1 Introduction

Deep photometric and spectroscopic searches in various nearby star-forming regions and young open clusters have revealed populations of very low mass stars ($\le$0.3$M_{\odot}$), brown dwarfs (see Basri 2000 for a review) with masses below the hydrogen-burning mass limit ($\sim$0.075$M_{\odot}$) and planetary-mass objects (Najita et al. 2000; Lucas et al. 2001; Zapatero Osorio et al. 2000) smaller than the deuterium-burning threshold at 0.013$M_{\odot}$(Saumon et al. 1996). Age is one of the most relevant parameters for their study and characterization. Traditionally, mass estimates of cluster members rely on evolutionary models, which predict luminosities and effective temperatures (hereafter $T_{\rm eff}$) as a function of time and mass. This procedure, namely isochrone fitting to observational photometric diagrams, is highly age dependent for the smallest objects because they cool down very quickly (e.g., D'Antona & Mazzitelli 1994; Burrows et al. 1997; Chabrier et al. 2000). To better constrain masses, it is desirable to date clusters with higher accuracy.

Lithium absorption features in optical spectra can be used as a tracer of the stellar internal structure. In addition, lithium is valuable to assess the age of stars in clusters. Dating young clusters and field objects based on lithium analysis is a procedure nearly independent of distance and reddening, in marked contrast to the isochrone-fitting technique. Moreover, lithium isochrones do not significantly depend on metallicity (D'Antona 2000), rendering the lithium dating technique very powerful. Pre-main sequence stars with large convective regions burn lithium efficiently on short time scales (see Pinsonneault 1997 for a review) as soon as the temperature at the base of the convective zone becomes hot enough to undergo the nuclear reaction ⁷Li+p $\rightarrow$⁴He+$\alpha$. Stars smaller than the Sun require only about 10-15Myr to deplete this element by one order of magnitude, and all M-type stars are observed to have destroyed their lithium at ages around 20-40Myr (e.g., Pinsonneault et al. 1990; D'Antona & Mazzitelli 1994, 1997; Baraffe et al. 1998). Furthermore, lithium detections in fully convective objects near and below the substellar limit have been successfully used to constrain the ages of clusters like the Pleiades (Basri et al. 1996; Martín et al. 1998; Stauffer et al. 1998), $\alpha$Persei (Stauffer et al. 1999), and IC2391 (Barrado y Navascués et al. 1999). Lithium dating, which is fundamentally a nuclear age calibrator, can be considered reliable even though some uncertainties (rotation, activity, mixing processes) may affect theoretical calculations.

Recently, various groups have investigated the stellar and substellar populations around the bright, massive and multiple O9.5V-type star $\sigma$Orionis, which gives its name to the association (Walter et al. 1994; Wolk 1996; Walter et al. 1998; Béjar et al. 1999; Zapatero Osorio et al. 1999, 2000; Béjar et al. 2001). These authors have adopted a cluster age between 1Myr and 7Myr (Blaauw 1964; Warren & Hesser 1978; Brown et al. 1994). This is the age interval estimated for the O9.5V-type star based on its physical properties, evolutionary stage (still burning hydrogen on the main sequence) and membership in the Orion OB1b subgroup (Blaauw 1991). Other properties of the $\sigma$Orionis cluster, e.g., distance (352pc) and reddening ( $A_V\,\le\,0.5$mag), are discussed in Béjar et al. (2001). Here we examine low mass stars and brown dwarfs with confirmed membership to determine the most likely age of the cluster. We report on observations of intermediate- and low-resolution optical spectroscopy in Sects. 3 and 4. A discussion and main conclusions are given in Sects. 5 and 6, respectively.

 

 

Table 1: Log of the observations (ordered by observing date).

Object	$\alpha$  (J2000)  $\delta$	I	Obs. date	Observ.	Disp.	Wl. range	Exp. time
	( $^{\rm h ~ m ~ s}$)    ( $^{\circ} ~ ' ~ ''$)	(mag)	(UT)		(Å/pix)	(Å)	(s)
4771-1075	05 39 05.3   -2 32 30	12.66	20 Nov. 1998	CAHA	0.55	6220-7297	700
4771-1097	05 38 35.7   -2 30 43	12.43	20 Nov. 1998	CAHA	0.55	6220-7297	800
r053907-0228	05 39 07.6   -2 28 23	14.33	20 Nov. 1998	CAHA	0.55	6220-7297	2$\times$1200
SOriJ053958.1-022619	05 39 58.1   -2 26 19	14.19	21 Nov. 1998	CAHA	0.55	6220-7297	2$\times$1200
SOriJ053920.5-022737	05 39 20.5   -2 27 37	13.51	21 Nov. 1998	CAHA	0.55	6220-7297	2$\times$1200
r053833-0236$^\ast$	05 38 33.9   -2 36 38	13.71	21 Nov. 1998	CAHA	0.55	6220-7297	2$\times$1500
			22 Nov. 1998	CAHA	2.41	6194-10000	650
			26 Jan. 1999	ORM	0.84	6034-6840	1200
SOriJ053949.3-022346	05 39 49.3   -2 23 46	15.14	21 Nov. 1998	CAHA	0.55	6220-7297	1800
4771-1051$^\ast$	05 38 44.1   -2 40 20	12.33	21 Nov. 1998	CAHA	0.55	6220-7297	900, 535
			26 Jan. 1999	ORM	0.84	6034-6840	1200
SOriJ053715.1-024202	05 37 15.1   -2 42 02	15.07	21 Nov. 1998	CAHA	2.41	6194-10000	600
SOriJ053951.6-022248	05 39 51.6   -2 22 48	14.59	22 Nov. 1998	CAHA	2.41	6194-10000	2$\times$600
SOri45	05 38 25.5   -2 48 36	19.59	21 Dec. 1998	Keck	0.85	6324-8025	3$\times$1800
SOri27	05 38 17.3   -2 40 24	17.07	21 Dec. 1998	Keck	0.85	6324-8025	2$\times$1200
r053820-0237$^\ast$	05 38 20.3   -2 37 47	12.83	25 Jan. 1999	ORM	0.84	6034-6993	2$\times$1200
r053831-0235$^\ast$	05 38 31.4   -2 35 15	13.52	25 Jan. 1999	ORM	0.84	6034-6840	600, 1800
4771-899$^\ast$	05 38 47.9   -2 27 14	12.08	25 Jan. 1999	ORM	0.84	6034-6840	300
SOriJ053847.5-022711	05 38 47.5   -2 27 11	14.46	26 Jan. 1999	ORM	0.84	6034-6840	2$\times$1800
SOriJ054005.1-023052	05 40 05.1   -2 30 52	15.90	26 Jan. 1999	ORM	0.84	6034-6840	2$\times$2700
SOriJ054001.8-022133	05 40 01.8   -2 21 33	14.32	26 Jan. 1999	ORM	0.84	6034-6840	2$\times$1200
r053838-0236$^\ast$	05 38 38.0   -2 36 38	12.37	27 Jan. 1999	ORM	0.84	6034-6840	2$\times$100
4771-41	05 38 27.1   -2 45 10	12.82	27 Jan. 1999	ORM	0.84	6034-6840	2$\times$1200
4771-1038$^\ast$	05 39 11.5   -2 36 03	12.78	28 Jan. 1999	ORM	0.84	6034-6840	2$\times$2400
r053840-0230$^\ast$	05 38 40.2   -2 30 19	12.80	28 Jan. 1999	ORM	0.84	6034-6840	2$\times$2400
r053820-0234	05 38 20.4   -2 34 09	14.58	29 Jan. 1999	ORM	0.84	6034-6840	900, 1800
r053849-0238$^\ast$	05 38 49.0   -2 38 21	12.88	03 Dec. 1999	McDonald	0.70	6150-6850	5$\times$1200
r053923-0233$^\ast$	05 39 22.7   -2 33 33	14.16	03 Dec. 1999	McDonald	0.70	6150-6850	8$\times$1200
SOriJ053827.4-023504	05 38 27.4   -2 35 04	14.50	05 Dec. 1999	McDonald	0.70	6150-6850	12$\times$1200
SOriJ053914.5-022834	05 39 14.5   -2 28 34	14.75	06 Dec. 1999	McDonald	0.70	6150-6850	2$\times$1200
SOriJ053820.1-023802	05 38 20.1   -2 38 02	14.41	06 Dec. 1999	McDonald	0.70	6150-6850	10$\times$1200

$^\ast$ Also detected in X-rays (Wolk 1996).

 

 

Table 2: Instrumental setups of different campaigns.

Run	Observ.	Teles.	Spectrograph	Grating	Detector	Spatial res.	Slit width
20 Nov. 1998	CAHA	3.5-m	TWIN	T06	SITe $2000\times800$pix	0.56 $^{\prime\prime}$/pix	1.2 $^{\prime\prime}$
21 Nov. 1998	CAHA	3.5-m	TWIN	T11	SITe $2000\times800$pix	0.56 $^{\prime\prime}$/pix	1.2 $^{\prime\prime}$
20 Dec. 1998	Keck	Keck II	LRIS	900/5500	$2048\times2048$pix	0.22 $^{\prime\prime}$/pix	1.0 $^{\prime\prime}$
25-28 Jan. 1999	ORM	INT	IDS	R1200Y	Tektronix $1024\times1024$pix	0.70 $^{\prime\prime}$/pix	1.7 $^{\prime\prime}$
03-06 Dec. 1999	McDonald	2.1-m	ES2	#25	Craf/Cassini $1024\times1024$pix	2.72 $^{\prime\prime}$/pix	2.1 $^{\prime\prime}$