The centroid speed as a characteristic of the group speed of solar coronal fast magnetoacoustic wave trains

The highly-filamented nature of the coronal plasma significantly influences dynamic processes in the corona such as magnetohydrodynamic waves and oscillations. Fast magnetoacoustic waves, guided by coronal plasma non-uniformities, exhibit strong geometric dispersion, forming quasi-periodic fast-propagating (QFP) wave trains. QFP wave trains are observed in extreme-ultraviolet imaging data and indirectly in microwaves and low-frequency radio, aiding in understanding the magnetic connectivity, energy, and mass transport in the corona. However, measuring the field-aligned group speed of QFP wave trains, as a key parameter for seismological analysis, is challenging due to strong dispersion and associated rapid evolution of the wave train envelope. We demonstrate that the group speed of QFP wave trains formed in plane low-$β$ coronal plasma non-uniformities can be assessed through the propagation of the wave train's effective centre of mass, referred to as the wave train's centroid speed. This centroid speed, as a potential observable, is shown empirically to correspond to the group speed of the most energetic Fourier harmonic in the wave train. The centroid speed is found to be almost insensitive to the waveguide density contrast with the ambient corona, and to vary with the steepness of the transverse density profile. The discrepancy between the centroid speed as the group speed measure and the phase speed at the corresponding wavelength is shown to reach 70\%, which is crucial for the energy flux estimation and interpretation of observations.