Cores Of Red Giant Stars Research Articles

Local stability of differential rotation in magnetized radiation zones and the solar tachocline

ABSTRACT We study local magnetohydrodynamical instabilities of differential rotation in magnetized, stably stratified regions of stars and planets using a Cartesian Boussinesq model. We consider arbitrary latitudes and general shears (with gravity direction misaligned from this by an angle $\phi$), to model radial ($\phi =0$), latitudinal ($\phi =\pm 90^\circ$), and mixed differential rotations, and study both non-diffusive [including magnetorotational instability (MRI) and Solberg–Høiland instability] and diffusive instabilities [including Goldreich–Schubert–Fricke (GSF) and MRI with diffusion]. These instabilities could drive turbulent transport and mixing in radiative regions, including the solar tachocline and the cores of red giant stars, but their dynamics are incompletely understood. We revisit linear axisymmetric instabilities with and without diffusion and analyse their properties in the presence of magnetic fields, including deriving stability criteria and computing growth rates, wave vectors, and energetics, both analytically and numerically. We present a more comprehensive analysis of axisymmetric local instabilities than prior work, exploring arbitrary differential rotations and diffusive processes. The presence of a magnetic field leads to stability criteria depending upon angular velocity rather than angular momentum gradients. We find MRI operates for much weaker differential rotations than the hydrodynamic GSF instability, and that it typically prefers much larger length-scales, while the GSF instability is impeded by realistic strength magnetic fields. We anticipate MRI to be more important for turbulent transport in the solar tachocline than the GSF instability when $\phi \gt 0$ in the Northern (and vice versa in the Southern) hemisphere, though the latter could operate just below the convection zone when MRI is absent for $\phi \lt 0$.

Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields

Context. Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. Aims. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. Methods. We used the powerful analytical Racah-Wigner algebra used in quantum mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various realistically plausible topologies of fossil magnetic fields. We also computed the induced perturbation of their frequencies. Results. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to the unraveling of the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Conclusions. Asymmetries of dipolar mixed modes provide a key bit of information on the geometrical topology of deep fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.

Evidence of structural discontinuities in the inner core of red-giant stars

Red giants are stars in the late stages of stellar evolution. Because they have exhausted the supply of hydrogen in their core, they burn the hydrogen in the surrounding shell . Once the helium in the core starts fusing, the star enters the clump phase, which is identified as a striking feature in the color-magnitude diagram. Since clump stars share similar observational properties, they are heavily used in astrophysical studies, as probes of distance, extinction through the galaxy, galaxy density, and stellar chemical evolution. In this work, we perform the detailed observational characterization of the deepest layers of clump stars using asteroseismic data from Kepler. We find evidence for large core structural discontinuities in about 6.7% of the stars in our sample, implying that the region of mixing beyond the convective core boundary has a radiative thermal stratification. These stars are otherwise similar to the remaining stars in our sample, which may indicate that the building of the discontinuities is an intermittent phenomenon.

Magnetic fields of 30 to 100 kG in the cores of red giant stars.

A red giant star is an evolved low- or intermediate-mass star that has exhausted its central hydrogen content, leaving a helium core and a hydrogen-burning shell. Oscillations of stars can be observed as periodic dimmings and brightenings in the optical light curves. In red giant stars, non-radial acoustic waves couple to gravity waves and give rise to mixed modes, which behave as pressure modes in the envelope and gravity modes in the core. These modes have previously been used to measure the internal rotation of red giants1,2, leading to the conclusion that purely hydrodynamical processes of angular momentum transport from the core are too inefficient3. Magnetic fields could produce the additional required transport4-6. However, owing to the lack of direct measurements of magnetic fields in stellar interiors, little is currently known about their properties. Asteroseismology can provide direct detection of magnetic fields because, like rotation, the fields induce shifts in the oscillation mode frequencies7-12. Here we report the measurement of magnetic fields in the cores of three red giant stars observed with the Kepler13 satellite. The fields induce shifts that break the symmetry of dipole mode multiplets. We thus measure field strengths ranging from about 30 kilogauss to about 100 kilogauss in the vicinity of the hydrogen-burning shell and place constraints on the field topology.

The RGB tip of galactic globular clusters and the revision of the axion-electron coupling bound

Context. The production of neutrinos by plasma oscillations is the most important energy sink process operating in the degenerate core of low-mass red giant stars. This process counterbalances the release of energy induced by nuclear reactions and gravitational contraction, and determines the luminosity attained by a star at the moment of the He ignition. This occurrence coincides with the tip of the red giant branch (RGB), whose luminosity is extensively used as a calibrated standard candle in several cosmological studies. Aims. We aim to investigate the possible activation of additional energy sink mechanisms, as predicted by many extensions of the so-called Standard Model. In particular, our objective is to test the possible production of axions or axion-like particles, mainly through their coupling with electrons. Methods. By combining Hubble Space Telescope and ground-based optical and near-infrared photometric samples, we derived the RGB tip absolute magnitude of 22 galactic globular clusters (GGCs). The effects of varying the distance and the metallicity scales were also investigated. Then we compared the observed tip luminosities with those predicted by state-of-the-art stellar models that include the energy loss due to the axion production in the degenerate core of red giant stars. Results. We find that theoretical predictions including only the energy loss by plasma neutrinos are, in general, in good agreement with the observed tip bolometric magnitudes, even though the latter are ∼0.04 mag brighter on average. This small shift may be the result of systematic errors affecting the evaluation of the RGB tip bolometric magnitudes, or, alternatively, it could be ascribed to an axion-electron coupling causing a non-negligible thermal production of axions. In order to estimate the strength of this possible axion sink, we performed a cumulative likelihood analysis using the RGB tips of the whole set of 22 GGCs. All the possible sources of uncertainties affecting both the measured bolometric magnitudes and the corresponding theoretical predictions were carefully considered. As a result, we find that the value of the axion-electron coupling parameter that maximizes the likelihood probability is gae/10−13 ∼ 0.60−0.58+0.32. This hint is valid, however, if the dominant energy sinks operating in the core of red giant stars are standard neutrinos and axions coupled with electrons. Any additional energy-loss process, not included in the stellar models, would reduce such a hint. Nevertheless, we find that values gae/10−13 > 1.48 can be excluded with 95% confidence. Conclusions. The new bound we find represents the most stringent constraint for the axion-electron coupling available so far. The new scenario that emerges after this work represents a greater challenge for future experimental axion searches. In particular, we can exclude that the recent signal seen by the XENON1T experiment was due to solar axions.

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.

Asteroseismology can reveal strong internal magnetic fields in red giant stars.

Internal stellar magnetic fields are inaccessible to direct observations, and little is known about their amplitude, geometry, and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, arising from a magnetic greenhouse effect that scatters and traps oscillation-mode energy within the core of the star. The Kepler satellite has observed a few dozen red giants with depressed dipole modes, which we interpret as stars with strongly magnetized cores. We find that field strengths larger than ~10(5) gauss may produce the observed depression, and in one case we infer a minimum core field strength of ≈10(7) gauss.

Angular momentum redistribution by mixed modes in evolved low-mass stars

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.

Stability of the stellar structure and nonequilibrium dynamical characteristics of (g ? T) effects in nuclear reactions in stellar cores

The nonequilibrium dynamical theory of thermonuclear reaction in the stars is used to analyse the stabilities of P-PI reactions in the solar core and 3α reactions of helium burning in the core of red giant stars. The constant stability of stars on the main sequence and the helium “flash” instability have been explained from a new point of view. Calculations show that the (g - T) term in the dynamical equation has a damaging effect on the stability of the thermonuclear reaction, but its intensity in the core of red giant stars is ~ 107 times that in the solar core. It may be intimately related to some instability of the stellar structure. The effect on the “flash” instability is especially analysed.

Hydrodynamical models of type II supernovae

A series of hydrodynamical models of type-II supernova outbursts (SNII) has been calculated. Approximate relations connecting the total outburst energy e, the mass of envelope ejectedM, the presupernova radiusR, and the amount of ionizing quanta radiated by the supernovaeN H with such values as the duration of the light curve plateau Δt, and absolute magnitude in the wavelength bandV and photospheric velocityU PH observed near the middle of the plateau have been established. Advantage has been taken of the relations to obtain a preliminary evaluation for the characteristics of the average SN II: e=7×1050 erg,M=6M ⊙,R=500R ⊙,N H=2×1058. The SNIIs with plateau-like light curves seem to be accounted for by thermonuclear explosions of degenerate cores of red giant stars and result in a total disruption of the star without any stellar remnant. To the contrary, SNIIs with linear light curves have substantially different properties (in particular, they throw considerably less massive envelopes off). These SNII must signify the birth of collapsed objects—neutron stars (pulsars) or black holes.

Nuclear Reactions in Stars. IV. Buildup from Carbon

Reactions leading to the formation of C, O, and Ne at temperatures T of about 10/sup 8/ deg K, in the core of red giant stars, were studied previously. The nuclear reactions and resulting nucleogenesis are now studied for a gas consisting of C/sup 12/, O/sup 16/, and Ne/sup 20/ at 6 x 10/sup 8/ to 10 x 10/s up 8/ deg K and densities around 10/sup 4/ g/cc. The basic reaction rates are calculated and a set of simultaneous differential equations for various abundances as a function of time is solved numerically. The C/sup 12/ is destroyed by compound nucleus formation from C + C collisions in about 10/sup 5/ and 1 years, respectively, at 6 x 10/sup 8/ and 8.5 x 10/sup 8/ deg K. The net result is the production of some additional amounts of O/sup 16/ and Ne/sup 20/; appreciable amounts of Na/sup 23/ and the three stable magnesium isotopes (mainly Mg/sup 24/) and decreasing amounts of Al/sup 27/, Si, etc. The ratio of Na/sup 23/ to Mg/sup 24/ produced is almost 1/2, appreciably larger than the cosmic ratio. During the carbon burning, protons and alphas are released. At temperatures below 7 x 10/sup 8/ degmore » K, neutrons are produced very copiously through the sequence C/sup 12/(p, gamma )N/sup 13/; N/sup 13/ yields C/sup 13/; C/sup 13/( alpha ,n)O/sup 16/. If small amounts of metals i n the Fe-region (up to about one metal nucleus per 1000 C/sup 12/ nuclei) were present originally, each metal nucleus will absorb about 30 neutrons, At temperatures above 8 x 10/sup 8/ deg K, N/sup 13/ is photodisintegrated and the neutron production is appreciably less. (auth)« less