arXiv:astro-ph/0511295v1 10 Nov 2005 Vcremyb xlie yteeitneo diinlplan additional of existence the by explained be may curve RV tpsil ovrf n xedterslsotie ihan with obtained results the periods. extend leading and verify to possible it Results. Methods. Aims. Context. accepted Received; Toru´n, Poland PL-87-100 Astronomy, for Toru´n Centre upsdt otJva opnosi ogpro orbits. long-period in companions Jovian host to supposed e words. Key mi and d 7–20 of range the indee in periods has orbital fits their single-planet estimate We of signifi yields residuals model the 2-planet of the variability when cases new four found We 20)anucdadsoeyof et discovery Rivera a recently, also Very announced been (2004). has (2005) al. planet et Neptune-like Butler a by an- time, discovered same been has the has at companion the Almost low-mass planet in A mass found (2004). 14-Earth al. been et year, Santos compan- by past Neptune-like nounced of the detection In of ions. limit p the extrasolar approach for surveys ets (RV) velocity radial precision The Introduction 1. D106 novn etn-aspae in planet Neptune-mass about a system involving multi-planet 190360 new a HD announced (2005) al. et Vogt ∼ i ihaJptrlk opno with companion Jupiter-like a with bit uhpaessest entrl h yaia eaaino relaxation dynamical The natural. be to existenc seems not the planets and such Nevertheless, signal observations. RV contributed enough the frequent of amplitude small detecte clearly of be cause cannot objects such present, At panions. smalle contain can planets Jupiter-like involving systems or system. Solar distant own relatively our in resemble to planets begin giant also involving en ment, their of th architecture rather systems. The bodies hot-Jupiters. multi-planet rocky gaseous massive are of likely planets view low-mass found the The change discoveries These edo Send etme 8 2018 28, September srnm Astrophysics & Astronomy dobtaottefmu lee86paeaysse.Also system. planetary 876 Gliese famous the about orbit 2d hr r led pcltosa owiho h extrasolar the of which to as speculations already are There bu uaieNpuelk xrslrpaeaycandida planetary extrasolar Neptune-like putative About ff ets yohssta h eiul fte1pae model 1-planet the of residuals the that hypothesis a test We rn eussto requests print u nlsscnrstepeec faproi opnn in component periodic a of presence the confirms analysis Our er-nlz h rcso ailvlct R)dt fH 2 HD of data (RV) velocity radial precision the re-analyze We epromagoa erhfrtebs t nteobtlpara orbital the in fits best the for search global a perform We xrslrpaesDplrtcnqe D288—D19036 208487—HD HD technique— planets—Doppler extrasolar ρ 1 [email protected] : acisse MAtu ta.2004). al. et (McArthur system Cancri aucitn.ms no. manuscript ∼ ryzo ozzesiadCzr Migaszewski Cezary Go´zdziewski and Krzysztof at-aspae in planet Earth-mass 7 ∼ 00 ria period. orbital 3000d ≃ lntr rgnte o-etn lnt a xs nth in exist may planets hot-Neptune then origin planetary a d 17 plcto fcmol sdFTbsdproormanalys periodogram FFT-based used commonly of application . com- r t nsotpro orbits. short-period in ets dor- 1d ia assaoto 0mse dteEarth. the od masses 20 of about masses nimal viron- atybte t oteR aata h et1pae soluti 1-planet best the than data RV the to fits better cantly be- d ABSTRACT bits, of e lan- al. an f fteR ra reua cte ftemaueet bu th about measurements the of scatter irregular an or RV the of eessaewt eei loihsadsmlxmto.Th method. simplex and algorithms genetic with space meters h Vo D106 hc a orsodt o-etn plan hot-Neptune a to correspond may which 190360 HD of RV the trhstesm-mltd fafwmtr e eod i.e., second, per meters ho few the a to of semi-amplitude close the revolving s has planets velocity star t Neptune-like radial in small, The lies of technique. still nal Doppler problem inevitable the the of but limitations field the in through 05 dye l 05 ut ta.20;Fshre l 2005) al. et Fischer 2005; al. a et et Curto Bonfils 2005; al. (e.g., et candidates Udry 2005; hot-Saturn and detect hot-Neptune new several of turn by In supported accretion. are sta works planetary type theoretical of these solar by-product to common com- a close of be planets could formation Neptune-like the of that systems simulatio show pact numerical (2005) The Cionco can & hot-Jupiters. Brunini they are by and as history frequent evolution as and origin be hot-Jupit same and the hot-Neptunes evapo- share that may significant suggests undergone work have This ration. which giants gas massive h xrslrPaesEccoei yJa Schneider, Jean by Encyclopedia Planets http: Extrasolar the t aotG 436, pl GJ hot-Neptune (about detected ets recently three the Bara star. that parent show eas the (2005) of can neighborhood close which a companions, in survive undetectable still may smaller, planets Jupiter-like tain ex distant many particular, containing In systems 2000). solar (Laskar availa orbits dynamically stable the of final up space to filling lead orbits can with 2003) configurations Laughlin & (Adams systems planetary 1 88,H 930 D181 n D142.Teesasare stars These 114729. HD and 188015 HD 190360, HD 08487, h eeto fNpuems xpaesi break- a is exoplanets Neptune-mass of detection The o rqetudtso h eeecs laesee please references, the of updates frequent For // www.obspm.fr —D181—D142—D147513 114729—HD 188015—HD 0—HD / planets. ρ 1 Cnc, µ re a rgnt rmmore from originate may Arae) s xrslrsystems. extrasolar ese sfrietfigthe identifying for is n.I h periodic the If ons. tes
c synthetic e S 2018 ESO ff smakes is tal. et e con- ions tra- an- ble ers ig- ily he ns et. rs at st 1 l. . , 2 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? a similar range as the measurement errors and chromospheric eccentricity, V0 is the velocity offset. There are some arguments variability of the RV. This can be a source of erroneous inter- that is best to interpret the derived fit parameters (K, P, e, ω, Tp) pretation of the observations. For instance, in a recent work, in terms of Keplerian elements and minimal masses related Wisdom (2005) claims that the orbital period of 2.38d of com- to Jacobi coordinates (Lee & Peale 2003; Go´zdziewski et al. panion d detected by McArthur et al. (2004) in ρ1 Cancri sys- 2003). tem is an alias of two periods originating from the orbital mo- To search for the best-fit solutions, we applied a kind of tion of planets b and c and, instead, he found an evidence of hybrid optimization. A single program run starts the genetic al- an another planet in ∼ 261 d orbit. Actually, a proper inter- gorithms (GAs) optimization. In particular, we use the PIKAIA pretation of the observations is still very difficult. Often, they code by Charbonneau (1995). The GAs has many advantages can be equally well modeled by qualitatively different config- over more popular gradient-type algorithms, for instance, the urations and even the number of planets cannot be resolved Levenberg-Marquardt scheme (Press et al. 1992). The power without doubt. An example will be given in this paper too. of GAs lies in their global nature, the requirement of knowing 2 1/2 In this work, for a reference and a test of our approach, only the (χν) function and an ease of constrained optimiza- we re-analyze the published RV data of two stars: HD 208487 tion. In particular, GAs permit to define parameter bounds or 2 1/2 (Tinney et al. 2005)— Gregory (2005a) claims that a second add a penalty term to (χν) (Go´zdziewski et al. 2003, 2005). planet accompanies a confirmed Jovian companion b, and In our code, the initial population of randomly chosen HD 190360 (Vogt et al. 2005)—the discovery team claims the 2048 members represents potential solutions to the RV model. existence of a hot-Neptune and a Jovian planet in long-period The code produce 128 new off-spring generations. The best orbit. Next, using the same method, we study other three extra- fit found by PIKAIA is refined by the simplex algorithm of solar systems: HD 188015 (Marcy et al. 2005b), HD 114729 Melder and Nead (Press et al. 1992). In that method, we set 2 1/2 −15 (Butler et al. 2003) and HD 147513 (Mayoret al. 2004), in the fractional tolerance for (χν) variability to 10 . Such which Jupiter-like companions have been discovered in long- procedure runs thousands of times for every analyzed data set. period orbits. However, the residuals of the 1-Keplerian fits Thanks to non-gradient character of both algorithms we may are either relatively large or we see ”suspicious” scatter of the bound the space of examined parameters, according to specific residuals. We use the available measurements to test a hypoth- requirements. Usually, due to a small number of measurements, esis that additional short-period planets exist in these systems the best-fit ec is barely constrained and tends to be large, in and their signals may be already hidden in the existing data, but particular in the range of very short periods. Nevertheless, we likely at the detection limit. Our reasoning follows the theoret- assumed that the tidal circularization limits the eccentricity of ical predictions that Neptune-like planets can easily form and the short-period orbit and we arbitrarily set its upper bound to survive close to the parent star. The main difficulty is a small 0.3. The orbital periods of putative planets are searched in the number of measurements, typically about of 30–40 data points range of [2,136] d. spread over several years. It makes it very difficult to determine The internal errors of the RV data are rescaled according 2 2 2 orbits of such planetary candidates without a doubt. In partic- to σ = σm + σj , where σ is the joint uncertainty, σm and ular, this concerns the identification of the orbital periods with σj is the internal error and adopted variance of stellar jitter, the application of somehow traditional Fourier-based analysis. respectively. Typically, we choose σj following estimates for Instead, we prefer a global search for the best-fit 2-planet con- Sun-like dwarfs (Wright 2005) or we set its value as quoted 2 1/2 figurations using the genetic algorithms and scanning (χν) in by the discovery teams. The particular estimates are given in the multidimensionalspace of orbital parameters. This couldbe Table 1. an alternative to the already classic Lomb-Scargle periodogram The best fits found in the entire hybrid search are illustrated (e.g., Butler et al. 2004) or sophisticated Bayesian-based anal- by projections onto planes of particular parameters of the RV ysis, which is recently proposed by Gregory (2005a,b). That model, Eq. 1. Usually, we choose the (P, K)- and (P, e)-planes. author claims an evidence of additional planets using the same Marking the elements within the formal 1σ, 2σ, 3σ confidence RV measurements which are modeled by 1-planet configura- intervals of the best-fit solution (which is always marked in the tions by the discovery teams, about HD 73526 and HD 208487. maps by two crossing lines) we have a convenient way of vi- 2 1/2 sualizing the shape of the local minima of (χν) and to obtain 2. The fitting algorithm, numerical setup and tests reasonable estimates of the fit errors (Bevington & Robinson 2003). In all cases studied in this paper, we assume that the second, Still, even we find very good best-fit configurations,a prob- putative planet is closer to the star than the already known com- lem persists: is the obtained fit not an artifact caused by specific panion b in relatively long-period orbit. To model the RV sig- time-distribution of measurements or the stellar jitter? In order nal, we use the standard formulae (e.g., Smart 1949). For every to answer for this question we apply the test of scrambled ve- planet, the contribution to the reflex motion of the star at time t locities (Butler et al. 2004). We remove the synthetic RV con- is the following: tribution of the firstly confirmed planet from the RV data, ac- cording to its best-fit parameters. Next, the residuals are ran- V (t) = K[cos(ω + ν(t)) + e cos ω] + V , (1) r 0 domly scrambled, keeping the exact moments of observations, where K is the semi-amplitude, ω is the argument of pericenter, and we search for the best-fit elements of the second (usually, ν(t) is the true anomaly involving implicit dependence on the inner) planet. For uncorrelated residual signal we should get 2 1/2 orbital period P and the time of periastron passage Tp, e is the close to the Gaussian distribution of (χν) . For every synthetic Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 3 data set, the minimization is performed with the hybrid method. 0.60 Let us note, that in this case we deal with 1-planet model (and 6 parameters only) thus the large population in the GA step and 0.50 precise simplex code assure that the best-fit solution can be re- c 0.40 liably found in one single run of the hybrid code. The runs of e b the code are repeated at least 20,000 times for every analyzed e data set. If the best fit correspondingto the real (not scrambled) 0.30 data lies on the edge of this distribution,such experimentassure us that the real data produce much smaller (χ2)1/2 (and an rms) 0.20 ν 0 0.2 0.4 0.6 0.8 1 1.2 than the most frequent outcomes obtained for the scrambled 5 data. Such a test provides a reliable indication that the residuals t [10 yr] are not randomly distributed. A likelihood pH that the residuals 2.03 are only a white noise can be measured by the ratio of the best 2 1/2 2.01 fits with (χν) less or equal to that one corresponding to the real data against all possible solutions. 1.99 Unfortunately, even with a positive outcome of the test
Fig. 1. The parameters of the best-fit solutions to the 2-planet model of the HD 208487 RV data projected onto the (P, e)- and (P, K)-plane. In this search, a more distant companion to the formerly known Jupiter-like body in ≃ 130 d orbit is assumed. 2 1/2 Upper plots are for the inner planet, bottom plots are for the outer companion. The values of (χν) of the best-fit solutions 2 1/2 are marked by the size of symbols. Largest circle is for (χν) equal to 0.619 ; smaller symbols are for 1σ solutions with 2 1/2 2 1/2 2 1/2 (χν) ∈ [0.619, 0.710), 2σ solutions with (χν) ∈ [0.710, 0.841) and 3σ solutions with (χν) ∈ [0.841, 1.0) (smallest, filled circles), respectively.
Fig. 2. The parameters of the best-fit solutions to the 2-planet model of the HD 208487 RV data projected onto (P, e)- and (P, K)-plane. In this search, an inner companion to the formerly known Jovian planet in ≃ 130 d orbit is assumed. Upper plots 2 1/2 are for the outer planet, bottom plots are for the inner companion. The values of (χν) of the best-fit solutions are marked 2 1/2 by the size of symbols. Largest circle is for (χν) = 0.581 (the best-fit solution, Table 1); smaller symbols are for solutions 2 1/2 2 1/2 within 1σ interval of the best-fit with (χν) ∈ [0.581, 0.677), 2σ solutions with (χν) ∈ [0.677, 0.813) and 3σ solutions with 2 1/2 (χν) ∈ [0.813, 0.98) (smallest, filled circles), respectively. Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 5
12 1200 HD208487 1000 10 HD 208487 800 8 600 6 400 for real data 2 ν number of fits Power √χ 4 200 2 √χν 2 0 0.5 0.6 0.7 0.8 0.9 1 1.1 0 2 1/2 2 5 10 25 50 100 250 500 1000 Fig. 6. A histogram of (χν) for Keplerian fits to 33,000 sets Period [d] of scrambled RV residuals of the synthetic signal of the Jupiter- like planet in ∼ 130 d orbit (HD 208487, see Table 1). The Fig. 4. Lomb-Scargle periodogram of the residuals of the position of the best-fit to the real data is marked with an arrow. Jupiter-like companion’s with Pb ∼ 130 d about HD 208487. 25
20 HD 190360
15 ity may contradict the requirement of a tidally circularized or- bit. However, the orbital evolution of the whole system reveals Power 10 large-amplitude variations of ec (Fig. 3) which areforced by the mutual interactions between companions. We also face an an- 5 other trouble, a small periastron-apoastron distance of the two putative planets ∼ 0.2 AU. Nevertheless, the system appears to 0 be dynamically stable. The evolution of the MEGNO indicator 2 5 10 25 50 100 250 500 1000 · 5 (Go´zdziewski et al. 2001) computed over 3 10 Pb is illustrated Period [d] in the lower panel of Fig. 3. Its oscillations about of 2 mean a quasi-periodic configuration and strictly confirm apparently Fig. 8. Lomb-Scargle periodogram of the residuals of the long- regular behavior of eb,c. period signal which is seen in the HD 190360 data. For a reference, we computed the Lomb-Scargle (LS) peri- odogram (Fig. 4) of the residuals of the dominant 1-planet sig- 2.2. Test case II: HD 190360 nal having the period of 130 d. The largest peaks about of 28 d In a recent paper, Vogt et al. (2005) published the precision RV and 998 d (the period of a hypothetic long-period planet) most data for HD 190360. The variability of the RV is explained by possibly are aliasing with the best-fit period ≃ 14.5 d. However, the existence of two planetary companions: a Jupiter-like planet this period is favored by the smallest (χ2)1/2. The aliasing of the ν in long-period orbit, P ∼ 3000 d, and a Neptune-like body two dominant periods is illustrated in Fig. 5. This figure shows b in ≃ 17.1 d orbit. The authors conclude that the existence of the synthetic RV signals of the putative configurations with the the smaller planet is the best explanation of the residual signal short- and long-period companions of planet b. Curiously, the of the single planet solution. Its contribution has small semi- orbital periods of the two planets in the model with the short- amplitude K ≃ 4.6 m/s. Yet the orbital period is about of a period orbit are very close to the 9:1 ratio. This again could be half of the rotational period of the star, 36–44 d, and the RV an effect of aliasing, nevertheless the best-fit solution with sin- variability may be an effect of spot complexes on the stellar gle planet has P about of 14.5 d and much larger rms ∼ 7m/s b surface (Vogt et al. 2005). than in the best 2-planet solution. The elements of a few hundred fits gathered by the hybrid Some more interesting results brings the test of scrambled search are illustrated in Fig. 7 (the elements of the best-fit are residuals, Fig. 6. It appears that the real residual signal lies far given in Table 1). The period of the inner planet corresponds to 2 1/2 from the maximum of the Gaussian-like distribution and it is a single, very deep minimum of (χν) . It is clear, that ec has a −5 unlikely that the residuals are only a white noise (pH ≃ 3·10 ). large error ∼ 0.15. Our fit is slightly better than that one quoted Also Kb ≃ 10.5m/s is much larger than the joint uncertainty of by Vogt et al. (2005) but ec ≃ 0.2 is also different as well as the measurements. Because HD 208487 is a very old and quiet we have got slightly larger Kc ≃ 5.2m/s. Note that we obtain a G-dwarf with low chromospheric activity (Tinney et al. 2005), similar uncertainties of 100 d for Kb and of 0.05 for eb. the hypothesis of a hot sub-Neptune planet in this extrasolar The Lomb-Scargle periodogram (Fig. 8) of the residuals system seems to be very appealing. A peculiarity of this system of the long-period orbit reveals a strong, dominant peak at could be the proximity to the 9:1 mean motion resonance of its 17.1 d. This an excellent confirmation of the results of the hy- companions. brid search. The test of scrambled residuals reveals that the 6 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates?
40
30
20
10 [m/s]
r
V 0
-10 -20 HD 208487 -30 1000 1500 2000 2500 3000 JD-2,450,000 [days] Fig. 5. Synthetic RV signals of the two solutions to the RV data of HD 208487. The thick line is for the outer companion to the known 130 d planet. The thin line is for the putative inner companion. The original RV data are marked with error-bars. For a clear illustration, only a part of the second curve is plotted.
0.5 28
26 0.4 b e [m/s] 24 b
0.3 K 22
0.2 20 2700 2800 2900 3000 3100 3200 2700 2800 2900 3000 3100 3200 Pb [d] Pb [d] 0.3 7.0
6.0 0.2 c
e 5.0 [m/s] c
0.1 K 4.0
0.0 3.0 16 16.5 17 17.5 18 16 16.5 17 17.5 18 Pc [d] Pc [d]
Fig. 7. The parameters of the best-fit solutions to the 2-planet model of the HD 190360 RV data projected onto the (P, e)- and 2 1/2 (P, K)-plane. Upper plots are for the outer planet, bottom plots are for the inner companion. The values of (χν) of the best- 2 1/2 fit solutions are marked by the size of symbols. Largest circle is for (χν) ≃ 0.679 (the best-fit solution, Table 1); smaller 2 1/2 2 1/2 2 1/2 symbols are for 1σ solutions with (χν) ∈ [0.679, 0.70),2σ solutions with (χν) ∈ [0.70, 0.74)and 3σ solutions with (χν) ∈ [0.74, 0.79) (smallest, filled circles), respectively.
2 1/2 residual signal is hardly random. The maximum of (χν) for Still, the best-fit period of the inner planet can be clearly 2 1/2 scrambled data is shifted by ≃ 0.4 from the value of (χν) for identified (Fig. 10) but the semi-amplitude Kc has been slightly the real data. shifted. The elements of the outer planet are determined with much larger errors than the uncertainties obtained for the full Now, having so clear picture, we analyze a smaller sample data. In particular, the error of P is about of 350 d. The domi- of measurements.To perform this test, we selected 38 first mea- b nant period is still well recognizable in the Lomb-Scargle peri- surements spanning ∼ 2200 d. The number of data points and odogram, Fig. 11. Finally, the test of scrambled residuals also their time-coverage are similar to other cases which we study give a clear picture, albeit the histogram (Fig. 12) has much in this work. The described above procedure was repeated on such synthetic data set. Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 7
Fig. 10. The parameters of the best-fit solutions to the 2-planet model of the RV data of HD 190360 limited to the first 38 measurements, projected onto (P, e)- and (P, K)-plane. Upper plots are for the outer planet, bottom plots are for the inner com- 2 1/2 2 1/2 panion. The values of (χν) of the best-fit solutions are marked by the size of symbols. Largest circle is for (χν) ≃ 0.733; 2 1/2 2 1/2 smaller symbols are for 1σ solutions with (χν) ∈ [0.733, 0.793), 2σ solutions with (χν) ∈ [0.793, 0.89 and 3σ solutions 2 1/2 with (χν) ∈ [0.89, 1.00) (smallest, filled circles), respectively. Vertical and horizontal lines mark the best-fit obtained for the full data (see Fig. 7 and Table 1).
1200 HD190360 12 HD 190360 1000 10 800 8 600
for real data 6 400 2 ν number of fits Power √χ 200 2 4 √χν 0 2 0.8 0.9 1 1.1 1.2 1.3 0 2 1/2 Fig. 9. A histogram of (χν) for Keplerian fits to 20,000 sets 2 5 10 25 50 100 250 500 1000 of scrambled RV residuals of the synthetic signal of the outer Period [d] planet in HD 190360 (see Table 1). The position of the best-fit to the real data is marked with an arrow. Fig. 11. Lomb-Scargle periodogram of the residuals of the long-period signal in HD 190360 when only 38 first measure- ments are analyzed. Compare with Fig. 8 for the full data set.
2 1/2 larger width and (χν) of the real data is closer to the maxi- than 1, similarly to the three systems which are described be- mum of the distribution. low. Even for a half of the available measurements, the peri- odic nature of the residual signal of the single-planet fit can be clearly recognized. One might conclude that the inner planet 3. HD 188015 around HD 190360 might be detected about 2–3 years ago. Recently, Marcy et al. (2005b) published the precision RV of The results obtainedfor the HD 190360data providea valu- HD 188015. The variability of the RV is explained by the pres- able test of our method and a good reference point to further ence of a planetary companion with minimal mass 1.26 mJ analysis. Let us recall, that the model with two planets yields and orbital period ∼ 1.25 yr. Our attention has been drawn on 2 1/2 low residuals with an rms of 3.5m/s and (χν) much smaller large rms of this 1-planet solution, ≃ 8.6m/s. The mean error 8 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates?
10 1000 HD190360 HD 188015 800 8
600 6
400 for real data 2 ν number of fits Power 4 √χ 200 2 √χν 0 2 0.8 0.9 1 1.1 1.2 1.3 0 2 1/2 Fig. 12. A histogram of (χν) for Keplerian fits to ∼ 27, 000 2 5 10 25 50 100 250 500 1000 sets of scrambled RV residuals of the synthetic signal of the Period [d] outer planet in HD 190360 for the first 38 measurements. The position of the best-fit for the real data is markedwith an arrow. Fig. 15. Lomb-Scargle periodogram of the residuals of the Compare with Fig. 9. long-period signal visible in the RV data of HD 188015.
of the RV data is about of 4.1 m/s and expected stellar jitter at the 1σ-level of the best-fit about of 30 d and ec ∼ 0.3, see ≃ 4 m/s (Marcy et al. 2005b). The mean measurement error Fig. 14. added in quadrature to the jitter is about of 5 m/s, still much The results of the hybrid search perfectly agree with the smaller than the rms of 1-planet solution. However, this can be LS periodogram (Fig. 15) of the signal after removal of the partially explained by a linear trend apparently present in the contribution from the outer planet. All the relevant periods RV signal. If one adds such a trend to the fit model, the rms can be found in the periodogram too. This assures us that the goes down by 1 m/s (Marcy et al. 2005b, also our Fig. 13a). GA search is robust in locating the best-fit solution even in 2 1/2 The trends in the RV data frequently indicate a distant body the case when (χν) has several equally deep local minima. (e.g., Marcy et al. 2005a; Jones et al. 2002; Go´zdziewski et al. Additionally, we did an independent gradient-based scan over 2003). Nevertheless, we assumed that the second putative body Pc and that test also confirmed the excellent performanceof the is not a distant companion, but rather a planet closer to the star GAs. than already detected companion b. The test of scrambled velocities which is illustrated in The elements of the best-fit solution found in the entire hy- Fig. 16 helps us to explain the trouble of finding a clear, sec- brid search are illustrated in Fig. 13 (panels b,c,d) and its el- ondly dominant short-period in the data. The histogram of 2 1/2 2 1/2 ements are given in Table 1. The synthetic Doppler signal is (χν) has the maximum about of 1.1 and (χν) ≃ 0.93 of the plotted over the data points in Fig. 13b. Surprisingly, the ap- real residuals is not well separated from this maximum. The es- parent slope of the RV data can be only an artifact related timated pH ≃ 0.03 is significant and indicates that the residual to a specific time-distribution of measurements. The value of signal is rather noisy. Yet the best 2-planet fit improves signifi- 2 1/2 (χν) ≃ 1.021 indicates a statistically good solution. Its rms cantly the 1-planet solution. is about of 5 m/s, consistent with the adopted estimate of the We are warned by the referee(and we quotehim againhere) mean uncertainty. The semi-amplitude of the inner planets’ sig- that the jitter estimate by Marcy et al. (2005b) comes from the nal is ∼ 7m/s. Assuming the mass of the host star ≃ 1.08 M⊙ study of jitter levels in the Carnegie planet search sample by (Marcy et al. 2005b), we derived its minimal mass about of Wright (2005). In that article, it turns out that at the activity 0.07 mJ and semi-major axis about of 0.08 AU. Thus, the new level of HD 188015 corresponds to an average jitter of the putative object can be classified as a hot-Neptune planet. quoted 4 m/s, but with a wide dispersion from case to case, 2 1/2 According to the 1σ-level of (χν) , marked in Fig. 14, the and that levels of 6-7 m/s are not at all uncommon. In fact, uncertainty of eb is ∼ 0.1, and of Kb is ∼ 5 m/s. Similarly, for low values of the Calcium index there is little activity-jitter the 1σ uncertainties of the elements of the inner planet can be correlation in Wright (2005), and any values between 1 and estimated by ∼ 0.3 and 1 m/s, respectively. There are visible 10 m/s are almost equally likely. This may invalidate our ar- 2 1/2 several local minima in the (Pb, eb)-plane, which are very nar- gument about the excess scatter and the value of (χν) in the row with respect to Pc,aboutof0.05datthe1σ level. It is clear 2-planet model. Nevertheless, what we can do is to adopt an that the eccentricity of the inner companion (also its argument uniform jitter variance for all measurements. Then a larger jit- 2 1/2 of periastron — not shown here) cannot be well fixed. ter will only ”flatten” (χν) , keeping its minimum at similar A local minimum at Pc ≃ 15.37 d which also well mod- position in the parameters space. The results for HD 190360 els the observations (at the 1σ confidence interval of the best- may be used as an argument supporting the planetary hypothe- fit solution) may correspond to an alias of the best-fit period sis —in that case the 2-planet fit also has an rms about of 1 m/s 8.386 d. It could be also an alias of the rotational period ∼ 30 d smaller than the joint uncertainty. Yet we encountered a similar of the star, assuming that it is smaller than the 36 d estimate problem when analyzing the next system, around HD 114729, 2 1/2 by (Marcy et al. 2005b). Indeed, there is a minimum of (χν) described below. Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 9
40 40 a) b) 20 20
0 0
[m/s] -20 [m/s] -20
r r V -40 V -40
-60 -60 RMS=7.46 m/s RMS=4.93 m/s -80 -80 1600 1800 2000 2200 2400 2600 2800 3000 3200 1600 1800 2000 2200 2400 2600 2800 3000 3200 JD-2,450,000 [days] JD-2,450,000 [days]
20 c) 30 d) 15 10 20 5 10
[m/s] 0 [m/s]
r r
V -5 V 0 -10 -10 -15 RMS=4.93 m/s -20 -20 0 1 2 3 4 5 6 2750 2800 2850 2900 2950 phase (φ) [rad] JD-2,450,000 [days] Fig. 13. The best-fit solutions to the RV data published by Marcy et al. (2005b) for HD 188015. a) 1-Kepler model with a 2 1/2 linear trend which is apparently present in the data. b) 2-Kepler model is consistent with the measurement error, (χν) ≃ 1.02, rms≃ 4.9m/s. c) Period-phased RV signal of the inner companion. d) A close-up of the synthetic signal of the best-fit 2-planet configuration (see Table 1).
1000 one, inner planet in the system in short-period orbit, [2,136] d. HD188015 To test this hypothesis, we did the same analysis of the RV data 800 as described in previous sections. The results are illustrated in Fig. 17a,b,c,d which is for the graphical illustration of the best- 600 fit parameters. Figure 18 is for the Lomb-Scargle periodogram
400 of the residual signal of the long-period companion. Figure 19
for real data 2 1/2 2 ν illustrates the shape of (χ ) about the best-fit and the distri- number of fits ν 200 √χ bution of the best fits obtained in the hybrid search. The or- 2 √χν bital parameters of the best fit are given in Table 1. Clearly, 0 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 the results of the hybrid search agree perfectly with the LS periodogram—the dominant peak about of 7 d is clearly vis- 2 1/2 2 1/2 Fig. 16. A histogram of (χν) for Keplerian fits to 20,000 sets ible in the (Pc, ec)-plane as the deepest minimum of (χν) in of scrambled RV residuals of the synthetic signal of the outer the region of short periods. The best-fit eccentricity of the in- planet in HD 188015 (see Table 1). The position of the best-fit ner planet is found close to the assumed limit of 0.3. However, to the real data is marked with an arrow. in a few tests with smaller jitter (∼ 3m/s) we obtained better 2 1/2 bounded minimum of (χν) and smaller best-fit ec ≃ 0.2, so this element is barely constrained by the RV data. 4. HD 114729 An inspection of the LS periodogramshows some other rel- Similarly to most of the stars monitored in precision RV sur- atively strong peaks, for instance about of 180 d, which most veys, the HD 114729 is a Sun-like star of G3V spectral type likely are aliasing with the period of 13.844 d. (G0V by Hipparcos). Its RV data indicate a Jupiter-like com- 2 1/2 panion with minimal mass 0.84 mJ, orbital period ≃ 3.1 yr Figure20 is for the histogramof (χν) obtained for scram- and eccentricity ≃ 0.32 (Butler et al. 2003). An rms of the sin- bled residuals of the outer planet’s signal. The probability that gle Keplerian fit to the data is 5.34 m/s. It is larger than the the residual signal of the outer companion has a random origin 2 1/2 mean of internal errors, ≃ 3.6m/s. The expected jitter is 4 m/s is very small, pH ≃ 0.003. The (χν) for the best-fit solution (Butler et al. 2003). The mean measurement error scaled in has well defined minimum about of 0.77.Its rms of ∼ 3.6m/s is quadrature with the jitter variance is comparable with the rms. very close to the mean of the internal errors. Assuming that the Nevertheless, having in mind a significant scatter of the mea- mass of the host star is equal to 0.93 M⊙, the derived minimal surements about some parts of the synthetic 1-planet RV curve mass of the inner planet is about of 0.065mJ and its semi-major (see Fig. 17a), and the presence of the distant giant planet, we axis ≃ 0.11 AU. Thus it would correspond to a hot Neptune- assumed (as in the previous case) that there exist an another like planet. 10 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates?
Fig. 14. The elements of the best-fit solutions to the 2-planet model of the HD 188015 RV data projected onto the (P, e)- and 2 1/2 (P, K)-plane. Upper plots are for the outer planet, bottom plots are for the inner companion. The (χν) of the best-fit solutions 2 1/2 are marked by the size of symbols. Largest circle is for (χν) = 1.021 (the best-fit solution, Table 1); smaller symbols are for 2 1/2 2 1/2 2 1/2 1σ solutions with (χν) ∈ [1.02, 1.07), 2σ solutions with (χν) ∈ [1.07, 1.14) and 3σ solutions with (χν) ∈ [1.14, 1.25) (smallest, filled circles), respectively.
10 1200 HD114729 1000 8 HD 114729 800
6 600
400 for real data number of fits Power 4 2 ν 200 √χ 2 √χν 2 0 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 2 1/2 2 5 10 25 50 100 250 500 1000 Fig. 20. A histogram of (χν) for Keplerian fits to 21,000 Period [d] sets of scrambled RV residuals of the synthetic signal of the outer planet in the HD 114729 planetary system (Table 1). The Fig. 19. Lomb-Scargle periodogram of the residuals of the position of the best-fit to the real data is marked with an arrow. long-period singal in the HD 114729 data.
We searched for the second planet in short-period orbit, 5. HD 147513 [2,136] d. The results of the hybrid search obtained for 2-planet fits are illustrated in Fig. 21 for the statistics of the gathered The last example which we examine is HD 147513. This star best-fits and in Fig. 22a,b,c,d for the graphical illustration of is observed by Mayor et al. (2004) who published 30 measure- the best-fit solution. These results remind us the HD 190360 2 1/2 ments covering 1690 d. In this case, an rms of 5.7 m/s of the case. The (χν) of the best-fit has well defined minimum at 1-planet fit is comparable with the mean of measurement er- Pc ≃ 7.894 d. Its rms ≃ 4.1m/s means a significant improve- rors, nevertheless our attention draws an irregular scatter of ment of the single-planet fit. This is seen in Fig. 22b,d; appar- the data about the synthetic RV curve, Fig. 22a. The discovery ently the synthetic RV curve is ideally close to the measure- team announced a Jupiter-like planet of minimal mass 1.21 mJ ments. A relatively large Kc ∼ 11 m/s and mass of the host star ′ in ≃ 528 d orbit. The host star is very active (RHK = −4.4). 1.11 M⊙ imply the minimal mass of the inner planet 0.115 mJ Following Wright (2005) we estimate its jitter ∼ 9m/s. and semi-major axis about of 0.08 AU. Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 11
20 a) 20 b)
10 10
0 0 [m/s] [m/s]
r r
V -10 V -10
-20 -20 RMS=5.34 m/s RMS=3.6 m/s -30 -30 500 1000 1500 2000 2500 500 1000 1500 2000 2500 JD-2,450,000 [days] JD-2,450,000 [days] 20 15 c) 15 d) 10 10 5 5 0 [m/s] [m/s]
r r V -5 V 0 -10 -15 -5 RMS=3.59 m/s -20 0 1 2 3 4 5 6 1560 1565 1570 1575 1580 1585 1590 1595 1600 phase (φ) [rad] JD-2,450,000 [days] Fig. 17. The best-fit solutions to the HD 114729 RV data published in Butler et al. (2003). a) Synthetic signal of 1-planet model. 2 1/2 b) 2-Kepler model is consistent with the measurement error, (χν) ≃ 0.775, an rms ≃ 3.6m/s. c) Period-phased RV signal of the inner companion. d) A close-up of the synthetic signal of the best-fit 2-planet configuration (see Table 1).
10 1200 HD147513
8 HD 147513 1000 800 6 600 for real data
400 2 ν number of fits Power 4 √χ 200 2 √χν 2 0 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0 2 1/2 2 5 10 25 50 100 250 500 1000 Fig. 24. A histogram of (χν) for Keplerian fits to 30,000 Period [d] sets of scrambled RV residuals of the synthetic signal of the outer planet in the HD 147513 planetary system (Table 1). The Fig. 23. Lomb-Scargle periodogram of the residuals of the position of the best-fit to the real data is marked with an arrow. long-period signal visible in the RV data of HD 147513. the host star, about of 4.7 d (Mayor et al. 2004), differs from The LS periodogram, Fig. 23, reveals features which recall the secondary period visible in the RV signal (about of 7.9 d), us the first system examined in this paper, about HD 208487. it is suspiciously close to this approximation. However, such The short period of ≃ 7.9 d seems to be aliased with a much coincidence of periods still does not exclude a planetary ex- longer period of 810.8 d. Figure 24 is for the histogram of planation (Santos et al. 2000, 2003) because the activity can be 2 1/2 (χν) computed for the scrambled residuals. The probability induced or amplified by relatively massive and close planetary of a random character of the residual signal is negligible. At companion. this time, such a characteristic is almost the same as for the HD 190360 system; in that case the 2-planet solution also pro- 6. Conclusions duces very small rms which is less than the joint measurement uncertainty. It is extremely difficult to interpret the RV measurements when Still, mostly due to the activity of the star, the periodic- their number is limited and their time coverage is poor. We are ity of the RV variations can be explained by jitter. According looking for signals which have an amplitude comparable with to Mayor et al. (2004), HD 147513 is a young G3/5V dwarf, noise. Although is already possible to pick up some promising only 0.3Gyr old. Its spectrum reveals a strong emission in the extrasolar systems in which one planet is clearly visible and an Ca II H line. Although the estimated short rotation period of another putative body is at the detection limit, a claim that the 12 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates?
Fig. 18. The parameters of the best-fits to the 2-planet model of the HD 114729 RV data projected onto the (P, e)- and (P, K)- 2 1/2 plane. Upper plots are for the outer planet, bottom plots are for the inner companion. The values of (χν) of the best-fit solutions 2 1/2 are marked by the size of symbols. Largest circle is for (χν) equal to 0.775 (the best-fit solution, Table 1); smaller symbols 2 1/2 2 1/2 2 1/2 are for 1σ solutions with (χν) ∈ [0.775, 0.83), 2σ solutions with (χν) ∈ [0.83, 0.915) and 3σ solutions with (χν) ∈ [0.915, 1.02) (smallest, filled circles), respectively.
Fig. 21. The projections of best-fit parameters to the 2-planet model of the HD 147513 RV data onto the (P, e)- and (P, K)-plane. 2 1/2 Upper plots are for the outer planet, bottom plots are for the inner companion. The values of (χν) of the best-fit solutions are 2 1/2 marked by the size of symbols. Largest circle is for (χν) ≃ 0.505 (the best-fit solution, Table 1); smaller symbols are for 1σ 2 1/2 2 1/2 2 1/2 solutions with (χν) ∈ [0.505, 0.619), 2σ solutions with (χν) ∈ [0.62, 0.773) and 3σ solutions with (χν) ∈ [0.773, 0.95) (smallest, filled circles), respectively. Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? 13
40 a) 40 b) 30 30 20 20 10 10 0 0 [m/s] [m/s]
r r
V -10 V -10 -20 -20 -30 -30 RMS=6.82 m/s -40 -40 RMS=4.1 m/s
1000 1500 2000 2500 1000 1500 2000 2500 JD-2,450,000 [days] JD-2,450,000 [days]
20 20 c) d) 15 10 10 5 0 0 [m/s] [m/s]
r r -10
V -5 V -10 -20 -15 RMS=4.1 m/s -20 -30 0 1 2 3 4 5 6 2360 2380 2400 2420 2440 2460 2480 2500 phase (φ) [rad] JD-2,450,000 [days] Fig. 22. The best-fit solutions to the RV data published in (Mayoretal. 2004) for HD 147513. a) 1-planet model. The thick line is for the fit found with GA, assuming σ j = 9 m/s; its parameters (K, P, e, ω, Tp − T0) are: ◦ 2 1/2 (28.40 m/s, 520, 49 d, 0.346, 288 .57, 3125.302 d), T0=JD 2,450,000, (χν) = 0.737, an rms=6.83 m/s. The thin line is for the fit without accounting for the jitter; its parameters are almost the same as in (Mayoret al. 2004): ◦ 2 1/2 (29.312 m/s, 528.112 d, 0.260, 282 .453, 2214.94 d), (χν) = 1.60, an rms = 7.26 m/s. b) 2-Kepler model is consistent with 2 1/2 the measurement errors, (χν) ≃ 0.505, an rms≃ 4.1m/s. c) Period-phased RV signal of the inner companion. d) A close-up of the synthetic signal of the best-fit 2-planet configuration, Table 1.
Table 1. Primary parameters of the model Eq. 1 and inferred elements of the best-fits found in this paper, T0 is JD 2,450,000. See the text and figures for error estimates.
HD 188015 HD 114729 HD 147513 HD 190360 HD 208487 Parameter cbcbcbcbcb M⋆ [M⊙] 1.08 0.93 1.11 0.95 0.96 m sin i [MJ] 0.076 1.81 0.066 0.88 0.115 1.15 0.064 1.62 0.121 0.46 a [AU] 0.08 1.22 0.11 2.12 0.08 1.35 0.13 3.93 0.11 0.49 P [d] 8.389 476.23 13.849 1171.19 7.894 541.00 17.104 2908.32 14.496 129.51 K [m/s] 7.21 44.75 5.87 17.71 10.95 26.85 5.20 24.90 10.47 19.08 e 0.23 0.24 0.25 0.30 0.30 0.09 0.21 0.37 0.43 0.26 ω [deg] 103.9 242.4 301.1 66.3 9.1 316.8 10.1 10.8 27.6 130.9 Tp [JD-T0] 859.67 2270.10 2496.77 1558.98 1047.23 2248.44 2370.38 3517.82 2815.87 2957.74 2 1/2 (χν ) 1.021 0.775 0.505 0.680 0.581 σj [m/s] 4.0 4.0 9.0 3.1 3.0 σ2 [m/s] 4.1 3.5 4.4 2.2 5.4 2 (σj2 + σ )1/2 [m/s] 5.7 5.3 10 3.8 6.2 rms [m/s] 4.93 3.59 4.07 2.97 2.82 V0 [m/s] -17.45 -3.22 -4.85 -4.81 7.97 residual signal has a planetary origin is always very risky. To ories supporting their origin, permit us to state and investigate confirm the existence of the putative hot-Neptune candidates, a hypothesis of the planetary nature of the RV variability. a deep astrophysical analysis is necessary (Mayor & Queloz Our results may be useful in some aspects. Even if the 1995; Santos et al. 2003; Butler et al. 2004), by far beyond our residual periodicities are of pure stellar origin, accounting them technical abilities. That includes many additional spectroscopic for may improve the single planet fits, because it makes it pos- and photometric observations. Nevertheless, the dynamical en- sible to remove a contribution of not-random RV signal from vironment of the putative new planetary companions, several the data. When we deal with a small number of measurements, recent discoveries of Neptune-like planets and cosmogonic the- the short-term contribution of jitter does not average out and it alters the long-period solution. Yet the stellar variations may 14 Go´zdziewski & Migaszewski: New Neptun-like extrasolar candidates? have origin in planetary-induced activity. This effect has been Lee, M. H. & Peale, S. J. 2003, ApJ, 592, 1201 analyzed by Santos et al. (2000, 2003). An elimination of the Marcy, G., Butler, R. P., Fischer, D., et al. 2005a, Progress of planetary hypothesis also requires additional observations and Theoretical Physics Supplement, 158, 24 analysis. Marcy, G. W., Butler, R. P., Vogt, S. S., et al. 2005b, ApJ, 619, Basically, we use an independent, FFT-free method of the 570 global analysis of the RV data and early detection of plausi- Mayor, M. & Queloz, D. 1995, Nature, 378, 355 ble planets. It can be used for checking the results of 1-dim Mayor, M., Udry, S., Naef, D., et al. 2004, A&A, 415, 391 periodogram-based analysis, extending it into the multidimen- McArthur, B. E., Endl, M., Cochran, W. D., et al. 2004, ApJ, sional space of the orbital elements. If some of our results will 614, L81 be confirmed, a similar approach can be used to detect smaller Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, bodies in short-period orbits in the other, already discovered B. P. 1992, Numerical Recipes in C. The Art of Scientific extrasolar systems. Such studies can be useful for planning fu- Computing (Cambridge Univ. Press) ture observing sessions. Rivera, E., Lissauer, J., Butler, R. P., et al. 2005, ApJ, submitted We did a similar but very preliminaryanalysis of the RV ob- Santos, N. C., Mayor, M., Naef, D., et al. 2000, A&A, 361, 265 servations of a few other stars hosting single Jupiter-like plan- Santos, N. C., Udry, S., Mayor, M., et al. 2003, A&A, 406, 373 ets. For instance, we found a short-term variability of the RV, Santos, N. C. et al. 2004, A&A, 426, L19 about of 7 d in the HD 19994 system (Mayor et al. 2004). The Smart, W. M. 1949, Text-Book on Spherical Astronomy second companion would have K ∼ 9m/s, larger than the mean (Cambridge Univ. Press) uncertainty of the measurements, about of 6.6 m/s. In the same Tinney, C. G., Butler, R. P., Marcy, G. W., et al. 2005, ApJ, paper, we found the RV data of HD 121504 and a curious RV 623, 1171 variability which may be well modeled by a new 2-planet sys- Udry, S. et al. 2005, A&A, submitted tem close to the 6:1 mean motion resonance. Likely, the data Vogt, S. S., Butler, R. P., Marcy, G. W., et al. 2005, ApJ, 632, collected and published by Doppler planet searches already 638 hide many interesting and unusual planetary configurations. Wisdom, J. 2005, AAS/Division of Dynamical Astronomy Meeting, 36, Acknowledgements. We thank the anonymous referee for comments Wright, J. T. 2005, PASP, 117, 657 and invaluable suggestions that improved the manuscript. We deeply acknowledge the pioniering work and publishing of the precision RV data by planet search teams. K.G. thanks Jean Schneider for the in- spiration to study the HD 208487 system. This work is supported by Polish Ministry of Sciences and Information Society Technologies, Grant No. 1P03D-021-29.
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