Luis A. Balona

Space photometry from the Kepler and TESS missions has resulted in the discovery of a large number of A and B stars with light variations consistent with rotation and starspots. At least 20% of early-type stars appear to be rotational variables. In addition, superflares in A-type stars have been detected. These are shown to originate in the A star itself and not on a cool companion. The implied presence of localized magnetic fields poses a challenge to the origin of surface magnetism. Either A and B stars have surface convective zones or there are other ways of generating surface magnetism other than by the dynamo mechanism. It is suggested that the Be phenomenon is an extreme case of such activity.

TESS observations of pulsating hot main sequence stars paint a very different picture from what is currently accepted. There are large numbers of delta Scuti (DSCT) stars hotter than the theoretical hot edge of the instability strip, continuing to what appear to be DSCT stars of mid-B type (historically known as Maia variables). The frequencies of maximum amplitude in DSCT stars are in poor agreement with unstable frequencies from the models. There is a well-defined upper envelope in the frequencies of maximum amplitude as a function of effective temperature for DSCT and MAIA stars which requires an explanation. The gamma Doradus (GDOR) stars should be regarded as DSCT stars with suppressed high frequencies rather than a separate class. They are found mostly among the cool DSCT stars, but occur throughout the DSCT instability strip and as early A-type stars, where they merge with the SPB variables. The mixture of DSCT and GDOR stars throughout the instability strip is one example of the unexplained large variation of frequency patterns in DSCT stars. The location of beta Cephei stars in the H-R diagram agrees quite well with the models, but the observed frequencies are generally higher than predicted. There are no discernible boundaries between the traditional classes of pulsating stars. Existing pulsation models do not describe the observations at all well and a re-evaluation is required.

Inspection of the periodograms of TESS delta Scuti stars indicates that there is little, if any, similarity between the frequencies of stars in the same region of the H-R diagram. This is difficult to understand because pulsation models predict that stars with similar physical parameters should have similar frequencies. To investigate the problem, a quantitative measure of similarity between frequency patterns is described. When applied to non-adiabatic pulsation models with similar temperatures and luminosities, a strong correlation is found between the frequency patterns, as expected. The correlation increases when rotational frequency splitting is included. When applied to observations, no correlation can be found, confirming the impression from visual inspection. It seems that each star has its own unique frequency pattern, unrelated to its position in the H-R diagram. This presents a problem in our understanding of stellar pulsation. The existence of a period-luminosity law and the effect of combination frequencies in delta Scuti stars is briefly discussed.

High-precision photometry from TESS has revealed over 500 stars, located between the δ Scuti and β Cephei instability strips, which pulsate with high frequencies. Models do not predict high pulsation frequencies in these stars. These anomalous variables may be identified with the historical “Maia” variables. From the projected rotational velocities, it is shown that the rotation rates of Maia variables are no different from main sequence or SPB stars in the same effective temperature range. Some Maia stars pulsate at frequencies typical of roAp stars. It is shown that Maia stars should be considered an extension of δ Scuti variables to effective temperatures as high as 18,000 K, rather than as a separate class. The TESS data show a continuous sequence of low-frequency pulsating stars linking the γ Doradus and SPB variables, which is not predicted by the models. There are, in fact, no well-defined instability strips at all among upper main sequence stars, which means that arbitrary choices of effective temperature and frequency ranges need to be made in order to assign a particular variability class. It seems that a mixture of driving mechanisms is present in which convection may play a very important role.

Visual classification of the variability classes of over 120,000 Kepler, K2 and TESS stars is presented. The sample is mainly based on stars with known spectral types. Since variability classification often requires the location of the star in the H--R diagram, a catalogue of effective temperatures was compiled. Luminosities were estimated from Gaia DR3 parallaxes. The different classes of variable found in this survey are discussed. Examples of light curves and periodograms for common variability classes are shown. A catalogue of projected rotational velocities is also included.

From TESS photometry, 493 mid- to late-B stars with high frequencies (Maia variables) have been identified. The distribution of projected rotational velocities shows that the rotation rates of Maia variables are no different from those of SPB stars. Moreover, many Maia stars pulsate with frequencies exceeding 60 c/d. Rapid rotation is ruled out as a possible factor in understanding the Maia variables. There is clearly a serious problem with current pulsational models. Not only are the models unable to account for the Maia stars, but they also fail to account for the fact that SPB and gamma Dor variables form one continuous instability strip from the cool end of the delta Sct region to the hot end of the beta Cep instability strip. Likewise, there is continuity between the distributions of delta Sct, Maia, and beta Cep variables. In fact, Maia stars seem to be an extension of delta Sct stars to the mid-B type. These observations suggest an interplay between multiple driving mechanisms rather than separate dominant mechanisms for each variability group.

The periods of 34,376 main sequence stars hotter than 6000 K are derived from Kepler, K2 and TESS light curves. From the effective temperatures and GAIA DR3 luminosities, the radii, and hence the equatorial rotational velocities, can be estimated. Comparison with the projected rotational velocities shows that the photometric periods are indistinguishable from the rotational periods. Rotational light modulation in cool stars appears to continue to the hottest B stars. In fact, it is the most common type of light variation and is seen in 20–50 percent of F, A and B stars. The rotation rates of Am, Ap and Bp stars do not appear to be very different from those of non-peculiar stars. Mixing of the surface layers by rotation cannot be the sole reason why element diffusion is not present in stars with normal surface abundances. The rotation rate of Be stars is well below the rate required to trigger mass loss by nonradial pulsation. Surface activity leading to ejection of material into co-rotating clouds is suggested as the mass-loss mechanism. The rotational amplitudes of non-Be stars increases rapidly with effective temperature, possibly due to an increasing proportion of incipient Be stars in the sample. The simplest way to explain these results is to assume that surface convection is present in all main sequence stars, from the coolest M star to the hottest B star.

From sector 1–44 TESS observations, 19 new rapidly oscillating Ap (roAp) stars, 103 ostensibly non-peculiar stars with roAp-like frequencies, and 617 δ Scuti stars with independent frequencies typical of roAp stars were found. Examination of all chemically peculiar stars observed by TESS resulted in the discovery of 199 Ap stars that pulsate as δ Sct or γ Dor variables. The fraction of pulsating Ap stars is the same as the fraction of pulsating chemically normal stars. There is no distinct separation in frequency or radial order between chemically peculiar δ Sct stars and roAp stars. In fact, all the features that originally distinguished roAp from δ Sct stars in the past have disappeared. There is no reason to assume that the high frequencies in roAp stars are driven by a different mechanism from the high frequencies in chemically normal stars. However, chemically peculiar stars are far more likely to pulsate with high frequencies. The term ‘roAp’ should be dropped: all roAp stars are normal δ Scuti stars.

Evidence of rotational light modulation in 30%–40% of normal B stars is presented, suggesting the presence of starspots and photospheric activity. On this basis, we propose that mass loss in Be stars is a result of magnetic reconnection coupled with rapid but not necessarily near-critical rotation. The ejected matter is trapped at two diametrically opposed locations where the magnetic and geometric equators intersect. Nonradial pulsation plays no role in the mass loss and in the short-period light and line profile variations, though Be stars may pulsate as SPB or β Cep variables. The model allows many of the major characteristics of Be stars to be understood, including the frequency pattern in the periodogram, allowing the approximate rotational frequency to be identified. From a large number of Be stars observed by TESS, it is shown that the resulting equatorial rotational velocities, v, are consistent with the projected rotational velocities, v sin i . Furthermore, it is shown that Be stars are rotating in a broad range of 30%–100% of the critical rotational velocity. This agrees with several statistical v sin i analyses, which all show that Be stars are very unlikely to be rotating at near-critical velocities.