The Geometry of Sagittarius Stream from Pan-STARRS1 3$\pi$ RR Lyrae

We present a comprehensive and precise description of the Sagittarius (Sgr) stellar stream's 3D geometry as traced by its old stellar population. This analysis draws on the sample of ${\sim}44,000$ RR Lyrae (RRab) stars from the Pan-STARRS1 (PS1) 3$\pi$ survey (Hernitschek et al. 2016,Sesar et al. 2017b), which is ${\sim}80\%$ complete and ${\sim}90\%$ pure within 80~kpc, and extends to ${\gtrsim} 120$~kpc with a distance precision of ${\sim} 3\%$. A projection of RR Lyrae stars within $|\tilde{B}|_{\odot}<9^\circ$ of the Sgr stream's orbital plane reveals the morphology of both the leading and the trailing arms at very high contrast, across much of the sky. In particular, the map traces the stream near-contiguously through the distant apocenters. We fit a simple model for the mean distance and line-of-sight depth of the Sgr stream as a function of the orbital plane angle $\tilde{\Lambda}_{\odot}$, along with a power-law background-model for the field stars. This modeling results in estimates of the mean stream distance precise to ${\sim}1\%$ and it resolves the stream's line-of-sight depth. These improved geometric constraints can serve as new constraints for dynamical stream models.