The transiting dust clumps in the evolved disk of the Sun-like UXor RZ Psc

1.9 MB·

by  Grant M. Kennedy

The transiting dust clumps in
the evolved disk of the
Sun-like UXor RZ Psc
rsos.royalsocietypublishing.org
1
Grant M. Kennedy , Matthew A.
2 3
Kenworthy , Joshua Pepper , Joseph E.
Research
4,5 6
Rodriguez , Robert J. Siverd , Keivan G.
5,7 1
7 Stassun , & Mark C. Wyatt
1 Articlesubmittedtojournal
1
0 InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,
2 CambridgeCB30HA,UK
n SubjectAreas: 2LeidenObservatory,LeidenUniversity,POBox9513,NL-2300
a astrophysics,extrasolarplanets,stars R3ALeiden,theNetherlands
J DepartmentofPhysics,LehighUniversity,16MemorialDrive

3 East,Bethlehem,PA18015,USA
2 Keywords: 4Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,
variablestars,protoplanetarydisks, MS-78,Cambridge,MA02138,USA
] 5DepartmentofPhysicsandAstronomy,VanderbiltUniversity,
R debrisdisks,circumstellarmatter
6301StevensonCenter,Nashville,TN37235,USA
S 6
LasCumbresObservatoryGlobalTelescopeNetwork,6740
.
h Authorforcorrespondence: CortonaDr.,Suite102,SantaBarbara,CA93117,USA
7
p GrantM.Kennedy DepartmentofPhysics,FiskUniversity,100017thAvenueNorth,
- Nashville,TN37208,USA
o e-mail:[email protected]
r
t
s RZPscisayoungSun-likestar,longassociatedwith
a
the UXorclassofvariable stars,which ispartiallyor
[
wholly dimmed by dust clumps several times each

1 year. The system has a bright and variable infrared
v
excess, which has been interpreted as evidence that
8
the dimming events are the passage of asteroidal
6
5 fragments in front of the host star. Here, we present
6 a decade of optical photometry of RZ Psc and take
0 a critical look at the asteroid belt interpretation. We
.
1 show that the distribution of light curve gradients
0 is non-uniform for deep events, which we interpret
7
as possible evidence for an asteroidal fragment-
1
like clump structure. However, the clumps are very
:
v likely seen above a high optical depth mid-plane,
i
X so the disk’s bulk clumpiness is not revealed. While
circumstantial evidence suggests an asteroid belt is
r
a more plausible than a gas-rich transition disk, the
evolutionary status remains uncertain. We suggest
that the rarity of Sun-like stars showing disk-related
variabilitymayarisebecausei)anyaccretionstreams
aretransparent,and/orii)turbulenceabovetheinner
rimisnormallyshadowedbyaflaredouterdisk.
(cid:13)c 2014TheAuthors.PublishedbytheRoyalSocietyunderthetermsofthe
CreativeCommonsAttributionLicensehttp://creativecommons.org/licenses/
by/4.0/, which permits unrestricted use, provided theoriginal author and
sourcearecredited.
1. Introduction
2
DisksofgasanddustsurroundessentiallyallyounganaloguesofourSun(e.g.[1]).Thelifetime
ofthegasinthesedisksisveryshortcomparedtothestellarlifetime,andwithinafewmillion ...rso
byueailrdsihnagspalcacnreettse.dTohneteovtohleutsitoanr,obfetehneldouststtodsupriancgetihnisphpohtaoseeviaspuonrcaetirvtaeinfl,obwust,tahnedexcoisntetrnicbeuotefdgatos .....s.roy
.a
giantplanetsmakesitclearthatplanetarybuildingblocks,andofcoursesomeplanets,formona ..ls
.o
similarorshortertimescale. ...cie
Beyondthefirstfewmillionyearsatypicalstarhostsaplanetarysystem,thecomponentsbeing ..ty
.p
theplanetsthemselvesandaresidualdiskofsmallbodies.These“planetesimals”–theasteroids ...ub
andcomets–makeupthe“debrisdisk”,wherethestandardpictureisthatdestructivecollisions ..lis
.h
betweenthemgenerateasizedistributionoffragmentsthatextendsdowntomicron-sizeddust ..in
.g
(e.g.[2–4]). ...o
The state ofplanetary systemsasthey emergefromthe gas-richphaseisuncertain. Planets’ ...rg
.
.R
locationsarenotfinalisedatthisepoch,but maymovebyinteracting withotherstars,planets, ...
.S
and/orplanetesimalsinthesystem(e.g.[5–7]).Similarly,thestateandoriginofthedebrisdiskis ...oc
uncertain.Atstellocentricdistancesnear1au,theregionofinterestinthisarticle,itcouldbethat ..
dustobservedatthistimeisrelatedtothefinalstagesofplanetformation(e.g.[8,9]),originates ...op
.e
in young analogues of our Asteroid belt [10], is a signature of comets scattered inwards from ..n
more distant regions (e.g. [11]), or is simply a remnant of the gas-rich disk that has yet to be ....sci.
dispersed[12].Intheabsenceofgasdetectionsthatargueforthelatterscenario,discerningamong ..0
.0
.0
thesevariousscenarios,whicharenotmutuallyexclusive,isdifficult. ..0
.0
Apromisingwaytoprobetheseinnerregionsisbyobservingtemporalvariability(e.g.[13]). .0
..0
OpticalandIRstellarvariationhasbeenstudiedfordecades(e.g.[14,15]),andhasrecentlybeen .
reinvigorated by large scale efforts (e.g. [16,17]) and as a side-effect of large-scale surveys for
transiting planets [18,19]. Of many different classes of variables, the ones of most interest and
relevance here are the “UXors”, named for the prototypical system UX Orionis [15]. These are
usuallyHerbigAeandlate-typeHerbigBestars[20],andtypicallyshowseveralmagnitudesof
extinction that is generally attributed to variable obscuration by circumstellar dust [15,21,22].1
Threerelatedargumentsthatfavourcircumstellardustasthecausearei)amaximumdepthof
dimmingeventsofroughly3magnitudes,suggestingthatafewpercentofthevisiblefluxisnot
directlyfromthe star, but scatteredoff adiskthat surroundsthe star and remainsvisible even
when the star itself is completely occulted, ii) “blueing”, where the star is reddened for small
(.1mag) levelsof dimmingbut returnsto the stellarcolour (i.e.becomes “bluer”) forthe very
deep (&1mag) events where the star is mostly occulted – the reddening indicates dimming by
circumstellardust,andastellarcolouristypicaloflightscatteredoffcircumstellardust[28],and
iii)increasedpolarisationfractionduringdimmingevents,causedbyagreaterfractionoftheflux
beingcontributedbydust-scatteredlight(e.g.[29],whichalsoshowsthatthesurroundingdust
does not residein a spherical shell). UXors thereforereveal information on the degreeof non-
axisymmetry,the“clumpiness”,ofdustorbitingastaronspatialscalessimilartothestaritself.
Theobservationscanspanmultipleorbitstotestforrepeateddimmingevents(e.g.[30]),andby
usingdifferentbandpassesandpolarisationcanestimatedustgrainsizes(e.g.[28,31]).
Inthe majorityofUXor-likecases(i.e.those relatedtoobscurationbydust),includingother
classessuchas“dippers”(e.g.[17,32]),theprocessescausingyoungstarstovaryareattributed
togas-richprotoplanetarydisks.ForHerbigAe/Bestarstheobscurationisthoughttobecaused
by hydrodynamic turbulence that lifts dust above the puffed up inner rim of a self-shadowed
disk[33].Forthedippers,whichareobservedaroundlow-massstars,theobscurationisattributed
todustinaccretionstreamsthatlinktheinnerdiskandthestellarsurface,and/ortovariations
intheheightoftheinnerdiskedge[30,32,34].Thecommonthemeisthereforethatthelocationof
1NotallstarsoccultedbydustareUXors.Twootherclassesare:thoseoccultedbycircumstellarmaterialbeyond&10au,such
asAATauandV409Tauwhichshow&year-longdimmingevents[23,24],andsystemssuchasǫAur,J1407,EECep,and
OGLE-LMC-ECL-11893wheretheoccultationsareattributedtocircumsecondarydisks(e.g.[18,25–27]).
theoccultingdustisasclosetothestarasphysicallypossible,beingsetbysublimation(e.g.[35]).
3
Thesesystemstellusaboutthenatureofturbulenceandaccretioningas-dominateddisks,butso
farreveallittleabouthowthesediskstransitiontothedebrisphaseandthesubsequentevolution.
HerewefocusonRZPsc,astarthatshowsUXor-likevariability(e.g.[36–38]).AsayoungK0V ...rso
.s
tuynpiqeustearamwiotnhgnoUeXvoirdsenacnedfomragyasparcocvriedtieonneawndinafsotrrmonagtiionnfraornedth(eIRs)teruxccteussre,thoifsisnynsetermplaapnpeetaarrys ......roya
systemsduringorfollowingdispersalof the gasdisk[39,40]. However,the IR excessindicates ...lso
.c
the over 5% of the starlight is intercepted by the disk, which is a level more akin to gas-rich ..ie
protoplanetaryand transition disksthan debrisdisks.Specifically,we use a decadeof ground- ...typ
basedopticalphotometryofRZPsc(section3)todrawconclusionsondustlocation(section4), ...ub
..lis
anddiscussthepossiblediskstructureandevolutionarystateinsection5.Weconcludeinsection .h
..in
6. .g
...o
...rg
2. A clumpy dust ring near 0.5 au? ..R
...
.S
There is significant evidence that the optical variations seen towards RZ Psc are caused by ...oc
..
circumstellar dust: i) during dimming events the colour becomes redder [36,41] in a way ...op
consistentwiththatexpectedfordust[42,43],ii)themaximumdepthisabout2.5magandduring .e
..n
tfhroemseleivgehnttsscathtteerceodlooufrfrtehteurcnirscutomnsetealrlasrtedlluasrtv(ai.leu.etsh,esustgagreisstifnuglltyhaotccthuelterdem[2a8in,4i2n]g, aenmdisisiiio)nthies ....sci.
..0
polarisationfractionincreasesduringthetransits,asexpectedifanincreasingfractionofthelight .0
.0
isscatteredoffadiskofcircumstellardust[28,38,44]. ..0
.0
.0
WhatseparatesRZPscfromotherUXors(anddippers)isi)thespectraltypeisK0Vratherthan ..0
.
HerbigAe/BeforUXorsandlateKtoM-typefordippers,ii)theoccultingdustlieswellbeyond
thesublimationradius,andiii)thestarisnotassociatedwithastar-formingregionsoisinferred
tobeafewtensofmillionsofyearsold.Thedustdistancehasbeeninferredfromthespeedof
ingress of dimming events, which was previouslyestimated as about 0.6au (for circular orbits
[40]).Corroboratingevidencecomesfromthe 500Ktemperatureofthedustseeninthemid-IR,
∼
whichplacesitnear0.4-0.7au(dependingonopticaldepth)andthereforeatalocationconsistent
withtheoccultingdust[40].ThedistancetoRZPscisunknown,butasanapparentlyisolatedstar
thatshowsLiabsorptiontheagehasbeenestimatedasafewtensofMyr,andthereforebeyond
theageatwhichagas-richdiskwouldnormallyexist[39,45].Furtherdistinguishingfeaturesare
thatthedurationofthedimmingeventsisconsistentlyshortcomparedtootherUXors,afewdays
ratherthandaystoafewweeks,andthatnonear-IR(i.e.K-band)excessoraccretionsignatures
areseen[45],sointerpretationsrelatedtoaccretionofdiskmaterialontothestar(e.g.[21,30,34])
areunlikely.
Thus, the potentially compelling and unique aspect for RZ Psc is that we are observing
dimmingeventsfromdustinamain-sequenceplanetarysystemthatresidesatabout0.5au.This
dust is also seen in thermal emission, so deriving joint constraints on the dust properties and
structuremaybepossible.AsarguedbydeWitetal.[40]apictureisemerginginwhichRZPsc
is surrounded by a massive young version of our own asteroid belt, in which planetesimals
are continually being destroyed. These collisions generate the large collective surface area of
smalldustthatemitsstronglyinthemid-IR,andthesystemgeometrymeansthatthisdustalso
sometimespassesinfrontofthestar.
Whilethisasteroidbeltpictureisintriguing,andmakesRZPscasystemthatcouldbeofgreat
interestandworthyofdetailedstudy,itisnottheonlypossibility.Wellover1%ofthestarlightis
reprocessedbythecircumstellardisk,whichismoretypicaloftheprimordialgas-richdisksseen
aroundnearlyallyoungstars.ThediscoveryofsystemslikeHD21997, thatappeartobeafew
tens ofMyroldand hostgas-richdisks[46], showsthat stellarageisnotaperfectindicatorof
diskstatus.Thus,aconsiderablepartofouranalysisfocusesonthequestionofthestatusofthe
diskaroundRZPsc.
Giventheproposedinterpretationrelatedtoindividualplanetesimaldisruptions,ratherthan
hydrodynamics, it is perhaps surprising that to date the dimming events are not seen to be
periodic[40,47].TheonlycyclicalvariationseeninlightcurvesforRZPscisa12.4yearvariation
4
withanamplitudeof0.5mag,whichisattributedtoeitheramagneticcycle,orprecessionofan
otherwiseunseenouterdiskduetoperturbationsfromanunseencompanion[40].
...rso
.s
3. Time series photometry .....roy
.a
..ls
.o
(a) Optical .c
..ie
..ty
TWoidset-uAdnyglteheSetaermchpoforarlPvlaanrieatbsil(iWtyAoSfPR[4Z8,4P9s]c),wanedunseinetwsoeasseoanssoonfsdoaftapufrbolmic tdhaetaKiflroodmegtrheee ......publis
ExtremelyLittleTelescopeNorth(KELT-North[50]).Wealsocollected,butultimatelydidnotuse, ...hin
photometricobservationsofRZPscfromawidevarietyofothersources([15,36,41,44,51–53],the ...g.o
CatalinaSkySurvey,theAmericanAssociationofVariableStarObservers,theAll-SkyAutomated ...rg
Survey).AsidefromtheHarvardplatephotometrypublishedbyGürtleretal.[37]wehavenot ..R
soughtunpublishedphotometrysothelightcurveremainsincomplete.2 ....S
HerewefocusontheWASPandKELT-Northdata,asithasnotbeenpreviouslyanalysedand ...oc
..
hasconsiderablyhighercadence(manymeasurementspernight)andtemporalcoverage(nightly, ...op
weatherpermitting)thanotherdatasets.TheWASPdatafrom2004and2006arepublicandwere ...en
obybt[a5in4]e,dwfrhoemreacnomonmlinoen-amrcohdiveev3a.rTihateisoendsawtaewreerreemproovceedssuesdininga50mqanunieetrnseimariblayrsttoatrhs.atTdheesWcriAbSePd ......sci.0
bandpass is broad, with roughly uniform transmission from 400-700nm [48]. The KELT-North ..00
..0
data,2006-2014,wereusedinrawform,theonlyspecifictreatmentbeinga4%relativecorrection .0
.0
beingmadetoensureobservationstakeninthe“east”and“west”telescopeorientationshavethe ..0
.
samecalibration.ThebandpassisredderthanforWASP,withmosttransmissionbetween500nm
and800nm[50].ForafulldescriptionoftheKELT-Northdatareduction,see[55].
We normalisedeachyear’sdatafromeachinstrument separatelyby convertingmagnitudes
to flux density and dividing out the sigma-clipped median so the light curve has an out-of-
occultationbaselineof1.Indoingsoweareassumingthatvariationsduetotheslightlydifferent
filterbandpassesareunimportant.EachrowinFigure1showsaseason’sdata,startingonMay
1eachyear(JDalsoindicated).Mostyear’sdatathereforeextendintothenextyear,sothe“2006
data”referstodatafromthe2006/2007observingseason.
(i)Qualitativelightcurveoverview
It is clear from Figure1 that RZ Psc undergoesthe very deep dimming events that are typical
ofUXors.Theseareseenafewtimeseachobservingseasonandvaryincomplexity,withafew
extendedevents(e.g.2006) andagreaternumber of“neater”singleevents (e.g.2010). Insome
yearsthereisalsosignificantvariabilityatshallowerdepths.Ofparticularnoteisthepairofdeep
eventsin2006;theseappeartobeabout70daysapart,andgiventhesuggestionthattheputative
asteroidbeltanalogueresidesnear0.5auanaturalinferenceisthatthesetwoeventsarerelated.If
true,thisrepetitioncorrespondstoasemi-majoraxisofabout0.3au,whichgivenuncertaintiesin
thetruediskspectrumcouldbeconsistentwiththelocationoftheasteroidbelt.In2004thereare
about100daysofnear-consecutivenightsofdataandnodeepevents,soeitherthetrueperiodis
longerthan100days,ordustclumpscanbecreated(andperhapsdestroyed)ontimescalesofa
yearorso.
InFigure2wehaveselectedmostoftheeventsfromeachyearandshownthematagreater
temporal resolution. The scale in each panel is the same, so wider boxes simply cover longer
events. Most events appear to last at least a few days, suggesting that only having nightly
coverage does not seriously hinder our ability to detect most events. However, the events are
sufficientlyshortandirregularthatthetrueshapeofeventsremainsuncertain.Whileitislikely
that interpolation of the photometry for the fourth event in 2011 (that is, the fourth box from
2Allnormalisedphotometryisavailableathttps://github.com/drgmk/rzpsc
3http://wasp.cerit-sc.cz
5

22450310264.5 ....rsos
......roya
..ls
.o
2006 ...cie
2453856.5 ...typ
...ub
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2007 ....hing
2454221.5 ......org
..R
...
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22450450878.5 ....oc.
...op
2009 .......ensci.
2454952.5 ..0
....000
.0
....00
2010
2455317.5

2011
2455682.5

2012
2456048.5

2013
2456413.5

x 1.2
e Flu 01..80
v 0.6
Relati 000...024 22450671784.5 WKAELSTP
5 0 10 0 15 0 20 0 25 0 30 0
Days since 1 May each year
Figure1.WASPandKELT-Northdata.Photometryisshownindimensionlessform,relativetoaquiescentlevelof1,and
wasconvertedfromobservedmagnitudesasdescribedinthetext.
6

2004 ...rso
.....s.roy
.a
..ls
..oc
2006 ....iety
....pub
..lis
...hin
2007 ...g.o
...rg
.
...R.
.S
2008 ...oc
......ope
..n
2009 ......sci.0
.0
...00
.0
....00
2010

1.00ux
0.75e Fl
0.50ativ
2011 00..0205Rel

2012

2013

2014

0 5 1 0 1 5 2 0
Days + offset
Figure2.WASPandKELT-Northdata,focussingondimmingevents.Theverticalandhorizontalscalesineachsub-panel
arethesame.
the leftinthe rowcorrespondingto 2011inFigure2) wouldresemblethe true lightcurve,this
7
assumptionseemsveryunlikelytoyieldthetrueevolutionofmorecomplexeventslikethosein
2006.
Nevertheless,Figure2showsanunprecedentedviewofdimmingeventsseentowardsRZPsc, ...rso
.s
arantdetishastukcheythinaftoirtmcaantiobneorensothlveeidngteremsspoarnadllye,garensdshoefndciemtmheinvgeleovceintytsainsdprraedseianlt.loTchaetidonimomfitnhge ......roya
dustclumps estimated.Whilesuch estimateshave beenmade inthe pastbased onone ortwo ...lso
.c
individualevents[36],thesedatamakethempossibleforanensembleoftensofevents. ..ie
..ty
A fairlybasicquestionis whether the lightcurve couldresultfromobjects that all have the .p
sameproperties,orwhetherarangeisrequired.Giventheexistenceofbothlongshallowevents ...ub
..lis
andshortdeepevents,ataminimumtheclumpsmustvaryinsizeand/orvelocityacrosstheface .h
..in
ofthestar,butprobablyalsohavedifferentopticaldepths.Thestarcanbecompletelyocculted, .g
sotheclumpscanbeopticallythickandstar-sized,butithasalreadybeenshownthattheevents ......org
arenotgreyincolour,sotheclumpsmusthaveadensitygradientratherthansharpedges.Where .
.R
sufficientdataexist,itisclearthatnotalleventshavethesamerelativeshape,sotheshapeofthe ...
.S
clumpsvaries.Thus,thebroadpictureisofroughlystar-sizedclumps,whoseshapeandorbital ...oc
..
elementsvary.Thefactthatthedimmingeventscanbeshowninaseriesofpanelswiththesame ...op
scaleinFigure2suggeststhattherangeoverwhichthesepropertiesvaryisoforderfactorsofa .e
..n
few,notmanyordersofmagnitude. ....sci.
..0
.0
(b) Infrared .0
..0
.0
.0
While the optical photometry reveals information about how RZ Psc is itself dimmed, IR ..0
.
photometry beyond a few microns is dominated by emission from the circumstellar disk.
Thus, IR variation reveals information about how the emitting surface area, temperature, and
perhapscomposition,ofthedustchangewithtime.Suchvariationisindeedapparent,bothfrom
comparisonofanAKARI18µmnon-detectionatalowerlevelthantheWISE22µmdetection,and
fromseveralindividualWISEmeasurementstakenat6-monthintervals.
Motivated by this variation, we obtained VLT/VISIR observations of RZ Psc; an N-band
(10µm)spectrumon2016August16andQ-band(18µm)photometryon2016July27(programme
097.C-0217). These data, and the related calibration observations, were reduced using the
standardESOesorexpipeline.Thewall-clockintegrationtimeforthespectrumwas50minutes
atanairmassof1.66,andwascalibratedusinganobservationofHD189831takenimmediately
afterwardsatanairmassof1.63.Thespectrainindividualchop/nodcyclesareconsistentsothe
shapeofthespectrumisreliable.Theabsolutecalibrationisuncertainat 10%levels[56],which
∼
issufficientlypreciseforourpurposeshere.Thespectrumwastrimmedtomaskhighlyuncertain
regions shortward of 8µm, and longward of 13 µm, and near the telluric absorption at 9.5µm.
TheQ-bandphotometrytook45minutesatanairmassof1.65-1.7,andwascalibratedagainstan
observationofHD2436takenimmediatelyafterwardsatanairmassof1.5.PhotometryofRZPsc
andHD2436wasdoneusinga0.9”radiusapertureandaskyannulusfrom1-2”.Inadditionto
theconversionfromadu/stoJanskyusingHD2436,weappliedanadditionalupwardcorrection
toaccountfortheslightlylowerairmassforthecalibrator(exp(0.3[1.675 1.5] 1.05,wherean
− ≈
extinctionof0.3perunitairmasswasused,derivedfromarchivalcalibrationdatausingamethod
similartothatofVerhoeffetal.[57]).Uncertaintieswereestimatedasthestandarddeviationof
thefluxdensityin50aperturesaroundRZPsc.Thefinalcalibratedfluxis86 10mJy.
±
The VISIR spectrum and photometry are shown in Figure 3, which also shows the other
availablenear-tofar-IRphotometry.TheabsolutelevelofthespectrumagreeswellwiththeIRAS,
WISE(fromtheALLWISEcatalogue),andAKARIobservations;thatfourobservationsspanning
over30yearsareconsistentsuggeststhatwhilethispartofthespectrummayvary,theshapeand
levelshown is typical. The same cannot be said near 18µm, where the AKARI and VISIR (and
perhaps WISE depending on the disk spectrum) flux densities are inconsistent. The flux near
10µm being relativelyconstant, and the 18µm flux changing could be indicative of shadowing
of an outerdiskby an inner disk;that is,evidence that the diskaround RZ Pschas significant
8
...rso
.s
.....roy
.a
..ls
.o
.c
..ie
..ty
.p
...ub
..lis
.h
..in
.g
...o
...rg
.
.R
...
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...oc
..
...op
.e
F(aipgpurroexim3.aFtelu)xyedaernsoiftyobdsisetrrvibautitoionn. TohfeRdZarPksbcl,ueinclilnuedinsghow2MsAaSsSt,elWlarISpEh,otAosKpAhReIr,eVmISoIdRe,laantdtheIRaApSprdoaxitmaaatendsttehlleairr ......nsci.
temperatureof5350K,andthelightbluelinea500Kblackbody. Thelatterisnotafit,butanapproximate continuum ...00
.0
levelthatillustratesthattheWISE3.4and22µmphotometrycannotbothbeaccountedforwithasingleblackbody,ifthe ..0
.0
silicatefeatureseenwithVISIRwaspresentin2010. ...00
.
9.5
9.4
W1 9.3
9.2
9.1
20102011201220132014201520168.6 8.7 8.8 8.9 9.0 9.1 6.0 6.1 6.2 6.3 4.854.904.955.005.055.105.15
year W2 W3 W4
Figure4.WISEepochphotometryat3.4,4.6,12,and22µm(W1,W2,W3,andW4,inmagnitudes).Theleftpanelshows
thetimevariationinW1over5.5years.SubsequentpanelsshowhowW1correlateswithW2,W3,andW4,whichdo
nothaveobservationsatallW1epochs.Thedashedlinesshowtheslopeexpectedforconstantdiskfluxvariationwith
wavelength(thevariationissmallerinW1/2becausethetotalfluxisnotdominatedbythedisk).
radialextent.Thistypeofbehaviourisseenas“seesaw”variabilityinIRspectratowardssome
transitiondisks(e.g.[58,59]).
Thespectrumclearlyshowssolid-stateemission(andthecontinuumlevelisnotactuallyclear),
whichindicatesi)thatthedustisofordermicronsinsize,andii)thatthedustincludessilicates.
The smooth rise and fall suggests that the silicates are largely amorphous; crystalline silicates
havesharperfeatures,notablyadepressionbetweentwopeaksat10and11µm,ratherthanthe
flattopseenhere.Othersystemsthoughttohostbrightasteroidbeltanalogues(ratherthangas-
rich disks), such as HD 69830, BD+20 307, and HD 113766A, tend to show crystalline features
(e.g.[60–62]),whichmayargueagainstsuchascenarioforRZPsc.However,suchcomparisons
arelargelyspeculativeasthereisalsoahighdegreeofvariationamongsilicatefeatures,forboth
gas-richandgas-poordisks.
To further explore this variability, we use the WISE “epoch” photometry, for which the
9
telescopescanningstrategyresultsinclustersofmeasurementsthatarespaced6monthsapart.
These data appear at approximately days 70 and 250 in the relevant years in Figure 1, but do
notcoincidewithany opticaldimmingevents.Photometryisnotavailable inallfourchannels ...rso
.s
sfrinomcemlauidnc2h01in1-e2a0r1l4y(2s0e1e0[,6d3u,6e4t]o).eTxhheasuestdioatnaoafrtehsehcoowolnanintaFfitgeurr7e.74m,wonhtehrseathnedlaef2t.5p-ayneealrshhiaotwuss ......roya
the 3.4µm magnitude as a function of time, and that there is significant variation on 6-month ...lso
.c
timescales,andanevengreatervariationoverall.Inspectionoftheindividualclusters,whichare ..ie
onhourtodaytimescales,showsno significantvariationwithtime.Thedashedlineshave the ...typ
slopeexpectedfordiskbrightnessvariationthatisindependentofwavelength;theslopesarenot ...ub
exactly1because the total flux is notdominated bythe disknear 3-5µm, and hence the slopes ...lish
..in
areslightlyflatter.Comparingtheobservedandexpectedcorrelations,weconcludethatthedata .g
do not show significant evidence for changes in the spectral shape (i.e. changing temperature ......org
orcomposition).However,theratiosincluding12and22µm observationsaremostsensitiveto .
.R
thesechanges,butonlyincludethe firsttwo setsofobservationswherethe brightnesschanges ...
.S
wererelativelysmall. ...oc
..
Nevertheless, the amplitude of the change in 3.4µm brightness over 5 years is about 30%. ...op
Consideringthat thediskflux densityisonly45% ofthe total fluxatthis wavelength, the disk .e
..n
bbryigchotmnepsasriinngcrethaese1d8fµrmomu2p0p1e0rtolim20i1t5frboymabAoKuAtaRfIaicnto2r0o0f7twanod.AousirmVilIaSrIRvamriaetaisounrecamnebnetiinnfe2r0r1e6d. ....sci.
..0
GiventheseincreasesisitsurprisingthattheN-bandspectrumdoesnotappearmuchhigherthan .0
.0
the IRAS, AKARI, and WISE photometry. A possible explanation would be that the increased ...00
.0
emissionoriginates in larger grains, which would result in greater continuum flux but similar ..0
.
levelsinspectralfeatures.However,withoutwiderspectralandmorefrequenttemporalcoverage
quantifyingsucheffectsisdifficult.ThislevelofIRvariationisseentowardsbothprotoplanetary
(e.g.[58,65]) and debrisdisks(e.g.[13,66,67]), so these data providelittle means to distinguish
betweenscenarios.
4. Where are the occulting bodies?
The main part of our analysis concerns attempts to extract information from the optical light
curve, taking advantage of the greatnumber of dimming events seen over ten seasons. In this
sectionwefocusontheradiallocationofthebodies(“clumps”)thatpassinfrontofRZPsc,first
searchingforperiodicityassociatedwithrepeatevents,andthenusingthelightcurvegradients
toconstraintheprojectedvelocities.Thisanalysisprimarilyfocussesonwhatcanbegleanedfrom
thelightcurves,andtheimplicationsoftheseresultsfordifferentclumporiginsarethenexplored
insection5.
(a) Search for periodic dimming events
We begin by estimating the lifetime of an occulting clump as a check on the plausibility that
dimmingeventsshouldrepeat.TheangularrateatwhichclumpsareshearedoutisRdΩ/dR=
3Ω/2. Accounting for shear inboth forward(interior)and backward (exterior)directionsthe
−
shearvelocityacrossaclumpofradiusRclisthen
vsh=3RclΩ, (4.1)
sothe clumpexpansionrateduetoshearinunitsofclumpradiiisonlythreetimesthe orbital
frequency.Thatis,afteroneorbitaclumpwillbestretchedbyafactorof6π,andtheradialand
vertical optical depth will be roughly 6π lower (though it might still be optically thick). Thus,
clumps that are not bound by their own self-gravity are expected to have a short lifetime at
opticaldepthsthatarelargeenoughtocausedetectabledimmingevents,butcouldcauserepeated
dimmingeventsiftheyareinitiallyopticallythick.
Thetemporalcoverageoftheobservationsinanindividualseasonis100-150days.Thus,ifthe
10
occultingmaterialresidesinanasteroidbeltcloserthan 0.5au,periodicityinthedimmingevents
∼
may be visible in a single season’s data. Longer orbital periods may be visible across seasons,
thoughthe six-monthgap betweenseasonsmakesunambiguouslylinkingevents harder.Non- ...rso
.s
dnoetteecxtiiosnt.oAfnpeinritoedrmicietdyiwatoeupldosismibpilliytythiasttthhaetdoactcaualtraetinoontssuhfafipcpieennt,woirththaatrsatnrigcetpoefrpioedriiocidtyicditoieess, ......roya
perhapsreflectingtheirorigininaradiallybroadregion,andthatdiscerningthisscenariofrom ...lso
.c
randomlyoccurringoccultationsisnotpossiblegiventhedata. ..ie
Inanattempttofindtheexpectedperiodicitywetriedseveralapproaches.Thesearesimilarin ...typ
thattheyaimtoquantifywhethersomefeatureinthelightcurveisrepeatedagainatalatertime, ...ub
..lis
butdifferinhowwelltheyrevealevidenceforaperiodicsignal.Wefoundnoevidenceforevents .h
..in
thatarerelatedfromoneyeartoanother,sofocusonstatisticsderivedfromindividualseasons’ .g
data(thoughthesearesometimescombined). ......org
.
.R
(i)Autocorrelation ...
.S
We first used autocorrelation to search for periodicity, rather than methods related to Fourier ....oc.
transforms (e.g. periodograms). The motivation being that an individual transit event may be ...op
.e
followed by another some number of days later, and perhaps repeat a few times, but other ..n
similarly(butnotexactly)separatedeventsmayhappenyearslaterorearlierwithaphasethat ....sci.
istotallydifferent.Wethereforeusedthediscreteautocorrelationfunction(DACF)proposedby ..0
.0
Edelson&Krolik[68], though donot include uncertainties on individualmeasurements.Fora ...00
tciumrvees,ehrieersewwiethumseedasthueresmigemntas-caliipaptetdimmeseatnitthoerDemAoCvFefithrsetdcoimmmpuintegsetvheenmtse.aTnhea¯nfrfoomretahcehlpigahirt .....000
ofpointsai,aj (withi=j)computesUij=((ai a¯)(aj a¯)/σa,witheachUij associatedwitha
6 − −
timelag∆tij=tj ti.Aseriesoftimelagscenteredattimestlagwithwidth∆tlagarethenused
−
asbins,andtheaverageineachbinistheDACF.TheDACFisnotcomputedforlagbinswithno
data.TheunitsoftheDACFarestandarddeviationsofthelightcurveσa(againcalculatedusing
sigmaclipping).
The results are shown in Figure5 for time lags (i.e. trial periods)of 10 to 155 days in half-
daybins.ComparisonofthesewiththelightcurvesshowsthattheDACFrecoversmost,butnot
all,events.Conversely,notallDACFpeaksarenecessarilyassociatedwithrealrepeatevents,as
theremayofcoursebemultipledistinctclumpsorbitingthestaratanygiventime.Notallpairs
of events showa strong DACFsignal, as they can compriseonly afew measurementsand the
mean for that tlag dominated instead by a much largernumber of measurements elsewherein
thelightcurveclosertothequiescentlevel(i.e.neara¯).Ourattemptstoavoidthisissuebyusing
autocorrelationoninterpolateddatayieldedmixedresults;heavyfiltering,suchassettingalldata
aboveagivenlevelto1,wasneededforresultssimilartotheDACFshowninFigure5.
WhileseveralstrongpeaksappearintheDACFofalldata,mostofthesearisefrom2006,ascan
beseenintheDACFwhenthesedataareexcluded.Somepeaksremainnear70days,aswellas
at120and145days,andthelattertwocouldbealiasesofperiodsnear60-70days,arisingsimply
becauseaneventwasmissed.Thatis,theirregularsamplingmeansthatabsenceofevidenceof
poweratsomeperiodintheDACFisnotevidenceofabsence.
Thepairofeventsseparatedby70daysin2006providesthestrongestsignal,andmostother
years also show events near this period (2007, 2009, 2011, 2012, 2013, 2014). To illustrate these
numbersthetopmostlineinFigure5quantifiesthenumberofyearsthatshowapeak,in10day
bins.Thepeakof7yearsisat65-75days,whichissuggestivebutnotconclusivebecauseaK-S
testshowsthatthisdistributionisconsistentwithbeinguniforminperiod.
(ii)Iterativeeventfinding
InanattempttoavoidsomeofthedifficultiesarisingfromtheDACF,wetriedasimilarapproach
that first identifies individual occultation events and then computes the time delays between
them.Themainaimwastoidentifyandusealleventsinawaythatavoidsbiasesrelatedtothe