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 ~10¹³ 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 deg² 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 ×10¹⁷ 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 10¹⁴ pc^-3-one order of magnitude greater than Whipple's estimate.