Since the external regions of the envelopes of rapidly rotating early-type stars are unstable to convection, a coupling may exist between the convection and the internal rotation. We explore what can be learned from spectroscopic and interferometric observations about the properties of the rotation law in the external layers of these objects. Using simple relations between the entropy and specific rotational quantities, some of which are found to be efficient at accounting for the solar differential rotation in the convective region, we derived analytical solutions that represent possible differential rotations in the envelope of early-type stars. A surface latitudinal differential rotation may not only be an external imprint of the inner rotation, but induces changes in the stellar geometry, the gravitational darkening, the aspect of spectral line profiles, and the emitted spectral energy distribution. By studying the equation of the surface of stars with non-conservative rotation laws, we conclude that objects undergo geometrical deformations that are a function of the latitudinal differential rotation able to be scrutinized both spectroscopically and by interferometry. The combination of Fourier analysis of spectral lines with model atmospheres provides independent estimates of the surface latitudinal differential rotation and the inclination angle. Models of stars at different evolutionary stages rotating with internal conservative rotation laws were calculated to show that the Roche approximation can be safely used to account for the gravitational potential. The surface temperature gradient in rapid rotators induce an acceleration to the surface angular velocity. A non-zero differential rotation parameter may indicate that the rotation is neither rigid nor shellular underneath the stellar surface.
Optical interferometry provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Through direct observation of rotationally distorted photospheres at sub-milliarcsecond scales, we are now able to characterize latitude dependencies of stellar radius, temperature structure, and even energy transport. These detailed new views of stars are leading to revised thinking in a broad array of associated topics, such as spectroscopy, stellar evolution, and exoplanet detection. As newly advanced techniques and instrumentation mature, this topic in astronomy is …
Near-infrared interferometers have recently imaged a number of rapidly rotating A-type stars, finding levels of gravity darkening inconsistent with theoretical expectations. Here, we present new imaging of both a cooler star β Cas (F2IV) and a hotter one α Leo (B7V) using the CHARA array and the MIRC instrument at the H band. Adopting a solid-body rotation model with a simple gravity darkening prescription, we modeled the stellar geometric properties and surface temperature distributions, confirming both stars are rapidly rotating and show gravity darkening anomalies. We estimate the masses an…
We have observed and spatially resolved a set of seven A-type stars in the nearby Ursa Major moving group with the Classic, CLIMB, and PAVO beam combiners on the CHARA Array. At least four of these stars have large rotational velocities ($v \sin i$ $\gtrsim$ 170 $\mathrm{km~s^{-1}}$) and are expected to be oblate. These interferometric measurements, the stars' observed photometric energy distributions, and $v \sin i$ values are used to computationally construct model oblate stars from which stellar properties (inclination, rotational velocity, and the radius and effective temperature as a func…
To fully understand the Be star phenomenon, one must have a reasonable degree of knowledge about the star beneath the disk, which is often found to be rapidly rotating. Rapid rotation complicates modelling because fundamental properties like the stellar luminosity and effective temperature require knowledge of the angle of inclina- tion at which the star is observed. Furthermore our knowledge of the structure of rapidly rotating stars is on a less sure foundation than for non-rotating stars. The uncertainties in the inclination and the surface properties of a few rapidly rotating stars have be…
Context. The circumstellar disks ejected by many rapidly rotating B stars (so-called Be stars) offer the rare opportunity of studying the structure and dynamics of gaseous disks at high spectral as well as angular resolution. Aims. This paper explores a newly identified effect in spectro-interferometric phase that can be used for probing the inner regions of gaseous edge-on disks on a scale of a few stellar radii. Methods. The origin of this effect (dubbed central quasi-emission phase signature, CQE-PS) lies in the velocity-dependent line absorption of photospheric radiation by the circumstell…
Interpretation of interferometric observations of rapidly rotating stars requires a good model of their surface effective temperature. Until now, laws of the form T_eff \propto g_eff^β have been used, but they are only valid for slowly rotating stars. We propose a simple model that can describe the latitudinal variations in the flux of rotating stars at any rotation rate. This model assumes that the energy flux is a divergence-free vector that is antiparallel to the effective gravity. When mass distribution can be described by a Roche model, the latitudinal variations in the effective temperat…
Magnetic fields influence the formation and evolution of stars and impact the observed stellar properties. Ap stars (magnetic A-type stars) are a prime example of this. Access to precise and accurate determinations of their stellar fundamental properties, such as masses and ages, is crucial to understand the origin and evolution of fossil magnetic fields. We propose using the radii and luminosities determined from interferometric measurements, in addition to seismic constraints when available, to infer fundamental properties of 14 Ap stars préviously characterised. We used a grid-based modelli…
The black holes (BH) in merging BH-BH binaries are likely progeny of binary O stars. Their properties, including their spins, will be strongly influenced by the evolution of their progenitor O stars. The remarkable observation that many single O stars spin very rapidly can be explained if they accreted angular momentum from a mass-transferring, O-type or Wolf-Rayet companion before that star blew up as a supernova. To test this prediction, we have measured the spin rates of eight O stars in Wolf-Rayet (WR) + O binaries, increasing the total sample size of such O stars' measured spins from two …
Spectral energy distributions are computed using 2D rotating stellar models and NLTE plane parallel model atmospheres. A rotating, 2D stellar model has been found which matches the observed ultraviolet and visible spectrum of ? Oph. The SED match occurs for the interferometrically deduced surface shape and inclination, and is different from the SED produced by spherical models. The p mode oscillation frequencies in which the latitudinal variation is modelled by a linear combination of eight Legendre polynomials were computed for this model. The five highest and seven of the nine highest amplit…
Main sequence, fully-convective M dwarfs in eclipsing binaries are observed to be larger than stellar evolutionary models predict by as much as $10-15\%$. A proposed explanation for this discrepancy involves effects from strong magnetic fields, induced by rapid-rotation via the dynamo process. Although, a handful of single, slowly-rotating M dwarfs with radius measurements from interferometry also appear to be larger than models predict, suggesting that rotation or binarity specifically may not be the sole cause of the discrepancy. We test whether single, rapidly rotating, fully convective sta…
Despite a century of remarkable progress in understanding stellar interiors, we know surprisingly little about the inner workings of stars spinning near their critical limit. New interferometric imaging of these so-called ``rapid rotators'' combined with breakthroughs in asteroseismology promise to lift this veil and probe the strongly latitude-dependent photospheric characteristics and even reveal the internal angular momentum distribution of these luminous objects. Here, we report the first high precision photometry on the low-amplitude delta cuti variable star Rasalhague (alpha Oph, A5IV, 2…
We present interferometric observations of six O-type stars that were made with the Precision Astronomical Visible Observations (PAVO) beam combiner at the Center for High Angular Resolution Astronomy (CHARA) Array. The observations include multiple brackets for three targets, $λ$~Ori~A, $ζ$~Oph, and 10~Lac, but there are only preliminary, single observations of the other three stars, $ξ$~Per, $α$~Cam, and $ζ$~Ori~A. The stellar angular diameters range from 0.55 milliarcsec for $ζ$~Ori~A down to 0.11 mas for 10~Lac, the smallest star yet resolved with the CHARA Array. The rotational oblateness…
The Debris Disk Host $β$ Piscis Austrinus is a Rapidly Rotating Star Seen Nearly Pole-On
Georgia State University（佐治亚州立大学）；The CHARA Array of Georgia State University, Mount Wilson Observatory（佐治亚州立大学CHARA阵列，威尔逊山天文台）；Centro de Astrobiología (CAB) CSIC-INTA（天体生物学中心（CAB）CSIC-INTA）；RECONS Institute（RECONS研究所）
Optical and infrared interferometers definitively established that the photometric standard Vega (alpha Lyrae) is a rapidly rotating star viewed nearly pole-on. Recent independent spectroscopic analyses could not reconcile the inferred inclination angle with the observed line profiles, preferring a larger inclination. In order to resolve this controversy, we observed Vega using the six-beam Michigan Infrared Combiner on the Center for High Angular Resolution Astronomy Array. With our greater angular resolution and dense (u,v)-coverage, we find Vega is rotating less rapidly and with a smaller g…
Rotating proto-neutron stars can be important sources of gravitational waves to be searched for by present-day and future interferometric detectors. It was demonstrated by Imshennik that in extreme cases the rapid rotation of a collapsing stellar core may lead to fission and formation of a binary proto-neutron star which subsequently merges due to gravitational wave emission. In the present paper, we show that such dynamically unstable collapsing stellar cores may be the product of a former merger process of two stellar cores in a common envelope. We applied population synthesis calculations t…
FU Orionis-type objects are young, low-mass stars with large outbursts in visible light that last for several years or decades. They are thought to represent an evolutionary phase during the life of every young star when accretion from the circumstellar disk is enhanced during recurring time periods. These outbursts are able to rapidly build up the star while affecting the circumstellar disk and thus the ongoing or future planet formation. In many models infall from a circumstellar envelope seems to be necessary to trigger the outbursts. We observed the J=1$-$0 rotational transition of $^{13}$…
Time series of spectroscopic, speckle-interferometric, and optical long-baseline-interferometric observations confirm that $ν$ Gem is a hierarchical triple system. It consists of an inner binary composed of two B-type stars and an outer classical Be star. Several photospheric spectral lines of the inner components were disentangled, revealing two stars with very different rotational broadening ($\sim$260 and $\sim$140 kms$^{-1}$, respectively), while the photospheric lines of the Be star remain undetected. From the combined spectroscopic and astrometric orbital solution it is not possible to u…
Two-dimensional models of rapidly rotating stars are already unavoidable for the interpretation of interferometric or asteroseismic data of this kind of stars. When combined with time evolution, they will allow the including of a more accurate physics for the computation of element transport and the determination of surface abundances. In addition, modeling the evolution of rotation will improve gyrochronology. Presently, two-dimensional ESTER models predict the structure and the large-scale flows (differential rotation and meridional circulation) of stars with mass larger than 1.7Msun at any …
Rapidly rotating neutron stars can be unstable to the gravitational-wave-driven CFS mechanism if they have a neutral point in the spectrum of nonaxisymmetric f-modes. We investigate the frequencies of these modes in two sequences of uniformly rotating polytropes using nonlinear simulations in full general relativity, determine the approximate locations of the neutral points, and derive limits on the observable frequency band available to the instability in these sequences. We find that general relativity enhances the detectability of a CFS-unstable neutron star substantially, both by widening …
Polarization in stars was first predicted by Chandrasekhar [1] who calculated a substantial linear polarization at the stellar limb for a pure electron-scattering atmosphere. This polarization will average to zero when integrated over a spherical star but could be detected if the symmetry is broken, for example by the eclipse of a binary companion. Nearly 50 years ago, Harrington and Collins [2] modeled another way of breaking the symmetry and producing net polarization - the distortion of a rapidly rotating hot star. Here we report the first detection of this effect. Observations of the linea…
Context: Massive stars are extremely important for the evolution of the galaxies; there are large gaps in our understanding of their properties and formation, however, mainly because they evolve rapidly, are rare, and distant. It may well be that almost all massive stars are born as triples or higher multiples, but their large distances require very high angular resolution to directly detect the companions at milliarcsecond scales. Aims: Herschel36 is a young massive system located at 1.3 kpc. It has a combined smallest predicted mass of 45 M_sun. Multi-epoch spectroscopic data suggest the exi…
A significant fraction of main sequence stars observed interferometrically in the near infrared have slightly extended components that have been attributed to very hot dust. To match the spectrum appears to require the presence of large numbers of very small (< 200 nm in radius) dust grains. However, particularly for the hotter stars, it has been unclear how such grains can be retained close to the star against radiation pressure force. We find that the expected weak stellar magnetic fields are sufficient to trap nm-sized dust grains in epicyclic orbits for a few weeks or longer, sufficient to…
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.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 …
