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I know similar questions have been asked and answered. However, it is still not clear to me, so please bear with me if this is duplicate to some extent. The explanation goes like this - the core collapses and the collapse bounces for some reason, creating a shock wave which causes the explosion of the outer layers.

I want clarification on couple of points:

  1. If gravity causes the collapse which bounces, how does gravity cause a collapse that bounces "stronger" than the collapse?

  2. If I am not mistaken, the supernova explosion beams along a specific axis. How does the explosion get focused along an axis instead of exploding in all directions?

Are there models that explain the behavior, or are these explanations more like speculation?

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A supernova explosion is caused by the collapse of the core. Some of the gravitational potential energy released in this collapse is (somehow) transferred to the envelope. The transferred energy is sufficient to unbind the envelope.

Some numbers: If a 1.25 solar-mass $(M_{\odot})$ stellar core (roughly the Chandrasekhar mass for an iron core), with the size of the Earth, collapses to a 10km radius (size of a neutron star) then it releases roughly $2\times 10^{46}$ J.

About 10% of this energy dissociates the iron nuclei (8.8 MeV/nucleon), but most of the rest ends up in neutrinos.

The gravitational binding energy of the $\sim 10M_{\odot}$ envelope depends on its density profile. An extreme upper limit would be to place this mass just above the original core radius - so less than a few $10^{45}$ J. But more realistically if we place most of this mass at a solar radius, then its binding energy is a few $10^{43}$ J.

Thus only about 1-2% of the gravitational energy released by the collapsing core, is required to unbind (and explode) the envelope. How this transfer takes place after core bounce is still debated, but there is no problem with the energy budget.

Your second question is a non-sequitur. It is not the case that all supernovae eject matter in the form of jets. Some supernovae may do so; the cause is open to question, but will involve rapid rotation and magnetic fields. The jet axis will be the rotation axis of the star. Sometimes this is called the collapsar model of supernovae.

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