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Appendix A: The two-layer model

Each inverse P-Cygni profile was fitted using the simple two-slab model described by Myers et al. (1996) with the modification introduced by Di Francesco et al. (2001) to take into account the continuum source, see also Kristensen et al. (2012). The model assumes that the central continuum source is optically thick, emitting as a blackbody of temperature T_c, and filling a fraction of the beam, Φ. Two layers of gas, front and rear, are infalling toward the central source with an infall velocity and velocity dispersion V_in and σ_v, respectively. The rear layer is illuminated by the background radiation, T_b. If for each layer the peak optical depth is τ₀, then the expected line emission at velocity V can be expressed as (A.1)where (A.2)and where V_LSR is the source velocity, and the radiation temperature is defined as (A.5)where T₀ ≡ hν₀/k_B, and ν₀ is the line rest frequency.

Since the front absorbing layer is probably subthermally excited, we assumed a conservative value for the excitation front layer of T_f = 3 K. The continuum temperature, T_c, was chosen such that the continuum radiation temperature, J_c(T_c), matches the peak continuum flux in the image. The continuum source beam filling fraction, Φ, which is not well constrained, was set to 0.3 to use the same value as Di Francesco et al. (2001), who modeled interferometric observations with a similar angular resolution as we did; this value is consistent with the line modeling results of coarse angular resolution Herschel data Kristensen et al. (2012). Although the value of Φ used here is arbitrary, we have also performed line profile fits with higher values of Φ and the obtained infall velocity and velocity dispersion are unchanged, while the values for T_r and τ₀ are increased and decreased, respectively.Similarly, if a higher value of T_c is used, T_r and τ₀ are increased and decreased, respectively, while we obtain the same results for V_in and σ_v. Therefore our results are robust to the value of Φ and T_c used. An initial set of models with the centroid velocity, V_LSR, as a free parameter were run, and all gave a V_LSR of 3.4 ± 0.1 km   s^-1. Given these results, we decided to fix the value of V_LSR at 3.4 km   s^-1and reduce the number of free variables in the fit.

The χ² was minimized using the mpfitfun procedure (Markwardt 2009), where a spectrum is generated for different parameters and then compared to the observed line profile. The following parameters were kept fixed during the minimization: V_LSR, T_c, T_f, and Φ.

Appendix B: Tables

Table B.1 lists the position of the continuum sources. Table B.2 lists the information for the spectral lines analyzed.

Appendix C: Inverse P-Cygni profiles, centroid velocity and position velocity maps

In this Appendix, we show the inverse P-Cygni profiles and their respective models in Fig. C.1. The centroid velocity maps for all three molecules studied, CH₃OCHO-A/E and H₂CCO, are shown in Fig. C.2. The position velocity diagrams along the cut shown in Fig. C.2 are shown in Fig. C.3

	Fig. C.1 Molecular line spectra from the ALMA data toward the continuum peak of I16293B. In each panel, a red line shows the best two-layer model of infall fit for each spectrum. The best-fit model parameters are listed in Table 1.
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Fig. C.2 Intensity-weighted velocity for the three lines studied, CH3OCHO-A (left panel) CH3OCHO-E (middle panel), and H2CCO (right panel). Contours are drawn to  − 3, 3, 10, 22, 39, 61, 88, 120, and 157 times the rms noise of the integrated intensity, 15 mJy   beam-1 km   s-1, where negative contours are plotted using dotted lines. The beam size is shown at the bottom left corner. The gray line is the cut used for the position velocity diagram shown in Fig. C.3.

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Fig. C.3 Position velocity maps of source A, along the direction shown in the rightmost panel of Fig. C.2, for the three lines studied. From left to right: CH3OCHO-A, CH3OCHO-E, and H2CCO. Contours are drawn to  − 3, 3, 10, 22, 39, 61, 88, 120, and 157 times the rms noise, 4.5 mJy   beam-1, where negative contours are plotted using dotted lines. The red dashed line and red solid circle show the 8 km   s-1   arcsec-1velocity gradient and position of source A (VLSR = 3.4 km   s-1), respectively. Notice that in all panels an adjacent molecular transition line is marked with a vertical blue line, which can also be identified in Fig. 2. The spatial resolution is shown at the bottom right corner.

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© ESO, 2012