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Register a new userThe interior rotation of a sample of gamma Doradus stars from ensemble modelling of their gravity mode period spacings
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CONTEXT. Gamma Doradus stars (hereafter gamma Dor stars) are known to exhibit gravity- and/or gravito-intertial modes that probe the inner stellar region near the convective core boundary. The non-equidistant spacing of the pulsation periods is an observational signature of the stars evolution and current internal structure and is heavily influenced by rotation. AIMS. We aim to constrain the near-core rotation rates for a sample of gamma Dor stars, for which we have detected period spacing patterns. METHODS. We combined the asymptotic period spacing with the traditional approximation of stellar pulsation to fit the observed period spacing patterns using chi-squared optimisation. The method was applied to the observed period spacing patterns of a sample of stars and used for ensemble modelling. RESULTS. For the majority of stars with an observed period spacing pattern we successfully determined the rotation rates and the asymptotic period spacing values, though the uncertainty margins on the latter were typically large. This also resulted directly in the identification of the modes corresponding with the detected pulsation frequencies, which for most stars were prograde dipole gravity and gravito-inertial modes. The majority of the observed retrograde modes were found to be Rossby modes. We further discuss the limitations of the method due to the neglect of the centrifugal force and the incomplete treatment of the Coriolis force. CONCLUSION. Despite its current limitations, the proposed methodology was successful to derive the rotation rates and to identify the modes from the observed period spacing patterns. It forms the first step towards detailed seismic modelling based on observed period spacing patterns of moderately to rapidly rotating gamma Dor stars.
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Gamma Doradus stars (hereafter gamma Dor stars) are gravity-mode pulsators of spectral type A or F. Such modes probe the deep stellar interior, offering a detailed fingerprint of their structure. Four-year high-precision space-based Kepler photometry of gamma Dor stars has become available, allowing us to study these stars with unprecedented detail. We selected, analysed, and characterized a sample of 67 gamma Dor stars for which we have Kepler observations available. For all the targets in the sample we assembled high-resolution spectroscopy to confirm their F-type nature. We found fourteen binaries, among which four single-lined binaries, five double-lined binaries, two triple systems and three binaries with no detected radial velocity variations. We estimated the orbital parameters whenever possible. For the single stars and the single-lined binaries, fundamental parameter values were determined from spectroscopy. We searched for period spacing patterns in the photometric data and identified this diagnostic for 50 of the stars in the sample, 46 of which are single stars or single-lined binaries. We found a strong correlation between the spectroscopic vsini and the period spacing values, confirming the influence of rotation on gamma Dor-type pulsations as predicted by theory. We also found relations between the dominant g-mode frequency, the longest pulsation period detected in series of prograde modes, vsini, and log Teff.
When a star evolves into a red giant, the enhanced coupling between core-based gravity modes and envelope-based pressure modes forms mixed modes, allowing its deep interior to be probed by asteroseismology. The ability to obtain information about stellar interiors is important for constraining theories of stellar structure and evolution, for which the origin of various discrepancies between prediction and observation are still under debate. Ongoing speculation surrounds the possibility that some red giant stars may harbour strong (dynamically significant) magnetic fields in their cores, but interpretation of the observational data remains controversial. In part, this is tied to shortfalls in our understanding of the effects of strong fields on the seismic properties of gravity modes, which lies beyond the regime of standard perturbative methods. Here we seek to investigate the effect of a strong magnetic field on the asymptotic period spacings of gravity modes. We use a Hamiltonian ray approach to measure the volume of phase space occupied by mode-forming rays, this being roughly proportional to the average density of modes (number of modes per unit frequency interval). A strong field appears to systematically increase this by about 10%, which predicts a ~10% smaller period spacing. Evidence of near integrability in the ray dynamics hints that the gravity-mode spectrum may still exhibit pseudo-regularities under a strong field.
A major uncertainty in the theory of stellar evolution is the angular momentum distribution inside stars and its change during stellar life. We compose a sample of 67 stars in the core-hydrogen burning phase with a $log,g$ value from high-resolution spectroscopy, as well as an asteroseismic estimate of the near-core rotation rate derived from gravity-mode oscillations detected in space photometry. This assembly includes 8 B-type stars and 59 AF-type stars, covering a mass range from 1.4 to 5,M$_odot$, i.e., it concerns intermediate-mass stars born with a well-developed convective core. The sample covers projected surface rotation velocities $vsin,i in[9,242],$km,s$^{-1}$ and core rotation rates up to $26mu$Hz, which corresponds to 50% of the critical rotation frequency. We find deviations from rigid rotation to be moderate in the single stars of this sample. We place the near-core rotation rates in an evolutionary context and find that the core rotation must drop drastically before or during the short phase between the end of the core-hydrogen burning and the onset of core-helium burning. We compute the spin parameter, which is the ratio of twice the rotation rate to the mode frequency (also known as the inverse Rossby number), for 1682 gravity modes and find the majority (95%) to occur in the sub-inertial regime. The ten stars with Rossby modes have spin parameters between 14 and 30, while the gravito-inertial modes cover the range from 1 to 15.
We provide a status report on the determination of stellar ages from asteroseismology for stars of various masses and evolutionary stages. The ability to deduce the ages of stars with a relative precision of typically 10 to 20% is a unique opportunity for stellar evolution and also of great value for both galactic and exoplanet studies. Further, a major uncalibrated ingredient that makes stellar evolution models uncertain, is the stellar interior rotation frequency $Omega(r)$ and its evolution during stellar life. We summarize the recent achievements in the derivation of $Omega(r)$ for different types stars, offering stringent observational constraints on theoretical models. Core-to-envelope rotation rates during the red giant stage are far lower than theoretical predictions, pointing towards the need to include new physical ingredients that allow strong and efficient coupling between the core and the envelope in the models of low-mass stars in the evolutionary phase prior to the core helium burning. Stars are subject to efficient mixing phenomena, even at low rotation rates. Young massive stars with seismically determined interior rotation frequency reveal low core-to-envelope rotation values.
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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