Remnant radio galaxies represent an important phase in the life-cycle of radio active galactic nuclei. It is suggested that in this phase, the jets have switched off and the extended emission is fading rapidly. This phase is not well-studied due to the lack of statistical samples observed at both low and high frequencies. In this work, we study a sample of 23 candidate remnant radio galaxies previously selected using the Low Frequency Array at 150 MHz in the Lockman Hole field. We examine their morphologies and study their spectral properties to confirm their remnant nature and revise the morphological and spectral criteria used to define the initial sample. We present new observations with the Karl G. Jansky Very Large Array at 6000 MHz at both high and low resolution. These observations allowed us to observe the presence or absence of cores and study the spectral curvature and steepness of the spectra of the total emission expected at these high frequencies for the remnant candidates. We confirm 13 out of 23 candidates as remnant radio sources. This corresponds to 7% of the full sample of active, restarted, and remnant candidates from the Lockman Hole field. Surprisingly, only a minority of remnants reside in a cluster (23%). The remnant radio galaxies show a range of properties and morphologies. The majority do not show detection of the core at 6000 MHz and their extended emission often shows ultra-steep spectra (USS). However, there are also remnants with USS total emission and a detection of the core at 6000 MHz, possibly indicating a variety of evolutionary stages in the remnant phase. We confirm the importance of the combination of morphological and spectral criteria and this needs to be taken into consideration when selecting a sample of remnant radio sources.
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