ON THE NATURE OF THE HERBIG B[e] STAR BINARY SYSTEM V921 SCORPII: GEOMETRY AND KINEMATICS OF THE CIRCUMPRIMARY DISK ON SUB-AU SCALES^*

Infrared interferometers, such as ESO's Very Large Telescope Interferometer (VLTI), coherently combine the light from separate apertures in order to achieve an unprecedented angular resolution of a few milliarcseconds at infrared wavelengths. With a spectral resolving power of up to R = λ/Δλ = 12, 000, these instruments now enable investigations both in the continuum emission and in spatially and spectrally resolved gas-tracing lines. The measured visibility amplitudes, closure phases, and wavelength-differential phases (DPs) provide powerful constraints for model-fitting or can be used for the reconstruction of interferometric images.

First spectro-interferometric observations on V921 Sco using the VLTI near-infrared beam combiner instrument AMBER (Petrov et al. 2007) were presented by Kraus et al. (2008a), Kreplin et al. (2012), and in Paper I and provided low (LR-HK, R = 35) and medium (MR-K, R = 1500) spectral resolution. Here, we present new observations using AMBER's unique high spectral resolution mode (HR-K, R = 12, 000). The new data sets were obtained on 2010 March 3 and 2010 August 26 using the 8.2 m unit telescopes UT2, UT3, and UT4 and cover a wavelength window around the Brγ 2.16602 μm line.

In order to yield sufficient signal-to-noise ratio (S/N) for our high spectral resolution observations, we employed the FINITO fringe tracker instrument (Gai et al. 2004; Le Bouquin et al. 2008). This instrument measures and corrects the atmosphere-induced phase perturbations and allowed us to record the optical path delay stabilized interferograms with a long detector integration time of 3 s. Unfortunately, the tracking performance of FINITO was degraded for the longest baselines due to the low visibility contrast in this baseline regime. Based on the poor S/N, we rejected the visibility measurements for one baseline from 2010 March 3 (UT2–UT4) and two baselines from 2010 August 26 (UT2–UT4, UT3–UT4). The remaining baselines exhibit fringe S/Ns up to 3.5, 4.5, and 14, and cover baseline lengths between 36.7 and 84.3 m and PAs between 22° and 292° (Figure 1). The data show a double-peaked, rising visibility profile in the Brγ line as well as non-zero DPs (Figure 2).

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The wavelength calibration was done using atmospheric telluric features close to the Brγ line and by applying a heliocentric–barycentric system correction with heliocentric velocities of +28.33 km s⁻¹ (2010 March 3) and −27.09 km ⁻¹ (2010 August 26), respectively.

Each observation on V921 Sco was accompanied by observations on the interferometric calibrator HD 161068, for which we assume a uniform-disk diameter of 1.448 ± 0.019 mas (Mérand et al. 2006). Both for the science and calibrator star observations, we extract raw visibilities, closure phases, and DPs using the amdlib (V3.0) data reduction software (Tatulli et al. 2007b; Chelli et al. 2009).

Due to the influence of residual vibration, it is known that AMBER+FINITO observations with long DIT, such as used for our HR-K mode observations, might result in a poor absolute visibility calibration, while the wavelength-differential observables are only marginally affected (e.g., Tatulli et al. 2007a). To recalibrate the absolute continuum visibility level of the HR-K observations, we make use of our earlier LR-HK observations (Paper I) and the best-fit continuum model (Model DISK), which will be described in more detail in Section 3. We investigated the influence of frame selection in the course of our data reduction procedure and find that the wavelength-differential signatures are very robust when selecting, for instance, the 80%, 50%, 20%, or 10% of frames with the best S/N. Given that the statistical noise increases with decreasing frame number and that low-S/N frames are downweighted during the averaging process in a natural fashion, we decided to employ the observables from the full, unselected data sets for our analysis.

In order to associate the closure phase sign with the on-sky orientation, we use a reference data set³ on the binary star θ¹ Orionis C (Kraus et al. 2009b). To calibrate the wavelength-differential phases, we make use of the fact that the continuum photocenter is systematically offset with respect to the Brγ-line emission due to the presence of a close companion star. Using the well-established continuum closure phase sign calibration, we first determine the position angle⁴ (P.A.) of the companion star (Section 3) and then adjust the DP sign in our spectro-interferometric and spectro-astrometric data in order to match the direction of the continuum photocenter displacement. This procedure calibrates the DP sign unambiguously and might serve also as a reference for other studies using AMBER's HR mode. Recently, we employed this calibration in order to determine the rotation sense of the disk around the classical Be star β CMi (Kraus et al. 2012b). Since β CMi was observed using both AMBER's MR and HR mode, we can also extend the calibration to AMBER MR-mode observations, which resulted in a recalibration of the ζ Tau rotation sense (Kraus et al. 2012b) compared with earlier studies (Štefl et al. 2009).

The statistical error bars on the DPs vary strongly for the different baselines, which is both a result of the low fringe contrast at the longest baselines and of differences in the vibration properties of the UTs. These differences might give overproportional weight to the short baselines in our χ²-fitting procedure. Therefore, based on the typical root-mean-square noise in the continuum channels, we include a minimum DP error of 20° for all baselines in the fitting procedure.

Spectro-astrometry uses high S/N long-slit spectra to measure the centroid position of an unresolved object as a function of wavelength. Since the centroid position can be measured with much higher precision than the size of the point-spread function (Bailey 1998b), this method allows one to measure sub-mas photocenter displacements in spectrally resolved emission lines. While the earliest astronomical applications in the field of star formation focused on the detection of close companions (e.g., Bailey 1998a), later studies also successfully applied spectro-astrometry to more general cases, such as outflow signatures (Takami et al. 2003; Whelan et al. 2005) or the characterization of the gas kinematics in protoplanetary disks (Pontoppidan et al. 2011; Goto et al. 2012).

Our spectro-astrometric observations on V921 Sco were obtained using the VLT near-infrared high-resolution spectrograph CRIRES (Kaeufl et al. 2004). The measurements were obtained on 2010 March 4, UT 07:51 to 08:58 using an integration time of 5 s and a slit width of 02, resulting in a spectral resolution of R = 100, 000. In order to apply the spectro-astrometry technique, we recorded spectra toward three different P.A.s (55°, 115°, 175°), and the corresponding anti-parallel P.A.s (235°, 295°, 355°), complementing the P.A.s probed by interferometry (Figure 1). To maximize the flux in the slit, the spectra were recorded using the STRAP adaptive optics system, resulting in a typical PSF Gaussian FWHM of ∼115 mas. The measured spectra were corrected to the heliocentric–barycentric system using a heliocentric velocity of +28.36 km s⁻¹. The spectra were extracted using the ESO CRIRES data reduction pipeline (version 1.12.0).

Besides the Brγ 2.166078 μm line, which was covered by CRIRES detector 3, our observation also covered the Mg ii 2.137 μm line in detector 1. This line has also been detected in other B[e] stars (Clark et al. 1999). To compute velocities in the local standard of rest, we assumed a systemic velocity of v₀ = −20 km s⁻¹, which we adopt from the forbidden line measurements by Borges Fernandes et al. (2007).

In order to correct the spectrum for telluric spectral features, we observed the early G-type star Hip84425 and we modeled the intrinsic Brγ absorption using an infrared solar spectrum recorded with ACE-FTS (Hase et al. 2010).

The final spectra are shown in Figure 3 and reveal a very narrow (FWHM 0.0006560 μm or ≈91 km s⁻¹) and double-peaked line profile with a very small peak separation of just ∼0.000184 μm (∼25 km s⁻¹). In addition to the Brγ-line spectrum, which will be discussed and modeled in Section 4, we have also recorded the Mg ii 2.137 μm line. For the Mg ii line, the peak separation is significantly wider (∼0.000500 μm or 70 km s⁻¹), indicating that this line originates at smaller stellocentric radii in the circumstellar environment. This finding is consistent with our non-detection of a spectro-astrometric signal within this line.

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To derive the astrometric signal, we compute for each spectral channel v the beam centroid position (Pontoppidan et al. 2011) in the spatial direction

$$\begin{equation} X^{p,a}(v) = K \frac{\sum _{i} x_{i}(v) F_{i}(v)}{\sum _{i} F_{i}(v)}, \end{equation} \tag{ 1 }$$

where i defines the size of the virtual aperture (we use ±1 pixel around the center of the PSF) and K is defined as the ratio between the flux in the virtual aperture and the total PSF (∼1.5). The astrometric signals are derived for each P.A. (X^p) and its anti-parallel counterpart (X^a) and then subtracted in order to remove potential artifacts (Brannigan et al. 2006):

$$\begin{equation} X(v)=(X^{p}(v)-X^{a}(v))/2. \end{equation} \tag{ 2 }$$

The interpretation of spectro-astrometric signals is complicated by the fact that this technique measures only the first-order momentum in the brightness distribution (relative position), but is insensitive to higher-order momenta (angular size, asymmetry, kurtosis; see Lachaume 2003) as well as the continuum-emitting geometry, which limits this technique to relatively simple cases or requires additional model assumptions. In this study, we make use of the fact that photocenter displacements measured with spectro-astrometry are mathematically equivalent to the DPs measured in spectro-interferometry, which allows us to directly combine the spectro-interferometric (visibility, DP, closure phases) and spectro-astrometric observables (photocenter displacements) for quantitative modeling (Section 4.2), providing unique constraints on the AU-scale spatial distribution and kinematics of the circumstellar gas and dust. For this purpose, we translate the measured astrometric signal into the equivalent DP using the relation

$$\begin{equation} \phi = -\frac{2\pi X(v)}{\sigma }, \end{equation} \tag{ 3 }$$

where σ is the FWHM of the PSF measured in the spectrum (typically ∼150 mas). In order to give a similar weight to the AMBER and CRIRES measurements, we assume a minimum DP error of 1° for our CRIRES DPs.

We recorded a high-resolution, high-S/N near-infrared spectrum of V921 Sco using the FIRE Echelle spectrograph (Simcoe et al. 2008) mounted at the Magellan/Baade 6.5 m telescope. With a 045 slit, this instrument provides a spectral resolution R = 8000 and a wide wavelength coverage from 0.8 to 2.5 μm. The spectrum was recorded on 2011 March 12 using an A–B–B–A dithering pattern with DITs of 10 s (high gain mode, to obtain high S/N in the z and J band) and 5 s (low gain mode, in order to avoid saturation in the H and K bands). The slit was oriented along the disk polar axis derived from our interferometric observations (P.A. = 56°). To correct for telluric features, we observed the A0V-type standard star HD 122945. The data reduction was performed using the standard FIRE data reduction pipeline developed at MIT, which performs also a spectro-photometric calibration based using the photometry of the standard star. Trying different combinations of target star/standard star data sets, we find that the derived spectral slopes are consistent on the level of a few percent, while the derived absolute flux levels show some larger scatter in the ∼5%–10% range. In order to improve on the calibration, we fit a fifth-order polynomial in order to extract the spectral slope and then use archival ISO photometry in order to recalibrate the absolute flux at 2.4 μm which yields also a satisfying match with 2MASS J-, H-, and K-band photometry (the derived flux densities match within 20%). The derived absolute-calibrated FIRE spectrum is corrected for reddening (A_V = 4.8 ± 0.2; Borges Fernandes et al. 2007) using the extinction law from Cardelli et al. (1989, R_V = 3.1).

At the longest wavelengths, the S/N in our final spectrum is reduced compared with the J and H bands since some of the recorded frames had to be rejected due to saturation in this part of the spectrum. In particular, the saturation occurs in sky lines, resulting in some narrow spikes in the final corrected spectrum.

For a first, qualitative interpretation (Section 4.1) of the gas kinematics, we derive the photocenter displacement of the line-emitting region with respect to the continuum emission using our CRIRES spectro-astrometric data. For this purpose, it is necessary to separate the line spectro-astrometric signal from the underlying continuum contributions. To determine the continuum level, we fit a high-order polynomial function X_c to the astrometric signal derived from the continuum channels. This function is then subtracted from the astrometric signal in the line channels and weighted by the continuum-to-line flux ratio F_c/F_l:

$$\begin{equation} X_{l}(v) = \left(X(v) - X_c(v) \right) \left(1+F_{c}(v)/F_{l}(v) \right). \end{equation} \tag{ 4 }$$

The derived photocenter of the line velocity channels is significantly offset with respect to each other (clearly indicating the gas kinematics) and also shows a displacement with respect to the photocenter of the continuum channels (Figure 5). This displacement reflects the fact that the center of gravity of the continuum emission does not coincide with the location of the primary star, but is displaced toward the position of the companion. We calculate the center of gravity both for the line channels and the continuum channels and compute their relative displacement vector $\textbf {\em v}_{c-l}$, which is related to the companion separation ρ, P.A. Θ, and the flux ratio F_B/F_tot by

$$\begin{equation} \textbf {\em v}_{c-l} = \rho \frac{F_{\rm B}}{F_{\rm tot}} \left(\begin{array}{c}\sin \Theta \\ \cos \Theta \end{array} \right). \end{equation} \tag{ 5 }$$

Based on our continuum model fits from 2008 and 2009 (Table 1), we fix ρ = 25.13 mas and then determine the companion P.A. Θ and the flux ratio F_B/F_tot from the CRIRES observations. Applying this procedure yields Θ = 353° ± 9° (which is in reasonable agreement with the astrometry determined with AMBER; Table 1) and F_B/F_tot = 0.053, which is lower than the flux ratio determined with interferometry for epochs 2008 and 2009, possibly indicating variability.

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The photocenters in the blue- and redshifted line wings are displaced in the opposite direction with respect to each other. Also, the highest gas velocities (dark red points and dark blue points in Figure 5) emerge from smaller stellocentric distances than intermediate velocities, which suggests a rotation-dominated velocity profile. From the distribution of the individual photocenter offsets, we derive the disk plane orientation to 1532 ± 06.

In contrast to CRIRES, AMBER is able to spatially resolve the geometry of the line-emitting region, entering a regime where higher-order geometric effects are probed. Therefore, in the following two sections, we will employ a quantitative modeling in order to interpret the combined spectro-astrometric and spectro-interferometric observations.

Given the indications for a rotation-dominated velocity field provided by our model-independent photocenter analysis (Section 4.1), we first test whether a Keplerian velocity field might reproduce our spectroscopic, spectro-astrometric, and spectro-interferometric data quantitatively.

For this purpose, we employ a Keplerian disk model ($v(r) = \sqrt{GM_{\star }/r}$), which we have already successfully applied to AMBER high spectral dispersion data on the classical Be star β CMi (Kraus et al. 2012b). The model assumes that the line-emitting gas is optically thin and located in a geometrically thin disk, where the radial intensity profile is parameterized with a power law (I_l(r)∝r^q). The gas emission extends from an inner truncation radius (R_in) to an outer truncation radius (R_out), which we parameterize with a Fermi-type function in order to avoid artificial edges (see Equation (1) in Kraus et al. 2008b, where the width of the truncation region was chosen to 0.1). In our study on β CMi (Kraus et al. 2012b), we investigated the DP signatures induced by photospheric absorption and found that even for a relatively extended stellar surface (equatorial radius of 0.36 mas), the induced DPs are <05. For V921 Sco, the influence of photospheric absorption is likely ∼50 times smaller due to the smaller apparent stellar radius (∼0.07 mas) and the significantly larger equivalent width of the Brγ emission line. Therefore, these signatures are about four orders of magnitude smaller than the disk kinematical signatures and can be safely neglected in our modeling process.

As discussed in Section 4.1, the elliptical distribution of the derived photocenter vectors might indicate opacity effects, which cause the more distant parts of the disk to appear fainter than the disk parts facing the observer. In order to include this effect in our model, we assume that the disk is embedded in a medium of constant density. After a distance x traveled, the emitted intensity I₀ is then reduced to I(x) = I₀exp (− κx). Combining this line-emission model with our best-fit continuum disk+companion model (DISK, Table 1) allows us to produce model channel maps (Figure 6, bottom), from which we compute line profiles, visibilities, and DPs for comparison with our data (Figure 6, top).

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As line broadening mechanisms, we include thermal and turbulent Doppler broadening (Piétu et al. 2007)

$$\begin{equation} \Delta V= \sqrt{\frac{2 kT_{\rm gas}}{m} + v^{2}_{\rm turb}}, \end{equation} \tag{ 6 }$$

where v_turb is the turbulent velocity, which is typically negligible for Herbig Ae/Be stars (≲ 0.5 km s⁻¹; e.g., Piétu et al. 2007). In the disk surface layer, the gas temperature T_gas will be significantly higher than the dust temperature at a given stellocentric radius. We assume T_gas = 5T_dust, as suggested by the thermally decoupled radiative-hydrodynamics simulations by Thi et al. (2011), but note that the precise value affects mainly the line width and does not affect our general conclusions (see also Section 5.1).

Free parameters in our model are the mass of the central star M_A, the inner and outer disk radius (R_in, R_out), the radial intensity power-law index q, the disk inclination i, and the opacity index κ.

We vary these parameters systematically on a parameter grid and select the best-fit model with the best χ²_r = χ²_{r, V} + χ²_{r, ϕ} + χ²_{r, F}, where χ²_{r, ϕ} and χ²_{r, F} are the reduced chi-squared between the model and measured different phase and spectrum, respectively.

Remarkably, this simple disk model can reproduce important features in our data, in particular:

• 1.  
  Our model can reproduce the double-peaked Brγ-line profile (Figure 6, first panel) reasonably well. One line profile characteristic that is not reproduced by our model concerns the weak asymmetry observed in Brγ-line profile, with a slightly stronger redshifted line wing.
• 2.  
  Our AMBER observations (Figure 6, second panel) reveal M-shaped visibility profiles on two of three baselines (36.7 m/61° and 53.4 m/89°), indicating that the angular extension of the line-emitting region increases for low gas velocities. This effect is expected for a rotation-dominated velocity field, where the azimuthal velocity decreases as a function of radius and the visibility profile shape is reasonably well reproduced by our model for these baselines. On the third baseline (46.6 m/22°), no central visibility drop has been observed. We suspect that this effect is related to more subtle radiative transfer or line broadening effects, which are not included in our simplistic model. The visibilities at low gas velocities (i.e., in the line center) would be most sensitive to such small-order effects and we leave it to future studies using full radiative transfer modeling to investigate this in more detail.
• 3.  
  The measured AMBER and CRIRES DPs (Figure 6, 3rd panel) show very interesting signatures, including asymmetric S-shaped signatures and V-shaped signatures, which appear sometimes in the blueshifted and sometimes in the redshifted line wing. These signatures constrain the disk kinematics primarily, but contain also contributions from the continuum photocenter displacement caused by the companion star. Our combined binary star plus Keplerian disk rotation model reproduces the large variety of signatures reasonably well. The strongest residuals between the model and the data are observed at the longest AMBER baselines, where the data are extremely sensitive to small-order kinematical effects, but where the S/N is also reduced due to the lower fringe contrast.

The parameters corresponding to the best-fit model are listed in Table 2 and will be discussed in more detail in Section 5.2.

We also investigated whether a significant fraction of the Brγ emission might be associated with the secondary star (V921 Sco B) instead of the circumprimary disk, possibly indicating active accretion from the circumbinary disk onto the secondary star. Considering the strong measured displacement of the line photocenter in the direction toward the primary (Figure 5, right) and the good quantitative agreement of the displacement vector with the flux-weighted binary astrometry vector (Section 4.1), it is clear that the secondary is not the dominant Brγ-emitting component. In order to further quantify these constraints, we introduced the fraction of Brγ emission associated with the secondary star to the total Brγ-flux (F_B/F_tot)_Brγ as an additional parameter in our kinematical model and find that (F_B/F_tot)_Brγ < 0.11.

Our FIRE observations (Figure 7) reveal a very rich near-infrared spectrum. Similar to the optical spectrum (Borges Fernandes et al. 2007), the near-infrared regime is dominated by strong hydrogen line emission. As listed in Table 3, we detect 27 lines from the Brackett series (Brγ to Br29), 24 lines from the Paschen series (Paα to Pa24), and at least 10 lines from the Pfund series (Pf14-24). Given that the recombination physics of hydrogen is well known, one can use these line decrements in order to derive information about physical conditions of the line-emitting gas.

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Table 3. Lines Identified in Our V921 Sco FIRE Spectrum and Measured Line Equivalent Widths (EW) and Integrated Line Fluxes, F

Wavelength	Line	EW	F
(μm)		(nm)	(10−16 W m−2)
0.8304	Pa24	−0.053a	14.7
0.8312	Pa23	−0.073	20.1
0.8321	Pa22	−0.079	21.6
0.8332	Pa21	−0.087	23.7
0.8343	Pa20	−0.110	29.7
0.8357	Pa19	−0.153	41.0
0.8372	Pa18	−0.175	46.4
0.8390	Pa17	−0.199	52.2
0.8411	Pa16	−0.242	62.7
0.8436	Pa15	−0.300	76.6
0.8447	O i	−1.343	340.4
0.8465	Pa14	−0.369	92.6
0.8500	Pa13	−0.443	108.9
0.8543	Pa12	−0.432	103.7
0.8596	Pa11	−0.339	79.1
0.8663	Pa10	−0.394	88.8
0.8748	Pa9	−0.348	75.3
0.8820	O i	−0.012	2.5
0.8860	Pa8	−0.447	92.2
0.8927	Fe ii	−0.097	19.5
0.9013	Pa7	−0.462	89.9
0.9127	Fe ii	−0.074	13.9
0.9177	Fe ii	−0.169	31.2
0.9202	Fe ii	−0.121	22.1
0.9227	Pa6	−0.500a	90.8
0.9256	Fe ii	−0.080a	14.4
0.9261	O i	−0.070a	12.6
0.9392	N i	−0.071a	12.3
0.9406	C i	−0.060	10.4
0.9543	Pa	−0.660	110.1
0.9893	Fe ii	−0.045	6.9
0.9910	Fe ii	−0.029	4.5
0.9956	Fe ii	−0.070	10.7
0.9997	Fe ii	−0.624	94.4
1.0047	Paδ	−1.132	169.9
1.0108	Al ii	−0.043a	6.4
1.0174	Fe ii	−0.143	21.0
1.0501	Fe ii	−0.549	76.6
1.0688	C i	−0.163	22.2
1.0829	He i	−0.760	101.7
1.0862	Fe ii	−0.503	67.1
1.0917	He i	−0.207	27.4
1.0935	Paγ	−1.793a	237.2
1.1127	Fe ii	−0.468	60.6
1.1290	O i	−1.874a	238.9
1.1755	C i	−0.117	14.3
1.2467	N i	−0.083a	9.6
1.2815	Paβ	−4.030a	457.5
1.3166	O i	−0.321	35.6
1.4798	Br29	−0.031a	3.1
1.4811	Br28	−0.030a	3.0
1.4827	Br27	−0.042a	4.2
1.4844	Br26	−0.051	5.1
1.4863	Br25	−0.057	5.7
1.4884	Br24	−0.072	7.3
1.4907	Br23	−0.075a	7.5
1.4934	Br22	−0.096	9.6
1.4963	Br21	−0.117	11.7
1.4997	Br20	−0.141	14.1
1.5035	Br19	−0.161	16.1
1.5078	Br18	−0.191	19.1
1.5129	Br17	−0.212	21.1
1.5188	Br16	−0.250	24.8
1.5256	Br15	−0.279	27.6
1.5338	Br14	−0.395	38.9
1.5435	Br13	−0.430	42.1
1.5552	Br12	−0.524a	51.0
1.5696	Br11	−0.544	52.6
1.5750	Fe ii	−0.105	10.1
1.5876	Br10	−0.570	54.7
1.6105	Br9	−0.631	59.9
1.6403	Br8	−0.667a	62.5
1.6435	[Fe ii]	−0.019a	1.8
1.6769	[Fe ii]	−0.076a	7.0
1.6787	Fe ii	−0.046a	4.2
1.6802	Br7	−0.719a	66.2
1.6873	Fe ii	−0.309	28.4
1.6894	Fe ii	−0.015a	1.4
1.7006	He i	−0.032a	2.9
1.7111	[Fe ii]	−0.013	1.2
1.7357	Br6	−0.521	47.1
1.7414	Fe ii	−0.102	9.2
1.7451	[Fe ii]	−0.054a	4.9
1.9440	Brδ	−0.808b	70.3
1.9738	Fe ii	−0.019	1.7
2.0590	Mg ii	−0.219b	19.1
2.1376	Mg ii	−0.051	4.5
2.1447	Mg ii	−0.018	1.6
2.1649	Brγ	−0.705b	62.5
2.3532	Pf23	−0.028	2.5
2.3591	Pf22	−0.036	3.2
2.3657	Pf21	−0.036	3.2
2.3731	Pf20	−0.054	4.9
2.3815	Pf19	−0.064	5.8
2.3912	Pf18	−0.078	7.0
2.4023	Pf17	−0.075	6.7
2.4151	Pf16	−0.092	8.2
2.4300	Pf15	−0.114	10.2
2.4477	Pf14	−0.162	14.4
2.4687	Pf13	−0.245	21.5

Notes. ^aThese lines suffer from line blending, which introduces some uncertainty to the derived EW values. ^bDue to the high K-band continuum flux and line brightness, these lines likely reached the nonlinearity regime of the FIRE detector, resulting in an underestimation of the real EW.

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In order to model the line flux in the optically thin approximation, we extracted from Storey & Hummer (1995) the line emissivities _ul for Case B recombination for all Balmer (l = 3), Brackett (l = 4), and Paschen (l = 5) hydrogen line transitions (u − l) with u ⩽ 25. The line emissivities include collisional transitions, which makes our computation applicable even for relatively high gas densities. Assuming that the emitting gas is isothermal (T = 10, 000 K) and uniformly distributed in the volume V, the received line flux at distance d is then given by

$$\begin{equation} F_{u-l} = \frac{N_e N_p \epsilon _{ul} V}{4 \pi d^2}, \end{equation} \tag{ 7 }$$

where N_e and N_p are the electron and proton density per unit volume. In order to approximate the emitting volume V, we estimate from our Brγ spectro-interferometric data the characteristic stellocentric emission radius. For this purpose, we generate a velocity-integrated line map and measure the half-light emission radius to r_line = 3.0 mas = 3.5 AU (for d = 1.15 kpc). Assuming that the line-emitting gas is located in a hot disk surface layer with a characteristic scale height h of h/r_line = 0.2, as suggested by the thermally decoupled simulations from Thi et al. (2011), the emitting volume is given by V = πr³_Brγ · (h/r_line). We employ an iterative procedure, where we start by assuming a low gas density, which is then adjusted in order to reproduce the measured line fluxes.

Then we recompute the line emissivities and repeated the computation until convergence is reached. As shown in Figure 8, we require rather high gas densities between N_e = N_p = 2 × 10¹⁹ m⁻³ and 6 × 10¹⁹ m⁻³, which supports the scenario that the gas is located in a dense disk instead of a low-density halo. For the high-level transitions (u > 16, i.e., Pa14-24, Br13-29, and Pf12-23), the line fluxes can be reproduced well with a single gas density (N_e = 6 × 10¹⁹ m⁻³), suggesting that the optical thin approximation is well justified. The low-level transitions (u ⩽ 16; i.e., Paβ-Pa13, Brγ-Br12) and more consistent with densities around N_e = 2 × 10¹⁹ m⁻³, which might indicating that these transitions originate from more extended disk regions, where the disk surface density is lower. We would like to note that the derived densities depend to some extend also on the assumed gas temperature. Varying the temperature from the assumed T = 10, 000 K to other realistic values (e.g., 5000–20,000 K), would change the derived densities by a factor of ∼2–3. Based on our simplistic modeling, the derived density should be treated as an order-of-magnitude estimate and future radiation-hydrodynamic modeling will be required in order to fully exploit the rich information provided by our combined spectro-interferometric and spectroscopic data set.

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It is interesting to compare the derived electron density to the values predicted by state-of-the-art disk models. For instance, for a typical disk around a Herbig Ae star (e.g., AB Aurigae, 2.4 M_☉) with a gas surface density of 10⁴ kg m⁻², the predicted midplane gas density is ∼6 × 10¹⁷ m⁻³ (Dullemond & Monnier 2010) at the dust sublimation radius (1.1 AU). Our density measurement of N_e = (2–6) × 10¹⁹ m⁻³ probes similar spatial scales in the V921 Sco disk and is one to two orders of magnitude higher than this value, suggesting that the disk around V921 Sco is exceptionally massive. This result is in line with the study by Henning et al. (1998), who determined the total gas mass in the millimeter cores around 25 Herbig Ae/Be and FU Orionis stars and measured the highest total gas mass in the core around V921 Sco (M_gas = 40 M_☉; core size: 27 × 27'' or ∼30, 000 × 30, 000 AU at 1.15 kpc). Observations with our spectroscopic and spectro-interferometric approach on a larger sample of protoplanetary disks will be necessary in order to determine whether the derived high gas density indicates an intrinsic property of the V921 Sco disk (possibly due to the young age of the source) or simply reflects the predicted disk surface density scaling law with stellar mass ($\Sigma \propto \dot{M} \propto M_{\star }^{2}$; Calvet et al. 2004).

Besides hydrogen recombination lines, other identified lines include Fe ii, [Fe ii], C i, He i, O i, N i, Mg ii, Al ii, which have also been identified in the B[e] stars CI Cam (Clark et al. 1999) and HD 50138 (Jaschek et al. 1992), or in the LBV η Car (Damineli et al. 1998; Smith & Davidson 2001). Besides the total of 90 identified lines, we detect in our spectra a few dozen additional, yet unidentified lines and we encourage detailed follow-up spectroscopic studies in order to investigate the rich chemistry of this source.

Our wavelength range also covers the CO first overtone bandheads between 2.3 and 2.4 μm, which allows us to search for the CO first overtone bandheads, which we detect neither in absorption nor emission. This is particularly interesting, since Kraus (2009) suggested that these lines provide a good diagnostic tool to distinguish between a pre- and post-main-sequence evolutionary phase in B[e] stars. According to her computation, observable ¹³CO bandhead emission can only be produced in evolved stars, but should be absent in pre-main-sequence B[e] stars.

Finally, we investigated whether we find indications for variability of the Brγ-line during the ∼6 months covered by our CRIRES and AMBER observations. For this purpose, we convolved the CRIRES and AMBER HR-K data to the same spectral resolution and overplot the line profiles in Figure 9, finding no indications for variability, neither in line strength nor line profile.

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Using a temperature-gradient disk model (DISK), we determine the inner continuum disk radius R_in to 1.59 mas. We can compare this value with the expected location of the dust sublimation radius, using the luminosity and distance estimate of Borges Fernandes et al. (2007), L_⋆ = (10 ± 3) × 10³ L_☉ and d = 1150 ± 150 pc. Assuming gray dust opacities and a standard dust sublimation temperature of T_subl = 1500 K, the expected dust sublimation radius (including the effect of backwarming from the disk) is $R_{\mathrm{subl}}=\sqrt{\vphantom{A^A}\smash{\hbox{${L_{\star }/4\pi \sigma T_{\mathrm{subl}}^{4}}$}}}$ (Dullemond et al. 2001), where σ denotes the Stefan–Boltzmann constant. With the given large luminosity and distance uncertainties, this corresponds to a value of 6.9 ± 1.1 AU or 6.0 ± 1.9 mas, which is considerably larger than the measured inner disk radius of R_in = 1.59 mas. Assuming higher dust sublimation temperatures of 2000 K (R_subl = 3.9 ± 0.6 AU or 3.4 ± 1.0 mas) also does not solve this discrepancy. Therefore, we conclude that V921 Sco belongs to the group of Herbig Be disks that are "undersized" with respect to the size–luminosity relation (Monnier & Millan-Gabet 2002), as already discussed by Kraus et al. (2008a) and Kreplin et al. (2012). Different physical scenarios have been proposed in order to explain this effect, including gas absorption (Monnier & Millan-Gabet 2002), the emission from gas located inside of the dust sublimation radius (Eisner et al. 2004; Monnier et al. 2005; Kraus et al. 2008b; Tannirkulam et al. 2008), or the presence of a highly refractive dust grain species (Benisty et al. 2010). Multi-wavelength interferometric studies with even longer baseline lengths as well as detailed gas and dust radiative transfer modeling will be required in order to ultimately settle this question.

We determine the outer disk radius to ∼9.7 mas. However, this value should be treated as a lower limit, since colder parts of the disk might extend to larger stellocentric radii. We can compare this derived lower limit with theoretical predictions for the disk truncation radius in binary systems. Artymowicz & Lubow (1994) computed the resonance-induced truncation radius for circumstellar and circumbinary disks and predicts the circumprimary disk to be truncated at r/a ∼ 40%–20% of the orbit major axis (for a binary mass ratio of 0.3), depending on the orbit eccentricity and disk viscosity parameter. This range agrees reasonably well with our derived value of R_out/ρ = 39%. For a detailed comparison, a full orbit determination and mid-infrared and sub-millimeter interferometric observations of the colder material in the outer regions of the circumprimary disk and in the circumbinary gas and dust reservoir will be required.

Both theoretical (e.g., Natta et al. 2001; Dullemond et al. 2001; Isella & Natta 2005) and observational studies (Monnier et al. 2006; Kraus et al. 2009a; Benisty et al. 2011) suggest that the inner dust rim in protoplanetary disks has a complicated, possibly puffed-up vertical structure, which can result in an asymmetric brightness distribution. Interferometric data, such as presented in this study, are able to detect these asymmetries and to constrain the corresponding disk models, in particular using phase-closure capabilities. However, it is clear that the closure phases in our AMBER data are dominated by the signatures of the newly detected companion, while potential asymmetries due to the vertical disk structure would appear only as secondary effects. Such signatures would appear in particular at long baseline lengths and close to visibility minima, where we also observe some significant deviations from our simple flat disk+companion model (Figure 10). However, it would be difficult to constrain these more complex physical models with the current uncertainties on the stellar parameters and the limited available uv-coverage. Therefore, we leave it to future investigations to better constrain the inner dust disk geometry around V921 Sco A. Alternatively, the remaining residuals might indicate the orbital motion of the companion within the five months during which the 2008 AMBER LR-HK data have been recorded (see Table 1 in Paper I).

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Using our kinematical modeling, we show that the velocity field in the disk is in Keplerian rotation (Section 4.2) and that the line-emission emerges from a relatively high-density region (N_e = (2–6) × 10¹⁹ m⁻³; Section 5.1), likely in a hot disk surface layer. Between the high-level (u > 16, i.e., Pa14-24, Br13-29, and Pf12-23) and low-level transitions (u ≲ 16, i.e., Paβ-Pa13, Brγ-Br12), we detect a change of slope in the Paschen/Brackett decrements, indicating that the high-level transitions emerge from high-density regions closer to the star than the low-level transitions. In our best-fit model (Table 2, Figure 6), the orientation of the opacity screen is such that the southwestern part of the disk appear brighter, which suggests that the northeastern disk axis is facing toward us (which is also consistent with the orientation of the large-scale bipolar nebula, Figures 11(A)–(C)). Arguably the most surprising parameter value in our best-fit model concerns the derived stellar mass. For an assumed distance of 1.15 kpc, we yield best agreement with 5.4 ± 0.4 M_☉, which is hardly consistent with the spectral classification⁵ and the prediction mass of 9 ± 1 M_☉ (Borges Fernandes et al. 2007).

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In order to explain this surprising result, we propose two plausible scenarios.

• 1.  
  The value of 1.15 ± 0.15 kpc (Borges Fernandes et al. 2007) might underestimate the real distance to V921 Sco. This distance has been determined based on the equivalent width of the Na i and Ca ii-K interstellar absorption lines and therefore relies on a statistically established calibration. In particular, Lopes et al. (1992) employed the same method (also on the Na i line) and determined the distance to 2.5 kpc. A distance estimate ≳ 2 kpc has also been obtained by McGregor et al. (1988) based on optical/near-infrared spectroscopy and photometry. Adopting such a larger distance would result in a stellar mass of 12 M_☉ (for 2.5 kpc) or 9 M_☉ (for 2 kpc), which would be more consistent with the spectral classification.
• 2.  
  The disk might not be associated with the massive (early B-type) star in the system, but orbit around the intermediate-mass (late B-type) companion instead. This would explain the relatively low derived mass, while the massive primary star could still provide sufficient ultraviolet flux to ionize the disk surface layer and the ambient low-density material resulting in the forbidden line emission. In this scenario, the accretion would occur from the circumbinary disk onto the disk around the late B-type star. The massive primary would rest closer to the center of mass and be effectively shielded from mass infall by the orbiting companion. A similar dynamical configurations seems also plausible for other Herbig B[e]-star binary systems such as MWC 361 A, where the active accretion is clearly associated with the less massive component in the system (Monnier et al. 2006; Alecian et al. 2008).

In order to distinguish between these scenarios, it will be necessary to accurately measure the flux ratio of the two stars as a function of wavelength. Our current measurement yield similar flux ratios between the two stars in the H and K bands, with some indications that V921 Sco A (i.e., the star associated with the circumstellar material) is of earlier spectral type (Paper I), favoring scenario (1). However, it should be noted that this color measurement is only significant at the 2σ level ((F_B/F_A)_H = 0.83 ± 0.15, (F_B/F_A)_K = 1.18 ± 0.12, Paper I) and might be biased, for instance in case of inhomogeneous extinction toward the two stars. In both scenarios, it is clear that a careful re-evaluation of the spectral classification based on the spectral energy distribution and the spectroscopic diagnostics will be necessary, but this is out of the scope of this paper.

Independent of these uncertainties, we can derive new insights on the evolutionary status of V921 Sco from our constraints on the disk gas velocity field. The decretion disks around post-main-sequence supergiant B[e] stars should exhibit a strong outflowing velocity component (Lamers & Pauldrach 1991), which is not observed in our data. On the other hand, our observation of a Keplerian rotation profile is consistent with the expected velocity field in a viscous accretion disk (Shakura & Sunyaev 1973) around a pre-main-sequence Herbig B[e] star.

Arguably, the most important advancement provided by our observational data set on V921 Sco is that it allows us to simultaneously constrain the geometry of the circumstellar dust disk and the spatial distribution and kinematics of the hot gas in the system (see Figure 6). Such constraints are important, in particular as earlier spatially unresolved studies have associated the origin of the Brγ-line emission with fundamentally different physical mechanisms, including mass infall (e.g., magnetospheric accretion, gaseous inner disks) and mass outflow processes (e.g., stellar winds, X-winds, or disk winds). For V921 Sco, we find that the Brγ-emitting gas clearly shows a rotation-dominated velocity field and orbits the star in the same plane (φ = 145.0 ± 13, i = 54 ± 2°, see Table 2) as the circumstellar dust disk (φ = 1450 ± 84, i = 488 ± 4°), as illustrated in Figure 11. On the other hand, Benisty et al. (2010) found for the Herbig Be-star component in the Z CMa binary system that the Brγ-line emission was displaced along the outflow axis, i.e., presumably perpendicular to the disk plane. Given that the Z CMa observations were obtained during an exceptionally strong outbursting phase of the Z CMa system in 2008, they likely do not represent typical conditions in a Herbig Be star. Another example is provided by MWC 297, where Weigelt et al. (2011) could reproduce important features of the measured wavelength-differential phases using a magnetospheric disk wind model. These examples, V921 Sco (where Brγ was found to trace orbiting gas in the disk plane), Z CMa (where the Brγ-emitting gas was observed in a bipolar wind), and MWC 297 (where the Brγ-emitting might trace a disk wind), illustrate that the Brγ emission is probably not associated with a single astrophysical process, but can trace both mass accretion and outflow processes, as we have already concluded from our small VLTI/AMBER Brγ-survey with spectral resolution R = 1500 (Kraus et al. 2008a). Spatially and spectrally resolved observations on a larger object sample will be essential in order to explore under which circumstances the Brγ-line traces a certain mechanism and to determine the relation with spectroscopic diagnostics.