%0 Generic %1 chilingarian2019estimating %A Chilingarian, Igor V. %A Grishin, Kirill A. %D 2019 %K dispersion fitting uncertainty velocity %T Estimating Statistical Uncertainties of Internal Kinematics of Galaxies and Star Clusters Derived Using Full Spectrum Fitting %U http://arxiv.org/abs/1912.05269 %X Pixel-space full spectrum fitting exploiting non-linear $\chi^2$ minimization became a 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 IDL and 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.

@misc{chilingarian2019estimating, 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.}, added-at = {2019-12-12T17:23:51.000+0100}, author = {Chilingarian, Igor V. and Grishin, Kirill A.}, biburl = {https://www.bibsonomy.org/bibtex/202cf69f4e896aaf4654bcb261f0062b5/heh15}, description = {Estimating Statistical Uncertainties of Internal Kinematics of Galaxies and Star Clusters Derived Using Full Spectrum Fitting}, interhash = {8b77829ff0594883b64fc9708df4645f}, intrahash = {02cf69f4e896aaf4654bcb261f0062b5}, keywords = {dispersion fitting uncertainty velocity}, note = {cite arxiv:1912.05269Comment: 8 pages, 2 figures, submitted to PASP; the code is available here https://bitbucket.org/extragalactic/pxf_kin_err/src/master/}, timestamp = {2019-12-12T17:23:51.000+0100}, title = {Estimating Statistical Uncertainties of Internal Kinematics of Galaxies and Star Clusters Derived Using Full Spectrum Fitting}, url = {http://arxiv.org/abs/1912.05269}, year = 2019 }