We present a detailed analysis of the white dwarf luminosity functions
derived from the local 40 pc sample and the deep proper motion catalog of Munn
et al (2014, 2017). Many of the previous studies ignored the contribution of
thick disk white dwarfs to the Galactic disk luminosity function, which results
in an erronous age measurement. We demonstrate that the ratio of thick/thin
disk white dwarfs is roughly 20\% in the local sample. Simultaneously fitting
for both disk components, we derive ages of 6.8-7.0 Gyr for the thin disk and
8.7 ± 0.1 Gyr for the thick disk from the local 40 pc sample. Similarly, we
derive ages of 7.4-8.2 Gyr for the thin disk and 9.5-9.9 Gyr for the thick disk
from the deep proper motion catalog, which shows no evidence of a deviation
from a constant star formation rate in the past 2.5 Gyr. We constrain the time
difference between the onset of star formation in the thin disk and the thick
disk to be 1.6−0.4+0.3​ Gyr. The faint end of the luminosity function
for the halo white dwarfs is less constrained, resulting in an age estimate of
12.5−3.4+1.4​ Gyr for the Galactic inner halo. This is the first time
ages for all three major components of the Galaxy are obtained from a sample of
field white dwarfs that is large enough to contain significant numbers of disk
and halo objects. The resultant ages agree reasonably well with the age
estimates for the oldest open and globular clusters.Comment: ApJ, in pres