Considerable discussion has occurred recently following the discovery that the spectral lines of this star are variable in shape as well as position, the period of variation being 4.23 days. When only the variation of line position was known, it seemed reasonable to interpret this variation as the 'reflex' motion of an orbiting planet pulling on the star. But with the new information, this planet hypothesis is no longer acceptable; a planet cannot alter the shapes of the spectral lines.
The variations in line profiles can be documented with several
different parameters such as the velocity span of the line bisectors,
the curvature of the line bisectors, and line-depth ratios. All
such parameters show the 4.23-day period. The following graph
is an example based on my article in Nature 385,
795, 1997.
Naturally, once the planet idea is dead, we all want to know what is causing the variations. Non-radial oscillations can explain all available observations. Artie Hatzes (Texas) and I have computed detailed kinematic models in which the velocities on the surface of the model star are represented by the standard sectoral spherical harmonics of non-radial oscillations. The important free parameters, i.e., the ones that alter the pattern of variations, are the amplitude of the oscillation and the order of the harmonic. The 4th order (and degree), with the motion of one wavelength along the equator corresponding to the 4.23 days, gives a perfect match to the radial velocity data and to the variation in line bisectors.
Data, analysis, models, and further discussion can be found in the more recent paper, now accepted for publication in the Astrophysical Journal. In summary, the probability of the line profile variation showing the same periodicity as the radial velocity variation is very small, only one in several hundred. But it is not small enough to be absolutely conclusive, and so we must be patient and collect more data.
The brightness of 51 Peg is known to be constant to a high degree of precision, and this has been raised as an objection to oscillations as an explanation of the variations. Constancy of brightness is a valuable constraint on our models, but by no means rules out oscillations. In fact, there are many models that will accommodate this constraint.
It is almost amusing that the work done on three nights at the McDonald Observatory is cited as proof against my observations. Within their uncertainty of measurement, the results of these three nights agree with the curves of variability shown by my data. It is correct to say that the McDonald observations did not detect the variability, but it is wrong to say that they supply any evidence against variability.
Objections have also been raised using arguments of ignorance; these are not proof of anything. A statement like: "I can't understand how a star can have such a long period of oscillation, so it can't be true," is not proof, not even an argument, against oscillations. Nature simply does not wait for us to understand something before doing it. Thank goodness.
In fact, no legitimate objection against the non-radial-oscillation
model for 51 Peg has been put forward that cannot be countered.
It is true that we do not yet know why some stars oscillate while
other similar stars don't. This is not a unique situation, but
a common one. Consider Ap stars, where only a few per cent of
them show non-radial oscillations; or stars near each other in
the instability strip of the HR diagram, where some vary and others
don't; and so on. We also do not know why the particular order
seen on 51 Peg should be the one to occur. There are still many
things to learn.