On adaptive wavelet estimation of a class of weighted densities

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples, including those arising in order statistics or when $g$ is related to the maximum or the minimum of $N$ (random or fixed) independent and identically distributed (\iid) random variables. We here construct a new adaptive non-parametric estimator for $g$ based on a plug-in approach and the wavelets methodology. For a wide class of models, we prove that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with $p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared error) over Besov balls. The theoretical findings are illustrated through several simulations

VLTI/MIDI observations of 7 classical Be stars

We measured the mid-infrared extension of the gaseous disk surrounding seven Be stars in order to constrain the geometry of their circumstellar environments and to try to infer physical parameters characterizing these disks. We used the VLTI/MIDI instrument with baselines up to 130 m to obtain an angular resolution of about 15 mas in the N band and compared our results with previous K band measurements obtained with the VLTI/AMBER instrument and/or the CHARA interferometer. We obtained one calibrated visibility measurement for each of the four stars, p Car, zeta Tau, kappa CMa, and alpha Col, two for delta Cen and beta CMi, and three for alpha Ara. Almost all targets remain unresolved even with the largest VLTI baseline of 130m, evidence that their circumstellar disk extension is less than 10 mas. The only exception is alpha Ara, which is clearly resolved and well-fitted by an elliptical envelope with a major axis a=5.8+-0.8mas and an axis ratio a/b=2.4+-1 at 8 microns. This extension is similar to the size and flattening measured with the VLTI/AMBER instrument in the K band at 2 microns. The size of the circumstellar envelopes for these classical Be stars does not seem to vary strongly on the observed wavelength between 8 and 12microns. Moreover, the size and shape of Alpha Ara's disk is almost identical at 2, 8, and 12microns

A snapshot of the inner dusty regions of a RCrB-type variable

R Coronae Borealis variable stars are suspected to sporadically eject optically thick dust clouds causing, when one of them lies on the line-of-sight, a huge brightness decline in visible light. Mid-infrared interferometric observations of RYSgr allowed us to explore the circumstellar regions very close to the central star (~20-40 mas) in order to look for the signature of any heterogeneities. Using the VLTI/MIDI instrument, five dispersed visibility curves were recorded with different projected baselines oriented towards two roughly perpendicular directions. The large spatial frequencies visibility curves exhibit a sinusoidal shape whereas, at shorter spatial frequencies visibility curves follow a Gaussian decrease. These observations are well interpreted with a geometrical model consisting in a central star surrounded by an extended circumstellar envelope in which one bright cloud is embedded. Within this simple geometrical scheme, the inner 110AU dusty environment of RYSgr is dominated at the time of observations by a single dusty cloud which, at 10mic represents ~10% of the total flux of the whole system. The cloud is located at about 100stellar radii from the centre toward the East-North-East direction (or the symmetric direction with respect to centre) within a circumstellar envelope which FWHM is about 120stellar radii. This first detection of a cloud so close to the central star, supports the classical scenario of the RCrB brightness variations in the optical spectral domain

Adaptive optics imaging of P Cygni in Halpha

We obtained Halpha diffraction limited data of the LBV star P Cyg using the ONERA Adaptive Optics (AO) facility BOA at the OHP 1.52m telescope on October 1997. Taking P Cyg and the reference star 59 Cyg AO long exposures we find that P Cyg clearly exhibits a large and diffuse intensity distribution compared to the 59 Cyg's point-like source. A deconvolution of P Cyg using 59 Cyg as the Point Spread Function was performed by means of the Richardson-Lucy algorithm. P Cyg clearly appears as an unresolved star surrounded by a clumped envelope. The reconstructed image of P Cyg is compared to similar spatial resolution maps obtained from radio aperture synthesis imaging. We put independent constraints on the physics of P Cyg which agree well with radio results. We discuss future possibilities to constrain the wind structure of P Cyg by using multi-resolution imaging, coronagraphy and long baseline interferometry to trace back its evolutionary status.Comment: 10 pages, 19 Encapsulated Postscript figure

The variable stellar wind of Rigel probed at high spatial and spectral resolution

We present a spatially resolved, high-spectral resolution (R=12000) K-band temporal monitoring of Rigel using AMBER at the VLTI. Rigel was observed in the Bracket Gamma line and its nearby continuum in 2006-2007, and 2009-2010. These unprecedented observations were complemented by contemporaneous optical high-resolution spectroscopy. We analyse the near-IR spectra and visibilities with the 1D non-LTE radiative-transfer code CMFGEN. The differential and closure phase signal exhibit asymmetries that are interpreted as perturbations of the wind. A systematic visibility decrease is observed across the Bracket Gamma. During the 2006-2007 period the Bracket Gamma and likely the continuum forming regions were larger than in the 2009-2010 epoch. Using CMFGEN, we infer a mass-loss rate change of about 20% between the two epochs. We further find time variations in the differential visibilities and phases. The 2006-2007 period is characterized by noticeable variations of the differential visibilities in Doppler position and width and by weak variations in differential and closure phase. The 2009-2010 period is much more quiet with virtually no detectable variations in the dispersed visibilities but a strong S-shape signal is observed in differential phase coinciding with a strong ejection event discernible in the optical spectra. The differential phase signal that is sometimes detected is reminiscent of the signal computed from hydrodynamical models of corotating interaction regions. For some epochs the temporal evolution of the signal suggests the rotation of the circumstellar structures.Comment: Paper accepted in the A&A journa

A dense disk of dust around the born-again Sakurai's object

In 1996, Sakurai's object (V4334 Sgr) suddenly brightened in the centre of a faint Planetary Nebula (PN). This very rare event was interpreted as the reignition of a hot white dwarf that caused a rapid evolution back to the cool giant phase. From 1998 on, a copious amount of dust has formed continuously, screening out the star which has remained embedded in this expanding high optical depth envelope. The new observations, reported here, are used to study the morphology of the circumstellar dust in order to investigate the hypothesis that Sakurai's Object is surrounded by a thick spherical envelope of dust. We have obtained unprecedented, high-angular resolution spectro-interferometric observations, taken with the mid-IR interferometer MIDI/VLTI, which resolve the dust envelope of Sakurai's object. We report the discovery of a unexpectedly compact (30 x 40 milliarcsec, 105 x 140 AU assuming a distance of 3.5 kpc), highly inclined, dust disk. We used Monte Carlo radiative-transfer simulations of a stratified disk to constrain its geometric and physical parameters, although such a model is only a rough approximation of the rapidly evolving dust structure. Even though the fits are not fully satisfactory, some useful and robust constraints can be inferred. The disk inclination is estimated to be 75+/-3 degree with a large scale height of 47+/-7 AU. The dust mass of the disk is estimated to be 6 10^{-5} solar mass. The major axis of the disk (132+/-3 degree) is aligned with an asymmetry seen in the old PN that was re-investigated as part of this study. This implies that the mechanism responsible for shaping the dust envelope surrounding Sakurai's object was already at work when the old PN formed.Comment: A&A Letter, accepte

A close look into the carbon disk at the core of the planetary nebula CPD-568032

We present high spatial resolution observations of the dusty core of the Planetary Nebula with Wolf-Rayet central star CPD-568032. These observations were taken with the mid-infrared interferometer VLTI/MIDI in imaging mode providing a typical 300 mas resolution and in interferometric mode using UT2-UT3 47m baseline providing a typical spatial resolution of 20 mas. The visible HST images exhibit a complex multilobal geometry dominated by faint lobes. The farthest structures are located at 7" from the star. The mid-IR environment of CPD-568032 is dominated by a compact source, barely resolved by a single UT telescope in a 8.7 micron filter. The infrared core is almost fully resolved with the three 40-45m projected baselines ranging from -5 to 51 degree but smooth oscillating fringes at low level have been detected in spectrally dispersed visibilities. This clear signal is interpreted in terms of a ring structure which would define the bright inner rim of the equatorial disk. Geometric models allowed us to derive the main geometrical parameters of the disk. For instance, a reasonably good fit is reached with an achromatic and elliptical truncated Gaussian with a radius of 97+/-11 AU, an inclination of 28+/-7 degree and a PA for the major axis at 345+/-7 degree. Furthermore, we performed some radiative transfer modeling aimed at further constraining the geometry and mass content of the disk, by taking into account the MIDI dispersed visibilities, spectra, and the large aperture SED of the source. These models show that the disk is mostly optically thin in the N band and highly flared.Comment: Paper accepted in A&

The expanding dusty bipolar nebula around the nova V1280 Sco

V1280 Sco is one of the slowest dust-forming nova ever historically observed. We performed multi-epoch high-spatial resolution observations of the circumstellar dusty environment of V1280 Sco to investigate the level of asymmetry of the ejecta We observed V1280 Sco in 2009, 2010 and 2011 using unprecedented high angular resolution techniques. We used the NACO/VLT adaptive optics system in the J, H and K bands, together with contemporaneous VISIR/VLT mid-IR imaging that resolved the dust envelope of V1280 Sco, and SINFONI/VLT observations secured in 2011. We report the discovery of a dusty hourglass-shaped bipolar nebula. The apparent size of the nebula increased from 0.30" x 0.17" in July 2009 to 0.64" x 0.42" in July 2011. The aspect ratio suggests that the source is seen at high inclination. The central source shines efficiently in the K band and represents more than 56+/-5% of the total flux in 2009, and 87+/-6% in 2011. A mean expansion rate of 0.39+/-0.03 mas per day is inferred from the VISIR observations in the direction of the major axis, which represents a projected upper limit. Assuming that the dust shell expands in that direction as fast as the low-excitation slow ejecta detected in spectroscopy, this yields a lower limit distance to V1280 Sco of 1kpc; however, the systematic errors remain large due to the complex shape and velocity field of the dusty ejecta. The dust seems to reside essentially in the polar caps and no infrared flux is detected in the equatorial regions in the latest dataset. This may imply that the mass-loss was dominantly polar

An interferometric study of the post-AGB binary 89 Herculis I Spatially resolving the continuum circumstellar environment at optical and near-IR wavelengths with the VLTI, NPOI, IOTA, PTI, and the CHARA Array

Binary post-AGB stars are interesting laboratories to study both the evolution of binaries as well as the structure of circumstellar disks. A multiwavelength high angular resolution study of the prototypical object 89 Herculis is performed with the aim of identifying and locating the different emission components seen in the SED. A large interferometric data set, collected over the past decade and covering optical and near-IR wavelengths, is analyzed with simple geometric models. Combining the interferometric constraints with the photometry and the optical spectra, we reassess the energy budget of the post-AGB star and its circumstellar environment. We report the first (direct) detection of a large (35-40%) optical circumstellar flux contribution and spatially resolve its emission region. Given this large amount of reprocessed and/or redistributed optical light, the fitted size of the emission region is rather compact and fits with(in) the inner rim of the circumbinary dust disk. This rim dominates our K band data through thermal emission and is rather compact, emitting significantly already at a radius of twice the orbital separation. We interpret the circumstellar optical flux as due to a scattering process, with the scatterers located in the extremely puffed-up inner rim of the disk and possibly also in a bipolar outflow seen pole-on. A non-LTE gaseous origin in an inner disk cannot be excluded but is considered highly unlikely. This direct detection of a significant amount of circumbinary light at optical wavelengths poses several significant questions regarding our understanding of both post-AGB binaries and the physics in their circumbinary disks. Although the identification of the source of emission/scattering remains inconclusive without further study on this and similar objects, the implications are manifold.Comment: Accepted for publication in A&A, 16 pages, 15 figure

GI2T/REGAIN spectro-interferometry with a new infrared beam combiner

We have built an infrared beam combiner for the GI2T/REGAIN interferometer of the Observatoire de la Cote d'Azur. The beam combiner allows us to record spectrally dispersed Michelson interference fringes in the near-infrared J-, H- or K-bands. The beam combiner has the advantage that Michelson interferograms can simultaneously be recorded in about 128 different spectral channels. The tilt of the spectrally dispersed fringes is a measure of the instantaneous optical path difference. We present the optical design of the beam combiner and GI2T/REGAIN observations of the Mira star R Cas with this beam combiner in the spectral range of 2.00 micron - 2.18 micron (observations on 22 and 25 August 1999; variability phase 0.08; V-magnitude approx. 6; seven baselines between 12m and 24m; reference stars Vega and Beta Peg). The spectrograph of the beam combiner consists of an anamorphotic cylindrical lens system, an image plane slit, and a grism. A system of digital signal processors calculates the ensemble average power spectrum of the spectrally dispersed Michelson interferograms and the instantaneous optical path difference error in real time. From the observed R Cas visibilities at baselines 12.0m, 13.8m and 13.9m, a 2.1 micron uniform-disk diameter of 25.3mas +/-3.3mas was derived. The unusually high visibility values at baselines >16m show that the stellar surface of R Cas is more complex than previously assumed. The visibility values at baselines >16m can be explained by high-contrast surface structure on the stellar surface of R Cas or other types of unexpected center-to-limb variations. The R Cas observations were compared with theoretical Mira star models yielding a linear Rosseland radius of 276Rsun +/-66Rsun and an effective temperature of 2685K+/-238K for R Cas at phase 0.08.Comment: 10 pages, 6 figures, see also http://www.mpifr-bonn.mpg.de/div/speckle, SPIE conf 4006 "Interferometry in Optical Astronomy", in pres