Falling Transiting Extrasolar Giant Planets

0.2 MB·

by  B. Levrard

Toappearin ApJ Letters
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
FALLING TRANSITING EXTRASOLAR GIANT PLANETS
B. Levrard1, C. Winisdoerffer and G. Chabrier
Ecolenormalesup´erieuredeLyon,CentredeRechercheAstrophysiquedeLyon,
Universit´edeLyon,46all´eed’Italie,F-69364LyonCedex07,France
To appear inApJ Letters
ABSTRACT
We revisit the tidal stability of extrasolar systems harboring a transiting planet and demonstrate
9
that, independently of any tidal model, none but one (HAT-P-2b) of these planets has a tidal equi-
0
librium state, whichimplies ultimately a collisionof these objects with their hoststar. Consequently,
0
2 conventionalcircularizationandsynchronizationtimescalescannotbedefinedbecausethecorrespond-
ing states do not represent the endpoint of the tidal evolution. Using numerical simulations of the
n
coupled tidal equations for the spin and orbital parameters of each transiting planetary system, we
a
confirmthesepredictionsandshowthatthe orbitaleccentricityandthestellarobliquitydonotfollow
J
the usually assumed exponential relaxation but instead decrease significantly, reaching eventually a
4
zero value, only during the final runaway merging of the planet with the star. The only character-
1
istic evolution timescale of all rotational and orbital parameters is the lifetime of the system, which

crucially depends on the magnitude of tidal dissipation within the star. These results imply that the
]
P nearly circular orbits of transiting planets and the alignment between the stellar spin axis and the
E planetaryorbitareunlikely to be due to tidaldissipation. Otherdissipative mechanisms,forinstance
. interactions with the protoplanetary disk, must be invoked to explain these properties.
h
Subject headings: celestial mechanics, planetary systems: formation, protoplanetary disks
p
-
o
r 1. INTRODUCTION Dobbs-Dixon et al. 2004), leading to an erroneous ap-
t plication of the tidal stability criterion derived by Hut
s Jupiter-like extra-solar planets have been detected
a (1980). More recently, numerical simulations of the or-
transiting their parent star at an unexpectedly small
[ bits of some transiting planets from the OGLE survey
distance of less than 0.1 AU (e.g. Pont 2008). Most
indicated a possible collapse with the host star but the
1 of these systems have nearly circular orbits (e.g. Pont
effect of tides raised by the star within the planet was
v 2008) and first measurements of the sky-projected an-
ignored (Pa¨tzold et al. 2004; Carone & Pa¨tzold 2007).
8 gle λ between the stellar rotation axis and the plane-
4 tary orbital axis through the Rossiter-MacLaughlin ef- Jacksonet al. (2008) noticed the importance of consid-
0 fect (for HD 209458, HD 149026, HD 189733, TrES-1, eringbothtides raisedbythe starandthe planetaswell
2 XO-1, HD 17156) indicate a nearly perfect spin-orbit as the non-linear coupled evolution of the eccentricity
. and the orbital distance, but the global stability of the
1 alignment(Winn et al.2005,2007;Gaudi & Winn2007;
system and the additional coupling with the rotational
0 Narita et al. 2007; Loeillet et al. 2008; Cochran et al.
evolution were not investigated.
9 2008). These observational properties are commonly in-
In this Letter, we reconsider the stability of transiting
0 terpretedas anoutcome of tidal dissipationbetween the
: host star and the planet and these same effects are also extra-solar planets to tidal dissipation through theoreti-
v calandnumericalconsiderationsandshowthatnonebut
believed to lead to synchronization of the planetary and
i
X stellar rotation with the orbital motion. As a conse- oneofthetransitingplanetshasatidalequilibriumstate.
We investigate the consequences for the tidal evolution
r quence,correspondingtimescalesassociatedtothesepro-
a cesses are usually evaluated by assuming an exponential timescales of orbital (semi-major axis, eccentricity) and
rotational (stellar obliquity, stellar and planetary rota-
relaxation towards equilibrium parameters as obtained
tionalvelocities)parameters,takingbothtides raisedby
fromanyevolutionperturbationcalculationnearanequi-
the planet and the star into account.
librium state (e.g. Hut 1981). This leads to timescale
estimates of spin-orbit alignment, synchronization and 2. TIDALSTABILITYOFTRANSITINGPLANETS
circularization which differ by several orders of magni-
tude, ranging typically from ∼105 yrs to a Hubble time A binary star-planet system that conserves the to-
tal angular momentum L but dissipates its energy is
(e.g.Rasio et al.1996;Sasselov2003;Dobbs-Dixon et al. tot
known to dynamically evolve towards only two possible
2004; Ogilvie & Lin 2008; Mazeh 2008). All these con-
solutions (Counselman 1973; Hut 1980). On one hand,
clusions,however,implicitly assumetheexistenceofsuch
if L <L , where L is the critical angular momentum
tidal equilibrium states. tot c c
defined by
It has already been suggested that short-period plan-
ets could be unstable to tidal dissipation but these cal- G2 M3M3 1/4
culations were based on the assumption of the existence L =4 ⋆ p (C +C ) , (1)
c p ⋆
27 M +M
of (unstable) tidal equilibrium states (Rasio et al. 1996; " ⋆ p #
where M ,C and M ,C denote the masses and polar
1also at IMCCE-CNRS UMR 8028, 77 Avenue Denfert- p p ⋆ ⋆
moments of inertia of the planet and the star, respec-
Rochereau,75014, Paris. [email protected]
tively, and G is the gravitational constant, no equilib-
2 B. Levrard et al.
rium state exists and the system ultimately merges, in-
dependently of any tidal model. On the other hand, if
L > L , two equilibrium states exist that are charac-
tot c
No tidal equilibrium state
terized by the coincidence between equatorial and or-
HAT−P−2b
bital planes, circularity of the orbit and synchroniza- HD 17156b (1.6 Gyr)
tionbetweenrotationalandorbitalperiods whennofur- TrES−4b (0.6 Gyr)
HD 149026b (1.1 Gyr).
ther dissipation occurs (Hut 1980). The furthest equi-
HAT−P−6b (2.1 Gyr)
librium orbital distance a is stable while the closest
1 OGLE−TR−10b (2.2 Gyr)
a2 is unstable, with a1 > ac > a2, where ac is the WASP−3b (72 Myr)
marginalequilibriumorbitaldistanceforL =L ,with HD 209458b (4.4 Gyr)
tot c
a ≃ 3C /M ∼ 0.064(M /M )1/2 AU for a planet HD 189733b (1.0 Gyr)
c ⋆ p Jup p OGLE−TR−111b (23.5 Gyr)
orbiting a Sun-like star. Therefore, exploring whether HAT−P−4b (0.53 Gyr)
a systpem is stable or not, and deriving characteristic WASP−1b (0.22 Gyr) Stable and
timescales, first requires to find out whether the condi- XO−1b (9.4 Gyr) u enqsutialibblrei utimdal
tion L <L is satisfied or not. Neglecting the spin of HAT−P−1b (4.8 Gyr) states
tot c TrES−1b (4.7 Gyr)
theplanet, thetotalangularmomentumofthesystemis TrES−2b (0.71 Gyr)
given by the sum of the orbital angular momentum and HAT−P−5b (0.80 Gyr)
the spin of the star: OGLE−TR−182b (4.3 Gyr)
TrES−3b (51 Myr)
L =C ω + MpM⋆ Ga(1−e2), (2) WASP−2b (0.79 Gyr)
tot ⋆ ⋆ OGLE−TR−113b (98 Myr)
M +M
p ⋆ HAT−P−3b (5.0 Gyr)
p XO−2b (1.8 Gyr)
assuming that the stelplar obliquity is zero to maximize GJ 436b (5.0 Gyr)
Ltot, where e is the eccentricity, ω⋆ is the rotational ve- OGLE−TR−56b (7.0 Myr)
locityofthestarandC⋆ =kM⋆R⋆2,wherekissettothe OGLE−TR−132b (52 Myr)
typicalvalue0.06forcentrallycondensedstarswithdom-
inantlyradiativeinteriors,characteristicofSun-likestars 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
(Claret & Gimenez 1989). In order to investigate the Ratio between the total angular momentum and the critical angular momentum value
fate of observed transiting planetary systems, we have
computed the ratio L /L for each of them. All the
tot c Fig. 1.—Listoftransitingplanetsclassifiedbyincreasingvalues
quantities relevant to our study and their uncertainties
of the ratio between the total angular momentum of the system
have been collected from up-to-date published estimates Ltot and the critical angular momentum Lc (see text). The er-
(Table 1). The mean value of L /L and its standard ror bar indicates the standard deviation of the ratio distribution
tot c
arounditsmeanvalue. Thetimeremainingforeachplanettocol-
deviationhave been estimated using a Monte-Carlopro-
lidewithitshoststarasobtainedfromournumericalcomputations
cedure by sampling the values of M⋆, R⋆, Mp, a and withQ′⋆=Q′p=106(SeeSection3)isindicatedbetweenbrackets.
ω⋆,consideredasnormallydistributedaroundtheirmost Note that this time is strongly model-dependent. The HAT-P-2
probablevalue. Whentheloweranduppererrorbarsfor system is tidally-unstable and very close to the marginally stable
avariablearenotthesame,themaximumofthetwoval- regimea1≃ac. Becauseitspresentorbitaldistance(∼0.068AU)
ues has beenconsideredas the standarddeviationofthe is larger than the stable equilibrium value (a1 ∼ 0.048 AU), the
systemwillreachthisstateasymptotically.
distribution. When only anupper limit ofthe rotational
velocity is available,as for very slowly rotatingstars, we the star and the planet into account. We follow the tra-
consideredaflatdistributionbetween0andthegivenup- ditional “viscous” approach of the equilibrium tide the-
per limit. Finally, we calculated the ratio L /L from ory(Darwin1908)whichassumesaconstanttimelagfor
tot c
a random set of the five variables and reproduced this any frequency component between the tidally deformed
procedure 106 times (Fig. 1). surface of the gaseous envelope and the tidal perturba-
For all but one case,the mean ratio L /L is smaller tion, although alternative models are possible given our
tot c
than 1, indicating that none but one (HAT-P-2b) of the very limited understanding of tidal processes in gaseous
observed transiting planets lies on a tidal equilibrium bodies (e.g. Ogilvie & Lin 2008). The rate of change in
stateandthattheywillultimatelyallfallontotheirpar- the semi-major axis is, at second order in eccentricity
entstar. Hence,theexponentialdampingtimescaleorig- (N´eron de Surgy & Laskar 1997)
inally put forth by Rasio et al. (1996) (as a/a˙ or e/e˙)
da 6M R5 27
is inappropriatebecause orbitalcircularization,synchro- = p ⋆ 1+ e2 cosεω −(1+23e2)n
nization of the spins and spin-orbit alignment do not dt Q′⋆M⋆a4 (cid:20)(cid:18) 2 (cid:19) ⋆ (cid:21)
correspond to the endpoint of tidal evolution. In the
following,we define by timescale, the characteristictime + 6M⋆Rp5 1+ 27e2 ω −(1+23e2)n , (3)
required to observe a significant evolution of orbital or Q′pMpa4 (cid:20)(cid:18) 2 (cid:19) p (cid:21)
rotational parameters.
whereω istheplanetaryrotationvelocity,εisthestellar
p
3. TIMESCALESFORTHEEVOLUTIONOFORBITALAND obliquityandQ′ (resp. Q′)theratiobetweenthepresent
⋆ p
ROTATIONALPARAMETERS annual stellar (resp. planetary) tidal quality factor Q
⋆
In order to determine the characteristic timescales of (resp. Q ) and the tidal Love number of degree 2 k
p 2,⋆
tidally-unstable extrasolar systems with no asymptotic (resp. k ). The first term in Equation (3) reflects the
2,p
equilibrium state, we have conducted long-term simu- effectsoftideswithinthestarwhiletheeffectsofthetide
lations of the fully coupled tidal equations for the or- raised by the star within the planet are reflected in the
bital and spin parameters, taking tides raised both by second term. We assume that the planetary obliquity
Falling extrasolar giant planets 3
0.08 0.016 25
HD 209458b’s eccentricity a) b)
0.014
HD 209458 ’s obliquity
Semi−major axis [AU]000...000246 O EGxpLoEn−eTnRtia−l 1ec3c2HebDn’ts r2i cs0iet9ym 4d5ia−8mmbp’aisnj ogs rea apmxpiri−somximajaotiro anxis 00000.....00000000114682 Eccentricity ation period [Days] 111024468 RotationR poetaritoiodn o pf eHriDo d2 0o9f 4H5D8 209458b 5112050 Stellar obliquity [Degrees]
0.002 Rot 2
1004 105 106 107 108 109 1010 1004 105 106 107 108 109 1010
Time [Years] Time [Years]
Fig. 2.— Long-term integrations of orbital and rotational parameters of some transiting planets and of their host star. Tidal quality
parameters Q′⋆ and Q′p are initially set to 106 but vary with the semi-major axis as Q⋆ = Qp = 1/(n∆t) where ∆t is a constant tidal
time lag. a) Semimajor axis of OGLE-TR-132b, HD 209458b (solid lines) and eccentricity of HD 209458b (dashed line) as a function of
time. The thin dashed line is the usual exponential damping approximation of e with a 4.1×108 yr relaxation time assuming that only
tidesraisedontheplanetareconsideredandstabletidalequilibrumstatesexist;b)Rotational periodsofHD209458, HD209458b(solid
lines)and HD 209458’s obliquity (dashed line)as a function of time. The initial rotational periodof HD 209458b and HD 209458 stellar
obliquityarearbitrarilysettohalfadayand20◦ toevaluatetherespectivetimescalesoftheirtidalevolution.
is zero. Similar equations for the evolution of e, ε, ω The evolution of the rotational parameters is illus-
p
and ω can be found in Hut (1981). Since the orbits trated for the HD 209458 system in Figure 2b. Despite
⋆
of transiting planets are nearly edge-on, the angle λ is the global tidal instability, the planetary rotation veloc-
related to the stellar obliquity ε by cosε ≃ cosλsini , ity is first pseudo-synchronized with the orbital motion
⋆
where i is the inclination of the stellar rotation axis n such that ω ∼ (1+6e2)n over the same timescale
⋆ p
relative to the sky plane (Winn et al. 2005). In order τ ∼ (C nQ′ a6)/(3GM2R5), as the one estimated
ps p p ⋆ p
to evaluate the typical timescale for the tidal evolution when tidal equilibrium states exist (Hut 1981). It is
of the projected spin-orbit separation, the initial stellar close to ∼ 105 yr for typical HD 209458b’s parameters,
obliquity was then modified and set to some arbitrary much smaller than the orbital decay timescale. This
non-zerovalues. Wenumericallyintegratedthecomplete stems from the fact that the angular momentum asso-
setoftidalequationsforwardintimeusingpresentvalues ciated with the planet’s rotation is much smaller than
as initialconditions for eachtransiting planetarysystem the orbital angular momentum. However, Figure 2b
and setting the same initial value 106 for Q′⋆ and Q′p. clearly shows that it only corresponds to a temporary
The typical evolution of the orbital parameters is statebecausetheultimate orbitalcollapsecausesthe or-
showninFigure2aforaneccentricplanet(HD209458b) bital mean motion to diverge and then the rotational
and for the “most unstable” transiting planet OGLE- period of the planet to spin up dramatically. The evolu-
TR-132bwhichlies ona circularorbit. As expected, the tion of HD 209458’s rotational period can be easily un-
evolutionofthe orbitscompletely departsfromanexpo- derstood in the framework of classical tidal theory (e.g.
nential relaxation, characteristic of the existence of sta- Hut 1981; Pa¨tzold et al. 2004; Carone & Pa¨tzold 2007):
bleorunstabletidalequilibriumstates. Bothsemi-major because HD 209458 rotates more slowly than its orbital
axis evolveslowlyuntil the planets abruptly collide with period, the tidal torque raised by the planet onto the
theirparentstar(within.10Myrand.0.5Gyr,respec- star yields the star to spin up with time until a runaway
tively), reaching a zero value in ∼ 52 Myr and 4.3 Gyr, spin-up occurs, due to the conservation of momentum.
respectively. We verified that the same issue holds true Hence, HD 209458 is expected to never reach synchro-
for the other unstable transiting planetary systems and nization, contrary to current assumptions. The stellar
the time required for each planet to reach its host star obliquity follows the same trends and tidal dissipation
is indicated in Figure 1 for an initial zero stellar obliq- actsto coplanarizethe orbitandthe stellarequatoronly
uity. It typically ranges from 7 Myr (OGLE-TR-56) to duringthe finalrunawayphaseofthe orbitaldecay. Fig-
23.5 Gyr (OGLE-TR-111). Similarly (see Fig. 2a), HD ure 2 shows that, except for the existence of a rapid
209458b’seccentricityremains alsonearlyconstantuntil pseudo-synchronization timescale for the planetary ro-
an ultimate runaway decrease occurs associated to the tation, the timescale for the tidal evolutionof all the or-
orbital shrinkage. For comparison, we evaluate for this bital and rotational parameters is the time required for
planet the timescales derived from the usual exponen- the semi-majoraxis to shrink to zero,i.e. the remaining
tial tidal damping solution, based on the erroneous as- lifetime of the system, that has to be evaluated.
sumption that transiting planets are close to their tidal There is no simple analytical solution for eqn.(3) but
equilibrium state : when only tides raised by the star some reasonable simplifications are possible. Indeed,
(resp. planet) on the planet (resp. star) are considered, once the planetary spin has rapidly reached its pseudo-
τe,p = (2/21) × (Q′p/n)(a/Rp)5(Mp/M⋆) ≃ 0.41 Gyr equilibrium state within ∼ 105 − 106 yrs, any further
(resp. τ = (2/21)× (Q′/n)(a/R )5(M /M ) ≃ 15 exchangeofangularmomentumbetweentheplanet’sro-
e,⋆ ⋆ ⋆ ⋆ p
Gyr), more than one order of magnitude smaller (resp. tation and its orbit only occurs through radial tides due
three times larger) than the afore correctly calculated to a non-zero eccentricity. Assuming that the planet’s
remaining time before the eccentricity reaches zero. orbitalperiod is short comparedwith the star’s rotation
4 B. Levrard et al.
period, which is true for all unstable transiting planets, planetary orbits are in resonance. Finally, because our
eqn.(3) shows that the rate of orbital decay driven by results show that both the orbital eccentricity and the
planetarytidesbecomessmallerthanthecontributionof stellarobliquity undergoasubstantialdecayonlyduring
tides raised by the planet on the star if the relation: the ultimate runaway orbital collapse, this implies that
tidal dissipation in the star and in the planet has prob-
M 2Q′ R 5/2 ably not played a dominant role in the current observa-
p p ⋆
e< (4)
M⋆s7Q′⋆ (cid:18)Rp(cid:19) toifonpslaonfetnaerayrltyr-acnirsciutilnagr osrybstitesmasn,dunspleisns-oerabciht aolfigtnhmementiss
isverified. Thisconditionisfulfilledforallunstabletran- now precisely in this final rapid merging state, a rather
sitingplanetarysystems(consideringQ′ ≃Q′)2. Inthis unlikely possibility. These results bear important conse-
p ⋆
context, eqn.(3) can be integrated, giving the remaining quences for our understanding of planet formation, mi-
time for the planet to reach its host star from its initial gration and planet-disk interaction. They suggest that
orbital distance a (at small eccentricity): either the systems were formed with a nearly circular
orbit and a stellar spin nearly aligned with the orbital
1 Q′ a 5 M angular momentum, or other processes such as gravi-
τ ≃ ⋆ ⋆ , (5)
a 48 n R M tational interactions with the protoplanetary disk have
(cid:18) ⋆(cid:19) (cid:18) p(cid:19) dissipated the initial eccentricity (Moorhead & Adams
which only depends on tidal dissipation within the star, 2008). In contrast, planet-planet scattering during the
not within the planet 3. We stress, however, that such early stages of planet formation (e.g. Chatterjee et al.
timescales are very uncertain, because of the large un- 2008)orgravitationalperturbationsbyacompanionstar
′
1ce0r5ta<intiQes′⋆ i<n t1h0e10e)st(iem.ga.tePoa¨ftzothldeeQt⋆al.va2l0u0e4)(.typOictahlelyr cdouucleddhlaarvgeereacncdeonmtriizceitdiessp(inR-aosriboit&alFigonrdme1n9t96a)n.dF/oorrsparkoe-
tidal models involving dissipation by turbulent viscosity of simplicity, we have considered that the total angu-
intheconvectivezoneprovideestimatesoftheremaining lar momentum of the system is constant over time. In
lifetime several orders of magnitude larger (Rasio et al. reality, angular momentum of the star is continually ex-
1996; Sasselov 2003; Pa¨tzold et al. 2004). We found the tracted by a magnetized stellar wind, so that the ratio
values obtained with eqn.(5) to be in good agreement L /L should decrease with time. This indicates that
tot c
with those determined from numerical computations for binarysystemscloseto the marginallystableregimelike
each transiting planet, except for HD 17156 and GJ 436 HAT-P-2b (for which a ≃ a ) may eventually become
1 c
which have significanteccentricities,leading to a net de- unstable to tidal dissipation. One also may argue that
crease of the system lifetime due to enhanced tidal in- tidal dissipation is mostly effective in stellar convective
teractions. A non-zero stellar obliquity also causes the layers (Zahn 1977) so that only the moment of inertia
lifetime of the system to be slightly reduced. of the outer convective envelope, about ∼ 5% of the to-
tal moment of inertia C for a Sun-like star, should be
4. DISCUSSIONANDCONCLUSIONS ⋆
consideredbothineqns(1)and(2). Inthatcase,thesys-
Basedonrigorousargumentsandcalculations,wehave temconvectivelayers+planetisnotisolatedbecausethe
demonstrated that none but one of the discovered tran- differentialrotationbetweentheconvectiveandradiative
siting extra-solar planet has a tidal equilibrium state, zones generates an extra dissipative torque until radia-
implying a collapse with their host star. The lack of tive and convective zones are synchronized. Although
tidal equilibrium states implies that all the orbital and thismayaffecttheevolutiontimescaleofthesystem,the
rotational parameters evolve over the same, only rele- final conclusion should remain the same. We postulate
vant timescale which corresponds to the lifetime of the that satellite missions like CoRot or Kepler should de-
system. We stress that these results are independent of tect transiting planets onstable equilibrium orbits,with
the tidal model and can probably be extended to most L >L and a>a , further awayfrom the tidal insta-
tot c 2
other close-ingiant planets detected by radialvelocities. bility limit.
Nevertheless, the exact evaluation of such a timescale
strongly depends on the nature of the tidal processes
which remain poorly constrained (see e.g. Zahn 1977;
Rasio et al. 1996; Sasselov 2003; Pa¨tzold et al. 2004).
The very existence of the currently observed transiting
planets suggests that the lifetime of these systems is at
leastequaltotheageofthesystems. Analternativepos- The authorsare endebted to P.Robutel for useful dis-
sibility is that one or several undetected planetary com- cussions. This researchis supportedby the CNRS “Pro-
panions maintain the stability of the present orbit if the gramme National de Plan´etologie”.
2 except for GJ 436 for which p2/7(Mp/M⋆)×(R⋆/Rp)5/2 ∼ ofthe tidalfrequency yields asimilarvalue (the factor 1/48 must
0.08.e∼0.14. bereplacedby2/39)(Pa¨tzoldetal.2004)
3 Usingatidalmodelforwhichthequalityfactorisindependent
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6
Table 1. Values and uncertainties of parameters relevant to tidal evolution of transiting planetary systems
Name Mp(MJ) ∆Mp(MJ) Rp(RJ) Rmpin(RJ) Rmpax(RJ) Torb(days) a(AU) ∆a(AU) M⋆(M⊙) ∆M⋆(M⊙) R⋆(R⊙) ∆R⋆(R⊙) vsini⋆(km/s) ∆vsini⋆ e ∆e
HD17156 3.12c,d 0.5d 1.15d 1.04d 1.26d 21.22a,b 0.15b 0.042∗ 1.2a,b 0.1a,b 1.47a,b 0.17c 2.6c 0.5c 0.67c 0.08c
HaT-P-2 8.04b 0.4b 0.952e 0.94b 1.02b 5?63341a,b 0.0677a 0.0017a 1.298a 0.08b 1.412e 0.05b 20.2∗∗ 1.6∗∗ 0.517e 0.002e
HD149026 0.36a,b 0.03a,b 0.71g 0.66g 0.76g 2.8766f 0.042f 0.000664∗ 1.3a,b 0.06b 1.45a,b 0.1a,b 6.4h 2.1h 0.0f 0.0f
HD189733 1.15a,b 0.04b 1.154b 1.137b 1.171b 2.218581b 0.031b 0.0006b 0.82b 0.03b 0.755b 0.011b 3.5h 1.0h 0.0b 0.0b
HD209458 0.657b 0.006b 1.320a,b 11.295a,b 1.345a,b 3.52474859a,b 0.047b 0.0005b 1.101b 0.064b 1.125b 0.022b 4.7h 0.16h 0.014j 0.009j
GJ436 0.071b 0.006b 0.374b 0.358b 0.390b 2.64385a,b 0.0287b 0.0003b 0.44b 0.04b 0.463b 0.02b 0.52∗∗∗ 0.05∗∗∗ 0.14k 0.01k
TrES-1 0.76b 0.05b 1.081a,b 1.052a,b 1.110a,b 3.0300737a,b 0.0393a,b 0.0011l 0.89b 0.035b 0.811b 0.020b 1.08n 0.3n 0.0b 0.0b
TrES-2 1.198b 0.053b 1.220b 1.178b 1.265b 2.47063a,b 0.0367a,b 0.001m 0.98a,b 0.062a,b 1.000a,b 0.036a,b 2.0m 1.5m 0.0b -
TrES-3 1.92a,b 0.23a,b 1.295a,b 1.214a,b 1.376a,b 1.30619a,b 0.0226a,b 0.013a 0.90b 0.15b 0.802b 0.046b <2.0p - 0.0b -
TrES-4 0.84a,b 0.20b 1.674a,b 1.580a,b 1.768a,b 3.553945a,b 0.0488a,b 0.0022a 1.22b 0.17b 1.738b 0.092b 9.5q 1.0q 0.0b -
XO-1 0.90a,b 0.07a,b 1.184a,b 1.166b 1.212b 3.941534a,b 0.0488a,b 0.0005a 1.0a,b 0.03a,b 0.928a,b 0.015b <3.0r - 0.0b -
HAT-P-1 0.53a,b 0.04a,b 1.203b 1.152b 1.254b 4.46529a,b 0.0551a,b 0.0015a 1.12a,b 0.09a,b 1.115b 0.043b 2.2s 0.2s 0.09s 0.02s B
HAT-P-3 0.599b 0.026b 0.890a,b 0.844a,b 0.936a,b 2.899703a,b 0.03894a 0.0007t 0.936a,b 0.062a,b 0.824a,b 0.043a,b 0.5t 0.5t 0.0b - .L
HAT-P-4 0.68a,b 0.04a,b 1.27a,b 1.22a,b 1.32a,b 3.056436a,b 0.446a,b 0.0012a 1.26a,b 0.14a,b 0.59a,b 0.07a,b 5.5u 0.5u 0.0b - e
v
HAT-P-5 1.06a,b 0.11a,b 1.26a,b 1.21a,b 1.31a,b 2.788491a,b 0.04075a 0.00076a 1.16a,b 0.062a,b 1.167a,b 0.049a,b 2.6v 1.5v 0.0b - r
– a
HAT-P-6 1.057a,b 0.119a,b 1.330a,b 1.269a,b 1.391a,b 3.852985a,b 0.05235a 0.0087a 1.29a,b 0.06a,b 1.46a,b 0.06a,b 8.7w 1.0w 0.0b - r
1 d
WASP-1 0.867b 0.073b 1.443b 1.404b 1.482b 2.519961a,b 0.0382a,b 0.0013a,b 1.15b 0.24b 1.453b 0.032b –5.79x 0.35x 0.0b - e
WASP-2 0.88a 0.07b 1.036b 0.988b 1.088b 2.152226a,b 0.0307a,b 0.0011a 0.79b 0.15b 0.813b 0.032b <5.0y - b - t
WASP-3 1.76a,b 0.11b 1.31a,b 1.17a,b 1.38a,b 1.846834a,b 0.0317a,b 0.001z 1.24a,b 0.11a,b 1.31a,b 0.12a,b 13.4z 1.5z 0.0b - al.
OGLE-TR-10 0.61b 0.13b 1.22i 1.15i 1.36i 3.101278b 0.04162a,b0.00069B 1.10b 0.05b 1.14b 0.11b 7.0A 1.0A 0.0b -
OGLE-TR-56 1.29a,b 0.12a,b 1.30a,b 1.25a,b 1.35a,b 1.211909a,b 0.0225a,b 0.0004a 1.17a,b 0.04a,b 1.32a,b 0.06a,b 3.2A 1.0A 0.0b -
OGLE-TR-111 0.52b 0.13b 1.01b 0.97b 1.05b 4.0144479a,b 0.07C 0.001C 0.81b 0.02b 0.831a 0.031a <5.0a - 0.0b -
OGLE-TR-113 1.32a,b 0.19a,b 1.09a,b 1.06a,b 1.12a,b 1.4324757a,b 0.0229a,b 0.0002a 0.78a,b 0.02a,b 0.77a,b 0.02a,b <5.0A - 0.0b -
OGLE-TR-132 1.14a,b 0.12a,b 1.18a,b 1.11a,b 1.25a,b 1.689868a,b 0.0306D 0.0008D 1.26a,b 0.03a,b 1.34a,b 0.08a,b <5.0A - 0.0b -
OGLE-TR-182 1.01a,b 0.15a,b 1.13a,b 1.05a,b 1.37b 3.97910a,b 0.051a,b 0.001a 1.15a,b 0.05a,b 1.15a,b 0.23a,b <5.0E - 0.0b -
Note. —MpandRpareplanetarymassandradius,respectively. Thestellarrotationvelocityisdeterminedfromavailabledataonstarchromosphericactivityand/orfromthevalueoftheprojectedvelocityvsini⋆,
obtainedfromDopplerspectroscopicmeasurements,wherei⋆istheanglebetweenthestellarrotationaxisandtheline-of-sight,thatweassumedtobecloseto≃90◦.
∗estimatedviaKepler’slaw
∗∗basedontheaverageofLoeilletetal. (2008),Bakosetal. (2007)andWinnetal. (2007)
∗∗∗estimatedviachromosphericactivity(≃45daysbyDemoryetal. 2007)