\documentclass {article}
\usepackage{graphicx}

\title{Searching for Quasi-Dyson Spheres}
\author{Al Globus
\and Dana Backman
\and Fred Witteborn
}

\begin{document}
\maketitle

\begin{quote}
"As the eons advanced, hundreds of thousands of worlds were constructed, all of this type, but gradually increasing in size and complexity. Many a star without natural planets came to be surrounded by concentric rings of artificial worlds. In some cases the inner rings contained scores, the outer rings thousands of globes adapted to life at some particular distance from the Sun." from \textit{Star Maker} by Olaf Stapledon.
\end{quote}

\section{Abstract}

A neighboring star orbited by very large numbers of space colonies hosting water based life may exhibit spectral signatures distiguishable from dust and debris. These signatures depend only on thermodyamics and may be detectable by current or soon-to-be operational instruments, making the existence of very large civilization of orbital space colonies around nearby stars a testable hypothesis. We describe the beginings of a search of online astronomical databases to detect such civilizations.

\section{Introduction}

Assume
\begin{enumerate}
\item there is no technological short-cut to the laws of thermodynamics, as we know them
\item our civilization continues to expand for perhaps a million years, a small fraction of the lifetime of a star
\item we start building orbital space colonies in the next thousand years or so
\end{enumerate}

\noindent
In this case, we might be observable to a civilization orbiting a nearby star possessing instruments similar to what we have today. Turning this around, if civilizations similar to ours a million years hence are common in our stellar neighborhood, we may be able to observe them with current or soon-to-be deployed instruments. Specifically, a star orbited by very large numbers of space colonies may 
have excess emissions in the infrared
or even be dimmed.
Such a star may be described as a Quasi-Dyson Sphere (QDS). Freeman Dyson [Dyson 1959, Dyson 1966] proposed artificial structures completely enclosing a star, but such structures are gravitationally unstable [reference]. However, sufficiently large numbers of orbital colonies around a star would partially block and convert a star's energy. If n\% of a star's energy is blocked, we may say that this star is a n\% QDS.  Given instruments that can detect an n\% QDS, the existence of such civilizations, at least in our stellar neighborhood, becomes a testable, falsafiable hypothesis.

The search for extraterrestrial intelligence (SETI) has been dominated by the attempt to detect radio  signals [reference] on the questionable assumption that other civilizations will attempt deliberate communications and/or that their communication systems are inefficient. While it is true that our present radio frequency communication systems are inefficient in the sense that much of the signal does not reach the intended recipients but is rather broadcast into space, this inefficiency is a function of our current technology and is unlikely to last more than a few centuries or millenia. As a fraction of the multi-billion year life of a star, this is an insignificant length of time. Thus, even if we point our radio telescopes in the right direction, we are unlikely to happen to be at the right time. By contrast, the signatures this paper proposes for detecting QDS should last millions or even billions of years, although only a restricted set of potential civilizations will emit these signals.

\section{Infrared Excess}
One approach to detecting a QDS is to look for the infrared emissions produced by artificial thermal radiators. Assuming there is no work-around to our laws of thermodynamics, colonies must absorb a star's energy (or produce new energy), use it and reject the heat to deep space.  The heat must be rejected at temperatures below utilization temperatures. The higher the temperature the more efficient the heat rejection. For water based life, therefore, the temperature of the heat rejection systems can be assumed to be in the range 273-373K (the temperature of liquid water).  Thus, a QDS star's energy output curve should be somewhat different than a purely natural solar system, with a small artificial peak in the 10-20 micron range. The hight of the peak is related the completeness of the QDS. Once a star with such an infrared excess is found, it is necessary to distinguish between the infrared excess of space colonies and naturally occurring dust or debris. There are two approaches to this discrimination: the temperature range of the source and the age of the star. The temperature of the dust is determined by the distance from the star and the size and composition of the dust. From these parameters the expected spectrum can be calculated. Since any given thermal technology should have an optimal temperature, artificial emissions should be closer to black body radiation. Thus, high spectral resolution data between 10-20 microns, as is available from the Keck infrared instrument [reference], may be able to distinguish between natural debris and large numbers of space colonies. Second, dust is usually associated with younger stars. If our star develops a QDS it will have taken at least 5 billion years. Thus, a reliable means for determining the age of stars would help distinguish QDS from dust. The literature contains at least two attempts to find an infrared excess associated with a QDS.

\begin{enumerate}

\item Jugaku, Noguchi, and Nishimura have searched 53 nearby stars with a 1.26 m infrared telescope in Japan and examined IRAS 
(http://space.gsfc.nasa.gov/astro/iras/iras\_home.html) 
data for 135 more looking for a 10-20 micron infrared excess [Jugaku, Noguchi, and Nishimura 1995]. They claim that the sensitivity of the instruments should be sufficient to detect a 1\% QDS. No candidates have yet been found.  This group has continued this search [Jugaku and Nishimura 1991, 1997, 2000].

\item Slysh [Slysh 1985] examined the IRAS data for 100\% DS candidates, specifically 0507+528 P05, 0453+444 P03, 0536+467 P05, and 0259+601 P02 without finding a candidates, however noted that G 357 .3-1.3 [Gautier et al. 1984] is strong source with a 220K blackbody spectrum and claims this is a good 100\% QDS candidate, however the temperature is suspiciously low. Slysh notes that it is difficult to distinguish a 100\% QDS from circumstellar dust shells around an evolved red giant.
\end{enumerate}

As new instruments become available a search of greater sensitivity becomes possible. For example, the SIRFT (Space Infrared Telescope Facility, see http://sirtf.caltech.edu/) is expected to launch soon. We may examine the capabilities of this instrument for QDS detection by
assuming a cloud of individual space colonies orbiting in a belt
where equilibrium T = 300 K.  Assuming the colonies would
not be confined to the same orbital plane because that limits the
number of colonies and also makes them shadow each other.  If
the are distributed about an ecliptic mid-plane the only way to do
that is to have them in orbits inclined to the ecliptic, i.e.
each individual colony will oscillate vertically about the mid-plane
as it orbits the star.  This oscillation
should not have a large amplitude otherwise the colonies would have
large velocities relative to each other and it would be difficult to
move personnel and supplies between colonies.  Traffic control problems also suggest 
small colony-colony relative velocity dispersion is desirable.

Assuming the torus/belt of colonies has a vertical extent
of order 1/1000 of their stellar orbit radius, i.e. 150,000 km
at 1 AU.  That makes cross-velocities between colonies of order
$V_{orb} / 1000 \approx 30 {meters}/{sec}$.  Further, assume the torus is
filled with colonies to the point that the "optical depth" for
a ray from the star to infinity would be no more than 0.1, i.e. viewed
from a given colony at most 10 percent of the sun is blockd by other colonies.

Following from these assumptions about 'vertical' extent of the
colony swarm and upper limit on mutual shadowing, the
total cross-sectional area of all the colonies around a solar-type
star would be:  $2 \pi \times10^{-4} AU^2$,  or $1.4 \times 10^{19} m^2$, which is
$10^5$ times the land area of Earth.   The total bolometric luminosity
of stellar radiation intercepted by the colonies and re-radiated in
the IR would be $5 \times 10^{-5} L_{sun}$.

The contrast to the star at specific wavelengths are found in table 1.

\begin{table*}
\begin{center}
\begin{tabular}{|c|c|} \hline
wavelength (microns) &total $F_{nu}$ from colonies relative to G2 photosphere (\%) \\ \hline
15  & 7 \\ \hline
24   &  16 \\ \hline
70    &  33 \\ \hline
\end{tabular}
\caption{????}
\end{center}
\end{table*}

To detect the IR excess from the colonies with 5-sigma
precision and do it in 500 sec integration time, the pre-launch
sensitivities for SIRTF imply the stellar photosphere must be brighter
than 2.3 mJy at 24 microns.  For a solar-type star this means distance
less than 120 pc. 24 microns appears to be the best compromise between rising relative
flux from the 300 K colonies vs. decreasing relative sensitivity of SIRTF.


\section{Temperature/Luminosity Anomaly}
Another approach to finding an n\% QDS, albeit with high n, is to search for main sequence stars with low luminosity relative to other main sequence stars of the same temperature. A main sequence star's mass determines it's temperature [reference] and therefor it's absolute magnitude.  If the distance to a star is accurately know, it's absolute luminosity can be calculated from it's apparent brightness. The European Hipparchos satellite (http://archive.ast.cam.ac.uk/hipp/) calculated very accurate distance to nearby stars using parallax. We have extracted 299 stars from the Hipparchos catalogue that exhibit low luminosity relative to other stars with similar temperatures. The stars were selected to have:
 
\begin{eqnarray}
p & \ge & 20 \\
T_c & = & \frac{7300}{B-V + 0.73} \\
T_c & \le & 8000 \\
M_h & \le & 27.31 - 0.002149 T_c \\
M_h & \ge & 17.805 - 0.001681 T_c
\end{eqnarray}

\noindent
where $p$ is the Hipparchos parallax, $B-V$ is from the Hipparchos catalogue, and $M_h$ is the Hipparchos (absolute) magnitude based on apparent magnitude and the Hipparchos distance. $T_c$ is the temperature as calculated from $B-V$.  
B-V is the difference between the magnitudes of an object in the
B (blue, centered at 450 nanometers) and V (visual, centered at 550
nanometers) passbands defined by astronomers.  One measures
the B and V magnitudes of an target object with respect to a network
of standard stars.  The B and V magnitudes are each logarithmic
expressions of flux reaching the Earth from an object, thus B-V
is a difference of two logarithms, representing the ratio of fluxes received from the object
at 450 versus 550 nm wavelength.  B-V is sometimes called the color,
or color index, of an object.  The (counter-intuitive) definition of
the magnitude scale means that increasing B-V means more flux at 550
relative to 450 nanometers, thus an object with B-V = 0.63 (this is
the Sun's color index) appears redder than an object with B-V = 0.00
(the star Vega, which is blue-white to the eye).  In fact Vega is
the fiducial object, T = 9700 K, its color defines B-V = 0.00.
Blackbodies and stars cooler than Vega have positive
color indices and hotter objects have negative color indices.  There
is a 1-1 mapping of blackbody temperatures to B-V color index values expressed by equation 2.


\begin{figure*}
\centering
%\scalebox{0.5}[0.38]{\includegraphics{allStars}}

\caption{All of the stars from the Hipparchos catalogue that satisfy eq. 1.}
\end{figure*}
\begin{figure*}
\centering
\scalebox{0.5}[0.38]{\includegraphics{candidateStars}}

\caption{All of the stars from the Hipparchos catalogue that satisfy eq. 1-5.  These are candidates for further evaluation.}
\end{figure*}

\section{Conclusion}

With the advent of internet accessible archives of astronomical data, such as the Hipparchos catalogue and the IRAS database [reference], it is possible to design computer searches for candidate QDSs. With new, more powerful infrared instruments becoming available, such as SIRTF [reference], pledged to put their data on the net, new opportunities for inexpensive, computerized search for QDS will become available.  Combined with a search for passive signatures of large scale orbital civilizations, we now have a testable hypothesis that can lead the quantification of an upper limit to the density and size of QDS in our stellar neighborhood.

\section{Acknowledgements}

\section{References}

\noindent
[Dyson 1959] Freeman J. Dyson "Search for Artificial Sources of Infrared Radiation," \textit{Science}, volume 131, page 1667 (1959).
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\noindent
[Dyson 1966] Freeman J. Dyson "The Search for Extraterrestrial Technology." in R. E. Marshak, editor, \textit{Perspectives in Modern Physics: Essays in Honor of Hans Bethe}. New York: John Wiley \& Sons 1966. 
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\noindent
[Gautier et al. 1984] T. Gautier et al., {\textit Ap J. (Letters)}, volume 278, page L57
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\noindent
[Jugaku and Nishimura 1991] Jugaku, J., and Nishimura, S. "A Search for Dyson Spheres Around Late-Type Stars in the IRAS Catalog," in \textit{Bioastronomy: The Search for Extraterrestrial Life}, J. Heidemann and M. J. Klein (Eds.), Lectures Notes in Physics 390, pp. 295-298. Berlin: Springer-Verlag. 
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\noindent
[Jugaku, Noguchi, and Nishimura 1995] Jun Jugaku, Kunio Noguchi, and Shiro Nishimura, "A Search for Dyson Spheres Around Late-Type Stars in the Solar Neighborhood," {\textit Progress in the Search for Extraterrestrial Life}, G. Seth Shostak editor, ASP Conference Series, Volume 74, 1995, pages 381-385.
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\noindent
[Jugaku and Nishimura 1997] Jugaku, J., and Nishimura, S. "A Search for Dyson Spheres Around Late-Type Stars in the Solar Neighborhood. II," No. 161 in IAU Colloquium, pp. 707-709. Bologna: Editrice Compositori.
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\noindent 
[Jugaku and Nishimura 2000] Jugaku, J., and Nishimura, S. "A Search for Dyson Spheres Around Late-Type Stars in the Solar Neighborhood. III," in G. Lemarchand and K. Meech, eds. \textit{A New Era in Bioastronomy}, vol. 213 of ASP Conference Series. San Francisco: Astronomical Society of the Pacific.
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\noindent
[Slysh 1985] V. I. Slysh, "A Search in the Infrared to Microwave for Astroengineering Activity," {\textit The Search for Extraterrestrial Life: Recent Developments}, M. D. Papagiannis, editor, IAI, 1985, pages 315-319.


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