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Could Dyson spheres affect the structure of the stars they surround?

Since the early days of the Search for Extraterrestrial Intelligence (SETI), researchers have recognized that an advanced technological species may take advantage of the huge and sustainable energy supplies provided by stars. First proposed by Freeman Dyson, this would take the form of large structures surrounding a star (often called a “Dyson sphere”) which gather starlight, use the energy for some technological purpose, and re-emit the waste heat in the infrared. But could these megastructures in turn affect the stars they surround? I explore how this effect might work and when it matters in my paper recently accepted to the Astrophysical Journal and posted to arXiv, co-authored with my adviser, Professor Jason Wright.

We start with a look at what happens to stars undergoing irradiation. In general, stars have negative gravitothermal heat capacity. This means that when they receive additional energy, they are expected to overall expand and cool. Tout et al. first explored this idea in more detail 1989, in relation to stars near quasars or active galactic nuclei, sources of intense radiation. They modelled the evolution of stars in temperature baths of up to 10,000 K. They found that, in general, stars with radiative envelopes were not strongly affected, while stars with convective envelopes increased in size. For stars like the Sun, they found that main sequence lifetimes could be very slightly increased. For a star half the mass of the Sun, they found that its central temperature actually increased, accelerating nuclear fusion and shortening main sequence lifetime. 

In this work, I recreated these simulations in MESA, more modern software for stellar modelling. My results matched well with those of Tout et al. for a Sun-like star. However, the low mass star, with a significant convective envelope, in my simulations actually cooled in its core and had a dramatically extended main sequence lifetime. We conclude that this discrepancy is likely caused by the improvement in opacity estimates for the atmospheres of cool stars in the ~30 years between their simulations and ours. My results (left) are shown below, alongside those of Tout et al. (right), with regular stars shown as dashed lines and stars in 10,000 K temperature baths as solid lines.

So, we know that irradiated stars can expand and cool, particularly when they have a significant convective envelope. How does this relate to Dyson spheres? Depending on the use case for such a structure, it may have a reflective surface and/or thermally re-emit waste heat in all directions. This means that some amount of the star’s energy output is expected to return back onto its surface, either by direct reflection or thermal re-emission. We use MESA again to model the structure and evolution of irradiated stars, this time with the irradiation luminosity as a function of the star’s luminosity, multiplied by some factor f representing the feedback level.

We model stars with masses of 0.2, 0.4, 1, and 2 solar masses, with feedback levels from 1% to 50% of the star’s luminosity. The simulations show the expansion and cooling of irradiated convective envelopes, while radiative envelopes are not significantly affected. Let’s take a look at the evolution of a fully convective star:

The figures show the evolution of the models’ nuclear burning rate and radius throughout their main sequence lifetimes. For high levels of feedback, the star dramatically expands, cools, and slows fusion. This results in substantially extended lifetimes. Next, let’s look at the same evolution process for a solar mass star:

This star is primarily radiative, with a small convective envelope. We see the expected expanding and cooling in this envelope, but the star’s center is not significantly affected, showing very minor changes to nuclear burning rate and main sequence lifetime. For a star twice the mass of the Sun, with a fully radiative exterior, bulk properties are not noticeably affected:

We also generate color-magnitude diagrams for an array of Dyson sphere types, including those with very little feedback to help guide future Dyson sphere searches. Here’s what that looks like for a solar mass star:

CMD for 1 solar mass star-Dyson sphere systems in Gaia and WISE absolute magnitudes. more detail about the shapes of the curves can be found in the paper on arxiv.

This CMD shows Gaia and Wise absolute magnitudes and colors for both hot and cold Dyson spheres. A black dot indicates the position of a bare star. Cold, reflective spheres with different feedback levels are shown along the dotted black line. Colored lines indicate the colors and magnitudes of hot/warm Dyson sphere systems for a set of starlight transmission fractions, with a line tracing along a range of Dyson sphere sizes. The gray lines mark lines of constant Dyson sphere radius.

So what does this mean for the search for Dyson spheres? Does it matter? Ultimately, the effects of Dyson sphere feedback on a star are only significant for convective envelope stars with very hot or very reflective Dyson spheres, which does not align with the classical conception of a Dyson sphere, which would be non-reflective and ~300 K. It may matter, however, for a “stellar engine,” or highly reflective megastructure used to physically move a star. But, we won’t know for sure what sort of technology is out there until we find it. Maybe this could even be done on purpose to extend the main sequence lifetime of a society’s host star!

Published inMy Papers

One Comment

  1. Jack Warfield

    Nice article, Macy!

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