Spherical harmonic animation.

Spherical harmonic animation.
Originally uploaded by Astro Guy.

So I'm still working on models to explain some extraneous frequencies in the echelle diagram for AQ Leo. The application of non-radial modes has been suggested - although I'm not really a fan. I think the science is more interesting just in explaining the existence of combination frequencies.

Well, to investigate the non-radial suggestion, one has to work with spherical harmonics, which are a set of solutions to Laplace's equation and are handy for decomposing pulsation modes in stars into a series of numbers. If you click on the photo above you'll be linked to my flickr account. Click on the "all sizes" button above the picture, and you'll get to see the animation of a pulsation mode described by the spherical harmonic of l=5, m=2. Of course a star does not pulsate with such large variations, but only a fraction of a percent of the radius, but it's much cooler to see the deformations amplified.

So now I'm inserting non-radial modes by brute force to see what kind of light curve is produced with the addition of rotation and radial pulsations. I don't expect to see anything dramatic, because the important physics is missing.. namely, boundaries and assymetrics within the star. Since an RR Lyrae is a helium burning horizontal branch star the pulsation should travel through convective and radiative zones. You dump a non-radial mode at a transition zone and the radial pulsation becomes preterbed, possibly setting up a standing wave from interference. In photometry this will show up as combination frequencies.

This is definitely work in progress.