Constraints on the low frequency spectrum of FRB 121102

While repeating fast radio bursts (FRBs) remain scarce in number, they provide a unique opportunity for follow-up observations that enhance our knowledge of their sources and potentially of the FRB population as a whole. Attaining more burst spectra could lead to a better understanding of the origin of these bright, millisecond-duration radio pulses. We therefore performed $\sim$20 hr of simultaneous observations on FRB 121102 with the Effelsberg 100-m radio telescope and the Low Frequency Array (LOFAR) to constrain the spectral behaviour of bursts from FRB 121102 at 1.4 GHz and 150 MHz. This campaign resulted in the detection of nine new bursts at 1.4 GHz but no simultaneous detections with LOFAR. Assuming that the ratio of the fluence at two frequencies scales as a power law, we placed a lower limit of $\alpha$ > -1.2 $\pm$ 0.4 on the spectral index for the fluence of the instantaneous broad band emission of FRB 121102. For the derivation of this limit, a realistic fluence detection threshold for LOFAR was determined empirically assuming a burst would be scattered as predicted by the NE2001 model. A significant variation was observed in the burst repeat rate R at L-band. During observations in September 2016, nine bursts were detected, giving R = 1.1 $\pm$ 0.4 hr$^{-1}$, while in November no bursts were detected, yielding R < 0.3 hr$^{-1}$ (95% confidence limit). This variation is consistent with earlier seen episodic emission of FRB 121102. In a blind and targeted search, no bursts were found with LOFAR at 150 MHz, resulting in a repeat rate limit of R < 0.16 hr$^{-1}$ (95% confidence limit). Burst repeat rate ratios of FRB 121102 at 3, 2, 1.4, and 0.15 GHz are consistent within the uncertainties with a flattening of its spectrum below 1 GHz.