Punctuated chaos and the unpredictability of the Galactic center S-star orbital evolution

#Description of the data. <br> Raw and processed data for the manuscript "Punctuated chaos and the unpredictability of the Galactic center S-star orbital evolution" by Simon Portegies Zwart, Tjarda Boekholt, and Douglas Heggie. <br> The initial conditions for the S-stars are taken from the observed 27 stars by 2009ApJ...692.1075G. We adopted those observed initial conditions and converted them into orbital elements adopting a distance to the black hole of 8178pc and a mass of 4.154e+6 Solar masses. we adopted a current time of 1 January 2021. <br> We subsequently calculate the orbital evolution of all particles (S-stars and black hole) for 10000years. Since the system is chaotic, we adopted Brutus (see 2018CNSNS..61..160P) with a tolerance of $10^{-24}$ to perform the calculations storing snapshots every 0.1yr. The raw data contains two of these data sets for the canonical S-star Cartesian coordinates as a function of time, and one set in which one star (S5) was displaced in the positive x-direction by $10^{-10}$ relative to it's current (1 Jan 2021) x-coordinate. <br> The calculation are performed within the AMUSE framework (2013CoPhC.183..456P). <br> Main conclusions from the paper and supported by our analysis of the data. <br> -The S-star cluster around the supermassive black hole has a Lyapunv time scale of about 450 years. <br> -The S-star cluster does not resembler a "Solar system" because of the orbits have a wide range in eccentricity and inclination. <br> -Chaos in the S-star cluster is driven by close encounters between stars, which happend to be near the supermassive black hole. <br> -The close near-black-hole encounters lead to the brownian motion of the black hole, which is reflected in changes in the S-star orbits. <br> -minitious differences in initial conditions lead to slightly different close encounters, which drive differences in the details of the black hole's Brownian motion. <br> more details in README.md <br> Running the scripts requires the Astrophysical Multipurpose Software Environment (AMUSE for short). AMUSE can be downloaded from git through:https://github.com/amusecode/amuse see https://www.amusecode.org/ for a more extensive description. <br> The data is organized in files in directories. <br> Files and directories: REDME.md # this file data_raw # raw data in AMUSE hdf5 format. data_processed # processed data files, typically in python pickle binary format src # contains the script for running Brutus in AMUSE figures # processed figures in pdf format generated from the scripts plot # plotting routins for making the figures from processed data process # processing routines, take the raw data and process them <br> Subcontent: * data_raw: Contains the raw data files in AMUSE hdf5 format. The data is generated using Brutus with a tolerance of $10^{-24}$ as indicated in the filename. similar files are availabelf for $10^{-18}$ and $10^{-21}$. -Sstar_pert_dx0_eta-24.0.amuse Raw snapshots of the S-stars at 1 January 2021 for 10000yr at time intervals of 0.1 yr. -Sstar_pert_dx-10.0_eta-24.0.amuse Raw snapshots of the S-stars at 1 January 2021 for 10000yr at time intervals of 0.1 yr. This calculation was performed using the same initial realization used to generate star_pert_dx0_eta-24.0.amuse but with star S5 displaced in the positive x-coordinate by a relative distance of $dx = 1.e-10$. Resulting in an x-coordinate ofr the star S5 of $S5.x = S5.x * (1+dx)$ <br> * data_processed: processed data files are python pickle files, written by the processing routines from the "process" directory. These files are used for the plotting routines in the "plot" directory. -Sstar_dx0_eta-24_BH_NN_distance.pkl Distance to the black hole and its nearest neighbor -Sstar_dx0_eta-24_orbits.pkl orbitsal parameters of the S-stars as a function of time of the canconical solution. -Sstar_dx0_eta-24_BHdistance.pkl Distance to the black hole -Sstars_dx0_eta-24_dxv.pkl file containting the difference between the canonical and the perturbed solution in terms of positional and velocity difference. -S5_dx-10_eta-24_dxv.pkl file containting the difference between the canonical and the perturbed solution in terms of positional and velocity difference. In this case the file presents the difference between the canconical solution and the solution in which star S5 is perturbed in the x-direction by $10^{-10}$. <br> -S5_dx-10_eta-24_orbits.pkl orbitsal parameters of the S-stars as a function of time of the solution in which star S5 is perturbed in the x-direction: $S5.x = S5.x * (1+dx)$ with $dx = 10^{-10}$ <br> * src contains runscripts and helper scripts for performing the calculations. Running these may take a long time. * figures contains the pdf file figures generated with the scripts in the "plot" directory * plot plotting routines. Takes the data from the data_processed directory and makes figures of the appropriate parameters. * process contains the scripts to process the raw simulation data (AMUSE hdf5 formatted) and turns them into specific reduced data sets (in binary python picle format). <br> <br> December 2022 Simon Portegies Zwart, Leiden Observatory <br> <br> <br>

# 数据集说明
本数据集对应Simon Portegies Zwart、Tjarda Boekholt与Douglas Heggie所撰论文《间断混沌与银心S星轨道演化的不可预测性（Punctuated chaos and the unpredictability of the Galactic center S-star orbital evolution）》的原始与处理后数据。

S星的初始条件取自2009ApJ...692.1075G文献中观测到的27颗恒星。我们采用该观测初始条件，结合8178秒差距（pc）的黑洞距离与4.154×10^6太阳质量的黑洞质量，将其转换为轨道根数，并设定当前时间为2021年1月1日。

随后我们计算所有粒子（S星与黑洞）10000年的轨道演化。由于该系统具有混沌特性，我们采用Brutus求解器（参见2018CNSNS..61..160P），设置精度容差为10^-24，每0.1年存储一次快照。原始数据包含两套标准S星笛卡尔坐标随时间变化的数据集，以及一套将S5恒星沿x轴正方向偏移其当前（2021年1月1日）x坐标10^-10倍的扰动数据集。

所有计算均在**天体物理多用途软件环境（Astrophysical Multipurpose Software Environment，简称AMUSE）**框架下完成（参见2013CoPhC.183..456P）。

本文的主要结论由本数据集的分析支撑，具体如下：
1. 环绕超大质量黑洞的S星团的**李雅普诺夫（Lyapunov）时间尺度**约为450年。
2. 由于轨道偏心率与倾角分布广泛，S星团的动力学特征与"太阳系"并不相似。
3. S星团中的混沌现象由恒星间的近距离交会驱动，此类交会发生在超大质量黑洞附近。
4. 近距离黑洞交会会引发黑洞的布朗运动，这一现象会体现在S星轨道的变化中。
5. 初始条件的微小差异会导致近距离交会出现细微差别，进而影响黑洞布朗运动的细节。

更多细节请参见README.md文件。

运行本数据集的处理脚本需依赖AMUSE，可通过Git从https://github.com/amusecode/amuse下载，更详细的说明请访问https://www.amusecode.org/。

本数据集以目录下的文件形式组织，各文件与目录说明如下：
- README.md：本说明文件
- data_raw：采用AMUSE HDF5格式存储的原始数据
- data_processed：处理后的数据文件，通常采用Python pickle二进制格式
- src：包含在AMUSE中运行Brutus的脚本
- figures：通过脚本生成的PDF格式处理后图像
- plot：用于从处理后数据生成图像的绘图程序
- process：数据处理程序，读取原始数据并完成格式转换

各子目录详细内容如下：
1. data_raw：包含AMUSE HDF5格式的原始数据文件，文件名中已标注Brutus求解器的容差参数为10^-24，此外还提供了容差为10^-18与10^-21的同类文件。
- Sstar_pert_dx0_eta-24.0.amuse：2021年1月1日起10000年时长内，每0.1年存储一次的S星原始快照数据。
- Sstar_pert_dx-10.0_eta-24.0.amuse：与Sstar_pert_dx0_eta-24.0.amuse采用相同初始配置生成的原始快照数据，仅将S5恒星的x坐标沿正方向偏移原坐标的10^-10倍，即S5.x = S5.x × (1+10^-10)。
2. data_processed：由process目录下的程序生成的Python pickle格式处理后数据文件，供plot目录下的绘图程序使用。
- Sstar_dx0_eta-24_BH_NN_distance.pkl：黑洞与其近邻恒星的距离数据
- Sstar_dx0_eta-24_orbits.pkl：标准解下S星轨道参数随时间的变化数据
- Sstar_dx0_eta-24_BHdistance.pkl：黑洞距离数据
- Sstars_dx0_eta-24_dxv.pkl：标准解与扰动解之间的位置与速度差数据
- S5_dx-10_eta-24_dxv.pkl：标准解与S5恒星x方向偏移10^-10的扰动解之间的位置与速度差数据
- S5_dx-10_eta-24_orbits.pkl：S5恒星x方向偏移10^-10的扰动解下，S星轨道参数随时间的变化数据
3. src：包含运行计算所需的主脚本与辅助脚本，运行此类脚本通常耗时较长。
4. figures：通过plot目录下脚本生成的PDF格式图像文件。
5. plot：绘图程序，读取data_processed目录下的数据，生成对应参数的可视化图像。
6. process：数据处理脚本，读取AMUSE HDF5格式的原始模拟数据，并将其转换为特定的精简数据集（Python pickle二进制格式）。

2022年12月
Simon Portegies Zwart，莱顿天文台