The substellar mass function in the central region of the open cluster Praesepe from deep LBT observations

Abstract

Context. Studies of the mass function (MF) of open clusters of different ages allow us to probe the efficiency with which brown dwarfs evaporate from clusters to populate the field. Surveys of older clusters (age 100 Myr) are not affected so severely by several problems encountered in young clusters, such as intra-cluster extinction and large uncertainties in brown dwarf models. Aims. We present the results of a deep photometric survey to study the MF of the central region of the old open cluster Praesepe (age 590 +150 −120 Myr, distance 190 +6.0 −5.8 pc), down to the substellar regime. Methods. We performed an optical (riz and Y-band) photometric survey of Praesepe using the Large Binocular Telescope Camera covering an area of 0.59 deg 2 in the cluster centre from i ∼ 19.0 mag (∼100 M Jup) down to a 5σ detection limit at i ∼25.6 mag (∼40 M Jup). The survey is approximately 95% complete at i = 23.8 mag and z = 22.0 mag (∼55 M Jup). Results. We identify 59 cluster member candidates, of which 37 are substellar, by comparing with the predictions of a dusty atmo-sphere model. The MF of those candidates rises from the substellar boundary until ∼67 M Jup and then declines. This is quite different from the form inferred for other open clusters older than 50 Myr, but seems to be similar to those found in very young open clusters, the MFs of which peak at ∼10 M Jup . Either Praesepe really does have a different MF from other clusters or they had similar initial MFs but a different dynamical evolution. Since most of the candidates are faint, we lack astrometric or spectroscopic follow-ups to test their memberships. However, the contaminations by field dwarfs, galaxies, or giants are found to have little effect on the shape of MF and therefore the MF of 'real' cluster members should have similar characteristics.

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arXiv:1010.4091v1 [astro-ph.SR] 20 Oct 2010
**Volume Title**
ASP Conference Series, Vol. **Volume Number**
**Author**
c ?**Copyright Year** Astronomical Society of the Pacific
The substellar mass function in the central region of the open
cluster Praesepe from deep LBT observations
W. Wang1, S. Boudreault1,2,3, B. Goldman1, Th. Henning1, J. A. Caballero4
and C. A. L. Bailer-Jones1
1Max-Planck-Institut f¨ ur Astronomie, K¨ onigstuhl 17, D-69117 Heidelberg,
Germany
2Mullard Space Science Laboratory, University College London, Holmbury St
Mary, Dorking, Surrey, RH5 6NT, United Kingdom
3Visiting Astronomer at the Department of Physics and Astronomy, State
University of New York, Stony Brook, NY 11794-3800, USA
4Centro de Astrobiolog´ ıa (CSIC-INTA), Carretera de Ajalvir km 4, 28850
Torrej´ on de Ardoz, Madrid, Spain
Abstract.
us to probe the efficiency with which brown dwarfs (BDs) are evaporated from clusters
to populate the field. Surveys in old clusters (age?100Myr) do not suffer so severely
from several problems encountered in young clusters, such as intra-cluster extinction
and large uncertainties in BD models. Here we present the results of a deep photo-
metric survey to study the MF of the old open cluster Praesepe (age 590+150
distance 190+6.0
tify 62 cluster member candidates, of which 40 are substellar, from comparison with
predictionsfrom a dusty atmospheremodel. The MF rises fromthe substellar boundary
until ∼60 MJupand then declines. This is quite differentfromthe form inferredfor other
open clusters older than 50Myr, but seems to be similar to those found in very young
open cluster, whose MFs peak at ∼10MJup. Either Praesepe really does have a different
MF from other clusters or they had similar initial MFs but have differed in their dynam-
ical evolution. We further have identified six foreground T dwarf candidates towards
Praesepe, which require follow-up spectroscopy to confirm their nature.
Studies of the mass function (MF) of open clusters of different ages allow
−120Myr and
−5.8pc), down to a 5σ detection limit at i ∼25.6 mag (∼40MJup). We iden-
1.Introduction
The mass functions (MFs) of stellar and substellar populations have been determined
from optical and near-infrared surveys for several open clusters at different ages, such
as the Orion Nebula Cluster, σ Orionis, ρ Ophiuchi, Taurus, IC 348, IC 2391, M35,
the Pleiades, and the Hyades. Studies of relatively old open clusters (age>100Myr)
are important for the following two reasons in particular: first, they allow us to study
the intrinsic evolution of basic properties of BDs, e.g. luminosity and effective temper-
ature, and to compare the evolution with structural and atmospheric models; second,
we may investigate how the BD and low-mass star populations as a whole evolve, e.g.
the efficiency with which BDs and low-mass stars evaporate from clusters. Such an
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Wang et al.
investigation has been carried out for the Hyades (Bouvier et al. 2008, and references
therein) and for Praesepe (Boudreault et al. 2010, and references therein).
Boudreault et al. (2010, hereafter B2010) observed a significant difference be-
tween the MFs of Praesepe and Hyades: While the Hyades MF is observed to have
a maximum at ∼0.6M⊙(Bouvier et al. 2008), the MF of Praesepe continues to rise
from 0.8M⊙down to 0.1M⊙. This is surprising, as both clusters share similar physical
properties (ages, mass, metallicity, and tidal radii). Disagreement between the Praesepe
and Hyades MFs could arise from variations in the clusters’ initial MFs, or from dif-
ferences in their dynamical evolution (Bastian et al. 2010). Although different binary
fractions could cause the observed (system) MFs to differ, there is no clear evidence for
varying binary fractions from measurements published in the literature (B2010).
2. Observations and analysis
The Large Binocular Cameras (LBCs) are two wide-field, high-throughput imaging
cameras, namely Blue (LBCB) and Red (LBCR), located at the prime focus stations of
the Large Binocular Telescope (LBT). Each LBC has a wide field of view (23’×23’),
with four CCD detectors of 2048×4608 pixels each, providing images with a sampling
of 0.23′′/pixel. The optical design and detectors of the two cameras are optimized for
different wavelength ranges: one for ultraviolet-blue wavelengths (including the Bessel
U, B, V and Sloan g and r bands), and one for the red-infrared bands (including the
Sloan i, z and Fan Y bands). In the full binocular configuration, both cameras are
available simultaneously, and both point in the same direction of the sky, thus doubling
the net efficiency of the LBT. The survey was carried out with the r filter using LBC-
blue and the izY filters using LBC-red, covering the central 0.59 deg2area of Praesepe.
The standard data reduction steps for the LBT data were performed using the IDL
astronomy package and IRAF. An astrometric solution was achieved using the Sloan
Digital Sky Survey (SDSS) catalogue as a reference. The root mean square accuracy of
our astrometric solution is 0.10-0.15arcsec. To correct for Earth atmospheric absorp-
tion on the photometry, we calibrated the infrared data using the r, i and z band values
of SDSS objects which were observed in the science fields. In order to calibrate our
Y band photometry, we used our LBT i and z photometry and the Y band photometry
from the United Kingdom Infrared Telescope Infrared Deep Sky Survey (UKIDSS).
3.Candidate Selection Procedure and mass determination
Thecandidate selection procedure and themassdetermination introduced byBoudreault & Bailer-Jones
(2009) and B2010 were adopted in the present work. We use the evolutionary tracks
from (Chabrier et al. 2000) and the atmosphere models from (Allard et al. 2001) as-
suming a dusty atmosphere (the AMES-Dusty model), to compute an isochrone for
Praesepe using an age of 590+150
we neglecting the reddening.
−120Myr, a distance of 190+6.0
−5.8pc, a solar metallicity and
3.1.Candidate Selection using colour-magnitude and colour-colour diagrams
Candidates were first selected from our CMD by keeping all objects which are no more
than 0.28mag redder or bluer than the isochrones in all CMDs. This number accom-
modates errors in the magnitudes and uncertainties in the model isochrones. We also

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Figure 1.
used for the first and second selection procedures. Solid lines are the isochrones
computedfrom an evolutionarymodel with a dusty atmosphere(AMES-Dusty). The
dashed lines delimit our selection band. The numbers indicate the masses (in MJup)
on the model sequence. In the right panel, the theoretical colours of six galaxies and
of red giants are shown as thin lines and as thick lines, respectively. The six galaxies
are two starbursts, one Sab, one Sbc, and two ellipticals of 5.5 and 15Gyr, with
redshifts from z=0 to z=2 in steps of 0.25 (evolution not considered). We assume
that all red giants have a mass of 5M⊙, 0.5 < log g < 2.5 and 2000K < Teff <
6000K.
Colour-magnitude diagram (Left) and colour-colour diagram (Right)
include the errors from age and distance of Praesepe. We additionally include objects
brighter than the isochrones by 0.753mag in order to include unresolved binaries. In
Figure 1 (left) we show the CMD where candidates were selected based on z vs. i–z.
The second stage of candidate selection involves retaining just those objects which
lie within 0.28mag of the isochrone in the colour-colour diagram. This value reflects
the photometric errors and uncertainties in the model isochrones. In addition, we also
include the uncertainty in the age estimation of Praesepe. The colour-colour diagram
with the selection limits is shown in Figure 1 (right), with the theoretical colours for red
giants using the atmosphere models of Hauschildt et al. (1999) and theoretical colours
of six galaxies with redshift from 0 to 2 from K. Meisenheimer et al. ( in prep. ) over-
plotted. Neither the red giants nor the galaxies are expected to be a significant source of
contamination; most of the low redshift galaxies can be easily rejected through visual
inspection. As these are the dominant potential contaminators, we conclude that there
is no significant contamination of non-Praesepe members in our sample (Praesepe is at
a Galactic latitude of b = +32.5◦).
3.2.Observed magnitude vs. predicted magnitude
Our determination of Teffis based on the spectral energy distribution of each object
and is independent of the assumed distance. The membership status of an object can
therefore be assessed bycomparing its observed magnitude in aband withits magnitude
predicted from its Teffand the Praesepe’s isochrone (which assumes a distance and an

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Wang et al.
age). This selection step is only a verification of the consistency between the physical
parameters obtained of the photometric cluster candidates with the physical properties
assume for the cluster itself when computing the isochrones. In order to avoid removing
unresolved binaries that are real members of the cluster, we keep all objects with a
computed magnitude of up to 0.753mag brighter than the observed magnitude. This
selection procedure is illustrated in Fig. 2.
Figure 2.
tude computedfrom the derived mass and Teff, as a functionof Teff. The vertical line
marks the location of L0 dwarfs. The dotted line (at −0.753mag) represents the off-
set due to the presence of unresolved binaries, the dashed-dotted lines represent the
erroron the magnitudedetermination,and the long-dashedlines for the uncertainties
on the age and distance of Praesepe. The horizontal solid line just traces zero.
Difference between the observed J magnitude and the model J magni-
4.Results
4.1. Selected photometric candidates
62 photometric candidates survive the selection procedures (based on isochrones as-
suming dusty atmospheres). This corresponds to ∼105 objects per square degree. Our
survey saturation occurs at ∼ 18 mag in z band, corresponding to ∼100 MJup. There-
fore, most of the low mass candidates discovered in previous surveys (e.g. Pinfield et al.
1997, Hambly et al. 1995) saturate in our LBT images. Only a few faint BDs classified
by Pinfield et al. (1997), Gonz´ alez-Garc´ ıa et al. (2006) and by B2010 are rediscovered
by the current survey.
There are also some targets which are previously identified as cluster members but
rejected by our selection procedures or visual inspection. For example, ten candidates
identified by B2010 are detected (not saturated) in our LBT survey, but six of them are
rejected by the z vs. i–z CMD, because they are bluer than the isochrones area. Another

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one is obviously not a point-like source in the LBT image, and another is rejected
because its observed J magnitude is not consistent with its model-predicted magnitude.
Only the remaining two targets are confirmed to be cluster dwarf stars. As the current
work employed more photometric bands than B2010 did, it is not surprising that we
achieve a more conservative selection.
Most of our candidates are in the substellar regime, and other than these ten, no
other accurate photometric observations are available from past epochs. This precludes
using proper motions as a mean of cluster membership assessment at this time.
4.2.Contamination by non-members
As mentioned before, the two main sources of contamination are the background red
giants and unresolved galaxies. Red giants occupy the high mass end of this study, as
seen in the i − J vs. z − Ksdiagram. Although some types of galaxies share similar
colours with Praesepe cluster members more massive than 60 MJup, such low-redshift
galaxies are in general extended sources and therefore easily rejected by our visual
inspection. Among the 74 candidates that passed our selection procedures, we identify
four as galaxies through their LBT images. Other possible sources are field L dwarfs
and high redshift quasars (for instance at z ∼6; Caballero et al. 2008). However, as such
quasars have spectral energy distributions similar to mid-T dwarfs whereas our faintest
candidates have colours of early L dwarfs, and given that they are rare (0.25 quasars at
5.5 < z < 6.5 in a 0.59deg2survey, Stern et al. 2007), the MF should not be affected
by quasar contamination.
The contamination by L dwarfs is also unimportant. Caballero et al. (2008) have
collected possible field dwarf contaminants covering spectral type from M3 to T8 from
the literature. From their Table 3, the spatial density for L dwarfs in the solar neigh-
bourhood is ∼ 7 × 10−3pc−3. Given that Praesepe has a Galactic latitude of +32.5deg
and distance of 190pc, the nearby spatial density of L dwarfs Praesepe should be
∼ 6 × 10−3pc−3, assuming an exponential decrease for stellar density perpendicular
to the Galactic disk and a scale height of 500pc. If we define a volume corresponding
the area of our survey, and use the distance uncertainties to the cluster as its depth, the
total volume is ∼ 80pc3. Therefore, we estimate that we have ∼0.5 L dwarf contami-
nants near the cluster, which amounts to a negligible contamination of merely 0.7%. A
similar calculation shows that we would have ∼4 M dwarf contaminants, about 6%.
We conclude that various contaminants are not important for this study and the
MF we derive for Praesepe should be accurate.
5. Mass function of very low mass and substellar population of Praesepe
The mass function, ξ(log10M), we present here is the total number of objects per square
degree in each logarithmic mass interval log10M to log10M + 0.1, Since we do not make
any corrections for binaries, we compute here a system MF.
Our optical photometry reaches lower masses than the NIR photometry that we
used. To compute the MF of Praesepe to the lowest mass bin, we first computed a MF
using only the optical iz photometry. This MF is presented on Fig. 3 as filled dots.
We computed a second MF from the list of candidates that pass the three selections
criteria which are also detected in the survey of B2010 in the NIR J and Ksbands
(presented on Fig. 3 as filled triangles). For each mass bin, we computed the number of
object removed because of adding the J and Ksfilters to our selection process and mass