Astron. Astrophys. 363, 958-969 (2000)

3. Analysis

3.1. Colour-magnitude diagrams

In Fig. 1 we show the V vs  and I vs   colour-magnitude diagrams where we combine our photometric data of the X-ray candidates (filled circles) with magnitudes and colours from known Coma Berenices stellar members (open circles, Trumpler 1938; Artyukhina 1955; Argue & Kenworthy 1969; De Luca & Weiss 1981; Bounatiro 1993; Odenkirchen et al. 1998). Also included in the figure are the companion objects #1b, #1c and #2b. VRI photometry for confirmed Trumpler's Coma members have been adopted from Johnson & Knuckles (1955) and Mendoza (1963); we have taken the data for the remaining members from the SIMBAD and Hipparcos databases. Overplotted to the observations are the main sequence (solid line) for field stars and the 600 Myr-isochrone by D'Antona & Mazzitelli (1998, dashed line), both shifted to the distance of Coma Berenices ( = 4.77, Hipparcos). The main sequence for F-K spectral types have been taken from Pickles (1985), while that for the M-classes was derived from Leggett et al.'s (1996) paper. The theoretical isochrone (, luminosity) has been converted into the observables using the colour- and colour-BC(V) calibrations provided by Alonso et al. (1995, 1996) for the warmer stars and by Leggett et al. (1996) for the cooler temperatures. Cluster members nicely fit both the main sequence and the 600 Myr-isochrone down to = 14, 13, respectively. The age of 600 Myr has been recently suggested as the most likely age for the Coma Berenices stellar cluster (Odenkirchen et al. 1998).

A first glance at the two panels of Fig. 1 suggests that most of the candidates in our sample are likely to be Coma Berenices cluster non-members based on their photometry, and only one of them (#1a) plus stars #1b and #1c have a position not inconsistent with membership (considering 3 error bars). All the objects that we regard as non-members (#2b, #4, #5, #8, #10, #11 and #12) lie well below ( mag) the main sequence and the 600 Myr-isochrone and are considerably fainter than known Coma members with similar colours. Whereas non-membership is easy to ascertain, it is more difficult to confirm membership. The star #1a (RXJ 1212.0+2232) lies very close both to the isochrone and the main sequence and to the position of two previously known members in the two diagrams, and thus it can be classified as a photometric member. The two other bright stars in the field (#1b and #1c) also show photometry marginally in agreement with the expected sequence for the cluster. On the contrary, the three coolest objects in our sample, #2a (RXJ 1220.5+2648), #3 (RXJ 1222.7+2711) and #7 (RXJ 1229.4+2259), are located considerably above the 600 Myr-isochrone by about 1.5-2 mag. The position of these stars is also inconsistent with that of two previously known members with similar magnitudes as it can be observed from the figure. However, these three stars could be younger than the mean age of the cluster (by a factor two - an age dispersion in the low-mass end of the Coma Berenices sequence cannot be ruled out), or could be binary systems, or could be a combination of both (X-ray surveys do present a clear bias in this respect toward young stars and close binary systems). Under these assumptions the location of each of the three stars in the colour-magnitude diagrams may well be explained. Thus, with photometry alone we cannot discard them as possible members of the Coma cluster. Proper motions and spectroscopy will allow us to unambiguously establish their membership status.

3.2. Spectral types, chromospheric activity and radial velocities

Spectral types are useful for studying cluster membership and estimating other stellar parameters (i.e., temperature, radius, and mass, etc.) which are utilized in detailed abundance studies or in interpreting additional data for these stars (e.g., X-ray fluxes, rotation periods, etc.). We have inferred the spectral types of our sample by comparing the spectra of the targets with those of spectroscopic standard stars both in the blue and in the red spectral ranges. Spectra of the following G5-M0-type standards (Jaschek 1978): HD 282025 (G5V), BD 2140 (G7V), HD 290982 (K0V), BD 2310 (K1V), BD-08 2823 (K3V), BD 2785 (K5V), BD 2874 (K7V) and BD 1311 (M0V), were obtained in the same run as for the program stars. For later spectral types we used data collected with the same instrumental setup in previous campaigns. In this case, only the red spectra have been considered for direct comparison between the target stars and the standards. We have derived the M spectral classification of the three coolest stars in our sample making use of molecular indices defined by Kirkpatrick et al. (1991) and Prosser et al. (1991). These indices are based on the relative strengths of CaH and TiO bands; TiO molecular absorptions dominate the optical energy distribution of the M-class objects. The Kirkpatrick et al.'s spectroscopic standards GL 338A (M0V), GL 767A (M1V), GL 767B (M2.5V), GL 569A (M3V), GL 402 (M4V) and GL 406 (M6V) have been used to transform Prosser et al.'s measured index values to a spectral type. A series of G5-M4III spectra were also available to us and we used them in order to investigate the luminosity class of the candidates. All of our stellar targets appear to be dwarfs rather than giants. We provide in Table 2 our determinations; the uncertainty in the K-M spectral classification is estimated at half a subclass. The final adopted spectral types are in the range G6V to M3.5V.

Fig. 3 shows clearly the changes in the spectral energy distribution for the stars of the sample. Photospheric Ca II H & K lines, which dominate at the earlier spectral types, progressively allow the appearance of the chromospheric components at the later types. The Na I D doublet at 5890-5896 Å increases with increasing spectral type, while H changes accordingly from absorption to emission. In the spectrum of the star #12 (K1V) H disappears in absorption as a result of a high chromospheric activity. This is consistent with the chromospheric emission observed at the bottom of the photospheric Ca II H & K lines in its spectrum. This is also the case for the star #10 (K6V), with both Ca II H & K and H clearly in emission. Chromospheric activity appears to be also present in the star #4 (K0V). The spectrum presented in the figure for the star #1a (K6V) shows an inverse P-Cygni profile for H. Changes from a P-Cygni profile to its inverse, passing through intermediate situations, were observed within periods of hours. This behaviour is associated with the binary nature of this W-type W UMa object (see Sect. 3.4). Finally, it is seen how the spectra of the latest objects are mainly dominated by the presence of TiO bands.

In order to obtain a more quantitative evaluation of the chromospheric activity exhibited by the stars of this sample, we followed a similar procedure than that of García López et al. (1993) to estimate the S index for Ca II H & K lines (see Vaughan et al. 1978) from the observed spectra. We applied a numerical mask to our spectra, comprising two narrow bands of triangular profile centred on the H and K lines, and two square-topped broad bands, shifted to the red (R) and to the blue (V) of H and K, respectively. These bands were identical to the original bands defined by Vaughan et al. (1978) for their H-K photometer. An index was obtained by computing the following ratio between the equivalent widths measured for the chromospheric and continuum bands: . To convert our index to the original scale for the S index, we repeated this procedure for 15 dwarf stars with Ca II H&K spectra available in Montes et al. (1997), spectral types in the range G2V to K7V, and measurements of the S index listed in the catalogue of Duncan et al. (1991) ⁴. Before applying the mask, the original spectra of these stars were degraded to match our lower spectral resolution. The resulting values, with the error bars associated with this procedure, are given in Table 2.

Fig. 4 shows the chromospheric activity estimated for our stars compared with the mean S values for a sample of measurements of G- to K-type stars from Noyes et al. (1984), complemented with mean values listed by Duncan et al. (1991) for M-type stars of the Woolley et al. (1970) catalogue of stars within 25 pc of the Sun. The compilation of comparison stars is by no means exhaustive but provides a reference frame to evaluate the behaviour of the chromospheric activity of the X-ray selected stars. It can be seen how our stars with spectral type later than K0 are located in the upper part of the distribution, showing in general a high level of activity as it was expected from their high coronal emission. The previous qualitative considerations about the chromospheric activity of stars #4 (K0), #12 (K1) and #10 (K6) are clearly confirmed. The star #11 (K3) shows a lower level of activity but still much higher than other values observed for its spectral type. The error bar shown for the binary star #1a (indicated by an arrow) includes the variability observed for its chromospheric activity in six different measurements. The corresponding individual values are listed in Table 5. The two M-type stars of our sample with available blue spectra show a very high level of activity. This is not the case for the two G-type stars. The S values estimated for them are located in the lower strip of the distribution, below the so called "gap" of Vaughan & Preston (1980), which is believed to separate "old" and "young" G-type stars (Barry 1988), although it has also been ascribed to the combined action of two phenomena: the time-dependence of the stellar spin down and the colour-dependent shape of the activity-rotation relation for stars earlier than K2 (Walter 1982; Rutten 1987). The error bars for these two stars allow them, however, to be potentially more active. This would be in better agreement with their coronal emission, for which we estimate a lower limit similar to those of the stars in the upper part of the distribution (and typically at least one order of magnitude larger than those of the stars in the lower part). It could also be possible that these stars are indeed quiescent and not the real optical counterparts to the X-ray sources detected by ROSAT. The lower limit for their chromospheric activity is given by the minimum (basal) flux for their spectral type (Schrijver et al. 1989).

Fig. 4. Values of the S index estimated from the blue spectra of our sample stars (filled circles) vs. spectral type, compared with mean S values taken from the literature for late-type dwarfs (open diamonds), obtained using the H-K photometer (see text). The location of the Sun is shown with the usual symbol and the variable star RXJ 1212.0+2232 is indicated with an arrow. Note that the X-ray selected stars exhibit, in general, a very high level of chromospheric activity.

The spectral types that we derived for our sample stars are in full agreement with their colours, with the only marginal exception of the star #10 (K6V), whose spectrum appears to be slightly earlier than that of the star #2b (K6.5V) which shows slightly bluer colours but within the error bars. This general good agreement could be an indication that the extinction is low towards the direction of the sources. Using the spectral type-magnitude relationship defined by Coma Berenices members, only four objects in our sample (#1a, #2a, #3 and #7) fit the spectral sequence of the cluster. This result is very similar to that derived from the optical photometry. The seven remaining X-ray candidates appear to have low-luminosity for their spectral types, and thus, they are more distant than the cluster and are not members.

Due to the limited resolution of our spectra, we cannot infer radial velocities with a precision better than 15-20 km ^-1 and, therefore, we cannot definitively confirm membership using radial velocities. A mean radial velocity of about 0 km s^-1 has been inferred for Coma Berenices (see Trumpler 1938, who derived km s^-1; Odenkirchen et al. 1998, who obtained km s^-1). When we performed the spectroscopic observations we already knew that the star #1a showed photometric variability. Because of this, we obtained a number of spectra on this target in order to also detect radial velocity changes (see Sect. 3.4 for further details). For deriving radial velocities we have cross-correlated the spectra of our target stars with the spectra of two standard stars for which radial velocities are available to high degree of accuracy (HD 107513 km s^-1, BD 2785 km s^-1; Duflot et al. 1995). These data were obtained with the same instrumental setup during our spectroscopic campaign. Before deriving the radial velocities, all the spectra were set to a common origin by shifting sky lines to laboratory wavelenghts. The cross-correlation was carried out between target stars and reference stars of similar spectral types. We present our measurements as a function of heliocentric Julian date in Table 3 where the template star used for each program star is indicated. Given the uncertainties in our measurements we will adopt an interval of km s^-1 around the mean radial velocity of the cluster as a plausible range for inferring the membership of our candidates. In this respect, and averaging the various measurements available for some stars, we cannot exclude any of the four photometric candidates as likely members of the Coma cluster.

Table 3. Radial velocities for the stellar X-ray candidates.
Notes:
Typical uncertainty is 15 km s^-1.
The complete list of radial velocity measurements for this star is provided in Table 5.

In addition to photometry, spectral type and radial velocity not inconsistent with being cluster members, the stars #1a, #2a, #3 and #7 show H in emission with equivalent widths (EWs) of few Angstroms. The H EWs that we measure from our spectra are tabulated in Table 2. All these four objects have emissions in agreement with their nature of X-ray emitters and with the status of members of the Coma star cluster. However, this property is neither a necessary nor a sufficient condition, since active field dMe stars also display H in emission, while a fraction of M dwarfs in the Hyades and Praesepe have H absorption (or very weak emission; e.g., Barrado y Navascués et al. 1998; Stauffer et al. 1997). None of our targets has been observed to show flares.

3.3. Proper motions

We have successfully obtained proper motion measurements for those targets for which there is a spectroscopic and/or photometric suspicion of membership in the Coma cluster, i.e. stars #1a-c, #2a, #3 and #7. Because they are bright sources, all the candidates are well detected in the two epochs of observations of the Palomar Observatory survey. We have digitized an area of 8´ 8´ of the Palomar plates centered at the coordinates of each of the program stars, and compared them to our IAC80 images. They are separated in time by 35.8 yr (Palomar epoch 1 and epoch 2) and 41.8 yr (Palomar epoch 1 and IAC80 data). This time baseline is enough for detecting an apparent motion of the cluster in comparison to the surrounding field stars. The mean proper motion of the Coma Berenices cluster is = -0.0123 0.0054"/yr, = -0.0097 0.0063"/yr (3 uncertainties). These numbers result from the average of 35 Trumpler's (1938) cluster member proper motion determinations available in the catalogue by Abad & Vicente (1999). None of our candidates is, however, included in that work. Unfortunately, the cluster motion is not large and high precision measurements are needed in order to assess cluster membership. Nevertheless, if we find that our stars present a proper motion in disagreement with that of the Coma stellar group, we can reasonably claim that the candidates do not belong to Coma Berenices. The astrometric procedures we have used for deriving proper motions are simple: we derived centroids for all stellar-like objects with S/N peak-detections larger than 5 in the images, and we proceeded to correlate their relative positions from the first epoch to the second and third epochs. Those objects with no apparent displacement were used to define the origin, and the movement of mobiles was then referred to them. Table 4 lists our final measurements together with 1 error bars. None of our five objects shows a stellar motion compatible with cluster membership; all of them move several times faster, and in some cases, the movement is in an opposite direction. Regarding the remaining X-ray candidates in our sample we have not detected significant motions in the time interval of our analysis.

Table 4. Proper motion measurements.
Notes:
These two stars share the same proper motion.

One interesting by-product from the proper motion study is that stars #1a (RXJ 1212.0+2232) and #1b share the same motion in the sky within 1 uncertainty. This suggests that the two stars are real physical companions. Their photometry is also consistent with this result; the sequence defined by #1a and #1b nicely fits that of the main sequence shifted to a distance of 80-110 pc. The angular separation of the secondary star with respect the primary star is W and S (see Fig. 2); adopting the previous estimate of distance, this separation translates into 5000-7000 AU. From the photometric measurements of the fainter companion we can estimate its spectral type around M1-M3-class.

3.4. The W-type W UMa binary RXJ 1212.0+2232

From the photometric observations we have discovered one eclipsing binary star in our sample. More than 400 measures in the I-band are available for RXJ 1212.0+2232 (#1a) which have led to the determination of its orbital period. Periodogram analysis was performed on the differential photometry following the prescription of Scargle (1982) for unevenly sampled data. A significant peak (probability 100%) was found at a period of 5.2920 0.0001 hr. Fig. 5 (upper panel) illustrates the light curve of RXJ 1212.0+2232 in the I-band folded in phase with the derived period and including all the data-points obtained at the two telescopes, IAC80 and OGS (different symbols are used). Individual photometric measurements of the OGS data for the two comparison stars present a scatter of about 0.006 mag, which is one order of magnitude smaller than the amplitude of modulation of RXJ 1212.0+2232, and do not show any correlation with phase. We do not tabulate individual measures in this paper, but will provide the data to anyone interested. The amplitude of the I-filter curve is determined at 0.78 0.01 mag; we cannot obtain the amplitude of the light curve at other wavelengths because of the lack of enough data. However, we have detected slight changes by 0.1 mag in the optical colours of this binary star as a function of the orbital phase. This could be related to the different temperature and mass of the two stellar components. We also note that around phase 0.25 (secondary maximum) the scatter in the magnitudes of the star is large. Such an effect is real and cannot be ascribed to poor photometric precision; it may be interpreted as a result of the different spot coverage in the stellar surfaces at the time of the observations. Twelve low-resolution spectra have been also obtained for this close binary. Double lines are barely resolved in some of them, and the cross-correlation technique used for deriving radial velocities is biased to the most intense lines. We provide our heliocentric radial velocity and H EW measurements for one of the components of the system in Table 5; these values are given as a function of phase and heliocentric Julian date, and do correlate well with the light curve as it can be seen in Fig. 5 (lower panel).

Fig. 5. (Upper panel). Phased I-band light curve for the star #1a (RXJ 1212.0+2232, K6V spectral type). Small dots correspond to the OGS observations (April 1999, uncertainties of 0.006 mag), while filled circles and triangles stand for the IAC80 data (February and March 1997, respectively). The period used is 5.2920 0.0001 hr. This light curve is typical of active W-type W UMa binaries. (Lower panel). Radial velocity measurements ( error bars) of one of the stellar components of the W UMa binary. The sinusoidal variation with phase is clearly seen.

Table 5. RXJ 1212.0+2232 radial velocity, H, and S index measurements.
Notes:
Typical uncertainty is 15 km s^-1.
Typical uncertainty is 0.10&_Aring;.
Typical uncertainty is 0.30.

The shape of the light curve of Fig. 5 corresponds to contact binary stars of the W UMa type. In the particular case of RXJ 1212.0+2232, the deeper light minimum results from the eclipse of the less massive (but hotter) component, implying that our star is a W-type W UMa binary system. This is also in accord with the late spectral type (K6V) of the source. We remark that the period we have inferred for this contact binary star is among the shortest values found in the literature for this kind of stars. Although the frequency of the W UMa binaries is about one or two such systems per a thousand of ordinary dwarfs (Rucinski 1993), the discovery of RXJ 1212.0+2232 in our X-ray sample is not a surprise since W UMa stars are known to be strong X-ray emitters. Assuming a distance of 80-110 pc (see previous section) and the X-ray flux  erg s^-1 cm^-2 given by RSP, we estimate for RXJ 1212.0+2232 an X-ray luminosity  erg s^-1. Such a luminosity is consistent with those of known W UMa systems (e.g., McGale et al. 1996). In this kind of binary the stars are as close as double stars can be, sharing the same atmospheric envelope and showing the least amount of angular momentum among binary stars. We note that RXJ 1212.0+2232 is also a visual companion of a cooler star, forming a multiple stellar system. Only a few percent of these contact binaries are known to be visual companions.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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