{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimating-statistical-uncertainties-of","title":"Estimating Statistical Uncertainties of Internal Kinematics of Galaxies and Star Clusters Derived Using Full Spectrum Fitting","arxiv_id":"1912.05269","date":"2019-12-11","proceeding":null,"authors":["Igor V. Chilingarian","Kirill A. Grishin"],"abstract":"Pixel-space full spectrum fitting exploiting non-linear $\\chi^2$ minimization became a \\emph{de facto} standard way of deriving internal kinematics from absorption line spectra of galaxies and star clusters. However, reliable estimation of uncertainties for kinematic parameters remains a challenge and is usually addressed by running computationally expensive Monte-Carlo simulations. Here we derive simple formulae for the radial velocity and velocity dispersion uncertainties based solely on the shape of a template spectrum used in the fitting procedure and signal-to-noise information. Comparison with Monte-Carlo simulations provides perfect agreement for different templates, signal-to-noise ratios and velocity dispersion between 0.5 and 10 times of the instrumental spectral resolution. We provide {\\sc IDL} and {\\sc python} implementations of our approach. The main applications are: (i) exposure time calculators; (ii) design of observational programs and estimates on expected uncertainties for spectral surveys of galaxies and star clusters; (iii) a cheap and accurate substitute for Monte-Carlo simulations when running them for large samples of thousands of spectra is unfeasible or when uncertainties reported by a non-linear minimization algorithms are not considered reliable.","url_abs":"http://arxiv.org/abs/1912.05269v1","url_pdf":"http://arxiv.org/pdf/1912.05269v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimating-statistical-uncertainties-of","repo_url":"https://bitbucket.org/extragalactic/pxf_kin_err","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}