  In the beginning of 2023 the Be transient X-ray pulsar RX J0440.9+4431
underwent a fist-ever giant outburst observed from the source peaking in the
beginning of February and reaching peak luminosity of $\sim 4.3\times10^{37}$
erg s$^{-1}$. Here we present the results of a detailed spectral and temporal
study of the source based on NuSTAR, INTEGRAL, Swift, and NICER observations
performed during this period and covering wide range of energies and
luminosities. We find that both the pulse profile shape and spectral hardness
change abruptly around $\sim2.8\times10^{37}$ erg s$^{-1}$, which we associate
with a transition to super-critical accretion regime and erection of the
accretion column. The observed pulsed fraction decreases gradually with energy
up to 20 keV (with a local minimum around fluorescence iron line), which is
unusual for an X-ray pulsar, and then rises rapidly at higher energies with the
pulsations significantly detected up to $\sim120$ keV. The broadband energy
spectra of RX J0440.9+4431 at different luminosity states can be approximated
with a two-hump model with peaks at energies of about 10-20 and 50-70 keV
previously suggested for other pulsars without additional features. In
particular an absorption feature around 30 keV previously reported and
interpreted as a cyclotron line in the literature appears to be absent when
using this model, so the question regarding the magnetic field strength of the
neutron star remains open. Instead, we attempted to estimate field using
several indirect methods and conclude that all of them point to a relatively
strong field of around $B\sim 10^{13}$ G.
