Evolutionary and Observational Consequences of Dyson Sphere Feedback (2024)

We begin with a look at the general effects of irradiation on stellar structure and evolution. Stars have negative gravitothermal heat capacity: the addition of energy causes them to expand and cool. In a simple theoretical demonstration, the total energy of a star is the sum of its thermal and gravitational energies:

We apply the virial theorem,

to relate each energy type directly to the total energy:

When energy is added to a star (E_* increases), gravitational energy increases and thermal energy decreases, so we see the star expand and cool both overall (because E_therm is lower) and on its surface (because, being larger at the same or a lower luminosity its effective temperature must drop). A larger star should also result in less pressure on a cooler core, so we also expect its luminosity to decrease.

To examine this effect quantitatively, we calculate the differences in radius and temperature between normal and irradiated stellar models. Foundational work on the irradiated stars was performed by Tout et al. (1989), who modeled the evolution up to the helium flash of 0.5, 0.8, 1, and 2 M_⊙ stars in constant-temperature radiation baths from 0 to 10⁴ K. Tout et al. explore their 1 M_⊙ model in great detail, finding that in the early main sequence in the 10⁴ K bath, the star's radius increases significantly (by a factor of 1.4) and that its central temperature and nuclear luminosity decrease very slightly (<1% and ∼1%, respectively). They suggest that this large radius increase appears to be caused by the outer convective region becoming radiative. Since a radiative temperature gradient is smaller than a convective gradient, the envelope must be larger to encapsulate a similar temperature drop. The lower luminosity results in a slightly extended main-sequence lifetime (∼2% for the 10⁴ K bath).

Since normal 2 M_⊙ models have radiative exteriors that are hotter to begin with, Tout et al. find that they are not significantly affected by irradiation while on the main sequence. The irradiated 0.8 M_⊙ models, normally with an outer convective zone and radiative core, behave similarly to the 1 M_⊙ models, expanding and cooling in the outer regions, but not strongly affecting their main-sequence lifetimes. Interestingly, Tout et al. find that the 10⁴ K irradiation decreased the main-sequence lifetime of their 0.5 M_⊙ star by roughly half. They found the star to expand and cool overall, but a radiative region formed, and the thermal energy was distributed in such a way that the central temperature actually increased.

There are two primary ways that a star may undergo feedback from its surrounding sphere: materials may directly reflect some amount of starlight back onto the star, and/or the sphere may become warm and emit thermally. In the classic idea of a Dyson sphere, the sphere's goal is to collect energy, not to reflect it back. As the sphere collects energy, it will heat up and inevitably emit thermally. Some of this emission may end up going back toward the star, so we can model this process as the diffuse reflection of some fraction of starlight.

Although not spherically symmetrical like the typical modeling of a Dyson sphere, the related concept of "stellar engines" proposes a partial sphere which uses a significant portion of a star's luminosity to do mechanical work on the star. First proposed by Shkadov (1987), this could be in the form of a large mirror placed at some distance from the star, disturbing the radiative symmetry of the radiation field and altering its space velocity. Badescu & Cathcart (2000) noted that this reflection will cause the photospheric temperature to increase and gradually change the star's steady state, but they assumed that the nuclear reaction rate is unchanged. In this scenario, a smooth, mirrored surface reflects back as much light as possible, so we can model it as the specular reflection of some fraction of starlight.

As originally suggested by Dyson (1960), and expanded upon by Sagan & Walker (1966), the search for Dyson spheres began as a search for infrared sources in the Galaxy, assuming that they would appear as blackbodies with a temperature of a few hundred Kelvins. The Infrared Astronomical Satellite (IRAS) survey revealed the presence of many infrared sources in the galaxy, but the issue remains of how to distinguish between artificial structures and natural objects of similar mid-infrared fluxes, such as young stars with circ*mstellar disks, or giant stars with dusty atmospheres. Several searches for Dyson spheres with IRAS were performed. Slysh (1985) and Timofeev et al. (2000) each found several objects with spectral energy distributions (SEDs) resembling that of a blackbody with effective temperature between 3 and 400 K. Each noted that further observations would be needed to rule out natural sources. A series of studies (Jugaku et al. 1995; Jugaku & Nishimura 1997, 2000, 2004) combined IRAS and Two Micron All Sky Survey data to search for partial Dyson spheres around solar-type (FGK) stars within 25 pc of the Sun; they found no candidates in their 384 stars studied. Carrigan (2009) explored IRAS Low Resolution Spectrometer (LRS) sources with temperatures below 600 K for Dyson spheres, finding 16 candidates in a study sensitive to solar luminosity objects out to 300 pc. Carrigan (2009) noted that most of these candidates have possible nontechnological explanations and that more information is needed to rule out or strengthen the case for any of them.

Teodorani (2014) proposed a more modern approach to the infrared search for Dyson spheres than could be done with IRAS, using the higher-resolution Spitzer space telescope to search for Sun-like stars with infrared excess. This proposed method, however, assumes that only 1% of total starlight is obscured, as it relies on optical detectability. Wright et al. (2014) laid out the AGENT formalism for describing Dyson spheres and mentioned backwarming as a complication in the prediction of star–Dyson sphere system SEDs. Their Wide-field Infrared Survey Explorer (WISE) search focused on Kardashev Type III civilizations, or galaxies full of Dyson spheres, and concluded that they are rare or nonexistent. Wright et al. also note that infrared waste heat is much easier to detect than blocked optical starlight, except in cases where a very large fraction of the starlight is blocked.

Observing a lack of or change in optical light has also been the focus of many Dyson sphere searches. One such method is looking for strange light curves that could be indicative of transiting megastructures (Arnold 2005; Teodorani 2014; Wright et al. 2016). Zackrisson et al. (2018) proposed and demonstrated the use of Gaia to search for optically underluminous stars, by identifying those with spectrophotometric distance estimates far larger than parallax distances. When the James Webb Space Telescope is available for use, Wright et al. (2019) propose that it, in combination with WISE and Gaia, can be used to put robust upper limits on stellar energy collection throughout our Galaxy and across others.

In this work, we use Modules for Experiments in Stellar Astrophysics (MESA; Paxton et al. 2011, 2013, 2015, 2018, 2019) to model the effects of Dyson sphere feedback on the structure and evolution of stars. We use the AGENT formalism of Wright et al. (2014) and the radiative feedback formulation of Wright (2020) to compute absolute magnitudes of many configurations of combined star–Dyson sphere systems. We produce color–magnitude diagrams (CMDs) for selected Gaia and WISE bands and specify when these internal changes in the stars are significant in observations.

Section 2 describes the MESA modeling methods used in this work. Section 3 describes our recreation of the irradiated stellar models of Tout et al. (1989) in MESA. Sections 4 and 5 discuss the impacts of the feedback model on stellar structure and evolution. In Section 6, we demonstrate the observational consequences of these effects. Section 8 concludes the work and motivates future Dyson sphere searches.

We first attempt to recreate the results of Tout et al. (1989) in MESA. We run simulations of 0.5, 0.8, 1, and 2 M_⊙ stars in temperature baths from 0 to 10⁴ K. This temperature bath is implemented using the run_star_extras function other_energy, which continually pours energy onto a star. For a constant-temperature bath, this is implemented as

where L_extra/dm is the input to MESA's other_energy function (in units of luminosity/mass), σ is the Stefan–Boltzmann constant, R_* is the star's radius, T_b is the bath temperature, and dm is the mass contained in the outermost cell in our model.

To replicate the radiation of a Dyson sphere, we pour some fraction of the star's luminosity back onto the surface of the star. Physically, the extra luminosity is a simple function of the star's luminosity,

where L_extra/dm is the input to MESA's other_energy function (in units of luminosity/mass), L_* is the star's luminosity, f is the fraction of the star's luminosity reflected back on itself, and dm is the mass contained in the outermost cell in our model.

However, MESA's finite and relatively long timesteps add some complications, so we have to add some corrections into our function. Without any feedback, the luminosity of the outer layer (L[1]) will be equivalent to that just below it (L[2]), so we start with

When Dyson sphere feedback hits the star, its surface heats up, and in steady state the surface luminosity increases to

which then increases feedback:

This again increases surface luminosity,

which increases feedback:

This feedback cycle happens much quicker than the MESA timescale, so we implement a correction factor which extends this cycle to infinity, following the limits taken in Equations (26) and (27) of Wright (2020). This results in a feedback luminosity of

In essence, because the "reflection" of light between the star and the sphere happens much faster than an evolutionary timestep in MESA, we have just treated the sphere and star as partial mirrors within a timestep. In the case of f = 1, the energy is completely trapped between the sphere and star and so L_extra diverges (because the number of reflections does).

We also need to correct for stellar luminosity evolution within a timestep; we found that without such a correction our simulations underirradiated the star by potentially significant amounts. We forecast our next-step luminosity as the current step's plus the difference between the current step and the one before it. So, we replace L[2] with 2L[2] − L_prev[2]. Thus, our final input for other_energy is

We found that for large values of f, this feedback could become unstable and generate large oscillations in the radiative feedback. To correct this, we also implement a gradual onset of the feedback over multiple steps for f > 0.25 cases to prevent instability. We checked the fidelity of our implementation of this model in the MESA simulations (all with f ≤ 0.50) by confirming that ∣L_extra − fL[1]∣ < 10⁻⁵.

The temperature structure of the fully convective 0.2 M_⊙ star models given 100 Myr to settle after Dyson sphere feedback onset are shown in Figure 2. We find significant decreases in central temperature in the Dyson sphere feedback cases, on the order of 10⁵ K. This internal temperature change dramatically decreases nuclear fusion, with luminosity decreasing by nearly 50% in the 50% feedback case. We also see an increase in radius throughout, particularly prominently in the outer half of the star (not shown).

Figure 3 shows the temperature structure of the 0.4 M_⊙ models 100 Myr after the Dyson sphere onset. This star has a radiative interior containing 35% of its mass, covered by a convective exterior. The border is shown with a dotted line and is where the temperature structure varies the most. We see a spike in temperature for the feedback models just above the bottom of the convective region, where the incoming energy piles up due to inefficient transport into the radiative region below. This is followed by a dramatic dip at the top of the radiative zone, where the irradiation that has made it through has caused expansion and cooling. The spike then settles out toward a central temperature which is reduced by up to hundreds of thousands Kelvin for the stars undergoing feedback. Luminosity decreases for the models with feedback. This effect is less dramatic here than in the 0.2 M_⊙ stars, but but it is still significant, decreasing nuclear luminosity by nearly 40% for the 50% feedback case.

The 1 M_⊙ star, shown in Figure 4, is primarily radiative, with a light convective exterior containing 2% of its mass. As the left side of the figure shows, the changes seen are quite small on the scale of the star's actual temperature, but the right panel shows that the small effects are still quite distinctive. Overall, we see a similar shape in the temperature differential as for the 0.4 M_⊙ star, which also has a convective exterior and radiative interior, though with quite different proportions. We see a large spike in increased temperature as one moves toward the convection–radiation border for the models with feedback. Near the bottom of this convective zone, the temperature difference rapidly declines and becomes negative, settling down to a slightly lower central temperature than the normal star. The central temperatures of the 1 M_⊙ models are much less strongly affected than the 0.4 M_⊙ set. This slight decrease in central temperature produces a very slight decrease in luminosity. We see little expanding and cooling in the radiative interior, but the outer convective zone grows significantly in radius (not shown).

The 2 M_⊙ star, shown in Figure 5, has a convective 0.21 M_⊙ core, surrounded by a large radiative region. While overall the left side of the figure shows that the star is not very strongly affected, the right side shows that some points throughout the star have patterns of temperature deviation. At the very surface of the star, we can see that irradiation has increased the surface temperature, though this quickly decreases and goes away as one moves further into the star. This effect is also reflected in the radius (not shown), which is inflated in the very outermost regions of the irradiated stars, then returns to roughly the level of the model with no feedback. Very little of the feedback reaches further into the star, but that which does produces interesting effects surrounding the radiation–convection border. As one moves deeper into the star approaching this border, temperature begins to decrease, where the nearby convective zone is able to effectively transport heat away. Near the top of this convective zone, the temperature spikes back up, evening out toward a central temperature that is slightly higher for the models with feedback. Also in this region, we see a nearly vertical dip and spike in the model with 50% feedback, which was found to be a numerical artifact. At this turnover point just below the radiative zone, the stars undergoing feedback also see a disturbance in radius (not shown), with a slight decrease before settling out to match up with the feedback-free model. The decreased central temperature is not strong enough to significantly impact nuclear burning. The star's luminosity is essentially unaffected in the core, though the outer region shows a very slightly decrease, where fusion is very slightly perturbed at the turnover point below the radiation–convection border.

Figure 6 shows the nuclear luminosity and radius evolution through the main sequence of the 0.2 M_⊙ models for a few selected feedback levels. The star with 15% luminosity feedback significantly decreases in nuclear burning and has its main-sequence lifetime extended from 970 Gyr to 1070 Gyr. The 50% feedback case decreases nuclear burning very dramatically and extends the main-sequence lifetime to 1500 Gyr, an increase of over one-third. We see a significant increase in radius for 15% feedback and even more so for 50%.

We see a similar but slightly less dramatic effect on the 0.4 M_⊙ models, shown in Figure 7. For higher feedback, nuclear burning decreases and radius increases as the star expands and cools. The 15% case extends the main-sequence lifetime from 199 Gyr to 215 Gyr. The 50% case has a main-sequence lifetime of 267 Gyr.

At the onset of the Dyson sphere feedback, the 0.2 M_⊙ star is completely convective, while the 0.4 M_⊙ star is radiative out to 35% of its mass and convective in the exterior. As predicted, we see a very strong cooling and expanding effect on these highly convective stars, significantly extending their lifetimes. The effect is stronger on a fully convective star than one with a radiative core.

Figure 8 shows the nuclear luminosity and radius evolution through the main sequence for selected feedback levels on a 1 M_⊙ star. We see very slight dips in luminosity at the onset of the Dyson sphere. The nuclear burning decreases very slightly, causing lifetimes to be slightly extended, from 8.88 Gyr to 8.90 Gyr for 15% feedback and 8.94 Gyr for 50% feedback. Interestingly, in contrast with the minor effects on fusion and lifetime, we see dramatic increases in stellar radius, by a factor greater than 3 for the 50% case. The evolution of our 2 M_⊙ models is shown in Figure 9. Feedback has no significant effect on the bulk evolution of these stars.

At the onset of the Dyson sphere feedback, a 1 M_⊙ star is primarily radiative (out to 98% of its mass) with a convective envelope. The 2 M_⊙ star has an inner convective core, while the exterior is fully radiative. In the 1 M_⊙ star, we see that the convective envelope carries some of the reflected energy into the stellar interior. The radiative core gets a slight cooling effect, slightly slowing fusion, while the envelope dramatically expands, radically changing the star's radius. With the 2 M_⊙ star's lack of an outer convective region, very little of the reflected energy is able to reach the interior of the star, and the evolution of its bulk properties is essentially unaffected.

MESA implements BCs to estimate absolute magnitudes in user-specified filter systems (Paxton et al. 2018). The BCs are calculated by linear interpolation over tables of , , and [M/H]. We input BC tables from MESA Isochrones and Stellar Tracks (MIST; Dotter 2016; Choi et al. 2016) for the Gaia and WISE filter systems.

We select one point in the evolution of each star as our characteristic luminosity and BC values. For the 1 and 2 M_⊙ stars, we select the point in time at which the star is halfway between the onset of its Dyson sphere and the end of its main sequence. For the 0.2 and 0.4 M_⊙ stars, whose lifetimes are significantly longer than the age of the universe, we select an age of 10 Gyr, as their properties do not evolve significantly between the Dyson sphere's onset and the age of the universe.

So far, the only aspect of the Dyson spheres that we have defined is the fraction of luminosity reflected back onto the star (f). To characterize the structure in an observable way, we apply the AGENT formalism of Wright et al. (2014) and Wright (2020). The AGENT formalism is named for the five defining parameters of the Dyson sphere system (all powers normalized by the star's power output): the power of starlight intercepted, α, the power produced from other sources (e.g., fossil fuels), , the power of the Dyson sphere's thermal waste heat, γ, the power of other waste energy disposal, ν, and the characteristic temperature of the Dyson sphere's waste heat, T_waste. In this work, we set = ν = 0, assuming that the structure does not generate its own energy or emit significant low-entropy emission (e.g., radio transmissions).

We adopt a spherical shell model, centered over a star of radius R_*, with radius R and Bond albedo a. Photons leaving the interior of the Dyson sphere have three possible fates: reflection, transmission, and absorption. We parameterize the fractional portions of radiation for each of these fates with

where a, t, and e are the fractions of photons that get reflected, transmitted, and absorbed, respectively. For our feedback effect, we also need the parameter s, representing the probability that a photon emitted from or reflected by the interior of the sphere in a random direction will not immediately strike the star:

We also assume that the structures radiate heat equally on the interior and exterior (i.e., there is no strong thermal management), indicated as ζ = 1/2 in the AGENT formalism.

We examine two limiting cases for the a, and e parameters. The first case, which we refer to as hot Dyson spheres, assumes black material, adopting a Bond albedo a = 0. The second case, which we call cold Dyson spheres, corresponds to a spherical, specularly reflecting mirror that returns all light it collects back to the star. Such material absorbs no heat, so e = 0. Intermediate cases will have properties that are a compromise between these extremes. In both cases, we vary t, which corresponds to the transmittance of the sphere, which can be interpreted as the fraction of the star's solid angle the sphere does not cover. Since our models are one-dimensional, this is not completely appropriate for stellar engines with large deviations from spherical symmetry.

6.2.1.Case 1: Hot Dyson Spheres

For the hot Dyson sphere case, we assume that the sphere's material is black, so its Bond albedo is a = 0. We assume that the sphere's transmissivity is equivalent at optical and infrared wavelengths, corresponding to opaque absorbers covering a fraction e = 1 − t of the star.

Applying these assumptions to the AGENT formalism, we calculate the parameters that describe a system's observability, α and γ. We start by filling in our assumptions in the equations for the fractions of photons from the star and sphere that end up absorbed by the star, absorbed by the sphere, or escaped, in the limit of purely diffuse reflection from the shell, based on Table 2 from Wright (2020). Our version is shown in Table 1.

Table 1.The Fractions of Stellar and Dyson Sphere Photons that end up Being Absorbed by the Star, Absorbed by the Sphere, or Escaping

	Starlight (*)		Thermal Emission from Sphere (s)
	hot	cold	hot	cold
Absorbed by Star (*)	0	1-t		⋯
Absorbed by Sphere (s)	1-t	0		⋯
Escape (e)	t	t		⋯

Note. This is the recreation of Table 2 of Wright for the two configurations we explore: hot black spheres and cold mirrored spheres.

Download table as: ASCIITypeset image

We apply these to Equations (32)–(33) in Wright (2020) to calculate luminosity ratios required for energy balance:

where L_* is the star's total luminosity, is the star's luminosity due to power generated in its core (equivalent to L[2] used in MESA and the above sections), and L_s is the luminosity of the Dyson sphere. We then plug these into Equations (34)–(35) to calculate our AGENT observability parameters:

where α is the fraction of the star's nuclear luminosity which does not escape the system as starlight and γ is the fraction that ultimately escapes the system as thermal emission from the Dyson sphere. From our above equations, our feedback parameter relates to this formalism as

For each of our stars at their selected point in time, we calculate a Dyson sphere's temperature and size for each of our feedback fractions f, for t values from 0 to 0.99 (or the maximum possible for nonnegative s values.) From Equations (37)–40 in Wright (2020), we calculate the temperature T_s of the Dyson sphere. Using our L_s from Equation (18), our effective temperature is

where R_* is the star's radius. For this configuration, our Dyson sphere has the same internal and external temperature, so we can rewrite Equation (14), given Equations (45)–(47) of Wright (2020), as

6.2.2.Case 2: Cold, Mirrored Dyson Spheres

We take a closer look at selected Gaia and WISE CMDs shown for low-mass stars in Figure 10 and intermediate-mass stars in Figure 11. From Gaia, we use the G (green), G_BP (blue), and G_RP (red) filters to characterize the systems at optical wavelengths. From WISE, we use the W4 (22 μm) filter to include an infrared component.

In each CMD, we show the bare star and a line tracing cold, mirrored sphere systems with reflection fractions from 0 to 0.50. We also show a series of curves tracing the magnitudes of hot, nonreflective Dyson spheres with different transmission levels. Along these curves, the feedback parameter f can range from 10⁻⁶ to 0.50, though unphysical f and t combinations which would require a Dyson sphere smaller than its host star are excluded. In addition, we trace select lines of constant hot Dyson sphere radii. The data behind the figures are available in machine-readable form.

For the hot-to-warm Dyson sphere configurations, high values of f begin in the upper-left of each CMD and extend downward toward lower f. For each stellar mass, we see similar general trends. In the left-side diagrams, moving toward higher f, we see the stars dim in absolute G magnitude, as they redden then bluen again in G_BP–G_RP. This happens because at very high feedback levels, the Dyson sphere's temperature is very close to that of the star. As feedback decreases, we see the Dyson sphere begin to cool, reddening the system. At very low feedback levels, the Dyson spheres become very cool and no longer contribute significantly to optical magnitudes, so we begin to see the star's natural color again. On the right-side figures, we see that each constant t line generally dims and reddens as we move toward lower feedback levels. We see continuous reddening here as we move to cooler and cooler Dyson spheres, as the G-W4 color can pick up the infrared output of these relatively low-temperature objects.

Moving from high t lines to lower, we see this effect exaggerated, as the Dyson spheres intercept more starlight and contribute more to the overall appearance. As in the classical idea of a Dyson sphere, we can examine a solar mass star with little transmission of starlight through the sphere and a Dyson sphere radius of roughly 1 au. We see that the feedback levels are very low and that the systems will appear, relative to a bare solar mass star, to be dimmed in the optical range and reddened in both optical and infrared colors.

Next, we examine the CMDs for cold, mirrored spheres. Low feedback levels (high transmission values) begin at the bare star point. For the 0.2 M_⊙ star, we see dimming in the G band and no significant change in color, as the star's effective temperature does not significantly change, and there is no Dyson sphere emission. For the 0.4 M_⊙ star, we see dimming in the G band and the star getting slightly bluer, as the star very slightly increases in effective temperature. The 1 M_⊙ star does not significantly dim in the G band and becomes bluer. Feedback significantly increases its effective temperature, making it bluer, but not appearing brighter due to decreased transmission. The 2 M_⊙ star dims and becomes bluer. Its spectrum peaks in UV wavelengths, so the effective temperature increase is not enough to counteract the decreased transmission by the higher-coverage mirror systems.

The feedback of energy back to a stellar surface resulting from a warm and/or reflective Dyson sphere can strongly affect the appearance of a star under certain circ*mstances, particularly low-mass stars and high-feedback f values. For low-mass stars, we have demonstrated that nuclear luminosity is significantly affected. To cause a 1% change in the star's nuclear luminosity, 0.2 and 0.4 M_⊙ stars require 1.2% and 1.3% feedback, respectively. Interestingly, we see a partial cancellation in the effects on the star's effective temperature. Feedback increases the temperature of the star's exterior, increasing luminosity, while the reduction in nuclear burning decreases luminosity. Ultimately, their effective temperatures do not change noticeably for the feedback levels explored (≤50%).

For higher-mass stars, feedback cannot penetrate far into the star, so a very large amount is required to affect nuclear burning, often above the limit of 50% explored here. To produce a 1% change in the 1 M_⊙ star's nuclear luminosity, 45% feedback is required. None of our models were able to significantly change the 2 M_⊙ star's nuclear burning. Since there is not a significant cooling effect in these stars, we see that their effective temperatures can be significantly impacted. For a 1% change in effective temperature for 1 and 2 M_⊙ stars, feedback levels of 5.8% and 5.5%, respectively, are required. For a cold, mirrored sphere, for example, these would be the fraction of the star's solid angle (f = a = 1 − t) required to be covered in mirrors for the feedback to significantly affect stars' effective temperatures.

To demonstrate how these feedback levels translate to the physical properties of hot Dyson spheres, we plot α (the fraction of stellar luminosity which does not escape as starlight) and for each stellar mass at the f values that cause significant changes to stars' appearances in Figure 12. Ultimately, these significant observable changes only occur for Dyson spheres on the order of a few thousand Kelvin and not for those of typically assumed Dyson sphere temperatures of a few hundred Kelvin.

We have limited our analysis to f < 0.5 because this represents an extreme outer limit to what might be expected from Dyson spheres used as energy collectors, and in part because higher values required additional modifications to MESA to capture the physics correctly. But higher values, even up to f = 1, might be interesting to consider as components of a stellar engineering project. As we have shown, returning starlight to a star can increase its lifetime, especially if a significant fraction of the star's outer mass is convective.

Whether such a project could succeed on a star with a substantial radiative component is unclear, but in principle "bottling up" a star completely should unbind it on a Kelvin–Helmholtz timescale and quench the nuclear activity in its core. Such a project might be desirable and thus be done intentionally, either to extend the star's life, prevent it from experiencing post-main-sequence evolution, or even extract its mass. Exploring such possibilities is a topic for future work.