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Register a new userPeriod spacings in red giants I. Disentangling rotation and revealing core structure discontinuities
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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.
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The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focuses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring the coupling factor of mixed modes is set up. It is derived from the method recently implemented for measuring period spacings. It runs in an automated way so that it can be applied to a large sample of stars. Coupling factors of mixed modes were measured for thousands of red giants. They show specific variation with mass and evolutionary stage. Weak coupling is observed for the most evolved stars on the red giant branch only; large coupling factors are measured at the transition between subgiants and red giants, as well as in the red clump. The measurement of coupling factors in dipole mixed modes provides a new insight into the inner interior structure of evolved stars. While the large frequency separation and the asymptotic period spacings probe the envelope and the core, respectively, the coupling factor is directly sensitive to the intermediate region in between and helps determining its extent. Observationally, the determination of the coupling factor is a prior to precise fits of the mixed-mode pattern, and can now be used to address further properties of the mixed-mode pattern, as the signature of the buoyancy glitches and the core rotation.
Oscillation modes with a mixed character, as observed in evolved low-mass stars, are highly sensitive to the physical properties of the innermost regions. Measuring their properties is therefore extremely important to probe the core, but requires some care, due to the complexity of the mixed-mode pattern. This work aims at providing a consistent description of the mixed-mode pattern of low-mass stars, based on the asymptotic expansion. We also aim at studying the variation of the gravity offset $varepsilon_{g}$ with stellar evolution. We revisit previous work about mixed modes in red giants and empirically test how period spacings, rotational splittings, mixed-mode widths and heights can be estimated in a consistent view, based on the properties of the mode inertia ratios. From the asymptotic fit of the mixed-mode pattern of a large set of red giants at various evolutionary stages, we derive unbiased and precise asymptotic parameters. As the asymptotic expansion of gravity modes is verified with a precision close to the frequency resolution for stars on the red giant branch (10$^{-4}$ in relative values), we can derive accurate values of the asymptotic parameters. We decipher the complex pattern in a rapidly rotating star, and explain how asymmetrical splittings can be inferred, as well as the stellar inclinations. This allows us to revisit the stellar inclinations in two open clusters, NGC 6819 and NGC 6791: our results show that the stellar inclinations in these clusters do not have privileged orientation in the sky. The variation of the asymptotic gravity offset along with stellar evolution is investigated in detail. We also derive generic properties that explain under which conditions mixed modes can be observed.
With recent advances in asteroseismology it is now possible to peer into the cores of red giants, potentially providing a way to study processes such as nuclear burning and mixing through their imprint as sharp structural variations -- glitches -- in the stellar cores. Here we show how such core glitches can affect the oscillations we observe in red giants. We derive an analytical expression describing the expected frequency pattern in the presence of a glitch. This formulation also accounts for the coupling between acoustic and gravity waves. From an extensive set of canonical stellar models we find glitch-induced variation in the period spacing and inertia of non-radial modes during several phases of red-giant evolution. Significant changes are seen in the appearance of mode amplitude and frequency patterns in asteroseismic diagrams such as the power spectrum and the echelle diagram. Interestingly, along the red-giant branch glitch-induced variation occurs only at the luminosity bump, potentially providing a direct seismic indicator of stars in that particular evolution stage. Similarly, we find the variation at only certain post-helium-ignition evolution stages, namely, in the early phases of helium-core burning and at the beginning of helium-shell burning signifying the asymptotic-giant-branch bump. Based on our results, we note that assuming stars to be glitch-free, while they are not, can result in an incorrect estimate of the period spacing. We further note that including diffusion and mixing beyond classical Schwarzschild, could affect the characteristics of the glitches, potentially providing a way to study these physical processes.
Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. Such modes have the potential to reveal information on the physics of the deep stellar interior. Different methods have been proposed to derive an observed value for the gravity-mode period spacing, the most prominent one relying on a relation derived from asymptotic pulsation theory applied to the gravity-mode character of the mixed modes. Our aim is to compare results based on this asymptotic relation with those derived from an empirical approach for three pulsating red-giant stars. We developed a data-driven method to perform frequency extraction and mode identification. Next, we used the identified dipole mixed modes to determine the gravity-mode period spacing by means of an empirical method and by means of the asymptotic relation. In our methodology, we consider the phase offset, $epsilon_{mathrm{g}}$, of the asymptotic relation as a free parameter. Using the frequencies of the identified dipole mixed modes for each star in the sample, we derived a value for the gravity-mode period spacing using the two different methods. These differ by less than 5%. The average precision we achieved for the period spacing derived from the asymptotic relation is better than 1%, while that of our data-driven approach is 3%. Good agreement is found between values for the period spacing derived from the asymptotic relation and from the empirical method. Full abstract in PDF file.
The relation of period spacing ($Delta P$) versus period ($P$) of dipole prograde g modes is known to be useful to measure rotation rates in the g-mode cavity of rapidly rotating $gamma$ Dor and slowly pulsating B (SPB) stars. In a rapidly rotating star, an inertial mode in the convective core can resonantly couple with g modes propagative in the surrounding radiative region. The resonant coupling causes a dip in the $P$-$Delta P$ relation, distinct from the modulations due to the chemical composition gradient. Such a resonance dip in $Delta P$ of prograde dipole g modes appears around a frequency corresponding to a spin parameter $2f_{rm rot}{rm(cc)}/ u_{rm co-rot} sim 8-11$ with $f_{rm rot}$(cc) being the rotation frequency of the convective core and $ u_{rm co-rot}$ the pulsation frequency in the co-rotating frame. The spin parameter at the resonance depends somewhat on the extent of core overshooting, central hydrogen abundance, and other stellar parameters. We can fit the period at the observed dip with the prediction from prograde dipole g modes of a main-sequence model, allowing the convective core to rotate differentially from the surrounding g-mode cavity. We have performed such fittings for 16 selected $gamma$ Dor stars having well defined dips, and found that the majority of $gamma$ Dor stars we studied rotate nearly uniformly, while convective cores tend to rotate slightly faster than the g-mode cavity in less evolved stars.
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