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

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3. Statistical properties

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


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

The observed [FORMULA] and [FORMULA] curves for AM Her are shown in Fig. 4. Note that the median value of [FORMULA] ([FORMULA]) 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 [FORMULA] - produced by smoothing and then differentiating [FORMULA] - are present at [FORMULA] 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.

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

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© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000