  Shock breakout (SBO) signal is the first signature of the supernova explosion
apart from gravitational waves and neutrinos. Observational properties of SBO,
such as bolometric luminosity and colour temperature, connect to the supernova
progenitor and explosion parameters. Detecting SBO or SBO-cooling will
constrain the progenitor and explosion models of collapsing stars. In the light
of recently launched eROSITA telescope, the rate for detection of SBO is a few
events during a year. In the current study, we examine the analytic formulae
derived by Shussman et al. (2016). We use four red supergiant models from their
study, while running explosions with the radiation hydrodynamics code STELLA.
We conclude that there is a good agreement between analytic and numerical
approaches for bolometric luminosity and colour temperature during SBO. The
analytic formulae for the SBO signal based on the global supernova parameters
can be used instead of running time-consuming numerical simulations. We define
spectral range where analytic formulae for the SBO spectra are valid. We
provide improved analytical expression for the SBO spectral energy
distribution. We confirm dependence of colour temperature on radius derived by
analytical studies and suggest to use early time observations to confine the
progenitor radius. Additionally we show the prediction for the SBO signal from
red supergiants as seen by eROSITA instrument.
