Monday, July 5, 2021

A Goldilocks Universe

Anyone with experience in astronomy has encountered the term 'Goldilocks planet'.  It pertains to a planet that is not too near a star, nor too far, such that it may have liquid water on the surface.  Many scientists believe that this is a necessary pre-cursor for life.  Earth is the only Goldilocks planet in our solar system, but exoplanet searches have identified others across this galaxy.

This morning I was thinking about the Universe, and noting that there could be no Goldilocks planets without, what we might call 'Goldilocks stars'.  I would define a Goldilocks star as one that has a main sequence that endures for billions of years at the least.  There are countless such stars in our galaxy.

Why are billions of years of stable star output important?  It is because such is the timeframe that it takes for the development of life (itself an unlikely event) on a planet (which itself may take hundreds of millions of years to develop into a potential host for life).

A star's main sequence describes its stable state where the gravity that holds it together is in balance with the internal pressure that pushes it outward.  It is achieved during the period of time when the core of the star is largely a mass of protons zooming about (these protons are denoted as H-1, as they are hydrogen isotopes that lack a neutron, known as 'protium' as they are effectively just protons).  Energy is created via nuclear fusion when these protons collide and enter into what is known as the unfortunately named 'p-p cycle'.

A complete p-p cycle is a complex series of nuclear fusion reactions that eventually convert six protons into two protons and one Helium atom.  Each link in the fusion chain spits out other matter including positrons, neutrinos, and gamma particles.  Most importantly, the fusion reaction releases thermal energy because the nuclear by-products have less mass than the nuclear fuel - the fusion process produces energy E in the amount of dm multiplied by the speed of light squared (Einstein's uber famous equation) where dm is the quantity of annihilated mass.

The big picture is far less complex than the details: hydrogen fuel converts to helium and releases energy at a specified rate until it runs out.  The amount of time that this dance will play out for is determined by just one thing: the star's mass.

Red Dwarfs are small stars and are the most common; they can burn for trillions of years.  Yellow Dwarfs (like the Sun) are medium-sized and less common but not uncommon; these burn for billions of years.  Supergiants are far more massive than the Sun and are far less common; these burn for just millions of years before they exhaust their fuel supply.

Given the brief period of time (in cosmological terms) that Supergiants undergo their main sequence, it is unlikely that its planets can ever harbor life.  We can deem these stars too big.  We do not yet know whether Red Dwarfs can sustain life on the planets that orbit them.  These stars might be too small.  We do know for certain that planets orbiting Yellow Dwarfs can harbor life (we know of one clear example of this).  These stars, it seems, are just right: Goldilocks stars.

But it all comes back to that p-p cycle.  The rate at which our Sun burns through its fuel depends upon the probability that a p-p cycle can be completed.  Smashing two protons (H-1) together does not guarantee that a deuteron (H-2) will be synthesized (step one in the p-p cycle)... Far from it!  It is actually extremely unlikely.  The probability that it will occur is on the order of 1 in 10 to the power of 26!  The reason that the Sun produces energy at such a high rate is that despite the low fusion rate, there are some 10 to the power of 57 protons zooming about.

It is the 1 in 10 to the 26 rate that confounds me.  I mean, like, why that rate?  Each proton-proton collision is a quantum event.  The particular fusion rate seems so random, arbitrary even.  But it is ultimately critical to our existence.  If this rate were, say, ten times higher than it is, our Sun would have burned out long before life emerged on this planet.

Physics reveals many instances where the conditions of the Universe, its matter and the laws that govern how it interacts, seem to be just right.  If the strong nuclear force that binds the nucleus of an atom were slightly weaker, the electrostatic repulsion of protons would exceed it and prevent the existence of any atom not called Hydrogen.  No atomic variety means no life, just as no long-burning stars means no life.

One can imagine a universe not so perfectly tuned; a universe where life is impossible instead of improbable.  We may live on a Goldilocks planet that orbits a Goldilocks star, but if we widen our gaze, we see that we reside in a Goldilocks universe.  Not that it matters, but it is a funny coincidence that like Goldilocks herself, I ate porridge for breakfast today.  I mixed it with leftover brownies.  It became just right