论文标题
使用修改的对数正态幂定律分布来建模NGC 1711的质量函数
Using the Modified Lognormal Power Law Distribution to Model the Mass Function of NGC 1711
论文作者
论文摘要
确定恒星簇的质量函数（MF）可以很大程度上取决于所测量质量的范围，拟合技术和适合数据的分析函数。在这里，我们将NGC 1711的HST/WFPC2数据（大型麦哲伦云中的恒星群集）作为测试用例，以探索从单个数据集中对MF的一系列可能确定。我们采用分析性修改的对数正态幂律（MLP）分布，这是一种杂种函数，具有峰值的对数正态体样的身体和中间和高质量的幂律尾巴。与MLP的拟合的优点是，所得的最佳拟合函数可以是函数不同限制的混合功能，纯对数正态或纯幂律。观察值的完整性限制意味着数据包含$ \ sim 0.90 \，m _ {\ odot} $的质量。在这种情况下，MLP拟合基本上会产生纯幂律MF。我们证明，由于不满足基本假设，因此非线性回归/最小二乘方法是没有道理的。通过使用独立于安装的最大似然估计，我们找到了最佳拟合功能形式$ dn/d \ ln m \ propto m^{ - α} $，其中$α= 1.72 \ pm 0.05 $或$ 1.75 \ $ 1.75 \ pm 0.05 $ 0.05 $，分别针对两种不同的理论异隆模型。此外，我们探讨了由于观测的深度，在确定幂律指数中系统错误的可能性。当我们将观测数据与从$ 0.90 \ $ 0.90 \，m _ {\ odot} $的群众群体IMF中的人为生成的数据结合在一起时，最佳拟合MLP是一种混合功能，但具有陡峭的渐近斜率，但具有较陡峭的渐近斜率，即$α= 2.04 \ pm 0.04 \ pm 0.07 $ 0.07 $。这说明了常用的MF参数中的系统不确定性，这些参数可能取决于拟合的数据范围。
A determination of the mass function (MF) of stellar clusters can be quite dependent on the range of measured masses, the fitting technique, and the analytic function that is being fit to the data. Here, we use HST/WFPC2 data of NGC 1711, a stellar cluster in the Large Magellanic Cloud, as a test case to explore a range of possible determinations of the MF from a single dataset. We employ the analytic modified lognormal power-law (MLP) distribution, a hybrid function that has a peaked lognormal-like body and a power-law tail at intermediate and high masses. A fit with the MLP has the advantage that the resulting best-fit function can be either a hybrid function, a pure lognormal, or a pure power law, in different limits of the function. The completeness limit for the observations means that the data contains masses above $\sim 0.90\,M_{\odot}$. In this case, the MLP fits yield essentially a pure power-law MF. We demonstrate that the nonlinear regression/least-squares approach is not justified since the underlying assumptions are not satisfied. By using maximum likelihood estimation, which is independent of binning, we find a best-fit functional form $dN/d\ln m \propto m^{-α}$, where $α= 1.72 \pm 0.05$ or $1.75 \pm 0.05$ for two different theoretical isochrone models, respectively. Furthermore, we explore the possibility of systematic errors in the determination of the power-law index due to the depth of the observations. When we combine the observational data with artificially generated data from the lognormal Chabrier IMF for masses below $0.90\, M_{\odot}$, the best fit MLP is a hybrid function but with a steeper asymptotic slope i.e., $α= 2.04 \pm 0.07$. This illustrates the systematic uncertainties in commonly used MF parameters that can depend on the range of data that is fitted.
