Magnetic field and radial velocities of the star Chi Draconis A

Magnetic field and radial velocities of the star Chi Draconis A Abstract We present high-resolution spectropolarimetric observations of the spectroscopic binary χ Dra. Spectral lines in the spectrum of the main component χ Dra A show variable Zeeman displacement, which confirms earlier suggestions about the presence of a weak magnetic field on the surface of this star. Within about 2 yr of time base of our observations, the longitudinal component BL of the magnetic field exhibits variation from −11.5 ± 2.5 to +11.1 ± 2.1 G with a period of about 23 d. Considering the rotational velocity of χ Dra A in the literature and that newly measured in this work, this variability may be explained by the stellar rotation under the assumption that the magnetic field is globally stable. Our new measurements of the radial velocities (RV) in high-resolution I-spectra of χ Dra A refined the orbital parameters and reveal persistent deviations of RVs from the orbital curve. We suspect that these deviations may be due to the influence of local magnetically generated spots, pulsations, or a Jupiter-size planet orbiting the system. stars: individual: χ Dra: binaries, stars: magnetic field 1 INTRODUCTION The spectroscopic binary system χ Dra is a classic spectroscopic binary first discovered by Campbell (1898). Since 1987 (Tomkin et al. 1987; Schoeller et al. 1998) the system is also known as an interferometric binary. The angular separation between components is 0.12 arcsec and the orbital period is 280.55 d (Tomkin et al. 1987; Schoeller et al. 1998). The primary component χ Dra A is an F7V 4th magnitude star with a projected rotational velocity of v sin i = 2.5 km s−1 (Gray 1984b) 1 and a radius of 1.2 R⊙ (Torres, Andersen & Giménez 2010). The secondary component is a convective K-type star, two magnitudes fainter than the primary. In a comparatively recent study by Monin, Fabrika & Valyavin (2002), it was suggested that the main component, χ Dra A, has a weak longitudinal field of up to a few tens of Gauss. This suggestion, along with the binarity of χ Dra, makes this system an interesting laboratory to study the formation and evolution of magnetic stars within multiple stellar systems. Motivated by this idea, we conducted an extensive set of high-resolution spectropolarimetric observations of χ Dra with spectropolarimetric facilities of the Bohyunsan Optical Astronomical Observatory (BOAO) of the Korea Astronomy and Space Science Institute (KASI) in Republic of Korea. Another goal of this study was a high-precision search for the radial velocity (RV) variations of the system’s main component. Observations, data reduction and measurements are described in the next section. Section 3 presents results of magnetic field and RV measurements. In Section 4, we discuss our findings. 2 OBSERVATIONS, DATA REDUCTION AND MEASUREMENTS Observations of χ Dra were carried out on 15 nights between 2006 and 2008. The BOES spectropolarimeter at the 1.8 m of the BOAO was used. The spectrograph and spectropolarimetric observational procedures are described by Kim et al. (2007). The instrument is a moderate-beam fibre-fed high-resolution spectrograph, which incorporates 3 STU Polymicro fibers of 300, 200 and 80 μm core diameter (corresponding spectral resolutions are λ/Δλ = 30 000, 45 000, and 90 000, respectively). We used a 3800–10 000 Å working wavelength range and a spectropolarimetric mode provided with a spectral resolution of 60 000 by using two additional fibre-fed channels. An overview of observations is given in Table 1, where we list the date of observations, total number of exposures, typical exposure time for an individual frame and sky conditions. Table 1. Observation log of the binary system χ Dra. Date  N  Exp(s)  Sky conditions  2006 September 27  4  360  Good  2007 January 22  12  600  Moderate  2007 January 24  16  400  Good  2007 January 25  8  600  Moderate  2007 January 28  4  600  Moderate  2007 January 31  6  480  Good  2007 February 02  8  500  Moderate  2007 February 03  24  360  Good  2007 February 04  4  360  Good  2007 April 25  4  360  Good  2007 April 26  4  720  Poor  2007 April 27  4  600  Poor  2007 May 02  24  600  Moderate  2008 June 13  4  800  Moderate  2008 September 10  4  360  Good  Date  N  Exp(s)  Sky conditions  2006 September 27  4  360  Good  2007 January 22  12  600  Moderate  2007 January 24  16  400  Good  2007 January 25  8  600  Moderate  2007 January 28  4  600  Moderate  2007 January 31  6  480  Good  2007 February 02  8  500  Moderate  2007 February 03  24  360  Good  2007 February 04  4  360  Good  2007 April 25  4  360  Good  2007 April 26  4  720  Poor  2007 April 27  4  600  Poor  2007 May 02  24  600  Moderate  2008 June 13  4  800  Moderate  2008 September 10  4  360  Good  View Large The reduction of spectropolarimetric data was carried out using the image processing program DECH 2 as well as an automatic pipeline program (Kang et al. 2005, 2006). The general steps are standard and include cosmic-ray hits removal, electronic bias and scatter light subtraction, extraction of the spectral orders, division by the flat-field spectrum, normalization to the continuum and wavelength calibration. RV measurements in the stellar spectra were carried out by calculating the gravity centres of all narrow and symmetric spectral lines and their comparison with laboratory wavelengths, which together with Lande factors and other atomic data necessary for data processing were derived from the VALD data base (Piskunov et al. 1995; Ryabchikova et al. 1999; Kupka et al. 1999). Measurements of the longitudinal magnetic field were made as described in detail by Kim et al. (2007). We identified several hundred lines in the spectrum of χ Dra A within the range of 3 800–10 000 Å from which we selected about 300 deepest (rc ≥ 0.4, where rc is the central depth of the line) single narrow and symmetric absorptions with non-zero Lande factors. By measuring Zeeman displacements individually in all these lines, weighting and averaging these measurements as described by Monin et al. (2002), we obtained the estimates and corresponding uncertainties of the star’s longitudinal magnetic field at paired exposures of different orientation of the quarter-wave plate following the scheme described in detail by Kim et al. (2007). Since the spin period of χ Dra A is much longer than several days, we integrated these individual estimates within a combined exposure for each observing night. The duration of such exposure are equal to N × Exp (see Table 1) and ranges from a few tens of minutes to a few hours. In order to control the sign and zero level of the measured field, we used typical magnetic stars (HD 215441, HD 32633, and HD 40312) that have magnetic field of different strengths as well as zero-field stars (for details, see Kim et al. 2007). To control our measurements, we used non-saturated telluric spectral lines and the star Procyon that has not demonstrated a magnetic field higher than one G (Kim et al. 2007) and has a spectral class very similar to χ Dra A. Since individual RV estimates obtained for each short-time exposure have shown no remarkable features, we averaged all RV measurements within combined exposures in the same manner as magnetic field estimates. 3 RESULTS Results of our measurements for each observing date are presented in Table 2 where column (1) is the date of observations, column (2) is a Heliocentric Julian Date of mid-exposure, columns (3) and (4) display a nightly mean value of RV and its uncertainty σ, columns (5) and (6) give corresponding estimates of the longitudinal magnetic field BL and its uncertainty σ. Let us consider the results of Zeeman and RV measurements independently. Table 2. Results of the radial velocity and magnetic field measurements for the star χ Dra A. Date  HJD-245 0000  RV  σ  BL  σ    (d)  (km s−1)  (km s−1)  (G)  (G)  2006 September 27  4006.096  38.78  0.05  +11.1  2.1  2007 January 22  4123.337  36.351  0.017  +5.3  0.9  2007 January 24  4125.334  34.836  0.013  −3.2  0.7  2007 January 25  4126.331  34.112  0.021  −2.3  1.1  2007 January 28  4129.320  32.126  0.029  −5.3  1.7  2007 January 31  4132.345  29.898  0.032  −10.5  3.4  2007 February 02  4134.093  27.019  0.017  −11.5  2.5  2007 February 03  4135.345  26.089  0.018  −7.8  0.7  2007 February 04  4136.347  24.421  0.045  −9.5  1.8  2007 April 25  4216.014  25.58  0.046  +5.8  2.0  2007 April 26  4216.999  25.55  0.045  +4.4  2.0  2007 April 27  4218.061  26.31  0.045  +5.0  2.8  2007 May 02  4223.218  26.88  0.023  −7.1  0.9  2008 June 13  4630.817  46.56  0.035  −8.9  1.9  2008 September 10  4719.988  12.24  0.040  −8.5  2.5  Date  HJD-245 0000  RV  σ  BL  σ    (d)  (km s−1)  (km s−1)  (G)  (G)  2006 September 27  4006.096  38.78  0.05  +11.1  2.1  2007 January 22  4123.337  36.351  0.017  +5.3  0.9  2007 January 24  4125.334  34.836  0.013  −3.2  0.7  2007 January 25  4126.331  34.112  0.021  −2.3  1.1  2007 January 28  4129.320  32.126  0.029  −5.3  1.7  2007 January 31  4132.345  29.898  0.032  −10.5  3.4  2007 February 02  4134.093  27.019  0.017  −11.5  2.5  2007 February 03  4135.345  26.089  0.018  −7.8  0.7  2007 February 04  4136.347  24.421  0.045  −9.5  1.8  2007 April 25  4216.014  25.58  0.046  +5.8  2.0  2007 April 26  4216.999  25.55  0.045  +4.4  2.0  2007 April 27  4218.061  26.31  0.045  +5.0  2.8  2007 May 02  4223.218  26.88  0.023  −7.1  0.9  2008 June 13  4630.817  46.56  0.035  −8.9  1.9  2008 September 10  4719.988  12.24  0.040  −8.5  2.5  View Large 3.1 Magnetic field As clearly seen from Table 2, ten out of fifteen estimates of the longitudinal field have a significance exceeding the 3σ level. Besides, a long observing run between 2007 January 22 and 2007 February 04 revealed monotonous change of the field BL from maximum to minimum with passing through the negative extremum. This may indicate the presence of a global magnetic field on the stellar surface. Due to the rotation of χ Dra A, the magnetosphere demonstrates different integral projections of the surface magnetic field to the line of sight. If the magnetosphere is stable, this process should be periodic with the spin period of the star. The two-year time base of our observations makes it possible to primarily investigate this possibility. In order to determine the time-scale over which the longitudinal magnetic field varies (which may be the rotation period of the star), we applied the Lafler & Kinman (1965) method. The method tests trial periods by requiring the sum of the squares of the field magnitude differences between observations of adjacent phase to be a minimum. Such a criterion effectively reveals smooth periodical signals on a limited number of observations. Analysis of the power spectrum (Fig. 1, upper plot) of the data obtained with the Lafler–Kinman revealed a strong signal indicating the presence of a period P = 23.39(9) d. Figure 1. View largeDownload slide Upper panel: power spectrum of the field variation. Middle panel: observed phase variation of the longitudinal field BL of the star χ Dra A (filled circles) and the best sinusoidal fit to the data (a solid line). Lower panel: control results of ‘zero-field’ measurements in the spectra of Procyon (filled triangles) and telluric lines in the spectra of χ Dra A (open circles) Figure 1. View largeDownload slide Upper panel: power spectrum of the field variation. Middle panel: observed phase variation of the longitudinal field BL of the star χ Dra A (filled circles) and the best sinusoidal fit to the data (a solid line). Lower panel: control results of ‘zero-field’ measurements in the spectra of Procyon (filled triangles) and telluric lines in the spectra of χ Dra A (open circles) The magnetic phase curve of χ Dra A constructed for the found period is shown in Fig. 1 (middle plot). The phase variation of the longitudinal field is symmetric with some deviations from the sinusoidal symmetry (for example, two points between ϕ = 0 and 0.25). If from minimum to maximum individual measurements of Bl vary from −11.5 ± 2.5 to +11.1 ± 2.1 G, the sinusoidal fit of these data by the Marquard χ2 minimization method (Bevington 1969) gives the field variation from −11.5 ± 1.5 to +5.2 ± 1.5 G. This discrepancy suggests that the field geometry is more complicated than a simple dipole. The moment of maximum of the mean longitudinal field can be calculated according to the following ephemeris: T0 = 2454006.095 + 23.39(9) E. 3.2 Radial velocities Good quality of the RV data owing to the high mechanical stability of the BOES makes it possible to reanalyse RVs of χ Dra A with an accuracy higher than achieved in previous studies. To the best of our knowledge, the most complete set of RV data for the system was presented and analysed by Tomkin et al. (1987). Using several tens of individual RV measurements as well as speckle observations, these authors determined the RV orbit for χ Dra. In more recent studies (Schoeller et al. 1998; Farrington et al. 2010), the orbit was further refined by interferometric method. Combining RV measurements published by Tomkin et al. (1987) with our new measurements described here, we get a modified orbital solution. The best-fitting results are summarized in Table 3, which lists the projected velocity semi-amplitude of χ Dra A (K), the periastron angle (W), the epoch of periastron (Tp), the orbital period (P), the eccentricity (e), the offset RV (V0) and the linear slope S of RV variation to remove the linear component of the variation. Table 3. Radial-velocity orbit of χ Dra A. Orbital element  Unit  Value  Uncertainty  K  km s−1  16.95  0.19  W  deg(°)  116.9  2.0  Tp  HJD  2437307.827  1.294  P  days  280.523  0.019  e    0.432  0.02  V0  km s−1  28.73  11.18  S  m s−1day−1  0.13  0.05  Orbital element  Unit  Value  Uncertainty  K  km s−1  16.95  0.19  W  deg(°)  116.9  2.0  Tp  HJD  2437307.827  1.294  P  days  280.523  0.019  e    0.432  0.02  V0  km s−1  28.73  11.18  S  m s−1day−1  0.13  0.05  View Large Fig. 2 (upper plot) illustrates our solution (solid line) with all known RV estimates for χ Dra A folded with the obtained value of the orbital period P = 280.523 d. Filled circles represent our measurements and open diamonds data from Tomkin et al. (1987). The standard deviation of the ‘O−C’ (Observed minus Calculated) values (lower plot in the Fig. 2) for the whole data set is 0.97 km s−1, and for our measurements it is 0.37 km s−1. This means that our data demonstrate much better agreement with the orbital curve thanks to the essential improvement in spectroscopic techniques since the 1980s. However, despite improved agreement, both our data and the data from Tomkin et al. (1987) demonstrate noticeable deviations of measured RVs from the calculated RV orbit. Considering that the orbital elements derived in this Letter (Table 2) are in excellent agreement with the latest speckle-interferometric data (Farrington et al. 2010), we suspect that these deviations are not due to uncertainties in the orbital solution. For example, inspecting our RV estimates obtained within the longest two-week observing run (2007 January 22–February 04 ) reveal an unexpectedly high scatter of the data (several times larger than observational uncertainties). Visual inspection of Fig. 2 hints a periodicity within days to tens of days in the deviations of observed RVs from the orbital curve. A similar picture can be seen in Fig. 2 from Tomkin et al. (1987). This suggests the presence of additional cause of RV variations in χ Dra A. In order to examine this variability, we have analysed the ‘O−C’ residuals from the spectroscopic orbital solution obtained here for all available RV measurements. Figure 2. View largeDownload slide Upper panel: observed radial velocities and constructed orbital curve. Open diamonds are data from Tomkin et al. (1987). Filled circles represent our data. Lower panel: residual radial velocities (the ‘O−C’ values) after subtraction of orbital curve from the individual RV estimates. Figure 2. View largeDownload slide Upper panel: observed radial velocities and constructed orbital curve. Open diamonds are data from Tomkin et al. (1987). Filled circles represent our data. Lower panel: residual radial velocities (the ‘O−C’ values) after subtraction of orbital curve from the individual RV estimates. The Lomb–Scargle power spectrum (Lomb 1976; Scargle 1982) of these ‘O−C’ residuals is presented in Fig. 3. A considerable peak at ∼ 12 d was found to suggest the presence of a periodical signal. Unfortunately, due to the strong inhomogeneity of the data, the very long time base of observations (tens of years), and insufficient amount of data limit ourselves to the illustration of the periodogogram only; we are presently unable to clearly identify the true periodicity in the residual RVs of χ Dra A. Additional high-precision spectral observations are needed for more reliable conclusions. Figure 3. View largeDownload slide Power spectrum of the residual of radial velocity variations of χ Dra A. Figure 3. View largeDownload slide Power spectrum of the residual of radial velocity variations of χ Dra A. 4 DISCUSSION We obtained high-resolution spectropolarimetric observations of the star χ Dra A. Analysis of these new and previously published data revealed the presence of variable longitudinal magnetic field. Within the two-yr time base of our observations the field varied from −11.5 ± 1.5 to +5.2 ± 1.5 G with the period P = 23.39(9) d. As discussed by Tomkin et al. (1987) and Torres et al. (2010), the star χ Dra A is a low-mass, low-metallicity old star. As such, the origin of the field on χ Dra A should be typical for low-mass stars of spectral classes from late F to cooler classes (Reiners 2012). For these stars, as it is for the Sun, magnetic fields are concentrated mainly into locally generated, dynamically unstable strong-magnetic tubes seen as dark spots on stellar surfaces. These spots monotonously migrate with different velocities, giving additional contribution to the field variation in addition to rotation. The found period P = 23.39 d is, in principle, consistent with typical rotation periods of low-mass stars with masses comparable to χ Dra  A, although it may be a bit longer than expected based on our measured longitudinal magnetic field strengths (Marsden et al. 2014). From this point of view, it is important to establish whether the star’s rotation period is indeed around 23 d. In order to clarify the situation with rotation, we have analysed Doppler widths of spectral lines in the spectrum of χ Dra  A. To measure the projected rotational velocity vsin i, we have chosen several single lines with small Lande factors. By modelling profiles of these lines using the ATLAS/WIDTHS atmosphere model programs (Kurucz 1993), we derived v sin i ≤ 3 km s−1, which is consistent with the estimate v sin i = 2.5 km s−1 by Gray (1984b). Surprisingly, v sin i = 2.5 km s−1 with the orbital inclination of about 75° (Tomkin et al. 1987) and the stellar radius of 1.2 R⊙ (Torres et al. 2010) yields the rotation period of 23.5 d, almost the same as the found period of P = 23.39 d. Thus, we suspect that the found 23.39 d period is mainly due to the rotation of the star. This result, if confirmed, may also imply the existence of a long-living (more than several years) global poloidal magnetic field. In contrast to the solar-type stars’ unstable magnetic fields, stable poloidal (say dipolar) morphology of the field suggests that we may be seeing a special case of fossil or generated magnetic field, originated and evolving within the frame of the binary system. However, this interesting possibility is based on our currently limited observational data, and we don’t exclude the possibility that this variation could have more complicated origin and may not be regular. The detailed interpretation of the nature of the magnetic field in χ Dra  A requires further accumulation of observational data on longer time base. In this Letter, we restrict ourself with presentation of new observational data confirming the presence of magnetized field structures on the surface of χ Dra A. Lastly, measured RVs of χ Dra A exhibit systematic deviations from the orbital curve. Despite the fact that the measurements presented in this Letter demonstrate improved agreement with the orbital solution, the deviation still exists. No explanation of this phenomenon has been found so far. It may result from additional line displacement due to magnetic nature of the star. For example, the presence of magnetic field with inhomogeneous distribution over the stellar surface (in particular, magnetically induced spots) may simply distort integral symmetry of spectral lines. Rotational modulation of such line profiles can, in turn, cause ‘artificial’ RV variations. However, the period found through the analysis of RV residuals is not consistent with the rotation period estimated by means of spectropolarimetric methods. Our data cannot exclude the existence of a hot Jupiter mass orbiting χ Dra A with a short period. Following this idea and taking into account that the system is seen almost edge-on, it seems reasonable to monitor χ Dra A photometrically in order to search for deep, 1–2 per cent, transit. New high-precision, high-resolution spectral observations of the star χ Dra A are also necessary to answer this particularly important question. Acknowledgements We thank the anonymous referee for useful comments. The authors acknowledge the Russian Science Foundation (grant N14-50-00043) for financial support of theoretical part of this study. B-CL acknowledges partial support by KASI grant 2017-1-830-03. NGB acknowledges the support of the RAS Presidium Program P-7. AFK thanks the RFBR grant 16-02-00604 A for support of experimental investigation of the observed data. Support for MGP was provided by the KASI under the R&D program supervised by the Ministry of Science, ICT and Future Planning and by the National Research Foundation of Korea to the Center for Galaxy Evolution Research (No. 2012-0027910). 1 Monin et al. (2002) lists erroneous value of v sin i = 11 km s−1 in Table 1, citing (Gray 1984a). 2 http://gazinur.com/DECH-software.html REFERENCES Bevington P. R., 1969, Data reduction and error analysis for the physical sciences , McGraw-Hill, New York Campbell W. W., 1898, ApJ , 8, 292 CrossRef Search ADS   Farrington C. D.et al.  , 2010, AJ , 139, 2308F CrossRef Search ADS   Gray D. F., 1984a, ApJ , 277, 640 CrossRef Search ADS   Gray D. F., 1984b, ApJ , 281, 719 CrossRef Search ADS   Kang, Dong-Ii, Park H.-S., Han, Inwoo, Valyavin G., Lee B.-C., Kim K.-M., 2005, Publ. Korean Astron. Soc. , 20, 97 Kang, Dong-Ii, Park, Hong-Suh; Han , In-Woo; Valyavin G., Lee, Byeong-Cheol; Kim , Kang-Min, 2006, Publi. Korean Astron. Soc. , 21, 101 CrossRef Search ADS   Kim, Kang-Minet al.  , 2007, PASP , 119, 1052 CrossRef Search ADS   Kupka F., Piskunov N. E., Ryabchikova T. A., Stempels H. C., Weiss W. W., 1999, A&AS , 138, 119 CrossRef Search ADS   Kurucz R. L., 1993, ATLAS9 Stellar Atmosphere Programs and 2 km s−1 Grid, SAO CD-ROM 13 . Smithsonian Astrophys. Obs., Cambridge Lafler J., Kinman T. D., 1965, ApJS , 11, 216 CrossRef Search ADS   Lomb N. R., 1976, ApSS , 39, 447 Marsden S. C.et al.  , 2014, MNRAS , 444, 3517 CrossRef Search ADS   Monin D., Fabrika S., Valyavin G., 2002, A&A , 396, 131 CrossRef Search ADS   Piskunov N. E., Kupka F., Ryabchikova T. A., Weiss W. W., Jeffery C. S., 1995, A&AS , 112, 525 Reiners, Ansgar 2012, Living Rev. Sol. Phys. , 9, 73 CrossRef Search ADS   Ryabchikova T. A., Piskunov N. E., Stempels H. C., Kupka F., Weiss W. W., 1999, in the 6th International Colloquium on Atomic Spectra and Oscillator Strengths, Victoria BC, Canada, 1998, Physica Scripta , T83, 162 Scargle J. D., 1982, ApJ , 263, 835 CrossRef Search ADS   Schoeller M.et al.  , 1998, Astron. Lett. , 24, 337 Tomkin J., McAlister H. A., Hartkopf W. I., Fekel F. C., 1987, AJ , 93, 1236 CrossRef Search ADS   Torres G., Andersen J., Giménez A., 2010, Astron. Astrophys. Rev. , 18, 67 CrossRef Search ADS   © 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society: Letters Oxford University Press
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Abstract

Abstract We present high-resolution spectropolarimetric observations of the spectroscopic binary χ Dra. Spectral lines in the spectrum of the main component χ Dra A show variable Zeeman displacement, which confirms earlier suggestions about the presence of a weak magnetic field on the surface of this star. Within about 2 yr of time base of our observations, the longitudinal component BL of the magnetic field exhibits variation from −11.5 ± 2.5 to +11.1 ± 2.1 G with a period of about 23 d. Considering the rotational velocity of χ Dra A in the literature and that newly measured in this work, this variability may be explained by the stellar rotation under the assumption that the magnetic field is globally stable. Our new measurements of the radial velocities (RV) in high-resolution I-spectra of χ Dra A refined the orbital parameters and reveal persistent deviations of RVs from the orbital curve. We suspect that these deviations may be due to the influence of local magnetically generated spots, pulsations, or a Jupiter-size planet orbiting the system. stars: individual: χ Dra: binaries, stars: magnetic field 1 INTRODUCTION The spectroscopic binary system χ Dra is a classic spectroscopic binary first discovered by Campbell (1898). Since 1987 (Tomkin et al. 1987; Schoeller et al. 1998) the system is also known as an interferometric binary. The angular separation between components is 0.12 arcsec and the orbital period is 280.55 d (Tomkin et al. 1987; Schoeller et al. 1998). The primary component χ Dra A is an F7V 4th magnitude star with a projected rotational velocity of v sin i = 2.5 km s−1 (Gray 1984b) 1 and a radius of 1.2 R⊙ (Torres, Andersen & Giménez 2010). The secondary component is a convective K-type star, two magnitudes fainter than the primary. In a comparatively recent study by Monin, Fabrika & Valyavin (2002), it was suggested that the main component, χ Dra A, has a weak longitudinal field of up to a few tens of Gauss. This suggestion, along with the binarity of χ Dra, makes this system an interesting laboratory to study the formation and evolution of magnetic stars within multiple stellar systems. Motivated by this idea, we conducted an extensive set of high-resolution spectropolarimetric observations of χ Dra with spectropolarimetric facilities of the Bohyunsan Optical Astronomical Observatory (BOAO) of the Korea Astronomy and Space Science Institute (KASI) in Republic of Korea. Another goal of this study was a high-precision search for the radial velocity (RV) variations of the system’s main component. Observations, data reduction and measurements are described in the next section. Section 3 presents results of magnetic field and RV measurements. In Section 4, we discuss our findings. 2 OBSERVATIONS, DATA REDUCTION AND MEASUREMENTS Observations of χ Dra were carried out on 15 nights between 2006 and 2008. The BOES spectropolarimeter at the 1.8 m of the BOAO was used. The spectrograph and spectropolarimetric observational procedures are described by Kim et al. (2007). The instrument is a moderate-beam fibre-fed high-resolution spectrograph, which incorporates 3 STU Polymicro fibers of 300, 200 and 80 μm core diameter (corresponding spectral resolutions are λ/Δλ = 30 000, 45 000, and 90 000, respectively). We used a 3800–10 000 Å working wavelength range and a spectropolarimetric mode provided with a spectral resolution of 60 000 by using two additional fibre-fed channels. An overview of observations is given in Table 1, where we list the date of observations, total number of exposures, typical exposure time for an individual frame and sky conditions. Table 1. Observation log of the binary system χ Dra. Date  N  Exp(s)  Sky conditions  2006 September 27  4  360  Good  2007 January 22  12  600  Moderate  2007 January 24  16  400  Good  2007 January 25  8  600  Moderate  2007 January 28  4  600  Moderate  2007 January 31  6  480  Good  2007 February 02  8  500  Moderate  2007 February 03  24  360  Good  2007 February 04  4  360  Good  2007 April 25  4  360  Good  2007 April 26  4  720  Poor  2007 April 27  4  600  Poor  2007 May 02  24  600  Moderate  2008 June 13  4  800  Moderate  2008 September 10  4  360  Good  Date  N  Exp(s)  Sky conditions  2006 September 27  4  360  Good  2007 January 22  12  600  Moderate  2007 January 24  16  400  Good  2007 January 25  8  600  Moderate  2007 January 28  4  600  Moderate  2007 January 31  6  480  Good  2007 February 02  8  500  Moderate  2007 February 03  24  360  Good  2007 February 04  4  360  Good  2007 April 25  4  360  Good  2007 April 26  4  720  Poor  2007 April 27  4  600  Poor  2007 May 02  24  600  Moderate  2008 June 13  4  800  Moderate  2008 September 10  4  360  Good  View Large The reduction of spectropolarimetric data was carried out using the image processing program DECH 2 as well as an automatic pipeline program (Kang et al. 2005, 2006). The general steps are standard and include cosmic-ray hits removal, electronic bias and scatter light subtraction, extraction of the spectral orders, division by the flat-field spectrum, normalization to the continuum and wavelength calibration. RV measurements in the stellar spectra were carried out by calculating the gravity centres of all narrow and symmetric spectral lines and their comparison with laboratory wavelengths, which together with Lande factors and other atomic data necessary for data processing were derived from the VALD data base (Piskunov et al. 1995; Ryabchikova et al. 1999; Kupka et al. 1999). Measurements of the longitudinal magnetic field were made as described in detail by Kim et al. (2007). We identified several hundred lines in the spectrum of χ Dra A within the range of 3 800–10 000 Å from which we selected about 300 deepest (rc ≥ 0.4, where rc is the central depth of the line) single narrow and symmetric absorptions with non-zero Lande factors. By measuring Zeeman displacements individually in all these lines, weighting and averaging these measurements as described by Monin et al. (2002), we obtained the estimates and corresponding uncertainties of the star’s longitudinal magnetic field at paired exposures of different orientation of the quarter-wave plate following the scheme described in detail by Kim et al. (2007). Since the spin period of χ Dra A is much longer than several days, we integrated these individual estimates within a combined exposure for each observing night. The duration of such exposure are equal to N × Exp (see Table 1) and ranges from a few tens of minutes to a few hours. In order to control the sign and zero level of the measured field, we used typical magnetic stars (HD 215441, HD 32633, and HD 40312) that have magnetic field of different strengths as well as zero-field stars (for details, see Kim et al. 2007). To control our measurements, we used non-saturated telluric spectral lines and the star Procyon that has not demonstrated a magnetic field higher than one G (Kim et al. 2007) and has a spectral class very similar to χ Dra A. Since individual RV estimates obtained for each short-time exposure have shown no remarkable features, we averaged all RV measurements within combined exposures in the same manner as magnetic field estimates. 3 RESULTS Results of our measurements for each observing date are presented in Table 2 where column (1) is the date of observations, column (2) is a Heliocentric Julian Date of mid-exposure, columns (3) and (4) display a nightly mean value of RV and its uncertainty σ, columns (5) and (6) give corresponding estimates of the longitudinal magnetic field BL and its uncertainty σ. Let us consider the results of Zeeman and RV measurements independently. Table 2. Results of the radial velocity and magnetic field measurements for the star χ Dra A. Date  HJD-245 0000  RV  σ  BL  σ    (d)  (km s−1)  (km s−1)  (G)  (G)  2006 September 27  4006.096  38.78  0.05  +11.1  2.1  2007 January 22  4123.337  36.351  0.017  +5.3  0.9  2007 January 24  4125.334  34.836  0.013  −3.2  0.7  2007 January 25  4126.331  34.112  0.021  −2.3  1.1  2007 January 28  4129.320  32.126  0.029  −5.3  1.7  2007 January 31  4132.345  29.898  0.032  −10.5  3.4  2007 February 02  4134.093  27.019  0.017  −11.5  2.5  2007 February 03  4135.345  26.089  0.018  −7.8  0.7  2007 February 04  4136.347  24.421  0.045  −9.5  1.8  2007 April 25  4216.014  25.58  0.046  +5.8  2.0  2007 April 26  4216.999  25.55  0.045  +4.4  2.0  2007 April 27  4218.061  26.31  0.045  +5.0  2.8  2007 May 02  4223.218  26.88  0.023  −7.1  0.9  2008 June 13  4630.817  46.56  0.035  −8.9  1.9  2008 September 10  4719.988  12.24  0.040  −8.5  2.5  Date  HJD-245 0000  RV  σ  BL  σ    (d)  (km s−1)  (km s−1)  (G)  (G)  2006 September 27  4006.096  38.78  0.05  +11.1  2.1  2007 January 22  4123.337  36.351  0.017  +5.3  0.9  2007 January 24  4125.334  34.836  0.013  −3.2  0.7  2007 January 25  4126.331  34.112  0.021  −2.3  1.1  2007 January 28  4129.320  32.126  0.029  −5.3  1.7  2007 January 31  4132.345  29.898  0.032  −10.5  3.4  2007 February 02  4134.093  27.019  0.017  −11.5  2.5  2007 February 03  4135.345  26.089  0.018  −7.8  0.7  2007 February 04  4136.347  24.421  0.045  −9.5  1.8  2007 April 25  4216.014  25.58  0.046  +5.8  2.0  2007 April 26  4216.999  25.55  0.045  +4.4  2.0  2007 April 27  4218.061  26.31  0.045  +5.0  2.8  2007 May 02  4223.218  26.88  0.023  −7.1  0.9  2008 June 13  4630.817  46.56  0.035  −8.9  1.9  2008 September 10  4719.988  12.24  0.040  −8.5  2.5  View Large 3.1 Magnetic field As clearly seen from Table 2, ten out of fifteen estimates of the longitudinal field have a significance exceeding the 3σ level. Besides, a long observing run between 2007 January 22 and 2007 February 04 revealed monotonous change of the field BL from maximum to minimum with passing through the negative extremum. This may indicate the presence of a global magnetic field on the stellar surface. Due to the rotation of χ Dra A, the magnetosphere demonstrates different integral projections of the surface magnetic field to the line of sight. If the magnetosphere is stable, this process should be periodic with the spin period of the star. The two-year time base of our observations makes it possible to primarily investigate this possibility. In order to determine the time-scale over which the longitudinal magnetic field varies (which may be the rotation period of the star), we applied the Lafler & Kinman (1965) method. The method tests trial periods by requiring the sum of the squares of the field magnitude differences between observations of adjacent phase to be a minimum. Such a criterion effectively reveals smooth periodical signals on a limited number of observations. Analysis of the power spectrum (Fig. 1, upper plot) of the data obtained with the Lafler–Kinman revealed a strong signal indicating the presence of a period P = 23.39(9) d. Figure 1. View largeDownload slide Upper panel: power spectrum of the field variation. Middle panel: observed phase variation of the longitudinal field BL of the star χ Dra A (filled circles) and the best sinusoidal fit to the data (a solid line). Lower panel: control results of ‘zero-field’ measurements in the spectra of Procyon (filled triangles) and telluric lines in the spectra of χ Dra A (open circles) Figure 1. View largeDownload slide Upper panel: power spectrum of the field variation. Middle panel: observed phase variation of the longitudinal field BL of the star χ Dra A (filled circles) and the best sinusoidal fit to the data (a solid line). Lower panel: control results of ‘zero-field’ measurements in the spectra of Procyon (filled triangles) and telluric lines in the spectra of χ Dra A (open circles) The magnetic phase curve of χ Dra A constructed for the found period is shown in Fig. 1 (middle plot). The phase variation of the longitudinal field is symmetric with some deviations from the sinusoidal symmetry (for example, two points between ϕ = 0 and 0.25). If from minimum to maximum individual measurements of Bl vary from −11.5 ± 2.5 to +11.1 ± 2.1 G, the sinusoidal fit of these data by the Marquard χ2 minimization method (Bevington 1969) gives the field variation from −11.5 ± 1.5 to +5.2 ± 1.5 G. This discrepancy suggests that the field geometry is more complicated than a simple dipole. The moment of maximum of the mean longitudinal field can be calculated according to the following ephemeris: T0 = 2454006.095 + 23.39(9) E. 3.2 Radial velocities Good quality of the RV data owing to the high mechanical stability of the BOES makes it possible to reanalyse RVs of χ Dra A with an accuracy higher than achieved in previous studies. To the best of our knowledge, the most complete set of RV data for the system was presented and analysed by Tomkin et al. (1987). Using several tens of individual RV measurements as well as speckle observations, these authors determined the RV orbit for χ Dra. In more recent studies (Schoeller et al. 1998; Farrington et al. 2010), the orbit was further refined by interferometric method. Combining RV measurements published by Tomkin et al. (1987) with our new measurements described here, we get a modified orbital solution. The best-fitting results are summarized in Table 3, which lists the projected velocity semi-amplitude of χ Dra A (K), the periastron angle (W), the epoch of periastron (Tp), the orbital period (P), the eccentricity (e), the offset RV (V0) and the linear slope S of RV variation to remove the linear component of the variation. Table 3. Radial-velocity orbit of χ Dra A. Orbital element  Unit  Value  Uncertainty  K  km s−1  16.95  0.19  W  deg(°)  116.9  2.0  Tp  HJD  2437307.827  1.294  P  days  280.523  0.019  e    0.432  0.02  V0  km s−1  28.73  11.18  S  m s−1day−1  0.13  0.05  Orbital element  Unit  Value  Uncertainty  K  km s−1  16.95  0.19  W  deg(°)  116.9  2.0  Tp  HJD  2437307.827  1.294  P  days  280.523  0.019  e    0.432  0.02  V0  km s−1  28.73  11.18  S  m s−1day−1  0.13  0.05  View Large Fig. 2 (upper plot) illustrates our solution (solid line) with all known RV estimates for χ Dra A folded with the obtained value of the orbital period P = 280.523 d. Filled circles represent our measurements and open diamonds data from Tomkin et al. (1987). The standard deviation of the ‘O−C’ (Observed minus Calculated) values (lower plot in the Fig. 2) for the whole data set is 0.97 km s−1, and for our measurements it is 0.37 km s−1. This means that our data demonstrate much better agreement with the orbital curve thanks to the essential improvement in spectroscopic techniques since the 1980s. However, despite improved agreement, both our data and the data from Tomkin et al. (1987) demonstrate noticeable deviations of measured RVs from the calculated RV orbit. Considering that the orbital elements derived in this Letter (Table 2) are in excellent agreement with the latest speckle-interferometric data (Farrington et al. 2010), we suspect that these deviations are not due to uncertainties in the orbital solution. For example, inspecting our RV estimates obtained within the longest two-week observing run (2007 January 22–February 04 ) reveal an unexpectedly high scatter of the data (several times larger than observational uncertainties). Visual inspection of Fig. 2 hints a periodicity within days to tens of days in the deviations of observed RVs from the orbital curve. A similar picture can be seen in Fig. 2 from Tomkin et al. (1987). This suggests the presence of additional cause of RV variations in χ Dra A. In order to examine this variability, we have analysed the ‘O−C’ residuals from the spectroscopic orbital solution obtained here for all available RV measurements. Figure 2. View largeDownload slide Upper panel: observed radial velocities and constructed orbital curve. Open diamonds are data from Tomkin et al. (1987). Filled circles represent our data. Lower panel: residual radial velocities (the ‘O−C’ values) after subtraction of orbital curve from the individual RV estimates. Figure 2. View largeDownload slide Upper panel: observed radial velocities and constructed orbital curve. Open diamonds are data from Tomkin et al. (1987). Filled circles represent our data. Lower panel: residual radial velocities (the ‘O−C’ values) after subtraction of orbital curve from the individual RV estimates. The Lomb–Scargle power spectrum (Lomb 1976; Scargle 1982) of these ‘O−C’ residuals is presented in Fig. 3. A considerable peak at ∼ 12 d was found to suggest the presence of a periodical signal. Unfortunately, due to the strong inhomogeneity of the data, the very long time base of observations (tens of years), and insufficient amount of data limit ourselves to the illustration of the periodogogram only; we are presently unable to clearly identify the true periodicity in the residual RVs of χ Dra A. Additional high-precision spectral observations are needed for more reliable conclusions. Figure 3. View largeDownload slide Power spectrum of the residual of radial velocity variations of χ Dra A. Figure 3. View largeDownload slide Power spectrum of the residual of radial velocity variations of χ Dra A. 4 DISCUSSION We obtained high-resolution spectropolarimetric observations of the star χ Dra A. Analysis of these new and previously published data revealed the presence of variable longitudinal magnetic field. Within the two-yr time base of our observations the field varied from −11.5 ± 1.5 to +5.2 ± 1.5 G with the period P = 23.39(9) d. As discussed by Tomkin et al. (1987) and Torres et al. (2010), the star χ Dra A is a low-mass, low-metallicity old star. As such, the origin of the field on χ Dra A should be typical for low-mass stars of spectral classes from late F to cooler classes (Reiners 2012). For these stars, as it is for the Sun, magnetic fields are concentrated mainly into locally generated, dynamically unstable strong-magnetic tubes seen as dark spots on stellar surfaces. These spots monotonously migrate with different velocities, giving additional contribution to the field variation in addition to rotation. The found period P = 23.39 d is, in principle, consistent with typical rotation periods of low-mass stars with masses comparable to χ Dra  A, although it may be a bit longer than expected based on our measured longitudinal magnetic field strengths (Marsden et al. 2014). From this point of view, it is important to establish whether the star’s rotation period is indeed around 23 d. In order to clarify the situation with rotation, we have analysed Doppler widths of spectral lines in the spectrum of χ Dra  A. To measure the projected rotational velocity vsin i, we have chosen several single lines with small Lande factors. By modelling profiles of these lines using the ATLAS/WIDTHS atmosphere model programs (Kurucz 1993), we derived v sin i ≤ 3 km s−1, which is consistent with the estimate v sin i = 2.5 km s−1 by Gray (1984b). Surprisingly, v sin i = 2.5 km s−1 with the orbital inclination of about 75° (Tomkin et al. 1987) and the stellar radius of 1.2 R⊙ (Torres et al. 2010) yields the rotation period of 23.5 d, almost the same as the found period of P = 23.39 d. Thus, we suspect that the found 23.39 d period is mainly due to the rotation of the star. This result, if confirmed, may also imply the existence of a long-living (more than several years) global poloidal magnetic field. In contrast to the solar-type stars’ unstable magnetic fields, stable poloidal (say dipolar) morphology of the field suggests that we may be seeing a special case of fossil or generated magnetic field, originated and evolving within the frame of the binary system. However, this interesting possibility is based on our currently limited observational data, and we don’t exclude the possibility that this variation could have more complicated origin and may not be regular. The detailed interpretation of the nature of the magnetic field in χ Dra  A requires further accumulation of observational data on longer time base. In this Letter, we restrict ourself with presentation of new observational data confirming the presence of magnetized field structures on the surface of χ Dra A. Lastly, measured RVs of χ Dra A exhibit systematic deviations from the orbital curve. Despite the fact that the measurements presented in this Letter demonstrate improved agreement with the orbital solution, the deviation still exists. No explanation of this phenomenon has been found so far. It may result from additional line displacement due to magnetic nature of the star. For example, the presence of magnetic field with inhomogeneous distribution over the stellar surface (in particular, magnetically induced spots) may simply distort integral symmetry of spectral lines. Rotational modulation of such line profiles can, in turn, cause ‘artificial’ RV variations. However, the period found through the analysis of RV residuals is not consistent with the rotation period estimated by means of spectropolarimetric methods. Our data cannot exclude the existence of a hot Jupiter mass orbiting χ Dra A with a short period. Following this idea and taking into account that the system is seen almost edge-on, it seems reasonable to monitor χ Dra A photometrically in order to search for deep, 1–2 per cent, transit. New high-precision, high-resolution spectral observations of the star χ Dra A are also necessary to answer this particularly important question. Acknowledgements We thank the anonymous referee for useful comments. The authors acknowledge the Russian Science Foundation (grant N14-50-00043) for financial support of theoretical part of this study. B-CL acknowledges partial support by KASI grant 2017-1-830-03. NGB acknowledges the support of the RAS Presidium Program P-7. AFK thanks the RFBR grant 16-02-00604 A for support of experimental investigation of the observed data. Support for MGP was provided by the KASI under the R&D program supervised by the Ministry of Science, ICT and Future Planning and by the National Research Foundation of Korea to the Center for Galaxy Evolution Research (No. 2012-0027910). 1 Monin et al. (2002) lists erroneous value of v sin i = 11 km s−1 in Table 1, citing (Gray 1984a). 2 http://gazinur.com/DECH-software.html REFERENCES Bevington P. R., 1969, Data reduction and error analysis for the physical sciences , McGraw-Hill, New York Campbell W. W., 1898, ApJ , 8, 292 CrossRef Search ADS   Farrington C. D.et al.  , 2010, AJ , 139, 2308F CrossRef Search ADS   Gray D. F., 1984a, ApJ , 277, 640 CrossRef Search ADS   Gray D. F., 1984b, ApJ , 281, 719 CrossRef Search ADS   Kang, Dong-Ii, Park H.-S., Han, Inwoo, Valyavin G., Lee B.-C., Kim K.-M., 2005, Publ. Korean Astron. 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Monthly Notices of the Royal Astronomical Society: LettersOxford University Press

Published: Jan 1, 2018

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