  Measurements of the quantity of radio-mode feedback injected by an active
galactic nucleus into the cluster environment have mostly relied on X-ray
observations, which reveal cavities in the intracluster medium excavated by the
radio lobes. However, the sensitivity required to accurately constrain the
dimensions of these cavities has proven to be a major limiting factor and is
the main bottleneck on high-redshift measurements. We describe a hybrid method
based on a combination of X-ray and radio observations, which aims to enhance
our ability to study radio-mode feedback. In this paper, we present one of the
first samples of galaxy clusters observed with the International LOFAR
Telescope (ILT) at 144 MHz and use this sample to test the hybrid method at
lower frequencies than before. By comparing our measurements with results found
in literature based on the traditional method using only X-ray observations, we
find that the hybrid method provides consistent results to the traditional
method. In addition, we find that the correlation between the traditional
method and the hybrid method improves as the X-ray cavities are more clearly
defined. This suggests that using radio lobes as proxies for cavities may help
to circumvent systematic uncertainties in the cavity volume measurements.
Encouraged by the high volume of unique ILT observations successfully
processed, this hybrid method enables radio-mode feedback to be studied at high
redshifts for the first time even for large samples of clusters.
