We have acquired between 127 and 150 h of time-resolved multicolour photometry for each of the three β Cephei stars IL Vel, V433 Car and KZ Mus over a time-span of 4 months from two observatories. All three objects are multiperiodic with at least three modes of pulsation. Mode identification from the relative colour amplitudes is performed. We obtain unambiguous results for the two highest-amplitude modes of IL Vel (both are l = 1) and the three strongest modes of KZ Mus (l = 2, 0 and 1), but none for V433 Car. Spectroscopy shows the latter star to be a fast rotator (υ sin i = 240 km s - 1 ), whereas the other two have moderate υ sin i (65 and 47 km s - 1 , respectively). We performed model calculations using the Warsaw-New Jersey stellar evolution and pulsation code. We find that IL Vel is an object of about 12 M O . in the second half of its main-sequence evolutionary track. Its two dipole modes are most probably rotationally split components of the mode originating as p 1 on the zero-age main sequence; one of these modes is m = 0. V433 Car is suggested to be an unevolved 13-M O . star just entering the β Cephei instability strip. KZ Mus seems less massive (12.7 M O .) and somewhat more evolved, and its radial mode is probably the fundamental one. In this case its quadrupole mode would be the one originating as g 1 , and its dipole mode would be p 1 . Two of our photometric comparison stars also turned out to be variable. HD 90434 is probably a new slowly pulsating B-type star, the dominant mode of which is a dipole, whereas the variability of HD 89768 seems to be a result of binarity. It is suggested that mode identification of slowly rotating β Cephei stars based on photometric colour amplitudes is reliable; we estimate that a relative accuracy of 3 per cent in the amplitudes is sufficient for unambiguous identifications. Owing to the good agreement of our theoretical and observational results we conclude that the prospects for asteroseismology of multiperiodic slowly rotating β Cephei stars are good.
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