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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19997 |
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| _version_ | 1866909623983800320 |
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| author | Zhang, Luyao Feng, Fabo Rui, Yicheng Xiao, Guang-Yao Wang, Wenting |
| author_facet | Zhang, Luyao Feng, Fabo Rui, Yicheng Xiao, Guang-Yao Wang, Wenting |
| contents | Accurate measurements of stellar positions and velocities are crucial for studying galactic and stellar dynamics. We aim to create a Cartesian catalog from Gaia DR3 to serve as a high-precision database for further research using stellar coordinates and velocities. To avoid the negative parallax values, we select 31,129,169 sources in Gaia DR3 with radial velocity, where the fractional parallax error is less than 20% ($0 < σ_\varpi/\varpi < 0.2$). To select the most accurate and efficient method of propagating mean and covariance, we use the Monte Carlo results with $10^7$ samples (MC7) as the benchmark, and compare the precision of linear, second-order, and Monte Carlo error propagation methods. By assessing the accuracy of propagated mean and covariance, we observe that second-order error propagation exhibits mean deviations of at most 0.5% compared to MC7, with variance deviations of up to 10%. Overall, this outperforms linear transformation. Though Monte Carlo method with $10^4$ samples (MC4) is an order of magnitude slower than second-order error propagation, its covariances propagation accuracy reaches 1% when $σ_\varpi/\varpi$ is below 15%. Consequently, we employ second-order error propagation to convert the mean astrometry and radial velocity into Cartesian coordinates and velocities in both equatorial and galactic systems for 30 million Gaia sources, and apply MC4 for covariance propagation. The Cartesian catalog and source code are provided for future applications in high-precision stellar and galactic dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Cartesian catalog of 30 million Gaia sources based on second-order and Monte Carlo error propagation Zhang, Luyao Feng, Fabo Rui, Yicheng Xiao, Guang-Yao Wang, Wenting Astrophysics of Galaxies Accurate measurements of stellar positions and velocities are crucial for studying galactic and stellar dynamics. We aim to create a Cartesian catalog from Gaia DR3 to serve as a high-precision database for further research using stellar coordinates and velocities. To avoid the negative parallax values, we select 31,129,169 sources in Gaia DR3 with radial velocity, where the fractional parallax error is less than 20% ($0 < σ_\varpi/\varpi < 0.2$). To select the most accurate and efficient method of propagating mean and covariance, we use the Monte Carlo results with $10^7$ samples (MC7) as the benchmark, and compare the precision of linear, second-order, and Monte Carlo error propagation methods. By assessing the accuracy of propagated mean and covariance, we observe that second-order error propagation exhibits mean deviations of at most 0.5% compared to MC7, with variance deviations of up to 10%. Overall, this outperforms linear transformation. Though Monte Carlo method with $10^4$ samples (MC4) is an order of magnitude slower than second-order error propagation, its covariances propagation accuracy reaches 1% when $σ_\varpi/\varpi$ is below 15%. Consequently, we employ second-order error propagation to convert the mean astrometry and radial velocity into Cartesian coordinates and velocities in both equatorial and galactic systems for 30 million Gaia sources, and apply MC4 for covariance propagation. The Cartesian catalog and source code are provided for future applications in high-precision stellar and galactic dynamics. |
| title | A Cartesian catalog of 30 million Gaia sources based on second-order and Monte Carlo error propagation |
| topic | Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2503.19997 |