A refinement of the rotation period of the roAp star HR 3831 and the discovery of a significant phase lag between the times of pulsation and magnetic extrema and the time of mean-light extremum

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Abstract
HR 3831 is a rapidly oscillating Ap star with a pulsational period of 11.67 min. The amplitude of this pulsation ranges from 0 to about 5 mmag as a function of the rotational aspect of the star. We use 268 hr of new high-speed photometric observations obtained in 1990 and 1991 plus 238 hi of published high-speed photometry from 1980, 1981, 1985 and 1986 to show that the period of pulsation amplitude modulation is equal to the period of mean-light variation. We use this to show that an interpretation of the pulsation-amplitude modulation as rotationally perturbed m-modes requires that |$C_{n\ell}\le2\times 10^{-5}$| at the 3σ confidence level, making that interpretation highly unlikely. We also show that the time of pulsation maximum precedes the time of mean-light extremum by 0.177 ± 0.007 d (0.062 ± 0.002 rotation periods), a 25σ difference. The time of magnetic extremum coincides with the time of pulsation-amplitude maximum but differs from mean-light extremum by 0.158 ± 0.032 d, a 5σ difference. This argues that HR 3831 is an oblique pulsator with the magnetic axis and pulsation axis aligned, rather than a spotted pulsator with amplitude modulation caused by surface inhomogeneities. It also indicates a deviation from cylindrical symmetry which makes the interpretation of the pulsation-amplitude modulation in terms of the oblique-pulsator model more complex than has yet been considered. By shifting the pulsation-amplitude variations into phase with the mean-light variations and normalizing both data sets, we refine the rotation frequency for HR3831 to be |$\upsilon_\text{rot}=0.3506333 \pm 0.0000006 \, \text d^{-1}=4058.256 \pm 0.007\,\text{nHz},\,\text{or}\, P_\text{rot}=2.851982 \pm 0.000005 \,\text{d}$|

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