Fast radio bursts 1,2 are astronomical radio flashes of unknown physical nature with durations of milliseconds. Their dispersive arrival times suggest an extragalactic origin and imply radio luminosities that are orders of magnitude larger than those of all known short-duration radio transients 3 . So far all fast radio bursts have been detected with large single-dish telescopes with arcminute localizations, and attempts to identify their counterparts (source or host galaxy) have relied on the contemporaneous variability of field sources 4 or the presence of peculiar field stars 5 or galaxies 4 . These attempts have not resulted in an unambiguous association 6,7 with a host or multi-wavelength counterpart. Here we report the subarcsecond localization of the fast radio burst FRB 121102, the only known repeating burst source 8-11 , using high-time-resolution radio interferometric observations that directly image the bursts. Our precise localization reveals that FRB 121102 originates within 100 milliarcseconds of a faint 180-microJansky persistent radio source with a continuum spectrum that is consistent with nonthermal emission, and a faint (twenty-fifth magnitude) optical counterpart. The flux density of the persistent radio source varies by around ten per cent on day timescales, and very long baseline radio interferometry yields an angular size of less than 1.7 milliarcseconds. Our observations are inconsistent with the fast radio burst having a Galactic origin or its source being located within a prominent star-forming galaxy. Instead, the source appears to be co-located with a low-luminosity active galactic nucleus or a previously unknown type of extragalactic source. Localization and identification of a host or counterpart has been essential to understanding the origins and physics of other kinds of transient events, including gamma-ray bursts 12,13 and tidal disruption events 14 . However, if other fast radio bursts have similarly faint radio and optical counterparts, our findings imply that direct subarcsecond localizations may be the only way to provide reliable associations.The repetition of bursts from FRB 121102 9,10 enabled a targeted interferometric localization campaign with the Karl G. Jansky Very Large Array (VLA) in concert with single-dish observations using the 305-m William E. Gordon Telescope at the Arecibo Observatory. We searched for bursts in VLA data with 5-ms sampling using both beam-forming and imaging techniques 15 (see Methods). In over 83 h of VLA observations distributed over six months, we detected nine bursts from FRB 121102 in the 2.5-3.5-GHz band with signalto-noise ratios ranging from 10 to 150, all at a consistent sky position.

FRB 121102 is the only known repeating fast radio burst source. Here we analyze a wide-frequency-range (1 − 8 GHz) sample of high-signal-to-noise, coherently dedispersed bursts detected using the Arecibo and Green Bank telescopes. These bursts reveal complex time-frequency structures that include sub-bursts with finite bandwidths. The frequency-dependent burst structure complicates the determination of a dispersion measure (DM); we argue that it is appropriate to use a DM metric that maximizes frequency-averaged pulse structure, as opposed to peak signal-to-noise, and find DM = 560.57 ± 0.07 pc cm −3 at MJD 57644. After correcting for dispersive delay, we find that the sub-bursts have characteristic frequencies that typically drift lower at later times in the total burst envelope. In the 1.1 − 1.7 GHz band, the ∼ 0.5 − 1-ms sub-bursts have typical bandwidths ranging from 100 − 400 MHz, and a characteristic drift rate of ∼ 200 MHz/ms towards lower frequencies. At higher radio frequencies, the sub-burst bandwidths and drift rate are larger, on average. While these features could be intrinsic to the burst emission mechanism, they could also be imparted by propagation effects in the medium local to the source. Comparison of the burst DMs with previous values in the literature suggests an increase of ∆DM ∼ 1 − 3 pc cm −3 in 4 years, though this could be a stochastic variation as opposed to a secular trend. This implies changes in the local medium or an additional source of frequency-dependent delay. Overall, the results are consistent with previously proposed scenarios in which FRB 121102 is embedded in a dense nebula.

The millisecond-duration radio flashes known as fast radio bursts (FRBs) represent an enigmatic astrophysical phenomenon. Recently, the sub-arcsecond localization (∼100 mas precision) of FRB121102 using the Very Large Array has led to its unambiguous association with persistent radio and optical counterparts, and to the identification of its host galaxy. However, an even more precise localization is needed in order to probe the direct physical relationship between the millisecond bursts themselves and the associated persistent emission. Here, we report very-long-baseline radio interferometric observations using the European VLBI Network and the 305 m Arecibo telescope, which simultaneously detect both the bursts and the persistent radio emission at milliarcsecond angular scales and show that they are co-located to within a projected linear separation of 40 pc (12 mas angular separation, at 95% confidence). We detect consistent angular broadening of the bursts and persistent radio source (∼2-4 mas at 1.7 GHz), which are both similar to the expected Milky Way scattering contribution. The persistent radio source has a projected size constrained to be  0.7 pc (0.2 mas angular extent at 5.0 GHz) and a lower limit for the brightness temperature of T 5 10 K b 7´. Together, these observations provide strong evidence for a direct physical link between FRB121102 and the compact persistent radio source. We argue that a burst source associated with a low-luminosity active galactic nucleus or a young neutron star energizing a supernova remnant are the two scenarios for FRB121102 that best match the observed data.

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Fast radio bursts (FRBs) are bright, millisecond-duration radio transients originating from extragalactic distances 1 . Their origin is unknown. Some FRB sources emit repeat bursts, ruling out cataclysmic origins for those events [2][3][4] . Despite searches for periodicity in repeat burst arrival times on time scales from milliseconds to many days 2, 5-7 , these bursts have hitherto been observed to appear sporadically, and though clustered 8 , without a regular pattern. Here we report the detection of a 16.35 ± 0.18 day periodicity from a repeating FRB 180916.J0158+65 detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project (CHIME/FRB) 4, 9 . In 28 bursts recorded from 16th September 2018 through 30th October 2019, we find that bursts arrive in a 4.0-day phase window, with some cycles showing no bursts, and some showing multiple bursts, within CHIME's limited daily exposure. Our results suggest a mechanism for periodic modulation either of the burst emission itself, or through external amplification or absorption, and disfavour models invoking purely sporadic processes.Last year the CHIME/FRB collaboration reported the discovery of eight new repeating FRB sources 4 , including FRB 180916.J0158+65, which was recently localized to a star-forming region in a nearby massive spiral galaxy at redshift 0.0337±0.0002 10 . From September 2018 to November 2019, CHIME/FRB has detected a total of 28 bursts from FRB 180916.J0158+65, which remains the most active source from this recent CHIME/FRB repeater sample. The barycentric arrival times for the 28 bursts (including those has been published before) from FRB 180916.J0158+65, corrected for delays from pulse dispersion, are listed in Extended Data Table 1.To search for periodicity, the burst arrival times (spanning a 400-day time range) were folded with different periods from 1.57 to 62.8 days (see Methods), with a Pearson's χ 2 test applied to each resulting profile with 8 phase bins 11 . A reduced χ 2 1 with respect to a uniform distribution indicates a periodicity unlikely to arise by chance. Furthermore, to account for the possible non-Poissonian statistics of the bursts 12 , we have applied the search with different weighting schemes that consider clustered bursts of different time range to be correlated events (see Methods).Searches with different weightings return periodograms of similar shape and have the same primary peak with significance varying between 3.5 − 8σ. As an example, the reduced χ 2 versus period using a weighting that counts only active days instead of individual events is shown in Figure 1a. A distinct peak is detected at 16.35 ± 0.18 days, with