  Since the asteroseismic revolution, availability of efficient and reliable
methods to extract stellar-oscillation mode parameters has been one of the
keystone of modern stellar physics. In the helio- and asteroseismology fields,
these methods are usually referred as peakbagging. We introduce in this paper
the apollinaire module, a new Python 3 open-source Markov Chains Monte Carlo
(MCMC) framework dedicated to peakbagging. The theoretical framework necessary
to understand MCMC peakbagging methods for disk-integrated helio- and
asteroseismic observations are extensively described. In particular, we present
the models that are used to estimate the posterior probability function in a
peakbagging framework. A description of the apollinaire module is then
provided. We explain how the module enables stellar background, p-mode global
pattern and individual-mode parameters extraction. By taking into account
instrumental specificities, stellar inclination angle, rotational splittings,
and asymmetries, the module allows fitting a large variety of p-mode models
suited for solar as well as stellar data analysis with different instruments.
After having been validated through a Monte Carlo fitting trial on synthetic
data, the module is benchmarked by comparing its outputs with results obtained
with other peakbagging codes. An analysis of the PSD of 89 one-year subseries
of GOLF observations is performed. Six stars are also selected from the Kepler
LEGACY sample in order to demonstrate the code abilities on asteroseismic data.
The parameters we extract with apollinaire are in good agreement with those
presented in the literature and demonstrate the precision and reliability of
the module.
