# Sunscreen: Photometric Signatures of Galaxies Partially Cloaked in Dyson
Spheres

Brian C. Lacki1 Breakthrough Listen, Astronomy Department, University of
California, Berkeley, CA, USA<EMAIL_ADDRESS>
###### Abstract

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 $L_{\rm
min}$ are cloaked. I find the photometric signatures of galaxies with $L_{\rm
min}\leq 1\ \textrm{L}_{\odot}$ are minor, especially for blue, galaxies with
continuing star formation. Larger luminosity thresholds ($\gtrsim 30\
\textrm{L}_{\odot}$) 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 $L_{\rm min}$ 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.

extraterrestrial intelligence — astrobiology — galaxies: photometry —
galaxies: peculiar

††software: CMD 3.0††software: CMD

##  1 Introduction

The search for astroengineering is growing into a prominent branch of the
broader Search for Extraterrestrial Intelligence (SETI; Tarter 2001).
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; Sagan & Newman, 1983; 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 stars. Just as traditional SETI can survey many more star systems (e.g.,
$10^{6}$ in the Breakthrough Listen survey; Worden et al. 2017) than searches
for extraterrestrial life, while hinging on intelligence commonly evolving
from life, so astroengineering searches 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, 1985; Ćirković, 2006; Wright et al., 2014a;
Lacki, 2015, 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; Armstrong & Sandberg, 2013; Olson, 2015; Hooper, 2018).

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).

Waste heat from Type III societies has been sought in mid-infrared (MIR;
characteristic of $300\ \textrm{K}$ habitable Dyson spheres) and microwaves
(characteristic of very cold $3\ \textrm{K}$ smart dust), based on the
proposed temperatures of megastructures (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 $\sim 2$ 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 or Ĝ), which looked for extended MIR emission in galaxies
observed by the Wide-field Infrared Survey Explorer (WISE Wright et al.,
2014b; Griffith et al., 2015). Ĝ found no signs of a Type III society
capturing $\geq 85\%$ 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 $\sim
10\text{--}100\ \textrm{K}$ (glowing in far-infrared) or $\gtrsim 600\
\textrm{K}$, the waste heat would not have been found yet (Lacki 2016; see
also Bradbury 2000; Osmanov & Berezhiani 2018). Perhaps they broadcast it in
neutrinos or some other nigh-undetectable particle, or beam it anisotropically
away from us111Beaming 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., 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 $\gtrsim
1,000\ \textrm{L}_{\odot}?$. 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 search strategy 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 $1\ \textrm{L}_{\odot}$ were shrouded – or $0.01\
\textrm{L}_{\odot}$ or $100\ \textrm{L}_{\odot}$? 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 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 $m\approx
28$ ($M\approx 0$) depth in its outer disk (Dalcanton et al., 2012). Even if
every M, K, and G dwarf ($M_{V}\gtrsim 5$; 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 $m\approx 28$ would only detect stars with
$M\lesssim 0$, 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. Spectroscopic
techniques for determining the abundance of dwarf stars in a galaxy could be
useful (Conroy & van Dokkum, 2012), but remain somewhat controversial in that
they imply bottom-heavy IMFs in massive elliptical galaxies (van Dokkum &
Conroy, 2010), in dispute with X-ray binary and lensing models (Smith & Lucey,
2013; Peacock et al., 2017). I therefore focus on integrated 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 luminosity-to-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 color-
magnitude 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.

##  2 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. This code will be available from the UC Berkeley SETI program’s
Github site.222https://github.com/UCBerkeleySETI The simulated spectroscopic
and photometric data will also be made available.

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 $M_{\star}$, 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:

$\frac{d^{2}N}{dM_{\star}dt}=\frac{dP}{dM_{\star}}\frac{dN_{\star}}{dt}={\rm
IMF}(M_{\star})\times\frac{{\rm SFH}(t)}{\langle M_{\star}\rangle}.$ (1)

I employed a Chabrier (2003) IMF for my baseline calculations, although I also
consider a bottom-heavy IMF as well, motivated by claims of the latter IMF in
elliptical galaxies (as in van Dokkum & Conroy, 2010; Spiniello et al., 2014;
Martín-Navarro et al., 2015; La Barbera et al., 2017). The bottom-heavy IMF
used in my calculations:

$\frac{dP}{dM_{\star}}=\left[\frac{dP_{\rm Chabrier}}{dM_{\star}}(1\
\textrm{M}_{\odot})\right]\left(\frac{M_{\star}}{1\
\textrm{M}_{\odot}}\right)^{-3.0},$ (2)

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 $1\ \textrm{M}_{\odot}$ stars is equal to its value for the Chabrier
IMF, because the red giants around this mass dominate the light of modern
quiescent galaxies.

A galaxy’s stellar luminosity distribution depends strongly on the amount of
recent star formation compared to stellar mass (proportional to specific star
formation). I consider eight SFHs (Figure 1) that bracket the range of
qualitative behaviors that are encountered in the bulk of main-sequence and
quiescent galaxies. These span a range of luminosity-weighted stellar ages
from $1$ to $13\ \textrm{Gyr}$, with specific star formation rates decreasing
from $0.2$ to $0\ \textrm{Gyr}^{-1}$. At one extreme are galaxies whose star
formation has not slowed down, called _continuing-SF_ (star formation)
galaxies here. They are typically bluer galaxies with late-type morphology.
They are represented by a constant SFH. I focus on two ages for this
population: 100 Myr, representative of an ongoing starburst, and 13.5 Gyr, for
a normal star-forming galaxy.333I also included a time-averaged version of the
mean empirical SFH that Weisz et al. (2014) derived for Local Group dwarf
irregular (dIrr) galaxies, in which the SFR increases during the past several
Gyr. This model population behaved similarly with respect to cloaking as the
old constant SFR galaxy.

Most galaxies have ongoing star formation at a level much smaller than at
$z\approx 1\text{--}2$: these are dubbed here _declining-SF_ galaxies. I
represent declining-SF galaxies with the simulated SFHs from the simulations
in (Behroozi et al., 2013, B13) for galaxies in dark matter halos with total
masses $10^{11}$, $10^{12}$, $10^{13}$, and
$10^{14}~{}\textrm{M}_{\odot}$.444I use these models, which are quantified by
total rather than stellar mass, because they are easily available. They
correspond to stellar masses of $10^{8.8}$, $10^{10.4}$, $10^{10.9}$, and
$10^{11.1}\ \textrm{M}_{\odot}$, respectively.

Lastly, most stellar mass at $z=0$ is now located in galaxies with no star-
formation, referred to as _quenched_ galaxies in this paper. I consider two
quenched galaxy SFHs: (1) an instantaneous burst of age $13.5\ \textrm{Gyr}$
and initial mass $10^{11}\ \textrm{M}_{\odot}$; and (2) the SFH that the
ATLAS3D project derived for $M_{\rm JAM}=10^{11}\text{--}10^{11.5}\
\textrm{M}_{\odot}$ early-type galaxies, for which there is a spread in
stellar ages. (McDermid et al., 2015, M15).555JAM stands for Jeans Anisotropic
Multi-Gaussian Expansion, a dynamical model of galaxies, and $M_{\rm JAM}$ is
approximately the stellar mass of a galaxy (Cappellari et al., 2013). M15
derived additional SFHs for other JAM masses, but their behavior would fall in
the range spanned by the declining-SF and the pure burst SFHs. The SFHs in M15
are not physical star-formation rates, but the rate the present-day stellar
mass built up. I converted to SFR using the prescription of Leitner & Kravtsov
(2011) for a Chabrier IMF. Of course, the general behavior of the SFHs can
apply to smaller populations like star clusters. Throughout the paper, I use
the constant SFH as representative of a continuing-SF galaxy and the M15 SFH
as a fiducial quenched galaxy, in both cases with age 13.5 Gyr.

Figure 1: Star-formation rates used in this work: a constant SFH with age 100
Myr (dark blue) and 13.5 Gyr (bright blue); the B13 SFHs for halo masses of
$10^{11}$, $10^{12}$, $10^{13}$, $10^{14}\ \textrm{M}_{\odot}$ (light grey to
dark grey, respectively); and the M15 SFH for $M_{\rm
JAM}=10^{11}\text{--}10^{11.5}\ \textrm{M}_{\odot}$ (dark red).

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 isochrones that are available online (Bressan et al., 2012;
Marigo et al., 2017).666At http://stev.oapd.inaf.it/cgi-bin/cmd My models use
a grid of stellar ages with $4.0\leq\log_{10}t\leq 10.13$, with the upper
limit being the oldest available population from the web interface.777I used
the default Reimers mass loss parameter value of $0.2$. The age increases in
$\log_{10}t$ steps of $0.01$, fine enough to resolve “AGB boosting” at 1.6 Gyr
(Girardi et al., 2013). 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 $0.1\
\textrm{Z}_{\odot}$, $1\ \textrm{Z}_{\odot}$, and $2\ \textrm{Z}_{\odot}$.
These isochrones include stars in pre main sequence to the Therally Pulsating
Asymptotic Giant Branch (TP-AGB) or carbon burning phases, but they do not
include post-AGB evolution (Bressan et al., 2012; Chen et al., 2015; Marigo et
al., 2017).888I ignored the single post-AGB data point terminating some of the
isochrones, because it’s only there for compatibility with some codes and its
luminosity is deliberately set to $\sim 0$, as stated in the CMD 3.0 FAQ.

Figure 2: Color-magnitude diagrams generated for stellar populations with my
code, and the effects of only including stars within chosen luminosity ranges:
$L\leq 1\ \textrm{L}_{\odot}$ (black), $1\leq L\leq 10^{3}\
\textrm{L}_{\odot}$ (yellow), $10^{3}\ \leq L\leq 10^{4.5}\
\textrm{L}_{\odot}$ (sky blue), and $10^{4.5}\leq L$ (reddish-purple). The
shown diagrams are for a representative continuing-SF (left) and quenched
(right) SFH.. Darker shading indicates more stars, using a logarithmic scale.

Finally, the spectrum of the galaxies require the spectra 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 $F_{\nu}$) are converted into luminosity spectra $L_{\nu}$ by
assuming stars are spherical with $L_{\nu}^{\star}=4\pi R_{\star}^{2}F_{\nu}$,
using the isochrone-supplied radii $R_{\star}$. 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. The code
models these with blackbody spectra.

From these ingredients, I calculate the total luminosity spectrum of a model
galaxy as

$L_{\nu}({\rm galaxy})=\int\int\frac{d^{2}N}{dM_{\star}dt}\times
L_{\nu}^{\star}(t,M_{\star},Z_{\star})\times\Theta(L_{\star},M_{\star}dM_{\star})dt.$
(3)

$\Theta$ 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. The code also allows for cuts on mass and by (approximate) stage of
stellar evolution.

Table 1: Photometry Systems Used

System | Filters | Type | Normalization | Reference
---|---|---|---|---
FUSE | FUV, NUV | AB | Given in reference | Morrissey et al. (2005)
Johnson-Cousins | $UBVRI$ | Vega | alpha_lyr_stis_008 | Bessell (1990)
SDSS | $ugriz$ | AB | $3631\ \textrm{Jy}$ | Doi et al. (2010)
Dark Energy Survey | $grizY$ | AB | $3631\ \textrm{Jy}$ | Burke et al. (2018)
PanSTARRS-1 | $grizyw$ | AB | $3631\ \textrm{Jy}$ | Tonry et al. (2012)
LSST | $ugrizy$ | AB | $3631\ \textrm{Jy}$ | LSST Science Collaboration et al. (2009)
_Gaia_ |  $G$, $G_{\rm BP}$, $G_{\rm RP}$ | Vega | alpha_lyr_mod_002 | Carrasco et al. (2016); Evans et al. (2018)
2MASS | $JHK_{s}$ | Vega | Given in reference | Cohen et al. (2003); Skrutskie et al. (2006)
UKIRT | $ZYJHK$ | Vega | alpha_lyr_stis_008 | Hewett et al. (2006)
_Spitzer_ IRAC | IRAC-1, -2, -3, -4 | AB | $3631\ \textrm{Jy}$ | Fazio et al. (2004)
WISE | W1, W2, W3, W4 | Vega | Given in reference | Wright et al. (2010)

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 downloaded the LSST filter throughput curves from the LSST Github site at
https://github.com/lsst/throughputs/tree/master/baseline.

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
$T_{x}(\nu)$ for a filter band $x$ (and the atmosphere, if relevant), an
absolute magnitude ${\cal M}_{x}$ in that band is calculated using

${\cal
M}_{x}=\displaystyle-2.5\log_{10}\frac{\displaystyle\int\frac{1}{h\nu}\frac{L_{\nu}}{4\pi
D_{0}^{2}}T_{x}(\nu)d\nu}{\displaystyle\int\dot{N}_{\nu}^{0}T_{x}(\nu)d\nu},$
(4)

where $D_{0}=10\ \textrm{pc}$ and $\dot{N}_{\nu}^{0}$ 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 $F_{\nu}=3631\ \textrm{Jy}$, 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.999ftp://ftp.stsci.edu/cdbs/current_calspec 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. Two stellar color-magnitude diagrams (CMDs) constructed by a
modification of the code are shown in Figure 2, for an old continuing-SF and a
quenched galaxy.

Because they are purely stellar models with no chemical evolution, my models
have several limitations.

  * •

Dust extinction in the Milky Way and the host galaxy is not modeled. The Milky
Way extinction towards the Galactic Poles is typically around $A_{V}\approx
0.05\text{--}0.1$ (Schlegel et al., 1998). Extinction in other galaxies
depends on their morphology and inclination. Face-on spiral galaxies at $z=0$
typically have $\langle A_{B}\rangle\approx 0.2\text{--}0.5$, while early-type
galaxies have $\langle A_{B}\rangle\approx 0.05\text{--}0.1$ (Calzetti, 2001).
The extinction is much greater in edge-on gas-rich galaxies and galaxies at
$z\gtrsim 1$. Reddening is particularly acute in the ultraviolet, with the
majority of UV light absorbed in star-forming galaxies (Lisenfeld et al.,
1996; Bell, 2003). The attenuation is patchy, however, because of the density
fluctuations in the multiphase ISM. High mass stars are initially veiled in
gaseous star forming regions and are preferentially extincted, but their
feedback excavates bubbles in these clouds over Myrs.

  * •

Nor do I include interstellar dust emission, which dominates the MIR and FIR
SEDs of star-forming galaxies(Purcell, 1976; Draine & Li, 2001; Li & Draine,
2001; Hwang et al., 2010).

  * •

Although my code calculates the megastructures’ thermal emission, I will not
discuss the results, since we do not know what temperature they would be.
Temperatures greater than $1,000\ \textrm{K}$ are necessary to contribute to
the galaxy’s SED at wavelengths less than $2\ \mu\textrm{m}$ (around K band).

  * •

I do not include nebular emission lines like H$\alpha$ 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), as 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, 2017). These
stars can have either oxygen- or carbon-rich atmospheres, affecting their
SEDs. Intermediate mass TP-AGB stars, with ages of $\sim 1\ \textrm{Gyr}$, 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) and near their centers (Henry & Worthey,
1999). 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 are not modeled. These include extreme
horizontal branch (HB) stars, suspected to be the source of the UV excess in
quiescent galaxies below 200 nm (Han et al., 2007), and supersoft X-ray
sources that contribute to extreme UV luminosity (Kahabka & van den Heuvel,
1997).

For these reasons, the models should not be considered accurate at MIR and
longer wavelengths, or in far-ultraviolet or shorter wavelengths.

##  3 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 on the
main sequence (blue line, top). The other peak, mostly consisting of the red
and near-infrared light from older red giants (red line, top), reaches its
maximum near $1\ \mu\textrm{m}$. The blue peak becomes more prominent as the
SFH progresses from quenched to continuing-SF galaxies, because the increasing
number of high-mass stars contribute more to the luminosity. In addition, an
optical plateau in the SED extending to $\sim 400\ \textrm{nm}$ is adjoined to
the red peak in continuing-SF galaxies.101010Note the flat top of the red peak
in Figure 3 for these galaxies, compared to the rounded top for the quenched
galaxies. Dwarf stars dominate this plateau’s luminosity when $\lambda\lesssim
650\ \textrm{nm}$, and this contribution is mostly from A and F dwarfs with
$1\ \textrm{M}_{\odot}\lesssim M\lesssim 3\ \textrm{M}_{\odot}$.

Figure 3: Stellar spectra of natural galaxies with different SFHs, from
continuing-SF to quenched. The contributions to the SED from pre-MS and MS
stars (blue) and post-MS stars (red) are also shown. In every case, the
stellar populations have a Chabrier IMF and a metallicity of $1\
\textrm{Z}_{\odot}$.

Figure 4: Stellar spectra of partially and cloaked (bottom) galaxies for
several values of $L_{\rm min}$. Within each subpanel, from top to bottom and
darker to lighter lines, these are the unscreened spectra and then $L_{\rm
min}=1\ \textrm{L}_{\odot}$, $10\ \textrm{L}_{\odot}$, $100\
\textrm{L}_{\odot}$, and $1,000\ \textrm{L}_{\odot}$. In every case, the
stellar populations have a Chabrier IMF and a metallicity of $1\
\textrm{Z}_{\odot}$.

Screening stars with luminosity below $L_{\rm min}$ (Figure 4) changes the
shape of the integrated SED. A small $L_{\rm min}\leq 1\ \textrm{L}_{\odot}$
means only low luminosity (GKM) dwarfs are cloaked. These stars are brightest
at wavelengths longer than $\sim 400\ \textrm{nm}$, so they contribute mostly
to the red peak and the optical plateau. Screening only these stars has
insignificant effects on the ultraviolet luminosity of a galaxy (Figure 4). At
visible to near-infrared wavelengths, a screening threshold $L_{\rm min}=1\
\textrm{L}_{\odot}$ leads to a $<20\%$ drop in specific luminosity, with a
more pronounced drop for quenched galaxies. Thus, galaxies missing these stars
would not have qualitatively different spectral energy distributions and
finding them must require careful analysis.

Figure 5: How the unscreened stellar bolometeric luminosity of a galaxy
depends on $L_{\rm min}$. The different SFHs are a 100 Myr old constant SFR
galaxy (top, dark blue), constant SFR after 13.5 Gyr (medium blue), B13 SFHs
for halo masses of $10^{11}$, $10^{12}$, $10^{13}$, and $10^{14}\
\textrm{M}_{\odot}$ (from top to bottom, grey), the M15 quenched SFH (dark
red), and a 13.5 Gyr old burst (bottom, medium red). The solid lines are for a
metallicity of $1\ \textrm{Z}_{\odot}$, while the dot–long-dashed lines are
for $2\ \textrm{Z}_{\odot}$, and the dotted lines are for $0.1\
\textrm{Z}_{\odot}$. All shown functions are for a Chabrier IMF and a stellar
population age of $13.5\ \textrm{Gyr}$, except for the 100 Myr old star-
forming population. Also marked as yellow bands are the luminosity ranges for
the SGB, HB, and TRGB phases for an isochronal population with age $13.5\
\textrm{Gyr}$ and Solar metallicity.

More dramatic changes in a galaxy’s starlight occur if $L_{\rm min}\gg 1\
\textrm{L}_{\odot}$. Figure 5 depicts the fraction of a galaxy’s stellar
luminosity that remains unscreened as a function of $L_{\rm min}$ for various
SFHs, denoted $1-\alpha$ in the Ĝ AGENT formalism. When $L_{\rm min}=1\
\textrm{L}_{\odot}$, this fraction remains at $80\text{--}99.9\%$, but it
falls to $64\text{--}99.7\%$ for $L_{\rm min}=10\ \textrm{L}_{\odot}$,
$41\text{--}98\%$ for $L_{\rm min}=100\ \textrm{L}_{\odot}$, and
$16\text{--}92\%$ for $L_{\rm min}=1,000\ \textrm{L}_{\odot}$. In all cases,
quenched galaxies fade more than galaxies with recent star formation because
they lack the additional light from high and intermediate-mass stars.

The increase in $\alpha$ does not occur steadily as $L_{\rm min}$ 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 5 mark the
luminosity of stars in the subgiant branch (SGB), horizontal branch or red
clump (RC), and tip of the RGB (TRGB) for an isochronal stellar population of
age $13.5\ \textrm{Gyr}$. In quenched galaxies, the first sudden growth in
$\alpha$ occurs as $L_{\rm min}$ approaches the main sequence turn-off
luminosity, followed by a plateau for the luminosity range occupied during the
short-lived SGB phase. Then, $\alpha$ slowly increases with $L_{\rm min}$ as
stars along the red giant branch are cloaked, but there’s a sudden jump near
$40\ \textrm{L}_{\odot}$ where nearly all the stars in the red clump (low mass
horizontal branch; Girardi 2016) are shrouded. Roughly $10\%$ of a quenched
galaxy’s bolometric luminosity is concentrated in the red clump stars. The
increase in $\alpha$ continues until the TRGB is reached (c.f., Salaris et
al., 2002), leaving only a few TP-AGB stars providing a residual luminosity.
With declining- and continuing-SF galaxies, these features are much more
subtle, because much of the luminosity is provided by bluer main sequence
stars that do not have “clumps” or breaks in their luminosity distribution.

Figure 6: The ratio of screened $L_{\nu}$ to the unscreened specific
luminosity, measuring the relative strength of the cloaking effect at each
wavelength for each SFH. A value of $1$ implies none of the galaxy’s
luminosity at that wavelength is screened, whereas a value of $0$ implies all
of it is screened. Effects are shown for $L_{\rm min}$ of
$0.1\textrm{L}_{\odot}$ (black), and $1$, $10$, $100$, and $1,000\
\textrm{L}_{\odot}$ (same line styles as Figure 4).

As seen in Figure 4, increasing $L_{\rm min}$ up to $\sim 1,000\
\textrm{L}_{\odot}$ erodes the red peak while leaving the blue peak mostly
untouched. The fading is most significant in the visible parts of the spectrum
($300\text{--}800\ \textrm{nm}$), as demonstrated when the ratio of the
screened and the unscreened spectra are plotted (in Figure 6). For the flat
SFH galaxies, as $L_{\rm min}$ grows from $10$ to $1,000\ \textrm{L}_{\odot}$,
A and F dwarfs are cloaked. The optical plateau adjoined to the red peak is
screened, leaving the integrated spectrum with two sharp peaks from OB dwarfs
and bright red giants. Meanwhile, in the same $L_{\rm min}$ range, the
luminosity at $\sim 300\ \textrm{nm}$ is virtually extinguished for quenched
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 $2.5-2.6\ \mu\textrm{m}$ as $L_{\rm min}$ 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.

Figure 7: Stellar spectra of partially cloaked galaxies with constant SFH
where stars below a luminosity-to-mass ratio are cloaked. From top to bottom,
we have $(L/M)_{\rm min}=0$, $1\ \textrm{L}_{\odot}/\textrm{M}_{\odot}$, $10\
\textrm{L}_{\odot}/\textrm{M}_{\odot}$, $100\
\textrm{L}_{\odot}/\textrm{M}_{\odot}$, and $1,000\
\textrm{L}_{\odot}/\textrm{M}_{\odot}$.

Figure 8: The luminosity-weighted distribution of stars in $L$ versus $(L/M)$
for an old continuing-SF galaxy (blue) and a quenched galaxy (red). Main
sequence stars mostly fall on $L\propto M^{4}$ (blue), while the majority of
post-main sequence stars have $M\approx 1\ \textrm{M}_{\odot}$.

I also considered the effects of using the luminosity-to-mass ratio as a cut
rather than the stellar luminosity.111111I used the initial mass of a star
when making this cut, which is appropriate if ETIs build megastructures before
mass loss sets in. 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 $(L/M)_{\rm min}$ increases largely
looked the same as when $L_{\rm min}$ is used (Figure 7). The reason is simply
because there are two distinct kinds of bright stars contributing most of the
light, and these groups have different colors. Furthermore, each population
lies on a nearly monotonic relation between $L$ and $L/M$. As seen in Figure
8, the main sequence stars have $L\propto M^{4}$, while most post main-
sequence stars have $M\approx 1\ \textrm{M}_{\odot}$ since low mass stars
dominate the IMF. Thus, whether looking in UV/blue light – where main sequence
stars dominate – or red/infrared light – where the red giants dominate –
there’s a one-to-one relation between $L$ and $L/M$, and which one is used as
the cut does not matter much. This monotonicity fails when both populations
contribute equally to the spectrum (as for continuing-SF galaxies near $0.5\
\mu\textrm{m}$), resulting in the galaxies being somewhat redder and fainter
when $(L/M)_{\rm min}$ is used instead of $L_{\rm min}$. It can also fail for
young stellar populations, including starbursts that are $\ll 100\
\textrm{Myr}$ old. Stellar populations of age $\sim 100\ \textrm{Myr}$ also
contain low mass pre-main sequence stars that have not yet settled on the
$L\propto M^{4}$ relation.

##  4 Photometry of Partially Cloaked Galaxies

Photometric surveys provide large datasets of galaxy colors and brightnesses
(e.g., Adelman-McCarthy et al., 2007; LSST Science Collaboration et al.,
2009). 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 $L_{\rm min}\gg 1\
\textrm{L}_{\odot}$.

Figure 9: The fraction of flux in representative bandpasses that remains
unscreened. Shown are GALEX NUV (top left), $u_{\rm SDSS}$ (top center),
$g_{\rm SDSS}$ (top right), $r_{\rm SDSS}$ (middle left), $i_{\rm SDSS}$
(middle center), $z_{\rm SDSS}$ (middle right), $H_{\rm 2MASS}$ (bottom left),
$\textrm{K}_{s_{\rm 2MASS}}$ (bottom center), and W2 (bottom right). Line
styles are the same as in Figure 5.

The declining luminosity in various filter bands as $L_{\rm min}$ increases
are plotted in Figure 9. I generalize the AGENT parameterization in Wright et
al. (2014b) to introduce the $\alpha_{x}$ value, the fraction of starlight
screened in some band $x$.

As described in Section 3, the effects of partial cloaking on a galaxy can be
understood from the relative contributions of main-sequence and post-MS stars.
The main sequence forms a smooth luminosity distribution, with bright stars
being bluer and younger, and it emits a galaxy’s light in blue bands (like
$u$). In a continuing-SF galaxy, therefore, increasing $L_{\rm min}$ causes
the dwarf stars’ integrated light to smoothly fade and become bluer, as
$L_{\rm min}$ slides up the main sequence (Figure 2). In quenched-SF galaxies,
all dwarf stars are cloaked once $L_{\rm min}$ passes the main sequence turn-
off, and the flux in blue bands is extinguished precipitously.

Post-MS stars have a more complicated luminosity distribution, resulting in
more complicated evolution in redder bands (like $z$) as $L_{\rm min}$
increases. The red giant and asymptotic giant branches together form a rough
sequence with bright stars being redder. But horizontal branch stars
complicate matters, since the low-mass HB stars tend to lie near the red
clump, with similar luminosities and colors. As $L_{\rm min}$ increases, the
giant stars’ integrated light fades and becomes redder, but there tends to be
a sudden drop in flux near $30\ \textrm{L}_{\odot}$ when red clump stars are
cloaked. Most low-mass red giants have $L<3,000\ \textrm{L}_{\odot}$, although
a few TP-AGB stars are brighter. Of course, actual galaxies are a combination
of these two groups.

Figure 10: Color magnitude diagram for partially cloaked galaxies. Unscreened
galaxies start at the terminus of its track marked by nearly-overlapping solid
points. The effect of increasing $L_{\rm min}$ is to move the galaxy in color
space along the track. Tracks have the same colors for each SFH as Figure 5. A
circle surrounds the points on the tracks with a threshold of $1\
\textrm{L}_{\odot}$, the triangle is around the point for a threshold
luminosity of $1,000\ \textrm{L}_{\odot}$, and the squares are at the red
clump luminosity ($10^{1.7}\ \textrm{L}_{\odot}$). Small filled dots mark out
powers of ten in $L_{\rm min}/\textrm{L}_{\odot}$, while small open dots mark
out half-powers of ten. On left, the absolute magnitudes of the model galaxies
are shown; on right, the change in $r$-band magnitudes are plotted. For
comparison, a sample of SDSS objects are plotted on left: $z<0.1$ galaxies in
grey shading and contours, $z\geq 0.1$ galaxies in reddish-purple shading, and
QSOs in sky blue shading.

Ultimately, when searching for these galaxies in a photometric survey, we are
interested in how partial cloaking moves a galaxy on color-magnitude (CMD) and
color-color diagrams. I show a visible-light CMD (Figure 10) and three color-
color diagrams (Figure 11)that demonstrate the qualitative range of behaviors
partial cloaking caused as compared to natural galaxies. To show how the
screened galaxies stand out from natural galaxies, I downloaded a sample of
500,000 objects in the SDSS spectroscopic database for SDSS Data Release 14,
which are broadly classed into galaxies, quasars, and stars.121212I performed
a query using the SkyServer,
http://cas.sdss.org/dr14/en/tools/search/SQS.aspx, retrieving the top 500,000
objects found in the spectroscopic database with clean redshifts and clean
photometry. I separated the galaxies into those with $z<0.1$ and those with
$z\geq 0.1$, but otherwise did not perform any distance selection. Nor did I
select on luminosity or object class. The sample should be a uniformly random
selection among objects with spectra in SDSS DR 14 that pass the simple data
quality cuts. Natural galaxies at $z=0$ clearly separate into the red sequence
and blue cloud in optical diagrams (Strateva et al., 2001; Baldry et al.,
2004, among many others). In infrared color-color diagrams (represented here
by $(g-i)\text{--}(g-z)$ and $(r-i)\text{--}(i-z)$), the natural $z=0$ galaxy
populations tend to be stretched into narrow lines, providing a relatively
clean way to find anomalous galaxies.

A galaxy with a fixed stellar population forms a track on these diagrams as
$L_{\rm min}$ increases, as shown in the Figures. The shapes of these tracks
can also be understood from the relative contribution of dwarf and red giant
stars to variation in $\alpha_{x}$. Galaxies with $L_{\rm min}\approx 0$ start
with positions on these diagrams near observed galaxies with similar SFHs:
among the blue cloud for continuing-SF galaxies (although the 100 Myr constant
SFR model is bluer than most observed galaxies; dark blue); in the green
valley for declining-SF galaxies; and in the red sequence for quenched
galaxies. My model galaxies are somewhat offset from the observed galaxies by
around 0.1–0.2 magnitudes. The offset seems to be especially noticeable in
diagrams with infrared colors, and is largest for continuing-SF galaxies.
Galaxies do not move appreciably until $L_{\rm min}\gtrsim 1\
\textrm{L}_{\odot}$ because the faintness of these stars cannot compensate for
their larger number (indicated by the pile up of points near the start of the
track).

Figure 11: Effects on the colors of partially cloaked galaxies in color-color
diagrams. The yellow shading represents stars selected from SDSS; all other
notations are the same as in Figures 5 and 10. Tracks have the same colors for
each SFH as Figure 5.

As brighter stars are cloaked, though, the tracks leave the red sequence and
blue cloud where most $z=0$ galaxies reside. In the $r\text{--}(g-r)$ CMD
(Figure 10), quenched and declining-SF galaxies veer towards red colors
because their luminosity is dominated by red giants. Continuing-SF galaxies
drift towards blue colors as red giants and low to intermediate-mass MS stars
are cloaked, while O and B dwarfs remain unscreened. Ultimately, all galaxies
with ongoing star formation start becoming bluer when all the red giants are
cloaked. Galaxies with recent star-formation end up along a terminal locus in
color-color diagrams (Figure 11), with blue colors reminiscent of quasars.

Observationally, the effects of increasing $L_{\rm min}$ can be summed up as:
_red galaxies get redder (especially in red bands), and blue galaxies get
bluer (especially in blue bands)._ In infrared colors, continuing SF galaxies
also initially get redder because the post-MS stars dominate in these bands –
only when all red giants are screened do these galaxies become bluer again..
The tracks from continuing-SF and quenched galaxies leave the main
concentrations of galaxies on the color-color diagrams, implying partially
cloaked galaxies with $L_{\rm min}\gtrsim 1\ \textrm{L}_{\odot}$ can be
selected with a color cut. Quenched galaxies have particularly large
excursions, becoming over a magnitude redder or more than the red sequence
once the red clump is screened (squares on Figure). The excursions are also
significant in the infrared color-color diagrams simply because stars and most
$z=0$ galaxies are so concentrated in these diagrams. Deviations from the
stellar line on $(g-i)\text{--}(g-z)$ plot arise from the changing balance of
the unscreened stellar populations that produce optical light and those
producing NIR light.

Despite these variations, the altered galaxies share color-color space with
other source populations. The extra-blue galaxies tend to have similar colors
as quasars, while the extra-red galaxies tend to have similar colors as high-
redshift galaxies. Other criteria must therefore be implemented to select out
these potential false positives: quasars are bright and compact, while
partially cloaked galaxies would be dim (as seen in the CMD) and are extended;
spectroscopically measured redshifts can weed out red, high-$z$ galaxies.

###  4.1 Variants

With the code, it is possible to investigate how galaxies with a variety of
different stellar populations are affected by partial cloaking. Among the
other effects I considered are metallicity, galaxy age, IMF, the use of
$(L/M)$ instead of $L$ as a selection cut, and the effects of cloaking the
brightest stars only. These variant tracks are plotted for a continuing-SF
galaxy and a quenched SFH galaxy in Figure 12.

Some of these parameters have little qualitative effect on the tracks of
galaxies on color-color and color-magnitude diagrams. For the reasons
described in Section 3, using luminosity-to-mass ratio as a cut (dotted line)
instead of luminosity does not substantially change the tracks. Changing the
population age – using the rest-frame colors of a galaxy as it was billions of
years ago instead of today – conceivably could matter, since the main sequence
turn-off location is shifted to more massive, bluer stars. For continuing-SF
galaxies, changing the population age to 6 Gyr ($10^{9.8}\ \textrm{yr}$) or 3
Gyr ($10^{9.5}\ \textrm{yr}$) has little effect (blue lines). Some currently
quenched galaxies were in fact still forming stars at these times, and $z=0$
declining-SF galaxies had more vigorous star formation back then, so these
galaxies would have behaved as though their luminosity-weighted ages were
smaller. Despite the larger main sequence turn-off mass, a galaxy with a pure
burst SFH at $z\approx 1$ would behave much like one at present day with
regards to partial cloaking. Another change with an effect similar to altering
the SFH is using a bottom-heavy IMF. It favors old, low mass red giants at the
expense of young blue dwarfs, making the galaxy behave as if its SFH were more
quenched (red line).

It is disputed whether or not a galaxy’s metallicity affects its chances of
hosting intelligent life (Gonzalez et al., 2001), but starfaring ETIs might
spread to a low metallicity galaxy and engineer it. While metallicity does not
generally affect the shapes of tracks on these diagrams, it does control how
far they venture from the bulk of $z=0$ galaxies. Low metallicity galaxies,
with $Z=0.1\ \textrm{Z}_{\odot}$, have brighter and bluer stars, with
$\alpha_{x}$ declining more slowly and more synchronously in optical bands
(Figure 9). Thus, these galaxies simply do not wander much on color-color
diagrams as $L_{\rm min}$ increases, and their tracks generally do not leave
the bulk of $z=0$ galaxies (solid black line). The fluxes from high
metallicity galaxies (here, $Z=2\ \textrm{Z}_{\odot}$), in contrast, are more
sensitive to partial cloaking, as demonstrated by their wider excursions on
the color-color plots (dash-dotted black line).

Figure 12: The tracks of partially cloaked galaxies on color-color diagrams
when I vary the assumptions. Representatives of old continuing-SF (left) and
quenched (right) galaxies are shown. Plotted variations are: fiducial (grey
solid), brightest stars screened (dashed), $(L/M)_{\rm min}$ as the threshold
for screening (dotted), low metallicity (black solid), high metallicity (black
dot-dashed), a bottom-heavy IMF (red solid), and galaxy ages of $6\
\textrm{Gyr}$ (pale blue) and $3\ \textrm{Gyr}$ (bright blue). The small,
filled pentagons mark the unscreened start of the track. Also shown are
unscreened colors and magnitudes for IMFs with masses below $1$, $2$, and $5\
\textrm{M}_{\odot}$ (marked by the turquoise circled numbers) and a young
starburst (turquoise star).

All other notations are the same as in Figures 5, 10, and 11.

One variation does display qualitatively different behavior: cloaking stars
brighter than a threshold luminosity $L_{\rm max}$ (dashed grey line). There
could be various motivations for preferentially shrouding bright stars. 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 application is to transmit
vast amounts of information across interstellar distances (Kardashev, 1964).

Interestingly, screening the very brightest stars in a stellar population
doesn’t affect its simulated photometry much. Stars with $L\gg 10^{3}\
\textrm{L}_{\odot}$ are characteristic of young stellar populations and are
present mainly in galaxies with recent star formation. Even in the old
constant-SFR galaxy model, they account for only 60% of the bolometric
luminosity (Figure 5), so decreasing $L_{\rm max}$ from $\infty$ to $1,000\
\textrm{L}_{\odot}$ increases the bolometric magnitude by at most $1$. As seen
in Figure 9, these stars emit the majority of the light in ultraviolet but a
minority of visible and infrared light. Thus, unless a galaxy has had a recent
or ongoing starburst, the changes in its colors induced by $L_{\rm max}\gg
1,000\ \textrm{L}_{\odot}$ screening do not stand out against the natural
variance in galaxy colors.

Even as $L_{\rm max}$ decreases to $1\ \textrm{L}_{\odot}$, the tracks do not
verge into unnatural regions of color-color space. For these luminosity
thresholds, the brightest and reddest post-MS stars are screened, as well as
more and more relatively blue dwarfs. The remaining stellar population,
forming the lower mass main sequence and the lower luminosity red giant
branch, combine together to maintain integrated colors that are not wildly
divergent from natural galaxies. There is a reversal of the normal rule-of-
thumb for color deviations in this $L_{\rm max}$ range – red galaxies get
slightly bluer and blue galaxies get slightly redder, especially in redder
bands – but the effect is comparatively minor. Only when $L_{\rm max}<1\
\textrm{L}_{\odot}$, leaving only cool dwarfs unscreened, does the integrated
stellar light become unnaturally red for all galaxies.

If the radiation is processed into infrared waste heat, however, it would be a
notable signature of these galaxies. In the AGENT formulation, $\alpha$ passes
the Ĝ threshold of $0.25$ for all types of galaxies when $L_{\rm max}\gtrsim
300\ \textrm{L}_{\odot}$; for old continuing-SF galaxies, the threshold is
$\sim 10^{5}\ \textrm{L}_{\odot}$ (Figure 5). Most of the starlight is
reprocessed when $L_{\rm max}$ is $\sim 30\ \textrm{L}_{\odot}$ in quenched
and $3,000\ \textrm{L}_{\odot}$ in old continuing-SF galaxies. The waste heat
would make these galaxies look like highly obscured active galactic nuclei
(AGNs), or starburst galaxies if the waste heat was cold enough – except that
the emission comes from an unusually extended region ($\sim 10\ \textrm{kpc}$)
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.

###  4.2 Degeneracies with Alternate IMFs and SFHs?

Some of the unnatural alterations to galaxy photometry described here are
degenerate with unusual IMFs. Because the main sequence forms a monotonic
relation with mass, screening parts of the main sequence is equivalent to
suppressing star formation in that mass range. A galaxy with $L_{\rm
min}\lesssim 1\ \textrm{L}_{\odot}$ looks much the same in the optical or UV
as one with no low mass dwarfs; one with $L_{\rm max}\gg 1,000\
\textrm{L}_{\odot}$ looks much like a galaxy where massive stars never formed
or have already died out.

In Figure 12 the circled numbers represent simulated photometry of galaxies
with all star formation suppressed below $1$, $2$, and $5\
\textrm{M}_{\odot}$, corresponding to main-sequence turnoff ages of roughly
10, 1, and 0.1 Gyr. The bluer optical colors of these bottom-light IMF
galaxies are comparable to those of partially cloaked continuing-SF galaxies.
A very young starburst can also have extreme blue colors, as shown by the star
point in the figures denoting a starburst that is only 1 Myr old. However, the
alternate IMFs suppress the red giant population of these galaxies – there are
no redward excursions like those seen for partially cloaked quenched galaxies,
particularly in infrared colors. Unnaturally red galaxies would require a
narrow peak in the IMF around $1\ \textrm{M}_{\odot}$.

Any level of cloaking can be emulated by adjusting the joint IMF-SFH
distribution arbitrarily. Stars of a given age and mass tend to all have
nearly the same luminosity: that’s what allows us to use isochrones in the
first place. So by adjusting the joint age-mass distribution for all stars
with a given luminosity, any degree of screening can be accommodated. In that
case, only non-optical methods could provide evidence for screening
specifically, like dynamical estimates of mass to light or waste heat
searches. When $L_{\rm min}\approx 10\text{--}1,000\ \textrm{L}_{\odot}$,
though, the joint distributions are likely to be contrived because of the
importance of red giants in this luminosity range. As noted before, red giants
tend to have nearly the same mass because the post-MS phase of stellar
evolution is relatively short.

More generally, it is an empirical fact that most galaxies don’t have the
extreme colors of the more divergent partially cloaked galaxies. Any galaxy
with such a strange IMF and SFH would stand out in a photometric survey. While
we could not be entirely sure that partial cloaking is responsible, it would
be a clear sign that something bizarre is going on and that it merits a closer
look.

##  5 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 $L_{\rm min}$
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).

My general result is that in visible light colors, when $1\
\textrm{L}_{\odot}\lesssim L_{\rm min}\lesssim 1,000\ \textrm{L}_{\odot}$,
_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
$10^{6}\ \textrm{L}_{\odot}$), while low mass red giants tend to have a peak
luminosity at $\sim 1,000\ \textrm{L}_{\odot}$. Thus, continuing-SF galaxies
get bluer in the optical because the red giants go “missing”, leaving the
brighter blue stars. Quenched galaxies get redder after negligible evolution
when $L_{\rm min}\ll 1\ \textrm{L}_{\odot}$ because the stars that next go
“missing” as $L_{\rm min}$ increases are the relatively hot G dwarfs, the
subgiants, and then the relatively hot red giants at the base of the RGB. In
near-infrared, all galaxies get redder, since starlight at these wavelengths
is dominated by red giants, and to a lesser extent, low mass main sequence
stars, just like in quenched galaxies.

When $L_{\rm min}\lesssim 1\ \textrm{L}_{\odot}$, there are only small effects
on the colors of a galaxy. The deviations are greatest for quenched 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. Most importantly, galaxies where only the brightest stars are
cloaked behave qualitatively different. They have colors typical of $z=0$
galaxies for luminosity cuts above $1\ \textrm{M}_{\odot}$ and then become
unnaturally red when only faint dwarf stars remain.

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 values. We could search for galaxies with a
large number of hypermassive stars, for example, much greater in mass than the
$\sim 100\text{--}200\ \textrm{M}_{\odot}$ stars we know of. The stellar
population of a galaxy might somehow have an unnaturally high metallicity,
moving the galaxy off the mass-metallicity 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 main sequence 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.

I wish to acknowledge the support of the Breakthrough Listen program. Funding
for _Breakthrough Listen_ research is sponsored by the Breakthrough Prize
Foundation131313https://breakthroughprize.org/. In addition, I acknowledge the
use of NASA’s Astrophysics Data System and arXiv. I also thank the referee for
their thorough review of this paper. The plots use data from the Sloan Digital
Sky Survey. Funding for the Sloan Digital Sky Survey IV has been provided by
the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of
Science, and the Participating Institutions. SDSS acknowledges support and
resources from the Center for High-Performance Computing at the University of
Utah. The SDSS web site is www.sdss.org. SDSS is managed by the Astrophysical
Research Consortium for the Participating Institutions of the SDSS
Collaboration including the Brazilian Participation Group, the Carnegie
Institution for Science, Carnegie Mellon University, the Chilean Participation
Group, the French Participation Group, Harvard-Smithsonian Center for
Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins
University, Kavli Institute for the Physics and Mathematics of the Universe
(IPMU) / University of Tokyo, the Korean Participation Group, Lawrence
Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP),
Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für
Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik
(MPE), National Astronomical Observatories of China, New Mexico State
University, New York University, University of Notre Dame, Observatório
Nacional / MCTI, The Ohio State University, Pennsylvania State University,
Shanghai Astronomical Observatory, United Kingdom Participation Group,
Universidad Nacional Autónoma de México, University of Arizona, University of
Colorado Boulder, University of Oxford, University of Portsmouth, University
of Utah, University of Virginia, University of Washington, University of
Wisconsin, Vanderbilt University, and Yale University.

## References

  *   * Adelman-McCarthy et al. (2007) Adelman-McCarthy, J. K., Agüeros, M. A., Allam, S. S., et al. 2007, ApJS, 172, 634
  * Andrews et al. (2013) Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129
  * Annis (1999) Annis, J. 1999, Journal of the British Interplanetary Society, 52, 33
  * Armstrong & Sandberg (2013) Armstrong, S., & Sandberg, A. 2013, Acta Astronautica, 89, 1
  * Atek et al. (2011) Atek, H., Siana, B., Scarlata, C., et al. 2011, ApJ, 743, 121
  * Badescu & Cathcart (2006) Badescu, V., & Cathcart, R. B. 2006, Acta Astronautica, 58, 119
  * Baldry et al. (2004) Baldry, I. K., Glazebrook, K., Brinkmann, J., et al. 2004, ApJ, 600, 681
  * Behroozi et al. (2013) Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57
  * Bell (2003) Bell, E. F. 2003, ApJ, 586, 794
  * Bessell (1990) Bessell, M. S. 1990, PASP, 102, 1181
  * Bessell (2005) Bessell, M. S. 2005, ARA&A, 43, 293
  * Bohlin & Gilliland (2004) Bohlin, R. C., & Gilliland, R. L. 2004, AJ, 127, 3508
  * Bradbury (2000) Bradbury, R. J. 2000, “Matrioshka Brains”, accessed 16 Mar 2016,
<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.692.6584
&rep=rep1&type=pdf>

  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Brin (1983) Brin, G. D. 1983, QJRAS, 24, 283
  * Burke et al. (2018) Burke, D. L., Rykoff, E. S., Allam, S., et al. 2018, AJ, 155, 41
  * Calzetti (2001) Calzetti, D. 2001, PASP, 113, 1449
  * Cappellari et al. (2013) Cappellari, M., McDermid, R. M., Alatalo, K., et al. 2013, MNRAS, 432, 1862
  * Cardamone et al. (2009) Cardamone, C., Schawinski, K., Sarzi, M., et al. 2009, MNRAS, 399, 1191
  * Carrasco et al. (2016) Carrasco, J. M., Evans, D. W., Montegriffo, P., et al. 2016, A&A, 595, A7
  * Carrigan (2009) Carrigan, R. A., Jr. 2009, ApJ, 698, 2075, arXiv:0811.2376
  * Carrigan (2012) Carrigan, R. A. 2012, Acta Astronautica, 78, 121
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763, arXiv:astro-ph/0304382
  * Charlot & Longhetti (2001) Charlot, S., & Longhetti, M. 2001, MNRAS, 323, 887
  * Chen et al. (2015) Chen, Y., Bressan, A., Girardi, L., et al. 2015, MNRAS, 452, 1068
  * Chennamangalam et al. (2015) Chennamangalam, J., Siemion, A. P. V., Lorimer, D. R., & Werthimer, D. 2015, New Astron., 34, 245
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102
  * Ćirković (2006) Cirkovic, M. M. 2006, arXiv:astro-ph/0606102
  * Ćirković (2009) Ćirković, M. M. 2009, Serbian Astronomical Journal, 178, 1, arXiv:0907.3432
  * Ćirković (2015) Ćirković, M. M. 2015, Serbian Astronomical Journal, 191, 1, arXiv:1601.05112
  * Cohen et al. (2003) Cohen, M., Wheaton, W. A., & Megeath, S. T. 2003, AJ, 126, 1090
  * Condon (1992) Condon, J. J. 1992, ARA&A, 30, 575
  * Conroy & van Dokkum (2012) Conroy, C., & van Dokkum, P. 2012, ApJ, 747, 69
  * Conroy (2013) Conroy, C. 2013, ARA&A, 51, 393
  * Criswell (1985) Criswell, D. R. 1985, in _Interstellar Migration and the Human Experience_ , ed. B. R. Finney, & E. M. Jones (Berkeley, California: University of California Press), 50
  * Dalcanton et al. (2009) Dalcanton, J. J., Williams, B. F., Seth, A. C., et al. 2009, ApJS, 183, 67
  * Dalcanton et al. (2012) Dalcanton, J. J., Williams, B. F., Lang, D., et al. 2012, ApJS, 200, 18
  * Doi et al. (2010) Doi, M., Tanaka, M., Fukugita, M., et al. 2010, AJ, 139, 1628
  * Draine & Li (2001) Draine, B. T., & Li, A. 2001, ApJ, 551, 807
  * Dyson (1960) Dyson, F. J. 1960, Science, 131, 1667
  * Evans et al. (2018) Evans, D. W., Riello, M., De Angeli, F., et al. 2018, arXiv:1804.09368
  * Fazio et al. (2004) Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10
  * Garrett (2015) Garrett, M. A. 2015, A&A, 581, L5, arXiv:1508.02624
  * Girardi et al. (2013) Girardi, L., Marigo, P., Bressan, A., & Rosenfield, P. 2013, ApJ, 777, 142
  * Girardi (2016) Girardi, L. 2016, ARA&A, 54, 95
  * Gonzalez et al. (2001) Gonzalez, G., Brownlee, D., & Ward, P. 2001, Icarus, 152, 185
  * Griffith et al. (2015) Griffith, R. L., Wright, J. T., Maldonado, J., et al. 2015, ApJS, 217, 25, arXiv:1504.03418
  * Han et al. (2007) Han, Z., Podsiadlowski, P., & Lynas-Gray, A. E. 2007, MNRAS, 380, 1098
  * Haqq-Misra & Baum (2009) Haqq-Misra, J. D., & Baum, S. D. 2009, Journal of the British Interplanetary Society, 62, 47
  * Hart (1975) Hart, M. H. 1975, QJRAS, 16, 128
  * Henry & Worthey (1999) Henry, R. B. C., & Worthey, G. 1999, PASP, 111, 919
  * Hewett et al. (2006) Hewett, P. C., Warren, S. J., Leggett, S. K., & Hodgkin, S. T. 2006, MNRAS, 367, 454
  * Hooper (2018) Hooper, D. 2018, arXiv:1806.05203
  * Horowitz & Sagan (1993) Horowitz, P., & Sagan, C. 1993, ApJ, 415, 218
  * Hwang et al. (2010) Hwang, H. S., Elbaz, D., Magdis, G., et al. 2010, MNRAS, 409, 75
  * Johnson et al. (2010) Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905
  * Jugaku & Nishimura (2004) Jugaku, J., & Nishimura, S. 2004, in IAU Symp. 213, Bioastronomy 2002: Life Among the Stars, ed. Norris, R. & Stootman, F. (San Francisco, CA: Astronomical Society of the Pacific), 437
  * Kahabka & van den Heuvel (1997) Kahabka, P., & van den Heuvel, E. P. J. 1997, ARA&A, 35, 69
  * Kardashev (1964) Kardashev, N. S. 1964, Soviet Ast., 8, 217
  * Kardashev (1985) Kardashev, N. S. 1985, in IAU Symp. 112, The Search for Extraterrestrial Life: Recent Developments, ed. Papagiannis, M. D. (Dordrecht: D. Reidel Publishing Co.), 497
  * La Barbera et al. (2017) La Barbera, F., Vazdekis, A., Ferreras, I., et al. 2017, MNRAS, 464, 3597
  * Lacki (2015) Lacki, B. C. 2015, arXiv:1503.01509
  * Lacki (2016) Lacki, B. C. 2016, arXiv:1604.07844
  * Leitner & Kravtsov (2011) Leitner, S. N., & Kravtsov, A. V. 2011, ApJ, 734, 48
  * Lejeune et al. (1997) Lejeune, T., Cuisinier, F., & Buser, R. 1997, A&AS, 125, 229
  * Li & Draine (2001) Li, A., & Draine, B. T. 2001, ApJ, 554, 778
  * Lisenfeld et al. (1996) Lisenfeld, U., Völk, H. J., & Xu, C. 1996, A&A, 306, 677
  * LSST Science Collaboration et al. (2009) LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, arXiv:0912.0201
  * Maddox et al. (1960) Maddox, J., Anderson, P., Sloane, E. A., & Dyson, F. J. 1960, Science, 132, 250
  * Maraston (2005) Maraston, C. 2005, MNRAS, 362, 799
  * Maraston et al. (2006) Maraston, C., Daddi, E., Renzini, A., et al. 2006, ApJ, 652, 85
  * Marigo et al. (2008) Marigo, P., Girardi, L., Bressan, A., et al. 2008, A&A, 482, 883
  * Marigo et al. (2017) Marigo, P., Girardi, L., Bressan, A., et al. 2017, ApJ, 835, 77
  * Martín-Navarro et al. (2015) Martín-Navarro, I., Pérez-González, P. G., Trujillo, I., et al. 2015, ApJ, 798, L4
  * McDermid et al. (2015) McDermid, R. M., Alatalo, K., Blitz, L., et al. 2015, MNRAS, 448, 3484
  * Morrissey et al. (2005) Morrissey, P., Schiminovich, D., Barlow, T. A., et al. 2005, ApJ, 619, L7
  * Olson (2015) Olson, S. J. 2015, arXiv:1507.05969
  * Osmanov & Berezhiani (2018) Osmanov, Z., & Berezhiani, V. I. 2018, arXiv:1804.04157
  * Peacock et al. (2017) Peacock, M. B., Zepf, S. E., Kundu, A., et al. 2017, ApJ, 841, 28
  * Pickles (1998) Pickles, A. J. 1998, PASP, 110, 863
  * Purcell (1976) Purcell, E. M. 1976, ApJ, 206, 685
  * Rayner et al. (2009) Rayner, J. T., Cushing, M. C., & Vacca, W. D. 2009, ApJS, 185, 289
  * Sagan & Walker (1966) Sagan, C., & Walker, R. G. 1966, ApJ, 144, 1216
  * Sagan & Newman (1983) Sagan, C., & Newman, W. I. 1983, QJRAS, 24, 113
  * Salaris et al. (2002) Salaris, M., Cassisi, S., & Weiss, A. 2002, PASP, 114, 375
  * Schlegel et al. (1998) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Slysh (1985) Slysh, V. I. 1985, in IAU Symp. 112, The Search for Extraterrestrial Life: Recent Developments, ed. Papagiannis, M. D. (Dordrecht: D. Reidel Publishing Co.), 315
  * Smith & Lucey (2013) Smith, R. J., & Lucey, J. R. 2013, MNRAS, 434, 1964
  * Spiniello et al. (2014) Spiniello, C., Trager, S., Koopmans, L. V. E., & Conroy, C. 2014, MNRAS, 438, 1483
  * Strateva et al. (2001) Strateva, I., Ivezić, Ž., Knapp, G. R., et al. 2001, AJ, 122, 1861
  * Tarter (2001) Tarter, J. 2001, ARA&A, 39, 511
  * Timmes et al. (1995) Timmes, F. X., Woosley, S. E., & Weaver, T. A. 1995, ApJS, 98, 617
  * Timofeev et al. (2000) Timofeev, M. Y., Kardashev, N. S., & Promyslov, V. G. 2000, Acta Astronautica, 46, 655
  * Tipler (1980) Tipler, F. J. 1980, QJRAS, 21, 267
  * Tonry et al. (2012) Tonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750, 99
  * Tremonti et al. (2004) Tremonti, C. A., Heckman, T. M., Kauffmann, G., et al. 2004, ApJ, 613, 898
  * Tully & Fisher (1977) Tully, R. B., & Fisher, J. R. 1977, A&A, 54, 661
  * van Dokkum & Conroy (2010) van Dokkum, P. G., & Conroy, C. 2010, Nature, 468, 940
  * Villarroel et al. (2016) Villarroel, B., Imaz, I., & Bergstedt, J. 2016, AJ, 152, 76, arXiv:1606.08992
  * Voros (2014) Voros, J. 2014, arXiv:1412.4011
  * Weisz et al. (2014) Weisz, D. R., Dolphin, A. E., Skillman, E. D., et al. 2014, ApJ, 789, 147
  * Worden et al. (2017) Worden, S. P., Drew, J., Siemion, A., et al. 2017, Acta Astronautica, 139, 98
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868-1881
  * Wright et al. (2014a) Wright, J. T., Mullan, B., Sigurdsson, S., & Povich, M. S. 2014a, ApJ, 792, 26, arXiv:1408.1133
  * Wright et al. (2014b) Wright, J. T., Griffith, R. L., Sigurdsson, S., Povich, M. S., & Mullan, B. 2014b, ApJ, 792, 27, arXiv:1408.1134
  * Yun et al. (2001) Yun, M. S., Reddy, N. A., & Condon, J. J. 2001, ApJ, 554, 803
  * Zackrisson et al. (2015) Zackrisson, E., Calissendorff, P., Asadi, S., & Nyholm, A. 2015, ApJ, 810, 23, arXiv:1508.02406