How eccentric orbital solutions can hide planetary systems in 21 resonant orbits

a r X i v :0809.1275v 1 [a s t r o -p h ] 8 S e p 2008In preparationPreprint typeset using L A T E X style emulateapj v.10/09/06HOW ECCENTRIC ORBITAL SOLUTIONS CAN HIDE PLANETARY SYSTEMS IN 2:1RESONANT ORBITSGuillem Anglada-Escud ´e 1,Mercedes L ´opez-Morales 1,2,John E.Chambers 1In preparationABSTRACTThe Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets.If several planets are present,their signals will appear combined in the radial motion of the star,leading to potential misinterpretations of the data.Specifically,two planets in resonant orbits can mimic very efficiently the signal of a single planet in an eccentric orbit.We quantify the physical implications of this solution degeneracy using the well known harmonic expressions of keplerian motion.We find that a significant fraction of the published eccentric one-planet solutions might instead be multiple planet systems in near circular orbits ,and that several planets with masses comparable to Earth could have already been detected.Subject headings:Exoplanets –Orbital dynamics –Planet detectionINTRODUCTIONMost of the +300exoplanets found to date have been discovered using the Doppler technique,which measures the reflex motion of the host star induced by the plan-ets (Mayor &Queloz 1995;Marcy &Butler 1996).The diverse characteristics of these exoplanets are somewhat surprising.Many of them are similar in mass to Jupiter,but orbit much closer to their host stars.This finding has lead to extensive work on planet formation and mi-gration theories to explain how those planets got to their present location (eg.Ward 1997;Ida &Lin 2004).Also,many of the planets seem to move in orbits with eccen-tricies significantly larger than those observed in the So-lar System (where e <0.1,except for Mercury which has e ∼0.2),This result poses a problem for the planet for-mation theories of Core Accretion (Pollack et al.1996)and Disk Instability (Boss 1997),since both predict that planets form in quasi–circular orbits.The current expla-nation is that large eccentricities are triggered by secu-lar interactions,i.e.the Kozai effect (Soderhjelm 1975),or by rare close-in encounters (Ford et al.2005).The true distribution of exoplanet eccentricities is therefore key to understand the formation of planetary systems (Thommes et al.2008).The first multi-planet system was discovered around the solar type star υAndromedae (Butler et al.1997).The second one was found around the M dwarf Gliese 876.In Gliese 876,the first detected planet was the one orbiting furthest from the star (Delfosse et al.1998).Better sampling of the Doppler curve led to the subse-quent discovery of the other two planets,one of them in the 2:1resonance (Laughlin &Chambers 2001).In-terestingly,every time an additional planet is found in a system,the eccentricities of the other planets tend to decrease.The most clear examples are the multiple systems in 55Cnc (Fischer et al.2008)and HD160691(Pepe et al.2007).None of the current four planets in HD160691nor the five planets in 55Cnc have eccentricities larger than 0.2.Electronic address:anglada@,mercedes@,chambers@ 1Carnegie Institution of Washington,Department of Terrestrial Magnetism,5241Broad Branch Rd.NW,Washington D.C.,20015,USA2Hubble Fellow In this letter we discuss in detail the case where a two–planet system can be confused with a single planet in an eccentric orbit.This happens when two planets are in 2:1circular (or quasi circular)resonant orbits;i.e.the inner planet completes two orbits while the outer body completes one.Since a single planet eccentric fit is usu-ally the first choice,this degeneracy introduces an obser-vational bias towards eccentric solutions.In the forth-coming sections we show how this bias can have deep implications:1)many very low mass planets might have been already detected,but misinterpreted as an eccen-tricity signal,and 2)a significant fraction of the reported eccentric planets may be multiple systems in nearly cir-cular orbits;a configuration more similar to our Solar System than currently assumed.The solution degeneracy is a direct consequence of the Fourier expansion of the Keplerian motion (see Moulton 1914,as an example).In Konacki &Maciejewski (1996),the method of frequency analysis was first applied to an extrasolar planetary system and Konacki &Maciejewski (1999)adapted it to Doppler measurements.The poten-tial confusion between eccentric orbits and resonant sys-tems has been briefly mentioned in (Marcy et al.2001)and Ford (2006),but this issue has not been specifically considered until now.1.MATHEMATICAL DEGENERACYMathematically,the degeneracy between the resonantand the eccentric solutions come from the fact that their equations of keplerian trajectories are identical up to first order in the eccentricity.Exact detailed analytical ex-pressions to describe the harmonic expansion of the kep-lerian motion have been previously published,for exam-ple,by Konacki &Maciejewski (1999).Here we present only the approximate expression to illustrate the nature of the degeneracy and its implications.In the case of a single eccentric planet,the reflex radial velocity motion of the star isv e r =v r 0+K cos [Ω(t −τ0)](1)+Ke cos [2Ω(t −τ0)−ω]+O (Ke 2),where v r 0is the linear radial velocity of the barycenter of the system,K is the semi-amplitude of the radial veloc-2Anglada-Escud´e,L´o pez-Morales&Chambers1a.1b.Fig. 1.—Seen from above,diagrams of the relevant orbital pa-rameters of one planet in an eccentric orbit(Left),and two planets in a2:1resonant circular orbit(Right).τ0is the instant of cross-ing of the line of nodes.The instants of transit and occulation are marked as T I and T II.ity variations induced by the planet,ωis the argument of the periastron(angle between the periastron of the orbit and the ascending node),τ0is the time of cross-ing of the ascending node,andΩ=2π/P is the orbital frequency,where P is the orbital period(see Fig.1a). The term proportional to Ke is called thefirst eccentric harmonic,while the term O(Ke2)contains all the higher order contributions.If instead we have a two–planet system,both in circu-lar orbits and the inner planet having an orbital period half of the outer one,i.e.Ω2=2Ω(see Fig.1b),the expression for the radial velocity of the star isv R r=v r0+k1cos[Ω(t−τ0)](2)+k2cos[2Ω(t−τ0)+φ0]+O(k1e1,k2e2,Ke2),where k1and k2are the radial velocity semi–amplitudes of the outer and the inner planet.Ωandτ0are the or-bital frequency and the time of crossing of the ascending node of the outer planet,and the angleφ0is the rela-tive phase between the two planets atτ0.Higher order terms,summarized here as O(k1e1,k2e2,Ke2),become significant if the orbits are allowed to be eccentric.To afirst order approximation,v e r and v R r are formally identical if k1=K,k2=Ke,andφ0=−ω.This implies that the signal k2of an inner lower-mass planet will be indistinguishable from thefirst eccentric harmonic Ke unless the observations can resolve signals at the level of the next term in the harmonic expansion whose ampli-tude is9/8Ke2∼Ke2.Figure2shows how the Doppler radial velocity curves would look like in each case(one-planet in an eccen-tric orbit versus two resonant planets in circular orbits), for different values ofωand e.Thefigure shows how easily the two configurations can be confused,specially when e<0.3in the single planet case(or equivalently, when the inner planet is significantly less massive than the outer one,i.e.k2<k1),or if the radial veloc-ity curves are sparsely sampled.In a typical situation where K∼100ms−1and e∼0.1,both orbital solutions are indistinguishable at the3–σlevel unless the preci-sion of the data is better than0.3ms−1.Only now, planet hunting groups are beginning to achieve preci-sions of0.2–0.3ms−1(Mayor et al.2008;Fischer etal.Fig.2.—Radial velocity signals normalized to K=1.The two planet case(red dashed line)can be barely distinguished from the one planet eccentric solution(solid line)for eccentricities less than 0.3(top panels).2008).In addition,the typical stellar jitter3is3–5ms−1 (Cumming et al.2008),so radial velocity instrumental precision alone might not be enough to distinguish be-tween these two solutions.2.IMPACT ON KNOWN PLANETARY SYSTEMSThe implications of this degeneracy are large,since160 of305exoplanets have reported e<0.1eccentricities. Assuming circular orbits,the mass of the inner compan-ion candidate m h can be estimated asm h sin i=eResonant planets vs.eccentric orbits3TABLE1List of low mass eccentric planets.The complete table can be found inTab.S1.Planet m sin i P e K Ke Ke2m h sin i(m earth)(days)(m s−1)(m s−1)(m s−1)(m earth)Gl581c 4.7412.930.16 3.160.510.080.60Gl581d7.2983.600.20 2.630.530.11 1.16HD69830b9.908.670.10 3.800.380.040.79GJ674b11.10 4.690.209.65 1.930.39 1.76HD69830c11.4031.560.13 2.850.370.05 1.18HD69830d17.40197.000.07 2.350.160.010.97 ........................Data extracted from the Extrasolar Planet Encyclopedia(http://exoplanet.eu,mantained by Jean Schneider.See the full table in the on–linematerial.Fig. 3.—Orbital eccentricity versus the amplitude Ke2whichcan brake the statistical degeneracy if measured.Even asuming asensitivity of0.2m/s,there are still70over300planets under the3–σdetection threshold.A question that needs to be addressed is whether the2:1resonant configurations in Table1are dynamicallystable.Several2:1resonant multi-planet systems havealready been found(i.e.GJ876,HD82943,HD73526,HD128311).Dynamical stability of2:1resonant config-urations has been also discussed by several authors.Forexample,Lee&Peale(2002)show that resonant lockingmay arise naturally during the migration of exoplanetsin the presence of a protoplanetary disk.The case wherethe outer planet is significantly more massive has beenrecently discussed in great detail by Michtchenko et al.(2008),concluding that long term stability is guaranteedand that the resonant capture during migration is partic-ularly favoured.Therefore,there is no theoretical objec-tion to the case addressed in this paper,on the contrary,recent work strongly support the existence and stabilityof k2<<k1systems in2:1resonant configurations.Eccentric hot Neptunes(m1sin i<50m earth),are par-ticularly interesting since their potentially hidden com-panions are of a few Earth-masses or less(see Table1).Their small Ke2makes extremely difficult to distinguishbetween solutions with the current instrumental accura-cies but are excellent targets to seek out for the effectsof dynamical interactions.3.BREAKING THE DEGENERACYThe question then becomes how to observationallyidentify eccentric impostors.We focus here on theDoppler and photometric methods,which are the onlytwo techiques with currently enough sensitivity to dis-cern between both cases.In the future,techniques suchas astrometry and direct imaging will be useful aswell.ing improved Doppler dataThe most direct approach is to increase the numberof radial velocity observations,N obs,and their precision,σobs,until the condition3σobs/√4Anglada-Escud´e ,L´o pez-Morales &Chambers0.000.010.020.030.040.05-10-50510V e l o c i t y (m /s )12345Time (years)-10-50510V e l o c i t y (m /s )Fig. 4.—Numerical integration of the three body problem in GJ 674.Top panel contains the Doppler signal on a few orbits of the best resonant solution to GJ674b.The mass of the hidden companion is 2.2±0.6m earth .The bottom panels shows that dy-namical interactions become apparent on time–scales of hundreds of periods and the 2–planet case can be identified.pose a limit to the precision of radial velocity studies,even if dynamical interactions are present.3.2.Photometric methodsA second approach is to use photometric observations.These can confirm or discard the presence of a second planet in some circumstances,either by detection of plan-etary transits and occultations,or by observing reflected light or thermal emission from the planets.Photometric methods are mostly efficient for planets in short period orbits,since those tend to be hot and have a higher prob-ability of transiting in front of their star.Assuming that the period P ,the eccentricity e ,and τ0are known from the Doppler solution and that the orbital inclination of the planet is close to 900(edge on),the predicted instant of transit T I depends on the eccentricity asT I =τ0+NP1π+O (e 2),(4)where N is the number of integer periods elapsed from τ0.If the system contains a hidden companion,then the true e will be small and the transit will occur almost exactly 1/4P after crossing the line of nodes.This test is only significant if τ0is well constrained.An unambiguous determination of the eccentricity is obtained when both the primary transit and the occultation (planet passes behind the star),can be observed.This is because the time interval between these two events is independent of τ0.If the orbit is circular,the occultation occurs half period after the transit.If the orbit of the planet is truly eccentric,the time difference between the transit T I and the occultation T II isT II −T I =Pπ+O (e 2),(5)which can be as large as several hours on some of the known transiting planets.A representative example is GJ 436.The star hostsa hot–neptune in an eccentric orbit (e ∼0.14)with a period of only 2.63days (Maness et al.2007).The potential hidden companion would have a mass as low as 2.57m earth .GJ 436b was recently found to transit (Gillon et al.2007),but because of the uncertainity in τ0,the detection of the primary transit alone was not sufficient to confirm the eccentric orbit.Shortly after,the occultation was observed in thermal emission with the Spitzer telescope at the instant predicted by an ec-centric solution (Deming et al.2007).If the orbit of GJ 436b had been circular,the time of the occultation would differ by three hours from the observed time.4.CONCLUSIONSWe show that the Doppler signal of a single eccentric planet can mimic the signal of a two-planet system in a 2:1circular or near–circular resonant orbit.This de-generacy can be affecting more than half of the known exoplanets.If confirmed,it may result in a significant reduction of the eccentricities and a significant increase of the number of multiplanetary systems.The only techniques currently able to distinguish be-tween two resonant planets and single eccentric planet systems are limited to the Doppler and photometric ap-proaches described above.In the future,other meth-ods such as astrometry and direct imaging,will also provide ways to uncover eccentric impostors .Astrom-etry will be the first one to become sensitive enough,once the upcoming space astrometric missions Gaia/ESA (Lindegren et al.2008,to be launched in 2011)and SIM/NASA (Unwin et al.2008,to be launched after 2015),go on-line.High precision astrometry will be most helpful if the resonant orbits are not coplanar.Other-wise,it will suffer from the same degeneracies as the Doppler technique Konacki et al.(2002).The ultimate test will be direct imaging,which will allow to measure whether the orbit of the detected planet is indeed eccen-tric.This will have to wait until spaceborne missions such as a Darwin/TPF launch.The implications of this paper make worth reconsid-ering many published orbital solutions,and future an-nouncements of eccentric planets should be carefully tested before publication.Also,we find that several reported radial velocity curves (Mayor et al.2008)may contain hidden signals of hot rocky planets.Acknowledgements.GAE thanks A.Boss &A.Wein-berger for financial support.MLM acknowledges support provided by NASA through Hubble Fellowship grant HF-01210.01-A awarded by the STScI,which is operated by the AURA,Inc.,for NASA,under contract NAS5-26555.JEC would like to thank NASA’s Origins of Solar Sys-tems Program for support.We also thank A.Bonanos and all the other members of the Astronomy group at CIW-DTM for fruitful discussions.REFERENCESBoss,A.P.1997,Science,276,1836Butler,R.P.,Marcy,G.W.,Williams,E.,Hauser,H.,&Shirts,P.1997,ApJL,474,L115+Resonant planets vs.eccentric orbits5Cumming,A.,Butler,R.P.,Marcy,G.W.,Vogt,S.S.,Wright, J.T.,&Fischer,D.A.2008,PASP,120,531Delfosse,X.,Forveille,T.,Mayor,M.,et al.1998,A&A,338,L67 Deming,D.,Harrington,J.,Laughlin,G.,et al.2007,ApJL,667, L199Fischer,D.A.,Marcy,G.W.,Butler,R.P.,et al.2008,ApJ,675, 790Ford,E.B.2006,ApJ,642,505Ford,E.B.,Lystad,V.,&Rasio,F.A.2005,Nature,434,873 Gillon,M.,Pont,F.,Demory,B.-O.,et al.2007,A&A,472,L13 Ida,S.,&Lin,D.N.C.2004,ApJ,604,388Konacki,M.,&Maciejewski,A.J.1996,Icarus,122,347—.1999,ApJ,518,442Konacki,M.,Maciejewski,A.J.,&Wolszczan,A.2002,ApJ,567, 566Laughlin,G.,&Chambers,J.E.2001,ApJL,551,L109Lee,M.H.,&Peale,S.J.2002,ApJ,567,596Lindegren,L.,et al.2008,in IAU Symposium,Vol.248,IAU Symposium,217–223Maness,H.L.,Marcy,G.W.,Ford,E.B.,et al.2007,PASP,119, 90Marcy,G.W.,&Butler,R.P.1996,ApJL,464,L147+Marcy,G.W.,Butler,R.P.,Fischer,D.,et al.2001,ApJ,556,296 Marcy,G.W.,Butler,R.P.,Vogt,S.S.,Fischer,D.,&Lissauer, J.J.1998,ApJL,505,L147Mayor,M.,&Queloz,D.1995,Nature,378,355Mayor,M.,Udry,S.,Lovis,C.,et al.2008,ArXiv e-prints,806 Michtchenko,T.A.,Beaug´e,C.,&Ferraz-Mello,S.2008,MNRAS, 387,747Moulton,F.R.1914,An introduction to celesctial mechanics(The MacMillan Company,[c1914])Pepe,F.,Correia,A.C.M.,Mayor,M.,et al.2007,A&A,462,769 Pollack,J.B.,Hubickyj,O.,Bodenheimer,P.,et al.1996,Icarus, 124,62Rivera,E.J.,Lissauer,J.J.,Butler,R.P.,et al.2005,ApJ,634, 625Soderhjelm,S.1975,A&A,42,229Thommes,E.W.,Bryden,G.,Wu,Y.,&Rasio,F.A.2008,ApJ, 675,1538Unwin,S.C.,Shao,M.,Tanner,A.M.,et al.2008,PASP,120,38 Ward,W.R.1997,Icarus,126,261APPENDIXON–LINE MATERIAL6Anglada-Escud´e,L´o pez-Morales&ChambersTABLE2Planet m sin i/m⊕P e K Ke Ke2m ei/m⊕(days)(m s−1)(m s−1)(m s−1)Gl581c 4.7412.930.16 3.160.510.080.60Gl581d7.2983.600.20 2.630.530.11 1.16HD69830b9.908.670.10 3.800.380.040.7955Cnc e10.20 2.820.07 5.030.350.020.57GJ674b11.10 4.690.209.65 1.930.39 1.76HD69830c11.4031.560.13 2.850.370.05 1.18Gl581b14.76 5.370.0213.040.260.010.23HD190360c17.1017.100.01 4.580.050.000.14HD69830d17.40197.000.07 2.350.160.010.97GJ436b21.60 2.640.1519.01 2.850.43 2.57HD285968b22.7110.240.2312.25 2.820.65 4.15HD99492b32.7017.040.2510.98 2.790.71 6.59HD11964b33.0037.820.15 6.510.980.15 3.93HD49674b34.50 4.940.2314.09 3.240.75 6.3055Cnc f43.20260.000.20 4.800.960.19 6.8655Cnc c50.7044.340.099.990.860.07 3.46HD102117b51.6020.670.1113.86 1.470.16 4.34HD117618b57.0052.200.3911.36 4.43 1.7317.64HD76700b59.10 3.970.1326.67 3.470.45 6.10HD107148b63.0048.060.0511.400.570.03 2.50HD88133b66.00 3.410.1127.68 3.040.33 5.76HD168746b69.00 6.400.0827.92 2.260.18 4.44HD16141b69.0075.560.2111.83 2.480.5211.50HD46375b74.70 3.020.0439.00 1.560.06 2.37HD109749b84.00 5.240.0130.340.300.000.67HD101930b90.0070.460.1118.98 2.090.237.86HD33283b99.0018.180.4826.3412.64 6.0737.72HD164922b108.001155.000.057.610.380.02 4.29HD93083b111.00143.580.1419.23 2.690.3812.33HD74156d118.80336.600.2510.83 2.710.6823.57HD83443b120.00 2.990.0169.070.550.000.76HD108147b120.0010.900.5037.7018.779.3547.43HD75289b126.00 3.510.0556.93 3.070.17 5.40HD208487b135.00123.000.3217.04 5.45 1.7434.2947Uma c138.002190.000.227.57 1.660.3724.10HD45652b141.0043.600.3830.6811.66 4.4342.53BD-103166b144.00 3.490.0767.87 4.750.338.00HD6434b144.0022.090.3038.1111.43 3.4334.29HD99109b150.60439.300.0914.79 1.330.1210.76HD155358c151.20530.300.1814.75 2.600.4621.12HD187123b156.00 3.100.0372.95 2.190.07 3.71HD160691e156.57310.550.0715.59 1.040.078.28HAT-P-1b157.20 4.470.0762.36 4.180.288.36Gliese876c168.0030.100.2784.8522.91 6.1936.00HD37124d180.00843.600.1414.51 2.030.2820.00HD37124b183.00154.460.0625.76 1.420.087.99HD175541b183.00297.300.3314.74 4.86 1.6047.93HD27894b186.0017.990.0560.97 2.990.157.23HD216770b195.00118.450.3732.4712.01 4.4557.27HD170469b201.001145.000.1112.55 1.380.1517.55HD37124c204.902295.000.2011.96 2.390.4832.53HD209458b207.00 3.520.0795.93 6.710.4711.50Ups And b207.00 4.620.0375.11 2.180.06 4.76HD11964c210.001940.000.3011.56 3.47 1.0450.00HD224693b213.0026.730.0541.77 2.090.108.45HD187085b225.00986.000.4715.897.47 3.5183.93HIP14810c228.0095.290.4139.0015.94 6.5273.98HD38529b234.0014.310.2957.2716.61 4.8253.86HD4208b240.00812.200.0519.140.960.059.52HD114729b246.001131.480.3118.45 5.72 1.7760.53Gj849b246.001890.000.0627.87 1.670.1011.7255Cnc b247.2014.650.0170.150.980.01 2.75HD121504b267.0064.600.1347.52 6.180.8027.55HD155358b267.00195.000.1136.00 4.030.4523.73HD10647b273.001040.000.1818.54 3.340.6039.00HD185269b282.00 6.840.3093.5628.078.4267.15HD154345b284.103340.000.0414.670.650.039.92HD179949b285.00 3.090.02117.54 2.590.06 4.98HD114386b297.00872.000.2827.777.78 2.1866.00HD114783b297.00501.000.1028.13 2.810.2823.57HD150706b300.00264.000.3837.3014.18 5.3990.48HD142b300.00337.110.3830.9711.77 4.4790.48HD108874c305.401605.800.2519.07 4.77 1.1960.60rho CrB b312.0039.840.0465.17 2.610.109.91HD20367b321.00500.000.2328.67 6.59 1.5258.60HD130322b324.0010.720.05121.85 5.850.2812.34HD52265b339.00118.960.2945.1613.10 3.8078.03HD100777b348.00383.700.3636.3413.08 4.7199.43GJ317b360.00692.900.1975.8214.63 2.8255.15Resonant planets vs.eccentric orbits7TABLE3Planet m sin i/m⊕P e K Ke Ke2m ei/m⊕(days)(m s−1)(m s−1)(m s−1)HD65216b363.00613.100.4135.0614.37 5.89118.13HD210277b369.00442.100.4736.7317.348.18138.24HD188015b378.00456.460.1533.19 4.980.7545.00HD27442b384.00423.840.0732.13 2.250.1621.33HD177830b384.00391.000.4331.7213.64 5.86131.06HD217107b399.007.130.13146.1319.29 2.5541.80HD149143b399.00 4.070.02155.82 2.490.04 5.07HD108874b408.00395.400.0739.45 2.760.1922.67HD75898b444.00204.200.3548.3416.92 5.92123.34HD216435b447.001442.920.3425.668.73 2.97120.63HD86081b450.00 2.140.01217.81 1.740.01 2.86HD23127b450.001214.000.4430.6513.49 5.93157.15HD190360b450.602891.000.3623.388.42 3.03128.75HD12661c471.001444.500.2028.77 5.75 1.1574.77HD134987b474.00260.000.2452.4212.58 3.0290.29γCephei b480.00902.900.1228.28 3.250.3743.81HD167042b480.00416.100.0332.750.980.0311.43HD142415b486.00386.300.5051.5025.7512.87192.87HD4203b495.00400.940.4651.4723.6810.89180.73HD160691b501.00654.500.3140.8112.65 3.92123.27HD50499b513.002582.700.2323.19 5.33 1.2393.65HD82943b525.00441.200.2244.809.81 2.1591.26HD231701b534.00141.600.1066.78 6.680.6742.38HD154857b540.00409.000.4752.5424.6911.61201.44κCrB b540.001191.000.1924.83 4.720.9081.43HD73256b561.00 2.550.03251.987.560.2313.36HD68988b570.00 6.280.14197.8127.69 3.8863.34HD190647b570.001038.100.1838.01 6.84 1.2381.43Gliese876b580.5060.940.02222.58 5.540.1411.47HR810b582.00311.290.2458.4014.02 3.36110.86HD5319b582.00675.000.1235.17 4.220.5155.43HD187123c585.003700.000.2526.58 6.62 1.65115.61υAnd c594.00241.520.2559.5215.12 3.84119.75HD70642b600.002231.000.1032.66 3.270.3347.62HD19994b600.00454.000.2046.179.23 1.8595.24HD210702b600.00341.100.1540.82 6.200.9472.39HD82943c603.00219.000.3667.9324.398.76171.82HD117207b618.002627.080.1630.69 4.910.7978.48HD216437b630.001294.000.3441.5814.14 4.81170.01HD118203b639.00 6.130.31226.2869.9221.61156.72HD128311b654.00448.600.2572.4118.10 4.53129.77HD8574b669.00228.800.4082.2632.9013.16212.39HD12661b690.00263.600.3577.7027.199.52191.68HD41004A b690.00655.000.3977.3830.1811.77213.586Lyn b720.00899.000.1337.41 5.010.6776.58HD202206c732.001383.400.2744.4611.87 3.17155.12HD43691b747.0036.960.14129.3118.10 2.5383.01HD73526c750.00377.800.1473.1510.24 1.4383.34HD192699b750.00351.500.1553.838.02 1.2088.7047Uma b780.001083.200.0552.74 2.580.1330.34HD23079b783.00738.460.1057.80 5.780.5862.15HD89307b819.003090.000.2741.3011.15 3.01175.51HD66428b846.001973.000.4649.2322.8910.64312.23HD169830b864.00225.620.3184.4026.168.11212.58HD62509b870.00589.640.0248.560.970.0213.81HD73526b870.00188.300.19107.9020.50 3.90131.20HD72659b888.003177.400.2045.119.02 1.80140.96HD196885b888.001349.000.4653.0124.4911.31325.62HD196050b900.001289.000.2854.8815.37 4.30200.01W ASP-10b918.00 3.090.06560.2531.93 1.8241.53HD221287b927.00456.100.0873.65 5.890.4758.86HD125612b960.00502.000.3987.0533.9513.24297.16HD128311c963.00919.000.1782.4214.01 2.38129.94HD40979b996.00267.200.23106.7424.55 5.65181.82HD183263b1107.00634.230.3888.7033.7112.81333.88HD195019b1110.0018.200.01286.96 4.020.0612.3355Cnc d1150.505218.000.0245.98 1.150.0322.83HIP14810b1152.00 6.670.15440.1064.699.51134.41HD92788b1158.00377.700.27113.1230.548.25248.16Ups And d1185.001274.600.2467.9116.44 3.98227.61Gl86b1203.0015.770.05396.8618.260.8443.92HD169830c1212.002102.000.3356.6418.69 6.17317.45HD213240b1350.00951.000.4595.1642.8219.27482.17HD16175b1350.00856.000.4893.8045.0321.61514.32HD17092b1380.00359.900.1779.9013.26 2.20181.8214Her b1392.001773.400.3793.7334.5912.76407.68HD11506b1455.001280.000.2286.4419.02 4.18254.06HD50554b1470.001279.000.42102.6843.1318.11490.03HD190228b1497.001127.000.4394.5440.6517.48510.918Anglada-Escud´e,L´o pez-Morales&ChambersTABLE4Planet m sin i/m⊕P e K Ke Ke2m ei/m⊕(days)(m s−1)(m s−1)(m s−1)HD132406b1683.00974.000.34120.3740.9213.91454.17HD28185b1710.00383.000.07144.4610.110.7195.01HD102272b1770.00127.580.05162.268.110.4170.24HD70573b1830.00851.800.40148.6459.4623.78580.99HD10697b1836.001077.910.11115.8812.75 1.40160.30HD178911B b1887.6071.490.12309.2438.44 4.78186.22HD104985b1890.00198.200.03174.87 5.250.1645.00HD11977b1962.00711.000.40110.1444.0617.62622.90HD111232b2040.001143.000.20165.5533.11 6.62323.834Uma b2130.00269.300.43224.3896.9341.87730.33HD23596b2157.001558.000.31117.9637.0411.63537.5770Vir b2232.00116.690.40329.88131.9552.78708.62ǫTau b2280.00594.900.15100.0215.10 2.28273.26W ASP-14b2317.50 2.240.101043.5499.149.42174.74HD74156c2409.002476.000.43120.5651.8422.29822.17HD33564b2730.00388.000.34241.8582.2327.96736.71HD30177b2751.002819.650.30148.7144.6113.38655.04HD141937b2910.00653.220.41258.87106.1343.52946.9618Del b3090.00993.300.08125.9610.080.81196.20NGC24233b3180.00714.300.21143.4030.11 6.32530.03HD114762b3306.0083.890.34633.60215.4273.24892.15XO-3b3537.00 3.190.261539.90400.37104.10729.90HD136118b3570.001209.000.37220.0381.4130.121048.40HD38529c3810.002174.300.36178.2464.1723.101088.64HD162020b4125.008.430.281714.82475.00131.58906.90HD13189b4200.00471.600.28145.8140.8311.43933.39HD202206b5220.00255.870.44590.34256.80111.711802.26ChaHa8b5400.001590.900.491711.10838.44410.832100.13HD168443c5430.001765.800.21309.8265.8413.99915.83HD41004B b5520.00 1.330.086381.26516.8841.87354.88NGC4349127b5940.00677.800.19196.3037.307.09895.77。