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Appendix A: Uncertainties of the analysis

In this appendix we discuss the limitations of our analysis due to non-simultaneous observations and thoroughly quantify the uncertainties on the inferred results.

The mentioned stellar variability does not have a strong impact on the determination of the stellar properties because it does not significantly affect the shape of the optical spectrum (used to determine the spectral type) and the J and H band fluxes (used to estimate luminosity and radius).

On the contrary, the estimate of the visual extinction is affected by large uncertainties. We firstly point out that the use of the (J − H) color as a tracer of the extinction relies on the assumption that the observed flux at those wavelengths is entirely emitted by the stellar photosphere. Secondly, the determination of the optical extinction A_V is fairly sensitive to the surface gravity of the assumed model. By varying the stellar radius or mass by 30%, we obtain A_V values between 1.2 and 2.5. This may add a further factor of 15% uncertainty to the estimates of stellar properties. However, that the accretion luminosity values estimated by using different tracers from 0.45 and 2.17 μm does not show any dependence on the wavelength (see Fig. A.1) is a strong sanity check for determining A_V. The fact that we find the same A_V values by using two independent methods (the observed colors, Sect. 3.1, and the modeling approach, Sect. 4.1) further reinforces our result. The large difference between our estimate of the stellar luminosity and the result from Rebull et al. (2010; see Table 1) is due to the determination of A_V which is in turn due to the assumed surface gravity.

The spectral type-T_eff relation can actually introduce an additional error. Differences up to some hundreds of Kelvin arise for M-type stars among different works (see e.g., Da Rio et al. 2010). Finally, further uncertainty in the determination of the stellar properties is provided by the PMS star tracks adopted to infer the stellar mass and age. Hartmann (2001) suggests that the age spread inferred for TTSs in Taurus may be due exclusively to uncertainties toward individual members.

In Sect. 3.2.2 we estimated the disk inner radius by measuring the width of the CO ro-vibrational lines. The largest

uncertainty in the determination of R_in is set by the adopted inclination. The width of the CO lines is equally reproduced by configurations with (i: R_in) = (60°: 0.05 AU), (45°: 0.03 AU), and (30°: 0.02 AU).

The estimates of the mass accretion and outflow rate may be affected by variability, since the optical and NIR spectra used to measure the line luminosities were flux-calibrated by using non-simultaneous photometry. This is particularly true for estimates based on optical lines (optical flux variability ~2.1, see Sect. 5.1). The variability implies uncertainties on the estimates of the accretion luminosity in addition to the scattering of the empirical correlations employed to derive L_acc (Sect. 3.3.1). The lowest and the highest estimates for L_acc have been found by means of emission lines from the same spectrum (thus taken simultaneously, see Table 7). This is indicating that the scattering of the empirical relations might play the major source of uncertainty on the accretion luminosity.

	Fig. A.1 Accretion luminosity estimated from the luminosity of emission lines at optical to NIR wavelengths (x axis) for different AV values. The gray stripe indicates the range of values inferred from the Brγ line, which is the least affected by extinction. The trend with wavelength for high and no extinction is clear. Slight displacement between points has been put for better visualization.
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