THE CALIFORNIA PLANET SURVEY IV: A PLANET ORBITING THE GIANT STAR HD 145934 AND UPDATES TO SEVEN SYSTEMS WITH LONG-PERIOD PLANETS ^**affiliationmark:

The possibility of “Earth 2.0”, and especially another planet that hosts life, drives much of the search for exoplanets. As of 2014 November, efforts over two decades have uncovered more than 1400 planets and almost 4000 planetary candidates (Han et al., 2014; Burke et al., 2014, ; exoplanets.org). The variety of discoveries, from lone Jupiter-mass planets in few-day orbits to packed systems with multiple planets that fit within Mercury’s orbit, raises a significant question as to the nature of our solar system: Are we unique?

To search for analogs of the solar system, we target multi-planet systems and long-period giant planets, reminiscent of our own outer solar system. Because we seek planets with orbits of at least a few hundred days, the radial velocity (RV) method of exoplanet detection is advantageous (e.g. Wright & Gaudi, 2013; Butler et al., 1996; Mayor & Queloz, 1995). The RV method is the longest running, with multiple surveys studying thousands of stars. In our study, we utilize up-to-date velocities from Keck observatory’s High Resolution Echelle Spectrometer (HIRES; Vogt et al., 1994) and complementary, published velocities from other telescopes, where available.

So far, the number of planets discovered by RVs with periods greater than 1000 days is 103, only 16 of which have periods longer than 3000 days. This is in contrast to the 336 such planets with shorter periods.¹¹1We follow Han et al. (2014), who adopt a upper limit on minimum mass of 24 times the mass of Jupiter Our intent is to enlarge this sample of long-period planets to search for planetary systems with Jupiter analogs. Of these 103 planets, 31 are in multi-planet systems. The study of multi-planet systems addresses planetary formation, migration, and dynamics. Having a large sample can also contribute to the understanding of the evolution and lifetime of stable planetary systems. Studies can examine the orbital eccentricities and perform dynamic simulations and probe migration.

For the purposes of this discussion, we follow Wang et al. (2012) and define a Jupiter analog as a planet with $P>8$ yr, $4>M\sin(i)>0.5M_{\rm Jup}$, and $e<0.3$, but we also adopt an upper period limit of $P<16$ yr. Of the confirmed RV planets, only 13 planets fit the above criteria (Han et al., 2014). Another motivation for studying systems with long-period Jupiter analogs is the role such a Jovian planet may play in the habitability of an Earth-like planet in the same system. Wetherill (1994) argued that Jupiter acts as a shield that deflects comets originating from the Oort Cloud or Kuiper Belt, protecting the inner solar system. Without Jupiter, Wetherill (1994) suggested an increase in the frequency of cometary impacts on Earth by 1000 – 10,000 times the present–day value. Multi-planet systems serve not only as examples of planet-planet interaction but also as models for plane–comet dynamics.

Section 2 gives an outline of the steps taken for characterizing the planetary systems. In Section 3, we describe the planetary systems orbiting seven stars. Each of these systems already has at least one planet known and exhibits RV residuals indicative of an outer companion. Additionally, each can have its planetary orbits significantly refined with our new velocities from Keck, and in some cases we show that an outer, decade-long planetary orbit has finally completed. We present a summary of the radial velocity data, mean uncertainties, and telescope offsets in Table 1. Table 2 lists the stellar parameters of the target stars. Table 3 lists the orbital parameters of the planets presented in this paper. We also present figures showing the RV curves and residuals for each system. Section 4 presents an analysis of a new planet, HD 145934 b. We discuss our findings and future prospects in Section 5.

We combine previously published data from other telescopes to complement the time span and quantity of Keck-HIRES observations obtained by the California Planet Survey (Howard et al., 2010; Johnson et al., 2010; Wright et al., 2011) for many purposes, including as part of the $\eta_{\oplus}$ survey (Howard et al., 2009, 2010, 2011a, 2011b). At the time of the first confirmed RV planet, 51 Pegasi b (Mayor & Queloz, 1995), several surveys were underway and actively monitoring stars for the signs of planets (e.g. Cochran & Hatzes, 1994; Fischer et al., 2014). The discovery team for 51 Pegasi used the ELODIE spectrograph (Baranne et al., 1996), which was part of the Northern Extrasolar Planet Search until the SOPHIE spectrograph (Bouchy & Sophie Team, 2006) replaced it in 2006. The CORALIE spectrograph (e.g.  Queloz et al., 2000) was situated in Chile as part of the Southern Sky extrasolar Planet search Programme. It has been joined by HARPS (Mayor et al., 2003), also located in Chile. We make use of literature data from all four spectrographs in this work. Other data come from High Resolution Spectrograph (HRS) of the Hobby-Eberly Telescope (Tull, 1998), the Tull Spectrograph at the 2.7-m telescope of McDonald Observatory (Tull et al., 1995), and the Hamilton spectrograph at Lick Observatory (Vogt, 1987).

To analyze and fit the data, we use the Wright & Howard (2009) RVLIN package written in IDL that naturally handles multiplanet systems using data from multiple telescopes in systems where planet–planet interactions are negligible given the precision and the span of the observations. In this package, RV curves are described by both non-linear and linear parameters, and the package performs least-squares fitting on them separately. The package uses a simple linear least-squares solution for the linear parameters, and the Levenberg–Marquardt algorithm for the nonlinear parameters. RVLIN supplies a sum-of-Keplerians model (plus optional secular trend and offsets between instruments) to MPFIT , the IDL implementation of the LM method developed by Markwardt (2009).

We fit for these new planetary system as follows: (1) we collect Keck RVs before and after the 2004 HIRES upgrade separately to account for any (small) offsets between the pre- and post-upgrade time series (e.g., Kane et al., 2014); (2) we collect literature RVs for the system from other telescopes, if available (3) we use the published orbital parameters (which we collect from the Exoplanet Orbit Database; Han et al., 2014) as initial guesses for the planets’ orbits; (3) we use RVLIN to fit the system anew (with additional planets contributing five model parameters each, if necessary); (4) we use the reduced $\chi^{2}$($\chi^{2}_{\nu}$) to describe the goodness of fit.

We calculate most orbital parameter uncertainties using BOOTTRAN (Wang et al., 2012), which uses RVLIN and a bootstrapping method to compute the distribution of parameters consistent with the data. Because uncertainties can be highly non-Gaussian for planets with incomplete orbits, we also examine the minimum $\chi^{2}$ surface in minimum mass-period space (Section 3).

For our fits, we choose values for the jitter (Wright, 2005, and references therein) that yield $\chi^{2}_{\nu}$ values close to 1; usually we pick a value similar to the rms of the initial fit which does not incorporate jitter. If a star has data from several (more than three) instruments taken by multiple teams, we apply jitter on an instrument-by-instrument basis. To do so, we ran the fit with no assumed jitter, calculated for each instrument the standard deviation of the residuals, and added that value in quadrature to the velocities. After that, we rerun the fit and that yielded the best-fit parameters. We utilized an instrument-by-instrument jitter for HD 24040, HD 74156, and HD 217107. In general, we are confident in the relative instrumental uncertainties in the pre- and post-upgrade HIRES data, and we use a common jitter value for both.²²2The effect of jitter on the best fit values of an orbital solution is to give more even weight to points with different measurement uncertainties; in the cases of the well-detected planets we discuss in this work, the exact value of the jitter has very little effect on these best-fit values. Because we determine most of our parameter uncertainties via bootstrapping, our uncertainties are not strongly affected by our choice of jitter, and so there is no need to find the precise jitter value that yields $\chi^{2}_{\nu}=1.0$. Table 2 lists the stellar parameters of host stars, and Table 3 lists the orbital parameters of the planets we discussed below. Corresponding RV plots and additional figures follow the text.

Sun-like stars are known to have magnetic cycles with periods comparable to the period of Jupiter (Baliunas et al., 1995). A persistent concern in the hunt for long-term RV signals from Jupiter analogs has been that they might be mimicked by the effects of such magnetic cycles, which could alter convective patterns such that the magnitude of the disk-integrated convective blueshift of a star might vary with the stellar cycle (Dravins, 1985; Walker et al., 1995; Deming et al., 1987; Santos et al., 2010).

A common way to check that magnetic effects are not responsible for RV variations is to measure correlations between the RVs and activity indices such as Ca II H & K. Previous work by Wright et al. (2008), Santos et al. (2010), and Lovis et al. (2011) find that the observed activity-cycle-induced RV amplitudes are typically quite small (a few m s^-1 or less), although there are suggestions that a few stars may show abnormally high levels of correlation (at the level of 10–20 m s^-1).

We have checked for activity cycles in these stars to see if they have similar periods and phases to the RV measurements. To do this, we have used the Ca II H & K chromospheric activity measurements from Wright et al. (2004, hereafter W04), Isaacson & Fischer (2010, hereafter IF10), and more recent measurements made using the same data stream and pipeline as the latter work. For some stars, there appear to be calibration differences between the measurements published by W04 and those made using the IF10 pipeline, necessitating a rescaling or application of an offset to one of the streams. This is most apparent in “flat activity” stars which show no variation but occasionally exhibit a large jump in activity level between the two data streams.

In six of our stars, there is no appreciable activity variation (i.e., they are “flat activity” stars, Saar et al., 1998), making it very unlikely that the large RV variations we see are due to solar-type activity cycles. The seventh star, HD 183263 does show a significant cycle, however. The W04 activity levels decrease from 2002 to 2004, and the IF10 show a continued decrease starting in late 2004, which bottoms out in a minimum in 2012. The actual velocities show a minimum in 2005 and a maximum in 2012, thus exhibiting a shorter period than the actual activity cycle. The negative correlation between 2005–2012 and the very high amplitude of the RV signals are inconsistent with typical stars with RV-activity correlation seen in Wright et al. (2008) and described by Lovis et al. (2011). It is thus very unlikely that any of the long-period signals we describe in this work are due to stellar magnetic activity cycles.

In some cases, we find that a secular increase or decrease in the observed radial velocities is present (a “linear trend”), which is presumably a small portion of a Keplerian signal from a massive companion, typically an outer planet, or a secondary star or brown dwarf (Crepp et al., 2012, 2013a, 2013b, 2014; Montet et al., 2014; Knutson et al., 2014).

When the trend shows no curvature and we have no AO imagery to put limits on the mass and angular separation of companions, we usually say very little about the companion beyond a minimum mass (and a maximum luminosity from the fact that its spectrum did not complicate the RV analysis). The scenario that gives the minimum mass to a companion generating a linear trend of a given magnitude is one that has $e\sim 0.5$, $\omega=90^{\arcdeg}$, which produces a sawtooth-like RV curve with a long, nearly linear component for $\sim 80\%$ of the orbit with a brief, high-acceleration component during periastron for the other $\sim 20\%$ (Wright (2006), and see top panel of Figure 1 for an example; other panels show other pathological cases with radically different periods and semiamplitudes that mimic the same trend).

The minimum mass of a planetary companion detected only by its strongly detected constant acceleration $\dot{\gamma}$, is thus derived by solving the mass function for the minimum mass (e.g., Wright & Howard, 2009) assuming $P\sim 1.25\tau$ (where $\tau$ is the span of the observations), $e\sim 0.5$, and $K\sim\tau\dot{\gamma}$:

Wright et al. (2007) reported a substellar companion to the star HD 24040 with a wide range of possible periods ($10$ yr $<P<100$ yr) and minimum masses ($5<M\sin i<20M_{\rm Jup}$). Boisse et al. (2012), combining velocities from HIRES, SOPHIE, and ELODIE, determined an orbit of $3668^{+169}_{-171}$ days (corresponding to  10 yr) and a minimum mass of $4.01\pm 0.49M_{\rm Jup}$ for HD 24040 b. Boisse et al. (2012) also found a linear trend of $3.85^{+1.43}_{-1.29}$ m s^-1 yr^-1, indicative of a third body in the system. Boisse et al. (2012) also investigated potential long-term correlation between SOPHIE measurements and stellar activity indices but did not find such behavior.

We present an updated fit with more recent Keck-HIRES velocities, seen in Figure 2 and Table 4. We use HIRES data and published SOPHIE and ELODIE data, so in our fit we applied jitter instrument-by-instrument. With 107 velocities in total, 47 of which are from HIRES, 13 from SOPHIE, and from 47 ELODIE (Boisse et al., 2012), we find for the best-fit one-planet Keplerian model an rms of 13.62 m s^-1 and $\chi^{2}_{\nu}$ of 0.93. HD 24040 b orbits at a semimajor axis of $4.637\pm 0.067$ AU, corresponding to a period of 9.5 yr, making it a good Jupiter analog in terms of its orbit (however, its minimum mass is $4.10\pm 0.12M_{\rm Jup}$). The linear trend is $1.8\pm 0.4$ m s^-1 yr^-1 (lower than reported in Boisse et al., 2012), a minimum mass of at least 1.44 $M_{\rm Jup}$ according to Equation (1). Our fit for HD 24040 b, with a period of $3490\pm 25$ days and minimum mass of $4.10\pm 0.12M_{\rm Jup}$, is in good agreement with the solution from Boisse et al. (2012).

Butler et al. (2006) announced HD 66428 b, a planet with $P=1973\pm 31$ d (5.4 yr), $e=0.465\pm 0.030$, and $M\sin(i)=2.82\pm 0.27M_{\rm Jup}$. We update the orbital parameters with a total of 55 velocities from HIRES (see Figure 3). The original fit used 29 velocities taken with HIRES from 2000 to 2006. Our new fit adds 26 new data points through late 2013. Capturing two complete orbits of HD 66428 b, the fit has an rms of 3.14 m s^-1 where we assumed a jitter of 3 m s^-1 and $\chi^{2}_{\nu}$ of 0.96. We determine a period of $2293.9\pm 6.4$ days, or 6.3 yr. We determine a minimum mass of $3.195\pm 0.066M_{\rm Jup}$, which is more massive than reported in Butler et al. (2006).

Given our larger set of radial velocities, it is understandable that our solution does not match with the solution announced in Butler et al. (2006). The final fit finds a previously unreported linear trend of $-3.4$ $\pm$ 0.2 m s^-1 yr^-1 (corresponding to a minimum mass for the outer companion of at least 1.77 $M_{\rm Jup}$, by Equation (1)).

We run the fit with no jitter and no trend in order to see the significance of the detected trend. For that case, $\chi^{2}_{\nu}$ is 52.56, and the rms of the residuals is 7.46 m s^-1. To compare, we found an rms of 3.14 m s^-1 and $\chi^{2}_{\nu}$ of 8.23 for seven free parameters (including the trend) and no jitter. Given the improvement in the fit with a trend included, the trend is significant. We also note that the eccentricity of the orbit is large: $0.442\pm 0.016$. The trend may indicate that the outer companion has influenced the orbit of the b component. Further monitoring will determine the nature of the source of the trend (i.e., whether it is due to a stellar or planetary companion).

Naef et al. (2004) described the HD 74156 two-planet system as a 1.86 $\pm 0.03M_{\rm Jup}$ planet in a 51.64 $\pm$ 0.011 day period with a 6.17 $\pm 0.23M_{\rm Jup}$ outer companion in a 5.5 yr orbit. Multiple authors have suspected a third planet in the system. Barnes & Raymond (2004) predicted one based on the Packed Planetary System hypothesis, and Bean et al. (2008) claimed the discovery of a companion with $P=336$ days as the third planet. Based on analysis of RV jitter, Baluev (2009) questioned the validity of HD 74156 “d” as a false detection due to annual systematic errors from HRS. Wittenmyer et al. (2009) concluded that the third planet was unlikely to be real, and Meschiari et al. (2011) updated the system with further observations and reached the same conclusion.

Here, we combine 226 velocities from CORALIE and ELODIE (44 and 51 observations Naef et al., 2004), HRS (82 Bean et al., 2008), and HIRES (52) (see Figure 4). We apply a two-planet Keplerian model. We added jitter instrument-by-instrument, and our fit has an rms of 11.03 m s^-1 and $\chi^{2}_{\nu}$ of 0.97. We have captured at least two orbits of HD 74156 c, making our orbital solution more robust than previously reported solutions. Table 3 lists the orbital parameters. HD 74156 c is one of the more massive planets we have examined, with minimum mass $7.997\pm 0.095M_{\rm Jup}$. Both planets have large orbital eccentricities ($e=0.64$ and $e=0.38$ for b and c respectively).

In Figure 5 we plot the Lomb–Scargle periodogram (Scargle, 1982; Horne & Baliunas, 1986) of the residuals to our best two-planet fit. There is no indication of any power at the period of the purported $d$ component, a result which is consistent with prior refutations of this signal (indeed, our analysis here uses much of the same data as previous work on the topic). Indeed, there is no hint of significant power at any period, indicating that there is no detectable third planetary companion in this system.

First reported by Marcy et al. (2005), the HD 183263 system showed a residual linear trend in addition to a 3.7$M_{\rm Jup}$ planet in a 634-day period. Wright et al. (2007) attributed the new and significant curvature in the residuals to an outer companion. Wright et al. (2009) followed up and constrained the minimum mass (3.57 $\pm$ 0.55 $M_{\rm Jup}$) and period (8.4 $\pm$ 0.3 yr) for the outer companion, HD 183263 c, to which we report an updated set of parameters.

With 66 velocities from HIRES, we implemented a fit with an rms of 3.68 m s^-1 and an assumed jitter of 3.2 m s^-1. Figure 6 presents the RV curves for the system as well as the residuals. The orbit for HD 183263 c appears to have finally closed, and it is significantly closer to circular ($e=0.051\pm 0.010$) and has a longer period than the solution from Wright et al. (2009), which found $e=0.239\pm 0.64$ and $P\sim 8.5$ yr. We find for HD 183263 c, that $P=4684\pm 71$ days, or 9.1 yr; $M\sin i$ is $6.90\pm 0.12M_{\rm Jup}$. While our best fit orbital solution does not match well with the previous orbital solution, our solution resides comfortably within the stable portion in the $P_{c}$–$M_{c}\sin i_{c}$ space found by Wright et al. (2009, see their Figure 3).

Butler et al. (1998) discovered HD 187123 b, a $0.52M_{\rm Jup}$ planet in a 3-day orbit. After many years of continued monitoring of this system, Wright et al. (2007) announced a long-period outer companion with $P>10$ yr and a minimum mass between 1.5 $M_{\rm Jup}$ and 10 $M_{\rm Jup}$. Wright et al. (2009) presented a solution that constrained the mass and period of an outer companion to within 20%, with $P=10.4\pm 1.2$ yr and $M\sin i=2.0\pm 0.3M_{\rm Jup}$. Figure 7 shows an updated fit with HIRES data. Naef et al. (2004) provide ELODIE velocities; however, since they have significantly worse precision and do not add temporal coverage, we do not use them here. The 108 Keck observations still cover multiple orbits of the planets; assuming a jitter of 2.23 m s^-1, we find an rms of 2.66 m s^-1. From our fit, the period of HD 187123 c is $9.1\pm 0.13$ yr and the minimum mass is $1.818\pm 0.035M_{\rm Jup}$. HD 187123 c appears to be a Jupiter analog, although its orbit is somewhat eccentric at $e=0.280\pm 0.022$.

Fischer et al. (1999) presented HD 217107 b as a 1.27 $M_{\rm Jup}$ planet in a 7.12-day period. A few years later, Fischer et al. (2001) identified a linear trend in the residuals, which was likely caused by an outer companion. Vogt et al. (2005) reported the first orbit for HD 217107 c, modestly constrained at $P=8.6$ yr and $M\sin i=2.1M_{\rm Jup}$. Wright et al. (2009) constrained the orbit and mass of HD 217107 c to almost within 10%, with $P\sim 11.7$ yr and the minimum mass $\sim 2.6M_{\rm Jup}$.

As with the case of HD 74156, we also have data taken by different teams from several instruments, we added jitter instrument-by-instrument. In our fit, we use velocities from Keck (128 observations), Lick (Wright et al., 2009, 121), and CORALIE (63 Naef et al., 2001) to find a fit an rms of 10.29 m s^-1 (see Figure 8).

Because the outer planet has only barely (apparently) completed an orbit, its orbital parameters may be especially uncertain (and are particularly sensitive to the assumption that there is not a third, longer-period planet contributing significantly to the velocities). To explore the robustness of our derived orbital period of the $c$ component as a function of its minimum mass, we have constructed a $\chi^{2}$ map in $P$–$M\sin{i}$ space (a variety of what Knutson et al. (2014) call “Wright diagrams”; see Patel et al. (2007), Wright et al. (2009) and similar approaches taken in, e.g., Dumusque et al. (2011); Boisse et al. (2012)). In this map all orbital parameters have been optimized (i.e., they are at their maximum likelihood in a $\chi^{2}$ minimum sense) for each pair of $P_{c}$ and $M_{c}\sin{i_{c}}$ in the map (except for the offsets among the four instruments, which are held constant at their overall best-fit values).

Figure 9 shows the $\chi^{2}$ contour map, revealing that the orbital period and minimum mass for HD 217107 c are well constrained with $P=14.215_{-0.04}^{+0.045}$ yr and $M\sin i=4.51_{-0.02}^{+0.07}M_{\rm Jup}$. These uncertainties are roughly consistent with the uncertainties determined via bootstrapping, which yields $P=14.215\pm 0.06$ yr and $M\sin i=4.51\pm 0.07M_{\rm Jup}$. This validates our choice of stellar jitter for this star, since the contours in the $\chi^{2}$ maps are sensitive to the choice of jitter, while the bootstrapping uncertainties are almost completely independent of it. We report the bootstrapping uncertainties in Table 3.

To test the importance of our assumption that there are only two planets contributing detectable accelerations to the star, we repeated our bootstrapping analysis with a model that includes an additional, linear trend to the data. Though there is no statistical need to include such a trend in our model, giving our model the freedom to include one could, in principle, affect the best-fit parameters for the outer planet. Indeed, though the parameters of the $b$ component do not change significantly in this model (as expected given its high frequency) we find a slightly different best-fit with such a model, with $P_{c},T_{{\rm p},c}$, and $K_{c}$ all changing by 2–4 $\sigma$, resulting in a minimum mass for the outer companion of $4.37M_{\rm Jup}$. The uncertainties on the parameters of the $c$ component in the with-trend model are larger by a factor of 2–4, comfortably including most of the parameter estimates from the no-trend model. We conclude that our choice not to include a linear trend does not have a large effect on our conclusions or parameter estimations.