arXiv subjects

M. Wittkowski

Publications and source records attributed to M. Wittkowski.

At least 73 records · Page 4Linked to original sources

arXiv2012

Radio and IR interferometry of SiO maser stars

Radio and infrared interferometry of SiO maser stars provide complementary information on the atmosphere and circumstellar environment at comparable spatial resolution. Here, we present the latest results on the atmospheric structure and the dust condensation region of AGB stars based on our recent infrared spectro-interferometric observations, which represent the environment of SiO masers. We discuss, as an example, new results from simultaneous VLTI and VLBA observations of the Mira variable AGB star R Cnc, including VLTI near- and mid-infrared interferometry, as well as VLBA observations of the SiO maser emission toward this source. We present preliminary results from a monitoring campaign of high-frequency SiO maser emission toward evolved stars obtained with the APEX telescope, which also serves as a precursor of ALMA images of the SiO emitting region. We speculate that large-scale long-period chaotic motion in the extended molecular atmosphere may be the physical reason for observed deviations from point symmetry of atmospheric molecular layers, and for the observed erratic variability of high-frequency SiO maser emission

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arXiv2012

Fundamental properties and atmospheric structure of the red supergiant VY CMa based on VLTI/AMBER spectro-interferometry

We investigate the atmospheric structure and fundamental properties of the red supergiant VY CMa. We obtained near-infrared spectro-interferometric observations of VY CMa with spectral resolutions of 35 and 1500 using the AMBER instrument at the VLTI. The visibility data indicate the presence of molecular layers of water vapor and CO in the extended atmosphere with an asymmetric morphology. The uniform disk diameter in the water band around 2.0 mu is increased by \sim20% compared to the near-continuum bandpass at 2.20-2.25 mu and in the CO band at 2.3-2.5 mu it is increased by up to \sim50%. The closure phases indicate relatively small deviations from point symmetry close to the photospheric layer, and stronger deviations in the extended H2O and CO layers. Making use of the high spatial and spectral resolution, a near-continuum bandpass can be isolated from contamination by molecular and dusty layers, and the Rosseland-mean photospheric angular diameter is estimated to 11.3 +/- 0.3 mas based on a PHOENIX atmosphere model. Together with recent high-precision estimates of the distance and spectro-photometry, this estimate corresponds to a radius of 1420 +/- 120 Rsun and an effective temperature of 3490 +/- 90 K. VY CMa exhibits asymmetric, possibly clumpy, atmospheric layers of H2O and CO, which are not co-spatial, within a larger elongated dusty envelope. Our revised fundamental parameters put VY CMa close to the Hayashi limit of recent evolutionary tracks of initial mass 25 Msun with rotation or 32 Msun without rotation, shortly before evolving blueward in the HR-diagram.

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arXiv2011

Near-infrared spectro-interferometry of three OH/IR Stars with the VLTI/AMBER instrument

We investigate the molecular and dusty environment of OH/IR stars in order to characterize the mass-loss process during the tip-AGB superwind phase. Employing the AMBER instrument at the VLT Interferometer we obtained near-infrared H- and K-band spectro-interferometric observations of the three OH/IR stars IRAS 13479-5436, IRAS 14086-6907 and IRAS 17020-5254 with a spectral resolution of about 35. We use a two-component geometrical model, consisting of a uniform disk and a Gaussian disk, to obtain characteristic angular sizes of the central stellar sources and their dust envelopes, as well as the flux ratios between these components. Angular uniform disk diameters of the three central components of the objects above have values between 3.2 mas and 5.4 mas. For their dust envelopes, we find FWHM values between 17.1 mas and 25.2 mas. According to distance estimates from the literature, the central stellar components have radii between 900 R_sun and 1400 R_sun, while their dust envelopes reach FWHM values between 9000 R_sun and 13000 R_sun. The visibility functions of all three sources exhibit wavelength variations that resemble those of earlier VLTI/AMBER observations of semi-regular and Mira variable AGB stars. These are interpreted as characteristic of atmospheric molecular layers lying above the photosphere. We also find that the dust envelopes have a clearly larger optical depth than those known for Mira stars. We interpret this as an expected result of the "superwind" phase, the final 10 000 to 30 000 years of AGB-evolution, when the mass-loss rate increases by a factor of 10-100. By their different optical depths, the three dust shells studied here may represent different stages of the "superwind" and different initial masses.

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arXiv2011

The 2011 outburst of the recurrent novaT Pyx. Evidence for a face-on bipolar ejection

We report on near-IR interferometric observations of the outburst of the recurrent nova T Pyx. We obtained near-IR observations of T Pyx at dates ranging from t=2.37d to t=48.2d after the outburst, with the CLASSIC recombiner, located at the CHARA array, and with the PIONIER and AMBER recombiners, located at the VLTI array. These data are supplemented with near-IR photometry and spectra obtained at Mount Abu, India. Slow expansion velocities were measured (<300km/s) before t=20d (assuming D=3.5kpc). From t=28d on, the AMBER and PIONIER continuum visibilities (K and H band, respectively) are best simulated with a two component model consisting of an unresolved source plus an extended source whose expansion velocity onto the sky plane is lower than 700km/s. The expansion of the Brgamma line forming region, as inferred at t=28d and t=35d is slightly larger, implying velocities in the range 500-800km/s, still strikingly lower than the velocities of 1300-1600km/s inferred from the Doppler width of the line. Moreover, a remarkable pattern was observed in the Brgamma differential phases. A semi-quantitative model using a bipolar flow with a contrast of 2 between the pole and equator velocities, an inclination of i=15^{\circ} and a position angle P.A.=110^{\circ} provides a good match to the AMBER observables (spectra, differential visibilities and phases). At t=48d, a PIONIER dataset confirms the two component nature of the H band emission, consisting of an unresolved stellar source and an extended region whose appearance is circular and symmetric within error bars.These observations are most simply interpreted within the frame of a bipolar model, oriented nearly face-on. This finding has profound implications for the interpretation of past, current and future observations of the expanding nebula.

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arXiv2011

Mid-infrared interferometric monitoring of evolved stars - The dust shell around the Mira variable RR Aql at 13 epochs

We obtained 13 epochs of mid-infrared interferometry with the MIDI instrument at the VLTI between April 2004 and July 2007, covering pulsation phases 0.45-0.85 within four cycles. The data are modeled with a radiative transfer model of the dust shell where the central stellar intensity profile is described by a series of dust-free dynamic model atmospheres based on self-excited pulsation models. We examined two dust species, silicate and Al2O3 grains. We performed model simulations using variations in model phase and dust shell parameters to investigate the expected variability of our photometric and interferometric data. The observed visibility spectra do not show any indication of variations as a function of pulsation phase and cycle. The observed photometry spectra may indicate intracycle and cycle-to-cycle variations at the level of 1-2 standard deviations. The best-fitting model for our average pulsation phase of 0.64+/-0.15 includes the dynamic model atmosphere M21n (T_model=2550 K) with a photospheric angular diameter of 7.6+/-0.6 mas, and a silicate dust shell with an optical depth of 2.8+/-0.8, an inner radius of 4.1+/-0.7 R_Phot, and a power-law index of the density distribution of 2.6+/-0.3. The addition of an Al2O3 dust shell did not improve the model fit. The photospheric angular diameter corresponds to a radius of 520^+230_-140 R_sun and an effective temperature of ~ 2420+/-200 K. Our modeling simulations confirm that significant visibility variations are not expected for RR Aql at mid-infrared wavelengths within our uncertainties. We conclude that our RR Aql data can be described by a pulsating atmosphere surrounded by a silicate dust shell. The effects of the pulsation on the mid-infrared flux and visibility values are expected to be less than about 25% and 20%, respectively, and are too low to be detected within our measurement uncertainties.

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arXiv2011

Inhomogeneities in molecular layers of Mira atmospheres

We obtained K-band spectro-interferometric observations of the Miras R Cnc, X Hya, W Vel, and RW Vel with a spectral resolution of 1500 using the VLTI/AMBER instrument. We obtained concurrent JHKL photometry using the the Mk II instrument at the SAAO. Our sources have wavelength-dependent visibility values that are consistent with earlier low-resolution AMBER observations of S Ori and with the predictions of dynamic model atmosphere series based on self-excited pulsation models. The wavelength-dependent UD diameters show a minimum near the near-continuum bandpass at 2.25 um. They increase by up to 30% toward the H2O band at 2.0 um and by up to 70% at the CO bandheads. The dynamic model atmosphere series show a consistent wavelength-dependence, and their parameters such as the visual phase, effective temperature, and distances are consistent with independent estimates. The closure phases have significantly wavelength-dependent non-zero values indicating deviations from point symmetry. For example, the R Cnc closure phase is 110 degr in the 2.0 um H2O band, corresponding for instance to an additional unresolved spot contributing 3% of the total flux at a separation of ~4 mas. Our observations are consistent with the predictions of the latest dynamic model atmosphere series based on self-excited pulsation models. The wavelength-dependent radius variations are interpreted as the effect of molecular layers. The wavelength-dependent closure phase values are indicative of deviations from point symmetry at all wavelengths, thus a complex non-spherical stratification of the extended atmosphere. In particular, the significant deviation from point symmetry in the H2O band is interpreted as a signature on large scales of inhomogeneities or clumps in the water vapor layer. The observed inhomogeneities might be caused by pulsation- and shock-induced chaotic motion in the extended atmosphere.

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arXiv2011

The extended atmospheres of Mira variables probed by VLTI, VLBA, and APEX

We present an overview on our project to study the extended atmospheres and dust formation zones of Mira stars using coordinated observations with the Very Large Telescope Interferometer (VLTI), the Very Long Baseline Array (VLBA), and the Atacama Pathfinder Experiment (APEX). The data are interpreted using an approach of combining recent dynamic model atmospheres with a radiative transfer model of the dust shell, and combining the resulting model structure with a maser propagation model.

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arXiv2011

Structure and shaping processes within the extended atmospheres of AGB stars

We present recent studies using the near-infrared instrument AMBER of the VLT Interferometer (VLTI) to investigate the structure and shaping processes within the extended atmosphere of AGB stars. Spectrally resolved near-infrared AMBER observations of the Mira variable S Ori have revealed wavelength-dependent apparent angular sizes. These data were successfully compared to dynamic model atmospheres, which predict wavelength-dependent radii because of geometrically extended molecular layers. Most recently, AMBER closure phase measurements of several AGB stars have also revealed wavelength-dependent deviations from 0/180 deg., indicating deviations from point symmetry. The variation of closure phase with wavelength indicates a complex non-spherical stratification of the extended atmosphere, and may reveal whether observed asymmetries are located near the photosphere or in the outer molecular layers. Concurrent observations of SiO masers located within the extended molecular layers provide us with additional information on the morphology, conditions, and kinematics of this shell. These observations promise to provide us with new important insights into the shaping processes at work during the AGB phase. With improved imaging capabilities at the VLTI, we expect to extend the successful story of imaging studies of planetary nebulae to the photosphere and extended outer atmosphere of AGB stars.

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arXiv2011

AMBER observations of the AGB star RS Cap: extended atmosphere and comparison with stellar models

We report on K-band VLTI/AMBER observations at medium spectral resolution ($\sim$1500) of RS Capricorni, an M6/M7III semi-regular AGB star. From the spectrally-dispersed visibilities, we measure the star diameter as a function of observing wavelength from 2.13 to 2.47 microns. We derive a Rosseland angular diameter of $7.95 \pm 0.07$ mas, which corresponds to an effective temperature of $3160 \pm 160$ K. We detect size variations of around 10% in the CO band heads, indicating strong opacity effects of CO in the stellar photosphere. We also detect a linear increase of the size as a function of wavelength, beginning at 2.29 microns. Models of the stellar atmosphere, based on the mass of the star as estimated from stellar-evolution models, predict CO-size effects about half of those observed, and cannot reproduce the linear size increase with wavelength, redward of 2.29 microns. We are able to model this linear size increase with the addition of an extended water-vapor envelope around the star. However, we are not able to fit the data in the CO bandheads. Either the mass of the star is overestimated by the stellar-evolution models and/or there is an additional extended CO envelope in the outer part of the atmosphere. In any case, neither the water-vapor envelope, nor the CO envelope, can be explained using the current models.

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arXiv2010

Ellipsoidal primary of the RS CVn binary zeta And: Investigation using high-resolution spectroscopy and optical interferometry

We have obtained high-resolution spectroscopy, optical interferometry, and long-term broad band photometry of the ellipsoidal primary of the RS CVn-type binary system zeta And. Based on the optical interferometry the apparent limb darkened diameter of zeta And is 2.55 +/- 0.09 mas using a uniform disk fit. The Hipparcos distance and the limb-darkened diameter obtained with a uniform disk fit give stellar radius of 15.9 +/- 0.8 Rsolar, and combined with bolometric luminosity, it implies an effective temperature of 4665 +/- 140 K. The temperature maps obtained from high resolution spectra using Doppler imaging show a strong belt of equatorial spots and hints of a cool polar cap. The equatorial spots show a concentration around the phase 0.75. This spot configuration is reminiscent of the one seen in the earlier published temperature maps of zeta And. Investigation of the Halpha line reveals both prominences and cool clouds in the chromosphere. Long-term photometry spanning 12 years shows hints of a spot activity cycle, which is also implied by the Doppler images, but the cycle length cannot be reliably determined from the current data.

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arXiv2009

VLTI/AMBER spectro-interferometric imaging of VX Sgr's inhomogenous outer atmosphere

Aims. We aim to explore the photosphere of the very cool late-type star VX Sgr and in particular the existence and characterization of molecular layers above the continuum forming photosphere. Methods. We obtained interferometric observations with the VLTI/AMBER interferometer using the fringe tracker FINITO in the spectral domain 1.45-2.50 micron with a spectral resolution of about 35 and baselines ranging from 15 to 88 meters.We perform independent image reconstruction for different wavelength bins and fit the interferometric data with a geometrical toy model.We also compare the data to 1D dynamical models of Miras atmosphere and to 3D hydrodynamical simulations of red supergiant (RSG) and asymptotic giant branch (AGB) stars. Results. Reconstructed images and visibilities show a strong wavelength dependence. The H-band images display two bright spots whose positions are confirmed by the geometrical toy model. The inhomogeneities are qualitatively predicted by 3D simulations. At about 2,00 micron and in the region 2,35 - 2,50 micron, the photosphere appears extended and the radius is larger than in the H band. In this spectral region, the geometrical toy model locates a third bright spot outside the photosphere that can be a feature of the molecular layers. The wavelength dependence of the visibility can be qualitatively explained by 1D dynamical models of Mira atmospheres. The best-fitting photospheric models show a good match with the observed visibilities and give a photospheric diameter of theta = 8,82+-0,50 mas. The H2O molecule seems to be the dominant absorber in the molecular layers. Conclusions. We show that the atmosphere of VX Sgr rather resembles Mira/AGB star model atmospheres than RSG model atmospheres. In particular, we see molecular (water) layers that are typical for Mira stars.

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arXiv2009

Resolving the asymmetric inner wind region of the yellow hypergiant IRC+10420 with VLTI/AMBER in low and high spectral resolution mode

We obtained near-infrared long-baseline interferometry of IRC+10420 with the AMBER instrument of ESO's Very Large Telescope Interferometer (VLTI) in low and high spectral resolution (HR) mode to probe the photosphere and the innermost circumstellar environment of this rapidly evolving yellow hypergiant. In the HR observations, the visibilities show a noticeable drop across the Brackett gamma (BrG) line on all three baselines, and we found differential phases up to -25 degrees in the redshifted part of the BrG line and a non-zero closure phase close to the line center. The calibrated visibilities were corrected for AMBER's limited field-of-view to appropriately account for the flux contribution of IRC+10420's extended dust shell. We derived FWHM Gaussian sizes of 1.05 +/- 0.07 and 0.98 +/- 0.10 mas for IRC+10420's continuum-emitting region in the H and K bands, respectively, and the BrG-emitting region can be fitted with a geometric ring model with a diameter of 4.18 +0.19/-0.09 mas, which is approximately 4 times the stellar size. The geometric model also provides some evidence that the BrG line-emitting region is elongated towards a position angle of 36 degrees, well aligned with the symmetry axis of the outer reflection nebula. The HR observations were further analyzed by means of radiative transfer modeling using CMFGEN and the 2-D Busche & Hillier codes. Our spherical CMFGEN model poorly reproduces the observed line shape, blueshift, and extension, definitively showing that the IRC+10420 outflow is asymmetric. Our 2-D radiative transfer modeling shows that the blueshifted BrG emission and the shape of the visibility across the emission line can be explained with an asymmetric bipolar outflow with a high density contrast from pole to equator (8-16), where the redshifted light is substantially diminished.

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arXiv2008

An Improved Model of SiO Maser Emission in Miras

We describe a combined dynamic atmosphere and maser propagation model of SiO maser emission in Mira variables. This model rectifies many of the defects of an earlier model of this type, particularly in relation to the infra-red (IR) radiation field generated by dust and various wavelength-dependent, optically thick layers. Modelled masers form in rings with radii consistent with those found in VLBI observations and with earlier models. This agreement requires the adoption of a radio photosphere of radius approximately twice that of the stellar photosphere, in agreement with observations. A radio photosphere of this size renders invisible certain maser sites with high amplification at low radii, and conceals high-velocity shocks, which are absent in radio continuum observations. The SiO masers are brightest at an optical phase of 0.1 to 0.25, which is consistent with observed phase-lags. Dust can have both mild and profound effects on the maser emission. Maser rings, a shock and the optically thick layer in the SiO pumping band at 8.13\micron appear to be closely associated in three out of four phase samples.

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arXiv2008

The structure of the protoplanetary disk surrounding three young intermediate mass stars. II. Spatially resolved dust and gas distribution

[Abridged] We present the first direct comparison of the distribution of the gas, as traced by the [OI] 6300 AA emission, and the dust, as traced by the 10 micron emission, in the protoplanetary disk around three intermediate-mass stars: HD 101412, HD 135344 B and HD 179218. N-band visibilities were obtained with VLTI/MIDI. Simple geometrical models are used to compare the dust emission to high-resolution optical spectra in the 6300 AA [OI] line of the same targets. The disks around HD 101412 and HD 135344 B appear strongly flared in the gas, but self-shadowed in the dust beyond ~ 2 AU. In both systems, the 10 micron emission is rather compact (< 2 AU) while the [OI] brightness profile shows a double peaked structure. The inner peak is strongest and is consistent with the location of the dust, the outer peak is fainter and is located at 5-10 AU. Spatially extended PAH emission is found in both disks. The disk around HD 179218 is flared in the dust. The 10 micron emission emerges from a double ring-like structure with the first ring peaking at ~ 1 AU and the second at ~ 20 AU. No dust emission is detected between ~ 3 -- 15 AU. The oxygen emission seems also to come from a flared structure, however, the bulk of this emission is produced between ~ 1 -- 10 AU. This could indicate a lack of gas in the outer disk or could be due to chemical effects which reduce the abundance of OH -- the parent molecule of the observed [OI] emission -- further away from the star. The three systems, HD 179218, HD 135344 B and HD 101412, may form an evolutionary sequence: the disk initially flared becomes flat under the combined action of gas-dust decoupling, grain growth and dust settling.

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arXiv2008

VLTI monitoring of the dust formation event of the Nova V1280 Sco

We present the first high spatial resolution monitoring of the dust forming nova V1280 Sco performed with the Very Large Telescope Interferometer (VLTI). Spectra and visibilities were obtained from the onset of the dust formation 23 days after discovery till day 145, using the instruments AMBER and MIDI. These interferometric observations are complemented by near-infrared data from the 1.2m Mt. Abu Infrared Observatory, India. The observations are first interpreted with simple models but more complex models, involving a second shell, are necessary to explain the data obtained from t=110d after outburst. This behavior is in accordance with the light curve of V1280 Sco which exhibits a secondary peak around t=106d, followed by a new steep decline, suggesting a new dust forming event. Spherical dust shell models generated with the DUSTY code are also used to investigate the parameters of the main dust shell. Using uniform disk and Gaussian models, these observations allow us to determine an apparent linear expansion rate for the dust shell of 0.35 +/- 0.03 mas/day and the approximate time of ejection of the matter in which dust formed as t_ejec=10.5+/-7d, i.e. close to the maximum brightness. This information, combined with the expansion velocity of 500+/-100km/s, implies a distance estimate of 1.6+/-0.4kpc. The dust mass generated was typically 2-8 10^-9 solar mass per day. Considering that the dust forming event lasted at least 200-250d, the mass of the ejected material is likely to have exceeded 10^-4 solar mass.

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arXiv2008

J, H, K spectro-interferometry of the Mira variable S Orionis

Aims: We present J, H, K interferometry with a spectral resolution of 35 for the Mira variable S Orionis. We aim at measuring the diameter variation as a function of wavelength that is expected due to molecular layers lying above the continuum-forming photosphere. Methods: Visibility data of S Ori were obtained at phase 0.78 with the VLTI/AMBER instrument using the fringe tracker FINITO at 29 spectral channels between 1.29 and 2.32 mu. Apparent uniform disk (UD) diameters were computed for each spectral channel. In addition, the visibility data were directly compared to predictions by recent self-excited dynamic model atmospheres. Results: S Ori shows significant variations in the visibility values as a function of spectral channel that can only be described by a clear variation in the apparent angular size with wavelength. The closure phase values are close to zero at all spectral channels, indicating the absence of asymmetric intensity features. The apparent UD angular diameter is smallest at about 1.3 and 1.7 mu and increases by a factor of ~1.4 around 2.0 mu. The minimum UD angular diameter is 8.1 pm 0.5 mas, corresponding to ~420 R_sun. The S Ori visibility data and the apparent UD variations can be explained reasonably well by a dynamic atmosphere model that includes molecular layers. Conclusions: The measured visibility and UD diameter variations with wavelength resemble and generally confirm the predictions by recent dynamic model atmospheres. [abridged]

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arXiv2007

Resolving the complex structure of the dust torus in the active nucleus of the Circinus galaxy

To test the dust torus model for active galactic nuclei directly, we study the extent and morphology of the nuclear dust distribution in the Circinus galaxy using high resolution interferometric observations in the mid-infrared with the MIDI instrument at the Very Large Telescope Interferometer. We find that the dust distribution in the nucleus of Circinus can be explained by two components, a dense and warm disk-like component of 0.4 pc size and a slightly cooler, geometrically thick torus component with a size of 2.0 pc. The disk component is oriented perpendicular to the ionisation cone and outflow and seems to show the silicate feature at 10 micron in emission. It coincides with a nuclear maser disk in orientation and size. From the energy needed to heat the dust, we infer a luminosity of the accretion disk corresponding to 20% of the Eddington luminosity of the nuclear black hole. We find that the interferometric data are inconsistent with a simple, smooth and axisymmetric dust emission. The irregular behaviour of the visibilities and the shallow decrease of the dust temperature with radius provide strong evidence for a clumpy or filamentary dust structure. We see no evidence for dust reprocessing, as the silicate absorption profile is consistent with that of standard galactic dust. We argue that the collimation of the ionising radiation must originate in the geometrically thick torus component. Our findings confirm the presence of a geometrically thick, torus-like dust distribution in the nucleus of Circinus, as required in unified schemes of Seyfert galaxies. Several aspects of our data require that this torus is irregular, or "clumpy".

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arXiv2007

The Mira variable S Ori: Relationships between the photosphere, molecular layer, dust shell, and SiO maser shell at 4 epochs

We present the first multi-epoch study that includes concurrent mid-infrared and radio interferometry of an oxygen-rich Mira star. We obtained mid-infrared interferometry of S Ori with VLTI/MIDI at four epochs between December 2004 and December 2005. We concurrently observed v=1, J=1-0 (43.1 GHz), and v=2, J=1-0 (42.8 GHz) SiO maser emission toward S Ori with the VLBA at three epochs. The MIDI data are analyzed using self-excited dynamic model atmospheres including molecular layers, complemented by a radiative transfer model of the circumstellar dust shell. The VLBA data are reduced to the spatial structure and kinematics of the maser spots. The modeling of our MIDI data results in phase-dependent continuum photospheric angular diameters between about 7.9 mas (Phase 0.55) and 9.7 mas (Phase 1.16). The dust shell can best be modeled with Al2O3 grains using phase-dependent inner boundary radii between 1.8 and 2.4 photospheric radii. The dust shell appears to be more compact with greater optical depth near visual minimum, and more extended with lower optical depth after visual maximum. The ratios of the SiO maser ring radii to the photospheric radii are between about 1.9 and 2.4. The maser spots mark the region of the molecular atmospheric layers just beyond the steepest decrease in the mid-infrared model intensity profile. Their velocity structure indicates a radial gas expansion. Al2O3 dust grains and SiO maser spots form at relatively small radii of 1.8-2.4 photospheric radii. Our results suggest increased mass loss and dust formation close to the surface near the minimum visual phase, when Al2O3 dust grains are co-located with the molecular gas and the SiO maser shells, and a more expanded dust shell after visual maximum. Silicon does not appear to be bound in dust, as our data show no sign of silicate grains.

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