Constraints on Long-Period Planets from an L' and M band Survey of Nearby Sun-Like Stars: Observations
A. N. Heinze, Philip M. Hinz, Suresh Sivanandam, Matthew Kenworthy, Michael Meyer, Douglas Miller
aa r X i v : . [ a s t r o - ph . E P ] M a r To be submitted to ApJ.
Constraints on Long-Period Planets from an L ′ and M band Survey of NearbySun-Like Stars: Observations A. N. Heinze
Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721 [email protected]
Philip M. Hinz
Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721 [email protected]
Suresh Sivanandam
Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721 [email protected]
Matthew Kenworthy
Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721 [email protected]
Michael Meyer
Department of Physics, Swiss Federal Institute of Technology (ETH-Zurich), ETH H´onggerberg,CH-8093 Zurich, Switzerland [email protected]
Douglas Miller
Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721 [email protected]
ABSTRACT Observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizonaand the Smithsonian Institution. L ′ and M band Adaptive Optics (AO)imaging survey of 54 nearby, sunlike stars for extrasolar planets, carried out using theClio camera on the MMT. We have concentrated more strongly than all other planetimaging surveys to date on very nearby F, G, and K stars, prioritizing stellar proximityhigher than youth. Ours is also the first survey to include extensive observations inthe M band, which supplement the primary L ′ observations. Models predict muchbetter planet/star flux ratios at the L ′ and M bands than at more commonly usedshorter wavelengths (i.e. the H band). We have carried out extensive blind simulationswith fake planets inserted into the raw data to verify our sensitivity, and to establisha definitive relationship between source significance in σ and survey completeness. Wefind 97% confident-detection completeness for 10 σ sources, but only 46% for 7 σ sources– raising concerns about the standard procedure of assuming high completeness at 5 σ ,and demonstrating that blind sensitivity tests to establish the significance-completenessrelation are an important analysis step for all planet-imaging surveys. We discovered apreviously unknown ∼ . ⊙ stellar companion to the F9 star GJ 3876, at a projectedseparation of about 80 AU. Twelve additional candidate faint companions are detectedaround other stars. Of these, eleven are confirmed to be background stars, and one isa previously known brown dwarf. We obtained sensitivity to planetary-mass objectsaround almost all of our target stars, with sensitivity to objects below 3 M Jup in thebest cases. Constraints on planet populations based on this null result are presented inour Modeling Results paper, Heinze et al. (2010).
Subject headings: planetary systems, planets and satellites:detection, intrumentation:adaptive optics, infrared: planetary systems, binaries:general, astrometry
1. Introduction
Nearly 400 extrasolar planets have now been discovered using the radial velocity (RV) method.RV surveys currently have good statistical completeness only for planets with periods of less thanten years (Cumming et al. 2008; Butler et al. 2006), due to the limited temporal baseline of theobservations, and the need to observe for a complete orbital period to confirm the properties ofa planet with confidence. The masses of discovered planets range from just a few Earth masses(Bouchy et al. 2009) up to around 20 Jupiter masses (M
Jup ). We note that a 20 M
Jup objectwould be considered by many to be a brown dwarf rather than a planet, but that there is no broadconsensus on how to define the upper mass limit for planets. For a good overview of RV planets todate, see Butler et al. (2006) or http://exoplanet.eu/catalog-RV.php .The large number of RV planets has enabled several good statistical analyses of planet pop-ulations (Fischer & Valenti 2005; Butler et al. 2006; Cumming et al. 2008). However, these applyonly to the short-period planets accessible to RV surveys. We cannot obtain a good understanding 3 –of planets in general without information on long period extrasolar planets; nor can we see how ourown solar system fits into the big picture of planet formation in the galaxy without a good censusof planets in Jupiter- and Saturn-like long-period orbits around other stars.Several methods (transit detection, RV variations, astrometry, and direct imaging) have yieldedrepeatable detections of extrasolar planets so far. While RV and astrometric surveys may eventuallydeliver important information about long-period extrasolar planets, direct imaging is the onlymethod that allows us to characterize them on a timescale of months rather than years or decades.Direct imaging of extrasolar planets is technologically possible at present only in the infrared,based on the planets’ own thermal luminosity, not on reflected starlight. The enabling technologyis adaptive optics (AO), which allows 6-10m ground-based telescopes to obtain diffraction lim-ited IR images several times sharper than those from HST, despite Earth’s turbulent atmosphere.Theoretical models of giant planets indicate that such telescopes should be capable of detectingself-luminous giant planets in large orbits around young, nearby stars. The stars should be youngbecause the glow of giant planets comes from gravitational potential energy converted to heat intheir formation and subsequent contraction: lacking any internal fusion, they cool and becomefainter as they age.Several groups have published the results of AO imaging surveys for extrasolar planets aroundF, G, K, or M stars in the last five years (see for example Masciadri et al. (2005); Kasper et al.(2007); Biller et al. (2007); Lafreni`ere et al. (2007); Chauvin et al. (2010)). Of these, most haveused wavelengths in the 1.5-2.2 µ m range, corresponding to the astronomical H and K S filters(Masciadri et al. 2005; Biller et al. 2007; Lafreni`ere et al. 2007; Chauvin et al. 2010). They havetargeted mainly very young stars. Because young stars are rare, the median distance to stars ineach of these surveys has been more than 20 pc.In contrast to those above, our survey concentrates on very nearby F, G, and K stars, withproximity prioritized more than youth in the sample selection. The median distance to our surveytargets is only 11.2 pc. Ours is also the first survey to include extensive observations in the M band, and only the second to search solar-type stars in the L ′ band (the first was Kasper et al.(2007)). The distinctive focus on older, very nearby stars for a survey using longer wavelengths isnatural: longer wavelengths are optimal for detecting objects with very red IR colors – that is, lowtemperature planets. These are most likely to be found in older systems, since planets cool andredden with age (Baraffe et al. 2003; Burrows et al. 2003). However old, low-temperature planetsalso have low luminosities, rendering them undetectable around all but the nearest stars.In Section 2 we describe the criteria used in choosing our sample, and present the characteristicsof our stars. In Section 3, we briefly describe our instrument, our observing strategy, and our imageprocessing pipeline. In Section 4 we detail our sensitivity estimation methods, and show how wecharacterized them using blind tests in which simulated planets were inserted into our raw data – apractice that should be standard for planet imaging surveys. In Section 5 we give astrometric andphotometric data for all the faint companions detected in our survey, as well as precise astrometry of 4 –the bright known binary stars in our sample. We present our conclusions in Section 6. Constraintson planet populations based on our survey null result are presented in Heinze et al. (2010).
2. The Survey Sample
The goal of our sample selection was to pick the nearest stars around which we could detectplanets of 10 M
Jup or below. This practically meant that very nearby stars were potential targetsup to ages of several Gyr, while at larger distances we would consider only fairly young stars. Weset out initially to investigate only FGK stars within 25pc of the sun, in order to make our samplecomparable in spectral type to the samples of the RV surveys, and to focus on the nearest stars, atwhich the L ′ and M bands are most useful relative to shorter wavelengths. In the end we includeda few M stars and a few stars slightly beyond 25pc, because these stars were very interesting andwe had exhausted most of the observable stars that lay within our more strict criteria. The starsof our sample are presented in Tables 1 and 2.Our survey focuses on markedly more nearby stars than all other surveys published to date.For example, the median distance to stars in the Masciadri et al. (2005) survey is 21.2 pc. For theKasper et al. (2007) survey the median distance is 37 pc, for Biller et al. (2007) it is 24.7 pc, andfor Lafreni`ere et al. (2007) it is 21.7 pc. Our median distance is 11.2 pc. 5 –Table 1. Age, Distance, and Spectral Type of Survey TargetsAge 1 Age 2 Adopted Dist. SpectralStar (Gyr) (Gyr) Age (Gyr) (pc) TypeGJ 5 0.11 a b c d τ Ceti · · · · · · c a ǫ Eri 0.56 a · · · e · · · · · · · · · · · · · · · f · · · a · · · g · · · e · · · h · · · a g c e i · · · i · · · c · · · a · · · c j c j · · · · · · g · · · c · · · c · · · < k · · · c · · · c · · · a · · · a · · · g · · · a g c · · · · · · · · · ξ Boo A 0.43 a c ξ Boo B 0.15 a · · · c · · · g · · · < l · · · < l · · · g · · · g · · · · · · · · · · · · · · · · · · · · · · · · · · · c · · · < k · · · < k · · · h · · · j · · · j · · · < h · · · < h · · · a Fischer (1998) b Bryden et al. (2006) c Wichmann et al. (2003) d L´opez-Santiago et al. (2006) e Age estimate from FEPS target list, courtesy M. Meyer. f Zuckerman et al. (2001) g King et al. (2003) h Barrado y Navascu´es (1998) i Wichmann & Schmitt (2003) j Montes et al. (2001) k The H¨unsch et al. (1998) catalog reports a ROSAT detection at a flux levelthat suggests an age of 1 Gyr or less. l Favata et al. (1998) <
100 Myr) planets by orders of magnitude, while for older planets themodels are more accurate. Lastly, L ′ surveys such as ours and that of Kasper et al. (2007) arean important complement to the shorter-wavelength work of Masciadri et al. (2005); Biller et al.(2007); Chauvin et al. (2010); and Lafreni`ere et al. (2007) in that they ensure that limits on planetpopulations do not depend entirely on yet-untested predictions of the flux from extrasolar giantplanets in a narrow wavelength interval. Until a sufficient number of extrasolar planets have beendirectly imaged that their spectra are well understood, surveys conducted at a range of differentwavelengths will increase the confidence that may be placed in the results. 9 –Table 2. Position and Magnitude of Survey TargetsStar RA DEC V H K L’GJ 5 00:06:36.80 29:01:17.40 6.13 4.69 4.31 4.25HD 1405 00:18:20.90 30:57:22.00 8.60 6.51 6.39 6.32 τ Ceti 01:44:04.10 -15:56:14.90 3.50 1.77 1.70 1.65GJ 117 02:52:32.10 -12:46:11.00 6.00 4.23 4.17 4.11 ǫ Eri 03:32:55.80 -09:27:29.70 3.73 1.88 1.78 1.72GJ 159 04:02:36.70 -00:16:08.10 5.38 4.34 4.18 4.14GJ 166 B 04:15:21.50 -07:39:22.30 9.50 · · · · · · · · ·
GJ 166 C 04:15:21.50 -07:39:22.30 11.17 5.75 5.45 5.05HD 29391 04:37:36.10 -02:28:24.80 5.22 4.77 4.54 4.51GJ 211 05:41:20.30 53:28:51.80 6.23 3.99 4.27 4.21GJ 216 A 05:44:27.80 -22:26:54.20 3.60 2.47 2.42 2.38BD+20 1790 07:23:43.60 20:24:58.70 9.93 7.61 7.51 7.42GJ 278 C 07:34:37.40 31:52:09.80 9.07 5.42 5.24 5.05GJ 282 A 07:39:59.30 -03:35:51.00 7.20 5.06 4.89 4.82GJ 311 08:39:11.70 65:01:15.30 5.65 4.28 4.17 4.12HD 77407 A 09:03:27.10 37:50:27.50 7.10 5.53 5.44 5.39HD 77407 B 09:03:27.10 37:50:27.50 · · · · · · · · · · · ·
HD 78141 09:07:18.10 22:52:21.60 7.99 5.92 5.78 5.72GJ 349 09:29:54.80 05:39:18.50 7.22 5.00 4.79 4.70GJ 355 09:32:25.60 -11:11:04.70 7.80 5.60 5.45 5.39GJ 354.1 A 09:32:43.80 26:59:18.70 7.01 5.24 5.12 5.06GJ 380 10:11:22.10 49:27:15.30 6.61 3.93 2.96 2.89GJ 410 11:02:38.30 21:58:01.70 9.69 5.90 5.69 5.46HD 96064 A 11:04:41.50 -04:13:15.90 7.64 5.90 5.80 5.75HD 96064 B 11:04:41.50 -04:13:15.90 · · · · · · · · · · · ·
GJ 450 11:51:07.30 35:16:19.30 9.78 5.83 5.61 5.40BD+60 1417 12:43:33.30 60:00:52.70 9.40 7.36 7.29 7.23HD 113449 13:03:49.70 -05:09:42.50 7.69 5.67 5.51 5.46GJ 505 A 13:16:51.10 17:01:01.90 6.52 4.58 4.38 4.31GJ 505 B 13:16:51.10 17:01:01.90 9.80 5.98 5.75 5.43GJ 519 13:37:28.80 35:43:03.90 9.07 5.66 5.49 5.28GJ 3860 14:36:00.60 09:44:47.50 7.51 5.63 5.55 5.49GJ 564 14:50:15.80 23:54:42.60 5.88 4.47 4.42 4.37 10 –As can be seen from Table 1, some estimates have placed the ages of some of our stars wellbelow 100 Myr. We have chosen to approximate these ages as 100 Myr. There are several reasonsfor this. First, the Burrows et al. (2003) models we have adopted do not give the type of observ-ables we need for planets younger than 100 Myr. Second, setting the ages of these stars slightlyolder than they are thought to be fits in with our generally conservative approach to the volatilesubject of extrasolar planet searches, and ensures that our survey results do not hang on just afew very young stars and will not be invalidated if the age estimates are revised upward. Finally,setting the ages conservatively hedges our results to some extent against the possibility suggested inMarley et al. (2007) that young massive planets may be far fainter than expected because much ofthe gravitational potential energy of the accreting material may get radiated away in an accretionshock and thus never get deposited in the planet’s interior. Figure 4 in Marley et al. (2007) showsthat in this accretion scenario planets start out at much lower luminosities than predicted by ‘hotstart’ models such as those of Burrows et al. (2003), but over time the predictions converge. By100 Myr, the differences are less than an order of magnitude for planets less massive than 10 M
Jup ,and are negligible for planets of 4 M
Jup and lower masses.
3. Observations and Image Processing3.1. The Instrument
The Clio instrument we used for our observations has been well described elsewhere (Freed et al.(2004), Sivanandam et al. (2006), and Hinz et al. (2006)). We present only a brief overview here.The MMT AO system delivers a lower thermal background than others because it uses theworld’s first deformable secondary mirror, thereby avoiding the multiple warm-mirror reflections(each adding to the thermal background) that are needed in other AO systems. This uniqueproperty makes the MMT ideal for AO observations in wavelengths such as the L ′ and M bandsthat are strongly affected by thermal glow. Clio was developed to take advantage of this to searchfor planets in these bands. It saw first light as a simple imager offering F/20 and F/35 modes.The design allowed for coronagrapic capability, which has since been developed (Kenworthy et al.2007) but was not used in our survey. In the F/20 mode, which we we used for all the observationsreported herein, Clio’s field of view is 15.5 × . ± . L ′ and M bands. For each star in our sample we sought to acquire about one hour or more of cumulativeintegration at the L ′ band. In most cases we achieved this. For some of our brightest nearby 11 –Table 2—ContinuedStar RA DEC V H K L’GJ 3876 14:50:20.40 82:30:43.00 5.64 4.19 3.92 3.87 ξ Boo A 14:51:23.40 19:06:01.70 4.55 2.82 2.75 2.70 ξ Boo B 14:51:23.40 19:06:01.70 6.97 4.45 4.34 4.24HD 139813 15:29:23.60 80:27:01.00 7.31 5.56 5.46 5.41GJ 625 16:25:24.60 54:18:14.80 10.40 6.06 5.83 5.60GJ 659 A 17:10:10.50 54:29:39.80 8.80 6.23 6.12 5.97GJ 659 B 17:10:12.40 54:29:24.50 9.29 6.13 5.97 5.83GJ 684 A 17:34:59.59 61:52:28.39 5.23 3.89 3.74 · · ·
GJ 684 B 17:34:59.59 61:52:28.39 8.06 · · · · · · · · ·
GJ 702 A 18:05:27.30 02:30:00.40 4.20 2.32 2.24 2.18GJ 702 B 18:05:27.30 02:30:00.40 6.00 3.48 3.37 3.2761 Cyg A 21:06:53.90 38:44:57.90 5.21 2.47 2.36 2.2561 Cyg B 21:06:55.30 38:44:31.40 6.03 3.02 2.87 2.74BD+48 3686 22:20:07.00 49:30:11.80 8.57 6.58 6.51 6.45GJ 860 A 22:27:59.47 57:41:45.15 9.59 5.04 4.78 · · ·
GJ 860 B 22:27:59.47 57:41:45.15 10.30 · · · · · · · · ·
GJ 879 22:56:24.10 -31:33:56.00 6.48 3.80 3.81 3.70HD 220140 A 23:19:26.60 79:00:12.70 7.54 5.74 5.66 5.60HD 220140 B 23:19:26.60 79:00:12.70 · · · · · · · · · · · ·
GJ 896 A 23:31:52.20 19:56:14.10 9.95 5.24 4.99 4.64GJ 896 B 23:31:52.20 19:56:14.10 12.40 6.98 6.68 6.28Note. — Coordinates are epoch J2000.0 and are mostly fromPerryman et al. (1997). H and K magnitudes are from Cutri et al.(2003), or else calculated from Simbad website spectral types and V magnitudes using Table 7.6 of Cox (2000). L ′ magnitudes are similarlycalculated from either V or K values. 12 –targets we acquired M band integrations as well. If possible we observed the star through transit,not only to minimize airmass, but also to obtain the greatest possible amount of parallactic rotation.Parallactic rotation is important because it causes image artifacts from the telescope to rotate withrespect to real sources, rendering them more distinguishable. To enhance this effect, we observedwith the instrument rotator off, so that rays and ghosts from the Clio instrument itself would alsorotate, and could be suppressed by the same procedures that suppressed telescope artifacts (seeSection 3.3).After acquiring each target with MMTAO, we determined a single-frame integration timefor our science images based solely on the sky background. This integration time was chosen sothat the sky background flux filled 60 −
80% of the detector full-well capacity. This ensured thatbeyond the speckle halo of the star the observations were background-limited rather than readnoiselimited. The optimal integration time changed due to night-to-night variations in sky brightness,usually ranging from 1.5 to 2.0 seconds in L ′ and from 100-200 msec at M ; see Table 3 for details.The science exposures generally saturated the primary star. When possible, we interleaved a fewshorter exposures providing unsaturated images. These could be used later to determine the truePSF delivered by the AO system during observations of a particular star.In normal operation Clio coadds several individual frames and saves them as a single FITSimage. We used this option except for our observations of the star GJ 380, for which we saved andprocessed the frames individually. The increased data volume and processing runtimes for GJ 380outweighed any minor advantages the single-frame approach may offer in terms of image quality.Coadding delivers good-quality data much more efficiently.Table 3 shows the date on which each of our target stars was observed, the nominal single-frame integration time, the coadds, and the number of coadded FITS images we acquired. Thetrue single-frame integration for Clio is the nominal integration plus 59.6 msec. Table 4 gives thefull science integration, parallactic rotation, and mean airmass for each star.We took our data using the standard IR imaging technique of nodding, in which a sequenceof images is taken in one position, the telescopes is moved (‘nodded’) slightly, and then anotherimage sequence is acquired. Images taken at one position can then be subtracted from imagestaken at the other position. In contrast to the on-source/off-source nodding used in some typesof observations, we place the science target on the detector in both nod positions to maximize theuseful data aquired. Artifacts of the bright sky interacting with the telescope and the detectorvanish on nod subtraction, while real celestial objects, including the target star itself, appear asbright and dark images separated by a distance set by the nod amplitude (typically about halfour field of view). Nodding is a powerful technique, and is practically indispensible for L ′ and M band observations. We typically nodded the telescope every 2-5 minutes. This was short enoughthat alterations in the sky background did not introduce appreciable noise into our data – in sharpcontrast to, e.g., 10 µ m N band observations, where a ‘chopping’ mirror must be used to switchbetween source and sky on a timescale of seconds or less. 13 –Table 3. Observations of Science Targets: Basic ParametersDate Obs.Star (yyyy/mm/dd) Band Clio int(msec) Coadds a ξ Boo AB a ξ Boo AB a a a a a ǫ Eri 2006/09/09 M 130 100 180GJ 5 2006/09/11 L’ 1500 15 210 ǫ Eri 2006/09/11 L’ 1500 15 184GJ 117 2006/12/01 L’ 1500 15 139GJ 211 2006/12/01 L’ 1500 15 170GJ 282 A 2006/12/01 L’ 1500 15 190HD 1405 2006/12/02 L’ 1500 15 98GJ 159 2006/12/02 L’ 1500 15 180 14 –Table 3—ContinuedDate Obs.Star (yyyy/mm/dd) Band Clio int(msec) Coadds a a τ Ceti 2007/01/04 L’ 1700 15 160HD 29391 2007/01/04 L’ 1700 15 200BD+20 1790 2007/01/04 L’ 1700 15 188HD 96064 AB a a b a a These stars were sufficiently close binaries that both stars appeared on the same Clio images,and meaningful sensitivity to substellar objects could be obtained around both. b A small fraction of the images of this star were accidentally taken with a 1500 msec ratherthan a 1700 msec nominal integration time.
15 –Table 4. Observations of Science Targets: Data AcquiredStar Band Exposure(sec) Mean Airmass Rotation Proc. MethodsGJ 659 A L’ 1853.64 1.113 15.80 ◦ a, b, d, eGJ 354.1 A L’ 4778.27 1.032 130.75 ◦ a, b, d, e, x, yGJ 450 L’ 5354.96 1.031 110.37 ◦ a, b, d, e, x, yGJ 625 L’ 4283.97 1.117 45.65 ◦ a, b, d, e, x, yGJ 349 L’ 4943.04 1.178 40.61 ◦ a, b, d, eGJ 564 L’ 3975.03 1.036 70.70 ◦ a, b, d, eGJ 3876 L’ 3501.32 1.601 27.23 ◦ a, b, d, eGJ3860 L’ 3976.98 1.086 47.09 ◦ a, b, d, eHD139813 L’ 3728.42 1.529 30.15 ◦ a, b, d, eGJ 702 AB a L’ 2393.24 1.149 25.50 ◦ a, b, d, e, f, g61 Cyg A L’ 3350.54 1.012 101.25 ◦ a, b, d, eBD+60 1417 L’ 4030.72 1.153 37.65 ◦ a, b, d, e ξ Boo AB a L’ 3955.14 1.047 71.20 ◦ a, b, d, e, f, g61 Cyg B L’ 3275.16 1.012 103.68 ◦ a, b, d, eGJ 519 L’ 4210.92 1.011 139.97 ◦ a, b, d, eBD+48 3686 L’ 3274.96 1.074 35.97 ◦ a, b, d, e ξ Boo AB a M 4149.60 1.060 46.142 ◦ a, b, d, e, f, gGJ 684 AB a L’ 3023.04 1.175 24.15 ◦ d, e, y, gGJ 505 AB a L’ 3753.61 1.070 45.30 ◦ a, b, d, e, f, g, x, yGJ 659 B L’ 4282.64 1.112 43.93 ◦ a, b, d, e61 Cyg A M 2808.96 1.025 44.24 ◦ a, b, d, eGJ 860 AB a L’ 2619.97 1.133 24.55 ◦ a, d, e, g, y61 Cyg B M 4373.04 1.018 118.96 ◦ d, e, yGJ 896 AB a L’ 3275.16 1.026 66.49 ◦ a, b, d, e, f, y ǫ Eri M 3412.80 1.334 23.406 ◦ d, e, yGJ 5 L’ 4912.74 1.011 146.98 ◦ a, b, d, e, x, y ǫ Eri L’ 4304.50 1.342 36.92 ◦ d, e, yGJ 117 L’ 3251.77 1.463 34.05 ◦ a, b, d, e, x, yGJ 211 L’ 3976.98 1.097 50.12 ◦ a, b, d, e, x, yGJ 282 A L’ 4444.86 1.281 30.28 ◦ a, b, d, e, x, yHD 1405 b L’ 2292.61 1.036 162.97 ◦ a, b, d, e, x, yGJ 159 L’ 4210.92 1.189 37.65 ◦ a, b, d, e, x, yGJ 216 A L’ 3696.25 1.739 30.10 ◦ a, b, d, e, x, y 16 – Image processing for AO planet search images tends to be complex and sophisticated. We havegiven a brief outline of our processing pipeline in Heinze et al. (2008), which is applicable to thecurrent work, and we hope to detail the unique aspects of our pipeline in a separate future paper.Here we will briefly describe the processing sequence, stressing aspects that were not covered inHeinze et al. (2008), but which become more important for the larger set of stars, processed over alonger period of time, that we describe herein.We begin the processing of each Clio image by normalizing it to a single coadd, subtractingan equal-exposure dark frame usually taken immediately before or after the science data sequence,and dividing by a flat frame. There follows an initial step of bad-pixel fixing. The next step isnod subtraction: from every image we subtract an identically processed copy of an image from theopposite nod position. This nod subtraction image is scaled (by a factor that is always very closeto unity) so that its mean sky brightness exactly matches that of the science image from whichit is being subtracted; the scaling is useful to compensate for small variations in sky brightness.Further bad-pixel fixing and bad-column correction follows. Finally, an algorithm to remove residualpattern noise is applied, and the image is zero-padded, shifted, and rotated in a single bicubic splineoperation so that celestial north is up and the center-of-mass centroid of the primary star is locatedin the exact center of the image. See Figure 1 for an example of our processing sequence, appliedto the nearby binary star GJ 896.The rotation places celestial north up on the images with an accuracy of about 0.2 degrees.Since we do not use the instrument rotator, a different rotation is required for each image: theparallactic angle plus a constant offset, which we determine by observing known binary stars (thisis further described in section 5.3). While parallactic rotation of bright binary stars over just tensof seconds has been detected due to the high internal precision of Clio astrometry, in no case doessufficient parallactic rotation occur during a Clio coadd sequence to appreciably blur the scienceimages.We have confirmed that the clean, symmetrical stellar images produced by the MMT AOsystem at the L ′ and M bands give accurate, consistent center-of-mass centroids even if saturated.This is important for our survey since our pre-stack registration of images is based in most cases oncentroids of a saturated primary. If the variation in such centroids is more than about one pixel,faint sources will be substantially blurred in the final stacks, and our point-source sensitivity willbe appreciably reduced. In practice, however, we find that faint sources (and bright secondariesin binary systems) do in fact appear sharp in our image stacks. Images we took of Procyon(unpublished) and of 61 Cyg A and B (see Figures 13 and 14) illustrate this in an especially strikingmanner, because our images of Procyon were more severly saturated than any reported herein, whileour 61 Cyg A and B images were among the most saturated in our survey. In all three of these cases,sharp images of faint companions (the orbiting white dwarf in the case of Procyon; background starsin the cases of 61 Cyg A and B) appeared in the final image stacks, which were registered solely based 17 –Table 4—ContinuedStar Band Exposure(sec) Mean Airmass Rotation Proc. MethodsGJ 278 C b L’ 3088.01 1.017 170.627 ◦ a, b, c, d, e, x, yGJ 355 L’ 3719.65 1.380 25.74 ◦ a, b, c, d, e, x, yGJ 879 L’ 1263.28 2.232 11.68 ◦ a, c, d, x, yHD 220140 AB a L’ 3976.98 1.494 14.14 ◦ a, b, d, e, f, g, x, yGJ 166 BC a L’ 3485.71 1.301 28.66 ◦ a, b, d, e, x, yGJ 311 L’ 2105.46 1.201 26.23 ◦ a, b, c, d, e, x, yGJ 410 L’ 2339.40 1.026 34.26 ◦ a, b, c, d, e, x, y τ Ceti L’ 4223.04 1.535 37.03 ◦ a, b, d, e, x, yHD 29391 L’ 5278.80 1.227 39.63 ◦ a, b, c, d, e, x, yBD+20 1790 L’ 4962.07 1.068 47.94 ◦ a, b, d, e, x, yHD 96064 AB a L’ 4750.92 1.252 41.74 ◦ a, b, d, e, x, yHD 77407 AB a L’ 2085.13 1.008 95.44 ◦ a, b, c, d, e, f, g, x, yHD 78141 c L’ 5297.98 1.022 109.11 ◦ a, b, c, d, e, x, yHD 113449 L’ 4444.86 1.263 35.36 ◦ a, b, d, e, x, yGJ 702 AB M 3738.24 1.171 32.70 ◦ d, e, g, yGJ 380 L’ 3222.13 1.341 20.58 ◦ a, b, d, e, x, yNote. — Proc. Methods refers not to the data that were acquired, but to different methodsused in processing the data. Each method represents a different master image produced bystacking the entire data set after applying a particular set of pre-stack processing algorithms.For example, four separate master images were made of the star GJ 659A. Each was a stackof all the images acquired, processed using a different method of pre-stack image processing:the ‘a’, ‘b’, ‘d’, and ‘e’ methods in the case of this star. The different processing methods areexplained in Section 3.3 a These stars were sufficiently close binaries that both stars appeared on the same Clio images, and meaningfulsensitivity to substellar objects could be obtained around both. b Though the rotation on this star is very large, difficulties arise because the star transited very near the zenithand almost all the rotation happened in a short span of time during which observations were not possible. PSFsubtraction had to be performed on a subset of the data with equal numbers of images on each side of transit. c A small fraction of the images of this star were accidentally taken with a 1500 msec rather than a 1700 msecnominal integration time. The total exposure time has been corrected accordingly.
18 –Fig. 1.— (A)
Raw image of the nearby binary star GJ 896. (B)
Same image after dark subtractionand flatfielding. Contrast stretched 5 × relative to (A). (C) Same image after nod subtraction.Contrast stretched 2.5 × relative to (B). (D) Same image after correction for bad pixels and badcolumns. (E)
Same image after shifting and rotation. (F)
Final stack made from 105 images like(E). Unsharp masking has not yet been applied. The field of view for each tile is 10.6 arcsec square. 19 –on center-of-mass centroids of the heavily saturated primary. The consistency of such centroidsis confirmed to an even tighter tolerence based on our observations of binary survey targets, inwhich both saturated and unsaturated images were aquired. For example, the total differencesbetween our saturated and unsaturated astrometry at M band for the binary stars GJ 702 and ξ Boo were only 0.0007 arcsec and 0.0039 arcsec, respectively (where differences in separation andposition angle have been combined). The same saturated vs. unsaturated differences for our L ′ astrometry of the binary stars ξ Boo, HD 77407, GJ 505, and GJ 166BC were 0.0088 arcsec,0.0038 arcsec, 0.0026 arcsec, and 0.0015 arcsec, respectively. These values are based on averages ofastrometric measurements performed on individual frames prior to stacking. The internal scatterin the astrometry of saturated images was also very low, even though the saturated measurementsspanned about an hour of time and tens of degrees of parallactic rotation in each case, giving ampleopportunity for any defects in the saturated astrometry to manifest themselves. In all cases tested,center-of-mass centroids of saturated images are self-consistent, and consistent with centroids ofunsaturated images, to considerably greater precision than necessary for the purposes of our survey.We stack our processed images to make a master image for each processing method usinga creeping mean combine. This method of image stacking uses a single parameter, the rejectionfraction, which we set to 20% for our standard master images. The mean of each given pixel throughthe image stack is computed, the most deviant value is rejected, and the mean is computed again.This procedure is iterated until the required fraction of data points have been rejected. One of us(S. S.) developed an N log( N ) implementation that greatly improved the speed of our processingpipeline. We chose the creeping mean over the more commonly used median with sigma-clippingbecause the creeping mean can deliver cleaner final stacks when, as with Clio, the raw imagescontain bright, slowly-rotating ghosts and diffraction rays. In clean sky away from all ghosts andrays, the median delivers slightly lower rms noise, since it rejects fewer data points.Our final stacked images contain dark, high-noise regions on either side of each bright star, dueto the negative star images from nod subtraction. Since we usually keep a constant nod directionreferenced to the telescope, for data sets with significant parallactic rotation the dark regions arespread into arcs and weakened by the creeping mean stack. To further alleviate the dark regionsand to enhance the visibility of faint point sources against the bright stellar halo itself, we unsharpmask the final, stacked images. We do this by convolving the image with a Gaussian kernel of σ = 5 pixels, and then subtracting this convolved version from the original image. The full widthat half maximum (FWHM) of the Gaussian kernel is 11.8 pixels, as opposed to a FWHM of about3 pixels for a typical PSF, so the unsharp masking does not strongly reduce the brightness of realpoint sources. This step marks the end of our image processing pipeline.The above describes our baseline processing method. We developed six specializations of thismethod, which we call the ‘b,’ ‘c,’ ‘d,’ ‘e,’ ‘x,’ and ‘y’ processing strategies, while the previouslydescribed baseline method itself is called ‘a’. The data from each star in our survey were processedseveral times, each time using a different one of these specialized methods, and each producing aseparate master image. Having multiple master images based on different processing methods is 20 –helpful because the different methods enhance sensitivity to planets in different parts of the images,and because the master images from different methods provide a quasi-independent check on thereality of suspected faint sources. We will now describe how these different specialized processingmethods function.In the ‘b’ processing method, we suppress the stellar PSF to increase our sensitivity to faintcompanions. To do this, we take advantage of the fact that long-lived PSF artifacts in stellarimages from AO-equipped telescopes tend to remain fixed with respect to the telescope and/orinstrument (Soummer et al. 2007). When observing with the instrument-rotator off, as we do,real sources slowly rotate with respect to artifacts as the telescope tracks. Science images mustbe digitally rotated before stacking, as described above. However, if a stack of un -rotated framesis made, a clear image of the instrumental PSF is obtained, while any real sources are stronglyattenuated by the creeping mean. We subtract a properly registered version of such a PSF imagefrom every science frame prior to final rotation and stacking, a technique called ADI (Marois et al.2006). In our specific implementation of ADI, we split the image set into a first and second half,and a PSF image is made using a 50% rejection creeping-mean stack of each half. The PSF imagefrom the second half of the data is subtracted from every image in the first half, while the PSFimage from the first half of the data is subtracted from the images in the second half. The resultis powerful attenuation of the stellar PSF and greatly increased sensitivity to close-in companions.Since parallactic angle changes monotonically with time in all our observing sequences, splitting thedata into first and second halves helps prevent real companions from being partially subtracted dueto appearing at a residual level in the PSF images. For stars with insufficient parallactic rotation,very close-in companions can still be partially subtracted, but a characteristic dark-bright-darksignature is created which is very noticeable for companions of sufficient brightness. However, inour sensitivity analyses, we have conservatively set the sensitivity of ADI images to zero inside theradius where such ADI self-subtraction first becomes significant.In the ‘c’ reduction method, an azimuthally smoothed version of the primary PSF is subtractedfrom the image. The smoothing is done using creeping-mean rejection in a sliding annular arccentered on the primary, with parameters set so that real sources vanish essentially completelyfrom the smoothed PSF and therefore cannot be dimmed in the subtraction. The quality of PSFsubtraction achieved is usually substantially inferior to the ‘b’ method, and the ‘c’ method istherefore used relatively seldom. Sometimes it is employed because insufficient parallactic rotationrenders the ‘b’ method less useful, or because the ‘c’ image with its different speckle pattern isdesired as a quasi-independent check on candidate sources detected in the ‘b’ method image.In the ‘d’ reduction method, each image is unsharp masked before the stack. The final stackedimage is unsharp masked again. While unsharp masking is a linear process, the creeping meanstack is not, so the results are different from simply unsharp-masking twice after the final stack.This is especially significant for bright stars with intense seeing halos. Due to our nod subtractionmethod, it often happens for such stars that a given x,y pixel location falls on a bright, positiveseeing halo for images taken in the first nod position, and on a negative, subtracted seeing halo 21 –for images taken in the other nod position: that is, the statistics through the image stack at thispixel location are strongly bimodal. Under such circumstances the creeping mean will settle oneither the positive or the negative side of the distribution – and which one it settles on can bedifferent for adjacent pixels. This causes intense ‘bimodality noise’ that is essentially an artifactof the stack. Note that using a median stack instead will not necessarily fix the problem, as theremay well be no middle ground between the positive and negative seeing halos. Pre-stack unsharpmasking removes the seeing halos and thus resolves the problem of bimodality noise, enormouslyimproving the quality of the final stacked image for bright stars. For fainter stars, the results aremore similar to simply unsharp-masking the final image twice. However, the specific noise pattern issubstantially changed, which can aid in confirming faint sources: the ‘d’ method image can providea quasi-independent confirmation for a faint source marginally detected in the baseline ‘a’ image.The ‘e’ data reduction method combines the ‘b’ and ‘d’ methods: ADI is applied, and then thepre-stack unsharp masking is performed.The ‘x’ data reduction method uses a variant on nod subtraction that avoids the dark negativeimages. Two master sky images are made, by combining the star-free portions of all images in thefirst and second halves of the data set. One of these star-free master sky images is then subtractedfrom each individual science image in lieu of the ordinary nod subtraction. To avoid subtractingreal sources, the sky image from the second half of the data set is subtracted from images inthe first half, and vice-versa. The usefulness of this processing method varies enormously fromone data set to another. If the sky background was very stable, the ‘x’ method final image isalmost indistinguishable from that of the baseline ‘a’ method, so that blinking the two gives theimpression that the dark nod-subtraction artifacts magically disappear. If the sky background washighly variable, the ‘x’ images are useless due to intense pattern noise. The ‘y’ image reductionmethod is a combination of the ‘x’ and ‘d’ methods, in which the images are unsharp masked afterthe subtraction of the master sky image but before the final stack. Figure 2 compares the resultsof the ‘a’ method (before and after the final unsharp masking step), the ‘d’ method, and the ‘y’method. The star is HD 96064, a binary system in which the secondary is itself a close binary. Afaint additional companion is also detected, but is confirmed based on proper motion and K S − L ′ color to be a background star rather than a substellar companion.Two additional processing methods could be applied to binary stars of near-equal brightnessfor which both components appeared on each Clio frame. A scaled version of the PSF of eachstar could be used to subtract the other, on a frame-by-frame basis, prior to the final stack. Theresulting PSF subtraction was substantially better than ADI. We labeled this reduction method‘f.’ A version that also included pre-stack unsharp masking was called ‘g’. Figure 3 illustrates ourdifferent PSF subtraction methods, both ADI and binary star subtraction, as applied to the binarystar GJ 896, which was also shown in Figure 1.We applied the ‘a,’ ‘b,’ ‘d,’ and ‘e’ processing methods to almost all of our stellar data sets,except a very few for which there was insufficient parallactic rotation to use the ADI methodswithout subtracting real sources. In many instances we also applied the ‘x’ and ‘y’ methods. We 22 –Fig. 2.— Different processing methods applied to the wide binary star HD 96064. The brightness ofthe faint source is L ′ = 13 .
7, corresponding to a mass of about 20 M
Jup if it were a true companion– however, it is confirmed to be a background star. (1)
Result of baseline processing (‘a’ method)before final unsharp mask. (2)
The ‘a’ method image after unsharp masking. Dark nod-subtractionartifacts are somewhat reduced but remain prominent. (3)
Same data set processed with the ‘d’method. Nod artifacts are greatly reduced, but still exist as high-noise regions where faint sourcescould not be detected. (4)
Same data set processed with the ‘y’ method. The nod artifacts areeliminated. Field shown in each tile is 17 arcsec square. 23 –Fig. 3.— (1)
Baseline ‘a’ method final image of GJ 896A. (2)
Same data set processed with ADI(‘b’ method). (3)
Same data set processed with ADI and pre-stack unsharp masking (‘e’ method). (4)
Same data set processed with binary star subtraction. Background noise is increased becausethe secondary had to be scaled up to match the brightness of the primary. (5)
Same data set, butnow showing the ‘a’ method image of the secondary, rather than the primary. (6)
Same data set,again showing the secondary, but now processed with binary star subtraction. The background isvery clean since the primary was scaled down to subtract away the secondary. Field shown in eachtile is 3.9 arcsec square. 24 –applied the ‘f’ and ‘g’ methods to every binary star where they would work.The methods involving pre-stack unsharp masking (‘d,’ ‘e,’ ‘y,’ and ‘g’) always gave cleanerimages, but we used the other methods as well because pre-stack masking slightly dimmed pointsources (by about 3-10%, depending on the AO-corrected FWHM), and there was a slight chancethis could cause a discovery to be missed. Our pattern-noise correction method also dimmed faintpoint sources by about 15-18%, based on tests. Near the end of our processing, one of us (M. K.)developed a superior pattern-noise correction that caused zero dimming, and we also developeda type of unsharp masking that produced zero dimming to within the measurement error of ourtests. Only the stars ǫ Eri ( L ′ and M band), GJ 684 A, GJ 684 B, GJ 702 A ( M band only), GJ702 B ( M band only), 61 Cyg B ( M band only), GJ 860 A, and GJ 860 B were processed usingthese improvements. For these stars, only the ‘d,’ ‘e,’ ‘y,’ and, where applicable, the ‘g’ processingmethods were used, since the downside of pre-stack unsharp masking had been eliminated.
4. Sensitivity Analysis4.1. Sensitivity Estimators
Our survey arrived at a null result: no planets were detected. Our science results, like thoseof previous surveys (Masciadri et al. 2005; Kasper et al. 2007; Biller et al. 2007; Lafreni`ere et al.2007; Chauvin et al. 2010), therefore take the form of upper limits on the abundance of extrasolarplanets. The accuracy of such an upper limit depends entirely on having a good metric for thesensitivity of the survey observations.A sensitivity estimator must translate some measurable statistic of an image into a realisticpoint-source detection limit. A procedure which has often been used (see for example Biller et al.(2007) and Chauvin et al. (2010)) involves calculating the single-pixel RMS standard deviation( σ pix ) in different regions on an image, and adopting a factor (often taken to be 5.0) by whichthe peak of a point-source image must exceed this σ pix to be cleanly detected. All that remains isto map the 5 σ pix PSF peak to a magnitude (or ∆-mag), and assign this as the sensitivity in theimage region under consideration. Biller et al. (2007) and Kasper et al. (2007), among others, havediscussed possible choices for the size and shape of the regions over which σ pix is calculated, withthe objective of obtaining smooth and accurate plots of point-source sensitivity vs. separation fromthe star.While the method above produces excellent results when correctly applied, we sought to adopta slightly more sophisticated approach. One reason for this is that calculating sensitivity based oncomparing the single-pixel RMS to the peak of the PSF does not take into account the FWHM ofthe PSF. If the PSF is several pixels wide, detection need not depend on the peak height alone:pixels other than the central peak contain additional flux that can in principle be used to detectthe point source at a lower peak flux than would be possible for a narrower PSF. We have explored 25 –three possible sensitivity estimation methods that attempt to consider all the flux contained in theimage of a point source, rather than only the peak of the PSF. The first solution we consideredwas calculating σ pix just as for the previous method, and then translating this to a detection limitusing simple √ n statistics: σ P SF = σ pix √ πr = σ pix r √ π. (1)Where σ P SF is the PSF-scale noise in the image, σ pix is the single-pixel RMS as before, and r is the radius of the image of a point source (i.e. about half the FWHM of the PSF). Since not all theflux of a real point source will fall within the aperture of radius r , an aperture correction must beapplied as a final step. Then, for example, the 5 σ point-source sensitivity will be 5 σ P SF times theaperture correction. This sensitivity limit would represent an actual integrated flux, which couldbe converted directly to magnitudes using a photometric calibration. We will call this sensitivityestimation technique ‘Method 1’.The simple √ n statistics used in Method 1 assume that the brightness of each pixel is a randomvariable independent of its neighboring pixels: that is, that the noise is spatially uncorrelated. Thisassumption is violated for speckle residuals close to a star, and for a host of other stellar artifactsthat are present in AO images (ghosts, diffraction rays, etc.). We have confirmed by careful teststhat in the presence of speckle noise, Method 1 overestimates the true point-source sensitivity byup to 0.9 magnitudes. This applies to a good implementation of the method in which σ pix iscalculated over image regions spanning many PSF sizes. When the statistics region used is toosmall, the sensitivity will be overestimated even more.The problem with Method 1 is that clumps of correlated bright or dark pixels introduce morePSF-scale noise into the image than can be predicted from the single-pixel RMS. Lafreni`ere et al.(2007) solved this problem by convolving their image with a circular disk of radius r , effectivelysumming up the brightness within many small circular apertures at this radius, one aperture cen-tered on each pixel throughout the image. Then σ P SF will simply equal the RMS variation of theaperture sums (that is, of the convolved image). This is sensitivity estimation by aperture photom-etry of the noise background. As with previously discussed methods, it is important to calculatethe statistic over an image region large enough to contain many PSFs. In our implementation,the region over which the statistic σ P SF is calculated is either a disk of 8 pixel radius, or, close tothe star, an annular arc one pixel wide and 45 pixels long, at constant radius from the star. Forsimplicity, we will sometimes refer to this Lafreni`ere et al. (2007) method as ‘Method 2’. As withMethod 1, an aperture correction must be applied as a final step.Method 3 has already been described in Heinze et al. (2008). It is analagous to Method2, but rather than performing aperture photometry centered on every pixel of the image, oneperforms PSF-fitting photometry. If the PSF has been properly normalized, no aperture correctionis necessary for this method. We used PSF images from the short, unsaturated exposures describedin Section 3.2. 26 –In tests using our own real data, we find that the Lafreni`ere et al. (2007) method and Method3 agree to within reasonable uncertainty everywhere, while Method 1 agrees with the other twoonly in regions of very clean sky. Method 1 overestimates the sensitivity by about 0.2 magnitudesin the presence even of very faint ghost residuals, and by about 0.9 magnitudes in the strongresidual speckle noise close to the star. Herein, as in Heinze et al. (2008), we have used Method 3for our final sensitivity maps. It seemed slightly more conservative close to the star than Method2, though, again, our tests showed no significant difference between Method 3 and the method ofLafreni`ere et al. (2007). Far from the primary star, the region we use for calculating the sensitivitystatistic is a disk of radius 8 pixels (0.39 arcsec, or about 3 λ/D ): that is, large enough to spanmany PSF-sizes, but small enough to sample the local noise properties. Close to the star (that is,within 60 pixels or 2.9 arcsec), we use instead an arc 45 pixels (2.2 arcsec) long and 1 pixel wide, ata fixed radius from the star. These disks or arcs are centered in turn on every pixel of each image,with the calculated statistics forming a sensitivity map.
After making a sensitivity map from the stacked image produced by each processing methodapplied to the data from a given star, we apply a slight smoothing to the different maps, andthen combine them into a single master sensitivity map. They are combined such that the mastersensitivity image shows at each location the best sensitivity obtained at that location by anyprocessing method that was applied. We quote 10 σ sensitivities: that is, the point source sensitivityis ten times the σ P SF statistic from Method 3. 10 σ is chosen as a nominal detection thresholdbecause we have over 95% completeness for 10 σ sources, with considerably less for 5 or 7 σ (seeSection 4.4).Our background-limited 10 σ sensitivity for one-hour exposures under fair conditions is typically L ′ = 16 .
0, or M = 13 .
0. Since we can detect some sources down to 5 σ significance, this correspondsto some chance of finding objects as faint as L ′ = 16 .
75 or M = 13 .
75. For exposures longer thanan hour or under very good conditions, our background limited 10 σ sensitivity ranged as high as L ′ = 16 . M = 13 .
3. Our median 10 σ sensitivities close to the stars were about ∆mag= 6 . . L ′ and M bands. See Heinze et al. (2008) for a detailed comparison of the efficaciesof different wavelengths for planet detection in the specific cases of Vega and ǫ Eri.Figures 4, 5, and 6 give example sensitivity contour maps for our L ′ observations of GJ 896and GJ 117, and our M band observations of 61 Cyg B, respectively, with 10 σ sensitivities given inapparent magnitudes. Figures of this type for all the stars observed in our survey can be downloadedfrom . 27 –Fig. 4.— Final sensitivity contour map for the binary star GJ 896 AB. 10 σ sensitivities fromour Method 3 estimator are presented, converted to apparent L ′ magnitudes. The grid squaressuperposed for astrometric reference are 2 × σ sensitivity in this data set never exceeded L ′ = 16 .
3. 28 –For use in the Monte Carlo simulations described in Heinze et al. (2010), we have convertedour sensitivity maps into plots of sensitivity vs. projected radius from each star. As can beseen from Figures 4 through 6, however, our sensitivity varied widely with position angle aroundthe star. To quantify this, we calculated ten different sensitivity values at each radius, givingthe percentiles in sensitivity from 0th to 90th percentile in 10% increments. Thus, e.g., the 0thpercentile at 2 arcsec is the very worst sensitivity obtained anywhere on the 2 arcsec-radius ringsurrounding the star, while the 50th percentile gives the median sensitivity at that radius. InFigures 7 and 8, we give example plots for GJ 896 A, GJ 117, 61 Cyg B ( M band), and ǫ Eri,with the sensitivities converted to minimum detectable planet mass in M
Jup using models fromBurrows et al. (2003), plotted against projected separation in AU. Plots of this type for all the starsin our survey, as well as the tabular data from which they were constructed, can be downloadedfrom . While our final sensitivity maps are constructed using only Method 3, as described above, weuse both Methods 2 and 3 for automated source detection. The use of both methods increases ourlikelihood of noticing faint sources at the limit of detectability. To search an image for sourcesusing either method, we query each pixel in turn to see if a source is present at that location. Tomake this query, we first calculate the sensitivity statistic (Method 2 or Method 3) over either adisk or an arc, just as described in Section 4.1, except that a PSF-sized region around the pixelbeing considered is not included, so that if a real source is present, it will not bias the sensitivityestimator. Finally, either aperture photometry (Method 2) or PSF-fitting (Method 3) is applied atthe location of the pixel itself, measuring the brightness of any source that may be present there. Ifthe resulting brightness is greater than the sensitivity statistic by a specified threshold factor (i.e.,5 for a 5 σ detection), a preliminary detection is reported.We would like to set the threshold as low as possible without getting an unmanageable numberof spurious detections. To this end, we divided each data set into the first half of the images andthe second half, and created a stacked image from each half. To be reported by our automateddetection code, a source had to appear at 4 . σ significance in the full stack, and at 3 σ significanceon each half-stack, at a location consistent to within 2 pixels. This eliminated residual ghostsand other artifacts, which would appear in different locations on the two halves of the data dueto parallactic rotation. Typically 10-20 spurious automated detections were nonetheless reportedaround each star.A real source could also be missed by the automatic algorithm but noticed manually. Forexample, due to parallactic rotation, a location might have valid data only for the first half ofthe data sequence, rendering an automated detection of a real source there impossible. Everyautomated detection, as well as candidate sources noticed only by eye, was carefully examinedmanually. Criteria applied included correct FWHM and symmetry, consistency in position and 29 –Fig. 5.— Final sensitivity contour map for the star GJ 117. 10 σ sensitivities from our Method 3estimator are presented, converted to apparent L ′ magnitudes. The grid squares superposed forastrometric reference are 2 × σ sensitivity in this data set never exceeded L ′ = 16 .
0. 30 –Fig. 6.— Final sensitivity contour map for our M band observations of the star 61 Cyg B (GJ 820B). 10 σ sensitivities from our Method 3 estimator are presented, converted to apparent M bandmagnitudes. The grid squares superposed for astrometric reference are 2 × σ detection limits from Method 3 are shown, converted to planet massusing models from Burrows et al. (2003). Planetary orbits around GJ 896 A would be destabilizedbeyond about 12 AU by the companion star GJ 896 B. In order from bottom to top, the curvesgive the 90th, 80th, 70th, 60th, 50th, 40th, 30th, 20th, 10th, and 0th percentile sensitivity at eachradius.Fig. 8.— Minimum detectable planet mass vs. projected separation in AU for 61 Cyg B ( M banddata; left), and ǫ Eri (right). 10 σ detection limits from Method 3 are shown, converted to planetmass using models from Burrows et al. (2003). In order from bottom to top, the curves give the90th, 80th, 70th, 60th, 50th, 40th, 30th, 20th, 10th, and 0th percentile sensitivity at each radius. 32 –brightness from one half-stack to the other, and inability to be explained away as an artifactof ghosts, diffraction rays, etc. If necessary, data stacks were split into quarters or even finerdivisions to verify sources where only a fraction of the images provided useful data. These manualinvestigations were very labor-intensive, especially since the master images and half-stacks fromseveral different processing methods (see Section 3.3) had to be examined for each star. Everysource that passed this final manual analysis was found to correspond to a real astronomical object.There were no false positives. The final demonstration of the validity of a sensitivity estimator is a blind sensitivity test,in which fake planets are inserted into the raw data and then recovered by an experimenter (orautomated process) without a-priori knowledge of their positions or their number. Such a blindtest is the surest way to evaluate any sensitivity estimator and establish the relationship betweennominal significance (i.e. 3 σ , 5 σ , etc.) and the true completeness level of the survey. This shouldbe standard procedure for all planet imaging surveys.We inserted simulated planets at random locations in the raw data for selected stars. Theflux of each simulated planet was scaled to 5, 7, or 10 σ significance based on the master sensitivitymap (see Section 4.2) for that star. The PSFs for the planets were taken from the short exposure,unsaturated images of the parent star, mentioned above in Section 3.2. The raw data with fakeplanets inserted was then processed exactly as for the real, unmodified science data for that star,and planets were sought in the fully processed images by the same combination of manual andautomatic methods used for the real images.The final result of each test was that every inserted planet was classified as ‘Confirmed’, ‘No-ticed’, or ‘Unnoticed’. ‘Confirmed’ means the source was confidently detected, with no significantdoubt of its being a real object. ‘Noticed’ means the source was flagged by our automatic detectionalgorithm, or noticed manually as a possible real object, but could not be confirmed beyond rea-sonable doubt. Many spurious sources are ‘Noticed’ whereas the false-positive rate for ‘Confirmed’detections is extremely low, with none for any of the data sets discussed here. ‘Unnoticed’ meansa fake planet was not automatically flagged or noticed manually.Tables 5 through 9 give the results of these simulations, showing how the detectable planetmasses vary with the distance and age of the stars, and with data quality. Note that simulatedplanets with masses ranging down to 3 M Jup and below were confirmed, the lowest mass planetconfirmed being one of 2.36 M
Jup in the GJ 117 simulation. Figure 9 shows an image from ourblind sensitivity test on HD 29391, with the simulated planets marked. The random positions ofthe planets, unknown by the experimenter attempting to detect the them, are an important aspectof our tests. 33 –Table 5. GJ 450 fake planet experiment.Sep Mass Detection(arcsec) L ′ Mag (M
Jup ) Significance Status0.51 12.53 >
20 10.00 σ Confirmed0.56 13.32 >
20 10.00 σ Confirmed0.95 15.35 11.26 10.00 σ Confirmed1.14 15.60 10.54 10.00 σ Confirmed1.27 15.96 9.51 10.00 σ Confirmed1.58 16.06 9.21 10.00 σ Confirmed1.90 16.51 7.93 10.00 σ Confirmed2.50 16.59 7.73 10.00 σ Confirmed2.69 16.57 7.78 10.00 σ Confirmed2.91 16.38 8.29 10.00 σ Confirmed2.98 16.60 7.70 10.00 σ Confirmed3.71 16.51 7.93 10.00 σ Confirmed3.90 16.59 7.73 10.00 σ Confirmed3.93 16.62 7.65 10.00 σ Confirmed5.02 16.49 7.98 10.00 σ Confirmed6.52 16.43 8.15 10.00 σ Confirmed6.53 16.27 8.61 10.00 σ ConfirmedNote. — All of the input planets were confirmed. Planetmagnitude to mass conversion carried out by interpolationbased on theoretical spectra from Burrows et al. (2003), us-ing our adopted distance and age for this star (8.1 pc, 1.0Gyr). 34 –Table 6. HD 29391 fake planet experiment.Sep Mass Detection(arcsec) L ′ Band Mag (M
Jup ) Significance Status0.42 11.59 >
20 10.00 σ Confirmed0.76 12.56 16.85 10.00 σ Confirmed1.23 15.35 4.97 10.00 σ Confirmed2.06 15.90 3.92 10.00 σ Confirmed2.27 16.10 3.63 10.00 σ Confirmed3.26 14.58 6.95 10.00 σ Confirmed3.60 15.77 4.15 10.00 σ Confirmed4.29 15.48 4.72 10.00 σ Confirmed4.41 16.22 3.46 10.00 σ Confirmed5.31 16.21 3.47 10.00 σ Confirmed8.92 16.15 3.56 10.00 σ Confirmed10.69 16.15 3.56 10.00 σ Confirmed1.25 15.17 5.40 7.00 σ Confirmed1.86 16.32 3.31 7.00 σ Confirmed2.00 16.47 3.09 7.00 σ Unnoticed2.69 16.54 2.99 7.00 σ Unnoticed2.92 16.61 2.93 7.00 σ Noticed3.29 16.47 3.09 7.00 σ Confirmed4.69 15.83 4.03 7.00 σ Noticed5.72 16.38 3.22 7.00 σ Confirmed6.28 15.97 3.82 7.00 σ Noticed10.53 15.94 3.86 7.00 σ Confirmed1.19 15.39 4.89 5.00 σ Confirmed1.93 16.77 2.78 5.00 σ Noticed5.76 16.57 2.97 5.00 σ Noticed6.68 16.25 3.41 5.00 σ Unnoticed7.70 16.18 3.51 5.00 σ UnnoticedNote. — Planets confirmed: 12/12 at 10 σ ; 5/10 at 7 σ ; 1/5at 5 σ . Planets noticed: 12/12 at 10 σ ; 8/10 at 7 σ ; 3/5 at 5 σ . 35 –Planet magnitude to mass conversion carried out by interpolationbased on theoretical spectra from Burrows et al. (2003), using ouradopted distance and age for this star (14.71 pc, 0.1 Gyr). 36 –Table 7. GJ 117 fake planet experiment.Sep Mass Detection(arcsec) L ′ Band Mag (M
Jup ) Significance Status0.67 10.41 > σ Confirmed0.94 11.54 15.42 10.00 σ Confirmed1.10 12.05 12.21 10.00 σ Confirmed2.11 15.01 3.42 10.00 σ Confirmed2.17 14.78 3.75 10.00 σ Confirmed3.31 14.93 3.53 10.00 σ Confirmed3.77 15.20 3.14 10.00 σ Confirmed6.40 14.72 3.84 10.00 σ Confirmed6.42 15.26 3.05 10.00 σ Confirmed8.60 15.06 3.35 10.00 σ Confirmed9.88 14.56 4.09 10.00 σ Confirmed1.14 12.54 9.77 7.00 σ Confirmed3.08 15.44 2.87 7.00 σ Noticed5.06 15.35 2.96 7.00 σ Confirmed6.37 14.67 3.91 7.00 σ Noticed7.04 14.66 3.93 7.00 σ Noticed7.88 15.27 3.05 7.00 σ Noticed1.04 12.31 10.83 5.00 σ Confirmed1.75 15.12 3.26 5.00 σ Unnoticed2.89 15.96 2.40 5.00 σ Unnoticed3.30 16.16 2.21 5.00 σ Unnoticed5.08 16.00 2.36 5.00 σ Confirmed7.80 15.32 2.98 5.00 σ Noticed8.03 15.65 2.68 5.00 σ Unnoticed10.21 15.30 3.00 5.00 σ NoticedNote. — Planets confirmed: 11/11 at 10 σ ; 2/6 at 7 σ ; 2/8 at5 σ . Planets noticed: 11/11 at 10 σ ; 6/6 at 7 σ ; 4/8 at 5 σ . Planetmagnitude to mass conversion carried out by interpolation based ontheoretical spectra from Burrows et al. (2003), using our adopted 37 –distance and age for this star (8.31 pc, 0.1 Gyr). Note that a fakeplanet with a mass of only 2.36 M Jup was confirmed. 38 –Table 8. GJ 355 fake planet experiment.Sep Mass Detection(arcsec) L ′ Band Mag (M
Jup ) Significance Status0.37 9.46 > σ Confirmed0.43 9.66 > σ Confirmed0.94 13.72 13.10 10.00 σ Confirmed1.67 15.61 5.74 10.00 σ Confirmed1.74 15.66 5.63 10.00 σ Confirmed1.85 15.74 5.43 10.00 σ Confirmed2.05 15.63 5.70 10.00 σ Confirmed2.37 15.87 5.11 10.00 σ Noticed3.08 15.60 5.78 10.00 σ Confirmed3.30 15.92 5.00 10.00 σ Confirmed3.44 15.73 5.46 10.00 σ Confirmed4.26 16.02 4.80 10.00 σ Confirmed5.55 15.87 5.12 10.00 σ Confirmed8.09 15.55 5.89 10.00 σ Confirmed8.70 15.34 6.46 10.00 σ Confirmed1.57 15.95 4.93 7.00 σ Noticed2.83 16.24 4.37 7.00 σ Noticed3.68 16.04 4.77 7.00 σ Confirmed4.34 16.01 4.82 7.00 σ Confirmed4.68 16.33 4.19 7.00 σ Noticed6.99 15.95 4.94 7.00 σ Confirmed1.92 16.58 3.78 5.00 σ Unnoticed3.24 16.52 3.87 5.00 σ Unnoticed5.61 15.93 4.99 5.00 σ Noticed5.99 15.86 5.16 5.00 σ Noticed7.17 15.94 4.97 5.00 σ Noticed10.07 16.31 4.23 5.00 σ Confirmed 39 –Note. — Planets confirmed: 14/15 at 10 σ ; 3/6 at 7 σ ; 1/6 at5 σ . Planets noticed: 15/15 at 10 σ ; 6/6 at 7 σ ; 4/6 at 5 σ . Planetmagnitude to mass conversion carried out by interpolation based ontheoretical spectra from Burrows et al. (2003), using our adopteddistance and age for this star (19.23 pc, 0.1 Gyr). 40 –The total statistics from all 5 blind tests are that 63 of 65 planets were confirmed at 10 σ , 13of 28 at 7 σ , and 4 of 25 at 5 σ . In percentages we have 97% completeness at 10 σ , 46% completenessat 7 σ , and 16% completeness at 5 σ .Note the very low completeness at 5 σ , which many past surveys have taken as a realisticdetection limit. Though sensitivity estimators (and therefore the exact meaning of 5 σ ) differ,ours was quite conservative. The low completeness we find at 5 σ should serve as a warning tofuture workers in this field, and an encouragement to establish a definitive significance-completenessrelation through blind sensitivity tests as we have done. Many more planets were noticed than wereconfirmed: for noticed planets, the rates are 100% at 10 σ , 86% at 7 σ , and 56% at 5 σ . However,very many false positives were also noticed, so sources that are merely noticed but not confirmeddo not represent usable detections. No false positives were confirmed in any of our blind tests.There are several reasons for our low completeness rate at 5 σ . First, some flux is lost fromfaint sources in our processing, as described above, so that sources input at 5 σ significance arereduced to a real significance of typically 4 σ in the final image. Second, since our images containspeckles, ghosts, diffraction rays, and pattern noise, the noise is not gaussian but rather has along tail toward improbable, bright events – a normal circumstance in AO images that has beencarefully described by Fitzgerald & Graham (2006) and Marois et al. (2008). Third, the area ofeach final image is over 10 times the size of a PSF, so the distribution of possible spurious planetimages arising from noise is sampled at least 10 times for each final image in our survey. Followupobservations of suspected sources are costly in terms of telescope time, so a detection strategy witha low false-positive rate is important.While background noise originating from photon statistics in astronomical images is gaus-sian, speckle noise in AO-corrected images close to bright stars has been shown to follow a longertailed, approximately rician distribution (Marois et al. 2008; Fitzgerald & Graham 2006). In fact,Marois et al. (2008) have shown that to obtain an acceptably low false positive rate, detectionthresholds must be set as high as 12 σ in the presence of severe speckle noise. They assume adetection strategy based on the single-pixel RMS standard deviation (e.g. Biller et al. (2007);Chauvin et al. (2010)) rather than sensitivity estimation methods like ours or that of Lafreni`ere et al.(2007). Even so, given their findings it may seem surprising not that we had low completeness at5 σ , but that we were able to detect some 5 σ sources while also maintaining a very low false-positiverate.Part of the explanation for this is the speckle-supression produced by ADI: Marois et al. (2008)found that ADI could be so powerful that it nearly restored gaussian statistics to an image, allowingthe viable detection threshold to drop from 12 σ to lower than 6 σ . Our implementation of ADI maynot be as effective as that of Marois et al. (2008), but it did substantially improve our imagestatistics. This is demonstrated by the fact that our blind sensitivity tests did not show any clearbias against detection of low-significance planets close to the star. However, some of our ability toconfirm low-significance planets is simply due to our painstaking detection strategy. Noise-bursts 41 –Table 9. BD+48 3686 fake planet experiment.Sep Mass Detection(arcsec) L ′ Band Mag (M
Jup ) Significance Status0.23 8.03 > σ Confirmed0.97 14.65 13.89 10.00 σ Noticed1.33 15.19 10.47 10.00 σ Confirmed2.05 15.51 9.05 10.00 σ Confirmed4.33 15.57 8.85 10.00 σ Confirmed5.08 15.70 8.41 10.00 σ Confirmed6.13 15.52 9.04 10.00 σ Confirmed6.34 14.70 13.53 10.00 σ Confirmed8.41 15.38 9.60 10.00 σ Confirmed9.73 15.46 9.26 10.00 σ Confirmed1.46 15.62 8.67 7.00 σ Confirmed2.55 15.86 7.87 7.00 σ Noticed3.76 16.15 7.05 7.00 σ Unnoticed5.25 15.72 8.32 7.00 σ Confirmed5.73 15.66 8.53 7.00 σ Unnoticed10.43 15.41 9.50 7.00 σ Confirmed1.08 15.63 8.66 5.00 σ Noticed3.04 16.39 6.45 5.00 σ Unnoticed3.34 16.29 6.70 5.00 σ Unnoticed5.69 16.40 6.42 5.00 σ Noticed9.19 16.17 7.00 5.00 σ Unnoticed10.22 15.97 7.56 5.00 σ NoticedNote. — Planets confirmed: 9/10 at 10 σ ; 3/6 at 7 σ ; 0/6 at5 σ . Planets noticed: 10/10 at 10 σ ; 4/6 at 7 σ ; 3/6 at 5 σ . Planetmagnitude to mass conversion carried out by interpolation based ontheoretical spectra from Burrows et al. (2003), using our adopteddistance and age for this star (23.6 pc, 0.15 Gyr). 42 –Fig. 9.— Fully processed ‘e’ method master image from the blind sensitivity test on HD 29391. Inthis data set there are 12 planets of 10 σ significance (indicated by arrows), 10 at 7 σ (circled), and5 at 5 σ (boxed). One 5 σ planet is hidden by the inset. Each planet was either confirmed (CNF),noticed (NTC), or unnoticed (UNN) in the blind test. All 10 σ planets were confirmed. The inset,3 arcsec square, shows the inner part of the image magnified 3 × and with display range increased10 × relative to the main image. The main image is 24 arcsec square. Two planets are marked inboth the main image and the inset. 43 –at 10 or 12 σ may occur in the speckle-dominated regions of AO images, but splitting the data inhalf, examining master images created using different processing methods, and other time-intensiveanalyses can powerfully sort out the real from the unreal – even, in some cases, when the spurioussources are substantially brighter.Accurate estimation of the sensitivity of AO images is a complex task, worthy, perhaps, ofmore attention than has been paid it in the AO planet-search literature up to this point. Betweenthis work, Lafreni`ere et al. (2007), Biller et al. (2007) and Kasper et al. (2007), and others, severaldifferent sensitivity estimators have been used, which may produce substantially different results.Statistical noise distributions can vary widely even on a single image (Marois et al. 2008), andcertainly exhibit further variability from instrument to instrument and telescope to telescope. Ablind sensitivity test such as we have carried out is an excellent way to determine the true sensitivityof a set of observations. Completeness vs. significance relations established by such blind sensitivitytests may represent the only real option for ‘apples-to-apples’ comparisons of the sensitivity obtainedwith different instruments on different telescopes – and such comparisons may be quite importantfor selecting optimal observing strategies as we move forward to the next generation of surveys todetect extrasolar planets.
5. Detections of Faint Real Objects5.1. Overview of Detected Companions
In all, thirteen faint sources were confirmed as real. Table 10 presents our astrometry andphotometry for each detected companion.Of these 13 faint companions, one is a newly discovered low mass star orbiting GJ 3876 (seeSection 5.2), one is a previously known binary brown dwarf companion to GJ 564 (Potter et al.2003), and the other eleven are background stars. Note that Lafreni`ere et al. (2007), operating inthe H band regime, found more than 300 background stars. Due to the red IR colors of planets, along wavelength survey such as ours can obtain good sensitivity to planets while remaining blindto all but the brightest stars, so that less telescope time is needed to follow up candidate objects.Also, a background star masquerading as a planet at L ′ can often be detected in a short integrationat shorter wavelengths, showing that the object is far too blue in IR color to be a planet. We haveapplied this strategy by taking K S band images of the brighter of the two companions of BD+201790, and the faint companions near HD 96064, BD+60 1417, and GJ 3860, in all cases obtainingbright K S band fluxes that indicate the objects have stellar K S − L ′ color, rather than the very red K S − L ′ colors expected for planets. Such color measurements can often rule out a planet candidateimmediately, in contrast to the waiting period required for proper motion confirmation.For planets near our detection limit, expected K S − L ′ colors are generally so red that a K S detection effectively rules out the candidate. However, for brighter candidates, the case is not 44 –Table 10. Confirmed Sources in Our SurveyStar Det. L ′ Sep DateName Sig. Mag (arcsec) PA (yyyy/mm/dd)GJ 354.1A 4.93 σ . ± .
20 4.93 187 . ◦ σ . ± .
20 2.60 103 . ◦ σ . ± .
20 1.85 118 . ◦ σ . ± .
20 9.68 144 . ◦ · · · . ± .
20 11.24 227 . ◦ σ . ± .
20 7.78 83 . ◦ · · · . ± .
20 9.85 145 . ◦ σ . ± .
20 1.93 301 . ◦ σ . ± .
20 3.01 358 . ◦ · · · . ± .
20 7.24 0 . ◦ σ . ± .
20 8.73 74 . ◦ · · · . ± .
20 6.42 336 . ◦ σ . ± .
20 5.57 212 . ◦ L ′ = 14 . ± .
10. According to themodels of Burrows et al. (2003), at the age and distance we adopted for this system, L ′ = 14 . Jup planet with K S − L ′ = 2 .
14. Using the models of Baraffe et al. (2003)instead yields a 9.1 M
Jup planet with K S − L = 3 .
9. Our measured color for the object was K S − L ′ = 0 . ± .
22, consistent with a background star of any spectral type between F and lateM (see Tables 7.6-7.8 in Cox (2000)), but dramatically inconsistent with a planetary interpretationbased on either the Burrows et al. (2003) or the Baraffe et al. (2003) models. The very differentprediction from the two model sets stems mainly from the different planet masses they imply for theobserved L ′ magnitude: the models do not disagree so widely on K S − L ′ color for a specific planetmass. While the descrepancy does indicate considerable model uncertainty, there is agreement thatplanets in the range of mass and age applicable to this candidate are much redder in K S − L ′ color than stars. This is, of course, also our first-order expectation given the far lower effectivetemperatures of planets. The conclusion that the object we detected near GJ 3860 is a backgroundstar rather than a planet seems secure.The case of BD+20 1790 is less clear-cut. Our measured L ′ magnitude is 14 . ± .
15. Thisimplies a planet mass of 16.75 M
Jup and a K S − L ′ color of 1.06 according to the Burrows et al.(2003) models. Our observed color is K S − L ′ = 0 . ± .
20. While formally excluded, theplanetary hypothesis does not seem as untenable as for GJ 3860. Using the Baraffe et al. (2003)models instead gives a 10.71 M
Jup planet with K S − L ′ = 2 .
71, much more comfortably excludedby the data. The low galactic latitude of BD+20 1790 (+16 ◦ ), combined with the presence ofanother apparent companion (which was shown to be a background object based on an archivalHST image), suggests that there is a comparitively rich star field behind BD+20 1790, and thatthe most plausible interpretation of the brighter companion is, again, a background star. Whileinterpretation as a planetary or brown dwarf companion is perhaps not absolutely excluded, it ismuch less likely a priori, and is inconsistent with the observed color under both the model sets wehave employed.The companion of GJ 354.1 A is confirmed to be a background star rather than a commonproper motion companion based on an image by Lowrance et al. (2005). The fainter of the twocompanions of BD+20 1790 is similarly shown to be a background object by an archival HST image.The companions of 61 Cyg A and B are background objects based on detections on POSS platesfrom 1991, when, due to the 61 Cyg system’s fast proper motion, the objects were much farther 46 –from the bright stars and therefore beyond the glare on the POSS images. The companion of GJ860 is confirmed to be a background star based on previous detections on POSS plates from 1953,and optical images of our own taken with the University of Arizona 1.5m Kuiper Telescope in 2005(the latter simply prove the object is too bright in the optical to be a planet). The POSS positionmatch is imperfect, and our optical detection is at low significance, but taken together they confirmthe object’s nature. The companion of GJ 684 is shown to be a background star based on propermotion in followup images we obtained using Clio in September 2008.Figures 10 through 15 show all of our detected companions, except the companion of HD 96064,which has already been shown in Figure 2. Each of these images is from a ‘d’ method reduction oflong exposure science data. The single discovery of our survey is the low-mass stellar companion of GJ 3876. We firstdetected it on L ′ images from April 13, 2006, and confirmed it as a common proper motion com-panion in L ′ , M , and K S images taken on April 11, 2007. Table 11 gives our photometric andastrometric results, complete with what the object’s position should have been in April 2007 if itwere a background star.GJ 3876 B is clearly a common proper motion companion. The distance to the primary staris about 43 pc, based on the parallax from Perryman et al. (1997). This translates to a projectedseparation of about 80 AU, which suggests an orbital period of around 700 yr for a one solar massprimary. The constant position angle over a year seems inconsistent with a face-on orbit at thisperiod, while the formally insignificant increase in separation may hint at motion in a more inclinedorbit – however, much more data is needed.Again using the Perryman et al. (1997) distance, the K S absolute magnitude of GJ 3876 Bis 8 . ± .
22. Based on the models of Baraffe et al. (1998), this translates into a mass of about0 . ± . ⊙ . This estimate could be further investigated using our L ′ and M band magnitudes,but model magnitudes for low mass stars in these bands are not readily available in the literature,and integrating them from theoretical spectra is beyond the scope of this paper. We calibrated the plate scale and orientation of the Clio camera using observations of knownwide, very long-period binary stars. We had previously obtained precise astrometry of these stars inthe optical using the University of Arizona’s 61 inch Kuiper telescope on Mt. Bigelow (Heinze et al.(2009); for more complete data see ).When selecting our survey sample, we rejected some binary stars with orbital properties that 47 –Fig. 10.— (A) L ′ image of GJ 564, showing the binary brown dwarf discovered by Potter et al.(2003). (B) L ′ image of GJ 3876, showing the low-mass stellar companion we discovered. (C) L ′ image of BD+60 1417, showing the faint background star we detected. (D) L ′ image of binary starGJ 684, showing the faint background star we detected. Each tile is 4.86 arcsec square; the bottomtiles are contrast stretched 10 × more than the top ones to reveal the faint companions. 48 –Fig. 11.— Left, L ′ image of GJ 354.1 A, showing the faint background star we detected. Right, L ′ image of binary star GJ 860, again showing a faint background star. Each image is 9.71 arcsecsquare, contrast stretched the same as the lower panels in Figure 10 to reveal the faint objects.Table 11. Discovery Data for GJ 3876 BDate Sep PA(yyyy/mm/dd) (arcsec) (degrees) K S L ′ M . ± . . ± . · · · . ± . · · · . ± . . ± .
24 11 . ± .
22 10 . ± .
08 10 . ± . · · · · · · · · · Note. — Astrometry and photometry of the single discovery of our survey, GJ 3876 B. Thefirst two rows give actual measured values; the last gives the predicted position for 2007/04/11if the object were a background star, based on the 2006/04/13 position and a proper motionmeasurement from Perryman et al. (1997). The background star hypothesis is rejected withgreat confidence. 49 –Fig. 12.— L ′ image of BD+20 1790, showing two faint background stars. Image is 24.29 arcsecsquare, contrast stretched 3 × less than the images in Figure 11, to give a clear view of thesesomewhat brighter stars. 50 –Fig. 13.— L ′ image of 61 Cyg A, showing two faint background stars. Image is 24.29 arcsec square,contrast stretched the same as the previous figure. 51 –Fig. 14.— L ′ image of 61 Cyg B, showing a faint background star. Image is 24.29 arcsec square,contrast stretched the same as the previous figure. 52 –Fig. 15.— L ′ image of GJ 3860, showing a faint background star. Image is 24.29 arcsec square,contrast stretched the same as the previous figure. 53 –seemed likely to destabilize any planets we could detect. After these rejections, twenty stars inknown binary systems remained in our sample. Since our AO images allow very accurate astrometry,which might be useful for refining the orbital parameters of these nearby binaries, we present ourmeasurements of them in Table 12.Note that these binary stars change position relatively quickly, and should not be used forcalibration except with a precise orbital solution. Those referred to in Heinze et al. (2009) andthe associated website are better for calibration purposes, but some of them may still have movedsignificantly since our measurements.The measurements in Table 12 are averages of astrometry based on individual frames. In manycases we had short, unsaturated images available in addition to our longer, saturated exposuresfor planet detection. This allowed us to compare the internal precision of both saturated and un-saturated images, and choose as our final astrometric result the average of whichever of the twoimage sets had the smaller internal scatter. As explained in Section 3.3, the agreement betweensaturated and unsaturated astrometry was generally excellent. Note that the Table 12 value forour L ′ observations of ξ Boo is based on unsaturated images; this was the binary star with thelargest (though still only 0.009 arcsec) saturated/unsaturated difference in the list given in Section3.3. The uncertainties given in Table 12 combine both measurement scatter and calibration uncer-tainty. The latter is generally the larger term, due to the necessity of calibrating Clio using lessprecise astrometry from seeing-limited optical observations. The true internal scatter of carefullyconducted astrometric observations using Clio and MMTAO is certainly several times smaller thanthe uncertainties quoted in the table. Despite the calibration uncertainties, however, clear orbitalmotion in the star GJ 702 is seen over an interval of only ten months. See Heinze et al. (2009) andthe previously-cited website for an analysis of the challenges and potential of using AO astrometryfor binary star orbital science.
6. Conclusion
We have surveyed unusually nearby, mature star systems for extrasolar planets in the L ′ and M bands using the Clio camera with the MMT AO system. We have developed a sophisticatedimage processing pipeline for data from this camera, including some interesting innovations. Wehave carefully and rigorously analyzed our sensitivity. Accurately determining the sensitivity of AOplanet-search images is a more complex task than, perhaps, has been widely appreciated. Our datasupport the conclusion of Marois et al. (2008) that 5 σ limits can substantially overestimate themeaningful sensitivity of an image. Blind tests involving fake planets inserted in raw data are thebest way to confirm the validity of any sensitivity estimator, and should be included in all futureplanet-search publications. By extensive use of such tests, we established a definitive significancevs. completeness relation for planets in our data. This relation is important for use in Monte Carlosimulations to constrain planet distributions. 54 –Table 12. Astrometry of Binary Survey TargetsDate Obs.Star Name (yyyy/mm/dd) Sep.(arcsec) PA(deg)GJ 166 BC 2006/12/03 8 . ± .
010 153.72 ± . ± .
004 356.37 ± . ± .
007 221.61 ± . ± .
010 26.60 ± . ± .
006 104.92 ± ξ Boo AB 2006/06/10 6 . ± .
006 312.15 ± ξ Boo AB ( M ) 2006/06/11 6 . ± .
005 312.14 ± . ± .
004 323.84 ± . ± .
005 135.79 ± M ) 2007/04/11 5 . ± .
004 134.69 ± . ± .
004 58.55 ± . ± .
006 86.16 ± . ± .
007 214.49 ± ∼ . ⊙ binary companion at a projected separationof 80 AU from the star GJ 3876. We have detected twelve additional candidate faint companions,one of which is the binary brown dwarf companion of GJ 564 discovered prior to our observationsby Potter et al. (2003). The remaining eleven are confirmed to be background stars. We notethat shorter wavelength surveys, such as that of Lafreni`ere et al. (2007) in the H band regime,have typically found a much larger number of background stars, necessitating extensive follow-upobservations. A long wavelength survey such as ours can obtain good sensitivity to planets, withtheir very red IR colors, while remaining blind to all but the brightest stars. This reduces theamount of telescope time spent following up planet candidates that turn out to be backgroundstars.We did not detect any planets, but have set interesting limits on the masses of planets or othersubstellar objects that may exist in the star sytems we surveyed. In Heinze et al. (2010), we useextensive Monte Carlo simulations to show how our null result constrains the mass and semimajoraxis distributions of extrasolar planets orbiting sun-like stars.
7. Acknowledgements
This research has made use of the SIMBAD online database, operated at CDS, Strasbourg,France, and the VizieR online database (see Ochsenbein et al (2000)).We have also made extensive use of information and code from Press et al. (1992).We have used digitized images from the Palomar Sky Survey (available from http://stdatu.stsci.edu/cgi-bin/dss_form ),which were produced at the Space Telescope Science Institute under U.S. Government grant NAGW-2166. The images of these surveys are based on photographic data obtained using the OschinSchmidt Telescope on Palomar Mountain and the UK Schmidt Telescope.We thank the anonymous referee for helpful suggestions.Facilities: MMT, SO:Kuiper
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