Initial conditions for star formation in clusters: physical and kinematical structure of the starless core OphA-N6
arXiv:1111.4424v1 [astro-ph.GA] 18 Nov 2011
Tyler L. Bourke1 , Philip C. Myers1 , Paola Caselli2 , James Di Francesco3 , Arnaud Belloche4 , Ren´e Plume5 , David J. Wilner1 ABSTRACT We present high spatial ( 0.05 over much of the core. The N2 H+ column density profile across the major axis of Oph A-N6 is well represented by an isothermal cylinder, with temperature 20 K, peak density 7.1 × 106 cm−3 , and N2 H+ abundance 2.7 × 10−10 . The mass of Oph A-N6 is estimated to be 0.29 M⊙ , compared to a value of 0.18 M⊙ from the isothermal cylinder analysis, and 0.63 M⊙ for the critical mass for fragmentation of an isothermal cylinder. Compared to isolated low-mass cores, Oph A-N6 shows similar narrow line widths and small velocity variation, with a deuterium fraction similar to “evolved” dense cores. It is significantly smaller than isolated cores, with larger peak column and volume density. The available evidence suggests Oph A-N6 has formed through the fragmentation of the Oph A filament and is the precursor to a low-mass star. The dust continuum emission suggests it may already have begun to form a star. Subject headings: ISM: individual (Oph-A N6) – stars: formation – stars: lowmass 1
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; email
[email protected] 2
School of Physics & Astronomy, E.C. Stoner Building, The University of Leeds, Leeds, LS2 9JT, UK
3
National Research Council Canada, Herzberg Institute of Astrophysics, Victoria, BC, Canada
5
Max-Planck-Institut f¨ ur Radioastronomie, Auf dem H¨ ugel 69, D-53121 Bonn, Germany
4
Department of Physics and Astronomy, University of Calgary, Calgary, AB, Canada
–2– 1.
Introduction
It is now well established that low-mass (i.e., solar-like) stars form from the collapse of dense cores within molecular clouds (e.g., Larson 2003). The initial conditions of isolated star formation are known from continuum and line observations of many tens of dense cores in molecular cloud complexes such as Taurus, with relatively sparse concentrations of young stars (Di Francesco et al. 2007). The best commonly observed molecular line tracers of the central few thousand AU of centrally condensed cores on the verge of star formation are NH3 (ammonia), N2 H+ , and N2 D+ (Caselli et al. 2002c; Tafalla et al. 2002; Crapsi et al. 2005, 2007). Observations of these lines and the dust continuum have enabled the properties of dense isolated starless cores thought to be near to or at the point of star formation to be well determined in recent years (Di Francesco et al. 2007; Bergin & Tafalla 2007). These properties include (i) a high degree of deuterium fractionation, (i.e., large N(N2 D+ )/N(N2 H+ )) (ii) a large central density (∼ 106 cm−3 ), (iii) depletion of CO and other C-bearing species, (iv) cold central regions ( 0.1), with the largest total opacities measured near to the map center at τ ∼ 2 − 3. Positions where the total optical depth was ≥ 1 were used to estimate a single excitation temperature for the whole map, for which we find Tex = 10.0 ± 3.3 K, so we assume a constant Tex of 10 K for N2 D+ . For N2 D+ , the total integrated line emission and Tex were used to calculate the column density N at each map position. The results are shown in Figure 9(a). The column density of N2 D+ ranges from 9.8 × 1011 cm−2 to 4.7 × 1012 cm−2 , with values greater than 2 × 1012 cm−2 over much of the map. The N2 H+ 3-2 emission was found to be very optically thick over much of N6, making it difficult to estimate τ , and thus determine Tex . In addition, the saturated lines means that the observed integrated line emission is only a lower limit of the true emission, and equation (1) is not valid for optically thick emission. To overcome this problem, a multistep approach was used to obtain an estimate of Tex and measure the integrated line emission, so that the column density could be determined. Most of the optical depth of N2 H+ 3-2 is due to the main-V hyperfine group. The low-V and high-V groups only account for 0.0742 of the total line strength (normalized to 1.0; Daniel et al. 2006; Pagani, Daniel, & Dubernet 2009). The total integrated line emission was thus found by integrating only over the low-V (0.22 − 1.58 km s−1 ) and high-V (5.07 − 6.18 km s−1 ) hf groups, and scaling by the inverse of their relative line strength. In the outer part of the N2 H+ map, the total optical depth drops to reasonable values (< 15), allowing the total line emission to be measured, and compared to the value obtained using only the low-V and high-V hf groups scaled by 1/0.0742. At these positions, the results were found to be in general agreement (better than 20%). Although the total optical depth is high, the individual hyperfine features are optically thin (39 hyperfine features in total, 17 in the low-V and high-V hyperfine groups), and the total optical depth of the low-V and high-V hf groups together are also thin in these data, or at most τ ∼ 2 with and uncertainty of similar size. While it was possible to obtain good fits to essentially every map position using only the low-V and high-V hf groups, in most cases this resulted in an optically thin fit (τ = 0.1 in CLASS), so that Tex is unconstrained. In order to obtain an estimate of Tex , full hf fitting is needed. Using only those positions away from the map center where the full hf fit gives τ < 20, we obtain Tex = 10.0 ± 2.2 K. A full hf fit to a spectrum generated from the inner 8 × 10 positions, gives a similar result. As we were unable to obtain a reliable estimate for each individual map position, we assume that Tex = 10 ± 2 K across the whole map. This value is significantly lower than the value of 17 K determined by DAM04 for N2 H+ 1-0, and
– 12 – the value of the kinetic temperature of 20 K. This difference could suggest that while the 1-0 line is thermalized, the 3-2 line is not. Alternatively, the denser interior of the core, better traced by the 3-2 line, could be colder. However, Tex is fairly constant over the region mapped in N2 H+ 3-2, and the temperature derived from dust observations is closer to 20 K, so this alternative is the less likely of the two possibilities. To determine the N2 H+ 3-2 column density, we assumed that the total column density Ntot = Nhf /0.0742, where Nhf is the column density of the outer hyperfines, calculated using the integrated line emission of the low-V and high-V hyperfine groups, and assuming a constant Tex of 10 K. As shown in equation (1), the column density N (whether Ntot or Nhf ) is simply a function of Tex , f (Tex ), times the integrated line intensity, W , so that N = W × f (Tex ). The column density of N2 H+ determined in this manner ranges from 3.5 × 1012 cm−2 to 4.6 × 1013 cm−2 , with most values being greater than 1013 cm−2 , and with a significant fraction of the inner map region having values > 2.5 × 1013 cm−2 (Figure 9(b)). +100% The typical uncertainty in a particular measurement of the column density is N−50% . Similar + values for the N2 H column density were found by DAM04. We have checked our results, using the outer hyperfine satellite groups and assuming optically thin emission, against N2 H+ column densities determined from hyperfine fits to the full hyperfine spectra (Caselli et al. 2002b; Di Francesco et al. 2004; Friesen et al. 2010a). We find that the results are consistent, in that the values from the full fit are within the uncertainties of the method we have used. However, N determined from the full fit case are typically, but not systematically, higher (but are sometimes lower) by up to 50%. Because the total optical depth is so high its actual value is not well constrained by the full fit at any particular position, so we prefer the method we have used for estimating N.
4.2.
Deuterium Fraction
The ratio of N2 H+ and N2 D+ column densities can be used to estimate the deuteration fraction within N6. This is shown in Figure 10, where the ratio N(N2 D+ )/N(N2 H+ ) is shown, compared to the integrated intensity maps of each molecule. From this Figure it can be seen that the D/H ratio is of order 0.05 over a large fraction of the map, reaching higher values toward the western side, of order 0.15. These values are larger than those determined by Pon et al. (2009), from lower resolution observations. Figure 10 also shows that the NW N2 D+ peak has a higher D/H ratio than the SE peak, as might be expected from Pon et al. (2009), where only the NW peak is clearly detected in the JCMT data. This result shows that Oph A-N6 has a high central degree of deuteration, and is similar to values found for isolated low-mass starless cores (Crapsi et al. 2005). In some map locations the D/H value
– 13 – is close to the dividing line of 0.1 used to characterize the isolated cores as prestellar or starless, with the idea that prestellar cores are those closest to star formation (Crapsi et al. 2005). Of the prestellar cores identified by Crapsi et al. (2005), all but one, like OphA-N6, have N(N2 H+ ) > 1013 cm−2 . It is notable that even though the kinetic temperatures are near to 20 K, where the D/H ratio should decrease dramatically (Caselli et al. 2008), and significantly higher than in isolated cores, the D/H ratio is as high as in most starless cores, if not higher.
4.3.
Structure & Mass
N6 is elongated and may represent a fragment of a filament. The simplest model of a filament is a self-gravitating isothermal cylinder, whose radial density profile is (Ostriker 1964; Johnstone et al. 2003), n(r) =
n0 1+
r2 8H 2
2 ,
(2)
where n0 is the peak number density, r is the radial offset, and the scale length H is H2 ≡
c2 , 4πGρ0
(3)
where c is the sound speed, ρ0 the peak density, and G is the gravitational constant. If N6 is viewed perpendicular to its axis, then the column density along the line-of-sight is
N(r) =
π n0 H h i3/2 2 r2 2 1 + 8H 2
= N0
π H h i3/2 4R r2 2 1 + 8H 2
(4)
(5)
where N0 is the peak column density and R is the radius. Figure 12 shows the radial column density profile across the minor axis of N6 derived from N2 H+ 3-2 compared to the profile of an isothermal cylinder (dark continuous curve).
– 14 – This profile was constructed from N2 H+ 3-2 data imaged with a 2.′′ 4 beam and 1.′′ 2 pixels (Nyquist sampling), using the method of “super-resolution” (Briggs 1994; Chandler et al. 2005), in order to better sample the radial profile. Eighteen independent, consecutive profiles were extracted across the major axis at 1.′′ 2 intervals along the major axis. The region over which the profiles were extracted is shown in Figure 11. Each profile was normalized to its peak values, and the normalized profiles averaged together to form the composite profile shown in Figure 12. This figure shows that the column density profile of N6 is very well represented by an isothermal cylinder, as the model matches the data within its 1σ uncertainties at eight consecutive positions across the peal of the profile. The model allows the peak density and hence abundance of N2 H+ to be estimated, keeping other parameters fixed at their previously determined values; radius R = 800 AU, temperature of 20 K (Pon et al. 2009), and peak N2 H+ column density of 4.6 ×1013 cm−2 . Using these values, we find a good match to the data, as shown in Figure 12, assuming a constant N2 H+ abundance 6 −3 XN2 H + = 2.7 ± 0.2 × 10−10 , resulting in values of peak density n0 = 7.1+0.6 −0.5 × 10 cm , and scale length H = 362+12 −14 AU. Allowing for a 5 pc uncertainty in the distance does not change these values. Even though N6 is not a local dust emission peak, DAM04 estimated the column density, N(H2 ), to be 3 × 1023 cm−2 using the dust continuum emission, assuming isothermal dust at a temperature of 20 K. From this and their value for N(N2 H+ ) they infer an abundance X(N2 H+ ) of 3 × 10−10 , in very close agreement with the value used here that provides an excellent match between the isothermal cylinder model and the data. This abundance is in good agreement with values inferred for isolated low-mass cores, including the evolved prestellar cores discussed above (Benson, Caselli & Myers 1998; Caselli et al. 2002c; Crapsi et al. 2005). The mass per unit length of an isothermal cylinder is
M(r) = 2πρ0
Z
0
R
rdr 1 +
r2 8H 2
−2
(6)
After integrating, the mass of a cylinder of length L can be written: −1 2c2 2c2 1+ . M =L G πGρ0 R2
(7)
For T = 20 K, n0 = 7.1 × 106 cm−2 , R = 800 AU, and L = 3100 AU, the mass is M = 0.18 ± 0.02 M⊙ , where the uncertainty is due to the uncertainties in n0 given above and the distance uncertainty.
– 15 – We can determine the total mass traced by N2 H+ , using the N2 H+ column density map (Fig. 9(b)), with the result for the N2 H+ abundance. The map gives the column density per pixel, from which the mass per pixel (Mp ) can be determined, and hence the total mass, using Mp = X µm Ap NX ,
(8)
where µm is the mean particle mass (2.37 amu; Stahler & Palla 2005; Kauffmann et al. 2008), Ap is the area per pixel, X is the abundance of the molecule used, and NX is its column density. In a Nyquist sampled map, the total mass is then just the sum over all pixels. For Tex = 10 K and XN2 H + of 2.7 × 10−10 , we measure M = 0.29+0.05 −0.04 M⊙ for positions within the half-power level of the column density map. The uncertainties come from the uncertainties in X and the distance. The change in mass by assuming Tex = 9 or 11 K is much smaller than either of these. The critical mass is the mass of a condensation whose radius is equal to the shortest wavelength of a periodic perturbation that will grow. Larson (1985) has studied the critical mass for fragmentation of a number of geometries, and for an isothermal filament (i.e., a cylinder) finds (Larson 1985, equation 21)
7.88c4 G2 µ m N 2 23 10 cm−2 T [M⊙ ]. = 1.1 20 K N
Mc =
(9) (10)
With T = 20 K and N = 1.7 × 1023 cm−2 (from the peak N2 H+ column density and X), Mc = 0.63+0.05 −0.04 M⊙ . This value is within about a factor of 2 of the mass computed for N6 of 0.29 M⊙ from eqn. (8). Given the uncertainties in computing masses, such as determining the “size” of a core, and our method of measuring N at each position, this result suggests that N6 is consistent with having formed from the fragmentation of an isothermal filament, in this case Oph A.
– 16 – 5. 5.1.
Discussion Kinematics
Internally, Oph A-N6 is rather quiescent. It shows very narrow N2 H+ and N2 D+ linewidths of about 0.25 km s−1 across its extent, barely more than the thermal line width for the measured gas temperature of 20 K, of 0.18 km s−1 . Its non-thermal motions are very sub-sonic, but the surrounding gas shows significantly larger line-widths (DAM04; Andr´e et al. 2007; Pon et al. 2009) suggesting that N6 has lost any turbulent motions it may have had. The lack of significant variation in line centroid velocity and line-width over the core indicate that N6 is an example of a coherent core, as has been seen in more isolated cores (Barranco & Goodman 1998; Goodman et al. 1998; Caselli et al. 2002a; Tafalla et al. 2004; Pineda et al. 2010). This result suggests that small non-thermal motions typical of isolated cores are found in some starless cores within turbulent molecular clouds. Observations of HCO+ and DCO+ 3-2 show the expected signature of inward motions (Evans 1999; Pon et al. 2009), but the complex hyperfine structure of N2 H+ and N2 D+ 3-2 makes identifying any similar signature in these lines impossible. In addition, the very narrow line widths of N2 H+ 1-0 together with the spectral resolution and signal-to-noise of the data make it difficult to identify any signature of inward motions (DAM04), regardless of the hyperfine structure. Data with finer spectral resolution and improved signal-to-noise are required to search for inward motions in N2 H+ . However, the very narrow line-widths already suggest that any inward motions on the size scales probed by N2 H+ (∼ 300 AU) must be small. The ratio of non-thermal-to-thermal line-width in N6 is about 0.3, which is lower than observed in most starless dense cores in Perseus (Walsh et al. 2007; H. Kirk et al. 2007; Rosolowsky et al. 2008), for dense cores elsewhere in Ophiuchus (Andr´e et al. 2007; Friesen et al. 2009), or for most isolated low-mass dense cores (Myers 1983). Further, the absence of line-broadening toward the center of N6 suggests a lack of a central source. The motions observed in HCO+ may be infall onto the core, rather than core collapse (Pon et al. 2009).
5.2.
Dust Emission
Starless cores are usually defined through observations of the dust continuum or molecular lines in single-dish observations at millimeter wavelengths, with angular resolution 10-20′′ (typically the line observations are of lower resolution than the continuum). As a result, by definition they generally only show a single peak of emission, and fairly simple structures, being round or elongated with small aspect ratios (less than 2). When observed with an
– 17 – interferometer, which acts as a spatial filter, many such cores are not detected, or still only appear as single peaks of emission, due to their smooth large-scale structure and lack of significant sub-structure (Williams & Myers 1999; Williams et al. 1999, 2006; Harvey et al. 2003a; Olmi et al. 2005; Schnee et al. 2010). Combining the single-dish and interferometer line data, as we have done here, allows the small scale structure to be studied, without concerns about missing flux. These studies usually show that starless cores do not break up into sub-cores on small scales. One exception is L183, which is composed of 3 sub-cores in N2 H+ 1-0 (J. Kirk et al. 2009), but it shows a very elongated structure in single dish maps, so perhaps this is not too surprising. The nature of the compact dust emission detected toward the peak of integrated N2 H+ emission is unclear, given that N6 is not a local maximum in single-dish continuum observations between 1300 and 450 µm, with 10-15′′ resolution (Motte et al. 1998; Wilson et al. 1999; Johnstone et al. 2000). However, a dust temperature map derived from the ratio of 450-to-850 µm flux, assuming a constant dust emissivity, shows a similar structure to the N2 H+ maps, although with lower resolution (Pon et al. 2009). The dust temperature map shows a peak of 20 K at the N2 H+ peak, and is elongated in the NW-SE direction. It is not yet known if the gas temperature varies in a similar manner on similar scales, as the NH3 observations only have a resolution of about 30′′ . However, NH3 may not probe the highest densities toward the center of N6, and so determining the gas temperature there with confidence will be difficult. Supporting evidence for a relatively constant gas temperature within N6 comes from the comparison of its column density profile with that of an isothermal cylinder (Fig. 12), and from the almost constant line-widths. N6 is embedded within the Oph A ridge, and the large column of dust due to the ridge may make it difficult to distinguish a compact core within it as a separate entity. The dust temperature map suggests that it is a local temperature maximum, at about 20 K (Pon et al. 2009). This result is unlike those in detailed studies of isolated starless cores, which show flat temperature profiles in low-resolution observations (Jijina et al. 1999; Tafalla et al. 2004), but a drop in temperature toward the core center in observations with finer resolution (Crapsi et al. 2007). The mass of dust seen in N6 is very low, only of order 0.005-0.01 M⊙ , and the inferred peak column density of ∼ 1.3 × 1022 cm−2 is an order of magnitude below that found from N2 H+ observations, and from single-dish continuum observations. Recently, interferometers have detected compact millimeter dust emission toward three “starless” cores (Chen et al. 2010; Enoch et al. 2010; Pineda et al. 2011; Dunham et al. 2011). Supporting evidence, in the form of CO outflows or faint, compact 70 µm emission, and SED modeling, suggests that in all cases the emission is due to an internal heating source of very low temperature (>100 K), and the inferred luminosities are very low (300 pc; Testi & Sargent 1998; Williams & Myers 1999), and for isolated cores in Taurus (140 pc; Ward-Thompson et al. 1994; Caselli et al. 2002a,b; Tafalla et al. 2002; J. Kirk et al. 2005). A comparison of the properties of N6 with the cores in these studies shows that N6 is denser than most starless cores, by about an order-of-magnitude (107 cm−3 cf. 106 cm−3 ). These observations typically do not have the resolution of our observations of N6, and derived average densities of 106 cm−3 over the central 1000 AU could be consistent with peak densities of ∼ 107 cm−3 (Keto & Caselli 2010).
– 19 – N6 is smaller than most cores in all three cluster-forming regions listed above, (Walsh et al. 2007; Friesen et al. 2009), but this could be partly an effect of resolution, as this study has finer resolution by at least a factor of two over previous work. The small size could also be partly due to the molecular transition used, as we have used higher J transitions that preferentially trace higher column density material. Walsh et al. (2007) list a few cores with sizes comparable to N6, but these are at the limit of their resolution. N6 is significantly smaller than all isolated cores that have been well resolved, whether studied in line-emission, dust continuum, or extinction (Ward-Thompson et al. 1999; Bacmann et al. 2000; Crapsi et al. 2005; Kandori et al. 2005; Kauffmann et al. 2008). As noted earlier, the N2 H+ linewidths in N6 are narrower than almost all other cluster cores (Andr´e et al. 2007; Walsh et al. 2007; H. Kirk et al. 2007; Friesen et al. 2010a), and are almost totally due to thermal motions (as discussed in detail in DAM04). The linewidth barely varies across N6, and it is an excellent example of a coherent core, a core where the non-thermal motions are subsonic, and constant, so that it appears to be cut-off from the surrounding turbulent gas (Mouschovias 1991; Myers 1998; Barranco & Goodman 1998; Goodman et al. 1998; Caselli et al. 2002c; Pineda et al. 2010). The N2 H+ column density in N6 is larger than most cores elsewhere in Ophiuchus (Friesen et al. 2010a) and Perseus (H. Kirk et al. 2007), with a peak value of ∼ 5 × 1013 cm−2 compared to values of ∼ 1013 cm−2 . This peak value is about three times greater than the peak value observed in a sample of 28 isolated starless cores, and about eight times greater than the sample mean (∼ 8 × 1012 cm−2 ; Crapsi et al. 2005; see also Daniel et al. 2007). Similarly, the N2 D+ column density of N6, ∼ 5 × 1012 cm−2 , is greater than that of cores in Oph B, where the peak value is ∼ 7 × 1011 cm−2 , and greater than the mean value of 25 isolated starless cores, of < 1012 cm−2 (Friesen et al. 2010b; Crapsi et al. 2005; see also Daniel et al. 2007). However, the peak value of N(N2 D+ ) for isolated starless cores, observed toward L1544, L429 and L694-2, is similar to N6 (Crapsi et al. 2005). The deuterium fraction, ranging from a mean near 0.05 to a maximum value of about 0.15, is similar to that seen in 28 isolated cores (range 0.03 – 0.44), where 22 of the cores have D/H < 0.1 (Crapsi et al. 2005). The range of values in N6 is also similar to that of the cluster-core Oph B2, which has a peak of 0.16 but with most of the core showing values around 0.03 (Friesen et al. 2010b). The mean temperature of the isolated cores is about 10 K, while the mean in Oph B2 is higher at around 13-14 K. The deuterium fraction is expected to be significantly higher in the cold (
