Multi-mode delta Sct stars from the Zwicky Transient Facility Survey

We obtain the largest catalog of multi-mode $\delta$ Sct stars in the northern sky to date using the Zwicky Transient Facility (ZTF) Data Release 20 (DR20). The catalog includes 2254 objects, of which 2181 are new to our study. Among these multi-mode $\delta$ Sct stars, 2142 objects are double-mode $\delta$ Sct, while 109 objects are triple-mode $\delta$ Sct and 3 are quadruple-mode $\delta$ Sct. By analyzing the light curves in the $r$ and $g$ bands of the ZTF, we determine the basic parameters of multi-mode $\delta$ Sct stars, including the periods and amplitudes. Periods are checked by comparison with the OGLE catalog of double-mode $\delta$ Sct stars. On the Petersen diagram, multi-mode $\delta$ Sct stars form six sequences. We find that in Galactic coordinates, the periods of 1O/F double-mode $\delta$ Sct stars at high latitudes are shorter than those of 1O/F double-mode $\delta$ Sct stars in the disk, due to metallicity variations. In the future, our catalog can be used to establish the period--luminosity relation and the period--metallicity relation of double-mode $\delta$ Sct stars, and to study the Galactic structure.