From Stardust to Planetesimals: Contributed Papers - NASA Lunar ...

The characteristic angular frequency Wchar of a blob about the star is given by(WKepler( r) = GM*r-3)1 XrRLIWchar = N 47rr2Wkepler( r )n ( r ) dr (4)r=As all blobs individually rotate with Keplerian angular frequency, the typical distancer,, of a blob from the star isGM* 1/sr`u =2W charThe characteristic radius ru, is determined by weighing the distribution n(r) withthe angular frequency. This is the typical radius for describing the motion of theplanetesimals. We regard vli, as the velocity that is also characteristic for the motionof the `tunnels' through which stellar light reaches the circumstellar dust directly.4.3. Results for the DynamicsIn Fig 3 is an example of a typical model for component A.(5)1010 ' m 1.000109z 107108 0.100106 ` 0.010105om104 0.0010 1 2 3 4 5 0 1 2 3 4 5—d log n d log — dlog n log1000 106— 105E100E 104101 1010 1 2 3 4 5 0 1 2 3 4 5—dlog nod log— dlog d log103102Figure 3. Results of model calculationsfor a planetesimal distributionaround a 0.8Mp, 4.8 RDstar (typical for V536 Aql-A). Theblob distribution extends from 2 R.to 35.2 AU. The planetesimals haveradii of 10 -2 R* . We give as a functionof x - —d log n/d log r the totalnumber of blobs (N, top left),the typical distance of planetesimalsfrom the star (rw/RnL; top right),their characteristic Keplerian velocity(rwWchar; bottom left) and theirprojected velocity at 100AU (bottomright). We achieve the required projectedvelocity of ; :t^ 500 km/s for x^_-1.9. This places the planetesimalscharacteristically to a distance rw3.1 AU.The general characteristics of the solutions can be summarized as follows:• Projected velocities at projected distances of the order of 10 2 AU (vproj,100AU)amount to several 10 2 km/s.This leads to an exponent x ti —2 for the radial .number distribution of blobs.This in turn indicates a characteristic radius of the distribution of planetesimalsof a few percent of rRL, i.e., of the order of a few AU. This is consistent withthe extent of the `stars' in the NIR observations. For the model shown in Fig 3we get xti1.9,ru,ti3.1 AU.7