Issue 
A&A
Volume 528, April 2011



Article Number  A3  
Number of page(s)  23  
Section  Interstellar and circumstellar matter  
DOI  https://doi.org/10.1051/00046361/201015897  
Published online  16 February 2011 
Online material
Appendix A: The effects of differential refraction on source position
In images extracted from each data cube the nominal “source” position was found to shift slightly with wavelength. This shift is largely due to extinction, although differential refraction and/or imperfect cube construction from the 2dimensional spectral images obtained with the IFS could also contribute.
To investigate this possibility, we examined images extracted from our standard star observations. Six images spread across the H and Kbands were extracted from seven standard star data cubes. We found that the x and y positions of the standard (measured from 2dimensional Gaussian fits) shifted very slightly with wavelength; a tight linear correlation was identified for each standard star: Δx = S_{x} × δλ and Δy = S_{y} × δλ (where Δx and Δy are the shift in pixels, λ is the wavelength in microns, and S is the slope of the linear fit). However, S_{x} and S_{y} were not the same for all standard stars. Rather, these proved to be a function of airmass, AM, as expected for differential refraction, with S_{x} = 3.5 − 2.38 × AM and S_{y} = 1.0 − 0.55 × AM. Overall, this effect was mild: we found that at low airmass, between [Fe ii] and Brγ (increasing wavelength), the source shifted down and to the right by only 0.45 pix, 0.21 pix (0.022″, 0.011″), at intermediate airmass the shift is insignificant in both x and y, while at high airmass the shift is to the left by 0.41 pix, 0.01 pix (0.021″, 0″). These shifts are very small when compared to the offsets measured in Table 2 and essentially only apply to the [Fe ii] offsets. They have therefore not been applied to the data.
Appendix B: H and Kband line flux measurements
Tables B.1 and B.2 list the observed line intensities measured towards each outflow source from the spectra displayed in Figs. 5 and 6.
Appendix C: H_{2} excitation diagrams
Molecular hydrogen excitation diagrams may in principal be used to simultaneously estimate the gas excitation temperature and the extinction towards the lineemitting region (e.g. Nisini et al. 2002; Caratti o Garatti et al. 2006).
Fig. C.1
The lefthand panel shows an H_{2} excitation diagram for HH 26IRS. The data, corrected for extinction (A_{v} = 27 in this case), have been fitted with a straight line and a secondorder polynomial (dashed line). The equations describing each fit are displayed; the R^{2} values represent the square of the correlation coefficient associated with each fit. Plots over a range of A_{v} values were generated and R^{2} measured for the two fits in each case. The righthand panel shows a plot of R^{2} against A_{v}. Data from the linear and polynomial fits are represented by a cross and an open square, respectively; the full and dashed lines represent thirdorder polynomial fits to these data. The peak in each curve in the righthand plot marks the extinction associated with the greatest value of R^{2}, which in turn is associated with the least scatter about the linear and polynomial fits in the excitation diagram. 

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In thermalised gas at a single temperature, all of the points in the H_{2} excitation diagram will lie on a single straight line, the slope of which is a measure of the temperature. In reality, when emission lines from a range of rovibrational states are detected, the full diagram is better fit with a curve (Schwartz et al. 1995; Gredel 2006, 2007), or by a separate straight line for each vibrational state (e.g. Giannini et al. 2002; Caratti o Garatti et al. 2006), since lines from higher vibrational states – which have higher critical densities for collisional excitation by hydrogen atoms – may not be fully thermalised. Moreover, the shocks in outflows are rarely planar so the gas in unresolved bow shocks will not be heated to a single temperature; nor will it be maintained at a single temperature as it flows through the shock front and postshock cooling zone. However, if one plots column densities derived from lines from only the first few vibrational states, a linear fit is usually quite adequate (e.g. Lorenzetti et al. 2002; Giannini et al. 2004; Davis et al. 2004; Gredel 2006; Caratti o Garatti et al. 2008; MartínHernández et al. 2008). By minimising the scatter of points about this line, one can then estimate the extinction.
The column density of a given v,J rovibrational level, N_{v,J}, is related to the line intensity, I(vJ → v′J′) (measured in W m^{2}), the wavelength of the transition, λ (in microns), and the v,J → v′,J′ transition probability, A(vJ → v′J′), by: (C.1)In thermodynamic equilibrium, the ratio of column densities between two levels, N_{v,J} and N_{v′,J′}, is given by the Boltzmann equation:
(C.2)where ΔE is the energy difference between the two levels, g_{v,J} is the statistical weight, and T_{ex} is the excitation temperature.
If we adopt an extinction law of the form A_{λ}/A_{v} = (λ_{v}/λ)^{1.6} (Rieke & Lebofsky 1985), then the column density may be corrected for extinction:
(C.3)For a given value of A_{v}, the (negative) reciprocal of the slope of a linear fit to a plot of ln(N_{v,J}/g_{v,J}) against E_{v,J} (the energy of the v,J rovibrational level) yields an estimate of T_{ex}. Increasing A_{v} will increase the value of N_{v,J}(corr) and alter the distribution of points around the fit. Minimising this scatter should then yield an estimate of the extinction towards the lineemission region.
In Fig C.1 we present an excitation diagram for HH 26IRS; similar plots were generated for the other five H_{2} lineemitters in our sample. Over a range of extinction values (A_{v} = 0 − 100) we plot corrected column densities (divided by the statistical weights listed in Table C.1) against upper level energies. An orthopara H_{2} ratio of 3 is assumed throughout (note that a ratio that deviates from the statistical value of 3 would offset the orthoH_{2} and paraH_{2} data points with respect to each other; an orthopara ratio of 3 is in any case usually observed in YSO outflows, e.g. Smith et al. 1997). In each plot we fit the data with a single straight line and a secondorder polynomial. We measure the extinction values that yield the least scatter about each fit; from the best linear fit we also measure the excitation temperature (see Fig. C.1 for further details).
Our results are listed in Table C.2. In SVS 13 and HH 999IRS we had insufficient data to measure A_{v} (although from the two observed lines we could at least estimate T_{ex} assuming A_{v} = 0; note that T_{ex} is relatively insensitive to A_{v}). Towards the other four sources a range of values were measured. Excluding the Qbranch emission lines, which are suspect due to their location at the edge of the Kband, had little effect on the results. Excluding the higherenergy lines (lines from the v > 1 levels and the 1–0 S(7)–S(9) transitions in the Hband) also had only a subtle effect on extinction estimates, although excitation temperatures were consistently lower, as expected.
© ESO, 2011
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