Brown dwarfs and very low mass stars in the Praesepe open cluster: a dynamically unevolved mass function?
S. Boudreault, C. A. L. Bailer-Jones, B. Goldman, T. Henning, J. A. Caballero
aa r X i v : . [ a s t r o - ph . S R ] N ov Astronomy&Astrophysicsmanuscript no. 13011 c (cid:13)
ESO 2018October 20, 2018
Brown dwarfs and very low mass stars in the Praesepe opencluster: a dynamically unevolved mass function? ⋆ S. Boudreault , C. A. L. Bailer-Jones , B. Goldman , T. Henning and J. A. Caballero Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germanye-mail: boudrea, calj, goldman, [email protected] Departamento de Astrof´ısica, Facultad de F´ısica, Universidad Complutense de Madrid, E-28040 Madrid, SpainReceived 30 July, 2009; accepted 23 October, 2009
ABSTRACT
Context.
Determination of the mass functions of open clusters of di ff erent ages allows us to infer the e ffi ciency with which browndwarfs are evaporated from clusters to populate the field. Aims.
In this paper we present the results of a photometric survey to identify low mass and brown dwarf members of the old opencluster Praesepe (age 590 + − Myr, distance 190 + . − . pc) from which we estimate its mass function and compare this with that of otherclusters. Methods.
We performed an optical ( I c -band) and near-infrared ( J and K s -band) photometric survey of Praesepe covering 3.1 deg .With 5 σ detection limits of I c = . J = .
0, our survey is predicted to be sensitive to objects with masses from 0.6 to 0.05 M ⊙ . Results.
We photometrically identify 123 cluster member candidates based on dust-free atmospheric models and 27 candidates basedon dusty atmospheric models. The mass function rises from 0.6 M ⊙ down to 0.1 M ⊙ (a power law fit of the mass function gives α = ± ξ (M) ∝ M − α ), and then turns over at ∼ ⊙ . This rise agrees with the mass function inferred by previous studies,including a survey based on proper motion and photometry. In contrast, the mass function di ff ers significantly from that measured forthe Hyades, an open cluster with a similar age ( τ ∼
600 Myr). Possible reasons are that the clusters did not have the same initial massfunction, or that dynamical evolution (e.g. evaporation of low mass members) has proceeded di ff erently in the two clusters. Althoughdi ff erent binary fractions could cause the observed (i.e. system) mass functions to di ff er, there is no evidence for di ff ering binaryfractions from measurements published in the literature. Of our cluster candidates, six have masses predicted to be equal to or belowthe stellar / substellar boundary at 0.072 M ⊙ . Key words. stars: low-mass, brown dwarfs – stars: luminosity function, mass function – stars: formation – Galaxy: open clusters andassociations: individual: Praesepe
1. Introduction
Several publications in the past decade have been concernedwith the mass function (MF) of low mass stellar and substellarpopulations in open clusters, including σ Orionis (B´ejar et al.2002, Caballero et al. 2007), the Orion Nebula Cluster(Hillenbrand & Carpenter 2000, Slesnick et al. 2004), IC 2391(Barrado y Navascu´es et al. 2004, Boudreault & Bailer-Jones2009), the Pleiades (Moraux et al. 2003, Lodieu et al. 2007),and the Hyades (Reid & Hawley 1999, Bouvier et al. 2008),to name just a few. Studies of relatively old open clusters(age &
100 Myr) are important for the following two reasons inparticular. First, they permit a study of the intrinsic evolutionof brown dwarfs (BDs), e.g. their luminosity and e ff ective tem-perature, which constrains structural and atmospheric models.Second, together with younger clusters we can investigate howBD populations as a whole evolve and thus probe the e ffi ciencywith which BDs evaporate from clusters to populate the Galacticfield. Numerical simulations of cluster evolution have demon-strated that the MFs can evolve through dynamical interaction(de la Fuente Marcos & de la Fuente Marcos 2000; Adams et al.2002b). These interactions result in a decrease of the open clus-ter BD (and low-mass star) population. This has been observed ⋆ Based in part on observations carried out at ESO / La Silla, Chileunder proposal number 078.A-9055(A). by Bouvier et al. (2008) from a comparison of the Pleiades(120 Myr) and Hyades (625 Myr) mass functions.Many earlier studies of the substellar MF have focused onyoung open clusters with ages less than ∼
100 Myr, and in manycases much younger ( <
10 Myr). This is partly because BDsare bright when they are young (lacking a significant nuclearenergy source, they cool as they age), thus easing detectionof the least massive objects. However, youth presents di ffi cul-ties. First, intra-cluster extinction plagues the determination ofthe intrinsic luminosity function from the measured photom-etry. Second, at these ages the BD models have large(r) un-certainties (Bara ff e et al. 2002). Estimates of the substellar MFin very young clusters (age . ff er less from these problems, but have the dis-advantage that much deeper surveys are required to detect them.The old open cluster Praesepe is an interesting target con-sidering its age and distance. It is located at a distance of190 + . − . pc (based on parallax measurements from the newHipparcos data reduction, van Leeuwen 2009) and has an ageof 590 + − Myr (by isochrone fitting in the Hertzsprung-Russelldiagram; Fossati et al. 2008). The extinction towards this clus-ter is low, E ( B − V ) = ± / H] = ± + ± ± Boudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster troscopy and 0.20 ± + ± ∼
19 deg survey of the Praesepe cluster down to masses of ∼ ⊙ and observed a rise of the MF at the lowest masses.They concluded that this implied a large population of BDs.A shallow survey complete to I = R = uncovered one spectrally confirmed very low-massstar or BD (spectral type of M8.5V) with a model-dependentmass of 0.063–0.084 M ⊙ (Magazz´u et al. 1998). A survey overthe central 1 deg with 10 σ limits of R = I = Z = study of Praesepe using 2MASS (Two-Micron AllSky Survey) data and Palomar survey photographic plates, fromwhich they derived proper motions. They determined the radialprofile of this cluster but their MF does not reach the substellarregime. A more recent proper motion survey of Praesepe cov-ers a much larger area (300 deg ; Kraus & Hillenbrand 2007),but does not reach the BD regime either (the limit is ∼ ⊙ ).Finally, the most recent substellar MF determination of Praesepewas published by Gonz´alez-Garc´ıa et al. (2006) and extends toa 5 σ detection limit of i = . ⊙ . They identified one new substellar candidate, but theirsurvey covers only 1177 arcmin .In this paper, we present the results of a program to study,in detail, the MF of Praesepe down to the substellar regime. Ourphotometric survey is, as with Gonz´alez-Garc´ıa et al. (2006), thedeepest so far in optical and near-infrared (NIR) bands, with 5 σ detection limits of I c = . J = . ⊙ ), but covers more than nine timesthe area. Our paper is structured as follows. We first present thedata set, reduction procedure and calibration in section 2. Wethen discuss our candidate selection procedure in section 3 andthe survey results in section 4 before discussing the derived MFin section 5. We conclude in section 6.
2. Observations, data reduction, calibration, andestimation of masses and effective temperatures
Our survey consists of 47 Omega 2000 (O2k) fields each ofsize 15.4 × observed in J and K s , plus the same re-gion observed in nine I c Wide Field Imager (WFI) fields eachof size 34 ×
33 arcmin . This gives a total coverage of 3.1 deg observed in all three bands, centred on RA(J2000) = h m s and DEC(J2000) =+ ◦ ′ ′′ .The near-infrared (NIR) observations were made on the3.5m telescope at Calar Alto, Spain (with observation runsof several nights from February 2005 to January 2007). O2k(Bailer-Jones et al. 2000; Baumeister et al. 2003) comprises aHAWAII-2 detector with 2k ×
2k pixels over a field of view of15.4 × / ESO 2.2m telescope at La Silla,Chile (Baade et al. 1999) during 17–22 March 2007. The WFI isa mosaic camera of 4 × ×
4k pixels, coveringa total field of view of 34 ×
33 arcmin at 0.238 arcsec per pixel.All fields were observed in the broad band filter I c . A detailedlist of the fields observed with pointing, filter, exposure time and5 σ detection limits is given in Table 1 for the NIR data and in Table 1.
Description of observations with the O2k infrared cam-era.
Field α δ t exp ( J ) t exp ( K s ) J (5 σ ) K s (5 σ )( h m s ) ( ◦ ′ ′′ ) [min] [min] [mag] [mag]001 08 40 04 +
19 40 00 60 40 19.9 18.6A01 08 41 04 +
19 54 00 60 130 20.6 19.4A02 08 40 04 +
19 54 00 40 40 19.5 18.5A03 08 39 04 +
19 54 00 40 40 19.7 18.7A04 08 39 04 +
19 40 00 20 40 19.0 18.6A05 08 39 04 +
19 26 00 20 40 20.3 18.8A06 08 40 04 +
19 26 00 20 40 19.9 18.6A07 08 41 04 +
19 26 00 40 60 20.3 19.0A08 08 41 04 +
19 40 00 20 40 18.0 17.6B01 08 42 04 +
20 08 00 40 40 19.7 18.4B02 08 41 04 +
20 08 00 40 40 18.8 18.6B03 08 40 04 +
20 08 00 20 40 20.0 18.5B04 08 39 04 +
20 08 00 20 40 19.7 18.6B05 08 38 04 +
20 08 00 20 40 20.3 18.7B06 08 38 04 +
19 54 00 20 40 20.0 18.5B07 08 38 04 +
19 40 00 20 40 19.5 18.5B08 08 38 04 +
19 26 00 20 40 17.4 17.8B09 08 38 04 +
19 12 00 20 40 18.0 18.8B10 08 39 04 +
19 12 00 20 40 20.1 18.8B13 08 42 04 +
19 12 00 20 40 20.1 18.8B14 08 42 04 +
19 26 00 20 40 20.1 18.7B15 08 42 04 +
19 40 00 20 40 19.3 18.3B16 08 42 04 +
19 54 00 20 40 18.4 18.1C01 08 43 04 +
20 22 00 20 40 20.4 18.8C02 08 42 04 +
20 22 00 20 40 20.1 18.7C04 08 40 04 +
20 22 00 20 40 20.0 18.8C05 08 39 04 +
20 22 00 20 40 19.1 18.2C06 08 38 04 +
20 22 00 20 40 20.1 18.7C07 08 37 04 +
20 22 00 20 40 19.8 18.2C08 08 37 04 +
20 08 00 20 40 19.9 18.7C09 08 37 04 +
19 54 00 20 40 20.1 18.0C10 08 37 04 +
19 40 00 20 40 20.3 19.3C11 08 37 04 +
19 26 00 20 40 19.6 18.6C12 08 37 04 +
19 12 00 20 40 20.3 18.9C13 08 37 04 +
18 58 00 20 40 20.4 18.7C14 08 38 04 +
18 58 00 20 40 19.9 18.4C15 08 39 04 +
18 58 00 20 40 20.4 18.6C16 08 40 04 +
18 58 00 20 40 19.4 18.4C17 08 41 04 +
18 58 00 20 40 19.3 18.3C18 08 42 04 +
18 58 00 20 40 20.6 18.3C19 08 43 04 +
18 58 00 20 40 20.3 18.4C20 08 43 04 +
19 12 00 20 40 19.6 18.6C21 08 43 04 +
19 26 00 20 40 20.3 18.8C22 08 43 04 +
19 40 00 20 40 20.3 18.7C23 08 43 04 +
19 54 00 20 40 19.8 18.7C24 08 43 04 +
20 08 00 20 40 19.1 18.4
Table 2 for the optical data. The passband functions for the fil-ters, multiplied with the quantum e ffi ciency of the detectors, areshown in Figure 1. The standard data reduction steps (overscan subtraction, trim-ming and flat-fielding for the WFI data; dark subtraction andflat-fielding for O2k data) were performed on a nightly basis,using the ccdred package under IRAF . For both WFI and O2kdata we used superflats (obtained by combining science image The O2k camera su ff ers from a stray light problem. It appears onevery image taken with the camera, forming a ring pattern centred inthe middle of the detector (Nicol 2009). The stray light is removed viaour global illumination correction and sky subtraction.oudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster 3 Table 2.
Description of observations with WFI optical camera.
Field α δ t exp ( I c ) I c (5 σ )( h m s ) ( ◦ ′ ′′ ) [min] [mag]1 08 40 04 +
19 40 00 24 22.62 08 42 24 +
20 15 00 30 23.33 08 40 04 +
20 15 00 36 23.24 08 37 44 +
20 15 00 24 23.45 08 37 44 +
19 40 00 36 23.66 08 37 44 +
19 05 00 36 23.17 08 40 04 +
19 05 00 36 23.58 08 42 24 +
19 05 00 36 22.89 08 42 24 +
19 40 00 36 22.8
Fig. 1.
Transmission curve of the filters used in our survey com-pared to the synthetic spectrum of a BD with T e ff = g = ffi ciency of the detectors.frames for each night) for pixel-to-pixel variation correction andfor correcting the global illumination. For our NIR data, the skybackground was subtracted using the median-combined imagesfor each filter and each field (on a nightly basis). For WFI data,we reduced each of the eight CCDs in the mosaic independentlyand in the final step scaled them to a common flux responselevel. We made an initial sky subtraction via a low-order fit tothe optical data, and for the infrared data by subtracting a mediancombination of all (unregistered) images of the science frames.Fringes were visible for the I c -band photometry. They were re-moved in the way described by Bailer-Jones & Mundt (2001) .Finally, the individual images of a given field were registered andmedian combined. We used the IRAF task daofind to automati-cally detect stellar objects in an image by approximating the stel-lar point spread function with a Gaussian. We visually inspectedthe images in order to remove from our cluster candidate list anyextended sources (i.e. galaxies) that were mistakenly identifiedas stars by daofind (see section 3.3). Sources were extracted andinstrumental magnitudes assigned via aperture photometry withthe IRAF task wphot . To this aperture photometry we have ap- A fringe correction frame was created, which is a median combina-tion of all science frames in a same filter with the same exposure time.This fringe correction frame was scaled by a factor, determined manu-ally for each science frame, and subtracted from the science image. plied an aperture correction following the technique described inHowell (1989). An astrometric solution was obtained using theIRAF package imcoords and the tasks ccxymatch , ccmap and cctran . For each WFI field, this solution was computed for the I c -band image (and for each O2k field using the J -band image)using the 2MASS catalogue as a reference. The root mean squareaccuracy of our astrometric solution is 0.15–0.20 arcsec for bothWFI and O2k data. For WFI data, the astrometry was performedon a CCD-by-CCD basis. To correct for Earth-atmospheric absorption on the photometry,we calibrated the infrared data using the J and K s -band mag-nitudes of 2MASS objects which were observed in our sciencefields. By determining a constant o ff set between the magnitudeof 2MASS and our instrumental magnitude, we obtained the zeropoint o ff set. Since this zero point o ff set was obtained with ob-jects in the same field of view in each science frame, and sincewe found the di ff erence between the 2MASS and O2k pass-bands to be insignificant, we did not need to perform an airmassor colour correction when reducing our NIR photometry. (Thatis, the determined coe ffi cients were statistically consistent withzero.)We followed a similar approach for our I c -band photom-etry, but using observations in our fields for which r and i -band magnitudes are available in the Sloan Digital Sky Survey(SDSS) catalogue. We first transformed the i -band magnitudesof SDSS to I c -band magnitudes using the transformation equa-tion of Jordi et al. (2006) I c = i − . − . × ( r − i ) (1)We then determined the zero point o ff set between this I c mag-nitude and our instrumental I c magnitude, again using the SDSSstars. A further colour correction was not necessary, and as thiscalibration is applied on a field-by-field basis (as with the NIRdata), an airmass correction was likewise unnecessary. After we identify candidates (section 3) we will use the multi-band photometry to derive their masses and e ff ective temper-atures, T e ff . We use the evolutionary tracks from Bara ff e et al.(1998) and atmosphere models from Hauschildt et al. (1999a)(assuming a dust-free atmosphere; the NextGen model) to com-pute an isochrone for Praesepe for an age of 590 Myr, a dis-tance of 190 pc, a solar metallicity and assuming zero extinc-tion. These models and assumptions provide us with a predic-tion of f λ , the spectral energy distribution received at the Earth(in erg cm − s − Å − ) from the source. We need to convert thesespectral energy distributions into magnitudes in the filters weused. Denoting as S A ( λ ) the (known) total transmission functionof filter A (including the CCD quantum e ffi ciency and assum-ing telescope and instrumental throughput are flat), then the fluxmeasured in the filter is f A = R ∞ f λ S A ( λ ) d λ R ∞ S A ( λ ) d λ , (2)The corresponding magnitude m A in the Johnson photometricsystem is given by m A = − . f A + c A , (3) Boudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster where c A is a constant (zero point) that remains to be determinedin order to put the model-predicted magnitude onto the Johnsonsystem. We derived this constant for each of the bands I c , J and K s in the standard way, namely by requiring that the spectrumof Vega produce a magnitude m A of 0.03 in all bands. Usingthe Vega spectrum from Colina et al. (1992) we derive valuesof c I c = − . c J = − . c K s = − . ff ective temperatures fromthese isochrones using our three filter measurements in the fol-lowing way. We first normalize the energy distribution of eachobject to the energy distribution of the model using the J filter.We then estimate the mass and e ff ective temperature via a leastsquares fit of the measured spectral energy “distribution” (ac-tually just two points) to the model spectral energy distributionfrom the isochrone. This involves estimating one parameter fromtwo measurements, because mass and T e ff are not independent.The above assumption of a dust-free atmosphere is validfor T e ff > > T e ff > T e ff ) based onisochrones predicted in the same way, but based on evolution-ary tracks of Chabrier et al. (2000) and the AMES-dusty modelof Allard et al. (2001). This give us a second dusty model list ofcandidates. A priori some observed stars could appear in bothlists (and in fact two do), but in our later discussions of the massfunction we do not mix stars from the two lists but rather makeseparate determinations of the mass function.There are various sources of error in the estimation of massand T e ff . These are the photon noise, the photometric calibration,the least squares fitting (imperfect model) and the uncertaintiesin the age of and distance to Praesepe. The uncertainties in theage and distance are the most significant errors and given rise touncertainties of 0.060 ± ⊙ and 1 990 ±
260 K for a substel-lar object, 0.072 ± ⊙ and 2 293 ±
201 K for an object at thehydrogen burning limit and 1.000 ± M ⊙ and 5 300 ±
50 K fora solar-type star.
3. Candidate selection procedure
The candidate selection procedure for BDs and very low-massstars is as follows (and explained in more detail in the remain-der of this section). Candidates were first selected based oncolour-magnitude diagrams (CMDs) and this further refined us-ing colour-colour diagrams. In the third and final selection, weused the known distance to Praesepe to reject objects based on adiscrepancy between the observed magnitude in J and the mag-nitude in this band computed with the isochrones and our estima-tion of T e ff . To be considered as a cluster member, an object hasto satisfy all three of these criteria. We make two independentselections: one using dust-free and one using dusty atmosphericmodels. Fig. 2.
Colour–magnitude diagram showing an example ofthe first selection step using the I c and J bands. The solidlines show the isochrone computed from an evolutionary modelwith a dust-free atmosphere (NextGen model) and the dashedlines show our selection band around this. The numbers indi-cate the masses (in M ⊙ ) of objects on the isochrone for var-ious I c magnitudes. Overplotted are measurements from oursurvey of candidate cluster members reported in Pinfield et al.(1997) ( stars ), Adams et al. (2002a) ( triangles ) [where we in-clude objects which have a probability of being a real memberhigher than 10%], Gonz´alez-Garc´ıa et al. (2006) ( squares ) andKraus & Hillenbrand (2007) ( circles ). Candidates were first selected from our CMDs by retaining onlyobjects which are no more than 0.14 mag redder or bluer than theisochrone in all CMDs. This number accommodates errors in themagnitudes, uncertainties in the model isochrones plus uncer-tainties in the cluster age and distance estimates. We addition-ally include objects brighter than the isochrones by 0.753 magin order to include unresolved binaries. In Figure 2 and 3 weshow two CMDs where candidates were selected based on I c vs. I c – J and K s vs. I c – K s . These figures also show low-masscluster member candidates from previous studies which we de-tected in our survey (Pinfield et al. 1997; Adams et al. 2002a;Gonz´alez-Garc´ıa et al. 2006; Kraus & Hillenbrand 2007). InFigure 3, we can observe three structures in this CMD. The twostructures at I c − K s ∼ I c − K s ∼ ff , and disk late-type and giant stars re-spectively) while the structure at I c − K s ∼ σ detection limit in all filters, 800 are retained as candidatecluster members (96.7% are rejected). If we instead use dustymodel isochrones, then out of the 23 891 objects, 357 are re-tained (98.5% are rejected) for our dusty model list. oudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster 5 Fig. 3.
As Figure 2 but with the I c and K s bands. The second stage of candidate selection involves retaining justthose objects which lie within 0.24 mag of the isochrone in the(single) colour-colour diagram. This value reflects the photomet-ric errors plus uncertainty in the age estimation of Praesepe. Onesuch colour-colour diagram with the selection limits is shownin Figure 4. The two main sources of contamination besidefield M dwarfs are background red giants and unresolved galax-ies (Praesepe is at a Galactic latitude of b =+ ◦ ). We showin Figure 5 the theoretical colours for red giants using the at-mosphere models of Hauschildt et al. (1999b) and theoreticalcolours of six galaxies from Meisenheimer et al. (2009). We seethat red giants could be a source of contamination in the massrange of 0.09–0.2 M ⊙ and at ∼ ⊙ , while unresolved galaxiesshould not be a major source of contamination below 0.6 M ⊙ . InFigure 5 we see the same three structures as in Figure 3: from topto bottom galaxies, disk late-type and giant stars, and Galacticdisk turn-o ff stars. Of the 800 objects selected in the first step,291 are kept here (63.6% are rejected) assuming a dust-free at-mosphere, and 110 out of 357 are kept (69.2% are rejected) whenusing the model for a dusty atmosphere. As indicated in section 2.4, our determination of T e ff is basedon the spectral energy distribution of each object and is inde-pendent of the assumed distance. The membership status of anobject can therefore be assessed by comparing its observed mag-nitude in a band with its magnitude predicted from its T e ff andPraesepe’s isochrone (which assumes a distance). The premiseis that the predicted magnitude of a background contaminantwould be lower (brighter) than its observed magnitude andhigher (fainter) for a foreground contaminant. In order to avoidremoving unresolved binaries that are real members of the clus-ter, we keep all objects with a computed magnitude of up to Fig. 4.
Colour-colour diagram used in the second selection step.The solid line is the isochrone computed from an evolutionarymodel with a dust-free atmosphere (NextGen model, the massesin M ⊙ for each I c − J colours are shifted up clarity) and the dashedlines show our selection band. Overplotted are the cluster can-didate members from Pinfield et al. (1997) ( stars ), Adams et al.(2002a) ( triangles ), Gonz´alez-Garc´ıa et al. (2006) ( squares ) andfrom Kraus & Hillenbrand (2007) ( circles ), which we detectedin our survey. Fig. 5.
As Figure 4, but now showing the theoretical coloursof six galaxies as thick dotted lines and the theoretical coloursof red giants as thick solid lines. The six galaxies are two star-bursts, one Sab, one Sbc, and two ellipticals of 5.5 and 15 Gyr,with redshifts from z = z = ⊙ ,0.5 < log g < < T e ff < Boudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster
Fig. 6. Di ff erence between the observed J magnitude and themodel J magnitude computed from the derived mass and T e ff , asa function of T e ff . The two vertical lines are at the positions of L0and M5 dwarfs (left to right), for orientation purposes. The dot-ted line (at − .
753 mag) represents the o ff set due to the possiblepresence of unresolved binaries, the dot–dash lines representsthe error on the magnitude determination, and the curved, long–dashed lines represent the uncertainties on the age and distanceof Praesepe.0.753 mag brighter than the observed magnitude. We also takeinto account photometric errors and uncertainties in the age anddistance of Praesepe. This selection procedure is illustrated inFigure 6. From 291 objects selected through CMDs and colour-colour diagrams in the first two steps, 144 are kept (50.5% arerejected) when using the dust-free atmospheres / models, and 35out of 110 are kept (68.2% are rejected) when using the dustyatmosphere / models.After this step, we perform a visual inspection directly onthe images to reject resolved galaxies and spurious detections.This inspection removes 21 and 8 objects from the dust-free anddusty selection respectively.
4. Results of the survey
We now present the selected candidates, discuss contaminationby cluster non-members and derive the magnitude and massfunctions for Praesepe.
The final selection reveals 123 photometric candidates using anisochrone based on dust-free atmospheres, and 27 objects usingan isochrone assuming dusty atmospheres . This corresponds to ∼
40 and ∼ respectively. All our photometriccandidates are presented in Table 3. Objects are given the no-tation PRAESEPE-YYY where YYY is a serial identificationnumber (ID). Numbers above 900 indicate candidate members Two objects in the dust-free atmosphere selection (PRAESEPE-089 and -093) were also identified in dusty atmosphere selection (PRAESEPE-915 and -917).
Table 4.
Photometric candidates in our survey that are also pho-tometric candidates in previous surveys. ID α δ Alternative name Ref. a ( h m s ) ( ◦ ′ ′′ )005 08 41 08.5 +
19 54 02.0 RIZpr18 [3]010 08 39 06.9 +
19 47 08.0 J0839069 + + +
19 50 33.3 J0838554 + + +
19 51 44.6 J08385420 + + + +
19 30 16.8 J08391272 + +
19 27 37.1 J0839544 + + +
19 28 03.1 RIZpr11 [3]029 08 42 50.50 +
20 20 03.8 J0842505 + + +
20 03 36.3 RIZpr23 [3]035 08 42 51.96 +
20 05 19.4 J0842519 + +
20 01 29.3 J0843107 + +
20 22 38.4 J0841110 + +
20 20 50.4 J0840106 + + +
20 01 19.1 J0839145 + +
20 04 54.6 J0839224 + + +
20 13 08.8 J0838551 + + +
20 05 24.3 J08405397 + +
20 22 33.8 J08363947 + +
20 08 45.7 J08364501 + +
20 13 45.8 J08371143 + +
20 03 50.1 J08380800 + +
20 08 02.5 J08381244 + +
20 05 35.7 J08382186 + +
19 41 40.1 J08383929 + +
19 47 11.9 J08372449 + +
19 52 07.3 RIZpr2 [3]101 08 41 20.32 +
18 57 42.9 J08412034 + +
19 02 14.8 J08421923 + +
19 43 11.9 J08430905 + +
19 49 59.8 RIZpr24 [3]117 08 42 11.47 +
19 52 50.2 RIZpr21 [3]110 08 43 01.9 +
19 54 04.5 J08430186 + +
19 51 45.9 J08425228 + +
19 48 57.6 J08421550 + +
19 28 06.1 J08430839 + +
19 34 28.9 J08431265 + a Objects [1] are from Adams et al. (2002a), [2] are fromKraus & Hillenbrand (2007) and [3] are from Pinfield et al. (1997). assuming a dusty atmosphere. Only the first 10 rows of the ta-bles are shown, all other data are available online. We also notein Table 4 which objects are candidate cluster members alsoidentified as such by Kraus & Hillenbrand (2007), Adams et al.(2002a) or Pinfield et al. (1997).Some Praesepe members from previous studies are not de-tected in our work. This is the case for the objects fromPace et al. (2008) and Fossati et al. (2008), for example. Sincethose studies focused on bright objects, these stars saturate in ourscience images. (Pace et al. 2008 and Fossati et al. 2008 wereconcerned with chemical abundances of A-type and solar-typestars, respectively, while our saturation occurs at ∼ ⊙ .) oudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster 7 Table 3.
All photometric cluster member candidates of our survey. Table 3 is published in its entirety in the electronic edition of
Astronomy & Astrophysics . A fraction is shown here for guidance regarding its form and content. ID α δ I c a J a K s a M a T e ff a J model a ( h m s ) ( ◦ ′ ′′ ) [mag] [mag] [mag] [M ⊙ ] [K] [mag]001 08 40 53.61 +
19 40 58.6 19.19 16.81 15.61 0.089 2665 17.00002 08 41 08.8 +
19 43 27.5 16.14 14.95 13.97 0.219 3321 14.86003 08 41 01.6 +
19 52 02.5 16.67 15.35 14.38 0.162 3189 15.48004 08 41 12.17 +
19 52 48.6 18.43 16.39 15.46 0.099 2805 16.72005 08 41 08.5 +
19 54 02.0 19.02 16.58 15.39 0.088 2636 17.06006 08 40 10.74 +
19 40 49.8 16.97 15.47 14.36 0.132 3061 15.95007 08 39 39.56 +
19 47 54.3 17.95 16.10 15.07 0.104 2860 16.58008 08 39 43.38 +
19 48 45.7 16.89 15.56 14.68 0.161 3186 15.50009 08 39 55.84 +
19 53 14.3 20.29 17.50 16.54 0.081 2520 17.32010 08 39 06.9 +
19 47 08.0 16.51 15.14 14.20 0.155 3166 15.57 a The 1 σ uncertainty in the determination of magnitude, e ff ective temperature and mass are the following : ∆ mag = ∆ T e ff =
140 Kand ∆ M = ⊙ for stars (M > ⊙ ), ∆ mag = ∆ T e ff =
230 K and ∆ M = ⊙ for very low-mass stars (0.072 ⊙ < M < ⊙ ), ∆ mag = ∆ T e ff =
420 K and ∆ M = ⊙ for BDs (M < ⊙ ). The magnitude J model is the predicted magnitude based on photomet-ric determination of T e ff and mass. Not all objects identified by other surveys as brown dwarfsor very low mass stellar member candidates – and detectedin our survey – are members based on our criteria. The twoobjects from the work of Gonz´alez-Garc´ıa et al. (2006), whoalso used photometry in order to select candidate members,we detect above our 5 σ limit (Prae J084039.3 + + I c − J coloursbluer than our selection band. (Prae J084130.4 + I c − K s for our selection band at I c − K s = + I c − K s = + + σ detection limit of the publicly available surveys used in theirwork. However, these objects failed our observed magnitude vs.predicted magnitude test and some are bluer than our isochroneof Praesepe in J − K s . With I c − K s colour of ∼ σ detection limits of our survey are I c = J = K s = ∼ ⊙ using the dust-free isochrone). However, we cannot expect todetect all objects down to these magnitudes. We estimate the Fig. 7.
Estimation of the completeness limit for our survey usingthe J band. The solid line is the best linear fit before the turn o ff ,the vertical dashed line is the 5 σ detection limit and the verticaldotted line is the magnitude at which detector saturation occurs.survey completeness by taking the ratio of the number of ob-jects detected to the predicted number of detections, the lattermade by assuming a uniform distribution of stars along the lineof sight in our survey fields. (This comparison distribution issomewhat crude, but it gives an approximate value without mak-ing too many assumptions.) The predicted number of detectionsis obtained from the histogram of the number of detections asa function of magnitude (Figure 7) and by observing where thedistribution drops o ff compared to a straight line extrapolation.Based on this, the completeness of the survey down to the 5 σ de-tection limit is 90% in I c , 88% in J and 87% in K s . The overalldetection completeness of our survey, from saturation to 5 σ de-tection corresponding to 0.05 M ⊙ , is therefore ∼ J band,we reach a completeness of 95% at J = ∼ ⊙ . Boudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster
Fig. 8.
Finding charts of the six new BD candidates of Praesepe( J -band). We observed objects very close to PRAESEPE-099and -909, although they do not influence the photometry. Thepanels are 50 ×
50 arcsec with North up and East to the left.
Six objects in our survey are cluster candidates with theoreti-cal masses equal to or below the stellar / substellar boundary at0.072 M ⊙ . We present the finding charts of the six objects inFigure 8. In Table 5, we present their coordinates and physi-cal parameters. These BD candidates have predicted masses be-tween 0.064 and 0.072 M ⊙ . A spectroscopic follow up (on a 8 mclass telescope or larger) will be needed in order to confirm orrefute their membership and their substellar status. As mentioned in section 3.2, the two main sources of con-tamination are the background red giants, which are the domi-nant source at masses of 0.09–0.2 M ⊙ and ∼ ⊙ , and unre-solved galaxies, mostly a ff ecting masses above 0.6 M ⊙ . Otherpossible contaminants are field M dwarfs and high redshiftquasars (for instance at z ∼
6; Caballero et al. 2008). However, assuch quasars have spectral energy distributions similar to mid-T dwarfs whereas our faintest candidates are early L dwarfs,and given that they are rare (3.3 quasars at 5.5 < z < survey, Stern et al. 2007), the MF should not be a ff ectedby quasar contamination.Let us estimate the contamination by M dwarfs, First, weconsider that close to the open cluster Praesepe, the space den-sity of M dwarfs is uniform . We assume that their density ( ρ )drops exponentially with vertical distance from the galactic disk( h ) such that ρ ( h ) = ρ e − hh , (4)assuming a scale height of h =
500 pc. We use the local spacedensity ( ρ ) for M dwarfs of 57 · − pc − (from the ResearchConsortium on Nearby Stars ; Henry et al. 2006). Given theGalactic latitude of Praesepe of b =+ · − pc − . If we define a volume corresponding to the areaof our survey (3.1 deg , 34 pc ) and use the distance uncertain-ties to the cluster (190 + . − . pc) as its depth, we estimate that wehave ∼
19 M dwarf contaminants near the cluster. From a totalof 150 photometric candidates, we estimate a contamination of ∼
13% (or even less, as the cluster depth is presumably closer to
Fig. 9. J band luminosity function. The solid line histogramrepresents the luminosity function based on a selection usinga dust-free atmosphere (NextGen model); the thick dotted his-togram uses a dusty atmosphere (AMES-Dusty model). The stel-lar / substellar limit is at J ∼ ⊙ ).For reference, the ordinate value of 1.11 at the histogram peak(magnitude bin J = √ = . We present in Figure 9 the luminosity function of Praesepe usingthe J -band magnitude of the cluster candidates. No correction ismade for binaries, so this is the system rather than single-starluminosity function.The mass function (MF), ξ (log M), is generally defined asthe number of stars per cubic parsec in the logarithmic mass in-terval log M to log M + d log M. Here, we do not computethe volume of Praesepe so instead we define the MF as the to-tal number of objects in each 0.1 log M bin per square degree.Since we do not make any corrections for binaries we computehere a system
MF. Our inferred MF is shown in Fig. 10. Thelog-normal form for a MF is ξ (log M) = k · exp " − (log M − log M ) σ , (5)where k = m = ⊙ and σ = dust-free and dusty MF data we obtain k = ± m = ± ⊙ and σ = ± ξ (log M) = k · M − α , (6)from the highest mass bin to the turn over at 0.1 M ⊙ , we obtain α = ± ξ (M) ∝ M − . ). If we exclude thetwo bins between 0.1 and 0.15 M ⊙ (possible contamination byred giants) and the two highest bins (possible incompleteness),the fit gives α = ± oudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster 9 Table 5.
Same as Table 3, but only the BD candidates are given and we include the spectral type expected. ID α δ I c J K s M T e ff J model SpT a ( h m s ) ( ◦ ′ ′′ ) [mag] [mag] [mag] [M ⊙ ] [K] [mag]055 08 41 04.5 +
20 14 58.0 21.61 18.29 17.12 0.068 2250 17.97 L0096 08 41 13.48 +
18 59 05.1 21.06 17.85 16.82 0.072 2335 17.75 M9099 08 41 45.16 +
19 18 07.7 21.30 17.98 17.01 0.068 2249 17.98 L0909 08 39 29.94 +
20 11 40.3 20.11 17.63 16.67 0.069 2259 17.95 L0910 08 40 34.00 +
20 14 56.2 20.08 17.60 16.65 0.069 2261 17.94 L0915 08 38 51.77 +
19 00 21.6 20.28 17.67 16.68 0.068 2238 18.01 L0 a Spectral type expected based on T e ff and the temperature scale of Kraus & Hillenbrand (2007), with L1 set to 2100 K. The error on thisestimation is one subclass. Fig. 10.
Mass function based on our survey photometry. Pointswith error bars represent the MF based on a selection and masscalibration assuming a dust-free atmosphere, whereas the opencircles with error bars are the MF based on the dusty atmospheremodel. We also overplot the log-normal and the power law MFfitted to our data (both solid line). Error bars are Poissonian aris-ing from the number of objects observed in each bin. The verticalthin dotted lines are the mass limits at which detector saturationoccurs in the I c , J and K s –bands (from left to right). The verticalthick dashed line is the mass at the 5 σ detection limit (complete-ness of ∼ M = − ⊙ ]) correspondsto 27 objects. The two dusty data points have been shifted to theright by log M =
5. Analysis and discussion of the stellar andsubstellar mass function of Praesepe
Our MF of Praesepe (Figure 10) shows a rise in the number ofobjects from 0.6 M ⊙ down to 0.1 M ⊙ , and then a turn-over at ∼ ⊙ . This turn-over is not due to incompleteness since it oc-curs well above the 5 σ detection limit corresponding to 0.05 M ⊙ .This behaviour is confirmed by the luminosity function in Figure9 which shows a rise from J =
13 to 16 mag (with candidates ob-tained using a dust-free atmosphere) and a drop at J =
17 mag (seen with both types of candidates). To help the analysis ofthese features in the mass function, we compare in Figure 11 themass functions of Praesepe obtained from several studies plusthe MF for the old open cluster Hyades (age of 625 Myr).The rise in our MF of Praesepe is also present in the MFs ob-tained in the three previous studies of Baker & Jameson (2009),Kraus & Hillenbrand (2007) and Hambly et al. (1995). On theother hand, we do not see this rise in the MF of Adams et al.(2002a). However, their MF is based on objects with a mem-bership probability higher than only 1% and within a radius of3.8 deg. Due to use of such a low probability threshold for se-lection, we expect that most of the objects used in the MF de-termination are simply field stars (which is their own conclu-sion in section 5.4; Adams et al. 2002a), so further comparison isnot warranted. As for the MFs of Gonz´alez-Garc´ıa et al. (2006)and Pinfield et al. (1997), since the highest mass bins are ∼ ∼ ⊙ (respectively), the rise observed from 0.6 M ⊙ to0.1 M ⊙ cannot be discussed.Only four MFs, in addition to our work, reach masses be-low 0.1 M ⊙ : Baker & Jameson (2009), Gonz´alez-Garc´ıa et al.(2006), Pinfield et al. (1997) and Hambly et al. (1995). Whilethe MFs of Baker & Jameson (2009) and Hambly et al. (1995)show a turn-over at 0.1 M ⊙ , the one obtained by Pinfield et al.(1997) does not. On the contrary, it presents a sudden rise at thestellar / substellar limit (with a ratio of ∼ ⊙ ).They used RIZ photometry for their survey, but not all objectswere observed in all bands, resulting in just one colour avail-able for membership determination in some cases (Pinfield et al.1997). From an analysis of MFs of other clusters and usinga multi-band photometric survey, Boudreault & Bailer-Jones(2009) have shown that use of a narrow spectral coverage withfew filters can lead to high contamination by field M dwarfs,and thus an apparent rise in the MF in the low mass regime. Wesuggest that this is the reason for the apparent rise at the low-mass end of the MF in Pinfield et al. (1997) (who also notedthat only one colour is available for many objects in their twolowest bins). As for the MF of Gonz´alez-Garc´ıa et al. (2006), asthey only have three points we cannot comment on any possibletrend.Although there are some discrepancies between the dif-ferent MFs of Praesepe from previous works and our MF,none agrees with the MF of the Hyades ( ∼
625 Myr) ob-tained by Bouvier et al. (2008) , in which the MF is ob-served to turn-over and decrease already at 0.35 M ⊙ . Thisis surprising, since Praesepe and the Hyades share a com- Like the MF of Praesepe we present, the MF of the Hyades pre-sented by Bouvier et al. (2008) is a system MF (no correction for bina-ries).0 Boudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster
Fig. 11.
MF of Praesepe from our present work ( open dots assuming a dusty atmosphere and filled dots assuming a dust-freeatmosphere), from previous work ( open triangles for survey using proper motion and filled triangles for survey using photometryonly), as well as the MF from the Hyades from Bouvier et al. (2008) ( open squares ). We also show the galactic field star MF fromChabrier (2003) as a thin dashed line and the substellar limit as a thick dashed line. We have normalized all the MFs to the log-normal fit of Chabrier et al. (2005) at ∼ ⊙ (log M = -0.5), except for those of Gonz´alez-Garc´ıa et al. 2006 Pinfield et al. 1997)which have no data here.parable age, size and mass: they have ages of 590 + − Myr(Fossati et al. 2008) and 625 ±
50 Myr (Bouvier et al. 2008),tidal radii of 11.5 ± ± ±
40 M ⊙ (Kraus & Hillenbrand 2007) and about 400 M ⊙ (Bouvier et al. 2008), respectively. Therefore, we can expectthat the potential well is the same (at least today). Only themetallicity may be slightly di ff erent, assuming the most re-cent measurement for Praesepe: [Fe / H] = + ± / H] = + ± + ± ff erence could explain the significantly di ff erentmass functions.It is a priori possible that di ff erent binary mass fractions inPraesepe and the Hyades could account for the di ff erence in theirobserved (i.e. system, rather than star) mass functions. The bi-nary fraction in Praesepe for di ff erent mass intervals was ob-tained by Pinfield et al. (2003): 17 + − % for 1.0–0.6 M ⊙ , 31 + − %for 0.6–0.35 M ⊙ , 44 ±
6% for 0.35–0.2 M ⊙ and 47 + − % for 0.11–0.09 M ⊙ . As for the Hyades, Gizis & Reid (1995) observed a bi-nary fraction of 27 ±
16% for their sample of stars ( . ⊙ ), which is consistent with another determination of the Hyades binaryfraction of 30 ±
6% from Patience et al. (1998) (for a primarymass of ∼ ⊙ ). From these figures we see no significantdi ff erence in the binary fractions of the two clusters (even if pri-marily because the uncertainties are quite large), so this cannotbe used to explain the di ff erence between in their mass functions.Of course, if the typical mass ratio in a binary system is di ff er-ent in the two clusters then this may be able to account for somedi ff erence in the mass functions, but their is also no evidence tosupport (or refute) this.A distinction between the two clusters could be the spa-tial distribution of the members. Indeed, Holland et al. (2000)observed that the Praesepe cluster might be composed oftwo merged clusters with di ff erent ages, one main cluster of630 M ⊙ and a second subcluster of 30 M ⊙ . It was even proposedthat faint low-mass members of the subcluster could appearas Praesepe brown dwarf candidates (Chappelle et al. 2005).However, Adams et al. (2002a) did not find evidence of a sub-cluster in Praesepe. Based on the spatial distribution of the maincluster and subcluster from Holland et al. (2000), our surveyonly overlaps the main cluster. In addition, a collision betweentwo clusters could not explain alone an increase of the MF down oudreault, S., et al.: Brown dwarfs and very low mass stars in the Praesepe cluster 11 to 0.1 M ⊙ , as such a collision would rather remove low-massmember of the clusters.By comparing the MF of the Hyades with the one of thePleiades ( ∼
120 Myr), Bouvier et al. (2008) concluded that dy-namical evolution was responsible for the deficiency observed inthe very-low mass star and BD regime in the Hyades. However,this deficiency is not seen in Praesepe. One possible implica-tion is that Praesepe has been less a ff ected by dynamical evolu-tion, i.e. evaporation of low mass members which are expectedto have higher speeds based on equipartition of energy. On theother hand, if dynamical evolution has a ff ected Praesepe in thesame way, then it cannot have had the same initial mass functionand / or initial conditions as the Hyades. Dynamical interactionbetween one of these clusters and another object (such as an-other open cluster in the past) could explain the discrepanciesbetween the two MFs.
6. Conclusions
We have presented the results of a survey to study the mass func-tion of the old open cluster Praesepe. The survey consisted ofoptical I c -band photometry and NIR J and K s -band photometrywith a total coverage of 3.1 deg , down to the substellar regime,with a 5 σ detection limit corresponding to 0.05 M ⊙ (the detec-tion completeness to this level is ∼ / substellar boundary at 0.072 M ⊙ .We observed that the MF of Praesepe is characterizedby a rise in the number of objects from 0.6 M ⊙ down to0.1 M ⊙ , followed by a turn-over in the MF at ∼ ⊙ . Therise is in agreement with the Praesepe MFs derived in sev-eral previous studies (Hambly et al. 1995; Kraus & Hillenbrand2007; Baker & Jameson 2009) but disagrees with Adams et al.(2002a).We have compared the mass function of Praesepe with onederived for the Hyades and have observed a significant di ff er-ence: while the Hyades has a maximum at 0.35 M ⊙ , Praesepehas a maximum at a much lower mass, 0.1 M ⊙ . Assuming thatthey have similar ages (as main sequence fitting suggests), weconclude that the clusters either had di ff erent initial mass func-tions or that dynamical interaction has modified the evolutionof one or both. More specifically, in the latter case, dynamicalevaporation does not seem to have influenced the Hyades andPraesepe in the same way. A di ff erence in the binary fraction ormass ratios could also cause a di ff erence in the mass functions,but determinations of these are not yet precise enough to suggestany di ff erence. Acknowledgements.
SB and CBJ acknowledge support from the DeutscheForschungsgemeinschaft (DFG) grant BA2163 (Emmy-Noether Programme)to CBJ. SB thanks the Calar Alto observatory sta ff for support and KesterSmith for observations performed in January 2007. We are grateful to the ref-eree, Nigel Hambly, for his constructive comments and suggestions. We ac-knowledge Klaus Meisenheimer and Marie-H´el`ene Nicol for useful discus-sions about galaxy contamination. IRAF is distributed by the National OpticalAstronomy Observatories, which are operated by the Association of Universitiesfor Research in Astronomy, Inc., under cooperative agreement with the NationalScience Foundation. Some data analysis in this article has made use of the freelyavailable R statistical package, http: // / California Institute of Technology, funded by the NationalAeronautics and Space Administration and the National Science Foundation.
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