Evidence of asymmetries in the Aldebaran photosphere from multi-wavelength lunar occultations
A. Richichi, V. Dyachenko, A.K. Pandey, S. Sharma, O. Tasuya, Y. Balega, A. Beskakotov, D. Rastegaev, V.S. Dhillon
MMon. Not. R. Astron. Soc. , 1–7 (2016) Printed 6 August 2018 (MN L A TEX style file v2.2)
Evidence of asymmetries in the Aldebaran photospherefrom multi-wavelength lunar occultations
A. Richichi, (cid:63) V. Dyachenko, A.K. Pandey, S. Sharma, O. Tasuya, Y. Balega, A. Beskakotov D. Rastegaev and V.S. Dhillon , National Astronomical Research Institute of Thailand, 191 Huay Kaew Road, Chiang Mai 50200 Thailand Special Astrophysical Observatory, Nizhnij Arkhyz, Karachai-Cherkessian Republic, Russia 369167 Aryabhatta Research Institute of Observational Sciences, Manora Peak, Naini Tal, 263002 India Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK Instituto de Astrof´ısica de Canarias, E-38205 La Laguna, Tenerife, Spain
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We have recorded three lunar occultations of Aldebaran ( α Tau) at different telescopesand using various band-passes, from the ultraviolet to the far red. The data have beenanalyzed using both model-dependent and model-independent methods. The deriveduniform-disc angular diameter values have been converted to limb-darkened values us-ing model atmosphere relations, and are found in broad agreement among themselvesand with previous literature values. The limb-darkened diameter is about 20.3 mil-liarcseconds on average . However, we have found indications that the photosphericbrightness profile of Aldebaran may have not been symmetric, a finding already re-ported by other authors for this and for similar late-type stars. At the sampling scaleof our brightness profile, between one and two milliarcsecond, the uniform and limb-darkened disc models may not be a good description for Aldebaran. The asymmetriesappear to differ with wavelength and over the 137 days time span of our measurements.Surface spots appear as a likely explanation for the differences between observationsand the models.
Key words: occultations – stars: individual: Aldebaran – stars: atmospheres
Aldebaran ( α Tau) is one of the brightest and most distinc-tive stars in the sky, and as a result it has one of the longestrecords of observations and publications. Being a K5 giantstar and located at just 20 pc from the Sun, it has also oneof the largest angular diameters among all stars and it hastherefore been the subject of numerous measurements in thissense using a number of techniques. Since Aldebaran is lo-cated on the Zodiac, it is regularly occulted by the Moon.We are at present in the middle of one such series of occul-tations, which will last until early 2018.Richichi & Roccatagliata (2005, RR05 hereafter) pre-sented accurate lunar occultation (LO) and long-baselineinterferometry measurements obtained in the near-infrared,and discussed them in the context of previously availabledeterminations. They concluded that the limb-darkened di-ameter of α Tau is 20 . ± .
03 milliarcseconds (mas), or44 R (cid:12) . Photometric variability is less than 0.01 mag andthe diameter is assumed to be reliably constant. Differences (cid:63) E-mail: [email protected] in the angular diameter values available in the literature areindeed present and sometimes significant when taken at facevalue, however they can often be justified in terms of uniformdisc to limb-darkening corrections or by intrinsic limitationsin the accuracy.We have recorded three LO events in the present se-ries, and we present here their detailed analysis. Our aim isnot so much to confirm or refine the angular diameter de-termination, but rather to investigate possible asymmetriesor surface structure features in the photosphere of this giantstar. Indications in this sense had already been presented byRR05.
We recorded three LO light curves of α Tau: in October 2015using the SAO 6-m telescope in Russia, and in March 2016using the Devasthal 1.3-m telescope in India and the TNT2.4-m telescope in Thailand. Details of the observations areprovided in Table 1.At SAO, a commercial 512x512 pixels Andor iXon Ul- c (cid:13) a r X i v : . [ a s t r o - ph . S R ] S e p A. Richichi et al.
Table 1.
Observations logTelescope SAO 6-m 1.3-m TNT 2.4-mSite Nizhny Arkhyz, Russia Devasthal, India Doi Inthanon, ThailandCoordinates 41 ◦ (cid:48) E, 43 ◦ (cid:48) N, 2100m 79 ◦ (cid:48) E, 29 ◦ (cid:48) N, 2450m 98 ◦ (cid:48) E, 18 ◦ (cid:48) N, 2450mDate, Time (UT) 2015-10-29, 23:32:01 2016-03-14, 14:40:29 2016-03-14, 15:15:32Event Reappearance Disappearance DisappearancePredicted PA, Rate 229 ◦ , − ◦ , 0.732 m/ms 125 ◦ , 0.734 m/msDetector ANDOR ANDOR ULTRASPECFilter ( λ , ∆ λ ) (nm) Filterless R (640, 130) u (cid:48) (356, 60) λ eff (nm) 752 644 371Sampling (ms) 2.58 1.85 6.29CAL, DIF Sampling (mas) 0.90 0.76 2.57 tra DU-897-CS0 detector was used. For this observation weused binning 16x16, readout rate 17 MHz, electron multi-plying gain = 100, shift speed = 0.5 µ s, 0.1 ms exposuretime, kinetic regime. This resulted in a kinetic cycle timeof 2.58 ms. The readout noise at this rate was 93 e − .Theresult was a FITS data cube, with 32x32 pixel size and150,000 frames. At Devasthal, a similar detector was used,namely a 512x512 pixels frame transfer ANDOR iXon EM-CCD (DU-897E-CS0-UVB-9DW). For this observation, thecentral 32x32 pixels were used in 2x2 binning mode. Read-out rate 10 MHz, shift speed 0.9 µ s, 1.38 ms exposure timeresulted in a kinetic cycle time of 1.85 ms. The final imagewas a FITS data cube containing 45,000 frames. At TNT,we used the ULTRASPEC frame-transfer EMCCD imager(Dhillon et al. 2014) in the so-called drift mode already usedpreviously for LO (Richichi et al. 2014, 2016). We used awindow of 8x8 pixels (3 . (cid:48)(cid:48) . (cid:48)(cid:48) u (cid:48) filter. The resulting FITS data cube consisted of 9371frames, with sampling time of 6.288 ms and integration timeof 6.123 ms.In all three cases, we built an effective wavelengthresponse of the instrument by convolving the filter withthe CCD quantum efficiency and the optics. The effective(weighted average) wavelengths λ eff for each case are listedin Table 1. We also included in our analysis the effects ofthe finite integration time, and of the primary diameter andobstruction.The data cubes were trimmed to include only a fewseconds around the occultation event, and converted to lightcurves using a mask extraction tailored to the seeing and im-age motion, as described in Richichi et al. (2008). The lightcurves were then analyzed using several methods. Firstly, aleast-square model-dependent (LSM) analysis was used, thedetails of which are given in Richichi et al. (1992). This ap-proach uses a uniform-disc (UD) model of the stellar discwith its angular diameter as a free parameter, and achievesconvergence in χ based a noise model built from data be-fore and after the occultation. Among other parameters, thismethod allows to determine in principle also the actual slopeof the lunar limb from the comparison between predictedand fitted lunar rate. However, in the specific case of a largeangular diameter such as that of α Tau all diffraction fringesexcept at the most the first one (see below) are almost com-pletely erased, and this benefit of the LSM method cannotbe realized (see also Sect. 3.1). Additionally, although ourimplementation of the LSM method allows in principle topartly account for scintillation by means of interpolation by Legendre polynomials, for the same reason as above thiscannot be done in practice for the α Tau LO data.Secondly, we used a composite algorithm (CAL) whichprovides a model-independent brightness profile of thesource in the maximum-likelihood sense (Richichi 1989). Fi-nally, we also used a simple differentiation (DIF) to recon-struct the brightness profile in a model-independent fashion.This latter method is applicable when the occultation canbe described by simple geometrical optics. This is the casewhen the source angular diameter φ , the wavelength λ andthe distance to the Moon D satisfy the relation φ > (cid:112) λ/ D.With an angular diameter of about 20 mas, Aldebaran sat-isfies this relationship marginally in the far red, and com-pletely in the ultraviolet. The difference between the CALand the DIF methods is that the first one modifies an initialbrightness profiles with small steps during a large numberof iterations (typically thousands), resulting in a relativelysmooth profile; the second method, instead, performs a sin-gle differentiation operation but is affected by point-to-pointnoise in the data. This noise can be reduced by rebinningthe data before differentiation, at the expense however ofthe final angular resolution.With the LSM method, the achieved angular resolutionis related to the time sampling but also to the quality of thefit (expressed by the normalized χ ) and the signal-to-noiseratio (SNR) of the data. In practice, this is the method whichwill yield the best resolution and accuracy, at least formally.For CAL and DIF, the resulting brightness profiles have astep in angular resolution which is related to the samplingtime, to the apparent speed of motion of the lunar limb,and to the distance to the Moon. The theoretical angularsampling of the brightness profiles for these two methods arelisted in Table 1. In case of data rebinning, the angular stepof the CAL and DIF profiles will be reduced accordingly. The three data sets are shown in Fig. 1, rescaled and offsetby arbitrary amounts to fit in a single, compact figure. Someaspects of the data can be appreciated prior to any quantita-tive analysis, such as for example the progressive transitionfrom the diffraction to the geometrical regime. The SAO6-m curve has a redder effective wavelength than the Dev-asthal 1.3-m curve, and indeed it shows a slightly more pro-nounced first fringe. It is however surprising that the TNT2.4-m curve, which should be completely within the geo- c (cid:13) , 1–7 symmetries in the Aldebaran photosphere I n t en s i t y Relative Time [ms]0 100 200 300ab c I n t en s i t y Relative Time [ms]
Figure 1.
Light curves (points) marked as a, b, c, from the SAO6-m, the Devasthal 1.3-m and the TNT 2.4-m telescopes, respec-tively. The data have been shifted in time, scaled and shifted inintensity, to fit in a single figure. The solid lines are the best fitby a uniform-disc (UD) model in each case, as discussed in thetext. metrical optics regime, appears to show in fact a diffractionfringe. It is also evident how the telescope diameter stronglyaffects the level of scintillation, as expected: with compara-ble wavelengths, the SAO 6-m data have indeed significantlylower scintillation than those from the Devasthal 1.3-m. Inthe remainder of this section, we report and illustrate theresults of the quantitative data analysis of these curves, firstby the model-dependent and then by the model-independentmethods.
We report on the data analysis using the LSM method first,the natural outcome of which is the best fitting angular di-ameter on the basis of a noise model built individually foreach light curve and each instrument as detailed above. Weassume a stellar model with a uniform disc (UD), since this iseasily described by one parameter only, i.e. the angular size.In reality the star is generally better described in terms of alimb-darkened disc (LD). Although it is possible to describeLD brightness profiles analytically, this requires a numberof additional parameters and in practice their effect on thefitting process is not sufficient to obtain well-determined val-ues unless the light curve has a very high SNR. We thus fol-low the customary approach of determining UD diametersfirst. The results are listed in Table 2. We note that, dueto the almost complete suppression of the diffraction fringesin the case of α Tau, the actual rate of the event is nota completely independent parameter as in other LO lightcurves of sources with smaller angular diameters. In fact, inthis particular situation the rate is correlated to the angularsize. For this reason, we have decided to keep the rate to itspredicted value in the three fits. More comments about thisare given in Sect. 4.UD diameters are wavelength dependent, and as ex-pected the three values listed in Table 2 do not agree witheach other given the different band-passes. It can be howeverappreciated how the UD diameter value increases monoton-ically with λ eff . It can also be noted that the accuracy of Table 2.
Uniform and limb-darkened diameter valuesTelescope SAO 6-m 1.3-m TNT 2.4-m λ eff (nm) 752 644 371UD (mas) 19.12 ± ± ± χ eff (see text) 1.07 1.09 1.15LD (mas) 20.42 ± ± ± the resulting diameter value is closely related to the SNR,as discussed in Sect. 2. In order to compare results obtainedat various wavelengths and to test atmospheric models, itis useful to convert the wavelength-dependent UD values totheir limb-darkened (LD) diameter equivalent.It is customary to generate LD/UD coefficients frommodel atmospheres. Davis et al. (2000) derived detailedLD/UD coefficients as a function of wavelength for a largegrid of stellar atmospheric models, based on the atlas dis-tributed by R.L. Kurucz on CD-ROMs in 1993. The coeffi-cients are tabulated in discrete steps of effective temperatureT eff , of surface gravity log g , and of metallicity Z=log [Fe/H].For the temperature, we adopt the value T eff =3920 ±
15 Kby Blackwell et al. (1991), which is in excellent agreementwith the value of 3934 ±
41 K derived by RR05. For log g ,we adopt the value of 1.25 ± α Tau is quoted in the literaturewith a range of values ranging from solar to less than halfsolar (Cayrel de Strobel et al. 1992). Recently, Jofr´e et al.(2014) have analyzed the data available on the metallicity ofa number of GAIA benchmark stars using several differentmethods. They find Z= − . ± .
02 for Aldebaran, and thisis our adopted value as well.We thus selected those curves among those provided byDavis et al. (2000) which bracket our adopted T eff , log g andZ, and proceeded to interpolate between them. The resultingLD/UD correction as a function of wavelength is shown inFig.2. It can be noted that the Davis et al. (2000) data stopat λ =400 nm. Since our TNT observation extends to about λ =325 nm, we took the simple approach of extrapolatingthe curve, as also shown in Fig.2.We note that as long as the LD/UD uncertainty is lessthan 0.03, which seems a reasonable upper limit also in thecase of the ultraviolet extrapolation, the effect on the error inthe LD diameter is less than the last digit shown in Table 2. It must be remarked that the LD/UD coefficients are strictlyapplicable only for monochromatic wavelengths, while ourdata and thus our UD diameter results are for broad-bandfilters. To account for this, we have computed an effectiveLD/UD correction for each of the three LO cases, by weigh-ing the LD/UD curve by the effective transmission of filter,CCD and optics, and normalizing. The results are listed inTable 2 as (LD/UD) eff . Using these corrections, we deriveLD diameter values which are also listed in Table 2. It canbe seen that the LD values from SAO and TNT are consis- c (cid:13) , 1–7 A. Richichi et al. L D / UD Wavelength [nm]
Figure 2.
Solid curve: the monochromatic LD/UD coefficients,interpolated from the database of Davis et al (2005) for our as-sumed Aldebaran atmospheric parameters. Dashed curve: extrap-olation below 400 nm. The three curves labeled a, b, c are shownin arbitrary vertical units: they represent the total transmissionof the instruments at SAO, Devasthal, and TNT, respectively.They include the effects of CCD, optics and filter. tent among themselves and in some agreement with the LDdiameter of 20 . ± .
03 mas reported by RR05 - althoughnot within the errors in the case of the SAO result. The re-sult from the Devasthal 1.3-m telescope however has to beconsidered discrepant.To investigate further this apparent discrepancy, wehave plotted in Fig. 3 the fit residuals (normalized in unitsof the light curve intensity) for the two light curves withthe best quality, those from SAO and from Devasthal, inthe central part where the intensity goes from unocculted toocculted. It can be noticed that the Devasthal data show aquasi-sinusoidal variation. Scintillation comes first to mindas a possible cause, but it would not be so regular and more-over its amplitude should be proportional to the stellar flux.The flux changes from full unocculted intensity at the leftof Fig. 3, to zero at the right. Therefore, scintillation canbe convincingly excluded as the cause of this beating in theresiduals for the Devasthal curve. We note that in the caseof the SAO data scintillation decreases from the right to theleft of Fig. 3, and indeed one might see that the right partof the residuals appears slightly noisier.We are inclined to conclude that the residuals indicate,at least in the Devasthal case, that the UD is not a goodmodel at the level of the accuracy present in the data. Theeven higher accuracy data from SAO however do not showthis effect with the same magnitude, and we can speculatethat the UD (and LD as a consequence) model is a betterapproximation in the infrared part of the visible range. An-other possible reason are time variable changes in the pro-file, which we discuss in Sect. 4. The case of the TNT datain the ultraviolet is harder to pin down from an analysis ofthe residuals, since the noise was so much higher in this casedue to a combination of poorer combined throughput on onehand, and of much higher background on the other. How-ever, we have already remarked that the TNT light curveshown in Fig. 1 seems to exhibit a first diffraction fringewhich is totally unexpected since diffraction effects should -0.05 0 0.05 0 10 20 30 40 50 N o r m a li z ed R e s i dua l s Relative Time [ms]
Figure 3.
The fit residuals for the central part of the SAO andDevasthal light curves shown in Fig. 1, top and bottom respec-tively. The residuals have been normalized by the intensity of theunocculted source, and shifted vertically by ± .
025 units for clar-ity. They have also been shifted horizontally into a common timewindow. have been negligible at this wavelength. One possible causeof such a fringe, if real, could be a compact area (about 20%of the diameter or less) of enhanced emission on the photo-sphere. The jagged ultraviolet brightness profiles discussedin Sect. 3.3 could point in this direction, although the errorsmake this far from conclusive.
LD diameters are ultimately the values which are employedin standard stellar atmospheric models, but they are the re-sult of assumed empirical conversions which are not directlymeasured or confirmed by observations. Moreover, the ex-tension from the monochromatic values to an effective con-version coefficient valid for a broad bandpass is prone tointroduce a possible bias. Even more significantly, the wholeissue of determining an accurate diameter depends on thechosen model brightness distribution which is assumed tobe axisymmetric and constant with time. The discrepancieswhich we have highlighted in Sect 3.2 all point to cracksin these assumptions. In the case of Aldebaran however weare in the fortunate position to be able to reconstruct thebrightness profile directly by model-independent methods.Profiles reconstructed by the DIF method are shownin Fig. 4. By its design, this method is sensitive to whitenoise in the data and this explains why the profiles of thecurves from SAO and India are noisier on the side wherescintillation is affecting the data, the right and left sides ofthe respective profiles. In the case of TNT, the dominantsource of noise is not scintillation but rather the shot-noisefrom the very intense background around the Moon in theultraviolet, and it can be seen that the noise in the profile ismore evenly distributed. Further, in all three cases a slightdip towards negative values of the profile is due to presenceof small residual diffraction fringe in the light curves: thiscan be seen to the right of the SAO profile, and to the leftin the other two cases. It can be appreciated how in allthree cases the profile does not appear to be completely c (cid:13) , 1–7 symmetries in the Aldebaran photosphere I n t en s i t y Angle [mas]
Figure 4.
Reconstructed brightness profiles, using differentiationas explained in the text. The curves a, b, c, are for the data setsfrom SAO 6-m, Devasthal 1.3-m and TNT 2.4-m, respectively,with the effective wavelengths listed in Table 1. The profiles areshifted by arbitrary amounts in intensity, for the sake of clarity.The arrows display the direction of the scan by the lunar limb,projected on the sky and in counter-clockwise direction from theNorth they are for b, c, a respectively. The length of the arrowsis inversely proportional to the speed of the scan. I n t en s i t y Angle [mas]
Figure 5.
Reconstructed brightness profiles, using the maximum-likelihood CAL method as explained in the text. The curves areshifted in intensity, labeled and with the same sky orientation asin Fig. 4. The crosses on the right reflect the uncertainties foreach profile, as explained in the text. symmetric. In the case of the ultraviolet data from TNT,a relatively flat central part of the profile is present. Limb-brightening as observed in far-ultraviolet solar images comesto mind, although our SNR is not sufficient to confirm thishypothesis.We have computed the profiles also by the CAL method,and they are shown in Fig. 5. The profiles are consistent withan approximate extent of 20 mas, but show structure whichis markedly different from the gaussian shape expected fora circularly symmetric uniform disc (Richichi 1989). In thefigure we have added error crosses for each profile: the extentin angle is simply the sampling step from Table 1, whilethe extent in intensity is derived from the SNR of the CALfit rescaled by the number of points inside the Aldebaran’s I n t en s i t y Angle [mas]
Figure 6.
Same as Fig. 5, for three unresolved sources observedat SAO (a), Devasthal (b) and TNT (c). The curve (d) is for a wellresolved star observed at SAO. The profiles do not display obviousasymmetries. The points mark the different angular sampling ofthe data sets. Details in the text. disc. To clarify: the total reconstructed SAO profile extendedfrom −
50 to +40 mas, and included 46 points with a SNR of177.8, or an error of 0.0056 on the normalized intensity. Thepoints effectively inside the ±
10 mas extent of the disc are22. Assuming that those outside the disc do not contributesignificantly to the noise total, we compute the effective errorin normalized intensity as 46 / × . . α Tau -albeit in different filters. In Fig. 6 we show the CAL profilesobtained for 1 Cnc observed at SAO on February 19, 2016;for SAO 94227 observed at Devasthal on February 16, 2016;and for HR 4418 observed at TNT on April 18, 2016. Wehave also added a recent LO observation of λ Aqr observedfrom SAO on June 25, 2016: this result will be discussedelsewhere, but it can be seen that the profile is very well re-solved and represents a case not too dissimilar from that of α Tau. It can be appreciated that, at the level of the discreteangular sampling of the three data sets, the profiles do notshow significant asymmetries, in contrast with those foundfor α Tau.We emphasize that DIF and CAL profiles should beused to investigate the general appearance of the brightnessprofiles only. They are not well suited to measure angulardiameters since they are not parametric and because theangular scale depends on the adopted limb rate. In our DIFand CAL analysis, we adopted the same limb rates as in theLSM method.
The main common denominator of the results just presentedis that while the data can be fitted in a first approxima-tion by UD models which can in turn be converted to LDvalues, in reality all three light curves show small devia-tions which seem to indicate the presence of asymmetries inthe brightness profile. RR05 hinted at a similar possibility c (cid:13) , 1–7 A. Richichi et al. from their high quality near-IR data, and they also mentionan unusual scatter in the VLTI long-baseline interferometrymeasurements. Similar findings were reported in earlier LOobservations of stars with very large angular diameters, e.g.asymmetries were hinted in the case of α Sco (Evans 1957;Richichi & Lisi 1990) - although the latter is a supergiant.For the late-type giant R Leo, di Giacomo et al. (1991) foundfrom a LO that the UD fit was unsatisfactory, and that thebrightness profile showed significant departures from the UDhypothesis. Studies on other evolved stars with very largeangular diameters have also revealed significant departuresfrom simple circularly symmetric models, the best exam-ple being α Ori for which many different techniques couldbe used by several authors ranging from adaptive optics tospeckle to long-baseline interferometry.One important consideration is that the DIF and CALprofiles that we obtain appear to be all significantly differentfrom each other. This is not surprising, when one considersthat the data SNR is quite different in the three cases, and soare the effective wavelengths. In particular, the u (cid:48) data fromTNT represent the shortest wavelength ever used to recorda LO of α Tau, and the photospheric appearance in the ul-traviolet is expected to be considerably different from thatin the red. Other important factors are of course the timevariability and the different scan directions. Setting aside fora moment the lower SNR data from TNT, when one consid-ers e.g. the Devasthal and SAO profiles in Fig. 4 it should benoted that the scan directions were almost orthogonal andthat the two LO events occurred 137 d apart. For compari-son, Hatzes et al. (2015) (who discovered a likely exoplanetaround α Tau with a 629 d period) attribute residual varia-tions in their radial velocity data to rotation modulation ofstellar surface features with a period of ≈ d . These varia-tions could well be related to the photospheric asymmetriesthat we have pointed out, but in this case the time lag be-tween our LO measurements would be a significant fractionof the modulation period and hence the comparison of theSAO and Devasthal data would be problematic. Obviously,any comparison between the present sets of data and earlierones, such as the LO light curve discussed by RR05 whereasymmetries were also suggested, is impossible.In our LSM analysis discussed in Sect. 3.1 we have as-sumed that the lunar limb rate was equal to the predictedvalue. We have already stated that the limb rate and theangular diameter are correlated in a quasi-geometrical op-tics case such as that of α Tau, so we tried to prove thatthis assumption is reasonable. We have thus fitted the SAOdata (the set for which we expect the most marked diffrac-tion effects) leaving the rate as a free parameter. The fittedbest rate was 2.6% slower than predicted, corresponding toa limb slope of 2 . ◦ χ =1.247 instead of 1.206), and UD angu-lar diameter would then be 18.50 mas instead of 19.12, alsoa change in the wrong direction. As expected, in this casethe cross-correlation factor between limb rate and angulardiameter was 0.91. In summary, we think that our approachof keeping the limb rate fixed to the predicted value wasnot detrimental, and in any case did not affect at all theconclusion on the presence of photospheric asymmetries.The most likely physical explanation for such asymme- tries in the brightness profiles would be the presence ofsurface structures such as cold spots. Indeed, such spotsare expected on stars like Aldebaran. Indirect detection ofstarspots has been made possible thanks to Doppler imag-ing, and among the stars included in the review by Strass-meier (2009), about half were K giants. However, starspotsare usually more prominent in fast rotators, and many ofthe giants for which starspots are well measured are in bi-nary systems in which tidal locking accelerates rotation. Anexample is the recent extensive study of XX Tri by K¨unstleret al. (2015).In single late-type giants, with periods of the order of1-2 years, starspots could not be detected until recently, buttechnological improvements are starting to reveal magneticfields (Korhonen 2014), which are the basis of starspots.Auri`ere et al. (2009); Auri`ere et al. (2015) have detectedsub-Gauss fields in β Gem and α Tau itself, and Sennhauser& Berdyugina (2011) on α Boo. One additional, indirectsupport of the starspot hypothesis is the fact that they areknown to have significantly different contrast in the red andin the blue: this would help justify further the differencesobserved in the brightness profiles. For example, the DEVand TNT data are taken at the same time and along posi-tion angles differing by less than 30 ◦ , but the difference inwavelength is dramatic.As for the magnitude of their effect on the generalbrightness profile, the range of starpot sizes is quite broad. Inextreme cases, spots have been observed to cover about 20%of the stellar surface, or down to just fractions of percent atthe other extreme. Their number distribution is also quitevaried since they can be present as single spots or in dozens.The direct detection of starspots has recently been demon-strated by long-baseline inteferometry in ζ And (Roetten-bacher et al. 2016). With this work, we show that LO ofstars with a large angular diameter (above ≈
10 mas) alsorepresent an excellent option presently available to measurestarspots directly. We note that the Aldebaran occultationseries is ongoing until the end of 2017, and we plan to ob-serve more events from various sites around the northernhemisphere.As a final remark, Aldebaran is surrounded by a fewother stars, at least one of which is suspected of being aphysical companion. They are all much fainter and withseparations of at least tens of arcseconds, and are thus un-detectable in our light curves and with no influence on ourfindings.
We have recorded three lunar occultation light curves ob-tained first at the Russian 6-m telescope in the far red, andthen 137 days later at the Devasthal 1.3-m telescope in thered and at the 2.4-m Thai National Telescope in the ul-traviolet. The analysis by conventional uniform disc (UD)and limb-darkened disc (LD) models leads to values whichare approximately consistent with the expected LD value of20 . ± .
03 mas derived by RR05 from the combination ofaccurate occultation and long-baseline interferometry deter-minations. However, the measurements do not agree at thelevel of the formal errors, and a close inspection of the fitresiduals showed that the UD (and therefore the LD) ap- c (cid:13) , 1–7 symmetries in the Aldebaran photosphere proximation may not be accurate for this K5 giant. This isconsistent with earlier indications of surface asymmetries forAldebaran as well as for other late-type giants.Analyis by model-independent methods has revealedthat the brightness profile of Aldebaran has significant de-partures from spherical symmetry, at least at the milliarcsec-ond level, or few percents of its diameter. These asymmetrieswould be well consistent with cool spots, and lunar occulta-tions provide the means of detecting such spots directly, ifcoordinated observations are performed for the same eventfrom several sites. We plan to observe more occultations ofAldebaran in the present series which will last until the endof 2017. ACKNOWLEDGEMENTS
This work has made use of data obtained at the Thai Na-tional Observatory on Doi Inthanon, operated by NARIT.We are grateful to Dr. W.J. Tango for providing thedatabase of limb-darkening corrections, and to an anony-mous referee for valuable comments and references. AR ac-knowledges support from the ESO Scientific Visitor Pro-gramme.
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