Accurate parametrization of galaxies detected in the 21-cm HI emission is of fundamental importance to the measurement of commonly used indicators of galaxy evolution, including the Tully-Fisher relation and the HI mass function. Here, we propose a new analytic function, named the 'busy function', that can be used to accurately describe the characteristic doublehorn HI profile of many galaxies. The busy function is a continuous, differentiable function that consists of only two basic functions, the error function, erf(x), and a polynomial, |x|n, of degree n ≥ 2. We present the basic properties of the busy function and illustrate its great flexibility in fitting a wide range of HI profiles from the Gaussian profiles of dwarf galaxies to the broad, asymmetric double-horn profiles of spiral galaxies. Applications of the busy function include the accurate and efficient parametrization of observed HI spectra of galaxies and the construction of spectral templates for simulations and matched-filtering algorithms. We demonstrate the busy function's power by automatically fitting it to the HI spectra of 1000 galaxies from the HI Parkes All-Sky Survey (HIPASS) Bright Galaxy Catalog, using our own C/C++ implementation, and comparing the resulting parameters with the catalogued ones. We also present two methods for determining the uncertainties of observational parameters derived from the fit. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.
Westmeier, T., Jurek, R. J., Obreschkow, D., Koribalski, B. S., & Staveley-Smith, L. (2014). The busy function: A new analytic function for describing the integrated 21-cm spectral profile of galaxies. Monthly Notices of the Royal Astronomical Society, 438(2), 1176-1190. https://doi.org/10.1093/mnras/stt2266