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EVIDENCE FOR THE TIDAL DESTRUCTION OF HOT JUPITERS BY

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Citation Schlaufman, Kevin C., and Joshua N. Winn. “EVIDENCE FOR THE TIDAL DESTRUCTION OF HOT JUPITERS BY SUBGIANT STARS.” The Astrophysical Journal 772, no. 2 (July 17, 2013): 143.

As Published http://dx.doi.org/10.1088/0004-637X/772/2/143

Publisher IOP Publishing

Version Author's final manuscript

Citable link http://hdl.handle.net/1721.1/89209

Terms of Use Creative Commons Attribution-Noncommercial-Share Alike

Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ arXiv:1306.0567v1 [astro-ph.EP] 3 Jun 2013 nepeain aebe rpsd h rtpos- first conflicting The of Two scarcity proposed. the stars. been finding, evolved have first around interpretations the Jupiters understand hot to sire 2010b). al. and et stars Johnson evolved metallic- (e.g., of systematic stars samples of main-sequence the possibility between compli- differences the ity more of is a because comparison Third, cated this long-period although evolved. host to , is appear giant stars evolved of host fraction are the Second, larger planets when giant 2010a). lower al. long-period typically et of eccentricities Johnson orbital 2010; the al. et (“hot Bowler stars planets main-sequence (e.g., than giant stars close-in evolved fewer around are Jupiters”) re- there three First, least or- at population spects. in the stars, main-sequence from solar-type differs biting popula- stars evolved giant around the tion that evidence provided has work a ta.(00,St ta.(00,Lee l 21,2013), a (2011, et al. Liu et Lee (2010), (2007), al. (2012). a et al. al. et Sato et et Liu (2010), Sato Omiya (2009), Hatzes al. al. D¨ollinger et et (2006), (2008), (2007), Han al. al. et et et al. Sato al. se Butler Sato et (2008), D¨ollinger et Fischer (2002), stars, (2005), al. giant al. et (2006), For et Frink (2007), Setiawan (1993), Johnson (2011a,b). Cochran (2003), (2010), & al. al. al. Hatzes et et et example Johnson Robinson Bowler and (2008), al. (2010a,c), et (2007), Johnson (2007), al. et Johnson ugatsas swl svr vle in stars. giant evolved very as evolved well moderately as include stars, also subgiant These planets have stars. giant evolved Jupiter-mass there around of discoveries stars, numerous FGKM been main-sequence targeted abig,Msahsts019 USA 02139, Massachusetts Cambridge, shafmteu [email protected] [email protected], 3 h okdsrbdhr a oiae ytede- the by motivated was here described work The lhuhrda eoiypae uvy aemainly have surveys planet velocity radial Although rpittpstuigL using typeset Preprint press in ApJ al nttt o srpyisadSaeRsac,Massa Research, Space and Astrophysics for Institute Kavli 2 1 o ugatsas e o xml azse l (2003), al. et Hatzes example for see stars, subgiant For hsc eatet ascuet nttt fTechnolog of Institute Massachusetts Department, Physics Fellow Kavli sterpro n cetiiydsrbtosadoealoccurren overall a and distributions though, J subg eccentricity Keywords: hot remain, and around of populations period Questions lack their planet the as the destruction. result, between th a of differences tidal glimpse As reported their a evolution. provide for and tidal age, after evidence main-sequence in and only planet-hosting planet-hosting differ before the the to both to likely of are mass motions samples th in two space of the similar formation Galactic be inhibited the they or that average been destruction, show has tidal we it to mas Here Consequently due more is be sample. Jupiters to main-sequence hot thought the also dominate are the that However, Jupit the stars. hot because that main-sequence should ambiguous, established around well it than is uncertain, it stars Jupit very Indeed, subgiant hot is stars. cause decay evolved to more orbital and for expected timescale is the momentum Although angular of transfer Tidal VDNEFRTETDLDSRCINO O UIESB SUBGIA BY JUPITERS HOT OF DESTRUCTION TIDAL THE FOR EVIDENCE 1. aay ieaisaddnmc lntsa neatos—planet — interactions planet-star — dynamics and kinematics : eeto tr:eouin—sas ieaisaddnmc sta — dynamics and kinematics stars: — evolution stars: — detection A INTRODUCTION T E tl mltajv 08/17/12 v. emulateapj style X ei .Schlaufman C. Kevin eevd21 ac ;acpe 03My31 May 2013 accepted 8; March 2013 Received .(2009), l. 3 This tal. et al. et for e ABSTRACT and hstsIsiueo ehooy abig,Massachuset Cambridge, Technology, of Institute chusetts al. y, l. 1 n ohaN Winn N. Joshua and ne icsinaemmeso h hnds fthe of disk thin the stars of the members of All are comparison. discussion a such under provide can stars main- the the velocity and radial stars in included evolved been surveys. have the that of stars com- would sequence masses for it method the meantime, model-independent the a paring have In to con- helpful 2013). claim be this al. over et progeni- debate (Johnson G-type The domi- tinues and A-type. sample F- than samples a rather with define tors in stars, that resulted lower-mass to argued have by used nated should He were stars was evolved that (2011). of models criteria Lloyd evolutionary selection by the those question of into fidelity called the though, vltoaymdl sinteesastesm masses (2.0–1.6 same stars the A5–A9 the stars main-sequence because their these as stars,” to assign A referred “retired models as (2007) evolutionary stars al. evolved rel- et of are Johnson sample stars evolved massive. tem- the atively effective that is stars confirm and It evolved which , the peratures), stellar-evolutionary surface of literature. , fitting properties observable (their the of the in results to favored models the generally by is supported mass, lar dis- disk the or example) disk, commonly timescale. (for protoplanetary sipation less the in 2009). of differences occur Currie structure to may the due 2009; Jupiters stars massive al. hot around et picture, Kretke this 2007; (e.g., In mass Ida stellar enhanced & the Burkert planet to the than linked is in massive are differences populations more possibility the (e.g., average and second stars, on stars main-sequence are The the stars al. evolved evolved et hot the Kunitomo 2012). that 2009; the the Livio al. Adam´ow & et destroyed orbited Villaver 2011; 1996; has al. once et evolution Rasio that tidal that Jupiters is sibility h bevdGlci pc oin knmtc)of (kinematics) motions space Galactic observed The h atrseai,atiuigtedffrne ostel- to differences the attributing scenario, latter The nepeaino hsfidn a been has finding this of interpretation at n ansqec tr,such stars, main-sequence and iants erates. ce r r on esfeunl around frequently less found are ers ieta h -adGtp stars G-type and F- the than sive ptr riigsbinsi clear is subgiants orbiting upiters s lnt rudmsiestars. massive around planets ose stars. host their into spiral to ers otteitrrtto fother of interpretation the bout efse o ytm ihlarger with systems for faster be -adGtp tr.Therefore stars. G-type and F- nla hte h bec of absence the whether unclear ugatsasdmn hton that demand stars subgiant 2 aeeolntpopulation same e s statistics rs: n satellites: and s TSTARS NT M s019 USA 02139, ts ⊙ .Recently, ). 2 SCHLAUFMAN & WINN

Milky Way, and empirically it is known that the velocity giant and samples.4 Figure 1 is a Hertzsprung- dispersion of a thin-disk population increases with age Russell (HR) diagram of planet-hosting stars identified (e.g., Binney et al. 2000). This is understood as follows. with the technique, with our three sub- Thin disk stars form from dense, turbulent gas in the samples highlighted. Galactic plane. Because that process is highly dissipa- Our samples are defined according to observable cri- tive, stellar populations are formed with a very cold ve- teria in color and absolute , as opposed to locity distribution. Over time, the velocity distribution is model-dependent stellar masses (i.e., masses determined heated due to interactions between the stars and molecu- by comparing the observable properties with the out- lar clouds (e.g., Spitzer & Schwarzschild 1951) and tran- puts of theoretical stellar-evolutionary models). This is sient spiral waves (e.g., Barbanis & Woltjer 1967). Mas- because the planet surveyors often define samples ac- sive stars spend only a short time on the , cording to color and , and because and there is very little time for collisions to kinemati- of the questionable reliability of the model-dependent cally heat a population of massive stars. On the other stellar masses for the subgiants (Lloyd 2011). Neverthe- hand, solar-mass stars spend a long time on the main se- less, one may wonder about the model-dependent masses quence, leaving plenty of time for collisions to kinemat- that have been determined for the stars in our sam- ically heat a population of solar-mass stars. One would ples. For the subgiants, the model-dependent masses re- therefore expect a main-sequence thin-disk stellar pop- ported in the literature are in the range 0.92–2.0 M⊙, 5 ulation’s space velocity dispersion to decrease with in- with all but six stars having M∗ > 1.4 M⊙. The gi- creasing . The same is true even for evolved ant stars have model-dependent masses reported to be stars, because a star spends such a small fraction of its in the range 0.92–2.7 M⊙, with all but 6 stars having life as a subgiant or giant relative to its main-sequence M∗ > 1.4 M⊙. The reported model-dependent masses lifetime. of the main-sequence F5–G5 stars are in the range 0.8– In this paper, we investigate the Galactic velocity dis- 1.4 M⊙. persion of the population of evolved planet-hosting stars. We also define two samples of main-sequence stars in The kinematic evidence shows that these stars are simi- the solar neighborhood (not necessarily planet-hosting lar in mass to F5–G5 main-sequence stars. Consequently, stars) using the Hipparcos catalog, requiring as be- the lack of host Jupiters around evolved stars cannot be fore that the parallax uncertainty be smaller than 20%. attributed to mass. The most plausible explanation is The first sample consists of main-sequence stars with that the hot Jupiters have been destroyed, after losing 0.15 < (B − V ) < 0.30 and 1.9 < MV < 2.7, cor- orbital angular momentum to their host stars. We de- responding to A5–F0 stars (2–1.5 M⊙) according to scribe our sample of planet-hosting stars in Section 2, we Binney & Merrifield (1998). Our intention with this detail our analysis procedures in Section 3, we outline sample is to provide a control sample that will allow scaling relations for tidal evolution timescales in Section a test of the hypothesis that the population of sub- 4, we discuss the results and implications in Section 5, hosts is dominated by “retired A stars”. and we summarize our findings in Section 6. The second sample consists of main-sequence stars with 0.44 < (B − V ) < 0.68 and 3.5 < MV < 5.1, cor- 2. SAMPLE DEFINITION responding to F5–G5 stars (1.3–0.9 M⊙) according to We first extract a list of exoplanet host stars identified Binney & Merrifield (1998). with the Doppler technique, using the online database We compute Galactic UV W velocities for all stars for .org (Wright et al. 2011). We cross-match which the systemic radial velocities are available in the those stars with the Hipparcos catalog (van Leeuwen catalogs of Gontcharov (2006), Massarotti et al. (2008), 2007) to obtain parallaxes and B−V colors, and with the or Chubak et al. (2012). In addition to radial veloci- Tycho-2 catalog (Høg et al. 2000) to obtain apparent V - ties, as inputs we use Hipparcos , parallaxes, band magnitudes. We transform the Tycho-2 BT and VT and proper motions (van Leeuwen 2007). Enough infor- magnitudes into approximate Johnson-Cousins V -band mation is available to compute UV W velocities for all magnitudes using the relation V = VT −0.090(BT − VT ). 35 subgiants, 23 of 24 giant stars, and 88 of 91 main- Photometry for some of the brightest planet-hosting stars sequence F5–G5 stars. We use the algorithm given in is missing from the Høg et al. (2000) catalog. For those gal uvw.pro available from The IDL Astronomy User’s cases we use the original Tycho photometry given by Library. We follow the convention that U is positive to- Perryman & ESA (1997). We remove from the list all wards the , V is positive in the direction planet-hosting stars with imprecise parallaxes (fractional of Galactic rotation, and W is positive towards the North uncertainty exceeding 20%). We also obtain the nomi- Galactic pole. We do not correct for motion of the nal parameters of the host stars and their planets from relative to the local standard of rest. For those inter- exoplanets.org. ested in replicating the results, a comparable data set is We then define three samples of the planet-hosting publicly available from E. Mamajek6. stars. The sample of subgiants is defined as those stars with 0.85 < (B − V ) < 1.1 and 1.6 < MV < 3.1. The 4 sample of giants consists of stars with MV < 1.6. Fi- We also constructed samples corresponding to F0–F5, F5–G0, nally, a sample of main-sequence F5–G5 planet-hosting and G0–G5 stars. We settled on F5–G5 for the analysis presented stars is defined by the criteria 0.44 < (B − V ) < 0.68 and here, because this sample gave the best match to the kinematics of the subgiant planet hosts; see Section 3.1. 3.5

giant hosts subgiant hosts ms F5−G5 hosts other rv planet hosts ] mag [

V M 8 6 4 2 0 −2 0.5 1.0 1.5 B − V [mag]

Figure 1. Hertzsprung-Russell diagram of exoplanet host stars identified with the radial-velocity technique listed at exoplanets.org (Wright et al. 2011). We isolate and plot three subsamples of the full exoplanet host population: F5–G5 main-sequence stars (light blue points), subgiant stars (dark blue points), and giant stars (green points). We plot all other exoplanet host stars as black points. We plot only those stars that have Hipparcos parallaxes with an uncertainty smaller than 20%. The background shading indicates the density of stars in the entire Hipparcos catalog with relative parallax uncertainties smaller than 20%. The B − V colors come from van Leeuwen (2007) and the V -band photometry is derived from Tycho-2 magnitudes given in Høg et al. (2000) according to the relation V = VT −0.090 (BT − VT ). Following Binney & Merrifield (1998), we define the F5–G5 sample as those stars with 0.44 < (B − V ) < 0.68 and 3.5 < MV < 5.1. We define the subgiant sample as those stars with 0.85 < (B − V ) < 1.1 and 1.6

ms A5−F0 stars ms A5−F0 stars ms A5−F0 stars a subgiant hosts b subgiant hosts c subgiant hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 [ −1] [ −1] [ −1] U km s U km s V km s

ms F5−G5 stars ms F5−G5 stars ms F5−G5 stars d subgiant hosts e subgiant hosts f subgiant hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100

−100 −50 0 − 50 100 −100 −50 0 − 50 100 −100 −50 0 − 50 100 U [km s 1] U [km s 1] V [km s 1] Figure 2. Galactic UVW kinematics of subgiant stars that host exoplanets discovered with the radial-velocity technique. In each panel, we plot the UVW space motions of the subgiant sample as blue points and the density of points in a control sample selected from the Hipparcos catalog as the background shading. We plot outliers in the control sample as gray points. In panels a, b, and c the control sample consists of main-sequence A5–F0 Hipparcos stars with 0.15 < (B − V ) < 0.30 and 1.9

ms A5−F0 stars ms A5−F0 stars ms A5−F0 stars a giant hosts b giant hosts c giant hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 [ −1] [ −1] [ −1] U km s U km s V km s

ms F5−G5 stars ms F5−G5 stars ms F5−G5 stars d giant hosts e giant hosts f giant hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100

−100 −50 0 − 50 100 −100 −50 0 − 50 100 −100 −50 0 − 50 100 U [km s 1] U [km s 1] V [km s 1] Figure 3. Galactic UVW kinematics of giant stars that host exoplanets discovered with the radial-velocity technique. In each panel, we plot the UVW space motions of the giant sample as green points and the density of points in a control sample selected from the Hipparcos catalog as the background shading. We plot outliers in the control sample as gray points. In panels a, b, and c the control sample consists of main-sequence A5–F0 Hipparcos stars with 0.15 < (B − V ) < 0.30 and 1.9 < MV < 2.7 (e.g., Binney & Merrifield 1998). In panels d, e, and f the control sample consists of main-sequence Hipparcos F5–G5 stars with 0.44 < (B − V ) < 0.68 and 3.5 < MV < 5.1 (e.g., Binney & Merrifield 1998). In each panel, the light (heavy) ellipse is the 68% (95%) velocity ellipsoid of the control sample in that panel. The UVW velocity distribution of the giant sample is kinematically much hotter than the UVW velocity distribution of the main-sequence A5–F0 sample. However, it is well matched by the UVW velocity distribution of the main-sequence F5–G5 stars. We quantify these observation in Section 3.1. As a result, the typical mass of a star in the giant population is more likely to be similar in mass to a F5–G5 star than an A5–F0 star. is indistinguishable from the solar-neighborhood main- deed more massive than the F5–G5 planet hosts. To sequence F5–G5 sample (Anderson-Darling p = 0.62). quantify the maximum fraction of massive stars that We conclude that the planet-hosting giant stars, like the could be present in the subgiant sample, we use a Monte subgiants, are on average similar in mass to the main- Carlo simulation. We create many random mixed con- sequence F5–G5 planet hosts. trol samples composed of both solar neighborhood main- One of the planet-hosting giants, β Geminorum (Pol- sequence A5–F0 and F5–G5 stars. We vary the fraction lux) happens to have a asteroseismic mass determina- of main-sequence A5–F0 stars and then compare the ve- tion placing it firmly in the “retired A star” category, locity dispersion of the subgiant sample to the resultant with M∗ = 1.91 ± 0.09 M⊙ (Hatzes et al. 2012). Reas- mixed control samples. We find that control samples in- suringly, we find that this star has a UV W velocity of cluding less than ≈40% main sequence A5–F0 stars are (−16, 5, −26) km s−1, placing it just outside of the 68% generally consistent with the subgiant sample. Conse- contour of the solar-neighborhood main-sequence A5–F0 quently, we expect that no more than 40% of the sub- sample. Therefore this particular star has a low space giant planet hosts were once A5–F0 stars.8 Based on a velocity as expected, and does not call into question the similar calculation, we also find that no more than 40% overall result that the sample of planet-hosting giants is of the stars in the giant sample were once A5–F0 stars. dominated by lower-mass stars. We perform a few additional tests of the claim that the Figure 4 compares the UV W velocities of the planet- subgiants that were selected for the Doppler planet sur- hosting F5–G5 stars, and of the solar-neighborhood sam- veys have a typical mass similar to that of F5–G5 stars. ples. As expected, we find that the main-sequence F5– First, we repeated the comparisons after swapping the G5 planet-hosting stars are kinematically hotter than subgiant planet-hosting sample for the sample of south- the solar-neighborhood A5–F0 stars, and they are kine- ern sky subgiants from the Pan-Pacific Planet Search matically indistinguishable from the solar-neighborhood presented by Wittenmyer et al. (2011). These are not main-sequence F5–G5 sample. necessarily planet-hosting stars, but they were selected Figures 2, 3, and 4 indicate that on average the sub- for Doppler surveillance in a similar fashion as the other giant planet-hosting stars are similar in mass to the main- subgiant planet hosts. We obtain quantitatively similar sequence F5–G5 planet hosts. However it is possible that some fraction of the subgiant planet hosts stars are in- 8 Based on similar tests we also expect that no more than 60% of the subgiant planet hosts were once F0–F5 stars. 6 SCHLAUFMAN & WINN

ms A5−F0 stars ms A5−F0 stars ms A5−F0 stars a ms F5−G5 hosts b ms F5−G5 hosts c ms F5−G5 hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 [ −1] [ −1] [ −1] U km s U km s V km s

ms F5−G5 stars ms F5−G5 stars ms F5−G5 stars d ms F5−G5 hosts e ms F5−G5 hosts f ms F5−G5 hosts ] ] ] 1 1 1 − − − s s s

km km km [ [ [

V W W

−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100

−100 −50 0 − 50 100 −100 −50 0 − 50 100 −100 −50 0 − 50 100 U [km s 1] U [km s 1] V [km s 1] Figure 4. Galactic UVW kinematics of main-sequence F5–G5 stars that host exoplanets discovered with the radial-velocity technique. In each panel, we plot the UVW space motions of the main-sequence F5–G5 sample as light blue points and the density of points in a control sample selected from the Hipparcos catalog as the background shading. We plot outliers in the control sample as gray points. In panels a, b, and c the control sample consists of main-sequence A5–F0 Hipparcos stars with 0.15 < (B − V ) < 0.30 and 1.9 < MV < 2.7 (e.g., Binney & Merrifield 1998). In panels d, e, and f the control sample consists of main-sequence Hipparcos F5–G5 stars with 0.44 < (B − V ) < 0.68 and 3.5 < MV < 5.1 (e.g., Binney & Merrifield 1998). In each panel, the light (heavy) ellipse is the 68% (95%) velocity ellipsoid of the control sample in that panel. As expected, the UVW velocity distribution of the main-sequence F5–G5 sample is kinematically much hotter than the UVW velocity distribution of the main-sequence A5–F0 sample but well matched by the UVW velocity distribution of the larger Hipparcos main-sequence F5–G5 star sample. We quantify these observations in Section 3.1. results; the Pan-Pacific search targets are kinematically important to compare the of the two sam- better matched to F5–G5 stars than to more massive ples. Based on the determinations reported stars. Second, we select subgiant stars from the Hippar- in the literature, we find the average metallicity of the cos catalog using the same color and magnitude crite- main-sequence sample ([Fe/H] = 0.05 ± 0.03) to over- ria that we applied to select the planet-hosting subgiant lap with the average metallicity of the subgiant sample sample. This is intended to mimic the parent population ([Fe/H] = 0.03 ± 0.03). Their distributions are consis- of subgiants from which the planet-hosting stars were tent with being drawn from the same parent distribution identified by the Doppler surveyors. We find that their (Anderson-Darling p-value = 0.3). Thus at face value kinematics are indistinguishable from the kinematics of the metallicity distributions appear to be equivalent, al- the planet-hosting subgiants (Anderson-Darling p-value though in Section 5.3 we discuss the possibility of sys- =0.30). We also find the Hipparcos subgiant sample to tematic biases in the reported metallicity values. be kinematically incompatible with an origin in the same parent population as the Hipparcos main sequence A5– 3.3. Orbital Parameters F0 sample (Anderson-Darling p-value < 10−6). In con- The radial velocity surveys are complete for planets trast, the subgiant planet hosts and the main-sequence −1 F5-G5 planet hosts are kinematically consistent with an with velocity semiamplitude K > 20 m s and orbital origin in the same parent population (Anderson-Darling distance a < 2.5 AU, corresponding to orbital period . p-value = 0.5). P 4 yr (Johnson et al. 2010b). We therefore focus attention on the population of known planets satisfying 3.2. these criteria. In Figure 5 we plot the P –e and P –K Metallicities distributions for the giant planets with K > 20 m s−1 The masses of the subgiant planet-hosting stars are and a < 2.5 AU, for all three samples of planet-hosting now seen to be similar to those of the main-sequence stars. F5–G5 planet-hosting stars. One may wonder, though, The planets orbiting both samples of evolved stars if there are systematic differences in other stellar param- (subgiants and giants) mainly have periods longer than eters that may have affected their planet populations. 100 days. Only one subgiant has a planet with a shorter A key parameter is metallicity, which is well known to period, in strong contrast to the main-sequence stars have a major influence on the properties of giant planets which frequently host short-period planets. Furthermore (Santos et al. 2004; Fischer & Valenti 2005). Thus it is the planets around the evolved stars are preferentially EVIDENCE FOR TIDAL DESTRUCTION 7

giant hosts ] giant hosts 1

subgiant hosts − subgiant hosts s

ms F5−G5 hosts ms F5−G5 hosts m [

Eccentricity Semiamplitude

Velocity 0 50 150 250 350 0.0 0.2 0.4 0.6 0.8 1.0 100 101 102 103 100 101 102 103 Period [days] Period [days]

Figure 5. Eccentricities, velocity semiamplitudes (K), and orbital periods for the planets in each of our samples: main-sequence F5–G5 stars (light blue), subgiants (dark blue), and giants (green). For each sample, we only include planets that reside in parts of parameter space in which radial velocity surveys are complete: K > 20 ms−1 and a< 2.5 AU (e.g., Johnson et al. 2010b). There are three significant differences between the samples: (1) there are fewer planets orbiting evolved stars at short periods, (2) the planets around subgiants have lower eccentricities, and (3) the planets around subgiants have smaller K values than those observed around main-sequence stars or giants. on circular orbits, compared to the more eccentric orbits matics and metallicities, the differences between their commonly seen for the planets around main-sequence planet populations are not easily attributed to differences F5–G5 stars. The mean eccentricities of the planets in mass or composition. Instead, the observed differences around subgiants, giants, and main-sequence stars are in planet populations are likely to be related to age or e¯ = 0.12 ± 0.02,e ¯ = 0.17 ± 0.03, ande ¯ = 0.36 ± 0.04, stellar radius (which are, of course, correlated). A mech- respectively. The eccentricity distributions for planets anism for altering planetary systems that is known to around subgiants, and for planets around giants, are con- depend sensitively on stellar radius is tidal dissipation. sistent with each other (Anderson-Darling p-value = 0.3). Theoretical rates of energy dissipation due to star-planet However the probability that the eccentricities of the tidal interactions scale as high powers of the stellar ra- 5 planets around subgiants are drawn from the same par- dius (∝ R∗ in the works cited below). In this section we ent distribution as the main-sequence sample is less than develop approximate formulas for tidal dissipation rates, 10−6. In the next section we will examine the hypothesis to support the discussion in the next section. that tidal evolution is responsible for these differences in Tidal interactions between a star and an orbiting the planet populations. planet allow for the exchange of angular momentum be- The right panel of Figure 5 also shows that the plan- tween the bodies while steadily draining energy from the ets orbiting subgiants are clustered at low velocity semi- system (Counselman 1973; Hut 1980, 1981). If the star’s amplitudes K ≈ 40ms−1, relative to the planets around rotation period is longer than the planet’s orbital period, main-sequence stars. This is despite the fact that plan- the star spins up and the orbit shrinks. If the total an- ets with larger K values would have been more easily de- gular momentum of the system exceeds a critical value, tected. The probability that the K distributions of plan- the orbit eventually circularizes and the bodies’ spins are ets around subgiants and main-sequence stars are drawn synchronized and aligned. If however the total angular from the same parent distribution is less than 10−6. momentum is too small, then there is no stable equilib- One finding that is not illustrated in Figure 5 is that rium: the orbit keeps shrinking until the planet is de- the evolved stars are more likely than the main-sequence stroyed. It is not yet possible to compute accurate dissi- stars to show evidence for additional longer-period com- pation timescales from first principles. The best that can panions, in the form of a long-term radial-velocity trend. be done is to establish plausible scaling relationships that At P > 100 days, long-term radial-velocity trends oc- are calibrated using observations, as we attempt here. cur around 9 of 34 subgiants. In contrast, long-term Eccentricity damping (orbit circularization) can occur trends occur in only 2 of 33 main-sequence stars (with either due to dissipation inside of the planet or inside of giant planets in the complete region of parameter space) the star. The timescales for eccentricity damping due to and in only 1 out of 24 giant stars. If the distribution of dissipation inside of the planet te,p, due to dissipation long-term trends were the same for subgiants as for main- inside of the star te,∗, and their ratio are (e.g., Mardling sequence stars, the chance of reproducing these numbers 2007; Mazeh 2008) would be less than 1 in 40,000. 5 ≈ 2P Qp Mp a 4. te,p , (2) TIDAL TIMESCALES 21 k M∗ R  p     p  If the subgiant planet-hosting stars and the main- 5 2P Q∗ M∗ a sequence F5–G5 planet-hosting stars have similar kine- te,∗ ≈ , (3) 21 k∗ M R∗    p    8 SCHLAUFMAN & WINN

2 5 te,∗ Q∗/k∗ M∗ Rp for orbital drift τa of a 1 MJup planet orbiting at P =5 = , (4) ∼ 6 te,p Qp/kp Mp R∗ days a Q∗/k∗ 10 ,1 M⊙, and1 R⊙ host star is τa = 10       Gyr, then we have where P is the orbital period, a is the orbital semimajor −5 axis, Qp and Q∗ are the tidal quality factors of the planet Q∗/k∗ R∗ a 13/2 and star, kp and k∗ are their tidal Love numbers, Mp ta = τa . (11) 106 R⊙ 0.06 AU and M∗ are their masses, and R and R∗ are their radii. p       Assuming constant Q , k , M , R , and M∗, the scaling p p p p Equations (9) and (11) were used to calculate t and relations for the timescale for orbit circularization due to e t as a function of orbital period and stellar radius, for dissipation inside of the planet and inside of its host star a a fiducial solar-mass star with a Jovian planet. The re- are sults are shown in Figure 6, which also displays the peri- t P a 5 ods and stellar radii of the various samples of exoplanet e,p,2 = 2 2 , (5) t P a systems considered in this paper. The stellar radii are e,p,1  1   1  based on the empirical calibration given by Torres et al. 5 5 te,∗,2 P2 Q∗,2/k∗,2 R∗,1 a2 (2010). = . (6) There are two other criteria that must be satisfied for te,∗,1 P1 Q∗,1/k∗,1 R∗,2 a1         tidal decay. First, since tides only cause orbital decay It is commonly understood that for main-sequence if the period is longer than the orbital stars with planets, orbital circularization is mainly due to period, we indicate in Figure 6 the maximum stellar ro- dissipation within the planet. This is because the usual tation period that would be expected for stars in the 6 5 assumptions Q∗/k∗ ∼ 10 , Qp/kp ∼ 10 , M∗ = 1 M⊙, different samples. These are based on the observed pro- Mp = 1 MJup, R∗ = 1 R⊙, Rp = 1 RJup lead to jected rotation rates (v sin i) and estimated radii of the te,∗/te,p ∼ 100. We use this fact to provide a rough planet host stars, using calibration for the dissipation timescale. Figure 5 shows 2πR∗ that planets orbiting main-sequence stars inside of P =5 Prot . v sin i . (12) days are on nearly circular orbits, while planets orbiting outside of P = 10 days are frequently on eccentric orbits. The upper limit on Prot was computed for each star. The timescale for orbit circularization in the shorter- Then, the median of these upper limits was computed for period systems must be significantly shorter than the each sample, and plotted in the left panel of Figure 6. ages of the systems. We will therefore assume that the Second, the total angular momentum of the system circularization timescale τe,p at P = 5 days for a solar- Ltot must be lower than the critical value Lcrit nec- 6 mass star with Q∗/k∗ ∼ 10 and a planet with the mass essary for a stable equilibrium (in which the star and and radius of Jupiter and Q /k ∼ 105 is τ = 1 Gyr. planet have achieved spin–orbit synchronization and p p e,p alignment). The total angular momentum can be writ- When the host star is a subgiant with R∗ =4 R⊙, then ten te,∗/te,p ∼ 0.01 and circularization should be mainly due to dissipation inside of the star (e.g., Rasio et al. 1996). L = L + L ∗ + L , (13) Using Equations (4), (5), and (6) plus the calibration tot orb rot, rot,p 2 1/2 presented above we may write Lorb = µ GMtota(1 − e ) , (14) 5 2 2 P a Lrot,∗ = g∗M∗R∗ω∗,  (15) te,∗ = τe,pΘ , (7) 2 2 5 days 0.06 AU L = g M∗R ω , (16)     rot,p p p p where where µ = (M∗Mp)/(M∗ + Mp) is the reduced mass and 2 5 ≡ Q∗/k∗ M∗ Rp Mtot = M∗ + Mp is the total mass of the system. Here Θ . (8) 2 2 Qp/kp Mp R∗ g∗ =0.06 and gp =0.25 are the radii of gyration of star       and planet, assuming the solar and Jovian values respec- Then, taking the overall eccentricity-damping timescale tively. Likewise, ω∗ and ωp are the angular velocities of te to be the smaller of the two dissipation timescales star and planet. The rotational angular momentum of (inside the planet or inside the star), we have the planet is negligible. The value of Lcrit is (e.g., Hut P a 5 1980; Matsumura et al. 2010) te = τe,p min (1, Θ). (9) 5 days 0.06 AU 1/4 2 3 3     G M∗ Mp As for tidal evolution of the orbital distance a, the Lcrit =4 (I∗ + Ip) , (17) 27 M∗ + M scaling relation is thought to be (e.g., Lin et al. 1996) " p #

1/2 13/2 2 2 2 2 M∗ (Q∗/k∗)a where I∗ = g∗M∗R∗ and Ip = gpMpRp. Assuming t ∝ . (10) a M R5 M∗ =1 M⊙, Mp =1 MJup, R∗ =4 R⊙, and Rp =1 RJup p ∗ characteristic of an evolved star with a giant planet, Figure 5 shows that there are many planets orbiting main then all systems with a . 0.35 AU, or approximately sequence stars at P ≈ 5 days, but few at P ≈ 1 day. P . 75 days, are tidally unstable. Such planets will ulti- Assuming this difference to reflect the tidal decay of the mately be engulfed, if the host star’s rotational angular shortest-period orbits leads to a rough calibration of the momentum was initially comparable to the current solar tidal decay timescales. If we assume that the timescale value. EVIDENCE FOR TIDAL DESTRUCTION 9

106 107 108 109 1010 1011 [ ] Semimajor Axis Evolution Time years Orbit Circularization 2 2

10 giant hosts 10 giant hosts subgiant hosts subgiant hosts ms F5−G5 hosts ms F5−G5 hosts ] ] Sun Sun R R [ [

inside star inside star 1 1 10 10 Radius Radius

Stellar Stellar corotation 0 0 10 10 100 101 102 103 100 101 102 103 Period [days] Period [days]

Figure 6. Tidal timescales as a function of period and stellar radius. Left: Timescale ta for semimajor axis evolution (orbital decay) for planets inside the corotation radius (marked approximately by the white line). Right: Timescale te for orbit circularization. The timescales 6 5 were computed as described in the text, assuming M∗ = 1 M⊙, Mp = 1 MJup, Rp = 1 RJup, Q∗/k∗ = 10 , and Qp/kp = 10 . For planets to the left of the white diagonal band, the calculated tidal timescale is short compared to the duration over which a solar-mass, solar-metallicity star exists as a subgiant or at the base of the giant branch (e.g., Dotter et al. 2008). The left-hand figure shows that the scarcity of P < 10 day planets around subgiants is a seemingly inevitable consequence of tidal decay. The right-hand figure shows that the tendency for planets around subgiants to have nearly circular orbits all the way out to P ≈ 200 days can only be explained if stars become 2 much more dissipative as they evolve off of the main sequence (Q∗/k∗ ∼ 10 ). Such a scenario would also imply enhanced rates for tidal decay, and could explain the scarcity of planets around subgiants all the way out to P ≈ 100 days.

5. DISCUSSION R∗ = 4 R⊙ would be 24 days. Had it not absorbed its 5.1. Hot Jupiters planet’s orbital angular momentum, then its rotational period would have been 130 days. This seems like a sig- The left panel of Figure 6 shows that there is no dif- nificant difference. However, the radii of subgiants are ficulty explaining the lack of hot Jupiters around sub- generally uncertain by a factor of two or more. If instead giants with periods between 1 and 10 days. Although the subgiant had a radius of R∗ = 8 R⊙, then its rota- such planets’ orbits may be stable for a Hubble time tion period after absorbing its planet’s orbital angular around a main-sequence stars, once the host star evolves momentum would be 94 days. Consequently, identifying and reaches a radius of 4 R⊙, tidal dissipation rates in- angular momentum enhancement in evolved stars will be ∼ 2 crease by a factor of 10 . Those same planets would difficult without accurate stellar radii. experience orbital decay in a few 100 Myr, comparable The of metal-enriched material from a dis- to the time that their host stars spend as subgiants (e.g., rupted giant planet could also affect the observed chemi- Dotter et al. 2008). Tidal destruction has already been cal abundances of an evolved star. Indeed, the accretion noted as a theoretical possibility by Villaver & Livio of solid material was initially considered as one possi- (2009) and Kunitomo et al. (2011), at least for giant ble explanation for the enhanced metallicity of the solar- stars with R∗ & 20 R⊙. It has also been suggested by type stars identified as giant planet hosts (e.g., Laughlin Lloyd (2011), among others. Now that the subgiants are 2000). Following the calculation by Laughlin (2000), the seen to have similar masses as the main-sequence sample, accretion of a Jupiter-mass planet with Z ≈ 0.1 into the tidal destruction seems to be the inevitable explanation 0.5 M⊙ convective envelope of an evolved solar metallic- for the lack of close-in giant planets orbiting subgiants ity star will only increase the star’s observed metallicity relative to main-sequence stars. by 0.01 dex – an imperceptibly small increase. One might wonder if it is possible to find additional supporting evidence for tidal destruction of hot Jupiters 5.2. Intermediate-period Giant Planets based on the observed rotation rates of subgiants, since Although tidal destruction is a natural explanation for the accretion of angular momentum from a disrupted gi- the lack of hot Jupiters around subgiants, the relative ant planet could affect the rotation rate. Suppose a star scarcity of giant planets with periods between 10 and with mass 1.3 M⊙, radius 1.1 R⊙, radius of gyration 2 100 days cannot be explained as the consequence of tidal I/MR = 0.06 (the solar value), and rotation period destruction unless the tidal dissipation rate for subgiants Prot = 10 d accretes a 1 MJup planet initially orbiting at is 3-4 orders of magnitude faster than estimated in the 0.1 AU, and absorbs all of its orbital angular momentum. previous section (and plotted in Figure 6). One possibil- The final rotation period of that star when it reaches ity is that dissipation becomes faster not only because of 10 SCHLAUFMAN & WINN an enlarged stellar radius, but also a decrease in Q∗/k∗ Some of the observed differences between the planet due to the changing . This could also populations around subgiants and main-sequence stars explain the observation that the shortest-period plan- have no obvious interpretation in terms of tidal interac- ets seen around subgiants (P ≈ 200 days) tend to have tions. First, there is no simple explanation for the higher circular orbits: such planets would be undergoing tidal occurrence rate of long-period giant planets around sub- eccentricity damping due to dissipation within the host giant stars. According to Bowler et al. (2010), the oc- star. This is in contrast to the hot Jupiters observed +9 currence rate of giant planets with a < 3 AU is 26−8% around main-sequence stars, for which dissipation within as compared to 5–10% for main-sequence stars. More the planet is likely to be the primary cause of eccen- recently, Johnson et al. (2010b) accounted for the effect tricity damping. Furthermore it would not be surpris- of metallicity on planet occurrence and determined that ing for a subgiant to have a lower Q∗/k∗ than a main- the occurrence rate of giant planets with a . 2.5 AU is sequence star. The strength of tidal evolution in evolved 11±2% for subgiants, as compared to 6.5±0.7% for main- stars is thought to depend on the mass of their con- sequence stars. In either case, these offsets represent a vective envelopes (Rasio et al. 1996), and the mass in 2-3σ difference. the convective envelope of a solar-type star increases by A second and related point is that tides cannot explain an order of magnitude as a subgiant between the main the higher incidence of velocity trends noted at the end sequence turnoff and the base of the branch of Section 3.3. Tides are too weak to affect planets with (Sackmann et al. 1993). such long periods that they are observed only as linear We digress momentarily to point out that Figure 1 re- trends in a subgiant’s radial velocity curve. veals that most of the giant planet-hosting stars (as op- Third, and most puzzling, is the clustering of K values posed to subgiants) are concentrated in the so-called “red between 10–50 m s−1 for the subgiants, as compared to clump” — a region of the HR diagram where the red the broader distributions 10–300 m s−1 for planets in the giant branch overlaps with the for a same period range around both main-sequence stars and solar-metallicity stellar population. Without asteroseis- giants. The timescale for tidal evolution is proportional mic observations, we cannot confidently assign individual to planet mass, raising the possibility that only low-mass stars to one or the other of those two populations. Un- planets (small K values) persist once a star evolves off fortunately this means the giants are less useful than the of the main sequence. But any tidal explanation would subgiants in understanding the tidal evolution of plane- struggle to explain why the giant stars (which are even tary systems, for the following reason. The stars on the more evolved than subgiants) still harbor more massive horizontal branch are currently burning in their planets. Future work is needed to understand these three cores after an initial ascent up the giant branch. They differences. very likely had larger radii at the tip of the red giant One possibility is that the average metallicity of branch than they currently possess. Since tidal effects the stars in the subgiant sample is higher than that depend strongly on stellar radius, the tidal evolution of of the main-sequence sample, despite the comparison any close-in exoplanets depends strongly on the sizes of made in Section 3.2 suggesting that the metallicities the giant stars at the tip of the red giant branch — which are similar. Giant planet occurrence rates are known are unobserved and poorly constrained. The subgiants to be strongly dependent on host star metallicity (e.g., invite a more straightforward interpretation, since they Santos et al. 2004; Fischer & Valenti 2005). In particu- are presently as large as they have ever been since the lar Fischer & Valenti (2005) found that the probability planet-formation epoch. of giant planet occurrence Pp scales as Putting these pieces together, a scenario that explains many of our observations is as follows. Stars become ∝ 2hFe/Hi more dissipative as they evolve off of the main sequence, Pp 10 . (18) both because the stellar radius increases and also be- In that case, the increased planet occurrence rate for cause Q∗/k∗ decreases by 3-4 orders of magnitude. Con- sequently, planets orbiting inside of the corotation ra- subgiants reported by Johnson et al. (2010b) could be dius (P . 100 days) lose angular momentum relatively explained by a residual systematic metallicity offset of quickly through tidal interactions. Planets just outside log ( 11/6.5) ≈ 0.1 dex in [Fe/H]. At the 1σ limits of the of corotation are pushed out and pile up at P ≈ 200 days, Johnson et al. (2010b) occurrence rates, even a residual while also undergoing eccentricity damping. Extending offsetp as small as log ( 9/7.2) ≈ 0.05 dex in [Fe/H] could this scenario to the giant stars is also possible. As the explain the apparently larger occurrence rate of giant host stars continue to move up the red giant branch, planets in the subgiantp sample. they expand and their rotation slows. As a consequence, Such an offset does not seem out of the ques- the corotation radius is enlarged. Those planets that tion. The metallicities of the subgiants and many FG were previously secure at P ≈ 200 days now find them- planet host stars in the control sample have been mea- selves losing orbital angular momentum. These planets sured with the Spectroscopy Made Easy package (SME; are not necessarily destroyed, though, because the host Valenti & Piskunov 1996) and other similar spectral- stars’ trip up the red giant branch is brief. The orbital fitting codes. The metallicity values returned by SME are distances may shrink only modestly before the host stars known to have systematic biases depending on effective start burning helium in their cores, contract, and settle temperature Teff (e.g., Section 6.4 of Valenti & Fischer onto the horizontal branch. 2005). Although Valenti & Fischer (2005) attempt to correct for this bias, perhaps there still exists a residual 5.3. Occurrence Rates of Giant Planets offset of 0.1 dex in [Fe/H] when comparing the main- sequence F5–G5 sample (Teff ≈ 6000 K) to the subgiant EVIDENCE FOR TIDAL DESTRUCTION 11 sample (≈5000 K). Indeed, strong correlations between is in the range 0.4 . η . 0.8 (e.g., Sackmann et al. 1993) the values of Teff and [Fe/H] generated by SME were and frequently set to η =0.5 (e.g., Kudritzki & Reimers recently identified by Torres et al. (2012), who demon- 1978; Hurley et al. 2000). Taking the median luminos- strated that SME reports cooler temperatures (100 K) ity, radius, and isochrone mass of our subgiant planet and higher metallicities (0.1 dex) than a line-by-line host sample L∗ = 9.5 L⊙, R∗ = 3.8 R⊙, and M∗ = MOOG-like analysis (Sneden 1973). A homogeneous 1.6 M⊙, the expected mass loss is rate is dM∗/dt ≈ −12 −1 MOOG-like line-by-line stellar parameter analysis of a 5 × 10 M⊙ yr . Over the 500 Myr a solar-type large sample of both FGK dwarf and subgiant planet- star spends as a subgiant, the total mass lost is only host stars might help to resolve this issue. Mloss . 0.01 M⊙. Thus, mass loss is unlikely to affect We also note that in calculating the dependence of gi- the orbital evolution of close-in giant planets orbiting ant planet occurrence rates on stellar mass and metal- subgiants or stars at the base of the red giant branch. licity, Johnson et al. (2010b) assumed that the effects of mass and metallicity were separable, even though there 6. is a significant positive correlation between the reported CONCLUSIONS stellar masses and metallicities (see their Figure 2). As Subgiant stars are observed to host fewer close-in giant we have shown, the subgiant stars are not likely to be planets than main-sequence stars, but have a systemati- especially massive. As a result, some of the increased cally higher giant planet occurrence rate when integrated planet occurrence signal in the subgiant sample was likely over all periods. These differences have been attributed misattributed to mass instead of metallicity. For that to the increased mass of the subgiant planet hosts relative reason, the metallicity corrections necessary to directly to main-sequence planet hosts. We find that the Galac- compare the giant planet incidence rate of main-sequence tic kinematics of subgiant stars that host giant planets FGK dwarfs and subgiants may have been underesti- demand that on average they be similar in mass to solar- mated by Johnson et al. (2010b). type main-sequence planet-hosting stars. Therefore, the More speculative is the possibility raised by Lloyd best explanation for the lack of hot Jupiters around (2011) that some of the radial-velocity signals detected evolved stars is tidal destruction of the hot Jupiters they for subgiant stars do not represent planets, but rather once possessed. If tidal dissipation inside their host stars stellar oscillations. The oscillations would need to be is also responsible for circularizing the orbits of the giant nonradial to avoid producing large brightness variations planets orbiting subgiants at P ≈ 200 days, then tides in contradiction with the observations. Nonradial oscil- should also have been strong enough to destroy any gi- lations can produce low-amplitude, sinusoidal radial ve- ant planets inside of corotation (P . 100 days). Planets locity variations (e.g., Hatzes 1996), though usually with outside of corotation may have extracted angular mo- smaller amplitudes and shorter periods. To our knowl- mentum from their host stars and moved to longer or- edge nonradial oscillations of subgiants producing sig- bital periods, explaining the sudden appearance of plan- nals as large as tens of m s−1 with periods of hundreds ets around subgiant stars at P ≈ 200 days. The apparent of days have never been empirically established, nor have 2-3σ increase in the incidence of long-period giant plan- they been theoretically predicted. We note, though, that ets around subgiant stars relative to main-sequence stars the literature does contain examples of similar quasi- is difficult to explain. It may be the result of system- sinusoidal variations that are at least suspected to be the atic underestimates of the metallicities of subgiant stars result of nonradial oscillations, in both more evolved and or (more speculatively) hitherto unknown modes of stel- less evolved stars (Hatzes & Cochran 1999; Desort et al. lar pulsation among the subgiants that masquerade as 2009). Perhaps the intense scrutiny of the subgiants by long-period giant planets. the Doppler surveyors has revealed a new mode of stellar It is also important to note that the kinematic equiva- pulsation. In addition to bringing the occurrence rate lence of the subgiant and main-sequence samples suggests of giant planets around subgiants into better agreement that the theoretical stellar-evolutionary models that were with the main-sequence stars, this might help to explain used to infer larger masses for the subgiants need to the clustering of K values. The physics of the hypothet- be re-evaluated. In particular, as suggested by Lloyd ical pulsations might naturally select a particular range (2011) it may be necessary to reassess the applicability of velocities, whereas the planet-induced velocity ampli- of a mixing-length model of that is calibrated tudes would depend on three different independent vari- for the Sun to low surface stars that are not even ables (Mp, i, and P ) and should combine to produce a quasi-stationary and that are developing shells of supera- wide range of K values. diabatic convection (e.g., Robinson et al. 2004; Cassisi 2012). 5.4. Stellar Mass Loss There are also potentially important implications of One might also wonder if stellar mass loss contributes our suggestion that stars become much more dissipa- tive as they evolve off of the main sequence, such that to the orbital evolution of planets around subgiant stars, ∼ 2−3 in addition to tidal effects. Mass loss on the red giant Q∗/k∗ 10 . If this is so, then the Earth will very branch is frequently parametrized using the Reimers re- likely be destroyed as the Sun expands to nearly 100 lation (e.g., Kudritzki & Reimers 1978) times its current size near the tip of the red giant branch. Previously it was thought that the orbital evolution of dM∗ −13 L∗(t)R∗(t) M⊙ the Earth could not even be predicted qualitatively as it = η 4 × 10 , (19) seemed to depend on the details of the Sun’s mass loss on dt M∗ yr the giant branch (e.g., Sackmann et al. 1993; Rasio et al.  where L∗, R∗, and M∗ are the stellar , radius, 1996). Thus the subgiant planet searches may have— and mass in solar units. The dimensionless parameter η quite unexpectedly—clarified the Earth’s ultimate fate. 12 SCHLAUFMAN & WINN

We thank John Johnson, Adam Kraus, Greg Laugh- Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. lin, Jamie Lloyd, Nevin Weinberg, and the anonymous 2010b, PASP, 122, 905 referee for their comments and constructive criticism. Johnson, J. A., Bowler, B. P., Howard, A. W., et al. 2010c, ApJ, 721, L153 This research has made use of NASA’s Astrophysics Johnson, J. A., Clanton, C., Howard, A. W., et al. 2011b, ApJS, Data System Bibliographic Services, the Exoplanet Or- 197, 26 bit Database and the at exo- Johnson, J. A., Fischer, D. A., Marcy, G. W., et al. 2007, ApJ, planets.org, and both the SIMBAD database and VizieR 665, 785 catalogue access tool, CDS, Strasbourg, France. The Johnson, J. A., Howard, A. W., Bowler, B. P., et al. 2010a, original description of the VizieR service was published PASP, 122, 701 Johnson, J. A., Marcy, G. W., Fischer, D. A., et al. 2008, ApJ, by Ochsenbein et al. (2000). 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