Determining an Upper Limit on the Density of Interstellar Comets

Bonnie Meinke
Mentor:
Robert Jedicke

Current theories of Solar System formation predict that
comets that accrete in a
protostellar nebula are later ejected by interactions with
the newly formed
giant planets. In such a process a large fraction (99%)
of all comets would be
ejected from the new planetary system, subsequently creating
a large population
in the interstellar medium. Due to the observational absence
of such objects,
Whipple (1975) set this limit to be ~10^{13} pc^{–3},
although he, and others
since (e.g., Stern 1990) contend that this liberal upper
limit could be reduced
by several orders of magnitude given a continued observational
absence in a
survey covering large areas of sky to faint magnitudes.
Since the early 1990s,
the University of Arizona's Spacewatch survey at Kitt Peak
has conducted such
wide-field observations to V ~ 21.7. Using the
breadth of observations and
the efficiency of detection of such objects in the Spacewatch
system, we refine
the upper limit on the number density of ISCs. Our new
limit on the
ISC space density has implications on the formation
of planetary
systems.

We have parameterized the number density of ISCs as ρ = ρ_{o}
10^{α(H-Ho)}, where H is the absolute
magnitude of an object, α is a
constant representing the slope of the number density
as a function of H,
and ρ_{o} is the space density at H_{o}.
We will use
H_{o} = 19.1, which
corresponds to a 1 km object with a typical cometary
albedo of p = 0.04.
The value of α is undetermined in our analysis
but, for a
self-similar equilibriated collision cascade (Dohnyany,
1969) in which a
set of objects that have strengths independent of their
size collisionally
grind against one another, the analytically expected
value of α is
0.5. It is expected that the slope is steeper (larger α)
for objects undergoing accretion as appropriate to the
ejected ISCs.

Considering the amount of sky covered by Spacewatch observations
and the
detection efficiency for objects as a function of their
rates of motion and
apparent magnitude, we determined the 97% upper C.L. on
the number of ISCs as a
function of the slope parameter α as shown in the
accompanying figure.
In the period corresponding to this study Spacewatch covered
about 4200 deg^{2}
in 1399 sky scans. From one scan, at α
= 0.5, the 97% upper limit on the cumulative number density of interstellar
comets larger than 1 km is 3.6 ×10^{17} pc^{-3} or ~ 40 AU^{-3}. This number is reduced over three orders of magnitude when the
efficiencies of all 1399 scans are considered, rendering
a final limit on the order of 10^{14} pc^{-3}-one order of magnitude greater than Whipple's estimate.