The interplay between X-ray photoevaporation and planet formation

0.41 MB·English

by  Giovanni P. Rosotti

Mon.Not.R.Astron.Soc.000,1–11(2012) Printed15January2013 (MNLATEXstylefilev2.2)
The interplay between X-ray photoevaporation and planet
formation
Giovanni P. Rosotti⋆1,2,3, Barbara Ercolano2,3, James E. Owen4, Philip J. Armitage5,6
1Max-Planck-Institutfu¨rextraterrestrischePhysik,Giessenbachstraße,D-85748Garching,Germany
3 2ExcellenceClusterUniverse,Boltzmannstr.2,D-85748Garching,Germany
1 3Universitats-SternwarteMu¨nchen,Scheinerstraße1,D-81679Mu¨nchen,Germany
0 4CanadianInstituteforTheoreticalAstrophysics,60St.GeorgeStreet,TorontoM5S3H8,Canada
2 5JILA,UniversityofColoradoandNIST,440UCB,Boulder,CO80309-0440,USA
6DepartmentofAstrophysicalandPlanetarySciences,UniversityofColorado,Boulder,USA
n
a
J
Accepted2012December28.Received2012December21;inoriginalform2012November8
4
1

] ABSTRACT
R
S We assess the potential of planet formation instigating the early formation of a photo-
. evaporation driven gap, up to radii larger than typical for photoevaporation alone. For our
h
investigationwe makeuse ofhydrodynamicsmodelsofphotoevaporatingdiscswithagiant
p
planetembedded.We findthat,byreducingthe massaccretion flowontothe star,discsthat
-
o formgiantplanetswillbedispersedatearliertimesthandiscswithoutplanetsbyX-raypho-
r toevaporation. By clearing the portion of the disc inner of the planet orbital radius, planet
t
s formationinducedphotoevaporation(PIPE)isabletoproducetransitiondiscthatforagiven
a
mass accretion rate have larger holes when compared to standard X-ray photoevaporation.
[
Thisconstitutesapossibleroutefortheformationoftheobservedclassofaccretingtransition

1 discs with large holes, which are otherwise difficult to explain by planet formationor pho-
v toevaporationalone.Moreover,assumingthataplanetisabletofilterdustcompletely,PIPE
5 produces a transition disc with a large hole and may provide a mechanism to quickly shut
1 downaccretion.Thisprocessappearstobetooslowhowevertoexplaintheobserveddesert
0
inthepopulationoftransitiondiscwithlargeholesandlowmassaccretionrates.
3
. Keywords: accretion,accretiondiscs–hydrodynamics–protoplanetarydiscs.
1
0
3
1
:
v 1 INTRODUCTION agreementwiththeobservations(Hartmannetal.1998)ofthemass
i accretionratesin“classical”T-Tauridiscs.
X The evolution and final dispersal of the gas and dust contained
r in protoplanetary discs surrounding young low-mass stars plays However, thefinal evolution of protoplanetary discs appears
a animportantroleinshapingthepropertiesofpotential planetsin nottobecompatiblewiththispicture.Discshaveacharacteristic
the system. In particular the disc dispersal time-scale sets an up- lifetimeof 3Myr(Haischetal.2001;Mamajek2009;Fedeleetal.
perlimitfortheformation of gasgiants. Itisthereforecrucial to 2010), as can be shown looking at the fraction of disc bearing
formulateatheorycapableofdescribingthediscevolutionanddis- young stellar objects (YSO) in clusters of different ages, but,
persalindetail,whichisanimportantinputfortheplanetformation ratherthanfromahomogeneousdrainingaspredictedbypurevis-
theory. cosity evolution, discs seem to have a fast, final stage of clear-
Formostoftheirlifetime,theevolutionofdiscsisdrivenby ingfromtheinsideout(Luhmanetal.2010;Ercolanoetal.2011;
viscosity. Currently, the most favoured mechanism for its origin Koepferletal. 2012) with a typical time-scale of 105 years. This
is the magnetorotational instability (Balbus&Hawley 1991), al- behaviourhasbeencalled“two-timescale”intheliterature.
though other mechanisms have been proposed, such as thetrans- “Transitionaldiscs”areobjectsbelievedtohavebeencaught
portofangularmomentumbyspiralwavesinself-gravitatingdiscs in the act of disc-dispersal and hence to be useful for shedding
(Lodato&Rice2004).Undersimplifyingassumptions,theevolu- light on the mechanism responsible for disc clearing. First spot-
tion in time of a disc can be described by an analytical solution ted by spectral energy distribution (SED) observations of YSOs
(Lynden-Bell&Pringle1974), which was showed tobe in rough more than two decades ago (Strometal. 1989; Skrutskieetal.
1990), although only more recently the Spitzer space telescope
gave the possibility to study them in detail (e.g. Calvetetal.
2005;Espaillatetal.2010),theylackemissionatthemidIRwave-
⋆ E-mail:[email protected] lengthswhencomparedto“standard”disc.Thisdeficitofopacity
(cid:13)c 2012RAS
2 G. P.Rosottiet al.
in the warm dust has been interpreted as the signature of an in- viscoustime-scale(∼ 105 years).Theresultisadiscthatexhibits
nerhole.SEDmodellingishoweveraratherdifficulttask,depend- an inner dust cavity (hence a dip in the mid-infrared emission),
ingonmanymodelparametersthatareoftendegenerate.Morere- and aninner gasdisc that isstilldraining, producing a stillmea-
cently, the advent of good quality data from sub-mm interferom- surable mass accretion signature. Much progress has been made
eters has permitted to obtain spatially resolved images of some in computing detailed mass-loss rates from the photoevaporative
of these objects, confirming indeed the presence of large cavities wind.Thisiscrucialtodeterminethemass-accretionrateatwhich
(Andrewsetal.2011),sometimesoforderoftensofAU.Thefre- thewindisabletoopenagap,thusdeterminingtheageofthedisc
quencyoftransitionaldisc(∼10percentoftotalnumberofpro- andthepropertiesoftheresultingtransitiondisc.Inparticularre-
toplanetary discs) is compatible with the interpretation that they centmodelshaveincludedinthecalculationFUVandX-rayradi-
representafast,finalphaseofdiscevolutionthatproceedsfromthe ation(Gorti&Hollenbach2009;Ercolanoetal.2009;Owenetal.
insideout(Kenyon&Hartmann1995).Ithastoberemarkedthat, 2011).
despitetheimagesconfirmlargecavitiesbothinthesub-mmand In particular, Owenetal. (2011) compared the statistics of
inthemicron-sizeddust,gasisinmanycasesstillpresent.Indeed, transitional discs with evolution models including X-ray photoe-
someofthesetransitionaldiscspresentmassaccretionratesofor- vaporationfromthecentralstar,showingthatitisindeedpossible
der10−8M⊙yr−1,comparablewiththatofclassicalT-Tauristars, toexplainalargenumberofobservedobjectswithphotoevapora-
indicatingthatasubstantialreservoirofgasisstillpresentnearthe tionalone. Thismodel however stillfailedtoreproduce the class
centralobject.Evenmoreremarkably,ithastobenotedthat such oftransitionaldiscswithlargeholesandlargemassaccretionrates,
massaccretionratesarenotageneralfeatureofalltransitiondiscs, duetothefactthat,bythetimephotoevaporationhascarvedalarge
andthatthereisinsteadahugerangeofvariationintheobserved enoughholeintheouterdisc,themassreservoiroftheinner disc
sample. hasdroppedsomuchthatnomassaccretionrateisdetectableany-
To explain the presence of this class of discs, many more.
physical processes have been invoked, including grain Apossiblescenario,assuggestedbyOwen&Clarke(2012),
growth (Dullemond&Dominik 2005), photoevaporation isthat“transitional”discsarenotahomogenous class,indicating
(Clarkeetal. 2001; Alexanderetal. 2006a) and planet for- thatdifferentphysicalprocessesmaybeatwork,andtheremaybe
mation (Armitage&Hansen 1999; Riceetal. 2003). However, differentpathstotransitionaldiscformation,depending onwhich
up to now none of these processes alone have been shown to be of thesephysical mechanisms isdominant. If thisisthecase, we
sufficienttoexplainallobservations. expectthatinsomecasestheremaynotbeasingledominantpro-
Growingthroughcollisions,dustparticlescanindeedbecome cess,anditmaybetheinterplayamongseveralofthemthatleads
largeenoughtobecomeessentiallyinvisibletoobservations.How- toagiventransitionaldiscformation.
ever, whilemodels of grain growth areable to reproduce the ob- Alongthisroute,thegoalofthispaperistostudyifthecombi-
serveddipsintheirinfraredSEDsoftransitionaldiscs,theypredict nationofphotoevaporationandplanetformation,whichhavebeen
that thedust should stillbe visibleat millimetricwavelengths, in up to now studied separately, can indeed help in interpreting the
contrastwithwhatisfoundinobservations(Birnstieletal.2012). puzzlingpopulationofaccretingtransitionaldiscs.Byreducingthe
Thepresenceofagiantplanetembeddedinthediscisableto surface density and the mass accretion rate in the inner disc, we
openagap,andactslikeadam,stoppingtheinflowofmatterfrom expect thatthepresence ofaplanet isabletotriggertheopening
theouterdiscreservoir.However,thedamisporous,andwhilethe of agapby photoevaporation at earlytimes. Wecall thisprocess
surface density in the inner disc is lowered and the mass accre- planet induced photoevaporation (PIPE). To investigate this sce-
tionratereduced,thematerialcanstillflowtowardsitswaytothe nario,wemakeuseofhydrodynamicsmodelsofaphotoevaporat-
star(e.g.Lubow&D’Angelo2006).Toreconcilethiswithobser- ing disc with a giant planet embedded. Our purpose is to assess
vations,itisnecessarytofindtherightcombinationofparameters howthepresenceofaplanetaffectstheclearingofthediscbyX-
thatmakestheinnerdiscopticallythin,whilestillallowingasen- rayphotoevaporation.
siblemassaccretionrate.AsshowedbyZhuetal.(2011),theoret- Thispaperisstructuredasfollows.Insection2wepresentthe
icalcalculationspredictthatonesingleplanetisnotabletoperturb numericalmethodweusedandtheresultsweobtained.Insection
enoughthesurfacedensityoftheinnerdisc,andmultipleaccreting 3wediscusstheresultsandinsection4wedrawourconclusions.
planetsarerequiredtoopenagapofasizecompatiblewithwhat
isfoundinobservations.Thisreduceshoweverthemassaccretion
ratesontothestaraswellasthesurfacedensity. Zhuetal.(2011)
concludethateveninthecaseofmultipleplanetsitisnotpossible 2 NUMERICALINVESTIGATION
tointerpretdiscsthatexhibitalargeholesizetogetherwithahigh
2.1 Methods
massaccretionrateontothestar.
Photoevaporation is the process through which high energy Westudy the disc-planet interaction process by means of the 2D
radiation (from the central star or from the environment) ther- grid-basedhydrodynamicscodeFARGO(Masset2000).Thecondi-
mally drives a wind from the disc. The mass-loss rates depend tionsatthetimet0 oftheformationoftheplanetareprovidedby
on thedetailedphysics of the radiationfield. Including the effect a 1D viscous evolution code, that takes care of evolving the disc
of EUV radiation from the central star, Clarkeetal. (2001) and fromtimet=0tot0.Thisallowstosavecomputationalresources
Alexanderetal.(2006b)showedthatthecoupledevolutionofavis- whendetailedevolutionofthediscisnotneeded.
couslyevolvingdiscwiththepresenceofaphotoevaporativewind
isabletoopenagapintheinnerdiscwhenthemassaccretionrate
through the disc becomes comparable with the mass-loss rate of
2.1.1 Initialconditions(1Devolution)
thewind.Owenetal(2012)furtherarguethatthedustintheinner
discrapidlydriftsontothestar(Alexander&Armitage2007)–on Asinitialconditions,weusethemodelsofOwenetal.(2011).We
atimescaleof ∼ 103 years–, thegasdrainson its(much longer) include the effects of viscous evolution and X-ray photoevapora-
(cid:13)c 2012RAS,MNRAS000,1–11
Photoevaporationandplanetformation 3
tion.Theevolutionof thesurface densityof thediscisdescribed aplanet.Thecode,whichhasbeenwidelyusedinstudiesofpro-
bythefollowingequation: toplanetarydiscs, solvestheequations ofhydrodynamics through
finitedifferencesonagridincylindricalcoordinates. FARGOuses
∂Σ 3 ∂ ∂
∂t = R∂RhR1/2∂R(cid:0)νΣR1/2(cid:1)i−Σ˙w(R), (1) thesamealgorithmsastheZEUScode(Stone&Norman1992)for
hydrodynamics,butemploysamodifiedazimuthaltransporttech-
whereΣisthesurfacedensity,Σ˙w(R)isthephotoevaporationpro- niquethatresultinasmallercomputationalrequestfordiscgeome-
file (as in the Appendix of Owenetal. 2012) and ν is the kine- tries.
matical viscositycoefficient, whichsetsthemagnitude of viscos- ThecodesolvesthecoupledsystemofNavier-Stokesandcon-
ity.WechoosethesamevaluesoftheparametersasinOwenetal. tinuityequation.Wemodifiedthecontinuityequationfromthepub-
(2011), that we summarise here. We evaluate ν using the α pre- liclyavailableversionofthecodetoincludetheeffectsofphotoe-
scription(Shakura&Sunyaev1973):ν = αcsH,wherecs isthe vaporationonthedisc.Thecontinuityequationnowreads:
sound speed of the gas, H is the vertical scale-height and α the
∂Σ
dimensionless Shakura-Sunyaev parameter. In our models we set +∇·(Σv)=−Σ˙w(R), (3)
α = 1.5 × 10−3. The sound speed is a fixed function of ra- ∂t
Rdiu1/s,4)a;ntdheisncohrmosaelnizattoiognivies achmosieldnlys-oflatrhiantgadtis1cA(iU.e.,thHe/aRspe∝ct twiohnereemΣ˙pwloyiesdthien stahmee1Dmaesvs-olloustsionp.roAfilesidmuielartoimphpoletmoeevnatpaotiroan-
ratio H/R = 0.0333. Our computational grid covers the range was also used to study planet scattering in transitional discs by
[0.0025 AU,2500 AU], and it is comprised of 1000 grid points. Moeckel&Armitage (2012).The removal of mass is done at the
ThemeshisuniforminascaledvariableX ∝ R1/2.Ourviscous beginningofthehydrotime-step.Tobeabletofollowtheevolution
code uses a flux-conserving donor-cell scheme, implicit in time. intimeofthedisc,weimplementedaminimumdensitythroughthe
Details about the implementation can be found in Birnstieletal. disc.Wheneverthedensitybecomessmallerthanagiventhreshold,
(2010). itisresettotheminimumallowedvalue.Weusethedimensionless
Theinitialsurfacedensityprofileisgivenby: valueof10−8forthisthreshold,whichisaboutfiveordersofmag-
M (0) nitudesmallerthantheinitialvalueofthedensityinthediscatthe
Σ(R,0)= d exp(−R/R1), (2) planetlocation.Forsafety,wemodifiedalsothetimestepcondition,
2πRR1
addinganother criterionthat doesnot permit tophotoevaporation
whereMd(0)istheinitialmassofthediscandR1 ascaleradius toremoveinasingletimestepmorethanagivenfractionf ofthe
describingtheexponentialtaperofthedisc’souterregion.Weseta
massinacell.Weusedforf thevalueof0.1.However,wenoted
valueofR1 =18AUandaninitialdiscmassof0.07M⊙. inoursimulationsthatthisconditionisneverrelevant,andthatthe
Forwhatconcernsthephotoevaporationprofile,therearetwo
otherusualconditionsonthetimesteparemorerestrictive.
parameters,themassofthecentralstarM∗andtheX-rayluminos- Wesettheparameterstothesamevaluesasinthe1Devolu-
ityLX.WechoseM∗ = 0.7M⊙,whileweperformcalculations tion.Wearehowevernotabletoresolvethewholediscina2dsim-
withdifferentvaluesoftheX-rayluminosity.Wedorunswiththe
ulation,thereforewerestrictourselvesintherange [0.1r ,10r ],
medianX-rayluminosityL =1.1×1030ergs−1,thatweevolve p p
X where r is the planet orbital radius. We employ a resolution of
p
for2Myrsbeforeinsertingtheplanet,andrunswithahigherX-
n = 256cellsintheazimuthal direction,uniformlydistributed.
φ
ray luminosity of logL = 30.8, that we evolve for 0.65 Myr.
X The radial resolution is then chosen so that each cell is approxi-
Thesevaluesfortheplanetformationtime-scaledonotcomefrom
mately square, which gives n = 188 cells. While considerably
r
aphysicalmodel,butratherwerechosentohaveasimilarreason-
higher resolution simulations can be found in the literature, we
ablesurfacedensityprofileatthemomentoftheplanetformation.
remark that here we are interested in the global evolution of the
SinceinthecaseofthehighX-rayluminositytheevolutionofthe
disc,ratherthancapturingsomelocalproperty.Evenifsomefea-
disc is faster due to the increased mass-loss rate, in that case we
tureisnotproperlyresolved(suchastheaccretionstreamsontothe
choseasmallervaluefortheageofdiscatthemomentofplanetfor-
planet),thishaslittleeffectontheglobalevolution.Forthisreason
mation.Inbothcasesthenormalizationat1AUisapproximately
similarstudiesofthediscevolutiononalongtimescalehaveem-
500gcm−2,whichisafactor3-4lowerthantheMinimumMass
ployedaresolutionsimilartoours(e.g.,Zhuetal.2011).Wehave
SolarNebula(Hayashi1981).However,itshouldbenotedthatthe
checked,runningsimulationM20atdoubletheresolutionandcom-
power-lawslopeis−1,ratherthan−3/2,sothatintheouterregion
paringtheresult,thatourresultsstaythesame, withamaximum
thesurfacedensityishigher.Thetotalmassinthediscatthemo-
10%differenceinthemassoftheinnerdiscuptothemomentof
mentofplanetformationisapproximately25Mjupforthemedian thediscclearing.
X-rayluminosity,and20forthehighX-rayluminosity(thediffer-
WeconsideraplanetembeddedinthediscwithamassM =
p
enceduetothediscbeingmorespreadoutinthefirstcase),which 10−3M∗ = 0.7 MJ, and we let the orbital radius of the planet
ishigherthantheMinimumMassSolarNebula.Wenotethatac-
vary from10to50 AU.Theplanet isnot allowed tomigrate,al-
cordingtocurrentplanetformationtheoriesitisdifficult,although
thoughwealsoperformedaruninwhichweincludethiseffect.In
stillplausible(Movshovitzetal.2010),toformagasgiantinthe
thesimulationinwhichweincludedalsomigration,weswitchedit
shorttime-scaleusedinthesecondcase;thereforethehigh X-ray
ononlyafter500orbitstorestricttothecaseofTypeIImigration
luminositycaseshouldberegardedasalimitingone.
andexcludeTypeImigration.Toreduceartefactsinthesolutions
duetoasuddeninsertionoftheplanet,weslowlyincreaseitsmass
duringthefirst100orbits,usingthetaperfunctionprovidedinthe
2.1.2 FARGOsimulations
publicly available version of FARGO. We use open inner bound-
Attimet=t0,weassumethatagasgiantplanetforms,andweuse aryconditionsandreflectingouterboundary(whichisthedefault
theoutputofthe1Dcodeasinputforthe2DFARGOcode.Weas- inFARGO.Totesttheimpactofthischoice,weimplementedan
sumethattheformationhappensonatime-scalefastenoughsothat outerboundarycondition,findingnosignificantdifference).Weuse
wecanswitchfroma1Ddiscwithouthaplanettoa2Ddiscwith planetaryaccretionasprescribedbyKley(1999)usingthepublicly
(cid:13)c 2012RAS,MNRAS000,1–11
4 G. P.Rosottiet al.
Time:2.107Myr Time:2.176Myr Time:2.192Myr
40
]
U
30
A
[
s
u
di
a
R20
10
0 π/2 π 3π/2 0 π/2 π 3π/2 0 π/2 π 3π/2
Azimuth Azimuth Azimuth
TTiimmee::22..110077MMyyrr TTiimmee::22..117766MMyyrr TTiimmee::22..119922MMyyrr
40
]
U
30
A
[
s
u
di
a
R20
10
0 π/2 π 3π/2 0 π/2 π 3π/2 0 π/2 π 3π/2
Azimuth Azimuth Azimuth
Figure1.Toprow:surfacedensityinthediscatthreedifferenttimesfromsimulationM20.Bottomrow:samequantitiesforsimulationM20o,whichdonot
includephotoevaporation.Whileinthefirstsnapshottheinnerdiscisstilltherealsointhecaseincludingphotoevaporation,itiscaughtintheactofclearing
inthesecondsnapshot.Finally,weareleftwithadiscwiththeouterpartonlyinthelastsnapshot.Inthecontrolsimulationinsteadtheinnerdiscisleft.
availableimplementationinFARGO.Ateachtimestep,afraction causeΣ˙w depends onthe(physical)radiusinthediscandonthe
ofthematerialinsidetheHillradiusoftheplanetisremovedand massofthestar.
accreted onto the planet. The fraction is controlled by a free pa-
rameter,f,thatrepresentstheinverseoftheaccretiontimescalein
2.2 Results
dynamicalunits.Weusef = 1forourstandardmodel,although
wetestalsoasituationwitha10timessloweraccretiontimescale. 2.2.1 Qualitativepicture
Table1summarisesthesimulationsrun.
Thesurface density in the disc at three different times from runs
M20andM20oisplottedinfigure1.Intheleftpanel,atanageof
Lastly,itshouldbenotedthattheinclusionofaphotoevapora- approximately2.1Myrs,thedynamicalgapclearedbytheplanetis
tionprofilebreaksdownthedegeneracyofthedimensionlessunits evident,butphotoevaporation hasnotyetstartedtoclearthedisc.
usedbyFARGO.Inthepurehydrodynamicalcase,wehaveonefree The surface density at this stage is very similar to a control run
massscaleandtheresultscanthenbescaledtodifferentcentralstar withoutphotoevaporation, themostnotabledifferencesarevisible
masses.Thisisnolongerthecaseincludingphotoevaporation,be- atthegapedges. Theplanet actslikeadamfortheviscousflow,
(cid:13)c 2012RAS,MNRAS000,1–11
Photoevaporationandplanetformation 5
Runname Orbitalradius[AU] logLX t0[Myr] Notes
M10 10 30.04 2
M20 20 30.04 2
M20m 20 30.04 2 migration
M20f 20 30.04 2 sloweraccretion
M20o 20 30.04 2 nophotoevaporation
M30 30 30.04 2
M40 40 30.04 2
M50 50 30.04 2
M20x 20 30.8 0.65
M40x 40 30.8 0.65
Table1.Thetablesummarisesthesimulationsrun.ThenumberinthenameoftherunspecifiesthepositionoftheplanetinAU;the“x”denotestherunswith
highX-rayluminosity.Inadditiontothestandardruns,whichlettheplanetpositionandtheX-rayluminosityvary,therealsotree“specialruns”,withnames
M20m,M20fandM20o,respectivelyincludingmigration,withaslowerplanetaryaccretiontimescaleemployedandwithoutphotoevaporation. Theinitial
planetmassisineverycase0.7M .
J
10−7
101
10−8
M]jup 100 −1yr]
[ M⊙ 10−9
Mass10−1 M˙[acc
10−2 10−10
10−3 10−11
2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20
Time[Myr] Time[Myr]
Figure2.Solidblueline:massoftheinnerdisc(i.e.,insidetheplanetor- Figure3.Greendashedline:massaccretionrateattheinnerboundary of
bitalradius)withphotoevaporation(runM20).Dottedredline:massofthe thegridasafunctionoftimeforsimulationM20.Forreference,theblue
innerdiscwithoutphotoevaporation(runM20o).Dashedgreenline:mass solidhorizontal lineshowsthemass-lossrateduetophotoevaporation in
oftheouterdisc(i.e.,outsidetheplanetorbitalradius)withphotoevapo- theinnerdisc,whilethereddottedlineisastraightlineaddedasavisual
ration(runM20).Dotted-dashedcyanline:massoftheouterdiscwithout aidtodistinguishthemomentoftheinnerdiscclearing.Thechangeinthe
photoevaporation (runM20o).IntherunM20withphotoevaporation, the slopeofthemassaccretionratecorrespondstotheinnerdiscclearing.This
innerdiscisrapidlydissipated,whileinthecontrolrunM20oitreachesa clearing happens when the mass accretion rate has dropped below some
sortofsteady-statevalue. factorofthemass-lossrate.
reducingthemassaccretionrateintheinnerpartofthedisc.This same initial value, the difference accumulates in time, and when
permitsphotoevaporation totakeover,andcleartheinnerdisc,as photoevaporationbecomesimportantitrapidlydissipatestheinner
canbeseenintheintermediatestepinwhichphotoevaporation is disc.Onthecontrary,inthecontrolrunwithoutphotoevaporation
clearingthediscfrominsideout.Finally,weareleftonlywiththe themassoftheinnerdiscreachessomekindofsteadystatevalue,
outerdisc,whenthediscisapproximately2.2Myrsold.Itshould slightlysmallerthanaJupitermass.Duetoouruseofafloorden-
benotedthattheclearingoftheinnerdiscisduetothecombined sity,aftertheclearingoftheinnerdiscthereisstillanon-zeromass
effectofphotoevaporationandplanetformation.Inthecontrolsim- insidetheorbitoftheplanet,withavaluethatisaround10−4Mjup
ulationM20owithoutphotoevaporation,themassoftheinnerdisc (outofscaleinthefigure).Itshouldbenotedalsothatthereislittle
is reduced, but not cleared completely, as can be seen from the differenceinthemassoftheouterdiscbetweenthetworuns,and
bottomrowoffigure1.Ontheotherhand,withphotoevaporation thatthefinalvalueisaround15Mjup.
alonethediscwouldhaveclearedonalongertime-scale,after3.3 Infigure3weplotthemassaccretionrateattheinnerbound-
Myrsyears.ItcanbeconcludedthatPIPE,i.e.thecombinedeffects aryofthegrid.Thechangeintheslopecorrespondstothemoment
ofphotoevaporationandplanetformation,isabletocleartheinner at which the inner disc starts to clear. In the figure we overplot
discatearliertimes,thatis,starswithgiantplanetswill dissipate also, as a horizontal line, the mass-loss rate due to photoevapo-
theirinnerdiscsquicker. ration (considering the inner disc only). It can be seen that only
Figure2showsthemassesoftheouterandinnerdisc(i.e.,at oncethemassaccretionratehasdroppedbelowsomefactorofthe
radii larger and smaller than the planet orbital radius) as a func- mass-loss rate the clearing begins. The qualitative understanding
tionoftime.Forreferenceweincludedalsotheresultofthe con- ofdiscclearingisthusnotreallydifferentfromtheevolutionofa
trolrunM20owithoutphotoevaporation.Whiletheystartfromthe disc without a planet, namely the two-timescale behaviour (as in
(cid:13)c 2012RAS,MNRAS000,1–11
6 G. P.Rosottiet al.
10−7
101
10−8
−1yr] M]jup 100
M⊙ 10−9 [
M˙[acc Mass10−1
10−10
10−2
10−11 10−3
2.05 2.10 2.15 2.20 2.25 2.0 2.1 2.2 2.3 2.4 2.5 2.6
Time[Myr] Time[Myr]
Figure4.Left:comparisonofthemassaccretionrateattheinnerboundaryasafunctionoftime,varyingtheplanetaryaccretiontimescale.Thebluesolid
lineisforthestandardvalue(f =1),runM20,andthegreendashedlinefortheslowaccretion(f =10),runM20f.Right:comparisonofthemassofthe
innerdiscasafunctionoftime.Thelineshavethesamestyleasintheleftpanel.
theUVswitchmodel):formostofitslifetimetheevolutionofthe inner disc is indeed cleared at later times, since we need to wait
discisdrivenbyviscosity,andonlywhenthemassaccretionrate moreforthemassaccretionratetodrop,duetothehigherporos-
dropsbelowthemass-lossrateduetophotoevaporation theclear- ityof thedam. However, itshould benoted that thedifferenceis
ingbegins.Theroleoftheplanetisthatofacceleratingthisprocess, notsodramaticasonecouldexpectbysuchabigvariationinthe
actinglikeadamthatreducesthemassaccretionrateintheinner timescale. Thisisconsistent withwhat otherauthors havefound,
disc.Weremarkthat,sincetheinnerdiscspendsmostofitslifetime namelythattheprocessofplanetaryaccretionisnotdramatically
withamassaccretionratethatishigherthanthemass-lossrate,the dependant onthevalueofthisparameter(Kley1999).Whatcan-
totalmassofthediscthathasbeenlostthroughaccretionisgreater not be seen from this plot however is that the way in which the
thantheonecarriedawaybyphotoevaporation. Thus,itistheac- discclearsisdifferent.Thiscanbeseenfromthemassofthe in-
cretionthatdoesmostofthe“dirtyjob”ofdissipatingthedisc,and nerdiscversustimecomparisonintherightpaneloffigure 4.We
photoevaporation onlycontributes inthelast stepof theremoval. canseethatwithareducedplanetaryaccretiontime-scalenotonly
Forwhatconcernsplanetaryaccretion,wehavecheckedthatmost theclearinghappensatlatertimes,butitisalsoslower.Visualin-
ofthemassthatendsupontheplanetcomesfromtheouterdisc. spectionofthesurfacedensitydistributionshowsthataninnerring
Thisdoesnotmeanthatplanetaryaccretiondoesnotplayarolein ofmaterialisleftjustinsidetheorbitoftheplanet,which isonly
thedispersaloftheinnerdisc.Indeed,itcontrolstheporosityofthe slowlyeroded.Weinterpretthisasduetothefactthat,becauseof
planetarydam,fixingtheamountoftheviscousflowfromtheouter thehigher massaccretionratethrough theplanetarygap, photoe-
discthatisintercepted.Thiseffectmakesthemassoftheplanetin- vaporation hasamuchmoredifficultjobatremovingthispart of
creasebyafactor6atthemomentofdiscdispersal.However, the thedisc,beingcontinuouslyreplenishedfromtheouterdisc.This
directeffect,namelythemassaccretedbytheplanetdirectlyfrom showsthecomplexstructuresthatmaybeformedduetotheinter-
theinnerdisc,islittlecomparedwiththemassleavingthegridfrom playbetweenthedifferentphysicalprocessesactinginthedisc.
theinnerboundary, apartforasmallinitialtransientinwhichthe
planetisaccretingfromtheregionthatwillbedynamicallycleared.
2.2.3 Varyingplanetposition
In the simulation shown so far the planet has a semi-major axis
2.2.2 Effectofplanetaccretiontimescale
of 20 AU. To find how the inner disc clearing depends on the
This qualitative picture implies that a crucial parameter for esti- planet position, we ran other simulations withdifferent values of
mating the impact of the presence of a planet in the disc is the thisphysicalparameter.Figure 5showsacomparisoninthemass
porosityofthedam.Wenoticethatina1Dsimulationtheplanet oftheinnerdisc(normalizedtotheinitialvalue) asafunctionof
acts as a complete dam, and no filtering is possible. Thus, one timeforthedifferentsimulationsrun,withtheplanetpositionvary-
has to insert by parametrization the porosity of the dam (e.g., ingfrom10to50AU(runsM10-M50).Thefurtherouttheplanet
Alexander&Armitage2009),inawaythatdoesnotconservean- is,theslowertheprocessofdispersal.Thisisexpected,sincemore
gularmomentum. Thiseffect isbetteraccounted forin2D simu- timeisrequiredforafurtheroutplanettoreducethemassaccre-
lations, wherethetransport of angular momentum across the gap tionrateneartothestar.However,wecanseethatinallcasesthe
istreatedinarealisticfashion,althoughthereisstilladependence disc dispersal is considerably faster than without the presence of
on the planet accretion time-scale. Totest how robust our results aplanetinthedisc.Afittotheinitialsurfacedensityprofilewith
arewithrespecttothevariationofthisparameter,werunasimula- equation2givesforR1avalueofapproximately80AU,sothatfor
tionwitha10timeshighervalue(i.e.,theplanetaccretes10times theusedvaluesoftheplanetpositiontheplanetisabletocutmost
slower),f =10,thatwecallM20f.Intheleftpaneloffigure4we ofthediscmassreservoirfromtheinnerradii.Fromthisargument
proposeacomparisonbetweenthemassaccretionrateattheinner weexpectthataplanetfurtheroutthanR1,ifabletoform,would
boundaryofthegridofthissimulationwiththestandardone.The nothaveasignificantimpactonthedisclifetime.
(cid:13)c 2012RAS,MNRAS000,1–11
Photoevaporationandplanetformation 7
the slower the process of disc dispersal. Visual inspection of the
100 imagesconfirmsthesamequalitativebehaviourweoutlinedinthe
previoussection.
)010−1 2.2.5 Effectofmigration
t(
ss Totestthesensitivityofourresultstomigration,thatweneglected
a
M so far, we run a simulation with migration included, M20m. The
s/ leftpaneloffigure7showsacomparisoninthemassesofthein-
s
Ma10−2 nerdisc,showingthatthereisverylittledifferenceinthe process
of disc clearing. This is a consequence of the fact that the clear-
ing proceeds from inside out, so that the beginning of the clear-
ingissetbythepropertiesofthediscintheinnerportion, rather
thanintheneighbourhood oftheplanetthatisaffectedbymigra-
10−3
2.0 2.1 2.2 2.3 2.4 2.5 tion.Therightpaneloffigure7showsthesemi-majoraxisafunc-
Time[Myr]
tionoftime,showingthattheplanethasnotmigratedmuchbefore
thedisc is dispersed, approximately 2 AU. It may be argued that
Figure5.Comparisonofthemassoftheinnerdiscnormalizedtotheinitial
valueforsimulationswithdifferentpositionoftheplanet,varyingfrom10 thisisaconsequenceoftheinitialconditions,namelythatwetook
to50AU(runsM10-M50).Thefurthertheplanet,theslowertheclearing quite an evolved disc. Inserting the planet at earlier times would
ofthedisc. have allowed more time to migrate, and therefore to be more in-
cisiveinmodifyingtheclearing.Thisiswhathasbeenstudiedby
Alexander&Armitage (2009) and Alexander&Pascucci (2012),
whocoupledthediscevolutiontotheplanetmigrationandstudied
100 theresultingplanetdistribution.Theeffectofmoremassiveplanets
insertedinmassive(self-gravitating)discsisthefocusofaforth-
comingstudybyClarkeetal.(inprep.),whileinthisworkwefocus
10−1 onthestudyoflessmassivedisc-planetsystems.
)
0
t(
s
s
a
M10−2
/ 3 DISCUSSION
s
s
a
M IntheprevioussectionweshowedhowPIPEisabletochangethe
10−3 pictureofdiscdispersalwithrespecttophotoevaporationorplanet
formation alone. The main finding is that discs with a planet are
likelytobedispersedearlierthandiscswithout.Aninterestingtest
10−4 ofthePIPEscenario,istocompareitspredictionswiththeobser-
0.65 0.70 0.75 0.80
vationsof transitional disc,that areinterpretedasdiscs caught in
Time[Myr]
theactofclearing.InparticularwestudytheM˙ −R parameter
hole
Figure6.Massoftheinnerdisc,normalizedtotheinitialvalue,asafunc- space.Foreachofourmodels,theaimistocomputeevolutionary
tionoftime,forsimulations withthehighvalue oftheX-ray luminosity tracksthatcanbeplottedinthisparameterspace.Incontrastwith
withpositionsoftheplanetof20and40AU,runsM20x(solidblueline) Owenetal.(2011),duetotheincreasedcomputationalcost,weare
andM40x(dashedgreenline). notableheretorunawholepopulationsynthesis;rather,wewillbe
limitedtocomparingwithindividual datapoints. Inparticular,we
wishtoanswerthequestioniftransitiondiscswithlargeholesand
2.2.4 VaryingX-rayluminosity
massaccretion ratescan be accounted forby PIPE.A similarat-
Asalimitingcase,werunsimulationswithahighvalueofX-ray tempthasbeenmadebyMorishima(2012)throughthemodelling
luminosity, equaltologLx=30.8. Thediscis0.65 Myroldatthe ofX-rayphotoevaporatingdiscswithdeadzones.
timewhenthegiantplanetisinserted.Whilethismaysoundlike Unfortunately, ourhydrodynamical modellingdoesnotyield
anunrealisticallyyoungageforplanetformation,wenotethatthe directlytheseparameters.Inparticular,themassaccretionratethe
relativediscagecanbeobtainedbytheappropriatescalingofini- observations measure is the one onto the star, that we cannot re-
tialparametersandherewechoseavaluethatgivesasimilarsur- solvefornumericalreasons. Therefore,wemaketwolimitingas-
facedensitynormalization(althoughthediscislessspread,being sumptionstothemodelling.
younger) tothepreviouscase.Thisshowshow evenquiteamas- Inthefirst,conservativeassumption,weassumethattheX-ray
sivedisccanberapidlydispersedbythecombinedeffectofX-ray photoevaporationdrivenclearingoftheinnermostdiscproceedsas
photoevaporationandplanetformation. itwoulddo intheabsence of aplanet, opening agapatapproxi-
The evolution of the mass of the inner disc as a function of mately1.5AU.Thisgapisinsidetheregionthatwecanresolvein
time,normalizedtotheinitialvalue,isshowninfigure6fordiffer- thesimulation.Thediscwillthenexhibittwogaps,thedynamical
entvaluesoftheplanetinitialposition.Becauseofthehighermass- oneclearedbytheplanetandtheoneopenedbyphotoevaporation,
loss rates of photoevaporation, everything is happening quicker, thatdividethediscinthreedistinctregions(namedA,BandCin
withadispersalthatcanhappensofastaslessthan105 yearsaf- thefollowingforclarity).Asinthephotoevaporationcase,weas-
ter the planet formation. Also in this case the further the planet, sumethatthedustintheinnermostdiscAwilldrainveryquickly
(cid:13)c 2012RAS,MNRAS000,1–11
8 G. P.Rosottiet al.
24
101
U]
A22
M]jup 100 axis[
Mass[10−1 major20
mi-18
e
10−2 S
16
10−3
2.00 2.05 2.10 2.15 2.20 2.00 2.05 2.10 2.15 2.20
Time[Myr] Time[Myr]
Figure7.ResultsfromthesimulationM20mincludingmigration.Leftpanel:themassoftheinnerdiscasafunctionoftimeforsimulationM20m(bluesolid
line).Forreferencehasbeenplottedalsothecasewithoutmigration,runM20(greendashedline).Rightpanel:semi-majoraxisoftheplanetasafunctionof
time.
102 25
101
20
]
2
−
m
c 100
[g U]15
y A
densit10−1 R[hole10
ce10−2
a
urf
S 5
10−3
10−4 0
5 10 15 20 25 30 0 1 2 3 4 5 6 7 8
Radius[AU] Timesincebeginningofclearing[104yr]
Figure8.Surfacedensityasafunctionofradiusjustbeforetheinnerdisc Figure9.Innerholeradiusafunctionoftime(sincetheclearing),forthe
clearingstartsinrunM20(bluesolidline),comparedwiththesurfaceden- PIPEM20calculation(bluesolidline)andthe1Dmodelwiththemedian
sityinthe1DcalculationsfromOwenetal.(2011)modelwiththemedian X-rayluminosity(greendashedline)fromOwenetal.(2011).Thedeple-
X-rayluminosity(greensolidline). Thesurface densityarequitesimilar tionofthesurfacedensitycausedbytheplanetmakestheopeningofthe
neartotheinnerboundary,whileatgreaterradiiinthecase withaplanet holemuchfaster.Theoscillationsthatcanbeseenintheradiusofthehole
thesurfacedensityprofileismuchflatter. inmodelM20areaconsequenceoftheoscillationsatgapedgesvisiblein
figure1.
(∼103yr)ontothestar,sothatregionAwillbeinvisibleinobser-
vations.Thediscwillthenlooklikeatransitiondiscandtheradius duetothepresenceoftheplanetthatmakesthisregiondevoidof
oftheholeissetbytheinnerradiusofdiscB,thatwecanmeasure gas. This motivates us to assume that the dependence with time
fromthe2Dsimulation.WhileAisdraining,thereisstillameasur- ofthemassaccretionrateontothestaristhesameasinthecase
ablemassaccretionrate.Weassumethatthedependenceontimeof withouttheplanet,comingfromthedrainingofthediscAontothe
themassaccretionrateontothestaristhesameasinthe1Dsimu- star,butnowwithadifferentR dependencethatisderivedfrom
hole
lation,wherewetakeasthebeginningofclearingthetimeatwhich the2D simulation.Infigure9wecompare theR dependence
hole
inthe1Dsimulationtheradiusoftheholeistheinnerboundaryof formodelM20andthecorrespondingmodelwithoutaplanet,i.e.
our2Dgrid.Wenotethatthedensitystructureintheregionwecan Owenetal. (2011) model with the median X-ray luminosity. We
resolveisquitesimilarbeforetheonsetofclearingoftheinnerdisc, definetheradiusoftheholesimplyastheminimumradiuswhere
asweshowinfigure8.Inthisfigurewecomparethesurfacedensity theazimuthallyaveragedsurfacedensityisabovetheimposedfloor
fromourFARGOsimulationM20justbeforetheinnerdiscbegins density(withanallowancefactorof10,duetothepresenceofnu-
toclearwiththeresultsfromthe1Drunwithouttheplanet,atthe mericaloscillationsabovethefloordensity).Becauseofthemen-
timeinwhichtheradiusoftheholeis2AU(namelytheinnerradius tioneddepletionofthesurfacedensity, theclearingofthe holeis
ofour2Dgrid).Thesurfacedensitiesneartheinnerboundaryare muchfasterinthecasewithphotoevaporation.Whencomparedto
verysimilar,whileatlargerradiithedensitydistributionislower, modelsthatincludeX-rayphotoevaporationalone,wethusexpect
(cid:13)c 2012RAS,MNRAS000,1–11
Photoevaporationandplanetformation 9
wetakeasinthepreviouscasethemassaccretionrateaspredicted
10−7 by the case without the planet. The resulting tracks in this case
(plottedingreen continuous infigure 10) looklike verticallines,
since there is littleevolution of the radius during the simulation,
and the mass accretion rate simply decreases. Using this second
10−8
assumption, onewouldthenconcludethat,whenthedust proper-
−1] tiesaretakenintoaccount,PIPEisabletoexplaindiscswithlarge
yr holesandmassaccretionrates.Whileuptonowthetheoreticalef-
M⊙ 10−9 forthasbeentopredictwhethertheappearanceofaplanetbearing
[
M˙acc dinisucnrdeesresmtabnldeisngthathteoefvtoraluntsiiotinonoaflsduicshc,slyistttleemws.orPkhohtaosevbaepeonradtoionne
10−10 couldpotentiallygiveareasonfortheshuttingdownofaccretion,
thatisrequestedfromthelackofobserveddatapointsintheregion
oftheplotwithlargeholesandlowmassaccretionrates.Toexplore
10−11 thispossibility,weplottedlightgreencrossesalongthetracksev-
0 10 20 Rhole30[AU] 40 50 60 ery104years.Thereisnothoweveraclearseparationbetweenthe
uppermost andthelowerpartofthetrack,withonlyalittlejump
Figure10.M˙ −Rholeparameterspaceoftransitiondiscs.Thegreyarea thatisnotenoughtoaccountforthedesertontheobserveddesert
is the area permitted by X-rayphotoevaporation alone, as in Owenetal. in the observed distribution. If this desert is real and not due to
(2011).Pointsaretheobserveddatapoints withhighmillimetrefluxfrom observationalbiases(e.g.discswithhighmassaccretionratesare
Owen&Clarke(2012).Diamondsarefordiscwithoutadetectedmassac- alsomoremassive),thenanewmechanismmustdestroytheouter
cretionrate.Bluedashedtracksareforthefirstassumption (seetext)and
disc.Suchamechanismcouldbegivenbythe“thermalsweeping”
greencontinuousforthesecond;crossesonthetracksareplottedevery104
effect,aninstabilityfoundinphotoevaporatingdiscswithaninner
years.
holebyOwenetal.(2012),abletodestroythediscintheorderof
thedynamicaltimescale.TheforthcomingworkofClarkeetal(in
PIPEmodelstoyieldhighermassaccretionratesforthesamehole prep.)presentsanalternativescenariobasedonthecarvingofmm-
size,orconverselylargerholesatthesamemassaccretionrate.The brightaccretingtransitiondiscsbymassiveplanetarycompanions
timet = 0intheplotreferstothebeginningoftheclearing,and embeddedandmigratinginself-gravitatingdiscs.
it is the one when in the 1D simulation the radius of the hole is Ourresultssuggest thattheinterplaybetweenX-rayphotoe-
2 AU. Weplot our results in the M˙ −R parameter space in vaporationandplanetformationisworthoffurtherstudy.Ourwork
hole
figure 10 as the blue dashed tracks. The cyan crosses are plotted alsoimpliesthatplanetsareanimportantingredientinthediscdis-
every104 years.RunsM20xandM40xaretheonesthatproduce persalprocess,andshouldbeincludedinthemodelling.Theabil-
thehighermassaccretionrates,whileonlyrunsM10andM20are ityoftheupcomingALMAfacilitywillbehopefullybeabletotell
visiblefromtherunswiththemedianX-rayluminosity.Thepoints more about the gas structure in transitional discs, which is at the
intheplotaretheobserveddatapointsthatexhibitahighmillime- momentverypoorlyconstrained.
treflux,asitisdescribedinOwen&Clarke(2012).Thedatapoints
showaweakcorrelationbetweentheholeradiusandthemassac-
3.1 Modellimitations
cretionrate,whichhasnotbeenexplainedyet.Thegreyareaisthe
areapermittedbyX-rayphotoevaporationalone,asinOwenetal. Inthispaperithasbeenassumedthatthephotoevaporationprofile
(2011).Usingthisconservativeassumption(bluelines),onewould isthesameascomputedbyOwenetal.(2011),whomodelledthe
thenconcludethatthePIPEscenarioisindeedabletoexpandthe photoevaporative flow in a disc without a planet. Large scale 3D
parameter space with respect to photoevaporation alone, but that simulations that include both photoevaporation and a planet em-
themassaccretionratesobtainedarestilltoolow compared with beddedarebeingcarriedoutandwillbepresentedinaforthcoming
theobservations. paper(Rosottietal,inprep.).
Theotherlimitingassumption,thatisabestcasescenariofor Theabsolutetimescalesdiscussedinthepapershouldbetaken
us,istheoneinwhichtheplanetisabletofilterthedust,sothatthe with caution as they strongly depend on a number of simplify-
discwouldlooklikeintransition,evenifthereisstillahugequan- ing assumptions. Firstof all, asource of uncertainty comes from
tityofgasinsidetheorbitoftheplanet.Insynthesis,bymodifying theunknown mechanism fortheangularmomentum transport. In
thesurfacedensityprofileofthedisc,theplanetcreatesapressure thisworkwehaveconsideredasimpleα-discandassumedacon-
maximum.Dustparticles,flowinginward,areunabletocrossthis stantvalueofα.Theassumptionofaconstantα-valueiscommon
maximum,sothatthedustisfilteredoutfromtheinnerportionof in many theoretical studies of discs (e.g. Alexanderetal. 2006b;
the disc, that becomes invisible to observations. This simple pic- Gortietal.2009;Owenetal.2011),andismotivatedbyalackof
tureiscomplicatedbytheotherdustprocessesthathappensimul- strongobservationalconstraintsandbysimplicity,necessarytoiso-
taneously(coagulation,fragmentation,diffusion,...).Thisprocess late the effect of the other processes that affect the evolution of
hasbeenstudiedindetailbyRiceetal.(2006),Pinillaetal.(2012) thedisc.However,noknown theoryofangularmomentumtrans-
andZhuetal.(2012).Inthiscase,wetaketheorbitalradiusofthe port predicts a constant value for α (Armitage 2011). Therefore,
planetastheradiusofthehole.Beforetheclearingstarts,wetake such an assumption should be regarded more as amatter of con-
themassaccretion rateattheinnerboundary ofthegrid,starting venience.Studiesaddressingtheissueofhowaphysicalmodelfor
from500orbitssincethebeginning ofthesimulation(toexclude theviscosity,e.g.thelayeredaccretionmodelproposedbyGammie
initial oscillations), under the assumption that the mass accretion (1996),changestheevolutionofthedischavebeenconductedby,
rateintheinnerportionofthegridthatwedonotsimulateissetby for example, Armitageetal. (2002); Morishima (2012). The lay-
theouterpartthatwecanresolve.Oncetheinnerdiscstartstoclear, ered accretion model predicts the formation of dead zones in the
(cid:13)c 2012RAS,MNRAS000,1–11
10 G. P.Rosottiet al.
disc, where the viscosity is significantly lower than in the active 4 CONCLUSIONS
partsofthedisc.Thisisduetotheinsufficientionizationlevelin
Inthispaperwepresentedresultsfrom2Dsimulationsofdiscswith
thecoldmidplaneofthedisc,whichisnotenoughtocouplethegas
giant planets embedded undergoing X-ray photoevaporation. Our
withthemagneticfieldandtriggerthemagnetorotationalinstability
results show that planet formation influences the process of disc
(MRI).Theaccretioncontinuesinathinlayer,wheretheionizing
dispersal by photoevaporation. The main consequences of planet
radiation(X-raysfromthestarandcosmicrays)areabletopene-
formationinducedphotoevaporation(PIPE)canbesummarizedas
trate. Thenet effect, once vertically averaged, istocreate azone
follows:
withareduced viscosity.Employingadifferentmodelofphotoe-
vaporation thantheoneusedinthispaper, Armitageetal.(2002) (i) byreducingthemassaccretionflowontothestar,discsthat
modelledthecombined evolutionofagiant planet migratingina formplanetswillbedispersedatearliertimesthandiscswithoutby
layereddisc.Theyfindthatthemaineffectoflayeredaccretionisto X-rayphotoevaporation.
slowdownplanetarymigrationduetothelongerviscoustimescale. (ii) Forwhatconcernstransitionaldiscs,PIPEisabletoproduce
However,asshowedinsection2.2.5,migrationisalreadyrelatively transitiondiscthatforagivenmassaccretionratehavelargerholes
unimportantforourresults,sothisisprobablyasecond-order ef- whencomparedtostandardX-rayphotoevaporation.Howeverfur-
fect.Morishima(2012)foundthattheinterplaybetweendeadzones thermodelling of thedust processes isneeded tobeabletofully
andphotoevaporationcanalsobeapossibleroutefortheformation exploittheobservationalconsequencesofthisprocess.
oftransitiondiscswithlargeholesandlargemassaccretionrates. (iii) Assuming that the planet is able to filter dust completely
Theirresultspredict that, neartheouteredgeof adead zone, the (Riceetal. 2006; Pinillaetal. 2012; Zhuetal. 2012), large hole
radialmotionofgasisdirectedoutwards,whileitisinwardsinside transitiondiscscouldbeproduced.PIPEmayinstigatetheshutting
thedeadzoneregion.Thiseffect,oncecoupledwithphotoevapora- downaccretion;however,oursimplifiedmodelscannotatpresent
tion,maybeabletoopenagapinthediscattheouteredgeofthe explaintheobserveddesertinthepopulationoftransitiondiscwith
deadzone,around 40AUintheircalculations.Thedeadzonein largeholesandlowmassaccretionrates.
theinnerdiscwillsurviveforalongtimeaftertheopeningofthe
gap,sothatM˙ remainshighevenafterthegapopens.Suchconsid-
erationsmayalsoapplytothesystemsexploredinthiswork.Itis
ACKNOWLEDGEMENTS
howeverdifficulttopredicttheeffectofavaryingviscosityinduced
bythepresenceofadeadzoneonthediscclearingtimescalescal- Giovanni Rosotti acknowledges the support of the International
culated here. The location and extent of the supposed dead-zone Max Planck Research School (IMPRS) and is grateful to CITA
withrespecttotheplanetwillhaveastronginfluenceonhowthe foritshospitalityduringpartofthiswork.PJAacknowledgessup-
dispersalisaffected.Eventhedirectionofthefeedbackfromdead- portfromNASAundergrantHST-AR-12814awardedbytheSpace
zoneformationisdifficulttopredict.Ontheonehand,adeadzone TelescopeScienceInstitute,whichisoperatedbytheAssociation
reducesthemassaccretionratesintheregion,hencereducingthe ofUniversitiesforResearchinAstronomy,Inc.,forNASA,under
massflowsthroughaplanetgap,yieldingtoafasterdecouplingof contactNAS5-26555.WewouldliketothankTilmanBirnstielfor
theinnerandouterdisc.Howeverifthedead-zone containsmost providingtheviscousevolutioncode. WethankGiuseppe Lodato
of the disc mass, as inthe Morishima (2012) calculations, its ef- andCathieClarkeforinterestingdiscussions.
fectcouldalsobeoneofstabilisationofthemassaccretionratesin
theinnerdisc,resultinginaslowerdrainingofthelatter.Clearlya
focussedexplorationoftherelevantparameterspacewould bere-
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