THE CALIFORNIA PLANET SURVEY. I. FOUR NEW GIANT EXOPLANETS^*

We observed HD 34445, HD 126614 A, HD 13931, and Gl 179 using the HIRES echelle spectrometer (Vogt et al. 1994) on the 10 m Keck I telescope. These stars were each observed 30–70 times each over 10–12 yr. Typical exposure times for these stars were 100, 357, 130, and 500 s, respectively. All observations were made with an iodine cell mounted directly in front of the spectrometer entrance slit. The dense set of molecular absorption lines imprinted on the stellar spectra provide a robust wavelength fiducial against which Doppler shifts are measured, as well as strong constraints on the shape of the spectrometer instrumental profile at the time of each observation (Marcy & Butler 1992; Valenti et al. 1995).

We measured the Doppler shift from each star-times-iodine spectrum using a modeling procedure modified from the method described by Butler et al. (1996). The most significant modification is the way we model the intrinsic stellar spectrum, which serves as a reference point for the relative Doppler shift measurements for each observation. Butler et al. use a version of the Jansson (1995) deconvolution algorithm to remove the spectrometer's instrumental profile from an iodine-free template spectrum. We instead use a new deconvolution algorithm developed by one of us (J.A.J.) that employs a more effective regularization scheme, which results in significantly less noise amplification and improved Doppler precision.

Figure 2 shows the RV time series for four stable stars with characteristics similar to the planet-bearing stars presented herein, demonstrating our measurement precision over the past decade on a variety of spectral types. In 2004 August, the Keck HIRES spectrometer was upgraded with a new detector. The previous 2K × 2K pixel Tektronix CCD was replaced by an array of three 4K × 2K pixel MIT-LL CCDs. The new detector produces significantly higher velocity precision due to its improved charge transfer efficiency and charge diffusion characteristics, smaller pixels (15 μm versus 24 μm), higher quantum efficiency, increased spectral coverage, and lower read noise. Our post-upgrade measurements exhibit a typical long-term rms scatter of ∼1.5 m s⁻¹ for bright, quiescent stars, compared to ∼2.5 m s⁻¹ for pre-upgrade measurements. (Measurements prior to JD 2,453,237 are pre-upgrade.) The pre- and post-upgrade measurements also lack a common velocity zero point, but we fit for and corrected this offset to within ∼2 m s⁻¹ for every star observed at Keck using a large set of stable stars with many pre- and post-upgrade observations. To further limit the impact of the velocity discontinuity, we let the offset float in the Keplerian fits below, effectively treating pre-upgrade and post-upgrade observations as coming from two different telescopes (except for HD 13931, which does not have enough post-upgrade measurements to allow for a floating offset).

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With the exception of Gl 179, these planet-bearing stars are bright G and K stars, and the Keck RVs have median single measurement uncertainties of 1.2–1.4 m s⁻¹. In some instances, we made two or more consecutive observations of the same star and binned the velocities in 2 hr time bins, thereby reducing the associated measurement uncertainties. Gl 179 is substantially fainter (V = 11.96), and its median measurement uncertainty of 4.2 m s⁻¹ is dominated by Poisson noise from photon statistics. For each of these stars, the measurement uncertainty is the weighted standard deviation of the mean of the velocity measured from each of the ∼700 2 Å chunks in the echelle spectrum (Butler et al. 1996).

We observed two of the stars, HD 34445 and Gl 179, with the HET (Ramsey et al. 1998) at the McDonald Observatory, as part of the ongoing Doppler surveys of FGK-type stars (Cochran et al. 2004) and M dwarfs (Endl et al. 2003). We use the High-Resolution-Spectrograph (HRS; Tull 1998) in combination with an I₂-cell at a resolving power of R = 60, 000 to measure precise RVs. The observing strategy and data reduction pipeline are detailed in Cochran et al. (2004) and a description of our I₂-data modeling code "Austral" can be found in Endl et al. (2000).

HET observations of HD 34445 begun in 2003 October and we collected a total of 50 HRS spectra since then. We started RV monitoring of Gl 179 a year later, in 2004 October, and so far we have obtained 13 spectra of this faint M dwarf.

For each of the four stars below, we present a single-planet Keplerian fit to the measured velocities. For HD 126614 A, we add a linear velocity trend to the model. Table 3 summarizes the observing statistics, best-fit Keplerian orbital parameters, and measures of the goodness-of-fit for these planets. In this subsection, we describe the Keplerian modeling and related topics associated for all of the stars. We discuss the planet-bearing stars individually in Sections 5–8.

With the measured velocities for each star we performed a thorough search of the orbital parameter space for the best-fit, single-planet Keplerian orbital model using the partially linearized, least-squares fitting procedure described in Wright & Howard (2009). Each velocity measurement was assigned a weight, w, constructed from the quadrature sum of the measurement uncertainty (σ_RV) and a jitter term (σ_jitter), i.e., w = 1/(σ²_RV + σ²_jitter). Following Wright (2005), and based on the values of S_HK, M_V, and B − V, we estimate σ_jitter for each of the stars (Table 3). These empirical estimates account for RV variability due to myriad sources of stellar noise, including the velocity fields of magnetically controlled photospheric turbulence (granulation, super-granulation, and meso-granulation), rotational modulation of stellar surface features, stellar pulsation, and magnetic cycles, as well as undetected planets and uncorrected systematic errors in the velocity reduction (Saar et al. 1998; Wright 2005). We adopt larger values of jitter for pre-upgrade Keck measurements (σ_jitter = 3 m s⁻¹) than for HET measurements and post-upgrade Keck measurements (σ_jitter = 2–2.5 m s⁻¹). The difference accounts for the slightly larger systematic errors incurred in the reduction of pre-upgrade spectra.

The Keplerian parameter uncertainties for each planet were derived using a Monte Carlo method (Marcy et al. 2005) and do not account for correlations between parameter errors.

For stars with small Doppler amplitudes (HD 34445 and HD 126614 A), we also explicitly considered the null hypothesis—that the velocity periodicity represented by the Keplerian orbital fit arose from chance fluctuations in the velocities—by calculating a false alarm probability (FAP) based on Δχ², the goodness-of-fit statistic (Howard et al. 2009; Marcy et al. 2005; Cumming et al. 2008). These FAPs compare the measured data to 1000 scrambled data sets drawn randomly with replacement from the original measurements. (The linear velocity trend seen in HD 126614 A was subtracted from the velocities before scrambling.) For each data set, we compare a best-fit Keplerian model to the null hypothesis (a linear fit to the data) by computing Δχ² = χ²_lin − χ²_Kep, where χ²_lin and χ²_Kep are the values of χ² for linear and Keplerian fits to the data, respectively. The Δχ² statistic measures the improvement in the fit of a Keplerian model compared to a linear model of the same data. The FAP is the fraction of scrambled data sets that have a larger value of Δχ² than for the unscrambled data set. That is, the FAP measures the fraction of scrambled data sets where the statistical improvement from a best-fit Keplerian model over a linear model is greater than the statistical improvement of a Keplerian model over a linear model for the actual measured velocities. We use Δχ² as the goodness-of-fit statistic, instead of other measures such as χ_ν for a Keplerian fit, to account for the fact that the scrambled data sets, drawn from the original velocities with replacement, have different variances, which sometimes artificially improve the fit quality (i.e., some scrambled data sets contain fewer outlier velocities and have lower rms). It is important to note that this FAP does not measure the probability of non-planetary sources of true velocity variation masquerading as a planetary signature.

HD 34445 (= HIP 24681) is spectral type G0 V, with V = 7.31, B – V = 0.66, and M_V = 4.04, placing it ∼0.8 mag above the main sequence as defined by Wright (2005). It is chromospherically quiet with S_HK = 0.15 and log R'_HK = −5.07 (Isaacson 2009), implying a rotation period of ∼22 days (Noyes et al. 1984). Valenti & Fischer (2005) measured a super-solar metallicity of [Fe/H] = +0.14 using SME. Its placement above the main-sequence and low chromospheric activity are consistent with an old, quiescent star of age 8.5 ± 2 Gyr.

We have 560 individual photometric observations of HD 34445 spanning seven consecutive observing seasons. The mean short-term standard deviation of HD 34445 is comparable to the mean standard deviations of the comparison stars (Table 2; Columns 7 and 8); both are within the range of our typical measurement precision for single observations. We performed periodogram analyses over the range of 1–100 days on the seven individual observing seasons and on the entire data sets and found no significant periodicity in either HD 34445 or the comparison stars. Therefore, our short-term variability measurements of 0.00155 and 0.00156 mag are upper limits to any real nightly brightness variability in the target and comparison stars.

Similarly, the long-term standard deviations of HD 34445 and the comparison stars are similar (Table 2; Columns 9 and 10), indicating that we have not resolved any intrinsic year-to-year variability in HD 34445. Henry (1999) and Wright et al. (2008) present data sets that have seasonal means with standard deviations as low as 0.0002 mag, which we take as our measurement precision for seasonal mean magnitudes. Thus, our non-detection of long-term variability in HD 34445 may be compromised by low-level variability in one or both of the comparison stars.

We monitored the RV of HD 34445 at Keck for the past 12 yr and at the HET for the past 6 yr. Table 4 gives the Julian Dates of the observations, the measured (relative) RVs, the associated measurement uncertainties (excluding jitter), and the telescope used. The 118 velocities listed in Table 4 have an rms of 12.0 m s⁻¹ and are plotted as a time series in Figure 3 along with the best-fit, single-planet Keplerian model.

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The velocities plotted in Figure 3 reveal a ∼2.8 yr periodicity that is apparent by visual inspection. We searched periods near 2.8 yr, and a wide variety of other periods, to find a single-planet Keplerian model with best-fit parameters, P = 2.87 ± 0.03 yr, e = 0.27 ± 0.07, and K = 15.7 ± 1.4 m s⁻¹, implying a planet of minimum mass M sin i = 0.79 M_Jup orbiting with semimajor axis a = 2.07 AU. The full set of orbital parameters is listed in Table 3.¹² This joint fit has an rms of 7.31 m s⁻¹ with χ_ν = 2.39. The planetary signal was detected in the Keck and HET data sets individually, which have an rms of 6.39 m s⁻¹ and 7.95 m s⁻¹ about the joint fit, respectively.

We also considered the null hypothesis—that the observed RV measurements are the chance arrangement of random velocities masquerading as a coherent signal—by calculating an FAP. As described in Section 4.3, we computed the improvement in Δχ² from a constant velocity model to a Keplerian model (without a trend) for 10³ scrambled data sets. We found that no scrambled data set had a larger value for Δχ² than for the measured velocities, implying an FAP of less than ∼0.001 for this scenario.

While the single-planet model appears secure, the rms of the velocity residuals (6–8 m s⁻¹) is a factor of ∼2 higher than expected based on the measurement uncertainties and jitter. Two possible explanations for this excess variability are underestimated jitter and additional planets. Jitter seems an unlikely explanation given this star's metallicity, color, and modest evolution. As a comparison, the five stars most similar to HD 34445 (B – V and M_V within 0.05 mag) with 10 or more Keck observations have velocity rms in the range 2.6–4.9 m s⁻¹. We searched a wide range of possible periods for a second planet and found several candidates, the strongest of which has P_c = 117 days, M_csin i = 52 M_⊕, and an FAP of a few percent. A significant number of additional measurements are required to confirm this planet and rule out other periods.

HD 126614 (= HIP 70623) is identified in the Henry Draper and Hipparcos catalogs as a single star. As described in Section 6.5, we directly detected by adaptive optics (AO) a faint M dwarf companion separated by 489 mas from the bright primary. We refer to the bright primary star as HD 126614 A and the faint companion as HD 126614 B. These stars are unresolved in the Doppler and photometric variability observations described below. The planet announced below orbits HD 126614 A and is named HD 126614 Ab. In addition, HD 126614 A is orbited by a second M dwarf, NLTT 37349, in a much wider orbit (Gould & Chanamé 2004). This outer stellar companion is separated from HD 126614 A by 42'' and does not contaminate the Doppler or photometric observations.

HD 126614 A is spectral type K0 V, with V = 8.81, B – V = 0.81, and M_V = 4.64, placing it ∼1.2 mag above the main sequence. It is chromospherically quiet with S_HK = 0.15 and log R'_HK = −5.44 (Isaacson 2009), implying a rotation period of 99 days, which is off the scale of the calibration, but suggests that it is longer than 50 days (Noyes et al. 1984). Valenti & Fischer (2005) measured an extremely high metallicity of [Fe/H] = +0.56 using SME. This is the highest metallicity measured in the 1040 stars in the SPOCS catalog (Valenti & Fischer 2005). The low chromospheric activity (S_HK = 0.15) is consistent with the age estimate of 7.2 ± 2.0 Gyr from the SME analysis (Valenti & Fischer 2005).

We have only 113 photometric observations of HD 126614 A covering two observing seasons. Periodogram analyses over the range of 1–100 days found no significant periodicity in either HD 126614 A or its comparison stars. The short-term variability of 0.00158 mag in the target star is comparable to 0.00163 mag in the comparison stars and to our measurement precision. The measurement of long-term variability in HD 126614 A is compromised by low-amplitude variability in one or both comparison stars. Thus, 0.0016 mag serves as an upper limit to both long- and short-term variability in HD 126624 A.

We monitored the RV of HD 126614 A at Keck for the past 11 yr. Table 5 gives the Julian Dates of the observations, the measured (relative) radial velocities, and the associated measurement uncertainties (excluding jitter). The 70 velocities listed in Table 5 and plotted as a time series in Figure 4 display a strong linear trend of 16.2 m s⁻¹ yr⁻¹ with an rms of 6.6 m s⁻¹ about that trend. For clarity, the same velocities are plotted in Figure 5 with the trend subtracted.

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After subtracting the linear trend, a Lomb–Scargle periodogram of the HD 126614 A velocities reveals a strong periodicity near 3.4 yr. This periodicity closely matches the period of the best-fit, single-planet Keplerian model, which was found after a thorough search of the Keplerian parameters. Our model of a single planet plus a linear velocity trend has a distinctive staircase-like appearance (Figure 4) and the following best-fit parameters: P = 3.41 ± 0.05 yr, e = 0.41 ± 0.10, K = 7.3 ± 0.7 m s⁻¹, and dv/dt = 16.2 ± 0.2 m s⁻¹ yr⁻¹, implying a planet of minimum mass M sin i = 0.38 M_Jup orbiting with semimajor axis a = 2.35 AU. The full set of orbital parameters is listed in Table 3. The time series velocities (with trend subtracted) are plotted with the Keplerian model in Figure 5.

This model of a single planet plus linear trend has rms velocity residuals of 3.99 m s⁻¹ and χ_ν = 1.42, implying an adequate fit. We computed an FAP for the single-planet model using the Δχ² statistic, as described in Section 4.3. We found that no scrambled data set had a larger value for Δχ² than for the measured velocities, implying an FAP of less than ∼0.001 for this scenario.

The significant linear trend of 16.2 m s⁻¹ yr⁻¹ is likely due to a long-period stellar or planetary companion. We tried fitting the observed velocities with a two-planet model, using the Keplerian parameters of HD 126614 Ab and an outer planet with a wide variety of long periods as initial guesses. We were unable to find any two-planet models that improved χ_ν with statistical significance. Put another way, with a time baseline of 10 yr we do not detect curvature in the residuals to the one-planet model.

We also considered NLTT 37349 (2MASS J14264583-0510194) as the companion responsible for the observed acceleration. Gould & Chanamé (2004) identified this object as a common proper-motion partner to HD 126614 A with a sky-projected separation of 42''. The observed photometric properties of this object are M_V = 12.02, V = 16.19, and V − J = 4.00. Presumably NLTT 37349 has the same parallax (13.8 mas) and distance (72.4 pc) as HD 126614 A. Taken together, these properties are consistent with being an M dwarf, roughly M4, implying a mass of m ∼ 0.2 M_☉. To compute the approximate gravitational influence of NLTT 37349, we assume that the line of sight separation between HD 126614 A and NLTT 37349 is comparable to their physical separation in the sky plane, r_sep ∼ 3000 AU. The acceleration predicted by this model, $\dot{v_r} \sim Gm/r_\mathrm{sep}^2 = 0.004$ m s⁻¹ yr⁻¹, is much too small to account for the observed acceleration of 16.2 m s⁻¹ yr⁻¹. Thus, NLTT 37349 is not the source of the observed linear velocity trend.

Secular acceleration is a potential cause of a linear velocity trend, especially for stars with significant proper motion (such as HD 126614 A). While our standard velocity pipeline removed this effect from the velocities reported Table 5, it is reassuring to confirm that the calculated secular acceleration is inconsistent with the observed velocity trend. (The pipeline also removed the motion of Keck Observatory about the barycenter of the Solar System.) As discussed in Kürster et al. (2003) and Wright & Howard (2009), a star's proper motion will cause the the radial component of its space velocity vector to change with position on the sky, resulting a secular acceleration of $\dot{v_r} = D\mu ^2$ (to first order), where v_r is the bulk RV of the star, D is the star's distance, and μ is the total proper motion in radians per unit time. For the most extreme cases of nearby stars with significant proper motion, $\dot{v_r}$ can be as high as a few m s⁻¹ yr⁻¹. For HD 126614 A, we find $\dot{v_r} \sim 0.1$ m s⁻¹ yr⁻¹, ruling out secular acceleration as the cause of the observed 16.2 m s⁻¹ yr⁻¹ trend.

Having ruled out the above reasons for the linear RV trend, we considered a stellar companion close enough to HD 126614 A to have been missed by prior imaging surveys. To search for such a companion, we obtained direct imaging of HD 126614 A in J, H, and K-short (K_s) bands on the Hale 200'' Telescope at Palomar Observatory on 2009 April 13 using the facility AO imager PHARO (Hayward et al. 2001). In each band, we co-added approximately one-fifty 431 ms exposures. As expected, the AO correction was best in K_s band, translating into the smallest errors. A nearby faint companion ∼500 mas to the Northeast of HD 126614 A was identified in each band by visual inspection (Figure 6). We constructed an empirical point-spread function (PSF) in each band from images of a calibrator, and images were fit with a two-PSF model. Parameter errors were calculated using the curvature of the χ² surface, and for consistency, the error in contrast ratio compared to the percent flux of the fit residuals. Combining the astrometric fits in all bands, we find a projected separation of 489.0 ± 1.9 mas at a position angle of 56.1 ± 0.3 deg.

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We are unaware of a previous detection of this faint companion to HD 126614 A, which we name HD 126614 B. We summarize the astrometric and photometric results of the AO observations and the inferred properties of HD 126614 B in Table 6.

HD 126614 A and HD 126614 B are unresolved in the spectroscopic and photometric observations described in previous sub-sections. We estimate the amount of V-band contamination from HD 126614 B in these observations using three methods: model isochrones, observations of a similar star, and an empirical calibration employing metallicity effects.

First, we interpolated the log(age) = 9.1, Z = 0.070 (corresponding very nearly to [Fe/H] = +0.56) Padova isochrones (Girardi et al. 2000) at these absolute NIR magnitudes. These interpolations yield mass estimates for HD 126614 B (Table 6), the average of which is 0.324 ± 0.004 M_☉, making HD 126614 B an M dwarf. The weighted average V-band magnitude implied by these measurements is M_V = 10.65 ± 0.03.

Second, we find that the M dwarf Gl 661 B has nearly identical NIR absolute magnitudes to HD 126614 B (Table 6; Reid & Hawley 2005). Nonetheless, its absolute V magnitude is in severe disagreement with the Z = 0.070 isochrones (and in even worse agreement with the solar metallicity isochrones). This suggests that the Padova isochrones significantly overestimate the V-band flux of M dwarfs. We thus consider the isochrone V magnitudes to be unreliable.

Finally, we have applied the M dwarf photometric calibration of Johnson & Apps (2009) to the absolute K_s magnitude derived from the AO photometry. This empirical calibration is based on G–M binaries with well-measured metallicities (from LTE spectral synthesis analysis of the primary) and K_s-band magnitudes of both components. Johnson & Apps find that a star with [Fe/H] = +0.56 and $M_{\mathrm{K_{s}}}$ = 6.75 should have M_V = 12.2. This estimate, which we feel is the most robust of the three we have performed, implies V = 16.5 and therefore negligible contamination in our optical spectra (ΔV = 7.8, < 0.1% contamination).

Knowledge of the mass of HD 126614 B from the isochrones combined with the observed RV trend of HD 126614 A allows us to constrain the true physical separation between the stars. Let θ be the angle between the line of sight to the primary and the line connecting the primary to the secondary, such that the secondary is behind the primary when θ = 0. The observed RV trend (the instantaneous acceleration along the line of sight) is related to θ, the mass of the secondary M_B, and the true physical separation r_AB by

$$\begin{equation} \dot{v_\mathrm{A}}=\frac{GM_\mathrm{B}}{r_\mathrm{AB}^2}\cos \theta, \end{equation} \tag{ 1 }$$

where r_AB is related to the apparent angular separation ρ_AB through

$$\begin{equation} \left(\frac{r_\mathrm{AB}}{\mathrm{AU}}\right)\sin \theta = \frac{\rho _\mathrm{AB}}{\pi _\mathrm{A}} \end{equation} \tag{ 2 }$$

and π_A, the Hipparcos parallax of HD 126614 A. Given the observed radial acceleration of 16.2 m s⁻¹ yr⁻¹ and the best separation and mass from Table 6, there are two solutions for the implied physical separation between the stars: r_AB = 40⁺⁷₋₄ and 50⁺²₋₃ AU (where the uncertainty is dominated by the uncertainty in the parallax), which we can crudely combine as 45⁺⁷₋₉ AU with the caveat that the probability distribution function is highly non-Gaussian.

Holman & Wiegert (1999) studied the dynamical stability of planetary orbits in binary systems. In the terms of that work, we find the mass ratio of the binary system to be μ = 0.22, at the edge of Hill's Regime. Holman & Wiegert find that for a binary in a circular orbit, planets in S-type orbits of semimajor axis a_b are generally stable when secondary stars orbit with semimajor axes a_B > a_b/0.38. For our system, this yields a_B > 6.2 AU, consistent with our AO astrometry. Indeed, the HD 126614 system unconditionally passes this weak test for stability for e_B < 0.6; beyond this regime more detailed knowledge of the binary orbit is required for further analysis.

Pfahl & Muterspaugh (2006) discuss the prevalence of planets in binary systems such as HD 126614. They note that the literature contains a few planet detections in systems separated by ∼20 AU, the most similar to HD 126614 being HD 196885 (Fischer et al. 2009). Thus, HD 126614 Ab appears to be in a stable orbit in a binary system that is not atypical, even among systems with detected planets.

The identification of HD 126614 as a stellar binary with a separation of ∼05 (unresolved by Keck/HIRES) raises the question of the origin of the periodic RV signal described in Section 6.3. We investigated the possibility that the RV variation was the result of distortions in the spectral line profiles due to contamination of the HD 126614 A spectrum by the much fainter HD 126614 B spectrum modulated by an orbital companion of its own. We present multiple lines of reasoning to argue against this alternative explanation and in favor of the Jovian-mass planet orbiting HD 126614 A described in Section 6.3.

From the AO observations in JHK bands, we estimated the V-band flux of HD 126614 B in several ways with the most reliable method giving a flux ratio (A/B) of 7.8 mag. Thus, in the iodine region of the spectrum, the lines from HD 126614 B are fainter by a factor of ∼10³. To produce a Doppler signal with K = 7 m s⁻¹ when diluted by HD 126614 A, the signal from HD 126614 B would have an amplitude of approximately K = 7 km s⁻¹(implying a companion orbiting HD 126614 B with mass 0.25 M_☉, an M dwarf). Yet, the stellar lines of HD 126614 A, with vsin i = 1.52 km s⁻¹, are narrower than the amplitude of the hypothetical K = 7 km s⁻¹ Doppler signal. Thus, the stellar line profiles of HD 126614 A and HD 126614 B would not be blended, but separated from each other for most of the 3.41 yr orbit. This inconsistency casts serious doubt on the blend scenario as an explanation for the observed RV variation.

Nevertheless, we investigated the blend scenario further with a spectral line bisector span test (Torres et al. 2005; Queloz et al. 2001). We chose a region of the spectrum (6795–6865 Å) to the red of the iodine region for increased sensitivity to the spectral features of HD 126614 B (an M dwarf) and a lack of telluric contamination. We cross-correlated each post-upgrade Keck spectrum against the solar spectrum using the National Solar Observatory solar atlas (Kurucz et al. 1984). From this representation of the average spectral line profile we computed the bisectors of the cross-correlation peak, and as a measure of the line asymmetry we calculated the "bisector span" as the velocity difference between points selected near the top and bottom of the cross-correlation peak. If the velocities were the result of a blend, we would expect the line bisectors to vary in phase with the 3.41 yr period with an amplitude similar to K = 7 m s⁻¹. Instead, we find no significant correlation between the bisector spans and the RVs after subtracting the 16.2 m s⁻¹ yr⁻¹ trend. The Pearson linear correlation coefficient between these two quantities, r = −0.28, demonstrates the lack of correlation. We conclude that the velocity variations are real and that the star is orbited by a Jovian planet.

HD 13931 (= HIP 10626) is spectral type G0 V, with V = 7.61, B – V = 0.64, and M_V = 4.32, placing it ∼0.4 mag above the main sequence. It is chromospherically quiet with S_HK = 0.16 and log R'_HK = −4.99 (Isaacson 2009), implying a rotation period of ∼26 days (Noyes et al. 1984). Valenti & Fischer (2005) measured an approximately solar metallicity of [Fe/H] = +0.03 using SME. Its placement above the main sequence and low chromospheric activity are consistent with an old, quiescent star of age 6.4–10.4 Gyr.

We have 181 photometric observations of HD 13931 over two consecutive observing seasons. Periodogram analyses found no significant periodicity over the range 1–100 days. The short-term standard deviations of the target and comparison stars (Table 2) provide an upper limit of 0.0016 mag for night-to-night variability. The long-term standard deviations suggest intrinsic low-level variability in HD 13931, but additional observations are needed to confirm it.

We monitored the RV of HD 13931 at Keck for the past 12 yr. Table 7 gives the Julian Dates of the observations, the measured (relative) radial velocities, and the associated measurement uncertainties (excluding jitter). The 39 velocities listed in Table 7 have an rms of 15.1 m s⁻¹. These velocities are plotted as a time series in Figure 7 along with the best-fit Keplerian model.

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A long period signal that has completed approximately one cycle is clearly seen in the velocities plotted in Figure 7. After trying a wide variety of trial periods, we found the best-fit, single-planet Keplerian model with P = 11.5 ± 1.1 yr, e = 0.02 ± 0.08, and K = 23.3 ± 2.9 m s⁻¹, implying a planet of minimum mass M sin i = 1.88 M_Jup orbiting with semimajor axis a = 5.15 AU. Note that the orbit is consistent with being circular. The full set of orbital parameters is listed in Table 3. This model, with χ_ν = 1.01 and 3.31 m s⁻¹ rms velocity residuals, is an excellent fit to the data. Under the assumption of a one-planet model, we observed three RV extrema with Keck that strongly constrain the orbital parameters.

Gl 179 (= HIP 22627) is spectral type M3.5 V, with V = 11.96, B – V = 1.59, and M_V = 11.5, placing it ∼0.3 mag above the main sequence. It is chromospherically active with S_HK = 0.96 (Isaacson 2009). Valenti & Fischer (2005) did not calculate stellar parameters using SME for Gl 179 because of its late spectral type. Similarly, the Noyes et al. (1984) calibration of stellar rotation does not apply for B − V > 1.4. Johnson & Apps (2009) find a high metallicity of [Fe/H] = 0.30 ± 0.10 for Gl 179 based on its absolute K-band magnitude, M_K, and V − K color.

We have not made photometric observations of Gl 179 from the APTs because at V = 11.96 the star is too faint.

We monitored the RV of Gl 179 at Keck for the past 10 yr and at the HET for the past 5 yr. Table 8 gives the Julian Dates of the observations, the measured (relative) radial velocities, the associated measurement uncertainties (excluding jitter), and the telescope used. The 44 velocities listed in Table 8 have an rms of 19.7 m s⁻¹. Because Gl 179 is a faint M dwarf, the measurements have lower signal-to-noise ratios and larger uncertainties compared to the other stars in this paper. The measured velocities are plotted as a time series in Figure 8 along with the best-fit Keplerian model.

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After trying a wide variety of trial orbital periods, we find the best-fit, single-planet Keplerian model has P = 6.26 ± 0.16 yr, e = 0.21 ± 0.08, and K = 25.8 ± 2.2 m s⁻¹, implying a planet of minimum mass M sin i = 0.82 M_Jup orbiting with semimajor axis a = 2.41 AU. The full set of orbital parameters is listed in Table 3. We allowed for floating offsets between the HET RVs, the pre-upgrade Keck RVs, and the post-upgrade RVs when fitting the data.

Note that the planet is clearly detected in the Keck RVs alone, but the HET measurements are crucial for the precise determination of orbital parameters, especially eccentricity and minimum mass. This single planet model, with χ_ν = 1.78 and 9.51 m s⁻¹ rms velocity residuals, is a statistically significant improvement over a model with no planets. However, the relatively large value of χ_ν implies that either additional planets remain undetected in the system or we have underestimated the measurement uncertainties or jitter. We will continue to observe Gl 179 to search for additional planets.