Differential Chromatic Refraction in the Context of the Legacy Survey of Space and Time

Differential chromatic refraction (DCR) is a largely untapped, but potentially powerful tool for classification and photo-z regression of astrophysical sources whose emission and absorption features cause significant deviations from a power-law continuum at UV wavelengths (Kaczmarczik et al. 2009; Lee et al. 2019).

In the Sloan Digital Sky Survey (SDSS; York et al. 2000), DCR manifested as an offset of the u- and g-band positions of objects, specifically relative to the fiducial R.A./decl. derived from the r-band position. For the Legacy Survey of Space and Time (LSST; Ivezić et al. 2019) that will be conducted at the Vera Rubin Observatory with the Simonyi Survey Telescope, it is as yet unclear in what form DCR information may be reported. The reason is that LSST will not make observations in all of the bands at the same time as SDSS did, moreover that LSST image analysis will involve both stacking of individual epochs to create deeper images and also difference imaging to look for changes with time. Both of those differences in survey design mean that LSST cannot afford to simply report the positional offset due to DCR, rather that positional offset must be corrected in the astrometric solution; these corrections are a necessary condition for the success of LSST. In principle, the information content provided by DCR could be reported simply as the DCR coefficients in the astrometric solution. A more user-friendly solution might be to instead report "sub-band" photometry as discussed in https://dmtn-037.lsst.io/.

We describe an investigation of the effects of DCR on LSST survey strategy as a function of different possible operations simulations (OpSims; Delgado & Reuter 2016) using the metrics analysis framework (Jones et al. 2014). Our analysis is non-parametric and independent of the spectral energy distribution (SED) of the source. That is, we do not need to know how DCR information is going to be reported in order to know what information is potentially available or to know the SED of the source to know the relative effect that DCR will have between different simulations.

Fundamentally DCR is the positional offset (relative to the zenith direction) of the observed position relative to the true position. To first order this positional offset, Δ, is linear in the tangent of the zenith angle, Z:

$$\begin{eqnarray}&&{\rm{\Delta }}=m\,\tan (Z)+b.\end{eqnarray} \tag{ 1 }$$

The intercept, b ≡ 0, as the DCR effect goes away at the zenith, Z ≡ 0. The slope, m, is set by the effective wavelength of the bandpass (which depends on the source SED). A significant DCR residual will be present when, near the edges of the u or g bandpasses, there are strong emission features (e.g., broad-emission lines in quasars and SNe), broad absorption features (e.g., damped Lyα absorption or broad-absorption-line troughs in quasars), or absorption edges (Lyman-limit, Lyα, Balmer, and 4000 Å break features in quasars and galaxies). However, the accuracy to which we can measure the slope is largely independent of the source SED, with dependence on the astrometric error of the survey and the airmass of the observation. Both of these quantities are available at every location on the sky in the LSST OpSims (where the astrometric error is a function of magnitude and atmospheric seeing). Thus the error on the slope is (to first order):

$$\begin{eqnarray}&&{\sigma }_{m}={\sigma }_{\mathrm{astrom}}/\tan (Z).\end{eqnarray} \tag{ 2 }$$

With this realization, we can make differential comparisons of LSST OpSims to determine which simulations are "better" in terms of the DCR signal available. As these comparisons are differential, the magnitude of the source drops out and depends on the distribution of airmasses of the observations. We can then compute a metric that is averaged over the full survey area or as a function of position on the sky (e.g., comparing wide-fast-deep and deep-drilling fields; Ivezić et al. 2019). The code is available for inspection from Yu et al. (2020).

In the left panel of Figure 1 we show the distribution of DCR slope errors for 20 different "families" of OpSims from the v1.5 release (Jones et al. 2020). Each family has multiple simulations, but we show just one from each here for the sake of illustration. The different OpSims have similar median values of the slope errors. The g = 22 result shown is in relative units; the extent of the distributions in physical units is 2.5–6.0 mas. The outlier with a larger metric value is from the family of OpSims that were designed to have more high-airmass observations in order to provide a testbed for DCR. Thus, we conclude that there is no strong reason to chose one set of parameters for the LSST survey over another when it comes to DCR. An exception to that conclusion is that there may be intrinsic value to some science cases for including some high airmass observations (which is degenerate with the desire for long observing seasons).

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A small number of high-airmass observations can improve photo-z estimates for sources with significant DCR signal. For example, quasars, with their strong emission features that redshift through the bandpasses, have some of the most significant DCR slopes we might expect to encounter. The maximum slopes expected are ≈ ∣70∣ mas in both the u- and g-bands. The expected astrometric error for LSST at r = 22 is 15 mas (per coordinate, per visit), degrading to 74 by r = 24 (LSST Science Collaboration et al. 2009). On the right we show the signal-to-noise ratio (S/N) of the DCR specifically for a quasar SED, as a function of redshift. See Kaczmarczik et al. (2009) or Richards et al. (2001) for illustration of how the emission lines shift through the optical bandpasses and change the effective wavelength of those bandpasses when convolved with the SED. Shown is the S/N of a fiducial quasar with g = 22 and u = 22.15 (as appropriate for the mean slope of quasar continua). At nearly all redshifts one or both of the u and g filters have DCR effects exceeding 3σ (with some redshifts having 20σ). By 24th magnitude, the single-epoch depth of LSST, only a small range of redshifts will still exhibit 3σ effects. Thus, DCR will be an important source of classification and regression information for bright objects and may provide a novel, if noisy, piece of information for sources as faint as the single-epoch depths of LSST.

We thank David Monet for highlighting the importance of DCR and Lynne Jones for assistance with the LSST OpSims. This research makes use of the SciServer science platform (www.sciserver.org).