Astron. Astrophys. 330, 990–998 (1998) ASTRONOMYAND

ASTROPHYSICS

Deep optical and near infrared imaging photometryof the Serpens cloud core?

P. Giovannetti1, E. Caux1, D. Nadeau2, and J.-L. Monin3

1 Centre d’Etude Spatiale des Rayonnements, 9 avenue du Colonel Roche, BP 4346, F-31028 Toulouse Cedex 04, France2 Observatoire du Mont Megantic et Departement de Physique, Universite de Montreal, C.P. 6128, Succ. A. Montreal, H3C 3J7 Quebec, Canada3 Laboratoire d’Astrophysique, Observatoire de Grenoble, Universite Joseph Fourier, BP 53, F-38041 Grenoble Cedex, France

Received 2 June 1997 / Accepted 20 August 1997

Abstract. We present results from a deep optical (VRI) andnear infrared (JHK) survey of the central part of the Serpensmolecular cloud. A total of 138 sources were detected in the 19arcmin2 surveyed area down to a limiting magnitude of 16.3 inK. We find that the form of the observed K Luminosity Func-tion (KLF) of stars belonging to the Serpens Molecular cloud isconsistent with that predicted from a Miller & Scalo (1979) In-terstellar Mass Function (IMF). We have investigated the KLFevolution with the age of a cluster by modeling KLFs of hy-pothetical clusters. Our results suggest that two phases of starformation 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 molec-ular clouds is of fundamental importance since it provides in-sights into the nature of star-forming mechanisms. Young StellarObjects (YSOs) are associated with varying amounts of gas anddust and it is expected that the youngest objects will be invisibleat optical wavelengths due to obscuration by opaque circumstel-lar dust. Therefore observations at infrared wavelengths provideone of the best methods for identifying the young stellar popu-lation within molecular clouds. In the past, infrared studies ofstar-forming regions were limited by the poor sensitivity of theinstruments as well as their low spatial resolution. Infrared arraytechnology has advanced considerably in the last few years, andis now at a stage allowing to survey large regions of star forma-tion (see De Poy et al. 1990, Lada et al. 1991, Zinnecker et al.1993). An increase in spatial resolution and sensitivity almostalways 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 anony-mous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html

Two distinct areas need to be addressed by such data: i) thedetermination of which stars in any given field are members ofthe embedded young stellar population, i.e. separating the youngPre-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 sec-ond point has recently been addressed by Lada & Adams (1992)who studied the location of known classes of YSOs (i.e. classicalT Tauri Stars - CTTS, Weak-line T Tauri Stars - WTTS, HerbigAe/Be - HAEBE stars, and IR protostars: the class I sourcesof Lada & Wilking 1984) in near-IR colour-colour diagrams.They concluded that these relatively well-known evolutionaryclasses occupy different regions of the near-IR colour-colourdiagram and that given the JHK photometry, the evolutionarystate of PMS stars can be inferred relatively unambiguously. Starclusters are important laboratories for studying the initial lumi-nosity function because they consist of statistically significantgroups of stars who share the common heritage of forming fromthe same parental cloud, and they are not old enough to havelost a significant number of members due to stellar evolutionor dynamical effects such as evaporation or violent relaxation(Lada & Wilking 1984, Lada et al. 1991). Moreover in thesevery young clusters (1 − 5 106yr), low-mass stars are brighterthan at any other time in their PMS evolution.

At a distance of 310pc (De Lara et al. 1991), this region hasreceived attention since Strom et al. (1976) reported a small rednebulosity, called the Serpens Object or the Serpens ReflectionNebula. Based on the more than fifty low-mass stars identifiedin the core by a near-infrared survey, the Serpens molecularcloud is one of the most spectacular examples of a protostellarnursery, harboring a stellar density exceeding 450 stars/pc−3

(Eiroa & Casali 1992). A Recent submillimeter continuum sur-vey has uncovered half a dozen mm/submillimeter peaks, fourof which lack an infrared counterpart (Casali et al. 1993). A lowresolution CO and H2CO survey revealed a dense core in thedark cloud complex (Loren et al. 1979). More recently, Hurt andBarsony (1996) found several sources sharing the characteris-

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.06/12 CFHT V 1.2 10 21.106/11 CFHT R 1.1 10 23.506/11 CFHT I 0.8 10 22.111/09 CFHT J 1.5 5 18.411/10 CFHT H 1.5 5 17.909/15 ESO K 1.7 2 16.3

tics of Class 0 protostars, the short-lived (a few 104 yr) earliestprotostellar stage (Andre, Ward-Thompson & Barsony 1993,Barsony 1994).

In this paper, we present new deep optical and near-infraredobservations of the Serpens cloud core using an array detector.Our results increase the number of sources detected in the centralpart of the cloud and allow to make a more complete census ofits 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, wecalculate models which predict the evolution of the luminosityfunction of a cluster of PMS stars. We compare these modelswith the Serpens K luminosity function to place constraints onthe star formation history of this cluster and on the nature of theunderlying mass function.

The optical and near IR observations are presented inSect. 2, and the results in Sect. 3. The interpretation of theseresults in terms of general properties of the cluster is presentedand discussed in Sect. 4 and our conclusions are summarized inSect. 5.

2. Observations

2.1. Optical and near infrared observations

Table 1 presents the details of the observations in the six wave-bands. The observations in the V, R and I bands were carriedout during June 1992 at the 3.6m CFHT (Canada France HawaiiTelescope) on Mauna Kea, Hawaii, using the FOCAM instru-ment with the RCA4 10242 CCD detector. Flat fields have beenobtained in each photometric band on the sky during twilight.The CCD electronics offset was measured several times dur-ing the night. For each photometric band, various standard starswere repeatedly observed during the night.

At the F/8 focus of the telescope, the CCD pixel scale was0.21”. The observations in the J and H bands have been ob-tained in November 1992, also at the CFHT, using the visitor”MONICA” Nicmos 3 infrared camera (Nadeau et al. 1994) atthe same F/8 focus. At these wavelengths, the resolution is 0.25”per pixel. The observations in the K band have been obtained onSeptember 1992 at the 2.2m telescope of the ESO observatoryof La Silla, Chile, using the common-user IRAC2a CCD camerawith a resolution of 0.49” per pixel. In the optical bands, twofields slightly overlapped were observed, surveying an area of16 square arcminutes. In the three NIR bands, sixteen fields were

observed toward the Serpens cluster, approximately covering anarea of 12 square arcminutes in J and H, and 19 square arcmin-utes in K. These fields were arranged in a 4x4 mosaic centeredon the Serpens Reflection Nebula (α1950 = 18h27m22s, δ1950 =1o12’30”). The fields were spatially overlapped by 30” in bothright ascension and declination, allowing an accurate position-ing of the mosaicked fields. Per image, the integration timesused were of 10 minutes in the optical bands, five seconds inJ and H, and two seconds in K, allowing the quoted sensitivitylimits presented in Table 1.

2.2. Data analysis

The NIR data were reduced by first subtracting from each dataframe a median filtered sky frame obtained from five nebulosity-free frames, observed immediately before and after the target ob-servation. The J and H band images were then flat-field and dis-torsion corrected with a dedicated software. Finally, the imageswere mosaicked together. Nominal atmospheric extinctions forMauna Kea are J = 0.117, H = 0.067 per air mass, and nom-inal atmospheric extinction for ESO La Silla is K = 0.086 perair mass. All infrared images were air-mass corrected.

Data analysis was done with standard Image Reduction andAnalysis Facility (IRAF) and Interactive Data Language (IDL)routines. As a first step, several isolated stars of different in-tensities were chosen manually to determine the Full Width atHalf Maximum (FWHM). Thus, for each image, source extrac-tion and aperture photometry were performed using DAOPHOT(Stetson, 1987), and the routine DAOFIND was used to extractstellar-like sources whose fluxes were significantly above thebackground (that is, sky) noise in each image. The results werevisually compared to the images at several contrast levels to en-sure that spurious identifications were minimized. Such spuri-ous detections were a problem in the area of the bright reflectionnebula where probably non stellar emission knots could be in-terpreted as stars. We removed all these spurious sources fromour data sample listed in Table 2. This led undoubtedly to thenon-detection of faint sources in the area of the image wherecontamination from extended emission was present. In addition,sources that were not bright enough to be detected by the findingroutine, but visually identified as stars, were appended to the co-ordinate list. Finally, the resulting images were mosaicked withan IDL routine. This routine eliminated bad pixels and adjustedthe relative background level of overlapping frames to a com-mon value. Using these procedures, 5, 12, 20, 44, 86 and 138stars were found in the V, R, I, J, H and K mosaic images, respec-tively. Aperture photometry was performed for all the extractedstars in each image. Fluxes were determined for each star withthe size of the software aperture used varying along with thebrightness of the source (the brighter the source, the larger thesoftware aperture).

Sky levels were determined around each star in a 5-pixelwide annulus. Sky levels were also obtained for annuli withsmaller inner radii and larger outer radii with no significantchange in the resulting stellar fluxes. Photometry was performedmanually for stars which were confused with nearby nebulos-

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 thesignal in the object aperture minus the contribution from theaverage 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 usedto assess α and δ coordinates of all our sources. Positions forthe cluster members observed in the other wavebands were thendirectly derived from the K mosaic image by applying the sameprocedure.

2.3. Magnitude uncertainties and sensitivity limits

For each detected source, we evaluated the magnitude uncer-tainty by ∆ν =

√Iν +Nσ2

ν , where Iν is the stellar flux in thesource aperture calculated with N pixels, and σν the standarddeviation of the sky annulus. Thus, the final magnitude is givenby:

mλ = M ± Mmax−Minf

2

where Mmax = 2.5 log(Iν − ∆ν), Minf = C −2.5 log(Iν + ∆ν), and M = C − 2.5 log(Iν)

In order to determine the sensitivity limits, we considereda 3σ detection limit, σ being the standard deviation of the skycalculated on nebulosity- and star-free regions. A star can beapproximated by a gaussian whose parameters are the positioncentre, the Full Width at Half Maximum along the two axes(FWHMx and FWHMy), the stellar luminous intensity (I)and the sky level. Thus, the stellar flux is given by:

F = πσxσyI where σi = FWHMi/2√

ln 2.

In this case, I = 3σ and Mlim = C − 2.5 log(3F ), leadingto the values quoted in Table 1.

3. Results

Fig. 1 shows a reconstructed K image of the Serpens molecularcloud core. Black stars represent sources belonging to the cloudwith their corresponding identification numbers, as quoted inTable 2 (see 3.1). Solid lines represent logarithmic contour plotof the central nebula. Filled circles correspond to the unidenti-fied sources. Figs. 2 and 3 show the image of the Serpens CloudCore in K and I wavebands; the scale adopted for these imagesis 0.25” per pixel.

3.1. Log of the sources of the survey

Table 2 presents the broad-band photometric data. The numberin brackets is the 3σ uncertainty on the computed magnitude asdescribed in 2.3. Crosses correspond to the regions of the skythat were not observed in the concerned photometric band. ’nd’corresponds to sources that were not detected. Identificationnumbers followed by a ’S’ as superscript correspond to Serpens

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Fig. 1. Reconstructed K image of the Serpens molecular cloud core.Black stars represent sources belonging to the cloud with their cor-responding identification numbers. Solid lines represent logarithmiccontour plot of the central nebula. Filled circles correspond to theunidentified sources. North is at the top and East to the right.

cloud members. Conversions from fluxes to magnitudes weremade using relations from Landolt-Bornstein (1982).

Before drawing any conclusion on the distribution of nearinfrared sources detected by the survey, we had to distinguishthe embedded sources from the background sources. K bandphotometry by itself will not discriminate between sources thatare embedded in the cloud and sources that are background stars.

Methods that have previously been employed to help in theseparation of reddened background sources from the true em-bedded PMS stars are: i) the observation of a control field lo-cated at approximately the same galactic coordinates as the sur-vey field but off the associated molecular cloud that containsthe embedded PMS population and, ii) the use of a model thatproduces a table of K source counts according to galactic co-ordinates. However, use of these techniques does not allow todetermine which particular stars in the survey field are PMSstars i.e. it is statistical in nature. Considering our survey, thenumber of detected sources is not large enough and such statis-tical methods can obviously lead to inaccurate results.

The Serpens objects are identified by using the same basiccriteria as those used by Eiroa and Casali (1992). (1) Stars asso-ciated with cometary or bipolar nebulae are considered as cer-tain members of the Serpens population. (2) Hα emission-linestars can also be identified as cloud members since Hα emissionmust imply the presence of (ionized) circumstellar material. (3)PMS stars having IR excess in the near infrared colour-colour

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 tothe left.

diagram (Rydgren & Cohen 1985). In such a diagram, stars lo-cated to the right of the reddening vector followed by an A0 starcan unambiguously be identified as Serpens cloud members.

3.2. The colour-colour (J-H,H-K) diagram

The optical/NIR photometry derived from our survey allows usto study, via colour-colour (c-c) and colour-magnitude (c-m) di-agrams, the combined effects of both the intrinsic properties ofthe sources and the overlying extinction. Thanks to NIR pho-tometry we can theoretically penetrate deeper into the molecularclouds, observe a much larger fraction of the embedded popu-lation and learn more about the global properties of the starformation region and its individual sources.

The J-H, H-K c-c diagram presented in Fig. 4 provides auseful mean of distinguishing between the effects of interstellarreddening and IR excess. In this work, we make the assumptionthat the Rieke & Lebofsky (1985, hereafter RL85) reddening lawcan be applied to the Serpens cloud and represents a reasonableapproximation of the NIR extinction caused by the associatedmolecular cloud since a) few sources lie above the upper ofthe two vectors, and b) the vectors generally follow the sameslope as that implied by stars of different colours. Also plottedas solid line in Fig. 4, are the locations of both unreddenedmain-sequence and giant stars. From the extreme points of thesecurves we have plotted two dashed lines representing RL85reddening vectors. The area between these lines correspondsto the reddening zone for normal stars. The crosses located onthe reddening lines are separated by distances correspondingto 10 mag of visual extinction. Open circles correspond to the

Fig. 3. I image of the Serpens Cloud Core. North is at the top, East tothe left.

unidentified sources. Filled circles represent Serpens sourcesidentified using criteria described in Sect. 3.1. It is clear fromFig. 4 that a significant fraction of the objects observed in theSerpens cloud is located between the two reddening vectorsand is consistent with reddened background stars seen throughthe cloud. More than one third of the sources, however, lies atpositions outside the reddening vectors. This region of the JHKcolour-colour diagram is known as the infrared excess region(Lada & Adams 1992) and corresponds to the location of PMSstars. However, naked-T Tauri stars, post-T Tauri stars and someclass I sources found in ρOphiuchus by Wilking & Lada (1983)do not show any NIR excess, and will be found between the tworeddening vectors in such a diagram.

Another interesting point that can be inferred from the di-agram is that sources located in the reddening zone for normalstars are found spread along the reddening band. This indicatesthat the extinction caused by the cloud or by the circumstellarmaterial is variable and can reach values up to 20 magnitudesof visual extinction.

This colour-colour diagram is somehow different to that pre-sented by Eiroa & Casali (1992) and Sogawa et al. (1997). Thisis not surprising since their surveys cover an area larger thanour, with lower sensitivities. Thus, sources plotted on these di-agrams, do not correspond exactly to the same population.

3.3. The colour-magnitude (K,J-K) diagram

The K versus J-K colour-magnitude (c-m) diagram for all ob-jects found in the Serpens cloud core is plotted in Fig. 5. Inthis diagram, ZAMS stars are plotted at the assumed distance

994 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core

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Serpens sourcesunidentified sources

(J-H

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Fig. 4. The NIR colour-colour diagram. The solid line represents thelocus of points occupied by unreddened main-sequence and giant stars.The short dashed lines define the reddening band for normal stars andare parallel to the reddening vector. Crosses are placed along these linesat intervals corresponding to ten magnitudes of visual extinction. Filledcircles are candidates we identified to be Serpens cloud members. Opencircles are unidentified stars.

of the Serpens cloud i.e. 310 pc (the solid line joining the opendiamonds). A representative RL85 reddening vector (AV = 10magnitudes) is plotted as an arrow and the dashed line indicatesthe effective detection limit of the survey. Filled circles repre-sent the Serpens objects while open circles are the unidentifiedsources.

With the K=16.3 detection limit, we would therefore observeunreddened and unextincted ZAMS stars down to spectral typeM4 at 310 pc. Using the mass-MK relation for ZAMS shownin Zinnecker et al. (1993), this corresponds to a stellar mass of0.3 M�. However, PMS stars are over-luminous for their masswhich would lower the effective PMS mass detection limit sig-nificantly. Zinnecker & McCaughrean (1991) present age de-pendent mass-luminosity functions over the range 2 105 yearsto 2 106 years derived from homogeneous tracks calculated byI. Mazzitelli. These suggest that over this age range, 0.08 M�PMS objects would show a relatively small change inMK from4.9 to 5.3. This corresponds to a mK range of 12.4-12.8 forstars in Serpens. This is over 3.5 magnitudes brighter than ourdetection limit and hence our survey would be sensitive enoughto detect stars with masses less than 0.08 M�. But these val-ues do not take into account the extinction due to the molecularcloud. At K, the effect of extinction is however minimized andthe range of AV values between 0-20 magnitudes (as impliedby our NIR c-c diagram) could lead the embedded populationto be 2.3 magnitudes fainter than the values quoted above. Thiswould suggest that 0.08M� PMS stars would havemK valuesin the range 14.7-15.1. This is still below our detection limit,

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Fig. 5. Colour-magnitude (K,J-K) diagram. Filled circles are candi-dates we identified to be Serpens cloud members. Open circles areunidentified stars. The continuous line shows the locus of the ZAMSstars at the distance of the Serpens cloud. A representative reddeningvector is plotted as an arrow and corresponds to ten magnitudes of vi-sual extinction. The dashed line corresponds to our 3σ-completenesslimit.

suggesting that we should be able to detect objects with massessignificantly less than the 0.08 M� mass limit.

4. The stellar population of the Serpens cloud

While theoretical work on PMS evolution is progressing, anobservational effort to understand star forming history in a cloudis needed in order to address the IMF question.

4.1. The luminosity functions

The Initial Mass Function (IMF) is of fundamental interestto several fields of astronomy. Current estimates of the IMFare based on observations of stars in the solar neighbourhood(Salpeter 1955, Scalo 1986). PMS stars undergo considerableluminosity evolution with poorly known time scales before theyarrive at the zero age main sequence (ZAMS). Thus the observedluminosity function is a result of the IMF, the PMS evolutionand the star forming history. The K-band luminosity function(KLF) of the identified Serpens sources and of all stars observedtoward the central part of the Serpens cloud core is presentedin Fig. 6. The KLF is displayed as histograms of the number ofsources versus the apparent K magnitude, with a bin size of 1mag.

The comparison of the distributions shows that all sourceswithK < 10 are Serpens objects, as well as 55% of the sourceswith K < 15. When considering only the distribution of allstars detected at K, irrespectively of their nature, we note thepresence of a peak occurring at K = 15 mag and a decrease inthe observed number of sources with decreasing K brightness

P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 995

Fig. 6. K magnitude distribution of the identified Serpens sources andof all detected NIR sources in the field.

beyond K = 15 mag. This apparent turnover is probably due toour K detection limit (K=16.3). On the other hand, the KLF ofthe identified Serpens sources presents a turnover beyond K=12that is well below our K detection limit and cannot be consideredas an artefact. Such a trend has been called a turnover becauseKLFs derived from Miller & Scalo (1979) or Salpeter (1955)IMF show the number of sources increasing with decreasing Kbrightness. However, these KLFs were derived using a mass-luminosity relationship appropriate for main sequence stars. Aswe demonstrate in the next section, turnovers in luminosity func-tions are not necessarily inconsistent with Miller & Scalo (1979)or Salpeter (1955) mass functions when the cluster members arenot yet on the main sequence. In a study of several star formingregions, Zinnecker et al. (1993) also find and discuss similarresults. We have determined the cumulative number of sourcesper square degree brighter than a given K magnitude detected byCasali & Wainscoat (quoted in Eiroa & Casali 1992, hereafterCW92) in a field close to Serpens (galactic coordinates l = 40◦,b = -4◦) and normalized to an area equal to that covered by ourK image. That curve can be fitted by logN = 0.38K − 3.47.This means that around 260 sources should be detected withK < 15.5 in the area we surveyed. However, the mean extinc-tion of the cloud is aboutAV = 10 mag (Zhang et al., 1988) and,therefore, the number of sources in the line of sight to Serpens isexpected to be lower. The results are presented in Fig. 7 whichplots the cumulative number of sources brighter than a given Kmagnitude versus that magnitude.

The CW92 line is plotted as a dashed line and normalizedto an area equal to that covered by our K image with an extinc-tion ofAK=1.1 (equivalent toAV =10, using the RL85 standardextinction law). In the range 9 < K < 15, the relation betweenlogN and the apparent K magnitude for all sources appearslinear and a least square analysis was performed on these data.The resulting fit is logN = 0.23K−1.36 with a correlation co-efficient of 0.99. This linear relation is not satisfied in the caseof the identified Serpens sources. The deficiency of stars with

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Fig. 7. Cumulative number of stars brighter than a given K magnitude.Identified Serpens sources are plotted as crosses while filled circlesrepresent all sources detected in the field. The dashed line representsthe expected number of background stars after the empirical star countsurvey of Casali & Wainscoat, normalized to a 19 square arcmin field.The continuous line is the least square fit in the range 9 < K < 15.

K > 13 reflects the apparent turnover in the K-distribution ofstars.

This plot shows another interesting point. There is an excessof stars with K < 15.5 with respect to the number of expectedsources from the star count survey of CW92. Since the majorityof these stars is related to the molecular cloud, this evidences aclustering process in Serpens.

4.2. KLF modeling

A fundamental consequence of the theory of stellar evolution isthat the life history of a star is almost entirely predetermined byits initial mass. Consequently, to understand the star formationhistory and the consequent luminosity evolution of an embed-ded population of young stars such as the one we observed,requires a detailed knowledge of both the initial distribution ofstellar masses at birth and how this quantity varies through spaceand time. Since the stars are young, a time-dependent main se-quence mass-luminosity relation must be used to determine thestellar mass. In this aim, we modeled the predicted form of the Kluminosity function using Miller & Scalo (1979) IMF and theo-retical PMS mass-luminosity relationships from the isochronesof D’Antona & Mazzitelli (1994). Our first objective was to di-rectly compare synthetic KLFs with observations to place con-straints on the star formation history and the underlying massfunction of the Serpens molecular cloud.

We then evaluated the following equation:

dN

dK=

dN

d logM× d logM

dK(1)

996 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core

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Fig. 8a–d. Time dependant mass-mk luminos-ity relation, as derived from evolutionary tracksof d’Antona & Mazzitelli (1994) for 0.3 Myr (a)PMS stars and model 2.2µm (mk) luminosityfunction for a coeval cluster of low-mass starsof 0.3 Myr (b). Figs. c and d: same as a and bfor 2 Myr PMS stars.

where d logM/dK is the slope of the mass-K luminosity re-lation and dN/d logM is the underlying stellar mass functiongiven by the half-gaussian form of the Miller & Scalo (1979)IMF:

dN

d logM= C0 exp[−C1(logM − C2)2] (2)

where C0 = 106.0, C1 =1.09 and C2 = -1.02. The PMS evolu-tionary tracks give, for each age ranging from 7 104yr to 108yr,and each mass from 0.02 to 2.5 M�, the effective temperatureand luminosity of the star. For simplicity we considered stars asblackbodies and the luminosities were converted into K mag-nitude. The tracks used in our models were derived assumingAlexander et al. (1989) opacities and the Canuto and Mazz-itelli (1990, 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 andwe assumed that our PMS stars were diskless. In any case, theinfrared excess present in some of the objects we observed issmaller than the bin size of the observed and modeled KLFs.

4.3. Comparison of models with the observations

In Fig. 8a and 8c, we have plotted the mass-mk luminosity re-lation that we used at two different ages (0.3 and 2 Myr.), whileFig. 8b and 8d show the corresponding KLFs for a coeval clus-ter 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 luminosityrelation. This point of inflection is due to the deuterium burn-ing in the contracting PMS star and it is seen to move towardslower masses as the cluster ages. A physical interpretation ofthis phenomenon is that while deuterium is burning strongly ina star of given mass, D-burning is ending in higher mass starsand has yet to begin in stars of lower masses, for a sample ofstars born at the same time. This leads to an increase in the valueof d logM/dK and a peak in the luminosity function at the cor-responding K magnitude. That is why features and turnovers inKLFs are not necessarily due to features in the IMF; rather theymay often reflect the complex process of PMS evolution.

The modeled KLFs were compared to the KLF observedfor the Serpens molecular cloud. None of the coeval models fitsthe shape of the observed KLF in a satisfactory way. This ledus to construct KLFs for clusters of different ages and to com-pare the resulting KLF with the observations. The best fit to thedata is obtained with two bursts of star formation at differentepochs. One is 105 yr old, the other is around 3 Myr old. Fig. 9presents histograms of the model KLF superimposed on the ob-served KLF for the identified Serpens sources, normalized to100 stars. To attempt to account for the effects of uniform fore-ground extinction, we extincted our models by 1.5 mag at K,which introduced a shift in the model KLF toward larger magni-tudes, without changing its shape. We can note some differencesbetween the two curves, but the general shape, the location andthe intensity of the peak of the observed luminosity function arequite well reproduced by the model. However, these results are

P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core 997

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es

apparent K magnitude

Fig. 9. Comparison of model and Serpens K luminosity function, nor-malized to 100 stars. To account for the effects of uniform foregroundextinction, we extincted our model KLF by 1.5 mag at K.

qualitative since we could not take into account the effects ofdifferential extinction seen toward the cloud (because we lackspectroscopic data), and the relatively poor statistic number ofsources identified as cloud members (55 stars), may partly ex-plain the differences observed between the two histograms.

4.4. Influence of the IMF upon KLFs

In order to evaluate the influence of the IMF upon the resultingK luminosity functions, we have used different IMFs. We stillkept the general shape of the half-gaussian form of MS79 IMF(given by Eq. 2), but we examined how the KLF does evolve bychanging the number of stars at the two extremes of the curve.The expressions used can be summarized as follows:

dN

d logM=

{C0 exp[−C1(logM − C2)2] if logM > C2

C0 otherwise(3)

dN

d logM=

{C0 exp[−C1(logM − C2)2] if logM > C2

0 otherwise(4)

dN

d logM=

{C0 exp[−C1(logM − C2)2]with C1 = 0.8, 0.9, 1.0

(5)

The results of these models are presented in Fig. 10, whichplots the shapes of each IMF used, while Fig. 11 shows thecorresponding luminosity functions.

We can learn from Fig. 11 that on the one hand, increasingthe value of C1 (i.e. increasing the number of high-mass stars)leads to an increase of the number of bright stars. On the otherhand, Eq. 3 produces a KLF which increases the number ofstars with fainter magnitudes (i.e. low-mass stars). However,changing the value ofC1 does not alter significantly the resultingKLFs, which remains within the error bars.

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5

Eq. 5 - C1=1.0

Eq.5 - C1=0.8

Eq. 4

Eq. 3

dN /

dlog

M

M (solar masses)

Fig. 10. IMFs resulting from Eq. 3 to Eq. 5. For logM > C2, Eq. 3and Eq. 4 are equivalent.

4.5. Star formation efficiency

The Star Formation Efficiency (SFE) is defined by: SFE =Mstars/(Mstars + Mgas), and represents the mass of gas con-verted into stellar mass in a molecular cloud. A realistic estimateof this parameter is not simple since: i) the cloud mass dependson the density tracers used and on the spatial resolution of theobservations, and ii) the estimate of the stellar masses cannotbe inferred directly from the observations. We used the valueof 1450 M� given by White et al. (1995) to estimate the cloudmass. This lower limit ofMgas comes from their high resolutionC18O observations of the Serpens Nebula.

To estimate the mass of stars, we used our KLF model thatgives the number of PMS stars for each magnitude bin (i.e. in-terval of mass). We found a total of 16.5M� for the 55 sourcesidentified as Serpens objects which gives a mean stellar mass of0.3 M� and then, a SFE of 1.1%. This estimate is comparablewith those obtained towards other dark cloud complexes, form-ing low- to intermediate-mass stars; Ophiuchus: 0.8% (Wilkinget al. 1989); Taurus: 0.7% (Kenyon et al. 1990); L1641: 0.6%(Evans & Lada 1991); L1630: 3− 4% (Lada 1990). These lowlimits to the SFE reflect the star forming activity that has oc-curred to date (Evans & Lada 1991, Leisawitz et al. 1989).

An upper limit of the SFE in the Serpens cloud can be esti-mated by the assumption that all the 138 objects detected belongto Serpens, and that they are 0.3M� stars in average. This leadsto 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 es-timate the cloud mass, they used the value of 450M� based onthe H2CO measurements by Loren et al. (1979). Their lowerlimit of the SFE was obtained by considering that stars withL < 0.5L� have 0.5M�, stars with 0.5L� < L < 5L� have1M�, and stars with L > 5L� have 2M�. The upper limit isobtained with the assumption that all the detected objects belongto Serpens and are 1M�. These values are significantly largerthan ours, because: i) the stellar masses may have been over-estimated, and ii) the low-resolution of Loren et al.’s (1979)observations were made with large beams and may present a

998 P. Giovannetti et al.: Deep optical and near infrared imaging photometry of the Serpens cloud core

0

5

10

15

20

25

30

35

4 6 8 10 12 14 16 18

Eq. 2

Eq. 5 - C1=1.0

Eq. 3

Eq. 5 - C1=0.8

Eq. 4

num

ber

of s

ourc

es

apparent K magnitude

Fig. 11. KLFs resulting from Eq. 2 to Eq. 5

factor of uncertainty of 3-5 for the estimated mass due to un-certainties in radiative transfer effects and geometry.

We conclude that the SFE in the Serpens cloud lies in therange 1.1 − 3.3%. This is in good agreement with the valueobtained by White et al. (1995), who found a SFE of 2.5%, witha total stellar mass of 37 M�, and confirm that the SFE in thisdark cloud is no more than a few percent.

5. Conclusion

We have obtained sensitive optical and NIR imaging observa-tions of the central part of the Serpens cloud core. A total of 165sources was detected in the 19 arcmin2 surveyed area. We ob-tained new photometric data for 90 sources, among which 73 arenew detections. We developed models to describe the evolutionof the infrared luminosity functions of young embedded clustersof 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 identifiedSerpens sources above 14 mag, well below our 3σ complete-ness limit. The form of the observed KLF appears consistentwith the half-gaussian form of the Miller & Scalo (1979) IMF.In regions where the extinction from the molecular cloud is lessthanAV = 20, our survey is sensitive enough to allow the detec-tion of objects with masses less than the 0.08 M� mass limit.We estimated a SFE in the range 1-3% , which is compara-ble to the values obtained towards other dark cloud complexesforming intermediate- to low-mass stars. We have investigatedvarious forms of IMF and the best fit to the data is reached withtwo bursts of star formation of different ages. One is 105 yearsold, the other is around 3 106 years old. This result confirmsthe one obtained by Casali et al. (1993), who made millimeterand submillimeter continuum observations of the Serpens cloudcore that revealed a significant dispersion in the source ages.

Acknowledgements. We thank the ESO La Silla and the CFHT staffsfor their help during the observations.

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