Asteroseismology of magnetic massive stars

About ten percent of stars with spectral type O, B, or A have a detectable, stable and strong large-scale magnetic field at their surface, which most often resembles a magnetic dipole. These large-scale magnetic fields extend into the radiative layers of the OBA stars and theory and simulations predict that they alter the internal structure and physical properties of these stars.  In particular, it is expected that these large-scale magnetic fields enforce uniform rotation in the radiative layers and may suppress convective core overshooting.  This has consequences for the evolution of these magnetic hot stars and it has implications for galactic evolution.  Indeed, the most massive stars are important chemical furnaces, producing much of the heavy elements in the Universe.  Therefore, we observed and investigated the internal structure of magnetic hot stars.  To do so, asteroseismology, i.e., the study of stellar pulsations, is the best method as the oscillation properties are directly related to the internal physical conditions.  Various types of stellar oscillations are known and they are classified based on their dominant restoring force.  Of these, gravity modes are governed by the buoyancy force and have their strongest probing power in the near core region, which is the domain of our interest.

Our first objective was to identify pulsating magnetic hot stars and characterize their magnetic and seismic properties.  To do so, we constructed a sample of 16 magnetic candidate stars by following indirect observational diagnostics for the presence of a large-scale magnetic field.   Ground-based high-resolution optical spectropolarimetry, taken with the ESPaDOnS instrument, enabled the confirmation of the presence of a large-scale magnetic field for 12 of the magnetic candidate stars.  The stars without a detected magnetic field still showed indications of the presence of a weak large-scale magnetic field through chemical peculiarities.  For two known magnetic stars, namely HD 43317 and o Lup, the geometry and strength of the large-scale magnetic field were characterized in detail by studying the variability in the measured longitudinal magnetic field at various rotation phases, and by analysing time series of spectropolarimetric observations obtained with the ESPaDOnS, Narval, and HARPSpol instruments.  For each star in our sample, we obtained high-cadence and high-precision space-based photometry from either the BRITE, CoRoT, or K2 mission with at least a 60 d timebase to investigate (periodic) variability.  Only for a few magnetic stars did we detect coherent periodic variability, uncorrelated to the rotation, that indicated the presence of stellar pulsations.  The stars HD 158596, HD 177765, and o Lup were indicative for one or a few stellar pulsation modes, while HD 43317 revealed tens of stellar pulsations mode frequencies that pointed towards gravity modes.  In HD 43317, many of the pulsation mode frequencies were lower or similar to the rotation frequency.  Hence, the Coriolis force acts as an additional restoring force for these modes, implying that they are gravito-inertial modes.

Following these results, we investigated the B3.5V star HD 43317 in detail to meet our objective of observationally determining the internal structure of a magnetic hot star.  We did this by means of forward seismic modelling, where the observed stellar pulsation mode frequencies in the CoRoT data covering ~150 d were fit to those of gravito-intertial modes computed with the pulsation code GYRE, coupled to MESA stellar structure models.  We identified the pulsation mode frequencies as overlapping (l,m) = (1,-1) and (2,-1) mode series.  The small convective core overshooting region derived from the seismic modelling was in line with the theoretical predictions.  Yet, some of the parameters for the best fitted models were also compatible with literature values for non-magnetic pulsators within the derived uncertainties.  This was due to degeneracies between stellar structure models with similar values for the asymptotic period spacing of the gravito-inertial modes, leading to skew and large confidence intervals for various model parameters.  We conclude that the CoRoT time series of ~150 d is too short to lead to stringent constraints and tests of the stellar interior to discriminate between magnetic and non-magnetic pulsating hot stars.

From our detailed modelling efforts of the best studied pulsating magnetic hot star HD 43317, we were unable to observationally corroborate the theoretical predictions of an altered internal structure for magnetic hot stars.  Simplifications and approximations were made during the forward seismic modelling due to the limited frequency resolution of the CoRoT data in terms of its time base. Further efforts to include magnetism in the pulsation codes, or magnetism, rotation, and angular momentum transport in the evolutionary models, are worthwhile to test whether magnetic signatures are present in the numerous (non-magnetic) gravito-inertial pulsators recently found in the nominal Kepler database (which has a ten times better frequency resolution compared to CoRoT).