Pulsation vs Rotation in Be/X-ray binaries

We think of stars as stable systems and indeed they take millions of years to evolve significantly. However, stable does not mean static. Many stars, from all masses and sizes display pulsations on timescales between minutes and years, as for instance the Be stars. The most obvious pulsation mode is the radial one, where the star becomes bigger and smaller periodically, and like any expanding/compressing gas also gets cooler and hotter. 

Many early-type stars are known to be pulsating in modes other than radial. The non-radial pulsations divide the stellar surface in regions with different velocity fields, which, in the presence of rotation, redistribute the flux over the absorption line profile to create moving patterns of peaks and troughs. Likewise, the non-radial pulsations divide the stellar surface in regions with different temperatures. If the amplitude of the pulsations is large enough, the temperature variations across the surface of the star can be detected photometrically as differences in brightness.

Fig. 1. Representative examples of the different types of periodogramsin BeXBs
Fig. 2. Raw TESS light curve of 1A 0535+26 and its periodogram

The Be phenomenon refers to the presence of a circumstellar disk around the equator of OB-type stars. This disks forms, grows and dissipates on time scales of years. The source of matter that feeds the disk is the photosphere of the Be star. The ultimate mechanism that expels matter with enough angular momentum is unknown. The most favoured model combines the fast rotational velocity of the Be stars with non-radial pulsations. When two or more pulsation modes are in phase, the resulting amplitude of the oscillations can grow significantly and trigger the ejection of matter.

BeXB occupy a very narrow range in spectral type O9-B2 and by definition they are III-V stars. In the HR diagram they occupy the upper left part. In this part there a number of pulsator systems. The Be in a BeXB have the same mass, luminosity, temperature ranges as  the group known as B Cepheids. So, we expect the Be in BeXB to pulsate. Is that the case?

Dr. Pablo Reig, Research Director at the Institute of Astrophysics, and his collaborator have analysed space-based  data from the TESS mission and ground-based photometry from the Skinakas observatory to investigate the pulsational properties of the optical counterparts to Be/X-ray binaries. Figure 1 shows some representative examples of periodograms in BeXBs. Figure 2 (top panel) shows a characteristic TESS light curve of the BeXB 1A0535+26, the same light curve normalised where the amplitude of the pulsation can be observed clearly, and the peridogram displaying a group of frequencies. 

Their study reveals that short-term optical photometric variability is a very common, if not ubiquitous, feature intrinsic to the Be optical companions in Be/X-ray binaries. The fact that all sources display multi-frequency oscillations and that some of the detected frequencies of the modulations are higher than the maximum allowed for rotation favors the interpretation that non-radial pulsations is the main driver of the fast time optical variability in BeXBs.

Article: "Fast time optical variability in Be/X-ray binaries. Pulsation and rotation" Reig, P.  & Fabregat J., 2022, A&A, 667, 18