Astron. Astrophys. 334, 381-387 (1998)

5. A semi-analytical relation between and

Our aim is to find a semi-analytical relation for the intervals and .
The first step is the determination of a function for a fixed value of . We solve Eq. (7) for and and by the least square method we find the function :

with:

The value of the correlation coefficient between this function and the numerical integration is . With this method we find for several values of inside the interval . We can write the dimensionless collapse time as the product:

where the function can be written as

and, for and , K is constant: . So:

A test performed between the values obtained for from the numerical integration and the values obtained from Eq. (7) gives the result: .

© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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