The rotation properties of $\delta$ Sct and $\gamma$ Dor stars

Abstract

Based on the LAMOST spectroscopy and TESS time-series photometry, we have obtained a main-sequence star sample of $\delta$ Scuti and $\gamma$ Doradus stars. The sample includes 1534 $\delta$ Sct stars, 367 $\gamma$ Dor stars, 1703 $\delta$ Sct$| \gamma$ Dor stars, 270 $\gamma$ Dor$| \delta$ Sct stars, along with 105 '$\delta$ Sct candidates' and 32 '$\gamma$ Dor candidates'. After correcting for projection effects, we derived the equatorial rotational velocity distribution for $\delta$ Sct and $\gamma$ Dor stars and compared it with that of normal stars. The rotational velocity distributions of $\delta$ Sct and $\gamma$ Dor stars are extremely similar, with the only difference potentially due to the rotational variable stars that have not been completely removed. In contrast, the rotational velocity distribution of normal stars is more dispersed compared to pulsating stars. Additionally, the peak rotational velocity of the pulsating stars is about 10 km s$^{-1}$ higher than that of normal stars. Unlike the normal stars, which show a monotonic increase in peak velocity with mass between 1.8 and 2.5 $M_{\odot}$, the rotational velocity distribution of $\delta$ Sct stars does not exhibit a strong mass dependence. We also found that normal stars accelerate during the late main-sequence evolutionary phase, while $\delta$ Sct stars decelerate. Furthermore, there may still be unclassified stars with diverse rotational properties in the normal star sample compared to the $\delta$ Sct stars, which is likely to be an important contributor to the broader dispersion observed in its rotational velocity distribution. The photometric amplitude in $\delta$ Sct stars is modulated with rotational velocity, with high-amplitude stars typically rotating slowly and low-amplitude stars showing a broad distribution of rotational velocities.