Could a planet support life if its only energy came from antimatter striking its atmosphere?

Question

This planet is a rogue planet without any star or without being volcanically active. Antimatter continually collides with the planet, and annihilates with hydrogen in the upper atmosphere. This provides heat and light for the planet.

Alternatively, the planet could be made out of antimatter, with regular matter colliding with it. The end result is the same.

Could these conditions allow the planet to support life and allow enough time for life to evolve (10-20 million years)?

Answer 1

Let's start with a quick sanity check. Earth receives approximately $$\underbrace{\frac{L_{\odot}}{4\pi(1\;\text{AU})^2}}_{\text{solar flux}}\times\overbrace{(\pi R_{\oplus}^2)}^{\text{Cross-section of Earth}}=1.73\times10^{17}\;\text{Watts}$$ of power from the Sun, and that does a pretty good job of supporting life. If this planet got all of its energy from matter-antimatter annihilation, this extra hydrogen would be depleted at a rate $$\dot{M}=L_{\odot}/c^2\simeq2\;\text{kg s}^{-1}$$ If you made this hydrogen envelope the mass of Earth's atmosphere, it could last for approximately 85 billion years. Powering the planet for tens of millions of years would require only a small reservoir of hydrogen.

It's worth going beyond the numbers and thinking about what form that energy will take. Electron-positron annihilation usually simply forms a pair of gamma rays. Proton-antiproton annihilation, on the other hand, is comparatively messy. Air showers from energetic cosmic rays or astronomical gamma rays produce short-lived pions and, secondarily, less-energetic protons, neutrons, muons, electrons, neutrinos and photons. Our influx of antimatter will not be moving at relativistic speeds, but similar principles will still apply.

My main concerns from the above are the following:

• Only a small fraction of this energy may be transferred to light at wavelengths suitable for photosynthesis (or whatever variants may be used). Air showers can produce visible light through Cherenkov radiation from relativistic secondary particles, but as mentioned above, fewer of the particles produced will move so quickly as the hydrogen and antihydrogen will, unlike cosmic rays, be comparatively low energy.
• A non-negligible chunk of energy will be transmitted in the form of gamma rays. Many of these will not make it to the ground, as they'll collide with atmospheric molecules and produce more air showers, but the flux will likely still be significant.
• As BMF notes, some fraction of the energy -- I'm not sure just how much -- will escape to space, so the first calculation is a slight underestimate of the annihilation rate.

With the above in mind, producing a significant amount of optical or near-optical light will require increasing the rate of annihilation, requiring a larger hydrogen reservoir, perhaps closer to the Earth atmosphere-esque envelope I mentioned near the start. Unfortunately, this will also lead to the production of more gamma rays.

Additionally -- and this is an important point -- simulations indicate that it's quite difficult for terrestrial planets to hold onto primordial hydrogen envelopes for the timescales we're talking about; they tend to lose them on timescales of tens to hundreds of millions of years after a planet's formation due to thermal escape. This planet would be prone to the same problem, albeit with thermal escape triggered not by a star but by the hydrogen-antihydrogen annihilation. Life would need to evolve starting basically at the formation of the planet, which is quite unrealistic.

My two cents, then, is that the numbers check out inasmuch as you could heat the planet with a reasonable amount of antimatter in a hydrogen envelope, but the forms of the transmitted energy would likely be unsuitable for life, and the phenomenon would not last long.