## Monday, January 25, 2010

### Poincaré Hyperbolic Disk

***

Hyperbolic Geometry

Geometric models of hyperbolic geometry include the Klein-Beltrami model, which consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. A two-dimensional model is the Poincaré hyperbolic disk.

Weisstein, Eric W. "Hyperbolic Geometry." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HyperbolicGeometry.html

***

A computer-generated image showing the pattern of a p-mode solar acoustic oscillation both in the interior and on the surface of the sun. (l=20, m=16 and n=14.) Note that the increase in the speed of sound as waves approach the center of the sun causes a corresponding increase in the acoustic wavelength.

Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun.

***

### SOHO Reads the Solar Flares

Measurements of the Sun's oscillations provide a window into the invisible interior of the Sun allowing scientists to infer the structure and composition as well as the rotation and dynamics of the solar interior.

(Extreme ultraviolet Imaging Telescope) images the solar atmosphere at several wavelengths, and therefore, shows solar material at different temperatures. In the images taken at 304 Angstroms the bright material is at 60,000 to 80,000 degrees Kelvin. In those taken at 171, at 1 million degrees. 195 Angstrom images correspond to about 1.5 million Kelvin. 284 Angstrom, to 2 million degrees. The hotter the temperature, the higher you look in the solar atmosphere.

p-Modes

The mysterious source of these oscillations was identified by way of theoretical arguments in 1970 and confirmed by observations in 1975. The oscillations we see on the surface are due to sound waves generated and trapped inside the sun. Sound waves are produced by pressure fluctuations in the turbulent convective motions of the sun's interior. As the waves move outward they reflect off of the sun's surface (the photosphere) where the density and pressure decrease rapidly..

***
It's Effect on Earth

The plots on this page show the current extent and position of the auroral oval at each pole, extrapolated from measurements taken during the most recent polar pass of the NOAA POES satellite. "Center time" is the calculated time halfway through the satellite's pass over the pole.

Today's Space Weather

Any threat to communications is always seriously assessed. What we want to see on the other side of the Sun is whether any outburst is coming, that could seriously affect those same communications.