LOFAR VLBI Studies at 55 MHz of 4C 43.15, a z=2.4 Radio Galaxy
  The correlation between radio spectral index and redshift has been exploited
to discover high redshift radio galaxies, but its underlying cause is unclear.
It is crucial to characterise the particle acceleration and loss mechanisms in
high redshift radio galaxies to understand why their radio spectral indices are
steeper than their local counterparts. Low frequency information on scales of
$\sim$1 arcsec are necessary to determine the internal spectral index
variation. In this paper we present the first spatially resolved studies at
frequencies below 100 MHz of the $z = 2.4$ radio galaxy 4C 43.15 which was
selected based on its ultra-steep spectral index ($\alpha < -1$; $S_{\nu} \sim
\nu^{\alpha}$ ) between 365 MHz and 1.4 GHz. Using the International Low
Frequency Array (LOFAR) Low Band Antenna we achieve sub-arcsecond imaging
resolution at 55 MHz with VLBI techniques. Our study reveals low-frequency
radio emission extended along the jet axis, which connects the two lobes. The
integrated spectral index for frequencies $<$ 500 MHz is -0.83. The lobes have
integrated spectral indices of -1.31$\pm$0.03 and -1.75$\pm$0.01 for
frequencies $\geq$1.4 GHz, implying a break frequency between 500 MHz and 1.4
GHz. These spectral properties are similar to those of local radio galaxies. We
conclude that the initially measured ultra-steep spectral index is due to a
combination of the steepening spectrum at high frequencies with a break at
intermediate frequencies.
