The LCES HIRES/Keck Precision Radial Velocity Exoplanet Survey
R. Paul Butler, Steven S. Vogt, Gregory Laughlin, Jennifer A. Burt, Eugenio J. Rivera, Mikko Tuomi, Johanna Teske, Pamela Arriagada, Matias Diaz, Brad Holden, Sandy Keiser
hhires survey paper version 33
Preprint typeset using L A TEX style AASTeX6 v. 1.0
THE LCES HIRES/KECK PRECISION RADIAL VELOCITY EXOPLANET SURVEY
R. Paul Butler , Steven S. Vogt , Gregory Laughlin , Jennifer A. Burt , Eugenio J. Rivera , Mikko Tuomi ,Johanna Teske , Pamela Arriagada , Matias Diaz , Brad Holden , and Sandy Keiser Department of Terrestrial Magnetism, Carnegie Institution for Science, Washington, DC 20015, USA UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA Department of Astronomy, Yale University, New Haven, CT 06511, USA University of Hertfordshire, Centre for Astrophysics Research, Science and Technology Research Institute, College Lane, AL10 9AB,Hatfield, UK Departamento de Astronom´ıa, Universidad de Chile, Camino el Observatorio 1515, Casilla 36-D, Las Condes, Santiago, Chile
ABSTRACTWe describe a 20-year survey carried out by the Lick-Carnegie Exoplanet Survey Team (LCES), usingprecision radial velocities from HIRES on the Keck-I telescope to find and characterize extrasolarplanetary systems orbiting nearby F, G, K, and M dwarf stars. We provide here 60,949 precisionradial velocities for 1,624 stars contained in that survey. We tabulate a list of 357 significant periodicsignals that are of constant period and phase, and not coincident in period and/or phase with stellaractivity indices. These signals are thus strongly suggestive of barycentric reflex motion of the starinduced by one or more candidate exoplanets in Keplerian motion about the host star. Of thesesignals, 225 have already been published as planet claims, 60 are classified as significant unpublishedplanet candidates that await photometric follow-up to rule out activity-related causes, and 54 arealso unpublished, but are classified as “significant” signals that require confirmation by additionaldata before rising to classification as planet candidates. Of particular interest is our detection ofa candidate planet with M sin( i ) = 3 . M ⊕ , and P = 9 . Keywords:
Stars: planetary systems INTRODUCTIONIn 1994, we initiated an extensive long term search for extrasolar planets around nearby F,G, K, and M dwarfstars using the Keck Observatory HIRES spectrometer on the Keck I telescope atop Mauna Kea. Over the years, theHIRES program has registered some notable successes, including the co-discovery of HD 209458b, the first transitingextrasolar planet (Henry et.al 2000), the first discovery of a Neptune-mass planet outside the solar system (Butler et.al2004), the first direct mass measurement (without sin( i ) ambiguity) of Gliese 876d, the first super-Earth (Rivera et.al2005), and many others. The first decade of the survey’s productivity was memorialized in 2008, with a then-completecompendium of the orbital characteristics of nearby exoplanets (Cumming et.al 2008). Now, as the survey moves intoits third decade, we are electing to publish a catalog of all of the precision Doppler velocity measurements that wehave obtained at Keck, with the hope that this data will be of value to the exoplanet community.To date, this Keck-based precision radial velocity survey of the Lick-Carnegie Exoplanet Survey Team (LCES)has amassed 60,949 precision radial velocities on a target list of 1,624 stars. Figure 1 shows an H-R diagram ofHIPPARCOS stars within 100 pc (purple points), and HIRES/Keck target stars (red points). With the exception of afew transiting or other planet signal cases discovered elsewhere, we have been targeting primarily nearby F, G, K, andM main sequence stars which have been heavily pre-selected for low activity (expected stellar jitter) based on log R (cid:48) hk chromospheric emission indices determined from emission reversals in the Fraunhofer H and K lines of Ca II. RADIAL VELOCITY OBSERVATIONS a r X i v : . [ a s t r o - ph . E P ] F e b Butler et al.
B-V A b s o l u t e V m agn i t ude Spectral TypeA0 F6 K4 M3 M5
Hipparcos stars within 100pcKeck/HIRES stars
Figure 1 . H-R diagram of the survey program stars.
We use the iodine cell technique pioneered by Butler et al. (1996). All velocities reported herein were obtainedwith the HIRES spectrometer (Vogt et al. 1994) at the Keck observatory. Radial velocities were measured usingan iodine gaseous absorption cell as a precision velocity reference, placed just ahead of the spectrometer slit in theconverging beam from the telescope as described in detail by Butler et al. (1996). The iodine gas in this absorption cellsuperimposes a rich forest of iodine lines on the stellar spectrum, providing a wavelength calibration and wavelengthdependent proxy for the point spread function (PSF) of the spectrometer. The iodine cell is sealed and temperature-controlled to 50.0 ± ◦ C, so that the column density of iodine remains constant over decades.For this survey, the HIRES spectrometer was configured to operate at a nominal spectral resolving power of R ∼ ,
000 and wavelength range of 3700 – 8000 ˚A, however only the region from 5000 – 6200 ˚A (with iodine lines) wasused in the Doppler analysis. Doppler shifts from the spectra are determined with the spectral synthesis techniquedescribed by Butler et al. (1996). For this velocity analysis, the iodine region of the echelle spectrum was subdividedinto ∼
700 wavelength chunks of 2 ˚A each. Each chunk provided an independent measure of the wavelength, PSF, andDoppler shift. The final measured velocity is the weighted mean of the velocities of the individual chunks. The finaluncertainty on each velocity is the standard deviation of all 700 chunk velocities about that mean. Also derived aretwo chromospheric activity indices. The first is the well-known S-index, obtained from measurement of the emissionreversal at the cores of the Fraunhofer H and K lines of Ca II at 3968˚A and 3934˚A respectively. The second activityindex, herein called the H-index, is a measure of the chromospheric emission component at the H α Balmer line ofhydrogen at 6563˚A (Gomes da Silva et al. 2011).HIRES was neither originally intended, nor specifically optimized for, extreme precision radial velocity work. Rather,
IRES/Keck Exoplanet Survey Figure 2 . HIRES 3-CCD mosaic focal plane upgrade of August 2004 it was optimized as a general-purpose instrument, to provide moderately high resolution (50,000-70,000) echelle-stylespectra with good sky background subtraction on faint targets (V ∼ −
22) such as quasars. In the latter stages ofHIRES assembly and test, however, we added an iodine gaseous absorption cell to facilitate precision radial velocitywork. We drew on a combination of HIRES commissioning time and early allocations of UC-Keck nights to developa precision velocity data reduction pipeline, in anticipation that HIRES could be employed to facilitate exoplanetdiscovery. When NASA secured a 1/6 share of Keck and issued calls for proposals to find exoplanets, we were ableto garner enough nights on the heavily-shared Keck facility to mount a significant exoplanet discovery program atKeck, combining all of our UC-Keck nights with those from the NASA-Keck TAC. While this program was remarkablysuccessful from 1995-2004, the original Tektronix/SITE 2K x 2K 2048 CCD was actually an engineering-grade backupdevice from the LRIS instrument, and it limited the radial velocity precision achievable with HIRES. Chief amongits drawbacks were comparatively large (24-micron) pixels, a non-flat (convex) focal plane, and a relatively poor andnon-linear Charge Transfer Efficiency (CTE).In August-2004, with partial NASA funding, we performed a major upgrade to HIRES. The Tektronix/SITE CCDwas replaced with a 3-chip mosaic of MIT-Lincoln Lab 2K x 4K CCD’s. These MIT/LL devices feature higher quantumefficiency (QE), smaller (15-micron) pixels, higher and more linear CTE, and a flat imaging surface. At the same time,we remade the final optical element of the HIRES super-camera (Epps & Vogt 1993) to take full advantage of thenow-flattened imager surface. Figure 2 shows a view of the focal plane upgrade (with its internal scattered light baffleremoved to better show the CCDs) that we installed in August 2004. The bottom, middle, and top CCD’s wereoptimized respectively for highest QE in the UV, visible, and near-IR. The upgrade was done such that all iodinelines fall onto the middle CCD of the 3-chip mosaic, simplifying data reduction. Also visible in Figure 2 is the new
Butler et al. fused silica lens that serves as the dewar window, and flattens the focal plane to match the flat CCD mosaic. Theresult of the upgrade was a marked improvement in limiting velocity precision, from ∼ − to 1-2 m s − . Werefer hereafter to velocities obtained prior to August 2004 as “pre-fix” velocities, and velocities obtained after August2004 as “post-fix” velocities. We find no significant velocity offset in our data reduction pipeline between pre-fix andpost-fix velocities, and thus do not invoke any velocity offset parameter between pre- and post-fix data in our analyses.Typical exposure times for target stars varied from a few minutes each, to a maximum of 10 minutes. In general,exposure times were made long enough to provide some averaging over low-degree stellar p-modes, which exhibittypical time scales of ∼ − error in the barycentriccorrection. This correction depends on Hour Angle and Declination as well. To optimize exoplanet detection, onemust determine the true time centroid of an observation to a level of ±
15 seconds to render barycentric correctionerror insignificant relative to an overall error budget totaling of order 1 m s − .In 1997, to aid the exposure centroiding, we commissioned an exposure meter for HIRES that uses a propeller mirrorto pick off a small fraction ( ∼ OBSERVING TARGET LIST BASIC PROPERTIESFigure 3 shows a histogram of the apparent V magnitudes of the stars in our target list. We generally avoidedobserving stars brighter than V ∼ ∼
700 spectral chunks across the iodine region of the echelle spectral format. The internal uncertainty for eachvelocity is simply the standard deviation of those velocities about that average. As such, it does not include any otherunknown systematic errors that may be present in the reduction pipeline. The external error associated with anyvelocity will generally be larger. To maximize chances of exoplanet detection, we used knowledge of the chromosphericactivity S-value to limit the survey primarily to the intrinsically quietest stars at any spectral type. In general, as canbe seen from Figure 5, we limited our survey to stars with expected stellar jitter below about 5 m s − .Our standard metric of chromospheric activity in target stars is the Mt. Wilson “S-value”. The S-value quantifiesthe ratio of flux from 1 ˚A bins located at the centers of the Ca II Fraunhofer H & K lines, as compared to two broaderbandpasses lying 250˚A to either side of these lines (Duncan et al. 1991). We computed this ratio for every spectrumtaken of each of the stars in the HIRES data sample using the procedure described in Wright et al. (2004). Theresults are then calibrated to standard Mt. Wilson S-values using those stars that overlap between our sample andthe original Mt. Wilson survey. We then used the (B-V) color of each star along with the median of its calibratedS-values to calculate its expected jitter (blue histogram in Figure 5) following the steps outlined in Isaacson and Fischer(2010). The median expected stellar jitter of our sample is 2.13 m s − , while the median of our internal uncertaintiesis somewhat smaller at 1.56 m s − and thus well-matched to the expected stellar jitter levels from the sample.Figure 6 shows a histogram of distances (from HIPPARCOS parallaxes) of the program stars out to 150 pc. Thesurvey is heavily biased toward the nearest stars, especially the nearest K and M dwarfs. The median distance of our IRES/Keck Exoplanet Survey Apparent V magnitude F r equen cy Figure 3 . Histogram of target star apparent V-band magnitudes program stars is 36 parsecs. Figure 7 shows a cumulative distribution of observation time baselines for all programstars. 80% of all target stars were observed over a time baseline of at least 1000 days, while 50% were observed for atleast 3000 days. The longest time baselines for stars is 6300 days or about 17 years.Figure 8 shows a histogram of the spectral resolution obtained for all survey spectra. As mentioned above, HIRESwas designed primarily for moderately-high spectral resolution on very faint objects, and thus is not ideally suitedto extreme precision radial velocities. As shown by Bouchy et al. (2001), the radial velocity information content or“quality factor”, Q of a stellar spectrum depends on spectral resolution. For resolutions lower than R < , Q scales roughly linearly with R . For resolutions, R > , Throughput (a figure of merit for grating spectrometers defined as the product of spectral resolution times slit widthin arc-seconds) of about 39,000 arc-seconds. This value is geometrically fixed by the blaze angle of the echelle, thecollimated beam diameter, and the telescope’s primary mirror diameter. At that
Throughput , the 0.861 arc-secondnominal slit guarantees that the resolution is never less than 45,300 (no matter how over-filled the slit becomes frompoor seeing). However, if the seeing is better than 0.861 arc-seconds, the spectral resolution for any exposure will behigher, especially if the guiding is stable and the exposure is short.Unlike fiber-fed approaches such as that pioneered by HARPS (Pepe et al. 2000), where the seeing disk overfillsthe fiber aperture, and the fiber itself provides a high degree of image scrambling, thus assuring a stable width pointspread function input to the spectrometer, HIRES uses a simple long slit, without any scrambling. The advantageof the long slit is less light lost at the slit, since the slit is typically much longer than the seeing disk’s full-width athalf-maximum (FWHM), and thus light lost at the long slit scales only as slit width, rather than as the square ofthe diameter of the fiber for the fiber-fed case. However, the lack of image scrambling and its attendant point spreadfunction (PSF) stabilization requires that the PSF be solved for explicitly as part of the RV reductions. The iodinecell’s thousands of unresolved absorption lines serve as the proxy for the PSF, allowing variations of the PSF from one
Butler et al.
Stellar B-V F r equen cy Figure 4 . Histogram of target star (B-V) colors observation to the next to be adequately modeled and removed from the analysis so as not to contribute systematicerrors in velocity.At the same time, with HIRES, the FWHM of the seeing at Keck is often less than the width of our standard 0.861arc-second slit, in which case the spectral resolution becomes a function of the seeing. For cases of very bad seeing,when the seeing disk mostly overfills the slit, resolution could, in principle, degrade to the value 39,000/0.861 set bythe
Throughput , or to about 45,000. In practice, we rarely see resolutions less than R ∼ , R = 85 ,
000 can be achieved, corresponding to animplied seeing FWHM of about 0.46 arc-seconds. The mean resolution across the 60,949 velocities of the survey is ∼ ∼ ∼ ◦ , the resolution typically ranges from 49,000 to75,000 depending on the seeing quality. Below elevations of 30 ◦ , the typical resolution degrades steadily with decreasingelevation (increasing air mass).Spectral resolution also affects the mean internal uncertainty, which represents the limiting precision of any singleobservation. This is shown in Figure 11, which plots the mean internal uncertainty of each velocity vs. the resolution IRES/Keck Exoplanet Survey (Meters/second) F r equen cy Mean Internal UncertaintyExpected Jitter
Figure 5 . Histogram of velocity internal uncertainties and expected stellar jitter of the spectrum from which the velocity was extracted. At our median resolution of about 58,000, the internaluncertainties are typically 0.8 m s − < σ < − (dependent also on stellar spectral type and stellar V sin i ).But for resolutions above 75,000, a large fraction of the median internal uncertainties are in the 1 - 2 m s − range.Extrapolating that distribution to the R = 115,000 typical of HARPS and its variants implies that per observationmedian internal uncertainties of about 1 m s − could be achieved with HIRES if its resolution could be increased.This can be done straightforwardly by simply narrowing the slit, albeit at the expense of substantial light loss.When comparing the effectiveness of HIRES for precision radial velocity work against facilities such as HARPS (thatwere explicitly optimized for such work at a resolution of 115,000), HIRES is at a distinct disadvantage by at leasta factor of two because of its factor of approximately two lower spectral resolution. HARPS is optimized for a muchsmaller 3.6-m telescope, and, even so, suffers the loss of typically 50% of the light at its 1 arc-second diameter fiber innominal seeing. Mounting a similar-sized HARPS-like instrument on a telescope as large as the Keck 10-m would meaneven more serious light loss at the entrance aperture. Options for improving the Throughput of HIRES are to invokeadaptive optics (AO), and/or to use an image-slicer. Doing adequate AO in the visible remains technically beyondthe immediate near term for HIRES at Keck. But adding an image slicer to HIRES to boost its spectral resolutionwithout losing additional light at the slit should be feasible.Work at HIRES to improve the spectral resolution for precision radial velocity acquisition has been reported by(Spronck et al. 2015, 2012). These authors equipped HIRES first with an image-sliced fiber scrambler feed (Sproncket al. 2012), and later with a fiber double-scrambler (Spronck et al. 2015). In the second of the two articles, Sproncket al. report values for their single measurement precision (SMP- equivalent to our internal uncertainty) obtainedwith the conventional slit-fed HIRES of 1.96 and 2.11 m s − for slit-fed observations of two test stars with HIRES.Their SMP on these two stars then improved to 1.49 m s − for both stars when HIRES was used with their dual fiber Butler et al.
Distance to star (pc) F r equen cy Figure 6 . Histogram of target star distances scrambler/slicer. Our survey’s median SMP, (Figure 5) obtained from ∼ − , with 50%of our velocities attaining significantly higher precisions of 0.5 - 1.0 m s − . From these results we infer that Sproncket al. (2015) may retain a significant component of noise intrinsic to the data reduction pipeline and/or observingprocedure, that is not yet mitigated by the higher spectral resolution and stabilization of the instrument Line SpreadFunction enabled by the installed fiber scrambler/slicer. Spronck et al’s work demonstrates that gains can be obtainedfrom image-slicing and PSF-scrambling HIRES up to a HARPS-like resolution of 120,000 with a fiber scrambler/slicer,but sub-m s − measurement precision with this approach has yet to be demonstrated with HIRES. STELLAR ACTIVITY INDICESThe usual proxy for monitoring stellar activity levels is the S-index and its corresponding derivative log R (cid:48) hk . TheS-index is a measure of the emission at the cores of the Fraunhofer H and K lines of singly-ionized calcium due tochromospheric activity. It is often useful in revealing the rotation period of the star, and any longterm activity cyclessimilar to the Sun’s 11-year activity cycle. Chromospheric emission variations due to either or both stellar rotationand longterm activity cycles can produce radial velocity variations that can mimic, and therefore be mistaken for,Keplerian motion of planets. Any periodicity detectable in either broadband photometry or S-index that coincideswith a planet candidate’s period would cast serious suspicion on the latter’s veracity. In some cases, the rotation periodof the star can be detected solely from S-index data, even when broadband photometric variations reveal nothing.We include in this paper, for the first time in such a large collection of HIRES spectra, an additional measure ofthe stellar chromospheric activity (hereafter called the H-index) as measured from the H α Balmer line of hydrogen at6563˚A. The motivation to use an additional activity index, besides the S-index, comes from the low flux of M dwarfstars in the Ca H&K wavelength region; these stars are intrinsically brighter at redder wavelengths. Several otherauthors have also explored how H α flux variations compare to other stellar activity indices, stellar properties, andradial velocity measurements, e.g. Pasquini & Pallavicini (1991), Gomes da Silva et al. (2011), Robertson et al. (2013),and Gomes da Silva et al. (2014). We can build on their work with a much larger sample that is both uniform (allfrom HIRES) and spanning a wide spectral type range (late F to early M). Since this index is new to HIRES data, a IRES/Keck Exoplanet Survey Observing baseline (days) N u m be r o f s t a r s ob s e r v ed f o r > X da ys Figure 7 . Cumulative distribution of observing time baselines brief description of its calculation and use is given here. A more detailed discussion of the HIRES H-index data is inpreparation (Teske et al. 2016, in preparation).Similar to the S-index, the H-index quantifies the amount of flux within the H α line core compared to the localcontinuum. We use the Gomes da Silva et al. (2011) prescription, which defines the H-index as the ratio of theflux within ± α line at 6562.808 ˚A to the combined flux of two broader flanking wavelength regions:6550.87 ± ± α echelle orderfrom Th-Ar lamps (rather than using the extrapolated wavelength solution from the iodine region of the spectrum)and divide out a simple third-order polynomial fit to the continuum (excluding the H α line wings). The wavelengthsolution is refined in each individual spectrum with cross-correlation against the NSO solar atlas , rebinned to theresolution of the object spectrum. This is necessary, as we do not a priori have the intrinsic stellar velocity measuredfor each spectrum. In a small subset of spectra, this solar atlas cross-correlation does not work properly because theH α line is in emission, or because the signal-to-noise of the spectrum is too low (making the H α absorption featurerelatively weak). In these cases, the object spectrum does not match well to the deep H α absorption feature in thesolar spectrum, and this leads to an incorrect wavelength solution. After the cross-correlation step, a second continuumnormalization is carried out by dividing the object spectrum by the solar atlas, smoothing this fit, and then multiplyingthe object spectrum by this smoothed fit. Any wavelength mismatches between the object and solar atlas then createwaves in the continuum. These issues cause anomalously large H-index values; examination by eye of individual spectrasuggests a cut-off of “good” versus “bad” H-index values between 0.062 and 0.064. Thus we advise caution when usingor drawing any conclusions from H-index values above 0.062; this affects only ∼
1% of the stars presented here, mostof which are late type. In addition, the H-index is presented only for post-fix HIRES spectra (that were collected after The development of the NSO Digital Library has been generously supported by the National Science Foundation through its NationalSpace Weather Program, and by NASA under the Upper Atmosphere Research Program. Butler et al.
Spectral Resolution F r equen cy Mean Resolution: 60025Median Resolution: 58320
Figure 8 . Histogram of spectral resolutions of all survey spectra the detector upgrade in August, 2004), and only when the H α region of the raw spectrum is not saturated ( ≥ eff may affect their interpretation (Robertson et al. 2013). What is clear from Figure 12 is that the H-index correlatesmuch more tightly with stellar color (and temperature) than does the S-index. As most of our program stars werespecifically chosen to be either main sequence or only slightly evolved sub-giants, this correlation also manifests as astrong correlation with absolute V-magnitude in Figure 12.In Figure 13 we compare the S-index dispersion with the H-index dispersion. As expected, as the dispersion in theS-index for a given star increases, so does the dispersion in its H-index. The stars with the largest variation in bothindices are late-type (almost exclusively M dwarf) stars. RADIAL VELOCITIES AND ANCILLARY DATATable 1 shows a small but representative portion of the full table of radial velocities and ancillary data for allobservations of all stars. The full table is available through links in the on-line version of the paper.
IRES/Keck Exoplanet Survey Julian Date - 2450000 S pe c t r a l R e s o l u t i on Figure 9 . Spectral resolutions of all survey spectra vs. Julian date
Table 1 . Radial velocities and chromospheric activity indices of all program stars. (Notethat H-index values H ≥ .
062 are to be considered with caution, see Section 4 text.)(
Sample: full table in electronic version ) Target BJD RV [m s − ] σ [m s − ] S-index H-index Exp Time [sec]HD 10002 2450462.767 -0.53 1.09 0.151 — 600HD 10002 2450715.062 -6.34 1.03 0.161 — 600HD 10002 2450805.761 -1.77 1.08 0.167 — 400... ... ... ... ... ... ...HD 10008 2453723.831 -0.66 0.82 0.423 0.038 264HD 10008 2453723.834 -2.75 0.87 0.422 0.038 235HD 10008 2454129.746 9.28 1.25 0.428 0.037 81... ... ... ... ... ... ...HD 10013 2453982.024 1.83 0.69 0.145 0.032 92HD 10013 2453982.976 2.20 0.78 0.147 0.032 96HD 10013 2453983.924 -2.21 0.73 0.148 0.032 92... ... ... ... ... ... ...HD 10015 2453981.918 2846.74 0.66 0.146 0.034 101HD 10015 2453982.979 2713.58 0.66 0.142 0.034 106HD 10015 2453983.917 2595.18 0.58 0.149 0.034 202 Table 1 continued on next page Butler et al.
10 20 30 40 50 60 70 80 90
Elevation (degrees) S pe c t r a l R e s o l u t i on Figure 10 . Spectral resolution vs. telescope elevation for all survey spectraTable 1 (continued)
Target BJD RV [m s − ] σ [m s − ] S-index H-index Exp Time [sec] Data presented in Table 1 are (from left to right): Target star name, Barycentric Julian Date, radial velocity (m/s),radial velocity internal uncertainty (m/s), S-index, H-index, and exposure time in seconds. We continue to reducenewly available Keck/HIRES precision velocity data from the NASA/Keck archive. Newly reduced data is madeavailable on the Earthbound Planet Search web site PLANETARY CANDIDATE SIGNALSThis large ∼ ∼ http://home.dtm.ciw.edu/ebps/ IRES/Keck Exoplanet Survey k = 0 (where k is the number of signals in themodel) by applying the AM algorithm to obtain parameter estimates. As in all parameter estimations with MCMCalgorithms in the current work, after rejecting n initial chain members (considered to be the burn-in phase in whichthe chain identified the most probable regions in the parameter space) we divided the remaining chain into three partsand tested non-convergence by applying the Gelman-Rubin statistics for all parameters (Gelman et al. 2003; Ford2006). If the Gelman-Rubin statistic R in Eq. (25) of Ford (2006) was above 1.1 we rejected the chain because it Spectral Resolution I n t e r na l U n c e r t a i n t y ( m / s ) Figure 11 . Mean internal uncertainty vs. spectral resolution for all survey spectra Butler et al. (B-V) M ed i an H α i nde x V ab s (V-K) M ed i an H α i nde x V ab s (B-V) M ed i an S i nde x V ab s (V-K) M ed i an S i nde x V ab s Figure 12 . H-index (top plots) vs. (B-V) color (left), and (V-K) color (right). S-index (bottom plots) vs. (B-V) color (left)and (V-K) color (right). Points are color-coded by stellar absolute V magnitude. Note that H-index values ≥ showed evidence in favor of non-convergence and increased the chain length to obtain a more statistically representativesample. Required chain lengths ranged from 10 for k = 0 to 10 or more for k > k signals in the data and that the maximum a posteriori (MAP) estimates had been obtained with the AM algorithm, we adopted a model with k + 1 signals by setting theinitial state of the chain such that all but the five Keplerian parameters of the k + 1th signal were set equal to their IRES/Keck Exoplanet Survey k Keplerian signals. The period parameter of the k + 1thsignal was set to a random value in the set [ P min , T obs ], where we set P min =1 day and T obs is the baseline of the dataset. The eccentricity ( e ), and amplitude ( K ) were set equal to zero. With this setting, our model accounted for thek detected signals and enabled the Markov chains to sample the parameter space of the k + 1th signal in a searchfor global maxima that could be interpreted as additional signals in the data. This is demonstrated in greater detailbelow by using the analyses of two data sets as examples (Sections 6.3 and 6.4).The searches for signals were, however, difficult when there was a very significant Keplerian signal in the datacorresponding to e.g. a massive giant planet. In such cases, the Markov chains identified the signal easily but allnewly proposed values were rejected because they corresponded to considerably lower posterior values than the MAPestimate in the period space. This stopped the chain from visiting the whole period space, thereby preventing us fromseeing whether there were even more significant maxima in other parts of the period space. In such cases, instead ofusing a likelihood function L , we instead used L β such that parameter β was gradually decreased. If the chains failedto visit the whole period space, we decreased parameter β by a factor of 1.1 as long as was necessary to enable thechain to visit all areas of the period space. We note that, although setting parameter β to values below unity changesthe likelihood function, the positions of the maxima remain unchanged enabling us to use such tempered samplingsfor the purpose of searching signals in the noisy radial velocity time-series.If the sampling of the parameter space of the model with k + 1 Keplerian signals identified a probability maximumsuch that the ratio of the two maximum likelihood values ∆ ln L k +1 = ln L k +1 − ln L k indicated a significant increasewith a 0.1% FAP, corresponding to ∆ ln L k +1 ≥ α = 16 .
27, we considered the signal to be significantly detected. Insuch a case we moved on to estimate the parameters of the model with k + 1 signals. However, if such a maximum -5 -4 -3 H α index dispersion -4 -3 -2 -1 S i nde x d i s pe r s i on Figure 13 . HIRES S-index dispersion vs. H-index dispersion All areas refers to the chain visiting all 1000 equally long intervals of the log P space that cover the period space [ln P min , ln T obs ]. Butler et al. could not be found, we concluded that there is only evidence for k signals in the data (possibly k = 0).Table 2 lists all signals in the Keck data sets with likelihood ratio ∆ ln L j = ln L ( j = k ) − ln L ( j = k −
1) betweenmodels with k and k − K , period P , and phase φ ). If the likelihood ratio exceeds 20.52 (correspondingto a 0.1% FAP threshold for a full 5-parameter Keplerian model) the signal is labelled as “Candidate” – otherwise itis called “signal requiring confirmation” (SRC). Some signals are interpreted as “Activity” according to the criteriapresented in the next subsection. 6.1. Analysis of activity indicators
We also analyzed the HIRES S-indices in order to assess whether the signals in the radial velocities could beinterpreted instead as stellar activity. The S-indices were analyzed simply by calculating likelihood-ratio periodogramsfor a simple model containing a sinusoidal signal and a linear trend (see Appendix A). We ignored signals with periodsbelow 2 days to avoid detecting daily and yearly aliases whose significance can occasionally exceed the significance ofthe true signal at longer periods. We applied a 5% FAP threshold for the detection of signals in S-indices correspondingto a likelihood ratio threshold of α = 7 .
82 for a sinusoidal signal with three parameters.Table 3 presents a list of estimates of maximum likelihood parameter estimates and standard errors for the “nuisance”parameters. ˙ γ , σ J , and c S represent respectively the linear acceleration, excess white noise or “jitter”, and the coefficientquantifying the linear dependence of the radial velocities on the S-index. ∆ ln L S = ln L S ( k = 1) − ln L S ( k = 0)represents the likelihood ratio statistic of model with a signal ( k = 1) in the S-index with respect to a model withouta signal ( k = 0). Only signals exceeding a ratio of 7.82 corresponding to 5% FAP are shown. P S denotes the periodof the signal in the S-index time-series. 6.2. Interpretation of signals
The likelihood ratio of α = 16 .
27 is based on the χ statistics with three degrees of freedom. We used this limit tosearch signals but applied a more robust value of 20.52 when considering that they were signals of Keplerian origin.This value is a similar threshold to a 0.1% FAP (which we have chosen in keeping with the precedent established by ? but for five degrees of freedom), as is the case when comparing models with k and k + 1 Keplerian signals. Wethus interpreted signals exceeding the former threshold as signals requiring confirmation (SRC) but those exceedingthe latter threshold as candidate planets if the following conditions were satisfied.We consider a periodic radial velocity signal to be a candidate planet if:1. The likelihood ratio ∆ ln L k exceeds a threshold of α = 20 . P has a counterpart in the activity indicators (S-index or H-index) such that theperiod of the activity signal P a satisfies 0 . P < P a < . P , we interpret the radial velocity signal as being likelyconnected to stellar activity (rotation, magnetic cycle, etc.). However, we interpret the signals as candidate planetsif they have been reported and interpreted as planetary signals in the literature. Finally, we classify all signals indata sets that are dominated by activity-induced variations as stellar activity. This means that if at least 50% of thevariance in the radial velocities ( σ ( m )) is connected to variations in the S-index, such that c S σ ( S ) > . σ ( m ), weconsider the corresponding data set to be dominated by activity-induced variations making the planetary nature of allthe corresponding signals doubtful. IRES/Keck Exoplanet Survey Figure 14 . Estimated posterior density of the period parameter of the signal in a one-Keplerian model given radial velocities ofHD 4208. Red arrow denotes the global probability maximum and the horizontal lines correspond to equiprobability contoursat 10% (dotted), 1% (dashed), and 0.1% (solid) of the maximum.
Example 1. HD 4208 – a strong signal
HD 4208 is a host to a well-known candidate planet in the Keck sample (Butler et al. 2006) with an orbital periodof 828.0 ± ± Jup , gives rise to a radial velocity signalwith an amplitude of 19.06 ± − (Butler et al. 2006).Our automatic search for signals identified the periodic signal corresponding to this candidate without complications.During the search, the tempering parameter β was decreased to a value of 0.29 before the chains could visit all areas inthe period space without getting “stuck” to the position of the probability maximum in the period space correspondingto the radial velocity signal of the candidate. As a result, we could obtain an estimated posterior probability densityas a function of the period of the signal indicating that this signal is uniquely well-constrained in the period space(Fig. 14)As the signal corresponding to the candidate planet reported by (Butler et al. 2006) was detected clearly andits inclusion in the statistical model yielded an increase in the log-likelihood ratio of ∆ ln L =62.90, far above thethreshold of α = 20 .
52 required for a classification of the signal as a candidate planet, we also increased the number ofKeplerian signals in the model to k = 2 and attempted to find additional signals in the data. This time, the chains did8 Butler et al.
Figure 15 . As in Fig. 14 but for the period parameter of the second signal in a model with k = 2. not identify any maxima corresponding to significant signals in the period space and we thus conclude that there isevidence for only one signal in the HD 4208 Keck radial velocities corresponding to the planet candidate first reportedin Butler et al. (2006). Our DRAM samplings of the posterior density identified a maximum in the period space at aperiod of 551 days (Fig. 15) but this maximum was not significant enough to enable classifying it as an SRC and itwas accompanied by several local maxima exceeding the 1% equiprobability threshold, which is a typical outcome inthe absence of evidence for additional signals. Although it can be stated that the most prominent period for a secondsignal in the HD 4208 data is 551 days, the corresponding significance with ∆ ln L =10.03 is not sufficiently high toconclude that there is evidence in favor of a second signal.6.4. Example 2. HD 150706 – a weak but significant signal
HD 150706 has been reported to be a host to a long-period candidate planet with an orbital period of 5894 +5584 − days and a minimum mass of 2.71 +1 . − . M Jup giving rise to a radial velocity signal with an amplitude of 31.1 +6 . − . ms − (Boisse et al. 2012). This detection was based on ELODIE and SOPHIE radial velocities but some of the Keck datawas also used to support the detection in Boisse et al. (2012).With a baseline of only 3970 days, the 58 Keck velocities did not show any evidence in favor of the candidate planetreported by (Boisse et al. 2012). Furthermore, we found no evidence for linear acceleration indicative of a long-period IRES/Keck Exoplanet Survey Figure 16 . As in Fig. 14 (based on the radial velocities measured for HD 4208) but for HD 150706. companion to the star. The estimated linear acceleration was found to be ˙ γ =0.68 ± − year − , which is notstatistically significantly different from zero.We do, however, find a signal that we classify as a candidate planet orbiting the star at a period of 20.8266 ± ± − . This signal was uniquely present in the data (Fig. 16) and correspondedto a log-likelihood ratio of ∆ ln L = 22.26 enabling us to classify it as a candidate planet orbiting the star. Althoughthe significance of the signal corresponding to this candidate was only barely above the threshold of α = 20 .
51, it wasdetected according to all our criteria and we did not identify any counterparts in the activity indicators suggestive ofstellar rather than planetary origin. HD 150706 thus serves as an example of a previously undetected albeit significantsignal that is barely detected in the data but can still be classified as a candidate planet according to our criteria. Wehave plotted the phase-folded radial velocities of HD 150706 in Fig. 17 for visual inspection. We note that althoughthe signal appears slightly eccentric in Fig. 17, the eccentricity is not statistically significantly different from zero. Noadditional signals were detected in the HD 150706 Keck radial velocities. DISCUSSION OF SELECTED PLANET CANDIDATES CASES7.1.
HD 68017 Butler et al.
Figure 17 . Keck radial velocities of HD 150706 folded on the phase of the signal in the data.
HD 68017 is a known double star with an M5V companion at a projected separation of 13 AU (Crepp et al. 2012).Given that we limited our signal searches for periods up to the data baseline, the 5844-day signal that we observein the Keck radial velocities is likely just a lower bound estimate for the orbital period of this companion, althoughwe cannot rule out a massive long-period planet orbiting the star either. Moreover, some of the apparent long-periodradial velocity variability could be connected to a magnetic activity cycle of the star that we observe in the S-indicesat a period of 5554 days. This period is also likely to be an estimate for a lower bound due to our choice to limit signalsearches by the data baseline. 7.2.
HD 75732
Although HD 75732 (55 Cancri) is reportedly a 5-planet system (Nelson et al. 2014), we could only obtain evidencefor 4 signals with the Keck data alone. However, due to the fact that we limited the period space of our signal searchesto the interval [ P min , T obs ], where P min = 1 days, the fourth signal that we detected in the Keck data at a period of2.80 days corresponds to the daily alias of the known transiting super-Earth with an orbital period of 0.74 days (Winnet al. 2011).Wright (2015) point out that the longest periodicity in the data is similar to the period of the stellar activityvariation, but notes that the two time series are out of phase, implying a coincidence between the durations of the IRES/Keck Exoplanet Survey c S estimated to have a valueof -27.3 ± σ level. If the longest periodicity was connectedto the variations in the S-index and thus stellar activity, we would not expect the signal to be modeled well witha Keplerian periodicity. Moreover, the phases of the two signals do not coincide (Fig. 18) leaving us without anyevidence supporting the activity-induced origin for the longest radial velocity periodicity apart from a coincidence inthe period that mostly arises from the fact that the periods of the two signals are constrained from above by thebaseline of the data. 7.3. HD 95735
The radial velocity measurements for HD 95735 (GJ 411, Lalande 21185) support the existence of a planet candidateorbiting the star with an orbital period of 9.8693 ± K = 1 . ± − and it occupies a unique maximum in the estimated posterior probability density of the one-Keplerian model (Fig. 19). With a Hipparcos parallax of 393.42 ± α Centauri triple system, Barnard’s star, andWolf 359. The planetary candidate has a minimum mass, M sin( i ) = 3 . M ⊕ , and receives an energy flux from thestar roughly 5.3 × larger than the flux received by Earth from the Sun (based on R (cid:63) = 0 . R (cid:12) , T eff = 3828, and M (cid:63) = 0 . M (cid:12) ). The a-priori geometric probability that the planet can be observed in transit is P = 2 . Table 2 . Signals in the Keck data sets with likelihood ratio ∆ ln L j = ln L ( j = k ) − ln L ( j = k −
1) between models with k and k − K , period P , and phase φ ). ( Sample: full table in electronic version )Target n signals ∆ ln L k P K
Interpretation Notes(days) (ms − )BD-103166 1 73.71 3.4879 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Note 1: Signal coincides with a photometric period based on ASAS V-band photometry.Note 2: Spurious signal that emerges from the use of Keplerian fitting functions for a system the requires an N-body model.Note 3: A corresponding signal in the S-index data at a very nearby period, is likely indicative of the star’s P rot
Note 4: Signal is not constrained in the parameter space (1 day < P < T obs ) of the analyses.Note 5: Signal coincides with the activity cycle in the S-index but is strong enough to be interpreted as a candidate planet.Note 6: Likely artifact signal caused by orbital evolution of the system.Note 7: Daily alias of the known transiting planet orbiting the star with an orbital period of 0.73 days (Winn et al. 2011).Note 8: The strongest S-index counterpart in our sample; signal is likely caused by activity. Butler et al.
Figure 18 . Differential S-index variability for HD 75732 with respect to the data mean (top panel) and the radial velocitieswith the three shortest periodicities subtracted (bottom). In the bottom panel, the black curve denotes the modeled Kepleriansignal.
IRES/Keck Exoplanet Survey L = 22.24, which is in excess of the detection threshold we required to interpret a signal as a candidate planet( α = 20 . HD 154345
Wright (2015) suggests that the radial velocity signal from this star, which was initially reported as a planetarydetection by (Wright et al. 2008), is better interpreted as a stellar activity cycle as a consequence of the apparentlyhigh correlation (that has persisted over a much longer time base since the initial discovery) between the RV andS-index variations. We find, however, no significant linear correlation between RVs and the S-index. In Table 3,the parameter, c S , quantifying this dependence of RV on S-index has a value of 6.9 ± Table 3 . Maximum likelihood parameter estimates and standard errors for the “nuisance” parameters. (
Sample: full table inelectronic version ) Target ˙ γ σ J c S ∆ ln L S P S (ms − year − ) (ms − ) (ms − ) (days)0748-01711-1 76.498 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Butler et al.
Figure 19 . Estimated posterior probability density as a function of the period parameter of the signal in a one-Keplerian modelgiven radial velocities of HD 95735. Red arrow denotes the global probability maximum and the horizontal lines correspond toequiprobability contours at 10% (dotted), 1% (dashed), and 0.1% (solid) of the maximum. variations are linearly connected to the S-index. The only connection between them is an apparent period coincidenceand phase coincidence observed by Wright (2015). Moreover, the signal in the S-indices appears to be quasiperiodic aswould be expected from a signal connected to a stellar magnetic cycle whereas the radial velocity signal with a periodof 3296 ± , in particularbetween JDs 2455000-2456000, the overall shape of the variability is different and the two time-series are therefore notcorrelated when accounting for the signal of the planetary companion. It is thus our interpretation that the signal inthe HD 154345 radial velocities is likely to be caused by a planet candidate analogous to our own Jupiter.7.5. HD 156668
The radial velocities of HD 156668 point towards a system with at least two planet candidates. With more data, wecan confirm the published 4.64-day periodicity (Howard et al. 2011) and likewise interpret it as a signal of a planetcandidate. The Keck data now show no evidence for the hypothesis that the 4.64-day periodicity is an alias of the 1.27-day true period Dawson & Fabrycky (2010). Moreover, according to our analyses, there is another planet candidateorbiting the star with an orbital period of 855 ±
23 days. We also find evidence in the S-indices for the stellar magneticcycle with a period of 3753 days but this cycle has no counterpart in the radial velocity data, and is unlikely to weakenan interpretation that the 855-day periodicity arises from the Keplerian motion of a planet.7.6.
HD 185144
The HD 185144 radial velocities contain a low amplitude ( K =1.39 ± − ) signal with a period of 2644 ± This coincidence can be contrasted with the example in our own system that the orbital period of Jupiter is approximately equal tothe Solar magnetic cycle.
IRES/Keck Exoplanet Survey Figure 20 . Keck radial velocities for HD 95735 folded on the phase of the detected signal at a period of 9.87 days. In thebottom panel, weighted averages (red filled circles) are shown on top of the velocities (grey circles) when dividing the orbitalphase into 30 bins. The solid curve denotes the modeled Keplerian radial velocity variability. Butler et al.
Figure 21 . S-index time series of HD 154345 with respect to the mean (top panel) and the radial velocity time-series with theKeplerian curve overplotted (bottom panel).
IRES/Keck Exoplanet Survey
HD 207832
Haghighipour et al. (2012) reported two Jovian-type planets orbiting HD 208732. We had no difficulties in detectingthe signals corresponding to these planet candidates in the Keck data. We find evidence, however, for a stellar magneticcycle in the S-indices at a period of 1369 days. This is reasonably close to the orbital period of the outer candidateof 1252 ±
65 days. However, the radial velocity signal is explained much better by a Keplerian model than simplelinear relationship between the radial velocities and S-indices – this is apparent because when modeling the candidatesreported by Haghighipour et al. (2012) there is no evidence for a dependence of the radial velocities on the S-indicesin the sense that parameter c S in Eq. (A1) would be statistically significantly different from zero.7.8. HD 265866
The radial velocities of the nearby M dwarf HD 265866 (GJ 251, HIP 33226) showed evidence in favor of two signalsthat we interpret are being caused by candidate planets orbiting the star. Our searches for a signal in the data witha one-Keplerian model identified a strong signal at a period of 1.74471 ± ± − (Fig. 22). We note that in Fig. 22, there are two local maxima in the period space at periods of 14 and 600days, respectively, suggestive of alternative solutions or additional signals in the data. However, the 1.74-day signalappears to explain the variations in the data the most convincingly and we thus adopt this periodicity as our preferredKeplerian periodicity. We have plotted the radial velocities folded on the phase of the signal in Fig. 23. We stronglyencourage future monitoring of this star to assess the nature of the observed local probability maxima shown in Fig.22. DISCUSSIONHIRES on Keck-I was a transformatively successful facility during the first decade of exoplanetary detection andcharacterization. In recent years, however, as thousands of additional exoplanets and planetary candidate detectionshave streamed in from other telescopes, both on the ground and in space, two factors have limited HIRES’ effectiveness:1) lack of adequate observing cadence, and 2) inadequate spectral resolution. The Keck telescopes are heavily-sharedfacilities that are also scheduled around the lunar calendar, and even the most successful planet detection consortia haverarely obtained more than a few dozen nights of time on HIRES per year. Furthermore, the lunation-driven schedulingmakes it very hard for bright-time observers to obtain full phase coverage for planets that have orbital periods nearintegral multiples of the lunar month. When one considers the most interesting cases of very low mass, potentiallyrocky terrestrial planets and super-Earths, it is now known from
Kepler that a large fraction of such exoplanet systemstypically harbor multiple low-mass planets (Batalha et al. 2013). When confronted with a signal containing severallow-amplitude periodicities, it is difficult to accurately measure orbital parameters without sufficient cadence. Theproblem is compounded by jitter stemming from stellar activity. As a consequence, the data presented here likelycontain a plethora of bona-fide signals that lie beneath our noise thresholds. The velocity measurements presentedin Table 1 will thus usefully support follow-on efforts that can access higher cadence and comparable (or improved)Doppler precision. An excellent recent example of this type of synergy was provided by the complex system of sixplanets around the star HD 219134 (Motalebi et al. 2015; Vogt et al. 2015). We amassed 331 precision velocities of thisstar with HIRES/Keck over seven years, and we were aware of at least 3 significant periodicities in this system as earlyas 2010. With the limited observing cadence achievable at Keck, however, we were unable to adequately parameterizethis complex 6-planet system until 2015, after we had obtained 101 additional higher-cadence observations over twoyears with the Automated Planet Finder at Lick Observatory (Vogt et al. 2014a).Speed and precision comparisons are sometimes drawn between the “iodine-based” technique employed with HIRES,and the super-stabilized, fiber-scrambled technique of HARPS and its similar cousins. The HARPS and HARPS-variants approach utilizes a dual-white-pupil spectrometer, with stabilization of the instrument’s line spread functionprovided by a fiber-feed image scrambler (or dual-scrambler), and spectrometer stabilization accomplished by enclosingthe spectrometer in vacuum, and/or in a highly temperature-stabilized chamber. The HARPS has distinct advantages.With no need for iodine lines as a wavelength reference, HARPS does not have to acquire a separate high S/N templateof each target star, and it circumvents the complex deconvolution issues that must be solved to adequately characterize8
Butler et al.
Figure 22 . Estimated posterior probability density as a function of the period parameter of the signal in a one-Keplerian modelgiven radial velocities of HD 265866. Red arrow denotes the global probability maximum and the horizontal lines correspondto equiprobability contours at 10% (dotted), 1% (dashed), and 0.1% (solid) of the maximum. the instrument line spread function when using the iodine technique. In addition, the HARPS approach is not restrictedto the relatively narrow (∆ λ ∼ both techniques, when properly implemented, are capableof reaching sub m s − precisions, albeit each with its own attendant difficulties.Direct comparisons of the “iodine-technique” vs. the “fiber-scrambled HARPS” approach, that cite HIRES as areference example for the former, are somewhat misleading. HIRES was neither specifically designed for, nor optimizedfor, extreme precision RV work, and certainly, HIRES possesses limited effectiveness in connection with the highestprecision radial velocity work primarily as a result of its inadequate spectral resolution. The highest resolution ofHIRES (with scientifically effective Throughput at the slit) was set at ∼ − levels of precision. HIRES’s resolution is almost a factor of two lowerthan the value R ∼ − mean internal uncertainties per observation. Even R ∼ R ∼ ,
000 resolution. The higher resolution enables the APF/Levyfacility to achieve the same level of RV precision as HIRES, with about a factor of 6 fewer photons on M dwarfs. ForM dwarf stars down to at least V=10, the APF facility achieves very comparable speed-on-sky as Keck, due largely tothe higher spectral resolution of its spectrometer.
IRES/Keck Exoplanet Survey Figure 23 . Radial velocities of HD 265866 folded of the phase of the detected signal.
We are currently using APF to follow up on many promising targets from our 20-year HIRES exoplanet survey withmuch higher cadence (Burt et al. 2014, 2015). In particular, combining the higher cadence available from APF withthe long time baseline of the HIRES program is proving to be very effective for characterizing complex multi-planetsystems such as HD 141399 and HD 219134 (Vogt et al. 2014b, 2015). We are also using PFS (in the south) and APF(in the north), and in combination over the declination overlap region, for K2 follow-up, and in the near future forTESS follow-up. CONCLUSIONIn this paper, we present 60,949 precision radial velocities of 1,624 stars obtained over the past 20 years from theLCES survey with the HIRES spectrometer on the Keck-I telescope. We also present a list of 117 unpublished likelyplanet-candidate signals gleaned from these data that appear to stem neither from stellar rotation nor from stellaractivity. Given the automated and by extension, fully standardized signal searches performed in the current work,we can now study the global occurrence rates of planets orbiting the stars in the Keck sample. This requires theestimation of the detection probability function for the sample (Tuomi et al. 2014). We are performing the requiredcomputations and expect to report them in a follow-up paper.It is hoped that this unique corpus of radial velocities, by and of themselves, and especially when combined withadditional RV and photometric data from other facilities, will be a valuable resource to the astronomical communityfor furthering the discovery and characterization of the galactic planetary census.We gratefully acknowledge the long assistance of former California Planet Search colleagues Geoff Marcy, DebraFischer, Jason Wright and Katie Peek for their help in tending many nights at the Keck I telescope. SSV gratefullyacknowledges support from NSF grants AST-0307493 and AST-0908870. SSV also gratefully acknowledges supportfrom NASA grant NNG04GE18G that partially funded the HIRES focal plane upgrade, and NASA grant NAG-4445that funded the commissioning of the HIRES exposure meter. RPB gratefully acknowledges support from NASAOSS Grant NNX07AR40G, the NASA Keck PI program, and from the Carnegie Institution of Washington. The workherein is based on observations obtained at the W. M. Keck Observatory, which is operated jointly by the University of0
Butler et al.
California and the California Institute of Technology, and we thank the UC-Keck and NASA-Keck Time AssignmentCommittees for their support. This research has made use of the Keck Observatory Archive (KOA), which is operatedby the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the NationalAeronautics and Space Administration. We also wish to extend our special thanks to those of Hawaiian ancestry onwhose sacred mountain of Mauna Kea we are privileged to be guests. Without their generous hospitality, the Keckobservations presented herein would not have been possible.REFERENCES
Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS,204, 24Boisse, I., Pepe, F., Perrier, C., et al. 2012, A&A, 545, A55Bouchy, F., Pepe, F., and Queloz, D. 2001, A&A, 374, 733.Breger, M. 2000, Delta Scuti and Related Stars, 210, 3Burt, J., Vogt, S.S., Butler, R.P., et al. 2014, ApJ, 789, 114.Burt, J., Holden, B., Hanson, R., et al. 2015, SPIE Journal ofAstronomical Telescopes, Instruments, and Systems, Volume 1.Butler, R. P., Marcy, G. W., Williams, E., et al. 1996, PASP,108, 500Butler, R.P., Vogt, S.S., Marcy, G.W., et al. 2004, ApJ, 617, 580.Butler, R. P., Wright, T. J., Marcy, G. W., et al. 2006, ApJ, 646,505Crane, J.D., Shectman, S.A., and Butler, R.P. 2010, SPIE, 7735.Crepp, J.R., Johnson, J.A., Howard, A.W., et al., ApJ, 761, 39.Cumming, A. 2004, MNRAS, 354, 1165Cumming, A., Butler, R.P., Marcy, G.W., et al. 2008, PASP,120, 531.Dawson, R. I. & Fabrycky, D. C. 2010, ApJ, 722, 937Duncan, D. K., Vaughan, A. H., Wilson, O. C., et al. 1991, ApJ,,76, 383.Epps, H.W., & Vogt, S.S. 1993, Applied Optics 32, 6270.Ford, E. B. 2006, ApJ, 642, 505Gelman, A., Carlin, J. B., Stern, H. S., & Rubin D. B. 2003,Bayesian Data Analysis (New York: Chapman & Hall)Haario, H., Saksman, E., & Tamminen, J. 2001, Bernoulli, 7, 223Haario, H., Laine, M., Mira, A., & Saksman, E. 2006, Stat.Comp., 16, 339Kibrick, R. I., Clarke, D.A., Deich, W.T.S., & Tucker, D. 2006SPIE, 6274.Goldreich, P., & Keeley, D. A. 1977, ApJ, 212, 243Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2011, A&A,534, A30.Gomes da Silva, J., Santos, N. C., Boisse, I., Dumusque, X., andLovis, C. 2014, A&A, 566, 66.Haghighipour, N., Butler, R.P., Rivera, E.J., Henry, G.W., andVogt, S.S. 2012, ApJ, 756, 91.Henry, G.W., Marcy, G.W., Butler, R.P., and Vogt, S.S. 2000,ApJ, 529, L41.Howard, A.W., Johnson, J.A., Marcy, G.W., et al. 2011, ApJ,726, 73.Isaacson, H., and Fischer, D. F. 2010, ApJ, 725, 875.Meschiari, S., Wolf, A. S., Rivera, E. et al. 2009, PASP, 121, 1016 Meschiari, S., Wolf, A. S., Rivera, E., et al. 2010, in PathwaysTowards Habitable Planets, proceedings of a workshop held14-18 September 2009 in Barcelona, Spain. Edited by VincentCoud du Foresto, Dawn M. Gelino, and Ignasi Ribas. SanFrancisco: Astronomical Society of the Pacific, p.503Meschiari, S., Wolf, A.S., Rivera, E., et al. 2012, AstrophysicsSource Code Library, record ascl:1210.018Motalebi, F., Udry, S., Gillon, M., et al. 2015, A&A, 584, A72Nelson, B.T., Ford, E.B., Wright, J.T., et al. 2014, MNRAS, 441,442.Pasquini, L., and Pallavicini, R. 1991, A&A, 251, 199.Pepe, F.; Mayor, M.; Delabre, B. et al. 2000, SPIE 4008, 582.Rivera, E.J., Lissauer, J.J., Butler, R.P., et al. 2005, ApJ, 634,625.Robertson, P., Endl, M., Cochran, W. D., and Dodson-Robinson,S. E. 2013, ApJ, 764, 3.Spronck, J. F. P., Fischer, D. A., Kaplan, Z. A., & Schwab, C.2012, Proc. SPIE, 8446, 84468ZSpronck, J. F. P., Fischer, D. A., Kaplan, Z., et al. 2015, PASP,127, 1027Teske, J. et al., 2016, in preparation.Tikhonov, A. N. & Arsenin, V. Y. 1977, Solutions of Ill-posedproblems (New York: Wiley).Tuomi, M., Jones, H. R. A., Jenkins, J. S., et al. 2013, A&A,551, A79Tuomi, M., Jones, H. R. A., Barnes, J. R., et al. 2014, MNRAS,441, 1545Tuomi, M. & Anglada-Escud´e 2013, A&A, 556, A111Tuomi, M. 2012, A&A, 543, A52van Leeuwen, F. 2007, A&A, 474, 653.Vogt, S. S. 1987, PASP. 99, 1214.Vogt, S. S., Allen, S. L., Bigelow, B. C., et al. 1994 SPIE, 2198,362.Vogt, S.S., Burt, J., Meschiari, S., et al. 2015, ApJ, 814, 12.Vogt, S.S., Radovan, M., Kibrick, R., et al. 2014a, PASP, 126,359.Vogt, S.S., Butler, R.P., Rivera, E.J., et al. 2014b, ApJ, 787, 97.Vogt, S.S., Burt, J., Meschiari, S., et al. 2015, ApJ, 814, 12.Winn, J. N., Matthews, J. M., Dawson, R. I. et al. 2011, ApJ,737, L18.Wright, J. T., Marcy, G. W., Butler, R. P., and Vogt, S. S. 2004,ApJ, 152, 261.Wright, J. T., Marcy, G. W., Butler, et al. 2008, ApJ, 683, L63.Wright, J.T. 2015, in Proceedings of colloquium “Twenty yearsof giant exoplanets” held at Observatoire de Haute Provence,France, October 5-9, 2015. Edited by I. Boisse, O. Demangeon,F. Bouchy and L. Arnold, p. 8-17. Published by theObservatoire de Haute-Provence, Institut Pythas.
IRES/Keck Exoplanet Survey A. STATISTICAL MODELThe statistical model for radial velocities consists of five additive parts: superposition of k Keplerian signals f k ,linear acceleration ˙ γ , reference velocity γ , correlated noise component, activity component, and white noise. Thesecan be modeled by a forward model of a radial velocity measurement m i obtained at time t i written as m i = f k ( t i ) + ˙ γ + γ + φ exp (cid:40) t i − − t i τ (cid:41) (cid:15) i − + cξ i + (cid:15) i , (A1)where φ quantifies the magnitude of the moving average component used to model correlated noise (Tuomi et al. 2013,2014) with exponential smoothing in a time-scale of τ , parameter c quantifies the linear dependence of the velocityon the activity index ξ i = S i − N − (cid:80) Ni =1 S i , where S i is the measured S-index based on CaII H&K emission at t i ,and (cid:15) i is a Gaussian random variable with a zero mean and a variance of σ i + σ J where σ J is also a free parameterof the model. N denotes the number of measurements. We fixed the exponential smoothing time-scale to τ = 4 daysbecause this parameter is typically not well-constrained (Tuomi et al. 2014) as long as it accounts for correlationsbetween nearby epochs arising from stellar activity and/or possible instrumental instability. This model has 5( k + 1)free parameters when k Keplerian signals are included in the model.This statistical model implies a likelihood function written as L ( m ) = L ( m ) · L ( m | m ) · · · L ( m N | m N − ) . (A2)For measurement m i , the likelihood function is written aslog L ( m i ) = −
12 log (cid:0) πσ i (cid:1) − R i σ i , (A3)where R i = m i − f k ( t i ) − ˙ γ − γ − φ exp (cid:40) t i − − t i τ (cid:41) (cid:15) i − − cξ i (A4)In addition to the likelihood function, we also used a prior probability density in our analyses. This prior was setuninformative such that π ( θ i ) = 1 for all free parameters θ i except the orbital eccentricity. For eccentricity, we set π ( e ) ∝ N (0 , σ e ) and σ e = 0 . φ = 0 and c = 0 ms −1