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

We discuss the wavelength dependence of angular diameters of M giants from an observational perspective. Observers cannot directly measure an optical-depth radius for a star, despite this being a common theoretical definition. Instead, they can use an interferometer to measure the square of the fringe visibility. We present new plots of the wavelength-dependent centre-to-limb variation (CLV) of intensity of the stellar disc as well as visibility for Mira and non-Mira M giant models. We use the terms 'CLV spectra' and 'visibility spectra' for these plots. We discuss a model-predicted extreme limb-darkening effect (also called the narrow-bright-core effect) in very strong TiO bands which can lead to a misinterpretation of the size of a star in these bands. We find no evidence as yet that this effect occurs in real stars. Our CLV spectra can explain the similarity in visibilities of R Dor (M8IIIe) that have been observed recently, despite the use of two different passbands. We compare several observations with models, and find that the models generally underestimate 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.     

Angular diameter and effective temperature of a sample of 15 M giants at 2.2 μm from lunar occultation observations

High angular resolution measurements of a sample of 15 M giants at 2.2 μm by the technique of lunar occultation are presented in this paper. We obtain angular diameters for 11 sources of which five are the first diameter measurements. For these resolved sources we have estimated the effective temperatures, which are consistent with previous calibrations. For the other four sources we put the first upper limits on their angular sizes to be 2 mas. Two sources, namely IRC+20090 and IRC+20067, yield appreciably low temperatures, which could point to their possible Mira nature. For sources with Hipparcos parallax measurements, we have calculated the linear radii.     

Accurate fundamental parameters for lower main-sequence stars

We derive an empirical effective temperature and bolometric luminosity calibration for G and K dwarfs, by applying our own implementation of the Infrared Flux Method to multiband photometry. Our study is based on 104 stars for which we have excellent   BV ( RI )_C JHK _S  photometry, excellent parallaxes and good metallicities.
Colours computed from the most recent synthetic libraries (ATLAS9 and MARCS) are found to be in good agreement with the empirical colours in the optical bands, but some discrepancies still remain in the infrared. Synthetic and empirical bolometric corrections also show fair agreement.
A careful comparison to temperatures, luminosities and angular diameters obtained with other methods in the literature shows that systematic effects still exist in the calibrations at the level of a few per cent. Our Infrared Flux Method temperature scale is 100-K hotter than recent analogous determinations in the literature, but is in agreement with spectroscopically calibrated temperature scales and fits well the colours of the Sun. Our angular diameters are typically 3 per cent smaller when compared to other (indirect) determinations of angular diameter for such stars, but are consistent with the limb-darkening corrected predictions of the latest 3D model atmospheres and also with the results of asteroseismology.
Very tight empirical relations are derived for bolometric luminosity, effective temperature and angular diameter from photometric indices.
We find that much of the discrepancy with other temperature scales and the uncertainties in the infrared synthetic colours arise from the uncertainties in the use of Vega as the flux calibrator. Angular diameter measurements for a well-chosen set of G and K dwarfs would go a long way to addressing this problem.     

Hipparcos parallaxes for Mira-like long-period variables

This paper concerns the calibration of the K period–luminosity relation for Mira variables using Hipparcos parallaxes. K magnitudes are available for 255 Mira-like variables which were observed by Hipparcos . Period–luminosity zero-points are evaluated for various subgroups of data. The best solution for oxygen-rich Miras, which uses 180 stars, omitting the short-period red group (which had different kinematics from the short-period blue stars) and the low-amplitude variables, provides a zero-point of     which implies a distance modulus for the Large Magellanic Cloud of     or perhaps slightly greater if a metallicity correction is required, in good agreement with the value derived from Cepheids. The zero-point of the period–luminosity relation for carbon stars is briefly discussed.
Linear diameters are derived for red variables with measured angular diameters and parallaxes, and are used to examine the long-standing question of the pulsation mode(s) of these stars. Evidence is presented to suggest that most of them are pulsating in the same mode and, if published model atmospheres are correct, this is probably the first overtone. Some discussion is given of sequences in the period–luminosity and period–colour diagrams and their bearing on the pulsation mode problem.     

A merger tree with microsolar mass resolution: application to γ-ray emission from subhalo population

Observations of the southern Cepheid ℓ Car to yield the mean angular diameter and angular pulsation amplitude have been made with the Sydney University Stellar Interferometer at a wavelength of 696 nm. The resulting mean limb-darkened angular diameter is 2.990 ± 0.017 mas (i.e. ± 0.6 per cent) with a maximum-to-minimum amplitude of 0.560 ± 0.018 mas corresponding to 18.7 ± 0.6 per cent in the mean stellar diameter. Careful attention has been paid to uncertainties, including those in measurements, in the adopted calibrator angular diameters, in the projected values of visibility squared at zero baseline, and to systematic effects. No evidence was found for a circumstellar envelope at 696 nm. The interferometric results have been combined with radial displacements of the stellar atmosphere derived from selected radial velocity data taken from the literature to determine the distance and mean diameter of ℓ Car. The distance is determined to be 525 ± 26 pc and the mean radius  169 ± 8 R_⊙  . Comparison with published values for the distance and mean radius shows excellent agreement, particularly when a common scaling factor from observed radial velocity to pulsation velocity of the stellar atmosphere (the p -factor) is used.     

New views of Betelgeuse: multi-wavelength surface imaging and implications for models of hotspot generation

We report contemporaneous multi-wavelength interferometric imaging of the red supergiant star Betelgeuse ( α Orionis), using the Cambridge Optical Aperture Synthesis Telescope (COAST) and the William Herschel Telescope (WHT), at wavelengths of 700, 905 and 1290 nm. We find a strong variation in the apparent symmetry of the stellar brightness distribution as a function of wavelength. At 700 nm the star is highly asymmetric, and can be modelled as the superposition of three bright spots on a strongly limb-darkened disc. However, at 905 nm only a single low-contrast feature is visible and at 1290 nm the star presents a featureless symmetric disc. The change in spot contrast with wavelength is consistent with a model in which the bright spots represent unobscured areas of elevated temperature, owing perhaps to convection, on a stellar disc that itself has a different appearance, i.e. geometrical extent and limb-darkening profile, at different wavelengths. The featureless centre-to-limb brightness profile seen at 1290 nm is consistent with this model and suggests that future interferometric monitoring of the star to quantify the size changes associated with radial velocity variations should be performed at similar wavelengths in the near-infrared.     

Supergiant temperatures and linear radii from near-infrared interferometry

We present angular diameters for 42 Luminosity Class (LC) I stars and 32 LC II stars that have been interferometrically determined with the Palomar Testbed Interferometer. Derived values of radius and effective temperature are established for these objects, and an empirical calibration of these parameters for supergiants will be presented as a function of spectral type and colours. For the effective temperature versus  ( V − K )₀  colour, we find an empirical calibration with a median deviation of  Δ T = 70 K  in the range of  0.7 < ( V − K )₀ < 5.1  for LC I stars; for LC II, the median deviation is  Δ T = 120 K  from  0.4 < ( V − K )₀ < 4.3  . Effective temperature as a function of spectral type is also calibrated from these data, but shows significantly more scatter than the T _EFF versus  ( V − K )₀  relationship. No deviation of T _EFF versus spectral type is seen for these high-luminosity objects relative to LC II giants. Directly determined diameters range up to  400 R_⊙  , though are limited by poor distance determinations, which dominate the error estimates. These temperature and radii measures reflect a direct calibration of these parameters for supergiants from empirical means.     

Structure and evolution of low-mass W Ursae Majoris type systems – III. The effects of the spins of the stars

In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low-mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low-mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non-contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast-rotating star after about 1200 cycles of evolution (about  7.0 × 10⁹ yr  ).     

The bright southern Cepheid β Doradus: the radial velocity curve, distance and size

A new high-accuracy velocity curve is presented for the bright southern Cepheid β Doradus (HR 1922), and an investigation into the long-term stability of the velocity curve is made. An upper limit of 0.57 km s⁻¹ is placed on cycle-to-cycle variations. This work is compared with a similar analysis previously applied to the long-period Cepheid ℓ Carinae (HR 3884).   Using a near-infrared variant of the Barnes–Evans method, the mean radius of and distance to β Dor are found to be R  = 67.8 ± 0.7 R⊙ and d  = 349 ± 4 pc. The systematic errors in these parameters are less than 3 per cent. If these systematics can be resolved, through the development of advanced theoretical models and/or the direct measurement of angular diameters, a calibration of the cosmic distance scale to better than 1 per cent can be achieved.     

The accurate determination of stellar angular diameters using broad-band stellar interferometry

The angular diameter of a star can be estimated from interferometric observations by fitting the data with the visibility function for a uniformly illuminated disc and then using published correction factors to convert the uniform-disc angular diameter to the limb-darkened angular diameter. The correction factors are strictly valid only for monochromatic light. We investigate the effect of using a broad bandwidth, and present a simple method for calculating broad-band correction factors from the monochromatic factors.
The technique of fitting the data with a uniform-disc visibility function is only useful for stars with compact atmospheres and 'typical' limb-darkening profiles. It should not be applied to stars with extended atmospheres or that show extreme limb darkening. These stars have visibility functions that are qualitatively different from a uniform-disc visibility function, so they can be distinguished observationally from compact-atmosphere stars.     

Disk luminosity and angular momentum for accreting,weak field neutron stars in the ‘Slow’ rotation approximation

For accretion on to neutron stars possessing weak surface magnetic fields and substantial rotation rates (corresponding to the secular instability limit), we calculate the disk and surface layer luminosities general relativistically using the Hartle & Thorne formalism, and illustrate these quantities for a set of representative neutron star equations of state. We also discuss the related problem of the angular momentum evolution of such neutron stars and give a quantitative estimate for this accretion driven change in angular momentum. Rotation always increases the disk luminosity and reduces the rate of angular momentum evolution. These effects have relevance for observations of low-mass X-ray binaries.     

On the Physical Processes in Contact Binary Systems

Three importantphysical processes occurringin contact binarysystems are studied. The first one is the effect of spin, orbital rotation and tide on the structure of the components, which includes also the effect of meridian circulation on the mixing of the chemical elements in the components. The second one is the mass and energy exchange between the components. To describe the energy exchange, a new approach is introduced based on the understanding that the exchange is due to the release of the potential, kinetic and thermal energy of the exchanged mass. The third is the loss of mass and angular momentum through the outer Lagrangian point. The rate of mass loss and the angular momentum carried away by the lost mass are discussed. To show the effects of these processes, we follow the evolution of a binary system consisting of a 12M and a 5M star with mass exchange between the components and mass loss via the outer Lagrangian point, both with and without considering the effects of rotation and tide. The result shows that the effect of rotation and tide advances the start of the semi-detached and the contact phases, and delays the end of the hydrogen-burning phase of the primary. Furthermore, it can change not only the occurrence of mass and angular momentum loss via the outer Lagrangian point, but also the contact or semi-contact status of the system. Thus, this effect can result in the special phenomenon of short-term variations occurring over a slow increase of the orbital period. The occurrence of mass and angular momentum loss via the outer Lagrangian point can affect the orbital period of the system significantly, but this process can be influenced, even suppressed out by the effect of rotation and tide. The mass and energy exchange occurs in the common envelope. The net result of the mass exchange process is a mass transfer from the primary to the secondary during the whole contact phase.     

Photometric Monitoring of ROSAT-Selected Weak Line T Tauri Stars

We monitored the light curves of 22 weak-line T Tauri stars (WTTSs) discovered among the X-ray sources in the field of the Taurus-Auriga cloud. For 12 of the 22 WTTSs photometric periodic variability is confirmed and their rational periods are determined using Phase Dispersion Minimization (PDM) and Fourier analysis. Most of them are found to have periods shorter than one day. This gives further evidence for the spin up of solar-type stars predicted by the models of angular momentum evolution of pre-main sequence stars.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

Rotation Periods of Nine ROSAT Selected Solar-Type Stars

We monitored 16 X-ray selected young solar-type stars for light variation and found appreciable periodic light variability with amplitudes of a few hundredths of a magni-tude in nine of the objects. Using the method of Phase Dispersion Minimization (PDM) and Fourier analysis (software PERIOD04), the rotation periods of these stars were determined from the photometric data. The rotation periods of all nine stars are shorter than about 3days. It is suggested that, as with the Pleiades cluster, small amplitude light variations are quite common among young solar-type stars with rotation periods around 3 days or less. This gives further evidence for the spin up of solar-type stars predicted by models of angular momentum evolution of pre-main sequence stars.     

The colours of the Sun

We compile a sample of Sun-like stars with accurate effective temperatures, metallicities and colours (from the ultraviolet to the near-infrared). A crucial improvement is that the effective temperature scale of the stars has recently been established as both accurate and precise through direct measurement of angular diameters obtained with stellar interferometers. We fit the colours as a function of effective temperature and metallicity, and derive colour estimates for the Sun in the Johnson–Cousins, Tycho, Strömgren, 2MASS and SDSS photometric systems. For  ( B − V )_⊙  , we favour the 'red' colour 0.64 versus the 'blue' colour 0.62 of other recent papers, but both values are consistent within the errors; we ascribe the difference to the selection of Sun-like stars versus interpolation of wider colour– T _eff–metallicity relations.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

On the time dependence of differential rotation in young late-type stars

A model for the angular momentum transfer within the convection zone of a rapidly rotating star is introduced and applied to the analysis of recent observations of temporal fluctuations of the differential rotation on the young late-type stars AB Doradus (AB Dor) and LQ Hydrae (LQ Hya). Under the hypothesis that the mean magnetic field produced by the stellar dynamo rules the angular momentum exchanges and that the angular velocity depends only on the distance s from the rotation axis and the time, the minimum azimuthal Maxwell stress  | B_sB _φ|  , averaged over the convection zone, is found to range from ∼0.04 to  ∼0.14 T²  . If the poloidal mean magnetic field   B _s   is of the order of 0.01 T, as indicated by the Zeeman–Doppler imaging maps of those stars, then the azimuthal mean field   B _φ  can reach an intensity of several teslas, which significantly exceeds equipartition with the turbulent kinetic energy. Such strong fields can account also for the orbital period modulation observed in cataclysmic variables and RS Canum Venaticorum systems with a main-sequence secondary component. Moreover, the model allows us to compute the kinetic energy dissipation rate during the maintenance of the differential rotation. Only in the case of the largest surface shear observed on LQ Hya may the dissipated power exceed the stellar luminosity, but the lack of a sufficient statistic on the occurrence of such episodes of large shear does not allow us to estimate their impact on the energy budget of the convection zone.     

Internal stellar rotation and orbital period modulation in close binary systems

The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.     

On a physical mechanism for extra mixing in globular cluster red giants

For the first time we propose a real physical mechanism for 'extra mixing' in red giants that can quantitatively interpret all the known star-to-star abundance variations in globular clusters. This is Zahn's mechanism. It considers extra mixing in a radiative zone of a rotating star as a result of the joint operation of meridional circulation and turbulent diffusion. It is shown that the only free parameter, the angular velocity at the base of the convective envelope, can be so adjusted as to fit the observed abundance correlations without leading to a conflict with available data on rotation velocities of blue horizontal branch stars in the same cluster. There are two critical assumptions in our model, that the top of the radiative zone is not in synchronous rotation with the stellar surface but rotates significantly faster and that the criterion for shear instability takes a particular form. These will eventually be tested by three-dimensional hydrodynamical simulations.