A double white dwarf with a paradoxical origin?

We present Hubble Space Telescope UV spectra of the 4.6-h-period double white dwarf SDSS J125733.63+542850.5. Combined with Sloan Digital Sky Survey optical data, these reveal that the massive white dwarf (secondary) has an effective temperature T2 = 13 030 ± 70 ± 150 K and a surface gravity log g2 = 8.73 ± 0.05 ± 0.05 (statistical and systematic uncertainties, respectively), leading to a mass of M2 = 1.06 M⊙. The temperature of the extremely low-mass white dwarf (primary) is substantially lower at T1 = 6400 ± 37 ± 50 K, while its surface gravity is poorly constrained by the data. The relative flux contribution of the two white dwarfs across the spectrum provides a radius ratio of R1/R2 ≃ 4.2, which, together with evolutionary models, allows us to calculate the cooling ages. The secondary massive white dwarf has a cooling age of ∼1 Gyr, while that of the primary low-mass white dwarf is likely to be much longer, possibly ≳5 Gyr, depending on its mass and the strength of chemical diffusion. These results unexpectedly suggest that the low-mass white dwarf formed long before the massive white dwarf, a puzzling discovery which poses a paradox for binary evolution.