论文标题
矮星系中恒星的适当运动：区分中央密度尖头与核心
The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores
论文作者
论文摘要
我们表明，在矮星系中测量$ {\ sim 2000} $星的适当运动，最多可确定不确定性为1 km/s，可以确定矮人的暗物质（DM）密度曲线是否具有中央核心或CUSP。我们通过构建模拟星目目录来得出这些限制，类似于未来的星体{\ it theia}类似的任务，包括天体坐标，径向速度和恒星的正确运动。矮人的DM光环的密度场是从扩展的Navarro-Frank-White（ENWF）球形模型中采样的，而星星的数量密度分布是垂坠球。星星的速度场是根据牛仔裤方程式设置的。蒙特卡洛马尔可夫链算法应用于$ n \ gtrsim 2000 $ stars的样本，返回了ENFW DM参数的无偏估计，以内的$ 10 \％$ $ \％$，并且具有$1σ$相对不确定性$ \ \ sillessim 20 $ \％。恒星的正确运动提高了ENFW参数之间的变性，而仅当视线速度可用时就会出现。 {我们的分析表明，通过估计半光线半径估计的质量密度曲线的对数斜率，$ n = 2000 $ stars的样本可以区分核心和尖端，以超过$8σ$。}适当的动作也可以返回型号的型号，同时又有$1σ$的尺寸。从$ n = 100 $到$ n = 6000 $星星。因此，适当动作的度量可以强烈限制DM在附近的矮人中的分布，并为理解DM的性质和特性提供了基本贡献。
We show that measuring the proper motion of ${\sim 2000}$ stars within a dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the Dark Matter (DM) density profile of the dwarf has a central core or cusp. We derive these limits by building mock star catalogues similar to those expected from future astrometric {\it Theia}-like missions and including celestial coordinates, radial velocity and proper motion of the stars. The density field of the DM halo of the dwarf is sampled from an extended Navarro-Frank-White (eNWF) spherical model, whereas the number density distribution of the stars is a Plummer sphere. The velocity field of the stars is set according to the Jeans equations. A Monte Carlo Markov Chain algorithm applied to a sample of $N\gtrsim 2000$ stars returns unbiased estimates of the eNFW DM parameters within $10\%$ of the true values and with $1σ$ relative uncertainties $\lesssim 20$\%. The proper motions of the stars lift the degeneracy among the eNFW parameters which appears when the line-of-sight velocities alone are available. {Our analysis demonstrates that, by estimating the log-slope of the mass density profile estimated at the half-light radius, a sample of $N=2000$ stars can distinguish between a core and a cusp at more than $8σ$.} Proper motions also return unbiased estimates of the dwarf mass profile with $1σ$ uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the size of the star sample increases from $N=100$ to $N=6000$ stars. The measure of the proper motions can thus strongly constrain the distribution of DM in nearby dwarfs and provides a fundamental contribution to understanding the nature and the properties of DM.
