Oscillations of 2D ESTER models

Context. Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotating δ Scuti stars that seem to match theoretical expectations. Aims. In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings. Methods. In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra. Results. Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1 dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

A theoretical framework for BL Her stars – I. Effect of metallicity and convection parameters on period–luminosity and period–radius relations

ABSTRACT We present a new grid of convective BL Herculis models using the state-of-the-art 1D non-linear radial stellar pulsation tool mesa-rsp. We investigate the impact of metallicity and four sets of different convection parameters on multiwavelength properties. Non-linear models were computed for periods typical for BL Her stars, i.e. 1 ≤ P(d) ≤ 4 covering a wide range of input parameters – metallicity (−2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5–0.8 M⊙), luminosity (50–300 L⊙), and effective temperature (full extent of the instability strip; in steps of 50 K). The total number of BL Her models with full-amplitude stable pulsations used in this study is 10 280 across the four sets of convection parameters. We obtain their multiband (UBVRIJHKLL′M) light curves and derive new theoretical period–luminosity (PL), period–Wesenheit (PW), and period–radius (PR) relations at mean light. We find that the models computed with radiative cooling show statistically similar slopes for PL, PW, and PR relations. Most empirical relations match well with the theoretical PL, PW, and PR relations from the BL Her models computed using the four sets of convection parameters. However, PL slopes of the models with radiative cooling provide a better match to empirical relations for BL Her stars in the Large Magellanic Cloud in the HKS bands. For each set of convection parameters, the effect of metallicity is significant in U and B bands and negligible in infrared bands, which is consistent with empirical results. No significant metallicity effects are seen in the PR relations.

Light and colour variations of Mira variables in the Small Magellanic Cloud

ABSTRACT The goal of this paper is to characterize the light variation properties of Mira variables in the Small Magellanic Cloud. We have investigated a combined optical and near-infrared multi-epoch data set of Mira variables based on our monitoring data obtained over 15 yr. Bolometric correction relations are formulated for various near-infrared colours. We find that the same bolometric correction equation holds for both the bolometricly brightest and faintest pulsation phases. Period–bolometric magnitude relations and period–colour relations were derived using time-averaged values. Phase lags between bolometric phase and optical and near-infrared phases were detected from the O-rich (the surface C/O number ratio is below unity) Mira variables, while no significant systematic lags were observed in most of the C-rich (the C/O ratio is over unity) ones. Some Miras show colour phase inversions, e.g. H–Ks at its bluest while J–H and J–Ks are at their reddest values at about the bolometricly brightest phase. Their occurrence conditions were studied but no clear direct or indirect trigger was found. A large NIR colour change unassociated with stellar pulsation was observed in Miras with long secondary periods, and its possible explanation is described.

Mass-loss rate and local thermodynamic state of the KELT-9 b thermosphere from the hydrogen Balmer series

KELT-9 b, the hottest known exoplanet, with Teq ~ 4400 K, is the archetype of a new planet class known as ultra-hot Jupiters. These exoplanets are presumed to have an atmosphere dominated by neutral and ionized atomic species. In particular, Hα and Hβ Balmer lines have been detected in the KELT-9 b upper atmosphere, suggesting that hydrogen is filling the planetary Roche lobe and escaping from the planet. In this work, we detected δ Scuti-type stellar pulsation (with a period Ppuls = 7.54 ± 0.12 h) and studied the Rossiter-McLaughlin effect (finding a spin-orbit angle λ = −85.01° ± 0.23°) prior to focussing on the Balmer lines (Hα to Hζ) in the optical transmission spectrum of KELT-9 b. Our HARPS-N data show significant absorption for Hα to Hδ. The precise line shapes of the Hα, Hβ, and Hγ absorptions allow us to put constraints on the thermospheric temperature. Moreover, the mass loss rate, and the excited hydrogen population of KELT-9 b are also constrained, thanks to a retrieval analysis performed with a new atmospheric model. We retrieved a thermospheric temperature of T = 13 200−720+800 K and a mass loss rate of Ṁ = 1012.8±0.3 g s−1 when the atmosphere was assumed to be in hydrodynamical expansion and in local thermodynamic equilibrium (LTE). Since the thermospheres of hot Jupiters are not expected to be in LTE, we explored atmospheric structures with non-Boltzmann equilibrium for the population of the excited hydrogen. We do not find strong statistical evidence in favor of a departure from LTE. However, our non-LTE scenario suggests that a departure from the Boltzmann equilibrium may not be sufficient to explain the retrieved low number densities of the excited hydrogen. In non-LTE, Saha equilibrium departure via photo-ionization, is also likely to be necessary to explain the data.

Overall variation of the H2O masers around W Hydrae in 28 years

In this paper, we present the distribution of H$_2$O masers associated with the semi-regular variable star W Hydrae (W Hya). We have collected the radio interferometric data of the maser distribution taken with the Very Large Array (VLA), the Kashima–Nobeyama InterFErometer (KNIFE), the Multi-Element Radio Link Network (MERLIN), the VLBI Exploration of Radio Astrometry (VERA), and the combined array of the Korean VLBI Network (KVN) and VERA (KaVA) in order to trace the maser distribution variation in two decades. Even though differences in the sensitivities and angular resolutions of the interferometric observations should be taken into account, we attempt to find possible correlation of the maser distribution with the stellar light curve. Our failure in the measurement of the annual parallax of the masers with VERA is likely caused by the properties of the maser features, which have been spatially resolved by the synthesized beam and survived for only half a year or less. No dependence of the maser spot flux density on its size is found in the KNIFE data, suggesting that maser spot size is determined by the physical boundary, as is expected for a clump affected by outward propagation of a stellar pulsation shock wave, rather than the (spherical) geometry of maser beaming in the maser gas clump.

High-resolution observations of gas and dust around Mira using ALMA and SPHERE/ZIMPOL

Context. The outflows of oxygen-rich asymptotic giant branch (AGB) stars are thought to be driven by radiation pressure due to the scattering of photons on relatively large grains, with sizes of tenths of microns. The details of the formation of dust in the extended atmospheres of these stars and, therefore, the mass-loss process, is still not well understood. Aims. We aim to constrain the distribution of the gas and the composition and properties of the dust grains that form in the inner circumstellar environment of the archetypal Mira variable o Cet. Methods. We obtained quasi-simultaneous observations using ALMA and SPHERE/ZIMPOL on the Very Large Telescope (VLT) to probe the distribution of gas and large dust grains, respectively. Results. The polarized light images show dust grains around Mira A, but also around the companion, Mira B, and a dust trail that connects the two sources. The ALMA observations show that dust around Mira A is contained in a high-gas-density region with a significant fraction of the grains that produce the polarized light located at the edge of this region. Hydrodynamical and wind-driving models show that dust grains form efficiently behind shock fronts caused by stellar pulsation or convective motions. The distance at which we observe the density decline (a few tens of au) is, however, significantly larger than expected for stellar-pulsation-induced shocks. Other possibilities for creating the high-gas-density region are a recent change in the mass-loss rate of Mira A or interactions with Mira B. We are not able to determine which of these scenarios is correct. We constrained the gas density, temperature, and velocity within a few stellar radii from the star by modelling the CO v = 1, J = 3−2 line. We find a mass (~3.8 ± 1.3) × 10−4 M⊙ to be contained between the stellar millimetre photosphere, R⋆338 GHz, and 4 R⋆338 GHz. Our best-fit models with lower masses also reproduce the 13CO v = 0, J = 3−2 line emission from this region well. We find TiO2 and AlO abundances corresponding to 4.5% and <0.1% of the total titanium and aluminium expected for a gas with solar composition. The low abundance of AlO allows for a scenario in which Al depletion into dust happens already very close to the star, as expected from thermal dust emission observations and theoretical calculations of Mira variables. The relatively large abundance of aluminium for a gas with solar composition allows us to constrain the presence of aluminium oxide grains based on the scattered light observations and on the gas densities we obtain. These models imply that aluminium oxide grains could account for a significant fraction of the total aluminium atoms in this region only if the grains have sizes ≲0.02 μm. This is an order of magnitude smaller than the maximum sizes predicted by dust-formation and wind-driving models. Conclusions. The study we present highlights the importance of coordinated observations using different instruments to advance our understanding of dust nucleation, dust growth, and wind driving in AGB stars.