643 research outputs found
The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications
The inverse spectral transform for the Zakharov-Shabat equation on the
semi-line is reconsidered as a Hilbert problem. The boundary data induce an
essential singularity at large k to one of the basic solutions. Then solving
the inverse problem means solving a Hilbert problem with particular prescribed
behavior. It is demonstrated that the direct and inverse problems are solved in
a consistent way as soon as the spectral transform vanishes with 1/k at
infinity in the whole upper half plane (where it may possess single poles) and
is continuous and bounded on the real k-axis. The method is applied to
stimulated Raman scattering and sine-Gordon (light cone) for which it is
demonstrated that time evolution conserves the properties of the spectral
transform.Comment: LaTex file, 1 figure, submitted to J. Phys.
A birational mapping with a strange attractor: Post critical set and covariant curves
We consider some two-dimensional birational transformations. One of them is a
birational deformation of the H\'enon map. For some of these birational
mappings, the post critical set (i.e. the iterates of the critical set) is
infinite and we show that this gives straightforwardly the algebraic covariant
curves of the transformation when they exist. These covariant curves are used
to build the preserved meromorphic two-form. One may have also an infinite post
critical set yielding a covariant curve which is not algebraic (transcendent).
For two of the birational mappings considered, the post critical set is not
infinite and we claim that there is no algebraic covariant curve and no
preserved meromorphic two-form. For these two mappings with non infinite post
critical sets, attracting sets occur and we show that they pass the usual tests
(Lyapunov exponents and the fractal dimension) for being strange attractors.
The strange attractor of one of these two mappings is unbounded.Comment: 26 pages, 11 figure
First light of the VLT planet finder SPHERE. I. Detection and characterization of the sub-stellar companion GJ 758 B
GJ758 B is a brown dwarf companion to a nearby (15.76 pc) 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 (~600K) companion ever directly imaged around a neighboring star.
We present new high-contrast data obtained during the commissioning of the
SPHERE instrument at the VLT. The data was obtained in Y-, J-, H-, and Ks-bands
with the dual-band imaging (DBI) mode of IRDIS, 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 8 photometric points for an
extended comparison of GJ758 B with empirical objects and 4 families of
atmospheric models. From comparison to empirical object, we estimate a T8
spectral type, but none of the comparison object can accurately represent the
observed near-IR fluxes of GJ758 B. From comparison to atmospheric models, we
attribute a Teff = 600K 100K, but we find that no atmospheric model can
adequately fit all the fluxes of GJ758 B. 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
GJ758 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-Square Monte Carlo and Markov Chain Monte Carlo.
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. [abridged]Comment: 20 pages, 15 figures. Accepted for publication in A&
SPICES: Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems
SPICES (Spectro-Polarimetric Imaging and Characterization of Exoplanetary
Systems) is a five-year M-class mission proposed to ESA Cosmic Vision. Its
purpose is to image and characterize long-period extrasolar planets and
circumstellar disks in the visible (450 - 900 nm) at a spectral resolution of
about 40 using both spectroscopy and polarimetry. By 2020/22, present and
near-term instruments will have found several tens of planets that SPICES will
be able to observe and study in detail. Equipped with a 1.5 m telescope, SPICES
can preferentially access exoplanets located at several AUs (0.5-10 AU) from
nearby stars (25 pc) with masses ranging from a few Jupiter masses to Super
Earths (2 Earth radii, 10 M) as well as circumstellar
disks as faint as a few times the zodiacal light in the Solar System
First light of the VLT planet finder SPHERE. II. The physical properties and the architecture of the young systems PZ Tel and HD 1160 revisited
[Abridged] Context. The young systems PZ Tel and HD 1160, hosting known
low-mass companions, were observed during the commissioning of the new planet
finder SPHERE with several imaging and spectroscopic modes. Aims. We aim to
refine the physical properties and architecture of both systems. Methods. We
use SPHERE commissioning data and REM observations, as well as literature and
unpublished data from VLT/SINFONI, VLT/NaCo, Gemini/NICI, and Keck/NIRC2.
Results. We derive new photometry and confirm the nearly daily photometric
variability of PZ Tel A. Using literature data spanning 38 yr, we show that the
star also exhibits a long-term variability trend. The 0.63-3.8 mic SED of PZ
Tel B allows us to revise its properties: spectral type M7+/-1, Teff=2700+/-100
K, log(g)<4.5 dex, log(L/L_Sun)=-2.51+/-0.10 dex, and mass 38-72 MJ. The 1-3.8
mic SED of HD 1160 B suggests a massive brown dwarf or a low-mass star with
spectral type M5.5-7.0, Teff=3000+/-100 K, [M/H]=-0.5-0.0 dex,
log(L/L_Sun)=-2.81+/-0.10 dex, and mass 39-168 MJ. We confirm the deceleration
and high eccentricity (e>0.66) of PZ Tel B. For e<0.9, the inclination,
longitude of the ascending node, and time of periastron passage are well
constrained. The system is seen close to an edge-on geometry. We reject other
brown dwarf candidates outside 0.25" for both systems, and massive giant
planets (>4 MJ) outside 0.5" for the PZ Tel system. We also show that K1-K2
color can be used with YJH low-resolution spectra to identify young L-type
companions, provided high photometric accuracy (<0.05 mag) is achieved.
Conclusions. SPHERE opens new horizons in the study of young brown dwarfs and
giant exoplanets thanks to high-contrast imaging capabilities at optical and
near-infrared wavelengths, as well as high signal-to-noise spectroscopy in the
near-infrared from low (R~30-50) to medium resolutions (R~350).Comment: 25 pages, 23 figures, accepted for publication in A&A on Oct. 13th,
2015; version including language editing. Typo on co-author name on astroph
page corrected, manuscript unchange
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