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The recent Chromatic periodic activity down to 120 MHz in a Fast Radio Burst contains two paragraphs in which X's are given "assuming an Euclidean fluence scaling".

To me, a non-astronomer, the wording feels like a reviewer may have raised this point and so the phase was quickly inserted to get it past review and to press with expediency rather than haggle about it, but maybe FRBs are so far away that space being non-Euclidian could really impact these very large error-barred limits.

Question: What is Euclidean fluence scaling in the context of bounding constraints on FRB all-sky rates? Would non-Euclidean scaling give a meaningfully different answer?


Remarkably, for bursts of the same fluence, FRB 20180916B is around over an order of magnitude more active at 150 MHz than at 1.4 GHz, as seen in Extended Figure 1. Our detections allow for the first bounded constraints on the FRB all-sky rate below 200 MHz. A lower limit is obtained by assuming FRB 20180916B is the only source in the sky emitting at these frequencies. Combining this with previously published upper limits, we find that there are 3–450 sky−1 day−1 above 50 Jy ms at 90% confidence. Assuming an Euclidean fluence scaling, this is equivalent to 90–14000 sky−1 day−1 above 5 Jy ms at 150 MHz, which is promising for future high-sensitivity low-frequency surveys.

and

As the LOFAR bursts are the sole unambiguous FRB detections below 200 MHz, we and other teams13 can now provide the first bounded limits on the all-sky event rate at low frequencies. A lower limit on the FRB rate at 150 MHz can be obtained by assuming FRB 20180916B is the only source in the sky emitting at these wavelengths. This lower bound can be combined with previous upper bounds from non detections by blind searches at LOFAR and MWA14, 15, 64–67. The repetition rate of FRB 20180916B implies that there are at least 0.6 sky−1 day−1 above 50 Jy ms at 110–190 MHz at 95% confidence. Assuming a Euclidean scaling in the brightness distribution that continues down to lower fluences, this is equivalent to more than 90 sky−1 day−1 above 5 Jy ms. An earlier blind LOFAR search15 placed an upper limit of 29 sky−1 day−1 above 62 Jy pulses with 5 ms duration. Combining these two limits, we obtain a 90% confidence region of 3–450 sky−1 day−1 above 50 Jy ms.

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