Pulsation Modes Research Articles

Viscous and centrifugal instabilities of massive stars

ABSTRACT Massive stars exhibit a variety of instabilities, many of which are poorly understood. We explore instabilities induced by centrifugal forces and angular momentum transport in massive rotating stars. First, we derive and numerically solve linearized oscillation equations for adiabatic radial modes in polytropic stellar models. In the presence of differential rotation, we show that centrifugal and Coriolis forces combined with viscous angular momentum transport can excite stellar pulsation modes, under both low- or high-viscosity conditions. In the low-viscosity limit, which is common in real stars, we demonstrate how to compute mode growth/damping rates via a work integral. Finally, we build realistic rotating $30\, \mathrm{M}_\odot$ star models and show that overstable (growing) radial modes are predicted to exist for most of the star’s life, in the absence of non-adiabatic effects. Peak growth rates are predicted to occur while the star is crossing the Hertzsprung–Russell gap, though non-adiabatic damping may dominate over viscous driving, depending on the effective viscosity produced by convective and/or magnetic torques. Viscous instability could be a new mechanism to drive massive star pulsations and is possibly related to instabilities of luminous blue variable stars.

Dependence of Pulsation Mode of Cepheids on Metallicity

Abstract The Cepheid variables in the Small Magellanic Cloud (SMC), the Large Magellanic Cloud (LMC), the Milky Way, M33, and M31 are used to examine the dependence of pulsation mode on metallicity, which was previously found in red supergiants. The initial samples of Cepheids are collected from the Cepheid catalogs identified from the Optical Gravitational Lensing Experiment, PS1, DIRECT, Wide-field Infrared Survey Explorer, and Zwicky Transient Facility surveys. The contaminants are removed with the help of the Gaia/EDR3 astrometric information for extra galaxies or by comparing the geometric distance and the distance from the P–L relation for the Milky Way. The division of fundamental (FU) and first-overtone (1O) modes is refined according to the gap between the two modes in the P–L diagram of the objects in each galaxy. The ratio of FU/(FU+1O) is found to be 0.59, 0.60, 0.69, 0.83, and 0.85 for the SMC, the LMC, the Milky Way, M33, and M31, respectively, in order of metallicity, which confirms that the pulsation mode depends on metallicity in the way that the ratio of FU/(FU+1O) increases with metallicity. This dependence is not changed if the incompleteness of the samples is taken into account.

Pulsating hydrogen-deficient white dwarfs and pre-white dwarfs observed with TESS

Context. The collection of high-quality photometric data by space telescopes, such as the completed Kepler mission and the ongoing TESS program, is revolutionizing the area of white-dwarf asteroseismology. Among the different kinds of pulsating white dwarfs, there are those that have He-rich atmospheres, and they are called DBVs or V777 Her variable stars. The archetype of these pulsating white dwarfs, GD 358, is the focus of the present paper. Aims. We report a thorough asteroseismological analysis of the DBV star GD 358 (TIC 219074038) based on new high-precision photometric data gathered by the TESS space mission combined with data taken from the Earth. Methods. We reduced TESS observations of the DBV star GD 358 and performed a detailed asteroseismological analysis using fully evolutionary DB white-dwarf models computed accounting for the complete prior evolution of their progenitors. We assessed the mass of this star by comparing the measured mean period separation with the theoretical averaged period spacings of the models, and we used the observed individual periods to look for a seismological stellar model. We detected potential frequency multiplets for GD 358, which we used to identify the harmonic degree (ℓ) of the pulsation modes and rotation period. Results. In total, we detected 26 periodicities from the TESS light curve of this DBV star using standard pre-whitening. The oscillation frequencies are associated with nonradial g(gravity)-mode pulsations with periods from ∼422 s to ∼1087 s. Moreover, we detected eight combination frequencies between ∼543 s and ∼295 s. We combined these data with a huge amount of observations from the ground. We found a constant period spacing of 39.25 ± 0.17 s, which helped us to infer its mass (M⋆ = 0.588 ± 0.024 M⊙) and constrain the harmonic degree ℓ of the modes. We carried out a period-fit analysis on GD 358, and we were successful in finding an asteroseismological model with a stellar mass (M⋆ = 0.584−0.019+0.025 M⊙), compatible with the stellar mass derived from the period spacing, and in line with the spectroscopic mass (M⋆ = 0.560 ± 0.028 M⊙). In agreement with previous works, we found that the frequency splittings vary according to the radial order of the modes, suggesting differential rotation. Obtaining a seismological model made it possible to estimate the seismological distance (dseis = 42.85 ± 0.73 pc) of GD 358, which is in very good accordance with the precise astrometric distance measured by Gaia EDR3 (π = 23.244 ± 0.024, dGaia = 43.02 ± 0.04 pc). Conclusions. The high-quality data measured with the TESS space telescope, used in combination with data taken from ground-based observatories, provides invaluable information for conducting asteroseismological studies of DBV stars, analogously to what happens with other types of pulsating white-dwarf stars. The currently operating TESS mission, together with the advent of other similar space missions and new stellar surveys, will give an unprecedented boost to white dwarf asteroseismology.

Hydrogen and Helium Shock Phenomena during Rising Light in RR Lyrae Fundamental Mode Pulsators

Abstract We present measurements of H and He emission and absorption lines produced in RRab fundamental mode pulsators during primary light rise. The lines define universal progressions of rise and decay in metal-poor RRab stars. Such a progression cannot be constructed for He in metal-rich RRab (those with [Fe/H] > −0.8) because weak He i emission is detected in only two of the six metal-rich RRab in our survey. Great variety exists in the phase variations of the blue- and red-shifted absorption components of the 5876 Å line during pre- and post-emission phases. Detection of measurable He ii 4686 Å emission in eight RRab, three of them Blazhko variables, provides an additional constraint on ionization of helium.

The CubeSpec space mission

Context. There is currently a niche for providing high-cadence, high resolution, time-series optical spectroscopy from space, which can be filled by using a low-cost cubesat mission. The Belgian-led ESA/KU Leuven CubeSpec mission is specifically designed to provide space-based, low-cost spectroscopy with specific capabilities that can be optimised for a particular science need. Approved as an ESA in-orbit demonstrator, the CubeSpec satellite’s primary science objective will be to focus on obtaining high-cadence, high resolution optical spectroscopic data to facilitate asteroseismology of pulsating massive stars. Aims. In this first paper, we aim to search for pulsating massive stars suitable for the CubeSpec mission, specifically β Cep stars, which typically require time-series spectroscopy to identify the geometry of their pulsation modes. Methods. Based on the science requirements needed to enable asteroseismology of massive stars with the capabilities of CubeSpec’s spectrograph, we combined a literature study for pulsation with the analysis of recent high-cadence time-series photometry from the Transiting Exoplanet Survey Satellite (TESS) mission to classify the variability for stars brighter than V ≤ 4 mag and between O9 and B3 in spectral type. Results. Among the 90 stars that meet our magnitude and spectral type requirements, we identified 23 promising β Cep stars with high-amplitude (non-)radial pulsation modes with frequencies below 7 d−1. Using further constraints on projected rotational velocities, pulsation amplitudes, and the number of pulsation modes, we devised a prioritised target list for the CubeSpec mission according to its science requirements and the potential of the targets for asteroseismology. The full target catalogue further provides a modern TESS-based review of line profile and photometric variability properties among bright O9–B3 stars.

A Fresh Look at AGB Stars in Galactic Open Clusters with Gaia: Impact on Stellar Models and the Initial–Final Mass Relation

Abstract Benefiting from the Gaia second and early third releases of photometric and astrometric data, we examine the population of asymptotic giant branch (AGB) stars that appear in the fields of intermediate-age and young open star clusters. We identify 49 AGB star candidates, brighter than the tip of the red giant branch, with a good to high cluster membership probability. Among them, we find 19 TP-AGB stars with known spectral type: 4 M stars, 3 MS/S stars, and 12 C stars. By combining observations, stellar models, and radiative transfer calculations that include the effect of circumstellar dust, we characterize each star in terms of initial mass, luminosity, mass-loss rate, core mass, period, and mode of pulsation. The information collected helps us shed light on the TP-AGB evolution at solar-like metallicity, placing constraints on the third dredge-up process, the initial masses of carbon stars, stellar winds, and the initial–final mass relation (IFMR). In particular, we find that two bright carbon stars, MSB 75 and BM IV 90, members of the clusters NGC 7789 and NGC 2660 (with similar ages of ≃ 1.2–1.6 Gyr and initial masses 2.1 ≳ M i /M ⊙ ≳ 1.9), have unusually high core masses, M c ≈ 0.67–0.7 M ⊙. These results support the findings of a recent work (Marigo et al. 2020) that identified a kink in the IFMR, which interrupts its monotonic trend just at the same initial masses. Finally, we investigate two competing scenarios to explain the M c data: the role of stellar winds in single-star evolution, and binary interactions through the blue straggler channel.

Heat Transfer in Pulsating Laminar Flow in a Pipe: Evaluation of the Reduction in the Heat Exchange Area of Oil Cooler

In this study, the heat transfer in a pipe was investigated by a numerical method with the pulsating flow of oil at Reynolds numbers 280, 350, 420. The diameter D of the pipe was 0.014 m. The pipe length was 100D. The flow pulsations were not harmonical. A numerical experiment was carried out using AnsysFluent. Based on the data obtained from the numerical experiment, an estimate of the reduction in the heat exchange area of the oil cooler was calculated. The reduction in the heat exchange area of the oil cooler ranged from 2.57% to 8.63%, depending on the pulsation mode.

Gas-liquid hydrodynamics and vortex motion of flame spread over jet fuel in longitudinal air stream

The gas-liquid hydrodynamic characteristics and pulsation behaviors of flame spread over jet fuel are investigated in various longitudinal air streams. The experiments are conducted in concurrent and opposed air streams by igniting fuels at opposite extremes of the tray. Six magnitudes of air stream speeds are used for the tests, namely 0.45, 0.88, 1.3, 1.73, 2.15 and 2.57 m/s. The liquid convection flow is monitored using a rainbow schlieren deflectometry which confirms that the liquid flows in vertical and horizontal direction act together to form a clockwise vortex. Based on non-dimensional parameter group, the effect of longitudinal air stream on liquid hydrodynamics is revealed. The movement of liquid convective flow is primarily driven by thermocapillary force, while the effect of buoyancy is relatively small, regardless of direction and magnitude of air stream speeds. Combined with the boundary layer theory, the flow velocities driven by expansion of hot gas product and opposed thermal buoyancy and local air stream are quantified. The threshold value of air flow speed for establishing gas-phase recirculation cell is determined, and the transformation mechanism of flame pulsation mode is analyzed.

Geomagnetic Pulsations, Blackout and Low-Latitude Aurorae Associated with Power Magnetic Storm

The research analyzed the regularities of the dynamics of geomagnetic pulsation regimes in the frequency range 0.002–5 Hz, the generation of which reflects the interaction with the Earth's magnetosphere of the solar filament ejected by a powerful solar flare of 3B. We compared the dynamics of the change in the types and modes of geomagnetic pulsations with the dynamics of the atmosphere glow in two spectral lines and the total ionospheric absorption of radio waves. The study developed a possible model of the observed phenomenon.

First Results on RR Lyrae Stars with the TESS Space Telescope: Untangling the Connections between Mode Content, Colors, and Distances

Abstract The Transiting Exoplanet Survey Satellite (TESS) space telescope is collecting continuous, high-precision optical photometry of stars throughout the sky, including thousands of RR Lyrae stars. In this paper, we present results for an initial sample of 118 nearby RR Lyrae stars observed in TESS Sectors 1 and 2. We use differential image photometry to generate light curves and analyze their mode content and modulation properties. We combine accurate light-curve parameters from TESS with parallax and color information from the Gaia mission to create a comprehensive classification scheme. We build a clean sample, preserving RR Lyrae stars with unusual light-curve shapes, while separating other types of pulsating stars. We find that a large fraction of RR Lyrae stars exhibit various low-amplitude modes, but the distribution of those modes is markedly different from those of the bulge stars. This suggests that differences in physical parameters have an observable effect on the excitation of extra modes, potentially offering a way to uncover the origins of these signals. However, mode identification is hindered by uncertainties when identifying the true pulsation frequencies of the extra modes. We compare mode amplitude ratios in classical double-mode stars to stars with extra modes at low amplitudes and find that they separate into two distinct groups. Finally, we find a high percentage of modulated stars among the fundamental mode pulsators, but also find that at least 28% of them do not exhibit modulation, confirming that a significant fraction of stars lack the Blazhko effect.

Towards a systematic treatment of observational uncertainties in forward asteroseismic modelling of gravity-mode pulsators

Context.In asteroseismology, the pulsation mode frequencies of a star are the fundamental data that are compared to theoretical predictions to determine a star’s interior physics. Recent significant advances in the numerical, theoretical, and statistical asteroseismic methods applied to main-sequence stars with convective cores have renewed interest in investigating the propagation of observational uncertainties within a forward asteroseismic modelling framework.Aims.We aim to quantify the impact of various choices made throughout the observational aspects of extracting pulsation mode frequencies in main-sequence stars with gravity modes.Methods.We use a well-studied benchmark slowly pulsating B star, KIC 7760680, to investigate the sensitivity of forward asteroseismic modelling to various sources of observational uncertainty that affect the precision of the input pulsation mode frequencies.Results.We quantify the impact of the propagation of the observational uncertainties involved in forward asteroseismic modelling. We find that one of the largest sources of uncertainty in our benchmark star is in the manual building of period spacing patterns, such that the inclusion of a potentially ambiguous pulsation mode frequency may yield differences in model parameters of up to 10% for mass and age depending on the radial order of the mode.Conclusions.We conclude that future asteroseismic studies of main-sequence stars with a convective core should quantify and include observational uncertainties introduced by the light curve extraction, iterative pre-whitening, and the building of period spacing patterns, as these propagate into the final modelling results.

Semi-regular red giants as distance indicators

Context. Semi-regular variables (SRVs) are similar to Miras in brightness, and they also follow one or more period–luminosity relations (PLRs), though not necessarily the same one as Miras. As potential standard candles they are more challenging than Miras because of their smaller variability amplitudes and less regular light curves, but they are substantially more numerous and especially promising for probing old stellar populations. Aims. We aim to characterise the variability of SRVs, specifically focusing on their connection with Miras, in order to prepare the ground for investigating their potential as distance indicators. Methods. We examine SRVs and Miras in the Magellanic Clouds from OGLE-III observations, with data from Gaia and 2MASS. After cleaning the sample of variability periods unrelated to pulsation, we classify each source by chemical type and combination of pulsation modes. We examine the results in terms of global photometric and pulsation properties. Results. We identify four SRV groups that fit the general evolutionary scenario predicted by theory. SRVs dominated by fundamental-mode pulsation are very similar to Miras, especially if mono-periodic. They further split into two subgroups, one of which follows the same sequence as Miras in the period–luminosity and period–amplitude diagrams, without discontinuity. Conclusions. The similarities between Miras and SRVs suggest that the latter can be adopted as distance indicators in a way that is complementary to the use of the former, thereby at least doubling the available number of long-period variables (LPVs) suitable for use as distance indicators. The traditional amplitude-based separation between Miras and SRVs is not necessarily appropriate, and a more physically sound criterion should also involve pulsation periods. While this would require comparatively longer time-series, they are expected to become accessible in the coming years even for weak sources thanks to current and future large-scale surveys. The table of reclassified LPVs is made public.

Rossby numbers and stiffness values inferred from gravity-mode asteroseismology of rotating F- and B-type dwarfs

Context.Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations.Aims.We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes.Methods.We relied on near-core rotation rates and asteroseismic models of 26 B- and 37 F-type dwarf pulsators derived from 4-yearKeplerspace photometry, high-resolution spectroscopy, andGaiaastrometry in the literature to deduce their convective and wave Rossby numbers. We computed the stiffness at the interface of the convective core and the radiative envelope from the inferred maximum buoyancy frequency at the interface and the convective turnover frequency in the core. We use those asteroseismically inferred quantities to make predictions of convective penetration levels, local flux levels of gravito-inertial waves triggered by the convective core, and of the cores’ potential rotational and magnetic states.Results.Our sample of 63 gravito-inertial mode pulsators covers near-core rotation rates from almost zero up to the critical rate. The frequencies of their identified modes lead to models with stiffness values between 102.69and 103.60for the B-type pulsators, while those of F-type stars cover the range from 103.47to 104.52. The convective Rossby numbers derived from the maximum convective diffusion coefficient in the convective core, based on mixing length theory and a value of the mixing length coefficient relevant for these pulsators, vary between 10−2.3and 10−0.8for B-type stars and 10−3and 10−1.5for F-type stars. The 17 B-type dwarfs with an asteroseismic estimate of the penetration depth reveal it to be in good agreement with recent theory of convective penetration that takes rotation into account. Theoretical estimates based on the observationally inferred convective Rossby numbers and stiffness values lead to local stochastically-excited gravito-inertial wave fluxes which may exceed those predicted for non-rotating cores, in agreement with observations. Finally, the convective core of rapid rotators is expected to have cylindrical differential rotation causing a magnetic field of 20–400 kG for B-type stars and of 0.1–3 MG for F-type stars.Conclusions.Our results provide asteroseismic calibrations to guide realistic (magneto-)hydrodynamical simultations of rotating (magnetised) core convection in stellar interiors of dwarfs and future modelling of transport and mixing processes in their interiors.

Multimode Pulsations In The Axisymmetric Cavern At Supersonic Flow

Experimental study results of flow structure and pressure pulsation spectral characteristics of axisymmetric cavern at supersonic flow with Mach number 2 is presented. Multimode pulsation existence is observed. Different modes dominate in different time moments. Maximum of one mode amplitude correspond to minimum value of another. Mode tuning nature is incidental. Time of one mode existence is much more than one of mode oscillation period. It is determine that pulsation mode exist in the form of toroidal and helical disturbances. Numerical calculation results qualitative reproduce multimode fluctuation and corresponded to experimental data

Pulsating subdwarf B stars in the oldest open cluster NGC 6791

ABSTRACT We report results of our analysis of the Kepler superaperture LC data of the open cluster NGC 6791 to search for pulsating sdB stars. We checked all pixels and we found only three sdB stars to be pulsating, KIC 2569576 (B3), KIC 2438324 (B4), and KIC 2437937 (B5). These stars were known to be pulsators before, though we extended data coverage detecting more frequencies and features in their amplitude spectra, i.e. new multiplets and more complete period spacing sequences that we used for identifying geometry of the pulsation modes. The multiplet splittings were also used to derive rotation periods. The remaining known sdBs do not show any pulsation-related light variation down to our detection thresholds. We analysed already existing spectroscopic observations taken with the HECTOSPEC at the MMT telescope in Smithsonian Arizona and with the Gemini Multi-Object Spectrograph at the Gemini North telescope, and fitted atmospheric parameters using the Balmer lines. Four stars, B3 – B6, show atmospheric parameters that are consistent with g-mode dominated sdBs. We detected hints of radial velocity variability in B3, B5, and B6, indicating these three stars may be in binaries.

Non-Radial Pulsations of Distorted Stellar Structures: Effect of Mass Variation

Eigen-frequencies (EF) of non–radial modes (NRM) of pulsations of differentially rotating (D R) and tidally distorted (T D) stellar models by considering the effect of mass variation (MV) on its equi-potentials surfaces inside a star. The method utilizes an averaging proposal of Kippenhahn and Thomas (K and T) with conjunction of the concept of Roche-equipotential. The study accolades and corrects earlier studies of non-radial (NR) pulsations of DR and TD stellar structures of different natures such as radial and non-radial oscillations, X-ray, gamma ray and other electromagnetic disturbances. The reflection of the work comes from the requirements of the inclusion of non-uniform densities that yield Lane-Emden equation to have reliable results up to second order disturbances.

Non-radial modes in classical Cepheids: what to look for in spectroscopy?

ABSTRACT Recent photometric observations of first-overtone classical Cepheids and RR Lyrae stars have led to the discovery of additional frequencies showing a characteristic period ratio of 0.60–0.65 with the main pulsation mode. In a promising model proposed by Dziembowski (2016), these signals are suggested to be due to the excitation of non-radial modes with degrees 7, 8, and 9 (Cepheids) or 8 and 9 (RR Lyrae). Such modes usually have low amplitudes in photometric data. Spectroscopic time series offer an unexplored and promising way forward. We simulated time series of synthetic line profiles for a representative first-overtone classical Cepheid model and added a low-amplitude non-radial mode. We studied sets of spectra with dense sampling and without noise, so-called ’perfect’ cases, as well as more realistic samplings and signal-to-noise levels. Besides the first-overtone mode and the non-radial mode, also the harmonics of both modes and combination signals were often detected, but a sufficiently high sampling and signal-to-noise ratio prove essential. The amplitudes of the non-radial mode and its harmonic depend on the azimuthal order m. The inclination is also an important factor determining the detectability of the non-radial mode and/or its harmonic. We compared the results obtained for the predicted high degrees with those for lower-degree modes. Finally, we studied the sampling requirements for detecting the non-radial mode. Our findings can be used to plan a spectroscopic observing campaign tailored to uncover the nature of these mysterious modes.

Outbursts and stellar properties of the classical Be star HD 6226

ABSTRACT The bright and understudied classical Be star HD 6226 has exhibited multiple outbursts in the last several years during which the star grew a viscous decretion disc. We analyse 659 optical spectra of the system collected from 2017 to 2020, along with a ultraviolet spectrum from the Hubble Space Telescope and high cadence photometry from both Transiting Exoplanet Survey Satellite (TESS) and the Kilodegree Extremely Little Telescope (KELT) survey. We find that the star has a spectral type of B2.5IIIe, with a rotation rate of 74 per cent of critical. The star is nearly pole-on with an inclination of 13${_{.}^{\circ}}$4. We confirm the spectroscopic pulsational properties previously reported, and report on three photometric oscillations from KELT photometry. The outbursting behaviour is studied with equivalent width measurements of H α and H β, and the variations in both of these can be quantitatively explained with two frequencies through a Fourier analysis. One of the frequencies for the emission outbursts is equal to the difference between two photometric oscillations, linking these pulsation modes to the mass ejection mechanism for some outbursts. During the TESS observation time period of 2019 October 7 to 2019 November 2, the star was building a disc. With a large data set of H α and H β spectroscopy, we are able to determine the time-scales of dissipation in both of these lines, similar to past work on Be stars that has been done with optical photometry. HD 6226 is an ideal target with which to study the Be disc-evolution given its apparent periodic nature, allowing for targeted observations with other facilities in the future.

Geometry of radio pulsar signals: The origin of pulsation modes and nulling

Radio pulsars exhibit an enormous diversity of single pulse behaviour that involves sudden changes in pulsation mode and nulling occurring on timescales of tens or hundreds of spin periods. The pulsations appear both chaotic and quasi-regular, which has hampered their interpretation for decades. Here I show that the pseudo-chaotic complexity of single pulses is caused by the viewing of a relatively simple radio beam that has a sector structure traceable to the magnetospheric charge distribution. The slow E × B drift of the sector beam, when sampled by the line of sight, produces the classical drift-period-folded patterns known from observations. The drifting azimuthal zones of the beam produce the changes in pulsation modes and both the intermodal and sporadic nulling at timescales of beating between the drift and the star spin. The axially symmetric conal beams are thus a superficial geometric illusion, and the standard carousel model of pulsar radio beams does not apply. The beam suggests a particle flow structure that involves inward motions with possible inward emission.

The GAPS Programme at TNG

Context. Giant planets in short-period orbits around bright stars represent optimal candidates for atmospheric and dynamical studies of exoplanetary systems. Aims. We aim to analyse four transits of WASP-33b observed with the optical high-resolution HARPS-N spectrograph to confirm its nodal precession, study its atmosphere, and investigate the presence of star-planet interactions. Methods. We extracted the mean line profiles of the spectra using the least-squares deconvolution method, and we analysed the Doppler shadow and the radial velocities. We also derived the transmission spectrum of the planet, correcting it for the stellar contamination due to rotation, centre-to-limb variations, and pulsations. Results. We confirm the previously discovered nodal precession of WASP-33b, almost doubling the time coverage of the inclination and projected spin-orbit angle variation. We find that the projected obliquity reached a minimum in 2011, and we used this constraint to derive the geometry of the system, and in particular its obliquity at that epoch (ϵ = 113.99° ± 0.22°) and the inclination of the stellar spin axis (is = 90.11° ± 0.12°). We also derived the gravitational quadrupole moment of the star J2 = (6.73 ± 0.22) × 10−5, which we find to be in close agreement with the theoretically predicted value. Small systematics errors are computed by shifting the date of the minimum projected obliquity. We present detections of Hα and Hβ absorption in the atmosphere of the planet, with a contrast almost twice as small as that previously detected in the literature. We also find evidence for the presence of a pre-transit signal, which repeats in all four analysed transits and should thus be related to the planet. The most likely explanation lies in a possible excitation of a stellar pulsation mode by the presence of the planetary companion. Conclusions. A future common analysis of all available datasets in the literature will help shed light on the possibility that the observed Balmer lines’ transit depth variations are related to stellar activity and pulsation, and to set constraints on the planetary temperature–pressure structure and thus on the energetics possibly driving atmospheric escape. A complete orbital phase coverage of WASP-33b with high-resolution spectroscopic (and spectro-polarimetric) observations could help us to understand the nature of the pre-transit signal.