A large number of new members ($sim$150) of the Cetus Stream (CS) were identified from their clustering features in dynamical space using 6D kinematic data by combining LAMOST DR5 and Gaia DR2 surveys. They map a diffuse structure that extends over at least 100 degrees in the northern and southern Galactic hemispheres, at heliocentric distances between 20 to 50 kpc. Taking advantage of this expanded dataset, we model the stream with a suite of tailored N-body simulations. Our findings exclude the possibility that the NGC 5824 globular cluster is the core of the progenitor of the stream, as postulated by previous studies. Our best models, which successfully reproduce the features of the CS indicate that the progenitor is likely a dwarf galaxy of $sim$ 2$times$10$^9$M$_{odot}$, with a diffuse disc morphology. The merger occured $sim$ 5 Gyr ago and since then it has experienced approximately eight apo-center passages. Our results suggest that NGC 5824 was either a globular cluster situated off-centre in the dwarf progenitor or, alternatively, it was the nuclear star cluster of another dwarf galaxy that has very similar orbit as the progenitor of the CS. In both scenarios, the progenitor systems would leave streams around NGC 5824, but with distinct distance distributions. To discriminate between these scenarios, the detection and accurate distance measurements of the predicted stream around the GC are crucial, which will be possible in the upcoming LSST era. Our simulations also predict that part of the Southern Cetus stream is very likely the newly discovered Palca stream, and possibly related to another, more diffuse Southern substructure, the Eridanus-Pheonix overdensity.
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