LOFAR discovery of a radio halo in the high-redshift galaxy cluster PSZ2
  G099.86+58.45
  In this Letter, we report the discovery of a radio halo in the high-redshift
galaxy cluster PSZ2 G099.86+58.45 ($z=0.616$) with the LOw Frequency ARray
(LOFAR) at 120-168 MHz. This is one of the most distant radio halos discovered
so far. The diffuse emission extends over $\sim$ 1 Mpc and has a morphology
similar to that of the X-ray emission as revealed by XMM-Newton data. The halo
is very faint at higher frequencies and is barely detected by follow-up 1-2 GHz
Karl G.~Jansky Very Large Array (JVLA) observations, which enable us to
constrain the radio spectral index to be $\alpha\leq 1.5-1.6$, i.e.; with
properties between canonical and ultra-steep spectrum radio halos. Radio halos
are currently explained as synchrotron radiation from relativistic electrons
that are re-accelerated in the intra-cluster medium (ICM) by turbulence driven
by energetic mergers. We show that in such a framework radio halos are expected
to be relatively common at $\sim150$ MHz ($\sim30-60\%$) in clusters with mass
and redshift similar to PSZ2 G099.86+58.45; however, at least 2/3 of these
radio halos should have steep spectrum and thus be very faint above $\sim 1$
GHz frequencies. Furthermore, since the luminosity of radio halos at high
redshift depends strongly on the magnetic field strength in the hosting
clusters, future LOFAR observations will also provide vital information on the
origin and amplification of magnetic fields in galaxy clusters.
