The roAp star $\alpha$ Circini as seen by BRITE-Constellation

11 MB·

by  W. W. Weiss

Astronomy&Astrophysicsmanuscriptno.alCirArchiv (cid:13)cESO2016
January20,2016
The roAp star αCir as seen by BRITE-Constellation(cid:63)
W.W.Weiss1†(cid:5),H.-E.Fröhlich2,A.Pigulski3†(cid:5),A.Popowicz4†(cid:5),D.Huber8,R.Kuschnig1†(cid:5),A.F.J.Moffat5†(cid:5),J.
M.Matthews6†,H.Saio10,A.Schwarzenberg-Czerny11†(cid:5),C.C.Grant7,O.Koudelka9†,T.Lüftinger1,S.M.
Rucinski12†(cid:5),G.A.Wade15†(cid:5),J.Alves1†,M.Guedel1†,G.Handler11†(cid:5),St.Mochnacki12†(cid:5),P.Orleanski13†,B.
Pablo5(cid:5),A.Pamyatnykh11†,T.Ramiaramanantsoa5(cid:5),J.Rowe14,G.Whittaker7(cid:5),T.Zawistowski13(cid:5),E.Zocłon´ska11(cid:5),
andK.Zwintz16†
1 UniversityofVienna,InstituteforAstrophysics,Vienna,Austria;e-mail:[email protected]
2 KleineStrasse9,D-14482Potsdam;Leibniz-InstitutfürAstrophysik(AIP),Potsdam,Germany;e-mail:[email protected]
3 AstronomicalInstitute,UniversityofWrocław,Poland;e-mail:[email protected]
6 4 InstituteofAutomaticControl,SilesianUniversityofTechnology,Gliwice,Poland;
1 5 Dept.dephysique,Universite´deMontre´al;
0 6 Dept.ofPhysicsandAstronomy,UniversityofBritishColumbia,Canada;
2 7 SpaceFlightLaboratory,UniversityofToronto;
8 SydneyInstituteforAstronomy,UniversityofSydney,NSW2006,Australia;SETIInstitute,MountainView,CA94043,USA;
n
StellarAstrophysicsCentre,AarhusUniversity,AarhusC,Denmark
a
9 GrazUniversityofTechnology,Austria;
J
10 AstronomicalInstitute,GraduateSchoolofScience,TohokuUniversity,Sendai,Japan;
9 11 NicolausCopernicusAstronomicalCenter,Warsaw,Poland;
1 12 Dept.ofAstronomyandAstrophysics,UniversityofToronto,Canada;
13 SpaceResearchCenter,Warsaw,Poland;
R] 14 NASAAmesResearchCenter;
15 Dept.ofPhysics,RoyalMilitaryCollegeofCanada,Ontario,Canada;
S 16 InstituteforAstro-andParticlePhysics,UniversityofInnsbruck;
.
h
Received/Accepted
p
-
o
ABSTRACT
r
t
s We report on an analysis of high-precision, multi-colour photometric observations of the rapidly-oscillating Ap (roAp) star αCir.
a TheseobservationswereobtainedwiththeBRITE-Constellation,whichisacoordinatedmissionoffivenanosatellitesthatcollects
[
continuousmillimagnitude-precisionphotometryofdozensofbrightstarsforupto180daysatatimeintwocolours(≈JohnsonB

1 andR). standsforBRightTargetExplorer.TheobjectαCiristhebrightestroApstarandanidealtargetforsuchinvestigations,facil-
¯
v itatingthedeterminationofoscillationfrequencieswithhighresolution.Thisstarisbrightenoughforcomplementaryinterferometry
3 andtime-resolvedspectroscopy.Four satellitesobservedαCirfor146dor33rotationalcycles.Phasingthephotometryaccordingto
3 the4.4790drotationalperiodreveals¯qualitativelydifferentlightvariationsinthetwophotometricbands.Thephasedred-bandpho-
8 tometryisingoodagreementwithpreviously-publishedWIREdata,showingalightcurvesymmetricaboutphase0.5withastrong
4 contribution from the first harmonic. The phased blue-lband data, in contrast, show an essentially sinusoidal variation. We model
0 bothlightcurveswithBayesianPhotometricImaging,whichsuggeststhepresenceoftwolarge-scale,photometricallybright(relative
. tothesurroundingphotosphere)spots.Wealsoexaminethehigh-frequencypulsationspectrumasencodedinthe photometry.Our
1 analysisestablishesthestabilityofthemainpulsationfrequencyoverthelast≈20years,confirmsthepresenceoffre¯quency f ,which
7
0
wasnotdetected(orthemodenotexcited)priorto2006,andexcludesquadrupolarmodesforthemainpulsationfrequency.
6
1 Key words. Asteroseismology–Stars:chemicalpeculiar,oscillation,rotation,spots,fundamentalparameters–Starsindividual:
: αCir(HR5463,HD128898)
v
i
X
r1. Introduction panion is faint enough and distant enough from the primary to
a be ignored in the following study.) The primary component of
αCir(HD128898,HR5463)isabinarysystemwhoseprimary
αCir was discovered as the fifth known rapidly oscillating Ap
componentisanA7VpSrCrEustar(V=3.19)withaK5Vcom-
(roAp)starin1981byKurtz&Cropper (1981),followedbya
panion(V=8.47)separatedby16(cid:48)(cid:48)(Wayman 1962).(Thecom-
frequencyanalysisof47hoursofhigh-speed,ground-basedpho-
Sendoffprintrequeststo:[email protected] tometry(Kurtz,Allen&Cropper 1981).Theseauthorspointed
(cid:63) BasedondatacollectedbytheBRITE-Constellationsatellitemis- toavariationintheamplitudeoftheprincipalpulsation,whichis
sion,built,launchedandoperatedthankstosupportfromtheAustrian suspectedtobeduetorotationalmodulation.PulsationofαCir
Aeronautics and Space Agency, the University of Vienna, the Cana- was confirmed by Schneider & Weiss (1983) and soon after,
dianSpaceAgency(CSA),theFoundationforPolishScience&Tech- Weiss&Schneider (1984)presentedthefirsttime-resolvedsi-
nology (FNiTP MNiSW), and National Centre for Science (NCN). multaneous multi-colour photometry of αCir in the Walraven
†MemberoftheBRITEExecutiveScienceTeam(BEST). system. The goal was pulsation mode identification (attempted
(cid:5)MemberofthePhotometryTigerTeam(PHOTT).
Articlenumber,page1of10
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alsobyKurtz&Balona (1984))basedonfrequencymultiplets theConstellationduringtheαCirrun.Asaconsequenceofthis
andamplitudechanges. dynamic, instructional operational environment, the αCir data
The first simultaneous time-resolved photometry and spec- setisnaturallysomewhatcomplicated.
troscopy of αCir were obtained at ESO by Schneider & Weiss Thedatacover25March–8August2014:146days,corre-
(1989). This yielded only marginal evidence for radial veloc- spondingtonearly33stellarrotationalcycles(seethenextSec.3
ityvariationsfortwoCaIlinesandtheauthorsremarkedonthe fordetails).
very uncertain value on the rotation period for this star (rang- αCirwasobservedinthebluebyBAbfor131daysandBLb
ingintheliteraturefromoneto12days).Fiveyearslater,Kurtz for 26 days; in the red by UBr for 145 days, and BTr for six
et al. (1994) provided a robust value of the rotation period (P days. The light curves consist of nearly 44000 blue exposures
(cid:39) 4.46d). Another 15 years elapsed before the first light curve and 69000 red exposures, each of duration 1s in both colours.
samplingthefullrotationcycleofαCirwaspublishedbasedon The sampling time was 21.3s, which is set by the amount of
WIREspacephotometry(Bruntt etal. 2009). processingtimeneededbetweenconsecutiveexposuresandthe
The quantity and quality of data, and the sophistication of maximum amount of data that could be stored on board owing
models, has improved dramatically over the subsequent years tolimiteddownloadcapacityatthetime.
(e.g.Kurtz etal. (1994);Audard etal. (1998);Balona&Laney αCirwasobservedduringindividual orbitsfor5to30min,
¯
(2003);Kochukhov etal. (2007);andmanyreferencestherein). depending on target visibility, the Earth Exclusion Angle (an-
Themostcompleteandrecentsummaryofourknowledgeabout gular distance between the illuminated limb of the Earth and
thepulsationofαCirispresentedbyBruntt etal. (2008,2009) the star-tracker field of view), the required warm-up period for
andofthecomplexatmosphericstructureandspectralsignatures thestartrackersafterreacquisitionofthetarget,andpassagesof
of pulsation by Ryabchikova et al. (2007) and Kochukhov et thesatellitesthroughtheSouthAtlanticAnomaly(whenhigher
al. (2009). fluxes of cosmic rays prevent useful signal from the star track-
αCirwasincludedinproposalssubmittedin2009and2010 ers). There were also brief interruptions of science data collec-
by several authors of this paper, responding to an Announce- tionwhendatawerebeingtransmittedtogroundstations.
ment of Opportunity for targets to be observed by BRITE- ThedailydatatransferratetogroundstationsinEuropewas
Constellation.Proposal#05(WW)focusedonroApstars,#19 lessthanplannedbecauseofheavyinterferencewithunidentified
(DH) on 50 bright stars with the most accurately known Hip- transmitters on the ground, which is particularly serious during
parcos parallaxes, and #25 (TL) on the rotation of chemically theCentaurusfieldobservations.Forexample,datatransferfrom
peculiarstars(inparticular,possiblechangesinrotationperiod). BAbtothestationinGraz,Austria,waslimitedtoamaximum
of15minperorbit.
2. BRITE-Constellationphotometry
2.2. Reduction: standardpipeline
The BRITE-Constellation is a coordinated mission of five ¯
DuringthecommissioningofBRITE-Constellation,thepartic-
nanosatellites located in low Earth orbits, each hosting an op-
ular challenges of on-orbit photometry were assessed. To de-
tical telescope of 3cm aperture feeding an uncooled CCD, and
velop an efficient pipeline for fast and optimum extraction of
observing selected targets in a 24◦ field of view (Weiss et al.
thephotometry,aPhotometryTigerTeam(PHOTT)wasestab-
2014).Eachnanosatisequippedwithasinglefilter;threehave
lished, consisting of three groups working independently and
aredfilter(∼620nm)andtwohaveabluefilter(centralwave-
pursuingdifferentprocessingandreductionstrategies.
length (∼420nm). The satellites have overlapping coverage of
Issues investigated included: CCD radiation defects (warm
the target fields to provide two-colour, time-resolved photome-
columns, hot and cold pixels), CCD temperature variations,
try.
charge-transfer inefficiencies, pixel-to-pixel sensitivity varia-
ThedetectorisaKAI-11002MCCDwith11million9×9µm
tions and intra-pixel inhomogenities, pointing errors, complex
pixels,a14-bitA/Dconverter,gainofabout3.3e−/ADU,anda
pointspreadfunctions(PSF)varyingoverthe24◦ fieldofview
darkcurrentof1e−/sat+20◦C.Thesaturationlimitofthepixels
and during long observing runs, identification of defective im-
atthistemperatureis∼ 13000ADU,andtheresponseislinear
ages(e.g.incompletePSFinasub-raster).Competingreduction
uptoabout8000ADU.Thepixelsizeis27.3(cid:48)(cid:48),projectedatthe
methodsemployedPSFfittingandaperturephotometryaswell
sky.
as various threshold criteria for elimination of bad data points
Thefivenanosatsaredesignated-Austria(BAb),Uni(UBr),
¯ ¯ (outliers), various fit-quality parameters, median vs. mean, etc.
-Lem (BLb), -Hewelius (BHr), and -Toronto (BTr), where the
¯lastletterindic¯atesthefilteronboardt¯hesatellite("b"=blue,"r" ThemethodswillbedescribedindetailbyPopowicz etal. (in
prep.).
= red). A sixth nanosat, -Montréal (BMb), did not detach from
¯ ThisinvestigationofαCirisbasedonthereductionpipeline
itslaunchvehicle.ThenanosatsBbandUBrwerelaunchedfirst,
developed by PHOTT member Adam Popowicz via aperture
followedbyBLb,BTr,andBHr.
photometry. Figure1 illustrates the impact of two optimisation
parameters on the light-curve quality. The parameters are the
2.1. αCirphotometry thresholdemployedforbad-pixelidentificationinthemeandark
frame (T ) and the aperture radius. To assess the light-curve
bad
αCir was one of the targets in the Centaurus field, the sec- quality,wecomputedthemedianabsolutedeviations(MAD)of
ondlong-termpointingofBRITE-ConstellationaftertheOrion results obtained for individual satellite orbits, as a robust mea-
field.Theearlydatawereobtainedduringsciencecommission- sureofscatterinthepresenceofoutliers.Thefinalqualitymea-
ing of the mission, which meant interruptions in science data sure(Q )isthemedianofMADsdefinedasfollows:
M
collectionforengineeringtests.Evenso,significantgapsinthe
timeserieswereinfrequent,causedmainlybyaccidentalspace-
(cid:40) (cid:41)
craft mode changes from fine-to-coarse pointing (or tumbling) MAD
Q =median √ i , (1)
withrecoverytimesshorterthan48hours.Newnanosatsjoined M N
i
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Weiss,Fröhlich,Pigulskietal.:roApstarαCir
x 10−3
2.6
T = 50 [ADU]
bad
2.4
ag] Tbad = 100 [ADU]
) [mM2.2 Tbad = 150 [ADU]
Q T = 200 [ADU]
bits ( 2 bad
or
n
D i 1.8
A
M
an 1.6
di
e
M
1.4
1.2
3 4 5 6 7 8 9 10
Circular aperture radius [pix.]
Fig.1.OptimisingpipelineparametersforUBrdata:badpixelelimina-
tion(T )andapertureradius.
bad
where MAD and N denote the median absolute deviation and
i i
thenumberofmeasurementsinthei-thorbitwithatotalnumber
oforbitsN .
O
Fig.3.Correlationsbetweenresidualmagnitudesandfourinstrumental
parametersofBAb.ThecontinuouslinefollowstheAkimainterpola-
BTr
tionofbinaverages.
UBr
3.5
While removing more outliers results in smaller scatter, it
also results in fewer data points. Consequently, the signal de-
e
ud tection threshold in a periodogram, which depends both on the
nit BAb numberofdatapointsandtheirscatter,canhaveaminimumasa
Mag4.0 functionofα.Weadoptedoptimumvaluesofα = 0.8forBAb
and UBr data, 0.5 for BLb, and 0.3 for BTr data, accepting a
smallincreaseinnoiselevel.Thestrongestintrinsicstellarvari-
BLb
ations (the rotation frequency f , 2f and the main pulsation
rot rot
4.5 frequency near 6.5min, f ) were filtered from the data prior to
1
760 780 800 820 840 860 880 theoutlierremoval.
HJD 2456000.0+
Inthenextstep,wedecorrelatedthedatawithtemperature,
Fig.2.PipelinelightcurvesofαCirforthefours.NoteoffsetsforBTr followedbyadecorrelationwiththepositionofthestellarcen-
¯
andBLbandthelargerscatterforthebluedata. tres in both coordinates and orbital phase, as is illustrated in
Fig.3forBAbdata.Aftereachdecorrelation,theoutlierremoval
Optimisation is the most time-consuming stage of this wasrepeatedwiththepreviouslyusedαparameter.
pipeline, so only four values for T (50, 100, 150, and 200 The next step towards the final light curve was rejection of
bad
ADU) and eight values for the aperture (ranging from 3 to 10 the worst orbits, based on a single threshold for a given . Al-
pixels) were adopted. This seems sufficient to optimise param- thoughitmaynotbeobviousinFig.2,therearefeworbits¯that
etersfortheαCirdata(seeminimainoptimisationcurvespre-
sentedinFig.1).Thefinalpipelinelightcurvesfromthefours
¯
thatobservedαCirareshowninFig.2. 60
2.3. Additionalreductions ag] 50
m
m
Figure2 reveals that the pipeline reduction does not produce a n [ 40
trulycleanlightcurveinthiscase,andthatsomeoutliersandin- o
strumentaleffectshavesurvivedthepipeline.Thepipelinedata viati 30
e
werefine-tunedinthreesteps:(i)removalofoutliers,(ii)decor- d
d
relations, and (iii) removal of the satellite orbits that returned ar 20
¯ d
the poorest quality of photometry. (More details on fine-tuning n
a
pipeline-reduceddatacanbefoundintheBRITEDataAnalysis St
¯Cookbookathttp://brite.craq-astro.ca/doku.php?id=cookbook.) 10
First, outliers were eliminated based on a Generalized Ex-
0
treme Studentized Deviate (GESD)test (Rosner 1983) applied 760 780 800 820 840 860 880
HJD 2456000.0+
todataobtainedduringasingleorbitofeachsatellite.Thenum-
ber of identified outliers depends on a single parameter α, in- Fig. 4. Standard deviations for individual orbits: BAb (open circles),
creasingwithlargerα. UBr(dots),BLb(x),BTr(+)
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BTr
UBr
3.5
e
d
u
nit
g
a
M
4.0
BAb
BLb
760 780 800 820 840 860 880
HJD 2456000.0+
Fig.5.αCirlightcurvesafterremovaloftheworstorbitsandoutliers
anddecorrelation.BTrandBLbdataareoffsetforbettervisibility.
Fig.6.RotationofαCirobservedbythered-sensitive(top)andblue-
returnedphotometryofpoorquality.ThisisbetterseeninFig.4,
sensitive (bottom) s, respectively, with P =4.4790d. Phase-bin aver-
whichshowsthestandarddeviationsinmmagforindividualor- ¯ rot
ageswith1-σerrorsaregiventogetherwiththetheoreticallightcurve
bits.Basedonthis,thechosenthresholdsare:26mmagforBAb,
obtainedfortherespectivespotmodel(seeSec.4).Phases0to1also
25mmagforBLb,17mmagforUBr,and8mmagforBTr. showthebinnedoriginal datawithanoverallr.m.s.noiseof9mmag
Comparing Fig.5 with Fig.2 illustrates the improvements fortheredandof15mmag¯ forthebluelightcurve.
achieved by fine-tuning the original pipeline data. The system-
aticdecreaseofBAbmagnitudes(forexample,earlyintheob-
servingrunandseeninFig.2)disappearedbecauseitwascaused
-5
by CCD temperature variations (Fig.3, upper left). After fine-
tuning,atotalof61988redand34592bluedataremain.
-4
3. RotationofαCir
-3
ThefirstindirectevidenceoftherotationperiodofαCirwasre- ntal)
ported by Kurtz et al. (1994) who deduced a rotation period me
u -2
of about 4.46 days from the amplitude modulation of the star’s nstr
mainpulsationmode.Thisinitialestimatewasrefinedto4.4790 g (i
days (Kurtz, op.cit) through photometry collected over the fol- mma -1
lowing 12 years from various observing campaigns. αCir was
observedbytheWIREsatellitestartrackerforatotalof84days
0
duringSeptember2000–July2006,supportedbyground-based
Johnson B photometry from SAAO. These data led to the first
rotationlightcurveofαCir(Bruntt etal. 2009). 1
BRITE-Constellation takes the analysis of αCir to a new -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
stage compared to WIRE by providing space-based photometry Phase (WIRE to HJD 2453937.2086)
intwocolours. Thephotometryis plottedinphasewiththe ro-
Fig.7.RotationofαCir.Greencircles:WIRE-2006Julydata(Fig.2
tationperiodinFig.6.Thenoiselevelforthebluedataislarger,
of Bruntt et al. (2009)). Dots: UBr and BTr data (red filter) with a
mostlyduetoproblemswiththeBAbstartrackerandasaresult
phasebinningof0.01(smallreddots)andof0.05(largeblackdots).
ofthespectraltype,whichproducesasmallercountrateforthe
The datawerescaledtofittheamplituderangeofWIREandshifted
blue s compared to the red BRITEs. The rotation light curves inph¯asetobecompatiblewiththedifferentreferencetimeinHJDfor
areob¯viouslydifferentinthetwocolours.Whileonemaximum WIREand.
atapproximatelyphaseφ = 0.8appearsinbothfilters,thesec- ¯
ond maximum in red at about φ = 0.2 is not present in blue
(seeFig.6).Thisdifferenceissignificant,likelyindicatingvery
peculiarspotpropertiesandposingachallengetointerpretphys-
4. Bayesianphotometricimaging(BPI)
ically.
Forcomparison,wedigitisedFig.2ofBruntt etal. (2009)
and,inourFig.7,plottedtheir100WIREdatapointsfromJuly Apstars,suchasαCir,arewellknowntoexhibitsurfaceabun-
2006alongwithour reddata(similarinbandpasstotheWIRE dance nonuniformities (abundance spots) produced as a conse-
data). We conclude t¯hat the rotational modulation pattern has quenceofchemicaldiffusioninthepresenceoftheirstrongmag-
been stable between 2006 and 2013/14. When comparing the neticfields.Asdescribedby,forexampleKrticˇkaetal. (2009),
scatter,oneshouldkeepinmindthat(1)BRITE-Constellation photometric variability of these stars is believed to result from
data are based on 1s integrations sampled every 21s, while fluxredistributionprincipallybecauseofvariablelineblanketing
WIRE data were obtained twice per second, co-added in 15s modulated by stellar rotation. αCir exhibits obvious photomet-
bins; and (2) the collecting area of the WIRE star-tracker tele- ricvariabilityontherotationaltimescalethatweinterprettobe
scopeisthreetimeslargerthanthe telescope. indicativeofsuchspots.
¯
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4.1. Likelihoodestimate Table 1. Parameters for circular spots for the -red, WIRE, and -blue
¯ ¯
solutions,assumingtwodarkspots.Welistexpectationvaluesand90%
TheBayesianphotometricimaging(BPI)techniquetoconstruct credibility limits for the central longitude (λ), latitude (β), and radius
aspotmodelbasedonalightcurvewellsampledintimeisde- (γ). Radii and their uncertainties are modelled for a spot intensity of
scribed in detail by Lüftinger et al. (2010a). Below we only 60%oftheunperturbedphotosphere.
commentontheconstructionofthelikelihoodfunction,vitalfor
Parameter -red WIRE -blue
anyparameterestimation.
¯ ¯
To save computation time, the fine-tuned data were com- firstspot
binedintobinswithamaximumwidthof36min.Thisbinwidth λ 74◦.3+2.4 89◦.4+0.8 209◦+24
corresponds to roughly one-third of the orbital period of one −2.4 −0.7 −29
satellite. The time difference between adjacent points within a β −72◦.7+5.5 −2◦.8+3.4 36◦+41
−5.2 −3.7 −33
¯
bin does not exceed 15min. With these chosen bin constraints, γ 58◦.2+6.2 8◦.0+0.4 6◦+2
nobincontainsfewerthantendatapoints.Eachofthe1368red −6.3 −0.3 −2
secondspot
and1200bluebinswasassignedaweightaccordingtothenum-
berofcontributingdatapointswithinabinandusedfortheBPI λ 248◦.5+6.2 263◦.4+1.3 118◦+12
−6.2 −1.3 −14
proceduredescribedbelow. β 6◦.0+44.8 −18◦.7+2.9 −24◦+25
We assume the residuals, deviations between observation −30.8 −3.1 −35
and model, are Gaussian-distributed, i.e. measurement errors γ 6◦.0+1.8 8◦.3+0.7 16◦+15
−2.2 −0.7 −11
augmentedbysystematic(model)errors.Toenhancerobustness, residuals ±2.1 ±0.14 ±4.8
thevarianceoftheresidualswasassumedtobeunknownandre-
garded as a mere nuisance parameter. The Gaussian likelihood
function was integrated by applying Jeffreys’ prior (Jeffreys
us to consider more than two spots. The WIRE data do contain
1961).Inourcase,theimproper(notnormalisable)priorvaries
more information, which we plan to explore in a future study.
withthereciprocalofthevariance.Wetookintoaccountthatthe
binned data points have different weights. This error-integrated Themainpicture,however,veryprobablywillremainthesame.
likelihoodwasthenintegratedanalyticallyoverallpossiblemag- In our model, two types of circular spots are allowed: dark
nitudeoffsets. spots with a brightness of 60% of the brightness of the undis-
Theresultinglikelihoodisafunctionofthedataalone,given turbedphotosphereandbrightspotswithabrightnessof125%.
asetofparametervalues.Itisacomfortingfeatureofthistype The latter values are similar to what has been reported for the
of data analysis that the error variance and any magnitude off- spots of HD50773 by Lüftinger et al. (2010a), based, as is
set, although they remain undetermined, can be ignored, which already mentioned, on an independent analysis of space-based
reducesthenumberoffreeparametersandenhancesrobustness. photometryandground-basedDopplerimaging.
To reduce the number of free parameters as much as pos- The reason for a fixed common spot brightness is the un-
sible, we took the star’s inclination to be i = 36◦. This value avoidable degeneracy between spot area and spot brightness,
resultsfromthemeasuredprojectedrotationalvelocity,v·sin(i), whichpreventstheMCMCmethodtoconvergetoarelaxedso-
theassumedvalueofthestellarradius(Bruntt etal. 2008),and lutionoftheposteriorprobabilitydensitydistribution.Thedata
therotationalperiodof4.4790days(Kurtz etal. 1994).Asthe simply do not constrain both parameters independently. Hence,
limb-darkeningcoefficientisunknown,itwasregardedasanui- wehadnochoicebuttoprescribethespotbrightnessparameter,
sanceparameterforthepresentstudy.Forthehigh-qualityWIRE butthesearebasedonexamplesintheliterature.Asatest,were-
data,however,inafollow-upstudyitmightalsobepossibleto peatedthemodellingwithaκarbitrarilysetto1.5andexpected
extractthemarginaldistributionofthecoefficientforlinearlimb the inferred spot size to be reduced by about 50%. Indeed, we
darkening. foundafactorof1.84,whichcorrespondstoaspotsizereduced
TheoutcomeofaBayesianparameterestimationisthepos- to0.54oftheoriginalsize.Interestingly,thisspotsizereduction
terior probability distribution in an high-dimensional parame- with increased kappa only holds for the spot that is fully visi-
terspace.Directnumericalbrute-forceintegrationoftenrequires ble. The large spot at the south pole, which basically is visible
prohibitivelylargecomputingresources,soweusedtheMarkov mostofthetime,butneverentirely,isonlyreducedby4%andits
chain Monte Carlo method (MCMC; cf. Press et al. (2007)). centremoves6degreestowardsthepole.Itishardlynecessaryto
The likelihood mountain in the six-dimensional space is ex- stressthatitwouldmakeevenlesssense(fromthedataanalysing
ploredbyupto64Markovchains.Inarelaxedstate,eachparam- point of view) to consider spots with individual surface bright-
eter’smarginaldistributionisrevealedbycountinghowoftenan nesses.Themodelspotparametersmustbethereforeconsidered
elementinparameterspaceisfrequentedbythechains. withreservationandtakenratherasanorder-of-magnitudeesti-
A marginal distribution describes a parameter’s probability mate.
distributionirrespectiveofthevaluesofalltheotherparameters, The following parameters were estimated for each circular
i.e. disregarding correlations between parameters. These distri- spot: the central longitude (λ), latitude (β), and angular radius
butions are reflected in Tables1 and 2 by presenting the corre- (γ). The longitude increases in the direction of stellar rotation,
spondingcredibilityintervals.ItisanadvantageoftheBayesian andthezeropointisthecentralmeridianfacingtheobserverat
approachthatparameteraverages,suchasexpectationormedian thebeginningofthetimeseries(HJD=2456742.188).
as well as credibility intervals, are deduced from the measured Table1and2summarisewhatwecansayaboutthelocations
dataalone. and sizes of spots on the surface of αCirbased on a Bayesian
analysis of the red and blue light curves and the WIRE light
¯
curve. The importance parameter,justifying the attribute “first"
4.2. Surfacespotmodels
and “second" to a spot, indicates the impact on the light curve.
We restrict our discussion to two-spot models since the infor- Listedareexpectationvaluesand90%credibilityintervals(not
mation content of the presently available data does not enable tobeconfusedwith±1σlimits).
¯
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Table2.ThesameasTable1,butassumingbrightspots.Notwo-spot and -red data, but not in the -blue data, which have the lowest
solutionwasobtainedforthe-bluedata.Radiiandtheiruncertaintiesare ¯ ¯
precision.
¯
modelledforaspotintensityof125%oftheunperturbedphotosphere.
Aninhomogeneoussurfacedistributionofelements,likeSi,
Cr,andFe,areknowntocausevariationsinthelightcurvesof
Parameter -red WIRE -blue
¯ ¯ many Ap stars detectable as bright spots in visual photometry
firstspot (e.g.Lüftinger etal. 2010a,b;Krticˇkaetal. 2009,2012,2015;
λ 326◦.5+7.8 356◦.9+0.9 356◦+8 Shulyaketal. 2010).Thisisastrongargumenttofavourbright
−7.4 −0.8 −8 spotsolutionsoverdarkspotsolutions,ifnootherinformationis
β 31◦.7+25.1 25◦.9+4.3 34◦+27
−21.9 −4.4 −23 available. The size of abundance spots is independent of wave-
γ 9◦.6+2.0 13◦.7+1.4 8◦+1 length, which is what we find for the bright spot model within
−2.0 −1.4 −1
twicethecredibilitylimits.
secondspot
Bayesian techniques provide an infinite number of feasible
λ 172◦.2+7.3 186◦.1+2.0 two-spot solutions, but these differ in credibility. A main prob-
−7.6 −2.0
β −73◦.8+5.2 −82◦.8+1.4 nosolution leminourcaseistheskewnessofthemarginaldistributionfor
−5.3 −1.5 theparameters,inparticular,forthe data,asisevidentfromthe
γ 64◦.2+−77..32 85◦.2+−43..46 asymmetric90%credibilityintervals¯,whichisalsolistedinboth
residuals ±2.1 ±0.13 ±4.9 tables. The focusof ourinvestigation is onthe expectation val-
uesoftheparameters’marginaldistributions.Suchaspotmodel
is,inacertainsense,themostrepresentative,butbecauseofthe
posterior’s skewness, this model may differ from the globally
mostprobablemodel(the‘best-fitmodel’).
4.3. SignificanceofBSImodels
In the previous Section we tried to model the observed light
curvesobtainedindifferentcolourswithcircularareasatthestel-
larsurface(spots),whichmanifestthemselvestotheobserveras
periodically varying disk averages obtained at various rotation
phases. Stellar surface structures can be very complicated be-
cause they depend on temperature, gravity, dynamics in the at-
mosphere,elementabundances,andmagneticfield,allofthese
as a functions of optical depth. In addition, insufficient knowl-
edge of atomic and molecular transition properties and energy
level splittings in the presence of a magnetic field can have se-
rious effects on how such surface areas are interpreted by ob-
servers.
Fig.8.Mapsofbrightspotsbasedon blue, red,andWIREaccording Thetransformationofaone-dimensionalfunction,thelight
¯ ¯
totheparametersgiveninTable2.Tworotationphasesshown(topand curve, into a two-dimensional surface map obviously requires
bottom)differby180◦.TheBayesiantechniquecannotidentifyaspot
simplifying assumptions. An adjustable model constrained by
at the stellar south pole with sufficient probability for the -blue data,
¯ disk-averaged flux measurements, obtained with three broad-
probablybecauseofalowerphotometricaccuracy.
bandfiltersatadiscretesetofrotationphases,cannotrepresent
the complex physics and chemistry of a stellar atmosphere, but
canindicatelocationsofinhomogeneities.Unfortunately,inthe
presentinvestigationweonlyhavealimitedamountofinforma-
Acomparisonofthetablesshowsthatdarkandbrightspots
tionavailableforαCirtomapthecomplexsurface.Photometric
individuallyfittheBRITE-ConstellationandWIREdataequally
surfacemodelscannotrecoverinformationaboutpropertiessuch
well, i.e. we find similar credibility limits. The model light
asabundancesandtemperature,buttheycanindicateareaswith
curves (full lines in Fig.6) look very much the same and give
inhomogeneities at the stellar surface. In addition from consis-
thesameresidualstotheobservations,regardlessofwhetherthe
tency arguments, they can indicate a preference for flux excess
spotsaredarkorbright.However,importantdifferencescometo
ordepressionwithnoreferencetoanunderlyingphysics.There-
lightinadetailedexamination.
fore, a realistic starting point is a model, which is as simple as
Thesurfacemappingfortwodarkcircularspotswiththered possibleandistestedagainsttheobservations,whichinourcase
and WIRE data requires a separation of 180◦ in longitude with islightcurves.
¯
spotsonoppositesidesofthestar.Twodarkspots,whichfitthe TheBayesianapproachofferstwoattractivefeatures:(a)the
blue data,however,areseparatedbynearly90◦inlongitudeand quantitative comparison of models differing in the number of
¯
donotagreewiththeredmap.Thissuggeststhatbrightspotsare spotsand(b)thederivationofcredibilityintervalsforthemodel
amorerealisticfittotheentiredatasetthandarkspots. parametersfromtheposteriorprobabilitydistribution.Ourtwo-
We only find a spot model that agrees with WIRE and both spot model is sufficient to reproduce the photometry with the
data sets in the case of bright spots. However, only one bright best probability distribution possible so far. Adding more fea-
¯
spotcouldbedetectedinthe bluedata,whichisnotsurprising, tures may suggest a better visual representation of the light
consideringthedifferencesin¯theredandblue lightcurves(see curve,butconsideringthenoiselevelofthedata,increasedcom-
¯
Fig.6).Aschematicofwhatwebelieveisthemostrealisticsur- plexityreducestheover-allcredibilityofthemodel.Indeed,we
facemodelforαCir(seeTable2)isprovidedinFig.8.Thespot have investigated more complex models (e.g. three spots, dif-
close to the stellar south pole is credibly present in the WIRE ferentlimbdarkeningcoefficients,andspotsofdifferentbright-
Articlenumber,page6of10
Weiss,Fröhlich,Pigulskietal.:roApstarαCir
ness), but had to accept that all these additional model features main amplitude (=0.55mmag for f and our red s ) and give a
1
¯
did not increase the credibility. Moreover, with too many free justification for this value within the framework of the oblique
parameters involved, the method does not work because the pulsatormodel.
Markov chains do not converge to a well-constrained posterior ThemiddleandbottompanelsofFig.10showtheamplitude
probabilitydensitydistribution.Theonlyremedyareadditional spectra after pre-whitening the data by the dominant mode f
1
observationsthataccessnewparameterspace,suchashighspec- and we detect f in the -red data, while in both data sets f re-
7 6
tral and time-resolved spectroscopy and/or spectropolarimetry. mainsbelowthedetectio¯nthreshold(S/Nratioof∼4).Thisratio
Thelimitedamountofpresentlyavailabledata,theirqualityand correspondstoasignificancelimitof10−5.46,ortoa99.9%de-
physicalinformationcontentsimplydonotallowforamoreso- tectionprobabilityofatruesignal(Kuschnig etal. 1997).The
phisticatedspotmodelling,forexamplefordisentanglingκ and amplituderatiosareA(f )/A(f )=3.468(±0.007)forWIREand
1 7
sizeofspots. 2.51(±0.10)for red.Bruntt etal. (2009)speculatethat f and
6
¯
Nevertheless,ourpresentmodelservesasareasonablestart- f firstappearedbetween2005and2006andinterpretedthemas
7
ingpointformoresophisticatedmodellingofthesurfacestruc- consecutive overtones of a new pulsation mode. Unfortunately,
ture, for example based on future analysis of spectroscopic thenoiseleveloftheblue datadoesnotenableadetectionof f ,
7
and/or spectropolarimetric data. This expectation is supported whichwouldbehelpfulin¯discussingthepulsationmode.Ithas
bytheresultsofLüftinger etal. (2010a)forHD50773,where tobeprovenbyfollow-upobservationsthatindeedamodethat
essentially the same surface pattern was determined indepen- isdifferentinparitythan f hasbeenexcited.Anewmodeofthe
1
dently from Bayesian spot modelling of space-based photome- sameparitywouldhaveproducedafrequencyseparationthatis
try(CoRoT)andfromDopplerimagingmodellingofspectropo- twiceaslarge(seediscussioninBruntt etal. (2009)).
larimetricdata.Evenmoresignificantly,Alentjev&Mkrtichian Using the frequencies identified with SigSpec, we applied
(2010) report surface abundance maps of CrII in their prelim- Period04 (Lenz & Breger 2005) to calculate least-squares fits
inary Doppler imaging analysis, which support our model (= for frequency, amplitude, and phase to each light curve. For f
1
coursemapofinhomogeneities)derivedfromphotometry. wefixedthefrequencytothebest-fitvaluesfromthebluedata,
whichhashighersignificancethanthereddata.Uncertaintieson
allvalueswerecalculatedwithMonteCarlosimulations,which
5. Pulsationfrequencies,amplitudes,andphases
areimplementedinPeriod04.Thefinalvalues,uncertainties,and
ThepulsationspectrumofαCirshowsadominantmodewitha significancesarelistedinTable3.
periodof∼ 6.5min(f ),whichisrotationallysplitintoatriplet
1
byrotation(Kurtz etal. 1994).Fouradditionallow-amplitude
5.2. Amplitudesandphases
frequencies (f to f ), attributed to roAp oscillations, were re-
2 5
portedbyKurtz etal. (1994).UsingWIREdata,Bruntt etal. The pulsation amplitude ratio for f measured from
1
(2009)confirmedtwooftheselow-amplitudemodes(f4and f5), observations is AB/AR = 3.15 ± 0.33, compared to
while f2and f3remainedundetected. ¯AB/AWIRE = 2.32 ± 0.11 by Bruntt et al. (2009) and
Bruntt etal. (2009)alsoreporteddetectionoftwonewfre- A /A = 2.28 ± 0.26 by Kurtz & Balona (1984). Formally,
B V
quencies (f6 and f7) that are symmetrical to f1, which had not all values agree within 2σ, and the amplitude ratio seems to
beenseeninpreviousground-basedcampaignsnorintheWIRE confirm the conclusion by Bruntt et¯al. (2009) that the WIRE
2000and2005data. bandpassislikelyclosetotheV band.
The mentioned pulsation amplitude ratio is consistent with
the relation among photometric amplitudes in different photo-
5.1. Frequencies
metric bands known from previous ground-based observations,
We first removed the contribution of rotational variability and i.e.amplitudedecreaseswithincreasingwavelength(e.g.Weiss
instrumental effects (1d−1, 2d−1, orbital frequency and its har- &Schneider 1984;Kurtz&Medupe 1996).
monics) from the light curves with a multi-sine fit provided by Consideringtheamplituderatiosfor f between andWIRE,
1
¯
Period04(Lenz&Breger 2005).Next,wecalculatedamplitude the expected amplitudes for f to f found by WIRE would be
4 6
spectra and estimated the statistical significance of frequencies 0.04to0.12mmagintheredfilterand0.12to0.40mmaginthe
via SigSpec (Reegen 2007, 2011), which has previously been blue filter. Given a typical noise of ∼ 0.06 mmag for red and
extensivelyappliedtospace-basedphotometryfromMOST,in- ∼0.13mmagforblue data,weconcludethatournon-detect¯ions
¯
cludingroApstars(Gruberbaueretal. 2008;Huberetal.2008). are consistent with the WIRE results by Bruntt et al. (2009).
Figure 9 shows the amplitude spectra of the red and blue data However, the amplitude ratio for f may not necessarily apply
1
centred on the frequency range where oscillations had alr¯eady for f and f ,whichmusthaveadifferentsphericaldegreethan
4 5
been observed in αCir. The dominant mode near ∼ 6.5min f , f and f ,ifthelargefrequencyseparationclaimedbyBruntt
1 6 7
(∼ 2442µHz)isclearlydetectedinbothdatasets.Asexpected, etal.(op.cit.)iscorrect.
the amplitude is significantly higher in the blue than in the red Kurtz&Balona (1984)andBruntt etal. (2009)noticeda
filter. slightphaseshiftofφ −φ =−7.4±5.1◦andφ −φ =5.8±
V B WIRE B
ThetoppanelsofFig.10showaclose-upof f demonstrat- 1.3◦. Using the pulsation phases calculated from the unbinned
1
ingthattherotationallysplitsidelobesremainundetectedinthe blue and red light curves (calculated at a fixed frequency f ),
1
data.Thisisnotduetotheremovaloftherotationalvariability the observatio¯ns yield a phase shift of φ −φ = 10.6±5.9◦,
R B
¯ ¯
from the light curve, since the multiplet is caused by rotational whichisconsistentwithpreviousresults.
amplitudemodulationof f asaconsequenceoftheobliquepul-
1
sator model (Kurtz & Shibahashi 1986). The apparent contra-
6. Discussion
dictionofan f amplitudechangingwithrotationperiodandthe
1
lackofrotationsidelobesseeninthefrequencyspectrumofour –Rotation:Our reddata(similartoaJohnsonRbandpass)con-
¯
data is due to very small amplitudes. Kurtz et al. (1994) esti- firmtherotationperiodof4.4790 daysandthelightcurvechar-
mated these side-lobe amplitudes to be about one-tenths of the acteristicsofαCirdeterminedbyWIRE(similartoJohnsonV),
Articlenumber,page7of10
A&Aproofs:manuscriptno.alCirArchiv
Red Blue
0.7 2.0
SSiigg==55..4466 SSiigg==55..4466
0.6
WWIIRREE WWIIRREE
) )
g g 1.5
a 0.5 a
m m
m m
0.4
( (
e e 1.0
ud 0.3 ud
mplit 0.2 mplit 0.5
A A
0.1
0.0 0.0
2200 2300 2400 2500 2600 2200 2300 2400 2500 2600
Frequency (µHz) Frequency (µHz)
0.30 0.7
0.25 0.6
) )
g g
a a 0.5
m 0.20 m
m m
0.4
( (
e 0.15 e
ud ud 0.3
mplit 0.10 mplit 0.2
A A
0.05 0.1
0.00 0.0
2200 2300 2400 2500 2600 2200 2300 2400 2500 2600
Frequency (µHz) Frequency (µHz)
Fig. 9. Amplitude spectrum of the red (left panels) and blue (right panels) light curves after removing rotational variability and instrumental
effects.Thetoppanelsshowamplitudespectraofthedata,whilethebottom¯panelsshowamplitudespectraafterpre-whiteningofthedominant
pulsationmodenear∼2442µHz.Thesidelobesseeninthetoppanelcorrespondtotheorbitalfrequencyofthesatellites.Verticaldottedlinesin
eachpanelarepublishedWIREfrequenciesbyBruntt etal. (2009),whiletheredhorizontallinesshowaspectralsignificancecorrespondingto
afalse-alarmprobabilityof10−5.46(orS/N∼4).
showingtwomaximaataboutφ=0.2and0.8inourFig.6.This Table3.αCirpulsationfrequenciesextractedfrom data
¯
agreementiscontrastedbyour bluedata(similartoJohnsonB),
whichshowonlyonemaximum¯ ataboutφ=0.7. Data Frequency Amplitude Phase Sig
This profound difference in the shape of light curves ob- (µHz) (mmag) (0-1)
Frequency f
tained in different filters has not been seen before and would 1
red [ 2442.0574 ] 0.545(47) 0.191(14) 33.2
normally cast doubts on the reliability of our blue data. How- ¯
blue 2442.0574(31) 1.72(10) 0.165(09) 63.1
ever,strongsupportisprovidedby: W¯IRE 2442.0566(2) 0.652(5)
i)RVmeasurementswhichareconsistentwitharotationphase Frequency f
7
plot having only one maximum (Mkrtichian & Hatzes, private red 2472.2401(88) 0.249(43) 0.057(32) 6.8
¯
communication); blue – – – –
¯
ii) magnetic field measurements, which also indicate a single- WIRE 2472.2272(5) 0.188(5)
wave variation of the magnetic field (Kochukhov, private com-
munication). Notes:Forthered¯data(≈JohnsonR),wefixed f1 tothebest-fitvalue
It is a known property of CP (Ap) star rotation light curves [in parentheses] from the blue data (≈Johnson B) since the pulsation
¯
that amplitudes depend on the photometric filter used (e.g. amplitudeislargerinblueandhashighersignificance,despitethelarger
HD30849: Hensberge et al. (1982)). Even maxima and min- noise level in blue. The last column lists the spectral significance de-
imacanswitch(e.g.HD53116,op.cit.)whenswitchingcolours rivedwithSigSpec.UncertaintiesarecalculatedviaMonteCarlosim-
(moreexamplesinSchöneich,Hildebrand&Fürtig (1976)),but ulationsimplementedinPeriod04.ThereferenceforWIRE(≈Johnson
thedisappearanceofonlyoneextremumandnotalsotheotheris V)isTable3ofBruntt etal. (2009).
unique.Otherreferencestochangesoftheshapeoflightcurves
withwavelengthare,e.g.Musieloketal. (1980);Kurtz&Mar-
still not well understood, might lead to considerably different
tinez (2000);Mikulasek&Ziznovsky (2001);Mikulaseketal.
shapesofαCirlightcurvesintheblueandredbandsobserved
(2004).
byBRITE-Constellation.
AbundanceanomaliesonthesurfacesofmagneticCPstars,
which imprint their signatures on the light curves and spectral – Spots: Current knowledge about flux redistribution results in
lineprofiles,producechangingredistributionsofstellarflux(pri- dark spots in short-wavelength regimes, but bright spots in the
marily from short to longer wavelengths). This effect, which is optical, if the spots are due to concentrations of elements like
Articlenumber,page8of10
Weiss,Fröhlich,Pigulskietal.:roApstarαCir
Red Blue 2.5
0.6 2.0 ag) 2.0
mmag) 00..45 SWSWiiggIIRR==EE55..4466 1.5 de (mm 1.5
de ( 0.3 1.0 plitu 1.0
u m
Amplit 00..12 0.5 f1 a 00..05
0.0 0.0 0.0 0.5 1.0 1.5 2.0
2438 2440 2442 2444 2446 2438 2440 2442 2444 2446 Rotation Phase
0.25 0.6
ag) 0.20 0.5 0.4
m
plitude (m 00..1105 000...234 hase (0-1) 00..23
Am 0.05 0.1 1 p 0.1
0.00 0.0 f
2410 2411 2412 2413 2410 2411 2412 2413 0.0
0.0 0.5 1.0 1.5 2.0
0.25 0.6 Rotation Phase
mmag) 00..1250 00..45 rFoitga.ti1o1n.pDhaespeenodfeαncCeir,oofbasmerpvleitdudbeybanludep(chraosseseosf)farnedqureednc(ydoft1s)osn. the
e ( 0.3 ¯
ud 0.10
plit 0.2
m 0.05 0.1
A for roAp stars. Since the amplitude decline rate (from Johnson
0.00 0.0
B to R filters) is much steeper for pulsating late A-type stars
2471 2472 2473 2474 2471 2472 2473 2474
Frequency (µHz) Frequency (µHz) thanthatofmain-sequenceB-typevariables,Medupe&Kurtz
(1998)explainedthecaseofαCirwithanoutwardsdecreasing
Fig.10.SameasFigure9butforacloseupoftherotationalmultiplet temperatureamplitudewithinanarrowrange(∼ 200km)ofthe
around f (top panels) as well as f (middle panels) and f (bottom
1 6 7 atmosphere.
panels).Greyandblacklinesshowthespectrumbeforeandafterpre-
The observed phase shift between the blue and red data of
whiteningof f1,respectively. 10◦ ±6◦ is consistent with previous determinations. Thi¯s small
phase difference between red and blue light curves is in sharp
contrast to considerable phase variations in the radial velocity
Si, Cr, or Fe (Krticˇka et al. 2012). Lüftinger et al. (2010b), oscillations of roAp stars, obtained from various spectral lines
Shulyaketal.(2010),andKrticˇkaetal. (2015)findthatvaria- and at various depths of the Hα line (Baldry et al 1998, 1999;
tionsofHD37776andθAurigaeintheu,v,b,andyStrömgren Ryabchikova et al. 2007). Such spectroscopic studies have
bands are caused by spots dominated by Si, Cr, and/or Fe, and shown that the pulsation properties vary significantly with at-
thoseofHD37776aredominatedbyHe.TheelementsFeandCr mosphericdepthduetochemicalstratification,leadingtophase
are primarily responsible for the variability of (cid:15)UMa (Shulyak shiftsbetweendifferentelements.
etal. 2010). Pulsation energy, generated below the photosphere, flows
outwardsintotheatmospherewithchangingphases.Thisphase
Consideringtheevidenceprovidedbyourredandblue light
¯ variation is faster in the outer parts of the atmosphere because
curves, it is not surprising that the derived spot models are un-
usual. We speculate that the second spot has a very different someoftheenergyleaksattheouterboundary,wherethenon-
adiabatic damping effects are stronger. On the other hand, the
chemical composition than the first spot, which results in an
phase variation is slow at the base of the atmosphere because
equilibrium of redistributed and absorbed flux for the blue fil-
non-adiabatic effects are weak. Hence, RV variations deduced
ter.
fromrareearthelementsandHαbisectorsrepresentpulsationin
Alentjev & Mkrtichian (2010) derived very preliminary
theouterpartoftheatmosphere.There,non-adiabaticdamping
spectroscopic surface maps for αCir with spots dominated by
is strong, while the photometric variations primarily represent
Si and Cr, and detected abundance variations of up to 2.4 dex,
temperatureeffectsduetopulsationnearthebottomofthepho-
whichsupportourmodelsolutionassumingbrightspots.
tosphere (optical depth τ ≈ 1), where non-adiabatic effects are
–Pulsation:Thedominant frequencynear6.5min(2442µHz) expectedtobeweak.
isclearlydetectedinboth datasets.WithaSigSpecsignificance All the evidence points to high-order p-mode pulsation in
of6.8(S/N>4),wefinda¯lso f7inthefrequencyspectrumofthe αCir. We refer to Fig.6 of Bruntt et al. (2009) where the au-
red data (Fig.10, bottom). However, f7 does not appear in our thorsdiscussamplitudechangesforvariousaxisymmetricpulsa-
¯
bluedata,evenifwelowerthethresholdtoafalse-alarmproba- tionmodesdependingontherotationphaseofαCir.OurFig. 11
bilityof0.1%(S/N∼3).Accordingtotheamplitudescalingwith compares amplitude and phase changes of f observed in the
1
wavelengths,however, f7 shouldappearinourbluedata,ifitis redandblueby nanosats,averagedover25%ofafullrotation
related to the pulsation mode of f1. We emphasise that f7 has cycle, respective¯ly; our figure also addresses Fig.10 of Kurtz
onlybeendetectedsince2006. et al. (1994). Our conclusion is that within the quoted errors,
The pulsation amplitude of f decreases from the blue to quadrupolar modes can be excluded for f , and (cid:96) = 1,m = 0
1 1
red wavelengths (see our Table3), a trend that is well known beingsupported.
Articlenumber,page9of10
A&Aproofs:manuscriptno.alCirArchiv
Investigationsoflong-termchangesofrotationandpulsation Krticˇka,J.,Mikulášek,Z.,Lüftinger,T.,Jagelka,M.2015,A&A,576A,82
properties are obvious next research goals. Right now the time Kurtz,D.W.1982,MNRAS,200,807
baseofhighqualitydataistooshort,butobserversareencour- Kurtz,D.W.,Cropper,M.S.1981, IBVS 1987
agedtomonitorαCir,asBRITE-Constellationwillaswell. Kurtz,D.W.,AlenS.,Cropper,M.S.1981, IBVS 2033
Kurtz,D.W.&Balona,L.A.1984, MNRAS 210,779
–Finalnote:High-resolutionspectroscopywithhighS/N,cov- Kurtz,D.W.,Shibahashi,H.1986,MNRAS223,557
Kurtz,D.W.,Sullivan,D.J.,Martinez,P.,Tripe,P.1994, MNRAS 270,674
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troscopywithhightimeresolutionwillberequiredtodetermine
Lüftinger,T.,Fröhlich,H.-E.,Weiss,W.W.,etal.2010a,A&A,509,43
thestellarstructureanomalies.
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Mikulasek,Z.&Ziznovsky,J.2001,IBVS5188
ofthebestroApstarstoconstrainthemodelofpulsationinthe
Mikulasek,Z.,Zverko,J.,Ziznovsky,J.&Janik,J.2004,IAUS224,657
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Acknowledgements. RKandWWweresupportedbytheAustrianScienceFunds
Orleanski,P.,Graczyk,R.,MiroslawRataj,R.,Schwarzenberg-Czerny,A.,Za-
(FWF)andbytheAustrianResearchPromotionAgency(FFG-ASAP),which
wistowski,T.,Zee,R.E.2010, Proc.SPIE 7745
also supported OK. AFJM is grateful for financial assistance from NSERC
Popowicz,A.etal.2015,inpreparation
(Canada)andFRQNT(Quebec).JMM,SMR,andGAWaregratefulforsup-
Press,W.H.,Teukolsky,S.A.,Vetterling,W.T.,&Flannery,B.P.2007,Numer-
portfromNSERC(Canada).ThePolishBRITEoperationsarefundedbythe
PMN grant 2011/01/M/ST9/05914. APi acknowledges the support from the icalRecipes,3rdEdition(CambridgeUniv.Press,Cambridge)
NCN grant No. 2011/03/B/ST9/02667 and APo was supported by the Polish Reegen,P.2007,A&A,467,1353
National Science Center, grant no. 2013/11/N/ST6/03051: Novel Methods of Reegen,P.2011,CoAst 163
Rosner,B.1983Technometrics 25,165
ImpulsiveNoiseReductioninAstronomicalImages.TheMCMCcomputations
Ryabchikova,T.,Sachkov,M.,KochukhovO.andLyashko,D.2007, A&A473,
havebeenperformedbyHEFattheAIP.GHandAPareceivedsupportbythe
PolishNCNgrant2011/01/B/ST9/05448.DHacknowledgessupportbytheAus- 907
Schneider,H.&Weiss,W.W.1983, IBVS 2306
tralianResearchCouncil’sDiscoveryProjectsfundingscheme(projectnumber
Schneider,H.&Weiss,W.W.1989, A&A 210,147
DE140101364)andsupportbytheNationalAeronauticsandSpaceAdminis-
Schöneich,W.,Hildebrand,G.&Fürtig,W.1976,AN297,39
trationunderGrantNNX14AB92GissuedthroughtheKeplerParticipatingSci-
Shulyak,D.,Krticˇka,J.,Mikulášek,Z.,etal.2010,A&A,524,A66
entistProgram.TLacknowledgesfundingoftheAustrianFFGwithinASAP11
Walker,G.,Matthews,J.,Kuschnig,R.,etal.2003, PASP 115,1023
andsupportbytheFWFNFNprojectsS11601-N16andS116604-N16.K.Z.ac-
Walker,G.,Matthews,J.,Kuschnig,R.,etal.2003, PASP 115,1023
knowledgessupportbytheAustrianFondszurFo¨rderungderwissenschaftlichen
Wayman,P.A.1962, Roy.Obs.Bull,Greenwich 50
Forschung(FWF,projectV431-NBL).Finally,theauthorswishtoacknowledge
Weiss,W.W.,Schneider,H.1984, A&A 135,148
thespacecraftoperationteamsinAustria(P.Romano&M.Unterberger),Canada
Weiss, W. W., Rucinski, S. M., Moffat, A. F. J., Schwarzenberg-Czerny, A.,
(MonicaChaumont,SusanChoi,DanielKekez,KaranSarda,PaulChoi&Laura
Koudelka, O. F., Grant, C. C., Zee, R. E., Kuschnig, R., Mochnacki, St.,
Bradbury)andPoland(GrzegorzMarciniszyn&GrzegorzWoz´niak),whoseef-
Matthews, J. M., Orleanski, P., Pamyatnykh, A., Pigulski, A., Alves, J.,
fortswereessentialforthecollectionofthedatausedinthispaper.
Guedel,M.,Handler,G.,Wade,G.A.,Zwintz,K.2014, PASP 126,573
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