7 Conclusions

We have used ISOCAM to survey the $\mbox{$\rho$ ~Ophiuchi}$ main cloud for embedded YSOs down to a completeness level of $\sim$10-15 mJy at 6.7$\,\mu$m and 14.3$\,\mu$m. Our main findings are as follows:

1.

A total of 425 point sources are detected in the $\sim$0.7 deg² field covered by the survey, of which 211 are seen at both 6.7$\,\mu$m and 14.3$\,\mu$m. The observed distribution of the flux density ratio $\mbox{$F_\nu^{14.3}$ }/\mbox{$F_\nu^{6.7}$ }$ is clearly bimodal with a gap separating two distinct groups of sources: a "red'' group corresponding to Class I and Class II YSOs with optically thick mid-IR excesses, and a "blue'' group consisting of Class III YSOs and background stars (cf. Fig. 3);

2.

The red group consists of 139 cluster members, 71 of them being newly identified YSOs. Based on their mid-IR colors from 2$\,\mu$m to $6.7\,\mu$m and $14.3\,\mu$m, essentially all of these new YSOs are low-luminosity Class II objects. This brings the total number of Class II members to 123, a factor of 2 larger than previously known. Only 50% of these Class II sources have a near-IR excess large enough to be recognizable in a near-IR color-color diagram;

3.

Combining near-IR data from Barsony et al. (1997) with our mid-IR photometry, we derive stellar luminosities for 123 Class II and 74 Class III YSOs. We also estimate bolometric luminosities for 16 Class I objects. The corresponding luminosity functions (Fig. 6) are complete down to $\sim$ $0.02\,L_\odot$, $\sim$ $0.03\,L_\odot$, and $\sim$ $0.2\,L_\odot$ for Class I, Class II, and Class III objects, respectively. The luminosity function of Class II YSOs is essentially flat (in logarithmic units) below $\sim$ $2\,L_\odot$, with a possible peak at $1.5\,L_\odot$ and dip at $0.5\,L_\odot$ seen in the four sub-regions Oph A, Oph B, Oph EF, and L1689S (Fig. 9);

4.

The large proportion of Class II objects observed above the completeness level for Class III sources ( $\mbox{$M_\star$ }\sim 0.2\,\mbox{$M_\odot$ }$) suggests that more than 50% of the $\mbox{$\rho$ ~Ophiuchi}$ embedded YSO population have optically thick circumstellar disks at mid-IR wavelengths. In a majority of cases, the luminosities of these disks are consistent with pure reprocessing of stellar light. Only $\sim$35% of the Class II objects have excess mid-IR luminosities suggestive of substantial disk accretion rates.

5.

The luminosity function of Class II objects is well modeled by a population of PMS stars with ages in the range $\sim$0.3-2 Myr and a roughly flat mass distribution below $\mbox{$M_\mathrm{flat}$ }\sim 0.5\,\mbox{$M_\odot$ }$, i.e., dN/d$\,$log $\mbox{$M_\star$ }\propto \mbox{$M_\star$ }^{-0.15}$ down to $\sim$ $0.06\,\mbox{$M_\odot$ }$;

6.

Pending the results of a deep X-ray census of Class III objects, we argue that the mass distribution of Class II YSOs is representative of the emergent IMF of the embedded cluster. If we account for the presence of unresolved binaries, this emergent mass function is well described by a two-segment power law with a low-mass index $\alpha_1 = -0.35 \pm 0.25$, a high-mass index $\alpha_2 = -1.7$, and a transition mass $\mbox{$M_\mathrm{flat}$ }=0.55\pm0.25\,\mbox{$M_\odot$ }$(where dN/d$\,$log $\mbox{$M_\star$ }\propto \mbox{$M_\star$ }^{\alpha}$). We find no evidence for a sharp turnover at low masses down to at least $\sim$ $0.06\,\mbox{$M_\odot$ }$;

7.

The shape of the mass function for Class II systems is statistically indistinguishable from the mass spectrum determined at 1.3$\,$mm by Motte et al. (1998) for the pre-stellar condensations of the protocluster. This supports the conclusion of these authors that the IMF may be primarily determined by fragmentation at the pre-stellar stage of star formation. It also suggests that the 1.3$\,$mm protocluster condensations should form stars/systems with an efficiency larger than $\sim$50-70%.

Acknowledgements

S.B. was supported by an ESA Research Fellowship during his stay at the Stockholm Observatory. The authors thank the referee, Andrea Moneti, for constructive criticisms.