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 T _ { 2 } = 13030 \pm 70 \pm 150 K and a surface gravity log g _ { 2 } = 8.73 \pm 0.05 \pm 0.05 ( statistical and systematic uncertainties respectively ) , leading to a mass of M _ { 2 } = 1.06 M _ { \odot } .
The temperature of the extremely low-mass white dwarf ( primary ) is substantially lower at T _ { 1 } = 6400 \pm 37 \pm 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 R _ { 1 } / R _ { 2 } ~ { } \simeq~ { } 4.2 , which , together with evolutionary models , allows us to calculate the cooling ages .
The secondary massive white dwarf has a cooling age of \sim 1 Gyr , while that of the primary low-mass white dwarf is likely to be much longer , possibly \gtrsim 5 Gyrs , 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 .