1 Introduction

The Initial Mass Function (IMF), i.e. the mass spectrum resulting from complex physical processes at work during star formation, is a formidable constraint for star formation models. Its determination at low stellar and substellar masses is therefore one of the main motivations for the rapidly expanding quest for brown dwarfs. Very low mass stars and brown dwarfs are also prime candidates to investigate the structure and dynamical evolution of large stellar systems, such as clusters. Searches for the lowest-mass isolated objects have been conducted in the galactic field, in young open clusters and in star-forming regions, brown dwarfs being brighter when younger. The identification of substellar candidates is often based on color magnitude diagrams (hereafter CMD) built from deep wide-field imaging surveys. One of the major shortcomings of this selection method is the contamination by older and more massive late-type field dwarfs which may lie in the same region of the CMD.

The Pleiades cluster (RA  $=3^{\rm h}46.6^{\rm m}$, Dec  $=+24^{\circ}04'$) is an ideal hunting ground for substellar objects. It is relatively nearby with a distance of about 125 pc, with the apparent magnitude of massive brown dwarfs bright enough for being easily detected on intermediate-size telescopes. Its age of approximately 120 Myr (Stauffer et al. 1998; Martin et al. 1998) makes the lithium test particularly useful for identifying brown dwarfs: at this age, the lithium depletion boundary (in mass) coincides with the hydrogen burning mass limit (hereafter HBML). Also, the Pleiades is a rich cluster with about 1200 members and its galactic latitude is relatively high ( $b=-23^{\circ}$), which minimizes the possible confusion between members and red giants from the Galactic disk. Moreover, the cluster motion ( $\mu_{\alpha}=+19$ mas/yr, $\mu_{\delta}=-43$ mas/yr) is large compared to that of field stars so that cluster kinematic studies are a powerful way to recognize true members among the photometric candidates.

   

Table 1: Previous imaging surveys of the Pleiades conducted for searching brown dwarfs.

Survey	Area	Completeness	Nb of new	IMF index	Mass range
	sq. degree	limit	BD candidates		($M_{\odot}$)
Stauffer et al. (1989)	0.25	$I\sim17.5$	4		0.2-0.08
Simons & Becklin (1992)	0.06	$I\sim19.5$	22		0.15-0.045
Stauffer et al. (1994)	0.4	$I\sim17.5$	2		0.3-0.075
Williams et al. (1996)	0.11	$I\sim19$	1		0.25-0.045
Festin (1997)	0.05	$I\sim21.6$	0	$\le1$	0.15-0.035
Cossburn et al. (1997)	0.03	$I\sim20$	1		0.15-0.04
Zapatero et al. (1997)	0.16	$I\sim19.5$	9	$1\pm0.5$	0.4-0.045
Festin (1998)	0.24	$I\sim21.4$	4	$\le1$	0.25-0.035
Stauffer et al. (1998)	1.	$I\sim18.5$	3		0.15-0.035
Bouvier et al. (1998)a,b	2.5	$I\sim22$	13	$0.6\pm0.15$	0.4-0.04
Zapatero-Osorio et al. (1999)b	1.	$I\sim21$	41		0.08-0.035
Hambly et al. (1999)	36.	$I\sim18.3$	6	$\le0.7$	0.6-0.06
Pinfield et al. (2000)b	6	$I\sim19.6$	13		0.45-0.045
Tej et al. (2002)	7	$K\sim15$		$0.5\pm0.2$	0.5-0.055
Dobbie et al. (2002)b,c	1.1	$I\sim22$	10	0.8	0.6-0.030

^a BD candidates have been confirmed by Martín et al. (2000) and Moraux et al. (2001) and the IMF index has been revised to $0.51\pm0.15$.
^b Jameson et al. (2002) have compiled these surveys and using new infrared data they find that the Pleiades mass function is well represented by a power law with index $\alpha=0.41\pm0.08$ for $0.3~M_{\odot}\ge M\ge 0.035~M_{\odot}$.
^c These authors used the results from Hodgkin & Jameson (2000) and Hambly et al. (1999) to conclude that the $\alpha=0.8$ power law is appropriate from $0.6~M_{\odot}$ down to $0.03~M_{\odot}$.

To date, several surveys have been conducted in this cluster. They are summarized in Table 1 in term of covered area, completeness limit and number of new brown dwarfs candidates. Only surveys with a magnitude limit larger or equal to  $I\simeq17.5$ are listed here (the HBML corresponds to Ic=17.8, Stauffer et al. 1998). Starting in 1997, several groups reported estimates for the Pleiades mass function in the upper part of the substellar domain, often represented by a single power law ${\rm d}N/{\rm d}M \propto M^{-\alpha }$ with $0.5\leq\alpha\leq 1.0$(see Table 1).

While these various estimates agree within uncertaintites, the substellar samples on which they rely are still relatively small and, in some cases, not fully corrected for contamination by field dwarfs. Some surveys are also quite limited spatially, and the derived mass function may not be representative of the whole cluster. In order to put the determination of the Pleiades substellar mass function on firmer grounds, we performed a deep and large survey of the Pleiades cluster in the I and Z-band, using the CFH12K camera at the Canada-France-Hawaii telescope. The survey covers 6.4 square degrees and reaches up to 3 degrees from the cluster center. It encompasses a magnitude range $I\simeq 13.5{-}24$, which corresponds to masses from 0.025 $M_{\odot}$ to 0.45 $M_{\odot}$ at the distance and age of the Pleiades.

In Sect. 2, we describe the observations and the data reduction. Results in the stellar and substellar domains are presented in Sect. 3. Forty brown dwarf candidates are identified, 29 of which are new discoveries. We discuss contamination of the photometric samples by field stars in the stellar and substellar domains, investigate the radial distribution of substellar objects, and derive the cluster substellar mass function. In Sect. 4, we discuss the overall shape of the cluster mass function over the stellar and substellar domains, the possible consequences of early cluster dynamical evolution on its present mass function and the implications for the brown dwarf formation process. A comparison is made between the Pleiades and the Galactic field mass functions, which reveals significant differences at the low mass end, a large part of which is probably attributable to unresolved cluster binaries.