White dwarf cosmochronometry. I. Monte Carlo simulations of proper-motion and magnitude-limited samples using Schmidt's 1/Vmax estimator
Wood, Matt A.
Oswalt, T. D.
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Observationally, white dwarf stars are a remarkably homogeneous class with a minimum observed Teff ∼ 4000 K. Theoretically, the physics that determines their cooling timescales is relatively more straightforward than that which determines main-sequence evolutionary timescales. As a result, the white dwarf luminosity function has for the last decade been used as a probe of the age and star formation rate of the Galactic disk, providing an estimated local disk age of ∼ 10 Gyr with estimated total uncertainties of roughly 20%. A long-standing criticism of the technique is that the reality of the reported downturn in the luminosity function (LF) hinges on just a handful of stars and on statistical arguments that fainter (older) objects would have been observed were they present. Indeed, the likely statistical variations of these small-number samples represent one of the primary uncertainties in the derived Galactic age, and the behavior of Schmidt's 1/Vmax estimator in this limit is not well understood. In this work, we explore these uncertainties numerically by means of a Monte Carlo population synthesis code that simulates the kinematics and relative numbers of cooling white dwarfs. The "observationally selected" subsamples are drawn using typical proper motion and V-magnitude limits. The corresponding 1/Vmax LFs are then computed and compared to the input-integrated LFs. The results from our (noise-free) data suggest that (1) Schmidt's 1/Vmax technique is a reliable and well-behaved estimator of the true space density with typical uncertainties of ∼ 50% for 50 point samples and 25% for 200 point samples; (2) the age uncertainties quoted in previously published observational studies of the LF are consistent with uncertainties in the Monte Carlo results - specifically, there is a ∼ 15% and ≲ 10% observational 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-JV limit - preclude using the white dwarf LF to obtain an estimate of the recent star formation rate as a function of time.