标题： 通过使用$1/V_{\rm max}$方法对本地盘白矮星的大小和自行样本进行数值模拟，研究观测误差之间的相互作用。 显示英文标题

标题： The interplay of observational errors through numerical simulations using the $1/V_{\rm max}$ method for magnitude and proper-motion samples of local disk white dwarfs.}

摘要： 白矮星冷却序列提供了一个有用的指标，可以用来衡量银河盘的演化时间尺度以及恒星形成历史，因此，白矮星的光度函数已成为研究银河系演化和形成的重要工具。 我们使用$1/V_{\rm max}$方法研究了盘状白矮星光度函数的微弱端（$M_V > +14$）行为，但首次全面考虑了实际观测误差对推导出的光度函数的影响。 我们发现，观测误差，尤其是辐射校正和三角视差中的误差，在很大程度上掩盖了光度函数中的小规模波动（真实或人为的）。 似乎模拟的中位数比平均值更能准确估计真实的光度函数。 当使用后者时，不能排除来自 Leggett、Ruiz 和 Bergeron（1998 年）样本的年龄为 100 亿年或更老的情况。 显示英文摘要

摘要： White dwarf cooling sequences provides a useful indicator of the evolutionary time scales involved in the chronometry and star formation history of the galactic disk and, for this reason, the luminosity function of white dwarfs has become a powerful tool for studies of the evolution and formation of the Milky Way. We examine the faint-end ($M_V > +14$) behavior of the disk white dwarf luminosity function using the $1/V_{\rm max}$ method, but, for the first time, fully including the effects of realistic observational errors in the derived luminosity function. We find that observational errors, mostly in the bolometric corrections and trigonometric parallaxes, play a major role in obliterating (real or artificial) small scale fluctuations in the luminosity function. A better estimator of the true luminosity function seems to be the median over simulations, rather than the mean. When using the latter, an age of 10 Gyr or older can not be ruled out from the sample of Leggett, Ruiz, and Bergeron (1998).