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

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&

Learning CHARME models with neural networks

In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. Under certain Lipschitz-type conditions on the autoregressive and volatility functions, we prove that this model is stationary, ergodic and $\tau$-weakly dependent. These conditions are much weaker than those presented in the literature that treats this model. Moreover, this result forms the theoretical basis for deriving an asymptotic theory of the underlying (non)parametric estimation, which we present for this model. As an application, from the universal approximation property of neural networks (NN), we develop a learning theory for the NN-based autoregressive functions of the model, where the strong consistency and asymptotic normality of the considered estimator of the NN weights and biases are guaranteed under weak conditions.Comment: 31 pages, 4 figure

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

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

AMBER on the VLTI: data processing and calibration issues

We present here the current performances of the AMBER / VLTI instrument for standard use and compare these with the offered modes of the instrument. We show that the instrument is able to reach its specified precision only for medium and high spectral resolution modes, differential observables and bright objects. For absolute observables, the current achievable accuracy is strongly limited by the vibrations of the Unit Telescopes, and also by the observing procedure which does not take into account the night-long transfer function monitoring. For low-resolution mode, the current limitation is more in the data reduction side, since several effects negligible at medium spectral resolution are not taken into account in the current pipeline. Finally, for faint objects (SNR around 1 per spectral channel), electromagnetic interferences in the VLTI interferometric laboratory with the detector electronics prevents currently to get unbiased measurements. Ideas are under study to correct in the data processing side this effect, but a hardware fix should be investigated seriously since it limits seriously the effective limiting magnitude of the instrument.Comment: 10 page

The 2008 outburst in the young stellar system ZCMa: I. Evidence of an enhanced bipolar wind on the AU-scale

Accretion is a fundamental process in star formation. Although the time evolution of accretion remains a matter of debate, observations and modelling studies suggest that episodic outbursts of strong accretion may dominate the formation of the protostar. Observing young stellar objects during these elevated accretion states is crucial to understanding the origin of unsteady accretion. ZCMa is a pre-main-sequence binary system composed of an embedded Herbig Be star, undergoing photometric outbursts, and a FU Orionis star. The Herbig Be component recently underwent its largest optical photometric outburst detected so far. We aim to constrain the origin of this outburst by studying the emission region of the HI Brackett gamma line, a powerful tracer of accretion/ejection processes on the AU-scale in young stars. Using the AMBER/VLTI instrument at spectral resolutions of 1500 and 12 000, we performed spatially and spectrally resolved interferometric observations of the hot gas emitting across the Brackett gamma emission line, during and after the outburst. From the visibilities and differential phases, we derive characteristic sizes for the Brackett gamma emission and spectro-astrometric measurements across the line, with respect to the continuum. We find that the line profile, the astrometric signal, and the visibilities are inconsistent with the signature of either a Keplerian disk or infall of matter. They are, instead, evidence of a bipolar wind, maybe partly seen through a disk hole inside the dust sublimation radius. The disappearance of the Brackett gamma emission line after the outburst suggests that the outburst is related to a period of strong mass loss rather than a change of the extinction along the line of sight. Based on these conclusions, we speculate that the origin of the outburst is an event of enhanced mass accretion, similar to those occuring in EX Ors and FU Ors.Comment: Accepted for publication in Astronomy and Astrophysics Letter

VLTI observations of the dust geometry around R Coronae Borealis stars

We are investigating the formation and evolution of dust around the hydrogen-deficient supergiants known as R Coronae Borealis (RCB) stars. We aim to determine the connection between the probable merger past of these stars and their current dust-production activities. We carried out high-angular resolution interferometric observations of three RCB stars, namely RY Sgr, V CrA, and V854 Cen with the mid-IR interferometer, MIDI on the VLTI, using two telescope pairs. The baselines ranged from 30 to 60 m, allowing us to probe the dusty environment at very small spatial scales (~ 50 mas or 400 stellar radii). The observations of the RCB star dust environments were interpreted using both geometrical models and one-dimensional radiative transfer codes. From our analysis we find that asymmetric circumstellar material is apparent in RY Sgr, may also exist in V CrA, and is possible for V854 Cen. Overall, we find that our observations are consistent with dust forming in clumps ejected randomly around the RCB star so that over time they create a spherically symmetric distribution of dust. However, we conclude that the determination of whether there is a preferred plane of dust ejection must wait until a time series of observations are obtained.Comment: Accepted for publication in MNRAS; 14 pages, 10 figures, 6 table

The Expanding Fireball of Nova Delphini 2013

A classical nova occurs when material accreting onto the surface of a white dwarf in a close binary system ignites in a thermonuclear runaway. Complex structures observed in the ejecta at late stages could result from interactions with the companion during the common envelope phase. Alternatively, the explosion could be intrinsically bipolar, resulting from a localized ignition on the surface of the white dwarf or as a consequence of rotational distortion. Studying the structure of novae during the earliest phases is challenging because of the high spatial resolution needed to measure their small sizes. Here we report near-infrared interferometric measurements of the angular size of Nova Delphini 2013, starting from one day after the explosion and continuing with extensive time coverage during the first 43 days. Changes in the apparent expansion rate can be explained by an explosion model consisting of an optically thick core surrounded by a diffuse envelope. The optical depth of the ejected material changes as it expands. We detect an ellipticity in the light distribution, suggesting a prolate or bipolar structure that develops as early as the second day. Combining the angular expansion rate with radial velocity measurements, we derive a geometric distance to the nova of 4.54 +/- 0.59 kpc from the Sun.Comment: Published in Nature. 32 pages. Final version available at http://www.nature.com/nature/journal/v515/n7526/full/nature13834.htm

Improving the surface brightness-color relation for early-type stars using optical interferometry

The aim of this work is to improve the SBC relation for early-type stars in the $-1 \leq V-K \leq 0$ color domain, using optical interferometry. Observations of eight B- and A-type stars were secured with the VEGA/CHARA instrument in the visible. The derived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V-K color index ranging from -1 to 0. We also took the opportunity to check the consistency of the SBC relation up to $V-K \simeq 4$ using 100 additional measurements. We determined the uniform disk angular diameter for the eight following stars: $\gamma$ Ori, $\zeta$ Per, $8$ Cyg, $\iota$ Her, $\lambda$ Aql, $\zeta$ Peg, $\gamma$ Lyr, and $\delta$ Cyg with V-K color ranging from -0.70 to 0.02 and typical precision of about $1.5\%$. Using our total sample of 132 stars with $V-K$ colors index ranging from about $-1$ to $4$, we provide a revised SBC relation. For late-type stars ($0 \leq V-K \leq 4$), the results are consistent with previous studies. For early-type stars ($-1 \leq V-K \leq 0$), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or $\simeq 7\%$ in terms of angular diameter.Comment: 13 pages, 5 figures, accepted for publication in A&