Non-parametric deprojection of NIKA SZ observations: Pressure
  distribution in the Planck-discovered cluster PSZ1 G045.85+57.71
  The determination of the thermodynamic properties of clusters of galaxies at
intermediate and high redshift can bring new insights into the formation of
large-scale structures. It is essential for a robust calibration of the
mass-observable scaling relations and their scatter, which are key ingredients
for precise cosmology using cluster statistics. Here we illustrate an
application of high resolution $(< 20$ arcsec) thermal Sunyaev-Zel'dovich (tSZ)
observations by probing the intracluster medium (ICM) of the \planck-discovered
galaxy cluster \psz\ at redshift $z = 0.61$, using tSZ data obtained with the
NIKA camera, which is a dual-band (150 and 260~GHz) instrument operated at the
IRAM 30-meter telescope. We deproject jointly NIKA and \planck\ data to extract
the electronic pressure distribution from the cluster core ($R \sim 0.02\,
R_{500}$) to its outskirts ($R \sim 3\, R_{500}$) non-parametrically for the
first time at intermediate redshift. The constraints on the resulting pressure
profile allow us to reduce the relative uncertainty on the integrated Compton
parameter by a factor of two compared to the \planck\ value. Combining the tSZ
data and the deprojected electronic density profile from \xmm\ allows us to
undertake a hydrostatic mass analysis, for which we study the impact of a
spherical model assumption on the total mass estimate. We also investigate the
radial temperature and entropy distributions. These data indicate that \psz\ is
a massive ($M_{500} \sim 5.5 \times 10^{14}$ M$_{\odot}$) cool-core cluster.
This work is part of a pilot study aiming at optimizing the treatment of the
NIKA2 tSZ large program dedicated to the follow-up of SZ-discovered clusters at
intermediate and high redshifts. (abridged)
