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A. N. Heinze

Publications and source records attributed to A. N. Heinze.

At least 19 recordsLinked to original sources

Analysing the Onset of Cometary Activity by the Jupiter-Family Comet 2023 RN3

We utilize serendipitous observations from the Asteroid Terrestrial-impact Last Alert System (ATLAS) and the Zwicky Transient Facility (ZTF) in addition to targeted follow-up observations from the Las Cumbres Observatory (LCO) and Liverpool Telescope to analyze the first observed instance of cometary activity by the newly-discovered Jupiter-family comet C/2023 RN3 (ATLAS), whose orbital dynamics place it close to residing on a Centaur-like orbit. Across our 7-month baseline, we observe an epoch of cometary activity commencing in August 2023 with an increase in brightness of >5.4 mag. The lightcurve of 2023 RN3 indicates the presence of continuous cometary activity across our observations, suggesting the onset of a new period of sustained activity. We find no evidence of any outbursts on top of the observed brightening, nor do we find any significant color evolution across our observations. 2023 RN3 is visibly extended in LCO and Liverpool Telescope observations, indicating the presence of a spatially-extended coma. Numerical integration of 2023 RN3's orbit reveals the comet to have recently undergone a slight increase in semimajor axis due to a planetary encounter with Jupiter, however whether this orbital change could trigger 2023 RN3's cometary activity is unclear. Our estimate for the maximum dust production metric of Afrho ~400 cm is consistent with previous measurements for the Jupiter-family comet and Centaur populations.

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The Discovery and Evolution of a Possible New Epoch of Cometary Activity by the Centaur (2060) Chiron

Centaurs are small Solar System objects on chaotic orbits in the giant planet region, forming an evolutionary continuum with the Kuiper belt objects and Jupiter-family comets. Some Centaurs are known to exhibit cometary activity, though unlike comets this activity tends not to correlate with heliocentric distance and the mechanism behind it is currently poorly understood. We utilize serendipitous observations from the Asteroid Terrestrial-impact Last Alert System (ATLAS), Zwicky Transient Facility (ZTF), Panoramic Survey Telescope and Rapid Response System (Pan-STARRS), Dark Energy Survey (DES), and Gaia in addition to targeted follow-up observations from the Las Cumbres Observatory, TRAnsiting Planets and PlanetesImals Small Telescope South (TRAPPIST-South), and Gemini North telescope to analyze an unexpected brightening exhibited by the known active Centaur (2060) Chiron in 2021. This is highly indicative of a cometary outburst. As of 2023 February, Chiron has still not returned to its pre-brightening magnitude. We find Chiron's rotational lightcurve, phase curve effects, and possible high-albedo surface features to be unlikely causes of this observed brightening. We consider the most likely cause to be an epoch of either new or increased cometary activity, though we cannot rule out a possible contribution from Chiron's reported ring system, such as a collision of as-yet unseen satellites shepherding the rings. We find no evidence for coma in our Gemini or TRAPPIST-South observations, though this does not preclude the possibility that Chiron is exhibiting a coma that is too faint for observation or constrained to the immediate vicinity of the nucleus.

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Most Rotational Variables Dominated by a Single Bright Feature are $α^2$ CVn Stars

We previously reported a rare class of variable star light curves isolated from a sample of 4.7 million candidate variables from the ATLAS survey. Dubbed `UCBH' light curves, they have broad minima and narrow, symmetrical maxima, with typical periods of 1-10 days and amplitudes of 0.05--0.20 mag. They maintain constant amplitude, shape, and phase coherence over multiple years, but do not match any known class of pulsating variables. A localized bright spot near the equator of a rotating star will produce a UCBH-type light curve for most viewing geometries. Most stars that exhibit rotational variability caused primarily by a single bright feature should therefore appear as UCBH stars, although a rotating bright spot is not the only thing that could produce a UCBH-type lightcurve. We have spectroscopically investigated fourteen UCBH stars and found ten of them to be Ap/Bp stars: A-type or B-type stars with greatly enhanced photospheric abundances of specific heavy elements. Rotationally variable Ap/Bp stars are referred to as $α^2$ CVn variables. Most ATLAS UCBH stars are therefore $α^2$ CVn stars, although only a minority of $α^2$ CVn stars in the literature have UCBH light curves. The fact that $α^2$ CVn stars dominate the UCBH class suggests that lone bright spots with sufficient size and contrast develop more readily on Ap/Bp stars than on any other type. The $α^2$ CVn UCBH stars may be characterized by a specific magnetic field topology, making them intriguing targets for future Zeeman-Doppler imaging.

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Phase Curves of Kuiper Belt Objects, Centaurs, and Jupiter Family Comets from the ATLAS Survey

The Kuiper belt objects, the Centaurs, and the Jupiter-family comets form an evolutionary continuum of small outer Solar System objects, and their study allows us to gain insight into the history and evolution of the Solar System. Broadband photometry can be used to measure their phase curves, allowing a first-order probe into the surface properties of these objects, though limited telescope time makes measuring accurate phase curves difficult. We make use of serendipitous broadband photometry from the long-baseline, high-cadence ATLAS survey to measure the phase curves for a sample of 18 Kuiper belt objects, Centaurs, and Jupiter-family comets with unprecedentedly large datasets. We find phase curves with previously reported negative slopes become positive with increased data and are thus due to insufficient sampling of the phase curve profile, and not a real physical effect. We search for correlations between phase curve parameters, finding no strong correlations between any parameter pair, consistent with the findings of previous studies. We search for instances of cometary activity in our sample, finding a previously reported outburst by Echeclus and a new epoch of increased activity by Chiron. Applying the main belt asteroid HG1G2 phase curve model to three Jupiter-family comets in our sample with large phase angle spans, we find their slope parameters imply surfaces more consistent with those of carbonaceous main belt asteroids than silicaceous ones.

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Weather on Other Worlds. VI. Optical Spectrophotometry of Luhman 16B Reveals Large-amplitude Variations in the Alkali Lines

Using a novel wide-slit, multi-object approach with the GMOS spectrograph on the 8-meter Gemini South telescope, we have obtained precise time-series spectrophotometry of the binary brown dwarf Luhman 16 at optical wavelengths over two full nights. The B component of this binary system is known to be variable in the red optical and near-infrared with a period of 5 hr and an amplitude of 5--20%. Our observations probe its spectrally-resolved variability in the 6000--10000 Angstrom range. At wavelengths affected by the extremely strong, broadened spectral lines of the neutral alkali metals (the potassium doublet centered near 7682 Angstroms and the sodium doublet at 5893 Angstroms), we see photometric variations that differ strikingly from the those of the 8000--10000 Angstrom `red continuum' that dominates our detected flux. On UT 2014 February 24, these variations are anticorrelated with the red continuum, while on Feb 25 they have a large relative phase shift. The extent to which the wavelength-dependent photometric behavior diverges from that of the red continuum appears to correlate with the strength of the alkali absorption. We consider but ultimately reject models in which our observations are explained by lightning or auroral activity. A more likely cause is cloud-correlated, altitude-dependent variations in the gas-phase abundances of sodium and potassium, which are in chemical equilibrium with their chlorides in brown dwarf atmospheres. Clouds could influence these chemical equilibria by changing the atmospheric temperature profile and/or through cloud particles acting as chemical catalysts.

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NEO Population, Velocity Bias, and Impact Risk from an ATLAS Analysis

We estimate the total population of near-Earth objects (NEOs) in the Solar System, using an extensive, `Solar System to pixels' fake-asteroid simulation to debias detections of real NEOs by the ATLAS survey. Down to absolute magnitudes $H=25$ and 27.6 (diameters of $\sim 34$ and 10 meters, respectively, for 15% albedo), we find total populations of $(3.72 \pm 0.49) \times 10^5$ and $(1.59 \pm 0.45) \times 10^7$ NEOs, respectively. Most plausible sources of error tend toward underestimation, so the true populations are likely larger. We find the distribution of $H$ magnitudes steepens for NEOs fainter than $H \sim 22.5$, making small asteroids more common than extrapolation from brighter $H$ mags would predict. Our simulation indicates a strong bias against detecting small but dangerous asteroids that encounter Earth with high relative velocities -- i.e., asteroids in highly inclined and/or eccentric orbits. Worldwide NEO discovery statistics indicate this bias affects global NEO detection capability, to the point that an observational census of small asteroids in such orbits is probably not currently feasible. Prompt and aggressive followup of NEO candidates, combined with closer collaborations between segments of the global NEO community, can increase detection rates for these dangerous objects.

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Asteroid models reconstructed from ATLAS photometry

The Asteroid Terrestrial-impact Last Alert System (ATLAS) is an all-sky survey primarily aimed at detecting potentially hazardous near-Earth asteroids. Apart from the astrometry of asteroids, it also produces their photometric measurements that contain information about asteroid rotation and their shape. To increase the current number of asteroids with a known shape and spin state, we reconstructed asteroid models from ATLAS photometry that was available for approximately 180,000 asteroids observed between 2015 and 2018. We made use of the light-curve inversion method implemented in the Asteroid@home project to process ATLAS photometry for roughly 100,000 asteroids with more than a hundred individual brightness measurements. By scanning the period and pole parameter space, we selected those best-fit models that were, according to our setup, a unique solution for the inverse problem. We derived ~2750 unique models, 950 of them were already reconstructed from other data and published. The remaining 1800 models are new. About half of them are only partial models, with an unconstrained pole ecliptic longitude. Together with the shape and spin, we also determined for each modeled asteroid its color index from the cyan and orange filter used by the ATLAS survey. We also show the correlations between the color index, albedo, and slope of the phase-angle function. The current analysis is the first inversion of ATLAS asteroid photometry, and it is the first step in exploiting the huge scientific potential that ATLAS photometry has. ATLAS continues to observe, and in the future, this data, together with other independent photometric measurements, can be inverted to produce more refined asteroid models.

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ASASSN-14ko is a Periodic Nuclear Transient in ESO 253-G003

We present the discovery that ASASSN-14ko is a periodically flaring AGN at the center of the galaxy ESO 253-G003. At the time of its discovery by the All-Sky Automated Survey for Supernovae (ASAS-SN), it was classified as a supernova close to the nucleus. The subsequent six years of V- and g-band ASAS-SN observations reveal that ASASSN-14ko has nuclear flares occurring at regular intervals. The seventeen observed outbursts show evidence of a decreasing period over time, with a mean period of $P_0 = 114.2 \pm 0.4$ days and a period derivative of $\dot{P} = -0.0017\pm0.0003$. The most recent outburst in May 2020, which took place as predicted, exhibited spectroscopic changes during the rise and a had a UV bright, blackbody spectral energy distribution similar to tidal disruption events (TDEs). The X-ray flux decreased by a factor of 4 at the beginning of the outburst and then returned to its quiescent flux after ~8 days. TESS observed an outburst during Sectors 4-6, revealing a rise time of $5.60 \pm 0.05$ days in the optical and a decline that is best fit with an exponential model. We discuss several possible scenarios to explain ASASSN-14ko's periodic outbursts, but currently favor a repeated partial TDE. The next outbursts should peak in the optical on UT 2020-09-7.4$ \pm $1.1 and UT 2020-12-26.5$ \pm $1.4.

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Design and operation of the ATLAS Transient Science Server

The Asteroid Terrestrial impact Last Alert System (ATLAS) system consists of two 0.5m Schmidt telescopes with cameras covering 29 square degrees at plate scale of 1.86 arcsec per pixel. Working in tandem, the telescopes routinely survey the whole sky visible from Hawaii (above $δ> -50^{\circ}$) every two nights, exposing four times per night, typically reaching $o < 19$ magnitude per exposure when the moon is illuminated and $c < 19.5$ per exposure in dark skies. Construction is underway of two further units to be sited in Chile and South Africa which will result in an all-sky daily cadence from 2021. Initially designed for detecting potentially hazardous near earth objects, the ATLAS data enable a range of astrophysical time domain science. To extract transients from the data stream requires a computing system to process the data, assimilate detections in time and space and associate them with known astrophysical sources. Here we describe the hardware and software infrastructure to produce a stream of clean, real, astrophysical transients in real time. This involves machine learning and boosted decision tree algorithms to identify extragalactic and Galactic transients. Typically we detect 10-15 supernova candidates per night which we immediately announce publicly. The ATLAS discoveries not only enable rapid follow-up of interesting sources but will provide complete statistical samples within the local volume of 100 Mpc. A simple comparison of the detected supernova rate within 100 Mpc, with no corrections for completeness, is already significantly higher (factor 1.5 to 2) than the current accepted rates.

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The Flux Distribution and Sky Density of 25th Magnitude Main Belt Asteroids

Digital tracking enables telescopes to detect asteroids several times fainter than conventional techniques. We describe our optimized methodology to acquire, process, and interpret digital tracking observations, and we apply it to probe the apparent magnitude distribution of main belt asteroids fainter than any previously detected from the ground. All-night integrations with the Dark Energy Camera (DECam) yield 95\% completeness at $R$ magnitude 25.0, and useful sensitivity to $R=25.6$ mag when we use an analytical detection model to correct flux overestimation bias. In a single DECam field observed over two nights, we detect a total of 3234 distinct asteroids, of which 3123 are confirmed on both nights. At opposition from the Sun, we find a sky density of $697 \pm 15$ asteroids per square degree brighter than $R = 25.0$ mag, and $1031 \pm 23$ brighter than $R = 25.6$ mag. We agree with published results for the sky density and apparent magnitude distribution of asteroids brighter than $R=23$ mag. For a power law defined by $dN/dR \propto 10^{αR}$, we find marginally acceptable fits with a constant slope $α= 0.28 \pm 0.02$ from $R=20$ to 25.6 mag. Better fits are obtained for a broken power law with $α=0.218 \pm 0.026$ for $R=20$ to 23.5 mag, steepening to $α=0.340 \pm 0.025$ for $R = 23.5$ to 25.6 mag. The constant or steepening power law indicates asteroids fainter than $R = 23.5$ mag are abundant, contrary to some previous claims but consistent with theory.

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PS18kh: A New Tidal Disruption Event with a Non-Axisymmetric Accretion Disk

We present the discovery of PS18kh, a tidal disruption event (TDE) discovered at the center of SDSS J075654.53+341543.6 ($d\simeq322$ Mpc) by the Pan-STARRS Survey for Transients. Our dataset includes pre-discovery survey data from Pan-STARRS, the All-Sky Automated Survey for Supernovae (ASAS-SN), and the Asteroid Terrestrial-impact Last Alert System (ATLAS) as well as high-cadence, multi-wavelength follow-up data from ground-based telescopes and Swift, spanning from 56 days before peak light until 75 days after. The optical/UV emission from PS18kh is well-fit as a blackbody with temperatures ranging from $T\simeq12000$ K to $T\simeq25000$ K and it peaked at a luminosity of $L\simeq8.8\times10^{43}$ ergs s$^{-1}$. PS18kh radiated $E=(3.45\pm0.22)\times10^{50}$ ergs over the period of observation, with $(1.42\pm0.20)\times10^{50}$ ergs being released during the rise to peak. Spectra of PS18kh show a changing, boxy/double-peaked H$α$ emission feature, which becomes more prominent over time. We use models of non-axisymmetric accretion disks to describe the profile of the H$α$ line and its evolution. We find that at early times the high accretion rate leads the disk to emit a wind which modifies the shape of the line profile and makes it bell-shaped. At late times, the wind becomes optically thin, allowing the non-axisymmetric perturbations to show up in the line profile. The line-emitting portion of the disk extends from $r_{\rm in}\sim60r_{\rm g}$ to an outer radius of $r_{\rm out}\sim1400r_{\rm g}$ and the perturbations can be represented either as an eccentricity in the outer rings of the disk or as a spiral arm in the inner disk.

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Seeing Double: ASASSN-18bt Exhibits a Two-Component Rise in the Early-Time K2 Light Curve

On 2018 Feb. 4.41, the All-Sky Automated Survey for SuperNovae (ASAS-SN) discovered ASASSN-18bt in the K2 Campaign 16 field. With a redshift of z=0.01098 and a peak apparent magnitude of B_{max}=14.31, ASASSN-18bt is the nearest and brightest SNe Ia yet observed by the Kepler spacecraft. Here we present the discovery of ASASSN-18bt, the K2 light curve, and pre-discovery data from ASAS-SN and the Asteroid Terrestrial-impact Last Alert System (ATLAS). The K2 early-time light curve has an unprecedented 30-minute cadence and photometric precision for an SN~Ia light curve, and it unambiguously shows a ~4 day nearly linear phase followed by a steeper rise. Thus, ASASSN-18bt joins a growing list of SNe Ia whose early light curves are not well described by a single power law. We show that a double-power-law model fits the data reasonably well, hinting that two physical processes must be responsible for the observed rise. However, we find that current models of the interaction with a non-degenerate companion predict an abrupt rise and cannot adequately explain the initial, slower linear phase. Instead, we find that existing, published models with shallow 56Ni are able to span the observed behavior and, with tuning, may be able to reproduce the ASASSN-18bt light curve. Regardless, more theoretical work is needed to satisfactorily model this and other early-time SNe~Ia light curves. Finally, we use Swift X-ray non-detections to constrain the presence of circumstellar material (CSM) at much larger distances and lower densities than possible with the optical light curve. For a constant density CSM these non-detections constrain rho<4.5 * 10^5 cm^-3 at a radius of 4 *10^15 cm from the progenitor star. Assuming a wind-like environment, we place mass-loss limits of Mdot< 8 * 10^-6 M_sun yr^-1 for v_w=100 km s^-1, ruling out some symbiotic progenitor systems.

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ASASSN-18ey: The Rise of a New Black-Hole X-ray Binary

We present the discovery of ASASSN-18ey (MAXI J1820+070), a new black hole low-mass X-ray binary discovered by the All-Sky Automated Survey for SuperNovae (ASAS-SN). A week after ASAS-SN discovered ASASSN-18ey as an optical transient, it was detected as an X-ray transient by MAXI/GCS. Here, we analyze ASAS-SN and Asteroid Terrestrial-impact Last Alert System (ATLAS) pre-outburst optical light curves, finding evidence of intrinsic variability for several years prior to the outburst. While there was no long-term rise leading to outburst, as has been seen in several other systems, the start of the outburst in the optical preceded that in the X-rays by $7.20\pm0.97~\rm days$. We analyze the spectroscopic evolution of ASASSN-18ey from pre-maximum to $> 100~\rm days$ post-maximum. The spectra of ASASSN-18ey exhibit broad, asymmetric, double-peaked H$α$ emission. The Bowen blend ($λ\approx 4650$Å) in the post-maximum spectra shows highly variable double-peaked profiles, likely arising from irradiation of the companion by the accretion disk, typical of low-mass X-ray binaries. The optical and X-ray luminosities of ASASSN-18ey are consistent with black hole low-mass X-ray binaries, both in outburst and quiescence.

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A First Catalog of Variable Stars Measured by the Asteroid Terrestrial-impact Last Alert System (ATLAS)

The Asteroid Terrestrial-impact Last Alert System (ATLAS) carries out its primary planetary defense mission by surveying about 13000 deg^2 at least four times per night. The resulting data set is useful for the discovery of variable stars to a magnitude limit fainter than r~18, with amplitudes down to 0.01 mag for bright objects. Here we present a Data Release One catalog of variable stars based on analyzing 142 million stars measured at least 100 times in the first two years of ATLAS operations. Using a Lomb-Scargle periodogram and other variability metrics, we identify 4.7 million candidate variables which we analyze in detail. Through Space Telescope Science Institute, we publicly release lightcurves for all of them, together with a vector of 169 classification features for each star. We do this at the level of unconfirmed candidate variables in order to provide the community with a large set of homogeneously analyzed photometry and avoid pre-judging which types of objects others may find most interesting. We use machine learning to classify the candidates into fifteen different broad categories based on lightcurve morphology. About 10% (430,000 stars) pass extensive tests designed to screen out spurious variability detections: we label these as `probable' variables. Of these, 230,000 receive specific classifications as eclipsing binaries, pulsating, Mira-type, or sinusoidal variables: these are the `classified' variables. New discoveries among the probable variables number more than 300,000, while 150,000 of the classified variables are new, including about 10,000 pulsating variables, 2,000 Mira stars, and 70,000 eclipsing binaries.

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The ATLAS All-Sky Stellar Reference Catalog

The Asteroid Terrestrial-impact Last Alert System (ATLAS) observes most of the sky every night in search of dangerous asteroids. Its data are also used to search for photometric variability, where sensitivity to variability is limited by photometric accuracy. Since each exposure spans 7.6 deg corner to corner, variations in atmospheric transparency in excess of 0.01 mag are common, and 0.01 mag photometry cannot be achieved by using a constant flat field calibration image. We therefore have assembled an all-sky reference catalog of approximately one billion stars to m~19 from a variety of sources to calibrate each exposure's astrometry and photometry. Gaia DR2 is the source of astrometry for this ATLAS Refcat2. The sources of g, r, i, z photometry include Pan-STARRS DR1, the ATLAS Pathfinder photometry project, ATLAS re-flattened APASS data, SkyMapper DR1, APASS DR9, the Tycho-2 catalog, and the Yale Bright Star Catalog. We have attempted to make this catalog at least 99% complete to m<19, including the brightest stars in the sky. We believe that the systematic errors are no larger than 5 millimag RMS, although errors are as large as 20 millimag in small patches near the galactic plane.

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ATLAS: A High-Cadence All-Sky Survey System

Technology has advanced to the point that it is possible to image the entire sky every night and process the data in real time. The sky is hardly static: many interesting phenomena occur, including variable stationary objects such as stars or QSOs, transient stationary objects such as supernovae or M dwarf flares, and moving objects such as asteroids and the stars themselves. Funded by NASA, we have designed and built a sky survey system for the purpose of finding dangerous near-Earth asteroids (NEAs). This system, the "Asteroid Terrestrial-impact Last Alert System" (ATLAS), has been optimized to produce the best survey capability per unit cost, and therefore is an efficient and competitive system for finding potentially hazardous asteroids (PHAs) but also for tracking variables and finding transients. While carrying out its NASA mission, ATLAS now discovers more bright ($m < 19$) supernovae candidates than any ground based survey, frequently detecting very young explosions due to its 2 day cadence. ATLAS discovered the afterglow of a gamma-ray burst independent of the high energy trigger and has released a variable star catalogue of 5$\times10^{6}$ sources. This, the first of a series of articles describing ATLAS, is devoted to the design and performance of the ATLAS system. Subsequent articles will describe in more detail the software, the survey strategy, ATLAS-derived NEA population statistics, transient detections, and the first data release of variable stars and transient lightcurves.

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Constraints on Long-Period Planets from an L' and M band Survey of Nearby Sun-Like Stars: Observations

We present the observational results of an L' and M band Adaptive Optics (AO) imaging survey of 54 nearby, sunlike stars for extrasolar planets, carried out using the Clio camera on the MMT. We have concentrated more strongly than all other planet imaging surveys to date on very nearby F, G, and K stars, prioritizing stellar proximity higher than youth. Ours is also the first survey to include extensive observations in the M band, which supplement the primary L' observations. Models predict much better planet/star flux ratios at the L' and M bands than at more commonly used shorter wavelengths (i.e. the H band). We have carried out extensive blind simulations with fake planets inserted into the raw data to verify our sensitivity, and to establish a definitive relationship between source significance in $σ$ and survey completeness. We find 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-completeness relation are an important analysis step for all planet-imaging surveys. We discovered a previously unknown, approximately 0.15 solar-mass stellar companion to the F9 star GJ 3876, at a projected separation of about 80 AU. Twelve additional candidate faint companions are detected around other stars. Of these, eleven are confirmed to be background stars, and one is a previously known brown dwarf. We obtained sensitivity to planetary-mass objects around almost all of our target stars, with sensitivity to objects below 3 Jupiter masses in the best cases. Constraints on planet populations based on this null result are presented in our Modeling Results paper.

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Constraints on Long-Period Planets from an L' and M band Survey of Nearby Sun-Like Stars: Modeling Results

We have carried out an L' and M band Adaptive Optics (AO) extrasolar planet imaging survey of 54 nearby, sunlike stars using the Clio camera at the MMT. Our survey concentrates more strongly than all others to date on very nearby F, G, and K stars, in that we have prioritized proximity higher than youth. Our survey is also the first to include extensive observations in the M band, which supplemented the primary L' observations. These longer wavelength bands are most useful for very nearby systems in which low temperature planets with red IR colors (i.e. H - L', H - M) could be detected. The survey detected no planets, but set interesting limits on planets and brown dwarfs in the star systems we investigated. We have interpreted our null result by means of extensive Monte Carlo simulations, and constrained the distributions of extrasolar planets in mass $M$ and semimajor axis $a$. If planets are distributed according to a power law with $dN \propto M^α a^β dM da$, normalized to be consistent with radial velocity statistics, we find that a distribution with $α= -1.1$ and $β= -0.46$, truncated at 110 AU, is ruled out at the 90% confidence level. These particular values of $α$ and $β$ are significant because they represent the most planet-rich case consistent with current statistics from radial velocity observations. With 90% confidence no more than 8.1% of stars like those in our survey have systems with three widely spaced, massive planets like the A-star HR 8799. Our observations show that giant planets in long-period orbits around sun-like stars are rare, confirming the results of shorter-wavelength surveys, and increasing the robustness of the conclusion.

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