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Multitechnique testing of the viscous decretion disk model I. The stable and tenuous disk of the late-type Be star $beta$ CMi

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 Added by Robert Klement
 Publication date 2015
  fields Physics
and research's language is English




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The viscous decretion disk (VDD) model is able to explain most of the currently observable properties of the circumstellar disks of Be stars. However, more stringent tests, focusing on reproducing multitechnique observations of individual targets via physical modeling, are needed to study the predictions of the VDD model under specific circumstances. In the case of nearby, bright Be star $beta$ CMi, these circumstances are a very stable low-density disk and a late-type (B8Ve) central star. The aim is to test the VDD model thoroughly, exploiting the full diagnostic potential of individual types of observations, in particular, to constrain the poorly known structure of the outer disk if possible, and to test truncation effects caused by a possible binary companion using radio observations. We use the Monte Carlo radiative transfer code HDUST to produce model observables, which we compare with a very large set of multitechnique and multiwavelength observations that include ultraviolet and optical spectra, photometry covering the interval between optical and radio wavelengths, optical polarimetry, and optical and near-IR (spectro)interferometry. Due to the absence of large scale variability, data from different epochs can be combined into a single dataset. A parametric VDD model with radial density exponent of $n$ = 3.5, which is the canonical value for isothermal flaring disks, is found to explain observables typically formed in the inner disk, while observables originating in the more extended parts favor a shallower, $n$ = 3.0, density falloff. Modeling of radio observations allowed for the first determination of the physical extent of a Be disk (35$^{+10}_{-5}$ stellar radii), which might be caused by a binary companion. Finally, polarization data allowed for an indirect measurement of the rotation rate of the star, which was found to be $W gtrsim 0.98$, i.e., very close to critical.



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66 - P. Harmanec 2019
Bright Be star beta CMi has been identified as a non-radial pulsator on the basis of space photometry with the MOST satellite and also as a single-line spectroscopic binary with a period of 170.4 d. The purpose of this study is to re-examine both these findings, using numerous electronic spectra from the Dominion Astrophysical Observatory, Ondv{r}ejov Observatory, Universitatssterwarte Bochum, archival electronic spectra from several observatories, and also the original MOST satellite photometry. We measured the radial velocity of the outer wings of the double Halpha emission in all spectra at our disposal and were not able to confirm significant radial-velocity changes. We also discuss the problems related to the detection of very small radial-velocity changes and conclude that while it is still possible that the star is a spectroscopic binary, there is currently no convincing proof of it from the radial-velocity measurements. Wavelet analysis of the MOST photometry shows that there is only one persistent (and perhaps slightly variable) periodicity of 0.617 d of the light variations, with a double-wave light curve, all other short periods having only transient character. Our suggestion that this dominant period is the stars rotational period agrees with the estimated stellar radius, projected rotational velocity and with the orbital inclination derived by two teams of investigators. New spectral observations obtained in the whole-night series would be needed to find out whether some possibly real, very small radial-velocity changes cannot in fact be due to rapid line-profile changes.
The observed emission lines of Be stars originate from a circumstellar Keplerian disk that are generally well explained by the Viscous Decretion Disk model. In an earlier work we performed the modeling of the full light curve of the bright Be star $omega$ CMa (Ghoreyshi et al. 2018) with the 1-D time-dependent hydrodynamics code SINGLEBE and the Monte Carlo radiative-transfer code HDUST. We used the V -band light curve that probes the inner disk through four disk formation and dissipation cycles. This new study compares predictions of the same set of model parameters with time-resolved photometry from the near UV through the mid-infrared, comprehensive series of optical spectra, and optical broad-band polarimetry, that overall represent a larger volume of the disk. Qualitatively, the models reproduce the trends in the observed data due to the growth and decay of the disk. However, quantitative differences exist, e.g., an overprediction of the flux increasing with wavelength, too slow decreases in Balmer emission-line strength that are too slow during disk dissipation, and the discrepancy between the range of polarimetric data and the model. We find that a larger value of the viscosity parameter alone, or a truncated disk by a companion star, reduces these discrepancies by increasing the dissipation rate in the outer regions of the disk.
We model the spectral energy distributions (SEDs) of 23 protoplanetary disks in the Taurus-Auriga star-forming region using detailed disk models and a Bayesian approach. This is made possible by combining these models with artificial neural networks to drastically speed up their performance. Such a setup allows us to confront $alpha$-disk models with observations while accounting for several uncertainties and degeneracies. Our results yield high viscosities and accretion rates for many sources, which is not consistent with recent measurements of low turbulence levels in disks. This inconsistency could imply that viscosity is not the main mechanism for angular momentum transport in disks, and that alternatives such as disk winds play an important role in this process. We also find that our SED-derived disk masses are systematically higher than those obtained solely from (sub)mm fluxes, suggesting that part of the disk emission could still be optically thick at (sub)mm wavelengths. This effect is particularly relevant for disk population studies and alleviates previous observational tensions between the masses of protoplanetary disks and exoplanetary systems.
A global disk oscillation implemented in the viscous decretion disk (VDD) model has been used to reproduce most of the observed properties of the well known Be star $zeta$ Tau. 48 Librae shares several similarities with $zeta$ Tau -- they are both early-type Be stars, they display shell characteristics in their spectra, and they exhibit cyclic $V/R$ variations -- but has some marked differences as well, such as a much denser and more extended disk, a much longer $V/R$ cycle, and the absence of the so-called triple-peak features. We aim to reproduce the photometric, polarimetric, and spectroscopic observables of 48 Librae with a self-consistent model, and to test the global oscillation scenario for this target. Our calculations are carried out with the three-dimensional NLTE radiative transfer code HDUST. We employ a rotationally deformed, gravity-darkened central star, surrounded by a disk whose unperturbed state is given by the VDD model. A two-dimensional global oscillation code is then used to calculate the disk perturbation, and superimpose it on the unperturbed disk. A very good, self-consistent fit to the time-averaged properties of the disk is obtained with the VDD. The calculated perturbation has a period $P = 12$ yr, which agrees with the observed period, and the behaviour of the $V/R$ cycle is well reproduced by the perturbed model. The perturbed model improves the fit to the photometric data and reproduces some features of the observed spectroscopic data. Some suggestions to improve the synthesized spectroscopy in a future work are given.
We apply the viscous decretion disc (VDD) model to interpret the infrared disc continuum emission of 80 Be stars observed in different epochs. In this way, we determined 169 specific disc structures, namely their density scale, $rho_0$, and exponent, $n$. We found that the $n$ values range mainly between $1.5$ and $3.5$, and $rho_0$ varies between $10^{-12}$ and $10^{-10},mathrm{g,cm^{-3}}$, with a peak close to the lower value. Our large sample also allowed us to firmly establish that the discs around early-type stars are denser than in late-type stars. Additionally, we estimated the disc mass decretion rates and found that they range between $10^{-12}$ and $10^{-9},mathrm{M_{odot},yr^{-1}}$. These values are compatible with recent stellar evolution models of fast-rotating stars. One of the main findings of this work is a correlation between the $rho_0$ and $n$ values. In order to find out whether these relations can be traced back to the evolution of discs or have some other origin, we used the VDD model to calculate temporal sequences under different assumptions for the time profile of the disc mass injection. The results support the hypothesis that the observed distribution of disc properties is due to a common evolutionary path. In particular, our results suggest that the timescale for disc growth, during which the disc is being actively fed by mass injection episodes, is shorter than the timescale for disc dissipation, when the disc is no longer fed by the star and dissipates as a result of the viscous diffusion of the disc material.
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