We present an overview of the sample of northern hemisphere white dwarfs within 40 pc of the Sun detected from $Gaia$ Data Release 2 (DR2). We find that 521 sources are spectroscopically confirmed degenerate stars, 111 of which were first identified as white dwarf candidates from $Gaia$ DR2 and followed-up recently with the William Herschel Telescope and Gran Telescopio Canarias. Three additional white dwarf candidates remain spectroscopically unobserved and six unresolved binaries are known to include a white dwarf but were not in our initial selection of white dwarfs in the $Gaia$ DR2 Hertzsprung-Russell diagram (HRD). Atmospheric parameters are calculated from $Gaia$ and Pan-STARRS photometry for all objects in the sample, confirming most of the trends previously observed in the much smaller 20 pc sample. Local white dwarfs are overwhelmingly consistent with Galactic disc kinematics, with only four halo candidates. We find that DAZ white dwarfs are significantly less massive than the overall DA population ($\overline{M}_\mathrm{DAZ} = 0.59\,\mathrm{M}_\odot$, $\overline{M}_\mathrm{DA} = 0.66\,\mathrm{M}_\odot$). It may suggest that planet formation is less efficient at higher mass stars, producing more massive white dwarfs. We detect a sequence of crystallised white dwarfs in the mass range from $0.6\ \lesssim M/\mathrm{M}_\odot \lesssim\ 1.0\,$ and find that the vast majority of objects on the sequence have standard kinematic properties that correspond to the average of the sample, suggesting that their nature can be explained by crystallisation alone. We also detect 56 wide binaries including a white dwarf and 26 double degenerates.

中文翻译：

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Gaiawhite dwarfs in 40 pc II: 体积受限的北半球样本

我们概述了从 $Gaia$ 数据发布 2 (DR2) 检测到的 40 pc 太阳范围内的北半球白矮星样本。我们发现 521 颗源是光谱确认的退化恒星，其中 111 颗首先被确定为来自 $Gaia$DR2 的白矮星候选者，最近用威廉·赫歇尔望远镜和加那利大望远镜进行了跟踪。另外三颗候选白矮星在光谱上仍未被观测到，已知六颗未解析的双星包括一颗白矮星，但不在我们最初选择的 $Gaia$ DR2 Hertzsprung-Russell 图 (HRD) 中的白矮星中。大气参数是根据样品中所有物体的 $Gaia$ 和 Pan-STARRS 测光计算得出的，证实了之前在小得多的 20 pc 样品中观察到的大部分趋势。本地白矮星与银河盘运动学极为一致，只有四个晕候选。我们发现 DAZ 白矮星的质量明显小于整个 DA 种群 ($\overline{M}_\mathrm{DAZ} = 0.59\,\mathrm{M}_\odot$, $\overline{M}_\ mathrm{DA} = 0.66\,\mathrm{M}_\odot$)。这可能表明行星形成在质量较大的恒星上效率较低，会产生更大质量的白矮星。我们检测到质量范围为 $0.6\ \lesssim M/\mathrm{M}_\odot \lesssim\ 1.0\,$ 的一系列结晶白矮星，并发现该序列上的绝大多数天体都具有标准运动学特性对应于样品的平均值，表明它们的性质可以单独通过结晶来解释。我们还检测到 56 个宽双星，包括一颗白矮星和 26 个双简并星。