Doradus Stars Research Articles

Asteroseismology of the dip structure in period-spacings of rapidly rotating γ Doradus stars caused by the coupling between core and envelope oscillations

ABSTRACT Recent asteroseismic observations by the Kepler space mission have revealed the dip fine structure in the period-spacing versus period diagram of rapidly rotating γ Doradus stars. Following the successful reproduction of the dip structure by numerical calculations in previous studies, we present in this paper the physical mechanism of how the dip is formed as a result of the interaction between the gravito-inertial waves in the radiative envelope and the pure inertial waves in the convective core. We analytically describe the wave solutions in both of the radiative envelope and the convective core, and match them at the interface to construct an eigenmode. We have found from the analysis the following points: the dip structure is mainly controlled by a parameter that has an inverse correlation with Brunt–Väisälä frequency at the interface; the depth and the width of the dip is shallower and larger, respectively, as the parameter gets large; the shape of the dip can be approximated by the Lorentzian function; the period at the central position of the dip is equal to or slightly smaller than that of the involved pure inertial mode in the convective core. We have also understood based on the evolutionary models of main-sequence stars that the parameter is inversely correlated with the chemical composition gradient at the convective-core boundary. The dip structure thus would provide information about the poorly-understood physical processes, such as diffusion, convective overshooting and rotational mixing, around the boundary between the convective core and the radiative envelope.

Classifying Kepler light curves for 12 000 A and F stars using supervised feature-based machine learning

ABSTRACT With the availability of large-scale surveys like Kepler and TESS, there is a pressing need for automated methods to classify light curves according to known classes of variable stars. We introduce a new algorithm for classifying light curves that compares 7000 time-series features to find those that most effectively classify a given set of light curves. We apply our method to Kepler light curves for stars with effective temperatures in the range 6500–10 000 K. We show that the sample can be meaningfully represented in an interpretable 5D feature space that separates seven major classes of light curves (δ Scuti stars, γ Doradus stars, RR Lyrae stars, rotational variables, contact eclipsing binaries, detached eclipsing binaries, and non-variables). We achieve a balanced classification accuracy of 82 per cent on an independent test set of Kepler stars using a Gaussian mixture model classifier. We use our method to classify 12 000 Kepler light curves from Quarter 9 and provide a catalogue of the results. We further outline a confidence heuristic based on probability density to search our catalogue and extract candidate lists of correctly classified variable stars.

The near-core rotation of HD 112429

Context. The Transiting Exoplanet Survey Satellite (TESS) provides us with high-precision photometric observations of large numbers of bright stars over more than 70% of the entire sky, allowing us to revisit and characterise well-known stars. Aims. We aim to conduct an asteroseismic analysis of the γ Doradus (γ Dor) star HD 112429 using both the available ground-based spectroscopy and TESS photometry, and assess the conditions required to measure the near-core rotation rate and buoyancy travel time. Methods. We collected and reduced the available five sectors of short-cadence TESS photometry of this star, as well as 672 legacy observations from six medium- to high-resolution ground-based spectrographs. We determined the stellar pulsation frequencies from both data sets using iterative prewhitening, did asymptotic g mode modelling of the star, and investigated the corresponding spectral line profile variations using the pixel-by-pixel method. Results. We validate the pulsation frequencies from the TESS data down to S/N ≥ 5.6, confirming recent reports in the literature that the classical criterion S/N ≥ 4 does not suffice for space-based observations. We identify the pulsations as prograde dipole g modes and r-mode pulsations, and measure a near-core rotation rate of 1.536 (3) d−1 and a buoyancy travel time Π0 of 4190 (50) s. These results are in agreement with the observed spectral line profile variations, which were qualitatively evaluated using a newly developed toy model. We establish a set of conditions that have to be fulfilled for an asymptotic asteroseismic analysis of g-mode pulsators. In the case of HD 112429, two TESS sectors of space photometry suffice. Conclusions. Although a detailed asteroseismic modelling analysis is not viable for g-mode pulsators with only short or sparse light curves of space photometry, it is possible to determine global asteroseismic quantities for a subset of these stars. Thanks to the ongoing TESS mission, this will allow us to characterise many more stars than only those with years of data.

Nine Bright γ Doradus Variables Discovered with Ground-based Photometry

Abstract We have used precise photometric and high-dispersion spectroscopic observations to study nine candidate γ Doradus (γ Dor) stars, identified as optically variable comparison stars in our photometric studies of Sun-like stars. In this paper, we confirm these nine candidates as new γ Dor variables. All exhibit sinusoidal variability with amplitudes between 6 and 65 mmag in Johnson B and periods from 0.28 to 1.13 days. All lie in the same region of the H-R diagram as our previously confirmed γ Dor stars. Of the nine systems, one is a single-lined spectroscopic binary (SB1), two are double-lined spectroscopic binaries (SB2), and the remaining six are single stars. We present orbits for the three binary systems: HD 34415, HD 144839, and HD 182735. Their periods are 6400 days or 17.5 yr (adopted), 995 ± 7 days, and 1052.4 ± 0.2 days, respectively. We compare our photometric periods with those we derive for six of the nine stars observed with the Transiting Exoplanet Survey Satellite to strengthen the confirmation of these new γ Dor variables. Finally, because the distribution of γ Dor stars in the H-R diagram overlaps with the red edge of the δ Scuti (δ Sct) instability strip, we use our ground-based photometric results for the 73 γ Dor stars confirmed with our Automatic Photoelectric Telescopes over the past two decades to look at the incidence of hybrid δ Sct/γ Dor stars; these are highly valuable targets for asteroseismology.

Far-ultraviolet Variables in M31: Concentration in Spiral Arms and Association with Young Stars

Abstract The Andromeda galaxy (M31) is an object of ongoing study with the Ultraviolet Imaging Telescope (UVIT) on AstroSat. Field 2, which is 6.4 kpc in diameter at the distance of M31, includes a substantial part of the NE spiral arms of the galaxy. We have obtained a second observation of Field 2 with the far-ultraviolet (FUV) F148W (148 nm) filter, separated from the first observation by 1465 days. Both observations are analyzed to detect sources that are variable at a >3σ confidence level. For sources with less than ∼2″ separation, we apply multi-Gaussian fits, to obtain reliable magnitudes in the presence of source crowding. The variable sources are found to be concentrated in the spiral arms, with fraction of variable to nonvariable sources ∼2 times higher than for interarm regions, indicating an association of FUV variables with young stellar populations. UVIT FUV-NUV color–magnitude diagrams confirm the association of FUV variables with young massive/hot stars. Using existing catalogs, we obtain counterparts for 64 of the 82 most variable sources (>5σ). The counterparts include 13 star clusters, three ionized hydrogen (H ii) regions, three novae, one S Doradus star, eight eclipsing binaries, 20 foreground sources, two regular variables, and 14 unspecified variables.

Spectroscopic frequency and mode identification of γ Doradus stars HD 109799 and HD 103257

ABSTRACT Following frequency and mode identification of two candidate γ Doradus stars, HD 103257 and HD 109799, both can be categorized as bona-fide members of the class. Over 250 high-resolution spectra of the two stars were collected at University of Canterbury Mount John Observatory (UCMJO) using the High Efficiency and Resolution Canterbury University Large Echelle Spectrograph (HERCULES) spectrograph. The spectra were cross-correlated with a synthetic δ-function template to produce line-profiles and further augmented with high-quality photometry from the Transiting Exoplanet Survey Satellite (TESS) mission, the Wide Angle Search for Planets (WASP) archive, and HIPPARCOS catalogue for frequency and mode analysis. Frequency analysis was carried out using FAMIAS and SigSpec. Two pulsation frequencies were identified in the spectra for HD 103257: 1.22496 ± 0.00001 and 1.14569 ± 0.00002 d−1, explaining 58.9 ${{\ \rm per\ cent}}$ of the variation across the line profiles. Both frequencies were characterized with best-fitting modes of (ℓ, m) = (1, 1). Two pulsation frequencies were identified in the spectra for HD 109799: 1.48679 ± 0.00002 and 1.25213 ± 0.00002 d−1, explaining 32.6 ${{\ \rm per\ cent}}$ of the variation across the line profiles. Both frequencies also yielded individual mode fits of modes (ℓ, m) = (1, 1). The excellent quality photometry from TESS observations has proven complementary to the work herein, and will provide a meaningful opportunity for deeper analysis of additional stars in the HERCULES catalogue. This will be a key component in the continued development of models relating to the processes within γ Doradus stars.

Constraining stellar evolution theory with asteroseismology of γ Doradus stars using deep learning

Context. The efficiency of the transport of angular momentum and chemical elements inside intermediate-mass stars lacks proper calibration, thereby introducing uncertainties on a star’s evolutionary pathway. Improvements require better estimation of stellar masses, evolutionary stages, and internal mixing properties. Aims. Our aim was to develop a neural network approach for asteroseismic modelling, and test its capacity to provide stellar masses, ages, and overshooting parameter for a sample of 37 γ Doradus stars; these parameters were previously determined from their effective temperature, surface gravity, near-core rotation frequency, and buoyancy travel time Π0. Here our goal is to perform the parameter estimation from modelling of individual periods measured for dipole modes with consecutive radial order rather than from Π0. We assess whether fitting these individual mode periods increases the capacity of the parameter estimation. Methods. We trained neural networks to predict theoretical pulsation periods of high-order gravity modes (n ∈ [15, 91]), and to predict the luminosity, effective temperature, and surface gravity for a given mass, age, overshooting parameter, diffusive envelope mixing, metallicity, and near-core rotation frequency. We applied our neural networks for Computing Pulsation Periods and Photospheric Observables (C-3PO) to our sample and compute grids of stellar pulsation models for the estimated parameters. Results. We present the near-core rotation rates (from the literature) as a function of the inferred stellar age and critical rotation rate. We assessed the rotation rates of the sample near the start of the main sequence assuming rigid rotation. Furthermore, we measured the extent of the core overshoot region and find no correlation with mass, age, or rotation. Finally, for one star in our sample, KIC 12066947, we find indications of mode coupling in the period spacing pattern which we cannot reproduce with mode trapping. Conclusions. The neural network approach developed in this study allows the derivation of stellar properties dominant for stellar evolution, such as mass, age, and extent of core-boundary mixing. It also opens a path for future estimation of mixing profiles throughout the radiative envelope, with the aim of inferring these profiles for large samples of γ Doradus stars.

Investigating variable stars in the open cluster NGC 1912 and its surrounding field

In this work, we studied the variable stars in the open cluster NGC 1912 based on the photometric observations and Gaia DR2 data. More than 3600 CCD frames in B, V, R filters were reduced, and we obtained the light curves that span about 63 hours. By analyzing these light curves, we detected 24 variable stars, including 16 periodic variable stars, seven eclipsing binaries and one star whose type is unclear. Among these 24 variable stars, 11 are newly discovered, which are classified as six γ Doradus stars, one δ Scuti star, three detached binaries and one contact binary. We also confirmed 13 previously known variable stars. Based on cluster members identified by Cantat-Gaudin et al. (), we inferred cluster memberships for these detected variable stars. Using Gaia DR2 data, we plotted a new color-magnitude diagram for NGC 1912, and showed the nature of variable cluster members in kinematical properties and heliocentric distance. Among the 24 variable stars, seven variables are probable cluster members, which show homogeneity in kinematic characters and space position with the established cluster members. Four of the seven variable cluster members are the previously discovered stars, consisting of two γ Dor stars and two δ Sct stars. The remaining three variable cluster members, which are all γ Dor stars, are firstly detected in this work. The main physical parameters of these variable cluster members estimated from the color-magnitude diagram are log(age/yr) = 8.75, [Fe/H] = –0.1, m – M = 10.03 mag, and E(B – V) = 0.307.

Investigating variable stars in the open cluster NGC 1912 and its surrounding field

In this work, we studied the variable stars in the open cluster NGC 1912 based on the photometric observations and $Gaia$ DR2 data. More than 3600 CCD frames in B, V, R filters were reduced, and we obtained the light curves that span about 63 hours. By analyzing these light curves, we detected 24 variable stars, including 16 periodic variable stars, seven eclipsing binaries and one star whose type is unclear. Among these 24 variable stars, 11 are newly-discovered, which are classified as six gamma Doradus stars, one delta Scuti star, three detached binaries and one contact binaries. We also confirmed 13 previously known variable stars. Based on cluster members identified by Cantat-Gaudin et al. (2018), we inferred cluster memberships for these detected variable stars. Using Gaia DR2 data, we plotted a new color-magnitude diagram for NGC 1912, and showed the nature of variable cluster members in kinematical properties and heliocentric distance. Among the 24 variable stars, seven variables are probable cluster members, which show homogeneity in kinematic characters and space position with the established cluster members. Four of the seven variable cluster members are the previously discovered stars, consisting of two gamma Dor stars and two delta Sct stars. The remaining three variable cluster members, which are all gamma Dor stars, are firstly detected in this work. The main physical parameters of these variable cluster members estimated from the color-magnitude diagram are log(age/yr)=8.75, [Fe/H]=-0.1, m-M=10.03 mag, and E(B-V)=0.307.

Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars

Using our non-local and time-dependent theory of convection and a fixed set of convective parameters (C1, C2/C1 , C3)= (0.70, 0.50, 3.0) calibrated against the Sun, the linear non-adiabatic oscillations for evolutionary models with masses 1–20 M⊙ are calculated. The results show that almost all the classical instability strips can be reproduced. The theoretical instability strips of δ Scuti and γ Doradusvariables agree well with Kepler spacecraft observations. There is no essential difference in the excitation mechanism for δ Scuti and γ Doradus stars. They are excited by the combined effects of the radiative κ-mechanism and coupling between convection and oscillations. They represent two subgroups of a broader type of δ Scuti and γ Doradus stars, located in the lower part of the Cepheid instability strip. δ Scuti is the p-mode subgroup and γ Doradus is the g-mode subgroup. The luminous variable red giants observed by MACHO and OGLE are low-order radial pulsators among low-mass red giant and asymptotic giant branch stars. The excitation and damping mechanism of oscillations for low-temperature stars is studied in detail. Convective flux and turbulent viscosity are consistent damping mechanisms. The damping effect of the convective enthalpy flux is inversely proportional to the frequency of the modes, so it plays an important role in stabilizing the low-order modes and defining the red edge of the Cepheid instability strip. The damping effect of turbulent viscosity reaches its maximum at 3ωτc/16∼1, where τc is the dynamic time scale of turbulent convection and ω is the angular frequency of the modes. Turbulent viscosity is the main damping mechanism for stabilizing the high-order modes of low-temperature variables. The turbulent pressure is, in general, an excitation mechanism; it reaches maximum at 3ωτc/4∼1, and it plays an important role for the excitation of red variables. Convection is not, in fact, a pure damping effect for stellar oscillations. The relative contributions of turbulent pressure, turbulent viscosity, and convective enthalpy flux for excitation and damping effects change with stellar parameters (mass, luminosity, effective temperature) and with the radial order and spherical harmonic degree of the oscillation mode; therefore, the combined effect of convection is sometimes damping, and sometimes the excitation of oscillations. Our research shows that, for low-luminosity red giants, the low-order modes are pulsationally stable, while the intermediate- and high-order modes are unstable. Toward higher luminosity, the range of unstable modes shifts gradually toward the lower order. All of the intermediate- and high-order modes become stable, and a few low-order modes become unstable for high-luminosity red giants. They show the typical pulsational characteristics of Mira-like variables. The variable red giants are, at least for the high-luminosity RGs, self-excited. For red giants, the frequency of the maximally unstable modes predicted by our theory is similar to that given by the semi-empirical scaling relation.

High-amplitude γ Doradus variables

ABSTRACT According to most literature sources, the amplitude of the pulsational variability observed in γ Doradus stars does not exceed 0.1 mag in Johnson V. We have analysed fifteen high-amplitude γ Doradus stars with photometric peak-to-peak amplitudes well beyond this limit, with the aim of unraveling the mechanisms behind the observed high amplitudes and investigating whether these objects are in any way physically distinct from their low-amplitude counterparts. We have calculated astrophysical parameters and investigated the location of the high-amplitude γ Doradus stars and a control sample of fifteen low-amplitude objects in the log Teff versus log L/L⊙ diagram. Employing survey data and our own observations, we analysed the photometric variability of our target stars using discrete Fourier transform. Correlations between the observed primary frequencies, amplitudes and other parameters like effective temperature and luminosity were investigated. The unusually high amplitudes of the high-amplitude γ Doradus stars can be explained by the superposition of several base frequencies in interaction with their combination and overtone frequencies. Although the maximum amplitude of the primary frequencies does not exceed an amplitude of 0.1 mag, total light variability amplitudes of over 0.3 mag (V) can be attained in this way. Low- and high-amplitude γ Doradus stars do not appear to be physically distinct in any other respect than their total variability amplitudes but merely represent two ends of the same, uniform group of variables.

The effect of tides on near-core rotation: analysis of 35 Kepler γ Doradus stars in eclipsing and spectroscopic binaries

ABSTRACT We systematically searched for gravity- and Rossby-mode period spacing patterns in Kepler eclipsing binaries with γ Doradus pulsators. These stars provide an excellent opportunity to test the theory of tidal synchronization and angular momentum transport in F- and A-type stars. We discovered 35 systems that show clear patterns, including the spectroscopic binary KIC 10080943. Combined with 45 non-eclipsing binaries with γ Dor components that have been found using pulsation timing, we measured their near-core rotation rates and asymptotic period spacings. We find that many stars are tidally locked if the orbital periods are shorter than 10 d, in which the near-core rotation periods given by the traditional approximation of rotation are consistent with the orbital period. Compared to the single stars, γ Dor stars in binaries tend to have slower near-core rotation rates, likely a consequence of tidal spin-down. We also find three stars that have extremely slow near-core rotation rates. To explain these, we hypothesize that unstable tidally excited oscillations can transfer angular momentum from the star to the orbit, and slow the star below synchronism, a process we refer to as ‘inverse tides’.

First evidence of inertial modes in γ Doradus stars: The core rotation revealed

The advent of space photometry with CoRoT and Kepler has allowed for the gathering of exquisite and extensive time series for a wealth of main-sequence stars, including γ Doradus stars, whose detailed seismology was not achievable from the ground. γ Doradus stars present an incredibly rich pulsation spectra, with gravito-inertial modes, in some cases supplemented with δ Scuti-like pressure modes – for the hybrid stars – and, in many cases, with Rossby modes. The present paper aims to show that in addition to these modes which have been established in the radiative envelope, pure inertial modes that are trapped in the convective core can be detected in Kepler observations of γ Doradus stars thanks to their resonance with the gravito-inertial modes. We started by using a simplified model of perturbations in a full sphere of uniform density. Under these conditions, the spectrum of pure inertial modes is known from analytical solutions of the so-called Poincaré equation. We then computed coupling factors, which helped select the pure inertial modes which interact best with the surrounding dipolar gravito-inertial modes. Using complete calculations of gravito-inertial modes in realistic models of γ Doradus stars, we are able to show that the pure inertial and gravito-inertial resonances appear as “dips” in the gravito-inertial mode period spacing series at spin parameters that are close to those predicted by the simple model. We find the first evidence of such dips in the Kepler γ Doradus star KIC 5608334. Finally, using complete calculations in isolated convective cores, we find that the spin parameters of the pure inertial and gravito-inertial resonances are also sensitive to the density stratification of the convective core. In conclusion, we have discovered that certain dips in gravito-inertial mode period spacings that have been observed in some Kepler stars are, in fact, signatures of resonances with pure-inertial modes that are trapped in the convective core. This holds the promise that it would be possible to finally access the central conditions, namely, the rotation and density stratification, of intermediate-mass stars in the main sequence.

Pulsation and rotation in NGC 6811: the Kepler short-cadence stars

ABSTRACT We have analysed a selected sample of 36 Kepler short-cadence stars in the field of NGC 6811. The results reveal that all the targets are variable: two red giant stars with solar-like oscillations, 21 main-sequence pulsators (16 δ Scuti and five γ Doradus stars), and 13 rotating variables. Three new γ Doradus (γ Dor) variables (one is a hot γ Dor star) are detected in this work together with five new rotating variables. An in-depth frequency analysis of the δ Scuti (δ Sct) and γ Dor stars in the sample shows that the frequency spectra are very rich, in particular for the δ Sct-type variables. They present very dense frequency distributions and wide diversity in frequency patterns, even for stars being members of the cluster and with very similar location in the Hertzsprung–Russell (H–R) diagram. Rotational modulation is found for a high percentage of these main-sequence pulsating stars, which is an indication of stellar activity being common on the surfaces of these hot stars. In some cases, activity dominates the luminosity variations. Significant amplitude variability is also detected in at least some of the pulsation modes of highest amplitude in almost all the δ Sct stars. One of the δ Sct pulsators is a member of a binary system with the pulsating component tidally distorted. This system also shows strong stellar activity, including several flares that probably originate in the δ Sct component.

Gravity-mode period spacings and near-core rotation rates of 611 γ Doradus stars with Kepler

Abstract We report our survey of γ Dor stars from the 4-yr Kepler mission. These stars pulsate mainly in g modes and r modes, showing period-spacing patterns in the amplitude spectra. The period-spacing patterns are sensitive to the chemical composition gradients and the near-core rotation, hence they are essential for understanding the stellar interior. We identified period-spacing patterns in 611 γ Dor stars. Almost every star pulsates in dipole g modes, while about 30% of stars also show clear patterns for quadrupole g modes and 16% of stars present r mode patterns. We measure periods, period spacings, and the gradient of the period spacings. These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the Traditional Approximation of Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes. Most stars have a near-core rotation rate around 1 d−1and an asymptotic spacing around 4000 s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. 11 stars show rotational splittings with fast rotation rates. We compared the observed slope–rotation relation with the theory and find a large spread. We detected rotational modulations in 58 stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5%.

The first view of δ Scuti and γ Doradus stars with the TESS mission

ABSTRACT We present the first asteroseismic results for δ Scuti and γ Doradus stars observed in Sectors 1 and 2 of the TESS mission. We utilize the 2-min cadence TESS data for a sample of 117 stars to classify their behaviour regarding variability and place them in the Hertzsprung–Russell diagram using Gaia DR2 data. Included within our sample are the eponymous members of two pulsator classes, γ Doradus and SX Phoenicis. Our sample of pulsating intermediate-mass stars observed by TESS also allows us to confront theoretical models of pulsation driving in the classical instability strip for the first time and show that mixing processes in the outer envelope play an important role. We derive an empirical estimate of 74 per cent for the relative amplitude suppression factor as a result of the redder TESS passband compared to the Kepler mission using a pulsating eclipsing binary system. Furthermore, our sample contains many high-frequency pulsators, allowing us to probe the frequency variability of hot young δ Scuti stars, which were lacking in the Kepler mission data set, and identify promising targets for future asteroseismic modelling. The TESS data also allow us to refine the stellar parameters of SX Phoenicis, which is believed to be a blue straggler.

γ Doradus stars as a test of angular momentum transport models

Helioseismology and asteroseismology of red giant stars have shown that distribution of angular momentum in stellar interiors, and the evolution of this distribution with time remains an open issue in stellar physics. Owing to the unprecedented quality and long baseline of Kepler photometry, we are able to seismically infer internal rotation rates in γ Doradus stars, which provide the main-sequence counterpart to the red-giants puzzle. Here, we confront these internal rotation rates to stellar evolution models which account for rotationally induced transport of angular momentum, in order to test angular momentum transport mechanisms. On the one hand, we used a stellar model-independent method developed by our team in order to obtain accurate, seismically inferred, buoyancy radii and near-core rotation for 37 γ Doradus stars observed by Kepler. We show that the stellar buoyancy radius can be used as a reliable evolution indicator for field stars on the main sequence. On the other hand, we computed rotating evolutionary models of intermediate-mass stars including internal transport of angular momentum in radiative zones, following the formalism developed in the series of papers started by Zahn (1992, A&A, 265, 115), with the CESTAM code. This code calculates the rotational history of stars from the birth line to the tip of the RGB. The initial angular momentum content has to be set initially, which is done here by fitting rotation periods in young stellar clusters. We show a clear disagreement between the near-core rotation rates measured in the sample and the rotation rates obtained from the evolutionary models including rotationally induced transport of angular momentum following Zahn’s prescriptions. These results show a disagreement similar to that of the Sun and red giant stars in the considered mass range. This suggests the existence of missing mechanisms responsible for the braking of the core before and along the main sequence. The efficiency of the missing mechanisms is investigated. The transport of angular momentum as formalized by Zahn and Maeder cannot explain the measurements of near-core rotation in main-sequence intermediate-mass stars we have at hand.

Period spacings of γ Doradus pulsators in the Kepler field: Rossby and gravity modes in 82 stars

Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $\gamma$\,Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is seen. For each pattern, the mean pulsation period, the mean period spacing, and the slope are measured. We find that the slope correlates with the mean period for Rossby mode patterns. The traditional approximation of rotation is used to measure the near-core rotation rate, assuming the star rotates rigidly. We report the near-core rotation rates, the asymptotic period spacings, and the radial orders of excited modes of these 82 main-sequence stars. The near-core rotation rates lie between $0.6\,\mathrm{d^{-1}}$ and $2.3\,\mathrm{d^{-1}}$. Six stars show surface rotation modulations, among which only KIC\,3341457 shows differential rotation while the other five stars have uniform rotations. The radial orders of excited modes show different distributions for the dipole and quadrupole gravity modes versus the Rossby modes.

Asteroseismic masses, ages, and core properties of γ Doradus stars using gravito-inertial dipole modes and spectroscopy

The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring $\Pi_0$), in combination with the effective temperature ($T_{\rm eff}$) and surface gravity ($\log g$) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 $\gamma~$Doradus ($\gamma~$Dor) stars whose rotation frequency has been derived from $\textit{Kepler}$ photometry. We make use of two 6D grids of stellar models, one with step core overshooting and one with exponential core overshooting, to evaluate correlations between the three observables $\Pi_0$, $T_{\rm eff}$, and $\log g$ and the mass, age, core overshooting, metallicity, initial hydrogen mass fraction and envelope mixing. We provide multivariate linear model recipes relating the stellar parameters to be estimated to the three observables ($\Pi_0$, $T_{\rm eff}$, $\log g$). We estimate the (core) mass, age, core overshooting and metallicity of $\gamma~$Dor stars from an ensemble analysis and achieve relative uncertainties of $\sim\!10$ per cent for the parameters. The asteroseismic age determination allows us to conclude that efficient angular momentum transport occurs already early on during the main sequence. We find that the nine stars with observed Rossby modes occur across almost the entire main-sequence phase, except close to core-hydrogen exhaustion. Future improvements of our work will come from the inclusion of more types of detected modes per star, larger samples, and modelling of individual mode frequencies.

Pulsation in Intermediate-Mass Stars

A new perspective of pulsation in stars within the δ Scuti instability strip has recently emerged as a result of Kepler observations. The majority of stars within the instability strip do not pulsate and practically all δ Scuti stars contain low frequencies. Because γ Doradus stars co-exist with δ Sct stars in the same region of the instability strip, it follows that γ Dor stars are driven by the same mechanism as δ Sct stars. The difference must be due to different mode selection processes. The search for an unknown damping factor which is missing from the models will be essential for further progress. Maia variables and hot γ Dor stars are briefly discussed. Luminosities of roAp stars obtained from Gaia DR2 parallaxes and spectroscopic effective temperatures show that the roAp stars are slightly evolved with temperatures in the range 6300–8300 K, considerably cooler than predicted by the models. The roAp stars and stars with solar-like oscillations share the same mass - temperature - luminosity relation, but with frequencies which are about 50 percent higher. This suggests that roAp frequencies are determined by the critical acoustic frequency, but this frequency is larger than in standard models, perhaps as a result of a temperature inversion in the atmosphere.