Estimating extragalactic Faraday rotation

NOTE:  This is a reupload of the data set originally hosted at http://www.mpa-garching.mpg.de/ift/faraday/ . Below follows the content of the corresponding webpage, with only slight changes concerning formatting and the removal of obsolete links and contact information.

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Note: Due to a minor bug in the original code, the files on this website have been updated on February 16th, 2015. The numbers have changed only slightly. However, if you have retrieved the files before this date, please download them again.

Estimating extragalactic Faraday rotation

Here you can download the results presented in the paper "Estimating extragalactic Faraday rotation" (arXiv:1404.3701) by Niels Oppermann, Henrik Junklewitz, Maksim Greiner, Torsten A. Enßlin, Takuya Akahori, Ettore Carretti, Bryan M. Gaensler, Ariel Goobar, Lisa Harvey-Smith, Melanie Johnston-Hollitt, Luke Pratley, Dominic H.F.M. Schnitzeler, Jeroen M. Stil, and Valentina VaccaThe results are provided as hdf5 files. See here for information about the file format and here for the python interface. Alternative fits files containing the same information are also provided.All results provided make use of the 'polar caps' data split described in the paper.

Galactic foreground

In the foreground.hdf5 file you find the reconstruction of the Galactic Faraday depth, stored in HEALPix format. The structure of the file is the following:

'angspec': The reconstructed angular power spectrum of the dimensionless auxiliary field as shown in Fig. 10 of the paper. The values correspond to multipoles from l=0 to l=383.'profile': The Galactic variance profile that relates the dimensionless auxiliary field and the Galactic Faraday depth, as shown in Fig. 11, in units of rad/m2.'maps/s': The reconstructed dimensionless auxiliary field, i.e., the Galactic Faraday depth divided by the Galactic variance profile.'maps/phi': The reconstructed Galactic Faraday depth in units of rad/m2.'uncertainty/s': The pixel-wise uncertainty of the reconstructed dimensionless auxiliary field.'uncertainty/phi': The pixel-wise uncertainty of the reconstructed Galactic Faraday depth in units of rad/m2.

The last five results are stored as RING-ordered HEALPix maps at a resolution of Nside=128. The last four results correspond to the top four panels of Fig. 15.

Alternatively, you may use the foreground.fits fits file, which contains six binary table extensions corresponding to the six data sets described above. The names of the extensions are the same as the names of the data sets in the hdf5 file (i.e. ANGSPEC, PROFILE, MAPS/S, MAPS/PHI, UNCERTAINTY/S, UNCERTAINTY/PHI).

Extragalactic contributions

Here we provide samples drawn from the approximate posterior probability distribution for the extragalactic contributions to each data point. Each sample consists of 41632 numbers, the extragalactic contributions to each of the data points, in rad/m2. We provide 1000 such samples in total. Each one of these samples represents a possible configuration of extragalactic Faraday rotation contributions that is not ruled out by the data.

How to use the samples

A range of values that is less likely appears less often in the samples and vice versa. Thus, the frequency with which the sample values lie within a certain interval gives the posterior probability for the true extragalactic contribution to lie within that interval.When calculating a quantity as a function of the extragalactic Faraday contribution for one or several sources, this function should be evaluated for each of the samples. This will yield 1000 different answers. The distribution of these answers corresponds roughly to the posterior distribution for the quantity of interest, given the data and assumptions used in our paper.Obviously, using a smaller number of samples is possible, but the more samples are used, the more accurate the resulting distribution.See Appendix D of the paper for a more detailed description of the suggested usage of these samples.

How to get the samples

We provide one file containing all 1000 samples (samples.hdf5 (1000 samples; 162 MB)) and one containing a subset consisting of the first 100 samples (samples_subset.hdf5 (100 samples; 19 MB)). The latter is provided to limit the data volume to be downloaded for testing purposes or if a smaller number of samples is to be used. The structue of the hdf5 files is the following. The file contains three groups, 'sourceinfo/', 'samples/', and 'summary/'. The contents of 'sourceinfo/' are:

'sourceinfo/catalog': The name of the catalogs from which the data points are taken, using the nomenclature of Table 1 of Oppermann et al. (2012) and "Mao 2012" for the newly added data points.'sourceinfo/Gal_lon': Galactic longitude of the data points in degrees.'sourceinfo/Gal_lat': Galactic latitude of the data points in degrees.'sourceinfo/observed': The observed Faraday rotation value, for cases for which this is public, in rad/m2.'sourceinfo/sigma_observed': The error bar of the observed value, for cases for which this is public, in rad/m2. For the data points of the `Taylor' catalog, the published error bars are multiplied by a factor 1.22.'sourceinfo/foreground': The reconstructed posterior mean for the Galactic Faraday depth at the source's location, in rad/m2.'sourceinfo/sigma_foreground': The estimated posterior uncertainty for the Galatctic Faraday depth at the source's location, in rad/m2.

The group 'samples/' contains the samples, named 'samples/sample000' to 'samples/sample999'. Each of these data sets also has an attribute 'randomseed' that coincides with the sample number (000 to 999).

The group 'summary/' summarizes the distribution of the sample values by providing the mean in a data set 'summary/mean' and the standard deviation in a data set 'summary/standarddev', both in rad/m2.

For easier identification, the data points of each individual catalog are used in the same order as they appear in the original catalogs, with the exception of the observations that appear in several catalogs. For these, both catalogs are mentioned in the 'sourceinfo/catalog' dataset; e.g., "Tabara / Broten". We again provide fits files as an alternative. The file with the complete set of samples (samples.fits (1000 samples; 162 MB)) has four binary table extensions, the file containing the subset of samples (samples_subset.fits (100 samples; 19 MB)) has three binary table extension.The first extension contains 41632 rows for the 41632 sources and seven columns for the catalog identifier, Galactic longitude in degrees, Galactic latitude in degrees, observed Faraday rotation value in rad/m2, its error bar in rad/m2, the reconstructed Galactic foreground in rad/m2, and its estimated uncertainty in rad/m2.The second and third (in the case of the large file) extension tables have 41632 rows for the 41632 sources and 500 columns each for the different samples (or 100 columns in the case of the smaller file). The values in this table are in rad/m2.The last extension contains 41632 rows for the 41632 sources and two columns for the summary of the distributions, given by their mean in rad/m2 and their standard deviation in rad/m2.The following table gives an overview over the information stored in the files. These first ten rows correspond to the first ten sources in the catalog. The large number of digits for the sky position is due to a coordinate conversion.<Table was not retrievable via the WayBack machine>   

Acknowledgments

The authors would like to thank the anonymous referee for constructive criticism, as well as Shane P. O'Sullivan for providing his unpublished rotation measure synthesis data and S. Ann Mao for providing her newest data set in digital form. The results in this publication have been derived using the NIFTy package (Selig et al. 2013), as well as the HEALPix package (Gorski et al. (2005). This research has made use of NASA's Astrophysics Data System. It was supported by the DFG Forschergruppe 1254 "Magnetisation of Interstellar and Intergalactic Media: The Prospects of Low-Frequency Radio Observations". T.A. is supported by the Japan Society for the Promotion of Science (JSPS). B.M.G. acknowledges the support of the Australian Research Council through grant FL100100114. Some of the calculations were carried out on the Canada Foundation for Innovation funded CITA Sunnyvale cluster. 

NOTE: below is the traceback  of the Wayback Machine that was used to download data and original webpage:

FILE ARCHIVED ON 01:14:00 May 03, 2022 AND RETRIEVED FROM THEINTERNET ARCHIVE ON 08:24:04 Dec 15, 2025.JAVASCRIPT APPENDED BY WAYBACK MACHINE, COPYRIGHT INTERNET ARCHIVE.

ALL OTHER CONTENT MAY ALSO BE PROTECTED BY COPYRIGHT (17 U.S.C.SECTION 108(a)(3)).

**注意**：本数据集为原托管于http://www.mpa-garching.mpg.de/ift/faraday/ 的数据集的重新上传版本。以下为对应网页的内容，仅对格式进行了小幅调整，并移除了已失效的链接与联系信息。

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**补充说明**：由于原始代码存在一处小漏洞，本网站的数据集文件已于2015年2月16日完成更新，数据数值仅发生了微小变动。若您在此日期前已下载过本数据集，请重新获取最新版本。

# 河外法拉第旋转量估算
您可在此下载论文"Estimating extragalactic Faraday rotation"（arXiv:1404.3701）的相关结果，论文作者包括Niels Oppermann、Henrik Junklewitz、Maksim Greiner、Torsten A. Enßlin、Takuya Akahori、Ettore Carretti、Bryan M. Gaensler、Ariel Goobar、Lisa Harvey-Smith、Melanie Johnston-Hollitt、Luke Pratley、Dominic H.F.M. Schnitzeler、Jeroen M. Stil以及Valentina Vacca。本结果以HDF5格式文件提供，文件格式说明与Python接口文档可分别参见此处与此处。同时我们也提供包含相同数据内容的FITS格式文件作为替代选项。所有提供的结果均采用论文中所述的"极盖（polar caps）"数据划分方案。

## 银河前景成分
在`foreground.hdf5`文件中，存储了以HEALPix（Hierarchical Equal Area isoLatitude Pixelization，分层等面积球面像素化）格式保存的银河法拉第深度重建结果。该文件的结构如下：
- `angspec`：论文中图10所示的无量纲辅助场的重建角功率谱，其数值对应多极矩( l )从0到383的范围。
- `profile`：连接无量纲辅助场与银河法拉第深度的银河方差分布廓线，如图11所示，单位为( mathrm{rad/m^2} )。
- `maps/s`：重建的无量纲辅助场，即银河法拉第深度除以银河方差分布廓线所得的结果。
- `maps/phi`：重建的银河法拉第深度，单位为( mathrm{rad/m^2} )。
- `uncertainty/s`：重建的无量纲辅助场的逐像素不确定性。
- `uncertainty/phi`：重建的银河法拉第深度的逐像素不确定性，单位为( mathrm{rad/m^2} )。

上述后五项结果均以RING序HEALPix地图格式存储，分辨率为( mathrm{Nside=128} )。其中后四项结果对应论文图15的上方四幅子图。

作为替代，您也可以使用`foreground.fits`文件，该文件包含六个二进制表扩展段，分别对应上述六个数据集。扩展段的名称与HDF5文件中的数据集名称一致（即ANGSPEC、PROFILE、MAPS/S、MAPS/PHI、UNCERTAINTY/S、UNCERTAINTY/PHI）。

## 河外贡献成分
本节提供从每个数据点的河外贡献近似后验概率分布中抽取的样本。每个样本包含41632个数值，对应每个数据点的河外法拉第旋转贡献量，单位为( mathrm{rad/m^2} )。我们共提供1000个此类样本，每个样本均代表一组未被观测数据排除的河外法拉第旋转贡献可能分布。

### 样本使用方法
数值出现频率越低，其在样本集中的占比也越低，反之亦然。因此，样本值落在某一区间内的频率，即可视为真实河外贡献量落在该区间内的后验概率。当针对单个或多个源计算以河外法拉第贡献量为变量的物理量时，需对每个样本分别计算该函数，最终将得到1000个不同的计算结果。结合本论文使用的观测数据与假设前提，这些结果的分布将近似对应目标物理量的后验分布。当然，使用更少的样本也是可行的，但样本数量越多，最终得到的分布精度也就越高。关于本样本集建议使用方式的详细说明，请参见论文附录D。

### 样本获取方式
我们提供两个文件：一个包含全部1000个样本（`samples.hdf5`，1000个样本，大小162 MB），另一个包含前100个样本的子集（`samples_subset.hdf5`，100个样本，大小19 MB）。后者用于在测试或仅需少量样本时，降低下载的数据量。HDF5文件的结构如下：该文件包含三个组：`sourceinfo/`、`samples/`与`summary/`。`sourceinfo/`的内容如下：
- `sourceinfo/catalog`：数据点所属的星表名称，沿用Oppermann等人(2012)的表1命名规范，新增数据点则标注为"Mao 2012"。
- `sourceinfo/Gal_lon`：数据点的银河经度，单位为度。
- `sourceinfo/Gal_lat`：数据点的银河纬度，单位为度。
- `sourceinfo/observed`：已公开的观测法拉第旋转量数值，单位为( mathrm{rad/m^2} )。
- `sourceinfo/sigma_observed`：已公开的观测值误差棒，单位为( mathrm{rad/m^2} )。针对`Taylor`星表的数据点，已发表的误差棒已乘以修正因子1.22。
- `sourceinfo/foreground`：源位置处重建得到的银河法拉第深度后验均值，单位为( mathrm{rad/m^2} )。
- `sourceinfo/sigma_foreground`：源位置处银河法拉第深度的后验不确定性估计值，单位为( mathrm{rad/m^2} )。

`samples/`组包含所有样本，命名为`samples/sample000`至`samples/sample999`。每个数据集均带有一个`randomseed`属性，其数值与样本编号（000至999）一致。

`summary/`组用于汇总样本值的分布情况，其中数据集`summary/mean`存储样本均值，`summary/standarddev`存储样本标准差，单位均为( mathrm{rad/m^2} )。

为便于识别，每个星表的数据点均按照其在原始星表中的顺序排列，仅对同时出现在多个星表中的观测数据例外：此类数据的`sourceinfo/catalog`字段会同时标注所有所属星表，例如"Tabara / Broten"。

我们同样提供FITS格式文件作为替代选项：包含全部1000个样本的文件（`samples.fits`，1000个样本，大小162 MB）包含4个二进制表扩展段，仅包含样本子集的文件（`samples_subset.fits`，100个样本，大小19 MB）包含3个二进制表扩展段。第一个扩展段包含41632行（对应41632个源）与7列数据，分别为星表标识符、银河经度（单位：度）、银河纬度（单位：度）、观测法拉第旋转量（单位：( mathrm{rad/m^2} )）、观测值误差棒（单位：( mathrm{rad/m^2} )）、重建银河前景分量（单位：( mathrm{rad/m^2} )）以及其不确定性估计值（单位：( mathrm{rad/m^2} )）。

（对于完整样本文件的）第二与第三个扩展段表包含41632行（对应41632个源），每个扩展段包含500列（子集文件则为100列），分别对应不同的样本，表中数值单位为( mathrm{rad/m^2} )。

最后一个扩展段包含41632行（对应41632个源）与2列数据，分别为样本分布的均值与标准差，单位均为( mathrm{rad/m^2} )。

下表汇总了文件中存储的所有信息，其前十行对应星表中的前十个源。天球坐标数值保留了大量小数位，这是坐标转换过程导致的。<该表格无法通过互联网档案馆（Wayback Machine）获取>

## 致谢
作者谨向提出建设性意见的匿名审稿人致谢，同时感谢Shane P. O'Sullivan提供其未发表的旋转量合成数据，以及S. Ann Mao以数字形式提供其最新数据集。本研究成果基于NIFTy软件包（Selig et al. 2013）与HEALPix软件包（Gorski et al. 2005）生成。本研究使用了NASA天体物理学数据系统（ADS）的资源，得到了德国研究基金会（DFG）合作研究组1254"星际与星系间介质磁化：低频射电观测的前景"的资助。T.A.得到了日本学术振兴会（JSPS）的支持。B.M.G.感谢澳大利亚研究委员会通过项目FL100100114提供的资助。部分计算工作在加拿大创新基金会资助的CITA Sunnyvale集群上完成。

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