Testing dark matter density profiles based on Pad\'e approximants of different orders

Abstract

We investigate whether low-order Pad\'e rational functions can be used as empirical density profiles for modeling dark matter halos from galaxy RCs. We introduce three parameterizations determined from Pad\'e series, denoted Pad\'e 02, Pad\'e 12 and Pad\'e 03, and compare them with pseudo-isothermal, Burkert, Beta, Brownstein, exponential-sphere and Persic models. The analysis is performed for eight galaxies under the assumption that RCs are dark matter dominated. The parameters are inferred from RC data and the relative statistical performance of the models is obtained through the Bayesian Information Criterion. We find that the Pad\'e profiles perform well, being comparable with the other profiles, albeit not universally preferred. In most galaxies, conventional two parameter profiles provide fits of comparable or better statistical quality, whereas the clearest improvement occurs for one particular galaxy, where the Pad\'e 03 profile gives the lowest BIC. Even though the Pad\'e profiles are often statistically less strong than other models, they appear plausible in explaining the dark matter nature. Hence, their empirical construction can therefore be used to reconstruct RCs phenomenologically.