标题： 总质量密度和IMF的低质量端斜率是否呈反相关？ 显示英文标题

标题： Are the total mass density and the low-mass end slope of the IMF anti-correlated?

摘要： 我们对来自X-Shooter透镜巡天（XLENS）的九个大质量透镜早期类型星系（ETGs）进行了详细的透镜效应、动力学和恒星群体分析。结合来自哈勃太空望远镜（HST）成像的引力透镜约束条件以及来自甚大望远镜（VLT）X-Shooter（XSH）光谱的空间分辨动力学和线指数约束条件，我们推断了恒星初始质量函数（IMF）的低质量斜率和低截止质量：分别为$x_{250}=2.37^{+0.12}_{-0.12}$和$M_{{\rm low}, 250}= 0.131^{+0.023}_{-0.026}\, M_{\odot}$，对应于参考点$\sigma \equiv 250\, {{\rm kms}}^{-1}$和 R$_{{\rm eff}} \equiv 10$千秒差距。所有XLENS系统均与比银河系更陡峭的IMF斜率一致。除了总动态质量密度与低质量IMF斜率之间存在87%置信水平上的反相关性 [$dx/d\log(\rho)$ = $ -0.19^{+0.15}_{-0.15}$] 外，我们没有发现IMF斜率与其他任何量之间有显著的相关性。这一反相关性与史密斯等人（2015年）发现的低红移透镜一致，这些透镜具有高视向速度弥散和高恒星质量密度，但出乎意料的是具有较浅的IMF斜率。 显示英文摘要

摘要： We conduct a detailed lensing, dynamics and stellar population analysis of nine massive lens early-type galaxies (ETGs) from the X-Shooter Lens Survey (XLENS). Combining gravitational lensing constraints from HST imaging with spatially-resolved kinematics and line-indices constraints from VLT X-Shooter (XSH) spectra, we infer the low-mass slope and the low cut-off mass of the stellar Initial Mass Function (IMF): $x_{250}=2.37^{+0.12}_{-0.12}$ and $M_{{\rm low}, 250}= 0.131^{+0.023}_{-0.026}\, M_{\odot}$, respectively, for a reference point with $\sigma \equiv 250\, {{\rm kms}}^{-1}$ and R$_{{\rm eff}} \equiv 10$ kpc. All the XLENS systems are consistent with an IMF slope steeper than Milky Way-like. We find no significant correlations between IMF slope and any other quantity, except for an anti-correlation between total dynamical mass density and low-mass IMF slope at the 87% CL [$dx/d\log(\rho)$ = $ -0.19^{+0.15}_{-0.15}$]. This anti-correlation is consistent with the low redshift lenses found by Smith et al. (2015) that have high velocity dispersions and high stellar mass densities but surprisingly shallow IMF slopes.