81 research outputs found
Distance and intersection number in the curve graph of a surface
In this work, we study the cellular decomposition of induced by a filling
pair of curves and , , and its connection
to the distance function in the curve graph of a closed orientable
surface of genus . Efficient geodesics were introduced by the first
author in joint work with Margalit and Menasco in 2016, giving an algorithm
that begins with a pair of non-separating filling curves that determine
vertices in the curve graph of a closed orientable surface and
computing from them a finite set of {\it efficient} geodesics. We extend the
tools of efficient geodesics to study the relationship between distance
, intersection number , and . The main result is
the development and analysis of particular configurations of rectangles in
called \textit{spirals}. We are able to show that, in some
special cases, the efficient geodesic algorithm can be used to build an
algorithm that reduces while preserving . At the end of the
paper, we note a connection of our work to the notion of extending geodesics.Comment: 20 pages, 17 figures. Changes: A key lemma (Lemma 5.6) was revised to
be more precise, an irrelevant proposition (Proposition 2.1) and example were
removed, unnecessary background material was taken out, some of the
definitions and cited results were clarified (including added figures,) and
Proposition 5.7 and Theorem 5.8 have been merged into a single theorem,
Theorem 4.
Regularized autoregressive model preserving spatial discontinuities for analysis of radio-frequency (RF) signals in echographic images
Cet article traite de l'estimation spectrale locale à partir de signaux radio-fréquence obtenus en imagerie médicale par échographie ultrasonore. Du fait de la nature particulière des signaux RF (signaux aléatoires fortement bruités et non-stationnaires et présence de plusieurs milieux tissulaires), l'objectif principal est de régulariser l'estimation paramétrique locale tout en préservant d'éventuelles discontinuités. Nous proposons un shéma de régularisation 2D basé sur les modèles autorégressifs, introduit dans un cadre Bayesien où l'a-priori de continuité spatiale est exprimé par l'intermédiaire des champs de Markov. L'utilisation de fonctions non quadratiques (phi-fonctions) dans le terme d'a-priori permet de preserver les discontinuités. Nous appliquons tout d'abord cette méthode sur des simulations où des discontinuités spectrales ont été générées par un décalage de la fréquence centrale entre 2 milieux. Nous montrons comment le shéma de régularisation permet d'améliorer considérablement l'estimation des coefficients AR. De plus, l'utilisation des Phi-fonctions s'avère très efficace pour préserver les discontinuités. Enfin, nous appliquons cette méthode sur des signaux radio-fréquence acquis à l'Université de Leuven avec un système développé pour l'acqisition de tels signaux et adapté à un échographe conventionnel. Ces résultats montrent l'intérêt de cette méthode pour l'étude de signaux réels acquis in-vivo sur des tissus biologiques en conditions cliniques
The secondary eclipses of WASP-19b as seen by the ASTEP 400 telescope from Antarctica
The ASTEP (Antarctica Search for Transiting ExoPlanets) program was
originally aimed at probing the quality of the Dome C, Antarctica for the
discovery and characterization of exoplanets by photometry. In the first year
of operation of the 40 cm ASTEP 400 telescope (austral winter 2010), we
targeted the known transiting planet WASP-19b in order to try to detect its
secondary transits in the visible. This is made possible by the excellent
sub-millimagnitude precision of the binned data. The WASP-19 system was
observed during 24 nights in May 2010. The photometric variability level due to
starspots is about 1.8% (peak-to-peak), in line with the SuperWASP data from
2007 (1.4%) and larger than in 2008 (0.07%). We find a rotation period of
WASP-19 of 10.7 +/- 0.5 days, in agreement with the SuperWASP determination of
10.5 +/- 0.2 days. Theoretical models show that this can only be explained if
tidal dissipation in the star is weak, i.e. the tidal dissipation factor Q'star
> 3.10^7. Separately, we find evidence for a secondary eclipse of depth 390 +/-
190 ppm with a 2.0 sigma significance, a phase consistent with a circular orbit
and a 3% false positive probability. Given the wavelength range of the
observations (420 to 950 nm), the secondary transit depth translates into a day
side brightness temperature of 2690(-220/+150) K, in line with measurements in
the z' and K bands. The day side emission observed in the visible could be due
either to thermal emission of an extremely hot day side with very little
redistribution of heat to the night side, or to direct reflection of stellar
light with a maximum geometrical albedo Ag=0.27 +/- 0.13. We also report a
low-frequency oscillation well in phase at the planet orbital period, but with
a lower-limit amplitude that could not be attributed to the planet phase alone,
and possibly contaminated with residual lightcurve trends.Comment: Accepted for publication in Astronomy and Astrophysics, 13 pages, 13
figure
Effective null Raychaudhuri equation
The effects on Raychaudhuri's equation of an intrinsically-discrete or
particle nature of spacetime are investigated. This is done through the
consideration of null congruences emerging from, or converging to, a generic
point of spacetime, i.e. in geometric circumstances somehow prototypical of
singularity issues. We do this from an effective point of view, that is through
a (continuous) description of spacetime modified to embody the existence of an
intrinsic discreteness on the small scale, this adding to previous results for
non-null congruences.
Various expressions for the effective rate of change of expansion are
derived. They in particular provide finite values for the limiting effective
expansion and its rate of variation when approaching the focal point. Further,
this results in a non-vanishing of the limiting cross-sectional area itself of
the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde
Direct constraint on the distance of y2 Velorum from AMBER/VLTI observations
In this work, we present the first AMBER observations, of the Wolf-Rayet and
O (WR+O) star binary system y2 Velorum. The AMBER instrument was used with the
telescopes UT2, UT3, and UT4 on baselines ranging from 46m to 85m. It delivered
spectrally dispersed visibilities, as well as differential and closure phases,
with a resolution R = 1500 in the spectral band 1.95-2.17 micron. We interpret
these data in the context of a binary system with unresolved components,
neglecting in a first approximation the wind-wind collision zone flux
contribution. We show that the AMBER observables result primarily from the
contribution of the individual components of the WR+O binary system. We discuss
several interpretations of the residuals, and speculate on the detection of an
additional continuum component, originating from the free-free emission
associated with the wind-wind collision zone (WWCZ), and contributing at most
to the observed K-band flux at the 5% level. The expected absolute separation
and position angle at the time of observations were 5.1±0.9mas and
66±15° respectively. However, we infer a separation of
3.62+0.11-0.30 mas and a position angle of 73+9-11°. Our analysis thus
implies that the binary system lies at a distance of 368+38-13 pc, in agreement
with recent spectrophotometric estimates, but significantly larger than the
Hipparcos value of 258+41-31 pc
Near-Infrared interferometry of Eta Carinae with high spatial and spectral resolution using the VLTI and the AMBER instrument
We present the first NIR spectro-interferometry of the LBV Eta Carinae. The K
band observations were performed with the AMBER instrument of the ESO Very
Large Telescope Interferometer using three 8.2m Unit Telescopes with baselines
from 42 to 89m. The aim of this work is to study the wavelength dependence of
Eta Car's optically thick wind region with a high spatial resolution of 5 mas
(11 AU) and high spectral resolution. The medium spectral resolution
observations (R=1,500) were performed in the wavelength range around both the
HeI 2.059 micron and the Br gamma 2.166 micron emission lines, the high
spectral resolution observations (R=12,000) only in the Br gamma line region.
In the K-band continuum, a diameter of 4.0 +/-0.2 mas (Gaussian FWHM, fit range
28-89m) was measured for Eta Car's optically thick wind region. If we fit
Hillier et al. (2001) model visibilities to the observed AMBER visibilities, we
obtain 50 % encircled-energy diameters of 4.2, 6.5 and 9.6mas in the 2.17
micron continuum, the HeI, and the Br gamma emission lines, respectively. In
the continuum near the Br gamma line, an elongation along a position angle of
120+/-15 degrees was found, consistent with previous VLTI/VINCI measurements by
van Boekel et al. (2003). We compare the measured visibilities with predictions
of the radiative transfer model of Hillier et al. (2001), finding good
agreement. Furthermore, we discuss the detectability of the hypothetical hot
binary companion. For the interpretation of the non-zero differential and
closure phases measured within the Br gamma line, we present a simple geometric
model of an inclined, latitude-dependent wind zone. Our observations support
theoretical models of anisotropic winds from fast-rotating, luminous hot stars
with enhanced high-velocity mass loss near the polar regions.Comment: 22 pages, 14 figures, 2 tables; A&A in pres
Constraining the wind launching region in Herbig Ae stars: AMBER/VLTI spectroscopy of HD 104237
This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.Aims. We investigate the origin of the Brγ emission of the Herbig Ae star HD 104237 on Astronomical Unit (AU) scales.
Methods. Using AMBER/VLTI at a spectral resolution R = 1500 we spatially resolve the emission in both the Brγ line and the adjacent continuum.
Results. The visibility does not vary between the continuum and the Brγ line, even though the line is strongly detected in the spectrum, with a peak
intensity 35% above the continuum. This demonstrates that the line and continuum emission have similar size scales. We assume that the K-band
continuum excess originates in a “puffed-up” inner rim of the circumstellar disk, and discuss the likely origin of Brγ.
Conclusions. We conclude that this emission most likely arises from a compact disk wind, launched from a region 0.2–0.5 AU from the star, with
a spatial extent similar to that of the near infrared continuum emission region, i.e., very close to the inner rim location.This work has been partly supported by the
MIUR COFIN grant 2003/027003-001 and 025227/2004 to the INAFOsservatorio
Astrofisico di Arcetri. This project has benefited from
funding from the French Centre National de la Recherche Scientifique
(CNRS) through the Institut National des Sciences de l’Univers
(INSU) and its Programmes Nationaux (ASHRA, PNPS). The authors
from the French laboratories would like to thank the successive
directors of the INSU/CNRS directors. C. Gil work was supported
in part by the Fundac¸˜ao para a Ciˆencia e a Tecnologia through
project POCTI/CTE-AST/55691/2004 from POCTI,with funds from
the European program FEDER
Interferometric data reduction with AMBER/VLTI. Principle, estimators, and illustration
This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.Aims. In this paper, we present an innovative data reduction method for single-mode interferometry. It has been specifically developed for the
AMBER instrument, the three-beam combiner of the Very Large Telescope Interferometer, but it can be derived for any single-mode interferometer.
Methods. The algorithm is based on a direct modelling of the fringes in the detector plane. As such, it requires a preliminary calibration of the
instrument in order to obtain the calibration matrix that builds the linear relationship between the interferogram and the interferometric observable,
which is the complex visibility. Once the calibration procedure has been performed, the signal processing appears to be a classical least-square
determination of a linear inverse problem. From the estimated complex visibility, we derive the squared visibility, the closure phase, and the
spectral differential phase.
Results. The data reduction procedures have been gathered into the so-called amdlib software, now available for the community, and are presented
in this paper. Furthermore, each step in this original algorithm is illustrated and discussed from various on-sky observations conducted with the
VLTI, with a focus on the control of the data quality and the effective execution of the data reduction procedures. We point out the present limited
performances of the instrument due to VLTI instrumental vibrations which are difficult to calibrate.The AMBER project4 was founded by the French Centre
National de la Recherche Scientifique (CNRS), the Max Planck Institute für
Radioastronomie (MPIfR) in Bonn, the Osservatorio Astrofisico di Arcetri
(OAA) in Firenze, the French Region “Provence Alpes Côte D’Azur” and
the European Southern Observatory (ESO). The CNRS funding has been
made through the Institut National des Sciences de l’Univers (INSU) and its
Programmes Nationaux (ASHRA, PNPS, PNP).
The OAA co-authors acknowledge partial support from MIUR grants to the
Arcetri Observatory: A LBT interferometric arm, and analysis of VLTI interferometric
data and From Stars to Planets: accretion, disk evolution and
planet formation and from INAF grants to the Arcetri Observatory Stellar and
Extragalactic Astrophysics with Optical Interferometry. C. Gil work was supported
in part by the Fundação para a Ciência e a Tecnologia through project
POCTI/CTE-AST/55691/2004 from POCTI, with funds from the European program
FEDER
Disk and wind interaction in the young stellar object MWC 297 spatially resolved with AMBER/VLTI
This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.The young stellar object MWC 297 is an embedded B1.5Ve star exhibiting strong hydrogen emission lines and a strong near-infrared continuum
excess. This object has been observed with the VLT interferometer equipped with the AMBER instrument during its first commissioning run.
AMBER/VLTI is currently the only near infrared interferometer that can observe spectrally dispersed visibilities. MWC 297 has been spatially
resolved in the continuum with a visibility of 0.50+0.08
−0.10 as well as in the Brγ emission line where the visibility decreases to 0.33±0.06. This change
in the visibility with wavelength can be interpreted by the presence of an optically thick disk responsible for the visibility in the continuum and
of a stellar wind traced by the Brγ emission line and whose apparent size is 40% larger. We validate this interpretation by building a model of the
stellar environment that combines a geometrically thin, optically thick accretion disk model consisting of gas and dust, and a latitude-dependent
stellar wind outflowing above the disk surface. The continuum emission and visibilities obtained from this model are fully consistent with the
interferometric AMBER data. They agree also with existing optical, near-infrared spectra and other broad-band near-infrared interferometric
visibilities. We also reproduce the shape of the visibilities in the Brγ line as well as the profile of this line obtained at an higher spectral resolution
with the VLT/ISAAC spectrograph, and those of the Hα and Hβ lines. The disk and wind models yield a consistent inclination of the system of
approximately 20◦. A picture emerges in which MWC 297 is surrounded by an equatorial flat disk that is possibly still accreting and an outflowing
wind that has a much higher velocity in the polar region than at the equator. The AMBER/VLTI unique capability of measuring spectral visibilities
therefore allows us for the first time to compare the apparent geometry of a wind with the disk structure in a young stellar system.The AMBER project4 was founded by the French Centre National de la
Recherche Scientifique (CNRS), the Max Planck Institute für Radioastronomie
(MPIfR) in Bonn, the Osservatorio Astrofisico di Arcetri (OAA) in Firenze,
the French Region "Provence Alpes Côte D’Azur" and the European Southern
Observatory (ESO). The CNRS funding has been made through the Institut
National des Sciences de l’Univers (INSU) and its Programmes Nationaux
(ASHRA, PNPS, PNP).
The OAA co-authors acknowledge partial support from MIUR grants to
the Arcetri Observatory: A LBT interferometric arm, and analysis of VLTI interferometric
data and From Stars to Planets: accretion, disk evolution and
planet formation and from INAF grants to the Arcetri Observatory Stellar and
Extragalactic Astrophysics with Optical Interferometry. C. Gil work was supported
in part by the Fundação para a Ciência e a Tecnologia through project
POCTI/CTE-AST/55691/2004 from POCTI, with funds from the European program
FEDER
Constraining the wind launching region in Herbig Ae stars: AMBER/VLTI spectroscopy of HD 104237
Astronomy and Astrophysics, 464, pp. 55-58, http://dx.doi.org./10.1051/0004-6361:20065719International audienc
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