SUBSTELLAR-MASS COMPANIONS TO THE K-DWARF BD+14 4559 AND THE K-GIANTS HD 240210 AND BD+20 2457

RVs of BD+14 4559 were measured at 43 epochs over the period of 1265 days between MJD 53546 and 54811 (Table 2). Typically, the signal-to-noise ratio per resolution element in the spectra was 150–260 at 594 nm in 10–25 minutes of integration, depending on the atmospheric conditions. The estimated mean RV uncertainty for this star was 8 m s⁻¹.

BD+14 4559 (AG +14 2370, HIP 104780, LTT 16221) is a high proper motion K5 (Turon et al. 1993) star with V = 963 (Weis 1986), B − V = 098 ± 0.08 (Høg et al. 2000), and π = 19.99 ± 1.61 mas (Perryman & ESA 1997). The trigonometric parallax is consistent with the photometric value of π = 24 mas derived by Weis (1986). The atmospheric parameters of BD+14 4559 as determined in Z09 indicate that it is a dwarf with log(g) = 4.60 ± 0.05, T_eff = 5008 ± 20 K, and [Fe/H] = 0.10 ± 0.07.

Using the existing Hipparcos (Perryman & ESA 1997) and Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) photometry and the empirical calibrations of Ramírez & Meléndez (2005), we have estimated the effective temperature of the star to be T_eff = 4814 ± 94 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 5.56 and −0.32, respectively. By comparing the stellar parameters to evolutionary tracks of Girardi et al. (2000), we have computed the mass of BD+14 4559 to be M/M_☉ = 0.86 ± 0.15 and R/R_☉ = 0.95 ± 0.2.

The projected rotational velocity of BD+14 4559, vsin i = 2.5 ± 1 km s⁻¹, was estimated using the cross-correlation method (Benz & Mayor 1984). From this value and the adopted stellar radius we have obtained an estimate of the rotation period of P_rot = 19 days, which is much shorter than the observed 267 day period of the RV variations. From the uncertainty of the vsin(i) determination alone, the stellar rotation period may range from 13 to 32 days.

RVs of HD 240210 were measured at 38 epochs over the period of 1655 days between MJD 53187 and 54842 (Table 3). Typically, the signal-to-noise ratio per resolution element in the spectra was 150–300 at 594 nm in 4–10 minutes of integration, depending on the atmospheric conditions. The estimated mean RV uncertainty for this star was 8 m s⁻¹.

HD 240210 (BD+56 2959) is a K7 (Cannon & Pickering 1924) star with V = 833, B − V = 165 ± 0.04 (Høg et al. 2000). The parallax of π = 7.6 ± 8.7 mas (Perryman & ESA 1997) is consistent with the π = 7.0 ± 2.6 mas of Gatewood et al. (1992). The atmospheric parameters of HD 240210 (Z09) indicate that the star is a giant with log(g) = 2.31 ± 0.11, T_eff = 4297 ± 25 K, and [Fe/H] = −0.18 ± 0.12.

Using the existing Hipparcos (Perryman & ESA 1997) and 2MASS (Skrutskie et al. 2006) photometry, and the empirical calibrations of Ramírez & Meléndez (2005), we have estimated the effective temperature of the star to be T_eff = 4290 ± 94 K. These values of effective temperature and log(g) are consistent with a K3-giant star.

The derived absolute bolometric magnitude of the star and log(L/L_☉) are 0.86 and 1.55, 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_☉ = 0.82 ± 0.15 and R/R_☉ = 10.5 ± 3.

The projected rotational velocity of HD 240210, vsin i< 1.0 ± 1 km s⁻¹, was estimated using the cross-correlation method. From this value and the adopted stellar radius we have obtained an estimate of the rotation period of P_rot > 530 days.

RVs of BD+20 2457 were measured at 37 epochs over the period of 1833 days between MJD 53033 and 54866 (Table 4). Typically, the signal-to-noise ratio per resolution element in the spectra was 140–260 at 594 nm in 12–30 minutes of integration, depending on the atmospheric conditions. The estimated mean RV uncertainty for this star was 7 m s⁻¹.

BD+20 2457 (AG +20 1166) is a K2 (Heckmann 1975) star with V = 975, B − V = 125 ± 0.09 (Høg et al. 2000) which is similar to V = 9.57 and B − V = 1.35 as measured photometrically by Busko et al. (1980), who observed it as a comparison star in their stellar variability study. The parallax of the star, π = 5.0 ± 26.50 mas (Perryman & ESA 1997), is obviously very poorly determined. The atmospheric parameters of BD+20 2457 (Z09) indicate that it is a dwarf with log(g) = 1.51 ± 0.05, T_eff = 4137 ± 10 K, and [Fe/H] = −1.00 ± 0.07.

Using the existing Hipparcos (Perryman & ESA 1997) and 2MASS (Skrutskie et al. 2006) photometry and the empirical calibrations of Ramírez & Meléndez (2005), we have estimated the effective temperature of the star to be T_eff = 4127 ± 94 K. We conclude that the spectral type of BD+20 2457 is K2II.

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 of Girardi et al. (2000), we have estimated the mass of BD+20 2457 to fall in the 1.3–4.3 M/M_☉ range (2.8 ± 1.5 M/M_☉), and R/R_☉ = 49 ± 26.

As for the other two stars, the projected rotational velocity of BD+20 2457, vsin i<1.0 km s⁻¹, was estimated using the cross-correlation method. This estimate is however very uncertain. We therefore assume as the upper limit of vsin i for BD+20 2457 the mean value of the rotational velocity for K2II stars of vsin i = 2.5 km s⁻¹ from de Medeiros et al. (1996). From this value and the adopted stellar radius we have obtained an estimate of the rotation period of the star, P_rot > 983 days.

As shown in Figure 2, the best-fit, single Keplerian orbit model for the RV variations of this star leaves behind a significant, non-linear trend, which reaches the amplitude of ∼50 m s⁻¹ and results in σ_RV = 17 m s⁻¹ over the 1300 day span of observations. At this point, rather than attempting to search the χ²_ν- space for a range of acceptable two-planet solutions, we have modeled the observed RV variations with a Keplerian orbit and a parabolic trend added to it. The best-fit χ²_ν value for this model drops from 4.4 for the single orbit case to 2.1 indicating, together with the FAP <0.1%, that the trend is significant.

The final solution (Table 5) includes a planet with the minimum mass of 1.5 M_Jup, in a 269 day, 0.78 AU, e = 0.29 orbit around the star. Given the stellar mass of 0.86 M_☉, the mass function of 2.5 × 10⁻⁸ M_☉, and the above RV amplitude and time span of the observed trend, one can broadly constrain a putative second companion to have a minimum mass of >2.4 M_Jup and the orbital radius >2.3 AU, assuming e = 0.

The remaining post-fit rms residual, σ_RV = 11 m s⁻¹, slightly exceeds the estimated 8 m s⁻¹ precision of our RV measurements for this star. This excess "jitter" is within the estimated, intrinsically generated RV noise of 5 m s⁻¹ due to solar-type oscillations in stable dwarfs (Wright 2005).

A single orbit fit to the RV data for this star (Figure 3, Table 6) gives χ²_ν = 9.8, the post-fit rms residual, σ_RV = 39 m s⁻¹, and the very clear unmodeled RV variations. Our search for a multiple orbit solution has resulted in several two- and three-planet models, which gave nearly identical improvements of the fit. This is illustrated in Figure 3 by a two-planet model, which produces χ²_ν = 5.0, σ_RV = 25 m s⁻¹, FAP < 0.1%, and the persistent lower-level systematics in the RV residuals. Because the existing measurements are obviously insufficient to obtain satisfactory constraints on the Keplerian model of the RV variations of this star, we list in Table 6 the initial one-planet solution and postpone further analysis until the time, when enough data become available. The provisional, best-fit orbit involves a 5.2 M_Jup planet in a 502 day orbit with the semimajor axis of 1.16 AU and e = 0.15.

We also note that the 25 m s⁻¹ post-fit residual from the multiplanet fits is about 3 times larger than the formal precision of the RV measurements for HD 240210. As mentioned above, this is in agreement with the estimated RV scatter in K-giants due to their internal activity.

A single, Keplerian orbit fit to the RV data for this star is shown in Figure 4. The residuals from this fit are characterized by χ²_ν = 13.7, σ_RV = 105 m s⁻¹, and a ∼600 day periodicity with the amplitude in excess of 100 m s⁻¹. Once again, as shown in Figure 6, the FAP for the existence of the second periodicity is less than 0.1%.

As shown in Figure 5, the best-fit, two-orbit solution offers a dramatic improvement to the Keplerian model of the RV variations observed in BD+20 2457, with the values of χ²_ν and σ_RV reduced to 5.2 and 60 m s⁻¹, respectively. The model parameters calculated for the stellar mass of 2.8 M_☉ and listed in Table 7 call for a system of two substellar-mass companions with the respective minimum masses of 21.4 M_Jup and 12.5 M_Jup, orbital periods of 380 and 622 days, semimajor axes of 1.45 and 2.01 AU, and mild eccentricities of 0.15 and 0.18.

As in the case of HD 240210, the estimated, 7 m s⁻¹ uncertainty of the RV measurements of BD+20 2457 is much smaller than the actual, 60 m s⁻¹ rms of the post-fit residuals. This additional RV "jitter" broadly agrees with the 138 m s⁻¹ amplitude of the solar-type oscillations extrapolated for this star from Kjeldsen & Bedding (1995).

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 Hipparcos and Tycho (Perryman & ESA 1997), the NSVS (Woźniak et al. 2004), and the ASAS experiment (Pojmański 1997). None of the four data sets reveal any periodic light variations. In particular, 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. In this case, the light variations are characterized by the mean value of V = 9.650± 0.021 mag, which is consistent with the earlier measurements. As an example, the Lomb–Scargle (LS) periodogram of the ASAS photometry data in shown in Figure 7.

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We have obtained 43 bisector and line curvature measurements, which resulted in the mean bisector velocity span, BVS = 4.6 ± 32 m s⁻¹, and the mean bisector curvature, BC = −8 ± 27 m s⁻¹ 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 of the star has shown that the EW of the Hα line exhibited a 3% rms scatter around its mean value of 396 ± 12 mÅ, 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 0.01 is r_21,0.01 = 0.53). The LS periodograms of the RVs, Hα EW, the BVS, and photometry for BD+14 4559 are shown in Figure 7. Clearly, the only observable that exhibits periodic time variations in time is the RV.

Using the scatter seen in the ASAS photometry of the star, and its rotational velocity determined above, we can estimate the amplitude of RV variations and of the BVS due to a possible presence of a spot on the stellar surface (Hatzes 2002). The observed RV amplitude of BD+14 4559 is 3 times larger than the 35 m s⁻¹ total RV amplitude predicted by Hatzes (2002) for a spot with a filling factor of f = 0.02, on a star rotating at vsin i = 2.5 km s⁻¹. Within the estimated uncertainty of the rotation velocity, the expected RV amplitude induced by a hypothetical spot is at least 2 times less than the observed one. The expected bisector variations of 5 m s⁻¹ are comparable to the precision of our RV measurements and cannot have a detectable effect on our results. To summarize, the facts that there is no variability in the available photometric measurements over the period of ∼19 yr, the observed period of the RV variations is much longer than the estimated rotation period of the star, a significant eccentricity must be included in the best-fit model of the RV curve, and that the observed RV variations have been consistent over the five consecutive cycles of the period, make their interpretation in terms of a rotating spot very unlikely.

In the case of this star, the only long-term photometry available comes from 129 Tycho measurements with the V_T filter (Perryman & ESA 1997), between MJD 47946 and 49016. These data give the mean V_T = 8.499 ± 0.012 and the scatter in V_T of 0.136 mag. No periodic variability has been detected in these measurements. In addition, there are 19 epochs of photometric observations of this star available from the NSVS (Woźniak et al. 2004), collected between MJD 51362 and 51493. These data are characterized by the median V = 7.965 ± 0.01 and the scatter of 0.038. Since the NSVS photometry is of a much better quality than the Tycho data, we consider this scatter more believable. As shown in Figure 8, the LS periodogram of the Tycho photometry of HD 240210 reveals no significant periodicities.

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The mean values of the BVS and the BC for this star are 62 ± 23 m s⁻¹ and 23 ± 27 m s⁻¹, respectively, with no statistically significant variability. No correlations between the RV residuals and the BVS and BC were found. The respective correlation coefficients are r = 0.08 for the BVS and r = −0.18 for the BC (r_36,0.01 = 0.40). Furthermore, the average EW of the Hα line measured over 28 epochs amounts to 602 ± 13, and the EW itself does not show any periodicities within 2%. We have considered a possible rotational modulation in Hα by calculating the Pearson correlation coefficient with the RV data residuals after removing the putative orbit. We found no correlation between the Hα EW and the RV residuals (r = −0.26, whereas r_26,0.01 = 0.48). The LS periodograms of the four observables for HD 240210 discussed above are shown in Figure 8. As in the case of BD+14 4559, RV is the only one that varies periodically.

The observed photometric scatter in HD 240210, if interpreted in terms of a spot rotating with the star would also be detectable in both the RV and the line bisector data. The estimated total RV variations should be of the order of 23 m s⁻¹ and the bisector variations should amount to 31 m s⁻¹ (Hatzes 2002). The semi-amplitude of the observed periodic signal in RV is much larger than the predicted variations induced by a hypothetical spot of size consistent with the existing photometeric variations. Periodic variations in line bisectors produced by a hypothetical spot should manifest themselves as the uncertainty in our BVS measurements, which is comparable to the predicted value. In any case, these variations should show a periodicity equal to the stellar rotation period, P > 530 days. Because no such variations are present in our bisector measurements for this star, we conclude that the observed scatter is a combination of low quality photometry and possible solar-type oscillations of the star. Such oscillations might account for 3.3 mmag in the photometric variability and V_osc = 13 m s⁻¹ in the BVS using the scaling relations of Kjeldsen & Bedding (1995).

As in the case of BD+14 4559, we have identified four photometric data sets that we could utilize in our analysis, but we have concentrated on the data from the ASAS project (Pojmański 1997), which contains extensive measurements that are contemporaneous with our RV observations. These data include 120 measurements made between MJD 52622 and MJD 53400 and the 191 additional ones made between MJD 52623 and MJD 54911. We have used 319 grade A measurements from the ASAS to derive the mean V = 9.693 ± 0.051 mag and to compute their LS periodogram in search for any periodicities. As shown in Figure 9, no significant periodicities are present in the spectrum. Similarly, no periodicities were found in the other three, lower quality time series.

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We have obtained 37 bisector and curvature measurements for this star, with the mean BVS = 105 ± 39 m s⁻¹, and the mean BC = 47 ± 30 m s⁻¹, both revealing no significant periodicities in the corresponding LS periodograms (Figure 9). We have also searched for correlations between the RV residuals and the BVS and BC after having removed the putative companions b and c. The respective correlation coefficients are r = −0.33 and r = −0.19 for BVS and r = −0.12 and r = −0.09 for BC, respectively (the critical value of Pearson correlation coefficient at the confidence level of 0.01 is r_35,0.01 = 0.42). The EW of the Hα line for BD+20 2457 is 653 ± 23, and this parameter shows no significant periodicities within 3.5% for 23 observations (Figure 9). As for the other two stars, we have searched for a possible rotational modulation in Hα by calculating the Pearson correlations coefficient with the RV data residuals after removing the individual orbits. We found that there is no significant correlation between the Hα EW and the RV residuals (r = −0.21 and −0.51, respectively, and r_21,0.01 = 0.53).

A photometric scatter resulting from a spot rotating with BD+20 2457 would induce the estimated total RV variations on the order of 84 m s⁻¹ and the bisector variations of 11 m s⁻¹ (Hatzes 2002). The semi-amplitude of the observed periodic signal in RVs is much larger. As in BD+14 4559, the anticipated variability in line bisectors produced by a periodic spot rotation is comparable to the precision of our RV measurements and cannot have a detectable effect on our results. These variations, if real, should show a periodicity equal to the star's rotation period, P > 983 days, which appears not to be the case. Since no measurable variations are present in the bisectors and line curvatures, we conclude that the observed photometric scatter is again a combination of low quality photometry and possible solar-type oscillations of the star. Such oscillations might account for 5.9 mmag and up to V_osc = 138 m s⁻¹ using the scaling relations of Kjeldsen & Bedding (1995).