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While spectroscopy is the standard method of measuring the redshift of luminous objects, it is a time-intensive technique, requiring, in some cases, hours of telescope time for a single source. Additionally, spectroscopy favours brighter objects, and therefore introduces an intrinsic bias towards luminous or closer sources. A simple method of estimating the redshift through photometry would prove invaluable to forthcoming surveys on the next generation of large radio telescopes, as well as alleviating the inherent bias towards the most optically bright sources. While there is a well-established correlation between the near-infrared K-band magnitude and redshift for galaxies, we find that the K-z relation breaks down for samples dominated by quasi-stellar objects (QSOs).  Current methods of estimating photometric redshift rely either on template spectra, which requires a high number of infrared photometry points, or computationally intensive machine learning methods.  Using photometric data from the Sloan Digital Sky Survey (SDSS) we investigate the relationship between combinations of magnitudes of a group of quasars, and their redshift. We find a high correlation between the colour relation (I-W2)/(W3-U) and redshift for a group of broad-line emission sources from the SDSS, and we conclude that this could be a robust estimator of the redshift.

Developing a photometric estimate of quasar redshifts: An independent measurement of the distances to the most powerful objects in the Universe