Sunscreen: Photometric Signatures of Galaxies Partially Cloaked in Dyson Spheres

The Search for Extraterrestrial Intelligence has so far come up negative for Kardashev Type III societies that capture all starlight from a galaxy. One possible reason is that shrouding a star in a megastructure is prohibitively expensive. Most of a galaxy's starlight comes from bright stars, which would require structures even larger than the classical Dyson sphere to enclose. Using a custom spectral synthesis code, I calculate what happens to the spectrum and colors of a galaxy when only stars below a luminosity L_min are cloaked. I find the photometric signatures of galaxies with L_min<= 1 L_sun are minor, especially for blue, galaxies with continuing star formation. Larger luminosity thresholds (>~ 30 L_sun) result in galaxies with unnatural colors and luminosities. Galaxies observed in NIR and galaxies without recent star formation observed at UV-NIR wavelengths become redder than uncloaked galaxies as L_min increases. Recently star-forming galaxies get bluer in UV and blue light when they are cloaked, with colors similar to quasars but very low luminosities. By selecting on color, we may find Type III societies in large photometric surveys. I discuss how different metallicities, ages, and initial mass functions affect the results.


INTRODUCTION
The search for astroengineering is growing into a prominent branch of the broader Search for Extraterrestrial Intelligence (SETI). Astroengineering involves the deliberate manipulation of matter and energy on astronomical scales. These scales can be planetary, stellar, galactic, or even intergalactic, corresponding to Types I, II, III, and IV on Kardashev (1964)'s famous scale. The classic picture of astroengineering is the Dyson sphere, proposed to be either a solid shell or swarm of space stations surrounding a host sun and consuming all of its energy (Dyson 1960;Badescu & Cathcart 2006).
As our catalogs of galaxies grow and our understanding of their evolution deepens, there is more attention on the possibilities of Type III societies. These scenarios necessarily require interstellar travel of some kind, in addition to the ability to re-engineer each solar system. Questions about whether these technologies are feasible, and whether any astroengineering program can be sustained for a long time, spark fierce debate in the literature (Hart 1975;Tipler 1980;Brin 1983;Ćirković 2009;Haqq-Misra & Baum 2009;Wright et al. 2014a). But Type III societies use so much energy and alter galaxies so deeply that they could be detected at cosmological distances. Thus, our effective reach is quadrillions of astrobrianlacki@gmail.com stars. Just as traditional SETI can survey many more star systems (e.g., 10 6 in the Breakthrough Listen survey) than searches for extraterrestrial life, while hinging on intelligence commonly evolving from life, so astroengineering searhes extend traditional SETI in exchange for additional uncertainty.
Type III societies might develop for a variety of reasons: perhaps resource consumption, ensuring a society's long-term survival, intergalactic communication, enormous science experiments, or stabilization of a galactic environment (Kardashev 1964(Kardashev , 1985Ćirković 2006;Wright et al. 2014a;Lacki 2015Lacki , 2016. Four scenarios for Type III astroengineering have been advanced in the literature. First, they can use large amounts of power to produce non-thermal radiation that we can detect. The typical example is the radio beacon designed to be found by astronomers within millions of light years (Horowitz & Sagan 1993), but this can also take the form of high energy radiation from pulsars or X-ray binaries, modulated to act as a beacon, or even as pollution from particle accelerators (Chennamangalam et al. 2015;Lacki 2015). Second, they can move stars and gas around within galaxies, making the galaxy look strange to us (Badescu & Cathcart 2006;Carrigan 2012;Voros 2014). Third, they may use their abilities to launch intergalactic travelers, spreading seeds across the entire Universe -in effect, the Type III society is just a base to build a final Type IV society (Kardashev 1985 Fourth, and most thoroughly studied, the primary manifestation of a Type III society could be its use of a galaxy's luminosity, particularly its starlight. One way to do this is to put a Dyson sphere around every star in a galaxy (Annis 1999, and later papers). Another is to capture the radiation with a pervasive screen in the form of interstellar dust (Lacki 2016). Galaxies shrouded in these ways will appear optically faint because of the missing starlight. Yet any dissipative use of the power (like running a heat engine or doing irreversible computation) will produce waste heat, likely in the form of an infrared or microwave glow, assuming they are bound by known physics (Kardashev 1985;Wright et al. 2014a;Garrett 2015;Lacki 2016). Already, infrared waste heat has been the main tracer sought for individual Type II societies within the Galaxy (Sagan & Walker 1966;Slysh 1985;Criswell 1985;Timofeev et al. 2000;Jugaku & Nishimura 2004;Carrigan 2009).
Indeed, there have been several surveys that search for engineered galaxies that are either optically-faint or infrared-bright. A galaxy can be verified to be optically-faint with the Tully-Fisher relation, which relates the brightness of a spiral galaxy with the motions of its stars (Tully & Fisher 1977). These surveys, which have had negative results, have constrained Type III societies to less than 1 in 1,000 galaxies (Annis 1999;Zackrisson et al. 2015).
Infrared-bright galaxies can be identified by the presence of strong emission in mid-infrared (MIR; characteristic of 300 K habitable Dyson spheres) or microwaves (characteristic of very cold 3 K smart dust) (Kardashev 1985;Wright et al. 2014a;Lacki 2016). They also will appear to lie off the far-infrared radio correlation (Garrett 2015), which holds for star-forming galaxies and has only a factor ∼ 2 scatter (Condon 1992;Yun et al. 2001). Potentially, these could find Type III societies among millions of galaxies. One of the most thorough surveys of this form has been Glimpsing Heat from Alien Technologies (GHAT orĜ), which looked for extended MIR emission in galaxies observed by WISE (Wright et al. 2014b;Griffith et al. 2015).Ĝ found no signs of a Type III society capturing ≥ 85% of the host galaxy's starlight in an estimated 100,000 galaxies. They set weaker limits on Type III societies that capture only some of a galaxy's starlight (Griffith et al. 2015).
These results are impressively constraining, and seem to have extreme implications for technological advancement and/or the prevalence of aliens. But it is important to check whether there are any loopholes, and there are at least two. First, would waste-heat appear in a visible form? Maybe the aliens maintain their artifacts at a non-Earthly temperature -if it's between ∼ 10-100 K or 600 K, the waste heat would not have been found yet (Lacki 2016; see also Bradbury 2000;Osmanov & Berezhiani 2018). Or maybe they broadcast it in neutrinos or some other nigh-undetectable particle, or beam it anisotropically away from us 1 , or dump it into black holes. Or maybe they are somehow storing the energy without dissipating it.
A second objection deals with the extrapolation of a Dyson sphere around one star to Dyson spheres around every star in a galaxy. A "classic" Dyson sphere, consisting of habitable structures, would use the entire mass of Jupiter to build (Dyson 1960). Many have expressed incredulity that something that big could be built, or economical (beginning with Maddox et al. 1960, immediately following Dyson's paper). But not all stars have the same luminosity: at a given habitable temperature, the Dyson sphere area increases proportionally with luminosity. So, where would the builders get the materials to build a Dyson sphere around a red giant or a blue dwarf, with a luminosity 1,000 L ⊙ ?. A realistic construction material would mostly contain elements other than hydrogen and helium, limiting the potential of a star to act as a mine. Even if we suppose the builders can mine more matter from massive stars (as in Criswell 1985), blue dwarfs have much smaller mass-to-light ratios than the Sun, and red giants are even worse, with high luminosities but masses comparable to the Sun. Yet, the vast majority of starlight from galaxies comes from these brilliant stars.
Of course, the screens don't have to take the form of classic Dyson spheres. Much less massive structures can be built from photovoltaic panels (Bradbury 2000) or microscopic antennas -although that does suggest their temperature doesn't have to be Earthlike (Lacki 2016). But another route is to take these as true limits: what happens if only the fainter stars in a galaxy are cloaked in Dyson spheres? How much would a galaxy dim if only stars fainter than 1 L ⊙ were shrouded -or 0.01 L ⊙ or 100 L ⊙ ? Would its color change significantly? One advantage of looking for these changes in direct starlight is that it doesn't matter what form (or whether) the waste heat comes out, answering the first objection as well.
Simply doing a deep census of the stellar population within other galaxies could directly find these partially cloaked galaxies, even if the shrouded stars are faint 1 Beaming is constrained by conservation of etendue, and ultimately thermodynamics. Basically, the beaming structure (a mirror, a lens) must be proportionally larger than the emitting structure as the solid angle of emission decreases. This is possible when beaming starlight, by using a Dyson sphere as a mirror -indeed, it is the idea behind a Shkadov thruster (Badescu & Cathcart 2006) -but becomes more difficult when trying to beam waste heat of entire Dyson spheres, or the galaxy as a whole.
dwarfs. This strategy is impractical much beyond the Milky Way's satellite system, though, because the individual stars are too faint to be observed and suffer confusion. For example, the most thorough coverage of M31 is in the Panchromatic Hubble Andromeda Treasury, which achieved m ≈ 28 (M ≈ 0) depth in its outer disk (Dalcanton et al. 2012). Even if every M, K, and G dwarf (M V 5; Pickles 1998) in M31 is shrouded, there would be no sign of it in PHAT. PHAT has even lower depth in M31's inner disk and bulge, because the stellar fields are crowded enough that stars are blended together (Dalcanton et al. 2012).
Outside of the Local Group, stellar censuses are shallower still; in the M81 group, HST images with a depth of m ≈ 28 would only detect stars with M 0, like Vega (Dalcanton et al. 2009). Compare this with the 137 galaxies investigated in Annis (1999), the earliest systematic search for galaxies with missing starlight. Searches for partial Type III societies are thus still reliant on measurements of integrated light. I therefore focus on photometric signatures in this paper.
The goal of this paper is to calculate the effects of cloaking only a part of a galaxy's stellar population on its brightness and colors, using luminosity or luminosityto-mass ratio as a threshold. In Section 2, I describe the spectral synthesis calculations I performed, modeling stellar populations that are missing their faint (or bright) stars. An overview of the effects of partial cloaking on the integrated spectrum of a stellar population is given in Section 3. Then, Section 4 presents the model results for the photometry of a partially cloaked galaxy. These include the tracks galaxies trace on colormagnitude and color-color diagrams as stars of greater luminosities are shrouded. Section 5 provides a summary of the results and further possibilities for how a stellar population may be engineered.

SPECTRAL SYNTHESIS METHOD
A spectral synthesis code able to simulate the screening of stars below a luminosity threshold is necessary to calculate a partially cloaked galaxy's spectrum. Since more advanced extant codes do not have this feature, I wrote a custom code.
First, the code calculates a population distribution for the stars in the simulated galaxy, parameterized by age and initial stellar mass. This distribution is a combination of the initial mass function (IMF), describing which fraction of stars are born with a mass M ⋆ , and a star-formation history (SFH), describing how many stars were born a time t ago. I assume the IMF doesn't change with time, so the population distribution is: has a surplus of low mass, low luminosity dwarf stars, and so the partial cloaking of a galaxy has an increased effect. I normalize it so that the number of 1 M ⊙ stars is equal to its value for the Chabrier IMF, because the red giants around this mass dominate the light of modern early-type galaxies.
For the SFHs (Figure 1), I included a constant starformation rate (like a bluer spiral galaxy) and a single instantaneous burst of star formation (like a redder elliptical galaxy). I also included the simulated SFHs from the simulations in (Behroozi et al. 2013, B13) for galaxies in dark matter halos with masses 10 11 , 10 12 , 10 13 , and 10 14 M ⊙ . In these, the star-formation rates (SFR) rise quickly in the early Universe and then decline, but star-formation is still ongoing at z = 0. The low mass halos have SFHs most like a constant rate, while star formation mostly happens during the early Universe in the high mass halos. To simulate a more realistic quiescent galaxy, I use the SFH that the ATLAS3D project derived for M JAM = 10 11 -10 11.5 M ⊙ early-type galaxies (McDermid et al. 2015). Finally, as an example of an ultra-late type SFH, I include the empirical SFH that Weisz et al. (2014) derived for Local Group dwarf irregular (dIrr) galaxies, in which the SFR increases after an initial pulse.
Next, isochrones describe the basic properties (like luminosity, size, and surface temperature) of stars with a specified age as a function of initial mass. I employ the CMD 3.0 isochrones that are available online (Bressan et al. 2012;Marigo et al. 2017). 2 My models use a grid of stellar ages with 6.5 ≤ log 10 t ≤ 10.12, with the upper limit being the oldest available population from the CMD web interface. The age increases in log 10 t steps of 0.01. The stellar population also depends on the metallicity of the stars, the abundance of elements heavier than hydrogen and helium. Old stars and low-mass galaxies have low metallicity, while young stars and high-mass galaxies tend to have high metallicity (e.g., Timmes et al. 1995;Tremonti et al. 2004). The metallicities I chose were 0.1 Z ⊙ , 1 Z ⊙ , and 2 Z ⊙ .
Finally, the spectrum of the galaxies require the spec- tra of individual stars in its population. The BaSeL models of Lejeune et al. (1997) provide the spectrum of radiation flux (specific luminosity per unit area) for stellar atmospheres with a wide range of temperature, metallicity, and surface gravity. Surface gravity parameterizes the pressure in the stellar atmosphere; it is large for dwarf stars like the Sun and small for giant stars. These flux spectra (denoted F ν ) are converted into luminosity spectra L ν by assuming stars are spherical with L ⋆ ν = 4πR 2 ⋆ F ν , using the isochrone-supplied radii R ⋆ . In some stars from the isochrones, the surface gravity of a star was greater (lesser) than available in the grid of BaSeL spectra for a temperature bin, so I used the flux spectrum for the greatest (smallest) available surface gravity. There were also a few cases of stars hotter than any of the model spectra, so then I just used a blackbody spectrum.
From these ingredients, I calculate the total luminosity spectrum of a model galaxy as (3) Θ is the threshold factor, which is 0 for stars that are screened after passing a specified luminosity (or luminosity-to-mass) cut, and 1 otherwise. Note-The Johnson-Cousins system assigns magnitude 0.03 to Vega in all bands (Bessell 2005), and the Gaia photometry sets Vega's apparent magnitude at 0.023 (Carrasco et al. 2016 I also calculate the absolute magnitude of the model galaxy through several filters using this luminosity spectrum. These magnitude were found using the photon number flux, rather than the energy flux. Given a transmission function T x (ν) for a filter band x (and the atmosphere, if relevant), an absolute magnitude M x in that Lacki band is calculated using where D 0 = 10 pc andṄ 0 ν is the photon number flux of a source with magnitude 0. I list the magnitude systems for which I calculated simulated photometry in Table 1. The references give the transmission curves. Broadly speaking, the systems are either AB magnitudes, in which the magnitude zero point is given by F ν = 3631 Jy, or the Vega magnitude system, in which the zero point is set using the spectrum of Vega, possibly with a small magnitude offset. For Vega magnitude system photometry, I normalize with the model spectra of Bohlin & Gilliland (2004), which are available online. 3 When discussing results in this paper, I focus on photometry in the SDSS and 2MASS filter systems. Unless otherwise indicated, ugriz refers to the SDSS passbands.
Because they are purely stellar models with no chemical evolution, my models have several limitations.
• I do not include the effects of dust extinction, whether in the Milky Way or the host galaxy. When looking towards the Galactic Poles, the dust extinction is typically around A V ≈ 0.05-0.1 magnitudes (Schlegel et al. 1998). We can expect a similar amount of extinction within a face-on latetype galaxy at z ≈ 0, and essentially none for most early-type galaxies. Edge-on late-type galaxies are much more reddened because of the larger column of gas they present, though, and galaxies at z 1 are subject to high levels of internal dust extinction. Dust extinction is also a potential issue when looking in the ultraviolet, since star-forming galaxies (including the Milky Way) absorb a large fraction of the UV light they emit (Lisenfeld et al. 1996;Bell 2003). Furthermore, the dust extinction that is present in late-type galaxies is concentrated around gaseous star-forming regions, so young blue stars may be preferentially extincted.
• Nor do I include interstellar dust emission, which dominates the mid-infrared and far-infrared SEDs of star-forming galaxies. While the bulk of the dust emission is in the far-infrared with a relatively narrow range of temperatures (∼ 10-40 K for most star-forming galaxies; Hwang et al. 2010), absorption of high-energy photons by small dust grains leads to complicated SEDs in mid-infrared (Purcell 1976 • I do not include nebular emission lines like Hα or OIII, which are bright in intensely star-forming galaxies (Charlot & Longhetti 2001). In some cases, the emission lines can be strong enough to give galaxies unusual colors (Atek et al. 2011), like with the Green Pea galaxies (Cardamone et al. 2009).
• Since I do not include the effects of circumstellar dust or different abundance patterns in the atmospheres of stars, my models do not treat Thermally Pulsating Asymptotic Giant Branch (TP-AGB) stars properly, although they are included in the PARSEC isochrones (Marigo et al. 2008(Marigo et al. , 2017. These stars can have either oxygen-or carbon-rich atmospheres, which has an effect on their SEDs. Intermediate mass TP-AGB stars, with ages of ∼ 1 Gyr, may actually dominate the NIR emission of post-starburst galaxies (Maraston 2005;Maraston et al. 2006). They are particularly significant as a source of MIR emission due to their circumstellar dust shells (Conroy 2013). The treatment of TP-AGB stars is widely considered a difficult but important issue to treat in stellar evolution models (Choi et al. 2016;Marigo et al. 2017), and for spectral synthesis based on those models (Maraston et al. 2006;Conroy 2013).
• Galaxies do not have a constant metallicity, but generally become more metal-rich with time (Timmes et al. 1995). Thus, in reality, there should be a spread in the metallicity in the dwarf star and low mass post-main sequence population.
• I do not include any treatment of binary star evolution.
Objects that are the result of binary star interactions, like supersoft X-ray sources contributing to the extreme UV luminosity (Kahabka & van den Heuvel 1997), are not included in the SEDs.
For these reasons, the models are generally inaccurate in MIR and longer wavelengths, or in far-ultraviolet or shorter wavelengths.

INTEGRATED SPECTRA OF PARTIALLY CLOAKED GALAXIES
The stellar spectra of natural, uncloaked galaxies qualitatively consist of two peaks (Figure 3). One peak reaches its maximum near the Lyman limit, composed of the blue and ultraviolet light from young, massive stars. The other peak, mostly consisting of the red and nearinfrared light from older red giants, reaches its maximum near 1 µm. The NIR peak becomes more prominent as the SFH progresses from late-to early-type SFHs, as more of the stellar mass is concentrated into older stars. In addition, a bluewards plateau extending from the red peak towards ∼ 400 nm in the constant SFH galaxy drops off with the early-type SFHs. This plateau, visible in late-type galaxy spectra, is mostly contributed by main sequence stars with luminosities of 10-1,000 L ⊙ , or masses of ∼ 2-6 M ⊙ .
The low luminosity (GKM) dwarfs are brightest at wavelengths longer than ∼ 400 µm, so they contribute mostly to the red peak and its bluewards extension. Screening only these stars has insignificant effects on the ultraviolet luminosity of a galaxy. At visible to nearinfrared wavelengths, a screening threshold L min = 1 L ⊙ leads to a 3 to 20% drop in specific luminosity, with a more pronounced drop for bursty SFHs. Thus, galaxies missing these stars would not appear qualitatively different spectroscopically and finding them must require careful analysis.
More dramatic changes in a galaxy's starlight occur if L min ≫ 1 L ⊙ . Figure 4 depicts the fraction of a galaxy's luminosity remains unscreened as a function of L min for various SFHs, denoted 1−α in theĜ AGENT formalism. When L min = 1 L ⊙ , this fraction remains at 80-97%, but it falls to 64-90% for L min = 10 L ⊙ , 41-75% for L min = 100 L ⊙ , and 16-60% for L min = 1,000 L ⊙ . In all cases, early-burst SFH galaxies fade more than flat SFH galaxies.
The increase in α does not occur steadily as L min increases, but happens in spurts. These can be related to the luminosity of stars at distinct phases of their evolutions. The yellow bands in Figure 4 mark the luminosity of stars in the subgiant branch (SGB), horizontal branch (HB) or red clump (RC), and tip of the RGB (TRGB) for an isochronal stellar population of age 10 10.1 yr. In early-type galaxies, the first sudden growth in α occurs as L min approaches the main sequence turn-off luminosity, followed by a plateau for the luminosity range occupied during the short-lived SGB phase. Then, α slowly increases with L min as stars along the red giant branch are cloaked, but there's a sudden jump near 40 L ⊙ where nearly all the stars in the red clump (low mass horizontal branch; Girardi 2016) are shrouded. Roughly 10% of an early galaxy's bolometric luminosity is concentrated in the red clump stars. The increase in α continues until the TRGB is reached (c.f., Salaris et al. 2002), leaving only a few TP-AGB stars providing a residual luminosity. With intermediate and late-type galaxies, these features are much more subtle, because much of the luminosity is provided by bluer main sequence stars with no prominent features.
As seen in Figure 3, increasing L min up to ∼ 1,000 L ⊙ erodes the red peak while leaving the blue peak mostly untouched. The fading is most significant in the visible parts of the spectrum (300-800 nm), as demonstrated when the ratio of the screened and the unscreened spectra are plotted (in Figure 5). For the flat SFH galaxies, L min ≈ 100-1,000 L ⊙ eliminates the visible light plateau in the red peak, so that the integrated spectrum has two sharp peaks. The luminosity at ∼ 300 nm is virtually extinguished for bursty SFH galaxies. Yet, even the NIR summit of the red peak is still eroded by screening low-to-mid luminosity stars, if not as quickly because the light from brilliant red giants remain. In addition, a fairly narrow dip appears in the spectrum around 2.5 − 2.6 µm as L min grows. It is due to a water molecule absorption band in the spectra of the brightest red giants (Rayner et al. 2009). Unfortunately, it is not covered by standard photometric filters, due to water vapor absorption in Earth's atmosphere, and neither Spitzer IRAC nor WISE covered that wavelength region either.
I also considered the effects of using the luminosityto-mass ratio as a cut rather than the stellar luminosity. 4 More massive stars tend to start with substantial protoplanetary disks and more massive planets (e.g., Johnson et al. 2010;Andrews et al. 2013), and so have more material around to build a megastructure. I found that the changes in the spectra as (L/M ) min increases largely looked the same as when L min is used (Figure 6).
The reason for the similar behaviors with (L/M ) min and L min cuts is that stars tend to fall on one of two relations between L and M (Figure 7). Main sequence stars, including the bright blue stars of late-type galaxies, generally have (L/L ⊙ ) = (M/M ⊙ ) 4 (blue). Postmain sequence stars, however, are mostly billions of years old and therefore have masses ∼ 1 M ⊙ . Thus they nearly all have (L/L ⊙ ) = (M/M ⊙ ). When only one of these two groups determines the luminosity of a galaxy, there is effectively a monotonic power-law re-  lationship between (L/M ) and L. Thus, for late-type galaxies in NIR and early-type galaxies, (L/M ) follows the post-main sequence relation; for late-type galaxies in ultraviolet and blue, (L/M ) follows the main sequence relation. Some differences in the spectral erosion do occur in late-type and intermediate-type galaxies in red light (∼ 0.5 µm), where neither stellar population entirely dominates the light. A (L/M ) min cut allows somewhat brighter massive, blue main sequence stars to be shrouded than post-main sequence stars. It therefore tends to result in galaxies having redder colors and somewhat fainter fluxes in this waveband than expected from a simple L min cut. In general, however, I found that these changes did not affect the qualitative behavior of partially cloaked galaxies.

PHOTOMETRY OF PARTIALLY CLOAKED GALAXIES
Photometric surveys provide large datasets of galaxy colors and brightnesses. Since the starlight screened by partially cloaked galaxies is broadband, these surveys may provide an opportunity to quickly search up to several billion galaxies for Type III societies with L min ≫ 1 L ⊙ .
The declining luminosity in various filter bands as L min increases are plotted in Figure 8. I generalize the AGENT parameterization in Wright et al. (2014b) to introduce the α x value, the fraction of starlight screened in some band x. Qualitatively, the behavior of α x is the same in all bands: most starlight remains unscreened until L min ≈ 1-10 L ⊙ , then there's a (possibly sharp) drop as brighter main sequence stars are cloaked. In bursty SFH galaxies, there's a plateau, since all main sequence stars are cloaked at this point, while the RGB remains entirely visible. Then there's another drop at L min ≈ 30 − 1,000 L ⊙ as red giants are cloaked, with a sharp fall at ∼ 40 L ⊙ in early-type galaxies when red clump HB stars are screened. Finally, flat SFH galaxies maintain a residual luminosity L min ≫ 1,000 L ⊙ from the brightest and most massive stars. In all bands, bursty SFH galaxies fade more than flat SFH galaxies.
There are distinct variations in the details of the falloff visible in Figure 8, both in the slope and the curvature. Once L min passes a threshold of ∼ 1 L ⊙ , the residual ultraviolet flux has a positive curvature, starting with a rapid drop-off followed by a slower decline at large L min . In contrast, visible and near-infrared fluxes start off with negative curvature, slowly accelerating in their decline until stalling at a shelf for L min ≈ 3-30 L ⊙ , the regime of the SGB for older populations. The shelf is especially prominent in redder bands, maintaining a small α x value in the near-infrared. Then there's another quick accelerating drop, with an initial fall possible if red clump stars are prominent in the band, until most of the flux is extinguished at L min ≈ 1,000 L ⊙ . The observational importance of these features is that they represent color evolution in the galaxies, a tracer well-suited for photometric surveys. Figure 9 is a visible-light color-magnitude diagram for partially cloaked galaxies. I downloaded magnitude information for a sample of 10,000 objects in the SDSS Data Release 14, including galaxies (violet), quasars (turquoise), and stars (gold in color-color plots). 5 The separation of galaxies into the blue cloud and red sequence (Strateva et al. 2001;Baldry et al. 2004, among many others) is visible on the plot, with quasars being much bluer than either; natural flat SFH galaxies lie in the blue cloud while the intermediate-to earlytype SFH galaxies lie in the green valley or the red sequence for a pure burst SFH. While a threshold luminosity L min = 1 L ⊙ causes small effects lost within the natural dispersion (large circles), early-type SFH galaxies start becoming redder than practically all red sequence galaxies when L min passes 10 L ⊙ . The reddening reaches a peak value of ∼ 0.2 magnitudes for the B13 massive halo SFH with L min ≈ 100 L ⊙ . Pure burst SFHs redden significantly more, ∼ 0.5 magnitudes at 300 L ⊙ . Then, early-type SFH galaxies start becoming bluer again. Interestingly, around 1,000 L ⊙ , the B13 massive SFH galaxies appear similar to faint blue sequence galaxies in this diagram, because only blue stars remain visible to observers.
The color evolution of flat SFH galaxies is more neutral at first. They mainly get fainter without changing g − r until L min 100 L ⊙ . Furthermore, the fading is slow at first, being only ∼ 1 magnitude when L min ≈ 100 L ⊙ . Thus these partially cloaked blue sequence galaxies would still appear as blue sequence galaxies in a color-magnitude diagram like this. Eventually, they start getting bluer than typical galaxies, with colors similar to quasars. Unlike quasars, these partially cloaked galaxies are very faint instead of very bright. Resolved observations of these galaxies would also reveal that the blue starlight is coming from an extended region across a galactic disk rather than a compact nucleus.
The color evolution varies between each pair of bands, causing partially cloaked galaxies to move on color-color diagrams ( Figure 10). A (u − g)-(g − r) diagram can be used to distinguish early, red galaxies and late, blue galaxies (Strateva et al. 2001). Early-type galaxies show small color deviations with L min < 1 L ⊙ . Then they start getting redder in both (u − g) and (g − r), becoming redder than any galaxy with L min ≈ 10 L ⊙ . The artificial reddening reaches a maximum for L min ≈ 100-300 L ⊙ , and then their color evolution reverses. Early-type galaxies with L min ≈ 1,000 L ⊙ have similar colors to uncloaked galaxies. Finally, their reddening oscillates wildly as the brightest red giant stars in these galaxies are cloaked.
Late galaxies in contrast become bluer as their stellar populations are progressively shrouded. They appear largely unaffected for L min 30 L ⊙ , and then they start getting bluer in (u − g) while remaining constant in (g − r). With L min 100 L ⊙ , the engineered galaxies have colors typical of quasars (turquoise points in Figure 10). In this regime, late type galaxies start moving along a line in this color space, getting bluer faster in (g − r) than in (u − g). The intermediate galaxies have tracks more like early-type galaxies for L min 10 L ⊙ , getting slightly redder, before they start looping back to the blue when L min ≈ 100 L ⊙ . Finally, they reach the same terminal color line that late galaxies do.
The color evolution is greater in visible-infrared colors. This is seen in the (u − r)-(i − z) plot in Figure 10. Young blue stars have a strong influence on (u − r), but old red giants affect the (i − z) color. In the diagram, galaxies slowly move "up" (redder in i−z) off the galaxy sequence as L min reaches 1 L ⊙ , and then migrate across  color space with greater L min . Late-type galaxies move up and left -bluer in (u − r) and redder in (i − z), as young blue stars and red giant stars remain uncloaked. This continues until L min 1,000 L ⊙ , at which point there are no red giants left to shroud. Then the partially cloaked late galaxies all travel along "down" (bluer in i − z) a locus in color-color space. Note this locus is actually bluer than quasars. Intermediate-type galaxies have a similar color evolution, even evolving along the same color line, except that they start out by wandering "right" (redder in u − r) at first. Early-type galaxies get redder, especially in (u − r), where they are redder than natural galaxies for 3 L ⊙ L min 500 L ⊙ . They achieve peak (u − r) at L min ≈ 100 L ⊙ . They start the loop back that intermediate galaxies do, getting bluer again in (u − r) while continuing to redden in (i − z), but never complete it by settling on the terminal color line.
Two more color-color diagrams are included in Figure 10 to show the unnatural behaviors of partially cloaked galaxies. The first, (g − i)-(g − z), is interesting because natural galaxies all lie along a thin line. The partially cloaked galaxies generally move above the line (redder in (g −z) when L min ≈ 100-10,000 L ⊙ . Late and (especially) intermediate type galaxies perform a loop, first moving along the line, then rising above it and circling above it, becoming bluer than quasars, before returning and settling on the blue side of the extrapolated line as L min increases. Early type galaxies just keep moving along the extrapolation of the line but getting redder than any natural galaxy.
Natural galaxies sit in a compact cloud in the (r − i)-(i − z) color diagram, which partially cloaked galaxies move out far away from. Late and intermediate type galaxies perform the familiar loop, first getting redder, and then getting bluer along a locus once L min 1,000 L ⊙ . Early type galaxies get continuously redder, until their terminal wander at L min 1,000 L ⊙ . As noted in the previous section, the behavior of galaxies is qualitatively the same when a luminosityto-mass ratio is used as the threshold instead of the luminosity itself. The resultant tracks in the visiblelight CMD, for example, are very similar when increasing (L/M ) min as to increasing L min (Figure 11). The (L/M ) min tracks for late-and intermediate-type galaxies venture to redder NIR colors as they loop in colorcolor diagrams, effectively stretching the tracks vertically in the (u−r)-(r−i) diagram (right). The difference amounts to ∼ 0.1 magnitude and the qualitative behavior is the same. Furthermore, these galaxies end up on the same terminal locus when only bright blue stars remain unshrouded. Likewise, in the (r − i)-(i − z) colorcolor diagram (not shown), late-and intermediate-type galaxies go further redwards by ∼ 0.1-0.2 magnitudes in both colors when using (L/M ) min before returning. The reason for these differences is that (L/M ) min threshold preferentially filters the massive, blue dwarfs over red giants.
To summarize, not only do galaxies get fainter, they change in color as L min rises. The evolution starts becoming significant when L min 1-10 L ⊙ , with higher thresholds needed to observe large changes in late type galaxies. There usually is an inflection point at around L min ≈ 1,000 L ⊙ , corresponding to the point where red giants are being shrouded. The alteration the optical colors of galaxies can be summarized as red galaxies get redder, blue galaxies get bluer. In infrared colors, all galaxies start out getting redder, with late and intermediate galaxies turning around at the inflection point and getting bluer again for larger L min . Late and intermediate galaxies fall along a color locus when L min ≫ 1,000 L ⊙ characterized by very blue colors (comparable or even bluer than quasars).

IMF effects
Early-type galaxies in particular may have a bottomheavy IMF, with more red dwarf stars than expected for the Chabrier IMF (van Dokkum & Conroy 2010, and later papers). I show the resulting CMD (M r vs. g − r) and color-color diagram (u − g vs. g − r) in Figure 12. For early-type galaxies, the tracks are basically identical to those for the Chabrier IMF (pale, thick lines).
Intermediate and late-type galaxies are more strongly affected by going to a bottom-heavy IMF. The overall effect of the alternate IMF is to make galaxies act like they have "earlier" type star-formation histories, be- cause young massive stars are underproduced and old low mass stars are overproduced. Thus, these galaxies dim more than they normally would, especially as the RGB and HB are being cloaked, because there are fewer blue stars remaining unshrouded. Likewise, these galaxies get redder as L min increases for the same reason. Eventually, the late-and intermediate-type galaxies settle on the same terminal locus in color-color space, when only the blue stars they do have remain visible.

Metallicity effects
Stellar metallicity is influenced by the age, environment, and mass of a stellar population. Low mass galaxies tend to be low metallicity, while high mass galaxies tend to be high metallicity up to a maximum value (Tremonti et al. 2004). There are also gradients of metallicity within disk galaxies, which are more metal-rich in their centers than on their peripheries (Henry & Worthey 1999). Whether or not life or intelligence can evolve in galaxies with different metallicities is an open question - Gonzalez et al. (2001) proposed that there was a galactic habitable zone because massive planets tend to be found around metal-rich stars, and dense environments host dangerous phenomena that can trigger mass extinctions, as well as having abundance patterns incompatible with plate tectonics. I include them, though, to allow for the possibility that most galaxies are habitable. . Color magnitude diagram for partially cloaked galaxies. Tracks have the same colors as in Figure 4. The large circle surrounds the points on the tracks with a threshold of 1 L ⊙ , the triangle is around the point for a threshold luminosity of 1,000 L ⊙ , and the squares are at the red clump luminosity (10 1.7 L ⊙ ). Small filled dots mark out powers of ten in L min /L ⊙ , while small open dots mark out half-powers of ten. For comparison, a sample of SDSS objects are plotted: galaxies in violet, AGNs in turquoise.
The metallicity of stars affects their spectra and colors, and this is reflected in the photometric signatures of partial cloaking. I generally find that partial cloaking weakens these signatures in low metallicity galaxies (Z = 0.1 Z ⊙ ). In the low-metallicity CMD (Figure 13, left), galaxies start out brighter and slightly bluer in optical colors. As L min rises, their tracks tend to loop around the main concentrations of galaxies on CMD without escaping. Early-type galaxies do eventually get redder than the majority of galaxies when L min 100 L ⊙ . Late-type galaxies mostly stay in the blue cloud. Furthermore, the dimming effect when 10 3 L min 10 6 L ⊙ is compressed.
While the qualitative shape of the tracks of low metallicity galaxies on a color-color diagram (Figure 13, middle and right) are similar to those of Solar metallicity galaxies (pale, dotted), the scale of the deviations is much smaller, especially for late-type galaxies. The late-type galaxies get only ∼ 0.2-0.4 magnitudes bluer in (u − g) color. The terminal color line in fact remains redder (towards the right) than quasars on the diagram. Natural early-type galaxies with low metallicity start out bluer, and need a higher L min of ∼ 100 L ⊙ before they "escape" from the color-color cloud of galaxies observed by SDSS. Unlike the Solar metallicity galaxies, they do not appear to loop back to the blue, and with L min ≈ 1,000 L ⊙ , they remain redder than any natural galaxies.
The color deviation is even more curtailed in nearinfrared (Figure 13, right). Galaxies not only start out bluer, but they redden by at most ∼ 0.2 magnitudes in (i − z) as L min increases. As a result, their tracks remain near the regions of color space occupied by SDSS galaxies. Late and intermediate galaxies with L min 1,000 L ⊙ have (i−z) and (u−r) colors similar to quasars, while early-type galaxies with large L min eventually get redder than natural galaxies in (u − r) but not (i − z).
The reverse happens for high metallicity stellar populations (dashed lines). Galaxies start out redder and dimmer, and their deviations as L min increases is qualitatively similar to Z = 1 Z ⊙ galaxies but greater in magnitude.

Population age effects
One of the advantages of using photometric criteria for SETI surveys is the growing availability of massive catalogs of galaxy colors. SDSS alone has photometric data on over a hundred million galaxies (Adelman-McCarthy et al. 2007), and LSST should provide photometric data for several billion (LSST Science Collaboration et al. 2009). The great reach of these surveys means that we observe galaxies at significantly earlier cosmic times, with younger stellar populations (as seen in Figure 1). Assuming that ETIs evolved early in cosmic history and partially cloaked galaxies, how would the photometric signatures change?
I show the rest-frame colors and magnitudes of galaxies as they appeared at a cosmic time of 10 9.8 yr (solid), at z ≈ 0.9, and 10 9.5 yr (z ≈ 2), in Figure 14. (Note that observer-frame colors and magnitudes can require a K-correction of 1 magnitude or more.) The CMD and color-color tracks of young, pure burst and pure flat SFH galaxies are largely similar to contemporary galaxies with the same SFH (pale, dotted lines). This is because either they do have young, blue stars or they don't -going back in time a few billion years does not matter since the oldest stars are still billions of years old.
However, the galaxies with more complex SFHs do have different tracks -they act more like late-type galaxies. In fact, the M15 SFH galaxy is still forming stars, so there remain blue stars once all of its red giants are cloaked. In addition, the SFR rapidly increases to z = 2 within low halo mass B13 galaxies, so they are essentially later in type than even the z = 0 W14 dIrr galaxy at 10 9.5 yr. All of the complicated SFH galaxies end up on the same terminal color line of contemporary latetype galaxies. The other main difference is that they are generally brighter than contemporary galaxies, because they have higher star-formation rates, with the

Reverse screening
What if ETIs preferentially cloak the brightest stars of a galaxy, instead of the faintest ones? There could be various reasons for this behavior. These stars have a high luminosity-to-mass ratio and are therefore especially suitable for "starlifting", in which a star's own luminosity is harnessed to unbind its envelope and mine it for materials (Criswell 1985). In general, if aliens want a site where vast amounts of power are concentrated on sub-parsec scales, if AGNs or compact objects are unsuitable sites, and if they are unable or unwilling to beam power across interstellar distances, they would preferentially enclose brighter stars. One possible appli-cation is to transmit vast amounts of information across interstellar distances (Kardashev 1964).
The very brightest stars, with L ≫ 10 3 L ⊙ , are characteristic of young stellar populations and only show up in the late and (to a lesser extent) the intermediate type galaxies. Even in the W14 dIrr galaxy, they account for only 60% of the bolometric luminosity (Figure 4), so decreasing L max from ∞ to 1,000 L ⊙ increases the bolometric magnitude by at most 1. As seen in Figure 8, these stars emit the majority of the light in ultraviolet but a minority of visible and infrared light. Therefore, even the late type galaxies show minor evolution in optical color-magnitude and color-color diagrams, and would appear like natural galaxies ( Figure 15).  Rest-frame color-magnitude (left) and color-color (middle, right) diagrams for partially cloaked galaxies with an age of 10 9.8 yr (solid) and 10 9.5 yr (dotted), corresponding to z ≈ 0.9 and 2 respectively. The default evolution with 10 10.1 yr old galaxies is shown with wide, pale racks. As L max falls from 1,000 L ⊙ to ∼ 10 L ⊙ , red giants and horizontal branch stars start being shrouded. Galaxies with all of the SFHs I considered get fainter by ∼ 1 magnitude in r-band, and bluer by ∼ 0.2 mag in (g−r) color. The deviation is greater for early-type galaxies. Latetype galaxies are bluest when L max ∼ 30 L ⊙ while earlytype galaxies are bluest when it is ∼ 3 L ⊙ . Even now, the galaxies still have colors and brightnesses characteristic of natural galaxies, although the infrared colors of early-type galaxies with L max ≈ 100 L ⊙ are slightly bluer than normal.
Then, as L max falls further, to 1 L ⊙ and below, progressively dimmer and redder main sequence stars start being cloaked. All galaxies have these stars, and they have been forming for billions of years. The result is that all the galaxies become dimmer and redder. On a CMD, the galaxies follow parallel tracks (Figure 15). On color-color diagrams, all of the galaxies move along the same track, with slightly different positions at the same L max for different SFHs. The partiallycloaked galaxies become redder than natural galaxies when L max 10 −0.5 L ⊙ , getting redder by several magnitudes when only the faintest stars are visible. At this point, the galaxies are quite faint, with even the B13 10 14 M ⊙ galaxy having M r −20. As L max continues to decrease, the reach of photometric surveys decreases, as their brightnesses sink to levels characteristic of dwarf galaxies.
In short, photometric signatures for reverse-screened galaxies are probably even harder to detect than those with faintest stars shrouded. Unlike the previous cases, where thresholds of ∼ 30 ≈ 100 L ⊙ led to unnatural colors, the colors of these engineered galaxies appear fairly normal until L max is below 1 L ⊙ . If the radiation is processed into infrared waste heat, however, it would be a notable signature of these galaxies. In the AGENT formulation, α passes theĜ threshold of 0.25 for all types of galaxies when L max 300 L ⊙ ; for late type galaxies, the threshold is ∼ 10 5 L ⊙ (Figure 4). Most of the starlight is reprocessed when L max is ∼ 30 L ⊙ in earlytype galaxies and 3,000 L ⊙ in late-type galaxies. The waste heat would make these galaxies look like highly obscured AGNs, or starburst galaxies if the waste heat was cold enough -except that the emission comes from an unusually extended region (∼ 10 kpc) rather than a compact core. If instead the waste heat is emitted with habitable temperatures, the galaxies would appear as diffuse sources emitting only MIR and no FIR, a very unusual combination.

CONCLUSIONS
Dyson spheres are hard to build, and they are especially hard to build around bright stars. Yet bright stars are the source of most of the bolometric luminosity in a non-active galaxy. A megastructure-oriented society that would otherwise be Type III may therefore fail to process most of a galaxy's starlight if it is based on the classic Dyson sphere concept. Instead, it might only enclose stars below a certain luminosity threshold L min determined by practical constraints. These societies could be easily missed by previous searches for Type III societies, those searching for vast amounts of waste heat or profound optical dimming. Alternatively, a nearly Type III society might only enclose the brightest stars.
I have developed a stellar population synthesis code that allows me to compute the spectrum of a galaxy that appears to be missing its brightest or dimmest stars. From the output spectra, I can then calculate the observed magnitude of the partially cloaked galaxy to search for signatures that could be sought in photometric surveys. The advantage of using photometric surveys is that they catalog enormous numbers of galaxies. In addition, by searching for magnitude-color signatures of missing stars, we do not need to know the form the waste heat takes or even whether there is waste heat. I calculated the spectra for a variety of SFHs (Figure 1), metallicities, and IMFs.
My general result is that in visible light colors, when 1 L ⊙ L min 1,000 L ⊙ , red galaxies get redder while blue galaxies get bluer. This can be understood from the fact that bright stars tend to be either young, massive, blue stars, or they are red giants. The former are responsible for one peak in a galaxy's spectrum at ultraviolet energies, while the latter are responsible for another peak in visible to NIR. The blue stars are the brightest (up to 10 6 L ⊙ ), while low mass red giants tend to have a peak luminosity at ∼ 1,000 L ⊙ . Thus, late-type galaxies get bluer in the optical because the red giants go "missing", leaving the brighter blue stars. Early-type galaxies get redder because the stars that go "missing" are the brightest, relatively blue dwarfs and the low luminosity, relatively blue subgiants and fainter red giants. In nearinfrared, all galaxies get redder, since starlight at these wavelengths is dominated by red giants, and to a lesser extent, main sequence stars.
Late and intermediate-type galaxies still shine even as L min ≫ 1,000 L ⊙ since they have had recent star formation and extremely luminous young stars. When the threshold luminosity is this high, the colors of galaxies fall along a terminal locus in color-color diagrams. They are roughly as blue as quasars, although they are much dimmer and not compact.
When L min 1 L ⊙ , in contrast, there are only small effects on the colors of a galaxy. The deviations are greatest for early-type galaxies, with no luminous young stars to smother the signal, and in the near-infrared for the same reason.
I also tested the effects of variant mode populations with different parameters. Using the luminosity-to-mass ratio as the threshold instead of simple luminosity leads to similar tracks on CMDs and color-color diagrams. I found that using a bottom-heavy IMF instead of a Chabrier IMF has relatively small effects on the galaxy's colors. Younger galaxies, observed earlier in cosmic history (z ≈ 0.5-1), effectively have later types since star formation was more intense back then, but otherwise behave like contemporary galaxies do. In contrast, the metallicity has relatively strong effects on the appearance of partially cloaked-galaxies. Low metallicity galaxies (Z = 0.1 Z ⊙ ) in particular display much smaller deviations than Solar metallicity galaxies. Hence, partially cloaked low metallicity galaxies may prove difficult to detect. Finally, I found that galaxies with only stars above a threshold L max 1 L ⊙ would appear relatively normal in optical and NIR, even if most of the bolometric luminosity is cloaked. Only with L max smaller than 10 −0.5 L ⊙ do galaxies become unnaturally red. They could also appear extremely bright in mid-or far-infrared from waste heat emission.
Assuming megastructure-building, galaxy-spanning societies exist within the observable Universe, should we expect to find partially cloaked galaxies with these spectra and colors? In this paper, I have assumed that there is one homogeneous threshold luminosity that applies throughout a galaxy. That may not be realistic, since different regions of a galaxy are so distant from each other that they may not be able to coordinate a unified program of megastructure building. In addition, different regions of a galaxy that we observe simultaneously are separated temporally from each other, and the agenda of a galactic society could change with time (as in Hart 1975;Wright et al. 2014a). Instead, it's possible that there are galaxies with patchworks of adjusted stellar populations. They would appear like a mosaic of tiles with diverse colors and brightnesses. They could be found by looking at resolved galaxies, but it would take a more detailed analysis. Over time, these stellar populations would mix together and dilute any signature, unless the stars are being actively steered (as described in Badescu & Cathcart 2006).
Galaxies in the Local Group are close enough that their color-magnitude diagrams can be constructed through direct observation. It should be possible to search among the Group for parts of galaxies that are "missing" stars below (or above) a certain luminosity. There would have to be a way to distinguish artificial engineering from IMF variations.
It's also possible that a galaxy-spanning society would not merely cloak stars, but shape their formation and evolution more directly. This could lead to galaxies with "impossible" types, or stellar phenomena appearing completely out of proportion to their natural val-ues. We could search for galaxies with a large number of hypermassive stars, for example, much greater in mass than the ∼ 100-200 M ⊙ stars we know of. The stellar population of a galaxy might somehow have an unnaturally high metallicity, moving the galaxy off the massmetallicity relation. Rampant starlifting might lead to a galaxy with most of its brighter stars in a planetary nebula phase (Lacki 2016). Artificial stars might be created, with unnatural properties, designed to create astronomical amounts of metals.
There are widescale interventions that we could look for, even if no stars with individually unnatural properties are fabricated. The IMF of a galaxy may be adjusted in unusual ways, producing only stars of a certain mass for millions of years. The SFH may also be adjusted in unnatural ways; for example, a late-type galaxy might completely shut off star-formation for a couple of billion of years despite having a supply of gas, and then resume it at its natural high rate for no apparent reason. Either of these interventions might be detectable for billions of years through a detailed analysis of a galaxy's stellar population.