Hamilton's Object Revisited: A challenging source redshift of a strong lensing configuration

Low-resolution spectrographs used to have difficulties to determine redshifts of galaxies at $z\approx1$ and $z\approx3$. Spectral emission and absorption lines of magnesium and iron redshifted to $z\approx1$ fall close to hydrogen, silicon, and oxygen lines at $z\approx3$. Here, we demonstrate that, even with modern, integrated field unit spectrographs, this task remains challenging. Hamilton's object, a blue star-forming galaxy, gravitationally lensed into three multiple images by the galaxy cluster SDSS J223010.47-081017.8 is such a case. Using the Blue Keck Cosmic Web Imager, its redshift was determined as $z=0.82$, while its MOIRCS spectrum hinted at $z=3.201$. To resolve the ambiguity, we completely re-analyse the Blue KCWI spectra of all three multiple images including the star-forming region in the outskirts. We employ a new data reduction pipeline, PypeIt, signal enhancement, and line fitting by Python-routines. The re-evaluation confirms the previous result based on 6 absorption features, $z=0.820 \pm 0.001$ and 4 emission features, $z=0.821 \pm 0.002$. The alternative $z=3.199\pm 0.003$, based on 6 absorption and 2 emission lines is a worse fit, also compared to other spectra. Moreover, we find the MOIRCS spectrum inconclusive: Observations cover two of three multiple images, with the slit for image C only covering its central bulge; furthermore the pixel-to-wavelength calibration requires a nightsky-emission-line calibration due to a missing calibration arc lamp. New MOIRCS observations are needed to verify that Hamilton's object has the smallest separation in angular diameter distance between lensing cluster and source galaxy among the known cluster-scale strong lenses.