2.136E-4 36.01976 3 5 2 . × − DCO + (3-2) 7.722E-4 36.01976 5 7 2 . × − N H + (1-0) 3.628E-5 46.586867 1 3 1 . × − Einstein A coefficients are taken from the Leiden Atomic and MolecularDatabase (Sch¨oier et al. 2005) b (Frerking et al. 1982) c (Gottlieb et al. 2003) d Standard molecular abundance, taken from literature except for N H + e (Crapsi et al. 2004) f (Goldsmith et al. 1997) g (Tafalla et al. 2002) h (Lee et al. 2003) i Average value derived across TMC–1C.
TABLE 5Gas Column Density and Depletion atDust Peak
Transition N f D a Percent Error b cm − C O c O d O d S d +d +e H +c a Depletion from dust-derived N H = 5 . × , N tot and X can b Error from noise in spectrum, not including ∼ c Derived from (1-0) transition d Derived from (2-1) transition e Derived from (3-2) transition
MC-1C: an accreting starless core 15
Fig. 1.—
The spectra taken at the (0,20) position, which is the peak of the dust emission map. The velocity scales on the spectrashowing hyperfine structure are only correct for the marked component, whereas the enlarged portion of the spectra has been recenteredat the frequency of the isolated component. The vertical dotted line shows the LSR velocity of the weakest component of the N H + (1-0)spectrum, as determined by a Gaussian fit, for comparison. Fig. 2.—
Spectra of the F ,F = 2,3 → H + across the whole TMC–1C mapped region. Red boxes markspectra consistent with inward motions, whereas blue boxes mark spectra with outflow signatures (see Sect. 4.3). Colored dots indicatethose positions displayed in Fig. 9. The red-filled box mark the position of the continuum dust emission peak. The asymmetry in the highdensity tracer N H + is observed in an extended region, larger than that previously found in other evolved pre–stellar cores. See Fig. 4 forcontours of column density based on dust emission. MC-1C: an accreting starless core 17
Fig. 3.—
Profile of the main F ,F = 23 →
12 hyperfine component of N H + (1–0) (white histogram) superposed on the spectrum of theweak F F = 10 →
11 component (yellow histogram) at the dust peak position. Note that the weak component is symmetric and peakswhere the absorption of the main component is steepest, suggesting that this component is optically thin and can be used to estimate thecolumn density and line width where the main group of hyperfines is affected by self-absorption.
Fig. 4.—
Integrated intensity maps of ( top left ) C O(1–0), ( top middle ) C O(2–1), ( top right ) C O(2–1), ( bottom left ) DCO + (2–1)and ( bottom right ) N H + (1–0). The C O(1–0), C O(2–1) and DCO + (2–1) integrated intensities have been scaled up by factors of 1.5,2.0 and 5.0, respectively. For all spectra showing self-absorption, the N H + integrated intensity has been calculated from the thinnesthyperfine component. The contours show the visual extinction derived from the dust emission, at levels of A V = 10, 25, 40, and 55 mag.The 1 σ uncertainties in the integrated intensity are ∼ ∼ ∼ ∼ ∼ − in C O(1–0), C O(2–1), C O(2–1),DCO + (2–1) and N H + (1–0) respectively. The positions with large N H + depletion and low column density have been marked with redcrosses. MC-1C: an accreting starless core 19
Fig. 5.— ( Top Panel ) N H + (1-0) observed line width across the TMC–1C core. ( Bottom Panel ) N H + (1-0) observed line width (in kms − ) vs. distance from the peak of the dust column density map. For those positions where the self–absorption is present, we used thewidth of the weak component as representative of the intrinsic line width of the (1-0) line. The crosses show the values at each positionin the map with S/N >
3, and the large squares are averages of the data with 15 ′′ bins. The horizontal dashed line shows the thermalFWHM at 10 K for reference. Fig. 6.—
The non-thermal line width plotted against the thermal line width for each transition observed, at the position of the dustemission peak. The thermal line width is calculated from an assumed gas temperature of 10 K. The error in the non-thermal line width isderived using the error in the FWHM of the Gaussian fit to the line. The line withs of C S(2–1) and DCO + (3–2) are highly uncertain,because of the strong absorption observed (see Fig. 2) and the plotted errors do not take the absorption into account. The NH intrinsic linewidth is taken from Barranco & Goodman (1998). To make a fair comparison, all of the spectral line maps have been spatially smoothedto the ∼ ′ resolution of the NH map. MC-1C: an accreting starless core 21
Fig. 7.—
Top Panels ) The velocity field for C O(1-0), C O(2-1) and C O(2-1). The black contour shows the A V = 10 mag boundary,and the arrows show the direction and magnitude of the line-of-sight velocity gradient, pointing from blue to red. The red box enclosesa region with a velocity gradient similar to that of rotation as seen in the isotopologues of CO. In each map the velocity shown is thedifference between the measured VLSR at each position and the velocity at the (0,0) position. The lengths of the arrows are proportionalto the magnitude of the gradient, and is scaled to the labeled arrow. ( Bottom Panels ) velocity field for DCO + (2–1) and N H + (1–0) inTMC-1C. The red box encloses a region with a velocity gradient in isotopologues of CO that looks similar to that of rotation. The whitebox shows the region observed in NH by Barranco & Goodman (1998). Fig. 8.—
The overall velocity gradient for each tracer in the region bounded by − < RA offset <
70 and − < DEC offset <
70, theregion in the red box in Fig. 7 and 7. The dotted circles show the magnitude of gradients equal to 0.5, 1.5, 2.5 and 3.5 km s − pc − . MC-1C: an accreting starless core 23
Fig. 9.— N H + (1–0) spectra (black histogram) along a South–East (bottom panel) to North–West (top panel) strip (see spectra labelledwith colored dots in Fig. 2). Filled red histograms are two–layer model results, whereas light blue filled histograms are simply fits to theline, assuming one emitting layer and constant T ex for the seven hyperfines. Offsets from Fig. 2 are in the top left of each panel. Numbersin the top right are the V LSR velocities (in km s − ) from gaussian fits to the hfs structure. The parameters of the fits are in Table 3. Notethat the redshifted absorption (and thus the infall velocity) is largest toward the dust peak and that the self-absorption is present towardsthe North–West but not towards the South–East. Fig. 10.—
Right ascension (left) and declination (right) cuts cross the TMC–1C core, passing through the dust peak position (blackdotted line), of A V (black curve), N (N H + ) (red curve), and X (N H + ) (blue curve) normalized to their maximum values (see text). Theblue dashed line is the abundance value observed across L1544 (see Vastel et al. 2006). X (N H + ) shows an anticorrelation with the dustprofile, suggestive of some N H + depletion toward the dust center. MC-1C: an accreting starless core 25
Fig. 11.—
The dust temperature plotted against the column density, derived from the dust emission maps at 450, 850 and 1200 µ m.The spatial resolution of the data is 14 ′′ , resolving the innermost region of the core, with A V ≃
90 mag and T dust ≃ T d − A V relation predicted for an externally heated pre-protostellar core by Zucconi et al. (2001, Eq. 26). Departures fromspherical symmetry are probably causing the observed discrepancy between observations and (spherically symmetric) model predictions. Fig. 12.— ( left ) Excitation temperature of the C O(2–1) line. If this line is in LTE, the present data suggest a gas temperature decreasefrom about 12 K at the dust peak, to about 10 K at ≥ ′ away from the dust peak (equivalent to a projected distance of ≥ O(2–1) line (see text for details). ( right ) Brightness temperature ratioof the C O(1–0) and C O(2–1) lines as a function of distance from the dust (or A V ) peak. The ratio increases with distance, suggestingthat some physical property ( T kin and/or n (H )) changes as well. MC-1C: an accreting starless core 27
Fig. 13.—
Ratio of the C O(1–0) and C O(2–1) brightness temperatures as a function of (
Top ) gas temperature, for a fixed value ofthe volume density ( n (H ) = 2 × cm − ), and ( Bottom ) volume density, for a fixed value of the gas temperature ( T kin = 11 K). In bothpanels, N (C O) = 10 cm − and ∆ v = 0.4 km s − . The dashed horizontal lines enclose the observed range of T mb ratios (see Fig. 12,right panel). Note that observations are both consistent with a gas temperature decrease (and high constant density), as well as with avolume density decrease (and constant gas temperature) away from the dust peak. We believe that the latter is a more plausible solutionthan the former. Fig. 14.— ( left ) The depletion factor derived from molecular transitions observed with the IRAM 30m plotted against the column densityderived from dust emission maps at 450, 850 and 1200 µ m. The median percent error in the depletion (calculated from the RMS of thespectrum) is given in each panel. ( right ) Same as left, except that the depletion factor is plotted against the dust temperature. Thosepoints with anomalously high N H + depletion factors ( N H < × and f D > .
6) are shown in red, and their positions are shown withred crosses in Fig. 4. The N H + depletion factor goes below 1 because of our arbitrary choice of the N H + column density (see text). MC-1C: an accreting starless core 29
Fig. 15.— ( Left panel ) Fractional abundances of important molecular ions as a function of radius, calculated by the best–fit model forTMC–1C (i.e. the one that best reproduces the observed column densities, see text). The red curves are depletion factors within