<figure><img src="image_16.png" /></figure>

**Fig. A.1.** LOFAR 50kpc-taper, discrete source-subtracted images of the RR in the LoTSS DR2 - PSZ2 sample, from Botteon et al. (2022). The images and $R_{500}$ (black circles) are centred on the PSZ2 coordinate. The image of PSZ2 G165.46+66.15 is centred on the X-ray centroid. PSZ2 G089.52+62.34, PSZ2 G091.79-27.00, and PSZ2 G165.46+66.15 have been re-imaged. A scalebar, denoting 1 Mpc, is shown in black. The beam is shown in the bottom-left corner, and the mass ($M_{500}$, in units of $10^{14} M_{\odot}$), redshift (z), and image noise (rms, in units of mJy beam$^{-1}$) are reported in the top-left corner. White crosses mark the location of the relics, as used throughout the paper (see Sec. 2.2 for a description of their calculation).
<figure><img src="image_16.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Fig. A.1. continued.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. A.2.** Chandra/XMM-Newton images of the relic-hosting clusters in our sample. The white contours show the corresponding radio images (Fig. A.1) spaced by a factor of 2, starting at $2\sigma_{rms}$. Black crosses mark the position of the X-ray centroid. We note that, for PSZ2 G107.10+65.32, only the X-ray centroid of the S subcluster is plotted. All other information is as in Fig. A.1.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Fig. A.2.** Chandra/XMM-Newton images of the relic-hosting clusters in our sample. The white contours show the corresponding radio images (Fig. A.1) spaced by a factor of 2, starting at $2\sigma_{rms}$. Black crosses mark the position of the X-ray centroid. We note that, for PSZ2 G107.10+65.32, only the X-ray centroid of the S subcluster is plotted. All other information is as in Fig. A.1.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Fig. A.2. continued.</figcaption></figure>
**Appendix B: Comparison with FdG14 powers**

In Fig. 6 we compare the power vs. mass scaling relations of the relics in this sample (150 MHz) and those used by FdG14 (1.4 GHz). To make a completely fair comparison, the cosmology used to calculate the relic powers should be the same. In Fig. B.1 we reproduce Fig. 6 (top) with the relic powers from our sample recomputed with the same cosmology as FdG14 (ΛCDM cosmology with $\Omega_{\Lambda} = 0.73$, $\Omega_{m} = 0.27$, and $H_{0} = 71$ km s⁻¹ Mpc⁻¹), since the scaling relation in FdG14 was calculated with this cosmology. The slope and intercept (orthogonal fit) of the line of best fit for the recomputed powers are $B = 5.84 \pm 1.31$ and $A = -60.74 \pm 19.27$.

<figure><img src="image_24.png" /><figcaption>**Fig. B.1.** Same as Fig. 6 (top) but the relic powers from the DR2 sample have been recomputed using the cosmology used by FdG14.</figcaption></figure>

**Appendix C: Fitting methods**

The slope and intercept obtained when fitting a regression line depends on the fitting method (see Tab. 2. In this paper we report the parameters for four different methods: orthogonal; Y|X; X|Y and the bisector of Y|X and X|Y. In Fig. C.1 we show the regression line (confirmed relics only) for each fitting method.

<figure><img src="image_25.png" /><figcaption>**Fig. C.1.** Relic power vs. cluster mass for confirmed relics only. The regression lines are shown for all four fitting methods.</figcaption></figure>
**Appendix B: Comparison with FdG14 powers**

In Fig. 6 we compare the power vs. mass scaling relations of the relics in this sample (150 MHz) and those used by FdG14 (1.4 GHz). To make a completely fair comparison, the cosmology used to calculate the relic powers should be the same. In Fig. B.1 we reproduce Fig. 6 (top) with the relic powers from our sample recomputed with the same cosmology as FdG14 (ΛCDM cosmology with $\Omega_{\Lambda} = 0.73$, $\Omega_{m} = 0.27$, and $H_{0} = 71$ km s⁻¹ Mpc⁻¹), since the scaling relation in FdG14 was calculated with this cosmology. The slope and intercept (orthogonal fit) of the line of best fit for the recomputed powers are $B = 5.84 \pm 1.31$ and $A = -60.74 \pm 19.27$.

<figure><img src="image_25.png" /><figcaption>**Fig. B.1.** Same as Fig. 6 (top) but the relic powers from the DR2 sample have been recomputed using the cosmology used by FdG14.</figcaption></figure>

**Appendix C: Fitting methods**

The slope and intercept obtained when fitting a regression line depends on the fitting method (see Tab. 2. In this paper we report the parameters for four different methods: orthogonal; Y|X; X|Y and the bisector of Y|X and X|Y. In Fig. C.1 we show the regression line (confirmed relics only) for each fitting method.

<figure><img src="image_26.png" /><figcaption>**Fig. C.1.** Relic power vs. cluster mass for confirmed relics only. The regression lines are shown for all four fitting methods.</figcaption></figure>