The pulsations of Cepheids or RR Lyrae are essentially acoustic vibrations, similar to those of a musical instrument, such as a flute or an organ pipe, the essential difference being that they are spherical rather than linear.
It is well know since the work of Bernoulli and Webster that the equations that describe these acoustic oscillations of many wind instruments are mathematically equivalent to the Schroedinger equation from quantum mechanics. In the case of a trumpet or horn the 'potential' in this equation is determined by the variations of the flare radius along the instrument. Thus a sharp opening at the end acts like a potential barrier that allows standing waves in the instrument, corresponding to the notes that can be played.
In the case of the pulsating stars, the 'potential' is caused by the rapid variations of sound speed through the partial ionization regions of hydrogen and helium. In particular the former causes a very large potential barrier near the surface where some modes can get trapped. These are the 'strange' modes.
A detailed linear theoretical analysis of the eigenmodes shows that the strange modes are generally strongly unstable (self-excited).
The novelty of our work is that it predicts that there can be Strange Cepheids and RR Lyrae on either side of the classical instability strip. The pulsation amplitudes of such Strange stars have been calculated to be very small, viz. milli-magnitudes in the light variations or a few hundred m/s in their radial velocities. In a recent search for ultra-low amplitude Cepheids in the MACHO and OGLE databases for the Large Magellanic Cloud we have uncovered two potential candidates of Strange Cepheids.
If one designed a horn to have the same (relative) frequencies as a Cepheid variable star it would look like that
(graphics by Z. Kollath)
Buchler, J. R. & Kollath, Z., 2001, Strange Cepheids and RR Lyrae, Astrophysical Journal, Vol. 555, p. 961-966; astro-ph/0101392 ApJ
Buchler, J.R., Yecko, P.E. & Kollath, Z., 1997, The Nature of Strange Modes in Variable Stars, Astronomy & Astrophysics, Vol. 326, 669-681. source    A&A
Buchler, J.R., Wood, P.R., Keller, S. & Soszynski, I. 2005, Ultra-low
Amplitude Cepheids in the Large Magellanic Cloud , Astrophysical
Journal Letters, Vol. 631, p. L151 - L154
http://xxx.lanl.gov/abs/astro-ph/0506114 .ps.gz file ApJ
Work supported by National Science Foundation.
updated November 2005