Such disks have been observed around other stars, and these disks are thought to be very commonplace To form planetary systems, small solid particles which condense out of the cooling gas of the primitive solar nebula must around young stars with masses similar to that of the Sun aggregate together to form larger bodies. Centimeter-sized par- (Beckwith and Sargent 1993). Recent detections of planeticles can grow out of micrometer-sized grains; planets can tary companions around stars such as 51 Pegasi (Mayor form from the coagulation of kilometer-sized planetesimals. and Queloz 1995), 70 Virginis (Marcy and Butler 1996), The formation of stable, long-lived kilometer-sized objects from and 47 Ursae Majoris (Butler and Marcy 1996) suggest centimeter-sized particles is, however, not so straightforward.
that planet formation may be a rather ubiquitous process.
Some sort of surface sticking force is needed to hold these
In these theories of planet formation, 10 4 -km terrestrial aggregates together against rotational forces as well as collisions planets and 10 4 -km outer planet cores must form from in a turbulent solar nebula. We have performed experiments to determine the surface sticking force of water frosts under a the population of micrometer-sized grains that condense variety of ambient conditions. Our primary results are listed (Prinn and Fegley 1989) out of the cooling gaseous disk below.
orbiting the central star. The aggregation of small objects 1. The structure of the frost is critical in determining its into large clusters must therefore play an important role sticking properties; thin, porous frosts are more likely to adhere in the formation of planets and has been a topic of investithan are thick, dense frosts.
gation for more than two decades (Safronov 1969, Kerridge 2. Sticking forces range up to 250 dyn/mm 2 . and Vedder 1972, Hartmann 1978, Weidenschilling 1984, 3. Temperature fluctuations can increase the sticking force 1987, Weidenschilling and Cuzzi 1993). To reach millimeter by significant amounts. sizes, researchers have used models in which van der Waals
- The frost bond acts like a spring: it stretches before breaking, with the displacement proportional to the applied force. bonding between the grains provides weak binding forces Measured spring constants for many different water frosts clus- (Weidenschilling 1980, Chokshi et al. 1993, Blum and ter between 10 5 and 10 6 dyn cm Ψ1 (over a total area of 78 mm 2 ). Mu Β¨nch 1993). However, for an aggregate to grow larger and Based on these findings, we suggest that frosts of volatiles eventually form a planetesimal (a kilometer-sized object), such as water could provide the necessary surface sticking some sort of surface sticking force above and beyond van mechanism in some low-temperature regions of the solar der Waals bonding is required in the centimeter-to-meter nebula. Β© 1997 Academic Press size range to hold the growing body together against collisions with other particles (Weidenschilling and Cuzzi 1993). We propose that frosts which form on the surfaces of small 1. INTRODUCTION particles in the outer nebula provide this sticking force.
From observations of molecular abundances in comets, Current theories hold that the planets formed from a disk of gas and dust orbiting the Sun (e.g., Cameron 1978, which are considered to be essentially unaltered remnants 539