M. Scholz

Dynamical opacity-sampling models of Mira variables – II. Time-dependent atmospheric structure and observable properties of four M-type model series

We present four model series of the CODEX dynamical opacity-sampling models of Mira variables with solar abundances, designed to have parameters similar to o Cet, R Leo and R Cas. We demonstrate that the CODEX models provide a clear physical basis for the molecular shell scenario used to explain interferometric observations of Mira variables. We show that these models generally provide a good match to photometry and interferometry at wavelengths between the near-infrared and the radio, and make the model outputs publicly available. These models also demonstrate that, in order to match visible and infrared observations, the Fe-poor silicate grains that form within 3 continuum radii must have small grain radii and therefore cannot drive the winds from O-rich Mira variables.

Inhomogeneities in molecular layers of Mira atmospheres

Abstract : Aims. We investigate the structure and shape of the photospheric and molecular layers of the atmospheres of four Mira variables. Methods. We obtained near-infrared K-band spectro-interferometric observations of the Mira variables R Cnc, X Hya, W Vel, and RW Vel with a spectral resolution of about 1500 using the AMBER instrument at the VLTI. We obtained concurrent JHKL photometry using the Mk II instrument at the SAAO. Results. The Mira stars in our sample are found to 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 corresponding wavelength-dependent uniform disk (UD) diameters show a minimum near the near-continuum bandpass at 2.25 mum. They then increase by up to 30% toward the H2O band at 2.0 mum and by up to 70% at the CO bandheads between 2.29 mum and 2.48 mum. 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 and non-zero values at all wavelengths indicating deviations from point symmetry.

The Keck Aperture Masking Experiment: Multiwavelength Observations of Six Mira Variables

The angular diameters of six oxygen-rich Mira-type long-period variables have been measured at various NIR wavelengths using the aperture-masking technique in an extensive observing program from 1997 January to 2004 September. These data sets span many pulsation cycles of the observed objects and represent the largest study of multiwavelength, multiepoch interferometric angular diameter measurements on Mira stars to date. The calibrated visibility data of ο Cet, R Leo, R Cas, W Hya, χ Cyg, and R Hya are fitted using a uniform disk brightness distribution model to facilitate comparison between epochs, wavelengths, and with existing data and theoretical models. The variation of angular diameter as a function of wavelength and time is studied, and cyclic diameter variations are detected for all objects in our sample. These variations are believed to stem from time-dependent changes of density and temperature (and hence varying molecular opacities) in different layers of these stars. The similarities and differences in behavior between these objects are analyzed and discussed in the context of existing theoretical models. Furthermore, we present time-dependent 3.08 μm angular diameter measurements, probing for the first time these zones of probable dust formation, which show unforeseen sizes and are consistently out of phase with other NIR layers shown in this study. The S-type Mira χ Cyg exhibits significantly different behavior compared to the M-type Mira variables in this study, in both its NIR light curves and its diameter pulsation signature. Our data show that the NIR diameters predicted by current models are too small and need to incorporate additional and/or enhanced opacity mechanisms. Also, new tailored models are needed to explain the behavior of the S-type Mira χ Cyg.

Pulsation of M-type Mira variables with moderately different mass: search for observable mass effects

Models of M-type Miras with masses of 1 and 1. 2M � , i.e. with envelope masses of about 0.4 and 0. 6M � ,h ave been constructed, and a comparison has been made of their observable properties. Geometric pulsation of continuum-forming layers is found to be little affected by the mass difference. The influence of molecular contamination of near-infrared continuum bandpasses upon interferometrically measured fit diameters ranges from undetectable to quite significant. Some pulsation cycles of the lower-mass model Mira show substantially stronger contamination than that found in any cycle of the higher-mass star. Observations which sample pulsation phase well and continuously are crucial for avoiding misinterpretations, because the assignment of absolute pulsation phases is inherently uncertain by at least 0.1 cycles, diameter changes may be strongly phase-dependent, and cycle-to-cycle variations may be substantial. In accord with expectations, we find that cycle-to-cycle variations that show up in light curves and in near-continuum diameters tend to be larger and more common in the low-mass models, leading to one possible way to discriminate mass. Two other methods, based on high-precision measurements of the pulsation amplitude and on derivation of pre-maximum effective temperatures from diameter measurements, are also discussed. High-layer features that may be strongly affected by mass are not well described by present dust-free models. Ke yw ords: techniques: interferometric ‐ stars: AGB and post-AGB ‐ stars: variables: other.

THE KECK APERTURE MASKING EXPERIMENT: SPECTRO-INTERFEROMETRY OF THREE MIRA VARIABLES FROM 1.1 TO 3.8 μm

We present results from a spectro-interferometric study of the Miras o Cet, R Leo, and W Hya obtained with the Keck Aperture Masking Experiment from 1998 September to 2002 July. The spectrally dispersed visibility data permit fitting with circularly symmetric brightness profiles such as a simple uniform disk (UD). The stellar angular diameter obtained over up to ~ 450 spectral channels spanning the region 1.1-3.8 μm is presented. Use of a simple UD brightness model facilitates comparison between epochs and with existing data and theoretical models. Strong size variations with wavelength were recorded for all stars, probing zones of H2O, CO, OH, and dust formation. Comparison with contemporaneous spectra extracted from our data shows a strong anticorrelation between the observed angular diameter and flux. These variations consolidate the notion of a complex stellar atmosphere consisting of molecular shells with time-dependent densities and temperatures. Our findings are compared with existing data and pulsation models. The models were found to reproduce the functional form of the wavelength versus angular diameter curve well, although some departures are noted in the 2.8-3.5 μm range.

Observable effects of dust formation in dynamic atmospheres of M-type Mira variables

The formation of dust with temperature-dependent non-grey opacity is considered in a series of self-consistent model atmospheres at different phases of an O-rich Mira variable of mass 1.2 M_⊙. Photometric and interferometric properties of these models are predicted under different physical assumptions regarding the dust formation. The iron content of the initial silicate that forms and the availability of grain nuclei are found to be critical parameters that affect the observable properties. For certain plausible parameter values, dust would form at 2–3 times the average continuum photospheric radius. This work provides a consistent physical explanation for the larger apparent size of Mira variables at wavelengths shorter than 1 μm than that predicted by dust-free fundamental-mode pulsation models.

Wavelength dependence of angular diameters of M giants: an observational perspective

ABSTRACTWe discuss the wavelength dependence of angular diameters of M giants from an observationalperspective. Observers cannot directly measure an optical-depth radius for a star, despite thisbeing a common theoretical definition. Instead, they can use an interferometer to measure thesquare of the fringe visibility. We present new plots of the wavelength-dependent centre-to-limb variation (CLV) of intensity of the stellar disk as well as visibility for Mira and non-MiraM giant models. We use the terms “CLV spectra” and “visibilit y spectra” for these plots. Wediscuss a model-predicted extreme limb-darkening effect (also called the narrow-bright-coreeffect) in very strong TiO bands which can lead to a misinterpretation of the size of a star inthese bands. We find no evidence as yet that this effect occurs in real stars. Our CLV spectracan explain the similarity in visibilities of R Dor (M8IIIe) that have been observed recentlydespite the use of two different passbands. We compare several observations with models andfind the models generally under-estimate the observed variation in visibility with wavelength.We present CLV and visibility spectra for a model that is applicable to the M supergiant α Ori.Key words: techniques:interferometric,stars: fundamentalparameters, stars: variables: Miras,stars: individual: R Dor, α Ori1 INTRODUCTIONThe radius of a star is considered to be one of its fundamen-tal properties. Stellar radii may be determined from interfer-ometric observations of stellar angular diameters, but starsdo not necessarily appear to us as sharp-edged disks of uni-formbrightness and size. Rather, two effects may be present:limb-darkeningwhich tapers the surface brightness down to-wards the star’s edge and line absorption which changes thestar’s apparent size. Both effects depend on the wavelengthof the observation and are particularly significant in M gi-ants.To determine the radii of M giants from interferomet-ric data, observers have relied upon comparisons with mod-els of the centre-to-limb variation (CLV) of the intensity ofthe stellar disk. The simplest CLV, a uniform disk, is oftenused for this. Alternatively we can use CLVs derived fromappropriate model photospheres of late M giants, since thisprocedure can lead to improvements in these models and agreater understandingof these stars. The model-photosphereCLVs are defined for a particular filter or spectral passband

Mira science with interferometry: a review

Model-predicted and observed properties of the brightness distribution on M-type Mira disks are discussed. Fundamental issues of limb-darkening and diameter definition, of assigning observational data to diameter-type quantities and of interpreting such quantities in terms of model diameters are outlined. The influence of model properties upon interpretation of measured data is clarified. The dependence of the center-to-limb variation (CLV) of intensity on wavelength, on stellar parameters and on variability phase and cycle may be used for analyzing the geometrical and physical structure of the Mira atmosphere, for determining fundamental stellar parameters, and for investigating the quality of models. Desirable future observations include simultaneous observations in different spectral features at different phases and cycles, observation of the position of the shock front and observation of the time- and wavelength-dependence of deviations from spherical symmetry.

Silicate condensation in Mira variables

We study whether the condensation of silicate dust in Mira envelopes could be caused by cluster formation by the abundant SiO molecules. For a simplified model of the pulsational motions of matter in the the outer layers of a Mira variable which is guided by a numerical model for Mira pulsations, the equations of dust nucleation and growth are solved in the co-moving frame of a fixed mass element. It is assumed that seed particles form by clustering of SiO molecules. The calculation of the nucleation rate is based on the experimental data of Nuth and Donn (1982). The quantity of dust formed is calculated by a moment method and the calculation of radiation pressure on the dusty gas is based on a dirty silicate model. Dust nucleation occurs in the model at the upper culmination of the trajectory of a gas parcel where it stays for a considerable time at low temperatures while subsequent dust growth occurs during the descending part of the motion and continues after the next shock reversed motion. It is found that sufficient dust forms that radiation pressure exceeds gravitational pull of the stars such that the mass element is finally driven out of the star. Nucleation of dust particles by clustering of the abundant SiO molecules could be the mechanism that triggers silicate dust formation in Miras.

Effects of moderate abundance changes on the atmospheric structure and colours of Mira variables

Aims. We study the effects of moderate deviations from solar abundances upon the atmospheric structure and colours of typical Mira variables. Methods. We present two model series of dynamical opacity-sampling models of Mira variables which have (1) 1 solar metallicity; and (2) “mild” S-type C/O abundance ratio ([C/O] = 0.9) with typical Zr enhancement (solar +1.0). These series are compared to a previously studied solar-abundance series which has similar fundamental parameters (mass, luminosity, period, radius) that are close to those of o Cet. Results. Both series show noticeable effects of abundance upon stratifications and infrared colours but cycle-to-cycle differences mask these effects at most pulsation phases, with the exception of a narrow-water-filter colour near minimum phase.