Astrometric Redshifts for Quasars

The wavelength dependence of atmospheric refraction causes differential chromatic refraction (DCR), whereby objects imaged at different optical/UV wavelengths are observed at slightly different positions in the plane of the detector. Strong spectral features induce changes in the effective wavelengths of broad-band filters that are capable of producing significant positional offsets with respect to standard DCR corrections. We examine such offsets for broad-emission-line (type 1) quasars from the Sloan Digital Sky Survey (SDSS) spanning 0<z<5 and an airmass range of 1.0 to 1.8. These offsets are in good agreement with those predicted by convolving a composite quasar spectrum with the SDSS bandpasses as a function of redshift and airmass. This astrometric information can be used to break degeneracies in photometric redshifts of quasars (or other emission-line sources) and, for extreme cases, may be suitable for determining “astrometric redshifts”. On the SDSS’s southern equatorial stripe, where it is possible to average many multi-epoch measurements, more than 60% of quasars have emission-line-induced astrometric offsets larger than the SDSS’s relative astrometric errors of 25-35 mas. Folding these astrometric offsets into photometric redshift estimates yields an improvement of 9% within Delta z+/-0.1. Future multi-epoch synoptic surveys such as LSST and Pan-STARRS could benefit from intentionally making 10 observations at relatively high airmass (AM1.4) in order to improve their photometric redshifts for quasars.

💡 Research Summary

The paper investigates how differential chromatic refraction (DCR) – the wavelength‑dependent bending of light by Earth’s atmosphere – can be turned from a nuisance into a useful signal for estimating quasar redshifts. In standard imaging pipelines, a single DCR correction is applied based on the mean atmospheric refraction for a given airmass, assuming that an object’s spectral energy distribution (SED) is smooth. However, type‑1 quasars possess strong broad emission lines that shift the effective wavelength of each broadband filter away from the continuum value. As a result, the DCR correction appropriate for a smooth SED no longer matches the true refraction experienced by the quasar, producing small but measurable positional offsets between filters even when the observations are taken at the same airmass.

The authors assembled a large sample of SDSS quasars spanning redshifts 0 ≤ z ≤ 5 and airmasses from 1.0 to 1.8. For each object they extracted the catalogued astrometric positions in the u, g, r, i, and z bands and compared them to the offsets predicted by convolving the Vanden Berk composite quasar spectrum with the SDSS filter transmission curves. By varying redshift and airmass they generated a model of the expected DCR‑induced shift for each band. The measured offsets matched the model very well, especially in redshift intervals where prominent lines such as Mg II (λ 2798 Å), C IV (λ 1549 Å), and Lyα (λ 1216 Å) move through the filter bandpasses. In the Southern Equatorial Stripe, where many repeat observations exist, the authors were able to average over epochs and reduce the relative astrometric error to 25–35 mas. More than 60 % of the quasars in this region exhibited line‑induced astrometric offsets larger than this error floor, confirming that the effect is robust and detectable in real data.

Having demonstrated the existence of a measurable signal, the authors incorporated the astrometric offsets into a photometric redshift (photo‑z) estimator. They treated the multi‑band positional differences as additional observables, modeled their dependence on redshift and airmass, and combined them with the usual color information within a Bayesian framework. The resulting “astrometric‑enhanced” photo‑z’s showed a 9 % improvement in the fraction of objects whose redshift estimates fall within Δz = ±0.1 of the spectroscopic value. The gain is most pronounced in redshift ranges where color degeneracies are severe (e.g., z ≈ 2.2 versus z ≈ 3.5), because the line‑driven astrometric signature breaks the symmetry that colors alone cannot.

The paper concludes with practical recommendations for upcoming time‑domain surveys such as the Large Synoptic Survey Telescope (LSST) and Pan‑STARRS. While these projects aim to minimize atmospheric effects by observing at low airmass, the authors argue that deliberately acquiring a modest number (≈10) of high‑airmass (AM ≈ 1.4) exposures per field would dramatically increase the leverage of DCR‑induced astrometry. Because LSST will obtain hundreds of visits per sky location, the additional high‑airmass data can be combined with the bulk of low‑airmass observations to produce high‑precision astrometric offsets without sacrificing overall survey depth. This strategy would not only improve quasar photo‑z’s but also benefit any emission‑line dominated source (e.g., active galactic nuclei, supernovae with strong line emission), opening the possibility of “astrometric redshifts” where the redshift is inferred primarily from the wavelength‑dependent positional shift rather than from photometric colors alone.

In summary, the study shows that the subtle positional shifts caused by differential chromatic refraction, once thought to be a systematic error, encode valuable spectroscopic information. By modeling and measuring these shifts, one can augment traditional photometric redshift techniques, achieving higher accuracy for quasars and potentially for a broader class of line‑rich astronomical objects. The work paves the way for future synoptic surveys to exploit atmospheric refraction as a scientific tool rather than merely a nuisance.