How can white dwarf form Oxygen ? (Temperature problem)

Question

I’ve got a question about white dwarfs and oxygen.

I read in a book that a temperature of 100 million degrees is required to fuse Helium in the core of a red giant. The Helium fuses into Carbon by the triple-alpha process.

It’s also written that, after a temperature of 350 million degrees is reached, the core of a red giant ceases to be degenerate. So, the core is able to expand and its temperature is controlled. The core won't reach a temperature of more than 350 million.

But my teacher has said that a temperature of 600 million degrees is needed to form Oxygen from Carbon: Carbon fuses into Neon and by photodisintegration gives Oxygen.

So, how can there be Oxygen in white dwarfs, if we don't reach a temperature higher than 350 million degrees? By what process can oxygen be formed in a red giant?

Answer 1

Some oxygen is produced during CNO cycle processing of hydrogen, starting with carbon nuclei. Oxygen is also produced by alpha capture onto carbon nuclei at temperatures well below 350 million K.

Both of these occur in and around the cores of low mass stars before they become white dwarfs. Neon production is not required.

Answer 2

Because the Red-Giant Sun can fuse carbon to oxygen

But, the process is extremely slow. The Sun is too light to actually fuse carbon to oxygen on a large scale. You need much more mass to do that.

So instead, the Sun simply fuses it passively. But the Sun does not do carbon+carbon=oxygen fusion. It instead uses carbon+helium, where a helium nucleus (essentially an alpha particle) is bombarded onto a carbon nucleus, forming oxygen.

But even this process is really slow, as there is not much mass. So this process is merely a byproduct, a trace product of the dominant helium-fusing core of a red-giant.