We present the results of a search for galaxy substructures in a sample of 11
gravitational lens galaxies from the Sloan Lens ACS Survey. We find no
significant detection of mass clumps, except for a luminous satellite in the
system SDSS J0956+5110. We use these non-detections, in combination with a
previous detection in the system SDSS J0946+1006, to derive constraints on the
substructure mass function in massive early-type host galaxies with an average
redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a
Bayesian inference on the substructure mass function, within a median region of
about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean
projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68
percent confidence level and a substructure mass function slope $\alpha$ < 2.93
at the 95 percent confidence level for a uniform prior probability density on
alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we
infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ =
1.90$^{+0.098}_{-0.098}$ at the 68 percent confidence level. Since only one
substructure was detected in the full sample, we have little information on the
mass function slope, which is therefore poorly constrained (i.e. the Bayes
factor shows no positive preference for any of the two models).The inferred
fraction is consistent with the expectations from CDM simulations and with
inference from flux ratio anomalies at the 68 percent confidence level.

研究了 11 个引力透镜星系中的星系亚结构，发现除了系统 SDSS J0956 + 5110 中的一个亮卫星外，没有发现质量块。通过这些非检测结果，结合先前在 SDSS J0946 + 1006 中的检测结果，我们得出了大质量类星体寄主星系的亚结构质量函数的约束条件，并进行贝叶斯推断得出其坡度和平均投影亚结构质量分数。其中，推断出的亚结构分数与 CDM 模拟的期望值相一致。