Exploring the water and carbon monoxide shell around Betelgeuse with VLTI/AMBER
Abstract
We present the results of the analysis of our recent interferometric observations of Betelgeuse, using the AMBER instrument of the VLTI. Using the medium spectral resolution mode () we detected the presence of the water vapour and carbon monoxide (CO) molecules in the H and K bands. We also derived the photospheric angular diameter in the continuum. By analysing the depth of the molecular lines and the interferometric visibilities, we derived the column densities of the molecules, as well as the temperature and the size of the corresponding regions in the atmosphere of Betelgeuse (the MOLsphere) using a single shell model around the photosphere. Our results confirm the findings by Perrin et al. ([2004]) and Ohnaka et al. ([2011]) that the HO and CO molecules are distributed around Betelgeuse in a MOLsphere extending to approximately 1.3 times the star’s photospheric radius.
Exploring the water and carbon monoxide shell around Betelgeuse with VLTI/AMBER^{0}^{0}footnotetext: Based on AMBER observations made with ESO Telescopes at the Paranal Observatory under programmes ID 086.D0351 and 286.D5036

and ^{1}^{1}1 LESIA, Observatoire de Paris, CNRS, UPMC, Université ParisDiderot, 5 place Jules Janssen, 92195 Meudon, France MaxPlanckInstitut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
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1 Introduction
Betelgeuse was observed in January and February 2011 with the ESO Very Large Telescope Interferometer (VLTI) using the Astronomical MultiBEam combineR, AMBER (the instrument is described in Petrov et al. [2007]) in the band from 1.45 to 1.80 m and in the band from 2.10 to 2.45 m with the E0G0H0, E0G0I1 and G0H0I1 triplets. The CO and water vapor absorption lines in the band were investigated using the medium spectral resolution of the instrument ().
2 Data reduction
The AMBER data reduction package version 3.0.3 also known as amdlib was used to obtain the calibrated interferometric observables (Tatulli et al. [2007]) : the three visibilities associated to the three baselines are directly the amplitude of the object’s Fourier Transform. It is not possible to measure directly the phase but the calibrated data contain three differential phases (DP) which are sensitive to the photocenter shift in a spectral line with respect to the continuum. The closure phase (CP) is the sum of three phases along the three baselines that form a triangle : . This quantity is independent from the atmospheric perturbations.
The wavelength calibration was performed using telluric lines in the spectrum of the interferometric calibrator HR1543 (spectral type F6V). The error bars in the visibilities and closure phases of Betelgeuse were underestimated, probably due to the low visibility of the fringes. We had to split each data file into five subsets to get a new estimation of these errors. We also noticed that some datasets were showing unusually low visibilities : we conclude it was caused by lock loss of the fringe tracker FINITO. These corrupted data sets were discarded.
3 Results
3.1 Continuum analysis
We used two different models to fit the continuum visibilities between 2.1 and 2.245 m : a uniform disk (UD) and a limbdarkened disk (LDD) using a power law () according to Hestroffer ([1997]). We only fitted the data from the first and second lobes in order to avoid contributions from small scale structures at higher spatial frequencies. We used 8752 visibility points over 31 577, from which we derived an angular diameter of for the uniform disk model giving a reduced of 5.27. For the limbdarkened model we obtained an angular diameter of and a power law coefficient of with a reduced of 4.91. The result of these fits is presented in Fig. 1 together with the coverage in the first and second lobes. Our value of the angular diameter may not be representative of the average angular diameter of the star as we are only probing one direction of the plane.
Our UD value is significantly lower than the previous ones found by Perrin et al. ([2004]) of mas and Ohnaka et al. ([2009] and [2011]) of which was obtained for this later with VLTI/AMBER observations in the same direction. This could be caused by the relative decrease of the diameter shown in Ohnaka et al. ([2011]) or by a change in the flux distribution on the photosphere of the star. On the other hand, our LDD value agrees well with the of Ohnaka et al. ([2011]).
3.2 HO and CO absorption lines : model fitting
The wavelengths longer than 2.245 m contain absorption lines from carbon monoxide (CO) and water vapor (HO) which are elements present in the MOLsphere described by Tsuji ([2000]) and Perrin et al. ([2004]). In this paper we restrain ourselves to the first two overtone band heads (m). It is clear from Fig. 2 (right panel) that the other bands are not well fitted when these first two are.
We modeled them using a Kurucz atmosphere model^{1}^{1}1http://kurucz.harvard.edu/ (Castelli & Kurucz [2003] and Kurucz [2005]) and a single layer containing both CO and HO at the same temperature and distance from the photosphere and the corresponding absorptions were computed from the line list of Goorvitch ([1994]) for CO and from Partridge & Schwenke ([1997]) for HO. This model contains five parameters : the photospheric diameter , the MOLsphere diameter , the MOLsphere temperature , the CO and HO column densities and . Its analytical expression is given by :
(3.1) 
if and otherwise :
(3.2) 
is the Planck function, is the angle between the line of sight and the center of the star and is the MOLsphere opacity computed from the line lists of Goorvitch ([1994]) and Partridge & Schwenke ([1997]). The squared visibility is then derived by computing the Hankel transform of this analytical expression :
(3.3) 
With , and the zeroth order Bessel function of the first kind.
An illustration of this model and an example of the corresponding spectrum of Betelgeuse model are given in Fig. 2, together with our AMBER observation.
The model contains five a priori independent parameters but there are some correlations between and and between the two column densities. Because of this degeneracy, we had to develop a strategy to perform our fit. We fixed to the value obtained by the uniform disk fit of the continuum data. Then we computed maps of our data by fitting and then at given and . :
(3.4) 
where is the spatial frequency. and are fitted on each cell of the grid . However, there was also a correlation between and the two column densities. We had to eliminate it by including the spectrum into our fit : this compensates for the lack of interferometric data in the band core caused by the band fringe fitting described in Sect. 2.
The maps are presented on Fig. 3 and we derived the following values for the parameters of the MOLsphere :
(3.5) 
Our two maps for carbon monoxide and water vapor present a minimum for the same couple of (). Therefore our hypothesis of a single layer containing both elements is validated. Our best fit values for the angular diameter and the temperature of the MOLsphere are close to those derived by Perrin et al. ([2004]) which were and .
4 Conclusion
Our analysis of the AMBER visibilities in the continuum allowed us to compute new uniform disk and limbdarkened disk angular diameters. Our absorption line analysis led us to new values for the MOLsphere parameters, consistent with the results from Perrin et al. ([2004]) and Ohnaka et al. ([2011]).
However, our analysis here only includes data from the first two CO overtone band heads : it must be extended to the other bands, that may probe a deeper molecular layer, closer to the star’s photosphere. Finally we will conclude this analysis by exploiting the closure phase signal. This work is currently undergoing and will allow us to search for asymmetries in the light distribution at the surface of the star.

This research has made use of the AMBER data reduction package of the JeanMarie Mariotti Center^{2}^{2}2Available at http://www.jmmc.fr/amberdrs
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