Orbital Refinement and Stellar Properties for the HD 9446, HD 43691, and HD 179079 Planetary Systems

Transiting exoplanets have become an integral part of exoplanetary science and provide not only detection and confirmation of exoplanets but also information about the radius and the atmospheric composition of the planet. Provided the star's size is known, the radius of the planet can be determined by the reduction in a star's flux as the planet passes in front of the star since the transit "depth" (or corrected depth if a close companion provides "third light" contamination) is directly proportional to the cross-sectional size of the planet. The atmospheric composition of the planet can be detected by the light from the star passing through the planet's atmosphere, through a method called transmission spectroscopy (Seager & Sasselov 2000).

Combined with the information gathered through the radial velocity (RV) method, transits enable studies of the mean density of a planet as well as its interior structure. Planets with both RV and transit observations are the most fully constrained and are the main data sources behind many statistical relationships that define our understanding of the formation and evolution of exoplanets, such as the mass–radius relationship and models of the composition of exoplanets. Thus detecting the potential transits of known RV planets is of great importance.

The Transit Ephemeris Refinement and Monitoring Survey (TERMS) is a project that seeks to detect transits of known RV planets with a broad range of orbital periods (Kane et al. 2009). The transit detection method is biased toward planets with short orbital periods close to their star as the probability of a planet transiting its star increases with decreasing distance from the star (Beatty & Gaudi 2008; Kipping & Sandford 2016). In order to detect planets further away from their star and broaden the catalog of transiting exoplanets, the TERMS team targets known intermediate- to long-period exoplanets with existing RV data in the literature. The orbital parameters of the known planets are first recalculated using the latest data from the Keck Observatory. Then a refined transit ephemeris is determined for the planet so that the planet host star can be observed during the predicted transit window. Photometry from various ground-based telescopes including two of Tennessee State University's automated photoelectric telescopes (APTs) and the Kilodegree Extremely Little Telescope (KELT) are then analyzed to determine if a transit was detected.

In this paper we present an analysis of both the host star and the planets in the HD 9446, HD 43691, and HD 179079 systems. We provide new RV data for each system, extending the time baseline of the observations and so improving the orbital parameters of the planets. From this new data, we calculated an accurate transit ephemeris and predicted the parameters of a potential transit of each known planet. We present precision photometry of HD 9446, HD 43691, and HD 179079 acquired with the APTs and KELT and determine the existence of transits of each of the known planets in these systems. We note that each of these stars falls within the gaps of the primary mission for TESS and so are unlikely to be observed by space-based instruments in the near future.

Each of the systems in this paper was detected by the RV method. The multiplanet system HD 9446 was first discovered by Hébrard et al. (2010) using the SOPHIE spectrograph. The initial orbital solution gave the inner planet (b) a period of 30.052 ± 0.027 days and the outer planet (c) a period of 192.9 ± 0.9 days. HD 43691 b was first discovered by da Silva et al. (2007), with orbital parameters updated in 2018 by Ment et al. (2018) including a refined orbital period for planet b of 36.9987 ± 0.0011 days. HD 179079 b was first discovered by Valenti et al. (2009), with updated orbital parameters including a period of 14.479 ± 0.010 days by Ment et al. (2018; see Table 1). As the precision of planetary and orbital parameters is inherently linked to how well the host star is known we present a spectral energy distribution (SED) analysis of each star in Section 3. Each of these systems has a planet that occupies the period space between 10 and 50 days and has relatively high transit probabilities (see Section 4) so were flagged as high-priority TERMS targets. Shown in Figure 1 are two diagrams that include the known transiting planets as small circles, where the data were extracted from the NASA Exoplanet Archive (Akeson et al. 2013) on 2019 December 1. Highlighted as orange circles are those transiting planets discovered using the RV method, such as HD 209458b (Charbonneau et al. 2000; Henry et al. 2000). The four planets in the three systems included in this study are indicated as large crosses. Note that these four planets are not known to transit, and so we use the radii estimates described in Section 4. The mass–radius diagram shown in the left panel indicates where the four planets fall with respect to the bulk of the known transiting planet population. HD 179079 b is expected to lie within the Neptune regime and could potentially be an interesting test of photoevaporation for low-mass giant planets (Laughlin et al. 2011; Lopez & Fortney 2013). The remaining three planets fall within the bulk of the known transiting giant planets. However, the period–mass diagram shown in the right panel demonstrates that the three largest planets in our sample are significantly removed from the bulk of the known transiting giant planet population when considering orbital period. The detection of transits for such planets would therefore be of high value in studies of mass–radius relationships for "cold" giant planets, particularly since the host stars for the three systems of our sample are all exceptionally bright (see Section 3).

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Table 1.  Stellar Properties

Parameter	HD 9446 ba	HD 9446 ca	HD 43691 bb	HD 179079 bb
Star
Spectral Type	G5 V	G5 V	G0	G5IV
V	8.35	8.35	8.03	7.95
Distance (pc)c	50.42 ± 0.35	50.42 ± 0.35	85.81 ± 0.37	69.848 ± 0.395
Teff (K)d	5793 ± 22	5793 ± 22	6093	5646
$\mathrm{log}g$ d	4.53 ± 0.16	4.53 ± 0.16	4.31 ± 0.07	4.11 ± 0.04
Fbol (${10}^{-8}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)d	1.245 ± 0.029	1.245 ± 0.029	1.764 ± 0.020	2.084 ± 0.049
[Fe/H] (dex)e	0.13 ± 0.06	0.13 ± 0.06	0.32 ± 0.03	0.35 ± 0.09
${M}_{* }\,({M}_{\odot })$ f	1.07 ± 0.08	1.07 ± 0.08	1.32 ± 0.09	1.25 ± 0.09
R* (R⊙)f	0.984 ± 0.01	0.984 ± 0.01	1.704 ± 0.023	1.792 ± 0.016
${\rho }_{* }\,({\rm{g}}\,{\mathrm{cm}}^{-3})$ f	1.59 ± 0.12	1.59 ± 0.12	0.375 ± 0.031	0.307 ± 0.023
Planet
P (days)	30.052 ± 0.027	192.9 ± 0.9	36.9987 ± 0.0011	14.479 ± 0.010
e	0.2 ± 0.06	0.06 ± 0.06	0.0796 ± 0.0067	0.0490 ± 0.0870
ω (°)	215 ± 30	100 ± 130	292.7 ± 4.8	308 ± 77
K (m s−1)	46.6 ± 3.0	63.9 ± 4.3	130.06 ± 0.84	6.22 ± 0.78
${M}_{p}\sin i\,({M}_{{\rm{J}}})$	0.7 ± 0.06	1.82 ± 0.17	2.55 ± 0.34	0.081 ± 0.02
a (au)	0.189 ± 0.006	0.654 ± 0.022	0.238 ± 0.015	0.1214 ± 0.0068

Notes.

^aPlanet parameters from Hébrard et al. (2010). ^bPlanet parameters from Ment et al. (2018). ^cGaia Collaboration et al. (2018). ^dSWEETcat catalog Santos et al. (2013). ^eHypatia Catalog Hinkel et al. (2014). ^fOur SED analysis.

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In order to detect the possible transit of the planetary systems, additional RV measurements were taken using the HIRES instrument on the Keck I telescope. Combining the newly obtained data with that already available for each system, the RV data was fit using the RV fitting tool RadVel (Fulton et al. 2018) to confirm each planet's orbital solution and look for linear trends (Section 5). These trends could potentially be indications of additional unidentified planets in the system. We search for unknown planets in the RV data and provide an analysis of the sensitivity of our search through RV injection-recovery tests in Section 5.3.

Using the transit window determined through RadVel along with the photometry from the KELT and the APTs, the newly calculated transit windows were then used to look for transits of each planet. These results are presented in Section 6.3.

The KELT and APT photometry were then used to characterize the stellar variability of each system. Starspots are a common cause of intrinsic stellar variability by inducing rotational modulation as the star rotates (e.g., Kipping 2012 and citations therein). The rotational modulation period is therefore a direct measurement of the rotational period of the star. When coupled with the spectroscopic measurement of the projected rotational velocity, it can be used to constrain the inclination of the stellar rotational axis, i_*.

As an independent determination of the basic stellar parameters, we performed an analysis of the broadband SED of each star together with the Gaia DR2 parallaxes (adjusted by +0.08 mas to account for the systematic offset reported by Stassun & Torres 2018), in order to determine an empirical measurement of the stellar radius, following the procedures described in Stassun & Torres (2016) and Stassun et al. (2017, 2018). We extracted the NUV flux from Galaxy Evolution Explorer, the B_TV_T magnitudes from Tycho-2, the Strömgren ubvy magnitudes from Paunzen (2015), the BVgri magnitudes from APASS, the JHK_S magnitudes from 2MASS, the W1–W4 magnitudes from WISE, and the G magnitude from Gaia, as available for each star. Together, the available photometry in general spans the full stellar SED over the wavelength range 0.2–22 μm (see Figure 2).

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We performed a fit using Kurucz stellar atmosphere models (Kurucz 2013), with the effective temperature (T_eff), metallicity ([Fe/H]), and surface gravity (log g) adopted from the systematic spectroscopic analyses provided in the SWEET catalog (Santos et al. 2013). The only free parameter is the extinction (A_V), which we restricted to the maximum line-of-sight value from the dust maps of Schlegel et al. (1998). The resulting fits are good (Figure 2) with a reduced χ² ranging from 1.9 to 3.4. Integrating the (unreddened) model SED gives the bolometric flux at Earth (F_bol). Taking the F_bol and T_eff together with the Gaia DR2 parallax, gives the stellar radius. Finally, we can use the empirical relations of Torres et al. (2010) and a 6% error from the empirical relation itself to estimate the stellar mass; this, in turn, together with the stellar radius provides an empirical estimate of the mean stellar density. We used the derived radius and mass to calculate a value for log g and compared our values to those from the SWEET catalog (Santos et al. 2013). We found there is a good agreement (within the uncertainties) between the values for each star. The full set of resulting parameters is summarized in Table 1 along with planet properties of the three systems drawn from the Hébrard et al. (2010) and Ment et al. (2018) papers. Note that while HD 9446 and HD 43691 are similar to the Sun, HD 179079 is an evolved star that has entered the subgiant branch.

We observed the star HD 9446 using CHIRON, a fiber-fed Echelle spectrometer with a resolution of R = 79,000 (Tokovinin et al. 2013; Brewer et al. 2014) in use at the 1.5 m telescope at Cerro Tololo Inter-American Observatory (CTIO). The CHIRON spectrum was analyzed using Spectroscopy Made Easy (SME), described in detail by Valenti & Piskunov (1996) and Valenti & Fischer (2005). The stellar parameters derived for HD 9446 from our SME analysis are consistent with those shown in Table 1. The distances to the stars shown in Table 1 are from the Gaia Data Release 2 parallaxes (Gaia Collaboration et al. 2018).

The three host stars were found within the Hypatia Catalog,¹⁵ an amalgamate database of stellar abundances for nearby FGKM-type stars (Hinkel et al. 2014). HD 9446 was observed by seven groups (Ramírez et al. 2007, 2009, 2012, 2013; Baumann et al. 2010; Brugamyer et al. 2011; Brewer et al. 2016), while HD 43691 and HD 179079 were both observed by six groups (Gonzalez et al. 2010a, 2010b; Brugamyer et al. 2011; Kang et al. 2011; Petigura & Marcy 2011; Brewer et al. 2016 and Petigura & Marcy 2011; Maldonado et al. 2013; Ramírez et al. 2014; Jofré et al. 2015; Brewer et al. 2016; Maldonado & Villaver 2016, respectively). All data sets are renormalized to the same solar scale within Hypatia, namely Lodders et al. (2009), such that they are more easily comparable. Then, when multiple groups measure the same element within the same star, the median value is used and the uncertainty is defined as the spread or range from all of the renormalized abundance determinations. The [Fe/H] values for the three target stars are consistent with those in Table 1. The other elements, including volatiles, refractory, iron-peak, and neutron-capture, are all enriched to a similar magnitude as the respective [Fe/H] values when compared to the Sun. Of note, the composition of HD 9446 is the most similar to the Sun, such that a few elements (N, O, Na, Mg, Si, S, Mn, and Cu) hover around 0.0 dex when uncertainty is taken into account. All three stars are relatively close and bright, making the systems ideal for additional characterization.

We also examine the stars for possible evidence of binary companions. HD 9446 was previously observed using speckle imaging by Wittrock et al. (2016), for which the data found no evidence of a stellar companion. Here we provide new results for one of the stars, HD 179079, using data from the Differential Speckle Survey Instrument (DSSI). DSSI is a dual-channel speckle imaging system that uses two narrowband filters with wavelengths centered on 692 and 880 nm. The details of the instrument hardware and data reduction are described in detail by Horch et al. (2009) and Howell et al. (2011). HD 179079 was observed using DSSI as part of a survey of known exoplanet host stars for binary companions (Kane et al. 2014, 2019; Wittrock et al. 2016, 2017). The star was observed using WIYN on 2016 April 19 and Gemini-South on 2016 June 29 during which periods DSSI was mounted as a guest instrument at these telescopes. No companion was detected in any of the images from our observations, with a detection limit of Δm ∼ 7 magnitudes in both channels within the range of 01–18. Given the distance to the star listed in Table 1, this corresponds to a projected range of 7–125 au for which companions of most spectral types can be excluded based on our analysis.

As TERMS targets, these planets had a relatively high likelihood of transiting their host star. Using the equation from Kane & von Braun (2008) the prior transit probability can be estimated by:

$$\begin{eqnarray}&&{P}_{t}=\displaystyle \frac{({R}_{p}+{R}_{* })[1+e\cos (\pi /2-\omega )]}{a(1-{e}^{2})},\end{eqnarray} \tag{ 1 }$$

where R_* is the radius of the star, e is the orbital eccentricity, ω is the argument of periastron, a is the semimajor axis, and the planet radius (R_p) is determined using the mass–radius relation code Forecaster developed by Chen & Kipping (2016). Our calculation does not compute the posterior transit probability, which includes prior information for the mass distribution of RV-discovered exoplanets (Ho & Turner 2011; Stevens & Gaudi 2013). Simulations by Stevens & Gaudi (2013) found only a ∼1% difference between prior and posterior transit probabilities for planets with masses in the range 100–1000 M_⊕, which likely includes HD 9446 b, HD 9446 c, and HD 43691 b. For HD 179079 b, the posterior transit probability is likely higher than the prior transit probability by ∼20% (Stevens & Gaudi 2013).

Calculating the transit probability (Equation (1)) with the planet radii estimated by Forecaster (Chen & Kipping 2016) we find that HD 9446 b, with an estimated planet radius of 1.238 ± 0.240 R_J, has a transit probability of ∼2.2% with a transit depth of 1.671 × 10⁻² ± 7.1 × 10⁻³. For HD 9446 c, with a radius of 1.197 ± 0.226 R_J, the transit probability is ∼0.7% with an expected transit depth of 1.563 × 10⁻² ± 6.4 × 10⁻³. For HD 179079 b, with a calculated radius of 0.471 ± 0.1935 R_J, the transit probability is ∼6.6% with a depth of 7.29 × 10⁻⁴ ± 7.2 × 10⁻⁴, and for HD 43691 b, with a calculated planet radius of 1.185 ± 0.218 R_J, transit probability is ∼3.1% with a depth of 5.107 × 10⁻³ ± 2.05 × 10⁻³.

We consider the transit probabilities of the four target planets with those of the full sample of RV-discovered exoplanets. We acquire the prior transit probabilities for 673 RV-discovered exoplanets from Dalba et al. (2019), which we display in Figure 3. These probabilities do not account for the known mass distribution of the sample of RV exoplanets and, therefore, are not posterior transit probabilities (Ho & Turner 2011; Stevens & Gaudi 2013). The transit probabilities we calculated with Equation (1) for HD 9446 b and c, HD 43691 b, and HD 179079 b are also prior probabilities, meaning they can be compared with those from Dalba et al. (2019). All four of these transit probabilities fall within one standard deviation of the median of the distribution (Figure 3). However, all probabilities except that of HD 9446 c are higher than the median. This suggests that these targets were relatively good candidates for transit searches especially considering their orbital periods.

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5.1. Data Acquisition: Spectroscopy

5.2. Orbital Solutions and Linear Trends

Here we present the revised orbital solutions for HD 9446, HD 43691, and HD 179079.

Each star's RV data was fit using the RV modeling toolkit RadVel (Fulton et al. 2018) in order to confirm the orbital solution and look for linear trends to determine if there were indications for additional planetary companions. RadVel enables users to model Keplerian orbits in RV time series. RadVel fits RVs using maximum a posteriori probability (MAP) and employs "modern Markov chain Monte Carlo (MCMC) sampling techniques and robust convergence criteria to ensure accurately estimated orbital parameters and their associated uncertainties" (Fulton et al. 2018). Once the MCMC chains are well mixed and the orbital parameters that maximize the posterior probability are found, RadVel then supplies an output of the final parameter values from the MAP fit, provides RV time series plots and MCMC corner plots showing all joint posterior distributions derived from the MCMC sampling.

RadVel also provides a mid transit time of each planet along with uncertainties, which when combined with the expected transit duration of the planet defines the estimated transit window of the planet.

A Keplerian orbital solution was fit to the RV data for HD 9446, HD 179079, and HD 43691 using RadVel in order to refine the orbital parameters and transit ephemeris of each system. Public RV data from SOPHIE and ELODIE published in da Silva et al. (2007) and Hébrard et al. (2010) was combined with our Keck HIRES data, which is provided in full in Tables A1, A2, and A3 in Appendix A. Gamma velocities of 21712.56 m s⁻¹, −28967.79 m s⁻¹, and −28958.18 m s⁻¹ were subtracted from the total RV values of the SOPHIE data for HD 9446, SOPHIE data for HD 43691 and ELODIE data for HD 43691, respectively, before being run through RadVel. Thus the gamma values in Tables 3–5 (σ) are in reference to these values. Tables 3–5 list the resulting median values of the posterior distributions for each parameter in the orbital solutions. The best-fit Keplerian orbital model for the system and planet orbital solutions are shown for the HD 9446 b and HD 9446 c planets in Figure 4, for planet HD 179079 b in Figure 5, and for planet HD 43691 b in Figure 6. Comparing these results with those from Table 1, each planet's orbital solution is in close agreement with the published values with the exception of HD 9446 c. Our fit presents a new best-fit period of this planet of 189.6 ± 0.13 days. Note all other variances for HD 9446 c fall within the uncertainties of the published values. We fit each system allowing the trend parameter to be free in order to look for linear trends. These trends could be indications of additional unknown planets in orbit around the host star. RadVel provides a model comparison summary with both Akaike information criterion (AIC) and Bayesian information criterion (BIC) values. The results from these model comparisons can be found in Tables B1, B2, and B3 in Appendix B. For HD 179079 both AIC and BIC methods preferred the model without a trend (see Table B3). For HD 43691 both the AIC and BIC preferred the model with a ∼1.75σ trend (see Tables 5 and B2). While this could indicate the presence of another unknown planet in the system, this is a low sigma result and so warrants only a small mention here. For HD 9446 both comparison methods prefer models with the trend parameter free, with the best fit including a ∼4.8σ trend (see Tables 3 and B1). As the results from our speckle imaging analysis in Section 3 indicated no evidence of a stellar companion, this significant trend likely indicates an additional planet in the HD 9446 system. Further RV observation of this system is required to determine the cause of this linear trend. Note the AIC and BIC comparisons of HD 9446 preferred different models (BIC preferred e_b as a fixed parameter). However, for the purposes of determining looking for linear trends, each comparison method preferred a model with a trend.

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Table 3.  MCMC Posteriors HD 9446

Parameter	Credible Interval	MAP	Units
MCMC
Pb	${30.0608}_{-0.0033}^{+0.0034}$	30.0607	days
$T{\mathrm{conj}}_{b}$	${2457790.96}_{-0.58}^{+0.56}$	2457790.98	JD
eb	${0.214}_{-0.041}^{+0.04}$	0.22
${\omega }_{b}$	$-{2.09}_{-0.22}^{+0.21}$	−2.08	radians
Kb	46.0 ± 2.1	46.1	m s−1
Pc	189.6 ± 0.13	189.58	days
$T{\mathrm{conj}}_{c}$	2457724.1 ± 2.6	2457724.1	JD
ec	${0.071}_{-0.032}^{+0.031}$	0.067
${\omega }_{c}$	$-{2.29}_{-0.65}^{+5.2}$	−3.0	radians
Kc	${60.8}_{-2.0}^{+1.9}$	61	m s−1
Other
γSOPHIE	≡44.2309	≡44.2309	m s−1
γHIRES	≡1.4458	≡1.4458	m s−1
$\dot{\gamma }$	${0.0115}_{-0.0023}^{+0.0025}$	0.0116	m s−1 day−1
$\ddot{\gamma }$	≡0.0	≡0.0	m s−1 day−2
σSOPHIE	$-{15.8}_{-1.7}^{+1.5}$	−15.0	${\rm{m}}\ {{\rm{s}}}^{-1}$
σHIRES	${11.4}_{-1.2}^{+1.4}$	10.5	${\rm{m}}\ {{\rm{s}}}^{-1}$
Derived
${M}_{b}\sin i$	${0.687}_{-0.055}^{+0.056}$	0.709	${M}_{{\rm{J}}}$
ab	${0.1892}_{-0.0065}^{+0.0061}$	0.1844	au
${M}_{c}\sin i$	1.71 ± 0.13	1.66	MJ
ac	${0.646}_{-0.022}^{+0.021}$	0.629	au

Note. Negative jitter values in the RadVel results are equal to the positive equivalent. Reference epoch for γ, $\dot{\gamma }$, $\ddot{\gamma }$: 2457752.165903.

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Table 4.  MCMC Posteriors HD 179079

Parameter	Credible Interval	MAP	Units
MCMC
Pb	${14.4708}_{-0.0035}^{+0.01}$	14.47	days
$T{\mathrm{conj}}_{b}$	${2454881.84}_{-0.29}^{+0.33}$	2454881.73	JD
eb	≡0.0	≡0.0
ωb	≡−0.0	≡−0.0	radians
Kb	${5.84}_{-0.66}^{+0.63}$	5.95	m s−1
Other
${\gamma }_{{\mathrm{HIRES}}_{\mathrm{PRE}2004}}$	$\equiv -2.2151$	$\equiv -2.2151$	m s−1
${\gamma }_{\mathrm{HIRES}}$	≡−2.0527	≡−2.0527	m s−1
$\dot{\gamma }$	${0.00048}_{-0.00037}^{+0.00039}$	0.00043	m s−1 day−1
$\ddot{\gamma }$	$\equiv 0.0$	$\equiv 0.0$	m s−1 day−2
${\sigma }_{{\mathrm{HIRES}}_{\mathrm{PRE}2004}}$	${7.4}_{-3.5}^{+7.9}$	4.6	${\rm{m}}\ {{\rm{s}}}^{-1}$
${\sigma }_{\mathrm{HIRES}}$	${4.13}_{-0.33}^{+0.35}$	3.97	${\rm{m}}\ {{\rm{s}}}^{-1}$
Derived
ab	${0.1214}_{-0.0071}^{+0.0064}$	0.1014	au
${M}_{b}\sin i$	0.076 ± 0.012	0.053	MJ

Note. Reference epoch for γ, $\dot{\gamma }$, $\ddot{\gamma }$: 2454872.463263.

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Table 5.  MCMC Posteriors HD 43691

Parameter	Credible Interval	MAP	Units
MCMC
Pb	${36.99913}_{-0.00092}^{+0.00095}$	36.99932	days
$T{\mathrm{conj}}_{b}$	${2456282.91}_{-0.14}^{+0.15}$	2456282.89	JD
eb	${0.085}_{-0.011}^{+0.012}$	0.087
ωb	−1.35 ± 0.12	−1.34	radians
Kb	130.4 ± 1.4	130.6	${\rm{m}}\ {{\rm{s}}}^{-1}$
Other
γSOPHIE	≡−12.4134	≡−12.4134	m s−1
${\gamma }_{{\mathrm{HIRES}}_{\mathrm{PRE}2004}}$	≡21.0278	≡21.0278	m s−1
γHIRES	≡21.6117	≡21.6117	m s−1
γELODIE	≡−45.0874	≡−45.0874	m s−1
$\dot{\gamma }$	$-{0.00121}_{-0.00068}^{+0.00069}$	−0.00124	m s−1 day−1
$\ddot{\gamma }$	≡0.0	≡0.0	m s−1 day−2
σSOPHIE	${10.7}_{-2.3}^{+3.3}$	9.8	${\rm{m}}\ {{\rm{s}}}^{-1}$
${\sigma }_{{\mathrm{HIRES}}_{\mathrm{PRE}2004}}$	$-{3.2}_{-9.6}^{+16.0}$	−6	${\rm{m}}\ {{\rm{s}}}^{-1}$
σHIRES	${4.85}_{-0.74}^{+0.95}$	4.16	${\rm{m}}\ {{\rm{s}}}^{-1}$
σELODIE	$-{3}_{-10}^{+16}$	−11	${\rm{m}}\ {{\rm{s}}}^{-1}$
Derived
ab	${0.238}_{-0.016}^{+0.014}$	0.227	au
${M}_{b}\sin i$	${2.57}_{-0.34}^{+0.31}$	2	${M}_{{\rm{J}}}$

Note. Negative jitter values in the RadVel results are equal to the positive equivalent. Reference epoch for γ, $\dot{\gamma }$, $\ddot{\gamma }$: 2456284.051544.

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As well as providing updated values for each planet's period, eccentricity, and semiamplitude, RadVel also derives the values for the planet semimajor axis (a) and mass (M_p sin i). These values are shown at the bottom of Tables 3–5.

Using the posteriors for the time of conjunction from the MCMC output, we calculated the transit window for each planet to use in determining if a transit of these planets had been detected (see Section 6).

5.3. Search for Additional Planets and Injection-recovery Tests

We searched for additional planet candidates in our radial velocity data using RVSearch (L. J. Rosenthal et al. 2020, in preparation), an iterative periodogram algorithm. First we define an orbital frequency/period grid over which to search, with sampling such that the difference in frequency between adjacent grid points is $\tfrac{1}{2\pi \tau }$, where τ is the observational baseline. Using this grid we compute a goodness-of-fit periodogram by fitting a sinusoid with a fixed period to the data for each period in the grid. We choose to measure goodness-of-fit as the change in the Bayesian Information Criterion (BIC) at each grid point between the best-fit one-planet model with the given fixed period, and the BIC value of the zero-planet fit to the data. We then fit a power law to the noise histogram (50%–95%) of the data and accordingly extrapolate a BIC detection threshold corresponding to an empirical false-alarm probability of our choice (we choose 0.003).

If one planet is detected we perform a final fit to the one-planet model with all parameters free, including eccentricity, and record the BIC of that best-fit model. We then add a second planet to our RV model and conduct another grid search, leaving the parameters of the first planet free to converge to a more optimal solution. In this case we compute the goodness-of-fit as the difference between the BIC of the best-fit one-planet model, and the BIC of the two-planet model at each fixed period in the grid. We set a detection threshold in the manner described above and continue this iterative search until the n+1th search rules out additional signals. Once we have a complete orbital model we can characterize the completeness of our search using injection-recovery tests, wherein we inject synthetic planet signals into the data and check whether RVSearch can recover that synthetic signal.

RVSearch was run on HD 9446, HD 43691, and HD 179079, and it successfully recovered each of the known planets in these systems. No additional planets were found via the search. Injection-recovery tests were then completed for each system to determine the completeness of the search, the results of which can be seen in Figure 7. Figure 7 shows the detection results of the injection-recovery tests for HD 9446 (top), HD 43691 (middle), and HD 179079 (bottom). The black dots indicate the known planets for each system whereas the smaller dots represent the injected planets. Dots that are purple are injected planets that were successfully recovered, and dots that are red are planets that were not recovered. The contouring shows the parameter spaces in which planets are likely to be recovered in light pink and those that have a low probability of detection in dark red. HD 9446 b and c and HD 43691 b are each in a parameter space with a high probability of recovery whereas HD 179079 b borders the area of low probability.

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Following the methods outlined in Brandt et al. (2019) and Kiefer et al. (2019) we then attempted to constrain the mass and period of the additional companion in the HD 9446 system by calculating the difference between the Gaia (Gaia Collaboration et al. 2018) and Hipparcos (van Leeuwen 2007) positions for HD 9446, deriving the proper motion and comparing the value with the Gaia proper motion. We found no evidence from the Hipparcos to Gaia positional difference to indicate there is an acceleration. The derived proper motion from the difference between the Hipparcos and Gaia positions is consistent to the Gaia proper motion to within 1σ, and so we did not attempt further to constrain the period and mass of the additional companion.

6.1. Data Acquisition: KELT Photometry

6.2. Data Acquisition: APT Photometry

6.3. Search for Transits

Using the refined transit ephemerides and orbital periods obtained in Section 5.2 along with the photometric data from KELT and the T10 and T12 APTs, transits of the known planets were searched for in each system.

The normalized observations from all observing seasons are plotted in the top panels of Figures 8 and 9 for HD 9446 b and c, HD 179079 b, and HD 43691 b respectively.

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The photometric observations within the transit window are shown for each system in the lower panels of Figures 8 and 9. The solid black line shows the transit baseline and the red line shows the binned average flux measurements for each planet. A dashed line shows the predicted transit signal expected for a central transit of the known planet. The vertical dotted lines give the ±1σ uncertainty in the timing of the transit window.

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A comparison of the in-transit and out-of-transit flux for each system reveals there is no significant difference in the flux received during these times. When compared to the expected transit depths calculated in Section 4 for each system, we can rule out a central transit for planet HD 9446 b to a certainty of 3.96σ. Due to gaps in the photometry data we can only rule out a transit of HD 9446 c to a certainty of 3.88σ for a planet with an impact parameter of up to b = 0.5778. Accounting for the data gap in the photometry of HD 43691 we can only rule out a transit to a certainty of 0.74σ for a transiting planet with an impact parameter of up to b = 0.898. For HD 179079 b a transit cannot be ruled out due to the combination of a relatively small planet with a large star and thus low signal-to-noise. Note that for grazing transits, limb darkening will cause a reduction in the transit depth and so these types of transits have not been ruled out in our analysis (Mandel & Agol 2002).

6.4. Photometric Variability of Host Stars

To check the photometric variability of all three host stars, we calculated and examined their Lomb–Scargle (L-S) periodograms (Lomb 1976; Scargle 1982). We calculated the L-S periodograms for each data set using astropy (Astropy Collaboration et al. 2013, 2018) for each observing season separately and also for the entire light curves, in the frequency range 0.01–1 cycles day⁻¹ with 10,000 equally spaced frequency steps. Frequencies above 0.98 were excluded from the analysis due to the strong periodicity peaks caused by the diurnal observing cycle.

In each periodogram, we identified the highest periodicity peak in the unexcluded frequency range as the candidate for periodic astrophysical variability. Next, we estimated the period uncertainty from the width of the periodicity peak, which we determined by fitting the peak with a Gaussian function in the frequency range equal to the inverse of the observing baseline centered at the peak's central frequency. We also scaled the period uncertainty with the peak significance by dividing it with the square root of the normalized power of the peak (VanderPlas 2018). Then, we phase folded each light curve on the identified variability period, and determined the variability amplitude and its uncertainty by fitting the phase curve with a sine function. We also calculated the rms for each light curve before and after the sinusoidal variability fit, and false alarm probability (FAP) for each periodogram and each highest peak using the Baluev approximation (Baluev 2008).

With the injection tests and by trial and error, we selected the following criteria for a statistically significant variability detection: (1) FAP of the periodicity peak has to be lower than 1%, (2) the full-amplitude of the variability has to be greater than the rms before variability fitting, and (3) the rms has to drop by at least 10% when removing the best-fit variability signal.

Following these criteria, we find that HD 9446 is variable with a period of 14.39 ± 0.19 days from our analysis of the whole APT light curve. We also detect the 14 day variability in every individual APT observing season (see Table 7). APT periodogram and variability phase curve of HD 9446 are shown in Figure 10. Given the small amplitude of about half a percent, the sinusoidal behavior of the variability, and the G5V spectral type of the host star, we conclude that the 14 day periodicity detected in the APT data is likely caused by starspots. This agrees with the expected stellar rotational period of ${12.5}_{-2.5}^{+4.1}\sin {i}_{* }$ days, which was calculated from the stellar projected rotational velocity and stellar radius, and ∼10 day period, which is based on the measurement of the chromospheric activity index (Hébrard et al. 2010).

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Table 7.  Results of the Periodicity Analysis for HD 9446 Using the APT Data

Season	Period (days)	Full Amplitude	L-S Power	FAP	Rms Before	Rms After
2015–16	14.7 ± 2.1	0.0051 ± 0.0010	0.3026	0.0003	0.0032	0.0027
2016–17	13.8 ± 2.1	0.0037 ± 0.0008	0.2186	0.0095	0.0025	0.0022
2017–18	14.1 ± 1.4	0.0096 ± 0.0013	0.3846	<0.0001	0.0055	0.0044
all	$14.39\pm 0.19$	$0.0063\pm 0.0007$	0.2697	<0.0001	0.0043	0.0037

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We did not detect the 14 day periodicity in the KELT data, which may be due to a number of reasons. First, the redder and broader KELT passband filter compared to the APT is dampening more variability amplitude, which typically peaks in the blue part of the spectrum (Oelkers et al. 2018). Second, the rms of most KELT observing seasons was higher than the APTs. Third, since the KELT and APT data sets do not temporally overlap (see Table 6), the starspots may have been absent or possibly distributed differently on the stellar surface during the KELT observations. However, the KELT periodograms of all observing seasons tentatively but consistently indicate a potential presence of around 7 day periodicity, which is compatible with half of the rotational period determined with APT, and might be interpreted as a bimodal distribution of starspots on the stellar surface. However, because the variability amplitudes indicated by the KELT are significantly lower than those detected in the APT data, and do not exceed our significance criteria, they should be regarded as tentative. Instead, we set a conservative upper limit for the variability amplitude of 0.005, equal to the rms of the entire KELT light curve.

For HD 43691 and HD 179079, we did not detect any significant periodic variability in any of the APT or KELT whole or seasonal light curves. For HD 43691 we set the APT and KELT variability amplitude upper limits to 0.002 and 0.008, and for HD 179079 to 0.002 and 0.006, respectively.

Stellar chromospheric activity is tightly linked with the stellar magnetic field and is correlated with the magnetic cycle (Hall 2008) and photometric rotational modulation (Cao & Gu 2014). We do not detect any periodicities in the Ca ii H and K chromospheric activity indices within the available observational timespans of HIRES observations (see Table 2) for any of the three host stars. The corresponding $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ measurements and their 1σ standard deviations for HD 9446, HD 43691, and HD 179079, are −4.71 ± 0.04, −4.85 ± 0.02, and −5.00 ± 0.01, respectively.

Using new RV data obtained from the Keck HIRES instrument we refined the orbital parameters of the known planets and looked for linear trends in the HD 9446, HD 179079, and HD 43691 systems. While our fits largely agreed with the published values for these systems, an improved solution for planet HD 9446 c was found, giving the outer planet an orbital period of 189.6 ± 0.13 days. We also found that for HD 9446 the best fit included a ∼4.8σ trend. As the results from our speckle imaging analysis in Section 3 indicated no evidence of a stellar companion, this likely indicates an additional planet in the HD 9446 system and so further RV monitoring of this system should be prioritized. As the discovery paper by Hébrard et al. (2010) did not report a linear trend for HD 9446, it is possible the original fit included some of the linear trend in the orbital solution for planet c. The best fit for HD 43691 included a ∼1.75σ trend. While this could also indicate the presence of another unknown planet in the system, this is a low sigma result and so warrants only a small mention here.

From the refined fits for each system we produced a transit ephemeris onto which we folded precise photometry acquired with the APTs and KELT. For planet HD 9446 b a transit can be ruled out to a certainty of 3.96σ. For HD 9446 c we can rule out a transit to a certainty of 3.88σ for a planet with an impact parameter of up to b = 0.5778, and for planet HD 43691 a transit can be ruled out to a certainty of 0.74σ for a planet with an impact parameter of up to b = 0.898. Each of these stars falls into the gaps of the primary planned mission for TESS and so are unlikely to be observed by any space-based instruments. Thus these ground-based observations are essential in determining the possible transit of the planets in these systems. Given the difficulties in ruling out a transit for HD 179079 b through ground-based photometry, the total effective success probability of the experiment is significantly lower than the transit probability described in Section 4. Excluding HD 179079 b, the maximum success probability of the remaining planets is 6% assuming HD 9446 b and HD 9446 c are coplanar, 5.3% if not.

Our analysis of the T10 APT light curve revealed a 14.39 ± 0.19 days variability period of host star HD 9446. We identify this as the rotational period of the host star. Host stars HD 43691 and HD 179079 showed no evidence of significant periodic variability.

The TERMS project aids in the detection of planetary transits by refining the orbital parameters of known RV planets and calculating a revised transit ephemeris for the planet, and now combined with TESS photometry the expected yield of this collaboration is expected to be significant (Dalba et al. 2019). Already there have been detections by TESS of known planets that utilized the ongoing RV observations made by the TERMS team (Mocnik et al. 2020; J. Pepper et al. 2020, in preparation). Precision photometry from the TESS mission will be combined with the improved orbital ephemerides from TERMS observations to search for additional transiting planets in observed systems, such as the case of Pi Mensae c (Huang et al. 2018). It is expected that many more systems observed by TERMS will have as-yet undetected additional planets that will be revealed through transits and trends seen in additional RV observations, such as that found in Wang et al. (2012). TERMS observations also contribute to the stellar characterization of exoplanet host stars (Dragomir et al. 2012).

The high quality transit ephemerides are essential for follow-up observations that will occur with future space missions. For example, transmission spectroscopic observations with the James Webb Space Telescope and direct imaging with missions such as WFIRST require that both the orbit of the planets within each system and the properties of the host star be determined to a high degree of certainty (Beichman et al. 2014; Kane et al. 2018). The refined orbital properties and transit ephemerides presented in this work will be used for observing strategy development of these systems for many years, and the ruling out of transits will allow for prioritization of other targets in future transit missions, saving valuable telescope time. The targets studied by the TERMS project provide critical refinement of the orbital parameters of known planets and enable further observations to detect the existence of additional planets in orbit about each system observed.

Thanks to the anonymous referee, whose comments greatly improved the quality of the paper. G.W.H. acknowledges long-term support from NASA, NSF, Tennessee State University, and the State of Tennessee through its Centers of Excellence program. The research shown here acknowledges use of the Hypatia Catalog Database, an online compilation of stellar abundance data as described in Hinkel et al. (2014), which was supported by NASA's Nexus for Exoplanet System Science (NExSS) research coordination network and the Vanderbilt Initiative in Data-Intensive Astrophysics (VIDA). This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of NASA's Astrophysics Data System. This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France (doi:10.26093/cds/vizier). The original description of the VizieR service was published in A&AS 143, 23.

Here we provide the as yet unpublished radial velocity measurements used in the analysis of this paper. Tables A1, A2, and A3 include the Keck HIRES radial velocity measurements of HD 43691, HD 9446, and HD 179079, respectively.

In this section we present the model comparison summary with both Akaike information criterion (AIC) and Bayesian Information criterion (BIC) values for HD 9446, HD 43691, and HD 179079, respectively.

Table B1.  Model Comparison HD 9446

AICc Qualitative Comparison	Free Parameters	Nfree	Ndata	Rms	$\mathrm{ln}{ \mathcal L }$	BIC	AICc	ΔAICc
AICc Favored Model	eb, Kb, ec, Kc, $\dot{\gamma }$, σ, γ	13	129	14.16	−522.62	1098.67	1064.66	0.00
Nearly Indistinguishable	Kb, ec, Kc, $\dot{\gamma }$, σ, γ	11	129	14.50	−526.08	1095.24	1066.04	1.38
Ruled Out	Kb, ec, Kc, σ, γ	10	129	15.54	−536.56	1110.87	1084.14	19.48
	eb, Kb, ec, Kc, σ, γ	12	129	15.29	−534.51	1117.00	1085.37	20.71
	eb, Kb, Kc, $\dot{\gamma }$, σ, γ	11	129	15.79	−536.49	1115.84	1086.64	21.98
	Kb, Kc, $\dot{\gamma }$, σ, γ	9	129	16.26	−540.43	1113.33	1089.11	24.45
	eb, Kb, Kc, σ, γ	10	129	16.44	−543.58	1124.53	1097.79	33.13
	Kb, Kc, σ, γ	8	129	16.88	−546.73	1120.75	1099.07	34.41
	Kb, $\dot{\gamma }$, σ, γ	6	129	33.75	−636.54	1292.58	1276.11	211.45
	eb, Kb, $\dot{\gamma }$, σ, γ	8	129	33.32	−635.00	1298.24	1276.57	211.91
	Kb, σ, γ	5	129	34.06	−638.04	1290.49	1276.68	212.02
	eb, Kb, σ, γ	7	129	33.74	−637.10	1297.53	1278.44	213.78
	Kc, $\dot{\gamma }$, σ, γ	6	129	43.66	−668.97	1357.00	1340.53	275.87
	Kc, σ, γ	5	129	44.08	−670.22	1354.68	1340.87	276.21
	ec, Kc, σ, γ	7	129	43.87	−669.74	1363.49	1344.40	279.74
	ec, Kc, $\dot{\gamma }$, σ, γ	8	129	43.53	−668.69	1366.22	1344.54	279.88
	σ, γ	2	129	53.53	−694.73	1389.28	1383.66	319.00
	$\dot{\gamma }$, σ, γ	3	129	53.20	−694.03	1392.73	1384.35	319.69
	eb, Kb, ec, Kc, $\dot{\gamma }$, γ	11	129	14.59	−1720.01	3483.12	3453.92	2389.26
	Kb, ec, Kc, $\dot{\gamma }$, γ	9	129	15.07	−1806.56	3646.11	3621.89	2557.23
	eb, Kb, Kc, $\dot{\gamma }$, γ	9	129	16.26	−2016.26	4064.95	4040.73	2976.07
	Kb, Kc, $\dot{\gamma }$, γ	7	129	16.76	−2101.19	4224.76	4205.66	3141.00
	eb, Kb, ec, Kc, γ	10	129	16.11	−2141.88	4318.99	4292.26	3227.60
	Kb, ec, Kc, γ	8	129	16.18	−2179.70	4384.89	4363.21	3298.55
	eb, Kb, Kc, γ	8	129	17.38	−2352.36	4729.83	4708.15	3643.49
	Kb, Kc, γ	6	129	17.65	−2412.14	4839.35	4822.88	3758.22
	eb, Kb, $\dot{\gamma }$, γ	6	129	34.00	−11728.06	23472.15	23455.67	22391.01
	Kb, $\dot{\gamma }$, γ	4	129	33.74	−12298.96	24604.46	24593.34	23528.68
	eb, Kb, γ	5	129	35.59	−12696.38	25397.32	25383.51	24318.85
	Kb, γ	3	129	35.02	−13079.73	26156.88	26148.49	25083.83
	ec, Kc, $\dot{\gamma }$, γ	6	129	44.71	−17516.10	35051.55	35035.08	33970.42
	Kc, $\dot{\gamma }$, γ	4	129	44.42	−17565.82	35141.27	35130.16	34065.50
	ec, Kc, γ	5	129	45.43	−18105.53	36225.48	36211.66	35147.00
	Kc, γ	3	129	45.07	−18160.39	36325.53	36317.14	35252.48
	$\dot{\gamma }$, γ	1	129	53.39	−27445.77	54886.50	54883.67	53819.01
	γ	0	129	53.60	−27570.93	55131.95	55131.95	54067.29

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Table B2.  Model Comparison HD 43691

AICc Qualitative Comparison	Free Parameters	Nfree	Ndata	Rms	$\mathrm{ln}{ \mathcal L }$	BIC	AICc	ΔAICc
AICc Favored Model	eb, Kb, $\dot{\gamma }$, σ, γ	10	67	11.47	−224.05	501.61	483.49	0.00
Nearly Indistinguishable	eb, Kb, σ, γ	9	67	11.48	−226.02	501.65	484.96	1.47
Ruled Out	Kb, σ, γ	7	67	13.41	−245.37	531.91	518.38	34.89
	Kb, $\dot{\gamma }$, σ, γ	8	67	13.37	−244.83	535.08	519.92	36.43
	σ, γ	4	67	89.30	−373.15	774.61	766.44	282.95
	$\dot{\gamma }$, σ, γ	5	67	88.39	−372.45	777.42	767.38	283.89

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Table B3.  Model Comparison HD 179079

AICc Qualitative Comparison	Free Parameters	Nfree	Ndata	Rms	$\mathrm{ln}{ \mathcal L }$	BIC	AICc	ΔAICc
AICc Favored Model	Kb, σ, γ	5	93	4.19	−268.46	549.03	537.06	0.00
Nearly Indistinguishable	Kb, $\dot{\gamma }$, σ, γ	6	93	4.16	−267.75	552.14	537.93	0.87
Ruled Out	σ, γ	2	93	6.06	−301.06	600.65	595.72	58.66
	$\dot{\gamma }$, σ, γ	3	93	6.05	−300.95	604.96	597.63	60.57

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