Planet formation in post-common-envelope binaries

0.23 MB·English

by  Dominik Schleicher

Astron.Nachr./AN999,No.88,789–795(2006)/DOIpleasesetDOI!
Planet formation in post-common-envelope binaries
Dominik R.G. Schleicher1,⋆, Stefan Dreizler1, Marcel Vo¨lschow2, Robi Banerjee2, and Frederic V.
Hessman1
1 Institutefu¨rAstrophysikGo¨ttingen,Friedrich-Hund-Platz1,37077Go¨ttingen,Germany
2 HamburgObservatory,Gojenbergsweg112,21029Hamburg,Germany
5
Received30May2005,accepted11Nov2005
1
Publishedonlinelater
0
2
n Keywords post-commonenvelopebinaries,commonenvelope,planetformation
a
Tounderstandtheevolutionofplanetarysystems,itisimportanttoinvestigateplanetsinhighlyevolvedstellarsystems,
J
andtoexploretheimplicationsoftheirobserved propertieswithrespecttopotentialformationscenarios. Observations

7 suggestthepresenceofgiantplanetsinpost-common-envelopebinaries(PCEBs).Aparticularlywell-studiedsystemwith
planetarymassesof1.7MJ and7.0MJ isNNSer.Weshowherethatapurefirst-generationscenariowheretheplanets
] formbeforethecommon envelope(CE)phaseandtheorbitsevolveduetothechanges inthegravitationalpotentialis
R
inconsistentwiththecurrentdata.Weproposeasecond-generationscenariowheretheplanetsareformedfromthematerial
S thatisejectedduringtheCE,whichmaynaturallyexplaintheobservedplanetarymasses.Inaddition,hybridscenarios
. wheretheplanetsformbeforetheCEandevolveduetotheaccretionoftheejectedgasappearasarealisticpossibility.
h
p
(cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
-
o
r
st 1 Introduction formation of planets in gaseous disks formed by stellar
a windsinbinarysystems.
[
1 While observational studies have predominantly focused Animportantclassofhighlyevolvedbinarieswherethe
on planetary systems around single stars, it is well-known
v presenceofplanetsisconsideredarethepost-commonen-
that mostof the stars are in binaries.It is thereforeimpor-
6 velope binaries (PCEBs). These are compact binary sys-
5 tantto understandwhetherplanetscanformin binarysys-
tems of only a few solar radii consisting of a white
6 tems, which is suggested by an increasing amount of re-
dwarf and a low-mass main sequence star. For the PCEB
1 centobservations.TheunevolveddG/dMbinaryKepler47
0 system NN Ser, different series of mid-eclipse times
harbors two planets with orbital periods of 49.5 days and
. have been obtained since the discovery of the eclipses
1 303.2 days (Oroszetal., 2012). The binary system Kepler
in 1998 (Beuermannetal., 2013, 2010; Brinkworthetal.,
0
16 hosts the Saturn-sized planet Kepler 16b (Doyleetal.,
5 2006; Haefneretal., 2004). In 2010, the quality of the
2011)andKepler34/35hostsaplanetwith1/5ofJupiter’s
1 data was good enough to obtain a two-planet solution
: mass(Welshetal.,2012).Fromatheoreticalpointofview, (Beuermannetal., 2010), which was shown to be dynam-
v
theformationofplanetsinbinarysystemshasbeenexplored
i icallystable(Beuermannetal.,2013).Themostrecentdata
X e.g.byHaghighipour&Raymond(2007).
suggest planetary masses of 1.7 M and 7.0 M with
J J
r To understand the evolution of planetary systems, it low eccentricities and semi-major axis of ∼ 3.3 AU and
a
is particularly relevant to search for planets in highly ∼5.4AU(Beuermannetal.,2013).Theplanetarysolution
evolved stellar systems, to determine if and under which hasbeenconfirmedbyMarshetal.(2014).
conditions they survive different phases of stellar evolu-
tion. The first exoplanets have been found around pul- At the same time, there is increasing evidence against
sars, which provideaccurateclocksfora precisemeasure- alternativeexplanationsof the eclipsingtime variations.A
ment(e.g.Konacki&Wolszczan,2003;Wolszczan&Frail, frequently considered mechanism are periodic changes in
1992; Yanetal., 2013). Recent observations have re- thestellarstructurerelatedtomagneticactivity,whichcould
vealedthe presenceofa protoplanetarydebrisdisk around give rise to regular changes in the star’s quadrupole mo-
the pulsar 4U 0142+61 (Ertanetal., 2007; Wangetal., ment and therefore affect the gravitational coupling in the
2006). Planet formation scenarios in highly evolved stel- binarysystem (Applegate, 1992). ForNN Ser,thismecha-
lar systems have been put forward by Perets (2010) and nismhasbeenexcludedonenergeticgrounds,duetothelow
Tutukov&Fedorova (2012), considering for instance the mass of the secondarystar and the limited energyproduc-
tion(Brinkworthetal.,2006).Indeed,onemayexpectthat
similarargumentscanbemadeformanysystemswithlow-
⋆ Corresponding author: e-mail: [email protected]
masscompanions(Zorotovic&Schreiber,2013).Thepos-
goettingen.de
sibility ofapsidalprecessionhasalso beenexcludedbased
(cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
790 D.R.G.Schleicher:Planetformationinpost-common-envelopebinaries
onrecentdata(Parsonsetal.,2014),leavingonlytheplan- of 3, we therefore expect planetary orbits on scales of ∼
etaryhypothesisasapossibleexplanation. 10AU,considerablylargerthantheobservedones.
In this article, we will first review the main argu- In these calculations, we have implicitly assumed that
ments againsta first-generationorigin of the planetsgiven the mass loss occurs almost instantaneously. This is plau-
by Vo¨lschowetal. (2014) in section 2, and subsequently sible, as most of the energy is released in the late stages
put forward a potential formation scenario for second- of the common envelope phase, where the secondary has
generation planets in section 3 (see Schleicher&Dreizler, spiraled down to scales close to the central core, and the
2014).Ourmainresultsandconclusionsaresummarizedin energy release occurs on very short timescales (see e.g.
section4. Kashi&Soker, 2011). However, the models for the com-
mon envelope phase are still highly uncertain, and it is
also conceivable that, at least for part of the evolution,
2 The caseagainstafirst-generation origin
the mass loss occurs more gradually. Such a scenario has
beenexploredbyPortegiesZwart(2013)fortheplanetsin
To assess the feasibility of a first-generation scenario, we HUAqua.Inthiscase,theorbitsoftheplanetswillgradu-
need to reconstructthe propertiesof the system beforethe allyadjustaccordingtothedecreasingmassofthesystem.
common envelopephase. We will here discuss the case of
From the conservationof angular momentum, one can
initiallysphericalorbits,andrefertoVo¨lschowetal.(2014) then show that r = r µ−1, with r and r the final and
f i f i
for the more general case. Following Beuermannetal.
initialradiusofthesphericalorbit.Withtheexpectedmass
(2010), we expect an initial size of the binary of about loss factor µ ∼ 0.3, we therefore find an orbital increase
1.44 AU, corresponding to the typical size of a red gi- by a factor of ∼ 3, suggesting that the observedplanetary
ant. The latter allows the system to enter the common en- orbits should be ∼ 10 AU, while in fact the planets have
velope phase during the later stages of the evolution. Us-
beendetectedwithsemi-majoraxesof3.3AUand5.4AU.
ing the binary star evolution code by Hurleyetal. (2002),
Additional arguments can be made based on the ec-
Mustilletal. (2013) have reconstructed the mass of the
centricities of the planets. In the orbital solution of
white dwarf progenitor to be between 1.875 M⊙ and Beuermannetal.(2013),thesearegivenasǫ =0.144and
1
2.25 M⊙, assuming metallicities between 0.01 and 0.03. ǫ = 0.222 for the outer and inner planet. In the case of
2
As the current mass of the white dwarf corresponds to
an instantaneousmassloss, onewouldexpecta significant
MWD = 0.535 M⊙, we have a mass loss factor µ = increaseoftheeccentricityas(Vo¨lschowetal.,2014)
M /M ∼ 0.3. The mass of the secondary corre-
current prev ǫ =µ−1−1. (4)
spondstoM2 = 0.111M⊙,andplaysonlyaminorrolein f
themassbudget.Insuchasystem,itiswell-knownthatthe For mass loss factors of µ ∼ 0.5, we thereforeexpect ec-
planetary orbits are dynamically unstable, unless they ex- centricitiesoforder1.Similarresultshavebeenreportedby
ceedatleastthreeHillradii.Asaresult,oneexpectssemi- Mustilletal.(2013)basedonadynamicalanalysis.
major axis of r ∼ 2.5 AU. Assuming Keplerian rotation, To avoid these constraints, gas drag forces are neces-
p
wehave sary to decrease the planetaryvelocitiesby frictioneffects
GM to keep them gravitationally bound and at low eccentric-
v2 = ini, (1)
p r ities. For this purpose, Vo¨lschowetal. (2014) considered
p
bothasphericallysymmetricoutflowassuminganexponen-
where M is the initial mass of the system. Due to the
ini tialdensityprofile,aswellasadisk-shapedejectionmecha-
mass loss of the system, the gravitational binding energy
nismintheorbitalplaneofthebinarysystem.Inthespher-
willdecrease,sotheorbitsoftheplanetswillwidenoreven
icallysymmetriccase,theircalculationshowsthatthedrag
become unbound. Considering that the escape velocity is forcesisclearlysubdominant,withatypicalratioof10−10
givenas
comparedtothegravitationalforce.Foradisk-shapedout-
2GM flow,therecanbesomeinitialdraginwards,whichiscom-
v2 = , (2)
esc r pensated during the subsequent evolution, where the drag
p
forces are reduced during the expansion of the disk, and
with M = µM the central mass after the ejection, the
ini evenanoutwardaccelerationmayoccurwhenthediskma-
planetswillbecomeunboundforamasslossfactorµ<0.5.
terialmovesbeyondthe planetaryorbit.Infact, inmostof
As mentioned above, a mass loss of µ ∼ 0.3 is expected
the simulations the planets are ejected, and it appears un-
for NN Ser, and it seems likely that the previous planets
likelythattheobservedlow-eccentricityorbitscouldbepro-
became gravitationally unbound. Even for more moderate
duced. A potential way to avoid the problem could be an
mass losses, one can show that the planetary orbits would
angular momentum exchange with an inhomogeneousgas
evolveas(Vo¨lschowetal.,2014)
distribution, which could however easily produce an infall
r
a = i , (3) oftheplanetsontothestar.Alternatively,onecouldincrease
f 2−µ−1
theeffectofthegasdragandtheresultingfrictionbymain-
with a the semi-major axis after the mass loss and r the taininghighgasdensitiesneartheplanetsforseveralorbital
f i
initial orbital radius. Assuming a typical expansion factor periods.Thelattercanbethecaseifsomematerialisejected
(cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org
Astron.Nachr./AN(2006) 791
butremainsgravitationallybound,leadingtotheformation at a radius of 0.9 R⊙. In general, one may therefore ex-
ofa fall-backdisk.Insuchacase,thegaswillbeaccreted pect the mass in the envelopeto be ejected, but one needs
ontotheplanetsandaffecttheirdynamicalevolution.Inthe todeterminewhichfractionofthemassbecomestruelyun-
nextsection,wewillconsidertheformationofsuchafall- bound. The latter requires to also determine the velocities
backdiskandtheformationofnewplanetsviagravitational of the ejected material. Clearly, the latter can be pursued
instabilities.Theseplanetsmayeitherformfromseedscre- onlyinanapproximatefashionwithinananalyticalframe-
atedbythegravitationalinstability,orpotentiallyalsofrom work(seee.g.Kashi&Soker,2011),whilenumericalsim-
the previous planets, which may become the cores of the ulations may not be able to address the later stages of the
newones.Inthefirstcase,weexpectatruelysecondgenera- evolution(cf.Passyetal.,2012).
tion,whilethesecondcasecorrespondstoahybridscenario
betweenfirst-andsecond-generationplanetformation.
3 Planetformationfrom the ejecta of
common envelopes
Inthissection,wedescribetheformationofafall-backdisk
afterthecommon-envelopephase,aswellastheformation
ofgiantplanetsviagravitationalinstabilitiesasoutlinedby
Schleicher&Dreizler(2014).
3.1 Ejectionandtheformationofafall-backdisk
Fortheejectionevent,weadoptthemodelofKashi&Soker
(2011) as employed by Schleicher&Dreizler (2014). We
assume the AGB star to consist of a core with M =
core
Fig.1 Comparisonofthegravitationalbindingenergyof
0.535 M⊙ and an envelopewith Menv = 1.465M⊙, con-
the envelopewith the gravitationalenergyreleased via the
sistentwiththeparametersinferredbyMustilletal.(2013).
inspiralin NN Ser. Both energiesbecomeequalforE =
Themassenclosedwithinradiusristhengivenas B
r EG ∼ 1.2×1047 ergataradiusof∼ 0.94R⊙,leadingto
M(r)=M + 4πr2ρ(r)dr, (5) theejectionoftheenvelope(Schleicher&Dreizler,2014).
core
Z
Rcore
with Rcore ∼ 0.01 R⊙. As in the models of
Nordhaus&Blackman (2006), Tauris&Dewi (2001) and In the following, we will assume that the energy in-
Soker(1992),weassumeapower-lawdensityprofileinthe jection occurs almost instantaneously, which may be jus-
envelopeoftheAGBstarwhere tified due to the short timescales once that the secondary
has reached small scales close to the central core. This is
ρ(r)=Ar−ω, (6)
also the stage where most of the gravitational energy will
withω = 2.Fromthemassoftheenvelope,thenormaliza- bereleased.Wecanthereforeemploytheself-similarSedov
tionfollowsas solutionfora powerlaw densityprofile(Sedov, 1959). As
M theinjectedenergyE ,weconsiderthesumofthebinding
A= env (7) 0
4πR∗ energyoftheenvelopeEB andtheavailablethermalenergy
intheenvelope,whichwecalculatefromthevirialtheorem
with R∗ the radius of the AGB star, for which we adopt a
typical value R∗ ∼ 185 R⊙. We consider now the inspi- as0.5EB.Thepositionoftheshockfrontisthenexpected
toevolveas
raaslsuomfethtehastecthoendejaercytisotnarowcciuthrsmoanscseMtha2t=the0r.e1l1e1asMed⊙graanvd- R (t)= E0t2 1/(5−ω), (10)
S
itationalenergyexceedsthebindingenergyoftheenvelope (cid:18) αA (cid:19)
massoutsideradiusr.Thelatterisgivenas wheretheconstantαcanbecalculatedfromenergyconser-
vation.Itisthenpossibletoobtainthepost-shockprofilesof
R∗ G(M(r)+M )
E = 2 4πr2ρ(r)dr, (8) theradialvelocity,densityandpressureas(Kashi&Soker,
B
Z r
r 2011;Schleicher&Dreizler,2014)
whiletheformeriscalculatedvia 2 r 1r
v = = , (11)
GM(r)M G(M +M )M 3γ−1t 2t
E = 2 − core env 2. (9)
G
2r 2R∗ ρ = A(γ+1)λ8/(γ+1) =4Ar−2λ3, (12)
Inthisequation,thefactor1/2reflectsthathalfofthegravi- rω(γ−1)
tationalpotentialisbalancedbythekineticenergy.Wecom- A 2(γ+1) 1
p = λ8/(γ+1) = At−2λ3, (13)
parebothexpressionsinFig.1andshowthattheyareequal rω−2t2(3γ−1)2 3
www.an-journal.org (cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
792 D.R.G.Schleicher:Planetformationinpost-common-envelopebinaries
where we assumed γ = 5/2 after the second equality and 3.2 Planetformationviagravitationalinstabilities
introducedtheself-similarvariable
Inthefollowing,weassumethatthegasofthegravitation-
Aα 1/(5−ω) allyboundmaterialsettlesintoadiskdescribedbyapower-
λ= rt−2/(5−ω) =r/R . (14)
(cid:18)E (cid:19) S lawprofileofthegassurfacedensity,
0
r n
FromtheconsiderationthatEtherm+Ekin = E0,onecan Σ(r)=Σ0 out , (19)
r
showthatα=π.Weevaluatethevelocityprofileatthetime (cid:16) (cid:17)
whereRS = R∗, andcomparewith theescapevelocityof whererout denotestheouterradiusofthedisk,Σ0 thedisk
thesystem, surfacedensityattheouterradius,andnthepower-lawin-
dex.WewillinparticularconsiderthecaseofaMesteldisk
2G(M +M ) 1/2 withn = 1(Mestel, 1963).We noteherethatΣ andr
v (r)= core 2 . (15) 0 out
esc (cid:18) r (cid:19) can be calculatedfromthedisk mass andangularmomen-
tumasoutlinedinSchleicher&Dreizler(2014),andthere-
As a result,we find thatthe masson scales above106R⊙ sultingsurfacedensityprofilesaregiveninFig.2.
becomesunbound.Theejectedmasswhichremainsbound
to the system correspondsto Mbound ∼ 0.133M⊙ or 140
Jupiter masses. In reality, the bound fraction may even be
higheriftheejectionprocessishighlyinhomogeneous.
Arelevantquestionconcernstheangularmomentumof
the ejected material. The total angular momentum that is
depositedintheenvelopebythesecondarycanbeestimated
as
GM
Ldep =M2R∗r R∗1, (16)
yieldingabout1.2×1052ergcm2 s−1.Itishoweverlikely
that the envelope was previously rotating, as angular mo-
mentum can be exchanged with the secondary via tidal
torques before the onset of the common envelope phase
(Hurleyetal., 2002; Hut, 1981; Soker, 1995; Zahn, 2008).
Fig.2 Thegassurfacedensityasafunctionofradiusfor
As shown by Bear&Soker (2010), the rotational velocity
the modelsoutlinedby Schleicher&Dreizler (2014), with
canreachf = 45%ofthebreakupvelocity.Theangular
rot
power-law indices from n = 0 to n = 1.5.The models
momentumduetorotationoftheenvelopeisthusgivenas
are normalized to reproduce the observed planetary mass
R∗ GM(r) 1/2 at5.4AU(Schleicher&Dreizler,2014).
L = f ·4πr2drρ(r)r , (17)
rot rot
Z (cid:18) r (cid:19)
0
yieldingacontributionofL ∼2.6×1052ergcm2s−1.To We expect that the disk efficiently cools through the
rot
determinethespatialextentofthedisk,themainquantityof emission of the dust grains, and the Toomre Q parameter
interest is howeverthe specific angularmomentum,which reachesasmarginallystablestatewith
weparametrizeas
c Ω
Q= s ∼1. (20)
L L πGΣ
disk =α dep. (18)
L
Mdisk Mej Wethereforehave
πGΣ
Both due to the inhomogeneous injection of the angu-
c = . (21)
s
lar momentum of the secondary, as well as due to the Ω
initial rotation of the envelope, one may expect that a WenotethatΩiscalculatedassumingKeplerrotationwith
value of αL ∼ 10 can be achieved (see discussion in acentralmasscorrespondingtothemassofthepresentsys-
Schleicher&Dreizler,2014).Similarenhancementsofthe tem.Thediskheightfollowsash(r) =c (r)/Ω(r)(Levin,
s
specificangularmomentumhavebeenobservedforinstance 2007;Lodato,2007).
inthegaseousdisksintheRedRectangle(Bujarrabaletal.,
The mass of the initial clumps forming by the grav-
2005, 2003). We also note that an independentanalysis of
itational instability is then given as (Boleyetal., 2010;
the angular momentum constraints has been pursued by
Meru&Bate,2010,2011;Rogers&Wadsley,2012)
Bear&Soker (2014), finding no relevant constraints for
planetformationinNNSer. M =Σ(r)h2(r). (22)
cl
(cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org
Astron.Nachr./AN(2006) 793
Theseclumpsmaygrowontheorbitaltimescaleuntilthey
reachthegapopeningmasswherethewholediskisevapo-
ratedneartheirorbit(Lin&Papaloizou,1986):
α 1/2 r 1/2
M =M 12π crit . (23)
f cl
0.3 h
h (cid:16) (cid:17)i (cid:16) (cid:17)
Here α denotesthe α-parameterforviscousdissipation
crit
for which fragmentation occurs. We adopt here a generic
valueofα ∼ 0.3(Gammie,2001).Theresultingclump
crit
masses are given in Fig. 3. We note in particular that it is
straightforward to reproduce the characteristic mass scale
of the planets, while the expected position has a stronger
dependenceonthespecificangularmomentum.Inaddition,
the potentialeffectof migration has to be considered(e.g.
Baruteauetal.,2011).Asaresultofsuchmigration,theob-
served resonances of the planets (Beuermannetal., 2013) Fig.4 Thegastemperatureinthepresenceofphotoheat-
mayformontimescalesofafeworbitalperiods. ingfromthestarinthecaseofaMesteldisk,corresponding
tomodelCdescribedbySchleicher&Dreizler(2014).We
explore the effect of different effective temperature of the
central star T∗. The minimum temperaturein the modelis
basedontheassumptionthatthediskshouldbemarginally
stable(Schleicher&Dreizler,2014).
adopttheminimumofEq.24andthetemperatureexpected
inamarginallystablestate(Q∼1).
TheresultingthermalevolutionisgiveninFig.4,show-
ing that radiative feedbackcan stabilize the disk on scales
aroundafewAU. Thelattermaynaturallyexplainthesta-
bility of the disk in the interior, and could in fact provide
a natural point to stop the migration, as it becomes easier
to create a gap in the disk once it is gravitationally stable
(Baruteauetal.,2011).
Fig.3 Thefinalclumpmassesasafunctionofradiusfor
themodelsbySchleicher&Dreizler(2014)intheabsence 3.4 Comparisonwiththeobservedpopulation
ofradiativefeedback,withpower-lawslopesfromn=0to
n=1.5(Schleicher&Dreizler,2014). While NN Ser is currently the system with the most de-
tailed data and the highest-quality fits to the planetary
orbits, Zorotovic&Schreiber (2013) have suggested 12
PCEB-systems which may harbor such massive planets,
some of which even indicate the presence of two plan-
3.3 Radiativefeedback
ets as in NN Ser. These systems include five detached
Radiationfromthecentralstarcansubstantiallyheatupthe systems with a hot subdwarf B (sdB), four detached sys-
diskandstabilizeitagainstgravitationalinstabilitiesinthe temswith a white dwarf(WD) andthreecataclysmic vari-
interior.WeadoptheretheapproachofChiang&Goldreich ables (CVs). For the system NSVS14256825, the two-
(1997) to estimate the temperature in the midplane of the planet solution was shown to be dynamically unstable
diskas (Wittenmyeretal., 2013), while the one-planet solution is
stable (Beuermannetal., 2012). In this case, we therefore
T = θ 1/4 r∗ 1/2T∗, (24) usethedataofBeuermannetal.(2012),whileweadoptthe
(cid:18)4(cid:19) (cid:16) r (cid:17) parametersinferredbyZorotovic&Schreiber(2013)inthe
whereT∗ istheeffectivetemperatureofthecentralstarand othercases.
r∗ its radius. We consider here the stage very early after The comparison of the theoreticalpredictions with the
theejection,andthereforeestimatetheradiusofthestarto observationallyinferredmasses is givenin Fig. 5. We find
becomparabletotheremainingradiusofthecore(seee.g. thatthereisapopulationshowinggoodagreementwiththe
Schleicher&Dreizler,2014).Thegrazingangleθdescribes theoreticalpredictions,as well as an additionalpopulation
the angle at which light from the star strikes the disk, and withevenhighermasses.Thelattermayhinteitheratadif-
is estimated as θ ∼ 0.4r∗/r. For the temperature,we then ferent origin of these planets, or the potential presence of
www.an-journal.org (cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
794 D.R.G.Schleicher:Planetformationinpost-common-envelopebinaries
additionaleffectsrelatedtomagneticactivity,whichcannot Acknowledgements. We thank Klaus Beuermann, Christiane
beruledoutinsomecases. Diehl, TimLichtenberg and Sonja Schuh for stimulating discus-
sions on the topic. DRGS thanks for funding fromthe Volkswa-
genfoundationviatheproject”Planetsbeyondthemainsequence:
4 Discussionandconclusions
theoryandobservations”.SDthankstheDeutscheForschungsge-
meinschaft (DFG)for funding viatheSFB963/1”Astrophysical
In this article, we have summarized the main arguments flowinstabilitiesandturbulence”(projectA5).
against a first-generation scenario for the planets in NN
Ser,andpresentedatheoreticalmodelexplainingtheforma-
tionofplanetsfromtheejectaduringthecommonenvelope References
phase.Themodelnaturallyexplainstheobservedplanetary
Applegate,J.H.1992,ApJ,385,621
masses in NN Ser, and is in good agreement with a num-
Baruteau, C., Meru, F., & Paardekooper, S.-J. 2011, MNRAS ,
ber of additionalsystems. In addition, there seems to be a
416,1971
population where the observationally inferred masses sig-
Bear,E.&Soker,N.2010,NewAstron.,15,483
nificantlyexceedthetheoreticalpredictions.Itisinteresting
Bear,E.&Soker,N.2014,MNRAS,444,1698
to notethatinexactlythesecases, itisdifficulttojustifya
Beuermann, K., Breitenstein, P., Debski, B., et al. 2012, A&A,
second-generationscenarioduetoangularmomentumcon- 540,A8
straints(Bear&Soker,2014).Thelattercanpotentiallyhint Beuermann,K.,Dreizler,S.,&Hessman,F.V.2013,A&A,555,
atadifferentplanetaryorigin.Wenotethatbeyondapurely A133
first-orsecond-generationorigin,alsohybridscenariosare Beuermann, K., Hessman, F. V., Dreizler, S., et al. 2010, A&A,
conceivable where the existing planets accrete additional 521,L60
massfromtheboundmaterialremainingaftertheejection. Boley, A. C., Hayfield, T., Mayer, L., & Durisen, R. H. 2010,
Icarus,207,509
Brinkworth,C.S.,Marsh,T.R.,Dhillon,V.S.,&Knigge,C.2006,
MNRAS,365,287
Bujarrabal, V., Castro-Carrizo, A., Alcolea, J., & Neri, R. 2005,
A&A,441,1031
Bujarrabal, V., Neri, R., Alcolea, J., & Kahane, C. 2003, A&A,
409,573
Chiang,E.I.&Goldreich,P.1997,ApJ,490,368
Doyle,L.R.,Carter,J.A.,Fabrycky,D.C.,&etal.2011,Science,
333,1602
Ertan,U¨.,Erkut,M.H.,Eks¸i,K.Y.,&Alpar,M.A.2007,ApJ,
657,441
Gammie,C.F.2001,ApJ,553,174
Haefner, R., Fiedler, A., Butler, K., & Barwig, H. 2004, A&A,
428,181
Haghighipour,N.&Raymond,S.N.2007,ApJ,666,436
Hurley,J.R.,Tout,C.A.,&Pols,O.R.2002,MNRAS,329,897
Hut,P.1981,A&A,99,126
Fig.5 Comparison of model predictons (diamonds) Kashi,A.&Soker,N.2011,MNRAS,417,1466
with planetary masses inferred from observations by Konacki,M.&Wolszczan,A.2003,ApJ,591,L147
Zorotovic&Schreiber(2013)(triangles).Thedataindicate Levin,Y.2007,MNRAS,374,515
Lin,D.N.C.&Papaloizou,J.1986,ApJ,309,846
the potentialpresence of two populations,one comparable
Lodato,G.2007,NuovoCimentoRivistaSerie,30,293
toourmodelpredictions,andonewithevenhighermasses
Marsh,T.R.,Parsons,S.G.,Bours,M.C.P.,etal.2014,MNRAS,
(Schleicher&Dreizler,2014).
437,475
Meru,F.&Bate,M.R.2010,MNRAS,406,2279
Meru,F.&Bate,M.R.2011,MNRAS,410,559
The scenario proposed here can be validated through Mestel,L.1963,MNRAS,126,553
thefurtherobservationoftheeclipsingbinarysystems,asa Mustill,A.J.,Marshall,J.P.,Villaver,E.,etal.2013,MNRAS,
strictperiodicityisexpectedinthecaseofplanetaryorbits. 436,2515
Inaddition,complementaryapproacheslikethedetectionof Nordhaus,J.&Blackman,E.G.2006,MNRAS,370,2004
theplanetsviatheirthermalemissioncouldprovideanim- Orosz,J.A.,Welsh,W.F.,Carter,J.A.,etal.2012,Science,337,
1511
portantpathwaytoconfirmtheirexistence.Telescopeslike
Parsons,S.G.,Marsh,T.R.,Bours,M.C.P.,etal.2014,MNRAS,
GeminiandALMAmayinadditionlookforremantsofthe
438,L91
gravitationallyboundgasin NN Ser to identifya potential
Passy,J.-C.,DeMarco,O.,Fryer,C.L.,etal.2012,ApJ,744,52
debrisdiskorthegasejectedduringthecommonenvelope
Perets,H.B.2010,ArXive-prints1001.0581
event.Thelattermayprovidefurtherinformationtosignifi-
PortegiesZwart,S.2013,MNRAS,429,L45
cantlyrefinesuchamodel. Rogers,P.D.&Wadsley,J.2012,MNRAS,423,1896
(cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org
Astron.Nachr./AN(2006) 795
Schleicher,D.R.G.&Dreizler,S.2014,A&A,563,A61
Sedov, L. I. 1959, Similarity and Dimensional Methods in Me-
chanics
Soker,N.1992,ApJ,389,628
Soker,N.1995,MNRAS,274,147
Tauris,T.M.&Dewi,J.D.M.2001,A&A,369,170
Tutukov,A.V.&Fedorova,A.V.2012,AstronomyReports,56,
305
Vo¨lschow,M.,Banerjee,R.,&Hessman,F.V.2014,A&A,562,
A19
Wang, Z., Chakrabarty, D., & Kaplan, D. L. 2006, Nature, 440,
772
Welsh,W.F.,Orosz,J.A.,Carter,J.A.,Fabrycky,D.C.,&etal.
2012,Nature,481,475
Wittenmyer,R.A.,Horner,J.,&Marshall,J.P.2013,MNRAS,
431,2150
Wolszczan,A.&Frail,D.A.1992,Nature,355,145
Yan,Z.,Shen,Z.-Q.,Yuan,J.-P.,etal.2013,MNRAS,433,162
Zahn,J.-P.2008,inEASPublicationsSeries,Vol.29,EASPubli-
cationsSeries,ed.M.-J.Goupil&J.-P.Zahn,67–90
Zorotovic,M.&Schreiber,M.R.2013,A&A,549,A95
www.an-journal.org (cid:13)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim