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Subsections

3 Results

The (I,I-Z) color magnitude diagrams of the point-like objects contained in the 17 Pleiades fields are shown in Figs. 5 and 6. The short and long exposures have been analysed separately corresponding respectively to the stellar and the substellar domains. In both cases we present our photometric selection of candidates before dealing with the field star contamination. We examine the spatial distribution of cluster members and attempt to measure their core radius. We then use these estimates to derive the Pleiades mass function.

3.1 Stellar domain

The (I,I-Z) color magnitude diagram for the short exposure images of our survey is presented in Fig. 5. The 120 Myr isochrone from the NEXTGEN models of Baraffe et al. (1998) shifted to the Pleiades distance ( $(m-M)_{\rm o}= 5.53$) is shown as a dashed line. On the basis of the location of this theoretical isochrone, we made a rather conservative photometric selection to include all possible stellar members between I=13.5 and I=17.5. This selection corresponds to the box drawn in Fig. 5.


  \begin{figure} \includegraphics[width=8.8cm,clip]{ms3257f5.ps} \end{figure} Figure 5: (I,I-Z) color-magnitude diagram for the short exposures. The dashed line is the 120 Myr isochrone from the NEXTGEN models of Baraffe et al. (1998) shifted to the Pleiades distance. The region corresponding to our photometric selection for stellar candidates corresponds to the box. Objects recovered by 2MASS and having a membership probability p based on their proper motion larger than 0.1 (Adams et al. 2001) are shown as filled triangles. Candidates too faint to be found in 2MASS but recovered by Hambly et al. (1999) and having a proper motion within $1\sigma $ of the cluster motion are indicated as open triangles.

To remove all the contaminating field stars from our sample, we compared our list of candidates to the results of other large Pleiades surveys. Adams et al. (2001) performed a large search for Pleiades stellar members using the photometry from the Two Micron All Sky Survey (2MASS) and proper motions determined from Palomar Observatory Sky Survey (POSS) plates. This search extends to a radius of 10 $\hbox{$^\circ$ }$around the cluster center, well beyond the tidal radius, which means that it covers the complete cluster area. The completeness limit of the POSS plates is $I\sim16.5$, i.e. $0.1~M_{\odot}$. The authors analysed the proper motion of all the objects previously selected on the basis of their 2MASS JHK photometry and defined a membership probability p(see Adams et al. 2001 for details). We cross-correlated our list of stellar candidates with the list of all the sources analysed by Adams et al. (2001) and we kept all the objects with p>0.1 so as to minimize the non-member contamination down to I=16.5 (Adams' survey completeness limit). All those sources are shown as filled triangles in Fig. 5.

For stars fainter than I>16.5 we compared our results with those from Hambly et al. (1999). They used photographics plates from the United Kingdom Schmidt Telescope to construct a $6\hbox{$^\circ$ }\times 6\hbox{$^\circ$ }$proper motion survey centered on the Pleiades. To minimize the contamination, we chose all the objects out of our photometric candidates having proper motion within $1\sigma $ ($\simeq$20 mas/yr) of the known cluster motion ( $\mu_{\alpha}=+19$ mas/yr, $\mu_{\delta}=-43$ mas/yr, Robichon et al. 1999). They are indicated as open triangles in Fig. 5.

We stopped our stellar selection at I=17.5 corresponding about to Hambly's survey completeness limit but also to the HBML. A short list of those very probable low mass stellar members in our survey is presented in Table 3. We considered that the residual contamination of this sample is low enough to be neglected. The analysis of the fainter objects, i.e. substellar candidates, has been done from the long exposure images and is explained hereafter.


   
Table 3: Stellar candidates identified from our survey. The whole electronic list can be found on the CDS website.
No. I I-Z ${\rm RA}_{J2000}$ ${\rm Dec}_{J2000}$
      (h m s) ( $^{\circ}$ ' '')
1 13.69 0.54 3:51:11.55 24:23:13.30
2 13.71 0.51 3:43:09.76 24:41:32.82
3 13.75 0.53 3:51:19.05 24:10:13.08
... ... ... ... ...
111 17.21 0.77 3:52:5.82 24:17:31.16
112 17.34 0.84 3:48:50.45 25:17:54.52

3.2 Substellar domain

3.2.1 Photometric selection

The (I,I-Z) color magnitude of the point-like objects contained in the long exposures of the 17 Pleiades fields is shown in Fig. 6. Candidates previously identified by Bouvier et al. (1998) and confirmed on the basis of spectroscopic data, infrared photometry (Martín et al. 2000) and proper motion (Moraux et al. 2001) are shown as open circles. These objects define the high mass part of the cluster substellar sequence from $I\simeq17.8$ down to about $I \simeq 19.5$. We note that the location of two Pleiades members (CFHT-PL-12 and CFHT-PL-16) suggest that they are likely binaries as already suspected by Bouvier et al. (1998) and Martín et al. (2000).


  \begin{figure} \par\includegraphics[width=15cm,clip]{ms3257f6.ps} \end{figure} Figure 6: (I,I-Z) color magnitude diagram for the long exposures. The small dots represent the field stars. Brown dwarf candidates down to  $0.03~M_{\odot}$ are shown as filled triangles. Previously identified Pleiades proper motion BDs from Moraux et al. (2001) recovered by our survey are shown as open circles. The 120 Myr NEXTGEN (dashed line) and DUSTY (dot-dashed line) isochrones from Baraffe et al. (1998) and Chabrier et al. (2000) are also shown. Error bars indicate the rms photometric error.

We overplotted the 120 Myr isochrones from the NEXTGEN and DUSTY models from Baraffe et al. (1998) and Chabrier et al. (2000) respectively, assuming a distance modulus for the Pleiades cluster of $(m-M)_{\rm o}= 5.53$, AV=0.12 and a solar metallicity. At a $T_{{\rm eff}}$ which corresponds to late-M and early L spectral types, dust grains begin to form, changing the opacity and resulting in objects having bluer I-Z colors than predicted by the NEXTGEN models. DUSTY models instead include a treatment of dust grains in cool atmospheres for $T_{{\rm eff}} \le$ 2300 K. To build our sample of Pleiades brown dwarf candidates for $17.8\le I\le 19$, we defined a line 0.1 mag bluer in I-Z than the NEXTGEN isochrone and we selected all the sources located on the right side of this line. For $I\ge19$, we selected all the objects redward of the DUSTY isochrone and we stopped our selection around the completeness limit, i.e. $M\simeq0.03~M_{\odot}$. All the candidates are shown in Fig. 6 as filled triangles. The photometry and coordinates of these objects are given in Table 4. Two sources are located $\sim$0.12 mag left on the NEXTGEN isochrone at about I=18.5 and have not been considered as brown dwarf candidates. The proper motion of the faintest of these two objects has been measured and indicates non-membership. The other source will be followed up but this will not change the mass function estimate.


   
Table 4: Brown dwarfs candidates identified from our survey. Objects written in bold characters (resp. in parenthesis) have proper motion indicating cluster membership (resp. non cluster membership).
CFHT-PLIZ I I-Z ${\rm RA}_{J2000}$ ${\rm Dec}_{J2000}$ Other Id.
      (h m s) ( $^{\circ}$ ' '')  
1 17.79 0.83 3:51:05.98 24:36:17.09  
2 17.81 0.90 3:55:23.07 24:49:05.01 BPL 327 ( $I_{{\rm KP}}=$ 17.72), IPMBD 11 ( $I_{\rm C}=$ 18.07)
3 17.82 0.90 3:52:06.72 24:16:00.76 CFHT-Pl-13 ( $I_{\rm C}=$ 18.02), Teide 2 (I= 17.82), BPL 254 ( $I_{{\rm KP}}=$ 17.59)
4 17.82 0.96 3:41:40.92 25:54:23.00  
5 17.84 0.84 3:53:37.96 26:02:19.67  
6 17.87 1.04 3:53:55.10 23:23:36.41 CFHT-Pl-12 ( $I_{\rm C}=$ 18.00), BPL 294 ( $I_{{\rm KP}}=$ 17.61)
7 18.46 1.12 3:48:12.13 25:54:28.40  
8 18.47 0.96 3:43:00.18 24:43:52.13 CFHT-Pl-17 ( $I_{\rm C}=$ 18.80), BPL 49 ( $I_{{\rm KP}}=$ 18.32)
9 18.47 1.11 3:44:35.19 25:13:42.34 CFHT-Pl-16 ( $I_{\rm C}=$ 18.66)
10 18.66 1.03 3:51:44.97 23:26:39.47 BPL 240 ( $I_{{\rm KP}}=$ 18.45)
(11) 18.85 1.03 3:44:12.67 25:24:33.62 CFHT-Pl-20 ( $I_{\rm C}=$ 18.96)
12 18.88 1.07 3:51:25.61 23:45:21.16 CFHT-Pl-21 ( $I_{\rm C}=$ 19.00), Calar 3 (I= 18.73), BPL 235 ( $I_{{\rm KP}}=$ 18.66)
13 18.94 1.14 3:55:04.40 26:15:49.32  
14 18.94 1.14 3:53:32.39 26:07:01.20  
15 19.32 1.11 3:52:18.64 24:04:28.41 CFHT-Pl-23 ( $I_{\rm C}=$ 19.33)
16 19.38 1.12 3:43:40.29 24:30:11.34 CFHT-Pl-24 ( $I_{\rm C}=$ 19.50), Roque 7 (I= 19.29), BPL 62 ( $I_{{\rm KP}}=$ 19.19)
17 19.44 1.08 3:51:26.69 23:30:10.65  
18 19.45 1.14 3:54:00.96 24:54:52.91  
19 19.56 1.10 3:56:16.37 23:54:51.44  
20 19.69 1.21 3:54:05.37 23:33:59.47 CFHT-Pl-25 ( $I_{\rm C}=$ 19.69), BPL 303 ( $I_{{\rm KP}}=$ 19.43)
21 19.80 1.17 3:55:27.66 25:49:40.72  
22 20.27 1.13 3:51:52.71 26:52:32.16  
23 20.30 1.10 3:51:33.48 24:10:14.16  
24 20.55 1.15 3:47:23.68 26:00:59.75  
(25) 20.58 1.16 3:52:44.30 24:24:50.04  
26 20.85 1.20 3:44:48.66 25:39:17.52  
(27) 20.90 1.14 3:55:00.38 23:38:08.05  
28 21.01 1.23 3:54:14.03 23:17:51.39  
29 21.03 1.27 3:49:45.29 26:50:49.88  
30 21.04 1.22 3:51:46.00 26:49:37.41  
31 21.05 1.26 3:51:47.65 24:39:59.51  
32 21.19 1.23 3:50:15.47 26:34:51.27  
33 21.25 1.17 3:50:44.68 26:42:09.36  
34 21.35 1.16 3:54:02.56 24:40:26.07  
35 21.37 1.18 3:52:39.17 24:46:30.03  
36 21.42 1.19 3:54:38.34 23:38:00.63  
37 21.45 1.40 3:55:39.57 24:12:52.12  
38 21.49 1.22 3:45:54.69 26:30:14.57  
39 21.55 1.19 3:53:40.30 26:16:18.15  
40 21.66 1.29 3:49:49.30 26:33:56.19  

Part of our survey overlaps with Bouvier et al.'s (1998) survey performed in 1996, so that we were able to derive proper motion for some of the objects identified in both surveys. The two epochs of observations are separated by approximately 4 years and the resulting proper motion uncertainty is typically $1\sigma\simeq 7$mas/yr. The details of the procedures used to derive proper motion are given in Moraux et al. (2001). Objects which have a proper motion less than $2\sigma$ from the cluster motion ( $\mu_{\alpha}=+19$ mas/yr, $\mu_{\delta}=-43$ mas/yr) are very likely Pleiades members. We have written those objects in bold characters in Table 4 and objects whose proper motion indicates non membership in parenthesis.

Two of our new candidates had already been identified as probable Pleiades members by Pinfield et al. (2000), CFHT-PLIZ-2 = BPL 327 and CFHT-PLIZ-10 = BPL 240, on the basis of their optical and infrared photometry and from their proper motion by Hambly et al. (1999). These objects are also written in bold characters in Table 4.

3.2.2 Contamination

An (I,I-Z) diagram alone cannot identify objects as certain Pleiades members as one expects some level of contamination by field stars. Due to the relatively high galactic latitude of the Pleiades cluster, heavily reddened distant objects should not contaminate our photometric sample of candidate members. However, the relative location in the CMD of the theoretical Pleiades isochrone and a zero age main sequence isochrone from DUSTY models indicates that some of the photometrically selected brown dwarfs candidates could in fact be field M-dwarfs at a distance about 30% closer than the Pleiades. Considering the whole selection range which extends from 0.5 mag below the cluster sequence to the binary cluster sequence, we find that contaminating field M-dwarfs can lie in a distance range from 60 to 125 pc. Then, taking into account the area of the survey, the volume occupied by contaminants is about 1150 pc3. The field star luminosity function for MI=12-14.5 can be approximated as a constant $\phi \sim 0.003$ stars/pc3 per unit MI as estimated from the DENIS survey (Delfosse 1997). We therefore expect to find about 7 field stars out of 21 candidates in the range I=17.8-19.8, i.e. a contamination level of about 33% as previously derived from proper motion measurements by Moraux et al. (2001).

At fainter magnitudes the contamination level cannot be derived from the field star luminosity function which is not very well known for MI>14.5. However, we can use the number of stars identified in the DENIS survey down to I=18 in a given color (or temperature) range in order to estimate the number of contaminants in our sample for this color interval. For example, the brown dwarf candidates with I between 20.2 and 21.7 have a temperature of $\sim$2000 K (Chabrier et al. 2000). We then consider the number of DENIS objects within a restricted temperature range around this value and I between 16.5 and 18, and multiply this number by two factors: a) the ratio of our CFHT survey area to the DENIS survey area, and b) the ratio of the two volumes corresponding to the two magnitude ranges (I= 20.2 to 21.7 and I= 16.5 to 18) for the DENIS survey. We thus predict 5 or 6 field dwarfs to occupy the region of the Pleiades color magnitude diagram corresponding to  $0.04~M_{\odot}\ge M\ge 0.03~M_{\odot}$. This indicates again a contamination level of $\sim$30%.

For redder objects, the statistics of the DENIS survey are very low so that it is difficult to estimate the contamination. Moreover, our survey starts to be incomplete in this domain and that is why we limited our analysis to $M=0.03~M_{\odot}$.

3.3 Radial distribution

In order to deduce the total number of Pleiades members and derive the cluster mass function from a survey covering only a fraction of the cluster area, we need to investigate the spatial distribution of cluster members and its dependence on mass.

The spatial distribution of our Pleiades brown dwarf candidates is shown in Fig. 2. Overplotted are circles of radii 0.75 to 3.5 degrees centered on the cluster center. From this diagram we estimated the covered area within annulii of $0.25\hbox{$^\circ$ }$ width and we counted the number of substellar objects found therein. We then obtained radial surface densities for brown dwarf candidates by dividing these numbers by the corresponding surveyed areas. We proceeded in the same way for low mass stars. The number of stellar and substellar objects per square degree as a function of the radial distance is shown in Fig. 7.


  \begin{figure} \includegraphics[width=8.5cm,clip]{ms3257f7a.ps}\hspace*{5mm} \includegraphics[width=8.5cm,clip]{ms3257f7b.ps} \end{figure} Figure 7: Left: The radial distribution of probable Pleiades stellar members found in our survey and having a mass between $0.48~M_{\odot}$ and $0.08~M_{\odot}$ (histogram). Overplotted is the best King profile fit which, assuming $r_{\rm t}=5.54^{\circ }$ (Pinfield et al. 1998), yields a core radius $r_{\rm c}=2.0^{\circ }$; Right: The plain histogram shows the radial distribution of our brown dwarf candidates and the shaded histogram represents those which are already confirmed by proper motion. Overplotted are King profiles with $r_{\rm t}=5.54^{\circ }$. The solid line is a fit of the shaded histogram which yields a lower limit of $r_{\rm c}=1.3^{\circ }$ for the substellar core radius. A King profile with a core radius of $r_{\rm c}=3.0^{\circ }$ is shown for reference (dashed line).

The stellar distribution ( 13.5<I<17.5, i.e. $0.48>M>0.08~M_{\odot}$) shown on the left panel is well fitted by a King distribution (King 1962):

 
$\displaystyle % f(x) = k~\left[\frac{1}{\sqrt{1+x}} - \frac{1}{\sqrt{1+x_{t}}}\right]^2$     (1)

where k is a normalisation constant, $x=(r/r_{\rm c})^2$ and $x_{\rm t}=(r_{\rm t}/r_{\rm c})^2$ with r the radius from the cluster center. The core radius $r_{\rm c}$ increases as the stellar mass decreases and the tidal radius $r_{\rm t}$ corresponds to the location where the gravitationnal potential of the galaxy equals the cluster potential. Using $r_{\rm t}=5.54\hbox{$^\circ$ }$ from Pinfield et al. (1998), we found $k\simeq110$ per square degrees and $r_{\rm c}\simeq2$ degrees for a median mass of our stellar sample of $M\simeq0.2~M_{\odot}$. From this radial distribution, we obtain a total of 557 stars between 0.08 and 0.48 $M_{\odot}$. For a dynamically relaxed cluster, the core radius is expected to vary with stellar mass as M-0.5 and Jameson et al. (2002) derived the relationship $r_{\rm c}=0.733~M^{-0.5}$ for the Pleiades stars. For $M\simeq0.2~M_{\odot}$, this yields $r_{\rm c}\simeq1.6\hbox{$^\circ$ }$, slightly smaller than our value.

The radial distribution of brown dwarf candidates is shown on the right side of the Fig. 7. The plain histogram corresponds to the whole list of candidates whereas the shaded histogram corresponds to objects having proper motion consistent with cluster membership (written in bold characters in Table 4). This histogram does not extend further than $r=2.25^{\circ}$ corresponding to the surveys of Pinfield et al. (2000) and Bouvier et al. (1998) from which proper motions have been derived. Those surveys were not as deep as ours so that only brown dwarf candidates brighter than I=20.9 were counted. A King profile fitted to this histogram yields $r_{\rm c}\simeq1.3$ degrees as a lower limit to the cluster substellar core radius. The plain histogram also decreases in the first few radius bins but then increases further away from the cluster center. Note, however, that the uncertainties due to small number statistics are large and the plain histogram is not corrected for contamination for field stars, whose rate is expected to increase away from the cluster center. An illustrative King profile with $r_{\rm c}\simeq3.0$degrees is shown as a possible fit to the brown dwarf distribution, mainly based on the few first radial bins. The median mass for the brown dwarfs candidates is $M\simeq0.05~M_{\odot}$ and the value expected by Jameson et al.'s (2002) relationship $r_{\rm c}=0.733~M^{-0.5}$ is 3.4 degrees.

With $r_{\rm c}\simeq3.0^{\circ}$ and k=28.5 per square degrees, integration of the King distribution yields a total of $\sim$130 brown dwarfs between 17.8<I<21.7, i.e. between 0.07 and 0.03 $M_{\odot}$ in the whole cluster. From this distribution, we expect to find $\sim$26 brown dwarfs Pleiades members in our survey out of the 40 selected candidates. This would correspond to a contamination level of 35%, quite consistent with our estimate above.

3.4 The Pleiades mass function

The Pleiades mass function can be estimated from our CFHT large survey over a continuous mass range from $0.03~M_{\odot}$ to  $0.45~M_{\odot}$. For the stellar part (down to I=17.5) we use our sample of candidates derived from short exposure images and decontaminated as explained above. We derived masses from I-band magnitudes using the 120 Myr isochrone from Baraffe et al. (1998). Below the HBML ($I\sim17.5$) we consider our selection of brown dwarf candidates (Table 4) and we apply a correction factor of 0.7, assuming a contamination level of 30%. We used the 120 Myr isochrone from the DUSTY models of Chabrier et al. (2000) to estimate masses.

In order to correctly estimate the mass function of the whole cluster from a survey which is spatially uncomplete, one has to take into account the different radial distribution of low mass stars and brown dwarfs. Our CFHT fields are located between 0.75 and 3.5 degrees from the cluster center. We now proceed to estimate the fraction of low mass objects located in this ring compared to the total number of such objects in the cluster. For a King-profile surface density distribution, the total number of stars seen in projection within a distance r of the cluster center is obtained by integrating Eq. (1):

 
$\displaystyle % n(x)= k\pi r_{\rm c}^{2} \left[\ln(1+x) - 4\frac{\sqrt{1+x}-1}{\sqrt{1+x_{\rm t}}} + \frac{x}{1+x_{\rm t}}\right]\cdot$     (2)

We consider stellar core radii following Jameson et al. (2002) relationship $r_{\rm c}=0.733~M^{-0.5}$ and assumed a substellar core radius $r_{\rm c}=3.0^{\circ }$ (see previous section). We then deduce from equation 2 that 74% of the $0.4~M_{\odot}$ stars and 80% of the brown dwarfs are located within a distance from the cluster center between 0.75 and 3.5 degrees. This indicates that the relative number of brown dwarfs compared to low mass stars deduced from our survey is representative to their relative number over the whole cluster. In other words, the area covered by this survey is large enough so that any correction to the mass function for a mass-dependent radial distribution is negligeable.

The derived mass function is shown in Fig. 8 as the number of objects per unit mass. Within the uncertainties, it is reasonably well-fitted by a single power-law ${\rm d}N/{\rm d}M \propto M^{-\alpha }$ over the mass range from $0.03~M_{\odot}$ to $0.45~M_{\odot}$. A possibility to explain why the $0.06~M_{\odot}$ data point is low is discussed in Dobbie et al. (2002). A linear regression through the data points yields an index of $\alpha=0.60~\pm~0.11$, where the uncertainty is the $1\sigma $ fit error[*]. This result is consistent with previous estimates (cf. Table 1) and is affected by smaller uncertainties thanks to the combination of relatively large samples of low mass stars and brown dwarfs, proper correction for contamination by fields stars, and extended radial coverage of the cluster.

In Moraux et al. (2001) the mass function index was found to be $\alpha=0.51\pm0.15$. Lacking a proper determination of the radial distribution of cluster members, the assumption was made that brown dwarfs and very low mass stars were similarly distributed. The index estimate was based on Bouvier et al.'s (1998) survey which covered fields spread between 0.75 and 1.75 degrees from the cluster center. From the radial distribution derived above, we find that this annulus contains 43% of the $0.4~M_{\odot}$ stars and 33% of the cluster brown dwarfs. Applying these correcting factors to the number of Pleiades members found in that survey, the mass function index becomes 0.63 instead of 0.51. This corrected value is in excellent agreement with our new estimate.

Extrapolating the power-law mass function down to $M=0.01~M_{\odot}$, we predict a total number of $\sim$270 brown dwarfs in the Pleiades for a total mass of about $10~M_{\odot}$. Clearly, while brown dwarfs are relatively numerous, they do not contribute significantly to the cluster mass. Adams et al. (2001) derived a total mass of $\sim$ $800~M_{\odot}$ for the Pleiades which means that, even though brown dwarfs account for about 25% of the cluster members, they represent less than 1.5% of the cluster mass.

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