5 Discussion

5.1 Structure of protostellar envelopes and comparison with collapse models

The millimeter continuum maps and radial profiles presented in Sects. 3 and 4 allow us to test, in Sect. 5.1.2 below, several theoretical predictions which we first summarize in Sect. 5.1.1.

5.1.1 Detailed model predictions

In the self-similar collapse theory of Shu and co-workers, the instantaneous structure of a protostellar dense core is primarily determined by the position of the expansion wavefront (see Sect. 1). For a typical cloud temperature $\mbox{$T_{\mbox{\tiny cloud}}$ }\approx 10\$K (e.g. Myers & Benson 1983), the isothermal sound speed is $\mbox{$a_{\mbox{\tiny s}}$ }= \sqrt{\displaystyle\frac{k_{\rm B}\, \mbox{$T_{\m... ...d}}$ }}{\mu\, \mbox{$m_{\mbox{\tiny H}}$ }}} \simeq 0.19\ {\mbox{km s$^{-1}$ }}$ (where $k_{\rm B}$ is the Boltzman constant, $\mu = 2.33$ the mean molecular weight, and $\mbox{$m_{\mbox{\tiny H}}$ }$the mass of atomic hydrogen). At the distance of the Taurus cloud, the head of the expansion wave should be located at angular radii $\theta_{\rm inf}\sim 3\hbox{$^{\prime\prime}$ }$, $\sim$ $30\hbox{$^{\prime\prime}$ }$ and $\sim$ $5\hbox{$^\prime$ }$, when t=10⁴ yr, t=10⁵ yr, and t=10⁶ yr, respectively. A power-law density profile of the form $\rho(r)\propto r^{-p}$ is expected, with $p \approx 1.5$ inside the expansion wavefront, and $p \approx 2$ further out. More generally, the work of Whitworth & Summers (1985) shows that, during the protostellar phase (i.e., $t \geq 0$), all isothermal similarity solutions converge at small radii toward a free-fall density profile of the type $\rho (r,t) = \frac{1}{4\pi} \, (\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }/2G)^{1/2} \: r^{-3/2} \: t^{-1/2}$, where $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }= w_0\, \mbox{$a_{\mbox{\tiny s}}$ }^3 / G$ is the accretion rate with w₀ ranging from 0.975 for the Shu case to $\sim$47 for the Larson-Penston case.

Hence, in all self-similar isothermal models, the mass enclosed within a given radius of the infall envelope should roughly scale as $\mbox{$M_{\mbox{\tiny env}}$ }(r < R) \propto t^{-1/2}$, where t is the age of the central protostar (i.e., the time elapsed since point mass formation). When the sound speed is $\mbox{$a_{\mbox{\tiny s}}$ }= 0.19\ {\mbox{km s$^{-1}$ }}$, the envelope masses predicted by the Shu model are: $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200, t\rm = 10^4\rm\, yr\rm )\simeq 0.35~\mbox{$M_\odot$ }$, $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200, t\rm = 10^5\rm\, yr\rm )\simeq 0.19~\mbox{$M_\odot$ }$, and $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200, t\rm = 10^6\rm\, yr\rm )\simeq 0.03~\mbox{$M_\odot$ }$ (see e.g. Fig. 5a). For t > 0, the envelope masses are expected to be a factor $\sim$7 larger in the Larson-Penston solution than in the Shu model. For comparison, at point mass formation (t=0), the mass enclosed by the (static) SIS at $\mbox{$T_{\mbox{\tiny cloud}}$ }=10\$K is $M_{\mbox{\tiny SIS}}(r<R\rm ) = \frac{2\:a^2}{G} \: R \simeq 0.37~\mbox{$M_\odot$ }$ for $R=4\,200\rm\ AU$, while the mass enclosed by the (dynamic) Larson-Penston flow is $\sim$4.4 times larger. In the magnetized case, a similar overdensity factor exists between the dynamical similarity solution of Contopoulos et al. (1998) around t = 0 and the (equilibrium) singular isothermal magnetic disk (see discussion in Basu 1998). When the collapse initial conditions are not self-similar but correspond to pressure-truncated Bonnor-Ebert isothermal spheres, the (inner) density profile is expected to approach that of the Larson-Penston similarity solution near point mass formation ( $t \lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }0$) but to relax toward the Shu density profile at later times, until the expansion wavefront reaches the finite outer radius of the cloud core (see Foster & Chevalier 1993).

In the alternative, non-isothermal description of the collapse by McLaughlin & Pudritz (1996, 1997), based on a logotropic equation of state of the type $P/P_{\rm c} = 1 + A\,$ln $(\rho/\rho_{\rm c})$(where $A \sim 0.2$, and $P_{\rm c}$ and $\rho_{\rm c}$ are the central values of the pressure and density), the initial conditions are taken to be a singular logotropic sphere with $\rho(r) = (A P_{\rm c}/2\pi G)^{1/2}r^{-1}$, truncated by external pressure at some outer radius $\mbox{$R_{\mbox{\tiny out}}$ }$. When the collapse of such a logotrope is initiated (by, e.g., a small increase in external pressure), the density distribution also approaches a free-fall $\rho(r) \propto r^{-1.5}$power-law inside the head of the expansion wave. The envelope mass enclosed within $R = 4\,200$ AU remains essentially constant during a first "redistribution'' phase. For a critical logotrope of total mass $M_{\mbox{\tiny tot}} \sim 92~\mbox{$M_\odot$ }$ and outer radius $\mbox{$R_{\mbox{\tiny out}}$ }\simeq 19\,000$ AU, this phase lasts for approximately 10⁶ yr and the enclosed mass is $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200, t\rm = 0-10^6\rm\ yr\rm )\simeq 0.15~\mbox{$M_\odot$ }$, assuming the nominal parameters adopted by McLaughlin & Pudritz (i.e., $\mbox{$T_{\mbox{\tiny cloud}}$ }=10\$K and a surface pressure $P_{\rm s} = 1.3~10^{5} \times k_{\rm B}~\cm3~\mbox{K}$). Thereafter, the stellar mass increases roughly as $\mbox{$M_\star$ }(t) \propto t^4$ and the envelope mass decreases accordingly [ $\mbox{$M_{\mbox{\tiny env}}$ }(t)=M_{\mbox{\tiny tot}}-\mbox{$M_\star$ }(t)$], until all the mass has been accreted and the accretion phase is terminated at $t\simeq 2.5~10^6$ yr. The accretion history predicted by this model is thus very different from that of the Shu et al. model.

5.1.2 Comparison with observations

Given observational uncertainties, the power-law density structure derived in Sect. 4 for the envelopes of bona-fide protostars in Taurus and Bok globules [ $\rho(r)\propto r^{-p}$ with $p \simeq 1.5-2$] is consistent with that expected for either a SIS (p = 2) or a free-fall configuration (p = 1.5). In the context of the standard protostellar model, the median circumstellar mass $\overline{\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }0.074~\mbox{$M_\odot$ }$ estimated for our complete sample of Taurus candidate protostars corresponds to a collapse age of $t\lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }3~10^5$ yr. This value is in rough agreement with the typical lifetime inferred for Taurus Class I sources based on statistical arguments ( $t \simeq 1-2~10^5\$yr - see, e.g., KHSS90). Furthermore, the median envelope mass of the "bona-fide'' Class I/0 protostars of Taurus, $\overline{\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }}\sim 0.28\ \mbox{$M_\odot$ }$, is within a factor of $\lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }2$ of $M_{\mbox{\tiny SIS}}(r<4\,200\, \rm AU)$, suggesting that these objects are still well into the main accretion phase with estimated collapse ages $t \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }5~10^4$ yr. By contrast, the median mass measured for the 11 undetected or unresolved Class I sources of Taurus (see e.g. Fig. 3g), is very low ( $\overline{\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }} < 0.01\ \mbox{$M_\odot$ }$), and corresponds to a very old collapse age $t\lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }9~10^6$ yr. This is much longer than the estimated lifetime of the protostellar embedded phase, implying that the peculiar Class I sources cannot be genuine protostars. Altogether, except perhaps for these peculiar sources (see also Sect. 5.2.1 below), our Taurus results are in fairly good agreement with the predictions of the standard collapse model.

On the other hand, the envelopes of Class 0 protostars in both Perseus and isolated globules tend to be a factor of $\sim$2 to $\sim$12 more massive than is predicted by the standard model, even if very young collapse ages are assumed: $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }\simeq 0.6-5\ \mbox{$M_\odot$ }$ is measured, while a maximum of $M_{\mbox{\tiny SIS}}(\r4200)\simeq 0.4\ \mbox{$M_\odot$ }$ is expected. As the gas temperature in the initial cloud core cannot be much larger than 10 K (e.g. Ladd et al. 1994), such large masses cannot be explained in the SIS picture unless non-thermal sources of support are included. A factor of $\sim$2 increase in mass can be accommodated by the standard model if a significant (static) magnetic field is present (e.g. Li & Shu 1996). In principle, turbulence may also contribute to the support of the initial dense core (e.g. Myers & Fuller 1992). However, the small-scale condensations or "kernels'' corresponding to the progenitors of protostars in star-forming clusters (e.g. MAN98) appear to be essentially "coherent'', i.e., largely devoid of turbulence (Goodman et al. 1998; Myers 1998; Belloche et al. 2001). We conclude that variants of the standard model can probably account for the masses measured in most Bok globules but are clearly insufficient to explain the $> 1.5\ \mbox{$M_\odot$ }$ envelopes observed toward L1157-MM and the Class 0 objects of Perseus. The most likely explanation in the latter cases is that the collapse started from non-singular initial conditions, resulting in a nonequilibrium density configuration similar to the Larson-Penston flow near point mass formation (see Sect. 5.1.1 above). Such a conclusion, which is consistent with the large accretion/ejection rates inferred for Perseus Class 0 objects (Bontemps et al. 1996 - hereafter BATC96), could be tested if direct observational constraints on the infall velocity field of these sources are obtained: large infall velocities are indeed expected.

In contrast to isothermal models, the logotropic model of McLaughlin & Pudritz (1997) accounts only marginally for our Taurus results: the radial density structure we observe ( $p \simeq 1.5-2$) is somewhat steeper than the predictions (i.e., p=0.5-1.5). The disagreement is most serious for the Taurus YSOs with the most massive envelopes, namely the young Class 0 objects IRAM 04191, K04166, and L1527, which have $p= (1.8-2.2)\pm 0.5$, while p=0.5-1 is expected at $t \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ } 10^6$ yr in this model. Moreover, the envelope mass predicted by the nominal critical model of McLaughlin & Pudritz during the collapse [ $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200) \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }0.15\ \mbox{$M_\odot$ }$ at most] is significantly lower than that implied by our observations in both Taurus and isolated globules. The case of B335 is discussed by McLaughlin & Pudritz (1997) who conclude that this object may correspond to a $1\ \mbox{$M_\odot$ }$collapsing logotrope at the end of its accretion phase. However, our measurements of the envelope mass [ $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }\simeq 0.9\ \mbox{$M_\odot$ }$] and power-law density index [ $p=2.2\pm 0.4$] are not consistent with such a model which predicts $\mbox{$M_{\mbox{\tiny env}}$ }(\r4200)\ll 0.034\ \mbox{$M_\odot$ }$ and p=1.5.

Furthermore, none of the low-mass pre-stellar cores studied in detail up to now has a density structure consistent with a pressure-truncated logotrope (Bacmann et al. 2000).

5.2 Protostellar evolution in Taurus-Auriga

5.2.1 The ${\mathsfsl M}_{\mathsf {env}} - {\mathsfsl L}_{\mathsf {bol}}$ evolutionary diagram

As shown by AM94 and Saraceno et al. (1996), the envelope mass ( $\mbox{$M_{\mbox{\tiny env}}$ }$) vs. bolometric luminosity ( $\mbox{$L_{\mbox{\tiny bol}}$ }$) diagram can be used as a practical evolutionary diagram for embedded YSOs. While $\mbox{$M_{\mbox{\tiny env}}$ }$provides a measure of the mass reservoir that remains to be accreted, the bolometric luminosity $\mbox{$L_{\mbox{\tiny bol}}$ }$ may be used to estimate the mass of the central star, $\mbox{$M_\star$ }$, via plausible mass-luminosity relations for protostars (see AM94 for details). Conceptually, Class 0 protostars were defined as YSOs with $\mbox{$M_{\mbox{\tiny env}}$ }> \mbox{$M_\star$ }$ by AWB93. Because of uncertainties in, e.g., the mass-luminosity relationship, the actual observational boundary between Class 0 and Class I objects is not a well-defined border line but a border zone. The original Class 0 criterion given by AWB93, namely $\mbox{$L_{\mbox{\tiny submm}}^{\mbox{\tiny$\lambda > 350~\mu$ m}}$ }/\mbox{$L_{\mbox{\tiny bol}}$ }> 0.5\%$, is based on a linear mass-luminosity relationship (i.e., $\mbox{$M_\star$ }\propto \mbox{$L_{\mbox{\tiny bol}}$ }$, as expected if $\mbox{$L_{\mbox{\tiny bol}}$ }$ derives only from accretion onto a star with a fixed $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }/\mbox{$R_\star$ }$ ratio) and typical dust properties for converting $\mbox{$L_{\mbox{\tiny submm}}^{\mbox{\tiny$\lambda > 350~\mu$ m}}$ }$ to $\mbox{$M_{\mbox{\tiny env}}$ }$ (cf. AWB93 and AM94). In terms of the $\mbox{$M_{\mbox{\tiny env}}$ }$- $\mbox{$L_{\mbox{\tiny bol}}$ }$ diagram, this roughly corresponds to $\mbox{$M_{\mbox{\tiny env}}$ }/\mbox{$L_{\mbox{\tiny bol}}$ }> 0.1\ \mbox{$M_\odot$ }/\mbox{$L_\odot$ }$. In practice, the status of sources lying close to this formal border line is uncertain, and only YSOs with $\mbox{$L_{\mbox{\tiny submm}}^{\mbox{\tiny$\lambda > 350~\mu$ m}}$ }/\mbox{$L_{\mbox{\tiny bol}}$ }>> 0.5\%$ are considered as bona-fide Class 0 objects (see AWB2000).

Figure 5: $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }$ vs. $\mbox{$L_{\mbox{\tiny bol}}$ }$ diagram in Taurus. Bona-fide protostars are shown as (open and filled) circles (for Class 0 and Class I objects, respectively), while peculiar Class I sources are denoted by open star-like markers. The solid straight lines are two $\mbox{$M_\star$ }$- $\mbox{$L_{\mbox{\tiny bol}}$ }$relations marking the conceptual border zone between the Class 0 stage ( $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }> \mbox{$M_\star$ }$) and the Class I stage ( $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }< \mbox{$M_\star$ }$): $\mbox{$M_\star$ }\propto \mbox{$L_{\mbox{\tiny bol}}$ }$ (cf. AWB93 and AM94) and $\mbox{$M_\star$ }\propto \mbox{$L_{\mbox{\tiny bol}}$ }^{0.6}$as suggested by the time-dependent accretion scenario of the text (see also AWB2000). Two distinct sets of evolutionary tracks (solid curves) are shown, based on: a) A constant accretion rate, $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }\approx 2~10^{-6}~\mbox{$M_\odot\: \mbox{yr}^{-1}$ }$, as in the standard model. Arrows mark time steps from $t=10^4\$yr to $t=4 \times 10^5\$yr. (The dotted curves illustrate the magnitude of the observational uncertainties on $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }$.) b) A time-dependent accretion rate, $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }\propto \mbox{$M_{\mbox{\tiny env}}$ }(t)$, as described in the text. Small arrows are plotted on the tracks every 104 yr, big arrows when $50\%$ and $90\%$ of the initial core mass has been accreted

Our $\mbox{$M_{\mbox{\tiny env}}$ }$- $\mbox{$L_{\mbox{\tiny bol}}$ }$ diagram for the embedded YSOs of Taurus is displayed in Figs. 5a,b, along with two sets of evolutionary tracks. The values of $\mbox{$M_{\mbox{\tiny env}}$ }$ (from Sect. 3.2) and $\mbox{$L_{\mbox{\tiny bol}}$ }$ (from the literature) used in this diagram can be found in Tables 1 and 2, respectively. Rather than the total masses detected in the maps, we have preferred to use our estimates of the inner envelope mass, $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }$ (see Sect. 3.2). Our maps suggest that the envelopes of bona-fide protostars in Taurus have a power-law density structure up to a fairly large radius, $\mbox{$R_{\mbox{\tiny out}}$ } \sim 4\,000$-$17\,000$ AU (cf. Col. 7 of Table 4). But the total mass measured within $\mbox{$R_{\mbox{\tiny out}}$ }$, which has a median value $\overline{\mbox{$M_{\mbox{\tiny c$\star$ }}^{\mbox{\tiny\mbox{$R_{\mbox{\tiny out}}$ }}}$ }}\sim 0.83\ \mbox{$M_\odot$ }$, is unlikely to be entirely accreted by the central object. As pointed out by, e.g., Ladd et al. (1998), the outflow will probably disperse a significant fraction of this mass. Our map of the L1527 envelope, which shows some evidence for a bipolar cavity oriented along the outflow axis (Fig. 1l), is consistent with this view. As the star formation efficiency in a single isolated core is expected to be $\sim$30% on theoretical grounds (Matzner & Mckee 2000), we believe that the initial core mass within $R = 4\,200$ AU should provide a better indicator of the final stellar mass than the total core mass.

The first set of evolutionary tracks, shown in Fig. 5a, corresponds to the predictions of the standard protostellar model (e.g. Adams et al. 1987) and assumes that $\mbox{$L_{\mbox{\tiny bol}}$ }= \mbox{$L_{\mbox{\tiny acc}}$ }= (G\,\mbox{$M_\star$ }\,\mbox{$\dot{M}_{\mbox{\tiny acc}}$ })/\mbox{$R_\star$ }$, with $\mbox{$a_{\mbox{\tiny s}}$ }=0.19~{\mbox{km s$^{-1}$ }}$ (i.e., $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }\simeq 1.6~10^{-6}~\mbox{$M_\odot\: \mbox{yr}^{-1}$ }$) and $\mbox{$R_\star$ }= 3\ \mbox{$R_\odot$ }$.

The second set of evolutionary tracks (Fig. 5b) shows the predictions of the accretion scenario advocated by BATC96 and AWB2000, in which protostars form from dense cores with finite initial masses, M₀, and both the envelope mass and the accretion rate are assumed to decline exponentially with time according to $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }(t) = \mbox{$M_{\mbox{\tiny env}}$ }(t)/\tau = M_0\, \exp(-t/\tau)/\tau$, where $\tau\approx 10^5$ yr is a characteristic time. Such a decline of $\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }$ is consistent with the decrease of outflow power observed from Class 0 to Class I protostars (BATC96), and is theoretically expected in the case of non-singular collapse initial conditions (e.g. Foster & Chevalier 1993; HAB97). The tracks of Fig. 5b further assume that the observed bolometric luminosities result from a combination of accretion and stellar contributions: $\mbox{$L_{\mbox{\tiny bol}}$ }= G\mbox{$M_\star$ }\mbox{$\dot{M}_{\mbox{\tiny acc}}$ }/\mbox{$R_\star$ }+ \mbox{$L_\star$ }$, where $\mbox{$R_\star$ }(\mbox{$M_\star$ }, \mbox{$\dot{M}_{\mbox{\tiny acc}}$ }) \approx 3\, \mbox{$R_\odot$ }$ is the stellar radius and $\mbox{$L_\star$ }(\mbox{$M_\star$ }, \mbox{$\dot{M}_{\mbox{\tiny acc}}$ })$ the stellar luminosity on the birthline for PMS stars (Stahler 1988).

It can be seen that the "standard'' tracks based on the self-similar theory of Shu et al. (1987) account relatively well for the locations of the bona-fide protostars of Taurus in the $\mbox{$M_{\mbox{\tiny env}}$ }$- $\mbox{$L_{\mbox{\tiny bol}}$ }$ diagram (see Fig. 5a). Furthermore, there is a good continuity between Class 0 and (bona-fide) Class I objects: In regions of isolated star formation, Class 0 objects (open circles in Fig. 5a) may merely correspond to extreme versions of bona-fide Class I sources (filled circles). A similar conclusion was reached by HAB97 based on a discussion of the outflow properties (see Fig. 10 of HAB97). In this respect, it is noteworthy that more than half of the bona-fide Class I sources of Fig. 5 lie above the solid straight lines marking the border zone between $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }> \mbox{$M_\star$ }$ and $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }< \mbox{$M_\star$ }$ in the diagram: They match the conceptual definition of the Class 0 stage given by AWB93 (see above). Our observations are thus consistent with the idea that all of the bona-fide Class 0 and Class I objects of Fig. 5 are in the main accretion phase of YSO evolution.

Despite this reasonably good agreement, two problems should be pointed out. First, as noticed by Kenyon et al. (1993a, hereafter KCH93) and summarized by Hartmann (1998), the accretion luminosities predicted by the standard model tend to be larger than the observed bolometric luminosities by up to an order of magnitude: the luminosity predicted at a typical collapse age of $\sim$2 10⁵ yr is $\mbox{$L_{\mbox{\tiny acc}}$ }\sim 5\, \mbox{$L_\odot$ }$, while the median Class I/0 luminosity in our sample is $\overline{\mbox{$L_{\mbox{\tiny bol}}$ }} \sim 0.8\, \mbox{$L_\odot$ }$. This discrepancy is quite severe even though it can be reduced by a factor of $\lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }2$ if non-spherical accretion effects and wind driving are properly taken into account (cf. Shu et al. 1996). The solution proposed by KCH93 is that envelope material does not fall directly onto the central star but piles up in a disk whose radius is substantially larger than the stellar radius, thereby reducing the infall luminosity. It remains to be seen, however, whether short episodes of high disk accretion ("FU Ori'' outbursts) can be made frequent enough to maintain $M_{\rm disk} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }0.1\, \mbox{$M_\odot$ }$ throughout the embedded phase, as measured by millimeter interferometers (e.g. Terebey et al. 1993; Looney et al. 2000).

A second problem with the evolutionary tracks of the standard model is that they do not account for the properties of the peculiar Class I sources identified here (open star markers in Fig. 5a). In spite of their Class I infrared SEDs (Adams et al. 1987; KCH93) and low bolometric temperatures ( $\overline{\mbox{$T_{\mbox{\tiny bol}}$ }}=350$ K according to Chen et al. 1995), these objects cannot be interpreted as accreting protostars in the framework of the inside-out collapse model. Possible interpretations are given in Sect. 5.2.3 below.

The tracks assuming an exponential decrease in the rate of envelope dissipation with time (Fig. 5b) explain the luminosities of the bona-fide Class 0/I protostars better than do the standard tracks (see also HAB97 and Myers et al. 1998), and account even marginally for the locations of the peculiar Class I sources.

Although obviously idealized, this time-dependent accretion scenario hints that the peculiar Class I sources may correspond to low-mass objects at the very end of the protostellar accretion phase. In this view, they would be the descendants of the lowest mass bona-fide protostars of Fig. 5. Physically, an exponential termination of the accretion phase may result from the finite mass reservoir available in the initial pre-collapse core. Indeed, our 1.3 mm continuum maps suggest that, even in Taurus, the initial core is bounded with $\mbox{$R_{\mbox{\tiny out}}$ }\lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }10\,000$AU (see, e.g., Fig. 3f). When the collapse expansion wave reaches $\mbox{$R_{\mbox{\tiny out}}$ }$ (which occurs at $t = \mbox{$R_{\mbox{\tiny out}}$ }/\mbox{$a_{\mbox{\tiny s}}$ }\lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }2.5~10^5\$yr in the standard picture), the circumstellar evolution is likely to change drastically in character: the central YSO should enter a phase of residual accretion and its remnant envelope may be quickly dispersed by the outflow. The peculiar Class I sources may be representative of this late accretion phase.

5.2.2 Comparison with $\rho$ Ophiuchi

For direct comparison with Fig. 5, we show in Fig. 6 the $\mbox{$M_{\mbox{\tiny env}}$ }$- $\mbox{$L_{\mbox{\tiny bol}}$ }$ diagram constructed for the self-embedded YSOs of $\rho$ Ophiuchi using data from AM94, MAN98, and Wilking et al. (1989). Since the protostars of $\rho$ Ophiuchi are surrounded by compact, finite-sized envelopes (cf. MAN98), $\mbox{$M_{\mbox{\tiny env}}$ }$ is here simply taken to be the total mass enclosed within a relatively well-defined envelope outer radius (cf. AM94). The same evolutionary tracks as in Fig. 5 are superposed. In this case, a clear contrast between Class 0 and Class I objects is apparent. The standard tracks, which would imply a continuum of protostars rather than two separate classes, do not fit the $\rho$ Oph diagram and cannot account for the observed Class I sources with $\mbox{$M_{\mbox{\tiny env}}$ }\lower.5ex\hbox{$\; \buildrel < \over \sim \;$ }0.1\, \mbox{$M_\odot$ }$ and $\mbox{$L_{\mbox{\tiny bol}}$ }\sim$ 1-2  $\mbox{$L_\odot$ }$.

On the other hand, the time-dependent accretion tracks explain all of the $\rho$ Oph objects reasonably well. It is also noteworthy that the sources are on average more luminous (by a factor $\sim$3-10) in Ophiuchus than in Taurus (see also Chen et al. 1995). This, coupled with the fact that the standard accretion scenario is satisfactory in Taurus, supports the suggestion of HAB97 (see also André 1997) that embedded YSOs follow different accretion histories in $\rho$ Ophiuchi and in Taurus. This is presumably the result of a marked difference in fragmentation lengthscale between the two clouds: $\mbox{$R_{\mbox{\tiny out}}$ }\sim 3\,000$ AU in $\rho$ Oph (cf. MAN98) versus $\mbox{$R_{\mbox{\tiny out}}$ }\lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }10\,000$ AU in Taurus (this paper).

Comparing Fig. 5 with Fig. 6, and Fig. 1 with the $\rho$ Oph 1.3 mm maps of AM94 and MAN98, we suggest that the circumstellar evolutionary state of the peculiar Class I YSOs of Taurus may be similar to that of the typical Class I sources of Ophiuchus: in both cases, only remnant, compact envelopes are present.

Figure 6: Same as Fig. 5 for the embedded YSOs of the $\rho$Ophiuchi main cloud (adapted from AM94). In this case, $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }$ is equivalent to the total envelope mass $\mbox{$M_{\mbox{\tiny env}}$ }$. Note that, in contrast to the Taurus diagram, there is a gap between Class 0 and Class I objects here

5.2.3 Nature of the unresolved Class I sources

A possible interpretation of the peculiar Class I objects is that they are in fact PMS stars seen in a particular configuration and/or environment. The very weak, if not absent, outflow activity observed toward the peculiar Class I sources (see BATC96) supports this view. First, some of these sources may be viewed through a high visual extinction due to a large inclination to the line of sight (cf. Sonnhalter et al. 1995). Existing near-infrared maps of scattered light toward K04302 show a pronounced dark lane and are indeed suggestive of a TTS surrounded by a circumstellar disk seen roughly edge-on (Padgett et al. 1999; see also Lucas & Roche 1997). Second, a PMS star with a very low envelope mass could also present a Class I SED if its disk is warped by the tidal effects of a close companion (Terquem & Bertout 1993, 1996). Possible examples of this could be M04108-B, M04295, and M04489, whose estimated extinctions are moderate and which appear point-like in near-infrared images (Kenyon et al. 1993b). Third, several sources, such as M04108-B, Elias6, and HH30-IRS, are observed on the same line of sight as diffuse cloud emission (see Col. 8 of Table 2). This may produce both substantial near-IR extinction and significant far-IR (IRAS) excess resulting in a Class I SED.

On the other hand, the near-infrared spectra observed by Greene & Lada (1996) for L1489, M04295, M04489 and M04181+2655 differ from those of T Tauri stars. If the near-IR spectroscopy scheme developped by Greene & Lada (1996) is correct, M04295, M04489 and M04181+2655 should be intermediate objects between protostars and PMS stars and L1489 should be surrounded by significant envelope material. We also note that Z04260 is not strictly point-like in our 1.3 mm data (see Fig. 11k). Furthermore, millimeter interferometric mapping of L1489 (e.g. Hogerheijde et al.1997, 1998; Ohashi 1999) reveals a $\sim$1000 AU rotating structure with possible infall motions, which is apparently different from the more compact disks typically observed in T Tauri stars (see, e.g., Dutrey et al. 1996).

Several peculiar Class I sources may thus be highly reddened PMS stars while others could be objects in transition between protostars and T Tauri stars. These sources illustrate that the interpretation of YSO SEDs is non unique and that mapping information, preferably at several wavelengths, is crucial to get at a proper physical picture (see also Miroshnichenko et al. 1999).

5.3 Cold dense fragments undetected by IRAS

As mentioned in Sect. 3, our 1.3 mm maps reveal the presence of at least seven new dense cores/condensations in the vicinity of the targeted YSOs (see Table 3). Since these cold cores do not coincide with IRAS point sources, they are good candidates for being at either the pre-stellar stage or the Class 0 protostellar stage of evolution (cf. AWB2000). One of these objects, IRAM 04191, has been studied in more detail (AMB99) and corresponds to the first clear-cut example of a Class 0 protostar in Taurus: It has a large envelope mass ( $\mbox{$M_{\mbox{\tiny env}}^{\mbox{\tiny 4200~AU}}$ }\sim 0.5\, M_\odot$), very low bolometric luminosity and bolometric temperature ( $\mbox{$L_{\mbox{\tiny bol}}$ }\sim 0.15\, L_\odot$, $\mbox{$T_{\mbox{\tiny bol}}$ }\sim 18\,$K), and features a jet-like CO outflow as well as extended infall motions. Some of the cores of Table 3 may also be associated with very young accreting protostars. On the other hand, the fact that five of these sources have flat inner intensity profiles (see Sect. 4.1 and Fig. 3h) suggests that they rather correspond to pre-stellar dense cores similar to those discussed by Ward-Thompson et al. (1994, 1999). Follow-up observations are required to assess their nature more firmly. In any event, the serendipitous discovery of these cold objects in the course of a pointed 1.3 mm mapping study of IRAS YSOs clearly emphasizes the need for deep, unbiased surveys of molecular clouds in the submillimeter band. Such surveys should soon become possible with, e.g., the Far InfraRed and Submillimeter Telescope (FIRST) of ESA.