Deep optical and near infrared imaging photometry of the Serpens cloud core

Transcription

1 Astron. Astrophys. 33, (1998) ASTRONOMY AND ASTROPHYSICS Deep optical and near infrared imaging photometry of the Serpens cloud core P. Giovannetti 1, E. Caux 1, D. Nadeau 2, and J.-L. Monin 3 1 Centre d Etude Spatiale des Rayonnements, 9 avenue du Colonel Roche, BP 4346, F-3128 Toulouse Cedex 4, France 2 Observatoire du Mont Megantic et Département de Physique, Université de Montréal, C.P. 6128, Succ. A. Montréal, H3C 3J7 Québec, Canada 3 Laboratoire d Astrophysique, Observatoire de Grenoble, Université Joseph Fourier, BP 3, F-3841 Grenoble Cedex, France Received 2 June 1997 / Accepted 2 August 1997 Abstract. We present results from a deep optical (VRI) and near infrared (JHK) survey of the central part of the Serpens molecular cloud. A total of 138 sources were detected in the 19 arcmin 2 surveyed area down to a limiting magnitude of 16.3 in K. We find that the form of the observed K Luminosity Function (KLF) of stars belonging to the Serpens Molecular cloud is consistent with that predicted from a Miller & Scalo (1979) Interstellar Mass Function (IMF). We have investigated the KLF evolution with the age of a cluster by modeling KLFs of hypothetical clusters. Our results suggest that two phases of star formation could have taken place in the Serpens core. Key words: stars: pre-main sequence ISM: open clusters: Serpens cloud stars: luminosity function infrared: stars star formation 1. Introduction The knowledge of the distribution of young stars within molecular clouds is of fundamental importance since it provides insights into the nature of star-forming mechanisms. Young Stellar Objects (YSOs) are associated with varying amounts of gas and dust and it is expected that the youngest objects will be invisible at optical wavelengths due to obscuration by opaque circumstellar dust. Therefore observations at infrared wavelengths provide one of the best methods for identifying the young stellar population within molecular clouds. In the past, infrared studies of star-forming regions were limited by the poor sensitivity of the instruments as well as their low spatial resolution. Infrared array technology has advanced considerably in the last few years, and is now at a stage allowing to survey large regions of star formation (see De Poy et al. 199, Lada et al. 1991, Zinnecker et al. 1993). An increase in spatial resolution and sensitivity almost always provides new insights into old problems. Send offprint requests to: P. Giovannetti, giova@cesr.cnes.fr Table 2 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr ( ) or via Two distinct areas need to be addressed by such data: i) the determination of which stars in any given field are members of the embedded young stellar population, i.e. separating the young Pre-Main Sequence (PMS) stars from the population of normal background/foreground main sequence and giant stars and, ii) to determine the nature (i.e. evolutionary state, age, luminosity, etc) of the derived young embedded PMS population. This second point has recently been addressed by Lada & Adams (1992) who studied the location of known classes of YSOs (i.e. classical T Tauri Stars - CTTS, Weak-line T Tauri Stars - WTTS, Herbig Ae/Be - HAEBE stars, and IR protostars: the class I sources of Lada & Wilking 1984) in near-ir colour-colour diagrams. They concluded that these relatively well-known evolutionary classes occupy different regions of the near-ir colour-colour diagram and that given the JHK photometry, the evolutionary state of PMS stars can be inferred relatively unambiguously. Star clusters are important laboratories for studying the initial luminosity function because they consist of statistically significant groups of stars who share the common heritage of forming from the same parental cloud, and they are not old enough to have lost a significant number of members due to stellar evolution or dynamical effects such as evaporation or violent relaxation (Lada & Wilking 1984, Lada et al. 1991). Moreover in these very young clusters (1 1 6 yr), low-mass stars are brighter than at any other time in their PMS evolution. At a distance of 31pc (De Lara et al. 1991), this region has received attention since Strom et al. (1976) reported a small red nebulosity, called the Serpens Object or the Serpens Reflection Nebula. Based on the more than fifty low-mass stars identified in the core by a near-infrared survey, the Serpens molecular cloud is one of the most spectacular examples of a protostellar nursery, harboring a stellar density exceeding 4 stars/pc 3 (Eiroa & Casali 1992). A Recent submillimeter continuum survey has uncovered half a dozen mm/submillimeter peaks, four of which lack an infrared counterpart (Casali et al. 1993). A low resolution CO and H 2 CO survey revealed a dense core in the dark cloud complex (Loren et al. 1979). More recently, Hurt and Barsony (1996) found several sources sharing the characteris-

2 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 991 Table 1. Log of observations in the V, R, I, J, H and K bands UT Date Tel. Band Seeing Exp. time 3σ limit (1992) ( ) (mn) mag. 6/12 CFHT V /11 CFHT R /11 CFHT I /9 CFHT J /1 CFHT H /1 ESO K tics of Class protostars, the short-lived (a few 1 4 yr) earliest protostellar stage (André, Ward-Thompson & Barsony 1993, Barsony 1994). In this paper, we present new deep optical and near-infrared observations of the Serpens cloud core using an array detector. Our results increase the number of sources detected in the central part of the cloud and allow to make a more complete census of its membership, determine the nature of its embedded members, and construct the infrared luminosity function of the cluster. To investigate the nature of the underlying mass function, we calculate models which predict the evolution of the luminosity function of a cluster of PMS stars. We compare these models with the Serpens K luminosity function to place constraints on the star formation history of this cluster and on the nature of the underlying mass function. The optical and near IR observations are presented in Sect. 2, and the results in Sect. 3. The interpretation of these results in terms of general properties of the cluster is presented and discussed in Sect. 4 and our conclusions are summarized in Sect.. 2. Observations 2.1. Optical and near infrared observations Table 1 presents the details of the observations in the six wavebands. The observations in the V, R and I bands were carried out during June 1992 at the 3.6m CFHT (Canada France Hawaii Telescope) on Mauna Kea, Hawaii, using the FOCAM instrument with the RCA CCD detector. Flat fields have been obtained in each photometric band on the sky during twilight. The CCD electronics offset was measured several times during the night. For each photometric band, various standard stars were repeatedly observed during the night. At the F/8 focus of the telescope, the CCD pixel scale was.21. The observations in the J and H bands have been obtained in November 1992, also at the CFHT, using the visitor MONICA Nicmos 3 infrared camera (Nadeau et al. 1994) at the same F/8 focus. At these wavelengths, the resolution is.2 per pixel. The observations in the K band have been obtained on September 1992 at the 2.2m telescope of the ESO observatory of La Silla, Chile, using the common-user IRAC2a CCD camera with a resolution of.49 per pixel. In the optical bands, two fields slightly overlapped were observed, surveying an area of 16 square arcminutes. In the three NIR bands, sixteen fields were observed toward the Serpens cluster, approximately covering an area of 12 square arcminutes in J and H, and 19 square arcminutes in K. These fields were arranged in a 4x4 mosaic centered on the Serpens Reflection Nebula (α 19 = 18h27m22s, δ 19 = 1 o 12 3 ). The fields were spatially overlapped by 3 in both right ascension and declination, allowing an accurate positioning of the mosaicked fields. Per image, the integration times used were of 1 minutes in the optical bands, five seconds in J and H, and two seconds in K, allowing the quoted sensitivity limits presented in Table Data analysis The NIR data were reduced by first subtracting from each data frame a median filtered sky frame obtained from five nebulosityfree frames, observed immediately before and after the target observation. The J and H band images were then flat-field and distorsion corrected with a dedicated software. Finally, the images were mosaicked together. Nominal atmospheric extinctions for Mauna Kea are J =.117, H =.67 per air mass, and nominal atmospheric extinction for ESO La Silla is K =.86 per air mass. All infrared images were air-mass corrected. Data analysis was done with standard Image Reduction and Analysis Facility (IRAF) and Interactive Data Language (IDL) routines. As a first step, several isolated stars of different intensities were chosen manually to determine the Full Width at Half Maximum (FWHM). Thus, for each image, source extraction and aperture photometry were performed using DAOPHOT (Stetson, 1987), and the routine DAOFIND was used to extract stellar-like sources whose fluxes were significantly above the background (that is, sky) noise in each image. The results were visually compared to the images at several contrast levels to ensure that spurious identifications were minimized. Such spurious detections were a problem in the area of the bright reflection nebula where probably non stellar emission knots could be interpreted as stars. We removed all these spurious sources from our data sample listed in Table 2. This led undoubtedly to the non-detection of faint sources in the area of the image where contamination from extended emission was present. In addition, sources that were not bright enough to be detected by the finding routine, but visually identified as stars, were appended to the coordinate list. Finally, the resulting images were mosaicked with an IDL routine. This routine eliminated bad pixels and adjusted the relative background level of overlapping frames to a common value. Using these procedures,, 12, 2, 44, 86 and 138 stars were found in the V, R, I, J, H and K mosaic images, respectively. Aperture photometry was performed for all the extracted stars in each image. Fluxes were determined for each star with the size of the software aperture used varying along with the brightness of the source (the brighter the source, the larger the software aperture). Sky levels were determined around each star in a -pixel wide annulus. Sky levels were also obtained for annuli with smaller inner radii and larger outer radii with no significant change in the resulting stellar fluxes. Photometry was performed manually for stars which were confused with nearby nebulos-

3 992 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core ity or other stars. For objects with associated NIR nebulosity, we considered that the true stellar flux is represented by the signal in the object aperture minus the contribution from the average sky plus nebulosity in the sky annulus. In the K band, a cross-correlation between our survey and the one of Eiroa & Casali (1992) on the brighter common sources has been used to assess α and δ coordinates of all our sources. Positions for the cluster members observed in the other wavebands were then directly derived from the K mosaic image by applying the same procedure Magnitude uncertainties and sensitivity limits For each detected source, we evaluated the magnitude uncertainty by ν = I ν + Nσ 2 ν, where I ν is the stellar flux in the source aperture calculated with N pixels, and σ ν the standard deviation of the sky annulus. Thus, the final magnitude is given by: m λ = M ± Mmax M inf 2 where M max = 2. log(i ν ν ), M inf = C 2. log(i ν + ν ), and M = C 2. log(i ν ) In order to determine the sensitivity limits, we considered a 3σ detection limit, σ being the standard deviation of the sky calculated on nebulosity- and star-free regions. A star can be approximated by a gaussian whose parameters are the position centre, the Full Width at Half Maximum along the two axes (FWHM x and FWHM y ), the stellar luminous intensity (I) and the sky level. Thus, the stellar flux is given by: F = πσ x σ y I where σ i = FWHM i /2 ln 2. In this case, I =3σand M lim = C 2. log(3f ), leading to the values quoted in Table Results Fig. 1 shows a reconstructed K image of the Serpens molecular cloud core. Black stars represent sources belonging to the cloud with their corresponding identification numbers, as quoted in Table 2 (see 3.1). Solid lines represent logarithmic contour plot of the central nebula. Filled circles correspond to the unidentified sources. Figs. 2 and 3 show the image of the Serpens Cloud Core in K and I wavebands; the scale adopted for these images is.2 per pixel Log of the sources of the survey Table 2 presents the broad-band photometric data. The number in brackets is the 3σ uncertainty on the computed magnitude as described in 2.3. Crosses correspond to the regions of the sky that were not observed in the concerned photometric band. nd corresponds to sources that were not detected. Identification numbers followed by a S as superscript correspond to Serpens Fig. 1. Reconstructed K image of the Serpens molecular cloud core. Black stars represent sources belonging to the cloud with their corresponding identification numbers. Solid lines represent logarithmic contour plot of the central nebula. Filled circles correspond to the unidentified sources. North is at the top and East to the right. cloud members. Conversions from fluxes to magnitudes were made using relations from Landolt-Bornstein (1982). Before drawing any conclusion on the distribution of near infrared sources detected by the survey, we had to distinguish the embedded sources from the background sources. K band photometry by itself will not discriminate between sources that are embedded in the cloud and sources that are background stars. Methods that have previously been employed to help in the separation of reddened background sources from the true embedded PMS stars are: i) the observation of a control field located at approximately the same galactic coordinates as the survey field but off the associated molecular cloud that contains the embedded PMS population and, ii) the use of a model that produces a table of K source counts according to galactic coordinates. However, use of these techniques does not allow to determine which particular stars in the survey field are PMS stars i.e. it is statistical in nature. Considering our survey, the number of detected sources is not large enough and such statistical methods can obviously lead to inaccurate results. The Serpens objects are identified by using the same basic criteria as those used by Eiroa and Casali (1992). (1) Stars associated with cometary or bipolar nebulae are considered as certain members of the Serpens population. (2) H α emission-line stars can also be identified as cloud members since H α emission must imply the presence of (ionized) circumstellar material. (3) PMS stars having IR excess in the near infrared colour-colour 1

4 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 993 Fig. 2. K image of the Serpens Cloud Core. North is at the top, East to the left. diagram (Rydgren & Cohen 198). In such a diagram, stars located to the right of the reddening vector followed by an A star can unambiguously be identified as Serpens cloud members The colour-colour (J-H,H-K) diagram The optical/nir photometry derived from our survey allows us to study, via colour-colour (c-c) and colour-magnitude (c-m) diagrams, the combined effects of both the intrinsic properties of the sources and the overlying extinction. Thanks to NIR photometry we can theoretically penetrate deeper into the molecular clouds, observe a much larger fraction of the embedded population and learn more about the global properties of the star formation region and its individual sources. The J-H, H-K c-c diagram presented in Fig. 4 provides a useful mean of distinguishing between the effects of interstellar reddening and IR excess. In this work, we make the assumption that the Rieke & Lebofsky (198, hereafter RL8) reddening law can be applied to the Serpens cloud and represents a reasonable approximation of the NIR extinction caused by the associated molecular cloud since a) few sources lie above the upper of the two vectors, and b) the vectors generally follow the same slope as that implied by stars of different colours. Also plotted as solid line in Fig. 4, are the locations of both unreddened main-sequence and giant stars. From the extreme points of these curves we have plotted two dashed lines representing RL8 reddening vectors. The area between these lines corresponds to the reddening zone for normal stars. The crosses located on the reddening lines are separated by distances corresponding to 1 mag of visual extinction. Open circles correspond to the Fig. 3. I image of the Serpens Cloud Core. North is at the top, East to the left. unidentified sources. Filled circles represent Serpens sources identified using criteria described in Sect It is clear from Fig. 4 that a significant fraction of the objects observed in the Serpens cloud is located between the two reddening vectors and is consistent with reddened background stars seen through the cloud. More than one third of the sources, however, lies at positions outside the reddening vectors. This region of the JHK colour-colour diagram is known as the infrared excess region (Lada & Adams 1992) and corresponds to the location of PMS stars. However, naked-t Tauri stars, post-t Tauri stars and some class I sources found in ρ Ophiuchus by Wilking & Lada (1983) do not show any NIR excess, and will be found between the two reddening vectors in such a diagram. Another interesting point that can be inferred from the diagram is that sources located in the reddening zone for normal stars are found spread along the reddening band. This indicates that the extinction caused by the cloud or by the circumstellar material is variable and can reach values up to 2 magnitudes of visual extinction. This colour-colour diagram is somehow different to that presented by Eiroa & Casali (1992) and Sogawa et al. (1997). This is not surprising since their surveys cover an area larger than our, with lower sensitivities. Thus, sources plotted on these diagrams, do not correspond exactly to the same population The colour-magnitude (K,J-K) diagram The K versus J-K colour-magnitude (c-m) diagram for all objects found in the Serpens cloud core is plotted in Fig.. In this diagram, ZAMS stars are plotted at the assumed distance

5 994 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 6 4 Serpens sources unidentified sources (J-H) K (H-K) J - K Fig. 4. The NIR colour-colour diagram. The solid line represents the locus of points occupied by unreddened main-sequence and giant stars. The short dashed lines define the reddening band for normal stars and are parallel to the reddening vector. Crosses are placed along these lines at intervals corresponding to ten magnitudes of visual extinction. Filled circles are candidates we identified to be Serpens cloud members. Open circles are unidentified stars. of the Serpens cloud i.e. 31 pc (the solid line joining the open diamonds). A representative RL8 reddening vector (A V =1 magnitudes) is plotted as an arrow and the dashed line indicates the effective detection limit of the survey. Filled circles represent the Serpens objects while open circles are the unidentified sources. With the K=16.3 detection limit, we would therefore observe unreddened and unextincted ZAMS stars down to spectral type M4 at 31 pc. Using the mass-m K relation for ZAMS shown in Zinnecker et al. (1993), this corresponds to a stellar mass of.3 M. However, PMS stars are over-luminous for their mass which would lower the effective PMS mass detection limit significantly. Zinnecker & McCaughrean (1991) present age dependent mass-luminosity functions over the range 2 1 years to years derived from homogeneous tracks calculated by I. Mazzitelli. These suggest that over this age range,.8 M PMS objects would show a relatively small change in M K from 4.9 to.3. This corresponds to a m K range of for stars in Serpens. This is over 3. magnitudes brighter than our detection limit and hence our survey would be sensitive enough to detect stars with masses less than.8 M. But these values do not take into account the extinction due to the molecular cloud. At K, the effect of extinction is however minimized and the range of A V values between -2 magnitudes (as implied by our NIR c-c diagram) could lead the embedded population to be 2.3 magnitudes fainter than the values quoted above. This would suggest that.8 M PMS stars would have m K values in the range This is still below our detection limit, Fig.. Colour-magnitude (K,J-K) diagram. Filled circles are candidates we identified to be Serpens cloud members. Open circles are unidentified stars. The continuous line shows the locus of the ZAMS stars at the distance of the Serpens cloud. A representative reddening vector is plotted as an arrow and corresponds to ten magnitudes of visual extinction. The dashed line corresponds to our 3σ-completeness limit. suggesting that we should be able to detect objects with masses significantly less than the.8 M mass limit. 4. The stellar population of the Serpens cloud While theoretical work on PMS evolution is progressing, an observational effort to understand star forming history in a cloud is needed in order to address the IMF question The luminosity functions The Initial Mass Function (IMF) is of fundamental interest to several fields of astronomy. Current estimates of the IMF are based on observations of stars in the solar neighbourhood (Salpeter 19, Scalo 1986). PMS stars undergo considerable luminosity evolution with poorly known time scales before they arrive at the zero age main sequence (ZAMS). Thus the observed luminosity function is a result of the IMF, the PMS evolution and the star forming history. The K-band luminosity function (KLF) of the identified Serpens sources and of all stars observed toward the central part of the Serpens cloud core is presented in Fig. 6. The KLF is displayed as histograms of the number of sources versus the apparent K magnitude, with a bin size of 1 mag. The comparison of the distributions shows that all sources with K<1 are Serpens objects, as well as % of the sources with K < 1. When considering only the distribution of all stars detected at K, irrespectively of their nature, we note the presence of a peak occurring at K = 1 mag and a decrease in the observed number of sources with decreasing K brightness

6 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core expected number of background sources from Casali & Wainscoat linear fit for K < 1. Serpens sources all sources 2 log N 1. 1 Fig. 6. K magnitude distribution of the identified Serpens sources and of all detected NIR sources in the field K beyond K = 1 mag. This apparent turnover is probably due to our K detection limit (K=16.3). On the other hand, the KLF of the identified Serpens sources presents a turnover beyond K=12 that is well below our K detection limit and cannot be considered as an artefact. Such a trend has been called a turnover because KLFs derived from Miller & Scalo (1979) or Salpeter (19) IMF show the number of sources increasing with decreasing K brightness. However, these KLFs were derived using a massluminosity relationship appropriate for main sequence stars. As we demonstrate in the next section, turnovers in luminosity functions are not necessarily inconsistent with Miller & Scalo (1979) or Salpeter (19) mass functions when the cluster members are not yet on the main sequence. In a study of several star forming regions, Zinnecker et al. (1993) also find and discuss similar results. We have determined the cumulative number of sources per square degree brighter than a given K magnitude detected by Casali & Wainscoat (quoted in Eiroa & Casali 1992, hereafter CW92) in a field close to Serpens (galactic coordinatesl=4, b=-4 ) and normalized to an area equal to that covered by our K image. That curve can be fitted by log N =.38K This means that around 26 sources should be detected with K<1. in the area we surveyed. However, the mean extinction of the cloud is about A V = 1 mag (Zhang et al., 1988) and, therefore, the number of sources in the line of sight to Serpens is expected to be lower. The results are presented in Fig. 7 which plots the cumulative number of sources brighter than a given K magnitude versus that magnitude. The CW92 line is plotted as a dashed line and normalized to an area equal to that covered by our K image with an extinction of A K =1.1 (equivalent to A V =1, using the RL8 standard extinction law). In the range 9 <K<1, the relation between log N and the apparent K magnitude for all sources appears linear and a least square analysis was performed on these data. The resulting fit is log N =.23K 1.36 with a correlation coefficient of.99. This linear relation is not satisfied in the case of the identified Serpens sources. The deficiency of stars with Fig. 7. Cumulative number of stars brighter than a given K magnitude. Identified Serpens sources are plotted as crosses while filled circles represent all sources detected in the field. The dashed line represents the expected number of background stars after the empirical star count survey of Casali & Wainscoat, normalized to a 19 square arcmin field. The continuous line is the least square fit in the range 9 <K<1. K>13 reflects the apparent turnover in the K-distribution of stars. This plot shows another interesting point. There is an excess of stars with K<1. with respect to the number of expected sources from the star count survey of CW92. Since the majority of these stars is related to the molecular cloud, this evidences a clustering process in Serpens KLF modeling A fundamental consequence of the theory of stellar evolution is that the life history of a star is almost entirely predetermined by its initial mass. Consequently, to understand the star formation history and the consequent luminosity evolution of an embedded population of young stars such as the one we observed, requires a detailed knowledge of both the initial distribution of stellar masses at birth and how this quantity varies through space and time. Since the stars are young, a time-dependent main sequence mass-luminosity relation must be used to determine the stellar mass. In this aim, we modeled the predicted form of the K luminosity function using Miller & Scalo (1979) IMF and theoretical PMS mass-luminosity relationships from the isochrones of D Antona & Mazzitelli (1994). Our first objective was to directly compare synthetic KLFs with observations to place constraints on the star formation history and the underlying mass function of the Serpens molecular cloud. We then evaluated the following equation: dk = d log M d log M dk (1)

7 996 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core. 3 log M (solar masses) τ = 3.1 ans a) N 3 τ = 3.1 yrs b) m k m k log M (solar masses). τ = ans c) m k N 3 3 τ = yrs d) m k Fig. 8a d. Time dependant mass-m k luminosity relation, as derived from evolutionary tracks of d Antona & Mazzitelli (1994) for.3 Myr (a) PMS stars and model 2.2µm (m k ) luminosity function for a coeval cluster of low-mass stars of.3 Myr (b). Figs. c and d: same as a and b for 2 Myr PMS stars. where d log M/dK is the slope of the mass-k luminosity relation and /d log M is the underlying stellar mass function given by the half-gaussian form of the Miller & Scalo (1979) IMF: d log M = C exp[ C 1 (log M C 2 ) 2 ] (2) where C = 16., C 1 =1.9 and C 2 = The PMS evolutionary tracks give, for each age ranging from yr to 1 8 yr, and each mass from.2 to 2. M, the effective temperature and luminosity of the star. For simplicity we considered stars as blackbodies and the luminosities were converted into K magnitude. The tracks used in our models were derived assuming Alexander et al. (1989) opacities and the Canuto and Mazzitelli (199, 1992) convection model. For statistical purposes, KLFs were constructed using intervals of one magnitude bin. We did not take into account the infrared excess emission and we assumed that our PMS stars were diskless. In any case, the infrared excess present in some of the objects we observed is smaller than the bin size of the observed and modeled KLFs Comparison of models with the observations In Fig. 8a and 8c, we have plotted the mass-m k luminosity relation that we used at two different ages (.3 and 2 Myr.), while Fig. 8b and 8d show the corresponding KLFs for a coeval cluster of low-mass stars. As pointed out by Zinnecker et al. (1993), features as peaks in the KLF are strongly correlated to the sharp inflection at the corresponding point in the mass-k luminosity relation. This point of inflection is due to the deuterium burning in the contracting PMS star and it is seen to move towards lower masses as the cluster ages. A physical interpretation of this phenomenon is that while deuterium is burning strongly in a star of given mass, D-burning is ending in higher mass stars and has yet to begin in stars of lower masses, for a sample of stars born at the same time. This leads to an increase in the value of d log M/dK and a peak in the luminosity function at the corresponding K magnitude. That is why features and turnovers in KLFs are not necessarily due to features in the IMF; rather they may often reflect the complex process of PMS evolution. The modeled KLFs were compared to the KLF observed for the Serpens molecular cloud. None of the coeval models fits the shape of the observed KLF in a satisfactory way. This led us to construct KLFs for clusters of different ages and to compare the resulting KLF with the observations. The best fit to the data is obtained with two bursts of star formation at different epochs. One is 1 yr old, the other is around 3 Myr old. Fig. 9 presents histograms of the model KLF superimposed on the observed KLF for the identified Serpens sources, normalized to 1 stars. To attempt to account for the effects of uniform foreground extinction, we extincted our models by 1. mag at K, which introduced a shift in the model KLF toward larger magnitudes, without changing its shape. We can note some differences between the two curves, but the general shape, the location and the intensity of the peak of the observed luminosity function are quite well reproduced by the model. However, these results are

8 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 997 number of sources observed KLF model KLF / dlogm Eq. 3 Eq. 4 Eq. - C 1 =1. Eq. - C 1 = M (solar masses) apparent K magnitude Fig. 1. IMFs resulting from Eq. 3 to Eq.. For log M>C 2, Eq. 3 and Eq. 4 are equivalent. 4.. Star formation efficiency Fig. 9. Comparison of model and Serpens K luminosity function, normalized to 1 stars. To account for the effects of uniform foreground extinction, we extincted our model KLF by 1. mag at K. qualitative since we could not take into account the effects of differential extinction seen toward the cloud (because we lack spectroscopic data), and the relatively poor statistic number of sources identified as cloud members ( stars), may partly explain the differences observed between the two histograms Influence of the IMF upon KLFs In order to evaluate the influence of the IMF upon the resulting K luminosity functions, we have used different IMFs. We still kept the general shape of the half-gaussian form of MS79 IMF (given by Eq. 2), but we examined how the KLF does evolve by changing the number of stars at the two extremes of the curve. The expressions used can be summarized as follows: d log M = d log M = d log M = { C exp[ C 1 (log M C 2 ) 2 ] if log M>C 2 C otherwise { C exp[ C 1 (log M C 2 ) 2 ] if log M>C 2 otherwise { C exp[ C 1 (log M C 2 ) 2 ] with C 1 =.8,.9, 1. The results of these models are presented in Fig. 1, which plots the shapes of each IMF used, while Fig. 11 shows the corresponding luminosity functions. We can learn from Fig. 11 that on the one hand, increasing the value of C 1 (i.e. increasing the number of high-mass stars) leads to an increase of the number of bright stars. On the other hand, Eq. 3 produces a KLF which increases the number of stars with fainter magnitudes (i.e. low-mass stars). However, changing the value of C 1 does not alter significantly the resulting KLFs, which remains within the error bars. (3) (4) () The Star Formation Efficiency (SFE) is defined by: SFE = M stars /(M stars + M gas ), and represents the mass of gas converted into stellar mass in a molecular cloud. A realistic estimate of this parameter is not simple since: i) the cloud mass depends on the density tracers used and on the spatial resolution of the observations, and ii) the estimate of the stellar masses cannot be inferred directly from the observations. We used the value of 14 M given by White et al. (199) to estimate the cloud mass. This lower limit of M gas comes from their high resolution C 18 O observations of the Serpens Nebula. To estimate the mass of stars, we used our KLF model that gives the number of PMS stars for each magnitude bin (i.e. interval of mass). We found a total of 16. M for the sources identified as Serpens objects which gives a mean stellar mass of.3 M and then, a SFE of 1.1%. This estimate is comparable with those obtained towards other dark cloud complexes, forming low- to intermediate-mass stars; Ophiuchus:.8% (Wilking et al. 1989); Taurus:.7% (Kenyon et al. 199); L1641:.6% (Evans & Lada 1991); L163: 3 4% (Lada 199). These low limits to the SFE reflect the star forming activity that has occurred to date (Evans & Lada 1991, Leisawitz et al. 1989). An upper limit of the SFE in the Serpens cloud can be estimated by the assumption that all the 138 objects detected belong to Serpens, and that they are.3 M stars in average. This leads to a SFE of 3.3%. This is lower than the value obtained by Eiroa & Casali (1992), who found a SFE in the 8 28% range. To estimate the cloud mass, they used the value of 4 M based on the H 2 CO measurements by Loren et al. (1979). Their lower limit of the SFE was obtained by considering that stars with L<.L have.m, stars with.l <L<L have 1M, and stars with L>L have 2M. The upper limit is obtained with the assumption that all the detected objects belong to Serpens and are 1M. These values are significantly larger than ours, because: i) the stellar masses may have been overestimated, and ii) the low-resolution of Loren et al. s (1979) observations were made with large beams and may present a

9 998 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core number of sources Eq. - C 1 =1. Eq. - C 1 =.8 Eq. 4 Eq. 3 Eq apparent K magnitude Fig. 11. KLFs resulting from Eq. 2 to Eq. factor of uncertainty of 3- for the estimated mass due to uncertainties in radiative transfer effects and geometry. We conclude that the SFE in the Serpens cloud lies in the range %. This is in good agreement with the value obtained by White et al. (199), who found a SFE of 2.%, with a total stellar mass of 37 M, and confirm that the SFE in this dark cloud is no more than a few percent.. Conclusion We have obtained sensitive optical and NIR imaging observations of the central part of the Serpens cloud core. A total of 16 sources was detected in the 19 arcmin 2 surveyed area. We obtained new photometric data for 9 sources, among which 73 are new detections. We developed models to describe the evolution of the infrared luminosity functions of young embedded clusters of pre-main sequence stars for comparison with observations. The results of our study can be summarized as follows. There is evidence for a turnover in the KLF of the identified Serpens sources above 14 mag, well below our 3σ completeness limit. The form of the observed KLF appears consistent with the half-gaussian form of the Miller & Scalo (1979) IMF. In regions where the extinction from the molecular cloud is less than A V = 2, our survey is sensitive enough to allow the detection of objects with masses less than the.8 M mass limit. We estimated a SFE in the range 1-3%, which is comparable to the values obtained towards other dark cloud complexes forming intermediate- to low-mass stars. We have investigated various forms of IMF and the best fit to the data is reached with two bursts of star formation of different ages. One is 1 years old, the other is around years old. This result confirms the one obtained by Casali et al. (1993), who made millimeter and submillimeter continuum observations of the Serpens cloud core that revealed a significant dispersion in the source ages. Acknowledgements. We thank the ESO La Silla and the CFHT staffs for their help during the observations. References Alexander D.R., Augason G.C., Johnson H.R., 1989, ApJ 34, 114 André P., Ward-Thompson D., Barsony M., 1993, ApJ 46, 122 Barsony M., 1994, in Clouds, Cores, and Low Mass Stars, Proceedings of the Fourth Haystack Conference, Eds D.P. Clemens & R. Barvainis, ASP Conference Series Vol. 6, p. 197 Canuto V.M., Mazzitelli I., 199, ApJ 37, 29 Canuto V.M., Mazzitelli I., 1992, ApJ 389, 724 Casali M.M., Eiroa C., Duncan W.D., 1993, A&A 27, 19 Churchwell E., Koorneef J., 1986,ApJ 3, 729 D Antona F., Mazzitelli I., 1994, ApJS 9, 467 De Lara E., Chavarria K.C., Lopez-Molina G., 1991, A&A 243, 139 De Poy D.L., Lada E.A., Gatley I., Probst R., 199, ApJ 36, L Eiroa C., Casali M.M., 1992, A&A 262, 468 Evans N.J., Lada E.A., 1991, in Fragmentation of Molecular Clouds and Star Formation, IAU Symposium 147, p293, D. Reidel Press Gómez de Castro A.I., Eiroa C., Lenzen R., 1988, A&A 21, 299 Horrobin M.J., Casali M.M., Eiroa C., 1997, A&A 32, L41 Hurt R.L., Barsony M., 1996, ApJ 46, L4 Kenyon S.J., Hartmann L.W., Strom K.M., Strom S.E., 199, AJ 99, 869 Lada C.J., Wilking B.A., 1984, ApJ 287, 61 Lada E.A., 199, PhD Thesis, University of Texas at Austin Lada E.A., De Poy D.L., Neal J.E., Gatley I., 1991, ApJ 371, 171 Lada C.J., Adams F.C., 1992, ApJ 393, 278 Landolt-Bornstein H., 1982, Astronomy & Astophysics, subvolume 2b, eds. Schaifers annd Voigt H.H., p. 3 Leisawitz D., Bash F., Thaddeus P., 1989, ApJS 7, 731 Loren R.B., Evans N.J. II, Knapp G.R., 1979, ApJ 234, 932 Miller G.E., Scalo J.M., 1979, ApJS 41, 13 Nadeau D., Murphy D.C., Doyon R., Rowlands N., 1994, PASP 16, 99 Rieke G.H., Lebofsky M.J., 198, ApJ 288, 618 (RL8) Rydgren A.E., Cohen M., 198, in: Protostars and Planets II, Black D.C., Mathews M.S. (eds), University of Arizona Press, Tucson, p. 371 Salpeter E.E., 19, ApJ 121, 161 Scalo J.M., 1986, Fund. Cosmic Phys. 11, 1 Sogawa H., Tamura M., Gatley I., Merrill K.M., 1997, AJ 113, 17 Stetson P.B., 1987, PASP 99, 191 Strom S.E., Vrba F.J., Strom K.M., 1976, AJ 81, 638 White G.J., Casali M.M., Eiroa C., 199, A&A 298, 94 Wilking B.A., Lada C.J., 1983, ApJ 274, 698 Wilking B.A., Lada C.J., Young E.T., 1989, ApJ 34, 823 Zhang C.Y., Laureijs R.J., Clark F.O., 1988, A&A 196, 236 Zinnecker H., McCaughrean M.J., 1991, Mem. Soc. Astron. It 62, 761 Zinnecker H., McCaughrean M.J., Wilking B.A., 1993, in Protostars and Planets III, edited by E.H. Levy, J.I. Lunine, and M.S. Mathews (University of Arizona Press, Tucson), p. 429 This article was processed by the author using Springer-Verlag LaT E X A&A style file L-AA version 3.