BD+15 2940 AND HD 233604: TWO GIANTS WITH PLANETS CLOSE TO THE ENGULFMENT ZONE

BD+15 2940 (HIC 78407) is a V_T = 9.185 ± 0.024, B − V = 1.006 ± 0.036 (van Leeuwen 2007) K0 (Cannon & Pickering 1924) star in Serpens. Its Hipparcos parallax π = 1.71 ± 1.33 points to a distance of 585 pc. The star belongs to the PTPS red clump giants sample (Zieliński et al. 2012). We collected 38 spectra of BD+15 2940 over 2362 days between 2005 March 23 and 2011 September 10 (MJD 53452-55814). The signal-to-noise ratio per resolution element (S/N) in the spectra was 120–330 at 594 nm in 316–919 s of integration, depending on the atmospheric conditions.

HD 233604 (BD+54 1280) is V_T = 10.406 ± 0.049 (Høg et al. 2000), B − V = 1.007 ± 0.115 (Perryman & ESA 1997), K5 (Cannon & Pickering 1924) star in Ursa Major. It belongs to the PTPS red clump giant sample and it was observed at 33 epochs over the period of 2956 days from 2004 January 11 to 2012 February 14 (MJD 53015-55971). The S/N in the spectra was 110–300 at 594 nm in 762–2100 s of integration, depending on the atmospheric conditions.

HD 209458 (BD+18 4917, V376 Peg) a V_T = 7.703 ± 0.012, B − V = 0.594 ± 0.015 (van Leeuwen 2007) G0 dwarf (Montes et al. 2001), is known (Henry et al. 2000; Mazeh et al. 2000) as a host of a transiting (Charbonneau et al. 2000), msin i = 0.689 ± 0.024 M_J planet at a = 0.04723 ± 0.00079 AU orbit (Butler et al. 2006; P = 3.52474859  ±  3.8 × 10⁻⁷ days; Knutson et al. 2007) with RV semi-amplitude of K = 84.67 ± 0.7 m s⁻¹ (Torres et al. 2008). This star is one of the PTPS test stars, which are known hosts to planetary systems that we have been monitoring as part of our long-term observing program. We have observed HD 209458 between 2004 July 11 and 2011 November 25 over 2693 days or 7.4 yr (MJD 53197-55890) and collected 29 epochs of RV measurements. The exposure times varied between 94 and 608 s depending on weather conditions, typically achieving the S/N of about 200.

HD 88133 (BD+18 2326), a V_T = 8.094 ± 0.013, B − V = 0.810 ± 0.015 (van Leeuwen 2007) G5 dwarf (Cannon & Pickering 1924), is another PTPS test star, a well-studied short-period host of a msin i = 0.299 ± 0.027 M_J planet in a = 0.04717 ± 0.00079 AU (P = 3.41587 ± 0.00059 days) with the RV semi-amplitude of K = 36.1 ± 3 m s⁻¹ (Fischer et al. 2005; Butler et al. 2006). It was occasionally observed between 2006 January 23 and 2012 February 20 (MJD 53758-55977). Twenty-three epochs of observations were gathered with S/N of 110–330 achieved in 141–800 s exposures, depending on actual weather conditions.

HD 166435 (BD+29 3190), a V_T = 6.901 ± 0.010, B − V = 0.633 ± 0.006 (van Leeuwen 2007) G1 sub-dwarf (White et al. 2007), has been known to exhibit a pronounced stellar activity due to spots that manifest themselves as the measured RV variations induced by the line bisector variability of an amplitude of ∼135 m s⁻¹ (Queloz et al. 2001). As one of the PTPS test stars, it was observed between 2011 February 19 and 2011 September 22 (MJD 55611-55826) at 23 epochs. The observations resulted in S/N of 290–540 obtained with 70–700 s exposures, depending on actual weather conditions.

The atmospheric parameters (T_eff, log g, [Fe/H], v_micro) of BD+15 2940 and HD 233604 were taken from Zieliński et al. (2012), who have estimated their values using the method of Takeda et al. (2002, 2005). With these values and the luminosities estimated from available data, stellar masses and ages were derived by fitting the ensemble of parameters characterizing the star (log L_⋆/L_☉, log T_eff, log g, and metallicity) to the evolutionary tracks of Girardi et al. (2000). The stellar radii were estimated using the derived masses and log g from the spectroscopic analysis as described in Zieliński et al. (2012). The stellar rotation velocities of BD+15 2940 and HD 233604 were taken from G. Nowak et al. (2013, in preparation), who have estimated their values using the cross-correlation technique and calibrations of Fekel (1997) and Hekker & Meléndez (2007). The stellar parameters are summarized in Table 1.

Table 1. Stellar Parameters of BD+15 2940 and HD 233604

Parameter	BD+15 2940	HD 233604
VT (mag)	9.185 ± 0.024	10.406 ± 0.049
(B − V) (mag)	1.006 ± 0.036	1.007 ± 0.115
Spectral type	K0	K5
π (mas)	1.71 ± 1.33	...
Teff (K)	4796 ± 117	4791 ± 45
log g	2.8 ± 0.45	2.55 ± 0.18
(Fe/H)	0.28 ± 0.07	−0.36 ± 0.04
log L⋆/L☉	2.01 ± 0.75	1.75 ± 0.18
M⋆/M☉	1.1 ± 0.2	1.50 ± 0.30
R⋆/R☉	14.7 ± 2.8	10.9 ± 0.6
Age (Gyr)	7.1 ± 4.2	2.4 ± 1.8
vrotsin i⋆ (km s−1)	2.3 ± 0.8	2.0 ± 0.8
Prot(sin i⋆)−1 (days)	317 ± 121	282 ± 111
Kosc (m s−1)	$22^{+137}_{-19}$	$9^{+9}_{-4}$
Posc (days)	$0.68^{+0.51}_{-0.31}$	$0.27^{+0.11}_{-0.07}$

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For HD 209458 and HD 88133 we adopted the stellar parameters determined in Valenti & Fischer (2005) and Fischer et al. (2005), respectively.

2.6.1. Li Abundance

As the HRS is a general purpose spectrograph, which is neither temperature- nor pressure-controlled, calibration of RV measurements with this instrument is best accomplished with the I₂ cell technique. We have improved the efficiency of the entire data analysis process by combining this method (Marcy & Butler 1992; Butler et al. 1996) with that of cross-correlation (Queloz 1995; Pepe et al. 2002) for the purpose of the respective RV, line bisector span (BS), and line bisector curvature (BC) measurements in the final version of the ALICE code.

A detailed implementation of the above approach is described in Nowak (2013). Briefly, we used the I₂ spectrum imprinted on the HRS flat-field spectrum to correct the initial ThAr lamp-derived wavelength scale and to determine the IP modeled as a sum of five Gaussian profiles. The wavelength scale was assumed to be linear over the 96-pixel segments that the spectra were divided into. The high S/N stellar template spectrum was then smoothed using optimal Wiener filtering (Rabiner & Gold 1975), deconvolved with the model IP using Jansson (1984) method, resampled to the corrected wavelength scale, and used as a model for RV determination from a remaining shift between the model and the stellar spectrum observed at a given epoch. The modeling process employed the nonlinear least squares Levenberg–Marquardt (L-M) method (Press et al. 1992). The RV for each epoch was derived as a mean value of 391 independent measurements from the 17 usable echelle orders, after rejecting those with outlying radial velocities (more than 3σ off the mean value) and those obtained for segments without stellar spectral lines, identified in the course of cleaning the combined stellar and iodine spectra from the I₂ lines. The RV uncertainty for each epoch was calculated as the error of the mean value ($={\rm rms}/\sqrt{n_{{\rm seg}}}$, where n_seg is the number of actually used segments).

A computation of the cross-correlation functions (CCFs) for the purpose of BS/BC determination was carried out as part of the above RV measurement procedure. To this end, the combined stellar and iodine spectra were first cleaned of the I₂ lines by dividing them by the corresponding iodine spectra imprinted in a flat-field, and then cross-correlated with a binary CCF mask. Typically the cleaned spectra and stellar template agree within 1%, consistent with the S/N ratio of 100. The mask was constructed from a synthetic K2 star spectrum of Kurucz (1993) Atlas 9 and contained about 300 lines.

The CCFs were computed in all the 17 HRS orders used for RV measurements over a wide, ±30 km s⁻¹, range after correcting the spectra for their absolute radial velocity and shifting them to the solar system barycenter (Stumpff 1980). Finally, the 17 CCFs were added together in the wavelength scale to form the integrated CCF used in further analysis. The absolute RVs at a given epoch of observations were measured from the position of a maximum of the CCF, while the CCF line bisectors and curvatures, defined in the usual way, were calculated using three reference ranges of (0.1–0.25), (0.375–0.525) and (0.65–0.8) of the central CCF intensity. The uncertainties of BS measurements were estimated with the formulae of Martínez Fiorenzano et al. (2005).

We fitted Keplerian orbits to the observed RV variations using a hybrid approach (Goździewski et al. 2003, 2007; Goździewski & Migaszewski 2006), which combines the global search for a plausible range of orbital parameters with the aid of the genetic algorithm (GA), followed by a nonlinear least squares or a downhill simplex fit to data to quickly converge to the preliminarily constrained χ² minimum.

In our implementation of this approach, once a periodic signal in a RV time series was identified in its Lomb–Scargle (L-S) periodogram (Lomb 1976; Scargle 1982), we searched for possible orbital solutions over a wide range of parameters with the PIKAIA-based GA code (Charbonneau 1995). The GA semi-global search usually identified a narrow parameter range of the search space, which was then explored using the L-M algorithm to locate the best-fit Keplerian solution. In the case of a single planet the RV scrambling method (Butler et al. 2004) was used to assess the false alert probability (FAP) of the final orbital solution. If a more complicated system was indicated by the presence of two or more periodicities in the RV data, the scrambled residua were used to quantify the goodness of the final solution. Uncertainties of the best-fit orbital parameters were estimated from either the covariance matrix of the L-M fits or from the scrambled residuals (Marcy et al. 2005).

Along with the target stars, we have been monitoring three stars of known RV behavior, HD 209458, HD 88133, and HD 166435, to track any possible changes in the data acquisition system that could affect the precision of RV measurements.

The RV and BS measurements for HD 209458 are listed in Table 2. The long-term RV uncertainty of 12 m s⁻¹ for this star was dominated by its high T_eff, which resulted in a correspondingly low number of spectral lines that could be used in RV measurements. The uncertainty of the BS estimates amounted to 38.9 m s⁻¹. The L-S periodogram of the observed RV variations revealed a clear, single period of 3.52 days and no trace of any long-term trend. The best fit Keplerian model of these data is shown in Figure 1 and the corresponding orbital parameters are given in Table 3. Within uncertainties, our results are identical to those of Butler et al. (2006).

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The RV and BS measurements for HD 88133 are listed in Table 4. In the case of this star, the 6.2 m s⁻¹ RV uncertainty was much lower than for HD 209458, and the respective uncertainty of BS measurements was 16.5 m s⁻¹. The L-S periodogram of the RV time series exhibited a highly significant signal at a 3.41 day period, and, as in the case of HD 209458, no long-period trend. The best-fit Keplerian orbit folded at the orbital period is presented in Figure 2 and the orbital parameters are listed in Table 3. Once again, within uncertainties, our results are identical to those of Butler et al. (2006).

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Table 3. Orbital Parameters of HD 209458 b and HD 88133 b

Parameter	HD 209458 b	HD 88133 b
P (days)	3.525 ± 0.009	3.415 ± 0.001
T0 (MJD)	53199.3 ± 0.9	53760.7 ± 0.9
K (m s−1)	87.7 ± 5.4	34.2 ± 3.6
e	0.007 ± 0.060	0.09 ± 0.07
ω (deg)	60 ± 108	15 ± 120
msin i (MJ)	0.714	0.284
a (AU)	0.0474	0.047
RV0 (m s−1)	11.1 ± 3.4	−0.7 ± 1.4
σ+ (m s−1)	0.0	0.0
$\chi ^2_\nu$	3.13	1.127
σO − C (m s−1)	20.54	5.46
$\overline{\sigma _{{\rm RV}}}$ (m s−1)	11.87	6.15
σj (m s−1)	16.76	⩽5.46
Nobs	29	23

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Finally, despite the fact that the 51.5 m s⁻¹ uncertainty of the BS measurements for HD 166435 (Table 5) was much larger than the respective RV uncertainty of 12.7 m s⁻¹, the correlation between the two quantities was obvious (r = 0.63, while the critical value of the Pearson correlation coefficient at the confidence level of 0.01 is r_{21, 0.01} = 0.52; Figure 3), in agreement with the results reported by Queloz et al. (2001) for this star. This confirms the reliability of our BS measurements. Unfortunately, given the poor phase coverage of our observations, we were not in position to confirm the periodic character of the RV and BS variations that mimic a planet.

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Overall, the results from RV and BS monitoring of the three stars discussed above demonstrate a satisfying long-term stability of our data acquisition scheme.

RV measurements of BD+15 2940 made at 38 epochs over a period of almost 6.5 yr are listed in Table 6 and shown in Figure 4. The estimated RV uncertainty for this star was σ_RV = 7 m s⁻¹ with the expected amplitude of solar-type oscillations of K_osc = 22 m s⁻¹ (Kjeldsen & Bedding 1995). The star exhibits RV variations with an amplitude of 65 m s⁻¹ which is ∼3 times the expected RV uncertainty.

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The L-S periodogram of the RV variations for this star revealed a single period of 137.5 days (Figure 5(a)) and no signature of any low frequency component. The best-fit Keplerian orbit is shown in Figure 4 and its parameters are listed in Table 7. When an additional scatter σ₊ of 18 m s⁻¹ determined from this fit was added in quadrature to the original RV uncertainties, it resulted in a $\chi ^2_\nu$ value of 0.989. Note that this increase in the long-term RV uncertainty is very close to the above K_osc estimate and the actual jitter derived as $\sigma _{j}=\sqrt{\vphantom{A^A}\smash{{\sigma ^{2}_{O-C} - \sigma ^{2}_{{\rm RV}}}}}$. The FAP < 0.001 for this orbital solution was estimated by performing 1000 Keplerian fits to the scrambled data points as shown in Figure 6.

Given the estimated stellar mass of 1.1 M_☉ and the orbital period of P = 137.5 days, the semi-major axis of the orbit of the planet is 0.54 AU, and the RV semi-amplitude of K = 43 m s⁻¹ gives its minimum mass of 1.1 M_J. The moderately eccentric orbit of e = 0.26 ± 0.10 makes the planet's distance to its star vary within 0.4–0.68 AU. Therefore, the BD+15 2940 planet is the closest one to a giant star detected so far by means of the Doppler velocity method, and the second least-massive one of all planets orbiting giants within 1 AU after BD+48 738 b (Gettel et al. 2012b).

Radial velocities of HD 233604 (BD+54 1280) measured at 33 epochs over the period of 2956 days (over 8 yr) are listed in Table 8 and presented in Figure 7. The estimated RV uncertainty for this star was 9.0 m s⁻¹, which is exactly the same as the estimated K_osc value. The measured RV amplitude was 213 m s⁻¹ or ∼17 times the expected RV uncertainty.

Table 7. Orbital Parameters of BD+15 2940 b and HD 233604 b

Parameter	BD+15 2940 b	HD 233604 b
P (days)	137.48 ± 0.34	192.00 ± 0.22
T0 (MJD)	53464 ± 16	53022 ± 77
K (m s−1)	42.7 ± 4.4	177.8 ± 4.3
e	0.26 ± 0.10	0.05 ± 0.03
ω (deg)	302 ± 33	281 ± 43
msin i (MJ)	1.11	6.575
a (AU)	0.539	0.747
RV0 (m s−1)	−2.5 ± 3.3	−16.9 ± 3.7
σ+ (m s−1)	18.0	9.0
$\chi ^2_\nu$	0.989	2.76
σO − C (m s−1)	17.89	19.13
$\overline{\sigma _{{\rm RV}}}$ (m s−1)	6.97	9.04
σj (m s−1)	16.48	16.86
Nobs	38	33

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The dominant feature in the periodogram of these RV data is the peak at a frequency corresponding to a 192 day period. The corresponding best-fit Keplerian orbit, presented in Table 7 and in Figure 7, gives the value of $\chi ^2_\nu$ of 2.76. An additional scatter of σ₊ = 9 m s⁻¹ was added to the original errors to account for an unresolved RV variability that has apparently degraded the precision of RV measurements for this star. As in the previous case, the FAP of <0.001 (Figure 6) was calculated for this best-fit model. The orbital solution for HD 233604, together with its estimated mass of M_⋆ = 1.5 M_☉ gives a msin i = 6.6 M_J companion in a 0.75 AU, nearly circular orbit with e = 0.05 ± 0.03.

With the estimated rotation velocity of v_rotsin i_⋆ = 2.3 ± 0.8 km s⁻¹ and the radius of R_⋆/R_☉ = 14.7 ± 2.8 the expected upper limit to the rotation period of BD+15 2940 is 317 days, but it may range between 196 and 438 days. Therefore, it is important to consider possible sources of stellar activity that may result in the observed periodic RV signal. Such processes include stellar pulsations and a spot rotating with a star.

The p-mode oscillations can be excluded, because their expected amplitude and period are K_osc = 22 m s⁻¹ and P_osc = 0.68 days, respectively (Kjeldsen & Bedding 1995). We do not resolve such a fast oscillation with our sampling that is focused on long-term RV variations. Consequently, this effect only contributes a RV-jitter to our measurements.

The mean values of the BS and the BC for this star are −5 ± 23 m s⁻¹, and −20 ± 32 m s⁻¹, respectively, with the corresponding uncertainties of 18 m s⁻¹ and 24 m s⁻¹. The BS and BC amplitudes are 45 m s⁻¹ and 75 m s⁻¹. Neither BS (Figure 5(c)) nor BC show any periodic signal above the f_n = 0.01 level. Pearson's correlation coefficients for RV and BS and BC are 0.12 and 0.17, respectively, and the critical value at the confidence level of 0.01 is r_{36, 0.01} = 0.41.

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Two archival photometry datasets are available for BD+15 2940. The existing Hipparcos photometry (Perryman & ESA 1997) includes 65 epochs that uniformly cover the 1159 days (3.2 yr) or ∼8.5 RV periods between MJD 47904-49063, over 12 yr earlier than our RV data. No periodic signal is present in these data, either. The 362 epochs of ASAS photometry (Pojmanski 1997) collected between MJD 52685-55089 cover ∼6.5 yr (2404 days) or ∼12 RV periods. These measurements, clumped in seven groups, are contemporaneous with ∼70% of our RV data. Again, no trace of a periodicity is present in these data (see Figure 5(d)).

Since the ASAS photometric uncertainty of σ = 0.015 mag is typically given the observed brightness of the star, it is unlikely that it may be a noise caused by a stellar spot. However, if we made such an assumption and postulated a rotating spot that covers 1.5% of the stellar surface, the expected semi-amplitudes of RV and BS variations would be 61–95 m s⁻¹ and 12–19 m s⁻¹, respectively, depending on the assumed model (Saar & Donahue 1997; Hatzes 2002; Desort et al. 2007). Although these values are in reasonable agreement with our RV and BS data, there is no periodicity in the ASAS data gathered over ∼12 RV periods, and no correlation between our RV and BS measurements. Adding to these results a moderate eccentricity of the assumed Keplerian orbit, we can practically rule out the possibility that the observed RV periodicity is caused by any of the stellar phenomena discussed above and is most likely the effect of an orbital motion of a substellar mass companion to the star.

The estimated upper limit of the rotation period of HD 233604 is 282 days and it is fairly close to the observed period of the RV variations of this star. Given the uncertainty in stellar radius and the precision of rotation velocity determination, the rotation period may range from 181 to 383 days. Obviously, it is critically important to examine the available data for a possible alternative explanation of the periodic RV signal.

Due to the length of the period of the observed RV variations and their high amplitude, we can confidently reject p-mode oscillations as a cause of the RV periodicity. The most likely alternative is a spot on the stellar surface moving with the star at its rotation period. Such a spot should be detectable in both the photometric and the line profile variations.

The amplitudes and mean values of the BS and BC measurements for this star are 65 m s⁻¹ and 9.6 ± 30.1 m s⁻¹, and 52 m s⁻¹ and −9.7 ± 32.3 m s⁻¹, respectively, and the corresponding uncertainties are 22 and 30 m s⁻¹. Neither BS (Figure 8(c)) nor BC variations show any evidence for a periodicity in the computed LS periodograms. Similarly, no correlations between the RV and the BS and BC variability were found. The respective Pearson's correlation coefficients are r = 0.34 for the BS and r = 0.20 for the BC (with critical value of r_{36, 0.01} = 0.44 for the confidence level of 0.01).

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In the case of this star, long-term photometric time series are available from the NSVS (Woźniak et al. 2004) and the WASP (Pollacco et al. 2006). SWASP photometry consists of 2767 measurements between MJD 54189 and 54575, which are contemporaneous with our spectroscopic observations but cover only a small part of their time baseline. In fact, most of the available epochs of photometry fall within 175 days between MJD 54400 through MJD 54575. The NSVS photometry is of a better quality and consists of 309 measurements made between MJD 51272 and MJD 51633, which amounts to 361 days of data collected about 4 yr earlier than our HET observations. These data are clustered in two groups, each covering a fraction of the orbital period.

The LS analysis reveals no periodic signal in SWASP data, but four significant periodicities are found in the NSVS photometry with f_n < 0.001. Two of them which are close to a 1 day period are most likely artifacts of the particular cadence of the RV observations. The other two at 28.1 and 27.7 days are most likely caused by the residual lunar illumination of the field that was not removed in the photometric data reduction process.

As in the case of BD+15 2940, we can make a very conservative assumption that the SWASP photometric uncertainty of σ = 0.018 mag is caused by a spot, covering 1.8% of the stellar surface. This gives the expected semi-amplitude of RV and BS variations of 70–111 m s⁻¹ and 13–20 m s⁻¹, respectively, depending on the assumed model (Saar & Donahue 1997; Hatzes 2002; Desort et al. 2007). The expected RV variations estimated under such an unfavorable assumption are 1.6–2.5 times smaller than those observed.

Altogether, the absence of the periodicity seen in the RV data in the available photometric data and no correlation between BC, BS, and RV variations make it unlikely that they are induced by stellar activity. Additional evidence supporting the Keplerian origin of the observed periodic RV variations is provided by the fact that they are much larger than expected under the assumption that the photometric data scatter is dominated by a rotating spot on the stellar surface.