Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=6cm,clip]{5577f1.eps} \end{figure}$ Figure 1: Spectrally dispersed AMBER/VLTI Michelson interferograms of $\eta$ Car. The two panels show the spectrally dispersed fringe signal (IF) as well as the photometric calibration signals from the three telescopes (P1-P3) in high (HR, upper panel) and medium spectral resolution mode (MR, lower panel). In both panels, the bright regions are associated with the Doppler-broadened Br $\gamma$ emission line.
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In the text

$\begin{figure} \includegraphics[width=13.2cm,clip]{5577f2.eps} \end{figure}$ Figure 2: AMBER observables derived from our $\eta$ Car data around the Br $\gamma$ line for three independent measurements ( Left: MR, 2004 December 26, Middle: MR, 2005 February 25, Right: HR, 2005 February 26). The first row shows the continuum-normalized spectra as extracted from the interferometric channels, followed by the derived calibrated visibilities and the differential visibilities. In the fourth and fifth row, the differential phase and the closure phase are presented. In the spectra we mark the wavelength regimes, which we defined as continuum for our analysis (shaded regions). The vertical grey line marks the rest-wavelength of Br $\gamma$ ( $\lambda_{\rm vac}=2.1661~\mu$ m; the small correction due to the system velocity of -8 km s^-1 (Smith 2004) has been neglected). We show different error bars within each panel: the left error bars correspond to the total (including statistical and systematic) error estimated for the continuum wavelength range, and the error bar towards the right visualizes the total error for the wavelength range within the line. For the HR 2005-02-26 measurement, data splitting showed that for a small wavelength range (hatched areas in the two lower right panels), the differential phase for the longest and middle baseline as well as the closure phase become very noisy and are therefore not reliable. Furthermore, the HR differential phase of the longest baseline is noisy at all wavelengths. See Sect. 2 for further details.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.3cm,clip]{5577f3.ps} \end{figure}$ Figure 3: uv coverage of the AMBER $\eta$ Car observations. The data obtained with medium spectral resolution in Dec. 2004 and Feb. 2005 are indicated by red squares and green bullets, respectively, while the high-resolution measurements are shown as blue triangles. Filled symbols denote observations around the Br $\gamma$ line, and open symbols denote observations around the He I line.
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In the text

$\begin{figure} \par\includegraphics[height=210mm,clip]{5577f4.eps} \end{figure}$ Figure 4: Similar to Fig. 2, but showing the MR measurement from 2004 December 26 covering the region around the He I line. The vertical grey line marks the He I rest-wavelength ( $\lambda_{\rm vac}=2.0586~\mu$ m).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=17.1cm,clip]{5577f5.eps} \end{figure}$ Figure 5: Comparison of the AMBER spectra and visibilities with the NLTE model predictions of Hillier et al. (2001). The figure displays the spectra ( upper row) and visibilities ( lower three rows, see labels for projected baselines) of the four AMBER measurements (green lines) and the corresponding data of the Hillier et al. NLTE model (red lines). The errors of the AMBER continuum and line visibility measurements are indicated by the two vertical error bars (see Figs. 2 and 4; the left bar is the continuum error bar), and the uncertainty of the AMBER wavelength calibration is indicated by the horizontal error bar. As the figure shows, we find good agreement between the AMBER data and the model predictions for the continuum visibilities as well as the shape and depth of the visibility inside the Br $\gamma$ line. In the case of the He I line, the wavelength dependence of the model visibility inside the line differs considerably from the AMBER measurements, indicating a different physical process involved in the line formation (see Sect. 3.1). The He I wavelength shift can be attributed to a combination of both Doppler shift (e.g. Hillier et al. 2006; Nielsen et al. 2006) and uncertainties in the wavelength calibration of the AMBER data. Note that no additional scaling has been applied to the Hillier et al. model. The model spectra and visibilities have a spectral resolution ( $\lambda/\Delta\lambda\sim20~000$ ) comparable to the HR measurements.
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In the text

$\begin{figure} \includegraphics[width=123mm,clip]{5577f6.eps} \end{figure}$ Figure 6: Left: comparison of the AMBER visibilities (filled green squares; baseline range 28-89 m) as a function of spatial frequency with the NLTE model predictions of Hillier et al. (2001) (solid red lines) for two continuum wavelengths (upper two panels; see labels for the exact wavelengths), the central wavelength of the Br $\gamma$ emission line (third), wavelengths in the blue and red wing of the Br $\gamma$ emission line (fourth and fifth row; at these wavelengths, the AMBER data show the strongest differential and closure phase signals), and the central wavelengths of the He I emission and P Cygni absorption (lower two panels). The blue triangles are the background-corrected VINCI K-band measurements from van Boekel et al. (2003). Right: center-to-limb variation (CLV; i.e. intensity as a function of angular radius) of the monochromatic Hillier et al. (2001) NLTE models for the wavelengths indicated by the labels. As the figures show, the typical FWHM diameter of the models is of the order of $\sim$ 2-4 mas for an assumed distance of 2.3 kpc for $\eta$ Car. See text for details.
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In the text

$\begin{figure} \par\includegraphics[width=90mm,clip]{5577f7t.eps}\\ \includegraphics[angle=-90,width=83mm,clip]{5577f7b.ps} \end{figure}$ Figure 7: Top: the solid and dashed red lines show the continuum-corrected visibility inside the Br $\gamma$ line of the HR measurement with the shortest projected baseline (29 m). The continuum correction follows Eq. (2). Except for the phase, all quantities entering Eq. (2) are indicated in the figure. We assume $F_{\rm tot} = F_{\rm cont} + F_{\rm line}$ and that $F_{\rm cont}$ inside the line is approximately equal to the level outside the line. The continuum-corrected visibility in the blue-shifted region of the emission line is shown with a dashed line since it is highly uncertain due to the presence of the P Cygni-like absorption component (see text for details). Bottom: continuum-corrected AMBER visibilities (filled blue squares) in the red region of the Br $\gamma$ line as a function of spatial frequency. To derive the visibilities according to Eq. (2), the data in the wavelength range 2.1661-2.1670 $~\mu$ m (red-shifted line region) were averaged before the continuum correction. The solid red line shows the continuum-corrected model visibility. Obviously, observations at shorter baselines are needed to further test the model predictions.
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In the text

$\begin{figure} \par\includegraphics[width=90mm,angle=0]{5577f8t.eps}\\ \includegraphics[width=60mm,angle=-90]{5577f8b.ps} \end{figure}$ Figure 8: Visibility in the He I line. Top: the figure is similar to Fig. 7 ( top) but displays the MR-2004-12-26 data with the shortest projected baseline (43 m). As in the case of the Br $\gamma$ emission, the figure reveals that the region dominated by line emission is fully resolved by the AMBER measurements. As in Fig. 7 (top), the continuum-corrected visibility is shown with a dashed line in the blue-shifted region of the emission line to indicate that in this region, the line visibility is highly uncertain due to the presence of the P Cygni absorption. Bottom: continuum-corrected AMBER visibilities (filled blue squares) in the red region of the He I emission line as a function of spatial frequency and continuum-corrected visibility curve (solid red line) according to the NLTE model of Hillier et al. (2001). To derive the visibilities according to Eq. (2), the data in the wavelength range 2.057-2.058 $~\mu$ m were averaged before the continuum correction. The model curve predicts much larger visibility values in the line, which indicates that the size of the line-emitting region in the model is probably underestimated by the model. A rescaling of the size of the model by a factor of $\sim$ 2.3 (green line) reveals better agreement with the AMBER measurements.
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In the text

$\begin{figure} \mbox{\includegraphics[width=50mm,angle=0]{5577f9l.eps} $\begin{... ...raphics[width=70mm,angle=0]{5577f9r4.ps}\\ [-6mm] \end{array}$ } \end{figure}$ Figure 9: Left: illustration of the components of our geometric model for an optically thick, latitude-dependent wind (see text for details). For the weak aspherical wind component, we draw the lines of latitudes to illustrate the 3D-orientation of the ellipsoid. Right ( a), b)): the upper row shows the brightness distribution of the modeled aspherical wind component (item (3) in the text) for two representative wavelengths. The figures below show the total brightness distribution after adding the contributions from the two spherical consituents of our model.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{5577f10.eps} \end{figure}$ Figure 10: Observables computed from our optically thick, latitude-dependent wind model (see Fig. 9 for a model illustration). The points (crosses) represent the measurements (as also shown in Fig. 2), and the solid lines give the observables computed from our model. The upper row shows the contributions from the various model components to the total flux. Besides the continuum emission (purple line), we introduced a spherical (blue line) and an aspherical (black line) wind component.
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In the text

$\begin{figure} $\begin{array}{ccc} \begin{array}{c} \textnormal{\textbf{a) Co... ...[width=110mm,angle=0]{5577f11aCMJN.eps} \end{array} \end{array}$ \end{figure}$ Figure 11: Simulation illustrating the signatures of a binary companion at the predicted position (for the orbital phase at the time of our continuum observations around the Br $\gamma$ line; separation $\sim$ 8 mas, $\rm PA \sim -36\hbox {$^\circ $ }$ ; see Nielsen et al. 2006). For the primary component, we assume a continuum emission CLV from Hillier et al. (2006), to which we add a uniform disk of 0.1 mas diameter to account for the binary companion (see a). b) Shows the 2D-visibility function of a single component model containing only the continuum-emitting object with Hillier-type CLV. c) Shows the 2D-visibility corresponding to the binary model shown in panel a) for a small K-band flux ratio q=10 between the continuum emitting region (Hillier-type CLV) and the companion. In d) the residuals of the visibilities (upper panel) and closure phases (lower panel) between the models with and without a companion are shown as a function of flux ratio q for baselines and PAs corresponding to the seven AMBER measurements. The dashed horizontal lines indicate the uncertainty of the measurements. Given these uncertainties, the figure illustrates that a companion signature should be visibile from the AMBER closure phase measurements, if the binary is less than $\sim$ 110 times fainter compared to the primary. See text for details.
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In the text

$\begin{figure} \includegraphics[width=85mm,angle=0]{5577fa1t.eps}\vspace*{-3mm} \par\includegraphics[width=58mm,angle=-90]{5577fa1b.ps} \par\end{figure}$ Figure A.1: Top: spectral calibration of the AMBER observations. The figure shows the spectrum of $\eta$ Car (blue) and the calibrator star L Car (green) around the Br $\gamma$ line obtained from the HR measurements in Feb. 2005. In addition, a telluric spectrum from the Kitt Peak Observatory is shown in red. The original telluric spectrum with a spectral resolution of R=40 000 was spectrally convolved to match the resolution of the AMBER measurements. For the flux calibration of the $\eta$ Car spectrum, the Br $\gamma$ line in the L Car spectrum was interpolated before the division. See text for further details. Bottom: same as top panel, but for both MR measurements around the He I emission line. Together with the $\eta$ Car spectra, the spectra of the calibrators HD 93030 and HD 89682 are displayed. In addition, the telluric spectrum obtained at Kitt Peak with R=40 000 and a spectrally convolved telluric spectrum is shown, which matches the spectral resolution of the MR measurements (R=1500). The figure illustrates that the forest of telluric lines forms a quasi-continuum which modulates the AMBER spectra.

In the text

$\begin{figure} \par\includegraphics[width=53mm,angle=-90]{5577fb1t.ps}\includegr... ...77fb1m.ps}\\ \includegraphics[width=53mm,angle=-90]{5577fb1b.ps} \end{figure}$ Figure B.1: 1-D visiblity fits of the AMBER continuum measurements. The upper two panels show uniform-disk and Gaussian fits for the averaged continuum around the He I and Br $\gamma$ lines, respectively. As both panels illustrate, neither a uniform disk nor a Gaussian is a good representation of the AMBER measurements. The panel on the left summarizes the fitting attempt for all continuum wavelength channels by displaying the fitted diameters of the UD and GAUSS models as a function of wavelength.

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.7cm,clip]{5577fb2.ps} \end{figure}$ Figure B.2: Dependence of the Gaussian FWHM diameter on the fit range. The figure shows the background-corrected visibilities obtained with VINCI/VLTI (see van Boekel et al. 2003) as well as Gaussian fits of (a) all four data points (long-dashed green line), (b) only the point with q=45 cycles/arcsec (short-dashed blue), (c) only the point corresponding to the longest baseline (dotted purple), and (d) only the point corresponding to the shortest baseline (dashed-dotted light blue). See the labels for the Gaussian FWHM diameters resulting from the different fits. The figure illustrates that the fitted diameter strongly depends on the spatial frequency range which is used to fit the data. The strong diameter variation (in this case, the diameter changes by a factor of $\sim$ 3) occurs since a Gaussian is not a good representation of the measured visibility function. See text for further discussion.

In the text

$\begin{figure} \par\includegraphics[angle=270,width=7.3cm,clip]{5577f3.ps} \end{figure}$	Figure 3: uv coverage of the AMBER $\eta$ Car observations. The data obtained with medium spectral resolution in Dec. 2004 and Feb. 2005 are indicated by red squares and green bullets, respectively, while the high-resolution measurements are shown as blue triangles. Filled symbols denote observations around the Br $\gamma$ line, and open symbols denote observations around the He I line.
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$\begin{figure} \par\includegraphics[height=210mm,clip]{5577f4.eps} \end{figure}$	Figure 4: Similar to Fig. 2, but showing the MR measurement from 2004 December 26 covering the region around the He I line. The vertical grey line marks the He I rest-wavelength ( $\lambda_{\rm vac}=2.0586~\mu$ m).
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