Non parametric reconstruction of distribution functions from observed galactic disks

A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields the unique distribution compatible with all the observables available. The derivation may be carried out from the measurement of the azimuthal velocity distribution arising from positioning the slit of a spectrograph along the major axis of the galaxy. More generally, it may account for the simultaneous measurements of velocity distributions corresponding to slits presenting arbitrary orientations with respect to the major axis. The approach is non-parametric, i.e. it does not rely on a particular algebraic model for the distribution function. Special care is taken to account for the fraction of counter-rotating stars which strongly affects the stability of the disk. An optimisation algorithm is devised -- generalising the work of Skilling & Bryan (1984) -- to carry this truly two-dimensional ill-conditioned inversion efficiently. The performances of the overall inversion technique with respect to the noise level and truncation in the data set is investigated with simulated data. Reliable results are obtained up to a mean signal to noise ratio of~5 and when measurements are available up to $4 R_{e}$. A discussion of the residual biases involved in non parametric inversions is presented. Prospects of application to observed galaxies and other inversion problems are discussed.Comment: 11 pages, 13 figures; accepted for publication by MNRA

A certification method for the milling process of free-form surfaces using a test part

International audienceIt is generally admitted that the manufacturing of free-form surfaces requires the use of a CAD-CAM system. The toolpath accuracy and the dimensional quality of the final shape have to be in accordance with the geometrical specifications. But most of the time, the final parts present deviations from the expected shape. These deviations may be due to either the toolpath calculation (CAM system) or the cutting process itself. In the paper, we propose an analysis of the whole milling process to point out the possible sources of errors. These errors generally lead to geometrical deviations and the final part does not meet the required specifications. As the errors can be linked to geometrical particularities of the shape, we propose a test part associated with check means to bring out problems. The milling of this part using two different techniques of toolpath generation shows that obviously both toolpaths are not error-free and that errors result from different geometrical particularities of the part surfaces

Dynamical Masses of Young Stars in Multiple Systems

We present recent measurements of the orbital motion in the young binaries DF Tau and ZZ Tau, and the hierarchical triple Elias 12, that were obtained with the Fine Guidance Sensors on the HST and at the Keck Observatory using adaptive optics. Combining these observations with previous measurements from the literature, we compute preliminary orbital parameters for DF Tau and ZZ Tau. We find that the orbital elements cannot yet be determined precisely because the orbital coverage spans only about 90 degr in position angle. Nonetheless, the range of possible values for the period and semi-major axis already defines a useful estimate for the total mass in DF Tau and ZZ Tau, with values of 0.90{+0.85}{-0.35} M_sun and 0.81{+0.44}{-0.25} M_sun, respectively, at a fiducial distance of 140 pc.Comment: 26 pages, 9 figures, accepted for publication in A

A Test of Pre-Main Sequence Evolutionary Models Across the Stellar/Substellar Boundary Based on Spectra of the Young Quadruple GG Tau

We present spatially separated optical spectra of the components of the young hierarchical quadruple GG Tau. Spectra of GG Tau Aa and Ab (separation 0".25 ~ 35 AU) were obtained with the Faint Object Spectrograph aboard the Hubble Space Telescope. Spectra of GG Tau Ba and Bb (separation 1".48 ~ 207 AU) were obtained with both the HIRES and the LRIS spectrographs on the W. M. Keck telescopes. The components of this mini-cluster, which span a wide range in spectral type (K7 - M7), are used to test both evolutionary models and the temperature scale for very young, low mass stars under the assumption of coeval formation. Of the evolutionary models tested, those of Baraffe et al. (1998, A&A, 337, 403) yield the most consistent ages when combined with a temperature scale intermediate between that of dwarfs and giants. The version of the Baraffe et al. models computed with a mixing length nearly twice the pressure scale height is of particular interest as it predicts masses for GG Tau Aa and Ab that are in agreement with their dynamical mass estimate. Using this evolutionary model and a coeval (at 1.5 Myrs) temperature scale, we find that the coldest component of the GG Tau system, GG Tau Bb, is substellar with a mass of 0.044 +/- 0.006 Msun. This brown dwarf companion is especially intriguing as it shows signatures of accretion, although this accretion is not likely to alter its mass significantly. GG Tau Bb is currently the lowest mass, spectroscopically confirmed companion to a T Tauri star, and is one of the coldest, lowest mass T Tauri objects in the Taurus-Auriga star forming region.Comment: 25 pages, 6 figures, accepted for publication in The Astrophysical Journa

Imaging the spotty surface of Betelgeuse in the H band

This paper reports on H-band interferometric observations of Betelgeuse made at the three-telescope interferometer IOTA. We image Betelgeuse and its asymmetries to understand the spatial variation of the photosphere, including its diameter, limb darkening, effective temperature, surrounding brightness, and bright (or dark) star spots. We used different theoretical simulations of the photosphere and dusty environment to model the visibility data. We made images with parametric modeling and two image reconstruction algorithms: MIRA and WISARD. We measure an average limb-darkened diameter of 44.28 +/- 0.15 mas with linear and quadratic models and a Rosseland diameter of 45.03 +/- 0.12 mas with a MARCS model. These measurements lead us to derive an updated effective temperature of 3600 +/- 66 K. We detect a fully-resolved environment to which the silicate dust shell is likely to contribute. By using two imaging reconstruction algorithms, we unveiled two bright spots on the surface of Betelgeuse. One spot has a diameter of about 11 mas and accounts for about 8.5% of the total flux. The second one is unresolved (diameter < 9 mas) with 4.5% of the total flux. Resolved images of Betelgeuse in the H band are asymmetric at the level of a few percent. The MOLsphere is not detected in this wavelength range. The amount of measured limb-darkening is in good agreement with model predictions. The two spots imaged at the surface of the star are potential signatures of convective cells.Comment: 10 pages, 10 figures, accepted for publication in A&A, references adde

VSI: the VLTI spectro-imager

The VLTI Spectro Imager (VSI) was proposed as a second-generation instrument of the Very Large Telescope Interferometer providing the ESO community with spectrally-resolved, near-infrared images at angular resolutions down to 1.1 milliarcsecond and spectral resolutions up to R=12000. Targets as faint as K=13 will be imaged without requiring a brighter nearby reference object. The unique combination of high-dynamic-range imaging at high angular resolution and high spectral resolution enables a scientific program which serves a broad user community and at the same time provides the opportunity for breakthroughs in many areas of astrophysic including: probing the initial conditions for planet formation in the AU-scale environments of young stars; imaging convective cells and other phenomena on the surfaces of stars; mapping the chemical and physical environments of evolved stars, stellar remnants, and stellar winds; and disentangling the central regions of active galactic nuclei and supermassive black holes. VSI will provide these new capabilities using technologies which have been extensively tested in the past and VSI requires little in terms of new infrastructure on the VLTI. At the same time, VSI will be able to make maximum use of new infrastructure as it becomes available; for example, by combining 4, 6 and eventually 8 telescopes, enabling rapid imaging through the measurement of up to 28 visibilities in every wavelength channel within a few minutes. The current studies are focused on a 4-telescope version with an upgrade to a 6-telescope one. The instrument contains its own fringe tracker and tip-tilt control in order to reduce the constraints on the VLTI infrastructure and maximize the scientific return.Comment: 12 pages, to be published in Proc. SPIE conference 7013 "Optical and Infrared Interferometry", Schoeller, Danchi, and Delplancke, F. (eds.). See also http://vsi.obs.ujf-grenoble.f

Phase Referencing in Optical Interferometry

One of the aims of next generation optical interferometric instrumentation is to be able to make use of information contained in the visibility phase to construct high dynamic range images. Radio and optical interferometry are at the two extremes of phase corruption by the atmosphere. While in radio it is possible to obtain calibrated phases for the science objects, in the optical this is currently not possible. Instead, optical interferometry has relied on closure phase techniques to produce images. Such techniques allow only to achieve modest dynamic ranges. However, with high contrast objects, for faint targets or when structure detail is needed, phase referencing techniques as used in radio interferometry, should theoretically achieve higher dynamic ranges for the same number of telescopes. Our approach is not to provide evidence either for or against the hypothesis that phase referenced imaging gives better dynamic range than closure phase imaging. Instead we wish to explore the potential of this technique for future optical interferometry and also because image reconstruction in the optical using phase referencing techniques has only been performed with limited success. We have generated simulated, noisy, complex visibility data, analogous to the signal produced in radio interferometers, using the VLTI as a template. We proceeded with image reconstruction using the radio image reconstruction algorithms contained in AIPS IMAGR (CLEAN algorithm). Our results show that image reconstruction is successful in most of our science cases, yielding images with a 4 milliarcsecond resolution in K band. (abridged)Comment: 11 pages, 36 figure

Observations of T-Tauri Stars using HST-GHRS: I. Far Ultraviolet Emission Lines

We have analyzed GHRS data of eight CTTS and one WTTS. The GHRS data consists of spectral ranges 40 A wide centered on 1345, 1400, 1497, 1550, and 1900 A. These UV spectra show strong SiIV, and CIV emission, and large quantities of sharp (~40 km/s) H2 lines. All the H2 lines belong to the Lyman band and all the observed lines are single peaked and optically thin. The averages of all the H2 lines centroids for each star are negative which may indicate that they come from an outflow. We interpret the emission in H2 as being due to fluorescence, mostly by Ly_alpha, and identify seven excitation routes within 4 A of that line. We obtain column densities (10^12 to 10^15 cm^-2) and optical depths (~1 or less) for each exciting transition. We conclude that the populations are far from being in thermal equilibrium. We do not observe any lines excited from the far blue wing of Ly_alpha, which implies that the molecular features are excited by an absorbed profile. SiIV and CIV (corrected for H2 emission) have widths of ~200 km/s, and an array of centroids (blueshifted lines, centered, redshifted). These characteristics are difficult to understand in the context of current models of the accretion shock. For DR Tau we observe transient strong blueshifted emission, perhaps the a result of reconnection events in the magnetosphere. We also see evidence of multiple emission regions for the hot lines. While CIV is optically thin in most stars in our sample, SiIV is not. However, CIV is a good predictor of SiIV and H2 emission. We conclude that most of the flux in the hot lines may be due to accretion processes, but the line profiles can have multiple and variable components.Comment: 67 pages, 19 figures, Accepted in Ap

The Schro¨\ddot{o}dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.Comment: Accepted for publication in the Euro. Phys. J.