© ESO, 2010

1. Introduction

There are already measurements of magnetic fields in single G and K giants (Konstantinova-Antova et al. 2008a; Aurière et al. 2008; Konstantinova-Antova et al. 2009), but M giants have not yet been studied in this respect. Despite theoretical predictions of possible dynamo operation on the asymptotic giant branch (AGB) (Blackman et al. 2001; Soker & Zoabi 2002; Nordhaus et al. 2008), actual evidence of magnetic activity in such evolved stars is sparse and indirect (Hünsch et al. 1998; Karovska et al. 2005; Herpin et al. 2006). Hence, we here present a study of the variable magnetic field of the single M giant EK Boo. This work is a part of a programme, that aims to detect magnetic fields in evolved, single late-type stars (Konstantinova-Antova et al. 2008a).

The source EK Boo = HD 130144 is a 6th magnitude M 5 giant and a semiregular variable star (Kholopov et al. 1998). This evolved giant attracted our interest by its unusual X-ray luminosity L_x, which is higher than 10³⁰ erg s^-1 (Hünsch et al. 1998). A further study revealed its variability of L_x, as well as its optical activity indicators Ca ii K&H and H_α (Hunsch et al. 2004). At the same time, EK Boo is considered to be a single star (Famaey et al. 2009) with a projected rotation velocity of vsini = 11 km s^-1 (Hünsch et al. 2004). A direct detection of its magnetic field was first reported by Konstantinova-Antova et al. (2009). To our knowledge, this was the first direct detection of a magnetic field in a single M giant. In the work we present here, we study the variability of the magnetic field and activity of EK Boo, its chemical composition and evolutionary stage, and we discuss possible reasons for a dynamo operation in such an evolved star. To see if this magnetically active M giant is a special case, or magnetic activity is common in such stars, we also present first magnetic field measurements obtained for other M giants.

2. Observations and methods

The observations of EK Boo were carried out at the 2-m Bernard Lyot Telescope (TBL) of the Pic du Midi observatory, with NARVAL, a new generation spectropolarimeter (Aurière 2003). It is a copy of the instrument ESPaDOnS, which was installed at CFHT at the end of 2004 (Donati et al. 2006). NARVAL is a fiber-fed echelle spectrometer, able to cover the whole spectrum from 370 nm to 1000 nm in a single exposure. Forty orders are aligned on the CCD frame, separated by 2 cross-disperser prisms. We used NARVAL in polarimetric mode, with a spectral resolution of 65 000. Stokes I (unpolarised) and Stokes V (circular polarization) parameters were measured by means of four sub-exposures, between which the retarders, Fresnel rhombs, were rotated in order to exchange the beams in the instrument and to reduce spurious polarization signatures.

We observed EK Boo during four consecutive nights in April 2008, then on 20 and 21 December 2008, 25 February 2009, and during three nights in March 2009. For the extraction of the spectra we used Libre-ESpRIT (Donati et al. 1997), a fully automatic reduction package installed at TBL. For the Zeeman analysis, a least-squares deconvolution (LSD, Donati et al. 1997) was then applied to all spectra. We used a mask, which was calculated for solar abundance, an effective temperature of 3500 K, log g = 0.5 and a microturbulence of 2.0 km s^-1. These parameters are consistent with the spectral class and luminosity of EK Boo (Dyck et al. 1998). This method enabled us to average a total of about 12 700 lines and to get Stokes I and Stokes V profiles. The null spectrum (N profile) given by the standard procedure (Donati et al. 1997) was also examined, but never showed any signal, confirming that the detected signatures in the V profiles are not spurious. From the obtained mean Stokes V for each night we computed the surface-averaged longitudinal magnetic field B_l in G, using the first-order moment method (Donati et al. 1997; Rees & Semel 1979).

At the same time, the magnetic activity of EK Boo was monitored by means of measurements of the relative intensity of the chromospheric activity indicator Ca ii K. In the core of this emission line, the S/N of our spectra exceeds 50. Table 1 gives the journal of our observations of EK Boo, including the dates, Heliocentric Julian Day (HJD), total exposure time, detection-level from the LSD statistics (Donati et al. 1997), B_l and its error (in G), and the relative intensity I(CaII K)/I(3950) for the maximum of the Ca ii K emission.

Fig. 1 LSD profiles of Stokes I, null polarization N and Stokes V (bottom, middle and upper curves) for EK Boo, as observed on 13 March 2009. For clarity, Stokes V and N profiles are enlarged 500 times, and the successive profiles are shifted vertically.

Fig. 2 LSD Stokes V profiles for EK Boo for the dates listed in Table 1, from 03 Apr. 08 (top) to 18 Mar. 09 (bottom). The dashed lines illustrate the respective zero levels. The scale of the Y-axis is in units of V/Ic, Ic is the intensity of the continuum. For clarity, successive profiles are shifted vertically.

Fig. 3 Magnetic field measurements (upper panel) and chromospheric activity indicator Ca ii K emission (lower panel) for EK Boo in the observed period. An inverse Y-axis is used for Bl to illustrate the magnetic field.

3. Observational results

3.1. Magnetic field and activity indicators of EK Boo

A significant Stokes V signal was detected at all times, except in December 2008. The measured B_l varies from  − 0.1 to  − 8 G. Figure 1 shows our best LSD profiles, obtained on 13 March 2009, under excellent sky conditions. Using the LSD statistics tool (Donati et al. 1997), the outstanding Stokes V signature (upper profile) corresponds to a definitive detection (DD) with a χ² of 4.7. The Stokes V signal is well centred on the Stokes I profile (bottom) and no signal at all is observed on the null polarization N profile (middle). This observation shows a complex Stokes V structure, maybe a result of a dynamo action. Figure 2 shows all observed Stokes V profiles for EK Boo. A very weak signal was observed in the two nights of December 2008, and we did not obtain any significant Zeeman detection. Nevertheless, a definitive detection can be attained by averaging all spectra taken during these two nights. On 25 February 2009, the magnetic field was definitely detected again and the resulting B_l is still close to 0. This challenges our much higher measurements obtained in the four nights of April 2008, when the magnetic field of EK Boo did not present significant variations. And there appears a rapid increase of B_l again in March 2009.

A significant Ca ii K&H emission is observed in every night. The ratio I/I(3950) of the K-line is given in Table 1. In Fig. 3 it can be compared with the B_l measurements. Both measurements are plotted over HJD. We can see that the Ca ii K emission increases smoothly and monotonically during the period monitored here, apparently without any significant short-time variation. This behaviour is different from that of the Stokes V profiles and B_l. For example, Ca ii is at the weakest when the magnetic field is strong in the nights in April 2008. And it becomes stronger when Stokes V and B_l are weak on 20 and 21 December 2008. This suggest the existence of areas with opposite magnetic polarity on the surface of EK Boo: contributions of both polarities to the mean magnetic field can cancel each other when both are present on the facing side of the star, while adding up to a maximum Ca ii emission line flux of the related chromospheric activity regions.

The Ca ii K emission profiles sometimes feature a single peak, but on other occations they show a double-peak structure (see Fig. 4). Their peak asymmetry changes from V/R > 1 on April 3, 2008, to V/R < 1 on December 21, 2008, where V/R is the ratio between the violet (V) and red (R) components of the double-peaked emission line. In the first case, this indicates vertical motions in the chromosphere, where the downward components appear stronger. This is typical for many red giants (Smith & Shetrone 2000). In the second case, V/R < 1, upward motions and possible outflow dominate the asymmetry. Hence, the chromosphere of EK Boo seems to be very dynamical on timescales of months and years, with episodic outflows from its lower layers, where Ca ii K and H emission lines are formed.

Fig. 4 Ca ii K emission line profiles, as observed for EK Boo in the period of April 2008 to March 2009.

3.2. Radial velocity, binarity, and pulsations

Radial velocity measurements (RV) for EK Boo have been carried out on the LSD Stokes I profiles using Gaussian fits. The RV accuracy of NARVAL is 20 − 30 m s^-1 (Moutou et al. 2007; Aurière et al. 2009). Variations of RV larger than 1 km s^-1 were observed on a time-scale of less than a month. But in averaging the RV measurements for each month (April 2008, December 2008, February 2009, and March 2009), we find a standard deviation of only about half a km s^-1. This compares well with the values (0.36 and 0.65 km s^-1 respectively) obtained by Hünsch et al. (2004) and Famaey et al. (2009) from measurements with CORAVEL (Udry et al. 1997). Famaey et al. (2009) included their EK Boo observations in two of their diagnosis plots and concluded that the star “appears amidst the non-binary M giants”.

EK Boo is also known as a semi-regular variable (Kholopov et al. 1998). A larger photometric sample is available from Hipparcos data, and though EK Boo is among stars with large HIP photometric amplitudes (0.38 mag, Adelman 2001), no clear periodicity can be derived (Koen et al. 2002).

The average of our much more recent RV measurement is shifted by about 5 km s^-1 with respect to the average given in the literature (about  − 27 km s^-1 with respect to about  − 22 km s^-1). This difference is one order of magnitude larger than any shift obtained for other M giants studied with NARVAL, even when observations were made during the same nights as EK Boo. Hence, this shift appears to be real, and it could be linked to pulsations, as discussed in the context of other semiregular variable stars (Lebzelter 1999; Lebzelter et al. 2000) or of multiple-mode asymptotic giant branch variable stars (Hinkle et al. 2002).

In summary, our RV measurements confirm that their variations on a time-scale of less than a month are of a magnitude of about 1 km s^-1. These variations must be considered as significant with respect to NARVAL’s accuracy (better than CORAVEL accuracy). The analysis by Famaey et al. (2009) favours an origin from pulsations, quite common in this type of stars. Furthermore, the shift in RV between our observations and those in the literature is not due to binarity, although slow orbital motion might, a priory, be a possible explanation: Hünsch et al. (1998) already considered the possibility of active, faint companions in detail, when discussing the origin of detected X-ray emission in M-giants. But in the case of EK Boo, spectral signatures of a secondary have never been found. On the other hand, clearly a Zeeman detection with NARVAL could only be caused by a bright object, which would have been easily detected spectroscopically. Hence, the M giant itself must be magnetically active.

3.3. Metallicity and atmospheric parameters determination

We used our NARVAL spectrum of 13 March 2009 to derive the metallicity and other parameters of EK Boo. For this purpose, we measured equivalent widths of the Fe i and Ni i lines in the “window” 7400 − 7580 Å, a spectral region relatively free of molecular absorption. Values for the respective oscillator strengths log gf were taken, if available, from Gurtovenko & Kostyk (1989). Otherwise, we used the values derived by Smith & Lambert (1985) or those offered by the VALD database (Kupka et al. 2000).

We then used spherically symmetric, LTE, hydrostatic model atmospheres as computed with the MARCS code (Gustaffson et al. 2008). The CNO abundances in atmospheres of M giants are known to be modified through the first dredge-up (see, e.g., Charbonnel 1994; Boothroyd & Sackmann 1999; and Sect. 4): ¹²C is depleted and ¹⁴N is enhanced. We therefore used MARCS models for moderately CN-cycled composition with  [C/Fe]  =  −0.13,  [N/Fe]  =  + 0.31, and ¹²C/¹³C = 20. This chemical composition agrees with the abundance ratios measured in field M giants by Smith & Lambert (1990):  [C/Fe]  =  −0.19 ± 0.13 and  [N/Fe]  =  +0.28 ± 0.11.

The stellar mass was taken to be M = 2   M_⊙ (see Sect. 4). But as shown by Plez (1990) and García-Hernandez (2007), the temperature and pressure structures of model atmospheres are practically identical for models of 1   M_⊙ and 10   M_⊙ stars. The current version of the LTE line analysis and spectrum synthesis code moog (Sneden 1973) was used here.

The microturbulence velocity was determined from the Fe i lines by requiring that the derived abundances shall be independent of the equivalent width. The effective temperature was derived by requiring that the abundance calculated for the Fe i lines shall not show any dependence on excitation potential (Fig. 5). The atomic line list, measured equivalent widths, and derived abundances are listed in Table 2.

Fig. 5 Iron abundance as derived from individual Fe i lines, log ε(Fe), versus excitation potential and reduced equivalent width, log    (Wλ/λ). An atmospheric model with Teff = 3400 K, log g = 0.0, and ξ = 2.0 km s-1 was used.

In the way described above, we derive an effective temperature of T_eff = 3400 K and a microturbulent velocity of ξ = 2.0 km s^-1. In adopting these values, a surface gravity of log g = 0.0 (estimated from M_bol, T_eff and the stellar masses obtained by comparison with evolutionary tracks, see Sect. 4 and Fig. 7), we then derived the following abundances: log ε(Fe) = 7.38 ± 0.13, log ε(Ni) = 6.12 ± 0.18 or  [Fe/H]  =  −0.14 ± 0.13 and  [Ni/H]  =  −0.13 ± 0.18¹ where the solar abundances of Fe and Ni are from Anders & Grevesse (1989). These values indicate a metallicity typical of M giants.

The accuracy of the above-derived metallicity of EK Boo depends on the uncertainties in the adopted atmospheric parameters. Spectral signatures of singly ionized elements are highly sensitive to the variations in log g, and to a lesser extent to the variations of T_eff. Small changes in the microturbulent velocity lead to larger changes in the derived abundances. Table 3 lists the abundance changes that are caused by individual changes in the various atmospheric parameters. In summary, we can state that the metallicity of EK Boo is comparable to the solar one.

3.4. Lithium abundance

In order to determine the lithium abundance of EK Boo, we used the Li i resonance doublet at 6707.8 Å. In this region, the spectrum is heavily blanketed by TiO molecular lines, especially by the γ electronic transition. In our computations of synthetic spectra we used the TiO line list given by Plez (1998), restricted to ⁴⁸TiO. In deed, when Plez et al. (1993) computed a restricted line list for the γ system of TiO around the 6708 Å Li i line for all five isotopes of Ti from ⁴⁶Ti to ⁵⁰Ti, they found that even if they included all isotopes to improve the match between calculated and observed spectra, this did not change the derived Li abundance.

Vacuum values of wavelengths (λ_vac) were transformed to air wavelengths (λ_air) according to the dispersion formula (see Birch & Downs 1994; Morton 2000). For the dissociation energy of TiO, a value of D₀ = 6.87 eV was used. CN lines in the vicinity of the Li i doublet were included in our line list, even though the CN red system lines near 6700 Å are very weak in M giants (Luck & Lambert 1982). Wavelengths and oscillator strength for the individual hyperfine and isotopic components of the lithium lines were taken from Hobbs et al. (1999). A solar ⁶Li/⁷Li isotopic ratio (⁶Li/⁷Li = 0.081) was adopted in the computations of our synthetic spectra. Atomic line data were taken from the VALD database (Kupka et al. 2000).

As mentioned above, the TiO veiling effect in the EK Boo spectrum is significant. This makes it difficult to place the continuum. For the local continuum, we adopted the highest point of the spectrum near the Li i line, at a wavelength of 6710.7 Å. Both the observed and synthetic spectra around 6708 Å line are shown in Fig. 6.

We cannot find any traceable presence of the Li i 6708 Å resonance line in the spectrum of EK Boo. Using alternative synthetic spectra, an upper limit to the lithium abundance of log ε(Li) ≤  − 0.8 was determined.

Fig. 6 Observed (dots) and synthetic (solid lines) spectra for EK Boo in the region around the Li i 6708 Å resonance line, the observed spectrum is scaled in intensity for a good match. The synthetic spectra represent lithium abundances of log ε(Li) =  − 1.0, 0.0, and +1.0.

4. Mass and evolutionary status of EK Boo

In Sect. 3.3 we derive an effective temperature of 3400 K for EK Boo. In the literature, values of 3420 K and 3577 K are given, according to Perrin et al. (1998) and Dyck et al. (1998), respectively. Hence, we here determine the mass and evolutionary status of EK Boo on the basis of both these effective temperatures. We use the parallax from the New Reduction Hipparcos catalogue by van Leeuwen (2007), the V magnitude from the 1997 Hipparcos catalogue, and bolometric corrections according to Buzzoni et al. (2010).

Figure 7 shows the positions of EK Boo (black circles, for the two T_eff quoted above) and other M giants (see Table 4) in the HR diagram, in comparison to standard stellar evolutionary tracks. These have been computed with the code STAREVOL by Lagarde & Charbonnel (in prep.) for solar metallicity (with Asplund et al. 2005, chemical composition), ignoring stellar rotation. Tracks are shown for models with masses between 1.0 and 5.0 M_⊙.

Fig. 7 Position in the H-R diagram of EK Boo and other M giants, adopting Teff from the literature, parallaxes from the New Reduction Hipparcos catalogue by van Leeuwen (2007), V magnitudes from the 1997 Hipparcos catalogue, and bolometric corrections from Buzzoni et al. (2010). EK Boo’s position (filled circles) is shown for two different effective temperatures (3420 K and 3577 K, see text). β And, another Zeeman detected M giant, is represented by a filled square. Standard evolutionary tracks for solar composition and various initial stellar masses (as indicated) are also plotted (Lagarde & Charbonnel, in prep.). Dotted lines show the evolution up to the tip of the first ascent (the RGB) for the low-mass models (1.0 to 2.2 M⊙), while AGBs are indicated by solid lines for the intermediate-mass stars (2.2 M⊙ and above). For clarity, only the 2.2 M⊙ model is shown with both RGB and AGB.

We focus here on the luminosity and effective temperature range of our sample stars, so that only the relevant RGB and AGB sequences (dashed and solid lines, respectively) appear on the graph. While low-mass stars ( ≤ 2.2 M_⊙) ignite He-burning in a degenerate core at the tip of the RGB, i.e., at very high luminosity and cool effective temperature, more massive stars start central-He burning at much lower luminosities and hotter T_eff. Hence, the short RGB-tracks of the latter fall outside Fig. 7, showing only their AGBs. Respectively, for the low-mass stars we have plotted only the RGB sequences. As an exception, the 2.2 M_⊙ model is shown with both RGB and AGB.

When an effective temperature of EK Boo of 3400 K is considered, this comparison leads to an estimate of the mass of 3.1 ± 0.5   M_⊙. The uncertainty quoted here reflects only the parallax error. And in this case, EK Boo is found to be evolving already on the AGB. At the luminosity of EK Boo our 3 M_⊙ model has just undergone a first and relatively weak thermal pulse. By contrast, an alternative effective temperature of 3577 K would lead to a lower initial mass of 2.3 ± 0.3   M_⊙, when compared to the tracks. Then the star would be either close to the tip of the first ascend (i.e., on the red giant branch, RGB), or on the AGB near the onset of the thermal pulse phase. In these two cases (i.e., 3.1 or 2.3 M_⊙, for T_eff = 3400 or 3577 K, respectively), the corresponding stellar radii are 200 and 109 R_⊙, respectively if one uses the 2007 parallax of EK Boo.

According to Aurière et al. (2009, see their Fig. 5), consideration of stellar rotation would neither change the derived mass value, nor the evolutionary status for such a bright giant. Let us point out, however, that the models presented here were computed without core overshooting. For a given stellar mass, introducing core overshooting actually leads to a more massive He-core at the end of the main sequence, and thus to He-ignition at a somewhat lower RGB luminosity. In that case, the RGB tip-luminosities for stars above  ~ 1.5 M_⊙ could actually be lower than those shown in Fig. 7. This makes an even stronger case for EK Boo being an AGB star.

Major uncertainties on the determination of the mass and evolutionary status of our other sample stars actually come from the errors on the effective temperature and on the parallax of the star, as can be seen in Fig. 7. However, uncertainties of the bolometric corrections are also significant. Here, we use the prescription by Buzzoni et al. (2010), who provide a fitting function for BC_V vs. T_eff, supposed to be valid in the range of 3300 ≤ T_eff ≤ 5000 K. For T_eff = 3400 K, as derived above for EK Boo, this gives BC_V =  −3.255.

Buzzoni et al. (2010) show that for stars with T_eff ≥ 4000 K the BC_V − T_eff relation does not depend on stellar metallicity as far as atomic transitions prevail as the main source of metal opacity in their spectra. However, for a star as cool as T_eff = 3400 K, molecular opacity (mainly due to TiO) becomes important in visual wavelength, which could in turn affect the derived BC_V value. To the cool end (T_eff ≤ 3700 K), the sample used by Buzzoni et al. (2010) is actually biased in this respect, since only giants from a metal-rich open cluster (NGC 6791,  [ Fe/H ]  =  + 0.4) were available for the bolometric correction determination.

Hence, we compared the Buzzoni-values of BC_V with those which would follow for our M giants from Flower (1996) or Bessel et al. (1998). For less cool stars, i.e. T_eff ≥ 3500 K, all these bolometric corrections do not differ significantly from each other, but for cooler stars they do. For T_eff = 3400 K, as derived for EK Boo, we get a BC_V =  − 2.70 according to Flower (1996), and  − 3.07 when using Bessel et al. (1998). Taking into account these significant uncertainties in BC, the best we can conclude is that the mass of EK Boo lies in the range of 2.0 − 3.6 M_⊙.

The absence of the ⁷Li enrichment in the atmosphere of EK Boo is consistent with what is expected for a star within this mass range and at this evolutionary stage. The star has indeed depleted in the previous phases of its evolution all the ⁷Li it was born with, and it is not massive nor bright enough to produce fresh ⁷Li via the so-called Cameron & Fowler (1971) mechanism on the TP-AGB (see e.g. Smith 2010, and reference therein)².

5. Rotation and dynamo operation in EK Boo

5.1. Rotation

As for most M giants, the rotational period of EK Boo is not known. But in this case, vsini has been determined. The CORAVEL value obtained on the basis of the cross-correllation method (Melo et al. 2001) is 11 ± 1 km s^-1 (Hünsch et al. 2004). Our NARVAL data and the spectral synthesis method (permitting us to account for rotational and macroturbulent broadening) yield vsini of 8.5 km s^-1 with an accuracy 0.5 km s^-1. To estimate the projected rotational velocity, several synthetic spectra were generated by moog with different values of vsini and v_macro. The best fit was found for the following combination of the line-broadening factors: vsini = 8.5 km s^-1 and v_macro = 2.0 km s^-1. An adoption of low projected rotation velocity combined with high macroturbulent velocity leads to synthetic spectra that are noticeably different from the observed one. However, we have to mention that we do not know the real geometry of macroturbulent motions in the atmosphere of EK Boo. In our calculations we used an assumption of radial-tangential macroturbulence profile (Gray 1992).

The difference between these two values could simply arise because of the different methods of vsini determination. In general, M giants as very evolved stars are expected to be slow rotators. In this respect, both values above are surprisingly high! Hence, EK Boo appears to be a single M giant with a relatively fast rotation, compared to the statistical value for its spectral class (Zamanov et al. 2008).

An estimate of the rotational period P of the star (upper limit only) could be made using the radius of the star, as derived from its angular diameter. Adopting θ of 7.90 ± 0.40 mas (Dyck et al. 1998), as well as a distance of 248 ± 25 pc (by the new Hipparcos parallaxes of van Leeuwen 2007), we obtain a radius of 210 ± 21   R_⊙. This value is about twice as high as the statistical value for an M 5 giant (120 R_⊙) given in Dumm & Schild (1998). It is however consistent with the value of 200 R_⊙ derived in Sect. 4 for EK Boo being an AGB star with a T_eff of 3400 K. Assuming rigid body rotation and vsini of 8.5 km s^-1, we obtain P ≤ 1247^d for the empirical radius of 210 R_⊙, and P ≤ 714^d for the statistical radius of 120 R_⊙. For vsini = 11 km s^-1, these values are 964^d and 552^d, respectively.

Of course, any tilt of the giant’s axis into the line of sight would in deed mean it is rotating even faster than suggested by the radial velocity measurement. Adopting the statistical value of sini = π/4 and the empirical radius, we then obtain a period of 846^d for vsini = 8.5 km s^-1 (or 654^d for vsini = 11 km s^-1).

In future, our observations and Zeeman Doppler Imaging (ZDI) method will be able to shed more light on the actual rotational period of EK Boo.

5.2. Dynamo operation and its origin

Indirect evidence for the magnetic activity of EK Boo has been reported before our NARVAL study. The star attracted the attention of Hünsch et al. (1998) because of its high X-ray luminosity. Later, Hünsch et al. (2004) studied its variability in X-ray and optical activity indicators. They too ruled out the possibility of a symbiotic nature of EK Boo.

Our study (see Sect. 3.1) revealed a variable longitudinal magnetic field in EK Boo for which a dynamo could be a possible explanation. A dipole (as a remnant of an Ap star on the main sequence) is an unlikely explanation, considering the big radius and big convective envelope at this evolutionary stage. We now attend to the question about the possible origin of the dynamo and its type in this evolved star.

A star of about 2.2 − 3.6   M_⊙ at the evolutionary stage of EK Boo has just entered the thermally-pulsing phase on the AGB. It has a complex internal structure with an O/C core surrounded by He- and H-burning shells, and a very deep and extended convective envelope.

Turbulent motions and fast rotation could result in dynamo action of the α − ω type, as described in Nordhaus et al. (2008). Could such a dynamo explain the magnetic field in EK Boo? We calculated the Rossby number (R_o), which is indicative for an efficient dynamo action of this type. For the statistical rotational period of 846 d (see Sect. 5.1) and a convective turnover time τ_c of 182 d, as obtained from the model of 2.5 M_⊙ described in Sect. 4, we determined a R_o of about 4.7. For a period of 654 d (as for a smaller, statistical radius, see Sect. 5.1), the value of R_o would be 3.6. For these values, we cannot expect a very efficient α − ω dynamo for EK Boo, but this dynamo might be still operationable (see Soker & Tylenda 2007). Our future observations and a direct determination of the rotational period could lead to a better knowledge of the Rossby number and the α − ω dynamo efficiency in this M giant.

Considering the high density and height difference between the photospheric layers of the giant and its bottom of the convection zone deep inside, it is well possible that the deep layers rotate a lot faster then the surface, which suffers from magnetic braking. In this way, the α − ω dynamo may yet be more efficient than expected on the basis of the surface rotational rate.

The question remains of where the required angular momentum should come from to run this dynamo. Schröder et al. (1998) studied the evolutionary status of evolved stars that have coronal X-ray emission, which is a good indicator of stellar activity among less cool giants. And Konstantinova-Antova et al. (2009) studied fast rotating single G and K giants with detected magnetic field. The most active giants in their samples are above 1.5 M_⊙, at different evolutionary stages after the main sequence (MS): first gap crossers, stars near the base of the RGB and its lower part. These stars had no convective outer layers and, consequently, no stellar activity on the MS. Hence, magnetic braking cannot yet have consumed their fast rotation and fresh activity has set in at these early post-MS stages. By contrast, EK Boo has evolved much further and its convective envelope is a lot more extended. It should have slowed down long ago, and fresh angular momentum is required here to run its faster rotation and a dynamo.

The possible source is the contracting core region of this giant: without any angular momentum transfer, the contracting core would be considerably speeding up its rotation rate, both in an RGB and an AGB giant of such a luminosity such as EK Boo. Its final product, a white dwarf, would have to rotate as fast as in minutes, which is physically impossible. Instead, we now have even direct evidence (see Charpinet et al. 2009) that white dwarfs are rotating a lot slower, with periods of the order of a day. Hence, evidently over 99% of the angular momentum of the core region is lost during the late evolutionary stages. As discussed by Talon & Charbonnel (2008), internal gravity waves may strongly contribute to the angular momentum redistribution in intermediate-mass stars such as EK Boo, when they reach the early-AGB phase. Hence, it may serve the expanded convective envelope to keep it spinning at a sufficient rate to run a dynamo process in M giants.

The other possible dynamo type operating in AGB giants is the turbulent dynamo, where the turbulent motions play the main role in the field amplification process and in the restoration of the poloidal component (Brandenburg 2001). However, for EK Boo this dynamo is less efficient than the α − ω one. Soker & Zoabi (2002) estimated that in AGB stars the magnetic field can reach only values of less than 1 G. This is inconsistent with the much larger net field strength, which we observe in EK Boo.

A second explanation for the magnetic field in this M giant could be given if EK Boo were a merger of a binary system, which would now be in its spin-down phase. Then an α − ω dynamo is well possible to operate (Soker & Tylenda 2007). The large radius of EK Boo together with the high vsini appears to support this idea. But for the moment, the accuracy of the angular diameter measurement and of the parallax are not high enough to give a reliable determination of the radius of the star. In future, we will need more precise values for these parameters, to be able to distinguish between these two possibilities for α − ω dynamo operation in the star.

Another possibility for spinning up a giant and to induce dynamo action is planet engulfment (Siess & Livio 1999). In this case, according to Melo et al. (2005), there should be an enhanced Li abundance. Indeed, Drake et al. (2002) found that among the rapid rotating (vsini ≥ 8 km s^-1) single K giants, there is a very large proportion (~50%) of Li-rich objects. By contrast, there is only a very small fraction (~2%) of Li-rich stars among the common type of slowly rotating K giants.

Unfortunately, we do not observe any enhanced lithium abundance in EK Boo, although we analysed this point carefully (see Sect. 3.4). However, note that only a recently engulfed big planet would cause a significant Li content on the star, since Li is a fragile element. The spin-down time, on the other hand, remains unclear, but it might exceed the lithium life-time. Hence, we cannot completely exclude the possibility that the enhanced rotation might be a result of a big planet engulfment.

6. Are there other magnetically active M giants?

If dynamo operation on the AGB is a result of the evolution of the star rather than an exotic case like binary merging or planet engulfment, we should expect more giants to have a magnetic field at the stage of EK Boo. As mentioned already in Sect. 1, there is indirect evidence for such activity, which stimulated us to begin observing several other M giants of interest in that respect.

Hence, we observed eight other M giants with the same procedures as for EK Boo (see Sect. 2). Three of them are known for their high X-ray emission: 15 Tri, 42 Her, and HD 187372 = HR 7547 (Hünsch et al. 1998, 2004). The sources 15 Tri and HD 187372 are also known as spectroscopic binaries of a long period (i.e., no synchronization), and 42 Her is considered to have a stable RV (Hünsch et al. 2004; Famaey et al. 2009). Our own NARVAL RV measurements confirm these findings (the specific case of EK Boo is discussed in Sect. 3.2). Five other M giants are fast rotators (Zamanov et al. 2008). These are HD 167006, HD 184786, 8 And = HD 219734, HD 18191, and β And = HD 6860. All these giants show no radial velocity variations and may be considered to be single stars (Famaey et al. 2005).

Data of all observed giants are presented in Table 4. The effective temperatures are from the VizieR catalogues. The X-ray luminosity L_x is from Hünsch et al. (2004); the measurements are both from the ROSAT and Einstein satellites. Positions in the HR diagram are shown in Fig. 7, assuming parallaxes from the New Reduction Hipparcos catalogue by van Leeuwen (2007), V magnitudes from the 1997 Hipparcos catalogue, and bolometric corrections from Buzzoni et al. (2010).

All these are stars in the mass interval 1.0 − 4.5   M_⊙, situated near the tip of the RGB or on the AGB. The least cool member of the sample, β And is among the more massive stars in our study (3.1 ± 0.5   M_⊙), and is located on the AGB. Note that at the adopted T_eff of β And, the uncertainty on the BC_V is much smaller than for EK Boo. Consequently, the uncertainty of its mass is mainly owing to the error of the Hipparcos parallax.

With the exeption of β And, which is much brighter, these M giants are in the same range of magnitude as EK Boo. For these reasons, their magnetic field detection and B_l measurements are of a similar accuracy as those of EK Boo. The three fast rotators (HD 18191, HD 184786, HD 219734) were observed only in one month (September 2008). The sources β And and HD 167006 were observed during two months. The three X-ray luminous giants were observed during two or three months: September and December 2008 (15 Tri), September 2008 and February 2009 (42 Her), and HD 187372 was observed in September 2008, February 2009, and November 2009.

A magnetic field was not detected with certainty for any of these stars within the limit of our accuracy (0.5 G). However, for β And, the brightest star in this sample, we obtained a marginal detection of magnetic field (see Fig. 8) in September 2008, after averaging 14 spectra. The measured B_l is  − 0.95 ± 0.2 G. New observations were obtained on 24 September 2009: a weak Stokes V signal is still visible, but at a non significant LSD statistical level (Donati et al. 1997).

Fig. 8 Averaged Stokes I (bottom), N (middle) and V (upper) profiles for β And. The spectra were obtained in September 2008.

This means, that magnetic fields may well be present in these stars, but with a weaker averaged longitudinal field, wherefore a different observational strategy might be necessary. However, a weak field seems an unlikely explanation for 15 Tri and HD 187372, which are X-ray sources as luminous as EK Boo, but which have to date not yet yielded any Zeeman detection of a mean magnetic field. As suggested in Sect. 3.1, magnetic areas with opposite polarities on the surfaces of these stars could produce averaged longitudinal magnetic fields close to zero, and that possibly for extended periods. Actually, EK Boo displays big differences in its magnetic field behaviour over an extended time interval (e.g. April − December 2008). Hence, we will need to monitor all suspected M giant stars both deeper and for longer periods of time.

For the X-ray luminous M giants, it may not entirely be excluded that a secondary star is the origin the X-ray radiation. Two of them, 15 Tri and HD 187372 are long-period spectroscopic binaries (Hünsch et al. 2004; Famaey et al. 2009), and 42 Her is a visual binary. Their vsini, however, are smaller than the value of EK Boo, which could simply mean that they are less active. All these stars have Ca ii emission, but their K emission cores show only little variability, much less than what we observe in EK Boo. This may support the idea that there is a link between their lower rotation velocity and a lower activity level in these three M giants.

The five fast rotating single M giants also exhibit Ca ii emission cores with a different strength. But we still lack sufficient observational data of them to judge their variability. In any case, all M giants (with one exception: HD 18191) have lower vsini values than EK Boo and a lower activity level could not be excluded, too.

More observations will answer the question of magnetic field in these M giants. In the future, we also want to expand our sample of M giants with some Mira variables, for which magnetic field detection has been reported from maser emission lines (Herpin et al. 2006). In this way, we will be able to draw a more complete picture of magnetic activity in AGB stars, and we will finally know, whether EK Boo is a special case, or rather whether this M giant is just the “tip of an iceberg” of magnetically active AGB stars.

7. Conclusions

• 1.

  The M 5 giant EK Boo wasobserved with NARVAL in the period of April 2008 to March2009 during 10 nights. We analysed the RV behaviour of the star and came to the conclusion that EK Boo is likely a single star, and that the observed variations of its RV are due to some kind of pulsation. Its position on the H − R diagram reveals that EK Boo is of 2.0 − 3.6   M_⊙, located on the AGB or near the tip of the RGB.

• 2.

  Magnetic field was definitely detected in the photosphere of EK Boo and its longitudinal component B_l was of the order of few Gauss. It is of a variable strength, and the activity indicators Ca ii K&H also show variability. EK Boo is the first M giant for which surface magnetic field is detected.

• 3.

  In March 2009, a complex structure in Stokes V was observed. This find may be indicative of a dynamo operation. In that case, EK Boo could be the first M giant with proof of dynamo operation.

• 4.

  A dynamo of the α − ω type is more likely to operate there than a turbulent dynamo. The driving mechanism for the α − ω dynamo operation could be angular momentum dredge-up from the interior, binary merging, or perhaps a planet engulfment, but the absence of a high Li abundance in EK Boo speaks against the latter (unless the spin-down time is significantly longer than the Li destruction time). A turbulent dynamo appears to be challenged by the high measured field strength of EK Boo.

• 5.

  For one more M giant, β And, we got a marginal detection of the magnetic field with a B_l strength of  − 0.95 G. A different observational strategy is required to be able to detect a weaker magnetic field in our other sample M giants, and to answer the question, what kind of a special case EK Boo is.

Note added in proof.   After this paper was accepted for publication, we obtained new spectra for some of the M giants of our sample. Two stars, V669 Her and RZ Ari are definitively Zeeman detected, and their longitudinal magnetic field is about 1G and 3G, respectively.

Acknowledgments

We thank the TBL team for their service observing support. Our observation time was granted under an OPTICON programme. We further acknowledge use of the Hipparcos database, the VizieR catalogue access tool (CDS, Strasbourg, France) and of the VALD data base in Vienna. R.K.-A. and I.S. acknowledge partial financial support under Bulgarian NSF contract DO 02-85/2009. R.K.-A. appreciates the possibility to work in LATT – Tarbes as an invited researcher in the spring 2009. C.C. acknowledges financial support from the French Programme National de Physique Stellaire (PNPS) from CNRS/INSU and from the Swiss National Science Foundation (FNS).

References

All Tables

All Figures

	Fig. 1 LSD profiles of Stokes I, null polarization N and Stokes V (bottom, middle and upper curves) for EK Boo, as observed on 13 March 2009. For clarity, Stokes V and N profiles are enlarged 500 times, and the successive profiles are shifted vertically.
In the text

	Fig. 2 LSD Stokes V profiles for EK Boo for the dates listed in Table 1, from 03 Apr. 08 (top) to 18 Mar. 09 (bottom). The dashed lines illustrate the respective zero levels. The scale of the Y-axis is in units of V/Ic, Ic is the intensity of the continuum. For clarity, successive profiles are shifted vertically.
In the text

	Fig. 3 Magnetic field measurements (upper panel) and chromospheric activity indicator Ca ii K emission (lower panel) for EK Boo in the observed period. An inverse Y-axis is used for Bl to illustrate the magnetic field.
In the text

	Fig. 4 Ca ii K emission line profiles, as observed for EK Boo in the period of April 2008 to March 2009.
In the text

	Fig. 5 Iron abundance as derived from individual Fe i lines, log ε(Fe), versus excitation potential and reduced equivalent width, log    (Wλ/λ). An atmospheric model with Teff = 3400 K, log g = 0.0, and ξ = 2.0 km s-1 was used.
In the text

	Fig. 6 Observed (dots) and synthetic (solid lines) spectra for EK Boo in the region around the Li i 6708 Å resonance line, the observed spectrum is scaled in intensity for a good match. The synthetic spectra represent lithium abundances of log ε(Li) =  − 1.0, 0.0, and +1.0.
In the text

Fig. 7 Position in the H-R diagram of EK Boo and other M giants, adopting Teff from the literature, parallaxes from the New Reduction Hipparcos catalogue by van Leeuwen (2007), V magnitudes from the 1997 Hipparcos catalogue, and bolometric corrections from Buzzoni et al. (2010). EK Boo’s position (filled circles) is shown for two different effective temperatures (3420 K and 3577 K, see text). β And, another Zeeman detected M giant, is represented by a filled square. Standard evolutionary tracks for solar composition and various initial stellar masses (as indicated) are also plotted (Lagarde & Charbonnel, in prep.). Dotted lines show the evolution up to the tip of the first ascent (the RGB) for the low-mass models (1.0 to 2.2 M⊙), while AGBs are indicated by solid lines for the intermediate-mass stars (2.2 M⊙ and above). For clarity, only the 2.2 M⊙ model is shown with both RGB and AGB.

In the text

	Fig. 8 Averaged Stokes I (bottom), N (middle) and V (upper) profiles for β And. The spectra were obtained in September 2008.
In the text