Re: Can a galaxy's core stars explode in a chain-reaction?

That's a very interesting question!  One might think that a stellar
explosion (called a supernova) could induce nearby stars to also go
supernova, but unlike explosions here on Earth (such as bombs), there is a
very different mechanism at work inside of a star.

Let's start with how a star shines:  nuclear fusion.  The temperature at
the center of a star is the hottest, and that allows fusion to occur.  At
first, when the star is just starting out on the main sequence (after
initial formation and starting to fuse) the star combines hydrogen to form
helium.  When it runs out of hydrogen in the center part where it is hot
enough to do this, the star contracts, turning gravitational potential
energy into thermal energy.  In other words, the star heats up.  Eventually
in the center it gets hot enough for helium to fuse to carbon.  For low
mass stars, such as the sun, that's where it stops (and some stars don't
even get to the He->C phase).  But for massive stars, this process can go
all the way up to fusing Silicon into iron -- but no further.  At that
point, it becomes energetically unfavorable to fuse iron into a higher
element (so one might ask where all the higher elements are formed!  We'll
see in a minute...)

The last stages before the massive star reaches iron in its core go very
very quickly because of the extremely hot temperatures in its center.  Once
the core is iron, the star no longer can support itself because the core is
not generating supporting energy.  The star then begins to collapse, but
essentially "bounces" off the iron core, resulting in the outer layers
exploding back outward in the supernova explosion.  (At this point there
are a lot of free neutrons flying around -- these combine with elements and
some decay to protons, thus forming the elements higher than iron!)

As the explosion goes outward, it becomes less and less dense because it is
spreading the same material out over a larger area.  At most, even near a
galactic center, this material will just add to the mass of another star --
although probably not too much, since a star is small compared to the area
the supernova ejecta is spread out over.  Since so little mass would be
added, it would not significantly affect whether or not that star would go
supernova (eventually, when it finished going through the cycle) unless
that star was already very close to the lower mass limit for a supernova. 
The largest effect will be to add heavier elements to the envelope of the
other star.

However, some galaxies have what are known as "starbursts".  This would
produce a simliar effect, even though the supernovae are not triggered by
each other.  In this case, something (often tidal interactions with another
galaxy) causes a lot of stars to form in a very short time within a galaxy.
 At first, these starburst regions put out an enormous amount of energy,
especially in the UV range, due to their hot, massive star components. 
This radiation would certainly affect any life nearby!  Then, as the very
massive stars age more quickly (because they are hotter) many of them will
go supernova within a short time (~1 million years), spreading an enormous
amount of energy and lots of heavy elements throughout the galaxy.  Again,
this would definitely cause some problems for nearby life!  Depending on
how far away the starburst occurred, life might be destroyed, or it might
be just fine.  Most of the radiation from a starburst is absorbed by
surrounding interstellar medium and re-radiatied in the infrared, which is
much less harmful.  So, if we lived 8.5 kiloparsecs (the distance from the
sun to the Galactic center) from a starburst, we would probably be just fine.

In terms of the galaxy, an event like this will often "blow out" columns
upward out of the galaxy (this generally occurs in a spiral, where there is
lots of gas to form stars in the first place).  However, the galaxy is
still very massive, so the starburst does not disrupt or tear apart the
galaxy itself.