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Fig. 4

image

Analysis of the empirical uncertainty for short-term repeat observations of vsini using order-sorting filter HR15N. Plot a) shows the variation of Evsini × (S/N)( [ vsini ] /C)2/ (1 + ( [ vsini ] /C)2)5/4 with S/N . The horizontal line indicates the value of parameter β in Eq. (3) fitted to the full dataset. Blue crosses show the estimated values β as a function of S/N corrected for the measured variation of β with Teff (see Sect. 4.4 and Table 3). Plot b) shows the variation of Evsini × S/N with vsini. The solid line show the relationship predicted using the theoretical value of C and the value of β from plot a). In plots a) and b) the y-axis shows an estimate of the standard deviation based on the MAD divided by 0.82 (for ν = 2, see Sect. 3.3). Plot c) shows the cumulative probability distribution (CDF) of the normalised uncertainty in vsini for short-term repeats. The red solid line shows results for measured data, the dashed line shows the cumulative distribution of a Gaussian with unit dispersion, and the diamond symbols show the cumulative distribution function for a Student’s t-distribution with ν = 2.

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