3 IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT DEBRIS DISK DATA FROM E.G. HERSCHEL, ALMA, AND SOON JWST, WE PROPOSE TO SELF-CONSISTENTLY INCORPORATE AN IMPORTANT NEW ELEMENT INTO THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS: PLANETESIMAL VELOCITY EVOLUTION. THE ANALYTIC AND MOST OF THE NUMERICAL WORKS ON COLLISIONAL CASCADES HAVE GENERALLY ASSUMED THAT THE BODIES VELOCITY DISPERSION IS INDEPENDENT OF SIZE AND CONSTANT IN TIME ONCE THE CASCADE BEGINS. NEVERTHELESS, WE EXPECT ALL BODIES TO BE CONSTANTLY SUBJECT TO VELOCITY EVOLUTION THROUGH VISCOUS STIRRING, COLLISIONAL DAMPING, DYNAMICAL FRICTION, AND STELLAR RADIATION EFFECTS. BECAUSE THESE PROCESSES ACT ON TIMESCALES COMPARABLE TO OR SHORTER THAN COLLISIONAL DESTRUCTION, AND BECAUSE RATES OF VELOCITY EVOLUTION DEPEND STRONGLY ON THE SIZES AND NUMBER DENSITIES OF THE OBJECTS, IT IS VERY UNCLEAR THAT THE VELOCITIES WOULD SIMPLY BE SIZE- AND TIME-INDEPENDENT. MOREOVER, VELOCITIES DETERMINE THE CATASTROPHIC COLLISION RATE: ACCURATE VELOCITIES ARE THEREFORE CRUCIAL IN DEDUCING THE CORRECT STEADY-STATE SIZE DISTRIBUTION AND DUST PRODUCTION RATE. Funding Only Action ($2) 4/23/19 Not listed IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT DEBRIS DISKDATA FROM E.G. HERSCHEL ALMA AND SOON JWST WE PROPOSE TO SELF-CONSISTENTLY INCORPORATE AN IMPORTANT NEW ELEMENT INTO THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS: PLANETESIMAL VELOCITY EVOLUTION. THE ANALYTIC AND MOST OF THE NUMERICAL WORKS ON COLLISIONAL CASCADES HAVE GENERALLY ASSUMED THATTHE BODIES VELOCITY DISPERSION IS INDEPENDENT OF SIZE AND CONSTANT IN TIME ONCE THE CASCADE BEGINS. NEVERTHELESS WE EXPECT ALL BODIES TO BE CONSTANTLY SUBJECT TO VELOCITY EVOLUTION THROUGH VISCOUS STIRRING COLLISIONAL DAMPING DYNAMICAL FRICTION AND STELLAR RADIATION EFFECTS. BECAUSE THESE PROCESSES ACT ON TIMESCALES COMPARABLE TO OR SHORTER THAN COLLISIONAL DESTRUCTION AND BECAUSE RATES OF VELOCITY EVOLUTION DEPEND STRONGLY ON THE SIZES AND NUMBER DENSITIES OF THE OBJECTS IT IS VERY UNCLEAR THAT THE VELOCITIES WOULD SIMPLY BE SIZE- AND TIME-INDEPENDENT. MOREOVER VELOCITIES DETERMINE THE CATASTROPHIC COLLISION RATE: ACCURATE VELOCITIES ARE THEREFORE CRUCIAL IN DEDUCING THE CORRECT STEADY-STATE SIZE DISTRIBUTION AND DUST PRODUCTION RATE. ($2) 4/23/19 Not listed IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT DEBRIS DISKDATA FROM E.G. HERSCHEL ALMA AND SOON JWST WE PROPOSE TO SELF-CONSISTENTLY INCORPORATE AN IMPORTANT NEW ELEMENT INTO THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS: PLANETESIMAL VELOCITY EVOLUTION. THE ANALYTIC AND MOST OF THE NUMERICAL WORKS ON COLLISIONAL CASCADES HAVE GENERALLY ASSUMED THATTHE BODIES VELOCITY DISPERSION IS INDEPENDENT OF SIZE AND CONSTANT IN TIME ONCE THE CASCADE BEGINS. NEVERTHELESS WE EXPECT ALL BODIES TO BE CONSTANTLY SUBJECT TO VELOCITY EVOLUTION THROUGH VISCOUS STIRRING COLLISIONAL DAMPING DYNAMICAL FRICTION AND STELLAR RADIATION EFFECTS. BECAUSE THESE PROCESSES ACT ON TIMESCALES COMPARABLE TO OR SHORTER THAN COLLISIONAL DESTRUCTION AND BECAUSE RATES OF VELOCITY EVOLUTION DEPEND STRONGLY ON THE SIZES AND NUMBER DENSITIES OF THE OBJECTS IT IS VERY UNCLEAR THAT THE VELOCITIES WOULD SIMPLY BE SIZE- AND TIME-INDEPENDENT. MOREOVER VELOCITIES DETERMINE THE CATASTROPHIC COLLISION RATE: ACCURATE VELOCITIES ARE THEREFORE CRUCIAL IN DEDUCING THE CORRECT STEADY-STATE SIZE DISTRIBUTION AND DUST PRODUCTION RATE. $0 9/8/17 2 IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT DEBRIS DISK DATA FROM E.G. HERSCHEL, ALMA, AND SOON JWST, WE PROPOSE TO SELF-CONSISTENTLY INCORPORATE AN IMPORTANT NEW ELEMENT INTO THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS: PLANETESIMAL VELOCITY EVOLUTION. THE ANALYTIC AND MOST OF THE NUMERICAL WORKS ON COLLISIONAL CASCADES HAVE GENERALLY ASSUMED THAT THE BODIES VELOCITY DISPERSION IS INDEPENDENT OF SIZE AND CONSTANT IN TIME ONCE THE CASCADE BEGINS. NEVERTHELESS, WE EXPECT ALL BODIES TO BE CONSTANTLY SUBJECT TO VELOCITY EVOLUTION THROUGH VISCOUS STIRRING, COLLISIONAL DAMPING, DYNAMICAL FRICTION, AND STELLAR RADIATION EFFECTS. BECAUSE THESE PROCESSES ACT ON TIMESCALES COMPARABLE TO OR SHORTER THAN COLLISIONAL DESTRUCTION, AND BECAUSE RATES OF VELOCITY EVOLUTION DEPEND STRONGLY ON THE SIZES AND NUMBER DENSITIES OF THE OBJECTS, IT IS VERY UNCLEAR THAT THE VELOCITIES WOULD SIMPLY BE SIZE- AND TIME-INDEPENDENT. MOREOVER, VELOCITIES DETERMINE THE CATASTROPHIC COLLISION RATE: ACCURATE VELOCITIES ARE THEREFORE CRUCIAL IN DEDUCING THE CORRECT STEADY-STATE SIZE DISTRIBUTION AND DUST PRODUCTION RATE. Other Administrative Action $0 9/8/17 1 IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT DEBRIS DISK DATA FROM E.G. HERSCHEL, ALMA, AND SOON JWST, WE PROPOSE TO SELF-CONSISTENTLY INCORPORATE AN IMPORTANT NEW ELEMENT INTO THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS: PLANETESIMAL VELOCITY EVOLUTION. THE ANALYTIC AND MOST OF THE NUMERICAL WORKS ON COLLISIONAL CASCADES HAVE GENERALLY ASSUMED THAT THE BODIES VELOCITY DISPERSION IS INDEPENDENT OF SIZE AND CONSTANT IN TIME ONCE THE CASCADE BEGINS. NEVERTHELESS, WE EXPECT ALL BODIES TO BE CONSTANTLY SUBJECT TO VELOCITY EVOLUTION THROUGH VISCOUS STIRRING, COLLISIONAL DAMPING, DYNAMICAL FRICTION, AND STELLAR RADIATION EFFECTS. BECAUSE THESE PROCESSES ACT ON TIMESCALES COMPARABLE TO OR SHORTER THAN COLLISIONAL DESTRUCTION, AND BECAUSE RATES OF VELOCITY EVOLUTION DEPEND STRONGLY ON THE SIZES AND NUMBER DENSITIES OF THE OBJECTS, IT IS VERY UNCLEAR THAT THE VELOCITIES WOULD SIMPLY BE SIZE- AND TIME-INDEPENDENT. MOREOVER, VELOCITIES DETERMINE THE CATASTROPHIC COLLISION RATE: ACCURATE VELOCITIES ARE THEREFORE CRUCIAL IN DEDUCING THE CORRECT STEADY-STATE SIZE DISTRIBUTION AND DUST PRODUCTION RATE. Funding Only Action $105.2k 9/20/16