5 Discussion

Ammonia cores are those regions of the interstellar medium where the volume density is between 10⁴-10⁵ cm^-3. In respect of physical properties they do not form a homogeneous group. Starless cores in most clouds have smaller nonthermal line widths and masses, and lower kinetic temperatures than those associated with IRAS sources. Moreover, the cores associated with embedded or nearby young clusters are the most massive and most turbulent objects in JMA's ammonia data base. The typical mass and turbulent energy of gas in the cores, moreover, varies from cloud to cloud. Most cores in Taurus form isolated stars, whereas some of them in Ophiuchus and Orion give birth to rich clusters (Motte et al. 1998; Mitchell et al. 2001). Several observational and theoretical studies suggest that the observed nonthermal line widths of cores are related to the initial conditions of star formation (e.g. Myers & Fuller 1993; Caselli & Myers 1995).

Figure 6: Average of 56 NH3(1,1) spectra in the region centred on the C18O peak position of clump B.

Dense cores of molecular clouds are thought to be created by shocks due to the supersonic turbulent velocity field of the ISM, referred to as turbulent fragmentation (e.g. Elmegreen 1993; Klessen et al. 2000). In this scenario several observed properties of core/cloud systems are related to the nature of interstellar turbulence (Padoan 1995; Padoan & Nordlund 2002). In particular, the slope $\alpha$ of the line width-size relation $\log \Delta v_{{\rm NT}} \propto \alpha~\log R$ reflects the power spectrum of the turbulence, so that $E(k) \propto k^{-\beta}$ and $\alpha = (\beta-1)/2$. Density ratio between cores and their environment, typical core diameter and mass, as well as the volume filling factor of the cores are related to the size L₀ and velocity dispersion $\sigma_{v,0}$ of the ambient cloud.

Cores of various size and velocity dispersion probably define the smallest scale of the self-similar structure of interstellar medium. In low-mass star forming regions they represent the size scale where the nonthermal velocity dispersion becomes subsonic (Goodman et al. 1998). Myers (1998) has shown that the strongly turbulent, massive cores having $\Delta v > 0.9$ km s^-1 and N(H $_2) > 1\times10^{22}$ cm^-2 may contain several critically stable condensations (kernels) cut off from MHD waves due to the high extinction of the core. This model suggests that massive, cluster-forming cores also represent an inner scale of the self-similar structure.

In this section we attempt to deduce some attributes of star formation from the derived properties of ammonia cores of L 1340 (Sect. 5.1), compare the features revealed by different tracers with each other (Sect. 5.2), and L 1340 with other star forming regions (Sect. 5.3).

   
5.1 Connection of ammonia cores with star formation

Table 2 shows that M(NH₃) $\ge M_{{\rm BE}}$ for most of the cores of L 1340. Several observations have shown that this is a necessary condition of star formation (Williams et al. 2000). Thus the observed cores probably highlight the positions of present and future star formation. The cores associated with embedded YSOs clearly differ from the starless cores in their nonthermal line widths. This is also true for the twin systems. The mean $\Delta v_{{\rm NT}}$ of cores without embedded or nearby IRAS point source, 0.28 km s^-1, corresponds to a velocity dispersion $\sigma_{{\rm NT}}=0.12$ km s^-1. This is smaller than the isothermal sound speed at 13 K, $c_{\rm s}=$ 0.21 km s^-1. Thus the detected starless cores are among the smallest clumps formed by turbulent fragmentation. Such objects may have a wide range of mass (e.g. Padoan & Nordlund 2002), including small clumps which do not collapse. The weak ammonia emission observed at the northern part of clump B probably originates from such small, dense regions. M(NH₃)  $\gg M_{{\rm BE}}$ for the starless cores, indicating that they are destined to collapse. Our observations thus suggest that these cores are prestellar. We note, however, that this conclusion has some uncertainties. First, magnetic fields, neglected here due to lack of data, may modify the critical mass so that it will be significantly larger than $M_{{\rm BE}}$. Furthermore, recent results by Tafalla et al. (2002) demonstrate that ammonia abundance is enhanced towards the centres of some starless cores. Detection of the central regions only, enriched in ammonia, may lead to overestimation of the mass. Finally, it is possible that these cores are not starless, but contain low-luminosity embedded YSOs below the detection threshold of IRAS. Observations in other molecular lines with high angular resolution and more sensitive infrared observations can clarify the nature of these cores.

Figure 7: a) Radial velocities in Clump C as a function of RA offset; b) linewidths observed in Clump C as a function of RA offset. Different declination offsets are marked with different symbols. Offsets are given in arcmin with respect to RA(2000) = 2 $^{\rm h}29^{\rm m}41\hbox{$.\!\!^{\rm s}$ }64$and Dec(2000) = +72$^\circ$43$^\prime$22 $.\!\!^{\prime\prime}$2.

Cores associated with embedded IRAS sources have average $\Delta v_{{\rm NT}} = 0.78$ km s^-1, comparable to the those of Orion B (JMA). From the six cores, column density and nonthermal line width of A4 and C3w fulfil the criteria set by Myers (1998) for cluster forming cores. In core A4 IRAS 02249+7230 closely coincides with the peak intensity of C¹⁸O, NH₃ and $A_{\rm V}$. $M_{{\rm BE}} \gg M$(NH₃) for this core, suggesting that it is disrupting. Morphology of HH 489, associated with the IRAS source, however, indicates that the direction of the bipolar outflow from this star lies close to the plane of the sky (Kumar et al. 2002). The large nonthermal velocity dispersion of this core thus cannot arise from the interaction of outflow with the core gas. It indicates either the presence of other YSOs with outflows along the line of sight, or might have been produced before the star formation. The other cluster-forming core candidate, C3w, has a common envelope with C2 and C3e. Our ammonia observations show this core to be the densest region of L 1340, though it lies far from the C¹⁸O peak, and is associated with a single low-luminosity IRAS source IRAS 02276+7225. No outflow, maser source or HH-object have been detected around this source. Core C3w is probably less evolved than A4.

Our observational results suggest that the large turbulent velocity dispersions of IRAS-associated cores cannot be attributed to YSO winds. These cores are not simply more evolved versions of the starless cores, but probably form more massive stars than their narrow-line counterparts, and some of them will evolve into small stellar groups similar to the two sparse young clusters RNO 7 and RNO 8, found in L 1340 (Kumar et al. 2002; Kun 2002a). In order to reveal the real nature and evolutionary state of the cores, their detailed density and velocity structures and stellar contents have to be studied via higher resolution molecular and submillimeter continuum observations.

   
5.2 Comparison with H I, ¹³CO, C¹⁸O, and A_V

The nonthermal line width-size relation for the structures shown by different tracers, called Type 3 line width-size relation by Goodman et al. (1998), is a useful indicator of the overall density structure of a cloud, which, in turn, is closely related to the mode of star formation. In order to derive this relation for L 1340 we supplemented our ammonia results with C¹⁸O, ¹³CO and H I data.

The $\Delta v_{{\rm NT}}$ and R data for the C¹⁸O and ¹³CO structures were taken from Paper I and from Yonekura et al. (1997), respectively. The size and line width of the H I structure associated with L 1340 were estimated from the Leiden-Dwingeloo H I survey data (Hartmann & Burton 1997). The main properties of the neutral hydrogen in the galactic environment of L 1340 are shown in Appendix A. The H I spectra in this region show definite peaks in the velocity interval $-18~{\rm km~s}^{-1} < v_{{\rm LSR}} < -8~{\rm km~s}^{-1}$whose characteristic FWHM is $7~{\rm km~s}^{-1}$, and the half-maximum size of the interstellar feature delineated by this gas component is 38 pc.

The $\log \Delta v_{{\rm NT}}$ vs. $\log R$ relation for the structures observed in NH₃, C¹⁸O, ¹³CO and H I is shown in Fig. 8. The R_1/2 values plotted have been corrected for the different beam sizes of the observations, and $\Delta v_{{\rm NT}}$ values have been corrected for spectral resolutions. We obtained the relation

$$% \log \Delta v_{{\rm NT}} = (0.41\pm0.06)~\log R + (0.12\pm0.06)$$ (1)

and the correlation coefficient 0.85.

This relationship reveals the self-similar hierarchy of substructures from the large H I cloud to the ammonia cores, i.e. on the 0.1-40 pc size scale, suggesting that they are parts of a physically connected structure shaped by interstellar turbulence (Larson 1981). The slope $\alpha=0.41$ is between those obtained for Taurus ( $0.53\pm0.07$) and Orion B ( $0.21\pm0.03$) cores (Caselli & Myers 1995), from the same tracers.

We compare properties of NH₃ cores and their embedding C¹⁸O clumps in Table 3. The data listed show that the average density ratio of the cores and their embedding clumps $n_{\rm c}/n_0$, the typical core diameter $l_{\rm c}$ and the volume filling factor of the cores are in accordance with the values predicted by the model of turbulent fragmentation (Padoan 1995; Padoan & Nordlund 2002). The size and velocity dispersion of the ¹³CO cloud are L₀= 3.7 pc and $\sigma_{v,0}=0.72$ km s^-1, respectively, thus the large-scale Mach number is $\mathcal{M}_{0}=\sigma_{v,0}/c_{\rm s} =3.4$. With these values the model gives $n_{\rm c}/n_0 \approx \mathcal{M}_{0}^2=11.6$, in accordance with the observed $n_{\rm c}/n_0 \approx 10$. The typical core diameter, $l_{\rm c} \sim L_0~\mathcal{M}_{0}^{-1/\alpha}=0.25$ pc, is also comparable to the observed average 0.16 pc. The volume filling factor of the cores, obtained from the probability density function of $n_{\rm c}/n_0$, is 0.02, compatible with the observed average shown in Table 3.

   

Table 3: Comparison of C¹⁸O and NH₃ cores in L 1340.

Clump	A	B	C	Mean
R(C18O) / pc	0.9	1.1	0.7	0.9
$\langle R \rangle$(NH3) / pc	0.07	0.13	0.09	0.10
$\Delta v_{{\rm tot}}$(C18O)a / km s-1	0.89	1.25	2.16	1.43
$\langle \Delta v_{{\rm tot}} \rangle$(NH3)	0.57	0.46	0.72	0.58
$T_{{\rm ex}}$(12CO) (K)	10.2	13.1	9.2	10.8
$\langle T_{k} \rangle$(NH3) / K	12.9	14.6	14.2	13.9
$N_{{\rm H_2}}$(C18O)b / 1021 cm-2	7.1	8.4	7.8	7.8
$N_{{\rm H_2}}$(NH3) / 1021 cm-2	8.6	6.8	14.0	9.8
$n_{{\rm H_2}}$(NH3)/ $n_{{\rm H_2}}$(C18O)	7.7	11.6	10.0	9.8
Area(NH3)/Area(C18O)	0.04	0.02	0.16	0.07
$M_{{\rm cores}}/M_{{\rm clump}}$	0.04	0.02	0.19	0.08
$V_{{\rm cores}}/V_{{\rm clump}}$	0.01	0.002	0.11	0.04

^a The total line width, $\Delta v_{{\rm tot}}$ of a C¹⁸O core was calculated from the mean line width $\langle \Delta v \rangle$ obtained by averaging for each observed position within
the half-maximum contour of the integrated intensity map and from the dispersion of the mean velocity ( $\delta v_{{\rm LSR}}$): $\Delta v_{{\rm tot}}^{2} = \langle \Delta v\rangle^{2} + 8 \ln 2 (\delta \langle v_{{\rm LSR}}\rangle)^{2}$.
^b Taking into account the revised calibration (Yonekura et al. 1997).

Figure 8: The nonthermal line width-size relation for different substructures (ammonia cores, C18O clumps and the whole 13CO cloud) of L 1340. Open circles mark the starless NH3 cores and those associated with optically visible stars, black circles represent the cores associated with IRAS point sources. Triangles are for the C18O clumps, and black square marks the whole 13CO cloud. The open square shows the H I feature, whose half-maximum size was estimated from Fig. A.2, and in estimating the nonthermal line width a kinetic temperature 80 K was assumed. The dashed line is fitted to all points.

Finally, in Fig. 9 we compare different density cross sections of L 1340, traced by ¹³CO, C¹⁸O, and NH₃, with the distribution of total column density shown by the visual extinction $A_{\rm V}$. Visual extinction map was constructed from star counts using the USNOFS Image and Catalogue Archive (see Appendix B for the details of obtaining $A_{\rm V}$). The angular resolution of ¹³CO, C¹⁸O and $A_{\rm V}$ maps is equally 3$^\prime$. Positions of ammonia cores, embedded YSOs and RNOs are also indicated. The amount of the foreground extinction was estimated and subtracted from the $A_{\rm V}$ values obtained from the star counts (see Appendix B). The three clumps can be recognized in the distribution of $A_{\rm V}$, but some remarkable differences can also be seen between the structures shown by the obscuring dust and molecular gas, At the southwestern edge of the cloud, in clump A, similarity of ¹³CO and $A_{\rm V}$ suggests that the total amount of $A_{\rm V}$ originates from the observed molecular gas. The steep gradients of both the column density and volume density suggest that the gas in this volume has suffered compression from an external shock. Both in Clump B and C large dark patches can be seen which do not correlate with the molecular emission (e.g. around offsets [ $14\hbox{$^\prime$ },-8\hbox{$^\prime$ }$], [ $-4\hbox{$^\prime$ },20\hbox{$^\prime$ }$]). These features indicate diffuse or overlapping clumps of high total column density. Together with the compact clump A they give asymmetric, cometary shape to the cloud with a `head' pointing towards southwest. Surface distribution of the ammonia cores suggests that they have been formed by external compression or magnetic fields instead of gravity. Most of them (A1, A2, B1, C1, C3) are found far from the bottom of the gravitational potential well of the embedding clumps, indicated either by the peaks of the C¹⁸O intensity or by the large-scale distribution of  $A_{\rm V}$.

Figure 9: 13CO (solid contours) and C18O (dotted contours) integrated intensity overlaid on the optical extinction map (shading) of L 1340 constructed from star counts. Coordinate offsets are given in arcmin with respect to RA(2000) = 2 $^{\rm h}29^{\rm m}42^{\rm s}$ and Dec(2000) = +72 $^{\rm o}43^{\prime }22^{\prime \prime }$. The lowest contour of 13CO is at 1.0 K km s-1, and the increment is 1.5 K km s-1. The C18O contours displayed are 0.45 and 0.75 K km s-1. Both the lightest shade and the increment is 1 mag. The $A_{\rm V}$ values displayed are corrected for the foreground extinction. Open circles indicate the ammonia cores, which probably represent the regions of highest volume densities. Dots are optically invisible IRAS point sources, and asterisks show the positions of the RNOs.

   
5.3 Comparison with other clouds

Comparison of properties of ammonia cores in L 1340 with JMA's data base (their Tables B9-B20) shows that the typical sizes, kinetic temperatures, line widths and masses of ammonia cores are increasing in the order of Taurus $\rightarrow$ Ophiuchus $\rightarrow$ Perseus $\rightarrow$ L 1340 $\rightarrow$ Orion B $\rightarrow$ Orion A. The IRAS luminosities do not show this trend, being lower in L 1340 than in Perseus. A reason for this departure from the trend may be the difference in cloud distances. L 1340 is the most distant among the clouds listed above, therefore a considerable fraction of YSOs born in it might remained undetected by IRAS. We have shown in Sect. 5.2 that the slope $\alpha$ of the line width-size relation also shows the Taurus $\rightarrow$ L 1340 $\rightarrow$ Orion B trend, suggesting that properties of cores and newborn stars are related to large-scale interstellar processes. Comparison of observational results with the continuously improving numerical simulations of such processes will lead to a better understanding of the cloud formation and evolution. This is, however, beyond the scope of the present paper.