英语翻译AO observations of the galactic center werecarried out between 2004 and 2012,with substantially,more data per epoch being obtained in2006 and onward.Previous publications containthe observational details for the first nine epochsof AO obs

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英语翻译AO observations of the galactic center werecarried out between 2004 and 2012,with substantially,more data per epoch being obtained in2006 and onward.Previous publications containthe observational details for the first nine epochsof AO obs
英语翻译
AO observations of the galactic center werecarried out between 2004 and 2012,with substantially,more data per epoch being obtained in
2006 and onward.Previous publications contain
the observational details for the first nine epochs
of AO observations (7,14–16).We collected 12
further epochs of AO observations between May
2008 and May 2012,using an observational
setup identical to those for all AO observations
obtained in 2006 and onward.For all but two
epochs,the high-order AO compensation was
based on observations of a bright [R band ∼ 10
magnitudes (mag)],on-axis,laser guide star,
generated with the Keck II sodium laser; and the
low-order (tip-tilt) AO corrections were determinedfrom measurements of the natural guide
star USNO 0600-28577051 (R = 13.7 mag and
ΔrSgrA* = 19′′) (ΔrSgrA*,distance to Sgr A*).
Table S2 provides the details of the 20 AO
epochs that are used here.
The data analysis for this study falls into several
distinct stages (17).First,for each epoch of
observations,we constructed an average image
of all the high-quality data collected as well as
three subset images,each composed of one-third
of the data (see Fig.1 for a zoom into the region
of an AO image where S0-102,S0-2,and the
electromagnetic manifestation of the black hole,
Sgr A*,reside).Second,both previously known
and newly detected stars were identified in the
images,along with their photometric and astrometric
characteristics,with the point spread
function (PSF) fitting program StarFinder (18).
Third,the positions of the stars in each epoch
were transformed into a common coordinate
system.Fourth,orbital model fits to the positions
of stars with significant orbital phase coverage
provided estimates of each star’s orbital
parameters.
The gravitational potentialin this region of
the Galaxy is dominated by the black hole,and to
a good approximation the stars follow Keplerian
orbits.Although deviations from a pure Keplerian
orbit will probably be detected in the future,this
cannot be expected with the current data set,and
we therefore assumed a point-mass potential and
Newtonian gravity.Within this framework,weused a c2-minimization routine to find the best-fit
orbital parameters (7).The six orbital elements
describing the star’s trajectory are the period,
eccentricity,time of closest approach (periapse
passage),inclination,angle to periapse,and angle
of the ascending node.The seven parameters
describing the gravitational potential are mass,
3D position (distance from Earth and focal point
of the orbital ellipse) and 3D velocity of the
point mass.

英语翻译AO observations of the galactic center werecarried out between 2004 and 2012,with substantially,more data per epoch being obtained in2006 and onward.Previous publications containthe observational details for the first nine epochsof AO obs
AO观察银河系中心werecarried在2004年和2012年之间,获得更多的具有划时代意义的数据.
2006年及以后,以前的出版物包含首九个月的时代观测资料AO观察（7月14-16日）.我们收集了12五月之间的AO观测的进一步的时代2008年和2012年5月,使用观察
设置相同的所有AO观察在2006年及以后获得.对于所有,但二时代的高阶AO补偿
根据光明的[R波段的观测〜10大小（MAG）,轴,激光导星,生成的凯克II钠激光;
低阶（尖倾斜）AO更正是determinedfrom的测量的自然指南明星USNO 0600-28577051（R = 13.7 mag和ΔrSgrA* = 19“）（ΔrSgrA,距离人马座A *）.表S2提供的20 AO的细节
历元,在这里使用.本研究的数据分析分为以下几个不同的阶段（17）.首先,为每个划时代
观察中,我们构建了一个平均图像所有的高品质的数据,以及收集三个子集图像,每个图像组成的三分之一的数据（参照图1到该区域中的变焦一个AO图像S0-102,S0-2,和电磁表现的黑洞,人马座A *,居住）.其次,无论是先前已知的新检测到的恒星中确定的图像,以及与他们的光测和天文的点扩散的特点,函数（PSF）的装修方案StarFinder（18）.第三,星星的位置,在每一个时代被转化成一个共同的坐标系统.四,轨道模型适合的位置具有显着的轨道阶段覆盖的明星估计每颗恒星的轨道参数.引力potentialin这一地区的银河系是占主导地位的黑洞,并
一个很好的近似遵循开普勒的明星轨道.虽然从一个纯粹的开普勒的偏差
轨道可能会在未来被检测到,这不能期望与当前的数据集,因此,我们假定一个点质量的潜力,牛顿引力.在此框架内,weused一个的C2最小化程序,以找到最合适的轨道参数（7）.6个轨道参数描述恒星的运动轨迹期间,偏心,时间最接近（近质通道）,倾角,角度近质心和角度
升交点.这七个参数描述引力势的质量,三维位置（距离地球和焦点轨道的椭圆形）和三维速度
点质量.

AO观测星系中心的werecarried出2004年和2012年之间,实质上,更多的数据被获得的每个时代
　　2006年及以后。之前的出版物包含
　　观测细节前九世
　　澳的观察(7,14 - 16)。我们收集了12
　　进一步观察的时代AO之间可能
　　2008年和2012年5月,使用一种观察
　　设置相同的所有AO观察
　　在2006年及...

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AO观测星系中心的werecarried出2004年和2012年之间,实质上,更多的数据被获得的每个时代
　　2006年及以后。之前的出版物包含
　　观测细节前九世
　　澳的观察(7,14 - 16)。我们收集了12
　　进一步观察的时代AO之间可能
　　2008年和2012年5月,使用一种观察
　　设置相同的所有AO观察
　　在2006年及以后的获得。除了两个
　　时代,高阶AO补偿

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