Magnetic characterization and variability study of the magnetic SPB star o Lup
B. Buysschaert, C. Neiner, A.J. Martin, M.E. Oksala, C. Aerts, A. Tkachenko, E. Alecian, MiMeS Collaboration
AAstronomy & Astrophysics manuscript no. Buysschaert_OmiLupvARXIV c (cid:13)
ESO 2018August 17, 2018
Magnetic characterization and variability study of the magneticSPB star o Lup (cid:63),(cid:63)(cid:63),(cid:63)(cid:63)(cid:63)
B. Buysschaert , , C. Neiner , A. J. Martin , M. E. Oksala , , C. Aerts , , A. Tkachenko , E. Alecian , andthe MiMeS Collaboration LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot,Sorbonne Paris Cité, 5 place Jules Janssen, F-92195 Meudon, France Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium Department of Physics, California Lutheran University, 60 West Olsen Road Dept. of Astrophysics, IMAPP, Radboud University Nijmegen, 6500 GL, Nijmegen, The Netherlands Université Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, FranceAugust 17, 2018
ABSTRACT
Thanks to large dedicated surveys, large-scale magnetic fields have been detected for about 10 % of early-type stars. We aim toprecisely characterize the large-scale magnetic field of the magnetic component of the wide binary o Lup, by using high-resolutionESPaDOnS and HARPSpol spectropolarimetry to analyse the variability of the measured longitudinal magnetic field. In addition,we investigate the periodic variability using space-based photometry collected with the BRITE-Constellation by means of iterativeprewhitening. The rotational variability of the longitudinal magnetic field indicates a rotation period P rot = . ff erences in the strength of the measuredmagnetic field occur for various chemical elements as well as rotational modulation for Fe and Si absorption lines, suggesting ainhomogeneous surface distribution of chemical elements. Estimates of the geometry of the large-scale magnetic field indicate i = ± ◦ , β = + − ◦ , and a polar field strength of at least 5.25 kG. The BRITE photometry reveals the rotation frequency and several ofits harmonics, as well as two gravity mode pulsation frequencies. The high-amplitude g-mode pulsation at f = . − dominatesthe line-profile variability of the majority of the spectroscopic absorption lines. We do not find direct observational evidence of thesecondary in the spectroscopy. Therefore, we attribute the pulsations and the large-scale magnetic field to the B5IV primary of the o Lup system, but we discuss the implications should the secondary contribute to or cause the observed variability.
Key words.
Stars: magnetic field - Stars: rotation - Stars: oscillations - Stars: early-type - Stars: individual: o Lup
1. Introduction
Large-scale magnetic fields are detected at the stellar surface ofabout 10 % of the studied early-type stars by measuring theirZeeman signature in high-resolution spectropolarimetry (e.g.,MiMeS, Wade et al. (2016); the BOB campaign, Morel et al.(2015); and the BRITE spectropolarimetric survey, Neiner et al.
Send o ff print requests to : [email protected] (cid:63) This work was based on data gathered with HARPS installed on the3.6-m ESO telescope (ESO Large Programme 187.D-0917 and ESONormal Programme 097.D.0156) at La Silla, Chile and on observationsobtained at the Canada-France-Hawaii Telescope (CFHT) which is op-erated by the National Research Council of Canada, the Institut Nationaldes Sciences de l’Univers of the Centre National de la Recherche Sci-entifique of France, and the University of Hawaii.. (cid:63)(cid:63)
Mode identification results obtained with the software packageFAMIAS developed in the framework of the FP6 European Coordina-tion Action HELAS (http: // (cid:63)(cid:63)(cid:63) Based on data collected by the BRITE Constellation satellite mis-sion, designed, built, launched, operated and supported by the AustrianResearch Promotion Agency (FFG), the University of Vienna, the Tech-nical University of Graz, the Canadian Space Agency (CSA), the Uni-versity of Toronto Institute for Aerospace Studies (UTIAS), the Foun-dation for Polish Science & Technology (FNiTP MNiSW), and NationalScience Centre (NCN). (2016)). These large-scale magnetic fields appear to be stableover a time scale of decades, have a rather simple geometry(most often a magnetic dipole), and have a polar strength rang-ing from about 100 G to several tens of kG. Because the fieldsremain stable and their properties do not depend on any observedstellar parameters, we expect that these large-scale magneticfields were produced during earlier stages of the star’s life, re-laxing into the observed configuration (e.g., Mestel 1999; Neineret al. 2015). In addition, a dynamo magnetic field is likely to oc-cur in the deep interior of early-type stars, produced by the con-vective motions of ionized matter in the convective core (Moss1989). However, no direct evidence of such a magnetic dynamohas ever been observed at the stellar surface, nor is it expected,since the Ohmic di ff usion time scale from the core to the surfaceis longer than the stellar lifetime.The large-scale magnetic fields detected at the surface ofearly-type stars have implications on the properties of the cir-cumstellar environment, the stellar surface, and the interior, al-tering the star’s evolution: – The ionized wind material follows the magnetic field lines,and can create (quasi-)stable structures in the circumstel-lar environment or magnetosphere. The precise properties ofthe magnetospheric material depend on the stellar and mag-netic properties (e.g., ud-Doula & Owocki 2002; Townsend
Article number, page 1 of 19 a r X i v : . [ a s t r o - ph . S R ] A ug & A proofs: manuscript no. Buysschaert_OmiLupvARXIV & Owocki 2005). In general, magnetospheres are subdi-vided into centrifugal magnetospheres, where material re-mains trapped by the magnetic field and supported againstgravity by rapid rotation, and dynamical magnetospheres.The latter has a region of enhanced density in the circum-stellar environment that continuously accumulates new windmaterial and loses matter to accretion by the star. – At the stellar surface, the large-scale magnetic field can a ff ectthe stratification and di ff usion of certain chemical speciesat the surface, which can cause surface abundance inhomo-geneities of certain chemical elements, and a peculiar globalphotospheric abundance composition. This would lead to ro-tational modulation of line profiles and photometric variabil-ity. Stars for which such peculiarities are observed are de-noted by the Ap / Bp spectral classification. – The structure and evolution of the deep stellar interior is an-ticipated to be altered by the large-scale magnetic field, dueto the competition of the Lorentz force with the pressureforce and gravity. This leads to a uniformly rotating radia-tive envelope (e.g., Ferraro 1937; Moss 1992; Spruit 1999;Mathis & Zahn 2005; Zahn 2011), altering the depth overwhich material overshoots the convective core boundary intothe radiative layer (e.g., Press 1981; Browning et al. 2004).Currently, this e ff ect has only been determined for two starswith a technique referred to as magneto-asteroseismology,which combines the analysis of the star’s pulsations withthat of its magnetic properties, and then performing for-ward seismic modelling. This was done for the magnetic β Cep pulsator V 2052 Oph (Neiner et al. 2012; Handler et al.2012; Briquet et al. 2012) and the magnetic g-mode pulsatorHD 43317 (Buysschaert et al. 2017a, 2018).Whenever present, the properties of the stellar pulsationsdepend on the strength, geometry and orientation of the large-scale magnetic field (e.g., Biront et al. 1982; Gough & Taylor1984; Dziembowski & Goode 1985; Gough & Thompson 1990;Goode & Thompson 1992; Shibahashi & Takata 1993; Takata& Shibahashi 1995; Dziembowski & Goode 1996; Bigot et al.2000; Hasan et al. 2005; Mathis & de Brye 2011; Lecoanet et al.2017). For stars with a spectral type from O9 to B2, β Cep-typepulsations are expected. These are low-order pressure modeswith periods of the order of several hours. For slightly less mas-sive stars (spectral types B2 to B9) Slowly Pulsating B-type(SPB) oscillations are predicted. These are low-degree, high-order gravity modes with a period of the order of a few days.Moreover, their pulsation modes show a regular pattern in theperiod domain. Both the β Cep and SPB pulsations are driven bythe κ -mechanism, related to the temperature dependent opacityof iron-like elements. In addition gravito-intertial modes, whichare excited by the motions of the convective core and have theCoriolis force and buoyancy as restoring forces, are anticipatedfor early-type stars with periods longer than the stellar rotationperiod (e.g., Mathis et al. 2014). Stellar pulsations remain thesole way to probe the interior of a single star, with the parame-ters of the pulsation modes dependent on the conditions insidethe star.Variability due to gravity waves (e.g., Press 1981; Rogerset al. 2013) was recently also found in photospheric and windlines of the O9Iab star HD 188209 (Aerts et al. 2017), the B1Iastar HD 2905 (Simón-Díaz et al. 2018), and the B1Iab star ρ Leo(Aerts et al. 2018), as well as in the close binary V380 Cyg(Tkachenko et al. 2014). The presence of gravity waves seemsto be a common property of hot massive stars that have evolvedbeyond half of the core-hydrogen burning stage, irrespective ofbinarity or a magnetic field. o Lup (HD 130807, HR 5528, HIP 72683, B5IV, V = . o Lup, at an angular separation of 0.115 arcsec.The most recent interferometric measurement indicated that thecomponents have an angular separation of 0.043 arcsec, with acontrast ratio of 0 . ± .
06 mag (Rizzuto et al. 2013). From thedistance to the Sco-Cen association, the authors deduced that thecomponents are 5.33 au apart with a mass ratio of 0.91. More-over, the distance to the Sco-Cen association implies that thelargest measured angular separation is above 17 au, such that theorbital period of the binary must be longer than 20 years (Alecianet al. 2011).Within the scope of the MiMeS survey, HARPSpol observa-tions were collected for o Lup. Alecian et al. (2011) concludedthat o Lup hosts a large-scale magnetic field, with variability ofthe measured longitudinal magnetic field indicating a rotationperiod between one and six days. This agrees well with the smallvalue of the projected rotation velocity, v sin i = ± − (determined by Głe¸bocki & Gnaci´nski 2005). Moreover, Alecianet al. (2011) determined T e ff = g = .
25 dexfor o Lup from a comparison with synthetic spectra using tlusty non-local thermal equilibrium atmosphere models and the syn - spec code (Lanz & Hubeny 2007; Hubeny & Lanz 2011). Theauthors also noted weaker He i lines and stronger Si ii than ex-pected from the solar abundances. Hence, the surface abundanceof certain chemical elements seems to be peculiar. Lastly, Si, N,and Fe exhibited line-profile variations (LPVs) on a time scale ofabout one day. Alecian et al. (2011) proposed surface abundanceinhomogeneities as the cause of these LPVs. o Lup has recently been observed by the BRITE-Constellation of nano-satellites to monitor its photometricvariability. This space-based photometry could aid in thedetermination of the rotation period of o Lup by observing therotational modulation caused by surface abundance inhomo-geneities due to the large-scale magnetic field. Moreover, itmight permit us to determine the precise value and the physicalprocess causing the variability with a period of about one daythat was noted by Alecian et al. (2011) as LPVs. Additionalground-based, high-resolution, optical spectropolarimetric datawere collected to characterize the magnetic field of o Lup moreprecisely.We introduce the various observational data sets in Sect. 2,and indicate how these were prepared and corrected for instru-mental e ff ects when needed. In Sect. 3, we estimate the stellarparameters of o Lup by fitting synthetic spectra to the observa-tions and we search for evidence of the secondary component inthe spectroscopy. The periodic photometric variability is inves-tigated in Sect. 4, while Sect. 5 covers the analysis of the large-scale magnetic field. The sub-exposures of the spectropolarimet-ric sequences are employed to detect and characterize the LPVsin Sect. 6. We end this work by discussing the obtained results inSect. 7 and by drawing conclusions and providing a summary inSect. 8.
Article number, page 2 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Fig. 1.
Top : Satellite-orbit averaged and reduced BRITE light curves for o Lup, where the UBr photometry is indicated in red ( left ) and theBAb photometry in blue ( right ). Photometric variability is indicated in parts-per-thousand (ppt).
Bottom : Corresponding satellite-orbit averagedtemporal variability of the on-board CCD temperature, showing di ff erent and discontinuous behaviour.
2. Observations o Lup was observed by three nano-satellites of the BRIght Tar-get Explorer (BRITE)-Constellation (Weiss et al. 2014) duringthe Centaurus I campaign. The BAb (BRITE Austria blue) nano-satellite monitored o Lup from 9 April 2014 until 18 August2014, with a large time gap (of about 76 days) in the mid-dle of the campaign, the UBr (UniBRITE red) nano-satelliteperformed continuous observations from 31 March 2014 until27 August 2014, and the BTr (BRITE Toronto red) nano-satellitehad a short campaign from 27 June 2014 until 3 July 2014. Lightcurves were constructed by the BRITE-team from the raw CCDimages using circular apertures (Pablo et al. 2016; Popowiczet al. 2017). These raw light curves were corrected for the in-trapixel sensitivity and additional metadata were added, suchas aperture centroid position and on-board CCD temperature.We retrieved these publicly available Data Reduction version 2(DR2) data from the BRITE data archive .The extracted BRITE photometry was further corrected byaccounting for known instrumental trends using our in-housetools (Buysschaert et al. 2017b, see its appendix for explicit de-tails). Here, we provide a short summary of the applied proce-dure. As a first step, we converted the timing of the observationsto mid-exposure times. Next, we subdivided the light curves ac-cording to the temporal variability of the on-board CCD tem-perature, T CCD , because strong discontinuities and di ff erences inits variability were noted (see bottom panels of Fig. 1). For eachof these data subsets, we performed an outlier rejection usingthe aperture centroid positions x c and y c , the on-board tempera-ture T CCD , the observed flux, and the number of datapoints pernano-satellite orbit. Once all spurious data were removed, werecombined the datasets to convert the photometric variability toparts-per-thousand (ppt). The data were then again subdividedinto the same subsets to correct for the fluctuating shape of thepoint-spread-function caused by the varying on-board tempera- https://brite.camk.edu.pl/pub/index.html Table 1.
Diagnostics related to the two BRITE light curves of o Lup.
UBr BAbrms raw [ppt] 4.57 3.50rms corr [ppt] 2.44 2.33length [d] 139.0 130.7time gap [d] 13.4 76.3 D sat , raw [%] 70.5 26.3 D sat , corr [%] 53.1 24.0 D orb , raw [%] 17.4 12.8 D orb , corr [%] 15.6 10.3 N orb , corr Notes.
For each light curve, we provide the rms scatter of the flux be-fore and after correction, the length of the light curve, the length of thelargest time gap, and the D sat and D orb duty cycles before and after cor-rection. The number of successful satellite orbits with observations isindicated as well. ture. The next correction step was a classical decorrelation be-tween the corrected flux and the other metadata (including thenano-satellite orbital phase) whenever the correlation was suf-ficiently strong. This detrending procedure was performed forthe complete UBr dataset and for the two BAb observing sub-campaigns (before and after the large time gap). We could notcorrect the BTr data, since the very short 6 days time span leadsto uncertain instrumental correction. Thus, we did not use thisBTr photometry in this work. Finally, we applied a local linearregression filter to the corrected BRITE photometry, detrendingand suppressing any remaining (instrumental) trend with a pe-riod longer than ∼
10 days. The last part consisted of determiningsatellite-orbit averaged measurements.The final corrected, detrended, and satellite-orbit averagedphotometry is given in Fig. 1. To assess the quality of the re-duced BRITE photometry, we also provide the values for somediagnostic parameters in Table 1. The first of these parameters is
Article number, page 3 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV the root mean square (rms) of the flux, given asrms = (cid:118)(cid:116) N N (cid:88) i σ i k i , (1)where σ i and k i are the standard deviation of the flux and thenumber of observations within orbital passage i , respectively,and N is the total number of orbital passages for a given BRITEdataset. Also listed are the median duty cycle per satellite or-bit D orb and the fraction of successful satellite orbits D sat . Theformer indicates the portion of the satellite orbit used for obser-vations, while the latter parametrizes the amount of successfulsatellite orbits over the total time span of the light curve.The two final BRITE light curves (UBr and BAb) formedthe basis of the photometric analysis of the periodic variabilityof o Lup discussed in Sect. 4.
The HARPSpol polarimeter (Piskunov et al. 2011) was em-ployed in combination with the High Accuracy Radial velocityPlanet Searcher (HARPS) spectrograph (Mayor et al. 2003) tomeasure the Zeeman signature indicating the presence of a large-scale magnetic field at the surface of o Lup. This combined in-strument is installed at the ESO 3.6-m telescope at La Silla Ob-servatory (Chile) and covers the 3800–6900 Å wavelength regionwith an average spectral resolution of 110 000. Standard settingswere used for the instrument, with bias, flat-field, and ThAr cal-ibrations taken at the beginning and end of each night. In total,36 spectropolarimetric sequences were obtained during three dif-ferent observing runs, in May 2011, July 2012, and April 2016.The first two campaigns were part of the Magnetism In MassiveStars (MiMeS) survey (Wade et al. 2016), and the third observ-ing run was performed for the BRITE spectropolarimetric survey(Neiner et al. 2016). Each spectropolarimetric sequence consistsof four consecutive sub-exposures with a constant exposure timeranging between 207 s and 1000 s. An overview of the spectropo-larimetric dataset is given in Table 2.The HARPSpol data were reduced using the reduce package(Piskunov & Valenti 2002; Makaganiuk et al. 2011), and resultedin a circular spectropolarimetric observation for each sequence.A minor update to the package enabled us to extract individ-ual spectra for each sub-exposure of the spectropolarimetric se-quence. The spectropolarimetric observations were normalizedto unity continuum using an interactive spline fitting procedure(Martin et al. 2018). This normalization method was performedper spectral order to achieve a smooth overlap between consecu-tive spectral orders. For the spectroscopy employed in this work,only the spectral orders of interest, taken from the spectropolari-metric sub-exposures, were normalized with the same interactiveprocedure. o Lup was also observed twice with the Echelle SpectroPo-larimetric Device for the Observation of Stars (ESPaDOnS, Do-nati et al. 2006) mounted at the Canada France Hawaii Tele-scope (CFHT) on Mauna Kea in Hawaii in April and June 2014(PI: M. Shultz). These spectropolarimetric sequences compriseof four consecutive sub-exposures with an exposure time of 85 s.They span the 3700–10500 Å wavelength region with an aver-age resolving power of 65 000. The data were reduced with the libre - esprit (Donati et al. 1997) and upena softwares available atCFHT. The resulting ESPaDOnS spectropolarimetric and spec-troscopic observations were normalized to unity continuum inthe same manner and using the same interactive tool as for the HARPSpol data. Details for the ESPaDOnS spectropolarimetryare provided in Table 2.
3. Comparison with synthetic spectra
An accurate magnetometric analysis (Sect. 5) starts from the ap-propriate spectral line pattern (also referred to as the line mask),which is defined by the atmospheric characteristics of the star.To this aim, we used a grid of synthetic spectra to model the ob-served Balmer lines (H α , H β , H γ , and H δ ) and selected heliumand metal lines, deriving a value for the e ff ective temperature, T e ff , and the surface gravity, log g , of o Lup. The selected linesincluded the He i ii T e ff and log g . The syn-thetic spectra produce a (good) first approximation of the stellarparameters, because the fainter secondary component and possi-ble surface abundance inhomogeneities will lead to an uncertainchemical abundance analysis.A model grid covering a range of T e ff spanning from 3500 Kto 55000 K and log g from 0.00 dex to 5.00 dex was calculatedusing atlas cossam _ simple (Martin et al. 2017).We varied the T e ff and log g of the synthetic spectra, applyingvarious values for the rotational broadening around the literaturevalue of v sin i =
27 km s − , and allowing for a radial velocity(RV) o ff set to fit the ESPaDOnS spectra. This resulted in a bestfit with T e ff = g = . v sin i =
35 km s − .The wings of the Balmer lines are generally well described bythe model, while the depths of the He i lines or several metallines, such as those of Mg ii , are overestimated. Peculiar surfaceabundances connected to the large-scale magnetic field can pro-duce such a discrepancy since the grid relies on a solar composi-tion for the synthetic data. We show the ESPaDOnS observationsand the best synthetic model in Fig. 2, as well as the residuals tothe fit.However, o Lup is a known interferometric binary system.The contrast ratio derived by Rizzuto et al. (2013) impliesthat about 40 % of the flux should originate from the sec-ondary component. Moreover, the angular separation betweenthe two components of o Lup is su ffi ciently small that both fallwithin the fiber of modern spectrographs. However, the sec-ondary has never firmly been detected in spectroscopy. Employ-ing the atlas cossam _ simple synthetic spectra, we investi-gated whether a binary spectrum describes the observations bet-ter than a single star.We varied T e ff for both components from 13000 K up to18000 K and log g from 3.5 dex up to 4.5 dex, allowing vari-ous v sin i values, light fractions from 0 % up to 50 %, and rel-ative RV o ff sets up to 50 km s − . The best fit occurs for T e ff , = T e ff , = g = . g = . v sin i =
50 km s − , v sin i =
25 km s − , RV = − − , RV = + − , and a light fraction of 50 %. This modelis indicated in Fig. 2. While the description of the helium andmetal lines improved, the fit to the Balmer lines did not nec-essarily improve. The binarity has a similar e ff ect on the metallines as a surface under-abundance, which is often observed formagnetic early-type stars. Moreover, the light fraction of the As T e ff increases, the range of the log g values covered reduces tovalues between 4 .
00 dex and 4 .
75 dex at 55000 K.Article number, page 4 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Table 2.
Observing log of the spectropolarimetric sequences.
ID HJD [d] t exp [s] φ rot complete He excluded He i Fe ii Si ii Balmer-2450000 S / N S / N S / N Detect. S / N S / N S / N Detect.H01 5704.72965 4 ×
100 0.754961 5186 4154 567 DD 2879 920 137 DDH02 5708.75948 4 ×
300 0.119465 4868 3959 595 ND 2768 933 143 DDH03 5709.73559 4 ×
750 0.449976 4875 3984 562 DD 2809 914 138 DDH04 5709.77216 4 ×
750 0.462360 4798 3816 547 ND 2752 897 143 DDH05 6123.56357 4 ×
300 0.572476 5101 3794 548 DD 2664 826 154 DDH06 6124.70439 4 ×
300 0.958758 5094 3862 627 DD 2767 916 134 DDH07 6125.45930 4 ×
300 0.214371 5300 4055 626 ND 3067 1012 140 NDH08 6125.57061 4 ×
300 0.252060 5289 4059 562 ND 3173 1038 128 NDH09 6126.56054 4 ×
300 0.587252 5130 3798 617 DD 2753 858 128 DDH10 6127.46812 4 ×
300 0.894560 5350 4064 534 ND 2943 955 147 DDH11 6129.59043 4 ×
600 0.613176 5010 3809 609 DD 2682 837 157 DDH12 6130.51806 4 ×
600 0.927273 5350 3997 581 DD 2861 933 152 DDE01 6758.06034 4 ×
85 0.413611 3214 2736 408 DD 2234 714 60 DDE02 6819.85180 4 ×
85 0.336251 3335 2664 611 ND 2383 676 60 DDH13 7481.61063 4 ×
207 0.408343 5134 4163 584 DD 3100 965 141 DDH14 7481.62175 4 ×
207 0.412107 5092 4041 582 DD 3006 958 138 DDH15 7481.63287 4 ×
207 0.415871 5251 4079 582 DD 2988 961 139 DDH16 7481.64398 4 ×
207 0.419634 5212 4119 579 DD 3039 960 158 DDH17 7481.65509 4 ×
207 0.423396 5133 4050 576 DD 2989 940 156 DDH18 7481.66620 4 ×
207 0.427159 5150 4035 576 DD 2974 943 151 DDH19 7481.67731 4 ×
207 0.430921 5099 4010 574 DD 2908 929 150 DDH20 7481.68842 4 ×
207 0.434684 4914 3884 537 DD 2857 922 154 DDH21 7481.82751 4 ×
207 0.481777 4513 3573 508 ND 2488 804 156 DDH22 7481.83862 4 ×
207 0.485539 3772 3138 589 ND 2170 740 143 NDH23 7482.65216 4 ×
207 0.761005 4810 3734 577 DD 2666 897 139 DDH24 7482.66327 4 ×
207 0.764767 4603 3639 561 ND 2585 883 159 MDH25 a ×
207 0.768530H26 7484.69562 4 ×
207 0.452922 4728 3707 570 DD 2737 886 155 DDH27 7484.70673 4 ×
207 0.456684 4738 3748 564 ND 2772 890 160 DDH28 7484.79338 4 ×
207 0.486023 4727 3710 563 DD 2693 866 153 DDH29 7484.80449 4 ×
207 0.489786 4749 3726 546 DD 2677 867 137 DDH30 7484.88788 4 ×
207 0.518020 4720 3682 545 DD 2621 812 146 DDH31 7484.89899 4 ×
207 0.521782 4759 3704 604 DD 2627 808 156 DDH32 7485.73598 4 ×
207 0.805188 5107 4035 604 DD 2908 951 153 DDH33 7485.74709 4 ×
207 0.808952 5073 3971 601 DD 2912 957 159 DDH34 7485.83035 4 ×
207 0.837143 5101 3939 600 DD 2828 895 157 DDH35 7485.84146 4 ×
207 0.840905 5072 3939 367 DD 2830 909 161 DD
Notes.
The first letter of the ID indicates whether the spectropolarimetric sequence was taken with HARPS (H) or ESPaDOnS (E). For eachsequence, the mid-exposure HJD, the exposure time, and the rotation phase, φ rot , are indicated. The latter was determined with P rot = . T = HJD 2455702 .
5. The provided S / N is that of the LSD Stokes I profile calculated with various line masks. In addition, the magneticdetection status is provided (DD = Definite Detection, MD = Marginal Detection, and ND = Non Detection) in case not all observations resultedin a DD for the given LSD line mask. a This observation was discarded because the last two sub-exposures in the sequence did not contain anysignal due to bad weather. secondary is higher than determined from interferometry, i.e.,the fitting algorithm tries to obtain a better description for the(weaker) metal lines. For these reasons, we rejected the morecomplex model, where both stars contributed equally to the spec-troscopic observations, and accepted the simpler model whereonly one star is visible. Further, we argue that if both compo-nents do contribute, we cannot distinguish between them in thespectroscopy due to their similar spectral types, small RV shifts,and expected chemical peculiarities. This is in agreement withthe results of Sect. 5.1, where we show that the Zeeman signa-ture spans the full width of the average line profiles. Therefore,we adopt T e ff = g = . T e ff or log g do impact the analysis of thelongitudinal magnetic field as an inappropriate set of lines will be used in the determination of the average line profile in themagnetometric analysis. However, slight discrepancies betweenthe adopted values and the real ones would only have a negligibleimpact, since the line depth in the line mask will be adjusted tothe observations (see also Sect. 5.1).
4. Periodic photometric variability
Magnetic early-type stars often show periodic photometric vari-ability due to co-rotating surface abundance inhomogeneitiescaused by the large-scale magnetic fields. Moreover, Alecianet al. (2011) discussed the possibility of stellar pulsations in o Lup, yet attributed the LPVs to surface abundance inhomo-geneities. To determine the cause of the LPVs, we investigatedthe BRITE photometry for coherent periodic variability. We em-
Article number, page 5 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV
Fig. 2.
Comparison between two ESPaDOnS spectra of o Lup, taken two months apart (shown in gray), and synthetic atlas / cossam _ simple spectra. The red line is the synthetic spectrum for a single star with T e ff = g = . v sin i =
35 km s − , and the blue lineis the synthetic spectrum for a binary star with T e ff , = T e ff , = g = . g = . v sin i =
50 km s − , v sin i =
25 km s − , RV = − − , RV = + − , and a light fraction of 50 %. Residuals to the fit are indicated with the same color codingand a small o ff set for increased visibility. The top row corresponds to the observed spectrum E01 and the bottom row to E02 (see also Table 2). ployed an iterative prewhitening approach to determine the fre-quencies of the periodic variability. Following the spectroscopicresults of Sect. 3, we attributed all photometric variability in theBRITE data to the primary component. However, implicationsand ambiguity caused by the binary system of o Lup are furtherdiscussed in Sect. 7.Iterative prewhitening is typically applied to recover andstudy the stellar pulsation mode frequencies of massive andearly-type stars in both ground-based and space-based photome-try (e.g. Degroote et al. 2009b). The method determines the mostsignificant periodic variability, fits a (sinusoidal) model to thedata with that frequency, calculates the residuals to the model,and iteratively continues this scheme to the residuals until nosignificant periodic variability remains. Adopting this approach,we searched for the significant frequencies in ten times oversam-pled Lomb-Scargle periodograms (Lomb 1976; Scargle 1982)of the BRITE photometry within the 0 – 8 d − frequency range.No variability was expected at higher frequencies. The signif-icance of frequency peaks was calculated using the signal-to-noise (S / N) criterion (Breger et al. 1993) with a frequency win-dow of 1 d − centered at the frequency of the variability andthis after its extraction. Frequency peaks were considered signif-icant if their S / N reached the threshold value of four. The peri-odograms for each BRITE light curve are shown in Fig. 3.This method resulted in six significant frequencies for theUBr photometry and three frequencies for the BAb photome-try, in the frequency domain of 0 – 1.5 d − . We report these inTable 3, together with their respective uncertainties. It was ex-pected that the analysis of the BAb would result in less clearperiodic variability, represented by the smaller amount of signif-icant frequencies, due to the large time gap, which complicatedthe analysis. We note that f is the second frequency harmonicof f and f is the third harmonic of f , making it very likely thatthese three frequencies are related to the rotational modulation ofthe magnetic component. (We confirm this hypothesis in Sect. 5.)Moreover, f is very close to 1.0 d − , which is a known instru- mental frequency for the BRITE photometry, related to the pe-riodic on-board temperature variability (e.g., Fig. A.4 of Buyss-chaert et al. 2017b). No significant amplitude changes were re-trieved during the length of the BRITE light curves.Periodic variability with the same frequency in both the UBrand BAb photometry had comparable amplitudes (see Table 3).The frequencies f and f are likely due to a g-mode pulsations.In this case, the slightly higher amplitude for f in the blue fil-ter was expected. Yet, without additional and simultaneous timeresolved photometry employing di ff erent bandpass filters, per-forming mode identification of the stellar pulsations with theamplitude ratio method was impossible (see e.g., Handler et al.2017, where this method was successfully applied for a pulsat-ing early-type star with BRITE and ground-based photometry).As the retrieved variability had similar amplitudes, we ignoredthe colour information of the individual BRITE light curves andcombined these into one light curve. This was done once with-out any weighting methods and once with a simple weightingmethod (using the rms corr values) to account for di ff erences indata quality, but overall no simple weighting method is availablefor BRITE photometry (see also Handler 2003, for more generalinformation on possible weighting methods). Subsequent itera-tive prewhitening did not result in any new significant periodicvariability compared to what was already obtained from the UBrdata.Once all significant periodic photometric variability was sub-tracted from the UBr photometry, the frequency diagram of theresiduals seems to be nearly constant with amplitudes well below1 ppt (see Fig. 3). No obvious variability remained in the residuallight curves in the time domain. Moreover, the noise level in theperiodogram of the residual BAb photometry was considerablyhigher than that of the UBr residuals, because it has less datapoints. Article number, page 6 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Fig. 3.
Lomb-Scargle periodograms showing the periodic variability for the UBr ( left ) and BAb ( right ) light curves.
Top : Periodograms coveringthe full investigated frequency domain. The periodograms of the light curve are given in red (UBr; left ) and blue (BAb; right ), while the variabilityof the residuals after the iterative prewhitening is given in black.
Bottom : Periodograms covering the frequency domain where significant periodicvariability is recovered. The amplitude of the periodic variability is given in parts-per-thousand (ppt). The frequencies of the extracted variabilityis given by the small black ticks in the top part of each panel.
Table 3.
Significant periodic photometric variability seen in the UBr and BAb BRITE photometry of o Lup.
ID Origin UBr BAb f δ f A S / N f δ f A S / N( d − ) (10 − d − ) ( ± .
17 ppt) ( d − ) (10 − d − ) ( ± .
35 ppt) f f rot f f rot f g mode 1.10572 0.9 7.14 10.0 1.10611 1.9 7.65 5.8 f f inst f f rot f g mode 1.29852 4.8 1.40 4.8 Notes.
We indicate the frequency and corresponding amplitude, A, together with their respective uncertainties, as well as the S / N of the detectionin the Lomb-Scargle periodogram during the iterative prewhitening procedure. The frequency and amplitude uncertainties are determined fromMontgomery & O’Donoghue (1999), under the assumption of white noise and uncorrelated data. These conditions are not always fullfilled andresult in a typical underestimation of the frequency error by a factor 10 (e.g., Degroote et al. 2009a). We also indicate the proposed origin of theobserved periodic photometric variability and remark that a more precise value for the rotation period was obtained through the magnetometricanalysis in Sect. 5.
5. Magnetic measurements
To reliably detect the Zeeman signature of a stable large-scalemagnetic field at the surface of an early-type star, mean lineprofiles are constructed from each high-resolution spectropo- larimetric observation to boost the S / N of the signature in theStokes V polarization. We employed the Least-Squares Decon-volution (LSD) technique (Donati et al. 1997) to create thesemean line profiles. We started from a pre-computed vald T e ff = g = . T e ff = Article number, page 7 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV and log g = . ff use interstellar bandsto ensure we only included absorption lines with similar lineprofiles (the only exception being the He i lines where pressurebroadening through the Stark e ff ect is still significant). All metallines with a depth smaller than 0.01 were also discarded. Lastly,the depths of the lines included in the line mask were adjusted tocorrespond to the observations (a technique sometimes referredto as "tweaking the line mask", see e.g., Grunhut et al. 2017).This resulted in a final line mask with 893 lines included, eachwith their respective wavelength, line depth, and Landé factor.An additional line mask (and corresponding LSD profiles) with-out (blends with) He i lines was also constructed and included821 metal lines. We show these mean line profiles in Fig. 4 forboth line masks. The Zeeman signature in the LSD Stokes V pro-file clearly varies between the various observations. Moreover,the LSD Stokes I profile exhibits clear LPVs, possibly due tothe rotational modulation caused by surface abundance inhomo-geneities or the stellar pulsation. Fortunately, the diagnostic nullprofiles (i.e., deconstructively added polarization signal withinthe sequence, Donati et al. 1997) suggest that no significant in-strumental e ff ects or LPVs have occurred during the spectropo-larimetric sequence, as they are flat.To determine whether an LSD Stokes V spectrum containeda Zeeman signature, we determined the False Alarm Probability(FAP; Donati et al. 1992, 1997) for each LSD profile. Defini-tive detections (DD) show a clear signature and correspond to aFAP < − %, while non-detections (ND) have a FAP > − %.Marginal detections (MD) fall in between DDs and NDs, with10 − % < FAP < − %. Based on these criteria, all LSD pro-files indicated a DD, irrespective whether the complete line maskor the He-excluded line mask was used. Thus, a large-scale mag-netic field is clearly detected in the high-resolution spectropo-larimetry.Figure 4 further indicates that the Zeeman signature in LSDStokes V spans the full width of the LSD Stokes I profile, demon-strating that this full width corresponds to the magnetic compo-nent. No additional spectroscopic component is identified in theLSD Stokes I profiles. Since the interferometric results of Riz-zuto et al. (2013) indicated that o Lup is a binary system with acomparable light fraction, both components must have a similarspectral type and have small RV shifts. This, together with thepresence of LPVs, makes it impossible to discern which compo-nent hosts the detected large-scale magnetic field. These resultsare in agreement with those from the spectroscopic analysis ofSect. 3. As such, we will likely underestimate the true strength ofthe magnetic field through an overestimated depth of the Stokes Iprofile in Eq. (2).
Since the large-scale magnetic fields of early-type stars are ex-pected to be stable over long time scales and inclined with re-spect to the rotation axis, the measured longitudinal magneticfield should exhibit rotational modulation (depending on the rel-ative orientation to the observer). This rotational modulation canbe used to accurately determine the rotation period of the mag-netic component of o Lup. The longitudinal magnetic field (in Gauss, see Rees & Semel1979) is measured as B l = − . · (cid:82) vV ( v )d v λ gc (cid:82) [1 − I ( v )]d v , (2)where V ( v ) and I ( v ) are the LSD Stokes V and I profiles for agiven velocity v . The parameters g , the mean Landé factor, and λ , the mean wavelength (in nm) come from the LSD method.The speed of light is given by c (in km s − ). We provide g and λ for the various line masks in Table 4 and the determined valuesfor B l in Table A.1. The integration limits to determine the B l should cover the full LSD Stokes I profile, and thus, also the fullZeeman signature. Following the plateau method (e.g., Fig. 3 ofNeiner et al. 2012), where we investigated the dependency of B l and σ ( B l ) with the integration limit for a near magnetic pole-onobservation, we determined an integration range of ±
65 km s − and ±
60 km s − around the line centroid to be the most appropri-ate for the complete and the He-excluded LSD profiles, respec-tively. These values were considerably larger than the literature v sin i =
27 km s − for o Lup, which did not capture the completewidth of the absorption profile or the Zeeman signature due tothe application of the LSD technique.When the large-scale magnetic field has a pure dipolar ge-ometry, the rotational modulation of the measured longitudinalmagnetic field can be characterized by a sine model: B l ( t ) = B + B sin (2 π ( f rot t + φ )) , (3)where B and φ are the amplitude and phase of the sine, B theconstant o ff set, and f rot the rotation frequency. However, whenthe large-scale magnetic field has a dipolar component with anon-negligible quadrupolar contribution, the longitudinal mag-netic field modulation is given by a second-order sine model: B l ( t ) = B + B sin (2 π ( f rot t + φ )) + B sin (2 π (2 f rot t + φ )) . (4)Again, B i and φ i are the amplitude and phase of the individualsine terms. We fitted both models to the longitudinal magneticfield measurements of the He-excluded LSD profiles using aBayesian Markov Chain Monte Carlo (MCMC) method (using emcee ; Foreman-Mackey et al. 2013) to determine the rotationperiod. We adopted the log-likelihood function for a weightednormal distribution: L ( Θ ) = − N ln (2 π ) − N N (cid:88) i = ln ( σ ( B l ( t i ))) − N (cid:88) i = (cid:32) ( B l ( t i ) − M ( Θ ; t i )) σ ( B l ( t i )) (cid:33) , (5)with ln the natural logarithm, M ( Θ ; t i ) the model of Eq. (3) orEq. (4) for a given parameter vector Θ at timestep t i . The mea-sured longitudinal magnetic field at t i is given by B l ( t i ), its re-spective error by σ ( B l ( t i )), and N is the number of observa-tions. We constructed uniform priors in the appropriate param-eter spaces for each free parameter describing the models ofEq. (3) and Eq. (4). For the rotation frequency, this was around f from the BRITE photometry with a range set by the Rayleighfrequency criterion employing the time length of the spectropo-larimetric dataset ( f res = . − ). Calculations were startedat random points within the uniform parameter space employ-ing 128 parameter chains and continued until stable frequencysolutions were reached. Article number, page 8 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Fig. 4.
Overplotted mean line profiles constructed with the LSD method using various line masks. Each panel shows (from top to bottom) the LSDStokes V profile, the diagnostic null profile, and the LSD Stokes I profile for the observations, that are o ff -set for increased visibility. Di ff erencesin the line depth of the LSD Stokes I profile, the strength and shape of the Zeeman signature in the LSD Stokes V profile, and the shape of theLPVs in the LSD Stokes I profile are clearly visible. We indicate the integration limits for the computation of the longitudinal magnetic field andthe FAP determination by the red dashed lines for each observation. For the Balmer lines, only the cores of the LSD Stokes I profiles were usedand shifted upwards to unity, following the technique of Landstreet et al. (2015, see text). Table 4.
Parameters related to the study of the longitudinal field measurements from various LSD line masks.
Parameter Complete He excluded Balmer Fe ii Si ii He i g . . . . . . λ [nm] 505 .
99 508 .
79 486 .
13 516 .
79 508 .
46 478 . (cid:104) EW (cid:105) [km s − ] 2 . ± .
10 1 . ± .
11 1 . ± .
10 3 . ± .
30 8 . ± . − ] ± ± ± ± ± ± B [G] 344 ± ±
11 531 ±
32 1679 ±
31 724 ±
22 27 ± B [G] 568 ± ±
15 913 ±
45 2905 ±
43 1053 ±
30 82 ± B [G] 61 ± ±
13 64 ±
46 383 ±
37 57 ±
29 1 ± φ . ± .
002 0 . ± .
002 0 . ± .
007 0 . ± .
002 0 . ± .
004 0 . ± . φ . ± .
02 0 . ± .
01 0 . ± .
10 0 . ± .
01 0 . ± .
08 0 . ± . Notes.
We provide the mean Landé factor g and the mean wavelength λ from the LSD calculation, as well as the resulting mean equivalent width(EW) of the LSD Stokes I profiles. The integration range around the line centroid for the calculation of the longitudinal magnetic field (see Eq. (2))and determination of the FAP is given, as well as the resulting parameters of the dipole with a quadrupole contribution model (i.e., Eq. (4)) fitted tothe measured longitudinal field. The detection status following the computed FAP value for a specific observation and LSD line mask is providedin Table 2, when not all observations had a definite detection for that specific line mask. The posterior probability distribution function (PDF; seeFig. 5) of the rotation frequency of Eq. (4) showed a maximumat f rot = . − , corresponding to a rotation period of P rot = . B and B ,and the o ff set B show a normal distribution centered at a non-zero value. The distributions for the phases φ and φ are nearlyuniform, which is expected as f rot was a free parameter duringthis process and each value of f rot from the PDF creates a normaldistribution for the phase φ i . The superposition of these normaldistributions for φ i creates the obtained nearly uniform distribu-tion. We indicate the recovered PDFs for the fitting parametersin Fig. 5 and list the deduced values for B , B , and B , with theirrespective uncertainties, in Table 4. The fit to the B l values com-puted from the He excluded LSD profile resulted in a non-zerovalue for B , indicating that the second-order term of the modelis needed, hence the quadrupolar component of the large-scale magnetic field is significant. This was further supported by theinformation criteria during the fitting process and model selec-tion. Once a value for each fitted parameter was obtained, we de-fined an initial epoch T around the first observations (i.e., H01),to place the maximum of the (sine-model) at a rotation phase of0.5.Assuming that both components of o Lup contribute to thespectropolarimetric data and that their rotation periods are sig-nificantly shorter than the length of the spectropolarimetric timeseries, we assert that only one component hosts a strong large-scale magnetic field. Indeed, there is a lack of variability in themeasured longitudinal magnetic field other than with a period P rot . A second magnetic component would severely distort therotational modulation indicated in Fig. 6. Only a binary systemwith synchronized rotation periods could reproduce this variabil- Article number, page 9 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV
Fig. 5.
Results of the MCMC analysis on the measured longitudinalmagnetic field of the He-excluded LSD profiles using the model ofEq. (4). The posterior probability distributions (PDF) are indicated foreach fitted parameter. When these had a normal distribution, we repre-sent it with the Gaussian description marked in red. ity, which is highly unlikely for the o Lup binary system givenits P orb >
20 years.We included the BRITE light curves, phase folded with P rot and the periodic variability not caused by the rotation removed,in Fig. 6 to compare the photometric rotational modulation withthat of the longitudinal magnetic field. The peak brightness in thefolded BRITE light curves occurs close to the phase where weobserved the magnetic poles (at rotation phases 0.0 and 0.5), sug-gesting that the brighter surface abundance inhomogeneities arelocated close to the magnetic poles. The remaining photomet-ric variability depends on the inclination angle i , the obliquityangle β , and the relative positions and sizes of the abundance in-homogeneities at the stellar surface, which requires tomographicimaging and / or spot modelling and is beyond reach of the currentdata. While adjusting the line depths of the metal lines used in theLSD line masks, we noted that the Zeeman signature shows dif-ferent strengths for di ff erent chemical species. Therefore, weconstructed three di ff erent line masks containing only 19 He i ,264 Fe ii , or 61 Si ii metal lines. Special care was taken to excludeany line blends with metal lines that had a stronger or similar linedepth than the considered chemical element. The correspondingmean Landé factors and mean wavelengths are given in Table 4,and the LSD profiles themselves are given in Fig. 4. Similar tothe LSD profiles constructed with the complete line mask, weobtained DDs for all LSD profiles constructed with either Si ii orFe ii lines. For the He i LSD profiles, however, we obtained tenNDs, and 26 DDs, most likely caused by the lower S / N, as fewer
Fig. 6.
Phase folded BRITE light curves (after subtracting the non-rotational variability); upper two panels ) and longitudinal magneticfield measurements from LSD profiles with various line masks, usinga P rot = . T = HJD 2455702 .
5, and indicated by the ob-serving campaign (black for MiMeS, red for BRITEpol, and green forESPaDOnS). The pure dipole model for the geometry of the large-scalemagnetic field of Eq. (3) is indicated by the dashed blue line and thedipole with a quadrupole contribution of Eq. (4) is indicated by the solidblack line. Note the di ff erences in strength of the measured B l values forthe various LSD line masks. lines were included in constructing the mean line profile. Indeed,the S / N in the LSD Stokes V and Stokes I profiles of the He i linemask was typically three times lower than that of the Fe ii LSDprofiles (see Table 2). Again, we noted strong LPVs for the LSDStokes I profiles of all single-element LSD line masks, while thediagnostic null profiles indicated that no LPVs or instrumentale ff ects have occurred during the spectropolarimetric sequence.We study these LPVs in more detail in Sect. 6.We used the single-element LSD line masks to measure thelongitudinal magnetic field associated with the large-scale mag- Article number, page 10 of 19. Buysschaert: Magnetic characterization and variability of o Lup netic field. Again, we employed the plateau method to determinethe integration range for the computations. This resulted in an in-tegration limit of 65 km s − , 60 km s − , and 60 km s − around theline centroid for the He i , Fe ii , and Si ii line masks, respectively.Keeping the rotation frequency fixed to the previously derivedvalue, we performed a Bayesian MCMC fit to model the rota-tional modulation of the measured longitudinal magnetic field.These models and the measured values are shown in Fig. 6.The rotational modulation of the measured B l values fromthe LSD profiles constructed with only Fe ii lines favored themodel of a dipolar magnetic field with a quadrupolar contribu-tion. This is in agreement with the results for the complete LSDline masks derived in Sect. 5.2. For the analysis of the measuredlongitudinal magnetic field of o Lup with only Si ii lines, we ob-tained a less clear distinction between both models for the rota-tional modulation of the measured B l values. Both models agreewith the measurements, within the derived uncertainties on the B l values. Yet, the fit with the model of dipolar magnetic fieldand a quadrupolar component was preferred from the informa-tion criteria. Lastly, the B l values measured from the He i LSDline mask were much smaller. This caused the rotational modu-lation of the measured B l values to be minimal, leading to a com-parable description by both models. Since the deduced errorbarson the measured B l values for the He i remained comparable tothose derived from the other LSD line masks, it seemed likelythat the noted di ff erences are (astro)physical. Surface abundanceinhomogeneities structured to the geometry of the large-scalemagnetic field at the stellar surface could be an explanation. El-ements that are concentrated at the magnetic poles will lead tolarger B l values, while elements located close to the magneticequator will result in smaller B l values. Such features shouldbe noted during tomographic analyses (i.e., Zeeman DopplerImaging; ZDI), but require a spectropolarimetric dataset whichis more evenly sampled over the rotation period than the currentobservations.Finally, we tried to model the Zeeman signature of the large-scale magnetic field, seen in the LSD Stokes V profile, using agrid-based approach (see e.g., Alecian et al. 2008, for further de-tails). However, we were not able to accurately model the chang-ing Zeeman profile with varying rotation phase. This was likelycaused by the insu ffi cient sampling of the rotation phase at keyphases. The magnetometric analysis of single-element LSD profiles ex-hibited a strong scatter in the strength of the measured B l values,suggesting surface abundance inhomogeneities for certain chem-ical elements (e.g., He, Si, and Fe). To measure the rotationalmodulation of the longitudinal magnetic field for an elementthat should be homogeneously distributed over the stellar surfacewe analyzed hydrogen lines. The wavelength regions around theBalmer lines in the spectropolarimetric observations were nor-malized with additional care, employing only linear polynomi-als, so as not to influence the depth of the line core or the broadwings.We constructed a mean line profile for the Balmer lines, in-cluding H α , H β , and H γ in the LSD line mask. Three of theseprofiles indicated a ND and one a MD of a Zeeman signature inthe observations, most likely due to the lower S / N in the Stokes Vprofiles for these observations. We then followed the method ofLandstreet et al. (2015) to measure the B l values. This methoduses only the core of the line and ignores the broad wings. More-over, to scale the measurements more in line with those from the metal lines, the (LSD) Stokes I profile was not integrated fromunity, but instead from the intensity level, I c , where the coretransitions into the wings. As the Zeeman signature in the LSDStokes V profile is slightly wider than the core of the Stokes Iprofile, we employed this width to set the integration range to100 km s − around the Stokes I line centroid. We present theseLSD profiles in Fig. 4, where the indicated Stokes I profile isshifted upwards to place I c at unity. While fixing the rotationfrequency, we performed a Bayesian MCMC fit to determine thefitting parameters for the description of the rotational modulationof the measured B l values. The fit of both models to the measured B l values is given in Fig. 6, with the parameters in Table 4.The rotational modulation of the measured longitudinal mag-netic field from the Balmer lines was more accurately repre-sented by the model for a dipolar magnetic field and a quadrupo-lar component. This result agreed with those of the other LSDprofiles. Yet, the discrepancies between this model and that of adipolar magnetic field were small at most of the rotation phases,due to large uncertainties in B l , caused by the low S / N in theLSD Stokes V profiles.
6. Line profile analysis
Pulsating early-type stars and magnetic early-type type stars areboth known to exhibit LPVs. Alecian et al. (2011) already notedsuch behaviour for o Lup. Therefore, we investigated the zerothand first moment of selected absorption lines for periodic vari-ability employing the software package famias (Zima 2008). Theanalysis of six absorption lines, using the sub-exposures of thespectropolarimetric sequences, is presented in Sect. 6.1. We alsoinvestigated the H α line for variability in Sect. 6.2, to try to diag-nose the presence of a magnetosphere. Lastly, we examined thepossibility of co-rotating surface abundance inhomogeneities byanalyzing the zeroth moment of six absorption lines in Sect. 6.3. To analyze the LPVs of stellar pulsations in absorption lines, itis preferred to work with deep and unblended absorption lines.This remains valid when investigating the signatures caused bythe rotational modulation of surface abundance inhomogeneities.During the analysis of the Zeeman signature in the LSD Stokes Vprofile, we noted di ff erences between di ff erent chemical species.Therefore, we selected absorption lines from various elements.For He, we selected and analyzed the He i i ii ff ective temperature of 15000 K, there are not many strongand suitable Si lines. Therefore, we opted for the Si ii ii ii ii line. Lastly, we chose the C ii ∼ ff erent shape for the LPVs forthe Fe ii and Si ii lines compared to the other selected absorption Article number, page 11 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV
Fig. 7.
LPVs for various selected absorption lines.
Top : all observations of the given line overlayed to illustrate the LPVs. As an additionaldiagnostic, we indicate the mean profile ( middle ) and standard deviation (std; bottom ) of all observations. The standard deviation, particularly,shows strong di ff erences when comparing the selected absorption lines. lines, such as the He i or C ii lines. This might indicate a di ff er-ent dominant variability, and hence a di ff erent origin or causefor the LPVs. The standard deviation of the selected Mg ii linealso looked slightly di ff erent, yet it seemed to be an intermediateprofile between the two studied He i lines.For each line selected, we set appropriate limits for the calcu-lation of their moments. These limits were set at similar flux lev-els for a given spectral line, close to the continuum level, unlessstrong pressure broadening (e.g. He i ii (cid:104) v (cid:105) , first, (cid:104) v (cid:105) , andsecond moment, (cid:104) v (cid:105) , (representative of the equivalent width, ra-dial velocity, and skewness, respectively) for each selected linewith the software package famias (Zima 2008). Here we con-tinue the discussion of the coherent periodic variability in thefirst moment. The zeroth moment is analyzed in Sect. 6.3. Fromthe BRITE photometry and the rotational modulation of the lon-gitudinal magnetic field, two phenomena were already knownto cause periodic variability, each with a distinct period. Thesephenomena are rotation modulation (with P rot = . f = . − ). We con-structed a model that included the (potential) periodic variability in the measured line moments: (cid:104) v (cid:105) ( t ) = C + (cid:88) i = A rot , i sin (cid:0) π (cid:0) i f rot t + φ rot , i (cid:1)(cid:1) + A puls sin (cid:16) π (cid:16) f puls t + φ puls (cid:17)(cid:17) , (6)where A rot , i and A puls are the amplitudes of the variability, φ rot , i and φ puls their respective phases, and C a constant o ff -set. Wededuced each free parameter with a Bayesian MCMC method.Uniform priors were assumed for all parameters in their appro-priate parameter spaces, in particular f puls had to agree withthe conservative result of the BRITE photometry (i.e., f = . ± . − , where the Rayleigh frequency limit wasassumed), and f rot was kept fixed to the value from the magne-tometric analysis. The quality of the fit was determined by theloglikelihood function for a (non-weighted) normal distribution: L ( Θ ) = − N ln (2 π ) − N ln ( σ ( (cid:104) v (cid:105) )) − N (cid:80) i = ( (cid:104) v (cid:105) ( t i ) − M ( Θ ; t i )) σ ( (cid:104) v (cid:105) ) , (7)where σ ( (cid:104) v (cid:105) ) is the error on all (cid:104) v (cid:105) , of the order of 1 km s − .Again, 128 parameter chains were used during the MCMC fit-ting, starting from random positions within the uniform priors, Article number, page 12 of 19. Buysschaert: Magnetic characterization and variability of o Lup and computations continued until stable solutions were reached.The computed values for the parameters in Eq. (6) and L ( Θ ) aregiven in Table 5. Furthermore, we phase-folded (cid:104) v (cid:105) with the de-termined f puls and with f rot and show these in Fig. 8.The derived amplitudes indicated that the rotational modula-tion and the dominant g-mode frequency cause the LPVs notedfor the absorption lines. However, the contribution (i.e., the am-plitude) of each variability term in (cid:104) v (cid:105) di ff ered greatly whencomparing the di ff erent absorption lines. Variability due to thestellar pulsation was dominant for the investigated C ii , Mg ii ,and He i lines, while the LPVs in the Fe ii line were due to therotational modulation. Contributions to the periodic variabilityof (cid:104) v (cid:105) for the studied Si ii line were almost equal. As such, theoccurrence of surface abundance inhomogeneities only occurredfor that particular chemical element, while LPVs due to the g-mode were always present. These observed features can alsobe seen in Fig. 8. Future tomographic analyses, such as ZDI,should indicate the distribution of the surface abundance inho-mogeneities more clearly.We also obtained a value for the pulsation mode frequency f puls from the Bayesian MCMC fit to each first moment of eachabsorption line. Yet, not all obtained values for the g-mode fre-quency agreed within the same confidence interval, pointing toheteroscedasticity of the first moment measurements. Magnetic early-type stars can host a magnetosphere in theirnearby circumstellar environment. The interactions of wind ma-terial with this magnetosphere could, cause rotationally modu-lated variability in certain spectroscopic lines, with emission fea-tures in H α the easiest to identify. For o Lup, we did not observesuch emission profiles, however, we did note variability in thecore of the H α line. We thus repeated the analysis of the linemoments, where we restricted their computation to the core ofthe line, fixing the integration limits where the broad line wingstarts.We performed the same analysis as for the other absorptionlines for the cores of the H α line of each complete spectropolari-metric sequence. The Bayesian MCMC fit indicated that we didnot detect any rotational modulation in the (cid:104) v (cid:105) of H α , because the A rot , i all agreed with zero. Therefore, we did not identify vari-ability coming from the (potential) magnetosphere. Similar tothe majority of the lines of the previous section, the MCMC fitsindicated that the g-mode pulsation frequency is the dominantsource for the LPVs. The significantly lower L ( Θ ) for the fit tothe core of H α is the result of using only 36 spectropolarimetricsequences compared to the 142 spectroscopic observations. The equivalent width or zeroth moment can be used as a firstapproximation to follow the change in the surface abundance ofchemical species. This has been employed before to confirm thepresence of co-rotating surface abundance inhomogeneities formagnetic stars (e.g., Mathys 1991). We repeated the analysis ofSect. 6.1 by replacing (cid:104) v (cid:105) by (cid:104) v (cid:105) in Eq. (6) and performing theBayesian MCMC fit to the (cid:104) v (cid:105) measurements. The determinedamplitudes and L ( Θ ) are provided in Table 5.For each fit to the (cid:104) v (cid:105) measurements of the di ff erent absorp-tion lines, we obtained a value for A puls compatible with zero.Moreover, the resulting PDFs for f puls were flat. These resultsindicated that the g-mode does not cause any significant periodic variability in the (cid:104) v (cid:105) measurements. This was expected, as most(non-radial) pulsation modes distort the shape of the line insteadof altering the equivalent width. Furthermore, the fit to the mea-surements from the He i lines and H α suggested that their abun-dances did not vary with the rotation period. For the remainingfour studied lines, some degree of periodic variability with f rot was deduced. We phase fold the (cid:104) v (cid:105) measurements with f rot andshow these in Fig. 9.The variability of (cid:104) v (cid:105) of the Fe ii line can be described bya second order sine function (see also Table 5), but heavily re-lies on the scarce measurements between rotation phase 0.20 and0.35. Moreover, the phase folded (cid:104) v (cid:105) of the Fe ii line seems to becoherent with the phase folded BRITE photometry (see top pan-els of Fig. 6). The simplest explanation for the LPVs in this Feline, thus, is the presence of surface abundance inhomogeneitiesthat are located close to the magnetic poles. Such a geometri-cal configuration agrees with the stronger measured longitudinalmagnetic field from LSD profiles with only Fe lines (Fig. 6) andis often encountered for magnetic Ap / Bp stars (an example forthe alignment between the large-scale magnetic field and (He)surface abundance inhomogeneities is presented in Oksala et al.2018).A di ff erent profile was obtained for the rotational modula-tion of the (cid:104) v (cid:105) of the Si ii line for which only a sinusoid wasneeded to capture the periodic variability (see Table 5). We re-call that the amplitudes of the variability caused by the g-modefrequency and the rotational modulation of (cid:104) v (cid:105) measurements forthis Si ii line were comparable. These results indicate that theSi surface abundance inhomogeneities have a di ff erent locationon the surface of o Lup than the Fe surface abundance inhomo-geneities. Because of the simple variation of (cid:104) v (cid:105) , we argue thatwe only observe one surface abundance inhomogeneity close tothe magnetic equator.For the two remaining absorption lines (i.e., C ii and Mg ii lines), the measured (cid:104) v (cid:105) followed a profile in between that of theFe ii line and the Si ii line, albeit with a smaller amplitude. Themeasured abundances of these lines are most likely following thechanges in the local atmosphere caused by the Si and Fe surfaceabundance inhomogeneities.
7. Discussion
Comparison between the ESPaDOnS spectroscopy and syntheticspectra did not indicate o Lup was an SB2 system, despite the in-terferometric results (Rizzuto et al. 2013). Either the secondarycomponent is not visible in the spectroscopy, or the RV shiftswere too small to detect due to two components of similar spec-tral type. Therefore, we continue this section under the assump-tion that only the primary component contributes to the variabil-ity and the large-scale magnetic field. We do comment, whereapplicable, what the implication would be in case of an indis-tinguishable secondary component in the spectropolarimetric orphotometric data.
The rotational modulation of the measured longitudinal mag-netic field favored the model a dipolar magnetic field with aquadrupolar contribution. The strength of the quadrupolar termin the model varied with the employed LSD line mask, but itwas typically about 10 % of the strength of the dipolar term (seeTable 4).Assuming a typical stellar radius of 3 – 4 R (cid:12) for a B5IV starwith T e ff = Article number, page 13 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV
Fig. 8.
Phase folded (cid:104) v (cid:105) for selected absorption lines with the average derived g-mode pulsation frequency ( f puls = . − and T = HJD 2455702 .
0; see Table 5); left and the rotation period from the magnetometric analysis ( P rot = . T = HJD 2455702 . right ).Thesame colours were used to indicate the di ff erent observations as in Fig. 6. ploying the measured rotation period of 2 . − and theliterature v sin i = ± − (Głe¸bocki & Gnaci´nski 2005),we estimated the inclination angle to be 27 ± ◦ (correspondingto an equatorial velocity of v eq = ± − ). These assump-tions lead to an obliquity angle β = + − ◦ , following the scalingrelation of Shore (1987) for a purely dipolar large-scale magneticfield. The quadrupolar contribution needed for the description ofthe modulated longitudinal magnetic field will only have a minore ff ect on this estimated value. Moreover, this value does not de-pend strongly on the LSD line mask used for the measurementsof the longitudinal magnetic field.A conservative lower limit for the polar strength of the large-scale magnetic field (when the geometry is a pure dipole) is 3.5times the maximal measured longitudinal magnetic field value(Preston 1967). Using the measurements of the LSD profilesfrom the Balmer lines, we obtained a lower limit of 5.25 kG for the polar strength of the magnetic field, since these were not in-fluenced by the surface distribution of the chemical elements.This value is typical for magnetic Bp stars.Detailed modelling of the Zeeman signatures or successfulZDI mapping of the stellar surface is required to verify the val-ues derived from simple assumptions. However, the current spec-tropolarimetric dataset is not su ffi cient to do so, because of miss-ing observations at several key rotation phases.In case the secondary component significantly contributesto the spectropolarimetric data, which was not confirmed atpresent, we underestimated the strength of the detected large-scale magnetic field, since the total Stokes I profile was used forthe normalization of the B l values. For a 40 % contribution of asecondary, the actual strength of the magnetic field will be un-derestimated by 40 % or 60 %, depending on which componentis hosting the large-scale magnetic field. Article number, page 14 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Table 5.
Values for some of the derived parameters and the loglikelihood for the Bayesian MCMC fits with Eq. (6) to the moments of the studiedabsorption lines. line moment
C A rot , A rot , A puls f puls L ( Θ )[km s − ] [km s − ] [km s − ] [km s − ] [ d − ]C ii (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -133.1Mg ii (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -133.1Fe ii (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -134.6He i (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -131.8Si ii (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -133.2H i (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -34.8He i (cid:104) v (cid:105) . ± . . ± . . ± . . ± . . ± . (cid:104) v (cid:105) . ± . . ± . . ± . . ± . − -133.4 Notes.
Results for the fits to either (cid:104) v (cid:105) or (cid:104) v (cid:105) of a given absorption line to determine the amplitude of the periodic variability with f rot and with f puls . The former was kept fixed during the analysis. The amplitudes A rot , i correspond to variability with i × f rot , the amplitude A puls with the g-modefrequency f puls and C is a constant o ff -set. No accurate values for f puls were recovered during the fit to (cid:104) v (cid:105) due to zero A puls and flat PDFs for f puls ,demonstrating that the model of Eq. (6) is overfitting these data. Fig. 9.
Phase folded (cid:104) v (cid:105) for absorption lines, for which non-zero val-ues for A rot , i were derived, with the rotation period ( P rot = . T = HJD 2455702 . ff erent observations as in Fig. 6. We consider it unlikely that both components of the o Lup bi-nary system host a large-scale magnetic field with the publishedlight ratio and the similar values for v sin i . In case both hosted alarge-scale magnetic field, the similar light contributions wouldlead to two overlapping Zeeman signatures in the LSD Stokes Vprofiles, resembling a highly complex magnetic field geometry.The similar values for the v sin i (and light ratio) would suggest asimilar rotation period, causing the longitudinal magnetic field tovary with two superimposed periods. This would lead to a strongbeating e ff ect. None of the above was observed (see Figs. 4 and 6). Only if both stars would rotate with exactly the same periodcould they pollute the observations unnoticed, and perhaps resultin the necessity of the high-order fit to the measured B l values.However, the synchronization time scale of a binary system withan orbital period of at least 20 years is su ffi ciently long to ex-clude this possibility. Strong di ff erences in the strength of the measured longitudinalmagnetic field from di ff erent chemical elements are not oftennoted for magnetic early-type stars. They are, however, observedhere. Surface abundance inhomogeneities are likely the cause ofthese di ff erences. We support this hypothesis with the analysis ofthe LPVs, since the chemical species having a stronger longitu-dinal magnetic field are also the same species that indicated therotation frequency as the dominant variability for the first mo-ment (i.e., Fe ii ). Moreover, the zeroth moment of some studiedabsorption lines suggested that the measured equivalent widthchanges with the rotation phase, implying a non-uniform surfacedistribution for these chemical elements. A similar conclusionwas obtained by Yakunin et al. (2015) for the magnetic helium-strong B2V star HD 184927. The larger measured B l values forLSD profiles with just Fe ii lines would indicate that their surfaceabundance inhomogeneities are located close to the magneticpole, while the weaker fields retrieved from the He i would locatetheir respective surface abundance inhomogeneities close to themagnetic equator. In addition, the weaker longitudinal magneticfield measurements for the He i lines could also be related to acontribution in the LSD Stokes I profile coming from the sec-ondary of the o Lup system, which is suggested to have a similarspectral type.We do not anticipate that the stellar pulsation is causing thesesevere di ff erences in the measured longitudinal magnetic fieldstrength. It would rather produce additional systematic o ff setsout of phase with the rotation period, as the pulsation frequencyis not a harmonic of the rotation frequency. For the secondary Article number, page 15 of 19 & A proofs: manuscript no. Buysschaert_OmiLupvARXIV component to cause these di ff erences, it must have a di ff erentspectral type, leading to di ff erent contributions to spectral linesof di ff erent chemical species. This is in contradiction to the bi-nary fitting process, that suggested a similar spectral type forboth components. Also, the interferometric results indicated arelatively similar spectral type for the secondary and a mass ra-tio of 0.91 (Rizzuto et al. 2013). The detected large-scale magnetic field for the primary compo-nent of o Lup is su ffi ciently strong to create a magnetosphere.However, the star is not su ffi ciently massive to have a consid-erable mass-loss rate, producing only a limited amount of windmaterial to fill the magnetosphere. Therefore, no observationalevidence of the magnetosphere is anticipated. Indeed, no ro-tational modulation, nor emission features were noted for theBalmer lines. No X-ray observations are available for o Lup todiagnose the interactions between wind material coming fromboth magnetic hemispheres.Petit et al. (2013) determined the star may host a centrifugalmagnetopshere, using the magnetic properties derived by Ale-cian et al. (2011). Repeating these computations for a 4 . M (cid:12) star with a 3 . R (cid:12) radius, the updated P rot = . .
25 kG (and assuming a mass-lossrate described by Vink et al. (2001)), we obtained R K = . R (cid:63) and R A = . R (cid:63) (and a mass-loss rate log ˙ M = − .
42 dexwith ˙ M given in M (cid:12) yr − ). This confirms the results of Petit et al.(2013) that the magnetic component of o Lup hosts a centrifu-gal magnetosphere. Yet, as previously indicated, the mass-lossrate is too low, particularly compared to the extend of the mag-netosphere ( R A (cid:29) R K ), to produce observational evidence ofmagnetospheric material. In addition, the binary orbit of o Lupis too wide to cause e ff ects in the circumstellar material of themagnetic component. The BRITE photometry indicated that two frequencies, namely f = . − and f = . − , were not explained as afrequency harmonic of the rotation frequency or as instrumentalvariability due to the spacecraft. Furthermore, we recovered f asthe dominant periodicity in the first moment of the C ii ii i i α . The frequency value and the stel-lar parameters of the primary suggest that this frequency is ag mode. The majority of stars exhibiting such pulsation modesshow a rich frequency spectrum, with sectoral dipole modes thatare quasi-constantly spaced in the period domain (e.g., Pápicset al. 2014, 2017; Kallinger et al. 2017). We only find two pul-sation mode frequencies due to the limited BRITE and ground-based data sets compared to the Kepler capacity in terms of alias-ing.The standard deviation of the lines (see Fig. 7) can serve asa proxy for the amplitude distribution from the pixel-by-pixelmethod (e.g., Gies & Kullavanijaya 1988; Telting & Schrijvers1997; Zima 2006) in case one dominant periodicity causes theLPVs. As such, the shape of these distributions for the absorp-tion lines that were dominantly variable with f suggested a low-degree mode (likely a dipole mode). Yet, detailed mode identi-fication with famias did not produce conclusive results on themode geometry. Furthermore, the frequency f = . − was also within the appropriate frequency domain for g-mode pulsations. In the absence of the secondary in the spectroscopy,we assumed that the g-mode pulsations originate from the mag-netic component, as the majority of the LPVs were explained by f . However, if the secondary contributed to the total flux, theperiodic variability with f or f could be produced by the com-panion since its anticipated similar spectral type would place itwithin the SPB instability strip as well.Without at least several detected pulsation modes, the mag-netic and pulsating component of o Lup is not a suitable candi-date for magneto-asteroseismology, and so does not provide theopportunity to investigate the influence of the large-scale mag-netic field on the structure and evolution of the stellar interior.
8. Summary and conclusions
We combined HARPSpol and ESPaDOnS spectropolarimetryto study and characterize the large-scale magnetic field of o Lup. Using the variability of the measured longitudinal mag-netic field, we determined the rotation period to be P rot = . o Lup sys-tem hosts the large-scale magnetic field, given the lack of firmdetection of a secondary component in the spectroscopy.Comparing the strength of the measured B l for various chem-ical elements, we noted large di ff erences, indicative of chemicalpeculiarity and abundance structures at the stellar surface. Thelargest values were obtained for Fe, while the smallest valueswere derived from He i lines. This suggests that Fe surface abun-dance inhomogeneities are located closer to the magnetic poles,while those for He are present near the magnetic equator. Yet, wecannot fully exclude a possible contamination by the secondarycomponent of o Lup in the LSD Stokes I profiles. ZDI is neededto verify the locations of the suggested surface abundance in-homogeneities. Yet, this is not feasible with the current spec-tropolarimetric dataset, as we are lacking observations at severalnecessary rotational phases.Fitting models to the rotational variability of the measured B l values favors a description of a dipolar magnetic field with aquadrupolar contribution. This remains valid for the LSD pro-files constructed with all metal lines, averaging out the e ff ectsof the surface abundance inhomogeneities, as well as for theLSD profiles from the Balmer lines. Typically, the strength ofthe quadrupolar contribution is about 10 % of that of the dipo-lar contribution. Using simple approximations, we estimated theinclination angle of the magnetic component of o Lup to be i = ± ◦ , which then leads to an obliquity angle β = + − ◦ . Aconservative lower limit on the polar strength of the large-scalemagnetic field, measured from the LSD profiles of the Balmerlines, would be 5 .
25 kG.The BRITE photometry for o Lup shows up to six significantfrequencies, indicating periodic photometric variability. Three ofthese frequencies ( f , f , and f ) correspond to the rotation fre-quency, and its second and third frequency harmonic. One fre-quency ( f ) is confirmed to be of instrumental origin, due to pe-riodic variability of the satellite on-board temperature that wasnot perfectly accounted for during the correction process. The re-maining two frequencies ( f and f ) fall in the frequency domainof SPB pulsations. In case f and f originate from the magneticcomponent, o Lup A would be classified as a magnetic pulsat-ing early-type star. However, the few detected pulsation modefrequencies are not su ffi cient for detailed magneto-asteroseismicmodelling. Article number, page 16 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Investigating selected absorption lines in the individual sub-exposures of the spectropolarimetric sequences indicates thepresence of LPVs. The first moment of these absorption lines al-most always indicate f as the dominant frequency, except forthe Fe ii line where f rot was the dominant frequency. This is,again, suggestive of surface abundance inhomogeneities for Fe.Moreover, the equivalent width of the studied Fe ii and Si ii linesdid change significantly with the rotation phase, demonstratingnon-uniform surface abundances for these chemical species. Theshape of the LPVs for the other selected absorption lines, where f was dominant, agreed with a low-order pulsation mode, con-firming that f is a pulsation mode frequency. Acknowledgements.
B.B. thanks the participants of the third BRITE scienceworkshop and the third BRITE spectropolarimetric workshop for the construc-tive comments on the presented work. In particular, Oleg Kochukhov for hissuggestion to analyse the zeroth moment in more detail. This work has made useof the VALD database, operated at Uppsala University, the Institute of Astron-omy RAS in Moscow, and the University of Vienna. This research has made useof the SIMBAD database operated at CDS, Strasbourg (France), and of NASA’sAstrophysics Data System (ADS). Some of the data presented in this paper wereobtained from the Mikulski Archive for Space Telescopes (MAST). STScI is op-erated by the Association of Universities for Research in Astronomy, Inc., underNASA contract NAS5-26555. Support for MAST for non-HST data is providedby the NASA O ffi ce of Space Science via grant NNX09AF08G and by othergrants and contracts. A. T. acknowledges the support of the Fonds Wetenschap-pelijk Onderzoek - Vlaanderen (FWO) under the grant agreement G0H5416N(ERC Opvangproject). The research leading to these results has (partially) re-ceived funding from the European Research Council (ERC) under the EuropeanUnion’s Horizon 2020 research and innovation programme (grant agreementN ◦ ffi ce (Belspo) un-der ESA / PRODEX grant "PLATO mission development".
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Appendix A: Additional tables
Article number, page 18 of 19. Buysschaert: Magnetic characterization and variability of o Lup
Table A.1.
Overview of the measured longitudinal magnetic field values.
HJD [d] φ rot B l [G] B l [G] B l [G] B l [G] B l [G] B l [G]-2450000 complete He excluded Balmer Fe ii Si ii He i ±
26 976 ±
41 618 ±
142 2038 ±
111 752 ±
79 66 ± − ± − ± − ± − ± − ± − ± ±
27 2243 ±
45 1239 ±
143 4770 ±
133 1904 ±
83 132 ± ±
32 2213 ±
51 1177 ±
165 4607 ±
147 1707 ±
97 66 ± ±
22 1976 ±
35 1446 ±
127 4285 ±
106 1617 ±
65 103 ± − ± − ± − ± − ± − ± − ± ±
29 204 ±
50 513 ±
155 56 ±
158 385 ± − ± ±
32 524 ±
56 570 ±
170 1167 ±
173 592 ±
115 1 ± ±
22 1967 ±
36 1327 ±
125 4260 ±
108 1649 ±
68 118 ± ±
23 93 ± − ±
123 268 ± − ± − ± ±
31 1896 ±
47 1227 ±
171 3881 ±
133 1567 ±
86 92 ± − ± − ± − ± − ± − ±
76 3 ± ±
31 1986 ±
51 1165 ±
137 4354 ±
156 1571 ±
85 106 ± ±
23 1443 ±
40 967 ±
98 3230 ±
130 1158 ± − ± ±
26 1948 ±
42 1275 ±
139 4148 ±
125 1642 ±
80 101 ± ±
25 1981 ±
41 1343 ±
136 4242 ±
122 1658 ±
77 53 ± ±
25 2018 ±
42 1327 ±
137 4391 ±
124 1609 ±
78 59 ± ±
25 2011 ±
41 1249 ±
133 4234 ±
119 1621 ±
76 65 ± ±
26 2043 ±
43 1399 ±
141 4228 ±
123 1684 ±
81 132 ± ±
27 2102 ±
43 1252 ±
145 4276 ±
124 1733 ±
81 78 ± ±
28 2109 ±
46 1225 ±
154 4440 ±
134 1716 ±
86 62 ± ±
34 2037 ±
54 1393 ±
183 4330 ±
157 1604 ±
101 112 ± ±
47 2201 ±
71 1238 ±
262 4835 ±
200 1805 ±
136 112 ± ±
72 2088 ±
109 1526 ±
396 5059 ±
335 1639 ±
209 24 ± ±
39 910 ±
62 611 ±
219 1989 ±
172 758 ±
124 96 ± ±
46 862 ±
73 758 ±
253 1932 ±
206 777 ±
146 91 ± ±
37 2083 ±
61 1535 ±
207 4765 ±
177 1747 ±
121 63 ± ±
35 2039 ±
58 1257 ±
201 4444 ±
167 1652 ±
115 76 ± ±
28 2145 ±
46 1267 ±
146 4486 ±
130 1893 ±
91 67 ± ±
29 2147 ±
47 1309 ±
159 4576 ±
133 1842 ±
93 97 ± ±
27 2179 ±
44 1392 ±
156 4677 ±
125 1876 ±
86 165 ± ±
27 2204 ±
43 1481 ±
157 4676 ±
123 1830 ±
84 62 ± ±
20 649 ±
34 164 ±
107 1174 ±
92 382 ±
72 30 ± ±
20 610 ±
33 212 ±
107 1128 ±
91 371 ±
71 25 ± ±
22 431 ±
35 222 ±
113 744 ±
93 194 ±
78 18 ± ±
23 472 ±
37 126 ±
120 875 ±
98 339 ±
83 14 ± Notes.
For each observation, the HJD at mid-exposure, the corresponding rotation phase, φ rot , calculated using P rot = . T = HJD 2455702 .
5, and the measured longitudinal magnetic field B ll