arXiv subjects

Daniel Apai

Publications and source records attributed to Daniel Apai.

At least 91 records · Page 5Linked to original sources

arXiv2014

HST Rotational Spectral Mapping of Two L-Type Brown Dwarfs: Variability In and Out of Water Bands Indicates High-Altitude Haze Layers

We present time-resolved near-infrared spectroscopy of two L5 dwarfs, 2MASS J18212815+1414010 and 2MASS J15074759-1627386, observed with the Wide Field Camera 3 instrument on the Hubble Space Telescope (HST). We study the wavelength dependence of rotation-modulated flux variations between 1.1 $μ$m and 1.7 $μ$m. We find that the water absorption bands of the two L5 dwarfs at 1.15 $μ$m and 1.4 $μ$m vary at similar amplitudes as the adjacent continuum. This differs from the results of previous HST observations of L/T transition dwarfs, in which the water absorption at 1.4 $μ$m displays variations of about half of the amplitude at other wavelengths. We find that the relative amplitude of flux variability out of the water band with respect to that in the water band shows a increasing trend from the L5 dwarfs toward the early T dwarfs. We utilize the models of Saumon & Marley (2008) and find that the observed variability of the L5 dwarfs can be explained by the presence of spatially varying high-altitude haze layers above the condensate clouds. Therefore, our observations show that the heterogeneity of haze layers - the driver of the variability - must be located at very low pressures, where even the water opacity is negligible. In the near future, the rotational spectral mapping technique could be utilized for other atomic and molecular species to probe different pressure levels in the atmospheres of brown dwarfs and exoplanets and uncover both horizontal and vertical cloud structures.

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arXiv2014

Cloud structure of the nearest brown dwarfs: Spectroscopic variability of Luhman 16AB from the Hubble Space Telescope

The binary brown dwarf WISE J104915.57$-$531906.1 (also Luhman 16AB), composed of a late L and early T dwarf, is a prototypical L/T transition flux reversal binary located at only 2 pc distance. Luhman 16B is a known variable whose light curves evolve rapidly. We present spatially resolved spectroscopic time-series of Luhman 16A and B covering 6.5 h using HST/WFC3 at 1.1 to 1.66 $μ$m. The small, count-dependent variability of Luhman 16A at the beginning of the observations likely stems from instrumental systematics; Luhman 16A appears non-variable above $\approx$0.4%. Its spectrum is well fit by a single cloud layer with intermediate cloud thickness (f_sed=2, Teff=1200 K). Luhman 16B varies at all wavelengths with peak-to-valley amplitudes of 7-11%. The amplitude and light curve shape changes over only one rotation period. The lowest relative amplitude is found in the deep water absorption band at 1.4 $μ$m, otherwise it mostly decreases gradually from the blue to the red edge of the spectrum. This is very similar to the other two known highly variable early T dwarfs. A two-component cloud model accounts for most of the variability, although small deviations are seen in the water absorption band. We fit the mean spectrum and relative amplitudes with a linear combination of two models of a warm, thinner cloud (Teff=1300 K, fsed=3) and a cooler, thicker cloud (Teff=1000-1100 K, f_sed=1), assuming out-of-equilibrium atmospheric chemistry. A cloud as for Luhman 16A but with holes cannot reproduce the variability of Luhman 16B, indicating more complex cloud evolution through the L/T transition. The projected separation of the binary has decreased by $\approx$0.3'' in 8 months.

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arXiv2014

High contrast imaging at the LBT: the LEECH exoplanet imaging survey

In Spring 2013, the LEECH (LBTI Exozodi Exoplanet Common Hunt) survey began its $\sim$130-night campaign from the Large Binocular Telescope (LBT) atop Mt Graham, Arizona. This survey benefits from the many technological achievements of the LBT, including two 8.4-meter mirrors on a single fixed mount, dual adaptive secondary mirrors for high Strehl performance, and a cold beam combiner to dramatically reduce the telescope's overall background emissivity. LEECH neatly complements other high-contrast planet imaging efforts by observing stars at L' (3.8 $μ$m), as opposed to the shorter wavelength near-infrared bands (1-2.4 $μ$m) of other surveys. This portion of the spectrum offers deep mass sensitivity, especially around nearby adolescent ($\sim$0.1-1 Gyr) stars. LEECH's contrast is competitive with other extreme adaptive optics systems, while providing an alternative survey strategy. Additionally, LEECH is characterizing known exoplanetary systems with observations from 3-5$μ$m in preparation for JWST.

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arXiv2014

Cloud structure of brown dwarfs from spectroscopic variability observations

Recent discoveries of variable brown dwarfs have provided us with a new window into their three-dimensional cloud structure. The highest variables are found at the L/T transition, where the cloud cover is thought to break up, but variability has been found to occur also for both cloudy L dwarfs and (mostly) cloud-free mid T dwarfs. We summarize results from recent HST programs measuring the spectral variability of brown dwarfs in the near-infrared and compare to results from ground-based programs. We discuss the patchy cloud structure of L/T transition objects, for which it is becoming increasingly certain that the variability does not arise from cloud holes into the deep hot regions but from varying cloud thickness. We present a new patchy cloud model to explain the spectral variability of 2MASSJ21392676+0220226. We also discuss the curious multi-wavelength variability behavior of the recently discovered very nearby early T dwarf WISE J104915.57-531906.1B (Luhman 16B) and the mid T dwarf 2MASS J22282889-431026.

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arXiv2014

LEECH: A 100 Night Exoplanet Imaging Survey at the LBT

In February 2013, the LEECH (LBTI Exozodi Exoplanet Common Hunt) survey began its 100-night campaign from the Large Binocular Telescope atop Mount Graham in Arizona. LEECH nearly complements other high-contrast planet imaging efforts by observing stars in L' band (3.8 microns) as opposed to the shorter wavelength near-infrared bands (1-2.3 microns). This part of the spectrum offers deeper mass sensitivity for intermediate age (several hundred Myr-old) systems, since their Jovian-mass planets radiate predominantly in the mid-infrared. In this proceedings, we present the science goals for LEECH and a preliminary contrast curve from some early data.

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arXiv2013

Brown Dwarf Photospheres are Patchy: A Hubble Space Telescope Near-infrared Spectroscopic Survey Finds Frequent Low-level Variability

Condensate clouds strongly impact the spectra of brown dwarfs and exoplanets. Recent discoveries of variable L/T transition dwarfs argued for patchy clouds in at least some ultracool atmospheres. This study aims to measure the frequency and level of spectral variability in brown dwarfs and to search for correlations with spectral type. We used HST/WFC3 to obtain spectroscopic time series for 22 brown dwarfs of spectral types ranging from L5 to T6 at 1.1-1.7 $μ$m for $\approx$40 min per object. Using Bayesian analysis, we find 6 brown dwarfs with confident $(p>95\%)$ variability in the relative flux in at least one wavelength region at sub-percent precision, and 5 brown dwarfs with tentative $(p>68\%)$ variability. We derive a minimum variability fraction $f_{min}=27^{+11}_{-7}\%$ over all covered spectral types. The fraction of variables is equal within errors for mid L, late L and mid T spectral types; for early T dwarfs we do not find any confident variable but the sample is too small to derive meaningful limits. For some objects, the variability occurs primarily in the flux peak in the J or H band, others are variable throughout the spectrum or only in specific absorption regions. Four sources may have broad-band peak-to-peak amplitudes exceeding 1%. Our measurements are not sensitive to very long periods, inclinations near pole-on and rotationally symmetric heterogeneity. The detection statistics are consistent with most brown dwarf photospheres being patchy. While multiple-percent near-infrared variability may be rare and confined to the L/T transition, low-level heterogeneities are a frequent characteristic of brown dwarf atmospheres.

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arXiv2013

Protoplanetary Disk Masses from Stars to Brown Dwarfs

We present SCUBA-2 850um observations for 7 very low mass stars (VLMS) and brown dwarfs (BDs): 3 in Taurus, 4 in the TWA, and all classical T Tauri (cTT) analogs. We detect 2 of the 3 Taurus disks, but none of the TWA ones. Our 3sigma limits correspond to a dust mass of 1.2 MEarth in Taurus and a mere 0.2 MEarth in the TWA (3--10x deeper than previous work). We combine our data with other sub-mm/mm surveys of Taurus, rho Oph and the TWA to investigate trends in disk mass and grain growth during the cTT phase. We find : (1) The minimum disk outer radius required to explain the upper envelope of sub-mm/mm fluxes is 100 AU for intermediate-mass stars, solar-types and VLMS, and 20 AU for BDs. (2) While the upper envelope of disk masses increases with Mstar from BDs to VLMS to solar-types, no increase is seen from solar-type to intermediate-mass stars. We propose this is due to enhanced photoevaporation around intermediate masses. (3) Many disks around Taurus and rho Oph intermediate-mass and solar-type stars evince an opacity index beta of 0--1, indicating large grains. Of the only four VLMS/BDs in these regions with multi-wavelength data, three are consistent with large grains, though optically thick disks are not ruled out. (4) For the TWA VLMS (TWA 30A, B), combining our fluxes with Mdot and ages suggests substantial grain growth by 10 Myr. The degree of grain growth in the TWA BDs (2M1207A, SSPM1102) remains largely unknown. (5) A Bayesian analysis shows that mean(log[Mdisk/Mstar]) = -2.4, roughly constant all the way from intermediate-mass stars to VLMS/BDs, and (6) the disk mass in close solar-type Taurus binaries is significantly lower than in singles (by a factor of 10), while that in wide solar-type Taurus binaries is closer to that in singles (lower by a factor of 3). (7) We discuss the implications for planet formation, and for the dependence of Mdot on Mstar.

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arXiv2013

HST Spectral Mapping of L/T Transition Brown Dwarfs Reveals Cloud Thickness Variations

Most directly imaged giant exoplanets are fainter than brown dwarfs with similar spectra. To explain their relative underluminosity unusually cloudy atmospheres have been proposed. However, with multiple parameters varying between any two objects, it remained difficult to observationally test this idea. We present a new method, sensitive time-resolved Hubble Space Telescope near-infrared spectroscopy, to study two rotating L/T transition brown dwarfs (2M2139 and SIMP0136). The observations provide spatially and spectrally resolved mapping of the cloud decks of the brown dwarfs. The data allow the study of cloud structure variations while other parameters are unchanged. We find that both brown dwarfs display variations of identical nature: J- and H-band brightness variations with minimal color and spectral changes. Our light curve models show that even the simplest surface brightness distributions require at least three elliptical spots. We show that for each source the spectral changes can be reproduced with a linear combination of only two different spectra, i.e. the entire surface is covered by two distinct types of regions. Modeling the color changes and spectral variations together reveal patchy cloud covers consisting of a spatially heterogenous mix of low-brightness, low-temperature thick clouds and brighter, thin and warm clouds. We show that the same thick cloud patches seen in our varying brown dwarf targets, if extended to the entire photosphere, predict near-infrared colors/magnitudes matching the range occupied by the directly imaged exoplanets that are cooler and less luminous than brown dwarfs with similar spectral types. This supports the models in which thick clouds are responsible for the near infrared properties of these underluminous exoplanets.

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arXiv2013

Weather on Other Worlds I: Detection of Periodic Variability in the L3 Dwarf DENIS-P J1058.7-1548 with Precise Multi-Wavelength Photometry

Photometric monitoring from warm Spitzer reveals that the L3 dwarf DENIS-P J1058.7-1548 varies sinusoidally in brightness with a period of 4.25 +0.26/-0.16 hours and an amplitude of 0.388 +/- 0.043% (peak-to-valley) in the 3.6 micron band, confirming the reality of a 4.31 +/- 0.31 hour periodicity detected in J-band photometry from the SOAR telescope. The J-band variations are a factor of 2.17 +/- 0.35 larger in amplitude than those at 3.6 microns, while 4.5 micron Spitzer observations yield a 4.5 micron/3.6 micron amplitude ratio of only 0.23 +/- 0.15, consistent with zero 4.5 micron variability. This wide range in amplitudes indicates rotationally modulated variability due to magnetic phenomena and/or inhomogeneous cloud cover. Weak H-alpha emission indicates some magnetic activity, but it is difficult to explain the observed amplitudes by magnetic phenomena unless they are combined with cloud inhomogeneities (which might have a magnetic cause). However, inhomogenous cloudcover alone can explain all our observations, and our data align with theory in requiring that the regions with the thickest clouds also have the lowest effective temperature. Combined with published v sin(i) results, our rotation period yields a 95% confidence lower limit of 0.111 solar radii on the radius of DENIS-P J1058.7-1548, suggesting upper limits of 320 Myr and 0.055 solar masses on the age and mass. These limits should be regarded cautiously because of 3-sigma inconsistencies with other data; however, a lower limit of 45 degrees on the inclination is more secure. DENIS-P J1058.7-1548 is only the first of nearly two dozen low-amplitude variables discovered and analyzed by the Weather on Other Worlds project.

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arXiv2013

Benchmark Tests for Markov Chain Monte Carlo Fitting of Exoplanet Eclipse Observations

Ground-based observations of exoplanet eclipses provide important clues to the planets' atmospheric physics, yet systematics in light curve analyses are not fully understood. It is unknown if measurements suggesting near-infrared flux densities brighter than models predict are real, or artifacts of the analysis processes. We created a large suite of model light curves, using both synthetic and real noise, and tested the common process of light curve modeling and parameter optimization with a Markov Chain Monte Carlo (MCMC) algorithm. With synthetic white-noise models, we find that input eclipse signals are generally recovered within 10% accuracy for eclipse depths greater than the noise amplitude, and to smaller depths for higher sampling rates and longer baselines. Red-noise models see greater discrepancies between input and measured eclipse signals, often biased in one direction. Finally, we find that in real data, systematic biases result even with a complex model to account for trends, and significant false eclipse signals may appear in a non-Gaussian distribution. To quantify the bias and validate an eclipse measurement, we compare both the planet-hosting star and several of its neighbors to a separately-chosen control sample of field stars. Re-examining the Rogers et al. (2009) Ks-band measurement of CoRoT-1b finds an eclipse $3190^{+370}_{-440}$ ppm deep centered at $ϕ_{me}$=$0.50418^{+0.00197}_{-0.00203}$. Finally, we provide and recommend the use of selected datasets we generated as a benchmark test for eclipse modeling and analysis routines, and propose criteria to verify eclipse detections.

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arXiv2012

Vertical Atmospheric Structure in a Variable Brown Dwarf: Pressure-dependent Phase Shifts in Simultaneous Hubble Space Telescope-Spitzer Light Curves

Heterogeneous clouds or temperature perturbations in rotating brown dwarfs produce variability in the observed flux. We report time-resolved simultaneous observations of the variable T6.5 brown dwarf 2MASSJ22282889-431026 over the wavelength ranges 1.1-1.7 microns and broadband 4.5 microns. Spectroscopic observations were taken with Wide Field Camera 3 on board the Hubble Space Telescope and photometry with the Spitzer Space Telescope. The object shows sinusoidal infrared variability with a period of 1.4 hr at most wavelengths with peak-to-peak amplitudes between 1.45% and 5.3% of the mean flux. While the light curve shapes are similar at all wavelengths, their phases differ from wavelength to wavelength with a maximum difference of more than half of a rotational period. We compare the spectra with atmospheric models of different cloud prescriptions, from which we determine the pressure levels probed at different wavelengths. We find that the phase lag increases with decreasing pressure level, or higher altitude. We discuss a number of plausible scenarios that could cause this trend of light curve phase with probed pressure level. These observations are the first to probe heterogeneity in an ultracool atmosphere in both horizontal and vertical directions, and thus are an ideal test case for realistic three dimensional simulations of the atmospheric structure with clouds in brown dwarfs and extrasolar planets.

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arXiv2012

The Gray Needle: Large Grains in the HD 15115 Debris Disk from LBT/PISCES/Ks and LBTI/LMIRcam/L' Adaptive Optics Imaging

We present diffraction-limited \ks band and \lprime adaptive optics images of the edge-on debris disk around the nearby F2 star HD 15115, obtained with a single 8.4 m primary mirror at the Large Binocular Telescope. At \ks band the disk is detected at signal-to-noise per resolution element (SNRE) \about 3-8 from \about 1-2\fasec 5 (45-113 AU) on the western side, and from \about 1.2-2\fasec 1 (63-90 AU) on the east. At \lprime the disk is detected at SNRE \about 2.5 from \about 1-1\fasec 45 (45-90 AU) on both sides, implying more symmetric disk structure at 3.8 \microns . At both wavelengths the disk has a bow-like shape and is offset from the star to the north by a few AU. A surface brightness asymmetry exists between the two sides of the disk at \ks band, but not at \lprime . The surface brightness at \ks band declines inside 1\asec (\about 45 AU), which may be indicative of a gap in the disk near 1\asec. The \ks - \lprime disk color, after removal of the stellar color, is mostly grey for both sides of the disk. This suggests that scattered light is coming from large dust grains, with 3-10 \microns -sized grains on the east side and 1-10 \microns dust grains on the west. This may suggest that the west side is composed of smaller dust grains than the east side, which would support the interpretation that the disk is being dynamically affected by interactions with the local interstellar medium.

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arXiv2012

First Light LBT AO Images of HR 8799 bcde at 1.65 and 3.3 Microns: New Discrepancies between Young Planets and Old Brown Dwarfs

As the only directly imaged multiple planet system, HR 8799 provides a unique opportunity to study the physical properties of several planets in parallel. In this paper, we image all four of the HR 8799 planets at H-band and 3.3 microns with the new LBT adaptive optics system, PISCES, and LBTI/LMIRCam. Our images offer an unprecedented view of the system, allowing us to obtain H and 3.3$ micron photometry of the innermost planet (for the first time) and put strong upper-limits on the presence of a hypothetical fifth companion. We find that all four planets are unexpectedly bright at 3.3 microns compared to the equilibrium chemistry models used for field brown dwarfs, which predict that planets should be faint at 3.3 microns due to CH4 opacity. We attempt to model the planets with thick-cloudy, non-equilibrium chemistry atmospheres, but find that removing CH4 to fit the 3.3 micron photometry increases the predicted L' (3.8 microns) flux enough that it is inconsistent with observations. In an effort to fit the SED of the HR 8799 planets, we construct mixtures of cloudy atmospheres, which are intended to represent planets covered by clouds of varying opacity. In this scenario, regions with low opacity look hot and bright, while regions with high opacity look faint, similar to the patchy cloud structures on Jupiter and L/T transition brown-dwarfs. Our mixed cloud models reproduce all of the available data, but self-consistent models are still necessary to demonstrate their viability.

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arXiv2011

Resolving the inner regions of the HD97048 circumstellar disk with VLT/NACO polarimetric differential imaging

Circumstellar disks are the cradles of planetary systems and their physical and chemical properties directly influence the planet formation process. As most planets supposedly form in the inner disk regions, i.e., within a few tens of AU, it is crucial to study circumstellar disk on these scales to constrain the conditions for planet formation. Our aims are to characterize the inner regions of the circumstellar disk around the young Herbig Ae/Be star HD97048 in polarized light. We use VLT/NACO to observe HD97048 in polarimetric differential imaging (PDI) mode in the H and Ks band. We spatially resolve the disk around HD97048 in polarized flux in both filters on scales between ~0.1"-1.0" corresponding to the inner ~16-160 AU. Fitting isophots to the flux calibrated H-band image between 13 - 14 mag/arcsec^2 and 14 - 15 mag/arcsec^2 we derive a apparent disk inclination angle of 34+-5 deg and 47+-2 deg, respectively. The disk position angle in both brightness regimes is almost identical and roughly 80 deg. Along the disk major axis the surface brightness of the polarized flux drops from ~11 mag/arcsec^2 at ~0.1" (~16 AU) to ~15.3 mag/arcsec^2 at ~1.0" (~160 AU). The brightness profiles along the major axis are fitted with power-laws falling off as ~r^(-1.78+-0.02) in H and ~r^(-2.34+-0.04) in Ks. As the surface brightness drops off more rapidly in Ks compared to H the disks becomes relatively bluer at larger separations possibly indicating changing dust grain properties as a function of radius. For the first time the inner ~0.1"-1.0" (~16-160 AU) of the surface layer of the HD97048 circumstellar disk have been imaged in scattered light demonstrating the power of ground-based imaging polarimetry. Our data fill an important gap in a large collection of existing data including resolved thermal dust and PAH emission images as well as resolved gas emission lines.

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arXiv2011

Measuring Organic Molecular Emission in Disks with Low Resolution Spitzer Spectroscopy

We explore the extent to which Spitzer IRS spectra taken at low spectral resolution can be used in quantitative studies of organic molecular emission from disks surrounding low mass young stars. We use Spitzer IRS spectra taken in both the high and low resolution modules for the same sources to investigate whether it is possible to define line indices that can measure trends in the strength of the molecular features in low resolution data. We find that trends in HCN emission strength seen in the high resolution data can be recovered in low resolution data. In examining the factors that influence the HCN emission strength, we find that the low resolution HCN flux is modestly correlated with stellar accretion rate and X-ray luminosity. Correlations of this kind are perhaps expected based on recent observational and theoretical studies of inner disk atmospheres. Our results demonstrate the potential of using the large number of low resolution disk spectra that reside in the Spitzer archive to study the factors that influence the strength of molecular emission from disks. Such studies would complement results for the much smaller number of circumstellar disks that have been observed at high resolution with IRS.

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arXiv2011

A Combined Subaru/VLT/MMT 1--5 Micron Study of Planets Orbiting HR 8799: Implications for Atmospheric Properties, Masses, and Formation

We present new 1--1.25 micron (z and J band) Subaru/IRCS and 2 micron (K band) VLT/NaCo data for HR 8799 and a rereduction of the 3--5 micron MMT/Clio data first presented by Hinz et al. (2010). Our VLT/NaCo data yields a detection of a fourth planet at a projected separation of ~ 15 AU -- "HR 8799e". We also report new, albeit weak detections of HR 8799b at 1.03 microns and 3.3 microns. Empirical comparisons to field brown dwarfs show that at least HR 8799b and HR8799c, and possibly HR 8799d, have near-to-mid IR colors/magnitudes significantly discrepant from the L/T dwarf sequence. Standard cloud deck atmosphere models appropriate for brown dwarfs provide only (marginally) statistically meaningful fits to HR 8799b and c for unphysically small radii. Models with thicker cloud layers not present in brown dwarfs reproduce the planets' SEDs far more accurately and without the need for rescaling the planets' radii. Our preliminary modeling suggests that HR 8799b has log(g) = 4--4.5, Teff = 900K, while HR 8799c, d, and (by inference) e have log(g) = 4--4.5, Teff = 1000--1200K. Combining results from planet evolution models and new dynamical stability limits implies that the masses of HR 8799b, c, d, and e are 6--7 Mj, 7--10 Mj, 7--10 Mj and 7--10 Mj. 'Patchy" cloud prescriptions may provide even better fits to the data and may lower the estimated surface gravities and masses. Finally, contrary to some recent claims, forming the HR 8799 planets by core accretion is still plausible, although such systems are likely rare.

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arXiv2010

First Results From VLT NACO Apodizing Phase Plate: 4-micron Images of the Exoplanet beta Pictoris b

Direct imaging of exoplanets requires both high contrast and high spatial resolution. Here, we present the first scientific results obtained with the newly commissioned Apodizing Phase Plate coronagraph (APP) on VLT/NACO. We detected the exoplanet beta Pictoris b in the narrow band filter centered at 4.05 micron (NB4.05). The position angle (209.13 +- 2.12 deg) and the projected separation to its host star (0."354 +- 0".012, i.e., 6.8 +- 0.2 AU at a distance of 19.3 pc) are in good agreement with the recently presented data from Lagrange et al. (2010). Comparing the observed NB4.05 magnitude of 11.20 +- 0.23 mag to theoretical atmospheric models we find a best fit with a 7-10 M_Jupiter object for an age of 12 Myr, again in agreement with previous estimates. Combining our results with published L' photometry we can compare the planet's [L' - NB4.05] color to that of cool field dwarfs of higher surface gravity suggesting an effective temperature of ~1700 K. The best fit theoretical model predicts an effective temperature of ~1470 K, but this difference is not significant given our photometric uncertainties. Our results demonstrate the potential of NACO/APP for future planet searches and provides independent confirmation as well as complementary data for beta Pictoris b.

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arXiv2010

Day-side z'-band emission and eccentricity of Wasp-12b

We report the detection of the eclipse of the very-hot Jupiter WASP-12b via z'-band time-series photometry obtained with the 3.5-meter ARC telescope at Apache Point Observatory. We measure a decrease in flux of 0.082+/-0.015% during the passage of the planet behind the star. That planetary flux is equally well reproduced by atmospheric models with and without extra absorbers, and blackbody models with f > 0.585+/-0.080. It is therefore necessary to measure the planet at other wavelengths to further constrain its atmospheric properties. The eclipse appears centered at phase = 0.5100 (+0.0072,-0.0061), consistent with an orbital eccentricity of |e cos w| = 0.016 (+0.011,-0.009) (see note at end of Section 4). If the orbit of the planet is indeed eccentric, the large radius of WASP-12b can be explained by tidal heating.

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