Effects Of Gravity Darkening Research Articles

CHEOPS observations confirm nodal precession in the WASP-33 system

We aim to observe the transits and occultations of which orbits a rapidly rotating delta Scuti pulsator, with the goal of measuring the orbital obliquity via the gravity-darkening effect, and constraining the geometric albedo via the occultation depth. We observed four transits and four occultations with CHEOPS, and employ a variety of techniques to remove the effects of the stellar pulsations from the light curves, as well as the usual CHEOPS systematic effects. We also performed a comprehensive analysis of low-resolution spectral and Gaia data to re-determine the stellar properties of system. We measure an orbital obliquity degrees, which is consistent with previous measurements made via Doppler tomography. We also measure the planetary impact parameter, and confirm that this parameter is undergoing rapid secular evolution as a result of nodal precession of the planetary orbit. This precession allows us to determine the second-order fluid Love number of the star, which we find agrees well with the predictions of theoretical stellar models. We are unable to robustly measure a unique value of the occultation depth, and emphasise the need for long-baseline observations to better measure the pulsation periods.

ZPEKTR: A code for spectral synthesis of fast-rotating stars

Estimating the physical states of the surfaces of fast-rotating stars is challenging due to several intrinsic processes, which include radiative flux inhomogeneities on the photosphere induced by rotation and circumstellar signatures in their spectra. The analysis of their spectra ultimately requires the use of synthetic grids of spectra accounting for all these physical processes. In this paper, we present the `von ZeiPEl's code for gravity darKening specTRal synthesis' (ZPEKTR) code, which is designed to perform the spectral synthesis of fast-rotating stars, accounting for gravity darkening, limb-darkening effects in the continuum and geometrical deformation induced by fast rotation. We consider colatitudinal temperature and surface-gravity variations, assuming both the classical prescription developed by von Zeipel and the new formulation by Espinosa-Lara. The code runs either with a rectangular or a triangular mesh on the stellar surface. We compare the temperature and gravitational distribution as a function of the stellar latitude arising from both models. The line profiles of 4388, 4471, 4922, and 6678 produced with both formalisms are compared at three different rotation rates and illustrate differences in shape and central intensity. We also illustrate the fittings of 31 line spectra of classical Be stars averaged from the Be Stars Observation Survey (BeSOS) database and make a comparison among their apparent physical parameters and ages determined from plane-parallel non-local thermodynamical equilibrium (non-LTE) models and parameters determined from classical von Zeipel models, finding a displacement of more evolved objects towards the zero-age main sequence. We also compare the distributions of projected rotation velocities of these objects obtained with and without the inclusion of gravity-darkening effects with ZPEKTR. We observe a shift of the histogram of rotation velocities calculated accounting for effects of gravity darkening concerning rotation velocities obtained through the fittings with classical plane-parallel non-LTE models. We show that models that do not account for gravity darkening can underestimate the rotation velocity, because the stellar latitudes that contribute the higher velocities are those in the equator with the least radiative flux. We envisage near-future improvements to the code, such as the inclusion of differential rotation and treatment of tidal forces in binary stellar systems.

Rapidly rotating stars and their transiting planets: KELT-17b, KELT-19Ab, and KELT-21b in the CHEOPS and TESS era

ABSTRACT Rapidly rotating early-type main-sequence stars with transiting planets are interesting in many aspects. Unfortunately, several astrophysical effects in such systems are not well understood yet. Therefore, we performed a photometric mini-survey of three rapidly rotating stars with transiting planets, namely KELT-17b, KELT-19Ab, and KELT-21b, using the Characterising Exoplanets Satellite (CHEOPS), complemented with Transiting Exoplanet Survey Satellite (TESS) data, and spectroscopic data. We aimed at investigating the spin-orbit misalignment and its photometrical signs, therefore the high-quality light curves of the selected objects were tested for transit asymmetry, transit duration variations, and orbital precession. In addition, we performed transit time variation analyses, obtained new stellar parameters, and refined the system parameters. For KELT-17b and KELT-19Ab, we obtained significantly smaller planet radius as found before. The gravity-darkening effect is very small compared to the precision of CHEOPS data. We can report only on a tentative detection of the stellar inclination of KELT-21, which is about 60 deg. In KELT-17b and KELT-19Ab, we were able to exclude long-term transit duration variations causing orbital precession. The shorter transit duration of KELT-19Ab compared to the discovery paper is probably a consequence of a smaller planet radius. KELT-21b is promising from this viewpoint, but further precise observations are needed. We did not find any convincing evidence for additional objects in the systems.

Automatic algorithm to obtain v sin i values via Fourier transform in the BeSOS database

ABSTRACT Be stars are found to rotate close to their critical rotation and therefore they are considered an important laboratory for the study of stellar rotation. In this context, we obtain the projected rotational velocity of a sample of classical Be southern stars in the BeSOS database via Fourier transforms in an automated way for several absorption lines at different epochs. A Gaussian profile is fitted to eight observed photospheric He i lines in order to select automatically from the profile the spectral signal given by areas under the curve of 95.45, 98.75, and 99.83 per cent, to obtain vsin i via the Fourier transform technique. The values obtained are in global agreement with the literature. Analysing only one line is not enough to set the vsin i value: depending on the line, the value in most cases is underestimated with respect to λ4471. When gravity-darkening effects are included, apparent values increase by ∼10 per cent. The resolution of the instrument Pontificia Universidad Catolica High Echelle Resolution Optical Spectrograph (PUCHEROS) used for BeSOS spectra ($R \sim 17\, 000$) constrains the theoretical lower bound possible to vsin i ∼ 100 km s−1. The procedure has limitations, using a linear limb-darkening function with ε = 0.6 for classical Be stars rotating close to the break-up velocity without gravity-darkening corrections, which cannot be negligible. Previous works measure vsin i values using just one spectral line and here we demonstrate that with more lines the results can vary. This could be due to the photospheric distribution of atomic transitions in classical Be stars.

The Effects of Stellar Gravity Darkening on High-resolution Transmission Spectra

Abstract High-resolution transmission spectroscopy is a powerful method for probing the extended atmospheres of short-period exoplanets. With the advancement of ultrastable echelle spectrographs and the advent of 30 m class telescopes on the horizon, even minor observational and physical effects will become important when modeling atmospheric absorption of atomic species. In this work we demonstrate how the nonuniform temperature across the surface of a fast rotating star, i.e., gravity darkening, can affect the observed transmission spectrum in a handful of atomic transitions commonly observed in short-period exoplanet atmospheres. We simulate transits of the ultrahot Jupiters KELT-9 b and HAT-P-70 b but our results are applicable to all short-period gas giants transiting rapidly rotating stars. In general, we find that gravity darkening has a small effect on the average transmission spectrum but can change the shape of the absorption light curve, similar to the effect observed in broadband photometric transits. While the magnitude of gravity-darkening effects are on the same order as the noise in transmission spectra observed with 10 m class telescopes, future high-quality spectroscopic light curves for individual atomic absorption lines collected with 30 m class telescopes will need to account for this effect.

Revisiting the Architecture of the KOI-89 System

Abstract While high stellar obliquities observed in exoplanetary systems may be attributed to processes that tilt the planetary orbits, it is also possible that they reflect misalignments between protoplanetary disks and stellar spins. This latter hypothesis predicts the presence of coplanar multiplanetary systems misaligned with their central stars. Here we reevaluate the evidence of such an architecture that has been claimed for the KOI-89 system. An early-type star, KOI-89 has one validated transiting planet, KOI-89.01/Kepler-462b (period 84.7 days, radius 3.0 R ⊕), and one transiting planet candidate, KOI-89.02 (period 207.6 days, radius 4.0 R ⊕), where the latter exhibits transit timing variations (TTVs). A previous modeling of the stellar gravity-darkening effect in the transit light curves inferred a high stellar obliquity of ≈70°. We perform photodynamical modeling of the Kepler transit light curves and use the resulting constraints on the orbital configuration and transit times to update the gravity-darkened transit model. As a result, we find no firm evidence for the gravity-darkening effect in the transit shapes and conclude that stellar obliquity is not constrained by the data. Given the evidence for low orbital eccentricities from the dynamical analysis, the system architecture can thus be consistent with many other multitransiting systems with flat, near-circular orbits aligned with the stellar spin. We find that the TTVs imparted on its neighbor imply that KOI-89.01 has a mass ≳20 M ⊕. This would render it one of the densest known sub-Neptunes, mostly composed of a solid core. Lower masses are possible if the TTVs are instead due to an unseen third planet.

Unveiling the power spectra of δ Scuti stars with TESS

Thanks to high-precision photometric data legacy from space telescopes like CoRoT and Kepler, the scientific community could detect and characterize the power spectra of hundreds of thousands of stars. Using the scaling relations, it is possible to estimate masses and radii for solar-type pulsators. However, these stars are not the only kind of stellar objects that follow these rules: δ Scuti stars seem to be characterized with seismic indexes such as the large separation (Δν). Thanks to long-duration high-cadence TESS light curves, we analysed more than two thousand of this kind of classical pulsators. In that way, we propose the frequency at maximum power (νmax) as a proper seismic index since it is directly related with the intrinsic temperature, mass and radius of the star. This parameter seems not to be affected by rotation, inclination, extinction or resonances, with the exception of the evolution of the stellar parameters. Furthermore, we can constrain rotation and inclination using the departure of temperature produced by the gravity-darkening effect. This is especially feasible for fast rotators as most of δ Scuti stars seem to be.

The envelope of the power spectra of over a thousand δ Scuti stars

CoRoT and Kepler high-precision photometric data allowed the detection and characterization of the oscillation parameters in stars other than the Sun. Moreover, thanks to the scaling relations, it is possible to estimate masses and radii for thousands of solar-type oscillating stars. Recently, a Δν − ρ relation has been found for δ Scuti stars. Now, analysing several hundreds of this kind of stars observed with CoRoT and Kepler, we present an empiric relation between their frequency at maximum power of their oscillation spectra and their effective temperature. Such a relation can be explained with the help of the κ-mechanism and the observed dispersion of the residuals is compatible with they being caused by the gravity-darkening effect.

Are the O stars in WR+O binaries exceptionally rapid rotators?

We examine claims of strong gravity-darkening effects in the O-star components of WR+O binaries. We generate synthetic spectra for a wide range of parameters, and show that the line-width results are consistent with extensive measurements of O stars that are either single or are members of `normal' binaries. By contrast, the WR+O results are at the extremes of, or outside, the distributions of both models and other observations. Remeasurement of the WR+O spectra shows that they can be reconciled with other results by judicious choice of pseudo-continuum normalization. With this interpretation, the supersynchronous rotation previously noted for the O-star components in the WR+O binaries with the longest orbital periods appears to be unexceptional. Our investigation is therefore consistent with the aphorism that if the title of a paper ends with a question mark, the answer is probably `no'.

Fourier analysis of He 4471/Mg 4481 line profiles for separating rotational velocity and axial inclination in rapidly rotating B-type stars

While the effect of rotation on spectral lines is complicated in rapidly-rotating stars because of the appreciable gravity-darkening effect differing from line to line, it is possible to make use of this line-dependent complexity to separately determine the equatorial rotation velocity (ve) and the inclination angle (i) of rotational axis. Although line-widths of spectral lines were traditionally used for this aim, we tried in this study to apply the Fourier method, which utilizes the unambiguously determinable first-zero frequency (sigma1) in the Fourier transform of line profile. Equipped with this technique, we analyzed the profiles of HeI 4471 and MgII 4481 lines of six rapidly-rotating (vesini~150-300km/s) late B-type stars, while comparing them with the theoretical profiles simulated on a grid of models computed for various combination of (ve, i). According to our calculation, sigma1 tends to be larger than the classical value for given vesini. This excess progressively grows with an increase in ve, and is larger for the He line than the Mg line, which leads to sigma1He > sigma1Mg. It was shown that ve and i are separately determinable from the intersection of two loci (sets of solutions reproducing the observed sigma1 for each line) on the ve vs. i plane. Yet, line profiles alone are not sufficient for their unique discrimination, for which photometric information (such as colors) needs to be simultaneously employed.

STELLAR ROTATION EFFECTS IN POLARIMETRIC MICROLENSING

ABSTRACT It is well known that the polarization signal in microlensing events of hot stars is larger than that of main-sequence stars. Most hot stars rotate rapidly around their stellar axes. The stellar rotation creates ellipticity and gravity-darkening effects that break the spherical symmetry of the source's shape and the circular symmetry of the source's surface brightness respectively. Hence, it causes a net polarization signal for the source star. This polarization signal should be considered in polarimetric microlensing of fast rotating stars. For moderately rotating stars, lensing can magnify or even characterize small polarization signals due to the stellar rotation through polarimetric observations. The gravity-darkening effect due to a rotating source star creates asymmetric perturbations in polarimetric and photometric microlensing curves whose maximum occurs when the lens trajectory crosses the projected position of the rotation pole on the sky plane. The stellar ellipticity creates a time shift (i) in the position of the second peak of the polarimetric curves in transit microlensing events and (ii) in the peak position of the polarimetric curves with respect to the photometric peak position in bypass microlensing events. By measuring this time shift via polarimetric observations of microlensing events, we can evaluate the ellipticity of the projected source surface on the sky plane. Given the characterizations of the FOcal Reducer and low dispersion Spectrograph (FORS2) polarimeter at the Very Large Telescope, the probability of observing this time shift is very small. The more accurate polarimeters of the next generation may well measure these time shifts and evaluate the ellipticity of microlensing source stars.

The GTC exoplanet transit spectroscopy survey

Context. The launch of the exoplanet space missions obtaining exquisite photometry from space has resulted in the discovery of thousands of planetary systems with very different physical properties and architectures. Among them, the exoplanet CoRoT-29b was identified in the light curves the mission obtained in summer 2011, and presented an asymmetric transit light curve, which was tentatively explained via the effects of gravity darkening.

Spectrally resolved interferometric observations ofαCephei and physical modeling of fast rotating stars

Context. When a given observational quantity depends on several stellar physical parameters, it is generally very difficult to obtain observational constraints for each of them individually. Therefore, we studied under which conditions constraints for some individual parameters can be achieved for fast rotators, knowing that their geometry is modified by the rapid rotation which causes a non-uniform surface brightness distribution.Aims. We aim to study the sensitivity of interferometric observables on the position angle of the rotation axis (PA) of a rapidly rotating star, and whether other physical parameters can influence the determination of PA, and also the influence of the surface differential rotation on the determination of the β exponent in the gravity darkening law that enters the interpretation of interferometric observations, using α Cep as a test star.Methods. We used differential phases obtained from observations carried out in the Hα absorption line of α Cep with the VEGA/CHARA interferometer at high spectral resolution, R = 30 000 to study the kinematics in the atmosphere of the star.Results. We studied the influence of the gravity darkening effect (GDE) on the determination of the PA of the rotation axis of α Cep and determined its value, PA = −157-10° +17° . We conclude that the GDE has a weak influence on the dispersed phases. We showed that the surface differential rotation can have a rather strong influence on the determination of the gravity darkening exponent. A new method of determining the inclination angle of the stellar rotational axis is suggested. We conclude that differential phases obtained with spectro-interferometry carried out on the Hα line can in principle lead to an estimate of the stellar inclination angle i . However, to determine both i and the differential rotation parameter α , lines free from the Stark effect and that have collision-dominated source functions are to be preferred.

Basic parameters and properties of the rapidly rotating magnetic helium-strong B star HR 7355*

The spectral and magnetic properties and variability of the B2Vnp emission-line magnetosphere star HR7355 were analyzed. The object rotates at almost 90% of the critical value, meaning it is a magnetic star for which oblateness and gravity darkening effects cannot be ignored any longer. A detailed modeling of the photospheric parameters indicate that the star is significantly cooler than suggested by the B2 spectral type, with T_eff=17500K atypically cool for a star with a helium enriched surface. The spectroscopic variability of helium and metal lines due to the photospheric abundance pattern is far more complex than a largely dipolar, oblique magnetic field of about 11 to 12kG may suggest. Doppler imaging shows that globally the most He enriched areas coincide with the magnetic poles and metal enriched areas with the magnetic equator. While most of the stellar surface is helium enriched with respect to the solar value, some isolated patches are depleted. The stellar wind in the circumstellar environment is governed by the magnetic field, i.e. the stellar magnetosphere is rigidly corotating with the star. The magnetosphere of HR7355 is similar to the well known \sigma Ori E: the gas trapped in the magnetospheric clouds is fairly dense, and at the limit to being optically thick in the hydrogen emission. Apart from a different magnetic obliquity, HR7355 and the more recently identified HR5907 have virtually identical stellar and magnetic parameters.

Rotation and Properties of Be Stars

The actual characteristic average surface angular velocity ratio of the Be phenomenon may be higher than Ω/Ωc= 0.8 ± 0.1 derived fromvsinivalues not corrected from gravity darkening effects. Late Be Stars need not only higher values of Ω/Ωc, but also larger main sequence age ratios τ/τMSthan early Be Stars to display the Be phenomenon. Galactic field Be Stars appear at any MS phase, but their frequency is higher for τ/τMS≳ 0.5. Be Stars are probably neat differential rotators, i.e. they rotate with energy ratios kinetic/|gravitational| larger than withstood by critical rigid rotators. Initial formation conditions must favor the existence of fast rotators, while only a small fraction of them could be accounted for by mass transfer in close binary systems. Bn stars could perhaps represent a pre-Be phase.

Inhibition of Wind-Compressed Disk Formation by Nonradial Line Forces in Rotating Hot-Star Winds

We investigate the effects of nonradial line forces on the formation of a wind-compressed (WCD) around a rapidly rotating B star. Such nonradial forces can arise both from asymmetries in the line resonances in the rotating wind and from rotational distortion of the stellar surface. They characteristically include a latitudinal force component directed away from the equator and an azimuthal force component acting against the sense of rotation. Here we present results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppression of the equatorward flow needed to form a WCD as well as a modest (~20%) spin-down of the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reduced mass loss, and thus lower density, in the wind from the equatorial region. Overall, the results here thus imply a flow configuration that is markedly different from that derived in previous models of winds from rotating early-type stars. In particular, a major conclusion is that equatorial wind compression effects should be effectively suppressed in any radiatively driven stellar wind for which, as in the usual CAK formalism, the driving includes a significant component from optically thick lines. This presents a serious challenge to the WCD paradigm as an explanation for disk formation around Be and other rapidly rotating hot stars thought to have CAK-type, line-driven winds.

Mass Loss from Rotating Hot-stars: Inhibition of Wind Compressed Disks by Nonradial Line-forces

We review the dynamics of radiatively driven mass loss from rapidly rotating hot-stars. We first summarize the angular momentum conservation process that leads to formation of a Wind Compressed Disk(WCD) when material from a rapidly rotating star is driven gradually outward in the radial direction. We next describe how stellar oblateness and asymmetries in the Sobolev line-resonance generally leads to nonradialcomponents of the driving force is a line-driven wind, including an azimuthal spin-down force acting against the sense of the wind rotation, and a latitudinal force away from the equator. We summarize results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppressionof the equatorward flow needed to form a WCD, as well as a modest (∼ 25%) spin-downof the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reducedmass loss, and thus lower density, in the wind from the equatorial region. Finally, we examine the equatorial bistability model, and show that a sufficiently strong jump in wind driving parameters can, in principle, overcome the effect of reduced radiative driving flux, thus still allowing moderate enhancements in density in an equatorial, bistability zone wind.

HD 93521, zeta Ophiuchi, and the effects of rapid rotation on the atmospheres and winds of 09.5 V stars

Both low- and high-resolution IUE spectra of the rapidly rotating 09.5 V stars HD 93521 and zeta Oph are used to develop a coherent picture of the effects of rapid rotation on the atmospheres and winds of late, main-sequence O stars. The observational consequences are by far the strongest on HD 93521, most likely because it is being viewed nearly equator-on. In particular, it is shown that HD 93521 (1) a much smaller UV optical flux ratio than expected, (2) UV photospheric lines indicative of a BO supergiant, (3) an abnormally strong N v wind doublet, and (4) wind profiles suggesting that its wind has latitudinally dependent properties. Because HD 93521 has a larger observed v sin i than zeta Oph and yet its H-alpha emission is no stronger than in zeta Oph, it is speculated that zeta Oph actually rotates as fast or faster than HD 93521, but has a smaller sin i. Because zeta Oph is significantly reddened, nothing can be determined about its intrinsic UV energy distribution. However, it is shown that its UV photospheric lines are a bit peculiar and that its C IV and N V wind doublets are abnormally strong and have unusual profiles. The C IV profile agrees with models of a rotationally distorted wind similar to the one in HD 93521, except viewed at an angle i approximately 60 deg-80 deg. The spectral peculiarities of both stars are attributed to the combined effects of gravity darkening of their atmospheres and rotational distortion of their winds. The differences between their spectra are interpreted as the result of being viewed at different inclination angles. Because of the gravity darkening, atmospheric analyses of either star based on single temperature and surface gravity model atmospheres are probably unreliable. Finally, I describe how different effects conspire to make the spectroscopic signatures of gravity darkening so pronounced at 09.5 V.