标题： 利用双重成像类星体的强引力透镜时间延迟累积分布测量$H_0$的 4% 精度 显示英文标题

标题： A 4% measurement of $H_0$ using the cumulative distribution of strong-lensing time delays in doubly-imaged quasars

摘要： 在大规模巡天的背景下，为了精确测量$H_0$而单独建模强引力透镜及其对应的时间延迟将会变得计算昂贵且极其复杂。 一种互补的方法是研究时间延迟的累积分布函数（CDF），其中全局透镜群体与$H_0$一起被建模。 本文中，我们使用一套流体动力学模拟来估计来自双像类星体的真实透镜分布的时间延迟 CDF。 我们发现，CDF 显示出大量的晕-晕方差，这些方差受密度剖面内斜率以及$5$千秒差距内的总质量调节。 为了拟合数据，我们使用主成分分析压缩了 CDF，并拟合了一个高斯过程回归器，其中包括三个物理特征：透镜的红移$z_{\rm L}$；晕的幂律指数$\alpha$，以及$5$千秒差距内的质量，再加上四个宇宙学特征。 假设宇宙是平坦的，我们将模型拟合到27个双重成像类星体上，得到 $H_0=71^{+2}_{-3}$公里/秒/百万千米，$z_{\rm L} = 0.36_{-0.09}^{+0.2} $，$\alpha=-1.8_{-0.1}^{+0.1}$，$\log(M(<5$千帕光年$)/M_\odot)=11.1_{-0.1}^{+0.1} $，$\Omega_{\rm M} = 0.3_{-0.04}^{+0.04} $和$\Omega_{\rm \Lambda}=0.7_{-0.04}^{+0.04}$。 我们将$z_{\rm L}$和$\log(M(<5$千秒差距$)/M_\odot)$的估计值与数据进行比较，并发现它们在数据的灵敏度范围内没有系统偏差。 我们生成了模拟的累积分布函数（CDF），并发现维拉·鲁宾天文台 (VRO) 可以测量$\sigma/H_0$到$<3\%$的范围，但受到模型精度的限制。 若要充分利用 VRO，我们需要进行模拟，以更大比例采样透镜星系群体，并采用多种反馈模型，探索所有可能的系统性影响。 显示英文摘要

摘要： In the advent of large scale surveys, individually modelling strong-gravitational lenses and their counterpart time-delays in order to precisely measure $H_0$ will become computationally expensive, and highly complex. A complimentary approach is to study the cumulative distribution function (CDF) of time-delays where the global population of lenses is modelled along with $H_0$. In this paper we use a suite of hydro-dynamical simulations to estimate the CDF of time-delays from doubly-imaged quasars for a realistic distribution of lenses. We find that the CDFs exhibit large amounts of halo-halo variance, regulated by the density profile inner slope and the total mass within $5$kpc. With the objective of fitting to data, we compress the CDFs using Principal Component Analysis and fit a Gaussian Processes Regressor consisting of three physical features: the redshift of the lens, $z_{\rm L}$; the power law index of the halo, $\alpha$, and the mass within $5$kpc, plus four cosmological features. Assuming a flat Universe, we fit our model to 27 doubly-imaged quasars finding $H_0=71^{+2}_{-3}$km/s/Mpc, $z_{\rm L} = 0.36_{-0.09}^{+0.2} $, $\alpha=-1.8_{-0.1}^{+0.1}$, $\log(M(<5$kpc$)/M_\odot)=11.1_{-0.1}^{+0.1} $, $\Omega_{\rm M} = 0.3_{-0.04}^{+0.04} $ and $\Omega_{\rm \Lambda}=0.7_{-0.04}^{+0.04}$. We compare our estimates of $z_{\rm L}$ and $\log(M(<5$kpc$)/M_\odot)$ to the data and find that within the sensitivity of the data, they are not systematically biased. We generate mock CDFs and find with that the Vera Rubin Observatory (VRO) could measure $\sigma/H_0$ to $<3\%$, limited by the precision of the model. If we are to exploit fully VRO, we require simulations that sample a larger proportion of the lens population, with a variety of feedback models, exploring all possible systematics.