Issue |
A&A
Volume 510, February 2010
|
|
---|---|---|
Article Number | A27 | |
Number of page(s) | 14 | |
Section | Galactic structure, stellar clusters, and populations | |
DOI | https://doi.org/10.1051/0004-6361/200913011 | |
Published online | 03 February 2010 |
Brown dwarfs and very low mass stars in the Praesepe open
cluster: a dynamically unevolved mass function?
,![[*]](/icons/foot_motif.png)
S. Boudreault1 - C. A. L. Bailer-Jones1 - B. Goldman1 - T. Henning1 - J. A. Caballero2
1 - Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
2 - Departamento de Astrofísica, Facultad de Física, Universidad Complutense de Madrid, 28040 Madrid, Spain
Received 29 July 2009 / Accepted 23 October 2009
Abstract
Context. Determination of the mass functions of open
clusters of different ages allows us to infer the efficiency with which
brown dwarfs 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 open
cluster Praesepe (age 590
+150-120 Myr, distance 190
+6.0-5.8 pc) from which we estimate its mass function and compare this with that of other clusters.
Methods. We performed an optical (-band) and near-infrared (J and
-band) photometric survey of Praesepe covering 3.1 deg2. With 5
detection limits of
and J = 20.0, our survey is predicted to be sensitive to objects with masses from 0.6 to 0.05
.
Results. We photometrically identify 123 cluster member
candidates based on dust-free atmospheric models and 27 candidates
based on dusty atmospheric models. The mass function rises from
0.6
down to 0.1
(a power law fit of the mass function gives
;
(M)
), and then turns over at
0.1
.
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 differs significantly from that measured for the
Hyades, an open cluster with a similar age (
Myr).
Possible reasons are that the clusters did not have the same initial
mass function, or that dynamical evolution (e.g. evaporation of low
mass members) has proceeded differently in the two clusters. Although
different binary fractions could cause the observed (i.e. system) mass
functions to differ, there is no evidence for differing binary
fractions from measurements published in the literature. Of our cluster
candidates, six have masses predicted to be equal to or below the
stellar/substellar boundary at 0.072
.
Key words: open clusters and associations: individual: Praesepe - stars: low-mass - stars: brown dwarfs - stars: luminosity function, mass function - stars: formation
1 Introduction
Several publications in the past decade have been concerned with the
mass function (MF) of low mass stellar and substellar populations in
open clusters, including Orionis (Béjar et al. 2002;
Caballero et al. 2007), the Orion Nebula Cluster
(Hillenbrand & Carpenter 2000; Slesnick et al. 2004), IC 2391
(Barrado y Navascués et al. 2004; Boudreault & Bailer-Jones 2009), 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
in particular. First, they permit a study of the intrinsic evolution
of brown dwarfs (BDs), e.g. their luminosity and effective
temperature, which constrains structural and atmospheric models.
Second, together with younger clusters we can investigate how BD
populations as a whole evolve and thus probe the efficiency with which BDs
evaporate from clusters to populate the Galactic field. Numerical
simulations of cluster evolution have demonstrated 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 cluster BD (and low-mass star) population. This has been
observed 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 on young open
clusters with ages less than 100 Myr, and in many cases much
younger (<10 Myr). This is partly because BDs are bright when they
are young (lacking a significant nuclear energy source, they cool as
they age), thus easing detection of the least massive objects.
However, youth presents difficulties. First, intra-cluster extinction
plagues the determination of the intrinsic luminosity function from
the measured photometry. Second, at these ages the BD models have
large(r) uncertainties (Baraffe et al. 2002). Estimates of the substellar MF in very young clusters (age
1 Myr) might be
unreliable due to these modelling uncertainties
(Chabrier et al. 2005). BDs in older clusters suffer less from
these problems, but have the disadvantage that much deeper surveys are
required to detect them.
The old open cluster Praesepe is an interesting target considering its
age and distance. It is located at a distance of
190
+6.0-5.8 pc (based on parallax measurements from the new
Hipparcos data reduction, van Leeuwen 2009) and has an age of
590
+150-120 Myr (by isochrone fitting in the
Hertzsprung-Russell diagram; Fossati et al. 2008). The extinction
towards this cluster is low,
mag
(Taylor 2006), while determinations of the metallicity of
Praesepe yield some discrepancies: [Fe/H] =
,
Friel & Boesgaard (1992); +
,
Boesgaard & Budge (1988);
from spectroscopy and
from photometry, An et al. (2007);
+
,
Pace et al. (2008). Hambly et al. (1995) presented a
19 deg2 survey of the Praesepe cluster down to masses of
0.1
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 = 21.2 mag,
R = 22.2 mag over 800 arcmin2 uncovered one spectrally
confirmed very low-mass star or BD (spectral type of M8.5V) with a
model-dependent mass of 0.063-0.084
(Magazzú et al. 1998). A
survey over the central 1 deg2 with 10
limits of
R = 21.5, I = 20.0 and Z = 21.5 mag revealed 19 BD
candidates and the first MF determination of Praesepe down to the
substellar limit, but without spectral confirmation
(Pinfield et al. 1997). Subsequent infrared photometry of the sample reduced this
number to nine candidates (Hodgkin et al. 1999). Adams et al. (2002a)
presented a 100 deg2 study of Praesepe using 2MASS (Two-Micron All
Sky Survey) data and Palomar survey photographic plates, from which they
derived proper motions. They determined the radial profile of this
cluster but their MF does not reach the substellar regime. A more
recent proper motion survey of Praesepe covers a much larger area
(300 deg2; Kraus & Hillenbrand 2007), but does not reach the BD regime
either (the limit is
0.12
). Finally, the most recent
substellar MF determination of Praesepe was published by
González-García et al. (2006) and extends to a 5
detection limit
of i = 24.5 mag corresponding to 0.050-0.055
.
They
identified one new substellar candidate, but their survey covers only
1177 arcmin2.
In this paper, we present the results of a program to study, in
detail, the MF of Praesepe down to the substellar
regime. Our photometric survey is, as with González-García et al. (2006),
the deepest so far in optical and near-infrared (NIR) bands, with
5
detection limits of
and J=20.0(corresponding to a mass limit of about 0.05
), but covers
more than nine times the area. Our paper is structured as follows. We
first present the data set, reduction procedure and calibration in
Sect. 2. We then discuss our candidate selection
procedure in Sect. 3 and the survey results in Sect. 4 before discussing the derived MF in Sect. 5. We conclude in Sect. 6.
2 Observations, data reduction, calibration, and estimation of masses and effective temperatures
2.1 Observations
Table 1: Description of observations with the O2k infrared camera.
Table 2: Description of observations with WFI optical camera.
Our survey consists of 47 Omega 2000 (O2k) fields each of size
arcmin2 observed in J and
,
plus the
same region observed in nine
Wide Field Imager (WFI)
fields each of size
arcmin2. This gives a total
coverage of 3.1 deg2 observed in all three bands, centred on
RA(J2000) = 08
40
04
and Dec(J2000) = + 19
40'00''.
The near-infrared (NIR) observations were made on the 3.5m telescope at Calar Alto,
Spain (with observation runs of several nights from February 2005 to
January 2007). O2k (Bailer-Jones et al. 2000; Baumeister et al. 2003)
comprises a HAWAII-2 detector with 2k 2k pixels over a field
of view of
arcmin delivering a pixel scale of 0.45 arcsec
per pixel. The optical observations were carried out with the Wide
Field Imager (WFI) on the MPG/ESO 2.2m telescope at La Silla, Chile
(Baade et al. 1999) during 17-22 March 2007. The WFI is a mosaic
camera of
CCDs, each with 2k
4k pixels,
covering a total field of view of
arcmin2 at
0.238 arcsec per pixel. All fields were observed in the broad band
filter
.
A detailed list of the fields observed with
pointing, filter, exposure time and 5
detection limits is
given in Table 1 for the NIR data and in
Table 2 for the optical data. The passband
functions for the filters, multiplied with the quantum efficiency of
the detectors, are shown in Fig. 1.
![]() |
Figure 1:
Transmission curve of the filters used
in our survey compared to the synthetic spectrum of a BD with
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2.2 Data reduction and astrometry
The standard data reduction steps (overscan subtraction, trimming and
flat-fielding for the WFI data; dark subtraction and flat-fielding for
O2k data) were performed on a nightly basis, using the ccdredpackage under IRAF. For both WFI and O2k
data we used superflats (obtained by combining science image
frames for each night) for pixel-to-pixel variation correction and for
correcting the global illumination. For our NIR data, the sky
background was subtracted using the median-combined images for each
filter and each field (on a nightly basis). For WFI data, we reduced
each of the eight CCDs in the mosaic independently and in the final
step scaled them to a common flux response level. We made an initial
sky subtraction via a low-order fit to the optical data, and for the
infrared data by subtracting a median combination of all
(unregistered) images of the science frames. Fringes were visible for
the
-band photometry. They were removed in the way
described by Bailer-Jones & Mundt (2001)
. Finally, the individual images of a given field were
registered and median combined. We used the IRAF task daofind
to automatically detect stellar objects in an image by approximating
the stellar point spread function with a Gaussian. We
visually inspected the images in order to remove from our cluster
candidate list any extended sources (i.e. galaxies) that were
mistakenly identified as stars by daofind (see Sect. 3.3). Sources were extracted and instrumental
magnitudes assigned via aperture photometry with the IRAF task
wphot. To this aperture photometry we have applied an
aperture correction following the technique described in Howell (1989).
An astrometric solution was obtained using the IRAF package
imcoords and the tasks ccxymatch, ccmap and
cctran. For each WFI field, this solution was computed for
the
-band image (and for each O2k field using the J-band
image) using the 2MASS catalogue as a reference. The root mean square
accuracy of our astrometric solution is 0.15-0.20 arcsec for both WFI
and O2k data. For WFI data, the astrometry was performed on a
CCD-by-CCD basis.
2.3 Photometric calibration
To correct for Earth-atmospheric absorption on the photometry, we
calibrated the infrared data using the J and -band magnitudes
of 2MASS objects which were observed in our science fields. By
determining a constant offset between the magnitude of 2MASS and our
instrumental magnitude, we obtained the zero point offset. Since this
zero point offset was obtained with objects in the same field of view
in each science frame, and since we found the difference between the
2MASS and O2k passbands to be insignificant, we did not need to
perform an airmass or colour correction when reducing our NIR
photometry. (That is, the determined coefficients were statistically
consistent with zero).
We followed a similar approach for our -band photometry,
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 magnitudes of SDSS to
-band magnitudes using the transformation equation of
Jordi et al. (2006)
![]() |
(1) |
We then determined the zero point offset between this


2.4 Mass and effective temperature estimates based on photometry
After we identify candidates (Sect. 3) we will use the multiband
photometry to derive their masses and effective temperatures,
.
We use the evolutionary tracks from Baraffe et al. (1998) and
atmosphere models from Hauschildt et al. (1999a) (assuming a dust-free
atmosphere; the NextGen model) to compute an isochrone for Praesepe
for an age of 590 Myr, a distance of 190 pc, a solar metallicity
and assuming zero extinction. These models and assumptions provide us
with a prediction of
,
the spectral energy distribution
received at the Earth (in erg cm-2 s-1 Å-1) from the
source. We need to convert these spectral energy distributions into magnitudes in the filters we used. Denoting as SA(
)
the (known) total
transmission function of filter A (including the CCD quantum
efficiency and assuming telescope and instrumental throughput are
flat), then the flux measured in the filter is
The corresponding magnitude mA in the Johnson photometric system is given by
where cA is a constant (zero point) that remains to be determined in order to put the model-predicted magnitude onto the Johnson system. We derived this constant for each of the bands




Assuming that all our photometric candidates belong to Praesepe, we
derive masses and effective temperatures from these isochrones using
our three filter measurements in the following way. We first normalize
the energy distribution of each object to the energy distribution of
the model using the J filter. We then estimate the mass and
effective temperature via a least squares fit of the measured spectral
energy ``distribution'' (actually just two points) to the model
spectral energy distribution from the isochrone. This involves
estimating one parameter from two measurements, because mass and
are not independent.
The above assumption of a dust-free atmosphere is valid for
3000 K, but objects with
3000 K
1800 K are expected to
have dust in equilibrium with the gas phase (Allard et al. 2001). We
therefore perform a second selection of candidates (and determination
of mass and
)
based on isochrones predicted in the same
way, but based on evolutionary tracks of Chabrier et al. (2000) and the
AMES-dusty model of Allard et al. (2001). This give us a second
dusty model list of candidates. A priori some observed stars
could appear in both lists (and in fact two do), but in our later
discussions of the mass function we do not mix stars from the two
lists but rather make separate determinations of the mass function.
There are various sources of error in the estimation of mass
and
.
These are the photon noise, the photometric
calibration, the least squares fitting (imperfect model) and the
uncertainties in the age of and distance to Praesepe. The uncertainties
in the age and distance are the most significant errors
and given rise to uncertainties of
and
K for a
substellar object,
and
K
for an object at the hydrogen burning limit and
and
K for a solar-type
star.
3 Candidate selection procedure
The candidate selection procedure for BDs and very low-mass stars is
as follows (and explained in more detail in the remainder of this
section). Candidates were first selected based on colour-magnitude
diagrams (CMDs) and this further refined using colour-colour
diagrams. In the third and final selection, we used the known distance
to Praesepe to reject objects based on a discrepancy between the
observed magnitude in J and the magnitude in this band computed with
the isochrones and our estimation of
.
To be considered
as a cluster member, an object has to satisfy all three of these
criteria. We make two independent selections: one using dust-free and
one using dusty atmospheric models.
3.1 First candidate selection step: colour-magnitude diagrams
Candidates were first selected from our CMDs by retaining only objects
which are no more than 0.14 mag redder or bluer than the isochrone in
all CMDs. This number accommodates errors in the magnitudes,
uncertainties in the model isochrones plus uncertainties in the
cluster age and distance estimates. We additionally include objects
brighter than the isochrones by 0.753 mag in order to include
unresolved binaries. In Figs. 2 and 3
we show two CMDs where candidates were selected based on vs.
-J and
vs.
-
.
These figures also show low-mass cluster member candidates from
previous studies which we detected in our survey
(Pinfield et al. 1997; Adams et al. 2002a;
González-García et al. 2006; Kraus & Hillenbrand 2007). In Fig. 3, we can observe three structures in this CMD. The
two structures at
mag and
mag are predominantly stars (Galactic
disk turn-off, and disk late-type and giant stars respectively) while
the structure at
mag is mostly composed
of galaxies. From a total of 23 891 objects detected above the
5
detection limit in all filters, 800 are retained as
candidate cluster members (96.7% are rejected). If we instead use
dusty model isochrones, then out of the 23 891 objects, 357 are
retained (98.5% are rejected) for our dusty model list.
![]() |
Figure 2:
Colour-magnitude diagram showing an example of
the first selection step using the |
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![]() |
Figure 3:
As Fig. 2 but with the |
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![]() |
Figure 4: Colour-colour diagram
used in the second selection step. The solid line is the isochrone
computed from an evolutionary model with a dust-free atmosphere
(NextGen model, the masses in |
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![]() |
Figure 5:
As Fig. 4, but now showing
the theoretical colours of six galaxies as thick dotted lines
and the theoretical colours of red giants as thick solid lines.
The six galaxies are two starbursts, one Sab, one Sbc, and two
ellipticals of 5.5 and 15 Gyr, 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 5 |
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3.2 Second candidate selection step: colour-colour diagram
The second stage of candidate selection involves retaining just those
objects which lie within 0.24 mag of the isochrone in the (single)
colour-colour diagram. This value reflects the photometric errors
plus uncertainty in the age estimation of Praesepe. One such
colour-colour diagram with the selection limits is shown in Fig. 4.
The two main sources of contamination beside field M dwarfs are
background red giants and unresolved galaxies (Praesepe is
at a Galactic latitude of
). We show in Fig. 5 the theoretical colours for red giants using the
atmosphere models of Hauschildt et al. (1999b) and theoretical colours of
six galaxies from Meisenheimer et al. (in prep.). We see that red giants
could be a source of contamination in the mass range of
0.09-0.2
and at
0.7
,
while unresolved
galaxies should not be a major source of contamination below
0.6
.
In Fig. 5 we see the same three
structures as in Fig. 3: from top to bottom galaxies,
disk late-type and giant stars, and Galactic disk turn-off stars. Of the
800 objects selected in the first step, 291 are kept here (63.6% are
rejected) assuming a dust-free atmosphere, and 110 out of 357 are kept
(69.2% are rejected) when using the model for a dusty atmosphere.
3.3 Third candidate selection step: rejection based on observed magnitude vs. predicted magnitude discrepancy
As indicated in Sect. 2.4, our determination of
is 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
by comparing its observed magnitude in a band with its
magnitude predicted from its
and Praesepe's isochrone (which assumes a distance).
The premise is that the predicted magnitude of a background
contaminant would be lower (brighter) than its observed magnitude and
higher (fainter) for a foreground contaminant. 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 0.753 mag
brighter than the observed magnitude. We also take into account
photometric errors and uncertainties in the age and distance of
Praesepe. This selection procedure is illustrated in Fig. 6. From 291 objects selected through CMDs and
colour-colour diagrams in the first two steps, 144 are kept (50.5% are rejected) when using
the dust-free atmospheres/models, and 35 out of 110 are kept (68.2%
are rejected) when using the dusty atmosphere/models.
![]() |
Figure 6:
Difference between the observed J magnitude and the model J magnitude computed from the derived
mass and
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After this step, we perform a visual inspection directly on the images to reject resolved galaxies and spurious detections. This inspection removes 21 and 8 objects from the dust-free and dusty selection respectively.
4 Results of the survey
We now present the selected candidates, discuss contamination by cluster non-members and derive the magnitude and mass functions for Praesepe.
4.1 Selected photometric candidates
The final selection reveals 123 photometric candidates using an
isochrone based on dust-free atmospheres, and 27 objects using an
isochrone assuming dusty atmospheres. This corresponds to
40 and
9 objects per deg2respectively. All our photometric candidates are presented in Table 3. Objects are given the notation
PRAESEPE-YYY where YYY is a serial identification number (ID).
Numbers above 900 indicate candidate members assuming a dusty
atmosphere. Only the first 10 rows of the tables are shown, all other
data are available online. We also note in Table 4 which objects are candidate cluster members
also identified as such by Kraus & Hillenbrand (2007), Adams et al. (2002a) or
Pinfield et al. (1997).
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.
Some Praesepe members from previous studies are not detected in our
work. This is the case for the objects from Pace et al. (2008) and
Fossati et al. (2008), for example. Since those studies focused on bright
objects, these stars saturate in our science images.
(Pace et al. 2008; Fossati et al. 2008, were concerned with chemical
abundances of A-type and solar-type stars, respectively, while our
saturation occurs at 0.7
).
Not all objects identified by other surveys as brown dwarfs or very
low mass stellar member candidates - and detected in our survey -
are members based on our criteria. The two objects from the work of
González-García et al. (2006), who also used photometry in order to
select candidate members, we detect above our 5
limit
(Prae J084039.3+192840 and Prae J084130.4+190449). Yet both objects are
non-members based on our selection criteria, because they have
colours bluer than our selection band.
(Prae J084130.4+190449
is also too blue in
for our selection band at
mag, whereas Prae J084039.3+192840 at
mag lies within it).
González-García et al. (2006) did not report any NIR photometry for
these two objects. Although the non-membership of
Prae J084039.3+192840 can be debated (high membership probability
based on González-García et al. 2006), Prae J084130.4+190449 is most
likely an unresolved galaxy (low membership probability;
González-García et al. 2006).
Table 4: Photometric candidates in our survey that are also photometric candidates in previous surveys.
Of the candidates from the photometric survey of Pinfield et al. (1997), seven fall within our survey and are detected, of which six are identified as candidates by our selection criteria. The non-selected object is RIZpr6 in Hodgkin et al. (1999). It is bluer than the isochrones in both CMDs in Figs. 2 and 3. From its positions in the CMDs and in the colour-colour diagram in Fig. 4, we suspect that this object is an unresolved galaxy.
11 of the the 14 objects from a survey based on proper motion and
photometry by Adams et al. (2002a) are identified by our selection. The
objects not recovered fail the observed magnitude vs. predicted
magnitude test. On the other hand, 27 cluster candidates of
Kraus & Hillenbrand (2007) out of 37 detected in our survey are selected. The
10 non-selected objects have membership probabilities from
Kraus & Hillenbrand (2007) based on proper motion greater than 95%, and are
brighter than the 10
detection limit of the publicly available
surveys used in their work. However, these objects failed our observed
magnitude vs. predicted magnitude test and some are bluer than our
isochrone of Praesepe in
.
With
colour of
2 mag, we suggest that these objects are more likely to be disk late-type stars or giant stars.
The 5
detection limits of our survey are
mag, J = 20.0 mag and
mag (which
correspond to
0.05
using the dust-free
isochrone). However, we cannot expect to detect all objects
down to these magnitudes.
We estimate the survey completeness
by taking the ratio of the number of objects
detected to the predicted number of detections, the latter made by assuming a uniform
distribution of stars along the line of sight in our survey fields.
(This comparison distribution is somewhat crude, but it gives
an approximate value without making too many assumptions). The
predicted number of detections is obtained from the histogram of the
number of detections as a function of magnitude (Fig. 7)
and by observing where the distribution drops off compared to a
straight line extrapolation. Based on this, the completeness of the
survey down to the
5
detection limit is 90% in
,
88% in J and 87%
in
.
The overall detection completeness of our
survey, from saturation to 5
detection corresponding to
0.05
,
is therefore
87%. In J band, we reach a completeness of 95% at J = 19.7 mag, which corresponds to
0.055
.
4.2 Substellar candidates in Praesepe
Six objects in our survey are cluster candidates with theoretical
masses equal to or below the stellar/substellar boundary at
0.072 .
We present the finding charts of the six objects in
Fig. 8. In Table 5, we
present their coordinates and physical parameters. These BD candidates
have predicted masses between 0.064 and 0.072
.
A
spectroscopic follow up (on a 8 m class telescope or larger) will be
needed in order to confirm or refute their membership and their
substellar status.
4.3 Contamination by non-members
As mentioned in Sect. 3.2, the two main sources of
contamination are the background red giants, which are the dominant
source at masses of 0.09-0.2
and
0.7
,
and unresolved galaxies, mostly affecting masses above
0.6
.
Other possible contaminants are field M dwarfs and high redshift quasars (for instance at
;
Caballero et al. 2008). However, as such 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 < 6.5 in a 8 deg2 survey,
Stern et al. 2007), the MF should not be affected by quasar
contamination.
Let us estimate the contamination by M dwarfs,
First, we consider that close to the open cluster Praesepe, the space
density of M dwarfs is uniform. We assume that their
density ()
drops exponentially with vertical distance
from the galactic disk (h) such that
![]() |
(4) |
assuming a scale height of h0 = 500 pc. We use the local space density (






4.4 Luminosity function and mass function
We present in Fig. 9 the luminosity function of Praesepe using the J-band magnitude of the cluster candidates. No correction is made for binaries, so this is the system rather than single-star luminosity function.
The mass function (MF),
), is generally defined as
the number of stars per cubic parsec in the logarithmic mass interval
to
.
Here, we do not compute
the volume of Praesepe so instead we define the MF as the total
number of objects in each
bin per square degree.
Since we do not make any corrections for
binaries we compute here a system MF. Our inferred MF is
shown in Fig. 10. The log-normal form for a MF is
![]() |
(5) |
where k = 0.086,





from the highest mass bin to the turn over at 0.1





5 Analysis and discussion of the stellar and substellar mass function of Praesepe
Our MF of Praesepe (Fig. 10) shows a rise in the
number of objects from 0.6
down to 0.1
,
and then
a turn-over at
0.1
.
This turn-over is not due to
incompleteness since it occurs well above the 5
detection
limit corresponding to 0.05
.
This behaviour is confirmed
by the luminosity function in Fig. 9 which shows a
rise from J = 13 to 16 mag (with candidates obtained using a dust-free
atmosphere) and a drop at J = 17 mag (seen with both types of candidates).
To help the analysis of these features in the mass function, we compare in
Fig. 11 the mass functions of Praesepe obtained from several studies plus the MF for the old open cluster Hyades (age of 625 Myr).
The rise in our MF of Praesepe is also present in the MFs obtained in the
three previous studies of Baker & Jameson (2009), Kraus & Hillenbrand (2007) and
Hambly et al. (1995). On the other hand, we do not see this rise in the
MF of Adams et al. (2002a). However, their MF is based on objects with a
membership probability higher than only 1% and within a radius of
3.8 deg. Due to use of such a low probability threshold for
selection, we expect that most of the objects used in the MF
determination are simply field stars (which is their own conclusion in
Sect. 5.4; Adams et al. 2002a), so further comparison is not
warranted. As for the MFs of González-García et al. (2006) and Pinfield et al. (1997), since the highest mass bins are 0.11 and
0.15
(respectively), the rise observed from 0.6
to
0.1
cannot be discussed.
![]() |
Figure 7:
Estimation of the completeness
limit for our survey using the J band. The solid line is the
best linear fit before the turn off, the vertical dashed line is
the 5 |
Open with DEXTER |
![]() |
Figure 8:
Finding charts of the six new BD
candidates of Praesepe (J-band). We observed objects very close
to PRAESEPE-099 and -909, although they do not influence the
photometry. The panels are
|
Open with DEXTER |
Table 5: Same as Table 3, but only the BD candidates are given and we include the spectral type expected.
![]() |
Figure 9:
J band luminosity function. The
solid line histogram represents the luminosity function based on a
selection using a dust-free atmosphere (NextGen model); the
thick dotted histogram uses a dusty atmosphere (AMES-Dusty
model). The stellar/substellar limit is at
|
Open with DEXTER |
![]() |
Figure 10:
Mass function based on our survey photometry. Points with error bars represent the MF based on a selection and
mass calibration assuming a dust-free atmosphere, whereas the open
circles with error bars are the MF based on the dusty atmosphere
model. We also overplot the log-normal and the power law MF fitted
to our data (both solid line). Error bars are Poissonian arising
from the number of objects observed in each bin. The vertical thin
dotted lines are the mass limits at which detector saturation occurs
in the |
Open with DEXTER |
Only four MFs, in addition to our work, reach masses below
0.1 :
Baker & Jameson (2009), González-García et al. (2006),
Pinfield et al. (1997) and Hambly et al. (1995). While the MFs of
Baker & Jameson (2009) and Hambly et al. (1995) show a turn-over at
0.1
,
the one obtained by Pinfield et al. (1997) does not.
On the contrary, it presents a sudden rise at the
stellar/substellar limit (with a ratio of
5 in the number of
objects at the mass bin at 0.07 to the number in the bin at
0.11
). They used RIZ photometry for their survey, but not all
objects were observed in all bands, resulting in just
one colour available for membership determination in some cases
(Pinfield et al. 1997). From an analysis of MFs of other clusters and
using a multi-band photometric survey, Boudreault & Bailer-Jones (2009) have
shown that use of a narrow spectral coverage with few filters can lead
to high contamination by field M dwarfs, and thus an apparent rise in
the MF in the low mass regime. We suggest that this is the reason for
the apparent rise at the low-mass end of the MF in Pinfield et al. (1997)
(who also noted that only one colour is available for many objects in
their two lowest bins). As for the MF of González-García et al. (2006),
as they only have three points we cannot comment on any possible
trend.
![]() |
Figure 11:
MF of Praesepe from our present
work (open dots assuming a dusty atmosphere and
filled dots assuming a dust-free atmosphere), from
previous work (open triangles for survey using proper
motion and filled triangles for survey using photometry
only), as well as the MF from the Hyades from Bouvier et al. (2008)
(open squares). We also show the galactic field star MF
from Chabrier (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 |
Open with DEXTER |
Although there are some discrepancies between the different MFs of
Praesepe from previous works and our MF, none agrees with the MF of
the Hyades (625 Myr) obtained by
Bouvier et al. (2008)
, in which the MF is observed to turn-over
and decrease already at 0.35
.
This is surprising, since
Praesepe and the Hyades share a comparable age, size and mass: they
have ages of 590
+150-120 Myr (Fossati et al. 2008) and
Myr (Bouvier et al. 2008), tidal radii of
pc (
deg, Kraus & Hillenbrand 2007) and 10.3 pc
(12.5 deg, Bouvier et al. 2008), and masses of
(Kraus & Hillenbrand 2007) and about 400
(Bouvier et al. 2008), respectively. Therefore, we can expect that
the potential well is the same (at least today). Only the metallicity
may be slightly different, assuming the most recent measurement for
Praesepe: [Fe/H] = +
for the latest metallicity
measurement of Praesepe (Pace et al. 2008) and
[Fe/H] = +
for the Hyades (Bouvier et al. 2008),
although a metallicity as low as +
(Friel & Boesgaard 1992) has been reported for Praesepe. It is unclear
how this metallicity difference could explain the significantly
different mass functions.
It is a priori possible that different binary mass fractions in
Praesepe and the Hyades could account for the difference in their
observed (i.e. system, rather than star) mass functions. The binary
fraction in Praesepe for different mass intervals was obtained by
Pinfield et al. (2003): 17
+6-4% for 1.0-0.6 ,
31
+7-6% for 0.6-0.35
,
% for
0.35-0.2
and 47
+13-11% for 0.11-0.09
.
As for the Hyades, Gizis & Reid (1995) observed a binary fraction of
% for their sample of stars (
0.4
), which
is consistent with another determination of the Hyades binary fraction
of
% from Patience et al. (1998) (for a primary mass of
0.6-2.8
).
From these figures we see no significant difference in the binary
fractions of the two clusters (even if primarily
because the uncertainties are quite large), so this cannot be used
to explain the difference between in their mass functions. Of course,
if the typical mass ratio in a binary system is different in the two
clusters then this may be able
to account for some difference in the mass functions, but their
is also no evidence to support (or refute) this.
A distinction between the two clusters could be the spatial
distribution of the members. Indeed, Holland et al. (2000) observed that
the Praesepe cluster might be composed of two merged clusters with
different ages, one main cluster of 630
and a second
subcluster of 30
.
It was even proposed that faint low-mass
members of the subcluster could appear as Praesepe brown dwarf candidates
(Chappelle et al. 2005). However, Adams et al. (2002a) did not find
evidence of a subcluster in Praesepe. Based on the spatial
distribution of the main cluster and subcluster from
Holland et al. (2000), our survey only overlaps the main cluster. In
addition, a collision between two clusters could not explain alone an
increase of the MF down to 0.1
,
as such a collision would
rather remove low-mass member of the clusters.
By comparing the MF of the Hyades with the one of the Pleiades
(120 Myr), Bouvier et al. (2008) concluded that dynamical
evolution was responsible for the deficiency observed in the very-low
mass star and BD regime in the Hyades. However, this deficiency is not
seen in Praesepe. One possible implication is that Praesepe has been
less affected by dynamical evolution, i.e. evaporation of low mass
members which are expected to have higher speeds based on
equipartition of energy. On the other hand, if dynamical evolution
has affected Praesepe in the same way, then it cannot have had
the same initial mass function and/or initial conditions as the
Hyades. Dynamical interaction between one of these clusters and
another object (such as another open cluster in the past) could
explain the discrepancies between the two MFs.
6 Conclusions
We have presented the results of a survey to study the mass function
of the old open cluster Praesepe. The survey consisted of optical
-band photometry and NIR J and
-band
photometry with a total coverage of 3.1 deg2, down to the
substellar regime, with a 5
detection limit corresponding to
0.05
(the detection completeness to this level is
87%).
Our final sample yields 123 photometric cluster member
candidates based on a selection assuming a dust-free atmosphere and 27
photometric cluster candidates based on a selection assuming a dusty
atmosphere. We estimate the contamination by field M-dwarfs to be
13% or less. Among our cluster candidates, six objects have theoretical
masses equal to or less than the stellar/substellar boundary at
0.072 .
We observed that the MF of Praesepe is characterized by a rise in the
number of objects from 0.6
down to 0.1
,
followed by
a turn-over in the MF at
0.1
.
The rise is in agreement with the Praesepe MFs derived in several previous studies (Hambly et al. 1995;
Kraus & Hillenbrand 2007; Baker & Jameson 2009) but disagrees with
Adams et al. (2002a).
We have compared the mass function of Praesepe with one derived for
the Hyades and have observed a significant difference: while the Hyades has
a maximum at 0.35 ,
Praesepe has a maximum at a
much lower mass, 0.1
.
Assuming that they have similar ages
(as main sequence fitting suggests), we conclude that the clusters
either had different initial mass functions or that dynamical
interaction has modified the evolution of one or both. More
specifically, in the latter case, dynamical evaporation does not seem
to have influenced the Hyades and Praesepe in the same way. A
difference in the binary fraction or mass ratios could also cause a
difference in the mass functions, but determinations of these are not
yet precise enough to suggest any difference.
S.B. and C.B.J. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) grant BA2163 (Emmy-Noether Programme) to CBJ. S.B. thanks the Calar Alto observatory staff for support and Kester Smith for observations performed in January 2007. We are grateful to the referee, Nigel Hambly, for his constructive comments and suggestions. We acknowledge Klaus Meisenheimer and Marie-Hélène Nicol for useful discussions about galaxy contamination. IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. Some data analysis in this article has made use of the freely available R statistical package, http://www.r-project.org. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.
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Online Material
Table 3: All photometric cluster member candidates of our survey.
Footnotes
- ... function?
- Based in part on observations carried out at ESO/La Silla, Chile under proposal number 078.A-9055(A).
- ...
- Full Table 3 is only available in electronic form at http://www.aanda.org
- ... under IRAF
- The O2k camera suffers from a stray light problem. It appears on every image taken with the camera, forming a ring pattern centred in the middle of the detector (Nicol 2009). The stray light is removed via our global illumination correction and sky subtraction.
- ...Bailer-Jones & Mundt (2001)
- A fringe correction frame was created, which is a median combination of all science frames in a same filter with the same exposure time. This fringe correction frame was scaled by a factor, determined manually for each science frame, and subtracted from the science image.
- ... atmospheres
- Two objects in the dust-free atmosphere selection (PRAESEPE-089 and -093) were also identified in dusty atmosphere selection (PRAESEPE-915 and -917).
- ...Bouvier et al. (2008)
- Like the MF of Praesepe we present, the MF of the Hyades presented by Bouvier et al. (2008) is a system MF (no correction for binaries).
All Tables
Table 1: Description of observations with the O2k infrared camera.
Table 2: Description of observations with WFI optical camera.
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.
Table 4: Photometric candidates in our survey that are also photometric candidates in previous surveys.
Table 5: Same as Table 3, but only the BD candidates are given and we include the spectral type expected.
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