Re: How is the limb darkening related with binary star?

The limb darkening effect is a fall-off
in brightness of the disk of the Sun or of
another star from the center to the limb, or
in other words, the edge.  This effect arises
because stellar atmospheres increase in
temperature with depth below the photospheric
surface.  Looking at the center of the Sun,
we see both the cooler, outer photospheric
layers, and the hotter inner layers.  On the
limb, however, we see mainly the cooler, outer
layers.  Hence, the center appears brighter;
the limb, darker.  If seen in blue or ultraviolet
light, the phenomenon is much more pronounced,
because such light is primarily generated in the
inner, hotter layers visible towards the center
of the Sun's disk.

When stars occur in binary systems, they may be
close enough to interact.  Gravitational forces
draw out matter from both stars in the direction
of the other.  This makes the photospheric layers
expand and cool slightly, and increases the limb
darkening effect in the hotter of the two stars.
However, in the cooler of the two stars, the
radiation from its interacting companion can heat
the outer layers and even reverse limb darkening,
a phenomenon called the "reflection effect" or
"gravity brightening".  Thus, in eclipsing binary
systems, light curves observed during the eclipse
cycle are either rounded off or exhibit sudden
brightening just before darkening.

You will not easily find comprehensive information
about limb darkening on-line, but your best bet
is to search with a good engine like Altavista
(http://altavista.digital.com).  Better yet, your
university library should have astronomy texts which
give descriptions of the phenomenon.  A good example
is Zeilik and Smith's "Introductory Astronomy and
Astrophysics", whose publisher has Tokyo and Sydney
offices, and thus should be available in Hong Kong.