Substellar-mass companions to the K-dwarf BD +14 4559 and the K-giants HD 240210 and BD +20 2457
aa r X i v : . [ a s t r o - ph . S R ] J un Substellar-mass companions to the K-dwarf BD +14 4559 and theK-giants HD 240210 and BD +20 2457
A. Niedzielski , G. Nowak , M. Adam´ow , A. Wolszczan , ABSTRACT
We present the discovery of substellar-mass companions to three stars by theongoing Penn State - Toru´n Planet Search (PTPS) conducted with the 9.2-mHobby-Eberly Telescope. The K2-dwarf, BD +14 4559, has a 1.5 M J companionwith the orbital period of 269 days and shows a non-linear, long-term radialvelocity trend, which indicates a possible presence of another planet-mass bodyin the system. The K3-giant, HD 240210, exhibits radial velocity variations thatrequire modeling with multiple orbits, but the available data are not yet sufficientto do it unambiguously. A tentative, one-planet model calls for a 6.9 M J planetin a 502-day orbit around the star. The most massive of the three stars, the K2-giant, BD +20 2457, whose estimated mass is 2.8 ± ⊙ , has two companionswith the respective minimum masses of 21.4 M J and 12.5 M J and orbital periodsof 380 and 622 days. Depending on the unknown inclinations of the orbits, thecurrently very uncertain mass of the star, and the dynamical properties of thesystem, it may represent the first detection of two brown dwarf-mass companionsorbiting a giant. The existence of such objects will have consequences for theinterpretation of the so-called brown dwarf desert known to exist in the case ofsolar-mass stars. Subject headings: planetary systems-stars: individual (HD 24210, BD +14 4559);brown dwarfs: individual (BD +20 2457) Toru´n Center for Astronomy, Nicolaus Copernicus University, ul. Gagarina 11, 87-100 Toru´n, Poland, [email protected], [email protected],[email protected] Department of Astronomy and Astrophysics, the Pennsylvania State University, 525 Davey Laboratory,University Park, PA 16802, [email protected] Center for Exoplanets and Habitable Worlds, the Pennsylvania State University, 525 Davey Laboratory,University Park, PA 16802
1. Introduction
Searches for planets around giant stars offer an efficient way to extend studies of plan-etary system formation and evolution to stellar masses substantially larger than 1 M ⊙ (Sato et al. 2003; Hatzes et al. 2006; Niedzielski et al. 2007; Hekker et al. 2008; Sato et al.2008a,b; D¨ollinger et al. 2009; Niedzielski et al. 2009; Liu et al. 2009). Although searches forthe most massive substellar companions to early-type stars are possible (Galland et al. 2005;Lagrange et al. 2009), it is much more efficient to utilize the power of the radial velocity(RV) method by exploiting the fact the GK-giants, the descendants of the main sequenceA-F type stars, have cool atmospheres and sufficiently many narrow spectral lines to makeachieving a <
10 m s − RV measurement precision possible.The GK-giant surveys are beginning to provide the statistics, which are needed toconstrain the efficiency of planet formation as a function of stellar mass and chemical com-position. In fact, the initial analyses by Johnson et al. (2007) and Lovis & Mayor (2007)extend to giants the correlation between planetary masses and the masses of their primariesobserved for the lower-mass stars. Most likely, this is simply because massive stars tendto have more massive disks. These results are in accord with the core accretion scenarioof planet formation (Kennedy & Kenyon 2008). Furthermore, Pasquini et al. (2008) haveused the apparent lack of correlation between the frequency of planets around giants andstellar metallicity to argue that this effect may imply a pollution origin of the observedplanet frequency - metallicity correlation for main sequence stars (Fischer & Valenti 2005).Similar conclusions have been reached in a preliminary study of our giant star sample by(Zieli´nski et al. 2009).The steadily extending baselines of the ongoing surveys of post-MS giants begin fur-nishing multiplanet system detections that are needed to study the dynamical evolution ofplanets around the off main-sequence stars. The multiplicity of planetary systems aroundMS stars has been firmly established (Udry & Santos 2007; Wright et al. 2009) and there isno reason why this tendency should not be present among giants. In fact, the ongoing searchfor planets around GK-giants with the Hobby-Eberly Telescope (HET) by our group (PennState-Toru´n Planet Search, hereafter PTPS) has already tentatively identified a two-planetsystem around the K0-giant HD 102272 (Niedzielski et al. 2009), and long-term trends inthe RV data have been seen in other surveys (e.g. Sato et al. (2008a)).In this paper, we describe the detection of a planet around the K3-giant, HD 240210,and show evidence that the star has more low-mass companions, and the intriguing discoveryof two brown dwarf-mass bodies orbiting the K2-giant, BD +20 2457. We also describe thediscovery of a Jupiter-mass planet and a non-linear RV trend in the K2-dwarf, BD +14 4559.This detection is the first result of the extension of the PTPS to evolved dwarfs in the upper 3 –envelope of the MS. This part of the project will be described in detail in a future paper.The plan of this paper is as follows. An outline of the observing procedure and adescription of the basic properties of the three stars are given in Section 2, followed by theanalysis of radial velocity measurements in Section 3. The accompanying analysis of rotationand stellar activity indicators is given in Section 4. Finally, our results are summarized andfurther discussed in Section 5.
2. Observations and properties of the stars
Observations were made with the Hobby-Eberly Telescope (HET) (Ramsey et al. 1998)equipped with the High Resolution Spectrograph (HRS) (Tull 1998) in the queue scheduledmode (Shetrone et al. 2007). The spectrograph was used in the R=60,000 resolution modewith a gas cell ( I ) inserted into the optical path, and it was fed with a 2 arcsec fiber.Details of our survey, the observing procedure, and data analysis have been described indetail elsewhere (Niedzielski et al. 2007; Niedzielski & Wolszczan 2008)Radial velocities were measured using the standard I cell calibration technique (Butler et al.1996). A template spectrum was constructed from a high-resolution Fourier Transform Spec-trometer (FTS) I spectrum and a high signal-to-noise stellar spectrum measured withoutthe I cell. Doppler shifts were derived from least-squares fits of template spectra to stellarspectra with the imprinted I absorption lines. The radial velocity for each epoch was de-rived as a mean value of the independent measurements from the 17 usable echelle orderswith a typical, intrinsic uncertainty of 6-8 m s − at 1 σ -level. This RV precision levels madeit quite sufficient to use the Stumpff (1980) algorithm to refer the measured RVs to the SolarSystem barycenter.The long-term precision of our RV measurements has been verified by the analysis ofdata derived from the monitoring of stars that do not exhibit detectable RV variations. Theresults for the K0 giant BD+70 1068 ( V=9.29, B-V=1.15 ± eff = 4580 ±
17 K) areshown in Figure 1 as an example. The relative RVs for this star vary with σ =12 m s − ,whereas our estimated intrinsic RV uncertainty for this series of observations was 7 m s − .The excess RV scatter is consistent with the approximate 10 m s − amplitude of solar-typeoscillations derived from the scaling relations of Kjeldsen & Bedding (1995).The atmospheric parameters of the stars under consideration were taken from Zielinskiet al. (2009, in preparation, hereafter Z09), who have estimated their values using the methodof Takeda et al. (2005a,b). With these values and the luminosities estimated from availabledata, stellar masses were derived by fitting the ensemble of parameters characterizing the 4 –star (log(L/L ⊙ ), log T eff , log (g), and metallicity) to the evolutionary tracks of Girardi et al.(2000). The parameters of the three stars are summarized in Table 1. Radial velocities of BD +14 4559 were measured at 43 epochs over the period of 1265days between MJD 53546 and 54811. Typically, the signal-to-noise ratio per resolutionelement in the spectra was 150-260 at 594 nm in 10-25 minutes of integration, depending onthe atmospheric conditions. The estimated mean RV uncertainty for this star was 8 m s − BD +14 4559 (AG +14 2370, HIP 104780, LTT 16221) is a high proper motion K5(Turon et al. (1993)) star with V=9 m .63 (Weis 1986), B-V=0 m .98 ± π = 19.99 ± π = 24 mas derived by (Weis 1986). The atmospheric parame-ters of BD +14 4559 as determined in Z09 indicate that it is a dwarf with log(g)=4.60 ± eff =5008 ±
20 K, and [Fe/H]=0.10 ± eff =4814 ±
26 K. As this value of T eff is too high for a K5 dwarf, we conclude that the spectral type of BD +14 4559 is K2V.The derived absolute bolometric magnitude of the star, M V , and log(L/L ⊙ ), are 5.56and -0.32, respectively. By comparing the stellar parameters to evolutionary tracks ofGirardi et al. (2000), we have computed the mass of BD +14 4559 to be M/M ⊙ =0.86 ± ⊙ = 0.95 ± vsini =2.5 ± − , was estimatedusing the cross-correlation method (Benz & Mayor 1984). From this value and the adoptedstellar radius we have obtained an estimate of the rotation period of P rot =19 days, which ismuch shorter than the observed 267-day period of the RV variations. From the uncertaintyof the vsin ( i ) determination alone, the stellar rotation period may range from 13 to 32 days. Radial velocities of HD 240210 were measured at 38 epochs over the period of 1655 daysbetween MJD 53187 and 54842. Typically, the signal-to-noise ratio per resolution elementin the spectra was 150-300 at 594 nm in 4-10 minutes of integration, depending on the 5 –atmospheric conditions. The estimated mean RV uncertainty for this star was 8 m s − HD 240210 (BD +56 2959) is a K7 (Cannon & Pickering 1924) star with V=8 m .33, B-V=1 m .The parallax of 6.5 ± π = 7.6 ± π = 7.0 ± ± eff =4297 ±
25 K, and [Fe/H]=-0.18 ± eff =4290 ±
13 K. These values ofeffective temperature and log(g) are consistent with a K3-giant star.The derived absolute bolometric magnitude of the star and log(L/L ⊙ ), are 0.38 and1.75, respectively. By comparing stellar parameters to evolutionary tracks of Girardi et al.(2000) we have computed the mass of HD 240210 to be M/M ⊙ =1.25 ± ⊙ = 13 ±
3. The projected rotational velocity of HD 240210 , vsini < ± − , was estimatedusing the cross-correlation method. From this value and the adopted stellar radius we haveobtained an estimate of the rotation period of P rot >
654 days.
Radial velocities of BD +20 2457 were measured at 37 epochs over the period of 1833days between MJD 53033 and 54866. Typically, the signal-to-noise ratio per resolutionelement in the spectra was 140-260 at 594 nm in 12-30 minutes of integration, depending onthe atmospheric conditions. The estimated mean RV uncertainty for this star was 7 m s − BD +20 2457 (AG +20 1166) is a K2 (Heckmann 1975) star with V=9 m .75, B-V=1 m .25 ± π = 5.0 ± ± eff =4137 ±
10 K, and [Fe/H]=-1.00 ± eff =4127 ±
17 K. We conclude thatthe spectral type of BD +20 2457 is K2II. 6 –The derived absolute bolometric magnitude of the star, M V , and log(L/L ⊙ ), are -3.0 and 3.17, respectively. By comparing the stellar parameters to evolutionary tracks ofGirardi et al. (2000), we have estimated the mass of BD +20 2457 to fall in the 1.3 - 4.3M/M ⊙ range (2.8 ± ⊙ ), and R/R ⊙ = 49 ± vsini < − , was estimated using the cross-correlation method. From this value and the adoptedstellar radius we have obtained an estimate of the rotation period of the star, P rot >
3. Analysis of the radial velocity data
The process of modeling the RV measurements of the three stars discussed in thispaper is documented in Figures 2-6. In the first step of the analysis, single, 6-parameter,Keplerian orbits were least-squares fitted to data using the Levenberg-Marquardt algorithm(Press et al. 1992). For the K-giants, HD 240210 and BD +20 2457, the estimated, 7-8 m s − errors in RV measurements were clearly insufficient to account for the observed RV variationsin the post-fit residuals. This excess RV variability is believed to originate in fluctuations ofthe stellar surface and radial and non-radial oscillations of the giant stars (de Ridder et al.2009) with the typical RV amplitudes around 20 m s − (Hekker et al. 2006). To account forthis effect, we have quadratically added 10 m s − and 30 m s − to the calculated RV errorsfor HD 240210 and BD +20 2457, respectively.Evidently, in all the three cases, the best-fit residuals from single orbit models leave non-random trends that need to be modeled further. A statistical significance of these trendswas assessed by calculating false alarm probabilities (FAP) for a null hypothesis that thetrends can be adequately accounted for by a single Keplerian orbit and noise. The FAPs werecalculated with the aid of the radial velocity scrambling method (Wright et al. (2007), andreferences therein). As illustrated in Figure 6, FAP < As shown in Figure 3, the best-fit, single Keplerian orbit model for the RV variations ofthis star leaves behind a significant, non-linear trend, which reaches the amplitude of ∼
50 ms − over the 1300-day span of observations. At this point, rather than attempting to search 7 –the χ - space for a range of acceptable two-planet solutions, we have modeled the observedRV variations with a Keplerian orbit and a parabolic trend added to it. The best-fit χ valuefor this model drops from 4.4 for the single orbit case to 2.1 indicating, together with theFAP < Jup , ina 269-day, 0.78 AU, e =0.29 orbit around the star. Given the stellar mass of 0.86 M ⊙ , themass function of 2.5 × − M ⊙ , and the above RV amplitude and time span of the observedtrend, one can broadly constrain a putative second companion to be another planet with theminimum mass > Jup and the orbital radius > e =0.The remaining post-fit rms residual, σ RV =11 m s − , slightly exceeds the estimated 8m s − precision of our RV measurements for this star. This excess ”jitter” is within theestimated, intrinsically generated RV noise of 5 m s − due to solar-type oscillations in stabledwarfs (Wright 2005). A single orbit fit to the RV data for this star (Figure 4, Table 2) gives χ =9.8, the post-fit rms residual, σ RV =39m s − , and the very clear unmodeled RV variations. Our searchfor a multiple orbit solution has resulted in several two- and three-planet models, whichgave nearly identical improvements of the fit. This is illustrated in Figure 4 by a two-planetmodel, which produces χ =5.0, σ RV =25 m s − , FAP < Jup planetin a 502-day orbit with the semi-major axis of 1.3 AU and e =0.15.We also note that the 25 m s − post-fit residual from the multiplanet fits is about 3times larger than the formal precision of the RV measurements for HD 240210. As mentionedabove, this is in agreement with the estimated RV scatter in K-giants due to their internalactivity. A single, Keplerian orbit fit to the RV data for this star is shown in Figure 4. The resid-uals from this fit are characterized by χ =13.7, σ RV =105 m s − , and a ∼ − . Once again, as shown in Figure 6, the FAP forthe existence of the second periodicity is less than 0.1%.As shown in Figure 5, the best-fit, two-orbit solution offers a dramatic improvementto the Keplerian model of the RV variations observed in BD +20 2457, with the values of χ and σ RV reduced to 5.2 and 60 m s − , respectively. The model parameters calculatedfor the stellar mass of 2.8 M ⊙ and listed in Table 3 call for a system of two substellar-masscompanions with the respective minimum masses of 21.4 M Jup and 12.5 M
Jup , orbital periodsof 380 and 622 days, semi-major axes of 1.45 and 2.01 AU, and mild eccentricities of 0.15and 0.18.As in the case of HD 240210, the estimated, 7 m s − uncertainty of the RV measurementsof BD +20 2457 is much smaller than the actual, 60 m s − rms of the post-fit residuals.This additional RV ”jitter” broadly agrees with the 138 m s − amplitude of the solar-typeoscillations extrapolated for this star from Kjeldsen & Bedding (1995).
4. Stellar photometry, rotation, and line bisector analysis
In order to verify that the observed RV periodicities are indeed caused by the Keplerianmotion, we have thoroughly examined the existing photometry data in search for any periodiclight variations, and performed a complete analysis of line bisectors and curvatures for eachof the three stars discussed in this paper. This analysis used the cross-correlation methodproposed by (Mart´ınez Fiorenzano 2005). For each star, the cross-correlation functionswere computed from ∼ lines removed from the spectra. Thisprocedure has been described in detail in Nowak et al. (2009).Because both the Ca II K emission line and the infrared Ca II triplet lines at 849.8-854.2nm are outside the range of our spectra, we have used the H α line as a chromospheric activityindicator. As the shape of the H α line in the spectra that showed significant telluric linecontamination could be affected by it, care was taken to omit such spectra from the analysis.Equivalent widths (EW) of the line profile, defined as I/I c ≤ A of the absorption profile, where the signature of stellar activity should be mostpronounced (the uncertainty of the EW defined this way depends on the actual depth of theH α line and the signal-to-noise ratio). 9 – The existing photometric databases for this star cover a wide range of epochs from,MJD 47891 to 54792, and include extensive time series of measurements from the Hipparcosand Tycho (Perryman & ESA 1997), the NSVS (Wo´zniak et al. 2004), and the ASAS exper-iment (Pojmanski 1997). None of the four data sets reveal any periodic light variations. Inparticular, the ASAS data, which are contemporaneous with our RV measurements of BD+14 4559, include observations made at 280 epochs between MJD 52754 and MJD 54792. Inthis case, the light variations are characterized by the mean value of V=9.650 ± ±
32 m s − , and the mean bisector curvature, BC=-8 ±
27 m s − with no trace of any periodic variability. No correlation between the BVS, BC,and RV was found (r=0.09 and r=0.08, respectively). Similarly, our analysis of 23 spectra ofthe star has shown that the EW of the H α line exhibited a 3% rms scatter around its meanvalue of 396 ± m ˚ A , which was not correlated with the observed RV variability (r = -0.15,while the critical value of the Pearson correlation coefficient at the confidence level of 0.01is r , . =0.53). The LS periodograms of the H α EW , the BVS, and BC for BD +14 4559are shown in Figure 7. Clearly, the only observable that exhibits periodic time variations intime is the radial velocity.Using the scatter seen in the ASAS photometry of the star, and its rotational velocitydetermined above, we can estimate the amplitude of radial velocity variations and of theBVS due to a possible presence of a spot on the stellar surface (Hatzes 2002). The observedradial velocity amplitude of BD +14 4559 is three times larger than the 35 m s − total RVamplitude predicted by Hatzes (2002) for a spot with a filling factor of f=0.02, on a starrotating at vsini =2.5 km s − . Within the estimated uncertainty of the rotation velocity,the expected RV amplitude induced by a hypothetical spot is at least two times less than theobserved one. The expected bisector variations of 5 m s − are comparable to the precision ofour RV measurements and cannot have a detectable effect on our results. To summarize, thefacts that there is no variability in the available photometric measurements over the periodof ∼
19 years, the observed period of the RV v ariations is much longer than the estimatedrotation period of the star, a significant eccentricity must be included in the best-fit modelof the RV curve, and that the observed RV variations have been consistent over the fiveconsecutive cycles of the period, make their interpretation in terms of a rotating spot veryunlikely. 10 –
In the case of this star, the only long-term photometry available comes from 129 Tychomeasurements with the V T filter (Perryman & ESA 1997), between MJD 47946 and 49016.These data give the mean V T =8.499 ± T of 0.136 mag. No peri-odic variability has been detected in these measurements. In addition, there are 19 epochsof photometric observations of this star available from the NSVS (Wo´zniak et al. 2004), col-lected between MJD 51362 and 51493. These data are characterized by the median V=7.965 ± ±
23 m s − , and 23 ±
27 m s, respectively, with no statistically significant variability. No correlations between theRV residuals and the BVS and BC were found. The respective correlation coefficients arer=0.08 for the BVS and r=-0.18 for the BC (r , . =0.40). Furthermore, the average EW ofthe H α line measured over 28 epochs amounts to 602 ±
13, and the EW itself does not showany periodicities within 2%. We have considered a possible rotational modulation in H α by calculating the Pearson correlation coefficient with the RV data residuals after removingthe putative orbit. We found no correlation between the H α EW and the RV residuals (r=-0.26, whereas r , . =0.48). The LS periodograms of the four observables for HD 240210discussed above are shown in Figure 8. As in the case of BD +14 4559, radial velocity is theonly one that varies periodical ly.The observed photometric scatter in HD 24210, if interpreted in terms of a spot rotatingwith the star would also be detectable in both the radial velocity and the line bisector data.The estimated total RV variations should be of the order of 23 m s − and the bisectorvariations should amount to 31 m s − (Hatzes 2002). The semi-amplitude of the observedperiodic signal in radial velocity is much larger than the predicted variations induced bya hypothetical spot of size consistent with the existing photometeric variations. Periodicvariations in line bisectors produced by a hypothetical spot should manifest themselves asthe uncertainty in our BVS measurements, which is comparable the the predicted value.In any case, these variations should show a periodicity equal to the stellar rotation period,P >
654 d. Because no such variations are present in our bisector measurements for thisstar, we conclude that the observed scatter is a combination of low quality photome try andpossible solar type oscillations of the star. Such oscillations might account for 3.3 mmag inthe photometric variability and V osc = 13 m s − in the BVS using the scaling relations ofKjeldsen & Bedding (1995). 11 – As in the case of BD +14 4559, we have identified four photometric data sets that wecould utilize in our analysis, but we have concentrated on the data from the ASAS project(Pojmanski 1997), which contains extensive measurements that are contemporaneous withour RV observations. These data include 120 measurements made between MJD 52622 andMJD 53400 and the 191 additional ones made between MJD 52623 and MJD 54911. We haveused 319 grade A measurements from the ASAS to derive the mean V=9.693 ± ±
39 m s − , and the mean BC=47 ±
30 m s − , both revealing no significantperiodicities in the corresponding LS periodograms (Figure 9). We have also searched forcorrelations between the RV residuals and the BVS and BC after having removed the putativecompanions b and c. The respective correlation coefficients are r=-0.33 and r=-0.19 forBVS and r=-0.12 and r=-0.09 for BC, respectively (the critical value of Pearson correlationcoefficient at the confidence level of 0.01 is r , . =0.42). The EQ of the H α line for BD+20 2457 is 653 ±
23, and this parameter shows no significant periodicities within 3.5% for23 observations (Figure 9). As for the other two stars, we have searched for a possiblerotational modulation in H α by calculating the Pearson correlations coefficient with the RVdata residuals after removing the individual orbits. We found that there is no significantcorrelation between the H α EW and the RV residuals (r=-0.21 and -0.51, respectively, andr , . =0.53).A photometric scatter resulting from a spot rotating with BD +20 2457 would inducethe estimated total RV variations on the order of 30 m s − and the bisector variations of 40m s − (Hatzes 2002). The semi-amplitude of the observed periodic signal in radial velocitiesis over one order of magnitude larger. As in HD 240210, the anticipated variability inline bisectors produced by a periodic spot rotation is similar to that observed in our BVSmeasurements, these variations should show a periodicity equal to the star’s rotation period,P > > osc = 138 m s − using the scaling relations ofKjeldsen & Bedding (1995). 12 –
5. Discussion
The most recent results from the Penn State-Toru´n search for extrasolar planets de-scribed in this paper add a Jupiter-mass planet to the large body of planets around main-sequence stars (Santos 2008) and increase the still modest number of substellar-mass objectsaround GK-giants (e.g. D¨ollinger et al. (2009); Liu et al. (2009); Niedzielski et al. (2009);Sato et al. (2008b); Niedzielski et al. (2007) and references therein) by at least three newdetections.In principle, the long period RV variations in red giants may be related to non-Keplerianeffects, including the stellar rotation modulation of surface inhomogeneities, intrinsic activity,or non-radial pulsations (e.g. Hatzes et al. 2006). Our analysis of the available photometricdata and the behavior of line bisectors in the three stars, following the established prac-tices (Queloz et al. 2001), has shown no significant correlations between the time variabilityof these stellar activity indicators and the RV variations. Consequently, our RV measure-ments find the most plausible explanation in terms of the Keplerian motion of substellar-mass companions around the observed stars. The details of this analysis can be found inNiedzielski et al. (2008).In the case of the K2-dwarf, BD +14 4559, the RV data reveal a planet with the minimummass of 1.5 M J in a 269-day, 0.78 AU, e=0.29 orbit around the star. An additional, long-termtrend seen in the data suggests the presence of another, long-period companion, which is verylikely to be another planet. This adds to the growing number of confirmed and anticipatedmultiplanet systems around solar-type stars (Wright et al. 2009).A single planet model of the RV variations in the K3-giant, HD 24210, leaves highlycorrelated post-fit residuals signaling a possible presence of additional substellar-mass bodiesorbiting the star. The presently available data are not sufficient to obtain an unambiguousmultibody solution for this system. The provisional parameters for one planet that can befitted for give a 6.9 M J body in a 502-day, 1.33 AU, e=0.15 orbit that will have to be revised,when another planet (or planets) are added to the current model. Nevertheless, the solutionis robust enough to conclude that HD 24210 has at least one planet with large minimummass. This result further emphasizes the observed correlation between the stellar mass andthe masses of orbiting planets (Johnson et al. 2007; Lovis & Mayor 2007).The RV variations observed in the K2-giant, BD +20 2457, can be unambiguouslymodeled by two Keplerian orbits with the periods of 380 and 622 days, 1.4 and 2 AU semi-major axes, and the respective eccentricities of 0.15 and 0.18. For the estimated stellar massof 2.8 M ⊙ , these parameters yield minimum masses of the orbiting bodies of 12.5 M J and21.4 M J , respectively. The ∼ J deuterium burning limit that conventionally separates planets from brown dwarfs.Further analysis of this intriguing system is complicated by the fact that, due to thehighly uncertain parallax of the primary, its mass is poorly known and spans a range thatis at least as wide as 1.3-4.3 M ⊙ (Section 2). This is illustrated in Figure 10, which showsthe constraints on the masses of the two substellar companions under the usual assumptionof a random distribution of orbital inclinations. There is a 95% probability that the massesof the two bodies fall in the respective ranges delimited by the inclinations of 18 ◦ and 90 ◦ .Clearly, high masses, approaching the hydrogen burning limit are very unlikely. Similarly,a possibility that both masses stay below the deuterium burning limit is marginal at best,unless one accepts an unrealistically low primary mass, approaching 1 M ⊙ or even less.Consequently, within the currently available constraints, it is reasonable to assume that thetrue masses of the two companions to BD +20 24 57 have masses in the brown dwarf range.An extensive study of the dynamics of this system will be described in a subsequent paper.The two brown dwarf - mass bodies discovered by our survey around BD +20 2457 addto the previous three detections of single objects of this kind around intermediate-mass stars(Hatzes et al. 2005; Lovis & Mayor 2007; Liu et al. 2008). Only one such two-companionsystem has been previously identified around a solar-mass star, HD 168443, by Marcy et al.(2001). On the basis of the facts presented above, it appears entirely reasonable to assumethat the two companions to this star have originated from a massive disk and acquired enoughmass to place them above the formal 13 M J brown dwarf limit. This raises an intriguingpossibility that, in the case of substellar-mass companions to giants, both the concept of thebrown dwarf desert (Marcy & Butler 2000) and the meaning of the deuterium burning limitwill have to be revisited. In fact, this problem has been remarked on by Lovis & Mayor(2007)in the context of the observed correlation between the stellar and the planetary mass.We thank the HET resident astronomers and telescope operators for support. AN andGN were supported in part by the Polish Ministry of Science and Higher Education grant1P03D 007 30. AW acknowledges support from NASA grant NNX09AB36G. GN is the recip-ient of a graduate stipend of the Chairman of the Polish Academy of Sciences. The Hobby-Eberly Telescope (HET) is a joint project of the University of Texas at Austin, the Pennsyl-vania State University, Stanford University, Ludwig-Maximilians-Universit¨at M¨unchen, andGeorg-August-Universit¨at G¨ottingen. The HET is named in honor of its principal benefac-tors, William P. Hobby and Robert E. Eberly. 14 – REFERENCES
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17 –Table 1. Stellar parameters of BD +14 4559, HD 24210 and BD +20 2457.Parameter BD +14 4559 HD 24210 BD +20 2457V 9.63 8.33 9.75B-V 0.98 ± ± ± π [mas] 19.99 ± ± ± eff [K] 5008 ±
20 4290 ±
13 4127 ± ± ± ± / H] 0.10 ± ± ± / L ⊙ -0.32 1.75 3.17M ⋆ / M ⊙ ± ± b P [days] 268.94 ± T [MJD] 53293.71 ± − ] 55.21 ± ± ω [deg] 87.64 ± m sin i [M J ] 1.47 a [AU] 0.777( χ ν ) / σ RV [m s − ] 11.43 18 –Table 3: Tentative orbital parameters of the new planet around HD 240210.Parameter HD 240210 b P [days] 501.75 ± T [MJD] 54486.76 ± − ] 161.89 ± ± ω [deg] 277.49 ± m sin i [M J ] 6.90 a [AU] 1.33( χ ν ) / σ RV [m s − ] 38.9Table 4: Orbital parameters of the sub-stellar-mass companions to BD +20 2457 derivedfrom the best fit of a two-body Keplerian model to the RV data.Parameter BD +20 2457 b BD +20 2457 c P [days] 379.63 ± ± T [MJD] 54677.03 ± ± − ] 322.35 ± ± ± ± ω [deg] 207.64 ± ± m sin i [M J ] 21.42 12.47 a [AU] 1.45 2.01( χ ν ) / σ RV [m s − ] 60.02 19 –Fig. 1.— Relative radial velocities for K0-giant BD+70 1068. The star shows RV variabilityat σ =12 m s − whereas the intrinsic RV measurement uncertainty for these observations was7 m s − . The remaining RV scatter can be attributed to solar - type oscillations at the levelof 10 m s −
20 –Fig. 2.—
Top:
Radial velocity measurements of BD +14 4559 (filled circles), the best-fit of asingle planet Keplerian model to data (solid line) and the fit of that model with a parabolictrend (dashed line).
Center:
The post-fit residuals for a single planet model.
Bottom:
Asabove for the planet with the trend fitted out. 21 –Fig. 3.—
Top:
Radial velocity measurements of HD 240210 (filled circles), the best-fit singleplanet Keplerian model (solid line), and a tentative, best-fit model of two planets to data(dashed line).
Center and bottom:
See Figure 2. 22 –Fig. 4.—
Top:
Radial velocity measurements of BD +20 2457 (filled circles) and the best-fitof a single planet Keplerian model to data (solid line).
Bottom:
The post-fit residuals forthe above model. 23 –Fig. 5.— A decomposition of the observed RV variations in BD +20 2457 (filled circles)into contributions from the orbital motions of two brown dwarf-mass companions.
From topto bottom:
The observed radial velocities (filled circles) and the best-fit Keplerian orbit forcompanion b (solid line) with the contribution from companion c fitted out. The same forcompanion c with companion b fitted out. The best fit of both b and c to the RV data. Thepost-fit residuals from the two-companion fit. 24 –Fig. 6.— Histograms of the values of p χ ν obtained from the fits of the Keplerian modelsto scrambled RVs used to estimate the FAPs for the three stars discussed in the text. Ineach case, 1000 sets of scrambled RVs have been generated. Vertical arrows point to therespective p χ ν values derived from fits to unscrambled velocities. In all three cases the FAPvalues are less than 0.1%. 25 –Fig. 7.— The Lomb-Scargle periodograms of (a) Radial velocities (b) Bisector Velocity Span(c) H α equivalent width and (d) ASAS (Pojmanski 1997) V photometry of BD +14 4559.The levels of FAP=1.0 % and 0.1% are shown. 26 –Fig. 8.— The Lomb-Scargle periodograms of (a) Radial velocities (b) Bisector VelocitySpan (c) H α equivalent width and (d) Tycho (Perryman & ESA 1997) V T photometry ofHD 240210. The levels of FAP=1.0 % and 0.1% are shown. 27 –Fig. 9.— The Lomb-Scargle periodograms of (a) Radial velocities (b) Bisector Velocity Span(c) H α equivalent width and (d) ASAS (Pojmanski 1997) V photometry of BD +20 2457.The levels of FAP=1.0 % and 0.1% are shown. 28 –Fig. 10.— Constraints on the masses of substellar companions to BD +20 2457. The solidlines delimit the masses of the inner companion computed from the mass function over theestimated 1.3-4.3 M ⊙ range for the stellar mass and orbital inclinations from 18 ◦ to 90 ◦◦