A HOT JUPITER ORBITING THE 1.7 M_☉ SUBGIANT HD 102956^*

The current state of knowledge of planets around intermediate-mass (M_⋆ ≳ 1.5 M_☉) stars is reminiscent of the general knowledge of exoplanets in 2001. At that time there were 32 planets known, mostly orbiting Sun-like stars. The distributions of semimajor axes and masses (M_Psin i) of these early exoplanet discoveries, drawn from the Exoplanet Orbit Database,⁷ are shown in Figure 1, illustrating the prevalence of giant planets in unexpectedly close-in orbits.⁸ As of 2010 May, there are 31 planets known to orbit intermediate-mass stars (M_⋆>1.5 M_☉), and the semimajor axes of planets in this new class were surprising, but for a different reason: there are no planets orbiting closer than 0.6 AU (Johnson et al. 2007; Sato et al. 2008). As Bowler et al. (2010) showed, the planet populations orbiting host stars on either side of 1.5 M_☉ are distinct at the 4σ level.

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Close-in, Jovian planets are relatively easy to detect using radial velocities because of the larger amplitude they induce and the increased number of orbit cycles per observing time baseline. Their absence therefore cannot be due to an observational bias given the large population of planets at longer periods. Instead, it appears that stellar mass has a dramatic effect on the semimajor axis distribution of planets. However, it is not clear whether this effect is a reflection of the process of planet formation and migration, or instead related to the effects of the evolution of the host stars.

Stellar evolution may be an important factor because Doppler surveys of intermediate-mass stars are largely restricted to post–main-sequence targets. While massive, main-sequence stars are poor Doppler targets due to their rapid rotation (V_rotsin i ≳50 km s⁻¹; Lagrange et al. 2009), their evolved counterparts on the giant and subgiant branches are much slower rotators (V_rotsin i ≲5 km s⁻¹) and therefore have the narrow absorption lines required for precise Doppler measurements. However, as stars evolve their atmospheres expand and may encroach upon the orbits of their planets. Simulations by Nordhaus et al. (2010), Carlberg et al. (2009), and Villaver & Livio (2009) have suggested that the engulfment planets by the expanding atmospheres of stars can account for the lack of close-in planets around K giants and clump giants (see also Sato et al. 2008).

While Doppler surveys have encountered a barren region around A stars inward of 0.6 AU, transit surveys have discovered two examples of hot Jupiters around intermediate-mass stars. OGLE2-TR-L9 and WASP-33 are 1.5 M_☉ stars orbited by Jovian planets with semimajor axes a = 0.041 AU and 0.026 AU, respectively (Snellen et al. 2009; Collier Cameron et al. 2010). These detections demonstrate that close-in planets exist around A-type dwarfs, adding additional concern that the lack of planets close to evolved intermediate-mass stars is the result of stellar engulfment. Unfortunately, the complicated observational and selection biases inherent to ground-based, wide-field transit surveys make it difficult to measure accurate occurrence rates that can be meaningfully compared to those measured from Doppler surveys (Gaudi et al. 2005).

Among the various types of evolved stars, subgiants offer a unique view of the population of hot Jupiters around intermediate-mass stars. The radii of subgiants have inflated by only a factor of ≈2 compared to their main-sequence values. The simulations of Villaver & Livio (2009) show that planets with a ≳ 0.1 AU should be safe from the tidal influence of stars near the base of the red giant branch (RGB; see their Figure 2). It is only after stars start to ascend the RGB and have their radii expand to an appreciable fraction of an AU that tidal influences become important. The occurrence rates and semimajor axis distribution of close-in planets around subgiants should therefore be representative of the properties of planets around A-type dwarfs.

We are conducting a Doppler survey of intermediate-mass subgiants at Keck and Lick Observatories to study the effects of stellar mass on the physical properties and orbital architectures of planetary systems. Our survey has resulted in the detection of 14 planets around 12 intermediate-mass (M_⋆ ≳ 1.5 M_☉) stars and four additional planets around less-massive subgiants (Johnson et al. 2006, 2007, 2008; Bowler et al. 2010; Peek et al. 2009; Johnson et al. 2010a, 2010b). In this Letter, we report the first Doppler-detected planet within 0.6 AU of a "retired" (former) A star: a hot Jupiter around a 1.68 M_☉ subgiant.

HD 102956 (= HIP 57820) is listed in the Hipparcos Catalog with V = 8.02, B − V = 0.971, a parallax-based distance of 126pc, and an absolute magnitude M_V = 2.5 (ESA 1997). Like most subgiants, HD 102956 is chromospherically quiet with an average S = 0.17 ± 0.02 and log R'_HK = −5.09 on the Mt. Wilson scale (Wright et al. 2004). We used the LTE spectral synthesis code Spectroscopy Made Easy (SME) described by Valenti & Fischer (2005) and Fischer & Valenti (2005) to estimate the spectroscopic properties. To constrain the low surface gravities of the evolved stars, we used the iterative scheme of Valenti et al. (2009), which ties the SME-derived value of log g to the gravity inferred from the Yonsei–Yale (Y²) stellar models. Our SME analysis gives T_eff = 5054 ± 44 K, [Fe/H] = +0.19 ± 0.04, log g = 3.5 ± 0.06, and V_rotsin i = 0.30 ± 0.5 km s⁻¹. We compared the star's temperature, luminosity, and metallicity to the Y² stellar model grids to estimate a stellar mass M_⋆ = 1.68 ± 0.11 M_☉ and radius R_⋆ = 4.4 ± 0.07 R_☉. All of the stellar properties are summarized in Table 1.

Table 1. Stellar Properties and Orbital Solution for HD 102956

Parameter	Value
V	8.02 ± 0.05
B − V	0.971 ± 0.01
Distance (pc)	126 ± 13
MV	2.5 ± 0.2
[Fe/H]	+0.19 ± 0.04
Teff (K)	5054 ± 44
Vrotsin i (km s−1)	0.30 ± 0.5
log g	3.5 ± 0.06
M⋆ (M☉)	1.68 ± 0.11
R⋆ (R☉)	4.4 ± 0.1
L⋆ (R☉)	11.6 ± 0.5
log R'HK	−5.09
Age (Gyr)	2.3 ± 0.5
P (days)	6.4950 ± 0.0004
K (m s−1)	73.7 ± 1.9
e	0.048 ± 0.027
TP (Julian date)	2455346 ± 0.7
ω (deg)	12 ± 40
MPsin i (MJup)	0.96 ± 0.05
a (AU)	0.081 ± 0.002
R⋆/a	0.253 ± 0.008
Nobs	22
rms (m s−1)	6.0
$\sqrt{\chi ^2_\nu }$	1.35

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We began monitoring the radial velocity (RV) of HD 102956 in 2007 April and we have gathered a total of 22 measurements. After two seasons of observing, we noticed RV variability with an rms scatter of 41 m s⁻¹, which is much larger than the scatter predicted by the measurement uncertainties and jitter levels typical of subgiants (Fischer et al. 2003; Wright 2005; Johnson et al. 2010a). Table 2 lists our RV measurements, times of observation, and internal errors (without jitter). Johnson et al. (2010a) estimate a typical jitter of 5 m s⁻¹ based on their analysis of 382 RV observations of 72 stable subgiants observed at Keck with High Resolution Echelle Spectrometer (HIRES). We add this jitter estimate in quadrature to the internal measurement errors to ensure proper weighting of the data in our orbit analysis.

To search for the best-fitting orbit, we used the partially linearized Keplerian fitting code RVLIN⁹ described by Wright & Howard (2009). As an alternative to a periodogram analysis, we first stepped through a grid of orbital periods sampled from 1 to 100 days in 5000 equal, logarithmically spaced intervals. At each step, we fixed the period, searched for the best-fitting orbit, and recorded the resulting¹⁰ $\sqrt{\chi ^2_\nu }$. We found a minimum ($\sqrt{\chi ^2_\nu }$ =1.15) at periods near 6.5 days. The next lowest minimum ($\sqrt{\chi ^2_\nu }$ =1.98) occurs at P = 3.47 days. However, with a best-fitting eccentricity of 0.95, the orbit solution is clearly unphysical.

We then allowed the period to float in our RVLIN analysis with an initial guess of P = 6.5 days and found that a single-planet Keplerian model with a period P = 6.4950 ± 0.0004 days, eccentricity e = 0.048 ± 0.027, and velocity semi-amplitude K = 73.7 ± 1.9 m s⁻¹. The fit produces RV residuals with an rms scatter of 6.0 m s⁻¹ and reduced $\sqrt{\chi ^2_\nu }$ =1.35, indicating an acceptable fit. We used the false-alarm analysis of Howard et al. (2009) to calculate FAP <0.001 (see also Johnson et al. 2010b). The resulting minimum planet mass is M_Psin i =0.96 M_Jup and the semimajor axis is a = 0.081 AU. The best-fitting solution is shown in Figure 2, where the plotted error bars are the quadrature sum of internal errors and 5 m s⁻¹ of jitter.

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After identifying the best-fitting model, we use a Markov Chain Monte Carlo (MCMC) algorithm to estimate the parameter uncertainties (see, e.g., Ford 2005; Winn et al. 2007; Bowler et al. 2010). MCMC is a Bayesian inference technique that uses the data to explore the shape of the likelihood function for each parameter of an input model. At each step, one parameter is selected at random and altered by drawing a random variate from a normal distribution. If the resulting χ² (not reduced by the number of free parameters ν) value for the new trial orbit is less than the previous χ² value, then the trial orbital parameters are added to the chain. If not, then the probability of adopting the new value is set by the difference in χ² from the previous and current trial steps. If the current trial is rejected then the parameters from the previous step are adopted. We adjusted the width of the normal distributions from which the steps are drawn until we achieved a 30%–40% acceptance rate in each parameter. The resulting "chains" of parameters form the posterior probability distribution, from which we select the 15.9 and 84.1 percentile levels in the cumulative distributions as the "one-sigma" confidence limits. In most cases, the posterior probability distributions were approximately Gaussian. The orbital parameters and their uncertainties are listed in Table 1.

As an additional check on the nature of the RV variations, we acquired photometric observations of HD 102956 with the T3 0.4 m automatic photometric telescope (APT) at Fairborn Observatory. A brief description of the T3 data acquisition and reduction procedures, as well as the utility of the APT observations for eliminating false positive detections, can be found in Johnson et al. (2010a).

The APT collected two dozen observations in the Johnson V and B photometric bands between 2010 May 30 and June 23, near the end of the 2010 observing season. The V observations scatter about their mean with a standard deviation of 0.0037 mag, consistent with T3's measurement precision for a single observation (e.g., Henry et al. 2000, Tables 2 and 3). A least-squares sine fit on the 6.4948 day radial velocity period yielded a semi-amplitude of 0.0012 ± 0.0010 mag. Identical results were obtained for the B observations. This tight upper limit to photometric variability provides strong support for the planetary interpretation of the radial velocity variations.

Our Keck and Lick Doppler surveys of subgiant stars have time baselines of three and six years, respectively, and the majority of the target stars have more than six observations with jitter-limited measurement precision ranging from 3 to 6 m s⁻¹. Our precision, cadence, and time baseline provide us with the opportunity to assess the fraction of intermediate-mass stars with hot Jupiters, which we define as planets with a < 0.1 AU. This definition is somewhat arbitrary, but it is consistent with definitions widely used by other studies of hot Jupiters, which typically focus on solar-mass stars and periods P ≲ 10 days. The most comprehensive study of this kind is that of Cumming et al. (2008), who measure an occurrence rate of f = 0.004 ± 0.003 for a < 0.1 AU, M_Psin i ⩾1 M_Jup, and primarily stars with masses M_⋆ < 1.4 M_☉. Their reported planet occurrence is consistent with f < 0.01 at 95% confidence.

Within our sample, we restrict our analysis to stars with M_⋆>1.45 M_☉ (the evolved counterparts of A-type stars), N_obs>3, V_rotsin i <20 km s⁻¹, and no evidence of double lines indicative of an SB2. Our sample contains 137 stars that meet these criteria. For each star, we first perform a periodogram analysis and use RVLIN to search for orbit solutions near the strongest periodicities using the same technique described by Marcy et al. (2005). We then evaluate the false alarm probability (FAP) by estimating the likelihood of improving χ²_ν over that of a linear fit (see Howard et al. 2009, for further details). For solutions with FAP <0.01, we record the rms of the residuals about the best-fitting orbit. For larger FAP values, we record the rms about the best-fitting linear fit to the RVs.

Next, we measure the largest velocity semi-amplitude K_up that is consistent with the observed rms scatter for simulated planets of various periods. Our method is similar to that of Lagrange et al. (2009) and Bowler et al. (2010). For each star, we sample a range of orbital periods corresponding to semimajor axes 0.04 ⩽ a ⩽ 0.10 AU.¹¹ At each fixed period, we generate a sample of 3000 simulated orbits with random phases and circular orbits sampled at the actual times of observation. For each simulated orbit, we also add 5 m s⁻¹ of random noise to simulate jitter. We then record the distribution of 3000 simulated velocity rms values and compare the distribution to the rms of the measurements. Finally, we adjust K until the measured rms is less than that of 99.7% of the simulated orbits and record the semi-amplitude as K_up at that period.

Repeating this procedure for all 137 stars provides a measure of the completeness of our survey for planets above a given M_Psin i at each semimajor axis sampled in our simulations. Figure 3 shows contours of constant completeness for our sample, together with the position of HD 102956, demonstrating that we are 95% complete for M_Psin i >1 M_Jup and a < 0.1 AU.

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Since each detection or non-detection of a hot Jupiter represents a Bernoulli trial, the fraction of stars with planets in our sampled range is given by the binomial distribution P(f|k, N) ∝ f^k(1 − f)^N−k, where N = 137 is the number of target stars containing k detections. For our sample, we measure an occurrence rate of f = 1.2^+1.2_−0.7, or f < 0.034 at 95% confidence for M_Psin i ⩾0.9 M_Jup, which includes a single detection, HD 102956 b with M_Psin i =0.96 ± 0.05. Restricting our analysis to planets more massive than 1 M_Jup, we find f < 0.025 at 95% confidence.

Based on their survey of main-sequence A-type stars, Lagrange et al. (2009) reported no planets with P < 10 days among a sample of 50 stars,¹² or f < 0.05 at 95% confidence. However, because their early-type stars are such rapid rotators, their achievable velocity precision only allowed them to rule out planets with M_Psin i ≳8 M_Jup. Thus, our estimate of the fraction of massive stars with hot Jupiters represents a significant refinement compared to the previous constraints. However, our sample size is still too small to provide a meaningful comparison with the planet fraction measured by Cumming et al. (2008) for less massive stars. An extension of our subgiants survey to the Southern sky is therefore warranted and is currently underway at the Anglo Australian Observatory (R. Wittenmyer 2009, private communication). Additional constraints will be provided by the Kepler space-based transit survey (Borucki et al. 2004).

We report the discovery of a hot Jupiter (e = 0.048 ± 0.027, M_Psin i =0.96 M_Jup, P = 6.4950 days) orbiting the subgiant HD 102956. At M_⋆ = 1.68 M_☉, HD 102956 is the most massive star known to harbor a hot Jupiter, and this short-period system is the first detected as part of a Doppler survey of evolved, intermediate-mass stars.

The existence of this planet demonstrates that the observed population of close-in planets around subgiants is largely representative of the "primordial" planet population, in that close-in planets have not been adversely affected by the relatively mild, post–main-sequence expansion of their host stars. This aspect of subgiants, together with their jitter-limited RV precision of ≈5 m s⁻¹, makes them ideally suited for studying the properties of short-period planets with a wide range of minimum masses around intermediate-mass stars.

Based on our current stellar sample, we estimate that 0.5%–2.3% of A-type stars harbor a planet with a < 0.1 AU and M_Psin i >1 M_Jup, compared to the 0.4 ± 0.3% occurrence rate around Sun-like stars (Cumming et al. 2008). While planets with a < 1 AU are unusually rare around A stars, it is possible that there exists a population of hot Jupiters (a < 0.1 AU) around intermediate-mass stars comparable to what is found around Sun-like stars. If so, then the close-in desert around A stars may simply be an exaggerated version of the "period valley" observed around Sun-like stars, marked by a deficit of planets with periods ranging from roughly 10 to 100 days, a sharp increase in the number of detected planets beyond 1 AU and a pile-up near P = 3 day (Udry & Santos 2007; Cumming et al. 2008; Wright et al. 2009). Doppler surveys of a larger number of massive subgiants, together with careful analyses of detections from transit surveys, will test this possibility.

We gratefully acknowledge the efforts and dedication of the Keck Observatory staff, especially Grant Hill, Scott Dahm, and Hien Tran for their support of HIRES, and Greg Wirth for support of remote observing. We are also grateful to the time assignment committees of NASA, NOAO, Caltech, and the University of California for their generous allocations of observing time. A.W.H. gratefully acknowledges support from a Townes Post-doctoral Fellowship at the U. C. Berkeley Space Sciences Laboratory. G.W.M. acknowledges NASA grant NNX06AH52G. G.W.H acknowledges support from NASA, NSF, Tennessee State University, and the State of Tennessee through its Centers of Excellence program. Finally, the authors wish to extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be guests. Without their generous hospitality, the Keck observations presented herein would not have been possible.