Does a Civilization have a Limit to Growth?

Growth of a planetary population, technology, productivity and energy consumption seems unstoppable - scaling to infinity over some finite time (millions of years??) When and if Earth becomes one large connected “city” the growth hits a wall, or, as Wong & Bartlett (2022) suggest - an asymptotic burnout - aka, civilization hits a limit of growth and either collapses or awakens. Is this the Fermi paradox and why we don’t see other extraterrestrial civilizations in the galaxy? Have most collapsed?

Read more here: Asymptotic burnout and homeostaticawakening: a possible solution to theFermi paradox?

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Terrestrial Planets in the Milky Way

Kepler 186f - NASA

In my last post I noted a paper that I used to roughly estimate the number of Earth-sized planets in habitable zones of their parent stars. Going a bit deeper in to some of the more recent works I've been trying to find other estimates that might confirm or adjust my estimate.

If you are interested in some of the published works, two terms that might be confusing are the differences between 'terrestrial planets' and 'Earth-sized' planets. Though not a fixed view, terrestrial planets are considered to be composed of silicates and metals unlike the lighter giant gaseous planets. For example, Zackrisson et al. 2016 define terrestrial planets as having radii in the range of 0.5 to 2.0 times that of Earth with a mass range of 0.5 to 10 times. In our Solar System this would include three of the four inner planets of Venus, Earth and Mars with Mercury just under their range (though it is still considered a terrestrial planet in our local Solar System). From a different perspective, Petragura et al. 2013 note that Earth-sized planets have radii in the range of 1 to 2 times Earth.

Interestingly, Zackrisson's estimate posits the total number of terrestrial planets in the Milky Way to be about 65 billion for stars with spectral types F, G, K and M. This is at least in the ballpark of my previous estimate of 4 billion Earth-sized planets in habitable zones of G and K stars. However, given the 65B estimate includes all terrestrial planets it would seem that Earth-sized planets in habitable zone might be modestly less than 4B.  Of the 65B only about 2.5B are considered orbiting spectral types of F, G and K stars with remaining 62.5B orbiting M stars (the number of M dwarf stars in the galaxy is about 3x greater than FGK stars - Zackrisson also mention the higher probability of finding terrestrial planets around M dwarf stars is about 2.5). What fraction of those are Earth-sized and in habitable zones is still in question - but the estimates seem to fall approximately around 0.1 to 1 billion Earth-sized planets in habitable zones around G and K stars.

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The Galactic Habitable Zone or GHZ

Re-emergence of life after catastrophic extinction event
(Chen & Benton 2012)

Many times we hear about habitability or the habitability zones within stellar exoplanetary systems which is closely related to the presence of liquid water as a precursor to life. However, to have the heavier elemental components making up planets much like our Solar System required generations of stellar evolution to create those elements in the abundances we measure today. If we make the assumption that life evolves in a similar environment, then there is a dependence on the age, evolution and position of an exoplanetary system in a galaxy--or, put another way, a galactic habitable zone (GHZ) (e.g., Lineweaver et al. 2004, Dosovic et al. 2019).

Another way to think of GHZs is to assess the components within a galaxy that could hinder or damage the formation of life on an exoplanet. For example, an exoplanetary system being too close to a number of supernovae or where the star formation rate is high creating gamma rays, X-rays and cosmic rays could strip atmospheres of UV blocking. Also, complex life seems to require complex heavy elements which implies that the location of the exoplanetary system in a galaxy would need to lie somewhere in the very narrow 'young thin disc' (how narrow? see Yoachim & Dalcanton 2006). This is the region where star formation and evolution is most active and produces the heavier elements through supernova explosions.

One hopeful component for habitability in general is that life seems robust. On Earth, for example, life rebounded quickly after catastrophic events or within millions or tens of millions of years (e.g. see Chen & Benton 2012) which is only approximately 1 to 5% of the age of the planet. Given that, any life on exoplanets would have the ability to rebound and evolve to some form of intelligence over 10x within a habitable galactic zone once critical local habitability conditions for life were established.

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Breakthrough Listen Optical

Breakthrough Listen is one of the most recent SETI efforts by to scan for signals across the optical, radio and near-infrared spectra. It is the largest program in history to search for extraterrestrial civilizations among 1 million of the closest stars (see Gajjar et al. 2019 for an excellent overview and Isaacson et al. 2017 for some suggested candidates). The Very Energetic Radiation Imaging Telescope Array System (VERITAS) at the Fred Lawrence Whipple Observatory in Amado, Arizona has just announced the search for optical signals using 4 12-meter optical telescopes.

Optical SETI is difficult due to multiple factors of distance, ISM and atmospheric absorption, parent starlight, etc. It is a bit of a needle in a haystack to find just the right amount of energy, pulse duration and optical frequency which calls for very high sensitivity in detection. I'll write more about this but 20 years ago Howard et al. (2000) wrote some good preliminary work.

Note: I'm all in support of more funding for SETI-like efforts but not overly pleased that Facebook is on the board.

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The Threat of Gamma Ray Bursts

Recently I stumbled into a paper estimating the number of supernovae (SN) in our galaxy (Adams et al. 2013). This reminded me of the number of news outlets that latched onto the potential of gamma ray bursts (GRBs) to create a catastrophic extinction event on Earth (here are some examples: Did Deadly Gamma-Ray Burst Cause a Mass Extinction on Earth?, Asteroids are not the only threat to life from space,  and shockingly from Nature -- 'Death Star' found pointing at Earth - that's a serious level of click-bate from such a prestigious journal).

You are welcome to read those articles and I'm not going to go into any deep detail in this post on GRB physics or planetary impacts. However, I did want to do some simple napkin math on what the probability of a direct gamma ray burst from a specific subset of core collapse SN might be on Earth. We're indebted to Dr. Enrico Cappellaro's dedicated research into SN rates within galaxies (see Cappellaro, Evans & Turatto 1999 and associated citations for newer work) for some of the broader rough estimates. There are a number of ways to determine the SN rate, but the most obvious way is to utilize observations across multiple galaxy surveys to measure the rate by look-back time. Other methods include measured pulsar birth rates (some percentage of SNs), the amount of SN remnant isotopes and future neutrino detection.

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Populating the Galaxy

The Jet Propulsion Laboratory recently hosted the 10th Global Trajectory Optimization Competition or GTOC X with a challenge to see how many star systems could be colonized with the the most uniform spacial distribution. The contest constraints were based on time to populate, a limit of 100,000 predefined stars, a fixed number of colonizing ships and as little propulsive velocity change as possible.

What's most interesting is that the nuances of the challenge require thinking about the motion of the ships as well as the motion of the stars around the center of the galaxy. Each ship has a limit of impulsive maneuvers to successfully rendezvous with a star system which forces some optimization on trajectories of the colonizing ships to keep the propulsive change to a minimum(use this link to the deeper descriptive rules in pdf).

Seems Team 7 from China of the College of Aerospace Science and Engineering, National University of Defense Technology and Key Laboratory of Astronautic Dynamics organizations bested all of the competition by colonizing 3798 systems (well above 2nd place).  You can see the results here.

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