Radiative Core Research Articles

TheGaia-ESO Survey: Stellar radii in the young open clusters NGC 2264, NGC 2547, and NGC 2516

Rapidly rotating, low-mass members of eclipsing binary systems have measured radii significantly larger than predicted by standard models. It has been proposed that magnetic activity is responsible for radius inflation. By estimating the radii of low-mass stars in three young clusters (NGC 2264, NGC 2547, NGC 2516, with ages of 5, 35 and 140 Myr respectively), we aim to establish whether similar radius inflation is seen in single, magnetically active stars. We use radial velocities from the Gaia-ESO Survey (GES) and published photometry to establish cluster membership and combine GES measurements of vsini with published rotation periods to estimate average radii for groups of fast-rotating cluster members as a function of their luminosity and age. The average radii are compared with the predictions of both standard evolutionary models and variants that include magnetic inhibition of convection and starspots. At a given luminosity, the stellar radii in NGC 2516 and NGC 2547 are larger than predicted by standard evolutionary models at the ages of these clusters. The discrepancy is least pronounced and not significant ~10 percent) in ZAMS stars with radiative cores, but more significant in lower-mass, fully convective pre main-sequence cluster members, reaching 30+/-10 percent. The uncertain age and distance of NGC 2264 preclude a reliable determination of any discrepancy for its members. The median radii we have estimated for low-mass fully convective stars in the older clusters are inconsistent (at the 2-3 sigma level) with non-magnetic evolutionary models and more consistent with models that incorporate the effects of magnetic fields or dark starspots. The available models suggest this requires either surface magnetic fields exceeding 2.5 kG, spots that block about 30 per cent of the photospheric flux, or a more moderate combination of both. [Abridged]

The role of mixing below the convective zone in evolution of solar lithium

We consider the evolution of lithium in the solar convective zone to explain its low content. The burning of lithium in a nuclear reaction 7Li(p,α)4He occurs intensely at an early stage from the moment of radiative core formation, and its content slowly decreases on the main sequence (MS). We study the percentage of lithium depletion at these two stages. The model without additional mixing below a convective zone predicts a sevenfold decrease of the lithium content, which is considerably less than that required by the observations (160-fold decrease). The new results of the helioseismic inversion indicate on existence of an overshooting region below the convective zone, the thickness of which cannot exceed 3.8% of the solar radius and is likely even thinner. The inclusion of this region in the evolution calculations indicates that lithium cannot burn out in a sufficient quantity on the MS stage. We conclude that lithium must be depleted at an early stage of evolution before the MS. At this early stage, even a relatively small overshooting in the region with a thickness of about 18% of the pressure scale height is sufficient to decrease the lithium content to the observed value.

Period spacings in red giants

Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. This work aims at disentangling the rotational splittings from the mixed-mode spacings, in order to open the way to a fully automated analysis of large data sets. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The \'echelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view on the radiative core.

Rotational evolution of slow-rotator sequence stars

The observed mass-age-rotation relationship in open clusters shows the progressive development of a slow-rotators sequence. The observed clustering on this sequence suggests that it corresponds to some equilibrium or asymptotic condition that still lacks a complete theoretical interpretation, crucial to our understanding of the stellar angular momentum evolution. We couple a rotational evolution model, which takes into account internal differential rotation, with classical and new proposals for the wind braking law, and fit models to the data using a MCMC method. The description of the evolution of the slow-rotators sequence requires taking into account the transfer of angular momentum from the radiative core to the convective envelope; we find that, in the mass range 0.85-1.10 $M_{\odot}$, the core-envelope coupling time-scale for stars in the slow-rotators sequence scales as $M^{-7.28}$. Quasi-solid body rotation is achieved only after 1-2 Gyr, depending on stellar mass, which implies that observing small deviations from the Skumanich law ($P \propto \sqrt{t}$) would require period data of older open clusters than available to date. The observed evolution in the 0.1-2.5 Gyr age range and in the 0.85-1.10 $M_{\odot}$ mass range is best reproduced by assuming an empirical mass dependence of the wind angular momentum loss proportional to the convective turnover time-scale and to the stellar moment of inertia. Period isochrones based on our MCMC fit provide a tool for inferring stellar ages of solar-like main-sequence stars from their mass and rotation period largely independent from the wind braking model adopted. These effectively represent gyro-chronology relationships that take into account the physics of the two-zone model for the stellar angular momentum evolution.

The Evolution of Surface Magnetic Fields in Young Solar-type Stars

AbstractSurface rotation rates of young solar-type stars display drastic changes at the end of the pre-main sequence through the early main sequence. This may trigger corresponding changes in the magnetic dynamos operating in these stars, which ought to be observable in their surface magnetic fields. We present here the first results of an observational effort aimed at characterizing the evolution of stellar magnetic fields through this critical phase. We observed stars from open clusters and associations, which range from 20 to 600 Myr, and used Zeeman Doppler Imaging to characterize their complex magnetic fields. We find a clear trend towards weaker magnetic fields for older ages, as well as a tight correlation between magnetic field strength and Rossby number over this age range. Comparing to results for younger T Tauri stars, we observe a very significant change in magnetic strength and geometry, as the radiative core develops during the late pre-main sequence.

OLDER AND COLDER: THE IMPACT OF STARSPOTS ON PRE-MAIN-SEQUENCE STELLAR EVOLUTION

We assess the impact of starspots on the evolution of late-type stars during the pre-main sequence (pre-MS) using a modified stellar evolution code. We find that heavily spotted models of mass 0.1-1.2\msun\ are inflated by up to $10$% during the pre-MS, and up to 4% and 9% for fully- and partially-convective stars at the zero-age MS, consistent with measurements from active eclipsing binary systems. Spots similarly decrease stellar luminosity and $T_{\rm eff}$, causing isochrone-derived masses to be under-estimated by up to a factor of $2 \times$, and ages to be under-estimated by a factor of 2-10$\times$, at 3 Myr. Consequently, pre-MS clusters and their active stars are systematically older and more massive than often reported. Cluster ages derived with the lithium depletion boundary technique are erroneously young by $\sim 15$% and $10$% at $30$ and $100$ Myr respectively, if 50% spotted stars are interpreted with un-spotted models. Finally, lithium depletion is suppressed in spotted stars with radiative cores, leading to a fixed-temperature lithium dispersion on the MS if a range of spot properties are present on the pre-MS. Such dispersions are large enough to explain Li abundance spreads seen in young open clusters, and imply a range of radii at fixed mass and age during the pre-MS Li burning epoch. By extension, this implies that mass, composition, and age do not uniquely specify the HR diagram location of pre-MS stars.

TOWARD AN EMPIRICAL THEORY OF PULSAR EMISSION. XI. UNDERSTANDING THE ORIENTATIONS OF PULSAR RADIATION AND SUPERNOVA “KICKS”

Two entwined problems have remained unresolved since pulsars were discovered nearly 50 years ago: the orientation of their polarized emission relative to the emitting magnetic field and the direction of putative supernova ``kicks' relative to their rotation axes. The rotational orientation of most pulsars can be inferred only from the (``fiducial') polarization angle of their radiation, when their beam points directly at the Earth and the emitting polar fluxtube field is $\parallel$ to the rotation axis. Earlier studies have been unrevealing owing to the admixture of different types of radiation (core and conal, two polarization modes), producing both $\parallel$ or $\perp$ alignments. In this paper we analyze the some 50 pulsars having three characteristics: core radiation beams, reliable absolute polarimetry, and accurate proper motions. The ``fiducial' polarization angle of the core emission, we then find, is usually oriented $\perp$ to the proper-motion direction on the sky. As the primary core emission is polarized $\perp$ to the projected magnetic field in Vela and other pulsars where X-ray imaging reveals the orientation, this shows that the proper motions usually lie $\parallel$ to the rotation axes on the sky. Two key physical consequences then follow: first, to the extent that supernova ``kicks' are responsible for pulsar proper motions, they are mostly $\parallel$ to the rotation axis; and second that most pulsar radiation is heavily processed by the magnetospheric plasma such that the lowest altitude ``parent' core emission is polarized $\perp$ to the emitting field, propagating as the extraordinary (X) mode.

High temperature thermal stability studies of ultrathin Al2O3 layers deposited on native oxide and sulphur passivated InGaAs surfaces

High resolution synchrotron radiation core level photoemission measurements have been used to undertake a comparative study of the high temperature stability of ultrathin Al2O3 layers deposited by atomic layer deposition (ALD) on both sulphur passivated and native oxide covered InGaAs. The residual interfacial oxides between sulphur passivated InGaAs and the ultrathin Al2O3 layer can be substantially removed at high temperature (up to 700°C) without impacting on the InGaAs stoichiometry while significant loss of indium was recorded at this temperature on the native oxide InGaAs surface.

Stellar acoustic radii, mean densities, and ages from seismic inversion techniques

Context. Determining stellar characteristics such as the radius, the mass or the age is crucial when studying stellar evolution, exoplanetary systems or characterising stellar populations in the Galaxy. Asteroseismology is the golden path to accurately obtain these characteristics. In this context, a key question is how to make these methods less model-dependant. Aims. Building on the work of Reese et al. (2012), we wish to extend the SOLA inversion technique to new stellar global characteristics in addition to the mean density. The goal is to provide a general framework in which to estimate these characteristics as accurately as possible in low mass main sequence stars. Methods. First, we describe our framework and discuss the reliability of the inversion technique and the possible sources of error.We then apply this methodology to the acoustic radius, an age indicator based on the sound speed derivative and the mean density and compare it to estimates based on the average large and small frequency separations. These inversions are carried out for several test cases which include: various metallicities, different mixing-lengths, non-adiabatic effects and turbulent pressure. Results. We observe that the SOLA method yields accurate results in all test cases whereas results based on the large and small frequency separations are less accurate and more sensitive to surface effects and structural differences in the models. If we include the surface corrections of Kjeldsen et al. (2008), we obtain results of comparable accuracy for the mean density. Overall, the mean density and acoustic radius inversions are more robust than the inversions for the age indicator. Moreover, the current approach is limited to relatively young stars with radiative cores. Increasing the number of observed frequencies improves the reliability and accuracy of the method.

Stellar oscillations - I - The adiabatic case

This lecture on adiabatic oscillations is intended to present the basis of asteroseismology and to serve as an introduction for other lectures of the EES 2014. It also exposes the state-of-the-art of solar-like oscillation analysis, as revealed by the space missions CoRoT and Kepler. A large part of the lecture is devoted to the interpretation of the modes with a mixed character that reveal the properties of the radiative cores of subgiants and red giants.

Zero-Energy and Beyond: A Paradigm Shift in Assessment

The world is on the eve of major changes in the way energy and material are used, and the building and construction sector is at the forefront. One of the revolutionary changes is that for 0-energy houses and buildings. Many countries already have some projects established, and legislation is following, first requiring near 0-energy, but undoubtedly this will evolve into 0-energy as basic requirement. Buildings will generate all required energy from within their building lot, from incoming free and renewable energy sources: solar radiation and earth core heat mainly. In other words, there are no polluting or depleting issues anymore related to energy consumed to operate a building. This will change the whole approach in evaluation and optimization of the environmental performance of buildings: while the energy-driven measures for buildings become obsolete, it will be materials needed for this transition that have to become the main focus, as argued in this paper.

The angular momentum transport by unstable toroidal magnetic fields

We demonstrate with a nonlinear MHD code that angular momentum can be transported due to the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. Only stationary current-free fields and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity are considered. We find that the dimensionless ratio of the effective over molecular viscosity, $\nu_T/\nu$;, linearly grows with the Reynolds number of the rotating fluid multiplied with the square-root of the magnetic Prandtl number - which is of order unity for the considered red sub-giant KIC 7341231. For the considered interval of magnetic Reynolds numbers - which is restricted by numerical constraints of the nonlinear MHD code - there is a remarkable influence of the magnetic Prandtl number on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm $\gtrsim$ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.

ANGULAR MOMENTUM TRANSPORT VIA INTERNAL GRAVITY WAVES IN EVOLVING STARS

Recent asteroseismic advances have allowed for direct measurements of the internal rotation rates of many subgiant and red giant stars. Unlike the nearly rigidly rotating Sun, these evolved stars contain radiative cores that spin faster than their overlying convective envelopes, but slower than they would in the absence of internal angular momentum transport. We investigate the role of internal gravity waves in angular momentum transport in evolving low-mass stars. In agreement with previous results, we find that convectively excited gravity waves can prevent the development of strong differential rotation in the radiative cores of Sun-like stars. As stars evolve into subgiants, however, low-frequency gravity waves become strongly attenuated and cannot propagate below the hydrogen-burning shell, allowing the spin of the core to decouple from the convective envelope. This decoupling occurs at the base of the subgiant branch when stars have surface temperatures of T ≈ 5500 K. However, gravity waves can still spin down the upper radiative region, implying that the observed differential rotation is likely confined to the deep core near the hydrogen-burning shell. The torque on the upper radiative region may also prevent the core from accreting high angular momentum material and slow the rate of core spin-up. The observed spin-down of cores on the red giant branch cannot be totally attributed to gravity waves, but the waves may enhance shear within the radiative region and thus increase the efficacy of viscous/magnetic torques.

High temperature thermal stability investigations of ammonium sulphide passivated InGaAs and interface formation with Al2O3 studied by synchrotron radiation based photoemission

High resolution synchrotron radiation core level photoemission measurements have been used to undertake a comparative study of the high temperature thermal stability of the ammonium sulphide passivated InGaAs surface and the same surface following the atomic layer deposition (ALD) of an ultrathin (∼1nm) Al2O3 layer. The solution based ex situ sulphur passivation was found to be effective at removing a significant amount of the native oxides and protecting the surface against re-oxidation upon air exposure. The residual interfacial oxides which form between sulphur passivated InGaAs and the ultrathin Al2O3 layer can be substantially removed at high temperature (up to 700°C) without impacting on the InGaAs stoichiometry while significant loss of indium was recorded at this temperature on the uncovered sulphur passivated InGaAs surface.

EFFECTS OF MAGNETIC FIELDS ON LITHIUM EVOLUTION IN F AND G STARS

To study the effects of magnetic fields on lithium depletion and to explain the characteristics of lithium evolution in F- and G-type stars in open clusters, we construct a stellar model that includes a Tayler-Spruit dynamo-type field. Through examining the features of extra-mixing caused by magnetic fields in stellar interiors and the relationship between lithium depletion and the input parameters (i.e., mass, metallicity, and the initial rotational condition), we find that the magnetic model produces extra-mixing processes different from other models. During pre-main sequence, the model exhibits very efficient extra-mixing, resulting in strong lithium depletion. As a star evolves, the efficiency of extra-mixing rapidly decreases and lithium depletion slows down at old ages. By setting up different initial rotating conditions, the model predicts dispersions of lithium abundance in both main sequence and pre-main sequence stages. The dispersion begins when a radiative core forms in the interior. The number sees a rapid growth afterward, reaching 0.1-0.5 dex at zero age main sequence in G and late-F stars. The increase of dispersion continues in the main sequence, which is slight in G and late-F stars while significant in mid-F stars. Finally, a comparison is carried out between the theoretical results and the observed data in four open clusters. Good agreements are obtained.

Observational Tests of Magnetospheric Accretion Models in Young Stars

Magnetically controlled accretion of disk material onto the surface of Classical T Tauri stars is the dominant paradigm in our understanding of how these young stars interact with their surrounding disks. These stars provide a powerful test of magnetically controlled accretion models since all of the relevant parameters, including the magnetic field strength and geometry, are in principle measureable. Both the strength and the field geometry are key for understanding how these stars interact with their disks. This talk will focus on recent advances in magnetic field measurements on a large number of T Tauri stars, as well as very recent studies of the accretion rates onto a sample of young stars in NGC 2264 with known rotation periods. We discuss how these observations provide critical tests of magnetospheric accretion models which predict a rotational equilibrium is reached. We find good support for the model predictions once the complex geometry of the stellar magnetic field is taken into account. We will also explore how the observations of the accretion properties of the 2264 cluster stars can be used to test emerging ideas on how magnetic fields on young stars are generated and organized as a function of their internal structure (i.e. the presence of a radiative core). We do not find support for the hypothesis that large changes in the magentic field geometry occur when a radiative core appears in these young stars.

MAGNETIC INHIBITION OF CONVECTION AND THE FUNDAMENTAL PROPERTIES OF LOW-MASS STARS. I. STARS WITH A RADIATIVE CORE

Magnetic fields are hypothesized to inflate the radii of low-mass stars---defined as less massive than 0.8$M_\odot$---in detached eclipsing binaries (DEBs). We investigate this hypothesis using the recently introduced magnetic Dartmouth stellar evolution code. In particular, we focus on stars thought to have a radiative core and convective outer envelope by studying in detail three individual DEBs: UV Psc, YY Gem, and CU Cnc. The results suggest that the stabilization of thermal convection by a magnetic field is a plausible explanation for the observed model-radius discrepancies. However, surface magnetic field strengths required by the models are significantly stronger than those estimated from the observed coronal X-ray emission. Agreement between model predicted surface magnetic field strengths and those inferred from X-ray observations can be found by assuming that the magnetic field sources its energy from convection. This approach makes the transport of heat by convection less efficient and is akin to reduced convective mixing length methods used in other studies. Predictions for the metallicity and magnetic field strengths of the aforementioned systems are reported. We also develop an expression relating a reduction in the convective mixing length to a magnetic field strength in units of the equipartition value. Our results are compared with those from previous investigations to incorporate magnetic fields to explain the low-mass DEB radius inflation. Finally, we explore how the effects of magnetic fields might affect mass determinations using asteroseismic data and the implication of magnetic fields on exoplanet studies.

High temperature thermal stability of the HfO2/Ge (100) interface as a function of surface preparation studied by synchrotron radiation core level photoemission

High resolution soft x-ray photoemission spectroscopy (SXPS) have been used to study the high temperature thermal stability of ultra-thin atomic layer deposited (ALD) HfO2 layers (∼1nm) on sulphur passivated and hydrofluoric acid (HF) treated germanium surfaces. The interfacial oxides which are detected for both surface preparations following HfO2 deposition can be effectively removed by annealing upto 700°C without any evidence of chemical interaction at the HfO2/Ge interface. The estimated valence and conduction band offsets for the HfO2/Ge abrupt interface indicated that effective barriers exist to inhibit carrier injection.

Stellar activity observed by the Kepler Space Telescope. The M dwarf of the Kepler-32 system with five orbiting planets

The activity of the central star of the Kepler-32 planetary system is studied using continuous 1141-day observations with the Kepler Space Telescope. The Kepler-32 system includes a slowly rotating Mdwarf (rotational period of 37.8 d) with a mass of 0.54M⊙ and five planets. One of the unique properties of the system is its compactness: the orbits of all five planets are less than a third of the size of the orbit of Mercury; the planet closest to the star is separated from it by only 4.3 stellar radii. Surface-temperature inhomogeneities of the central star are studied using precise photometric observations of Kepler-32, and their evolution traced. In total, 42 624 individual brightness measurements in the 1141-day (3.1-year) observing interval were selected for the analysis. The calculated amplitude power spectra for the first and second halves of the interval of the Kepler-32 observations indicate appreciable variability of the photometric period, corresponding to the evolution of active regions at various latitudes on the stellar surface. Evidence for the existence of two active regions on the stellar surface separated in phase by 0.42 has been found. Time intervals in which the longitudes of the active regions changed (“flip-flops”) with durations of the order of 200–300 days have been established. The spotted area of the star was, on average, about 1% of the total visible surface, and varied from 0.3 to 1.7%. The results for the dwarf Kepler-32 are compared with those from a spectropolarimetric survey of 23 M dwarfs, including both fully convective stars and stars with weakly radiative cores. For a more detailed comparison, temperature inhomogeneities on the surface of one of the survey stars, DS Leo, was reconstructed using the ground-based observations (316 individual measurements of the V-band brightness of the star during seven observing seasons in an all-sky automated survey). The general properties and evolution of the active regions on DS Leo and Kepler-32 are considered. The positions of the active regions on the surface of Kepler-32 yields no evidence for differential rotation of this star. The possibility of detecting the magnetic field of Kepler-32 is proposed. The analysis of the photometric data for Kepler-32 are also compared to the previous results for the fully convective, low-mass M dwarfs GJ 1243 and LHS 6351. This demonstrates that the observed manifestations of activity on Kepler-32 correspond to those for active G-K stars and to M dwarfs with masses of the order of 0.5M⊙, rather than Mdwarfs with masses from 0.2 to 0.5M⊙.

Do Magnetic Fields Actually Inflate Low-Mass Stars?

AbstractMagnetic fields have been hypothesized to inflate the radii of low-mass stars—defined as less than 0.8 M⊙–in detached eclipsing binaries (DEBs). We evaluate this hypothesis using the magnetic Dartmouth stellar evolution code. Results suggest that magnetic suppression of thermal convection can inflate low-mass stars that possess a radiative core and convective outer envelope. A scaling relation between X-ray luminosity and surface magnetic flux indicates that model surface magnetic field strength predictions are consistent with observations. This supports the notion that magnetic fields may be inflating these stars. However, magnetic models are unable to reproduce radii of fully convective stars in DEBs. Instead, we propose that model discrepancies below the fully convective boundary are related to metallicity.