We study the abundance of substructure in the matter density near galaxies
using ALMA Science Verification observations of the strong lensing system
SDP.81. We present a method to measure the abundance of subhalos around
galaxies using interferometric observations of gravitational lenses. Using
simulated ALMA observations, we explore the effects of various systematics,
including antenna phase errors and source priors, and show how such errors may
be measured or marginalized. We apply our formalism to ALMA observations of
SDP.81. We find evidence for the presence of a $M=10^{8.96\pm 0.12} M_{\odot}$
subhalo near one of the images, with a significance of $6.9\sigma$ in a joint
fit to data from bands 6 and 7; the effect of the subhalo is also detected in
both bands individually. We also derive constraints on the abundance of dark
matter subhalos down to $M\sim 2\times 10^7 M_{\odot}$, pushing down to the
mass regime of the smallest detected satellites in the Local Group, where there
are significant discrepancies between the observed population of luminous
galaxies and predicted dark matter subhalos. We find hints of additional
substructure, warranting further study using the full SDP.81 dataset
(including, for example, the spectroscopic imaging of the lensed carbon
monoxide emission). We compare the results of this search to the predictions of
$\Lambda$CDM halos, and find that given current uncertainties in the host halo
properties of SDP.81, our measurements of substructure are consistent with
theoretical expectations. Observations of larger samples of gravitational
lenses with ALMA should be able to improve the constraints on the abundance of
galactic substructure.

使用 ALMA 对 SDP.81 的观测结果，研究了星系周围物质密度中的子结构丰度，并得出了关于重子物质子谷物的丰度下限以及与 ΛCDM 半径的一致性的结论。

使用 ALMA 观测尘埃星系 SDP.81 探测透镜引力微弱信号

Detection of lensing substructure using ALMA observations of the dusty  galaxy SDP.81

We devise a method to measure the abundance of satellite halos in
gravitational lens galaxies, and apply our method to a sample of 7 lens
systems. After using Monte Carlo simulations to verify the method, we find that
substructure comprises fraction f=0.02 (median, 0.006<f<0.07 at 90% confidence)
of the mass of typical lens galaxies, in excellent agreement with predictions
of CDM simulations. We estimate a characteristic critical radius for the
satellites of 0.0001<b/arcsec<0.006 (90% confidence). For a satellite mass
function of dn/dM M^x with x=-1.8 and M_l<M<M_h, the critical radius provides
an estimate that the upper mass limit is 10^6Msun < M_h < 10^9Msun. Our
measurement confirms a generic prediction of CDM models, and may obviate the
need to invoke alternatives to CDM like warm dark matter or self-interacting
dark matter.

基于引力透镜的天体，我们设计了一种方法来测量卫星晕的丰度，这种方法被应用于 7 个透镜系统的样本中。经过使用蒙特卡罗模拟验证该方法后，我们发现亚结构占典型透镜星系质量的 f = 0.02（中位数，0.006 <f <0.07，置信度为 90％），与 CDM 模拟的预测非常吻合。我们估计卫星天体的特征临界半径为 0.0001<b/arcsec<0.006（置信度为 90％）。对于质量函数 dn /dM M ^ x，其中 x =-1.8 且 M_l < M <M_h，临界半径提供了一种估计上限质量为 10 ^6Msun <M_h <10 ^9Msun 。我们的测量确认了 CDM 模型的一般预测，并可能避免使用 CDM 的替代方案，如暖暗物质或自相互作用暗物质的需要。