We introduce MulensModel, a software package for gravitational microlensing
modeling. The package provides a framework for calculating microlensing model
magnification curves and goodness-of-fit statistics for microlensing events
with single and binary lenses as well as a variety of higher-order effects:
extended sources with limb-darkening, annual microlensing parallax, satellite
microlensing parallax, and binary lens orbital motion. The software could also
be used for analysis of the planned microlensing survey by the NASA flag-ship
WFIRST satellite. MulensModel is available at
this https URL

MulensModel 是一款用于引力微透镜建模的软件包，支持计算具有单个和双重透镜以及大量高阶效应（包括带有 limb-darkening 的扩展源、年度微透镜视差、卫星微透镜视差和二进制透镜轨道运动）的微透镜模型放大曲线和拟合优度统计，也可用于分析 NASA 旗舰 WFIRST 卫星计划的微透镜调查。

用 MulensModel 建模微引力透镜事件

Modeling microlensing events with MulensModel

Gravitational microlensing is the only method capable of exploring the entire
population of free-floating planets down to Mars-mass objects, because the
microlensing signal does not depend on the brightness of the lensing object. A
characteristic timescale of microlensing events depends on the mass of the
lens: the less massive the lens, the shorter the microlensing event. A previous
analysis of 474 microlensing events found an excess of very short events (1-2
days) - more than known stellar populations would suggest - indicating the
existence of a large population of unbound or wide-orbit Jupiter-mass planets
(reported to be almost twice as common as main-sequence stars). These results,
however, do not match predictions of planet formation theories and are in
conflict with surveys of young clusters. Here we report the analysis of a six
times larger sample of microlensing events discovered during the years
2010-2015. Although our survey has very high sensitivity (detection efficiency)
to short-timescale (1--2 days) microlensing events, we found no excess of
events with timescales in this range, with a 95% upper limit on the frequency
of Jupiter-mass free-floating or wide-orbit planets of 0.25 planet per
main-sequence star. We detected a few possible ultrashort-timescale events
(with timescales of less than 0.5 day), which may indicate the existence of
Earth- and super-Earth-mass free-floating planets, as predicted by
planet-formation theories. [abridged]

我们对 2010-2015 年间的一个六倍大的引力微透镜事件样本进行了分析，发现没有 1-2 天时间尺度范围内的事件频率超过预期，但有可能存在预期的地球质量和超级地球质量的游离行星。

没有大量未绑定或宽轨道木星质量行星

No large population of unbound or wide-orbit Jupiter-mass planets

Searches for extrasolar planets have uncovered an astonishing diversity of
planetary systems, yet the frequency of solar system analogs remains unknown.
The gravitational microlensing planet search method is potentially sensitive to
multiple-planet systems containing analogs of all the solar system planets
except Mercury. We report the detection of a multiple-planet system with
microlensing. We identify two planets with masses of ~0.71 and ~0.27 times the
mass of Jupiter and orbital separations of ~2.3 and ~4.6 astronomical units
orbiting a primary star of mass ~0.50 solar masses at a distance of ~1.5
kiloparsecs. This system resembles a scaled version of our solar system in that
the mass ratio, separation ratio, and equilibrium temperatures of the planets
are similar to those of Jupiter and Saturn. These planets could not have been
detected with other techniques; their discovery from only six confirmed
microlensing planet detections suggests that solar system analogs may be
common.

通过引力微透镜技术以及确认的六个微透镜行星发现了一个具有多个行星系统的行星系统，包括质量与距离与我们的太阳系类似的巨行星，这表明太阳系类似物可能很常见。

利用引力微透镜探测类木行星 / 土星类行星

Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing

Hundreds of gravitational microlensing events have now been detected towards
the Galactic bulge, with many more to come. The detection of fine structure in
these events has been theorized to be an excellent way to discover extra-solar
planetary systems along the line-of-sight to the Galactic center. We show that
by focusing on high magnification events the probability of detecting planets
of Jupiter mass or greater in the lensing zone (.6 -1.6 $R_E$) is nearly 100%,
with the probability remaining high down to Saturn masses and substantial even
at 10 Earth masses. This high probability allows a nearly definitive statement
to made about the existence of lensing zone planets in each such system that
undergoes high magnification. One might expect lightcurve deviations caused by
the source passing near the small primary lens caustic to be small due to the
large distance of the perturbing planet, but this effect is overcome by the
high magnification. High magnification events are relatively rare (e.g. $\sim
1/20$th of events have peak magnifications greater than 20), but they occur
regularly and the peak can be predicted in advance, allowing extra-solar planet
detection with a relatively small use of resources over a relatively small
amount of time.

高倍率引力微透镜事件是发现系外行星系统的有效方法，可能性接近 100％，即使是类土星和类地的行星也有很高的可能性，而这种事件相对稀少但可预测。