Online material

Appendix A: Detailed physical parameters of Cha I and III cores

Tables A.1 and A.2 provide a detailed list of the observationally derived physical parameters of the cores for each transition separately. The method for extracting these values is described in Sects. 3 and 4. For the spectra that have two velocity components, the derived properties based on both components are listed. The integrated intensities are listed only for the transitions that were used to derive column densities.

Appendix B: Critical densities

For the calculation of critical densities we use the Einstein A-coefficients, the collisional rate coefficients, and energies from the Leiden Atomic and Molecular Database (LAMDA⁴).

The critical density is the density at which the rate of spontaneous emission is equal to the rate of collisional de-excitation,(B.1)where A_ul is the Einstein coefficient for spontaneous emission (s^-1), C_ul = n_H2γ_ul the collision coefficient (collision de-excitation rate, s^-1), and γ_ul the collision rate (cm³ s^-1). The critical densities we derive are listed in Table B.1 for various molecular transitions.

Appendix C: Optical depths

Appendix C.1: C¹⁸O 2–1 opacity

C¹⁸O 2–1 was observed toward all 60 cores in Cha I and C¹⁷O 2−1 toward 32. We estimate the optical depth of the C¹⁸O 2–1 transition for this sample of 32 cores. We assume an isotopic ratio [¹⁸O]/[¹⁷O] of ~4.11, as was found for the nearby (140 pc) low-mass star forming cloud ρ Ophiuchus (Wouterloot et al. 2005), to derive the opacity of C¹⁸O 2−1 with the relation (C.1)where I_C¹⁸O and I_C¹⁷O are the integrated intensities of the two transitions, τ_C¹⁸O and τ_C¹⁷O their opacities, and τ_C¹⁷O = τ_C¹⁸O/4.11. Table C.1 lists the opacity estimates for the sample of 32 cores in Cha I. Approximately half of them are somewhat optically thick (4.2 >τ_C¹⁸O ≥ 1) in C¹⁸O 2–1.

We can only calculate the C¹⁸O 2–1 opacities for the two cores in Cha III that were also observed in C¹⁷O 2–1, Cha3-C1 and Cha3-C4. Cha3-C1 is borderline optically thick/thin with an opacity of ~ 1, while Cha3-C4 is optically thin (Table C.2). They are both optically thin in C¹⁷O 2–1.

Appendix C.2: CS 2–1 opacity

We assume an isotopic ratio of [³²S]/[³⁴S] ~ 22 (Frerking et al. 1980) to calculate the opacity of the CS 2–1 line in Cha I. All 57 CS 2–1 spectra feature detections and 23 out of the 57 are detected in C³⁴S 2–1. We follow the same method as above to estimate the CS 2–1 opacities toward the 23 cores that are detected in both transitions. The results are given in Table C.3.

For the remaining 34 spectra we calculate upper limits for the CS 2–1 opacity by using the ratio of the CS 2–1 integrated intensity to the value of 3 × rms of the C³⁴S 2–1 spectra. The opacity upper limits are listed in Table C.4. All 23 cores that have detections in C³⁴S 2–1 are optically thick in CS 2–1, with opacities ranging from ~2–10.

Two cores in Cha III are detected in C³⁴S 2−1 and their CS 2−1 opacity is listed in Table C.5. Both have CS 2−1 opacities greater than one, while they are optically thin in C³⁴S 2−1. CS 2−1 is detected toward all remaining cores, for which we calculate upper limits (Table C.6) in the same way as for the Cha I cores.

Appendix D: Density conversions

For the conversion of hydrogen densities to free-particle densities and vice versa we use the mean molecular weight per free-particle, μ ~ 2.37 (see Appendix A.1 in Kauffmann et al. 2008). The cosmic mass ratio of hydrogen to the total mass of matter is ~ 0.71, while that of helium is ~0.27 (Cox 2000). The total hydrogen density, n_H, is equivalent to (D.1)which gives (D.2)with n_fp the free-particle density.

Appendix E: Spectra of Cha I and III cores

The spectra of the transitions used to search for signatures of contraction motions in the sources listed in Table 7 are displayed in Fig. E.1.

Fig. E.1 Spectra obtained with APEX and the Mopra telescope toward the Cha I and III sources listed in Table 7, displayed in main-beam temperature scale. Spectra that were rescaled to fit in the figure have their scaling factor indicated on the right. The vertical dashed line marks the systemic velocity as derived from a Gaussian fit to the CH3OH 20–10 A+ transition, except for sources Cha1-C6, Cha1-C24, Cha1-C27, Cha1-C35, and Cha3-C10 for which the C18O 2–1 transition was used.

Open with DEXTER

	Fig. E.1 continued.
Open with DEXTER

	Fig. E.1 continued.
Open with DEXTER

© ESO, 2015