arXiv:1210.6985v1 [astro-ph.EP] 25 Oct 2012 Henry Dragomir H ICVR FH 37605 HD OF DISCOVERY THE e,C 42,USA 94720, CA ley, USA 94720, DK- CA ley, 120, Munkegade Denmark Ny C, University, Aarhus 8000 Aarhus Astronomy, and Canada V6T1Z1, BC Vancouver, Columbia, USA 21218, MD timore, 3261 9501, FL Box Gainesville, 112055, Box Blvd., P.O. USA Center, Merritt Science Space A. John USA 3500 37209, Nashville,TN University, State USA 91125, CA Pasadena, Avenue, Wilson South USA 78712, USA Pa University 16802, University, State Pennsylvania The oratory, and [email protected] to Pa correspondence University Send University, [email protected] USA; State 16802, Pennsylvania PA The Foundation. Keck oratory, M. finan- W. generous the the Califor of by of support possible University made cial was the Observatory at by Keck Texas operated The the is of which at University Observatory, Augus obtained the observations Georg of UniveUniversit¨at Universit¨at G¨ottingen, and M¨unchen, and Stanford project Maximilians University, joint State Ludwig Pennsylvania a the is Austin, which scope, rpittpstuigL using typeset Preprint hrnXeogWn ( Wang Xuesong Sharon 1 12 11 10 9 8 7 6 5 4 3 2 eateto hsc srnm,Uiest fBritish of University Astronomy, & Physics of Bal Department Dr., Martin San 3700 Institute, Science Telescope Space Bryant 211 Florida, of Tennessee University Astronomy, of Systems, Department Information in Excellence of 770 Center 100-22, MS Caltech, Institute, Science Exoplanet NASA TX Austin, Texas, of University The Observatory, McDonald Lab- Davey 525 Worlds, Habitable and Exoplanets for Center Lab- Davey 525 Astrophysics, and Astronomy of Department ae nosrain bandwt h ob-bryTele- Hobby-Eberly the with obtained observations on Based pc cecsLbrtr,Uiest fClfri,Berk California, of University Laboratory, Sciences Space Berke- California, of University Astronomy, of Department Physics of Department (SAC), Centre Astrophysics Stellar 6 ate .Payne J. Matthew , hsscn lnt D37605 HD planet, second This tbiga l,iatv tr ihatnaiertto eido 57 of period rotation tentative of a with activity star, stellar inactive the the old, Though characterized an it being satellite. window, it (MOST) transit Photoe Stars Automatic the 0.8-m of capture T12 performe Oscillations the we by and ephemeris, taken Microvariability predicted data photometric the the Using with variation. time transit VI akg n ro asb OTRNwt hs rdcdb produced those fi with headings: orbital BOOTTRAN Subject our by between bars consistency MCMC. error unc found and parameter and package comparison orbital RVLIN tr a dep Keplerian non-grazing made predicted calculating We a edge-on for of package an detection BOOTTRAN exclude null we window, dispositive transit a predicted report the to us enabled er,w rvd odobtlslto fteH 70 ytm a system, obs 37605 velocity HD radial the 137 of of solution orbital total 37605 precis good a HD provide a With provide to we follow-up. effort years, transit (TERMS) for Survey planets Monitoring ma and observations including Refinement Observatory, Keck and Telescope Eberly D365 hc a led nw ohs neccentric, an host to known already was which 37605, HD ∼ n xld n rni iha matparameter impact an with transit any exclude and erpr h ailvlct icvr fascn lntr mass planetary second a of discovery radial-velocity the report We 3 9 ameM Matthews M. 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1. INTRODUCTION 2009, the residuals to a one-planet fit were giving rea- 1.1. Context sonable constraints on the orbit of a second planet, HD 37605c, and by early 2011 the orbital parameters of the c Jupiter analogs orbiting other stars represent the first component were clear, and the Texas team was preparing signposts of true Solar System analogs, and the eccentric- the system for publication. ity distribution of these planets with a> 3 AU will reveal how rare or frequent true Jupiter analogs are. To date, 1.3. TERMS Data only 9 “Jupiter analogs” have been well-characterized in 13 The Transit Ephemeris Refinement and Monitor- the peer reviewed literature (defined here as P > 8 ing Survey (TERMS; Kane et al. 2009) seeks to re- years, 4 >M sin i> 0.5 MJup, and e< 0.3; Wright et al. fine the ephemerides of the known exoplanets orbit- 2011, exoplanets.org). As the duration of existing planet ing bright, nearby stars with sufficient precision to ef- searches approach 10–20 years, more and more Jupiter ficiently search for the planetary transits of planets analogs will emerge from their longest-observed targets with periastron distances greater than a few hundredths (Wittenmyer et al. 2012; Boisse et al. 2012). of an AU (Kane et al. 2011b; Pilyavsky et al. 2011a; Of the over 700 exoplanets discovered to date, Dragomir et al. 2011). This will provide the radii of plan- nearly 200 are known to transit their host star ets not experiencing continuous high levels of insolation (Wright et al. 2011, exoplanets.org; Schneider et al. around nearby, easily studied stars. 2011, exoplanet.eu), and many thousands more candi- In 2010, S.M. and J.T.W. began radial velocity obser- dates have been discovered by the Kepler telescope. Of 14 vations of HD 37605b at HET from Penn State Univer- all of these planets, only three orbit stars with V < 8 sity for TERMS, to refine the orbit of that planet for and all have P < 4 days. Long period planets are less a future transit search. These observations, combined likely than close-in planets to transit unless their orbits with Keck radial velocities from the California Planet are highly eccentric and favorably oriented, and indeed Survey (CPS) consortium from 2006 onward, revealed only 2 transiting planets with P > 20 days have been that there was substantial curvature to the radial velocity discovered around stars with V < 10, and both have residuals to the original Cochran et al. (2004) solution. e > 0.65 (HD 80606, Laughlin et al. 2009, Fossey et al. In October 2010 monitoring was intensified at HET and 2009; HD 17156, Fischer et al. 2007, Barbieri et al. 2007; at Keck Observatory by A.W.H., G.W.M., J.T.W., and both highly eccentric systems were discovered first with H.I., and with these new RV data and the previously radial velocities). published measurements from Wittenmyer et al. (2007) Long period planets not known to transit can have they obtained a preliminary solution for the outer planet. long transit windows due to both the large duration of The discrepancy between the original orbital fit and the any edge-on transit and higher phase uncertainties (since new fit (assuming one planet) was presented at the Jan- such uncertainties scale with the period of the orbit). uary 2011 meeting of the American Astronomical Society Long term radial velocity monitoring of stars, for in- (Kane et al. 2011c). stance for the discovery of low amplitude signals, can produce collateral benefits in the form of orbit refine- 1.4. Synthesis and Outline ment for a transit search and the identification of Jupiter In early 2011, the Texas and TERMS teams combined analogs (e.g., Wright et al. 2009). Herein, we describe an efforts and began joint radial velocity analysis, dynam- example of both. ical modeling, spectroscopic analysis, and photometric observations (Kane et al. 2012). The resulting complete 1.2. Initial Discovery and Followup two-planet orbital solution allows for a sufficiently pre- The inner planet in the system, HD 37605b, was the cise transit ephemeris for the b component to be calcu- first planet discovered with the Hobby-Eberly Telescope lated for a thorough transit search. We herein report the (HET) at McDonald Observatory (Cochran et al. 2004). transit exclusion of HD 37605b and a stable dynamical It is a super Jupiter (M sin i =2.41 MJup) on an eccen- solution to the system. tric orbit e =0.67 with an orbital period in the “period In 2, we describe our spectroscopic observations and § valley” (P = 55 days; Wright et al. 2009). analysis, which provided the radial velocities and the stel- W.C., M.E., and P.J.M. of the University of Texas at lar properties of HD 37605. 3 details the orbital solu- § Austin, continued observations in order to get a much tion for the HD 37605 system, including a comparison better orbit determination and to begin searching for with MCMC Keplerian fits, and our dynamical analysis. transits. With the first new data in the fall of 2004, We report our photometric observations on HD 37605 it became obvious that another perturber was present in and the dispositive null detection15 of non-grazing tran- the system, first from a trend in the radial velocity (RV) sits of HD 37605b in 4. After 5, Summary and Con- § § residuals (i.e., a none-zero dv/dt; Wittenmyer et al. clusion, we present updates on M sin i of two previously 2007), and later from curvature in the residuals. By published systems (HD 114762 and HD 168443) in 6. In the Appendix we describe the algorithm used in§ the 13 HD 13931b (Howard et al. 2010), HD 72659b (Moutou et al. package BOOTTRAN (for calculating orbital parameter 2011), 55 Cnc d (Marcy et al. 2002), HD 134987c (Jones et al. error bars; see 3.2). 2010), HD 154345b (Wright et al. 2008, but with possibility of be- § ing an activity cycle-induced signal), µ Ara c (Pepe et al. 2007), 15 A dispositive null detection is one that disposes of the ques- HD 183263c (Wright et al. 2009), HD 187123c (Wright et al. 2009), tion of whether an effect is present, as opposed to one that merely and GJ 832b (Bailey et al. 2009). fails to detect a purported or hypothetical effect that may yet lie 14 55 Cnc e (McArthur et al. 2004; Demory et al. 2011), HD beneath the detection threshold. The paragon of dispositive null 189733 (Bouchy et al. 2005), and HD 209458 (Henry et al. 2000; detections is the Michelson-Morley demonstration that the luminif- Charbonneau et al. 2000). erous ether does not exist (Michelson & Morley 1887). 3

2. SPECTROSCOPIC OBSERVATIONS AND ANALYSIS TABLE 1 2.1. HET and Keck Observations STELLAR PARAMETERS Observations on HD 37605 at HET started Decem- ber of 2003. In total, 101 RV observations took place Parameter Value over the course of almost eight years, taking advantage Spectral typea K0 V of the queue scheduling capabilities of HET. The queue a scheduling of HET allows for small amounts of telescope Distance (pc) 44.0 ± 2.1 ± time to be optimally used throughout the year, and for V 8.661 0.013 Teff (K) 5448 ±44 new observing priorities to be implemented immediately, log g 4.511 ± 0.024 rather than on next allocated night or after TAC and [Fe/H] 0.336 ± 0.030 scheduling process (Shetrone et al. 2007). The observa- BC -0.144 tions were taken through the High Resolution Spectro- Mbol 5.301 graph (HRS; Tull 1998) situated at the basement of the L⋆ (L⊙) 0.590 ± 0.058 c HET building. This fiber-fed spectrograph has a typical R⋆ (R⊙) 0.901 ± 0.045 −1 c long-term Doppler error of 3 – 5 m s (Baluev 2009). M⋆ (M⊙) 1.000 ± 0.050 The observations were taken with the spectrograph con- v sin i < 1 km s−1 figured at a resolving power of R =60,000. For more Ageb ∼ 7 Gyr details, see Cochran et al. (2004). a ESA (1997); van Leeuwen (2008). Observations at Keck were taken starting August b Isaacson & Fischer (2010), see § 4.1. 2006. A set of 33 observations spanning over five years c 5% relative errors, not the SME intrinsic errors. were made through the HIRES spectrometer (Vogt et al. See footnote 17 for details. 1994) on the Keck I telescope, which has a long-term Doppler error of 0.9 – 1.5 m s−1 (e.g. Howard et al. 2009). The observations were taken at a resolving power HET/HRS observations and one from Keck/HIRES. of R =55,000. For more details, see Howard et al. (2009) Throughout this work, we use the Keck DSST, which and Valenti et al. (2009). is of better quality thanks to a better known IRF of Both our HET and Keck spectroscopic observations HIRES and a superior deconvolution algorithm in the were taken with an iodine cell placed in the light path CPS pipeline (Howard et al. 2009, 2011). to provide wavelength standard and information on the Then the pipeline proceeds with barycentric correc- instrument response function16 (IRF) for radial velocity tion and radial velocity extraction for each observa- extraction (Marcy & Butler 1992; Butler et al. 1996). In tion. We have adopted the Doppler code from CPS (e.g. addition, we also have observations taken without iodine Howard et al. 2009, 2011; Johnson et al. 2011b). The cell to produce stellar spectrum templates – on HET and code is tailored to be fully functional with HET/HRS- Keck, respectively. The stellar spectrum templates, after formatted spectra, and it is capable of working with ei- being deconvolved with the IRF, are necessary for both ther an HET DSST or a Keck one. radial velocity extraction and stellar property analysis. The 101 HET RV observations include 44 observations The typical working wavelength range for this technique which produced the published velocities in Cochran et al. ˚ ˚ (2004) and Wittenmyer et al. (2007), 34 observations is roughly 5000 A– 6000 A. also done by the Texas team in follow-up work after 2007, 2.2. Data Reduction and Doppler Analysis and 23 observations taken as part of TERMS program. We have performed re-reduction on these 44 observations In this section, we describe our data reduction and together with all the rest 57 HET observations through Doppler analysis of the HET observations. We re- our pipeline. This has the advantage of eliminating one duced the Keck data with the standard CPS pipeline, free parameter in the Keplerian fit – the offset between as described in, for example, Howard et al. (2011) and two Doppler pipelines. Johnson et al. (2011b). Two out of the 101 HET observations were excluded We have constructed a complete pipeline for analyz- due to very low average signal-to-noise ratio per pixel ing HET data – from raw data reduction to radial ve- (< 20), and one observation taken at twilight was also locity extraction. The raw reduction is done using the rejected as such observation normally results in low accu- REDUCE package by Piskunov & Valenti (2002). This racy due to the significant contamination by the residual package is designed to optimally extract echelle spectra solar spectrum (indeed this velocity has a residual of over from 2-D images (Horne 1986). Our pipeline corrects for 100 m s−1 against best Keplerian fit, much larger than cosmic rays and scattered light. In order to make the the 8ms−1 RV error). data reduction process completely automatic, we have All∼ the HET and Keck radial velocities used in this developed our own algorithm for tracing the echelle or- work (98 from HET and 33 from Keck) are listed in Table ders of HRS and replaced the original semi-automatic 7. algorithm from the REDUCE package. After the raw data reduction, the stellar spectrum tem- 2.3. Stellar Analysis plate is deconvolved using IRF derived from an iodine flat on the night of observation. There were two decon- HD 37605 is a K0 V star (V 8.7) with high proper ∼ volved stellar spectrum templates (DSST) derived from motion at a distance of 44.0 2.1 pc (ESA 1997; van Leeuwen 2008). We derived± its stellar properties 16 Some authors refer to this as the “point spread function” or based on analysis on a high-resolution spectrum taken the “instrumental profile” of the spectrograph. with Keck HIRES (without iodine cell in the light path). 4

Table 1 lists the results of our analysis17, including the ef- to predict the phase of a planet at any point in the fective temperature Teff , surface gravity log g, iron abun- future in principle, but the uncertainties in those param- dance [Fe/H], projected rotational velocity v sin i, bolo- eters alone are insufficient to compute the uncertainty metric correction BC, bolometric magnitude Mbol, stellar in orbital phase without detailed knowledge of the luminosity L⋆, stellar radius R⋆, stellar mass M⋆ and age. covariances among the parameters. HD 37605 is found to be a metal rich star ([Fe/H] 0.34) This problem is particularly acute when determining ∼ with M 1.0 M⊙ and R 0.9R⊙. transit or secondary eclipse times for planets with near ⋆ ∼ ⋆ ∼ We followed the procedure described in circular orbits, where σTp and σω can be highly covariant. Valenti & Fischer (2005) and also in Valenti et al. In such cases the circular case is often not excluded by (2009) with improvements. Briefly, the observed the data, and so the estimation of e includes the case spectrum is fitted with a synthetic spectrum using Spec- e = 0, where ω is undefined. If the best or most likely troscopy Made Easy (SME; Valenti & Piskunov 1996) value of e in this case is small but not zero, then it is to derive Teff , log g, [Fe/H], v sin i, and so on, which associated with some nominal value of ω, but σω will are used to derive the bolometric correction BC and L⋆ be very large (approaching π). Since Tp represents the consequently. Then an isochrone fit by interpolating epoch at which the true anomaly equals 0, Tp will have a tabulated Yonsei-Yale isochrones (Demarque et al. 2004) similarly large uncertainty (approaching P ), despite the using derived stellar parameters from SME is performed fact that the phase of the system may actually be quite to calculate M⋆ and log giso values (along with age and precisely known! stellar radius). Next, Valenti et al. (2009) introduced In practice even the ephemerides of planets with well an outside loop which re-runs SME with log g fixed at measured eccentricities suffer from lack of knowledge of log giso, followed by another isochrone fit deriving a new the covariance in parameters, in particular Tp and P log log giso using the updated SME results. The loop (whose covariance is sensitive to the approximate epoch continues until log g values converge. This additional chosen for Tp). To make matters worse, the nature of iterative procedure to enforce self-consistency on log g is “1σ” uncertainties in the literature is inconsistent. Some shown to improve the accuracy of other derived stellar authors may report uncertainties generated while holding parameters (Valenti et al. 2009). The stellar radius all or some other parameters constant (for instance, by and log g reported here in Table 1 are derived from the seeing at what excursion from the nominal value χ2 is re- final isochrone fit, which are consistent with the purely duced by 1), while others using bootstrapping or MCMC spectroscopic results. The gravity (log g = 4.51) is also techniques may report the variance in a parameter over consistent with the purely spectroscopic gravity (4.44) the full distribution of trials. In any case, covariances are based on strong Mg b damping wings, so for HD 37605 rarely reported, and in some cases authors even report the iteration process is optional. the most likely values on a parameter-by-parameter basis Cochran et al. (2004) reported the values of Teff , log g, rather than a representative “best fit”, resulting in a set and [Fe/H] for HD 37605, and their estimates agree with of parameters that is not self-consistent. ours within 1σ uncertainty. Santos et al. (2005) also es- The TERMS strategy for refining ephemerides there- timated Teff , log g, [Fe/H], and M⋆, all of which agree fore begins with the recalculation of transit time uncer- with our values within 1σ. Our stellar mass and radius tainties directly from the archival radial velocity data. estimates are also consistent with the ones derived from We used bootstrapping (see Appendix) with the time of the empirical method by Torres et al. (2010). conjunction, Tc (equivalent to transit center, in the case Our SME analysis indicates that the rotation of the of transiting planets) computed independently for each star (v sin i) is likely < 1km s−1 (corresponding to rota- trial. For systems whose transit time uncertainty makes tion period & 46 days). We have used various methods to definitive observations implausible or impossible due to estimate stellar parameters from the spectrum, including the accumulation of errors in phase with time, we sought the incorporation of color and absolute magnitude infor- additional RV measurements to “lock down” the phase mation and the Mg b triplet to constrain log g, and var- of the planet. ious macroturbulent velocity prescriptions. All of these approaches yield results consistent with an undetectable 3.2. The 37605 System level of rotational broadening, with an upper limit of 1-2 −1 There are in total 137 radial velocities used in the Kep- km s , consistent with the tentative photometric period lerian fit for the HD 37605 system. In addition to the 98 57.67 days derived from the APT data (See 4.1). § HET velocities and 33 Keck ones (see 2.2), we also in- 18 § 3. ORBITAL SOLUTION cluded six velocities from Cochran et al. (2004) which 3.1. Transit Ephemeris were derived from observations taken with the McDon- ald Observatory 2.1 m Telescope (hereafter the 2.1 m The traditional parameters for reporting the telescope). ephemerides of spectroscopic binaries are P,K,e,ω, We used the RVLIN package by Wright & Howard and Tp, the last being the time of periastron passage (2009) to perform the Keplerian fit. This package is (Wright & Howard 2009). This information is sufficient based on the Levenberg–Marquardt algorithm and is

17 made efficient in searching parameter space by exploiting Note that the errors on the stellar radius R⋆ and mass M⋆ the linear parameters. The uncertainties of the parame- listed in Table 1 are not intrinsic to the SME code, but are 5%×R⋆ and 5%×M⋆. This is because the intrinsic errors reported by SME do not include the errors stemming from the adopted stellar mod- 18 The velocity from observation on BJD 2, 453, 101.6647 was els, and a more realistic precision for R⋆ and M⋆ would be around rejected as it was from a twilight observation, which had both low −1 ∼ 5%. Intrinsic errors reported by SME are 0.015 L⊙ for R⋆ and precision (σRV = 78.12ms ) and low accuracy (having a residual −1 0.017 M⊙ for M⋆. against the best Keplerian fit of over 100 m s ). 5

200 100 - HET - Keck - 2.1m

) 100 )

-1 -1 0 0 -100 -100 -200 HD 37605b -200 P = 55.013 days e = 0.6767

Velocity (m s -300 Velocity (m s -300 -400 -400 2004 2006 2008 2010 2012 0.0 0.2 0.4 0.6 0.8 1.0 Year Orbital Phase 40 60

) - HET - Keck - 2.1m ) 40 -1 20 -1 HD 37605c 20 P = 2720 days e = 0.013 0 0 20 -20 Velocity (m s Residual (m s 40 -40 60 2004 2006 2008 2010 2012 2004 2006 2008 2010 2012 Year Year

Fig. 1.— Radial velocity and Keplerian model plots for the HD 37605 system. In all panels, HET observations are labeled with black filled circles, Keck observations are labeled with red crosses, and the velocities from the 2.1 m telescope (Cochran et al. 2004) are labeled with blue triangles. Best Keplerian fits are plotted in black solid lines. Top left: The best-fit 2-planet Keplerian model (solid line) and the observed radial velocities from 3 telescopes. The HET and Keck velocities have been adjusted to take into account the velocity offsets (i.e., subtracting ∆HET and ∆Keck from the velocities, respectively; see Table 2 and § 3.2). Bottom left: Residual velocities after subtracting the best-fit 2-planet Keplerian model. The lengend gives the typical size of the error bars using the ± median RV error for each telescope (for 2.1 m telescope only the lower half is shown). Top right: RV signal induced by HD 37605b alone, phased up to demonstrate our coverage. Bottom right: RV signal induced by HD 37605c alone. The two vertical dashed lines denote the date of our first observation, and the date when HD 37605c closes one orbit, respectively. (A color version of this figure is available in the online journal.) ters are calculated through bootstrapping (with 1, 000 bootstrap replicates) using the BOOTTRAN package, which is described in detail in the Appendix19. The best-fit Keplerian parameters are listed in Table 2. The joint Keplerian fit for HD 37605b and HD 37605c has 13 free parameters: the orbital period P , time of perias- tron passage Tp, velocity semi-amplitude K, eccentricity e, and the argument of periastron referenced to the line of nodes ω for each planet; and for the system, the ve- locity offset between the center of the mass and barycen- ter of solar system γ and two velocity offsets between the three telescopes (∆Keck and ∆HET, with respect to the velocities from the 2.1 m telescope as published in Cochran et al. 2004). We did not include any stellar jit- ter or radial velocity trend in the fit (i.e., fixed to zero). The radial velocity signals and the best Keplerian fits for the system, HD 37605b only, and HD 37605c only are 2 Fig. 2.— χν map for the best Keplerian fits with fixed values plotted in the three panels of Fig. 1, respectively. of period P and minimum planet mass M sin i for HD 37605c. Adopting a stellar mass of M⋆ =1.000 0.017 M⊙ (as This is showing that both P and M sin i are well-constrained for in Table 1), we estimated the minimum± mass (M sin i) this planet. The levels of the contours mark the 1σ (68.27%), 2σ 2 for HD 37605b to be 2.802 0.011 MJup and 3.366 (95.45%) and 3σ (99.73%) confidence intervals for the 2-D χ dis- ± ± tribution. 0.072 MJup for HD 37605c. While HD 37605b is on a close-in orbit at a = 0.2831 0.0016 AU that is highly ± 19 The BOOTTRAN package is made publicly available online eccentric (e = 0.6767 0.0019), HD 37605c is found to at http://exoplanets.org/code/ and the Astrophysics Source Code be on a nearly circular± orbit (e = 0.013 0.015) out at Library. a = 3.814 0.058 AU, which qualifies it± as one of the ± 6

i.e. high values are penalized. For a detailed discussion TABLE 2 of priors, strategies to deal with correlated parameters, KEPLERIAN FIT PARAMETERS the choice of the proposal transition probability distri- bution function, and other details of the algorithm, we Parameter HD 37605b HD 37605c refer the reader to the original papers: Ford (2005, 2006); P (days) 55.01307 ± 0.00064 2720 ± 57 Ford & Gregory (2007). The likelihood for radial veloc- a Tp (BJD) 2453378.241 ± 0.020 2454838 ± 581 ity terms assumes that each radial velocity observation b Tc (BJD) 2455901.361 ± 0.069 ··· (vi) is independent and normally distributed about the −1 2 2 K (m s ) 202.99 ± 0.72 48.90 ± 0.86 true radial velocity with a variance of σi +σj , where σi is e 0.6767 ± 0.0019 0.013 ± 0.015 the published measurement uncertainty. σj is a jitter pa- ω (deg) 220.86 ± 0.28 221 ± 78 rameter that accounts for additional scatter due to stel- M sin i (MJup) 2.802 ± 0.011 3.366 ± 0.072 lar variability, instrumental errors and/or inaccuracies in a (AU) 0.2831 ± 0.0016 3.814 ± 0.058 the model (i.e., neglecting planet-planet interactions or γ (m s−1) −50.7 ± 4.6 −1 c additional, low amplitude planet signals). ∆Keck (m s ) 55.1 ± 4.7 −1 c We used an MCMC method based upon Keplerian or- ∆HET (m s ) 36.7 ± 4.7 2 bits to calculate a sample from the posterior distribu- χν 2.28 (d.o.f. = 124) −1 tion (Ford 2006). We calculated 5 Markov chains, each rms (m s ) 7.61 8 −1 d with 2 10 states. We discarded the first half of Jitter (m s ) 3.6 ∼ × a the chains and calculate Gelman-Rubin test statistics Time of Periastron passage. for each model parameter and several ancillary variables. b Time of conjunction (mid-transit, if the system transits). c Offset with respect to the velocities from the 2.1 m telescope. We found no indications of non-convergence amongst the d −1 2 4 If a jitter of 3.6 m s is added in quadrature to all RV errors, χν individual chains. We randomly drew 3 10 solutions becomes 1.0. from the second half of the Markov chains,× creating a “Jupiter analogs”. sample set of the converged overall posterior distribu- In order to see whether the period and mass of tion of solutions. We then interrogated this sample on the outer planet, HD 37605c, are well constrained, we a parameter-by-parameter basis to find the median and 2 mapped out the χν values for the best Keplerian fit in 68.27%(1σ) values reported in Table 3. We refer to this the Pc-Mc sin i space (subscript ‘c’ denoting parameters solution set below as the “best-fit” MCMC solutions. 2 for the outer planet, HD 37605c). Each χν value on the We note that the periods of the two planets found in P -M sin i grid was obtained by searching for the best-fit this system are very widely separated (Pc/Pb 50), c c ∼ model while fixing the period Pc for the outer planet and so we do not expect planet-planet interactions to be requiring constraints on Kc and ec to maintain M sin i strong, hence we have chosen to forgo a numerically fixed. As shown in Fig. 2, our data are sufficient to have intensive N-body DEMCMC fitting procedure (see e.g. both Pc and Mc sin i well-constrained. This is also con- Johnson et al. 2011a; Payne & Ford 2011) as the non- sistent with the tight sampling distributions for Pc and Keplerian perturbations should be tiny (detail on the Mc sin i found in our bootstrapping results. magnitude of the perturbations is provided in 3.4). The rms values against the best Keplerian fit are 7.86 However, to ensure that the Keplerian fits generated§ ms−1 for HET, 2.08 m s−1 for Keck, and 12.85 m s−1 for are stable, we took the results of the Keplerian MCMC the 2.1 m telescope. In the case of HET and Keck, their fits and injected those systems into the Mercury n-body rms values are slightly larger than their typical reported package (Chambers 1999) and integrated them forward RV errors ( 5ms−1 and 1ms−1, respectively). This for 108 years. This allows us to verify that all of the might be due∼ to stellar jitter∼ or underestimated system- selected∼ best-fit systems from the Keplerian MCMC anal- 2 atic errors in the velocities. We note that the χν is re- ysis are indeed long-term stable. Further details on the duced to 1.0 if we introduce a stellar jitter of 3.6 m s−1 dynamical analysis of the system can be found in 3.4. (added in quadrature to all the RV errors). We assumed that all systems are coplanar and edge-on§ for the sake of this analysis, hence all of the masses used 3.3. Comparison with MCMC Results in our n-body analyses are minimum masses. We compared our best Keplerian fit from RVLIN As shown in Table 3 and Fig. 3, the parameter es- and uncertainties derived from BOOTTRAN (abbrevi- timates from RVLIN+BOOTTRAN and MCMC meth- ated as RVLIN+BOOTTRAN hereafter) with that from ods agree with each other very well (all within 1-σ er- a Bayesian framework following Ford (2005) and Ford ror bar). In some cases, the MCMC analysis reports (2006) (referred to as the MCMC analysis hereafter). Ta- error bars slightly larger than bootstrapping method ble 3 lists the major orbital parameters from both meth- ( 20% at most). We note that the relatively large ∼ not ods for a direct comparison. Fig. 3 illustrates this com- MCMC confidence intervals are significantly reduced if one conducts an analysis at a fixed jitter level (e.g. parison, but with the MCMC results presented in terms −1 of 2-D confidence contours for P , e, K, M sin i, and ω of σJ =3.5m s ) unless one goes to an extremely low jitter value (e.g. 1.5m s−1). That is, the larger MCMC er- both planets, as well as for Tc of HD 37605b. ∼ For the Bayesian analysis, we assumed priors that ror bars do not simply result from treating the jitter as a are uniform in log of orbital period, eccentricity, argu- free parameter. For the uncertainties on minimum planet ment of pericenter, mean anomaly at epoch, and the mass M sin i and semi-major axes a, the MCMC analy- velocity zero-point. For the velocity amplitude (K) sis does not incorporate the errors on the stellar mass and jitter (σj ), we adopted a prior of the form p(x) = estimate. Note here, as previously mentioned in 3.1, −1 −1 −1 that the “best-fit” parameters reported by the MCMC§ (x + xo) [log(1 + x/xo)] , with Ko = σj,o =1ms , 7 2900 0.08 2850 0.07 0.06 2800 0.05 c

2750 e 0.04 [days]

c 0.03

P 2700 0.02 2650 0.01 2600 0 55.01 55.012 55.014 0.668 0.672 0.676 0.68

Pb [days] eb

52 3.55

51 ] 3.5 J 3.45 50

) [M 3.4 49 c 3.35 [m/s] c 3.3 K 48 sin(i c 3.25 47 M 3.2 46 3.15 201 202 203 204 205 206 207 2.78 2.8 2.82 2.84

Kb [m/s] Mb sin(ib) [MJ]

360 315 0.1 270 225 180 [deg] 0.05 c 135 ω 90 Fraction 45 0 0 220 221 222 0 0.2 0.4 0.6 ω b [deg] TC [JD - 2455901] Fig. 3.— Comparison between the Bayesian (MCMC) analysis and RVLIN+BOOTTRAN results. Top four and bottom left: Contours of the posterior distributions of selected orbital parameters (P , e, K, M sin i, and ω) based on the MCMC analysis (dashed dotted line). The x-axes are orbital parameters of the inner planet, b, and the y-axes are those of the outer planet, c. The inner contours mark the 68.27% (‘1σ’) 2-D confidence regions and the outer ones are 95.45% (‘2σ’) ones. Also plotted are the best Keplerian fit from RVLIN (blue squares) and ±1σ error bars estimated via bootstrapping (blue bars). Bottom right: Marginalized posterior distribution of time of conjunction (mid-transit) Tc of HD 37605b in dashed dotted line. The solid grey vertical line is the median of the distribution, and the dashed grey vertical lines mark 1σ confidence interval. The blue square and its error bars are for the best estimate of Tc from RVLIN+BOOTTRAN and its ±1σ errors. See § 3.3 for details. (A color version of this figure is available in the online journal.) analysis here listed in Table 3 are not a consistent set, We used the best-fit Keplerian MCMC parameters as as the best estimates were evaluated on a parameter-by- the basis for a set of long-term numerical (n-body) in- parameter basis, taking the median from marginalized tegrations of the HD 37605 system using the Mercury posterior distribution of each. Assuming no jitter, The integration package (Chambers 1999). We used these best Keplerian fit from RVLIN has a reduced chi-square integrations to verify that the best-fit systems: (i) are 2 value χν = 2.28, while the MCMC parameters listed in long-term stable; (ii) do not exhibit significant variations 2 Table 3 give a higher χν value of 2.91. in their orbital elements on the timescale of the observa- tions (justifying the assumption that the planet-planet interactions are negligible); (iii) do not exhibit any other unusual features. We emphasize again that the planets in 3.4. Dynamical Analysis this system are well separated and we do not expect any 8

TABLE 3 COMPARISON WITH MCMC RESULTS

Parameter HD 37605b HD 37605c RVLIN+BOOTTRAN MCMCa RVLIN+BOOTTRAN MCMCa

P (days) 55.01307 ± 0.00064 55.01250 +0.00073 −0.00075 2720 ± 57 2707 +57 −42 Tp (BJD) 2453378.243 ± 0.020 2453378.243 +0.025 −0.024 2454838 ± 581 2454838 +354 −435 Tc (BJD) 2455901.361 ± 0.069 2455901.314 +0.077 −0.081 ······ K (m s−1) 202.99 ± 0.72 203.91 +0.92 −0.88 48.90 ± 0.86 48.93 +0.82 −0.82 e 0.6767 ± 0.0019 0.6748 +0.0022 −0.0023 0.013 ± 0.015 0.025 +0.022 −0.017 ω (deg) 220.86 ± 0.28 220.75 +0.33 −0.32 221 ± 78 223 +50 −52 M (deg)b 62.31 ± 0.15 62.27 +0.18 −0.18 117 ± 78 118 +56 −51 M sin i (MJup) 2.802 ± 0.011 2.814 +0.012 −0.012 3.366 ± 0.072 3.348 +0.065 −0.062 a (AU) 0.2831 ± 0.0016 0.2833364 +0.0000027 −0.0000027 3.814 ± 0.058 3.809 +0.053 −0.040 Jitter (m s−1)c 3.6 2.70 +0.53 −0.46 a Median values of the marginalized posterior distributions and the 68.27% (‘1σ’) confidence intervals. b Mean anomaly of the first observation (BJD 2, 453, 002.671503). c Like RVLIN, BOOTTRAN assumes no jitter or fixes jitter to a certain value, while MCMC treats it as a free parameter. See § 3.3.

3.759 3.765 c 3.757 3.76 a 3.755 3.755 0.00016 0.00016 8e-05 8e-05 - 0.2839

b 0 0 a 0.675 0.67

b 0.6749 0.65

e 0.6748 0.63 0.04 0.61 0.15

c 0.035 0.11 e 0.07 0.03 0.03 0 1 2 3 4 5 6 7 8 9 10 1e+06 3e+06 5e+06 7e+06 9e+06 time [yrs] time [yrs]

0.6

0.4

0.2 ω 0

e sin -0.2

-0.4

-0.6

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 e cosω Fig. 4.— Dynamic evolution of the best-fit MCMC system. On the left we plot the short-term evolution over 10 years, on the right we plot the evolution over 107 years (< 1/10 of our dynamic simulation time scale). The top plots describe the evolution of the semi-major axes and eccentricities of the inner planet (ab & eb, blue dotted lines) and the outer planet (ac & ec, red solid lines), while the bottom plot describes the parameter space covered by the e cos ω,e sin ω quantities over 108 years (the blue and larger ring for inner planet, and the red and smaller ring for outer planet). We find that over the short-term (e.g., our RV observation window of ∼ 10 years), the parameter variations are negligible, but in the long term significant eccentricity oscillations can take place (particularly noticeable in the eccentricity of the outer planet). See § 3.4 for details. (A color version of this figure is available in the online journal.) instability to occur: for the masses and eccentricities in 1993), so while Hill stability does not preclude outward question, a planet at ab 0.28 AU will have companion scatter of the outer planet, the fact that ac 3.8 0.83 orbits which are Hill stable∼ for a & 0.83 AU (Gladman AU suggests that the system will be far from∼ any≫ such 9 instability. Sun-like stars, including the precise radial velocity stan- We integrated the systems for > 108 years ( 107 dard star HD 185144 (σ Dra) show similar activity vari- the orbital period of the outer planet and > 10∼2 the× ations and that rarely, if ever, are these signals well- secular period of the system), and plot in Fig. 4 the× evo- correlated with signals similar in strength to that seen in lution of the orbital elements a, e,& ω. On the left-hand HD 154345 ( 15 m s−1), and concluded that the simi- side of the plot we provide short-term detail, illustrat- larity was therefore∼ likely just an inevitable coincidence. ing that over the 10 year time period of our observa- Put succinctly, activity cycles in Sun-like stars are com- tions, the change∼ in orbital elements will be very small. mon (Baliunas et al. 1995), but few Jupiter analogs have On the right-hand side we provide a much longer-term been discovered, meaning that the early concern that ac- view, plotting 107 out of > 108 years of system evolution, tivity cycles would mimic giant planets is not a severe demonstrating that (i) the secular variation in some of problem. the elements (particularly the eccentricity of the outer Nonetheless, there is growing evidence that activity cy- planet; see e in red) over a time span of 4 105 years cles can, in some stars, induce radial velocity variations c ∼ × can be significant: in this case we see 0.03 < ec < 0.11, (Santos et al. 2010; Lovis et al. 2011; Dumusque et al. but (ii) the system appears completely stable, as one 2012), and the example of HD 154345 still warrants care would expect for planets with a period ratio Pc/Pb 50. and concern. Most significantly, Dumusque et al. (2011) Finally, at the bottom of the figure we display the range∼ found a positive correlation between chromospheric ac- of parameter space covered by the ei cos ωi, ei sin ωi pa- tivity and precise radial velocity in the average measure- rameters (i = b in blue for inner planet and i = c in red ments of a sample of HARPS stars, and provided a for- for outer planet), demonstrating that the orbital align- mula for predicting the correlation strength as a function ments circulate, i.e. they do not show any signs of res- of the metallicity and effective temperature of the star. −1 onant confinement, which confirms our expectation of Their formulae predict a value of 2 m s for the most minimal planet-planet interaction as mentioned before. suspicious case in the literature, HD 154345 (compared to As noted above, our analysis assumed coplanar plan- an actual semiamplitude of 15 m s−1), but are rather ets. As such the planetary masses used in these dynam- uncertain. It is possible that∼ in a few, rare cases, the ical simulations are minimum masses. We note that for formula might significantly underestimate the amplitude inclined systems, the larger planetary masses will cause of the effect. increased planet-planet perturbations. To demonstrate The top panel of Fig. 5 plots the T12 APT observations this is still likely to be unimportant, we performed a 108 from all five observing seasons (data provided in Table year simulation of a system in which 1/ sin i = 10, push- 4; see details on APT photometry in 4.1). The dashed § ing the planetary masses to 30 MJup. Even in such a line marks the mean relative magnitude (∆(b + y)/2) of pathological system the eccentricity∼ oscillations are only the first season. The seasonal mean brightness of the increased by a factor of 2 and the system remains com- star increases gradually from year to year by a total of pletely stable for the duration∼ of the simulation. 0.002 mag, which may be due to a weak long-term We also performed a separate Transit Timing Variation magnetic∼ cycle. However, no evidence is found in support (TTV) analysis, using the best-fit MCMC systems as the of such a cycle in the Mount Wilson chromospheric Ca ii basis for a set of highly detailed short-term integrations. H & K indices (Isaacson & Fischer 2010), although the From these we extracted the times of transit and found S values vary by approximately 0.1 over the span of a a TTV signal 100 s, or 0.001 day, which is much few years. The formulae of Lovis et al. (2011) predict a ∼ ∼ −1 smaller than the error bar on Tc ( 0.07 day). Therefore corresponding RV variation of less than 2 m s due to we did not take into account the∼ effect of TTV when activity, far too small to confound our planet detection performing our transit analysis in the next section. with K =49ms−1. Since we do not have activity measurements for this 3.5. Activity Cycles and Jupiter Analogs target over the span of the outer planet’s orbit in HD 37605, we cannot definitively rule out activity cycles as The coincidence of the Solar activity cycle period of the origin of the effect, but the strength of the outer 11 years and Jupiter’s orbital period near 12 years illus- planetary signal and the lack of such signals in other trates how activity cycles could, if they induced apparent stars known to cycle strongly dispels concerns that the line shifts in disk-integrated stellar spectra, confound at- longer signal is not planetary in origin. tempts to detect Jupiter analogs around Sun-like stars. Indeed, Dravins (1985) predicted apparent radial velocity 4. THE DISPOSITIVE NULL DETECTION OF TRANSITS variations of up to 30 m s−1 in solar lines due to the So- OF HD 37605b lar cycle, and Deming et al. (1987) reported a tentative We have performed a transit search for the inner planet detection of such a signal in NIR CO lines of 30 m s−1 in of the system, HD 37605b. This planet has a tran- just 2 years, and noted that such an effect would severely sit probability of 1.595% and a predicted transit dura- hamper searches for Jupiter analogs. That concern was tion of 0.352 day, as derived from the stellar parame- further amplified when Campbell et al. (1991) reported a ters listed in Table 1 and the orbital parameters given positive correlation between radial velocity and chromo- in Table 2. From the minimum planet mass (M sin i = 1 spheric activity in the active star κ Cet, with variations 2.802 0.011 MJup; see Table 2) and the models of of order 50–100 m s−1. Bodenheimer± et al. (2003), we estimate its radius to be Wright et al. (2008) found that the star HD 154345 Rp =1.1 RJup. Combined with the stellar radius of HD has an apparent Jupiter analog (HD 154345 b), but that 37605 listed in Table 1, R⋆ =0.901 0.015 R⊙, we esti- this star also shows activity variations in phase with mate the transit depth to be 1.877%± (for an edge-on tran- the radial velocity variations. They noted that many sit, i = 90◦). We used both ground-based (APT; 4.1) § 10

Fig. 6.— Brightness variability in HD 37605 possibly induced by stellar rotation at P = 57.67 ± 0.30 days. Top panel is the periodogram of the complete, normalized data set. Bottom panel shows the normalized photometry folded with this possible rotation period. The peak-to-peak amplitude is 0.00120 ± 0.00021 mag. See § 4.1 for more.

TABLE 4 PHOTOMETRIC OBSERVATIONS OF HD 37605 FROM THE T12 0.8m APT Fig. 5.— Photometric observations of HD 37605 acquired over five years with the T12 0.8m APT. The top panel shows the entire Heliocentric Julian Date ∆(b + y)/2 five-year data set; the dotted line represents the mean brightness of (HJD − 2,400,000) (mag) the first observing season. A long-term brightening trend is evident with a total range in the seasonal means of 0.002 mag. The middle 54,481.7133 1.4454 panel shows the photometric data normalized so that each season has the same mean as the first and then phased to the orbital 54,482.6693 1.4474 period of HD 37605b (55.01307 day). The solid line is the predicted 54,482.7561 1.4442 transit light curve, with Phase 0.0 being the predicted time of mid- 54,483.6638 1.4452 transit, Tc. A least-squares sine fit of the phased data produces the 54,495.7764 1.4469 very small semi-amplitude of 0.00031 ± 0.00011 mag, providing 54,498.7472 1.4470 strong evidence that the observed radial-velocity variations are not produced by rotational modulation of surface activity on the star. Note. — This table is presented in its The bottom panel plots the observations near Tc at an expanded entirety in the electronic edition of the As- scale on the abscissa. The horizontal bar below the transit window trophysical Journal. A portion is shown here represents the ±1σ uncertainty in Tc. Unfortunately, none of the APT observations fall within the predicted transit window, so we for guidance regarding its form and content. are unable to rule out transits with the APT observations. See § 4.1 for more. comparison of the differential magnitudes of these three and space-based (MOST; 4.2) facilities in our search. § comp stars demonstrates that all three are constant to 0.002 mag or better from night to night, consistent with 4.1. APT Observations and Analysis typical single-measurement precision of the APT (0.0015- The T12 0.8-m Automatic Photoelectric Telescope 0.002 mag; Henry 1999). (APT), located at Fairborn Observatory in south- Fig. 5 illustrates the APT photometric data and our ern Arizona, acquired 696 photometric observations of transit search. As mentioned in 3.5, the top panel HD 37605 between 2008 January 16 and 2012 April 7. shows all of our APT photometry§ covering five observ- Henry (1999) provides detailed descriptions of observing ing seasons, which exhibits a small increasing trend in and data reduction procedures with the APTs at Fair- the stellar brightness. To search for the transit signal born. The measurements reported here are differential of HD 37605b, the photometric data were normalized so magnitudes in ∆(b + y)/2, the mean of the differential that all five seasons had the same mean (referred to as magnitudes acquired simultaneously in the Str¨omgren b the “normalized photometry” hereafter). The data were and y bands with two separate EMI 9124QB bi-alkali then phased at the orbital period of HD 37605b, 55.01307 photomultiplier tubes. The differential magnitudes are days, and the predicted time of mid-transit, Tc, defined computed from the mean of three comparison stars: as Phase 0. The normalized and phased data are plot- HD 39374 (V = 6.90, B V = 0.996, K0 III), HD 38145 ted in the middle panel of Fig. 5. The solid line is the (V = 7.89, B V = 0.326,− F0 V), and HD 38779 (V = predicted transit light curve, with the predicted transit 7.08, B V =− 0.413, F4 IV). This improves the precision duration (0.352 day or 0.0064 phase unit) and transit of each− individual measurement and helps to compensate depth (1.877% or 0.020 mag) as estimated above. The for any real microvariability in the comp stars. Inter- scatter of the phased∼ data from their mean is 0.00197 11

TABLE 5 PHOTOMETRIC OBSERVATIONS OF HD 37605 ON MOST

Heliocentric Julian Date Relative Magnitude (HJD − 2,451,545) (mag)

4355.5105 -0.0032 4355.5112 -0.0047 4355.5119 -0.0018 4355.5126 -0.0026 4355.5133 -0.0018 4355.5140 -0.0039 Note. — This table is presented in its entirety in the electronic edition of the As- trophysical Journal. A portion is shown here for guidance regarding its form and content. Fig. 7.— Photometric observations of HD 37605 by the MOST satellite, which rule out the edge-on transit of HD 37605b at a ≫ mag, consistent with APT’s single-measurement preci- 10σ level. The solid line is the predicted transit light curve, and the sion, and thus demonstrates that the combination of our dashed vertical lines are the 1σ transit window boundaries defined by adding σTc (0.069 day) on both sides of the predicted transit photometric precision and the stability of HD 37605 is window (0.352-day wide). See § 4.2 for more details. easily sufficient to detect the transits of HD 37605b in our phased data set covering five years. A least-squares sine As noted earlier, the near-integer period of HD 37605b fit of the phased data gives a very small semi-amplitude makes it difficult to observe from a single longitude. The of 0.00031 0.00011 mag (consistent with zero) and ± brightness of the target and the relatively long predicted so provides strong evidence that the observed radial- transit duration creates additional challenges for ground- velocity variations are not produced by rotational mod- based observations. We thus observed HD 37605 during ulation of surface activity on the star. 2011 December 5–6 (around the predicted Tc at BJD The bottom panel of Fig. 5 plots the phased data 2, 455, 901.361 as listed in Table 2) with the MOST (Mi- around the predicted time of mid-transit, Tc, at an ex- crovariability and Oscillations of Stars) satellite launched panded scale on the abscissa. The horizontal bar below in 2003 (Walker et al. 2003; Matthews et al. 2004) in the the transit window represents the 1σ uncertainty on ± Direct Imaging mode. This observing technique is simi- Tc (0.138 day or 0.0025 phase unit for Tc’s near BJD lar to ground-based CCD photometry, allowing to apply 2, 455, 901.361; see 3.2). The light curve appears to § traditional aperture and PSF procedures for data extrac- be highly clustered, or binned, due to the near integral tion (see e.g. Rowe et al. 2006, for details). Outlying orbital period (P 55.01 days) and consequent incom- ∼ data points caused by, e.g., cosmic rays were removed. plete sampling from a single observing site. Unfortu- MOST is orbiting with a period of 101 minutes nately, none of the data clusters chance to fall within the (14.19 cycles per day, cd−1), which leads to∼ a periodic ar- predicted transit window, so we are unable to rule out tifact induced by the scattered light from the earthshine. transits of HD 37605b with the APT observations. This signal and its harmonics are further modulated with Periodogram analysis of the five individual observing a frequency of 1 cd−1 originating from the changing seasons revealed no significant periodicity between 1 and albedo of the earth. To correct for this phenomenon, 100 days. This suggests that the star is inactive and the we constructed a cubic fit between the mean background observed K 200 m s−1 RV signal (for HD 37605b) is ∼ and the stellar flux, which was then subtracted from the unlikely to be the result of stellar activity. data. The reduced and calibrated MOST photometric Analysis of the complete, normalized data set, how- data are listed in Table 5. ever, suggests a week periodicity of 57.67 0.30 days The MOST photometry is shown in Figure 7 for the with a peak-to-peak amplitude of just 0.0012± 0.0002 ± transit window observations. The vertical dashed lines mag (see Fig. 6). We tentatively identify this as the stel- indicate the beginning and end of the 1 σ transit window lar rotation period. This period is consistent with the −1 defined by adding σTc (0.069 day) on both sides of the projected rotational velocity of v sin i< 1kms derived predicted transit duration of 0.352 days. The solid line from our stellar analysis described in 2.3. It is also con- § shows the predicted transit model for the previously de- sistent with the analysis of Isaacson & Fischer (2010), scribed planetary parameters. The mean of the relative who derived a Mount Wilson chromospheric Ca ii H& ′ photometry is 0.00% (or 0.00 mag), with a rms scatter K index of S =0.165, corresponding to log RHK = 5.03. of 0.17%, and within the predicted transit window there −& Together, these results imply a rotation period 46 are 58 MOST observations. Therefore, the standard er- days and an age of 7 Gyr (see Table 1). Similarly, √ Ibukiyama & Arimoto∼ (2002) find an age of > 10 Gyr ror on the mean relative photometry is 0.17%/ 58 = using isochrones along with the Hipparcos parallax and 0.022%. This means that, for the predicted transit win- space motion, supporting HD 37605’s low activity and dow and a predicted depth of 1.877%, we can conclude long rotation period. a null detection of HD 37605b’s transit with extremely high confidence (149σ). 4.2. MOST Observations and Analysis Note that the above significance is for an edge-on tran- sit with an impact parameter of b = 0.0. A planetary 12 trajectory across the stellar disk with a higher impact parameter will produce a shorter transit duration. How- TABLE 6 Updated M sin i and Errors for HD 114762b ever, the gap between each cluster of MOST measure- and HD 168443b, c ments is 0.06 days which is 17% of the edge-on tran- sit duration. In order for the duration to be fit within the data gaps, the impact parameter would need to be Planet M sin i ± std. error (MJup) b > 0.996. To estimate a more conservative lower limit HD 114762ba 11.086 ± 0.067 for b, we now assume the most unfortunate case where HD 114762bb 11.069 ± 0.063 the transit center falls exactly in the middle of one of the HD 168443b 7.696 ± 0.015 measurement gaps, and also consider the effect of limb HD 168443c 17.378 ± 0.044 darkening by using the non-linear limb darkening model a For best orbital fit with RV trend (dv/dt). by Mandel & Agol (2002) with their fitted coefficients for b For best orbital fit without RV trend HD 209458. Even under this scenario, we can still con- (dv/dt). clude the null detection for any transit with b< 0.951 at of 1.877% at a 10σ level, with a 5σ lower limit on the & 5σ (taking into account that there are at least 20 ob- ≫ ∼ impact parameter of b 0.951. This transit exclusion is servations will fall within the transit window in this case, a further demonstration≤ of the TERMS strategy, where though only catching the shallower parts of the transit follow-up RV observations help to reduce the uncertainty light curve). on transit timing and enable transit searches. All of the above is based on the assumption that the Our best-fit orbital parameters and errors from planet has the predicted radius of 1.1 RJup. If in reality RVLIN+BOOTTRAN were found to be consistent with the planet is so small that even a b = 0 transit would fall those derived from a Bayesian analysis using MCMC. below our detection threshold, it would mean that the Based on the best-fit MCMC systems, we performed dy- planet has a radius of < 0.36 RJup (a density of > 74.50 3 namic and TTV analysis on the HD 37605 system. Dy- g/cm ), which seems unlikely. It is also very unlikely namic analysis shows no sign of orbital resonance and that our MOST photometry has missed the transit win- very minimal planet-planet interaction. We derived a dow completely due to an ill-predicted Tc. In the sam- TTV of 100 s, which is much smaller than σTc . pling distribution of Tc from BOOTTRAN (with 1000 We have∼ also performed a stellar analysis on HD 37605, replicates; see 3.2 and Appendix), there is no Tc that which shows that it is a metal rich star ([Fe/H]=0.336 § ± would put the transit window completely off the MOST 0.030) with a stellar mass of M = 1.000 0.017 M⊙ ⋆ ± coverage. In the marginalized posterior distribution of with a radius of R⋆ =0.901 0.015. The small variation Tc calculated via MCMC (see 3.3 and Fig. 3), there is seen in our photometric data± (amplitude < 0.003 mag 4 § only 1 such Tc out of 3 10 (0.003%). over the course of four years) suggests that HD 37605 is × 5. SUMMARY AND CONCLUSION consistent as being an old, inactive star that is probably slowly rotating. We tentatively propose that the rotation In this paper, we report the discovery of HD 37605c period of the star is 57.67 0.30 days, based on a weak and the dispositive null detection of non-grazing tran- periodic signal seen in our± APT photometry. sits of HD 37605b, the first planet discovered by HET. HD 37605c is the outer planet of the system with a pe- 6. NOTE ON PREVIOUSLY PUBLISHED ORBITAL FITS riod of 7.5 years on a nearly circular orbit (e =0.013) ∼ In early 2012, we repaired a minor bug in the BOOT- at a =3.814 AU. It is a “Jupiter analog” with M sin i = TRAN package, mostly involving the calculation and er- 3.366 MJup, which adds one more sample to the currently ror bar estimation of M sin i. As a result, the M sin i still small inventory of such planets (only 10 including values and their errors for two previously published sys- HD 37605c; see 1). The discovery and characterization § tems (three planets) need to be updated. They are: of “Jupiter analogs” will help understanding the forma- HD 114762b (Kane et al. 2011a), HD 168443b, and HD tion of gas giants as well as the frequency of true solar 168443c (Pilyavsky et al. 2011b). Table 6 lists the up- system analogs. This discovery is a testimony to the dated M sin i and error bars. power of continued observation of planet-bearing stars. One additional system, HD 63454 (Kane et al. 2011d), Using our RV data with nearly 8-year long baseline, we was also analyzed using BOOTTRAN. However, the refined the orbital parameters and transit ephemerides mass of HD 63454b is small enough compared to its host of HD 37605b. The uncertainty on the predicted mid- mass and thus was not affected by this change. transit time was constrained down to 0.069 day (at and near Tc = 2, 455, 901.361 in BJD), which is small com- pared to the transit duration (0.352 day). In fact, just The authors thank John A. Johnson for providing a the inclusion of the two most recent points in our RV copy of his Doppler code and his help with our incorpo- data have reduced the uncertainty on Tc by over 10%. ration of the code into the HET pipeline. The authors We have performed transit search with APT and the also thank Debra Fischer for her assistance in this re- MOST satellite. Because of the near-integer period of gard. We thank Peter Plavchan, Scott Dolim, Charley HD 37605b and the longitude of Fairborn Observatory, Noecker, and Farhan Feroz for useful discussions on the the APT photometry was unable to cover the transit win- term “dispositive null”. dow. However, its excellent photometric precision over This work was partially supported by funding from five observing seasons enabled us to rule out the possi- the Center for Exoplanets and Habitable Worlds, which bility of the RV signal being induced by stellar activity. is supported by the Pennsylvania State University, the The MOST photometric data, on the other hand, were Eberly College of Science, and the Pennsylvania Space able to rule out an edge-on transit with a predicted depth Grant Consortium. 13

The authors appreciate the significant Keck observing edge the very significant cultural role and reverence that time and associated funding support from NASA for the the summit of Mauna Kea has always had within the in- study of long period planets and mulitplanet systems. digenous Hawaiian community. We are most fortunate to J.T.W. and S.X.W. acknowledge support from NASA have the opportunity to conduct observations from this Origins of Solar Systems grant NNX10AI52G. The work mountain. of W.D.C., M.E., and P.J.M. was supported by NASA The Hobby-Eberly Telescope is a joint project of the Origins of Solar Systems Grant NNX09AB30G. E.B.F. University of Texas at Austin, the Pennsylvania State and M.J.P. were supported by NASA Origins of Solar University, Stanford University, Ludwig Maximillians Systems grant NNX09AB35G. D.D. is supported by a Universit¨at M¨unchen, and Georg August Universit¨at University of British Columbia Four Year Fellowship. G¨ottingen. The HET is named in honor of its principal The work herein is based on observations obtained at benefactors, William P. Hobby and Robert E. Eberly. the W. M. Keck Observatory, which is operated jointly This work has made use of the Exoplanet Orbit by the University of California and the California Insti- Database at exoplanets.org, the Extrasolar Planets En- tute of Technology. The Keck Observatory was made cyclopedia at exoplanet.eu, and of NASA’s Astro- possible by the generous financial support of the W.M. physics Data System Bibliographic Services. Keck Foundation. We wish to recognize and acknowl-

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APPENDIX UNCERTAINTIES VIA BOOTSTRAPPING 20 The uncertainties listed for the orbital parameter estimates and transit mid-time Tc are calculated via boot- strapping (Freedman 1981; Davison & Hinkley 1997) using the package BOOTTRAN, which we have made publicly available (see 3.2). It is designed to calculate error bars for transit ephemerides and the Keplerian orbital fit param- eters output by§ the RVLIN package(Wright & Howard 2009), but can also be a stand-alone package. Thanks to the simple concept of bootstrapping, it is computationally very time-efficient and easy to use. The basic idea of bootstrap is to resample based on original data to create bootstrap samples (multiple data repli- cates); then for each bootstrap sample, derive orbital parameters or transit parameters through orbital fitting and calculation. The ensemble of parameters obtained in this way yields the approximate sampling distribution for each estimated parameter. The standard deviation of this sampling distribution is the standard error for the estimate. We caution the readers here that there are regimes in which the “approximate sampling distribution” (a frequentist’s concept) is not an estimate of the posterior probability distribution (a Bayesian concept), and there are regimes (e.g., when limited sampling affects the shape of the χ2 surface) where there are qualitative differences and the bootstrap method dramatically underestimates uncertainties (e.g., long-period planets when the observations are not yet sufficient to pin down the orbital period; Ford 2005; Bender et al. 2012). In situations with sufficient RV data, good phase coverage, a sufficient time span of observations and a good orbital fit, bootstrap often gives a useful estimate of the parameter uncertainties. For the data considered in this paper, it was not obvious that the bootstrap uncertainty estimate would be accurate, as the time span of observations is only slightly longer than the orbital period of planet c. Nevertheless, we find good agreement between the uncertainty estimates derived from bootstrap and MCMC calculations. The radial velocity data are denoted as ~t, ~v, ~σ , where each t , v , σ represents radial velocity v observed at { } i i i i time (BJD) ti with velocity uncertainty σi. Extreme outliers should be rejected in order to preserve the validity of our bootstrap algorithm. We first derive our estimates for the true orbital parameters from the original RV data via orbital fitting, using the RVLIN package (Wright & Howard 2009): β~ = µ(~t, ~v, ~σ), (1)

21 where β~ is the best fitted orbital parameters . From β~, we derive ~t, ~vbest(β~) , the best-fit model (here ~t are treated as predictors and thus fixed). Then we can begin resampling to crea{ te bootstrap} samples. Our resampling plan is model-based resampling, where we draw from the residuals against the best-fit model. For data that come from the same instrument or telescope, in which case no instrumental offset needs to be taken into account, we simply draw from all residuals, ~v ~vbest , with equal probability for each (vi vbest,i). This new ensemble ∗ { − } − ∗ 22 of residuals, denoted as r~ , is then added to the best-fit model ~vbest to create one bootstrap sample, v~ . Associated ∗ ∗ with r~ , the uncertainties ~σ are also re-assigned to v~ – that is, if vj vbest,j is drawn as rk and added to vk to generate ∗ ∗ − vk, then the uncertainty for vk is set to be σj . For data that come from multiple instruments or multiple telescopes, we incorporate our model-based resampling plan to include stratified sampling. In this case, although data from each instrument or telescope are close to homoscedastic, the entire set of data are usually highly heteroscedastic due to stratification in instrument/telescope radial velocity precision. Therefore, the resampling process is done by breaking down the data into different groups, ~v1, ~v2,... , according to instrument and/or telescope, and then resample within each subgroup of data with the algorithm{ described} in last paragraph. The bootstrap sample is then v~∗ = v~∗ , v~∗ ,... . { 1 2 } To construct the approximate sampling distribution of the orbital parameter estimates β~, we compute β~∗ = µ(~t, v~∗, σ~∗) (2)

∗ ∗ for each bootstrap sample, ~t, v~ , σ~ . The sampling distribution for each orbital parameter estimate βi can { } (1) (2) be constructed from the multiple sets of β~∗ calculated from multiple bootstrap samples (β~∗ , β~∗ ,... from

20 Through out the paper and sometimes in this Appendix, we 21 As described in §3.2, this includes the P , T , K, e, and ω for estimates p refer to the “ of the parameters” (as distinguished from each planet, as well as γ, dv/dt (if applicable), and velocity offsets the “true parameters”, which are not known and can only be esti- between instruments/telescopes (if applicable) for the system. mated) simply as the “parameters”. 22 We simply use the raw residual instead of any form of modified residual, because the RV data for any single instrument or telescope are usually close enough to homoscedasticity. 15

(1) (2) v~∗ , v~∗ ,...). The standard errors for β~ are simply the standard deviations of the sampling distributions23. The sampling distribution of the estimated transit mid-time, Tc, is calculated likewise. Here Tc is the transit time for a certain planet of interest in the system, and is usually specified to be the first transit after a designated time T . However, the situation is complicated by the periodic nature of Tc. Our approach is to first calculate, based on the original RV data, Tc0, the estimated mid-time of the first transit after time T0 (an arbitrary time within the RV observation time window of [min(~t), max(~t)]; Tc0 is also within this window). Then T = N P + T , (3) c · c0 where P is the best-estimated period for this planet of interest, and N is the smallest integer that is larger than (T T )/P . Next we compute T ∗ for each bootstrap sample ~t, v~∗, σ~∗ . Given that within the time window of − c0 c0 { } radial velocity observations ([min(~t), max(~t)]), the phase of the planet should be known well enough, it is fair to ∗ assume that Tc0 is an unbiased estimator of the true transit mid-time. Therefore we assert that Tc0 has to be well ∗ ∗ ∗ constrained and within the range of [Tc0 P /2,Tc0 + P /2], where P is the period estimated from this bootstrap − ∗ ∗ sample. If not, then we subtract or add multiple P ’s until Tc0 falls within the range. Then naturally T ∗ = N P ∗ + T ∗ . (4) c · c0 ∗ ∗ The ensemble of Tc ’s gives the sampling distribution of Tc and its standard error. Note that Tc is not necessarily within the rage of [T P/2,T + P/2]. c − c Provided with the stellar mass M⋆ and its uncertainty, we calculate, for each planet in the system, the standard errors for the semi-major axis a and the minimum mass of the planet Mp,min (denoted as M sin i in the main text as commonly seen in literature, but this is a somewhat imprecise notation). As the first step, the mass function is calculated for the best-fit β~ and each bootstrap sample β~∗, 3 3/2 3 PK (1 e) (Mp sin i) f(P,K,e)= − = · 2 . (5) 2πG (M⋆ + Mp) The sampling distribution of f(P,K,e) then gives the standard error of the mass function. The minimum mass of the planet Mp,min is then calculated by assuming sin i = 1 and solving for Mp. Standard error of Mp,min is derived through simple propagation of error, as the covariance between M⋆ and f(P,K,e) is probably negligible. For the semi-major axis a, P 2G(M + M ) P 2G(M + M ) a3 = ⋆ p ⋆ p,min . (6) 4π2 ≈ 4π2 The standard error of P 2 is calculated from its bootstrap sampling distribution, and via simple propagation of error 2 we obtain the standard error of a (neglecting covariance between P , Mp,min, and M⋆).

23 The standard deviation of a sampling distribution is estimated in a robust way using the IDL function robust sigma, which is writ- ten by H. Fruedenreich based on the principles of robust estimation outlined in Hoaglin et al. (1983). 16

TABLE 7 HET and KECK RADIAL VELOCITIES FOR HD 37605

Velocity Uncertainty BJD−2440000 (m s−1) (ms−1) Telescope

13002.671503 122.4 8.8 HET 13003.685247 126.9 5.6 HET 13006.662040 132.1 5.2 HET 13008.664059 130.4 4.8 HET 13010.804767 113.4 4.7 HET 13013.793987 106.2 4.9 HET 13042.727963 -120.0 4.7 HET 13061.667551 126.5 4.0 HET 13065.646834 111.3 5.8 HET 13071.643820 106.7 5.5 HET 13073.638180 91.7 4.6 HET 13082.623709 53.4 5.7 HET 13083.595357 45.1 6.4 HET 13088.593775 30.7 11.3 HET 13089.595750 0.8 5.5 HET 13092.597983 -25.5 6.2 HET 13094.586570 -51.0 5.9 HET 13095.586413 -72.2 6.2 HET 13096.587432 -75.0 9.3 HET 13098.576213 -173.1 6.4 HET 13264.951365 -194.0 9.8 HET 13265.947438 -238.2 10.5 HET 13266.945977 -264.2 13.1 HET 13266.959470 -286.8 11.6 HET 13283.922407 118.8 9.6 HET 13318.819260 -142.8 6.6 HET 13335.921770 143.4 6.3 HET 13338.906008 132.1 5.4 HET 13377.819405 -279.6 6.1 HET 13378.811880 -161.3 5.2 HET 13379.802247 -39.7 5.2 HET 13381.644284 74.4 4.7 HET 13384.646538 112.5 5.8 HET 13724.855831 88.1 5.3 HET 13731.697227 57.8 5.0 HET 13738.674709 36.4 4.9 HET 13743.810196 14.1 5.7 HET 13748.647234 -17.8 5.6 HET 14039.850147 -104.1 5.5 HET 14054.964568 68.8 7.3 HET 14055.952778 49.3 6.5 HET 14067.762810 22.1 6.0 HET 14374.924086 32.7 8.6 HET 14394.864468 -12.1 8.5 HET 14440.883298 11.9 8.5 HET 14467.826532 -121.9 6.3 HET 14487.613032 40.4 5.6 HET 14515.689341 -55.6 5.7 HET 14550.600301 23.1 5.5 HET 14759.878895 34.3 4.9 HET 14776.839187 2.0 6.7 HET 14787.793398 -40.8 5.1 HET 14907.617522 -94.4 5.1 HET 15089.968860 76.4 4.1 HET 15104.917965 54.0 4.6 HET 15123.882222 -44.4 4.6 HET 15172.734743 -0.4 4.6 HET 15172.749345 3.0 4.9 HET 15180.715307 -65.0 5.3 HET 15190.692697 -257.0 4.9 HET 15190.704818 -252.3 6.3 HET 17

TABLE 7 — Continued

Velocity Uncertainty BJD−2440000 (m s−1) (ms−1) Telescope

15195.678923 -47.7 5.1 HET 15200.809909 85.1 4.5 HET 15206.665616 75.9 4.5 HET 15208.646672 72.6 5.7 HET 15266.634586 81.1 4.6 HET 15274.598361 57.1 4.6 HET 15280.605398 24.3 5.6 HET 15450.974863 25.2 5.2 HET 15469.928975 -81.7 4.4 HET 15481.884352 110.8 4.8 HET 15494.004309 71.2 4.9 HET 15500.853302 41.1 6.0 HET 15505.824457 21.2 4.8 HET 15510.809500 -13.9 5.5 HET 15511.813809 -18.4 4.7 HET 15518.798148 -139.1 4.9 HET 15518.943518 -148.8 4.6 HET 15524.791579 -97.7 6.0 HET 15526.759230 51.2 5.8 HET 15526.767959 56.5 6.1 HET 15527.921902 89.2 4.6 HET 15528.921753 105.1 5.5 HET 15530.757847 120.6 5.3 HET 15532.760658 117.6 4.8 HET 15544.730827 81.8 4.9 HET 15545.871710 87.7 5.2 HET 15547.717980 78.6 6.5 HET 15547.720596 81.2 7.8 HET 15550.703130 75.8 5.5 HET 15556.688398 43.4 5.0 HET 15557.842853 40.1 4.9 HET 15566.657803 -18.4 5.6 HET 15566.666973 -19.0 4.9 HET 15569.670948 -50.7 4.5 HET 15571.659560 -94.0 7.4 HET 15571.662188 -99.5 7.5 HET 15582.777052 75.1 5.4 HET 13982.116400 -312.6 1.1 Keck 13983.110185 -291.6 1.1 Keck 13984.104595 -175.0 1.1 Keck 14024.076794 -39.9 1.2 Keck 14129.848461 -17.1 1.1 Keck 14131.926354 -32.2 1.3 Keck 14138.913472 -98.8 1.2 Keck 14544.815162 54.2 1.0 Keck 14545.799155 50.4 1.0 Keck 14546.802812 48.1 1.0 Keck 15172.939733 21.7 1.1 Keck 15435.133695 97.5 1.0 Keck 15521.851677 -244.2 1.2 Keck 15522.947381 -268.1 1.1 Keck 15526.936103 78.6 1.1 Keck 15528.877669 118.4 1.0 Keck 15543.032113 115.5 1.2 Keck 15545.105481 110.3 1.2 Keck 15546.046328 110.6 1.2 Keck 15556.071287 69.6 1.1 Keck 15556.954989 66.4 1.1 Keck 15558.027806 62.3 1.2 Keck 15584.769501 128.2 1.2 Keck 15606.952224 91.6 1.2 Keck 15634.789262 -81.0 1.0 Keck 18

TABLE 7 — Continued

Velocity Uncertainty BJD−2440000 (m s−1) (ms−1) Telescope

15636.793990 80.7 1.0 Keck 15636.799360 85.6 1.1 Keck 15663.738831 87.6 1.0 Keck 15671.731754 45.8 1.2 Keck 15672.732058 37.1 1.0 Keck 15673.745070 27.6 1.0 Keck 15793.124325 -86.7 1.2 Keck 15843.017282 -6.4 1.3 Keck