Basically, since we know that the central region of these galaxies is occupied by a black hole, accretion by this black hole can power relativistic jets which result in radio emission. Radio emission from jets is most likely for high mass elliptical galaxies as they tend to host black holes with mass toward the high end of the supermassive black hole mass range. This seminal paper by Merritt and Ekers (2002) offers some context. They used this as a basis to hypothesize the double lobed radio galaxies (X-shaped radio galaxies) as originating from a spin flip due to a galactic merger.
Although the reorientation of a SBH’s spin axis due to coalescence is not directly ob-
servable, any gaseous accretion onto the SBH is constrained by relativistic frame dragging
to be axisymmetric with respect to the black hole, and it is widely believed that the
jets emitted from the centers of active galaxies are launched perpendicularly to the inner
accretion disk; hence a jet should point in the same direction as the spin axis of the SBH
at its center. The extraordinary long-term stability of the jet direction in many radio
galaxies is strong evidence that jet orientations are regulated by black hole spins.
Because powerful radio galaxies comprise only a fraction, of order 1%, of all bright ellipti-
cal galaxies and because radio power is a rapidly increasing function of galaxy luminosity, we would expect only the more massive of the two merging galaxies to harbor a jet.
Hence a likely consequence of SBH coalescence in a radio galaxy is a sudden change in
the direction of the jet associated with the larger SBH, followed by the generation of a
new radio lobe at some (possibly large) angle with respect to the original lobe.
They state further:
In fact there is a class of radio sources which fit this description: the so-called
“winged” or “X-type” radio sources. X-shaped sources are characterized by two low-
surface-brightness radio lobes (the “wings”) oriented at an angle to the “active,” or
high-surface-brightness, lobes (Fig. 2); both sets of lobes pass symmetrically through
the center of the associated elliptical galaxy. The first winged source discovered, NGC
326, was initially interpreted by a model in which a single SBH undergoes slow geodetic
precession due to torques from an external mass, resulting in an S-shaped radio morphol-
ogy; later observations revealed the X shape of this source indicating a more
rapid change of jet direction. Other explanations for the origin of X-shaped sources have
been proposed but none has proved satisfactory; black holes are nearly perfect gyroscopes
and reorienting them via external forces is difficult. One proposed model is based on a
warping instability of accretion disks, but this model fails to explain why jet reorien-
tation occurs only once in the X-shaped sources and why most radio galaxies have stable
jet directions. Capture of a dwarf galaxy with mass comparable to M1 could reorient a
black hole but it is more likely that the infalling galaxy would be disrupted by tidal forces
before being accreted.
So, as they state, the stability of the radio lobes is explained well by black holes since they "are essentially perfect gyroscopes and reorienting them via external forces is difficult." They go on to explain how this is the case for several observed radio galaxies. They cite this seminal paper which explains that the observed radio emission generally requires relativistic flows, for which black hole accretion is a natural explanation. This continues to be a promising explanation for systems, see e.g.'s this, this.
For an in depth explanation of the relevant physics and uncertainties, this review by Heckman and Best (2014) is very helpful. Here is the free version on arxiv. See for example Figure 3 which shows that both the main types of AGN, i.e., radiative and jet modes, involve a radio jet being sourced by a central supermassive black hole. The jet-mode AGN is more powerful and generally provides for stronger radio emission. Their Fig 4 summarizes this info nicely. See section 2.3.3 for how the mass of the black hole can be estimated.
