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Appendix A: ρ Ophiucus

The ρ-Oph sample is particularly interesting, because it is similar to the σ Ori one in being an IR-selected sample of class II, complete to a limiting mass of about 0.05 M_⊙ (Bontemps et al. 2001). Natta et al. (2006) computed mass accretion rates from the luminosity of Paβ assuming a distance of 160 pc; since no extensive spectral type determinations were available, they followed the method outlined by Bontemps et al. (2001) and derived the stellar parameters assuming coeval star formation at 0.5 My and the evolutionary tracks of D’Antona & Mazzitelli (1998, the isochrone method). They found that the mass accretion rates could be fitted by a linear relation  ∝ M ∗ ^1.8 ± 0.2 over a mass interval 0.03–3 M_⊙, with a very large spread for any given M_∗. However, the Natta et al. (2006) results need to be reconsidered, since new measurements of the ρ-Oph distance yield considerably low values, 120–130 pc (Lombardi et al. 2008; Loinard et al. 2008; Snow et al. 2008). The corresponding decrease in luminosity implies an older age for the region. We have redetermined stellar parameters and mass accretion rates for all objects in Natta et al. (2006), adopting a distance of 130 pc and evolutionary tracks of Baraffe et al. (1998) for 1 My. The new values of Ṁ_acc are somewhat lower than previous ones, and M_∗ higher, especially for higher masses (see Fig. A.1).

As a consequence, if fitted with a single power-law, the correlation between Ṁ_acc and M_∗ is flatter, with a slope of 1.3 ± 0.2. The new distance, the older age and the different evolutionary tracks contribute to this result. In particular, the dependence of the Ṁ_acc – M_∗ relation on the adopted evolutionary tracks is well known (see Fang et al. 2009) and is particularly strong in ρ-Oph, given the method used to determine the stellar parameters.

	Fig. A.1 Mass accretion rate versus stellar masses for the star of the ρ-Oph sample. The stellar parameters and the accretion properties were recalculated assuming a distance of 130 pc (Lombardi et al. 2008) instead of 160 pc assumed by Natta et al. (2006), and 1 My age.
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Appendix B: BD and very low-mass stars from the Lodieu et al. photometric survey

An independent sample of very low-mass stars and brown dwarfs has been selected from the list of σ Ori members and candidate members of Lodieu et al. (2009). We applied a first selection criterium on the z,(z − J) diagram computed T_eff by comparing observed z,Y,J colors to synthetic ones from the theoretical models of Baraffe et al. (1998) for log g = 4.0 and luminosities from the observed J mag and model-predicted bolometric corrections. We then performed a further selection based on the location of the objects on the HR diagram, excluding all stars with M_∗  > 0.13 M_⊙. Our sample of candidate young very low-mass stars and BDs in σ Ori is then formed by 80 objects, 40 of which were included in the U-band FORS1 survey.

Spitzer IRAC detections exist for 21/40 objects; three of them are uncertain members according to Hernandez et al. (2007). Of the 21, six are classified as class II, one is a transitional disk, one an evolved disk and 13 are class III objects. The 18 confirmed members are included in the sample analyzed in the main text of the paper. Note that the determination of the stellar parameters, T_eff in particular is performed using different photometric bands with respect to the bands used in the main text; the difference in T_eff are in general within the uncertainties discussed in Sect. 3.1; however, some of the objects in Table 2, although included in the Lodieu sample, were not selected with the criteria applied here.

Of the 40 objects in our sample, 20 have been detected in the U-band, while for the other 20 we have upper limits only. We derived the accretion luminosity and mass accretion rates as in Sect. 4.3. The calibration of the photospheric colors (U − J) and (U − I) as function of T_eff using our U-band photometry of Class III objects extends to T_eff  ~ 2900 K (Sect. 4.1); we compare it to synthetic colors from the Baraffe et al. (1998) model atmosphere to extend the relations to lower T_eff. The Class III colors agree well with the models; the results are shown in Fig. B.1.

Fig. B.1 U-λ colors as function of Teff. The red circles are objects with measured U-band fluxes, arrows are objects with U-band upper limits. The squares are model-predicted colors for different gravity, from 5.5 (black squares, top) to 3.5 (blue squares, lowest). The solid lines show the best-fit relations for Class III derived in Sect. 4.1, extrapolated to lower Teff; dashed lines are  ± 2σ. We will consider as accretors objects with colors below the photospheric strip: five BDs have clear evidence of U-band excess (note that for two we only have two colors), one only marginal evidence (from (U − I) and (U − J), while (U − Z) is photospheric). Hereafter we mark the upper limit as dashes for clarity. (A color version of this figure is available in the online journal.)

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Figure B.2 shows Ṁ_acc vs. M_∗; we find that only five objects (all with M_∗0.06 M_⊙) have Ṁ_acc  > −10.8, the median in Sect. 6.1. of these, two are class II sources (SO500 and SO848, also in Table 2), one is a class III (SO641, possibly misclassified), three have no Spitzer detections. No other object with higher values of Ṁ_acc is detected.

Fig. B.2 Mass accretion rate as function of M∗. Dots are class II objects with measured Ṁacc, the cross is a class III stars with measured Ṁacc, and diamonds refer to object with no Spitzer data. Arrows are objects with upper limits (both U-band detections and non-detections). Colors (only in the on-line version) indicate the SED Class : red for class II, blue for class III; black for objects with no Spitzer data. (A color version of this figure is available in the online journal.)

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Appendix C: SEDs and H_α of EV and TD objects

In this section, we show SEDs (Fig. C.1) and Hα profiles (Fig. C.2) of a subset of two TD and four EV stars observed with SARG@TNG (Sect. 2.4) and Giraffe (Sacco et al. 2008). A summary of the Hα properties is given in Table C.1, where 10% Hα represents the width of Hα at 10% of the line’s peak intensity, and pEW is the pseudo-equivalent width. Below we will briefly comment on each object.

SO587. This EV disk was extensively studied by Rigliaco et al. (2009). It exhibits modest excess emission (well below the lower quartiles of the distributions) in the IRAC bands and at 24 μm. It shows a symmetric and narrow Hα emission profile with the peak close to the line center (type I profile following the classification of Reipurth et al. (1996)). Based on the available U-band photometry (Wolk 1996), the narrow Hα and the strength and profiles of the [S ii] and [N ii] forbidden lines, Rigliaco et al. (2009) suggested that the disk was being photoevaporated and that the forbidden lines were coming from the photoevaporation flow, possibly driven and certainly illuminated by the star σ Ori. A crucial ingredient of this model was the high ratio between the mass-loss and the mass-accretion rate. Our results confirm this interpretation. Although relatively bright in U, the object does not have a measurable U-band excess (i.e., it lies inside the photospheric strip of Fig. 4) and we estimate an upper limit to log  Ṁ_acc of −9.45 M_⊙/y, consistent with the value −9.52 M_⊙/y derived in Rigliaco et al. (2009).

SO615. This is a relatively massive, luminous star. Its SED is typical of a flat disk up to 24 μm. We cannot measure Ṁ_acc from the U-band, which is already saturated by the photospheric emission alone, but we can estimate a value of log  Ṁ_acc = −8.25 M_⊙/y from the U = 15.96 mag measurement of Wolk (1996). The Hα has a complex profile, with broad wings, deep redshifted and blueshifted absorption and a narrow, slightly redshifted emission in the center. Similar profiles are observed for higher numbers of the Balmer series (“YY Orionis like profiles”; Walker 1972) and are associated with extensive infall and outflow rates, consistent with the very high value of Ṁ_acc. Unfortunately, the SARG SO615 spectrum is rather noisy.

SO759. Classified as EV disk star by Hernandez et al. (2007). The SED has negligible excess up to 8 μm, but a significant one at 24 μm, not very different from the SED of some TD objects. The Hα is rather narrow and symmetric, with a moderate red/blue asymmetry (type I profile, Reipurt et al. 1996). The 10% Hα width of 157 ± 12 km s^-1 and the upper limit log  Ṁ_acc  < −9.67 M_⊙/y is not stringent for an object of 0.3 M_⊙, but, combined with the Hα properties, it suggests that this is a low accretor (if any).

SO818. Classified as TD. This star shows significant excess emission, in the higher quartile at 3.6, 4.5, 5.8 and at 24 μm. We measure Ṁ_acc= −9.45 M_⊙/y, typical of optically thick disks. The Hα is broad (10% width of 332 ± 25 km s^-1) and shows an inverse P-Cygni profile, with the emission peak at the line center position. The red-shifted absorption goes below the continuum (type IVR), confirming the evidence of a high accretion rate.

SO897. Classified as TD; the IRAC excess emission is clearly detected, but lower than the σ Ori medians, while the 24 μm excess is strong. We measure a lower limit to Ṁ_acc(>−9.13 M_⊙/y), but the star is clearly accreting. We have two measurements of the Hα profile, one with Giraffe in October 2004 and one with SARG acquired in January 2009. Within these two epochs the maxima change in position and strength, with the primary one blue-shifted in 2004 and red-shifted in 2009, and the secondary one with opposite behaviour. The wavelength separation of the blue and red emission peaks decreases from 2004 and 2009, while the central reversal seems to be at the line center in the first epoch and then slightly blue-shifted in the second epoch. The profile changes from IIR to IIB, following the Reipurt et al. (1996) scheme, where these types are characterized by secondary peaks exceeding half the strength of the primary peaks, as we observe. This is a common phenomenon in accreting T Tauri stars, probably due to the interplay of variable accretion and mass-loss.

SO908. EV disk, with excess emission within the lower quartiles at all IRAC wavelengths, and significant excess at 24 μm. We measure Ṁ_acc = –9.37 M_⊙/y, typical of optically thick disks. The Hα is broad and asymmetric, with less emission in the red than in the blue. This type of profile (IIIR) is the less frequent in the scheme classification of Reipurt et al. (1996). Following the radiative transfer models developed by Kurosawa et al. (2006), this profile morphology requires some obscuration by the dusty disk, i.e. a high inclination, explaining the rarity of the profile. A highly inclined disk is consistent with the SED properties.

	Fig. C.1 SEDs of four EV disks and 2 TD. The squares shows the observed fluxes (see Table C.2). The lines plot the model atmosphere from Allard et al. (2000) at the appropriate Teff, log g = 4.0, normalized to the J band. Each panel gives the name of the star (see Table C.1) and the mass accretion rate.
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	Fig. C.2 Hα line profiles of six stars of the sample normalized to the continuum. The spectra have been obtained either in 2004 with FLAMES/Giraffe by Sacco et al., with a spectral resolution R = 17000, or by Rigliaco et al., in 2009 with SARG, with a spectral resolution R = 29000, as indicated in Table C.1.
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