5 General considerations on the star formation process in the S140 IRS region

5.1 The stellar population of S140 IRS

Figure 3: Color-magnitude diagram of stars in the S140 IRS region (solid dots). We have included the individual objects resolved in our speckle images; for these, no colors can be determined and we assume each component to have the same color as reported for the unresolved systems. All objects for which only K'-band magnitudes could be derived are plotted as small crosses at J-K'= 5.8. The thick solid line in the left part of the diagram shows theoretical colors and magnitudes based on the PMS models of Palla & Stahler (2000) and Bernasconi & Maeder (1996) for an age of $1 \times 10^6$ yr for masses from $0.1\,M_\odot$ to $15\,M_\odot$. Tick marks are shown for masses of 0.1, 0.4, 1, 2, 3, 4, 6, and $15\,M_\odot$. The long arrow shows the reddening path for AV = 25 mag starting at the location for a $1 \times 10^6$ yr old $1\,M_\odot$ star.

Near-infrared images (e.g. Fig. 2; see also Hodapp 1994) show a small cluster of fainter point sources around the nebulosity surrounding IRS1. It seems very likely that most of these objects are associated with the S140 star forming region for two reasons: first, the extinction of the S140 molecular cloud was estimated to be up to $A_V \sim 100$ mag based on the determination of $N({\rm C}^{18}{\rm O})$ by Minchin et al. (1995); it therefore provides an essentially opaque shield for the stellar background, and we can assume that all stars we see in this region are either foreground stars or associated with the S140 cloud. Second, the optical images of the region show only very few stars within a few arcminutes of the position of IRS1, clearly demonstrating that the foreground population cannot be very large.

Our deep J- and K'-band data offer a good opportunity to examine the stellar population of the S140 star-forming region. For this, we used DAOPHOT to locate point sources in our deep J- and K'-band images and performed aperture photometry. The central 20'' region had to be excluded from this analysis because of the extremely strong diffuse emission in the image center. In the circular region with radius 4' around IRS1, photometric data could be determined for 388 stars in the K'-band image and for 272 stars in the J-band image. The magnitudes were calibrated via observations of other regions and comparison with the corresponding magnitudes from the 2MASS catalogue. Due to the strong diffuse emission in the S140 IRS region the accuracy of the photometry is limited to $\sim$0.2 mag. Nevertheless, this is sufficiently accurate to consider the positions of the stars in the color-magnitude diagram.

Our color-magnitude diagram (CMD) is shown in Fig. 3. The comparison with the expected colors and magnitudes for pre-main sequence stars shows that our sample of K'-band sources should be complete for $1\,M_\odot$ stars suffering up to 25 mag of visual extinction (expected magnitude $K' \sim 14.4$). The number of stars for which the NIR data are consistent with being cluster members with $M \ge 1\,M_\odot$ is 39 (this includes 20 stars with K' < 12.5 for which we could only measure K'-band magnitudes.) Four out of these 39 stars, namely IRS1, IRS2, IRS3a, and IRS3b, are probably more massive than $5\,M_\odot$.

We can now compare these numbers with the expectation from the field star IMF. In the IMF representation by Scalo (1998), which has the form

   $$\frac{{\rm d}N}{{\rm d}M} \propto \left\{ \begin{array}{lcrcr... ...2.7} & \; \mbox{for} \;&1\!&< M/M_\odot <&10\end{array}\right.$$

the presence of 4 stars in the $[5 \dots 10]\,M_\odot$ range would imply a total number of 83 stars with masses between $1\,M_\odot$ and $10\,M_\odot$. The IMF representation given by Kroupa (2001) which has the form

   $$\frac{{\rm d}N}{{\rm d}M} \propto \left\{ \begin{array}{lcrcr... ...3} & \; \mbox{for} \;&0.5\!&< M/M_\odot <&10\end{array}\right.$$

would predict a total number of 48 stars in the $[1{-}10]\,M_\odot$ range. Our detection of 39 stars above $1\,M_\odot$ is lower than both predictions. However, we have to take into account that we certainly miss some fraction of low-mass members, for two main reasons: first, our photometry does not cover the central 20'' area due to extremely strong diffuse emission. Second, our sample can be expected to be complete only up to mag, while the total cloud extinction near the center is probably $A_V \approx 100$ mag. This suggests that our images probably reveal only about half of the low mass members in the cloud. Considering this, we conclude that the number of stars we see in our image is not inconsistent with the assumption that the cluster mass function follows the field star IMF.

5.2 Stellar masses versus cloud mass

We can estimate the total mass of the stars in the cluster by assuming that the mass function is the same as the field star IMF (as demonstrated above). In that case, the total mass of all stars ( $0.1 {-} 10\,M_\odot$) in the cloud would be $\sim$340$M_\odot$ based on the Scalo (1998) IMF and $\sim$240$M_\odot$ based on the Kroupa (2001) IMF.

We can estimate the total mass of the stars in the cluster in the following way: For a very conservative lower limit, we consider only the objects IRS1-IRS7. The sum of the estimated masses of these objects is $\sim$40$M_\odot$.

The mass of the gas and dust in the S140 IRS cloud has been determined in various radio and submm studies. For example, Hayashi & Murata (1992) derived a mass of $60\,M_\odot$ within a radius of r = 0.15 pc ( $\mathrel{\mathchoice {\hbox{$\widehat=$ }}{\hbox{$\widehat=$ }} {\hbox{$\scriptstyle\hat=$ }} {\hbox{$\scriptscriptstyle\hat=$ }}}$34''). Van der Tak et al. (2000) found $M =46\,M_\odot$ in r = 0.15 pc from submm maps. Bally & Lada (1983) derived a total mass of $\sim$64$M_\odot$ within r = 0.46 pc ( $\mathrel{\mathchoice {\hbox{$\widehat=$ }}{\hbox{$\widehat=$ }} {\hbox{$\scriptstyle\hat=$ }} {\hbox{$\scriptscriptstyle\hat=$ }}}$1.7') from CO observations. From these numbers one can see that the mass of the stars is considerably higher than the cloud mass.

A similar result is obtained for the center of the starforming region: Considering only the objects IRS1-IRS7, the sum of their estimated masses is $\sim$40$M_\odot$. On the other hand, the mass of the three submm cores within 25'' of IRS1 is only $\sim$29$M_\odot$ (Minchin et al. 1995).

These considerations make it quite clear that the inferred total mass in young stars exceeds the mass in gas significantly. This implies that a high fraction of the original cloud mass has been converted to stars or that the formation of a protostar leads to the escape of a much larger mass.

5.3 Cloud destruction by outflows?

In S140, there is clear evidence for the ejection of a large fraction of the cloud. Numerous outflows are found here in the warm shocked molecular gas, which reveals that even the present outflows contain sufficient thrust to eject material from the cloud. This is not surprising given that 10-30% of the mass accreting from the dense envelope around a core must be ejected into the jets observed from Class 0 protostars (e.g. Smith 2000) and the jet speed is of order 100kms^-1. The jets' thrust is thus sufficient to gravitationally unbind roughly ten times more mass than goes into the protostar. Hence, the total mass of the initial cloud out of which the stars formed may have been much larger than the sum of the star + gas mass presently found.

Given this picture, outflow activity must have influenced the cloud for its full lifetime. We could expect perhaps 100 outflows within a few million years. This would still be detectable in the CO rotational lines which contain a long-term record of outflow activity. And, indeed, the CO high-velocity gas possesses a complex distribution, consisting of numerous widely spread clumps, but bordered in the south and west by high density gas.

A problem with jet/outflow feedback scenarios is that a well collimated outflow only influences its immediate surroundings and not the cloud as a whole. It is not plausible to assert that an outflow can provide turbulent support to a cloud since turbulence decays faster than it could spread laterally, from an outflow, across a cloud given the rapid decay of turbulence found in MHD simulations (e.g. Mac Low 1999). Hence, even though the momentum inherent in the outflows may be sufficient (Yu et al. 2000), they will not be present to support the cloud as it evolves. A large number of outflows, however, distributed over space and the cloud life, may still be effective in dispersing the cloud with the following argument. If each outflow is represented as a cone with a half opening angle of just 10$^\circ$, then 103 outflows would fill the cloud volume. Hence, over the cloud lifetime, and given random outflow directions over the cloud lifetime, a large fraction of the cloud can be ejected.

In contrast, the H₂ gas is observed from hot shocks which are driven by the latest energetic outflows. Even so, we have found here evidence for several outflow directions, related to at least three outflows. The kinematic ages of the outflow have been estimated to be just a few thousand years. We suspect that the outflows are much older and penetrate far into the surrounding lower density halo where they are not detectable because of both the low density and possibly a low molecular fraction. Therefore, deep optical H$\alpha$ imaging in the NE region beyond 4' from IRS1 could reveal Herbig-Haro objects.

5.4 Triggered star formation

Triggered star formation by external compression might also lead to an enhancement of the star formation efficiency. This could also contribute to the high ratio of stellar mass versus gas mass we found above for the S140 region.

The S140 region is probably a good example for triggered star formation. A sequence of triggered star formation events in the Cepheus bubble has been suggested by Patel et al. (1998): initially, a cluster containing high-mass stars formed in a molecular cloud. The winds and the ionizing radiation of the massive stars then created an expanding shell around this cluster. Gravitational instabilities in the expanding ring lead to fragmentation, cloud collapse and the formation of a second generation of stars, which now constitute the Cep OB2 association, which has a presumed age of about 5-7 Myr. The massive stars in Cep OB2 now affect the dense gas remaining from the parent shell and seem to trigger the formation of the third generation of stars in the dense cloud cores, including S140, along the edge of the bubble (see also Ábráhám et al. 2000).

The shape of the S140 cloud strongly suggests that the gas is being compressed by external pressure from the south-west direction. One source for this compression is the B0 star HD 211880, the exciting source of the S140 HII region, at a projected distance of 2.5 pc from S140 IRS. Another factor may be the general expansion of the Cepheus bubble, the center of which is located to the south-west of the S140 cloud.

5.5 Spatial distribution of the young stellar objects

Figure 4: Radial distance distribution of the stars around IRS1. All objects with J - K' > 1.5 (corresponding to objects with strong infrared excess or suffering from at least $\sim$3 mag of visual extinction) are considered to be cluster members. In the two innermost bins our sample is incomplete due to the very strong diffuse nebulosity, hampering the detection of faint point sources.

It is interesting to consider the spatial distribution of the cluster members. In Fig. 4 we plot the number of objects with J - K' > 1.5, i.e. objects that either show strong infrared excess or suffer strong extinction and therefore can be considered cluster member candidates, in several bins of radial separation from the center. One can see that the radial distribution of these stars is more or less uniform. The interpretation of this uniform radial distribution is not fully conclusive. We could interpret the embedded stars as objects which have formed at a uniform rate within a very dense central core over the star formation lifetime of S140 and which form an expanding spherical distribution. Or, the stars formed in a rapid burst with a linear distribution of escape speeds. Such a burst, followed by dispersal of a large fraction of dense ambient material (reducing the confining gravitational force), would result in the free expansion of the young stars. A third possibility is that the stars formed in situ with an efficiency related to both the local density and the compression of a passing shock wave which would sweep up material into an inner clumpy ring, possibly as now observed in CS with a radius of 30 $^{\prime\prime}$ (Hayashi & Murata 1992). In this case, the stars could be younger. The age of the embedded stars could be tested by searching for excess H-K band emission (the H-band filter failed during the run described here).