Robust Measurement of Stellar Streams around the Milky Way: Correcting Spatially Variable Observational Selection Effects in Optical Imaging Surveys

Observations of density variations in stellar streams are a promising probe of low-mass dark matter substructure in the Milky Way. However, survey systematics such as variations in seeing and sky brightness can also induce artificial fluctuations in the observed densities of known stellar streams. These variations arise because survey conditions affect both object detection and star–galaxy misclassification rates. To mitigate these effects, we use Balrog synthetic source injections in the Dark Energy Survey (DES) Y3 data to calculate detection rate variations and classification rates as functions of survey properties. We show that these rates are nearly separable with respect to survey properties and can be estimated with sufficient statistics from the synthetic catalogs. Applying these corrections reduces the standard deviation of relative detection rates across the DES footprint by a factor of 5, and our corrections significantly change the inferred linear density of the Phoenix stream when including faint objects. Additionally, for artificial streams with DES-like survey properties we are able to recover density power spectra with reduced bias. We also find that uncorrected power-spectrum results for Legacy Survey of Space and Time (LSST)-like data can be around 5 times more biased, highlighting the need for such corrections in future ground-based surveys.