PROBING LOCAL DENSITY INHOMOGENEITIES IN THE CIRCUMSTELLAR DISK OF A Be STAR USING THE NEW SPECTRO-ASTROMETRY MODE AT THE KECK INTERFEROMETER

The disk continuum emission, emitted by bound-free and free–free thermal emission in the disk, is clearly resolved. To facilitate the comparison of our results with other published disk diameters, we give the size of a disk-only fit to the continuum visibilities (θ^FWHM_cont = 0.95  ±   0.03 mas) in Table 2. We model the disk continuum by a maximally inclined Gaussian profile, with a position angle of 50° which is orthogonal to the axis of polarization (McDavid 1999). However, the measured continuum emission consists of both stellar and disk contributions. Taking into account that the disk continuum of 48 Lib contributes one third of the K-band emission (Dougherty et al. 1994), the resulting disk size scale (θ^FWHM_cont,disk = 1.65 ± 0.05 mas) is seven times larger than the stellar photospheric diameter. Source variability may compromise this estimation of θ^FWHM_cont,disk, but a flux calibration of the KI photometry of 48 Lib, based on HD 145607, is consistent with the Two Micron All Sky Survey point source flux of our target (Skrutskie et al. 2006) to better than 10%, which is the precision level of our absolute flux calibration. Lefèvre et al. (2009) report an irregular variability in the Hipparcos band at the 5% level. Therefore, we can expect that variability of the star-disk flux ratio has no strong effect on the θ^FWHM_cont,disk value reported above. Note that although important for the estimation of the disk size, we cannot derive the NIR disk excess from the visibility data due to our small u, v coverage. Similarly, two-dimensional physical or phenomenological disk models of the continuum emission are not well constrained by a single baseline measurement. Gies et al. (2007) showed that, for several Be stars, even for significantly two-dimensional u, v coverages, physical models, using radiative transfer calculations, and phenomenological models, using Gaussian intensity profiles, are difficult to distinguish by the visibility data alone. Physical and phenomenological FWHM estimates of the average disk compactness may differ by 50%–100% (Gies et al. 2007). This may be used as an accuracy estimate for a physical interpretation of the θ^FWHM_cont,disk derived here. Since near-infrared disk excess and θ^FWHM_cont,disk of 48 Lib are within the typical range of Be-star disks, we can expect that a physical modeling of the disk continuum, as done by Gies et al. (2007), would lead to similar densities as described therein.

Table 2. Measured and Derived Properties of the Circumstellar Shell of 48 Lib^a

K'cont (Gauss-disk only)	θFWHMcont	0.94 ± 0.03 mas
K'cont (Gauss-disk + star)	θFWHMcont,disk	1.65 ± 0.05 mas
Br γ	$V_{(-250\,,\,-100\,{\rm km\,s^{-1})}}$	$R_{(100\,,\,250\,{\rm km\,s^{-1})}}$	V/R
Fline (norm.)	0.29 ± 0.01	0.16 ± 0.01	1.80 ± 0.2
Fcorrline (norm.)	0.23 ± 0.01	0.14 ± 0.01	1.66 ± 0.2
θFWHMline (mas)	1.7 ± 0.2	1.4 ± 0.2	1.2 ± 0.2
PC shiftline (mas)	2.2 ± 0.2	1.9 ± 0.2	1.2 ± 0.2
Pfavg(5:24...28)	$V_{(-325\,,\,-175\,{\rm km\,s^{-1})}}$	$R_{(175\,,\,325\,{\rm km\,s^{-1})}}$	V/R
Fline (norm.)	0.029 ± 0.01	0.028 ± 0.01	1.0 ± 0.1
Fcorrline (norm.)	0.024 ± 0.01	0.024 ± 0.01	1.0 ± 0.1
θFWHMline (mas)	1.9 ± 0.3	1.5 ± 0.2	1.2 ± 0.3
PC shiftline (mas)	0.9 ± 0.3	0.9 ± 0.3	1.1 ± 0.3

Notes. ^aAll uncertainties given in the table are derived from the standard deviations of the mean total flux and correlated flux spectra shown in the figures. These uncertainties reflect the differential, relative precision of the values, and are adequately used throughout this article for intercomparison of the different components. However, the absolute accuracy of the individual estimates is 10% for continuum and Br γ values and 25% for the Pf_avg values.

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The estimated disk continuum to stellar radii ratio matches other interferometrically observed edge-on systems with comparable properties (e.g., ζ Tau in Gies et al. 2007). The typically found moderate extent of the K-band emission size (5–10 times the stellar radius) is significantly smaller than recently modeled (Stee & Bittar 2001), confirming the need for interferometric constraints to understand the physical conditions in the stellar outflows of Be stars.

There are several indications in our data that the disk continuum emission zone is inside the Br γ and smaller than or equal to the Pf-recombination line emission zones. All fitted linear characteristics of the violet and the red part of the Br γ (Pf_avg) line emission zones (that is, θ^FWHM_line and the photocenter shifts PC^shift_line, for details see the next section; violet and red labels negative and positive Doppler shifts, following the standard Be-star terminology) indicate that the majority of the line emission is created at stellocentric radii larger than (comparable to) the radii dominating the continuum emission. Furthermore, the Pf_avg line center in the total and correlated flux drops below the continuum level (Figure 3). This points to a significant absorption of the continuum flux by gas in front of the continuum source; that is, the continuum emission is embedded and surrounded by the zone dominating the line emission. Therefore, we confirm the findings of Gies et al. (2007, studied H α versus continuum size) and Štefl et al. (2009) that the observed Br γ (and Pf_avg) hydrogen line emission in Be stellar shells seems to occur at larger (or equal) stellocentric radii than the disk continuum emission.

The emission line widths of Be stars are dominated by large-scale kinematic Doppler broadening (due to the fact that the ionized gas is located in a rotating disk around the star), without significant contributions of non-kinematic scattering processes (Hanuschik 1989; Gies et al. 2007). The disk of 48 Lib is known to be edge-on, which simplifies the geometric and kinematic interpretation of the line profiles (Hanuschik & Vrancken 1996). The spectrometer does not fully Nyquist sample the double peak of the Br γ and Pfund lines, but the central dip in the flux and the shape of the dϕ signal show that the violet (V) and the red (R) part of the disk are clearly separated by the spectrometer and that meaningful V/R ratios can be derived.

Pf-24...34 have been detected for the first time in an interferometric spectrum. The five strongest individual Pf-lines are clear detections (∼5σ–8σ) above the differential precision level of the flux ratio, visibility, and dϕ. To improve on the S/N for the Pf-lines and to minimize the effects of the limited sampling of the line profile, we average over the five strongest detected Pf-lines (24...28). To do so, the Pf-25...28 lines were scaled to match the flux levels of Pf-24. This avoids that the final average profile (Pf_avg) being affected by the individual line fluxes. We checked that none of the features of Pf_avg discussed below is significantly altered or vanishes when averaged over all 11 detected Pfund lines. However, our choice of averaging over the five strongest lines to create Pf_avg leads to the highest S/N. In addition, the omitted higher order Pfund lines are closer in the rest wavelength, and therefore, overlapping of adjacent line profiles would become apparent and compromise the profile of Pf_avg. Similarly, at velocities ⩾330 km s⁻¹ (indicated by the dashed region in Figure 3), the average profile is affected by adjacent lines. We purposefully show in the figure a large velocity space including these artifacts to demonstrate that Pf_avg emerges even out of these averaging artifacts. Unless indicated otherwise, we use a linear flux ratio continuum fit. Using a blackbody instead of a linear shape for the flux ratio continuum leads to a comparably good fit and slightly increases the off-center line emission of Pf_avg. We include this uncertainty in the shape of the continuum at the red end of the K'-band in the errors given in Table 2. The statistical precision of the averaged profiles is shown as red error bars.

We compared the individual properties (flux, visibility, and differential phase) of the Pf-(24...28) included in Pf_avg to check if meaningful geometric constraints on the Pfund line emission zone can be derived from Pf_avg. The decreasing signature in visibility and phase with increasing excitation level is consistent with the Pf-n/Pf-24 line flux ratios. This means that a similar geometry is encoded in the measured visibility and phase of each line, suggesting a common origin of the lines and justifying the averaging. The individual line ratios used match the respective Pfund-line ratio trends measured for other Be-star envelopes, such as γ Cas (Hony et al. 2000) and BK Cam (Granada et al. 2010). Furthermore, these flux ratios vary by no more than up to about 30% (Pf-28/Pf-24), which indicates, together with a similarly moderate variation of the respective Einstein coefficients, that the lines included in Pf_avg are emitted under similar conditions. Therefore, they most likely originate from similar regions in the disk. The geometric constraints, derived from Pf_avg, cannot be more accurate than this level, which matches the numbers given in Table 2.

The precision of the V/R estimate of the individual Pfund lines is clearly limited by our spectral resolution and the sampling of the line profile. Apparent ratios of up to 20% above and below unity for the Pfund lines included in Pf_avg are regarded as not significantly different from unity. Therefore, the lines show comparable V/R. Given the previous arguments for a common origin of the individual lines in the disk, we can expect that averaging does improve the V/R signal for the Pfund emission zone.

We concentrate on qualitatively answering the key question: are KI-SPR data suitable to measure directly, and efficiently in a single data set, the core parameters such as radial extent and radius dependence of the often discussed slowly rotating density inhomogeneity in the gas around Be stars? To do so, violet and red velocity bins outside the line center were defined to derive average V–R properties of the lines, while avoiding the zone of highest absorption and uncertain continuum (see below). The velocity bins enclose the maximum line emission with a width of 150 km s⁻¹, which is chosen to be comparable to the spectral resolution (bins are marked as a colored background in Figures 2 and 3). The profile averages for each bin are given in the figures. We derived intrinsic line emission sizes and photocenter shifts from the data (Table 2) by assuming the superposition of a linear continuum and additional Br γ disk emission (for the derivation of the relevant formulae see Appendix C in Weigelt et al. 2007). Note that the intrinsic photocenter shifts are on the order of the fringe spacing (λ/2B), which requires the use of the exact complex relation between the measured phase and the intrinsic phase (Equation (C3) in Weigelt et al. 2007) to derive the correct PC^shift_line. Table 2 reports the mean linear properties fitted to the linearly interpolated data for each velocity bin.

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For our analysis, we used a linear continuum extrapolation of the continuum flux ratio into the line center to derive the quantitative constraints in Table 2. However, the actual continuum at the Br γ line center may deviate from this linear continuum. The stellar continuum has some photospheric Br γ absorption, and since we observe an edge-on disk in emission with, at least partially, optically thick Br γ emission, additional absorption and emission makes it difficult to estimate the exact continuum shape at the line center. This presents a difficulty for isolating the correlated flux, visibility, and intrinsic dϕ of the line emission at the line center from the measured data, which contain a flux-weighted average of both continuum and line emission. An absorbed continuum profile (in contrast to the linear extrapolation of the off-line continuum assumed here) at the center of Br γ would increase the (correlated) line flux, and therefore decrease the derived intrinsic photocenter shift. To quantify this, we also applied a B4III Br γ template to the data (see also footnote "c" in Table 1). This would not change the measured V/R asymmetries significantly, but it would increase the given θ^FWHM_line by about 40% and decrease PC^shift_line by 20%, which gives the order of magnitude of this systematic uncertainty in our quantitative analysis.

Br γ and Pf_avg profiles differ. Above all, they show different V/R ratios and central absorption levels. The total and correlated Br γ line profiles are with V/R ∼ 1.8 and 1.6, respectively, which is significantly asymmetric. In contrast, θ^FWHM_line and PC^shift_line of the violet and red Br γ emitting regions coincide within the uncertainties. Štefl et al. (2009) resolved the Br γ disk emission of ζ Tau with the Very Large Telescope Interferometer with a spectral and spatial resolution similar to our data. They found a larger intrinsic line photocenter shift of the brighter wing, emitted at the time of their observation from the southeastern, red part of the disk of ζ Tau. A non-LTE disk model can explain such a trend in the dϕ as well as an extensive multi-wavelength and multi-technique data set with a global oscillation of a spiral density pattern (Carciofi et al. 2009). Our data might show a similar trend of a slightly larger PC^shift_line of the brighter side of Br γ. However, this trend is not significant with respect to the estimated uncertainties. We would encourage a similar, complex modeling effort of the disk of 48 Lib, including the new differential constraints from the Pfund emission based on repeated observations to improve on the significance of the dϕ trend of Br γ. Here, we concentrate on the overall line emission zone properties.

The bulk of the Br γ emission appears to come from similar stellocentric radii, and the enhanced emission on the violet side indicates a locally enhanced density. The observed asymmetry is inline with the ∼9 yr periodicity of cyclic changes of V/R (H α) (Hanuschik et al. 1995). The H α spectra of 48 Lib, provided by the BeSS database¹³ also report a V/R > 1 in 2008. In contrast, the Pf_avg profile appears to be symmetric in all properties within the errors. Again, θ^FWHM_line and PC^shift_line of Pf_avg are comparable for both sides, but the smaller PC^shift_line points to significantly smaller stellocentric radii of the bulk of the Pf_avg emission, if compared to Br γ. Both measured V/R (Br γ) and V/R (Pf_avg) can be reconciled with a one-armed density perturbation, if a radial dependence of the perturbation is allowed, as in the case of a spiral density wave, precessing through the disk.

There are several indications that the Pfund emission emerges from inside the bulk of the Br γ emission. The mean PC^shift_line(Br γ) is with 2.1 mas about twice as large as PC^shift_line(Pf_avg). Furthermore, the bins are centered at different stellocentric radii and velocities. The peak velocities appear offset (Br γ: 150 ± 50 km s⁻¹ versus Pf_avg: 230 ± 30 km s⁻¹). These velocity and PC^shift_line numbers are consistent with Keplerian gas motion, a typical assumption for a Be-star disk. The Keplerian rotation assumption is further supported by the measured double-peaked line profiles (in contrast to highly disordered or asymmetric profiles).

Since Be-star disks are (at least partially) optically thick in the hydrogen emission lines (see the central absorption in Figure 3 and the Be-star disk study of Lenorzer et al. 2002), it is expected that the stellocentric radius of the respective line anti-correlates with the specific line absorption properties. Comparing the respective Einstein absorption coefficients, we find B_5,24 <  B_4,7 <  B_2,3, which suggests that the Pf_avg is emitted inside the Br γ as described by our data. Br γ should be emitted at smaller stellocentric radii than H_α, as indirectly confirmed by the data of Wisniewski et al. (2007) (similarly for ζ Tau; Carciofi et al. 2009). Also the smaller H_α peak velocities (the spectrum in Figure 1 of Wisniewski et al. 2007, suggests about 110 km s⁻¹) are consistent with larger stellocentric radii compared to Br γ and Pf_avg.

Other indications for a different location of the Pfund line emission are the total and correlated flux profiles. Both show a clear absorption below the continuum emission level. This together with the symmetric line profile might indicate that the gas dominating the Pfund emission is located in front of the inner disk and the star (responsible for the continuum; see the extensive line profile modeling of Hummel & Hanuschik 1994; Telting et al. 1994). As discussed, we cannot estimate what fraction of this continuum absorption is due to intrinsic photospheric absorption, but a domination of the measured continuum absorption by photospheric absorption is unlikely for a Be star. Having the majority of the Br γ emission at larger stellocentric radii on the violet side but the Pfund emission at smaller radii in front of the star suggests that the overdensity pattern follows a radial, one-armed spiral pattern (Wisniewski et al. 2007; Carciofi et al. 2009). We depict the radial structure of the disk emission as measured by the KI in a schematic way in Figure 4. However, our single data set obviously cannot distinguish a spiral wave from other radius-dependent perturbation patterns.

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Our data provide a further quantitative test of Papaloizou's density wave model. Papaloizou et al. (1992) discuss that the temporal prediction of V/R cycles of about 10 year periods fits the available spectroscopic observations. Interferometric observations directly resolve the expected linear scale of the predicted density waves, as opposed to indirect methods such as polarimetry (as discussed for instance in Wisniewski et al. 2010). The mean photocenter shifts result in stellocentric radii of about 18 (8) R_* for Br γ (Pf_avg), which is consistent with both hydrogen emission line modeling of Be stars (e.g., Hummel & Vrancken 2000; Hony et al. 2000) and density wave models predicting that the local density perturbation, induced by the rotational flattening of the Be stars disappears outside a few stellar radii (Papaloizou et al. 1992).