It is possible to learn about the stellar formation history (SFH) in the disk of the Milky Way from volume complete samples of stars, hence obtain insights on how our Galaxy formed and evolved. Various studies have been aimed at identifying the SFH from stars, but often with conflicting results. Different approaches were employed , such as using the stellar activity in low-mass stars as an indicator of age, relying on empirical age versus metallicity relations, and applying statistical methods to HR diagrams (magnitude vs. color). It is difficult to determine the age of local Sun-like stars with any method because their outside layers do not change significantly with time. We have relied instead on white dwarfs as precise cosmic clocks. These former stars slowly cool with time, and their atmospheric temperature is a direct measure of their cooling age.
We rely on the 20 pc sample of 117 white dwarfs , which is estimated to be 80-90% complete. The significant advantage of this sample is that the remnants have precise distances, masses, and cooling ages. This allows for a direct conversion of the remnant parameters to initial stellar parameters (see Figure 1), employing the well studied initial-final mass relation calibrated from clusters and binaries .
Figure 1. Initial mass of the stars (in solar mass units) that are currently white dwarfs in the local 20 pc sample of  as a function of the time since formation. The dashed curve identifies the total main-sequence lifetime, hence below which white dwarfs have not yet formed. The remnants with a fixed log g = 8 value due to incomplete observations are identified with open circles.
Figure 2 presents the number of white dwarfs in 1 Gyr age bins (red). We also display our best SFH estimate considering the sum of two observational biases (black histogram). To begin, the total SFH is the sum of objects that are at present day white dwarfs, stars, and in much smaller number giants. Figure 1 would be populated with H-burning stars below the dashed line, although these objects are excluded from our sample, and we have corrected for this effect assuming a Salpeter initial mass function. The second bias comes from the fact that old stars have larger velocities in the vertical Galactic coordinate, and have a smaller probability to cross the solar neighborhood at present day. We correct for this bias with the observed dispersion of the vertical component of the velocity of stars in Galactic coordinates UVW as a function of age .
Figure 2. Our derived stellar formation history for the Galactic disk in 1 Gyr total age bins (black histogram), taking into account the biases due to the missing main-sequence stars and the velocity dispersion in the Galactic coordinate W. The error bars take into account number statistics uncertainties. The red dashed curve shows the raw uncorrected number of white dwarfs with the data from Figure 1. Both distributions have been normalized for the same total number of stars.
The two-step feature of the SFH, with an enhanced formation rate in the last 5 Gyr compared to the range 5 < Age (Gyr) < 10, is a significant detection for the 20 pc sample, which is unlikely to be compromised by biases. We believe that white dwarfs may be the most powerful cosmic clocks to derive the SFH at intermediate and large lookback times. For stars formed in the last ~2 Gyr, very few of them became white dwarfs hence it is difficult to recover a precise history. The largest limitation of the current analysis is the small size of the 20 pc white dwarf sample and Gaia will soon improve this situation.
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