tokens: a comparison needs to be made statistically using a large sample of stars. Unfortunately measurements are available for very few A and B stars in Kepler and K2 . A comparison using 30 stars with T eff in the range 8300–12 000 K supports the identification of the photometric period with the rotation period (Balona 2017 ). A similar study using TESS observations of B stars comes to the same conclusion (Balona et al. 2019 ). Both these studies involve small numbers of stars. TESS observations have revealed the rotation frequencies of many more A and B stars for which measurements are available. Table 2 shows that there are 274 stars with both rotation frequencies and . In Fig. 1 a comparison between and the photometric v is made for 193 stars with T eff > 8000 K. The temperature limit was chosen to minimize contamination by stars in which surface convection may still be present. Since cannot exceed v , the points are expected to lie below the line in the figure. Figure 1. The projected rotation velocity, , as a function of the equatorial rotation velocity, v , estimated from the photometric period for stars with effective temperatures T eff > 8000 K. The straight line is . The 1σ error bars are shown on the top left. Table 2. The number of stars with known photometric periods, n , and the total number of stars, N , in the given effective temperature range, T eff , is given. The number of stars with both photometric periods and measurements is . The number of stars used in the frequency distribution is . The increase in numbers of stars above the line at low rotation rates is to be expected. Measurements of are mostly obtained by measuring the widths of selected spectral lines and applying a calibration to convert to . The calibration is obtained using high-dispersion spectra and modelling line profiles. The error in is approximately constant at all values of . Analysis of the rotational velocity catalogue of Glebocki Gnacinski ( 2005 ) gives a standard deviation of of about 30 km s −1 . This means that at low values of , the error is comparable to, or larger than, itself and many points will lie above the line. This is further compounded by the fact that is constrained to be greater than or equal to zero, although measurements of line width may lead to negative values of on applying the calibration. As the rotation rate tends to zero, measurements of ever increasing precision are required to ensure that stays below the line. This is clearly not possible to attain. Another consideration is that low photometric frequencies are more difficult to measure because a longer time span is required to resolve the frequency peak in the periodogram. Thus instrumental drift becomes important. This is further compounded by the fact that the periodogram noise increases sharply towards zero frequency. Thus the uncertainty in v increases as v approaches zero, contributing to moving the point above the line. The standard deviation for v is about 40 km s −1 as
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