tokens: −0.61. This is approximately Δα ≃ 0.15 flatter than the measured average spectral index in radio α R ∼ −0.765. The flattest indices are obtained at the locations of assumed active particle acceleration with high shock velocities, such as near the forward shock and the south-west quadrant of the remnant. These locations also coincide with the regions that are brightest in non-thermal X-ray emission. The flattening of the spectrum at high frequencies is in qualitative agreement with non-linear DSA theory. The spectral index is, however, still steeper than the predictions of the non-linear models without magnetic field amplification (see Malkov Drury 2001 , and references therein). We assess the possibility of a cooling break being present in the remnant. We place the break frequency lower limit at ν br ∼ 5 × 10 12 Hz in the likely most affected regions. Considering 100 yr as the age of the shocked plasma, this indicates allowed magnetic field strength up to B ∼ 2–2.5 mG in the south-east/north-east and B ∼ 1 mG in the south-west of the remnant. This is higher than the average magnetic field limits inferred for Cas A, but probes the magnetic field values suggested locally by Atoyan et al. ( 2000 ). Using the age of Cas A (∼340 yr) as the age of the plasma puts the upper limits close to the magnetic field estimates obtained with other methods. Further investigations are still necessary and south-east/north-east regions are the best candidate locations for further investigation of the cooling break. Doing this may put constraints on the history of electron acceleration in Cas A. APPENDIX A: EXAMPLE OF OBTAINING SPECTRAL INDICES PER PIXEL USING MONTE CARLO SIMULATIONS In order to illustrate our procedure for measuring a spectral index for a single pixel and to prove the overall robustness of our results given the statistical and systematic errors, we show here our procedure for a given pixel, and how it leads to a likelihood range in the spectral index. We chose a pixel in the south-east location at coordinates (RA 23h 23m 391, Dec. 58 47′ 238) as our example pixel to provide a more complete picture of our data-handling process. The location is ideal to showcase the effect of the strongest effect of background subtraction as this region provides the lowest mid-infrared flux. We use a Monte Carlo approach in order to propagate the uncertainties and to obtain the result. The basis of this method is to take a value and its uncertainty of a given parameter and to simulate a normal distribution around it. In our case, we produce one-dimensional arrays of 10 000 elements. These arrays are then used as input into equations as if it would be a single value. However, as we do it on 10 000 elements we are saving the information about parameter’s possible values and effectively we also propagate its uncertainty. A.1 Background subtraction The flux in the chosen pixel is 190.1 × 10 −7 Jy px −1 with an uncertainty 9.1 × 10 −7 Jy px −1 . The mid-infrared
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