Aims. This work aims at presenting the first two-dimensional models of an isolated rapidly rotating star that include the derivation of the differential rotation and meridional circulation in a ...self-consistent way. Methods. We use spectral methods in multidomains, together with a Newton algorithm to determine the steady state solutions including differential rotation and meridional circulation for an isolated non-magnetic, rapidly rotating early-type star. In particular we devise an asymptotic method for small Ekman numbers (small viscosities) that removes the Ekman boundary layer and lifts the degeneracy of the inviscid baroclinic solutions. Results. For the first time, realistic two-dimensional models of fast-rotating stars are computed with the actual baroclinic flows that predict the differential rotation and the meridional circulation for intermediate-mass and massive stars. These models nicely compare with available data of some nearby fast-rotating early-type stars like Ras Alhague (α Oph), Regulus (α Leo), and Vega (α Lyr). It is shown that baroclinicity drives a differential rotation with a slow pole, a fast equator, a fast core, and a slow envelope. The differential rotation is found to increase with mass, with evolution (here measured by the hydrogen mass fraction in the core), and with metallicity. The core-envelope interface is found to be a place of strong shear where mixing will be efficient. Conclusions. Two-dimensional models offer a new view of fast-rotating stars, especially of their differential rotation, which turns out to be strong at the core-envelope interface. They also offer more accurate models for interpreting the interferometric and spectroscopic data of early-type stars.
Context. Interpretation of interferometric observations of rapidly rotating stars requires a good model of their surface effective temperature. Until now, laws of the form ...\hbox{$T_\mathrm{eff}\propto g_\mathrm{eff}^\beta$}Teff∝geffβ have been used, but they are only valid for slowly rotating stars. Aims. We propose a simple model that can describe the latitudinal variations in the flux of rotating stars at any rotation rate. Methods. This model assumes that the energy flux is a divergence-free vector that is antiparallel to the effective gravity. Results. When mass distribution can be described by a Roche model, the latitudinal variations in the effective temperature only depend on a single parameter, namely the ratio of the equatorial velocity to the Keplerian velocity. We validate this model by comparing its predictions to those of the most realistic two-dimensional models of rotating stars issued from the ESTER code. The agreement is very good, as it is with the observations of two rapidly rotating stars, α Aql and α Leo. Conclusions. We suggest that as long as a gray atmosphere can be accepted, the inversion of data on flux distribution coming from interferometric observations of rotating stars uses such a model, which has just one free parameter.
Context. Interpretation of light curves of many types of binary stars requires the inclusion of the (cor)relation between surface brightness and local effective gravity. Until recently, this ...correlation has always been modeled by a power law relating the flux or the effective temperature and the effective gravity, namely Teff ∝ geffβ . Aims. We look for a simple model that can describe the variations of the flux at the surface of stars belonging to a binary system. Methods. This model assumes that the energy flux is a divergence-free vector anti-parallel to the effective gravity. The effective gravity is computed from the Roche model. Results. After explaining in a simple manner the old result of Lucy (1967, Z. Astrophys., 65, 89), which says that β ~ 0.08 for solar type stars, we first argue that one-dimensional models should no longer be used to evaluate gravity darkening laws. We compute the correlation between log Teff and log geff using a new approach that is valid for synchronous, weakly magnetized, weakly irradiated binaries. We show that this correlation is approximately linear, validating the use of a power law relation between effective temperature and effective gravity as a first approximation. We further show that the exponent β of this power law is a slowly varying function, which we tabulate, of the mass ratio of the binary star and the Roche lobe filling factor of the stars of the system. The exponent β remains mostly in the interval 0.20,0.25 if extreme mass ratios are eliminated. Conclusions. For binary stars that are synchronous, weakly magnetized and weakly irradiated, the gravity darkening exponent is well constrained and may be removed from the free parameters of the models.
Context.
Solar Orbiter strives to unveil how the Sun controls and shapes the heliosphere and fills it with energetic particle radiation. To this end, its Energetic Particle Detector (EPD) has now ...been in operation, providing excellent data, for just over a year.
Aims.
EPD measures suprathermal and energetic particles in the energy range from a few keV up to (near-) relativistic energies (few MeV for electrons and about 500 MeV nuc
−1
for ions). We present an overview of the initial results from the first year of operations and we provide a first assessment of issues and limitations. In addition, we present areas where EPD excels and provides opportunities for significant scientific progress in understanding how our Sun shapes the heliosphere.
Methods.
We used the solar particle events observed by Solar Orbiter on 21 July and between 10 and 11 December 2020 to discuss the capabilities, along with updates and open issues related to EPD on Solar Orbiter. We also give some words of caution and caveats related to the use of EPD-derived data.
Results.
During this first year of operations of the Solar Orbiter mission, EPD has recorded several particle events at distances between 0.5 and 1 au from the Sun. We present dynamic and time-averaged energy spectra for ions that were measured with a combination of all four EPD sensors, namely: the SupraThermal Electron and Proton sensor (STEP), the Electron Proton Telescope (EPT), the Suprathermal Ion Spectrograph (SIS), and the High-Energy Telescope (HET) as well as the associated energy spectra for electrons measured with STEP and EPT. We illustrate the capabilities of the EPD suite using the 10 and 11 December 2020 solar particle event. This event showed an enrichment of heavy ions as well as
3
He, for which we also present dynamic spectra measured with SIS. The high anisotropy of electrons at the onset of the event and its temporal evolution is also shown using data from these sensors. We discuss the ongoing in-flight calibration and a few open instrumental issues using data from the 21 July and the 10 and 11 December 2020 events and give guidelines and examples for the usage of the EPD data. We explain how spacecraft operations may affect EPD data and we present a list of such time periods in the appendix. A list of the most significant particle enhancements as observed by EPT during this first year is also provided.
Contact.
Rotation is a key ingredient in the theory of stellar structure and evolution. Until now, stellar evolution codes operate in a one-dimensional framework for which the validity domain in ...regards to the rotation rate is not well understood.
Aims.
In this Letter, we present the first results of self-consistent stellar models in two spatial dimensions, which compute the time evolution of a star and its rotation rate along the main sequence (MS). We also present a comparison to observations.
Methods.
We make use of an extended version of the
ESTER
code, which solves the stellar structure of a rotating star in two dimensions with time evolution, including chemical evolution, and an implementation of rotational mixing. We computed evolution tracks for a 12
M
⊙
model, once for an initial rotation rate equal to 15% of the critical frequency, and once for 50%.
Results.
We first show that our model initially rotating at 15% of the critical frequency is able to reproduce all the observations of the
β
Cephei star HD 192575, which was recently studied with asteroseismology. Beyond the classical surface parameters, such as effective temperature or luminosity, our model also reproduces the core mass along with the rotation rate of the core and envelope at the estimated age of the star. This particular model also shows that the meridional circulation has a negligible influence on the transport of chemical elements such as nitrogen, for which the abundance may be increased at the stellar surface. Furthermore, it shows that in the late MS, nuclear evolution is faster than the relaxation time needed to reach a steady state of stellar angular momentum distribution.
Conclusions.
We demonstrate that we have successfully taken a new step towards two-dimensional evolutionary modelling of rotating stars. This opens new perspectives on the understanding of the dynamics of fast rotating stars and on the way rotation impacts stellar evolution.
Context. Recent results from interferometry and asteroseismology require models of rapidly rotating stars that are more and more precise. Aims. We describe the basic structure and the hydrodynamics ...of a fully radiative star as a preliminary step towards more realistic models of rotating stars. Methods. We consider a solar mass of perfect gas enclosed in a spherical container. The gas is self-gravitating and rotating, and is the seat of nuclear heating, and heat diffusion is due to radiative diffusion with Kramers type opacities. Equations are solved numerically with spectral methods in two dimensions with a radial Gauss-Lobatto grid and spherical harmonics. Results. We computed the centrifugally flattened structure of such a star: the von Zeipel model, which says that the energy flux is proportional to the local effective gravity is tested. We show that it overestimates the ratio of the polar to the equatorial energy flux by almost a factor 2. We also determine the Brunt-Vaeisaelae frequency distribution and show that outer equatorial regions in a radiative zone are convectively unstable when the rotation is fast enough. We compute the differential rotation and meridional circulation stemming from the baroclinicity of the star and show that, in such radiative zones, equatorial regions rotate faster than polar ones. The surface differential rotation is also shown to reach a universal profile when rotation is slow enough (less than 36% of the breakup one), as long as viscosity and Prandlt number remain small.
The first orbit of Solar Orbiter provided comprehensive measurements of six corotating interaction regions (CIRs) within 1 au. Five of these CIRs were also observed by ACE at 1 au, allowing for ...comparisons of the suprathermal ion intensities and spectra at different radial distances. Only subtle modulations of the
4
He spectral slopes are observed between Solar Orbiter and ACE. Additionally, the radial gradients of 226−320 keV/nuc
4
He ion intensities between Solar Orbiter and ACE are similar to that of 1.53 MeV H reported by Van Hollebeke et al. (1978, J. Geophys. Res., 83, A10). These observations provide a new addition to the study of the radial dependence of CIR-associated suprathermal ions in the inner heliosphere.
We report observations of a relatively long period of 3He-rich solar energetic particles (SEPs) measured by Solar Orbiter. The period consists of several well-resolved ion injections. The ...high-resolution STEREO-A imaging observations reveal that the injections coincide with extreme ultraviolet jets and brightenings near the east limb, not far from the nominal magnetic connection of Solar Orbiter. The jets originated in two adjacent, large, and complex active regions, as observed by the Solar Dynamics Observatory when the regions rotated into the Earth's view. It appears that the sustained ion injections were related to the complex configuration of the sunspot group and the long period of 3He-rich SEPs to the longitudinal extent covered by the group during the analyzed time period.
Context.
On 2020 November 29, the first widespread solar energetic particle (SEP) event of solar cycle 25 was observed at four widely separated locations in the inner (≲1 AU) heliosphere. ...Relativistic electrons as well as protons with energies > 50 MeV were observed by Solar Orbiter (SolO), Parker Solar Probe, the Solar Terrestrial Relations Observatory (STEREO)-A and multiple near-Earth spacecraft. The SEP event was associated with an M4.4 class X-ray flare and accompanied by a coronal mass ejection and an extreme ultraviolet (EUV) wave as well as a type II radio burst and multiple type III radio bursts.
Aims.
We present multi-spacecraft particle observations and place them in context with source observations from remote sensing instruments and discuss how such observations may further our understanding of particle acceleration and transport in this widespread event.
Methods.
Velocity dispersion analysis (VDA) and time shift analysis (TSA) were used to infer the particle release times at the Sun. Solar wind plasma and magnetic field measurements were examined to identify structures that influence the properties of the energetic particles such as their intensity. Pitch angle distributions and first-order anisotropies were analyzed in order to characterize the particle propagation in the interplanetary medium.
Results.
We find that during the 2020 November 29 SEP event, particles spread over more than 230° in longitude close to 1 AU. The particle onset delays observed at the different spacecraft are larger as the flare–footpoint angle increases and are consistent with those from previous STEREO observations. Comparing the timing when the EUV wave intersects the estimated magnetic footpoints of each spacecraft with particle release times from TSA and VDA, we conclude that a simple scenario where the particle release is only determined by the EUV wave propagation is unlikely for this event. Observations of anisotropic particle distributions at SolO, Wind, and STEREO-A do not rule out that particles are injected over a wide longitudinal range close to the Sun. However, the low values of the first-order anisotropy observed by near-Earth spacecraft suggest that diffusive propagation processes are likely involved.
The evolved fast rotator Sargas Domiciano de Souza, A.; Bouchaud, K.; Rieutord, M. ...
Astronomy & astrophysics,
11/2018, Letnik:
619
Journal Article
Recenzirano
Odprti dostop
Context. Gravity darkening (GD) and flattening are important consequences of stellar rotation. The precise characterization of these effects across the Hertzsprung–Russell (H-R) diagram is crucial to ...a deeper understanding of stellar structure and evolution. Aims. We seek to characterize such important effects on Sargas (θ Scorpii), an evolved, fast-rotating, intermediate-mass (∼5 M⊙) star, located in a region of the H-R diagram where they have never been directly measured as far as we know. Methods. We use our numerical model CHARRON to analyze interferometric (VLTI/PIONIER) and spectroscopic (VLT/UVES) observations through a MCMC model-fitting procedure. The visibilities and closure phases from the PIONIER data are particularly sensitive to rotational flattening and GD. Adopting the Roche approximation, we investigate two GD models: (1) the β-model (Teff ∝ geff β), which includes the classical von Zeipel’s GD law, and (2) the ω-model, where the flux is assumed to be anti-parallel to geff. Results. Using this approach we measure several physical parameters of Sargas, namely, equatorial radius, mass, equatorial rotation velocity, mean Teff, inclination and position angle of the rotation axis, and β. In particular, we show that the measured β leads to a surface flux distribution equivalent to the one given by the ω-model. Thanks to our results, we also show that Sargas is most probably located in a rare and interesting region of the H-R diagram: within the Hertzsprung gap and over the hot edge of the instability strip (equatorial regions inside it and polar regions outside it because of GD). Conclusions. These results show once more the power of optical/infrared long-baseline interferometry, combined with high-resolution spectroscopy, to directly measure fast-rotation effects and stellar parameters, in particular GD. As was the case for a few fast rotators previously studied by interferometry, the ω-model provides a physically more profound description of Sargas’ GD, without the need of a β exponent. It will also be interesting to further investigate the implications of the singular location of such a fast rotator as Sargas in the H-R diagram.
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