We present a chemo-dynamical study of the Orphan stellar stream using a catalog of RR~Lyrae pulsating variable stars for which photometric, astrometric, and spectroscopic data are available. Employing low-resolution spectra from the Sloan Digital Sky Survey (SDSS), we determined line-of-sight velocities for individual exposures and derived the systemic velocities of the RR~Lyrae stars. In combination with the stars spectroscopic metallicities and textit{Gaia} EDR3 astrometry, we investigated the northern part of the Orphan stream. In our probabilistic approach, we found 20 single mode RR~Lyrae variables likely associated with the Orphan stream based on their positions, proper motions, and distances. The acquired sample permitted us to expand our search to nonvariable stars in the SDSS dataset, utilizing line-of-sight velocities determined by the SDSS. We found 54 additional nonvariable stars linked to the Orphan stream. The metallicity distribution for the identified red giant branch stars and blue horizontal branch stars is, on average, $-2.13pm0.05$ dex and $-1.87pm0.14$ dex, with dispersions of 0.23 and 0.43dex, respectively. The metallicity distribution of the RR~Lyrae variables peaks at $-1.80pm0.06$ dex and a dispersion of 0.25dex. Using the collected stellar sample, we investigated a possible link between the ultra-faint dwarf galaxy Grus II and the Orphan stream. Based on their kinematics, we found that both the stream RR~Lyrae and Grus II are on a prograde orbit with similar orbital properties, although the large uncertainties on the dynamical properties render an unambiguous claim of connection difficult. At the same time, the chemical analysis strongly weakens the connection between both. We argue that Grus II in combination with the Orphan stream would have to exhibit a strong inverse metallicity gradient, which to date has not been detected in any Local Group system.
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