4 Analysis and results

4.1 Spectral types

We inferred spectral types by comparing our target spectra to data of spectroscopic standard stars (Gl820A, K5V; Gl820B, K7V; Gl338A, M0V; Gl182, M0.5V; Gl767A, M1V; Gl767B, M2.5V; Gl569A, M3V; Gl873, M3.5; Gl402, M4V; Gl905, M5V; and Gl406, M6V). The reference spectra were obtained with similar instrumentations in previous campaigns. In addition, we observed several K- and M-type standards with the McDonald telescope. For the spectral classification, we also used molecular indices that are based on the relative strengths of CaH and TiO bands (Kirkpatrick et al. 1991; Prosser et al. 1991), and the pseudocontinuum PC3 index given in Martín et al. (1996), which is valid for types later than M3. Our measurements, with an uncertainty of half a subclass, are provided in Table 3. The spectral types of SOri27 and 45 have been taken from Béjar et al. (1999). The final adopted spectral classes are in the range K6-M8.5.

 

 

Table 3: Spectroscopic data.

Objecta	I	R-I	Sp.T.b	MJDc	pEWd (H$\alpha$)	pEWe (Li I)	log $L_{\rm H\alpha}/L_{\rm bol}$	vr	Template
				(-51000)	(Å)	(Å)		(kms-1)
4771-1075	12.66	0.87	K7.0	137.9536	$0.7\pm0.1$	$0.59\pm0.09$	- $4.25\pm0.09$	$29.7\pm7$	4771-1051
4771-1097	12.43	0.79	K6.0	137.9686	$2.2\pm0.8$	$0.47\pm0.07$	- $3.77\pm0.19$	$34.9\pm7$	4771-1051
r053907-0228	14.33	1.41	M3.0	137.9881	$3.6\pm0.7$	$0.67\pm0.08$	- $3.63\pm0.13$	$39.0\pm7$	4771-1051
J053958.1-022619	14.19	1.41	M3.0	138.0676	$4.0\pm0.8$	$0.73\pm0.10$	- $3.59\pm0.13$	$47.4\pm7$	4771-1051
J053920.5-022737	13.51	1.34	M2.0	138.1046	$3.2\pm0.7$	$0.65\pm0.10$	- $3.66\pm0.14$	$33.0\pm7$	4771-1051
r053833-0236	13.71	1.54	M4.0	138.1237	$14.0\pm2.0$	$0.60\pm0.10$	- $3.10\pm0.11$	$35.8\pm7$	4771-1051
			M3.0	139.1788	$2.7\pm0.3$	$0.47\pm0.05$	- $3.82\pm0.10$	$35.8\pm7$	-
			M3.5	204.0726	$2.2\pm0.8$	$0.61\pm0.08$	- $3.90\pm0.19$	$35.6\pm10$	4771-1051
J053949.3-022346	15.14	1.80	M4.0	138.1696	$42.0\pm6.0$	$0.71\pm0.15$	- $2.78\pm0.11$	$38.0\pm7$	4771-1051
4771-1051	12.33	0.79	K7.5	138.2073	$6.4\pm1.0$	$0.58\pm0.09$	- $3.31\pm0.12$	$32.8\pm7$	Gl14
			K8.0	204.0912	$5.5\pm1.0$	$0.59\pm0.05$	- $3.37\pm0.13$	$32.8\pm7$	-
J053715.1-024202	15.07	1.63	M4.0	138.9739	$4.9\pm0.5$	$0.42\pm0.08$	- $3.61\pm0.10$	$35.9\pm25$	r053833-0236
J053951.6-022248	14.59	1.91	M5.5	139.0881	$60.0\pm7.0$	$0.35\pm0.10$	- $2.71\pm0.10$	$40.5\pm25$	r053833-0236
SOri45	19.59	2.88	M8.5	168.4644	$33.0\pm9.0$	$2.40\pm1.00$	- $3.74\pm0.16$	-$13.0\pm15$	vB10
SOri27	17.07	2.13	M6.5	168.5276	$5.7\pm0.5$	$0.74\pm0.09$	- $3.89\pm0.09$	$35.5\pm10$	vB10
r053820-0237	12.83	0.94	M5.0	203.8482	$10.2\pm0.8$	$0.66\pm0.10$	- $3.09\pm0.09$	$50.7\pm10$	4771-1051
r053831-0235	13.52	1.09	M0.0	203.8849	$4.5\pm0.5$	$0.47\pm0.07$	- $3.44\pm0.10$	$35.1\pm10$	4771-1051
4771-899	12.08	0.82	K7.0	203.9329	$3.1\pm0.5$	$0.48\pm0.07$	- $3.61\pm0.12$	$31.0\pm10$	4771-1051
J053847.5-022711	14.46	1.74	M5.0	203.9476	$7.8\pm1.0$	$0.53\pm0.08$	- $3.47\pm0.11$	$40.5\pm10$	4771-1051
J054005.1-023052	15.90	1.80	M5.0	204.0101	$20.5\pm6.0$	$0.72\pm0.15$	- $3.09\pm0.17$	$33.6\pm10$	4771-1051
J054001.8-022133	14.32	1.52	M4.0	204.0382	$46.5\pm9.0$	$0.65\pm0.15$	- $2.57\pm0.13$	$41.9\pm10$	4771-1051
r053838-0236	12.37	0.86	K8.0	205.9079	$2.9\pm0.5$	$0.53\pm0.05$	- $3.68\pm0.12$	$41.6\pm10$	4771-1051
4771-41	12.82	0.82	K7.0	205.9222	$53.5\pm9.0$	$0.50\pm0.06$	- $2.38\pm0.12$	$47.7\pm10$	4771-1051
4771-1038	12.78	0.90	K8.0	206.0002	$2.0\pm0.5$	$0.58\pm0.09$	- $3.79\pm0.15$	$38.7\pm10$	4771-1051
r053840-0230	12.80	0.94	M0.0	206.0299	$6.7\pm0.6$	$0.52\pm0.05$	- $3.27\pm0.09$	$46.3\pm10$	4771-1051
r053820-0234	14.58	1.59	M4.0	207.0720	$28.0\pm4.0$	$0.45\pm0.15$	- $2.83\pm0.11$	$47.7\pm10$	4771-1051
r053849-0238	12.88	1.00	M0.5	515.2615	$2.6\pm0.3$	$0.55\pm0.05$	- $3.67\pm0.10$	$29.0\pm10$	Gl873, Gl182
r053923-0233	14.16	1.23	M2.0	515.3933	$4.1\pm0.5$	$0.54\pm0.08$	- $3.51\pm0.10$	$31.0\pm10$	Gl873, Gl182
J053827.4-023504	14.50	1.33	M3.5	517.4297	$21.2\pm3.0$	$0.52\pm0.05$	- $2.83\pm0.11$	$36.7\pm10$	Gl873, Gl182
J053914.5-022834	14.75	1.48	M3.5	518.2596	$4.2\pm0.7$	$\le$0.44	--	$31.3\pm10$	Gl873, Gl182
J053820.1-023802	14.41	1.60	M4.0	518.3899	$9.6\pm2.0$	$0.57\pm0.07$	- $3.30\pm0.14$	$29.2\pm10$	Gl873, Gl182

^a Note the drop of "SOri'' for some objects.
^b Uncertainty of half a subclass.
^c Modified Julian date at the beginning of the exposure.
^d In emission. Whenever more than one spectrum available, the pEW has been measured over the combined data.
^e In absorption. Whenever more than one spectrum available, the pEW has been measured over the combined data.

We note that our spectral classification relies on field dwarf objects with high gravities. The gravity of $\sigma$Orionis cluster members is expected to be around logg=4.0 (CGS units) according to the evolutionary models of Baraffe et al. (1998) and D'Antona & Mazzitelli (1994). Older K-type stellar counterparts in the field ($\sim$5Gyr) display similar gravities, but early-M and late-M stars have values 0.5dex and 1.0dex larger, respectively. Cool giants are characterized by very low gravities (logg=1.5-2, Bonnell & Tell 1993; van Belle 1999). Therefore, it is reasonable to base the spectral classification of young late-type objects on a scheme intermediate between that of dwarfs and that of giants. Luhman (1999) successfully applied this exercise to members of the young cluster IC348, inferring that the spectral classification of objects like those of $\sigma$Orionis can be obtained from dwarfs with an accuracy up to half a subclass. We have confirmed this by comparing the optical spectrum of our M8.5 brown dwarf with brown dwarfs of identical types in $\rho$Oph and IC348 (Luhman et al. 1997; Luhman 1999). The three spectra overlap very nicely. We are confident that the spectral types given in Table 3 are reliable within the quoted uncertainty.

Figure 10: I magnitude against spectral type for $\sigma$Orionis members. Symbols are as in Fig. 1. The lower "end'' of the sequence (asterisks) is completed with data taken from Béjar et al. (1999), Barrado y Navascués et al. (2001a) and Martín et al. (2001). Typical uncertainties in spectral type are half a subclass, except for the coolest objects ($\ge$L2), where an uncertainty of one subclass is expected.

Since the spectral classification reflects effective temperatures, cluster members should lie along a defined sequence in magnitude vs. spectral type diagrams. The $\sigma$Orionis spectroscopic sequence is depicted in Fig. 10, where we have combined data presented here with data taken from Béjar et al. (1999), Barrado y Navascués et al. (2001a) and Martín et al. (2001). We note that the figure covers a wide range of masses: stars, brown dwarfs and planetary-mass objects. Free-floating low mass stars and isolated planetary-mass objects in the $\sigma$Orionis cluster have luminosities in the I-band that differ by about 3 orders of magnitude. Because substellar objects contract and fade very rapidly, such a difference becomes incredibly large at older ages, e.g., 8 orders of magnitude at 100Myr (Chabrier et al. 2000).

4.2 Rotational velocities

Given the poor velocity resolution of our spectra (68kms^-1, CAHA, first run; 176kms^-1, CAHA, second run; 78kms^-1, ORM; 120kms^-1, Keck; and 65kms^-1, McDonald), we are able to detect extremely fast rotators. These are defined as objects with projected rotational velocities, $v\,{\rm sin}\,i$, larger than 55kms^-1. The only case in Table 3 is 4771-1097, which was observed with the largest dispersion. This star (K6) is the most massive object in our sample ($\sim$0.9-1.2$M_{\odot}$). We measured the rotational velocity by comparing its spectrum to a slowly rotating template selected from our sample. The spectrum of 4771-1075 (observed with the same instrumentation) has very sharp lines and a similar spectral type, as can be seen from Fig. 6. The full width at half-maximum of the atomic lines of this "reference'' star indicates that its spectral broadening is mainly instrumental. Our procedure was to produce a set of artificial spectra spinned up to velocities of 75, 80, 95 and 110kms^-1. We then compared the observed spectrum of 4771-1097 to the synthetic rotational spectra and performed an analysis using the minimum squares technique. Spectral regions free of emission lines and telluric absorptions were considered. We derived $v\,{\rm sin}\,i=80\pm15$kms^-1. Wolk (1996) found clear evidence of optical photometric variability in 4771-1097 and inferred a likely rotational period of $\sim$1day. Combining these results with predicted radii for masses in the range 0.9-1.2$M_{\odot}$ and ages between 3 and 5Myr (D'Antona & Mazzitelli 1994; Baraffe et al. 1998), we conclude that 4771-1097 is rotating with an inclination of i=50$^{\circ}$-90$^{\circ}$.

4.3 Radial velocities

We computed radial velocities via Fourier cross-correlation of the target spectra with templates of similar spectral type. Our CAHA and ORM measurements were calibrated with the radial velocity standard star Gl14 ( $v_{r}=3.3\pm0.3$ km s^-1, Marcy & Benitz 1989; Marcy & Chen 1992), which was observed with the largest dispersion at CAHA on 1998 Nov. 20. We used this star to derive the radial velocity of 4771-1051, and then correlated the rest of our CAHA targets of the same resolution against it. We also adopted 4771-1051 as the template for the ORM data. Whether this star has a variable radial velocity is unknown to us. Thus, our ORM radial velocities might be shifted by a certain amount. However, this is unlikely (at least within the error bars of the measurements) since there is another $\sigma$Orionis member, r053833-0236, observed at CAHA and ORM. After correlating the ORM spectra of these two stars, we obtained for r053833-0236 a heliocentric radial velocity similar to the one derived from the CAHA data. We note that the relative radial velocity of each target with respect 4771-1051 is reliable. We adopted r053833-0236 as the reference star for the low-resolution CAHA spectra, and the M8 field star vB10 was used as the template ( $v_{\rm r}=35.3\pm1.5$kms^-1, Tinney & Reid 1998) for the Keck spectra. The spectrum of vB10 was taken from Martín et al. (1996). Our McDonald spectra were cross-correlated against the radial velocity standard stars Gl182 ( $v_{\rm r}=32.4\pm1.5$kms^-1, Jeffries 1995) and Gl873 ( $v_{\rm r}=0.47\pm0.24$kms^-1, Marcy et al. 1987), which were observed with the same instrumentation and on the same nights.

Radial velocities, their uncertainties and the templates used are provided in Table 3. We took special care in cross-correlating spectral windows (e.g. 6100-6800Å, 8400-8800Å) that are not affected by telluric absorptions and that contain many photospheric lines. In addition, we considered only parts of the spectra free of emission lines. The error bars in the table point to a possible 1/4 pixel uncertainty in the Fourier cross-correlation technique (Martín et al. 1999; Lane et al. 2001). We have checked this by cross-correlating the McDonald spectra against two reference stars. The spectrum of SOri45 is rather noisy, and the quoted error bar comes from the dispersion observed after cross-correlating different spectral regions. The majority of our radial velocities are obtained to an accuracy of the order of 10kms^-1. After discarding the largest and smallest radial velocity values from Table 3 (i.e., r053820-0237 and SOri45, respectively), the mean heliocentric radial velocity of our $\sigma$Orionis sample is $<v_{\rm r}>$=37.3kms^-1 with a standard deviation of 5.8kms^-1. This is comparable to the systemic radial velocity of the cluster's central star, which has been determined to be in the range 27-38kms^-1 (Bohannan & Garmany 1978; Garmany et al. 1980; Morrell & Levato 1991). Additionally, these velocities (except for one, see Sect. 5) are consistent with our sample belonging to the Orion OB association (Alcalá et al. 2000), and their distribution is significantly different from that of field stars.

4.4 H$\alpha$ emission

We derived H$\alpha$ pseudo-equivalent widths via direct integration of the line profile with the task SPLOT in IRAF. We note that given the cool nature of our sample, equivalent widths in the optical are generally measured relative to the observed local pseudo-continuum formed by (mainly TiO) molecular absorptions (Pavlenko 1997). We will refer to these equivalent widths as "pseudo-equivalent widths'' (pEWs).

Because of the resolution of our observations, broad H$\alpha$ lines appear blended with other nearby spectral features. The results of our measurements, given in Table 3, have been extracted by adopting the base of the line as the continuum. The error bars were obtained after integrating over the reasonable range of possible continua. Although this procedure does not give an absolute equivalent width, i.e., measured with respect the real continuum, it is commonly used by various authors, and allows us to compare our values with those published in the literature. We note that all of our program objects show H$\alpha$ in emission and that no significant H$\alpha$variability is found in any of them, except for r053833-0236 and SOri45. We also note that the H$\alpha$ emission of the fast rotator 4771-1097 is not stronger than that of other similar-type cluster members.

Figure 11: Pseudo-equivalent widths of H$\alpha$ emission as a function of spectral type (Table 3). Objects with other emission lines are plotted with filled triangles, except for r053833-0236 (M3.5). Typical uncertainty in spectral type is half a subclass. The stellar-substellar borderline takes place at M5-M6 at the age of the cluster. Effective temperatures in Kelvin and masses in solar units are also given.

Figure 11 shows the distribution of H$\alpha$ pEWs as a function of spectral type. Effective temperatures are given on the basis of the temperature - spectral-type relationships by Leggett et al. (1996), Jones et al. (1995) and Bessell (1991). Masses as inferred from the 5Myr evolutionary isochrone of Baraffe et al. (1998) are also indicated in the figure. In general, there is a trend of increasing H$\alpha$emission for cooler spectral classes, i.e., for lower masses. This behavior has been observed in various young clusters, like the Pleiades and Hyades (Stauffer et al. 1994), IC4665 (Prosser 1993), $\alpha$Persei (Prosser 1994), and Praesepe (Barrado y Navascués et al. 1998). The relative increase of H$\alpha$ in M-dwarfs may be (at least partially) explained by the drop of the flux continuum and the larger TiO molecular absorptions in the optical as a consequence of cooler $T_{\rm eff}$s. We note that, on average, H$\alpha$ for a given spectral type is slightly larger in $\sigma$Orionis than in other open clusters. This is very likely a direct consequence of the marked youth of $\sigma$Orionis.

Figure 12: Double-peak H$\alpha$ profiles. From top to bottom, the base of the emission line spreads over $\sim$$\pm$400kms-1, $\pm$350kms-1 and $\pm$270kms-1.

In Fig. 11 H$\alpha$ emission appears very strong ($pEWs\ge20$Å) and dispersed for late spectral classes ($\ge$M3.5), corresponding to masses below 0.25$M_{\odot}$ at the age of $\sigma$Orionis. Various authors have found an apparent "turnover'' in the distribution of H$\alpha$ emission in the Pleiades (Stauffer et al. 1994; Hodgkin et al. 1995) and $\alpha$Persei (Zapatero Osorio et al. 1996). Pleiades and $\alpha$Per stars with spectral types later than M3.5-M4 show a lower level of emission than stars with warmer classes. The authors suggest that this turnover is due to the transition from radiative to convective cores. By inspecting D'Antona & Mazzitelli (1994) pre-main sequence evolutionary models, we find that this transition takes place at masses 0.3-0.2$M_{\odot}$ regardless of age. In $\sigma$Orionis we do not see a drop in the H$\alpha$ emission of fully convective objects, but an enhacement. The source of such large emission clearly diminishes by the age of the $\alpha$Persei cluster (90Myr, Stauffer et al. 1999). However, the emission level of more massive stars remains with similar strengths.

Figure 13: Ratio of H$\alpha$ luminosity of the object to its bolometric luminosity as a function of optical spectral type. $\sigma$Orionis members are plotted with filled circles. For comparison we have also indicated Pleiades mean values with open triangles and a dotted line (Hodgkin et al. 1995). Uncertainty in spectral type is half a subclass.

Three stars in our sample, namely 4771-41 (K7), SOriJ054001.8-022133 (M4) and 4771-899 (K7), show profiles of H$\alpha$ emission similar to those of classical TTauri (CTT) stars, i.e., double peak structure and very broad lines spanning over $\pm$300kms^-1 from the line center. We illustrate in Fig. 12 the region around H$\alpha$ for these objects. While the emission intensity is rather large in 4771-41 and SOriJ054001.8-022133 (pEWs above 45Å), it is moderate in 4771-899.

   

Table 4: Pseudo-equivalent widths (pEWs) of emission lines.

		[O I]		[N II]			He I	[S II]
Object	MJDa	$\lambda$6300Å	$\lambda$6364Å	$\lambda$6548Å	$\lambda$6583Å	H$\alpha$	$\lambda$6678Å	$\lambda$6716Å	$\lambda$6731Å
	(-51000)	(Å)	(Å)	(Å)	(Å)	(Å)	(Å)	(Å)	(Å)
r053833-0236	138.1237	$2.29\pm0.10$	$0.75\pm0.05$	$0.80\pm0.05$	$2.50\pm0.10$	$14.0\pm2.0$	$\le$0.1	$1.15\pm0.08$	$1.65\pm0.08$
	138.1433	$2.00\pm0.10$	$0.57\pm0.05$	$0.88\pm0.05$	$2.54\pm0.10$	$14.1\pm2.0$	$0.15\pm0.05$	$0.85\pm0.05$	$1.49\pm0.05$
J053949.3-022346	138.1696	$1.80\pm0.50$	$\le$0.2	$\le$1.0	$0.35\pm0.08$	$42.0\pm6.0$	$1.18\pm0.08$	$\le$0.15	$\le$0.15
SOri45b	168.4644	-	$\le$1.5	$\le$1.5	$5.0\pm3.0$	$33.0\pm9.0$	$\le$1.5	$5.0\pm3.0$	$3.56\pm2.0$
J054001.8-022133	204.0382	$1.27\pm0.10$	$0.33\pm0.05$	$0.26\pm0.05$	$0.33\pm0.05$	$47.0\pm9.0$	$1.05\pm0.08$	$\le$0.15	$\le$0.15
	204.0531	$0.45\pm0.10$	$\le$0.1	$0.10\pm0.05$	$0.15\pm0.05$	$46.0\pm9.0$	$0.38\pm0.08$	$\le$0.15	$\le$0.15
4771-41	205.9222	$0.96\pm0.10$	$\le$0.1	blended	$0.25\pm0.05$	$53.2\pm9.0$	$0.21\pm0.05$	$0.16\pm0.08$	$0.42\pm0.05$
	205.9366	$1.00\pm0.10$	$0.18\pm0.08$	$\le$0.1	$0.30\pm0.05$	$54.0\pm9.0$	$0.42\pm0.07$	$\le$0.1	$0.45\pm0.05$
r053840-0230	206.0299	$\le$0.15	$\le$0.15	$0.42\pm0.05$	$1.10\pm0.10$	$6.5\pm0.6$	$\le$0.1	$\le$0.15	$0.31\pm0.05$
	206.0582	$0.55\pm0.05$	$0.15\pm0.05$	$0.54\pm0.05$	$1.10\pm0.10$	$6.9\pm0.6$	$\le$0.1	$\le$0.15	$0.31\pm0.05$
r053849-0238	515.2615	$0.36\pm0.10$	$\le$0.1	$\le$0.1	$0.32\pm0.05$	$2.6\pm0.3$	$\le$0.1	$\le$0.1	$\le$0.1
J053827.4-023504	517.4297	$1.25\pm0.50$	$\le$0.3	$\le$0.3	$\le$0.3	$21.2\pm3.0$	$0.26\pm0.08$	$\le$0.3	$\le$0.3

^a Modified Julian date at the beginning of the exposure.
^b Measures over the combined spectrum. Individual H$\alpha$ pEWs were 20.0, 49.4 and $22.0\pm7.0$Å, respectively.

We have calculated the H$\alpha$ luminosity ( $L_{\rm H\alpha}$) for our sample as in Herbst & Miller (1989) and Hodgkin et al. (1995). The ratio of $L_{\rm H\alpha}$ to bolometric luminosity ( $L_{\rm H\alpha}/L_{\rm bol}$) is independent of the surface area and represents the fraction of the total energy output in H$\alpha$. To derive $L_{\rm bol}$ we have used bolometric corrections provided by Monet et al. (1992) and Kenyon & Hartmann (1995). The logarithmic values of $L_{\rm H\alpha}/L_{\rm bol}$ are listed in Table 3; uncertainties take into account errors in photometry and in H$\alpha$ pEWs. Figure 13 shows the distribution of log( $L_{\rm H\alpha}/L_{\rm bol}$) with spectral type. For comparison purposes, we have also included the Pleiades mean values (Hodgkin et al. 1995). In the Pleiades, the $L_{\rm H\alpha}/L_{\rm bol}$ ratio clearly increases to a maximum at around the M3 spectral type and then turns over. This is not observed in the $\sigma$Orionis cluster, where cooler objects present larger H$\alpha$ output fluxes than the older Pleiades spectral counterparts. Discarding $\sigma$Orionis members with $\log (L_{\rm H\alpha}/L_{\rm bol})\ge-3.2$dex, cluster data appear to display a flat distribution from late K to late M (i.e., no dependence on color and mass) at around log( $L_{\rm H\alpha}/L_{\rm bol}$)=-3.61dex, with a standard deviation of 0.18dex.

4.5 Other emission lines

Our targets are pre-main sequence objects characterized by significant H$\alpha$ emission and the presence of lithium in their atmospheres (see Sect. 4.6.2). All show properties that resemble TTauri stars. The nominal definition of weak-lined TTauri (WTT) stars is usually based on H$\alpha$ emission: pEWs smaller than 10Å for K and early-M stars (Herbig & Bell 1988) and smaller than 20Å for later M-types (Martín 1998). This is accomplished by many of our objects.

Some of our program targets display, however, other permitted (He I $\lambda$6678Å) and forbidden ([O I] $\lambda$6300Å, [N II] $\lambda$6548, $\lambda$6583Å, [S II] $\lambda$6716, $\lambda$6731Å) emission lines. We have measured their pEWs; values are given in Table 4 as a function of Julian date. We note that some contamination from terrestrial night-sky emission lines may be expected in the measurements of the faintest sources. The objects of Table 4 are plotted with different symbols in various figures of this paper, except for r053833-0236 (for this star we have used the "quiet'' ORM data). The majority of the targets from Wolk (1996) are, in addition, classified as strong X-ray emitters by this author. In contrast to the younger CTT stars, WTT objects are not accreting mass from disks. However, the presence of He I and [O I], [N II], [S II] emission lines is related to jets and outflows, which are typical of CTT stars and accretion processes (Edwards et al. 1987; Hartigan et al. 1995). These lines are generally detected in objects with strong H$\alpha$ emissions ($pEWs\ge10$Å, see Fig. 11). The coexistence of $\sigma$Orionis members with properties of WTT and CTT stars is indeed indicative of ages of a few Myr. It may also indicate that small objects are accreting for longer periods than are more massive stars (Hillenbrand et al. 1998; Haisch et al. 2001), provided that their strong H$\alpha$ emissions are due to disk accretion.

The star r053833-0236 shows strong H$\alpha$ emission and noticeable forbidden lines of [O I], [N II] and [S II] in two consecutive CAHA spectra (Fig. 2, upper panel). However, its H$\alpha$ intensity clearly decreased, and no other emission lines were present in data collected on the following night (Fig. 2, lower panel) or with the INT (Fig. 3). The sources of this episodic flarelike event are not continuous in r053833-0236, probably indicating inhomogeneus mass infall onto the star surface.

The case of the brown dwarf SOri45 ($\sim$0.02$M_{\odot}$) is particularly interesting and noteworthy. Albeit the detection of [N II] and [S II] emission lines is affected by large uncertainties because of the modest quality of the Keck spectrum, this finding is very encouraging. It suggests that substellar objects, even those with very low masses, can sustain surrounding disks from which matter is accreted. Muzerolle et al. (2000) has recently reported on the evidence for disk accretion in a TTauri object at the substellar limit. The presence of disks around brown dwarfs in the Trapezium cluster ($\sim$1Myr) has been proved by Muench et al. (2001). The emission lines observed in SOri45 indicate that "substellar'' disks can last up to ages like those of the $\sigma$Orionis cluster. It is also feasible that the probable binary nature of SOri45 (see Sect. 5) triggers the formation of these emission lines. Nevertheless, further spectroscopic data will be very valuable to confirm the presence of forbidden emission lines in SOri45. The rapid H$\alpha$variability of this brown dwarf is also remarkable.

4.6 Li I absorption

4.6.1 Synthetic spectra

We have computed theoretical optical spectra in the wavelength range 6680-6735Å around the Li I $\lambda$6708Å resonance doublet for gravity logg=4.0 (CGS units) and for $T_{\rm eff}$=4000-2600K by running the WITA6 code described in Pavlenko (2000). This code is designed to opperate in the framework of classical approximations: local thermodynamic equilibrium (LTE), a plane-parallel geometry, neither sources nor drops of energy. The synthetical spectra have been obtained using the atmospheric structure of the NextGen models published in Hauschildt et al. (1999). We have adopted a microturbulent velocity value of $v_{\rm t}$=2kms^-1, solar elemental abundances (Anders & Grevesse 1989), except for lithium, and solar isotopic ratios for titanium and oxygen atoms. The ionization-dissociation equilibria were solved for about 100 different species, where constants of chemical equilibrium were taken from Tsuji (1973) and Gurvitch et al. (1979). For the particular case of the TiO molecule, we have adopted a dissociation potential of D₀=7.9 eV and the molecular line list of Plez (1998). The atomic line parameters have been taken from the VALD database (Piskunov et al. 1995), and the procedure for computing damping constants is discussed in Pavlenko et al. (1995) and Pavlenko (2001).

Synthetic spectra were originally obtained with a step of 0.03Å in wavelength, and were later convolved with appropiate Gaussians to match a resolution of 1.68Å, which corresponds to the majority of our data. We have produced a grid of theoretical spectra for nine different abundances of lithium [logN(Li)=1.0, 1.3, ..., 3.1, 3.4, referred to the usual scale of logN(H)=12] and seven values of $T_{\rm eff}$ (4000, 3600, 2400, 3200, 3000, 2800 and 2600K), covering the spectral sequence of our program targets. Determinations of the meteoritic lithium abundance (Nichiporuk & Moore 1974; Grevesse & Sauval 1998) lie between logN(Li)=3.1 and 3.4. Extensive lithium studies performed in solar metallicity, intermediate-age clusters like the Pleiades (Soderblom et al. 1993), $\alpha$Per (Balachandran et al. 1996), Blanco 1 (Jeffries & James 1999), NGC2516 (Jeffries et al. 1998), and IC2602 and IC2391 (Randich et al. 2001), as well as in the Taurus star-forming region (Martín et al. 1994) show that non-depleted stars preserve an amount of lithium compatible with a logarithmic abundance between 2.9dex and 3.2dex. We will adopt the mean value of logN₀(Li)=3.1 as the cosmic "initial'' lithium abundance.

Figure 14: The upper panel shows theoretical spectra computed for $T_{\rm eff}$=3400K, logg=4.0 and three different lithium abundances. The lower panel illustrates spectra for logg=4.0, logN(Li)=3.1 and various temperatures. The spectral resolution is $\sim$1.7Å. The absorption feature centered at 6707.8Å is due to the atomic Li I resonance doublet, while the rest of the spectral features are mainly molecular TiO absorptions.

 

 

Table 5: LTE Li I $\lambda$6708Å resonance doublet curves of growth: predicted pseudo-equivalent widths (pEWs).

$T_{\rm eff}$	logN(Li)
(K)	1.0	1.6	1.9	2.5	3.1	3.4
2600	.357	.444	.479	.552	.617/.644$^\ast$	.656/.694$^\ast$
2800	.346	.440	.475	.551	.623/.675$^\ast$	.669/.728$^\ast$
3000	.312	.404	.441	.522	.596/.666$^\ast$	.652/.741$^\ast$
3200	.296	.386	.423	.504	.578/.639$^\ast$	.637/.729$^\ast$
3400	.266	.350	.385	.456	.544/.634$^\ast$	.604/.720$^\ast$
3600	.262	.337	.373	.442	.536/.566$^\ast$	.609/.665$^\ast$
4000	.189	.281	.319	.403	.507/.537$^\ast$	.588/.620$^\ast$

Notes - pEWs are given in Å. In all computations we have
used logg=4.0 and solar metallicity, except for the columns
labelled with an asterisk, where we have used logg=4.5.

Figure 14 depicts some of our theoretical spectra for different values of lithium abundance and surface temperature. The observed spectrum of SOri27 is compared to a few computations in Fig. 15. Optical spectra at these cool temperatures are clearly dominated by molecular absorptions of TiO. Only the core of the lithium line is observable, since the doublet wings are completely engulfed by TiO lines (Pavlenko 1997). We have obtained the theoretical Li I $\lambda$6708Å pEWs via direct integration of the line profile over the spectral interval 6703.0-6710.8Å. Many of the lithium LTE curves of growth employed in this work are presented in Table 5. Various authors (e.g., Magazzù et al. 1992; Martín et al. 1994; Pavlenko et al. 1995; Pavlenko 1998) have shown that the differences between LTE and non-LTE calculations for cool temperatures are negligible compared to uncertainties of pEW, $T_{\rm eff}$ and gravity. Similarly, the effects of chromospheric activity on the line formation are found to be of secondary importance (Pavlenko et al. 1995; Houdebine & Doyle 1995; Pavlenko 1998) and have not been included in our calculations. The Li I resonance doublet appears to have very light dependence on the temperature structure of the outer layers (see also Stuik et al. 1997). We find a rather poor agreement between the predicted Li I pEWs of Table 5 and those provided in Pavlenko & Magazzù (1996). These authors' values are considerably larger because they measured theoretical equivalent widths (note the drop of "pseudo'') relative to the computed "real'' continuum, while we have determined pEWs relative to the computed pseudo-continuum formed by molecular absorptions.

Figure 15: Synthetic spectra ( $T_{\rm eff}$=3000K, logN(Li)=3.1) compared to the observed spectrum of the brown dwarf SOri27 (thick dotted line). Computed spectra have been degraded to the same resolution as the observations. The location of the Li I resonance doublet is indicated with a vertical dotted line.

   
4.6.2 Observed spectra

We have also obtained the Li I $\lambda$6708Å pEWs from our observed spectra. To compensate for the different resolution of the data, the integration of the line profile has always been performed over the spectral range 6703.0-6710.8Å. Our measurements and their uncertainties are listed in Table 3. Li I is detected in absorption in all of our program objects, except for SOriJ053914.5-022834 (M3.5). It might be a cluster non-member, but its optical spectrum is the noisiest amongst the McDonald data, and even the Ca I line at 6717Å lies barely undetected (see Fig. 9). We impose a 1$\sigma$ upper limit of pEW=0.44Å by considering the strongest possible feature in the region around the line and taking into account the S/N ratio and resolution of the spectrum.

Figure 16: Pseudo-equivalent widths of Li I $\lambda$6708Å as a function of spectral type. Symbols are as in Fig. 1. Note that the coolest cluster member of our sample (the brown dwarf SOri45) is not included in the figure for clarity. Overplotted onto the data are three LTE theoretical curves of growth provided in this paper. Typical uncertainty in spectral type is half a subclass. The stellar-substellar borderline takes place at M5-M6 spectral type at the age of the cluster. Effective temperatures in Kelvin and masses in solar units are also given.

Li I pEWs are plotted against spectral type in Fig. 16. SOriJ053914.5-022834 is excluded from the diagram. Overplotted onto the data are the theoretical pEWs for logg=4.0 and two different lithium abundances: logN₀(Li)=3.1 ("initial'') and logN(Li)=1.9 (about one order of magnitude of destruction). We have also included in the figure the "initial'' curve of growth for a slightly larger gravity, $\log\,g=4.5$. The trend of the observations is nicely reproduced by the logN₀(Li) curves, implying that lithium is still preserved at the age of the $\sigma$Orionis cluster. We will discuss this issue further in Sect. 5.2. We note the differences due to gravity in the Li I curves of growth. Although these differences are rather small ( $pEW\le0.03$Å) for $T_{\rm eff}$$\ge$3700K, they become twice as large for cooler temperatures. Given the error bars of the observed Li I pEWs, we cannot easily discriminate between gravities.

The scatter of the Li I pEWs is considerable for spectral types cooler than M3.5 (Fig. 16). The problem of the lithium star-to-star dispersion occurring at $T_{\rm eff}$$\le$5300K has been widely discussed in the literature (e.g., Soderblom et al. 1993; Pallavicini et al. 1993; Russell 1996; Randich et al. 1998; Barrado y Navascués et al. 2001b). Nevertheless, this phenomenon still remains obscure and proves challenging to explain theoretically. The dispersion could be ascribed to a variability in the Li I line as a consequence of stellar activity, different mixing processes, presence or absence of circumstellar disks, binarity, or different rotation rates from star to star. Recently, Fernández & Miranda (1998) have found that the Li I $\lambda$6708Å line in the WTT star V410Tau varies according to its rotational period. From Figs. 11 and 16 we observe that the region of the largest lithium scatter coincides with that of the strongest H$\alpha$ emissions. This might indicate that some hot continuum is "veiling'' the optical spectra (Joy 1945; Basri & Batalha 1990; Basri et al. 1991), thereby affecting our pEW measurements. We note, however, that if any "veiling'' exists around H$\alpha$ and Li I in our spectra, it has to be small compared with that of many other CTT stars, because there is no clear correlation between strong H$\alpha$ emission and low values of Li I pEWs (except for SOriJ053951.6-022248). There are other possible explanations for the significant Li I pEW scatter, such as different gravities (objects with low Li I pEWs might have lower gravities, and therefore, younger ages), and contamination by lithium-depleted interlopers.