New evidence for the precession of tilted disc in SDSS J081256.85+191157.8

Superorbital signals and negative superhumps are thought to be related to the reverse precession of the nodal line in a tilted disc, but the evidence is lacking. Our results provide new evidence for the precession of the tilted disc. Based on the TESS and K2 photometry, we investigate the superorbital signals, negative superhumps, positive superhumps, and eclipse characteristics of the long-period eclipsing cataclysmic variable star SDSS J0812. We find superorbital signals, negative superhumps, and positive superhumps with periods of 3.0451(5) d, 0.152047(2) d, and 0.174686 (7) d, respectively, in the K2 photometry, but all disappear in the TESS photometry, where the positive superhumps are present only in the first half of the same campaign, confirming that none of them is permanently present in SDSS J0812. In addition, we find for the first time a cyclic variation of the O-C of minima, eclipse depth, and negative superhumps amplitudes for 3.045 (8) d, 3.040(6) d, and 3.053 (8) d in SDSS J0812, respectively, and all reach the maximum at similar to 0.75 precession phases of the tilted disc, which provides new evidence for the precession of the tilted disc. We suggest that the O-C and eclipse depth variations may come from a shift of the brightness centre of the precession tilted disc. Our first finding on the periodic variation of negative superhumps amplitude with the superorbital signals is significant evidence that the origin of negative superhumps is related to the precession of the tilted disc.