WHITE-DWARF COSMOCHRONOMETRY - I - MONTE-CARLO SIMULATIONS OF PROPER-MOTION-LIMITED AND MAGNITUDE-LIMITED SAMPLES USING SCHMIDT 1 V-MAX ESTIMATOR/

Observationally, white dwarf stars are a remarkably homogeneous class with a minimum observed T(eff)similar to 4000 K. Theoretically, the ph ysics that determines their cooling timescales is relatively more stra ightforward than that which determines main-sequence evolutionary time scales. As a result, the white dwarf luminosity function has for the l ast decade been used as a probe of the age and star formation rate of the Galactic disk, providing an estimated local disk age of similar to 10 Gyr with estimated total uncertainties of roughly 20%. A long-stan ding criticism of the technique is that the reality of the reported do wnturn in the luminosity function (LF) hinges on just a handful of sta rs and on statistical arguments that fainter (older) objects would hav e been observed were they present. Indeed, the likely statistical vari ations of these small-number samples represent one of the primary unce rtainties in the derived Galactic age, and the behavior of Schmidt's 1 /V-max estimator in this limit is not well understood. In this work, w e explore these uncertainties numerically by means of a Monte Carlo po pulation synthesis code that simulates the kinematics and relative num bers of cooling white dwarfs. The ''observationally selected'' subsamp les are drawn using typical proper motion and V-magnitude limits. The corresponding 1/V-max LFs are then computed and compared to the input- integrated LFs. The results from our (noise-free) data suggest that (1 ) Schmidt's 1/V-max technique is a reliable and well-behaved estimator of the true space density with typical uncertainties of similar to 50 % for 50 point samples and 25% for 200 point samples; (2) the age unce rtainties quoted in previously published observational studies of the LF are consistent with uncertainties in the Monte Carlo results-specif ically there is a similar to 15% and less than or similar to 10% obser vational uncertainty in the ages inferred from 50 point and 200 point samples, respectively; and (3) the large statistical variations in the bright end of these LFs-even in the large-N limit-preclude using the white dwarf LF to obtain an estimate of the recent star formation rate as a function of time.