Astron. Astrophys. 361, 952-958 (2000)

3. Statistical properties

The simplest description of the statistical properties of the mass-transfer history is the differential probability of having a particular mass-transfer rate . For convenience, we will use the relative mass-transfer rate , where (Fig. 3) and is the relative "spottedness" (i.e. 0 if no spots are present and 1 if spots block the mass-transfer completely). is derivable from the cumulative probability distribution function , defined as

can be trivially derived from the observed values of by noting that it is simply one minus the rank of the sorted values divided by the number of measurements minus one.

The observed and curves for AM Her are shown in Fig. 4. Note that the median value of () is 0.75, i.e. on average, the L₁-point in AM Her yields no more than 25% of the observed mean maximum mass-transfer rate and even less of the maximum ever observed rate. Local peaks in - produced by smoothing and then differentiating - are present at 0.96-1.0, 0.4-0.65, and 0.77-0.88, indicating that there are some propensities (of unknown origin) for certain mass-transfer rates.

Fig. 4. The cumulative and differential probability distribution functions and for the relative spottedness (Fig. 3). The dashed curves indicate the changes in due to uncertainties in .

© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000
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