We propose a new scenario for compound chondrule formation named as “ fragment-collision model , ” in the framework of the shock-wave heating model .
A molten cm-sized dust particle ( parent ) is disrupted in the high-velocity gas flow .
The extracted fragments ( ejectors ) are scattered behind the parent and the mutual collisions between them will occur .
We modeled the disruption event by analytic considerations in order to estimate the probability of the mutual collisions assuming that all ejectors have the same radius .
In the typical case , the molten thin ( \sim 1 { mm } ) layer of the parent surface will be stripped by the gas flow .
The stripped layer is divided into about 200 molten ejectors ( assuming that the radius of ejectors is 300 { \mu m } ) and then they are blown away by the gas flow in a short period of time ( \sim 0.01 { s } ) .
The stripped layer is leaving from the parent with the velocity of \sim 4 { cm s ^ { -1 } } depending on the viscosity , and we assumed that the extracted ejectors have a random velocity \Delta v of the same order of magnitude .
Using above values , we can estimate the number density of ejectors behind the parent as n _ { e } \sim 800 { cm ^ { -3 } } .
These ejectors occupy \sim 9 \% of the space behind the parent in volume .
Considering that the collision rate ( number of collisions per unit time experienced by an ejector ) is given by R _ { coll } = \sigma _ { coll } n _ { e } \Delta v , where \sigma _ { coll } is the cross-section of collision ( e.g. , Gooding & Keil 1981 , Meteoritics 16 , 17 ) , we obtain R _ { coll } \sim 36 { collisions / s } by substituting above values .
Since most collisions occur within the short duration ( \sim 0.01 { s } ) before the ejectors are blown away , we obtain the collision probability of P _ { coll } \sim 0.36 , which is the probability of collisions experienced by an ejector in one disruption event .
The estimated collision probability is about one order of magnitude larger than the observed fraction of compound chondrules .
In addition , the model predictions are qualitatively consistent with other observational data ( oxygen isotopic composition , textural types , and size ratios of constituents ) .
Based on these results , we concluded that this new model can be one of the strongest candidates for the compound chondrule formation .

It should be noted that all collisions do not necessarily lead to the compound chondrule formation .
The formation efficiency and the future works which should be investigated in the forthcoming paper are also discussed .