4 Luminosity estimates and luminosity function

Most of the new YSOs identified by ISOCAM are weak IR sources which were not detected by IRAS and were not observed in previous ground-based mid-IR surveys (dedicated to bright near-IR sources). They likely correspond to low-luminosity, low-mass young stars. In Sect. 4.1 below, we derive stellar luminosity estimates for Class II and Class III objects using published near-IR photometry from Barsony et al. (1997). In Sect. 4.2, we provide mid-IR estimates of the disk luminosities, $\mbox{$L_\mathrm{disk}$ }$, for Class II YSOs. Finally, calorimetric estimates of the bolometric luminosities, $\mbox{$L_\mathrm{bol}$ }$, for Class I YSOs are calculated in Sect. 4.3. The luminosity function of the $\mbox{$\rho$ ~Ophiuchi}$ embedded cluster is then assembled in Sect. 4.4.

4.1 Dereddened J-band stellar luminosities for Class II and Class III sources

The J-band flux provides a good tracer of the stellar luminosity for late-type PMS stars (i.e., T Tauri stars) because the J-band is close to the maximum of the photospheric energy distribution for such cool stars. It is also a good compromise between bands too much affected by interstellar extinction at short wavelengths (very few $\mbox{$\rho$ ~Ophiuchi}$ YSOs have been detected in the V, R, or I bands), and the H, K and mid-IR bands which are contaminated by intrinsic excesses. Greene et al. (1994) showed that there is a good correlation between the dereddened J-band flux and the stellar luminosity derived by other methods. They pointed out that in $\mbox{$\rho$ ~Ophiuchi}$ this correlation is roughly consistent with a more theoretically based correlation expected for 1-Myr old PMS stars following the D'Antona & Mazzitelli (1994) evolutionary tracks. More recently, Strom et al. (1995) and Kenyon & Hartmann (1995) used the same model PMS tracks to directly convert dereddened J-band fluxes into stellar masses. We adopt a similar approach here.

4.1.1 Extinction estimates from near-IR colors

The main difficulty and source of uncertainty with this method is due to the foreground extinction affecting the J-band fluxes. One must estimate the interstellar extinction toward each source in order to correct the observed J-band fluxes. We have used the observed near-IR colors to estimate the J-band extinction. The (J-H) color excess is most suitable for this purpose (e.g. Greene et al. 1994) since the dispersion in the intrinsic (J-H) colors of CTTSs is small and observationally well determined (cf. Strom et al. 1989; Meyer et al. 1997).

The reddening law quoted by Cohen et al. (1981), which is determined for the standard CIT system, should be applicable to the JHK photometry of Barsony et al. (1997). We have thus used:

$$A_V = 9.09\times [(J-H)-(J-H)_0]$$ (1)

when the (J-H) color is available, and

$$A_V = 15.4\times [(H-K)-(H-K)_0]$$ (2)

otherwise, where we have adopted (J-H)₀ = 0.85, and (H-K)₀ = 0.55 from the CTTS results of Meyer et al. (1997). The dereddened J₀ magnitude is then obtained as $J_{0} = J-0.265\times A_V$, or $H_{0} = H-0.155\times A_V$ for those stars not detected in J (with A_V estimated from H-K). The dereddened J₀ (or H₀) can then be converted into an absolute J-band (H-band) magnitude, M_J (M_H), via the distance modulus of the ${\rho}$ Ophiuchi cloud equal to 5.73 (for d = 140 pc).

The uncertainties on M_J and M_H result from the typical uncertainties on the J, H, Kmagnitudes and on the intrinsic colors (J-H)₀ and (H-K)₀. With $\sigma(J)=0.1$, $\sigma(H)\sim\sigma(K)=0.05$ (Barsony et al. 1997), and $\sigma$( (J-H)₀)$\,= 0.1$, $\sigma$( (H-K)₀)$\,= 0.2$ (Meyer et al. 1997), we obtain the following typical uncertainties: $\sigma$( M_J) = 0.39 mag, and $\sigma$( M_H) = 0.60 mag. In addition, the uncertainty on the cluster distance ( $140 \pm 10$ pc) induces a maximum systematic error of $\pm 0.15$ mag on M_J and M_H.

4.1.2 Relationship between $\mathsfsl M_{\mathsfsl J}$ and $\mathsfsl L_\star$ for young T Tauri stars

The absolute J-band magnitude M_J can be directly converted into a stellar luminosity $\mbox{$L_\star$ }$ if the effective stellar temperature $\mbox{$T_\mathrm{eff}$ }$ is known: $\log_{10}(\mbox{$L_\star$ })=1.89-0.4\times(M_{J}+BC_{J}(\mbox{$T_\mathrm{eff}$ }))$, where BC_J is the bolometric correction for the J band depending only on $\mbox{$T_\mathrm{eff}$ }$. Pre-main sequence objects in the mass range $0.1\, \lower.5ex\hbox{$\buildrel < \over \sim$ }\, M_\star\, \lower.5ex\hbox{$\buildrel < \over \sim$ }\, 2.5\, M_\odot$ are cool sub-giant stars with typical photospheric temperatures $\mbox{$T_\mathrm{eff}$ }\sim$ 2500-5500 K (e.g. Greene & Meyer 1995; D'Antona & Mazzitelli 1994). In this temperature range (0.34 dex wide), the photospheric blackbody peaks close to the J band (1.2 $\mu$m), so that the J-band bolometric correction spans only a limited range, $1\, \lower.5ex\hbox{$\buildrel < \over \sim$ }\, BC_{J}\, \lower.5ex\hbox{$\buildrel < \over \sim$ }\, 2$, corresponding to a total shift in luminosity of only 0.4 dex. Therefore, if we use a (geometrical) average value for the effective temperature, $\mbox{$T_\mathrm{eff}$ }^0 \sim 3700$ K, we should not make an error larger than $\pm 0.2$ dex on $\log_{10}(\mbox{$L_\star$ })$.

Figure 4: MJ  - log10( $\mbox{$T_\mathrm{eff}$ }$) "HR'' diagram showing the well-defined strip of the HR diagram occupied by the PMS tracks of D'Antona & Mazzitelli (1998). For MJ = 4.0 for instance, we see that log10( $\mbox{$T_\mathrm{eff}$ }$) can span a range of only $\sim$0.15 dex for stellar ages between $0.1\,$Myr and $3\,$Myr. We thus adopt the MJ  - log10( $\mbox{$T_\mathrm{eff}$ }$) linear relationship displayed as a heavy dashed line which corresponds to the conversion: $\log_{10}(\mbox{$L_\star$ }) = 1.49-0.466\times M_{J}$.

Furthermore, since bright M_J sources tend to be of earlier spectral type than faint sources, we can in fact achieve more accurate luminosity estimates. Indeed, PMS stars are predicted to lie within a well-defined strip of the HR diagram. This is illustrated in Fig. 4 which displays model evolutionary tracks and isochrones from D'Antona & Mazzitelli (1998) on a M_J-log $_{10}(\mbox{$T_\mathrm{eff}$ })$ diagram for PMS stars with ages between $0.1\,$Myr and $3\,$Myr. We have used the compilations of Hartigan et al. (1994), Kenyon & Hartmann (1995), and Wilking et al. (1999) to derive an approximate linear interpolation for BC_J: $BC_J = 1.65+3.0\times$log₁₀( $3700/\mbox{$T_\mathrm{eff}$ }$). Figure 4 shows that, for a given observed value of M_J, the possible range of log₁₀( $\mbox{$T_\mathrm{eff}$ }$) is reduced to less than $\sim$0.15 dex, inducing a maximum error of $\pm 23\,$% ($\pm 0.09$ dex) on $\mbox{$L_\star$ }$. Based on Fig. 4, we have adopted a linear relationship between M_J and $\mbox{$T_\mathrm{eff}$ }$: log $(\mbox{$T_\mathrm{eff}$ }/3700) = -0.055\times (M_{J}-4.0)$(see the heavy dashed line in Fig. 4). This leads to the following $\mbox{$L_\star$ }-M_J$ conversion:

$$\log_{10}(\mbox{$L_\star$ }) = 1.49-0.466\times M_{J}. \hspace{0.7cm}$$ (3)

The uncertainty resulting from this conversion should be on the order of 0.045 dex for $0.01 \le \mbox{$L_\star$ }\le 10.0\,L_\odot$. We therefore estimate that the total uncertainty on $\log_{10}(\mbox{$L_\star$ })$ is $\sigma$( $\log_{10}\mbox{$L_\star$ }$) $= (0.045^2+(0.466\times\sigma$( M_J) )²)^1/2= 0.19 dex.

The $\mbox{$L_\star$ }-M_J$ conversion described above cannot be applied to sources undetected in the J band. Instead, we use the H-band magnitude, along with the extinction estimate derived from the (H-K) color, but with the additional complication that the circumstellar (disk) emission cannot be neglected. Meyer et al. (1997) found that the H-band circumstellar excess is on the order of 20% of the stellar flux, on average, for the Taurus CTTS sample of Strom et al. (1989) (for a $\mbox{$\rho$ ~Ophiuchi}$ sample, see Greene & Lada 1996). This excess, expressed as a veiling index $r_{H} = F_{\nu_{\rm exc}}^H /F_{\nu_{\star}}^{H}$ (e.g. Greene & Meyer 1995), is equal to $\sim$0.2. Accordingly, we have applied a systematic correction $\delta$H  $=\,-2.5\,\log_{10}(1+r_{H}) \sim 0.2$ mag. The $\mbox{$L_\star$ }- M_{H}$ relationship obtained in a way similar to the J-band relation is then:

$$\log_{10}(\mbox{$L_\star$ })=1.26-0.477\times (M_{H}+0.2).$$ (4)

The total uncertainty on $\log_{10}(\mbox{$L_\star$ })$ derived from M_H is then $\sigma$( $\log_{10}\mbox{$L_\star$ }$) $= (0.045^2+(0.477\times\sigma$( M_H) )²)^1/2= 0.29 dex.

This method can also be applied to Class III YSOs, using different values for (J-H)₀ and (H-K)₀. We have derived $\mbox{$L_\star$ }$for all Class III YSOs using the following relationships: $A_V = 9.09 \times [(J-H)-0.6]$, or $A_V = 15.4 \times [(H-K)-0.15]$; and log $(\mbox{$L_\star$ }) = 1.49-0.466 \times (J-0.265 \times A_V-5.73)$, or log $(\mbox{$L_\star$ }) = 1.26-0.477 \times (H-0.155 \times A_V-5.73)$ (the H-band IR excess for Class III YSOs is negligible).

The resulting M_J, M_H, A_V, and $\mbox{$L_\star$ }$ estimates are listed in Table 3 for Class II YSOs, and in Tables 4 and 5 for Class III YSOs.

4.2 Disk luminosities for Class II YSOs

Since the SED of an embedded Class II YSO peaks in the mid-IR range, the ISOCAM fluxes should be approximately valid tracers of the total, bolometric luminosities ( $\mbox{$L_\mathrm{bol}$ }$). To estimate $\mbox{$L_\mathrm{bol}$ }$ for weak Class II sources, an empirical approach thus consists in using this $F_\nu^\mathrm{MIR}$- $\mbox{$L_\mathrm{bol}$ }$ relationship after proper calibration on a sub-sample of (brighter) objects for which the luminosity can be derived by a more direct method. This approach has been adopted by, e.g., Olofsson et al. (1999). Here, we have used the $\mbox{$L_\star$ }$ estimates of Sect. 4.1 to check that a correlation is actually present between $\mbox{$L_\star$ }$ and the mid-IR fluxes. Figure 5 displays $\mbox{$F_\nu^{14.3}$ }$ (corrected for extinction) as a function of $\mbox{$L_\star$ }$ for the 104 Class II sources detected both in the near-IR and in the mid-IR range.

Figure 5: Correlation between $\mbox{$F_\nu^{14.3}$ }$ (corrected for interstellar extinction with $A_{14.3}=0.03\times\mbox{$A_V$ }$) and $\mbox{$L_\star$ }$. The observations are compared with a purely reprocessing disk model with $\mbox{$L_\mathrm{disk}$ }=0.25\times\mbox{$L_\star$ }$ and a stellar contribution given by Eq. (6). The continuous line corresponds to an average disk inclination ( $i = 60\hbox {$^\circ $ }$), while the dotted and dashed lines correspond to more extreme inclinations ( $i = 0\hbox {$^\circ $ }$ and $i = 85\hbox {$^\circ $ }$).

A correlation is found, showing that, despite some scatter, the ISOCAM fluxes can be used to give rough estimates of the stellar luminosities of Class II YSOs. This is useful for the few ISOCAM sources of our sample which have not been detected at near-IR wavelengths.

The mid-IR emission of Class II YSOs is usually interpreted as arising from warm dust in an optically thick circumstellar disk. Using a simplified disk model (e.g. Beckwith et al. 1990), it is easy to show that any observed monochromatic flux in the optically thick, power-law range of the disk SED is simply proportional to the total disk luminosity $\mbox{$L_\mathrm{disk}$ }$ divided by the projection factor cos(i), where i is the disk inclination angle to the line of sight. In the Beckwith et al. (1990) model, the disk is parameterized by a power-law temperature profile with three free parameters, T₀, r₀, and q, such that: $T(r) = T_0 \times (r/r_0)^{-q}$. Here, we have adopted T₀ = 1500 K, meaning that the disk inner radius is at the dust sublimation temperature, and q=2/3, corresponding to an IR spectral index $\mbox{$\alpha_\mathrm{IR}$ }=2/q-4=-1.0$ typical of CTTS spectra.

We must, however, account for the fact that the stellar emission itself is not completely negligible in the mid-IR bands, especially at 6.7 $\mu$m. A simple blackbody emission at $T_\star=3700$ K gives

$$F_{\nu\hspace{0.1cm}\star}^{\,\,\,6.7}=0.082\times(\mbox{$L_\star$ }/1\,L_\odot)\,\,\mathrm{Jy}$$ (5)

$$\mbox{$F_{\nu\hspace{0.1cm}\star}^{14.3}$ }=0.021\times(\mbox{$L_\star$ }/1\,L_\odot)\,\,\mathrm{Jy}.$$ (6)

Since $\mbox{$F_{\nu\hspace{0.1cm}\star}^{14.3}$ }$ is significantly smaller than $\mbox{$F_{\nu\hspace{0.1cm}\star}^{6.7}$ }$, only $\mbox{$F_\nu^{14.3}$ }$ is used to estimate $\mbox{$L_\mathrm{disk}$ }$. Assuming cos(i)=0.5 ( $i = 60\hbox {$^\circ $ }$) in all cases, we have computed $\mbox{$L_\mathrm{disk}$ }$ for each of the Class II YSOs with $\mbox{$L_\star$ }$ and $\mbox{$A_V$ }$ estimates from Sect. 4.1, based on the following relationship:

$$\mbox{$L_\mathrm{disk}$ }/1\,L_\odot = (\mbox{$F_\nu^{14.3}$ ... ...box{$F_{\nu\hspace{0.1cm}\star}^{14.3}$ })/1.80\,\mathrm{Jy},$$ (7)

where $A_{14.3}=0.03\times\mbox{$A_V$ }$ and $\mbox{$F_{\nu\hspace{0.1cm}\star}^{14.3}$ }$ from Eq. (6). The results are given in the last column of Table 3.

According to this model, the mid-IR flux is a direct tracer of the disk luminosity, and the $F_\nu^\mathrm{MIR} - \mbox{$L_\star$ }$ correlation of Fig. 5 simply expresses that $\mbox{$L_\mathrm{disk}$ }$ correlates with $\mbox{$L_\star$ }$. The origin of $\mbox{$L_\mathrm{disk}$ }$ is either the release of gravitational energy by accretion in the disk, or the absorption/reprocessing of stellar photons by the dusty disk. In the latter case, $\mbox{$L_\mathrm{disk}$ }$ is naturally proportional to $\mbox{$L_\star$ }$. The fraction $\mbox{$L_\mathrm{disk}$ }/\mbox{$L_\star$ }$ of stellar luminosity reprocessed by the disk depends on the spatial distribution of dust. In the ideal case of an infinite, spatially flat disk, this fraction is 0.25 (Adams & Shu 1986). If the disk is flared, $\mbox{$L_\mathrm{disk}$ }/\mbox{$L_\star$ }$ is larger, while it is smaller if the disk has a inner hole. The theoretical $F_\nu^\mathrm{MIR} - \mbox{$L_\star$ }$ correlations plotted in Fig. 5 correspond to $\mbox{$L_\mathrm{disk}$ }=0.25\times\mbox{$L_\star$ }$ and to three representative inclination angles. The fact that this simple model accounts for the observed correlation quite well, suggests that the disks of most $\mbox{$\rho$ ~Ophiuchi}$ Class II YSOs are passive disks dominated by reprocessing. This is consistent with recent estimates of the disk accretion level in Taurus CTTSs (e.g. Gullbring et al. 1998). The typical disk accretion rate of a CTTS is estimated to be $10^{-8}\,\mbox{$M_\odot$ }/$yr, corresponding to an accretion luminosity $\mbox{$L_\mathrm{acc}$ }=0.025\,L_\odot$ for $\mbox{$R_\star$ }=3\,\mbox{$R_\odot$ }$ and $\mbox{$M_\star$ }= 0.25\,\mbox{$M_\odot$ }$ (i.e., $\mbox{$L_\star$ }\sim 0.25\,L_\odot$ at 1$\,$Myr). In this case, the luminosity due to reprocessing is $\sim$5 times larger than the accretion luminosity in the disk.

On the other hand, 37 sources (among a total of 104) are located above the passive disk model lines in Fig. 5. These are good candidates for having an active disk with an accretion rate typically larger than $\sim 5\times(\mbox{$L_\star$ }/0.25~L_\odot)\times10^{-8}\,\mbox{$M_\odot$ }/$yr.

Overall, we find that the median $\mbox{$L_\mathrm{disk}$ }/\mbox{$L_\star$ }$ ratio is 0.41 for the 93 Class II sources detected in the near-IR and with $\mbox{$F_\nu^{14.3}$ }>\,15\,$mJy (i.e. the completeness level derived in Sect. 2.4). Using this ratio, we have derived rough estimates of the stellar luminosities of the 15 Class II YSOs which have no near-IR photometry (see Table 3) as follows:

$$\mbox{$L_\star$ }(L_\odot) \approx \mbox{$L_\mathrm{disk}$ }/0.41$$

$$\approx (0.97\times1.6/0.41)\times (\mbox{$F_\nu^{14.3}$ }/1.8\,\mathrm{Jy}).$$ (8)

[The factor 0.97 corresponds to a typical stellar contribution of 3% at 14.3 $\mu$m, while the factor 1.6 is an average extinction correction at 14.3 $\mu$m (corresponding to $< A_V > \, = 17$ mag).]

4.3 Calorimetric luminosities for Class I sources

The most direct method of estimating the total luminosities $\mbox{$L_\mathrm{bol}$ }$ of embedded YSOs consists in integrating the observed SEDs (cf. WLY89). However, since most of the ${\rho}$ Ophiuchi Class II and Class III YSOs are deeply embedded within the cloud ( $A_V \lower.5ex\hbox{$\buildrel > \over \sim$ }10$), only a negligible fraction of their bolometric luminosity can be recovered by finite-beam IR observations (e.g. Comerón et al. 1993). We thus do not attempt to derive calorimetric estimates of $\mbox{$L_\mathrm{bol}$ }$ for these sources. In contrast, the calorimetric method is believed to be appropriate for Class I YSOs since these are self-embedded in substantial amounts of circumstellar material which re-radiate locally the absorbed luminosity (cf. WLY89 and AM94). Using our new mid-IR measurements, we have evaluated the calorimetric luminosities ( $\mbox{$L_\mathrm{cal}$ }$) of the 16 Class I YSOs observed in our survey. Only 7 of them have reliable IRAS fluxes up to 60 or 100 $\mu$m (IRS54, IRS44, GSS30, IRS43, EL29, IRS48, IRS51). For these, the median of the ratio of $\mbox{$L_\mathrm{cal}$ }$(6.7-14.3 $\mu$m) to $\mbox{$L_\mathrm{bol}$ }$ is found to be 9.8, suggesting that the typical fraction of a Class I source's luminosity radiated between 6.7 and 14.3 $\mu$m is $\sim$10%. Assuming that this ratio is representative of all Class I YSOs, we have derived estimates of $\mbox{$L_\mathrm{bol}$ }$ for the remaining 9 weaker Class I sources (i.e., CRBR85, LFAM26, LFAM1, WL12, IRS46, CRBR12, IRS67, CRBR42, WL6). These luminosities are listed in Table 2.

4.4 Luminosity function of the $\mbox{$\rho$ ~Ophiuchi}$ embedded cluster

Combining the $\mbox{$L_\star$ }$ luminosities determined in Sect.  4.1 for the sources detected in the near-IR with the $\mbox{$L_\star$ }$ estimates from $\mbox{$L_\mathrm{disk}$ }$ for the sources without near-IR measurements (Sect. 4.2), we have built a luminosity function for Class II YSOs which represents a major improvement over previous studies (see Fig. 6a). In terms of $\mbox{$L_\star$ }$, the completeness level for this population can be estimated from the $\mbox{$F_\nu^{14.3}$ }$ completeness limit derived in Sect. 2.4 ( $\mbox{$F_\nu^{14.3}$ }\sim 15\,$mJy) using Eq. (8): $\mbox{$L_\star$ }^{\rm comp} (\rm {Class II}) = 0.032\,L_\odot$. While the luminosity function previously published by Greene et al. (1994) included only 33 (bright) Class II sources and suffered from severe incompleteness below $\mbox{$L_\star$ }\sim 1-2\,L_\odot$, our present completeness level is a factor $\sim$30-50 lower. The new luminosity function shows a marked flattening in logarithmic units at $\mbox{$L_\star$ }\sim 2\,L_\odot$, well above our completeness limit. This important new feature is discussed in Sect. 5 below.

Figure 6: Luminosity functions (LF) a) for the 123 Class II YSOs (continuous histogram with statistical error bars). The function corresponding to a similar histogram shifted by half the 0.2 dex bin size is shown as a thin curve to illustrate the level of statistical fluctuations due to binning. The LF of 33 Class II sources from Greene et al. (1994) is displayed as a darker histogram (rebinned to 0.2 dex bins, and rescaled to d=140 pc for better comparison with the new LF). The typical $\pm 1\sigma$ uncertainty on the position of each bin resulting from the individual uncertainties on $\mbox{$L_\star$ }$ is indicated, along with the effect of the distance uncertainty; b) for the 16 Class I YSOs ; and c) for the sample of 55 (19 confirmed + 36 candidate) Class III sources from Tables 4 and 5. The LF of a) is shown in the background for comparison. The dashed vertical lines show the respective completeness levels.

Based on the $\mbox{$L_\mathrm{cal}$ }$ estimates of Sect. 4.3, a new bolometric luminosity function for the 16 Class I YSOs of $\mbox{$\rho$ ~Ophiuchi}$ is displayed in Fig. 6b. The associated completeness level is derived from $\mbox{$F_\nu^{6.7}$ }= 10\,$mJy and $\mbox{$F_\nu^{14.3}$ }= 15\,$mJy (Sect. 2.4) using $\mbox{$L_\mathrm{bol}$ }/\mbox{$L_\mathrm{cal}$ }$(6.7-14.3 $\mu$m)  $\approx~9.8$ (Sect. 4.3): $\mbox{$L_\star$ }^\mathrm{comp} (\rm {Class I}) = 0.017\,L_\odot$. The median $\mbox{$L_\mathrm{bol}$ }$ for Class I YSOs is $1.6\ L_\odot$, which is $\sim$8 times larger than the median $\mbox{$L_\star$ }$ of Class II YSOs ( $0.20\,L_\odot$). The luminosities of Class I YSOs span a range of two orders of magnitude between $\sim$0.1$L_\odot$ and $\sim$10$L_\odot$, which is roughly as wide as the luminosity range spanned by Class II YSOs. The comparatively large value of $\mbox{$L_\mathrm{bol}$ }$ for Class I YSOs is probably due to a dominant contribution of accretion luminosity as expected in the case of protostars.

In Fig. 6c, we plot the luminosity function of the 55 Class III sources that are located within the CS contours of Fig. 1 and for which we have enough near-IR data to derive $\mbox{$L_\star$ }$ according to the procedure described in Sect. 4.1. This sample comprises 19 confirmed Class IIIs from Table 4 together with 36 candidate Class III sources from Table 5. It might be contaminated by a few background/foreground sources but is characterized by a relatively well defined completeness luminosity. From the completeness level $\mbox{$F_\nu^{6.7}$ }= 10\,$mJy and using Eq. (5) with an average extinction correction corresponding to A_V = 17 mag, we get $\mbox{$L_\star$ }^{\rm comp} (\rm {Class III}) = 0.20\,L_\odot$, which is $\sim$6 times higher than $\mbox{$L_\star$ }^{\rm comp} (\rm {Class II})$. Deep X-ray observations with XMM should improve the completeness luminosity for Class III YSOs by an order of magnitude in the near future (cf. discussion by Grosso et al. 2000 in a companion paper).