Why are red giants big?

Red giants form at the end of a stars life, when its supply of hydrogen in the core has dwindled. The slowing of the fusion reaction causes the star to shrink yet somehow this leads to a massive increase in its size.
Wiki says that the core is now all helium and fusion occurs in a shell around the core.
Two questions

  1. can’t the helium in the core fuse in this situation
  2. how does the contraction lead to an increase in size

From the wiki article (linked for future readers)

Second question:

First question:
Yes, if it’s massive enough.

Only if the core temperature is high enough. You need a higher core temperature to fuse helium than you do to fuse hydrogen.

Quote:
Since the inert helium core has no source of energy of its own, it contracts and heats up, and its gravity compresses the hydrogen in the layer immediately above it, thus causing it to fuse faster. This in turn causes the star to become more luminous (from 1,000 to 10,000 times brighter) and expand; the degree of expansion outstrips the increase in luminosity, thus causing the effective temperature to decrease.

I guess this is the part that gets me. How can a contraction of the core cause the
gases above the core to compress?

WAG: When the core contracts, it becomes denser, and the gas above it is now closer to the center of gravity, which causes it to compress.

Really just repeating the previous poster, but if the earth suddenly shrank a size (without loosing weight… maybe it bought a special corset or something) surface gravity would increase. This would cause air density at sea level to increase.
When hydrogen fusion in the core stops, it contracts, you now have the same mass in a smaller space, so “surface” gravity is higher, and pressure in the hydrogen around the core increases.

Or so I gather from today’s reading…

H. A. Bethe, Energy production in stars, Nobel Lecture, 1967-12-11

At about page 14 in the PDF file:

The lecture is a good overview, even if it’s a bit old.