Towards the global magnetic field of the planet-hosting red giant eps Tau
aa r X i v : . [ a s t r o - ph . S R ] F e b Received 26 April 2016; Revised 6 June 2016; Accepted 6 June 2016DOI: xxx/xxxx
ARTICLE TYPE
Towards the global magnetic field of the planet-hosting red gianteps Tau
S.I. Plachinda* | V.V. Butkovskaya | N.F. Pankov Stellar Physics Department, CrimeanAstrophysical Observatory of RAS,Nauchny, Russia
Correspondence *S. I. Plachinda, Crimean AstrophysicalObservatory of RAS, Nauchny 298409,Russia. Email: [email protected]
Funding Information
Ministry of Science and HigherEducation of the RussianFederation, 075-15-2020-780(N13.1902.21.0039).
We present the results of a search for the magnetic field inhomogeneity for thered giant 𝜖 Tau. This research is based on observations obtained over 10 nights in2008-2010 with the ESPaDOnS CFHT spectropolarimeter. We found a previouslyundescribed instrumental effect in the ESPaDOnS spectra, consisting in randompolarization outliers. Therefore, to measure the magnetic field from the unblendedindividual lines, we preliminarily cleared the initial array of spectral lines from thelines distorted by polarization outliers. On only one date from ten, the magneticfield of 𝜖 Tau was found to exceed 3 𝜎 . We also revealed that during two nights thetime series of the magnetic field values shows a distribution that is different fromthe normal distribution. A hypothesis was put forward that this may be due to theinhomogeneity of the magnetic field of this star. KEYWORDS: stars: late-type – stars: magnetic fields – stars: individual ( 𝜖 Tau, 𝜈 Oph) 𝜖 Tau (Sp G9.5 III, HR 1409, HD 28305) is a weakly activered giant belonging to the open cluster of Hyades. Its mass is 𝑀 = 2 . . 𝑀 ☉ , radius is 𝑅 = 13 . 𝑅 ☉ , X-ray luminos-ity is 𝐿 x = 2 × 10 erg s −1 , and 𝜖 Tau has a massive planet( 𝑀 p = 7 . . 𝑀 J ) orbiting it with a period of 594.9 ± 𝑇 eff =4901 ± 20 K, a surface gravity log 𝑔 = 2 .
64 ± 0 .
07 cm s −2 , amicroturbulent velocity 𝑣 t = 1 .
49 ± 0 .
09 km s −1 , and a metal-licity [Fe∕H] = 0 .
17 ± 0 . , which is consistent with the meanmetallicity of the Hyades. Gray (1982) derived a projectedrotational velocity of the star 𝑣 sin 𝑖 = 2 . −1 .Aurière et al. (2015) detected a weak magnetic field of 𝐵 e ∼−1 . . G for 𝜖 Tau via Zeeman signatures revealed bythem during the spectropolarimetric monitoring of a numberof giant stars with the twin spectropolarimeters ESPaDOnS atthe Canada-France-Hawaii Telescope (CFHT) and Narval at Télescope Bernard Lyot (TBL, Pic du Midi Observatory) over11 nights in 2008 – 2010.To measure the magnetic field, the authors used the LSD(Least Square Deconvolution) technique, which calculates themean Stokes 𝑉 and 𝐼 profiles over all spectral lines, includ-ing blends (Donati, Semel, Carter, Rees, & Collier Cameron,1997).The LSD method usually uses the most complete arrayof spectral lines (including blends) to reconstruct pseudo-mean Stokes profiles, which makes it possible to dramaticallyincrease the signal-to-noise ratio in the case of a sun-like spec-trum and to register weak magnetic fields up to one tenth ofGauss. This method was used to carry out extensive observa-tional campaigns to measure magnetic fields in stars of differ-ent spectral classes and luminosity types. In the last decade,LSD profiles have been actively used to construct magneticmaps of stellar surfaces using Zeeman-Doppler imaging (ZDI).Certainly, the original LSD method and its later modificationsrevolutionized the technique of studying the weak magneticfields of stars.If we want to achieve maximum signal-to-noise ratio,the LSD method is preferable (for example, to detect weak PLACHINDA
ET AL magnetic fields), but if our goal is to investigate inhomo-geneous physical conditions on the surface of the star, theSingle Line (SL) method (Butkovskaya & Plachinda, 2007;S. I. Plachinda, 2004; S. I. Plachinda & Tarasova, 1999) ismore suitable. Different spectral lines in the stellar atmospherecan be formed under different physical conditions, both onthe surface and with depth. Therefore, measuring the mag-netic field using the pseudo average spectral line profiles canlead to the distortion of information about the geometry of themagnetic field (S. Plachinda, Shulyak, & Pankov, 2019).For high-precision measurements of the magnetic field onthe Sun as a star, single spectral lines are usually used, anddifferent lines give different values of the magnetic field(Stenflo, Demidov, Bianda, & Ramelli, 2013). It is also knownthat different lines in the solar spectrum can have differentasymmetries (Dravins, 2008; Sheminova, 2020). These effectscan be caused both by different depth of spectral lines forma-tion and by the formation of spectral lines in different areas ofsupergranules. These facts are true for all stars with convectiveenvelopes. If there are also different types of active regions onthe surface of the star, this, in addition, complicates the phys-ical conditions in which the spectral lines are formed. Unlikethe LSD method, the SL method requires a higher signal-to-noise ratio in the observed spectra, because it usually usesfewer suitable spectral lines.Modern large telescopes allow us to measure the stellarmagnetic field using single lines, thereby making it possibleto study in detail the physics of the magnetic field, includingrevealing subtle patterns in the structure of the magnetic field.Our SL-method (the center of gravity method for singlelines) calculates the longitudinal magnetic field from individ-ual spectral lines using four polarized spectra normalized to thecontinuum, obtained in two consecutive exposures at different(orthogonal) angular positions of the input quarter-wave plate: 𝐵 𝑒 = 𝑘 (( 𝜆 𝑟 − ( 𝜆 𝑙 + Δ 𝜆 𝑖𝑛𝑠 ))∕2−( 𝜆 𝑙 − ( 𝜆 𝑟 + Δ 𝜆 𝑖𝑛𝑠 ))∕2)∕2 = 𝑘 (( 𝜆 𝑟 − 𝜆 𝑙 )∕2 + ( 𝜆 𝑟 − 𝜆 𝑙 )∕2)∕2 = 𝑘 Δ 𝜆 𝐵 , (1)where 𝜆 𝑟 and 𝜆 𝑙 - the wavelength of the center of gravity ofthe line in right and left polarized spectra in the first exposure; 𝜆 𝑟 and 𝜆 𝑙 - the wavelength of the center of gravity of the linein right and left polarized spectra in the second exposure; Δ 𝜆 𝑖𝑛𝑠 - the instrumental shift; 𝑘 = 1∕(4 .
67 × 10 −13 𝑧𝜆 ) , where 𝑧 isthe Lande factor.The normalized to continuum circular polarization (Stokes 𝑉 ) can be written as 𝑉 ∕ 𝐼 𝑐 = (( 𝐼 𝑟 −( 𝐼 𝑙 +Δ 𝐼 𝑖𝑛𝑠 ))∕2−( 𝐼 𝑙 −( 𝐼 𝑟 +Δ 𝐼 𝑖𝑛𝑠 ))∕2)∕2 =(( 𝐼 𝑟 − 𝐼 𝑙 )∕2 + ( 𝐼 𝑟 − 𝐼 𝑙 )∕2)∕2 . (2) The center of gravity of each polarized component of thespectral line is calculated with using cubic spline interpolationor least-squares cubic spline fitting (Lawson & Chiu, 2015).In the case of statistically homogeneous array, the entire arrayof magnetic field measurements, 𝑁 = 𝑁 𝑝𝑎𝑖𝑟 𝑜𝑓 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑠 ⋅ 𝑁 𝑙𝑖𝑛𝑒𝑠 ,is used to calculate mean per night magnetic field and its stan-dard error. To test the statistical homogeneity of the resultingarray of magnetic field measurements, the Monte Carlo methodunder the assumption of a normal probability distribution isused. If the time series of the measured magnetic field is uni-form, the difference between the experimental standard errorand the Monte Carlo simulated standard error is only a few per-cent: see section
4. The Reliability of the “Flip-Flop” ZeemanMeasurement Technique in S. I. Plachinda (2004). The arrayof magnetic field measurements can become statistically inho-mogeneous for a number of reasons: unaccounted instrumentaleffects, variability of the magnetic field during the observationnight, inhomogeneity of the magnetic field in the photosphere,inhomogeneity of physical conditions on the surface of the star,and so on.Despite the fact that the measured magnetic field for mostof the weakly active giants from the sample of Aurière et al.(2015) is close to zero, we selected 𝜖 Tau, for which thereare 10 nights of observations with the ESPaDOnS spectropo-larimeter and on some nights a magnetic field was registered, tosearch for the signatures of inhomogeneity of its magnetic fieldusing SL technique. Another red giant, 𝜈 Oph (Sp G9 III, HR6698, HD 163917), was taken as a control object for which nomagnetic field was detected. The stellar parameters of 𝜈 Oph, 𝑇 eff = 4831 K, 𝑀 = 3 . ☉ (Aurière et al., 2015; Sato et al.,2012); 𝐿 x = 7 × 10 erg s −1 (Gondoin, 1999), are close tothe stellar parameters of 𝜖 Tau.
Spectropolarimetric observations of 𝜖 Tau and 𝜈 Oph wereperformed at CFHT ESPaDOnS over 10 nights in 2008 –2010 and over 2 nights in 2008, respectively. From 2006to 2011A, ESPaDOnS was equipped with an EEV CCD42-90-1-941 detector with 2k × 4.5k 0.0135 mm square pixels.Since 2011A, EEV CCD42-90-1-941 has been replaced by anew detector E2V CCD42-90-1-B32 named Olapa (see, forexample, Wade et al. (2015)).Each Stokes 𝑉 exposure sequence consists of four subexpo-sures that are recorded at the following consecutive positionsof the entrance quarter-wave plate: +45 ◦ , −45 ◦ , −45 ◦ , +45 ◦ .The integration and read-out time during one subexposure is 32s and 25 s in 2008 and 60-70 s and 40 s in 2009-2010, respec-tively. The typical signal-to-noise ratio of a single spectrum is LACHINDA
ET AL -0.03-0.02-0.010.000.010.020.03 P ( V /I c ) Tau
Pixel P ( V /I c ) Aql -0.03-0.02-0.010.000.010.020.03 P ( V /I c ) Oph
FIGURE 1
Circular polarization in the spectrum of 𝜖 Tau (2008-10-18), 𝜈 Oph (2008-10-18), and 𝜂 Aql (2017-08-08). TheY-axis shows the Stokes V profile, and the X-axis shows the pixel numbers. The edges of the spectra on the blue and red sidesare cut off due to the low signal-to-noise ratio.390 in 2008 and 500-600 in 2009-2010. The resolving powerof spectra is 𝑅 = 68 000 . For the magnetic field calculation,we used spectral lines in the range 4100-7000 Å.The reduction and calibration of these spectra were per-formed using the standard IRAF software. In order to avoidthe distortion of the circular polarization in line profiles dur-ing continuum normalization, the continuum functions of eachorder of the spectra were calculated using the Fortran codedeveloped by S. Plachinda. This procedure according to formula (2) allows us to controlthe presence of polarization artifacts in the spectra normalizedto the continuum. The examples of such polarization artifactsin the spectrum after normalization to the continuum is shownin Fig. 1 for 𝜖 Tau (top panel) and 𝜈 Oph (middle panel). Theabsence of such polarization outliers for 𝜂 Aql is illustratedin bottom panel of Fig. 1. All three stars were observed withESPaDOnS.The upper and middle panels of Fig. 1 show circular polar-ization artifacts in the spectra of the same order for the stars
PLACHINDA
ET AL
TABLE 1
Magnetic field of 𝜖 Tau and 𝜈 Oph
Date HJD 𝐵 ∗e 𝜎 ∗B 𝐵 e 𝜎 B ND Be 𝐵 null 𝜎 Bnull ND Bnull 𝑁 t / 𝑁 s UT (2450000+) G G G G G G 𝜖 Tau2008-08-23 4702.02 1.40 0.58 0.80 1.43 Y 3.22 1.39 Y 784/5992008-10-18 4757.94 0.68 0.45 5.48 1.56 Y 0.97 1.28 Y 785/5082008-12-17 4817.80 − − − − − − − − − − − − − − 𝜈 Oph2008-08-24 4702.74 − − − − 𝜖 Tau and 𝜈 Oph obtained on 2008-10-18. The amplitudeof these polarization outliers reaches several percent. Obser-vations were obtained with the EEV1 detector and similarpolarization artifacts were detected by us in all orders on allobservation nights.A cross-correlation analysis of arrays of polarization val-ues obtained for both stars from observations on 2008-10-18 was performed. The analysis showed the absence of anycorrelations. Thus, we supposed the process to be sporadi-cal. Obviously, this effect cannot be caused by the optics ofthe polarimeter and spectrograph. Consequently, it could becaused by sporadical malfunctions in the electronics of theCCD camera. The bottom panel of Fig. 1 shows a similar dia-gram of circular polarization for the classical Cepheid 𝜂 Aqlfor comparison. The star was observed at ESPaDOnS in 2017with the new E2V CCD detector (Olapa). There are no circularpolarization artifacts in this graph.It should be noted that we did not detect polarization arti-facts from observations in 2006 (EEV1 detector) of the slowlyrotating magnetic star 33 Lib (Butkovskaya & Plachinda,2019). We also found no such polarization artifacts in observa-tions of the classical magnetic star 𝛽 CrB with other telescopes:over 32 nights in 1993-2004 with the coude long-slit spectro-graph at the 2.6 m Shajn reflector of the Crimean AstrophysicalObservatory, and over 6 nights in 2007-2009 with the high-resolution echelle spectropolarimeter BOES at the BohyunsanOptical Astronomy Observatory (Han et al., 2018).The calculation of the magnetic field longitudinal com-ponent (see formula (1) above) for 𝜖 Tau and 𝜈 Oph hasbeen performed by measuring the Zeeman splitting in indi-vidual spectral lines, using the procedure discussed in detail by (Butkovskaya & Plachinda, 2007; S. I. Plachinda, 2004;S. I. Plachinda & Tarasova, 1999). The SL-method (SingleLine) developed at CrAO makes it possible to measure themagnetic field by the centers of gravity of the polarized com-ponents of individual spectral lines. For each date, its own“mask” is built, which includes a set of spectral lines and theirparameters. It should be noted that the number of spectral linesin the “mask” can vary from date to date (see the last columnin Table 1). This is due to the variation of the number of weakspectral lines, which are appropriate for inclusion their in the“mask”. Then the resulting array of measurements of the mag-netic field along individual lines is tested for uniformity. If thearray is statistically heterogeneous, then at the next step thepossibility of dividing it into statistically significantly differentsubarrays of lines formed under similar physical conditions isinvestigated. The detection of two or more subarrays of linesgiving reliably different values of the magnetic field may indi-cate an inhomogeneity of the magnetic field on the surface ofthe star (S. Plachinda et al., 2019).The SL method uses some approaches to estimate the relia-bility of the obtained results (see Section 4 in S. I. Plachinda(2004):1. The control of polarization signal distortion and thedetection of apparent outliers when the spectra are nor-malized to the continuum.2. The analyzing of the statistical distribution of magneticfield values.3. The checking of the coincidence between the Monte-Carlo simulated and experimental standard error using
LACHINDA
ET AL N u m be r o f m ea s u r e m en t s B null origin B e origin -200 -100 0 100 200050100150200 B null cleared N u m be r o f m ea s u r e m en t s B null , G -200 -100 0 100 200 B e cleared B e , G FIGURE 2
Distribution of the “null” field and the magnetic field of 𝜖 Tau measured from individual spectral lines on the date2008-10-18. The normal distribution curves are shown by solid lines. In the upper panels, “ 𝐵 null origin ” is a distribution of the“null” field measured over all the unblended spectral lines, “ 𝐵 e origin ” is a distribution of the magnetic field of 𝜖 Tau measuredover all the unblended spectral lines. In the bottom panels, “ 𝐵 null cleared ” is a distribution of the “null” field measured with thearray of spectral lines, cleared from the lines distorted by outliers, “ 𝐵 e cleared ” is a distribution of the magnetic field measuredwith the array of spectral lines, cleared from the lines distorted by outliers.the normal distribution of a probability function.It is allowed to use the normal distribution, because whenthe read-out noise is neglected with respect to a highsignal-to-noise, the signal in each pixel of the CCD-detector is typically normal-distributed. Such an approachenables us to calculate the Monte-Carlo standard devia-tions for each single magnetic field measurement.4. Application of the homogeneous array of measurementsfor estimation of the mean and its standard error.5. Calculation of the “null” field is an internal spectropo-larimeter test for presence of significant stochastic out-liers or spurious wavelength- or time-dependent Stokessignatures. In the absence of instrumental effects, the“null” field should be statistically insignificant. Result of magnetic field measurements for 𝜖 Tau and 𝜈 Ophis shown in Table 1. The first and second columns contain thedates and Heliocentric Julian Dates of observations. The thirdand fourth columns show the mean magnetic fields and their errors from Aurière et al. (2015). The fifth and sixth columnspresent the magnetic fields and their errors obtained in thisstudy. Column 7 indicates whether the distribution of the mag-netic field (ND Be - Normal Distribution) measured from theundistorted individual spectral lines is normal (Y – distribu-tion is normal, N - distribution is not normal). The next threecolumns are the same as columns 5-7, but for the “null” field.The last column shows the initial number of unblended spec-tral lines ( 𝑁 t - total) and the final number of spectral linesundistorted by polarization outliers ( 𝑁 s - selected).A preselection of the unblended lines in the spectralrange 4100-7000 Å was performed using the appropri-ate temperature and gravity for each star from the dataprovided by the Vienna Atomic Line Database VALD(Kupka, Piskunov, Ryabchikova, Stempels, & Weiss, 1999).Since a number of lines in the spectra of 𝜖 Tau and 𝜈 Oph weredistorted by instrumental outliers, we excluded them fromthe total array of unblended spectral lines used to measurethe magnetic field. To determine the presence of instrumentalartifacts in the lines, we calculated a “null” field for each line.Ideally, the “null” field should not exceed ±3 𝜎 , where the errorof a single measurement, 𝜎 , is calculated by the Monte-Carlo PLACHINDA
ET AL method under the assumption of a normal distribution. In thiscase, we used the ±4 𝜎 criterion due to the possible presenceof unaccounted effects that can lead to an increase in scatter ofthe field values. Having extracted an array of the “null” fieldfor each spectral line, we excluded from further calculationsthose spectral lines for which this “null” field exceeded ±4 𝜎 .Analysis of the obtained arrays of the “null” field showedthat for both stars on each date up to 50% of the spectrallines give a field, the absolute value of which exceeds 𝜎 andin some cases reaches two dozen 𝜎 . Moreover, on differentdates, a statistically significant “null” field was recorded ondifferent spectral lines. We found no mention of this effectin the literature describing observations with ESPaDOnS. Itseems impossible to detect it using methods that involve auto-matic processing of observations and/or measurements of themagnetic field from averaged profiles.Figure 2 shows histograms of the “null” field and the mag-netic field distribution for 𝜖 Tau (2008-10-18) before cleaningthe array from the distorted lines (top panel) and after cleaning(bottom panel). The histograms of the “null” field and mag-netic field distributions before removing the distorted spectrallines demonstrate a significant deviation from the normal dis-tribution, while the arrays cleaned from the distorted linesexhibit the normal distribution with a confidence level higherthan 99.9%. The arrays were tested for normal distributionusing the Kolmogorov-Smirnov test (JASP & Team, 2020) fora significance level of 0.001 (0.1%).It should be noted that on 2 dates there is a deviation ofhistograms of the magnetic field of 𝜖 Tau from the normaldistribution (see Table 1). On these nights, 2008-12-17 and2010-11-16, three and two sets of observations were carriedout respectively, while on other dates, only one set of observa-tions was conducted. One of the reasons for the deviation fromthe normal distribution may be the inhomogeneity of the mag-netic field, which is difficult to detect based on a small numberof measurements. However, further observations are requiredto confirm or refute this hypothesis.We roughly estimated the discrepancy in accuracy betweenLSD and SL methods for 𝜈 Oph, i.e. determined the effect ofrandom instrumental outliers on measurement accuracy. Wedid it as follows:The measurement accuracy limit in this case is set by theSL Monte Carlo method assuming a normal distribution ofthe measured values of the magnetic field. According to theMonte Carlo method, the 𝜈 Oph magnetic field array is homo-geneous. Therefore, we can use the standard errors from Table1. Aurière et al. (2015) used from 6500 to 14000 spectral linesfor LSD magnetic field calculation. We took minimal num-ber of spectral lines 𝑁 𝐿𝑆𝐷 = 6500 . The standard errors forthe first and second dates are 𝜎 𝐿𝑆𝐷 = 0 . G and 𝜎 𝐿𝑆𝐷 =0 . G. The number of spectral lines, which were used for SL-method, 𝑁 𝑆𝐿 = 523 and 𝑁 𝑆𝐿 = 484 , as well as stan-dard errors, are presented in Table 1. Using 𝑁 𝐿𝑆𝐷 ≈ 𝑁 𝑆𝐿 ⋅ ( 𝜎 𝑆𝐿 ∕ 𝜎 𝐿𝑆𝐷 ) the number of spectral lines are roughly esti-mated as 𝑁 𝐿𝑆𝐷 ) = 2722 and 𝑁 𝐿𝑆𝐷 ) = 3237 . Therefore, inthis particular case, when the instrumental random outliers ofpolarization are absent, the LSD method needs in about 3000lines instead of 6500 to achieve standard errors 𝜎 𝐿𝑆𝐷 ) = 0 . G and 𝜎 𝐿𝑆𝐷 ) = 0 . G. A search for the inhomogeneity of the magnetic field on thered giant 𝜖 Tau was carried out using spectropolarimetricobservations acquired over 10 nights in 2008-2010 with theESPaDOnS CFHT spectropolarimeter. The red giant 𝜈 Ophwith the zero magnetic field, whose physical parameters areclose to the physical parameters of 𝜖 Tau, was taken as a con-trol star. We found some of the lines in spectra of both stars tobe distorted by random polarization outliers, presumably of aninstrumental nature. These lines were excluded from the gen-eral array of spectral lines used for calculating the magneticfield of stars. For 𝜖 Tau, a magnetic field exceeding 3 𝜎 wasrecorded on one from ten nights. No statistically significantmagnetic field on 𝜈 Oph was found. We also noticed that ontwo nights the statistical distribution of the magnetic field val-ues of 𝜖 Tau shows a deviation from the normal distribution.We assume that this may be due to the inhomogeneity of themagnetic field. However, further observations are required toconfirm or refute this hypothesis.
ACKNOWLEDGMENTS
We are grateful to the anonymous referee for a careful reviewof the manuscript, resulting in insightful recommendationsand kind suggestions leading to its improvement. Plachinda S.acknowledge the support of
Ministry of Science and HigherEducation of the Russian Federation under Grant number . This study is basedon observations obtained at the Canada–France–Hawaii Tele-scope (CFHT). This research used the facilities of the CanadianAstronomy Data Centre operated by the National ResearchCouncil of Canada with the support of the Canadian SpaceAgency.
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S.I. Plachinda, V.V. Butkovskaya, N.F. Pankov(2020), Towards the global magnetic field of the planet-hosting redgiant eps Tau, AN , . AUTHOR BIOGRAPHY
Sergei Plachinda
PhD, Leading Scientific Researcher atCrimean Astrophysical Observatory.
How cite this article:
S.I. Plachinda, V.V. Butkovskaya, N.F.Pankov (2020), Towards the global magnetic field of theplanet-hosting red giant eps Tau, AN ,2016;00:1–6