Office of the Secretary of Defense: 02_Physical_Constraints_Paper

4
et al. 2021). This implies that self-replicating probes could reach ∼ 1010 habitable planets around Sun-like stars in less
than a billion years. Since most stars formed more than a billion years before the Sun (Madau & Dickinson 2014), it
is possible that other technological civilizations predated ours by the amount of time needed for their devices to reach
Earth.
Here we can use time as another constraint. In the propulsion scheme where an interstellar self-replicating au-
tonomous system is travelling at 10−4c, the above analysis argues that ∼ 1010 habitable planets around Sun-like stars
could be reached within ∼ 0.5 Gyr. These self-replicating systems would necessarily be looking for water in order
to generate fuel, and would necessarily have to take into account the relative motion of the planet in order to reach
escape velocities after completion of the exploration mission. 1 Gyr ago Earth had water coverage and some simple
algae plant life. In the extreme, detection of Earth 1 Gyr ago from a technological civilization near the center of the
Milky Way 0.5 Gyr ago would be needed to decide to intentionally navigate here. In doing so, the navigators would
need to plan for where the solar system would be located 1 Gyr in the future from their point of observation. Under
such considerations, it becomes more likely that either: (i) such interstellar probes are the result of an unintended
arrival to a planetary system; (ii) a technological civilization much closer to us than the center of the Milky Way; or
(iii) an alternative propulsion scheme like the mothership/probe system is used.
A detailed statistical analysis by Ezell & Loeb (Ezell & Loeb 2022) showed that the inferred abundance of probes
is distinctly different in case of objects being targeted towards particular regions of the galaxy, specifically habitable
zones containing planets. ‘Oumuamua was detected at a distance of ≈ 0.2 AU from Earth, and it passed through the
habitable zone of our solar system. The estimated total number of ‘Oumuamua-like objects would then fall by a factor
of ∼ 2 × 1010 in the case of targeted probes compared to probes on random trajectories.
The interstellar meteor IM1 had an estimated diameter of ∼ 0.45 m and velocity of 60 km s−1, but it was detectable
when it burned up within the atmosphere of the Earth (Siraj & Loeb 2022a). The estimated detection rate for
meter-size interstellar meteors is at least ∼ 0.1yr−1 (Siraj & Loeb 2022a), resulting in a local density estimate of
∼ 106 AU−3 = 1022 pc−3. This implies 8 × 1034 IM1-like objects bound by the thin disk of the Milky Way. However,
if objects with the properties of IM1 were targeted towards habitable zones containing planets, the required number
of such objects is merely ∼ 4 × 1024. IM2 had a similar inferred number density to IM1 and a velocity of 40 km s−1
relative to the Local Standard of Rest (Siraj & Loeb 2022a). This implies ≈ 3 × 1034 IM2-like objects, with a reduction
to 1.5 × 1024 if such objects were targeted towards habitable zones.
The actual abundance of interstellar objects can be calibrated through future surveys such as the Legacy Survey
of Space and Time (LSST) on the Vera C. Rubin Observatory in Chile. Parallax data from the James Webb Space
Telescope may identify the nature and 3D trajectory of more ‘Oumuamua-like or smaller interstellar objects crossing
through or trapped within the solar system.
Below we show that any supersonic motion by such devices through the Earth’s atmosphere would inevitably be
accompanied by bright optical emission and detectable characterization signatures.
4. OPTICAL EMISSION
An object made of known matter with a frontal cross-sectional area A, moving at a supersonic speed, v, must create
a bow shock in the Earth’s atmosphere and dissipate a mechanical power,
P ≈ 1
2 Aρav3 = 1.5TW(A/10 m2)(ρa/0.3 kg m−3)(v/10 km s−1)3, (1)
where ρa is the ambient air density which depends on elevation, normalized here by a representative value at an
altitude of 10 km.
Data on meteors shows that the fraction of the kinetic power which is radiated away in the optical band is ≈ 10%
[see equation (1) and figure 2 in Brown et al. (Brown et al. 2002)], implying an optical luminosity,
Lopt ≈ 150GW(A/10m2)(ρa/0.3 kg m−3)(v/10 km s−1)3. (2)
For a path length ℓ, this luminosity will persist over a period of time, ∼ 1s × (ℓ/10 km)/(v/10 km s−1). Since
Lopt ∝ Av3, the fireball luminosity scales with inferred distance to the 5-th power because A scales as distance squared
and v scales as distance.
5. OTHER OBSERVABLE SIGNATURES02Page determined to be Unclassified
Reviewed by Chief of Staff, AARO
IAW FY24 NDAA, Section 1841 (a)(1)(C)
Date: 2/5/2025