Giant planet and brown dwarf formation

0.93 MB·

by  G. Chabrier

Giant planet and brown dwarf formation
GillesChabrier
EcoleNormaleSupe´rieuredeLyon
UniversityofExeter
AndersJohansen
LundUniversity
MarkusJanson
PrincetonUniversity
4 Queen’sUniversityBelfast
1
0
RomanRafikov
2
PrincetonUniversity
n
a
J Understandingthedominantbrowndwarfandgiantplanetformationprocesses, andfindingoutwhether

9 theseprocessesrelyoncompletelydifferentmechanismsorsharecommonchannelsrepresentsoneofthema-
2 jorchallengesofastronomyandremainsthesubjectofheateddebates.Itistheaimofthisreviewtosummarize

thelatestdevelopmentsinthisfieldandtoaddresstheissueoforiginbyconfrontingdifferentbrowndwarfand
]
R giantplanetformationscenariostopresentlyavailableobservationalconstraints. Asexaminedinthereview,if
objectsareclassifiedas”BrownDwarfs”or”GiantPlanets”onthebasisoftheirformationmechanism,ithas
S
. nowbecomeclearthattheirmassdomainsoverlapandthatthereisnomasslimitbetweenthesetwodistinct
h
populations. Furthermore,whilethereisincreasingobservationalevidencefortheexistenceofnon-deuterium
p
burningbrowndwarfs,somegiantplanets,characterizedbyasignificantlymetalenrichedcomposition,might
-
o bemassiveenoughtoignitedeuteriumburningintheircore. Deuteriumburning(orlackof)thusplaysnorole
r
t ineitherbrowndwarforgiantplanetformation. Consequently,wearguethattheIAUdefinitiontodistinguish
s
thesetwopopulationshasnophysicaljustificationandbringsscientificconfusion. Incontrast,browndwarfs
a
[ andgiantplanetsmightbearsomeimprintsoftheirformationmechanism,notablyintheirmeandensityand

in the physical properties of their atmosphere. Future direct imaging surveys will undoubtedly provide cru-
1
cialinformationandperhapsprovidesomeclearobservationaldiagnosticstounambiguouslydistinguishthese
v
9 differentastrophysicalobjects.
5 .
5
7
.
1
1. INTRODUCTION nate”browndwarfs”(1)allfreefloatingobjectsbelowthe
0
4 hydrogen-burning minimum mass, ∼ 0.075M(cid:12) for solar
The past decade has seen a wealth of sub-stellar object
1 composition(Chabrieretal.,2000b),nomatterwhetheror
v: (SSO) discoveries. SSO’s are defined as objects not mas- not they are massive enough to ignite deuterium burning,
sive enough to sustain hydrogen burning and thus encom-
i and (2) objects that are companions to a parent star or an-
X passbrowndwarfs(BD)andplanets, morespecificallygi-
otherBD,butexhibitcompositionalandmechanical(mass-
r ant planets (GP), we will focus on in the present review.
radius) properties consistent with the ones of a gaseous
a
For sake of clarity, we will first specify which objects we
sphereofglobalchemicalcompositionsimilartotheoneof
refer to as ”brown dwarfs” and ”giant planets”, respec-
theparentstar/BD.Incontrast,”giantplanets”aredefined
tively. For reasons which will be detailed in the review,
ascompanionsofacentral,significantlymoremassiveob-
we do not use the IAU definition to distinguish between
ject,anecessarycondition,whosebulkpropertiesstrongly
these two populations. Instead, we adopt a classification
depart from the ones just mentioned. We are well aware
which, as argued along the lines below, (1) appears to be
of the fact that these definitions do retain some ambiguity
more consistent with observations, (2) is based on a phys-
insomecases(e.g. someplanetsmightbeejectedontoan
ically motivated justification, invoking two drastically dif-
hyperbolic orbit and become genuine ”free floating plan-
ferent dominant formation mechanisms, (3) allows a mass
ets”) but, as argued in the review, these ambiguous cases
overlapbetweenthesetwopopulations,asindeedsupported
arelikelytobestatisticallyrare. Wewillcomebacktothis
byobservationsbutexcludedbythepresentofficialdefini-
issueintheconclusionofthereview.
tion. Thisclassificationisthefollowing. Wewilldenomi-
1
According to the above classification, the detection of domain. Finally, as the outcome of these confrontations,
BD’s now extends down to objects nearly as cool as our we will try in the conclusion to determine what is or are
jovianplanets,bothinthefieldandinclusterassociations, thedominantformationmechanismsforbrowndwarfsand
closely approaching the bottom of the stellar initial mass planets and whether or not they may share some common
fonction (IMF). Extrasolar planets, on the other hand, are channels.
discoveredbyradialvelocitytechniquesandtransitsurveys
atanamazingpace. Thewealthofdiscoveriesnowextends 2. OBSERVATIONAL PROPERTIES OF BROWN
fromgaseousgiantsofseveralJupitermassestoEarth-mass DWARFS
objects.
An excellent summary of BD observational properties
Bothtypesofobjectsraisetheirownfundamentalques-
canbefoundinLuhmanetal.(2007)andLuhman(2012).
tions and generate their own debates. Do brown dwarfs
We refer the reader to these reviews, and all appropriate
form like stars, as a natural extension of the stellar forma-
referencestherein,foradetailedexaminationofBDobser-
tionprocessinthesubstellarregime? Orarebrowndwarfs
vational properties. We will only briefly summarize some
issued from a different formation scenario and represent a
resultshere.
distinctiveclassofastrophysicalbodies? Similarly,cangi-
ant planets form in a fashion similar to stars, as the result 2.1. Thebrowndwarfcensusandmassfunction
ofagravitationalinstabilityinaprotoplanetarydisk,ordo
It is now widely admitted that the stellar initial mass
theyemergefromacompletelydifferentprocess,involving
function,definedhereafterasdN/dlogM(Salpeter,1955),
theearlyaccretionofplanetesimals? Whatarethedistinc-
flattens below a mass ∼ 0.6M compared to a Salpeter
tive observational signatures of these different processes? (cid:12)
IMF (Kroupa, 2001; Chabrier, 2003). Although the IMF
From a broader point of view, major questions concerning
belowthismassisoftenparametrisedbyaseriesofmulti-
theveryidentificationofbrowndwarfsandgaseousplanets
plepower-lawsegments,suchaformdoesnothavephysical
remain to be answered. Among which, non exhaustively:
foundation. In contrast, the IMF can also be parametrised
do the mass domains of brown dwarfs and giant planets
byapower-law+lognormalform,abehaviorwhichhasbeen
overlap or is there a clear mass cut-off between these two
showntoemergefromthegravoturbulentpictureofstarfor-
populations? Does deuterium burning (resp. lack of) play
mation (Hennebelle and Chabrier, 2008; Hopkins, 2012).
adeterminantroleinbrowndwarf(resp. planet)formation,
The behavior of such a stellar IMF in the BD regime can
providingakeydiagnostictodistinguishthesetwopopula-
nowbeconfronteddirectlytoobservationsbothinthefield
tionsoristhisprocessinconsequential? Withaconnected,
and in young clusters and star-forming regions. Figure 1
crucialquestion:whatistheminimummassforstar/brown
compares the predictions of the number density distribu-
dwarfformationandthemaximummassforplanetforma-
tions of BD’s as a function of T and J-absolute magni-
tion? eff
tudeforanageof∼1Gyr,assumingaGalacticconstantstar
Itistheaimofthepresentreviewtoaddresstheseques-
formation rate, a double-exponential Galactic disk density
tions and to find out whether or not we have at least some
distributionandaChabrier(2005;hereafterC05)IMF(see
reasonablyrobustanswersaboutBDandGPdominantfor-
Chabrier(2002,2005)fordetailsofthecalculations),with
mationmechanismsbyconfrontingpredictionsofthevari-
themostrecentobservationaldeterminations.TheC05IMF
ous suggested formation scenarios with observations. The
isbasedonaslighlyrevisedversionoftheChabrier(2003)
general outline of the review is as follows. In sections 2
IMF(Chabrier,2003)(seeChabrier, 2005). Theobserva-
and 3, we first summarize the most recent observational
tionsincludeinparticulartherecentresultsfromtheWISE
determinationsofbrowndwarfandgiantplanetproperties.
survey,whichnearlyreachesthebottomendoftheBDmass
Thisincludesbothfieldandstarformingregionsforbrown
distribution(T < 500K)inthefield(Kirkpatricketal.,
dwarfs as well as transit and radial velocity surveys for eff
2011). It is striking to see how the WISE discoveries, as
planets. We will particularly focus on direct imaging ob-
wellastheonesfromprevioussurveys,areconsistentwith
servationsofJupiter-massbodiesaswidecompanionsofa
aC05IMFextendingfromthestellarregimeintototheBD
central star, which may encompass both types of objects.
one. As shown in Table 1 of Chabrier (2005), the BD-to-
In §4, we briefly summarize the observable properties of
starratiopredictedwiththisIMFwas∼1/4,whiletheratio
protostellar and protoplanetary disks and examine the re-
revealedsofarbythe(stillpartlyincompleteatthe∼20%
quiredconditionsforsuchdiskstobegravitationalunstable
level)WISEsurveyis∼1/5. Thedeterminationoftheage
and fragment. Section 5 is devoted to a brief summary of
of the WISE objects is an extremely delicate task. Evo-
thedifferentexistingformationscenariosforbrowndwarfs
lutionary models (mass, age) and synthetic spectra (T ,
and planets. We will identify the distinctive concepts and eff
log g)inthistemperaturerangeremainsofartoouncertain
physicalmechanismsattheheartofthesescenariosandex-
to provide a reliable answer. The WISE survey, however,
aminetheirviabilitybyconfrontingthemwiththeprevious
probesthelocalthin-diskpopulation,sothediscoveredBDs
observational constraints. In section 6, we will examine
shouldbeonaveragelessthanabout3Gyrold. According
whether BD’s and GP’s can be distinguished according to
to BD theoretical evolution models (Baraffe et al., 2003;
various signatures which have been suggested in the liter-
Burrows et al., 2003; Saumon and Marley, 2008), for an
ature, namely early evolution, deuterium burning or mass
2
T Y
L
L T
Fig.1.—BrowndwarfnumberdensityasafunctiionofT (top)andabsoluteJ-magnitude(bottom)predictedwithaChabrier(2005)
eff
IMFforresolvedobjects(dash)andunresolvedbinarysystems(solid). TheL,TandYletterscorrespondtothevariousBDspectral
types. Thesolidtriangles,squaresandcirclesindicatevariousobservationaldeterminations(Burgasseretal.,2004;Cruzetal.,2007;
Metchevetal.,2008;Burninghametal.,2010;Reyle´etal.,2010),whilethehistogramwiththearrowsportraystheWISE(uncomplete)
observations(Kirkpatricketal.,2011).
ageof3Gyr(resp.1Gyr)BD’switheffectivetemperatures below the D-burning limit (Lucas et al., 2006; Caballero
below400K(resp. ∼550-600K)mustbelessmassivethan etal.,2007;LuhmanandMuench,2008;Marshetal.,2010;
0.012 M , i.e. below the D-burning limit for solar com- Scholz et al., 2012b,a; Lodieu et al., 2011; Delorme et al.,
(cid:12)
position(Chabrieretal.,2000a). Sofar,theWISEsurvey 2012a).Althoughtheseobjectsaresometimesdenominated
hasevendiscovered1fieldBDwithT (cid:46) 350K,reach- free floating ”planetary mass objects”, based on the IAU
eff
ingthetemperaturedomainofJupiter-likeobjects. Asjust definition,suchadistinctappelationisnotjustified,asthese
mentioned,thedeterminationoftheeffectivetemperaturein objectsareregulargenuineBDsnotmassiveenoughtoig-
this regime still retains significant uncertainties and these niteD-burning. Thesamewaystarsnotmassiveenoughto
values should be taken with due caution but these results igniteH-burningviatheCNOcyclesarestillcalled”stars”
suggestthatsomeofthefieldobjectsdiscoveredbyWISE andhaveneverbeennameddifferently.
liebelowtheD-burninglimit.Atanyrate,theWISEsurvey, All these BD discoveries are consistent with the very
asbothstatisticsandmodelsimprove,holdstheperspective same underlying ”universal” IMF extending continuously
tonaildowntheminimummassforstar/BDformationand fromthestellarregimeintotheBDonedowntoaboutthe
theIMF,aresultofmajorimportance. opacity fragmentation limit, with no noticeable variations
Notice that a C05 IMF would correspond globally to a betweenvariousregions(underMilkyWaylikeconditions)
negative α value, in terms of dN/dM ∝ M−α, below nor evidence whatsoever for a discontinuity near the H-
about T (cid:46) 1300 K, indicating a decreasing number of burning limit. This strongly argues in favor of a scenario
eff
BD’swithdecreasingmassbelow∼30M foraageof1 inwhichBD’sandstarssharedominantlythesameforma-
Jup
Gyr. Thisisinstarkcontrastwiththeplanetarymassfunc- tionmechanism.
tion, whichrevealsanincreasingnumberofobjectsbelow Therehasbeensomeclaimsbasedonmicrolensingob-
about the same mass (Mayor et al., 2011; Howard et al., servations (Sumi et al., 2011) for an excess of a very-low
2010). Similarly, the BD mass distribution has now been massobjectpopulation(∼afewM )inthefield,formed
Jup
determined in more than a dozen clusters or star-forming inproto-planetarydisksandsubsequentlyscatteredintoun-
regionsdownto∼ 0.02M orlessandthesedistributions bound orbits. The validity of these results, however, can
(cid:12)
are found to agree quite well, with some expected scatter, be questioned for several reasons. First of all, the excess
with the very same C05 IMF for unresolved systems (see number is based on 5 events - which depart form the ex-
e.g. Fig. 8and9ofJeffries(2012)). pecteddistributiononlyatthe∼1σ limit-andthushasno
Browndwarfsarenowroutinelydiscoveredwithmasses statisticalsignificance. Second,whenobservingashortdu-
3
ration isolated event with low S/N and non-complete cov- rityfrequencywithmass(seebelow). Therefore,presently
erage, the symmetryof theevent, acharacteristic property observedvaluesareoflimitedrelevancetoinferprimordial
oflensingevents,isverydifficulttoassessproperly,incon- multiplicity properties and their dependence on formation
trasttothecasewhentheplanetaryeventoccursasacaustic conditions.
during a stellar lensing event. Free-floating planet candi- Keeping that in mind, observations today point to star
date events are thus much more uncertain than star-planet and BD binary properties which appear to be continuous
candidate events and should be considered with extreme fromthestellartotheBDregime,withbinaryfractionsand
caution. Third, planet-planet scattering usually produces average separations decreasing continuously with primary
objects with high velocity dispersions compared with the mass,andmassratiosincreasingwithit(e.g.Fahertyetal.,
parentstar. Asexaminedbelow(§2.2),nosuchpopulation 2011; Kraus and Hillenbrand, 2012; Luhman, 2012). The
ofhighvelocityobjectsintheBDorplanetmassrangehas continuityofthemultiplicitypropertiesthusmirrorstheone
been discovered so far, at least down to present observa- foundfortheIMF.
tionallimits. Mostimportantly,theexcessoflow-massob- AnimportantobservationalconstraintforBDformation
jectsclaimedbythemicrolensingresultswouldcorrespond theoriesalsostemsfromtheobservationsofwidebinaries.
to a population of free-floating Jupiter-mass objects in the AparticularexampleisthewidebinaryFUTaua,b,withno
fieldalmosttwiceascommonasstars,acensusclearlyex- identified stellar companion in its vicinity (Luhman et al.,
cludedsofarbyobservations(e.g.Scholzetal.,2012b). 2009). ThisisthebestexamplethatBDscanforminisola-
tion, with no nearby stellar companion, in low-density en-
2.2. Browndwarfvelocityandspatialdistributions vironments(stellardensityn ∼ 1-10pc−3). Severalwide
(cid:63)
Available radial velocity measurements of BD’s in (≈ 400-4000 AU) binary substellar companions, down to
youngclustersandstar-formingregionsclearlyindicatethat ∼ 5MJup(Luhman et al., 2011; Aller et al., 2013), have
young BD’s and young stars have similar velocity disper- also been observed in star-forming regions. One of these
sions (e.g. Joergens, 2006; White and Basri, 2003; Kuro- objects has an extreme mass ratio q = M2/M1 ≈ 0.005.
sawa et al., 2006). Similar observations show that BD’s Worth mentioning are also the isolated and rather fragile
have the same spatial distributions as stars (e.g. Parker BDwidebinary2MASSJ12583501/J12583798(6700AU)
et al. (2011); Bayo et al. (2011); Scholz et al. (2012b) for (Radiganetal.,2009)orthequadrupolesystemcontaining
recent determinations). These observations clearly con- 2MASS 04414489+23015113 (1700 AU) (Todorov et al.,
tradict at least the early versions of the accretion-ejection 2010). All these systems seem rather difficult to explain
model for BD formation (5.2.2) (Reipurth and Clarke, withdynamicalprocessesordiskfragmentationandclearly
2001; Kroupa and Bouvier, 2003) which predicted that indicate that these mechanisms are not necessary for BD
young BD’s should have higher velocities than stars and formation. As discussed in §5.2.4, such wide binaries are
thusshouldbemorewidelydistributed. mostlikelytheindicationthatcorefragmentationintobina-
ries might occur at the very early stages of star formation
2.3. Brown dwarfs or giant planets as star or brown (see§5.2.4below).
dwarfcompanions Other relevant observational inputs for understanding
Thestatisticsofbrowndwarfandgiantplanetcompan- BDandGPformationincludethebrowndwarfdesert(e.g.
ionstostarsorBD’spotentialybearsimportantinformation Grether and Lineweaver, 2006), which is a lack of com-
on the formation process of these objects. Various stud- panions in the mass range 10–100 MJup (i.e., 1–10% of
ies have indeed compared the multiplicity distributions of theprimarymass)intheseparationrangecoveredwithra-
prestellarcorefragmentationsimulationswiththepresently dial velocity (up to a few AU) around Sun-like stars. The
observedvaluesinyoungclustersorstarformingenviron- frequency of companions increases with smaller mass be-
ments. Such comparisons, however, are of limited utility low the desert (e.g. Howard et al., 2010), and increases
to infer the very formation process. Indeed, while simula- with larger mass above the desert, clearly indicating sep-
tionsaddresstheveryprestellarcloud/corecollapsestages, arate formation mechanisms between planetary and stellar
i.e. theveryinitialepoch(∼ 105 yr)ofstarformation,ob- companions. Moreover, giant planets appear to become
servationsprobepresentconditions,i.e. typicalagesof1to less frequent around lower-mass stars and more frequent
severalMyr’s.Dynamicalinteractionsandinteractionswith around higher-mass stars (e.g. Johnson et al. 2010), and
thediskhavekeptoccuringbetweenthesetwoepochsand meanwhile, brown dwarf companions become more fre-
have strongly influenced the multiplicity properties. It is quentaroundlow-massstarsandbrowndwarfsinthesame
well establihed and intuitively expected, for instance, that separationrange(e.g.Joergens,2008). Thisfurtherimplies
the most weakly bound systems, which include preferen- that the desert is primarily determined by system mass ra-
tiallythosewithBDorvery-low-massstarcompanions,are tios, and is not specific to brown dwarf secondaries. As
more prone to disruption than more massive ones, so that mentionedin§2.1,thefactthatthemassfunctionofplane-
low-mass binary properties are expected to differ substan- tarycompanionstostars(Mayoretal.,2011;Howardetal.,
tially from their primordial distribution (e.g. Ducheˆne and 2010) differs drastically, qualitatively and quantitatively,
Kraus,2013). Thisnaturallyexplainsthedecreasingbina- from the BD mass function, clearly points to a different
dominantformationmechanismforthesetwopopulations.
4
More quantitative results about the statistics of wide orbit low-masscoresisexpectedtodecreaseexponentially,mak-
SSO’saroundstarsandBD’sintheBD/GPmassrangewill ingtheirdiscoveriesverychallenging.
begivenin§3.2.
2.5. Summary
2.4. Observational identifications of isolated proto-
In summary (again see Luhman (2012) for a more
andpre-browndwarfcores
throughout review), it seems rather robust to affirm that
The recent results of the HERSCHEL survey confirm young brown dwarfs and young stars: (1) exhibit similar
that the mass function of pre-stellar cores (the so-called radial velocity dispersions; (2) have similar spatial distri-
CMF)inmolecularcloudsresemblesthestellarIMFdown bution in young clusters; (3) have mass distributions con-
to the present observational sensitivity limit, which lies sistent with the same underlying IMF; (4) have both wide
within the BD domain (Andre´ et al., 2010; Ko¨nyves et al., binarycompanions;(5)exhibitsimilaraccretion+disksig-
2010)(seealsochapterbyOffneretal.). Althoughcaution naturessuchaslargeblue/UVexcess,withlargeasymetric
is necessary at this stage before definitive answers can be emission lines (UV, H , Ca II etc...), with accretion rates
α
claimed, these results strongly argue in favor of the stel- scaling roughly with the square of the mass, M˙ ∝ M2,
lar+BD IMF been determined at the very early stages of from 2 down to about ∼ 0.01M , signatures all consis-
(cid:12)
starformationratherthanatthefinalgas-to-starconversion tent with a natural extension of the CTT phase in the BD
stage,anissuewewillcomebacktoin§5.2. domain; (6) have similar disk fractions; (7) both exhibit
Severalclass0objectshavebeenidentifiedwithSpitzer outflows; (8) have both been identified at the early pre-
surveyswithluminositiesL < 0.1L ,indicativeofyoung stellar/BDstageofcoreformationinisolatedenvironments.
(cid:12)
proto-BDs (e.g. Huard et al., 2006; Dunham et al., 2008; Itseemsthatthemostnaturalconclusionwecandrawatthis
Kauffmannetal.,2011)(seefurtherreferencesinLuhman, stage from such observational results is that star and BD
2012). Althoughsomeoftheseobjectsmayeventuallyac- formations seem to share many observational signatures,
crete enough material to become stars, some have such a pointing to a common dominant underlying mechanism,
small accretion reservoir that they will definitely remain andthatdynamicalinteractions,diskfragmentationorpho-
in the BD domain (Lee and Kim, 2009; Kauffmann et al., toionizingradiationarenotessentialforBDformation.
2011; Lee et al., 2013). Most importantly, there are now
emerging discoveries of isolated proto-brown dwarfs (Lee 3. OBSERVATIONAL PROPERTIES OF GIANT
et al., 2009a,b; Palau et al., 2012; Lee et al., 2013). The PLANETS
existence of such isolated proto-BD’s again indicates that
3.1. Observedcorrelations
dynamical interactions, disk fragmentation or photoioniz-
ingradiationarenotessentialforBDformation. Duringthetwodecadesoverwhichexoplanetaryobser-
Ofnoticeableimportancealsoisthediscoveryoftheiso- vation has been an active area in astronomy, the field has
lated, very low-mass brown dwarf OTS 44 (spectal type expanded rapidly, both in terms of the number of detected
M9.5,M ∼12M ),withsignificantaccretionandasub- planetsandintermsoftheparameterspaceofplanetsthat
Jup
stantialdisk(Joergensetal.,2013). Thisdemonstratesthat hasopenedupforstudy. Asaresult,giantplanetscannow
theprocessesthatcharacterizethecanonicalstar-likemode be studied with good completeness over a rather wide do-
of formation apply to isolated BD’s down to few Jupiter mainofparameters. Bycombiningradialvelocityandtran-
masses. sits,bothradiusandmassaswellasarangeofotherprop-
But the most striking result concerning BD formation ertiescanbestudied, andadditionalconstraintscanbeac-
is the recent observation of an isolated pre-brown dwarf quiredfromastrometryandmicrolensing,aswellasdirect
core (Andre´ et al., 2012). The mass and size of this core imaging,whichisdescribedseparatelybelow.Furthermore,
havebeendeterminedwiththePdBI,yieldingacoremass the host star properties can be studied and correlated with
∼ 30M with a radius < 460 AU, i.e. a mean den- planet occurrence, in order to gain additional clues about
Jup
sityn ∼ 107-108 cm−3,consistentwiththeoreticalpredic- planetformation.
tions of the gravo-turbulent scenario (§5.2.3). It should be One of the most well-known and important relations
stressed that this core lies outside dense filaments of Oph between host star properties and planet occurrence is the
and thus is not expected to accrete a significant amount of planet-metallicitycorrelation(e.g.Santosetal.,2004;Fis-
mass(seeSupplementaryMaterialofAndre´ etal.(2012)). cher and Valenti, 2005), which refers to the rapid increase
Indeed,thesurroundinggashasbeendetectedinfollow-up ingiantplanetfrequencyasafunctionofstellarhostmetal-
observationswiththeIRAMtelescopeandthemostconser- licity. While only a few percent of solar abundance stars
vativeestimatessuggestatmostafactor2growthinmass, havegiantplanetswithorbitalperiodsoflessthan4years,
leavingthefinalobjectintheBDregime. Thisistheunam- ∼25% of stars with with [Fe/H] >0.3 have such planets.
biguousobservationofthepossibilityforBDcorestoform Thisisastrongpieceofevidenceinfavourofcoreaccretion
in isolation by the collapse of a surrounding mass reser- (hereafterCA)asaformationscenario, sinceaframework
voir,asexpectedfromgravoturbulentcloudfragmentation. in which planets grow bottom-up from solids in a proto-
GiventhenatureoftheCMF/IMF,however,thenumberof planetarydiskfavorsahighconcentrationofdustandices.
Equally interesting in this regard is the fact that the corre-
5
lation appears to weaken for lower planetary masses (e.g. thefewstellarspinmeasurementsthathavebeenperformed
Sousa et al., 2008; Mayor et al., 2011; Buchhave et al., forsmall-planetsystemsimplyco-planarityalsoinaspin-
2012). Thisagainfitswellintothecoreaccretionscenario, orbitsense(e.g.Albrechtetal.,2013). Ifthesetrendshold
sinceitwouldbenaturaltoassumethatthegasgiantplan- upwithincreasingdata,itcouldindicatethatwhilegasgi-
etsaremostdependentonhighconcentrationsofsolids,as ants and smaller planets probably pass through a similar
they need to rapidly reach the critical core mass for gas stage of evolution (core formation), there may be differ-
accretion, before the gas disk dissipates. It also appears ences in the evolutionary paths that bring them into small
that planet frequency and/or mass scales with stellar mass orbits.
(e.g.LovisandMayor,2007;Hekkeretal.,2008;Johnson Sincetransitinggiantplanetscanberelativelyeasilyfol-
etal.,2010),althoughthereisnotasclearaconvergenceon lowed up with radial velocity, both mass and radius can
this issue in the literature as for the metallicity correlation be determined in general for such planets, which allows
(see e.g. Lloyd, 2011; Mortier et al., 2013). In any case, tomakeinferencesabouttheircomposition. Duetonearly
this is once again easy to understand in the core accretion equal compensation between electron degeneracy and in-
paradigm, as more mass in the star means more mass in terionic electrostatic interactions (Chabrier and Baraffe,
thedisk,andthusamoregenerousreservoirfromwhichto 2000), an isolated gas giant planet without a substantial
growplanetsrapidlyandtolargesizes. core or other heavy element enrichment will have a radius
Anaspectinthestudyofgiantplanetsthathasreceived thatonlyveryweaklydependsonmass. Indeed,theradius
considerableattentioninrecentyearsisthestudyofalign- willconsistentlybeclosetothatofJupiter,apartfromdur-
ment (or mis-alignment) between the orbital plane of the ingtheearliestevolutionaryphases,whentheplanetisstill
planet and the rotational plane of the star. A projection of contracting after formation (e.g. Baraffe et al., 2003; Bur-
thedifferentialanglebetweentheseplanescanbemeasured rowsetal.,2003). However,withalargerfractionofheavy
intransitingsystemsusingtheRossiter-McLaughlin(RM) elements, the radius decreases, thus providing a hint of
effect(Rossiter,1924;McLaughlin,1924). TheRMeffect thiscompositionaldifference(Fortneyetal.,2007;Baraffe
is a sequence of apparent red/blue-shift of the light from etal.,2008;Leconteetal.,2009). Inpractice,whenstudy-
a rotating star, as a planet blocks approaching/receding ing transiting planets for this purpose, there is a primary
parts of the stellar surface during transit. This is the most complicating factor: the planets under study are far from
commonlyusedmethodformeasuringspin-orbitalignment beingisolated,butratheratasmalldistancefromtheirpar-
(e.g. Queloz et al., 2000; Winn et al., 2005), but other entstar. Theinfluenceofthestarmaysubstantiallyinflate
methods have recently been implemented as well. These theplanet,sometimesbringingtheradiusashighas2R
Jup
include spot crossings during transit (e.g. Sanchis-Ojeda (e.g. Hartman et al., 2011; Anderson et al., 2011; Leconte
et al., 2012) and independent determinations of the incli- et al., 2009). Many different mechanisms have been pro-
nation of the stellar plane; the latter can be accomplished posed to account for precisely how this happens, but it re-
throughrelatingtheprojectedrotationalvelocitytothero- mains so far an unsolved and interesting problem. For the
tational period and radius of the star (e.g. Hirano et al., purpose of our discussion, however, we merely establish
2012), or through observing mode splitting in asteroseis- thatitisacomplicatingfactorwhenevaluatingthecompo-
mology(e.g.Chaplinetal.,2013). sitionoftheplanet. Nonetheless,sometransitinggasgiants
In almost all of the above cases, the measurement only do feature sub-Jovian radii (e.g. HD 149026 b, Sato et al.
gives a projection of the relative orientation. As a conse- 2005;HAT-P-2b,Bakosetal.2007a),whichhasledtothe
quence,aplanetcanbemisaligned,butstillappearaligned inference of very large cores with tens or even hundreds
throughtheprojection,soitistypicallynotpossibletodraw of Earth masses (e.g. >200 M for HAT-P-2b; Baraffe
⊕
conclusions from single cases. However, firm statistical et al., 2008; Leconte et al., 2009, 2011). Although it is
conclusionscanbedrawnfromstudyingpopulationsofob- unclear how exactly these large cores could form, such a
jects. The studies that have been performed show that gi- heavy material enrichment can hardly be explained by ac-
antplanetsaresometimeswell-alignedwiththestellarspin, cretion of solids on a gaseous planet embryo, as produced
butsometimesstronglymisalignedorevenretrograde(e.g. by gravitational instability (see §4.2). This may thus im-
Triaud et al., 2010). Since there are indications for a cor- plythattheformationoftheseobjectsoccurredthroughthe
relation between orbital misalignment and expected tidal processofcoreaccretion,possiblyinvolvingcollisionsbe-
timescale, where systems with short timescales have low tweenJupiter-massplanets(Baraffeetal.2008).
obliquities(Albrechtetal.,2012),ithasbeenhypothesized Otherrelevantobservationalinputsforunderstandinggi-
that all systems with a close-in giant planet may feature ant planet formation include the brown dwarf desert and
a misalignment between the stellar spin and planetary or- the brown dwarf mass function, an issue we have already
bit, but that alignment occurs over tidal timescales. There addressed in §2.3. The observations show that the fre-
is a possible contrast here with lower-mass planets, which quency of companions increases with smaller mass below
often occur in multiply transiting configurations (e.g. Lis- the desert and increases with larger mass above the desert
saueretal.,2011b;Johansenetal.,2012b;Fabryckyetal., (Mayor et al., 2011; Howard et al., 2010), clearly indicat-
2012). This implies a high degree of co-planarity, at least ingseparateformationmechanismsbetweenplanetaryand
between the planes of the different planets. Furthermore, stellar/BDcompanions.
6
Finally,bothmicrolensingdata(e.g.Gouldetal.,2010) thechoiceofinitialconditionsinexistingtheoreticalmass-
aswellastheasymptotictrendsinradialvelocitydata(e.g. luminosityrelationships,andthusasimilarreliabilityinits
Cummingetal.,2008)indicatethatgiantplanetsaremore classification.ThemostpuzzlingpropertiesoftheHR8799
commonbeyondtheicelinethantheyareatsmallersepara- planetsinatraditionalplanet-formingframeworkaretheir
tions.Thismayagainconstituteaclueregardingtheforma- largeorbitalseparations(∼10–70AUforHR8799b/c/d/e),
tion, although it should probably be regarded primarily as aswillbefurtherdiscussedinsection5.3.
providingconstraintsonmigration,ratherthanformation. Besides the above relatively clear-cut cases, it is infor-
mative to probe some of the more ambiguous cases which
3.2. Directimagingconstraints
may or may not be counted as planets, depending on defi-
Thanks to developments in both adaptive optics-based nitions and uncertainties. The B9-type star κ And hosts a
instrumentation and high-contrast imaging techniques, di- companion with a mass of ∼10–20 MJup (Carson et al.,
rectimagingofwidemassiveplanetshasbecomepossible 2013), straddling the DB limit. However, due to the very
over the past decade. This has led to a number of surveys massiveprimary,themassratiooftheκAndsystemisonly
being performed, ranging from large-scale surveys, cover- 0.5–1.0%. This is very similar to the HR 8799 and β Pic
ing a broad range of targets (e.g. Lowrance et al., 2005; planets,andthecompanionresidesatacomparableorbital
Chauvin et al., 2010), to more targeted surveys of specific separation of ∼40 AU. This might imply a similar forma-
categories, such as low-mass stars (e.g. Masciadri et al., tion mechanism, which would support the fact that planet
2005;Delormeetal.,2012b),intermediate-massstars(e.g. formationcanproducecompanionsthatapproachorexceed
Lafrenie`re et al., 2007; Biller et al., 2007; Kasper et al., the DB limit, as has been suggested by theoretical models
2007),high-massstars(e.g.Jansonetal.,2011;Viganetal., (seechapterbyBaraffeetal.).
2012; Nielsen et al., 2013), or stars hosting debris disks A candidate planet presently in formation has been re-
(e.g. Apai et al., 2008; Janson et al., 2013; Wahhaj et al., ported in the LkCa15 system (Kraus and Ireland, 2012).
2013). Acommontraitofallsuchsurveysisthattheygen- Withthepotentialforconstrainingthetimescaleofforma-
erally aim for quite young targets (a few Myr to at most a tionandinitialconditionsofaformingplanet,suchsystems
few Gyr). This is due to the fact that distant giant planets would have a clear impact on our understanding of planet
(whicharenotstronglyirradiatedbytheprimarystar)con- formation,butmoredatawillbeneededtobetterestablish
tinuously cool over time, and hence become continuously the nature of this candidate before any conclusion can be
fainterwithage,whichincreasesthebrightnesscontrastbe- drawninthatregard. TheyoungSolaranalog1RXS1609
tween the planet and star and makes the planet more diffi- has a companion with a mass of ∼6–11 MJup (Lafrenie`re
culttodetectatoldstellarages. et al., 2008) and a system mass ratio of 1%, but the pro-
The number of giant exoplanets that have been imaged jectedseparationis330AU,whichmaybelargerthanthe
sofarisproblematictoquantifyexactly. Thisispartlydue sizeoftheprimordialdisk. Itisthereforeunclearifitcould
to the lack of a clear consensus concerning the definition haveformedinsuchadisk,unlessitwas,e.g.,scatteredout-
ofwhataplanetis,intermsof(e.g.) massversusformation wardinthree-bodyinteractions.Oneoftheclearesthintsof
criteria,andpartlyduetouncertaintiesinevaluatingagiven incompatibilitybetweenaDB-basedandaformation-based
object against a given criterion. For instance, the errors definition is 2M 1207 b (Chauvin et al., 2005), which is
in the mass estimate often lead to an adopted mass range a ∼4 MJup companion to a ∼20 MJup brown dwarf (e.g.
that encompasses both deuterium-burning (DB) and non- Mamajek,2005). Thus,thecompanionisfirmlyinthenon-
DBmasses. Likewise,itisoftendifficulttoassessthefor- DBmassregime,butwithasystemmassratioof20%,the
mation scenario for individual objects, given the relatively couple appears to be best described as an extension of the
fewobservablesthataretypicallyavailable. Asaresult,the browndwarfbinarypopulation,ratherthanaplanetarysys-
directly imaged planet count could range between ∼5 and tem.
∼30 planets in a maximally conservative and maximally Despitethesedetections,thegeneralconclusionfromthe
generous sense, respectively. Two systems that would ar- direct imaging surveys performed so far is that very wide
guablycountasplanetarysystemsunderanycircumstance and massive objects in the giant planet mass domain are
are HR 8799 (Marois et al., 2008a, 2010) and β Pic (La- rare,withmanyofthesurveysyieldingnullresults. These
grange et al., 2009, 2010). All the four planets around results can be used to place formal constraints on the un-
HR8799andthesingledetectedplanetaroundβ Pichave derlyingplanetpopulation. Forexample,theGDPSsurvey
best-fitmasseswellintothenon-DBregime(∼5–10M ), (Lafrenie`re et al., 2007) has indicated that the fraction of
Jup
mass ratios to their primaries of less than 1%, and indica- FGKM-type stars harboring >2 MJup objects in the 25–
tionsofsharingacommonorbitalgeometry,bothwitheach 420 AU range is less than 23%, at 95% confidence. For
other (for the HR 8799 system) and with the debris disks >5MJup objects, thecorrespondingupperlimitis9%. In
that exist in both systems. Recently, another planet has ordertoexamine howthistranslatesintototalgiant planet
been imaged around the Sun-like star GJ 504 (Kuzuhara frequencies, Lafrenie`re et al. (2007) assume a mass distri-
et al., 2013), which has a similarly small mass ratio and a butionofdN/dM ∝ M−1.2 andasemi-majoraxisdistri-
mass that remains in the non-DB regime independently of bution of dN/da ∝ a−1. This leads to the conclusion (at
95%confidence)thatlessthan28%ofthestarshostatleast
7
one 0.5–13 M planet in the semi-major axis range of significantly fainter than under hot-start conditions. This
Jup
10–25AU,lessthan13%hostacorrespondingplanetat25– would lead to overly restrictive upper limits on planet fre-
50AU,andlessthan9%at50–250AU.NielsenandClose quency in the statistical analyses. However, the measured
(2010) combine the GDPS data with spectral differential temperaturesofmostoftheplanetsthathavebeenimaged
imaging (SDI) data from VLT and MMT. They find that sofarareconsistentwithhotstartpredictions,androbustly
ifpowerlawdistributionsinmassandsemi-majoraxisthat excludeatleastthecoldestrangeofinitialconditions(e.g.
fit the radial velocity distribution (Cumming et al., 2008) MarleauandCumming,2013;Bowleretal.,2013),anissue
are adopted, and extrapolated to larger distances, planets wewilladdressfurtherin§6.1.Aswillbeshowninthissec-
followingtheseparticulardistributionscannotexistbeyond tion, cold vs hot/warm-start conditions are not necessarily
65 AU at 95% confidence. This limit is moved out to equivalenttoformationbycoreaccretionvsdiskinstability.
82AUifstellarhostmassistakenintoconsideration,since Nonetheless, the fact remains that the detection limits are
themoststringentdetectionlimitsinimagingareacquired based on mass-luminosity models that have not been fully
aroundthelowest-massprimaries,whichisalsowherethe calibrated in this mass and age range, which is an uncer-
giantplanetfrequencyisexpectedtobethelowestfromRV taintythatshouldbekeptinmind. Inanycase,directimag-
data(e.g.Johnsonetal.,2010). ing surveys have already started to put meaningful con-
Theabovestudiesassumeacontinuousdistributionfrom straintsonthedistributionsofdistantgiantplanetmassob-
small separation planets to large separation planets, and jects,andnear-futureinstrumentssuchasSPHERE(Beuzit
thus essentially assume the same formation mechanism et al., 2008), GPI (Macintosh et al., 2008) and CHARIS
(primarilycoreaccretion)forallplanets. However,atwide (Peters et al., 2012) will substantially enhance the capac-
separations, disk instability becomes increasingly efficient ityofthistechnique,thusleadingtotighterconstraintsand
(andcoreaccretionlessefficient),suchthatonemightimag- moredetectionsofcloser-inandlessmassiveobjects.
ine that two separate populations of planets exist, formed Asidefromprovidinginformationaboutthedistributions
byseparatemechanisms. Hence,analternativeapproachto of planet mass objects, the future instruments mentioned
statistically examine the direct imaging data is to interpret above will also be able to provide substantial information
theminthecontextofpredictionsfromdiskinstabilityfor- aboutatmosphericproperties,throughtheircapacityofpro-
mation. This was done in Janson et al. (2011), where the vidingplanetaryspectra. Thishasalreadybeenachievedin
detectionlimitsfromdirectimagingwerecomparedtothe theHR8799systemwithpresent-dayinstrumentation(e.g.
calculatedparameterrangeintheprimordialdiskinwhicha Jansonetal.,2010;Bowleretal.,2010;Oppenheimeretal.,
formingplanetorbrowndwarfcouldsimultaneouslyfulfill 2013;Konopackyetal.,2013),butcanbedeliveredatmuch
theToomrecriterionandthecoolingcriterionforfragmen- higher quality and for a broader range of targets with im-
tation(see§4.2foradiscussionofthesecriteria),forasam- provedinstruments. Spectroscopyenablesstudiesofchem-
ple of BA-type stars. It was concluded that less than 30% ical abundances in the planetary atmospheres, which may
of such stars can host disk instability-formed companions inturnprovidecluestotheirformation. Forinstance,core
at99%confidence. ThisworkwaslaterextendedtoFGKM accretionmightresultinageneralmetallicityenhancement,
type stars in Janson et al. (2012) using the GDPS sample, similartohowthegiantplanetsintheSolarSystemareen-
whereadditionaleffectssuchasdiskmigrationweretaken richedinheavyelementswithrespecttotheSun. Thismay
intoaccount,assumingawiderangeofmigrationratesfrom bepossibletoprobewithmetal-dominatedcompoundssuch
virtuallynomigrationtoveryrapidmigration.There,itwas asCO (e.g.LoddersandFegley,2002). Anotherpossibil-
2
found that <10% of the stars could host disk instability- ity is that the formation may leave traces in specific abun-
formedcompanionsat99%confidence.Sinceamuchlarger dance ratios, such as the ratio of carbon to oxygen (e.g.
fractionthanthisareknowntohostplanetsbelievedtohave Madhusudhan et al., 2011; O¨berg et al., 2011). The C/O
formedbycoreaccretion(e.g.Mayoretal.,2011;Batalha ratio of planets should remain close to stellar if they form
etal.,2013),itstronglysuggeststhatdiskinstabilitycannot throughgravitationalinstability. However, iftheyformby
beadominantmechanismofplanetformation. Thisupper core accretion, the different condensation temperatures of
limitistightenedfurtherbythediscoveryofrapidbranches water and carbon-bearing compounds may lead to a non-
ofthecoreaccretionscenariowhichcanleadtoformation stellar abundance ratio in the gas atmosphere that is ac-
ofgasgiantsinwideorbits,asdiscussedbelowin§5.3. cretedontotheplanetduringformation,unlessitgetsreset
It is important to note that several assumptions are in- through subsequent planetesimal accretion. The most ro-
cluded in the various analyses described above, some of bustobservationalstudyaddressingthisissuetodateisthat
which are quite uncertain. In particular, all of the above ofKonopackyetal.(2013),butwhiletheresultsdoindicate
studies translate brightness limits into mass limits using amodestlynon-stellarC/Oratio,theyarenotyetunambigu-
evolutionarymodelsthatarebasedonso-called”hot-start” ous. Again,futurestudieshavegreatpromiseforclarifying
conditions (e.g. Baraffe et al., 2003; Burrows et al., 2003) theseissues.
(see§6.1). Ithasbeensuggestedthattheinitialconditions
may be substantially colder (e.g. Fortney et al., 2008a) or
have a range of values in between (Spiegel and Burrows,
2012a),whichcouldmakeplanetsofagivenmassandage
8
4. PROTOSTELLAR AND PROTOPLANETARY tiveanalysisofitsoperationwasnotarounduntiltheworks
DISKS ofSafronov(1960)andGoldreichandLynden-Bell(1965).
They were the first to show that a 2D (i.e. zero thickness)
4.1. Observations of protostellar and protoplanetary
diskofrotatingfluidbecomesunstableduetoitsowngrav-
disks
ityprovidedthattheso-calledToomreQsatisfies
Circumstellar disks around young objects are generally
Ωc
studied via their thermal and line emission at IR and mm Q≡ s <1, (1)
wavelengths,wheretheydominatethestellarradiation.Un- πGΣ
fortunately, the determination of the radii of most disks wherec andΣarethesoundspeedandsurfacedensityof
s
cannot be done with current technology. Noticeable ex- thedisk. ThisparticularformassumesaKeplerianrotation,
ceptionsarenearlyedge-ondiskswhichcanbedetectedin when the so-called epicyclic frequency coincides with the
scatteredlightwhileoccultingthestar. UsingSpitzerspec- angularfrequencyΩ.
troscopy and high-resolution imaging from HST, Luhman The physics behind this criterion is relatively simple
et al. (2007b) were able to determine the disk radius of a andliesinthecompetitionbetweentheself-gravityofgas,
young BD in Taurus, and this latter was found to be small which tends to destabilize the disk, and stabilizing influ-
size,withR≈20-40AU. ence of both pressure and Coriolis force. If we consider a
Thisisalsowhatseemstobefoundattheearlyclass0 parcel of gas with characteristic dimension L and surface
stagewithobservationsofisolated,massive,compact(R∼ density Σ in a zero-thickness differentially rotating disk,
20AU)disks(Rodr´ıguezetal.,2005)whilesofarlargeand onecanevaluatetheattractiveforceitfeelsduetoitsown
massivediskspronetofragmentationappeartobeveryrare self-gravity as F ∼ GΣ2L2. However, at the same time
G
atthisstageofevolution(Mauryetal.,2010). Twonotice- itfeelsarepulsivepressureforceF ∼ c2ΣL,wherec is
P s s
ableexceptionsaretheR ∼ 70-120AU,M ∼ 0.007 M(cid:12) thesoundspeed.Inaddition,differentialrotationofthedisk
disk around the ∼ 0.2 M(cid:12) protostar L1527 (Tobin et al., causes fluid element to spin around itself at the rate ∼ Ω,
2013a)andtheR ∼ 150AU,M ∼ 0.02 M(cid:12) diskaround resulting in a stabilizing centrifugal force FC ∼ Ω2ΣL3.
VLA1623 (Murillo et al., 2013). Moreover, Tobin et al. Gravityovercomespressure(F > F )whenthegasele-
G P
(2013b) observed density structures around the Class 0/I ment is sufficiently large, L (cid:38) c2/(GΣ), which is in line
s
protostars CB230 IRS1 and L1165-SMM1 that they iden- with the conventional Jeans criterion for instability in a
tifyascompanionprotostars,becauseofthestrongionizing three-dimensionalhomogeneousself-gravitatinggas. How-
radiation,alongwithanextended(∼100AU),possiblycir- ever,inadiskcaseself-gravityalsohastoexceedtheCori-
cumbinary disc-like structure for L1165-SMM1. Whether olisforce(F >F ),whichresultsinanupperlimitonthe
G C
these companions indeed formed in an originally massive fluidparcelsize,L(cid:46)GΣ/Ω2. Gravitywins,andfluidele-
disk or during the very collapse of the prestellar core it- mentcollapseswhenbothoftheseinequalitiesarefulfilled,
self, however, remains an open question. In contrast, the which is only possible when the condition (1) is fulfilled.
extendedemissionaroundtheClass0L1157-mmissugges- This condition is often recast in an alternative form, as a
tiveofarathersmall((cid:46)15AU)disc. Itshouldbenoticed, lowerlimitonthelocalvolumetricgasdensityρ(cid:38)M /a3
(cid:63)
however, that L1527, CB230 IRS1 and L1165-SMM1 are atsemi-majoraxisa.
moreevolvedthangenuineClass0objectslikeL1157-mm, Applying this criterion to a disk around Solar type star
and protostellar discs are expected to expand significantly one finds that disk gravitational instability (hereafter GI)
withtimeduetointernalangularmomentumredistribution canoccuronlyifthedisksurfacedensityisveryhigh,
(e.g.Basu,1998;Machidaetal.,2010;Dappetal.,2012).
Large disks are indeed observed at later Class 0/I or Class Ωc (cid:18)AU(cid:19)7/4
Σ> s ≈105gcm−2 , (2)
I-IIstages(seechapterbyZ.-Y.Lietal.). Atsuchepochs, πG r
however,theyareunlikelytobemassiveenoughrelativeto
thecentralstartobepronetofragmentation(seenextsec- whereweusedtemperatureprofileT(r)=300K(r/AU)−1/2.
tion). Indeed,observedClassIdiskshavegenerallymasses Thisconsiderably(bymorethananorderofmagnitude)ex-
lessthan10%ofthestarmass. ceeds surface density in the commonly adopted minimum
Clearly,thisissueofmassivediscsattheearlystagesof mass solar nebula (MMSN). Such a disk extending to 50
starformationisnotquitesettledfornowandwillstrongly AUwouldhaveamassclosetoM . Forthatreason,with
(cid:12)
benefitfromALMA.Inanycase,asdiscussedindetail§5.1, thedevelopmentofthecoreaccretionparadigmintheend
compactdiskobservationsareinagreementwithMHDsim- of 1970th the interest in planet formation by GI has gone
ulations and thus suggest that magnetic field is a key ele- down,butseeCameron(1978).
mentinshapingupprotostellardisks. Situationstartedchanginginthe1990s,whenproblems
with the CA scenario for planet formation at large sepa-
4.2. Diskinstability
rations mentioned in §2 started emerging. Stimulated by
Theideathatmassivegaseousdisksmayfragmentunder this, Boss (1997) resurrected the GI scenario in a series
the action of their own gravity into bound, self-gravitating ofpapers,whichwerebasedongrid-basednumericalsim-
objectsisratherold(Kuiper,1951). However,thequantita- ulations of three-dimensional disks. These calculations
9
adoptedisothermalequationofstate(thevalidityofthisas- formula
sumptionwillbediscussedbelow)andfoundthatmassive Σc2 Σ(k /µ)
disks with Σ exceeding the limit (2) indeed readily frag- tc ∼ σT4s = σT3Bf(τ), (4)
ment, which would be expected if disk fragmentation was eff
governedbythecriterion(1)alone. where Teff is the effective temperature at the disk photo-
However,thelogicbehindlinkingtheoutcomeofgravi- sphere, related to the midplane temperature T via T4 =
tationalinstabilityunambiguouslytothevalueofToomreQ T4 f(τ). Theexplicitformofthefunctionf(τ)depends
eff
is not without caveats. Indeed, both the simple qualitative onaparticularmodeofverticalenergytransportinthedisk,
derivationpresentedaboveandthemorerigorousanalyses butitisexpectedtoscalewiththeopticaldepthofthedisk
of the dispersion relation explicitly assume that pressure τ. Asdiskcoolingisinefficientbothintheopticallythick
of collapsing fragment is the unperturbed pressure. This (τ (cid:29) 1)andthin(τ (cid:28) 1)regimes,f(τ) (cid:29) 1inbothlim-
is a good approximation in the initial, linear phase of the its. Inparticular, ifenergyistransportedbyradiationthen
instability, meaning that Toomre Q is a good predictor of f(τ) ≈ τ +τ−1 and similar expression has been derived
whether the instability can be triggered. However, in the by Rafikov (2007) if energy transport is accomplished by
nonlinearcollapsephasegasdensitygrowsandpressurein- convection. Interestingly,thecoolingconstraintiseasierto
creases, eventually stopping contraction provided that F satisfy at higher disk temperatures since, for a fixed f(τ),
P
grows faster than F as the gas element contracts. In real theradiativefluxfromthedisksurfaceincreaseswithtem-
G
disksthisispossiblee.g.ifcontractionisisentropicandgas perature as T4. This is a much faster scaling than that of
hasadiabaticindexγ >4/3,whichisthecaseformolecu- thethermalcontentofthedisk,whichislinearinT. Thus,
largasinprotoplanetarydisks.Asaresult,intheabsenceof tosatisfyequation(4)onewouldliketoincreaseT,forcing
radiativelossesgravitationalinstabilitycannotresultindisk Σ to grow to keep Q (cid:46) 1. As a result, at a given radius,
fragmentation,whichagreeswithnumericalcalculations. fragmentationofagravitationallyunstablediskispossible
Coolingofcollapsingfluidelementslowerstheirentropy onlyifthediskishotenough(shortcoolingtime)andvery
thus reducing pressure support and making fragmentation dense(Rafikov,2005,2007).
possible. Using2Dhydrosimulationsintheshearing-sheet Even under the most optimistic assumptions about the
approximation Gammie (2001) has shown that fragmenta- efficiencyofcooling(f(τ) ∼ 1)agravitationallyunstable
tionofagravitationallyunstablediskpatchispossibleonly diskwithasurfacedensityprofile(2)has
ifthelocalcoolingtimeofthedisktcsatisfies Ω2 (cid:18)k (cid:19)3/2 (cid:18)AU(cid:19)7/4
t Ω∼ B T−5/2 ≈600 (5)
t Ω(cid:46)β, (3) c πGσ µ r
c
for the previously adopted temperature profile. Fragmen-
whereβ ≈3. Intheoppositelimitoflongcoolingtimethe
tation criterion (3) is clearly not fulfilled at separations of
disksettlesintoaquasi-stationarygravitoturbulentstate,in
several AU in such a disk, making planet or BD forma-
whichitismarginallygravitationallyunstable.
tion via GI problematic in the inner regions of the pro-
A simple way to understand this result is to note that
toplanetary disk (Rafikov, 2005). Boss (2002) resorted to
the fluid element contracts and rebounces on dynamical
convective cooling as a possible explanation of rapid heat
timescale ∼ Ω−1, so unless cooling proceeds faster than
transport between the disk midplane and photosphere but
that, pressure forces would at some point become strong
Rafikov(2007)hasdemonstratedthatthisisunlikelypossi-
enoughtopreventcollapse. Thisresulthasbeengenerally
bility. Subsequently,BoleyandDurisen(2006)haveinter-
confirmed in different settings, e.g. in global 3D geome-
preted vertical motion seen in Boss (2002) simulations as
try, and with both grid-based and SPH numerical schemes
being the shock bores rather than the true convective mo-
(Riceetal.,2005). Theonlydifferencefoundbydifferent
tions.
groupsistheprecisevalueofβ atwhichfragmentationbe-
Combining gravitational instability and cooling criteria
comespossible,forexampleRiceetal.(2005)findβ ≈5in
(1) and (4) one can make more rigorous statements and
their3DSPHcalculations. Thevalueofβisalsoafunction
show that disk fragmentation is very difficult to achieve
of the gas equation of state (EOS), with lower γ resulting
closetothestar, withinseveraltensofAU(Rafikov,2005,
in higher β (Rice et al., 2005). This is natural as gas with 2007). Inparticular,forthediskopacityscalingasκ∝T2
softer EOS needs less cooling for the role of pressure to
thoughttobeappropriateforouter,cooldiskregions,frag-
be suppressed. It should nevertheless be noted that some
mentation of the optically thick disk is inevitable outside
authorsfoundthecoolingcriterion(3)tobenon-universal,
60−100AUaroundaSolartypestar(MatznerandLevin,
withβ dependeningonresolutionofsimulations,theirdu-
2005a; Rafikov, 2009), but cannot occur interior to this
ration and size of the simulation domain (Meru and Bate,
zone. This result may be relevant for understanding the
2011; Paardekooper, 2012). It is not clear at the moment
origin of the outermost planets in the HR8799 system, al-
whethertheseclaimeddeviationsfromsimplecoolingcrite-
though,asdiscussedin§5.3,theseplanetsmightalsohave
rionhavephysicalornumericalorigin(Paardekooperetal.,
formedbycoreaccretion.
2011;MeruandBate,2012).
In optically thin disks this boundary is pushed consid-
Cooling time in a disk can be estimated using a simple
erably further from the star (Matzner and Levin, 2005a;
10