Measuring quasar variability with pan-STARRS1 and SDSS

We measure quasar variability using the Panoramic Survey Telescope and Rapid Response System 1 Survey (Pan-STARRS1 or PS1) and the Sloan Digital Sky Survey (SDSS) and establish a method of selecting quasars via their variability in 10⁴ deg² surveys. We use 10⁵ spectroscopically confirmed quasars that have been well measured in both PS1 and SDSS and take advantage of the decadal timescales that separate SDSS measurements and PS1 measurements. A power law model fits the data well over the entire time range tested, 0.01-10 yr. Variability in the current PS1-SDSS data set can efficiently distinguish between quasars and nonvarying objects. It improves the purity of a griz quasar color cut from 4.1% to 48% while maintaining 67% completeness. Variability will be very effective at finding quasars in data sets with no u band and in redshift ranges where exclusively photometric selection is not efficient. We show that quasars' rest-frame ensemble variability, measured as a root mean squared in Δ magnitudes, is consistent with V(z, L, t) = A ₀(1 + z)^0.37(L/L 0) ^-0.16(t/1 yr)^0.246, where L ₀ = 10⁴⁶ erg s^-1 and A ₀ = 0.190, 0.162, 0.147, or 0.141 in the g P1, r P1, i P1, or z P1filter, respectively. We also fit across all four filters and obtain median variability as a function of z, L, and λ as V(z, L, λ, t) = 0.079(1 + z)^0.15(L/L ₀) ^-0.2(λ/1000 nm)^-0.44(t/1 yr)^0.246.