BOTH ANSWERS ARE YES ! YOU ARE EXACTLY RIGHT !
1. Isn't it also a possibility that our sun has a much older history than now accepted? Maybe it was a supernova itself, then neutron star, which "evaporated" into a new much lower mass star of mostly hydrogen gas. Some of remnants of the supernova are the matter orbiting our sun today, including the Earth and us.
2. Now the question is how would a neutron star evaporate?
ANSWERS:
1a. Our Sun has a much older history.
1b. It exploded as the supernova 5 Gyr ago
---[Based on combined U/Pb and Pu/Xe age dating.
1c. It ejected all of the material that now orbits the Sun.
1d. Neutron stars "evaporate" by neutron emission
---[Driven by repulsive interactions between neutrons].
1e. The free neutrons decay to protons and electrons.
1f. Strong magnet fields at the core accelerate protons upward by strong.
---[Protons from the core are the carrier gas that maintains mass separation]
1g. Most protons are fused into He-4 during the upward journey
---[This generates 35% of solar luminosity; 100% of solar neutrinos]
1h. 50,000 billion metric ton of H reach the solar surface annually
---[This generates 100% of the solar wind Hydrogen].
2. Neutron-emission, driven by repulsive interactions between neutrons.
All this was explained in detail over the past 30 years and is summarized in "The Sun is a plasma diffuser that sorts atoms by mass," Physics of Atomic Nuclei 69 (2009) 1847-1856; Yadernaya Fizika 69, number 11, (November 2006); PAC: 96.20.Dt DOI: 10.1134/S106377880611007X
http://arxiv.org/.../0609509
With kind regards,
Oliver K. Manuel