1. |
- Bonnefoy, M., et al.
(author)
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First light of the VLT planet finder SPHERE IV. Physical and chemical properties of the planets around HR8799
- 2016
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 587
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Journal article (peer-reviewed)abstract
- Context. The system of four planets discovered around the intermediate-mass star HR8799 offers a unique opportunity to test planet formation theories at large orbital radii and to probe the physics and chemistry at play in the atmospheres of self-luminous young (similar to 30 Myr) planets. We recently obtained new photometry of the four planets and low-resolution (R similar to 30) spectra of HR8799 d and e with the SPHERE instrument (Paper III).Aims. In this paper (Paper IV), we aim to use these spectra and available photometry to determine how they compare to known objects, what the planet physical properties are, and how their atmospheres work.Methods. We compare the available spectra, photometry, and spectral energy distribution (SED) of the planets to field dwarfs and young companions. In addition, we use the extinction from corundum, silicate (enstatite and forsterite), or iron grains likely to form in the atmosphere of the planets to try to better understand empirically the peculiarity of their spectrophotometric properties. To conclude, we use three sets of atmospheric models (BT-SETTL14, Cloud-AE60, Exo-REM) to determine which ingredients are critically needed in the models to represent the SED of the objects, and to constrain their atmospheric parameters (T-eff, log g, M/H).Results. We find that HR8799d and e properties are well reproduced by those of L6-L8 dusty dwarfs discovered in the field, among which some are candidate members of young nearby associations. No known object reproduces well the properties of planets b and c. Nevertheless, we find that the spectra and WISE photometry of peculiar and/or young early-T dwarfs reddened by submicron grains made of corundum, iron, enstatite, or forsterite successfully reproduce the SED of these planets. Our analysis confirms that only the Exo-REM models with thick clouds fit (within 2 sigma) the whole set of spectrophotometric datapoints available for HR8799 d and e for T-eff = 1200 K, log g in the range 3.0-4.5, and M/H = +0.5. The models still fail to reproduce the SED of HR8799c and b. The determination of the metallicity, log g, and cloud thickness are degenerate.Conclusions. Our empirical analysis and atmospheric modelling show that an enhanced content in dust and decreased CIA of H-2 is certainly responsible for the deviation of the properties of the planet with respect to field dwarfs. The analysis suggests in addition that HR8799c and b have later spectral types than the two other planets, and therefore could both have lower masses.
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2. |
- Zurlo, A., et al.
(author)
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First light of the VLT planet finder SPHERE III. New spectrophotometry and astrometry of the HR 8799 exoplanetary system
- 2016
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 587
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Journal article (peer-reviewed)abstract
- Context. The planetary system discovered around the young A-type HR8799 provides a unique laboratory to: a) test planet formation theories; b) probe the diversity of system architectures at these separations, and c) perform comparative (exo)planetology.Aims. We present and exploit new near-infrared images and integral-field spectra of the four gas giants surrounding HR8799 obtained with SPHERE, the new planet finder instrument at the Very Large Telescope, during the commissioning and science verification phase of the instrument (July-December 2014). With these new data, we contribute to completing the spectral energy distribution (SED) of these bodies in the 1.0-2.5 mu m range. We also provide new astrometric data, in particular for planet e, to further constrain the orbits.Methods. We used the infrared dual-band imager and spectrograph (IRDIS) subsystem to obtain pupil-stabilized, dual-band H2H3 (1.593 mu m, 1.667 mu m), K1K2 (2.110 mu m, 2.251 mu m), and broadband J (1.245 mu m) images of the four planets. IRDIS was operated in parallel with the integral field spectrograph (IFS) of SPHERE to collect low-resolution (R similar to 30), near-infrared (0.94-1.64 mu m) spectra of the two innermost planets HR8799 d and e. The data were reduced with dedicated algorithms, such as the Karhunen-Loeve image projection (KLIP), to reveal the planets. We used the so-called negative planets injection technique to extract their photometry, spectra, and measure their positions. We illustrate the astrometric performance of SPHERE through sample orbital fits compatible with SPHERE and literature data.Results. We demonstrated the ability of SPHERE to detect and characterize planets in this kind of systems, providing spectra and photometry of its components. The spectra improve upon the signal-to-noise ratio of previously obtained data and increase the spectral coverage down to the Y band. In addition, we provide the first detection of planet e in the J band. Astrometric positions for planets HR8799 bcde are reported for the epochs of July, August, and December 2014. We measured the photometric values in J, H2H3, K1K2 bands for the four planets with a mean accuracy of 0.13 mag. We found upper limit constraints on the mass of a possible planet f of 3-7 M-Jup. Our new measurements are more consistent with the two inner planets d and e being in a 2d:1e or 3d:2e resonance. The spectra of HR8799 d and e are well matched by those of L6-8 field dwarfs. However, the SEDs of these objects are redder than field L dwarfs longward of 1.6 mu m.
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3. |
- Vigan, A., et al.
(author)
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First light of the VLT planet finder SPHERE I. Detection and characterization of the substellar companion GJ 758 B
- 2016
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 587
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Journal article (peer-reviewed)abstract
- GJ 758 B is a brown dwarf companion to a nearby (15.76%) solar-type, metal-rich (M/H = +0.2 dex) main-sequence star (G9V) that was discovered with Subaru/HiCIAO in 2009. From previous studies, it has drawn attention as being the coldest (similar to 600 K) companion ever directly imaged around a neighboring star. We present new high-contrast data obtained during the commissioning of the SPHERE instrument at the Very Large Telescope (VLT). The data was obtained in Y-, J-, H-, and K-s-bands with the dual-band imaging (DBI) mode of IRDIS, thus providing a broad coverage of the full near-infrared (near-IR) range at higher contrast and better spectral sampling than previously reported. In this new set of high-quality data, we report the re-detection of the companion, as well as the first detection of a new candidate closer-in to the star. We use the new eight photometric points for an extended comparison of GJ 758 B with empirical objects and four families of atmospheric models. From comparison to empirical object, we estimate a T8 spectral type, but none of the comparison objects can accurately represent the observed near-IR fluxes of GJ 758 B. From comparison to atmospheric models, we attribute a T-eff = 600 +/- 100 K, but we find that no atmospheric model can adequately fit all the fluxes of GJ 758 B. The lack of exploration of metal enrichment in model grids appears as a major limitation that prevents an accurate estimation of the companion physical parameters. The photometry of the new candidate companion is broadly consistent with L-type objects, but a second epoch with improved photometry is necessary to clarify its status. The new astrometry of GJ 758 B shows a significant proper motion since the last epoch. We use this result to improve the determination of the orbital characteristics using two fitting approaches: Least-Squares Monte Carlo and Markov chain Monte Carlo. We confirm the high-eccentricity of the orbit (peak at 0.5), and find a most likely semi-major axis of 46.05 AU. We also use our imaging data, as well as archival radial velocity data, to reject the possibility that this is a false positive effect created by an unseen, closer-in, companion. Finally, we analyze the sensitivity of our data to additional closer-in companions and reject the possibility of other massive brown dwarf companions down to 4-5 AU.
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4. |
- Olofsson, J., et al.
(author)
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Resolving faint structures in the debris disk around TWA 7 Tentative detections of an outer belt, a spiral arm, and a dusty cloud
- 2018
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 617
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Journal article (peer-reviewed)abstract
- Context. Debris disks are the intrinsic by-products of the star and planet formation processes. Most likely due to instrumental limitations and their natural faintness, little is known about debris disks around low mass stars, especially when it comes to spatially resolved observations. Aims. We present new VLT/SPHERE IRDIS dual-polarization imaging (DPI) observations in which we detect the dust ring around the M2 spectral type star TWA 7. Combined with additional angular differential imaging observations we aim at a fine characterization of the debris disk and setting constraints on the presence of low-mass planets. Methods. We modeled the SPHERE DPI observations and constrain the location of the small dust grains, as well as the spectral energy distribution of the debris disk, using the results inferred from the observations, and performed simple N-body simulations. Results. We find that the dust density distribution peaks at similar to 0.72 '' (25 au), with a very shallow outer power-law slope, and that the disk has an inclination of similar to 13 degrees with a position angle of similar to 91 degrees east of north. We also report low signal-to-noise ratio detections of an outer belt at a distance of similar to 1.5 '' (similar to 52 au) from the star, of a spiral arm in the southern side of the star, and of a possible dusty clump at 0.11 ''. These findings seem to persist over timescales of at least a year. Using the intensity images, we do not detect any planets in the close vicinity of the star, but the sensitivity reaches Jovian planet mass upper limits. We find that the SED is best reproduced with an inner disk at similar to 0.2 '' (similar to 7 au) and another belt at 0.72 '' (25 au). Conclusions. We report the detections of several unexpected features in the disk around TWA 7. A yet undetected 100 M-circle plus planet with a semi-major axis at 20-30 au could possibly explain the outer belt as well as the spiral arm. We conclude that stellar winds are unlikely to be responsible for the spiral arm.
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5. |
- Cockell, C.S., et al.
(author)
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Darwin - an experimental astronomy mission to search for extrasolar planets
- 2009
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In: Experimental Astronomy. - 0922-6435 .- 1572-9508. ; 23:1, s. 435-461
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Journal article (peer-reviewed)abstract
- As a response to ESA call for mission concepts for its Cosmic Vision 2015–2025 plan, we propose a mission called Darwin. Its primary goal is the study of terrestrial extrasolar planets and the search for life on them. In this paper, we describe different characteristics of the instrument.
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6. |
- Milli, J., et al.
(author)
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Near-infrared scattered light properties of the HR4796A dust ring A measured scattering phase function from 13.6 degrees to 166.6 degrees
- 2017
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 599
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Journal article (peer-reviewed)abstract
- Context. HR4796A is surrounded by a debris disc, observed in scattered light as an inclined ring with a high surface brightness. Past observations have raised several questions. First, a strong brightness asymmetry detected in polarised reflected light has recently challenged our understanding of scattering by the dust particles in this system. Secondly, the morphology of the ring strongly suggests the presence of planets, although no planets have been detected to date.Aims. We aim here at measuring with high accuracy the morphology and photometry of the ring in scattered light, in order to derive the phase function of the dust and constrain its near-infrared spectral properties. We also want to constrain the presence of planets and set improved constraints on the origin of the observed ring morphology.Methods. We obtained high-angular resolution coronagraphic images of the circumstellar environment around HR4796A with VLT/SPHERE during the commissioning of the instrument in May 2014 and during guaranteed-time observations in February 2015. The observations reveal for the first time the entire ring of dust, including the semi-minor axis that was previously hidden either behind the coronagraphic spot or in the speckle noise.Results. We determine empirically the scattering phase function of the dust in the H band from 13.6 degrees to 166.6 degrees. It shows a prominent peak of forward scattering, never detected before, for scattering angles below 30 degrees. We analyse the reflectance spectra of the disc from the 0.95 mu m to 1.6 mu m, confirming the red colour of the dust, and derive detection limits on the presence of planetary mass objects.Conclusions. We confirm which side of the disc is inclined towards the Earth. The analysis of the phase function, especially below 45 degrees, suggests that the dust population is dominated by particles much larger than the observation wavelength, of about 20 mu m. Compact Mie grains of this size are incompatible with the spectral energy distribution of the disc, however the observed rise in scattering efficiency beyond 50 degrees points towards aggregates which could reconcile both observables. We do not detect companions orbiting the star, but our high-contrast observations provide the most stringent constraints yet on the presence of planets responsible for the morphology of the dust.
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7. |
- Defrere, D., et al.
(author)
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L'-band AGPM vector vortex coronagraph's first light on LBTI/LMIRCam
- 2014
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In: Adaptive Optics Systems IV. - : SPIE. - 9780819496164
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Conference paper (peer-reviewed)abstract
- We present the first observations obtained with the L'-band AGPM vortex coronagraph recently installed on LBTI/LMIRCam. The AGPM (Annular Groove Phase Mask) is a vector vortex coronagraph made from diamond subwavelength gratings. It is designed to improve the sensitivity and dynamic range of high-resolution imaging at very small inner working angles, down to 0.09 arcseconds in the case of LBTI/LMIRCam in the L' band. During the first hours on sky, we observed the young A5V star HR8799 with the goal to demonstrate the AGPM performance and assess its relevance for the ongoing LBTI planet survey (LEECH). Preliminary analyses of the data reveal the four known planets clearly at high SNR and provide unprecedented sensitivity limits in the inner planetary system (down to the diffraction limit of 0.09 arcseconds).
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8. |
- Kasper, M., et al.
(author)
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NEAR: : Low-mass Planets in α Cen with VISIR
- 2017
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In: The Messenger. ; 169, s. 16-20
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Journal article (peer-reviewed)abstract
- ESO, in collaboration with the Breakthrough Initiatives, is working to modify the Very Large Telescope mid-IR imager (VISIR) to greatly enhance its ability to search for potentially habitable planets around both components of the binary Alpha Centauri, part of the closest stellar system to the Earth. Much of the funding for the NEAR (New Earths in the Alpha Cen Region) project is provided by the Breakthrough Initiatives, and ESO mostly provides staff and observing time. The concept combines adaptive optics using the deformable secondary mirror at Unit Telescope 4, a new annular groove phase mask (AGPM) coronagraph optimised for the most sensitive spectral bandpass in the N-band, and a novel internal chopper system for noise filtering based on a concept for longer wavelengths invented by the microwave pioneer Robert Dicke. The NEAR experiment is relevant to the mid-infrared METIS instrument on the Extremely Large Telescope, as the knowledge gained and proof of concept will be transferable.
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9. |
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10. |
- Milli, J., et al.
(author)
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Discovery of a low-mass companion inside the debris ring surrounding the F5V star HD 206893
- 2017
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 597
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Journal article (peer-reviewed)abstract
- Aims. Uncovering the ingredients and the architecture of planetary systems is a very active field of research that has fuelled many new theories on giant planet formation, migration, composition, and interaction with the circumstellar environment. We aim at discovering and studying new such systems, to further expand our knowledge of how low-mass companions form and evolve.Methods. We obtained high-contrast H-band images of the circumstellar environment of the F5V star HD 206893, known to host a debris disc never detected in scattered light. These observations are part of the SPHERE High Angular Resolution Debris Disc Survey (SHARDDS) using the InfraRed Dual-band Imager and Spectrograph (IRDIS) installed on VLT/SPHERE.Results. We report the detection of a source with a contrast of 3.6 × 10−5 in the H-band, orbiting at a projected separation of 270 milliarcsecond or 10 au, corresponding to a mass in the range 24 to 73MJup for an age of the system in the range 0.2 to 2 Gyr. The detection was confirmed ten months later with VLT/NaCo, ruling out a background object with no proper motion. A faint extended emission compatible with the disc scattered light signal is also observed.Conclusions. The detection of a low-mass companion inside a massive debris disc makes this system an analog of other young planetary systems such as β Pictoris, HR 8799 or HD 95086 and requires now further characterisation of both components to understand their interactions.
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11. |
- Reggiani, M, et al.
(author)
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Discovery of a point-like source and a third spiral arm in the transition disk around the Herbig Ae star MWC 758
- 2018
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In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 611
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Journal article (peer-reviewed)abstract
- Context. Transition disks offer the extraordinary opportunity to look for newly born planets and to investigate the early stages of planet formation. Aims. In this context we observed the Herbig A5 star MWC 758 with the L'-band vector vortex coronagraph installed in the near-infrared camera and spectrograph NIRC2 at the Keck II telescope, with the aim of unveiling the nature of the spiral structure by constraining the presence of planetary companions in the system. Methods. Our high-contrast imaging observations show a bright (Delta L' = 7.0 +/- 0.3 mag) point-like emission south of MWC 758 at a deprojected separation of similar to 20 au (r = 0 ''.111 +/- 0 ''.004) from the central star. We also recover the two spiral arms (southeast and northwest), already imaged by previous studies in polarized light, and discover a third arm to the southwest of the star. No additional companions were detected in the system down to 5 Jupiter masses beyond 0 ''.6 from the star. Results. We propose that the bright L'-band emission could be caused by the presence of an embedded and accreting protoplanet, although the possibility of it being an asymmetric disk feature cannot be excluded. The spiral structure is probably not related to the protoplanet candidate, unless on an inclined and eccentric orbit, and it could be due to one (or more) yet undetected planetary companions at the edge of or outside the spiral pattern. Future observations and additional simulations will be needed to shed light on the true nature of the point-like source and its link with the spiral arms.
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12. |
- Serabyn, E, et al.
(author)
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The W. M. Keck Observatory infrared vortex coronagraph and a first image of HIP79124 B
- 2017
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In: Astronomical Journal. - : American Astronomical Society. - 0004-6256 .- 1538-3881. ; 153:1, s. 1-7
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Journal article (peer-reviewed)abstract
- An optical vortex coronagraph has been implemented within the NIRC2 camera on the Keck II telescope and used to carry out on-sky tests and observations. The development of this new L′-band observational mode is described, and an initial demonstration of the new capability is presented: a resolved image of the low-mass companion to HIP 79124, which had previously been detected by means of interferometry. With HIP 79124 B at a projected separation of 186.5 mas, both the small inner working angle of the vortex coronagraph and the related imaging improvements were crucial in imaging this close companion directly. Due to higher Strehl ratios and more relaxed contrasts in L′ band versus H band, this new coronagraphic capability will enable high-contrast, small-angle observations of nearby young exoplanets and disks on a par with those of shorter-wavelength extreme adaptive optics coronagraphs.
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13. |
- Tinyanont, S., et al.
(author)
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Infrared spectropolarimetric detection of intrinsic polarization from a core-collapse supernova
- 2021
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In: Nature Astronomy. - : Springer Nature. - 2397-3366. ; 5:6, s. 544-551
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Journal article (peer-reviewed)abstract
- Massive stars die an explosive death as a core-collapse supernova (CCSN). The exact physical processes that cause the collapsing star to rebound into an explosion are not well understood1–3, and the key to resolving this issue may lie in the measurement of the shape of CCSNe ejecta. Spectropolarimetry is the only way to perform this measurement for CCSNe outside the Milky Way and Magellanic Clouds. We present the infrared spectropolarimetric detection of a CCSN enabled by the new highly sensitive WIRC+Pol instrument at Palomar Observatory, which can observe CCSNe (magnitude M = −17 mag) out to 20 Mpc at ~0.1% polarimetric precision. Infrared spectropolarimetry is less affected than optical spectropolarimetry by dust scattering in the circumstellar and interstellar media, thereby providing a less biased probe of the intrinsic geometry of the supernova ejecta. SN 2018hna, a SN 1987A-like explosion, shows 2.0 ± 0.3% continuum polarization in the J band oriented at ~160° on sky 182 days after the explosion. Assuming a prolate geometry as in SN 1987A, we infer an ejecta axis ratio of <0.48 with the axis of symmetry pointing at a 70° position angle. The axis ratio is similar to that of SN 1987A, suggesting that the two CCSNe may share intrinsic geometry and inclination angles. Our data do not rule out oblate ejecta. We also observe one other CCSN and two thermonuclear supernovae in the J band. Supernova 2020oi, a stripped-envelope type Ic SN in Messier 100 has broadband p = 0.37 ± 0.09% at peak light, indicative of either a 10% asymmetry or host interstellar polarization. The type Ia SNe 2019ein and 2020ue have <0.33% and <1.08% polarization near peak light, indicative of asymmetries of less than 10% and 20%, respectively.
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14. |
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15. |
- Delacroix, C., et al.
(author)
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A diamond AGPM coronagraph for VISIR
- 2012
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In: Proceedings of SPIE. - : SPIE. - 9780819491473 ; , s. 84468K-
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Conference paper (peer-reviewed)abstract
- In recent years, phase mask coronagraphy has become increasingly efficient in imaging the close environment of stars, enabling the search for exoplanets and circumstellar disks. Coronagraphs are ideally suited instruments, characterized by high dynamic range imaging capabilities, while preserving a small inner working angle. The AGPM (Annular Groove Phase Mask, Mawet et al. 20051) consists of a vector vortex induced by a rotationally symmetric subwavelength grating. This technique constitutes an almost unique solution to the achromatization at longer wavelengths (mid-infrared). For this reason, we have specially conceived a mid-infrared AGPM coronagraph for the forthcoming upgrade of VISIR, the mid-IR imager and spectrograph on the VLT at ESO (Paranal), in collaboration with members of the VISIR consortium. The implementation phase of the VISIR Upgrade Project is foreseen for May-August 2012, and the AGPM installed will cover the 11-13.2 μm spectral range. In this paper, we present the entire fabrication process of our AGPM imprinted on a diamond substrate. Diamond is an ideal material for mid-infrared wavelengths owing to its high transparency, small dispersion, extremely low thermal expansion and outstanding mechanical and chemical properties. The design process has been performed with an algorithm based on the rigorous coupled wave analysis (RCWA), and the micro-fabrication has been carried out using nano-imprint lithography and reactive ion etching. A precise grating profile metrology has also been conducted using cleaving techniques. Finally, we show the deposit of fiducials (i.e. centering marks) with Aerosol Jet Printing (AJP). We conclude with the ultimate coronagraph expected performances.
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16. |
- Kuzuhara, Masayuki, et al.
(author)
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Gliese 12 b: A Temperate Earth-sized Planet at 12 pc Ideal for Atmospheric Transmission Spectroscopy
- 2024
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In: Astrophysical Journal Letters. - 2041-8213 .- 2041-8205. ; 969:1
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Journal article (peer-reviewed)abstract
- Recent discoveries of Earth-sized planets transiting nearby M dwarfs have made it possible to characterize the atmospheres of terrestrial planets via follow-up spectroscopic observations. However, the number of such planets receiving low insolation is still small, limiting our ability to understand the diversity of the atmospheric composition and climates of temperate terrestrial planets. We report the discovery of an Earth-sized planet transiting the nearby (12 pc) inactive M3.0 dwarf Gliese 12 (TOI-6251) with an orbital period (P(or)b) of 12.76 days. The planet, Gliese 12 b, was initially identified as a candidate with an ambiguous P-orb from TESS data. We confirmed the transit signal and P-orb using ground-based photometry with MuSCAT2 and MuSCAT3, and validated the planetary nature of the signal using high-resolution images from Gemini/NIRI and Keck/NIRC2 as well as radial velocity (RV) measurements from the InfraRed Doppler instrument on the Subaru 8.2 m telescope and from CARMENES on the CAHA 3.5 m telescope. X-ray observations with XMM-Newton showed the host star is inactive, with an X-ray-to-bolometric luminosity ratio of log L-X/L-bol approximate to - 5.7. Joint analysis of the light curves and RV measurements revealed that Gliese 12 b has a radius of 0.96 +/- 0.05 R-circle plus, a 3 sigma mass upper limit of 3.9M(circle plus), and an equilibrium temperature of 315 +/- 6 K assuming zero albedo. The transmission spectroscopy metric (TSM) value of Gliese 12 b is close to the TSM values of the TRAPPIST-1 planets, adding Gliese 12 b to the small list of potentially terrestrial, temperate planets amenable to atmospheric characterization with JWST.
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17. |
- Piron, P., et al.
(author)
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A Mach-Zehnder interferometer based on orbital angular momentum for improved vortex coronagraph efficiency
- 2015
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In: Techniques And Instrumentation For Detection Of Exoplanets Vii. - : SPIE. - 9781628417715
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Conference paper (peer-reviewed)abstract
- The Annular Groove Phase Mask (AGPM) is a vectorial vortex phase mask. it act, as a half-wave plate with a radial fast axis orientation operating in the mid infrared domain. When placed at the the focus of a telescope element provides a continuous helical phase ramp for an on axis sources, which creates the orbital angular momentum. Thanks to that phase, the intensity of the central source is canceled by a down-stream pupil stop, while the off axis sources are not affected. However due to experimental conditions the nulling is hardly perfect. To improve the null, a Mach-Zehnder interferometer containing Dove prisms differently oriented can be proposed to sort out light based on its orbital angular momentum (OAM). Thanks to the differential rotation of the beam, a 7 phase shift is achieved for the on axis light affected by a non zero OAM Therefore the contrast between the star and its faint companion is enhanced. Nevertheless, due the Dove prisms birefringence, the performance of the interferometer is relatively poor. To solve this problem, we propose to add a birefringent wave-plate in each arm to compensate this birefringence. In this paper, we will develop the mathematical model of the wave front using the Jones formalism. The performance of the interferometer is at first computed for the simple version without the birefringent plate. Then the effect of the birefringent plate is be mathematically described and the performance is re-computed.
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