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K M Rajwade, M B Mickaliger, B W Stappers, V Morello, D Agarwal, C G Bassa, R P Breton, M Caleb, A Karastergiou, E F Keane, D R Lorimer, Possible periodic activity in the repeating FRB 121102, Monthly Notices of the Royal Astronomical Society, Volume 495, Issue 4, July 2020, Pages 3551–3558, https://doi.org/10.1093/mnras/staa1237
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ABSTRACT
The discovery that at least some Fast Radio Bursts (FRBs) repeat has ruled out cataclysmic events as the progenitors of these particular bursts. FRB 121102 is the most well-studied repeating FRB but despite extensive monitoring of the source, no underlying pattern in the repetition has previously been identified. Here, we present the results from a radio monitoring campaign of FRB 121102 using the 76 m Lovell telescope. Using the pulses detected in the Lovell data along with pulses from the literature, we report a detection of periodic behaviour of the source over the span of 5 yr of data. We predict that the source is currently ‘off’ and that it should turn ‘on’ for the approximate MJD range 59002−59089 (2020 June 2 to 2020 August 28). This result, along with the recent detection of periodicity from another repeating FRB, highlights the need for long-term monitoring of repeating FRBs at a high cadence. Using simulations, we show that one needs at least 100 h of telescope time to follow-up repeating FRBs at a cadence of 0.5–3 d to detect periodicities in the range of 10–150 d. If the period is real, it shows that repeating FRBs can have a large range in their activity periods that might be difficult to reconcile with neutron star precession models.
1 INTRODUCTION
Fast Radio Bursts (FRBs) are bright radio pulses that last for no more than a few milliseconds (Lorimer et al. 2007; Thornton et al. 2013). While their nature is still a mystery, we know they are extragalactic on account of their anomalously high dispersion measures as well as the measured redshifts of the host galaxies of localized FRBs (Ravi, Shannon & Jameson 2015; Tendulkar et al. 2017; Bannister et al. 2019). Although subject to large variance at lower redshifts (Masui et al. 2015), the DM acts as a reasonable proxy for distance on cosmological scales (Keane 2018). In spite of detections only at radio wavelengths, the data not only contain information on the intergalactic medium but also about the progenitor and its local environment (Masui et al. 2015).
To date, more than one hundred FRBs have been published (Petroff et al. 2016), yet only some of these have so far been observed to repeat (Spitler et al. 2016; Shannon et al. 2018; Kumar et al. 2019; The CHIME/FRB Collaboration 2019) and there is no clear evidence favouring a specific progenitor model. The first repeater, FRB 121102, was discovered in 2014 (Spitler et al. 2014) though its repeating nature was not revealed until 2016 (Spitler et al. 2016). This discovery was crucial as it implied that not all FRB progenitors were of cataclysmic origin. Since then, 19 more repeaters have been discovered (CHIME/FRB Collaboration 2019; Kumar et al. 2019; Fonseca et al. 2020). While the new discoveries suggest the possibility of multiple populations of FRBs, a lack of urgent follow-up and monitoring of all known FRBs precludes a definitive conclusion. Of all the repeating sources, FRB 121102 has been studied extensively across a broad range of radio frequencies from 600 MHz (Josephy et al. 2019) to 8 GHz (Gajjar et al. 2018a). Though numerous pulses have been detected to date, no underlying pattern has been discovered so far. The shortest separations between two apparently distinctive pulses are 26 ms (Gourdji et al. 2019), 34 ms (Hardy et al. 2017), and 37 ms (Scholz et al. 2016). The recent discovery of periodic activity from FRB 180906.J0158+65 (The CHIME/FRB Collaboration 2020) has rekindled interest in this question and leads us to wonder whether all repeating FRBs show this kind of behaviour. The 16.35 d periodicity in FRB 180906.J0158+65 has led to models being invoked such as; binary orbits to explain the observed periodic behaviour (Lyutikov, Barkov & Giannios 2020; Ioka & Zhang 2020) while some authors have proposed a precession of flaring, highly magnetized neutron stars (Levin, Beloborodov & Bransgrove 2020; Zanazzi & Lai 2020). If true, it will provide a vital clue into the origins of these mysterious bursts. In this paper, we present the results of a long-term monitoring campaign of FRB 121102 using the 76 m Lovell telescope (LT) located at the Jodrell Bank Observatory. The observing campaign is presented in Section 2. We then describe our search for periodic activity in Section 3. We discuss the results obtained in Section 4 before providing concluding remarks in Section 5.
2 OBSERVATIONS AND DATA PROCESSING
Since the discovery of repeating pulses from FRB 121102, it was followed up on a pseudoregular basis using the LT. Starting from MJD 57363, the source was followed up on a near-weekly cadence, with some daily observations, until MJD 57723. From that point, it was observed nearly every day through MJD 57843. After that, there were a few sparse observations until 58483. The cadence of the monitoring campaign was non-uniform, the observations are interspersed with large gaps due telescope maintenance. The top panel of Fig. 2 shows the cadence of observations over the last 4 yr. Details of all observations with LT are shown in Table 1.
ID . | MJD start . | MJD end . | No. of detections . |
---|---|---|---|
0 | 57363.9001968 | 57363.9842014 | 0 |
1 | 57365.0012963 | 57365.0853009 | 0 |
2 | 57371.1676968 | 57371.2515278 | 0 |
3 | 57379.2055208 | 57379.289537 | 0 |
4 | 57389.0533796 | 57389.1374074 | 0 |
5 | 57402.0379051 | 57402.1219213 | 0 |
6 | 57407.1136111 | 57407.1976273 | 0 |
7 | 57428.8283333 | 57428.9998611 | 0 |
8 | 57429.0005556 | 57429.9993519 | 0 |
9 | 57430.0000463 | 57430.079213 | 0 |
10 | 57463.5381713 | 57463.6265741 | 0 |
ID . | MJD start . | MJD end . | No. of detections . |
---|---|---|---|
0 | 57363.9001968 | 57363.9842014 | 0 |
1 | 57365.0012963 | 57365.0853009 | 0 |
2 | 57371.1676968 | 57371.2515278 | 0 |
3 | 57379.2055208 | 57379.289537 | 0 |
4 | 57389.0533796 | 57389.1374074 | 0 |
5 | 57402.0379051 | 57402.1219213 | 0 |
6 | 57407.1136111 | 57407.1976273 | 0 |
7 | 57428.8283333 | 57428.9998611 | 0 |
8 | 57429.0005556 | 57429.9993519 | 0 |
9 | 57430.0000463 | 57430.079213 | 0 |
10 | 57463.5381713 | 57463.6265741 | 0 |
ID . | MJD start . | MJD end . | No. of detections . |
---|---|---|---|
0 | 57363.9001968 | 57363.9842014 | 0 |
1 | 57365.0012963 | 57365.0853009 | 0 |
2 | 57371.1676968 | 57371.2515278 | 0 |
3 | 57379.2055208 | 57379.289537 | 0 |
4 | 57389.0533796 | 57389.1374074 | 0 |
5 | 57402.0379051 | 57402.1219213 | 0 |
6 | 57407.1136111 | 57407.1976273 | 0 |
7 | 57428.8283333 | 57428.9998611 | 0 |
8 | 57429.0005556 | 57429.9993519 | 0 |
9 | 57430.0000463 | 57430.079213 | 0 |
10 | 57463.5381713 | 57463.6265741 | 0 |
ID . | MJD start . | MJD end . | No. of detections . |
---|---|---|---|
0 | 57363.9001968 | 57363.9842014 | 0 |
1 | 57365.0012963 | 57365.0853009 | 0 |
2 | 57371.1676968 | 57371.2515278 | 0 |
3 | 57379.2055208 | 57379.289537 | 0 |
4 | 57389.0533796 | 57389.1374074 | 0 |
5 | 57402.0379051 | 57402.1219213 | 0 |
6 | 57407.1136111 | 57407.1976273 | 0 |
7 | 57428.8283333 | 57428.9998611 | 0 |
8 | 57429.0005556 | 57429.9993519 | 0 |
9 | 57430.0000463 | 57430.079213 | 0 |
10 | 57463.5381713 | 57463.6265741 | 0 |
For each observation, a polyphase filter coarsely channelized a 400 MHz band into 25 subbands of 16 MHz each using a ROACH-based backend (Bassa et al. 2016). Each 16 MHz subband was further channelized into 32 × 0.5 MHz channels using digifil from the dspsr software suite (van Straten & Bailes 2011), and downsampled to a sampling time of 256 μs. The 800 total channels, spanning 400 MHz, were then combined in frequency. After MJD 57729, all observations (75 per cent of data reported here) had a bandwidth of 336 MHz, to mitigate the effect of radiofrequency interference (RFI) on the data. We also masked frequency channels in the data containing narrow-band RFI.
ID . | Topocentric MJD . | Fluence . | Width . | S/N . | DM . |
---|---|---|---|---|---|
. | . | Jy ms . | ms . | . | . |
1 | 57473.846689 | 1.29(10) | 3.5 | 12 | 559.5 |
2 | 57611.452953 | 1.50(7) | 1.6 | 21 | 560.5 |
3 | 57625.246712 | 0.40(6) | 1.2 | 6 | 559.5 |
4 | 57625.247667 | 1.63(10) | 3.2 | 16 | 562.4 |
5 | 57636.489603 | 2.16(10) | 3.6 | 20 | 571.2 |
6 | 57758.162612 | 5.23(15) | 7.2 | 34 | 557.5 |
7 | 57762.155348 | 1.74(7) | 1.7 | 23 | 559.8 |
8 | 57763.975657 | 0.57(7) | 1.6 | 8 | 559.8 |
9 | 57768.159477 | 1.28(8) | 2.2 | 15 | 562.1 |
10 | 57769.143333 | 0.85(8) | 2.2 | 10 | 558.6 |
11 | 57771.954804 | 0.88(8) | 1.9 | 11 | 558.6 |
12 | 57771.958773 | 0.59(8) | 2.2 | 7 | 560.9 |
13 | 57779.957530 | 5.84(10) | 3.6 | 54 | 562.1 |
14 | 57779.978393 | 1.21(7) | 1.7 | 16 | 563.3 |
15 | 57781.770722 | 4.80(9) | 2.5 | 53 | 562.1 |
16 | 57781.771322 | 3.35(12) | 5.0 | 26 | 569.1 |
17 | 57785.973376 | 1.15(9) | 2.8 | 12 | 560.9 |
18 | 57787.822048 | 0.85(8) | 2.2 | 10 | 562.1 |
19 | 57787.844951 | 11.34(11) | 3.9 | 99 | 563.3 |
20 | 57791.942210 | 0.72(8) | 1.9 | 9 | 562.1 |
21 | 57791.946845 | 1.12(9) | 1.9 | 14 | 569.1 |
22 | 57797.926712 | 0.81(10) | 3.2 | 8 | 560.9 |
23 | 57797.930046 | 0.53(7) | 1.7 | 7 | 565.6 |
24 | 57798.872124 | 11.42(12) | 4.5 | 94 | 565.6 |
25 | 57805.959486 | 4.89(9) | 2.5 | 54 | 559.8 |
26 | 57821.785328 | 1.28(8) | 2.2 | 15 | 563.3 |
27 | 57821.789488 | 3.22(12) | 5.0 | 25 | 571.5 |
28 | 57826.841596 | 1.02(8) | 2.2 | 12 | 563.3 |
29 | 57826.845833 | 1.93(7) | 1.6 | 27 | 560.9 |
30 | 57826.851906 | 0.68(7) | 1.7 | 9 | 560.9 |
31 | 57826.862280 | 0.44(6) | 1.2 | 7 | 562.1 |
32 | 57826.865941 | 0.45(7) | 1.7 | 6 | 560.9 |
ID . | Topocentric MJD . | Fluence . | Width . | S/N . | DM . |
---|---|---|---|---|---|
. | . | Jy ms . | ms . | . | . |
1 | 57473.846689 | 1.29(10) | 3.5 | 12 | 559.5 |
2 | 57611.452953 | 1.50(7) | 1.6 | 21 | 560.5 |
3 | 57625.246712 | 0.40(6) | 1.2 | 6 | 559.5 |
4 | 57625.247667 | 1.63(10) | 3.2 | 16 | 562.4 |
5 | 57636.489603 | 2.16(10) | 3.6 | 20 | 571.2 |
6 | 57758.162612 | 5.23(15) | 7.2 | 34 | 557.5 |
7 | 57762.155348 | 1.74(7) | 1.7 | 23 | 559.8 |
8 | 57763.975657 | 0.57(7) | 1.6 | 8 | 559.8 |
9 | 57768.159477 | 1.28(8) | 2.2 | 15 | 562.1 |
10 | 57769.143333 | 0.85(8) | 2.2 | 10 | 558.6 |
11 | 57771.954804 | 0.88(8) | 1.9 | 11 | 558.6 |
12 | 57771.958773 | 0.59(8) | 2.2 | 7 | 560.9 |
13 | 57779.957530 | 5.84(10) | 3.6 | 54 | 562.1 |
14 | 57779.978393 | 1.21(7) | 1.7 | 16 | 563.3 |
15 | 57781.770722 | 4.80(9) | 2.5 | 53 | 562.1 |
16 | 57781.771322 | 3.35(12) | 5.0 | 26 | 569.1 |
17 | 57785.973376 | 1.15(9) | 2.8 | 12 | 560.9 |
18 | 57787.822048 | 0.85(8) | 2.2 | 10 | 562.1 |
19 | 57787.844951 | 11.34(11) | 3.9 | 99 | 563.3 |
20 | 57791.942210 | 0.72(8) | 1.9 | 9 | 562.1 |
21 | 57791.946845 | 1.12(9) | 1.9 | 14 | 569.1 |
22 | 57797.926712 | 0.81(10) | 3.2 | 8 | 560.9 |
23 | 57797.930046 | 0.53(7) | 1.7 | 7 | 565.6 |
24 | 57798.872124 | 11.42(12) | 4.5 | 94 | 565.6 |
25 | 57805.959486 | 4.89(9) | 2.5 | 54 | 559.8 |
26 | 57821.785328 | 1.28(8) | 2.2 | 15 | 563.3 |
27 | 57821.789488 | 3.22(12) | 5.0 | 25 | 571.5 |
28 | 57826.841596 | 1.02(8) | 2.2 | 12 | 563.3 |
29 | 57826.845833 | 1.93(7) | 1.6 | 27 | 560.9 |
30 | 57826.851906 | 0.68(7) | 1.7 | 9 | 560.9 |
31 | 57826.862280 | 0.44(6) | 1.2 | 7 | 562.1 |
32 | 57826.865941 | 0.45(7) | 1.7 | 6 | 560.9 |
ID . | Topocentric MJD . | Fluence . | Width . | S/N . | DM . |
---|---|---|---|---|---|
. | . | Jy ms . | ms . | . | . |
1 | 57473.846689 | 1.29(10) | 3.5 | 12 | 559.5 |
2 | 57611.452953 | 1.50(7) | 1.6 | 21 | 560.5 |
3 | 57625.246712 | 0.40(6) | 1.2 | 6 | 559.5 |
4 | 57625.247667 | 1.63(10) | 3.2 | 16 | 562.4 |
5 | 57636.489603 | 2.16(10) | 3.6 | 20 | 571.2 |
6 | 57758.162612 | 5.23(15) | 7.2 | 34 | 557.5 |
7 | 57762.155348 | 1.74(7) | 1.7 | 23 | 559.8 |
8 | 57763.975657 | 0.57(7) | 1.6 | 8 | 559.8 |
9 | 57768.159477 | 1.28(8) | 2.2 | 15 | 562.1 |
10 | 57769.143333 | 0.85(8) | 2.2 | 10 | 558.6 |
11 | 57771.954804 | 0.88(8) | 1.9 | 11 | 558.6 |
12 | 57771.958773 | 0.59(8) | 2.2 | 7 | 560.9 |
13 | 57779.957530 | 5.84(10) | 3.6 | 54 | 562.1 |
14 | 57779.978393 | 1.21(7) | 1.7 | 16 | 563.3 |
15 | 57781.770722 | 4.80(9) | 2.5 | 53 | 562.1 |
16 | 57781.771322 | 3.35(12) | 5.0 | 26 | 569.1 |
17 | 57785.973376 | 1.15(9) | 2.8 | 12 | 560.9 |
18 | 57787.822048 | 0.85(8) | 2.2 | 10 | 562.1 |
19 | 57787.844951 | 11.34(11) | 3.9 | 99 | 563.3 |
20 | 57791.942210 | 0.72(8) | 1.9 | 9 | 562.1 |
21 | 57791.946845 | 1.12(9) | 1.9 | 14 | 569.1 |
22 | 57797.926712 | 0.81(10) | 3.2 | 8 | 560.9 |
23 | 57797.930046 | 0.53(7) | 1.7 | 7 | 565.6 |
24 | 57798.872124 | 11.42(12) | 4.5 | 94 | 565.6 |
25 | 57805.959486 | 4.89(9) | 2.5 | 54 | 559.8 |
26 | 57821.785328 | 1.28(8) | 2.2 | 15 | 563.3 |
27 | 57821.789488 | 3.22(12) | 5.0 | 25 | 571.5 |
28 | 57826.841596 | 1.02(8) | 2.2 | 12 | 563.3 |
29 | 57826.845833 | 1.93(7) | 1.6 | 27 | 560.9 |
30 | 57826.851906 | 0.68(7) | 1.7 | 9 | 560.9 |
31 | 57826.862280 | 0.44(6) | 1.2 | 7 | 562.1 |
32 | 57826.865941 | 0.45(7) | 1.7 | 6 | 560.9 |
ID . | Topocentric MJD . | Fluence . | Width . | S/N . | DM . |
---|---|---|---|---|---|
. | . | Jy ms . | ms . | . | . |
1 | 57473.846689 | 1.29(10) | 3.5 | 12 | 559.5 |
2 | 57611.452953 | 1.50(7) | 1.6 | 21 | 560.5 |
3 | 57625.246712 | 0.40(6) | 1.2 | 6 | 559.5 |
4 | 57625.247667 | 1.63(10) | 3.2 | 16 | 562.4 |
5 | 57636.489603 | 2.16(10) | 3.6 | 20 | 571.2 |
6 | 57758.162612 | 5.23(15) | 7.2 | 34 | 557.5 |
7 | 57762.155348 | 1.74(7) | 1.7 | 23 | 559.8 |
8 | 57763.975657 | 0.57(7) | 1.6 | 8 | 559.8 |
9 | 57768.159477 | 1.28(8) | 2.2 | 15 | 562.1 |
10 | 57769.143333 | 0.85(8) | 2.2 | 10 | 558.6 |
11 | 57771.954804 | 0.88(8) | 1.9 | 11 | 558.6 |
12 | 57771.958773 | 0.59(8) | 2.2 | 7 | 560.9 |
13 | 57779.957530 | 5.84(10) | 3.6 | 54 | 562.1 |
14 | 57779.978393 | 1.21(7) | 1.7 | 16 | 563.3 |
15 | 57781.770722 | 4.80(9) | 2.5 | 53 | 562.1 |
16 | 57781.771322 | 3.35(12) | 5.0 | 26 | 569.1 |
17 | 57785.973376 | 1.15(9) | 2.8 | 12 | 560.9 |
18 | 57787.822048 | 0.85(8) | 2.2 | 10 | 562.1 |
19 | 57787.844951 | 11.34(11) | 3.9 | 99 | 563.3 |
20 | 57791.942210 | 0.72(8) | 1.9 | 9 | 562.1 |
21 | 57791.946845 | 1.12(9) | 1.9 | 14 | 569.1 |
22 | 57797.926712 | 0.81(10) | 3.2 | 8 | 560.9 |
23 | 57797.930046 | 0.53(7) | 1.7 | 7 | 565.6 |
24 | 57798.872124 | 11.42(12) | 4.5 | 94 | 565.6 |
25 | 57805.959486 | 4.89(9) | 2.5 | 54 | 559.8 |
26 | 57821.785328 | 1.28(8) | 2.2 | 15 | 563.3 |
27 | 57821.789488 | 3.22(12) | 5.0 | 25 | 571.5 |
28 | 57826.841596 | 1.02(8) | 2.2 | 12 | 563.3 |
29 | 57826.845833 | 1.93(7) | 1.6 | 27 | 560.9 |
30 | 57826.851906 | 0.68(7) | 1.7 | 9 | 560.9 |
31 | 57826.862280 | 0.44(6) | 1.2 | 7 | 562.1 |
32 | 57826.865941 | 0.45(7) | 1.7 | 6 | 560.9 |
3 PERIODICITY
To confirm the periodic behaviour in the activity of FRB 121102, we first tried a Lomb–Scargle periodogram (Scargle 1982). Since the LT observations are spread along a long baseline and tend to be densely sampled closer to periods of activity, a periodogram of the resulting time-series was biased. One needs to sample multiple active and inactive periods to get a correct period from the periodogram even though the sampling is non-uniform (see VanderPlas 2018, for more details). To overcome this, we used a Fast Folding Algorithm (FFA) to search for periodicity in the activity of the source. The FFA is designed to search for periodic pulsar signals in time-series data, and provides the highest possible period resolution for that purpose (Staelin 1969). To make the algorithm applicable to our data set, we first binned the list of detected pulse MJDs available in the literature, 215 MJDs in total from Spitler et al. (2014), Scholz et al. (2016, 2017), Hardy et al. (2017), Gourdji et al. (2019), Spitler et al. (2016), Chatterjee et al. (2017), Marcote et al. (2017), Law et al. (2017), Spitler et al. (2018), Gajjar et al. (2018b), Hessels et al. (2019), Oostrum et al. (2020) (see Table 3 for more details) and this paper, into a histogram with a time resolution of 0.05 d. We do not use the most recent active phase that was reported by multiple telescopes (MJD > 58500) (Caleb et al. 2019; Di et al. 2019; Pearlman et al. 2019). Using an FFA implementation3 (Morello et al. 2020), we then phase-coherently folded these data at all distinguishable trial periods between 2 and 365 d, which generated sets of profiles representing source activity as a function of phase for all trial periods. When the FFA is used for pulsar searching, the folded profiles it produces are usually tested for significance with sets of matched filters reproducing an expected pulse shape, or a χ2 test. Here, however, such methods would be ineffective as most of the detections are concentrated within short time spans and therefore tend to be folded in only a few distinct phase bins regardless of trial period. We therefore used a modified metric: in each fold trial, we measured the length of the longest contiguous phase segment (in units of period) without any source activity. Higher values denote that the activity of the source is concentrated within a smaller phase window, which indicates a periodic activity pattern. The fraction of source inactivity as a function of period is plotted in Fig. 3. We find that for a trial period P0 = 157 ± 7 d, the source remains inactive for a contiguous 44 per cent of the time within each putative cycle. The behaviour of the inactivity metric as a function of trial period cannot be modelled analytically which precludes deriving a mathematically rigorous uncertainty on P0, and thus the error bars provided correspond to the full width at half-maximum of the periodogram peak. We produced an activity profile of the source by folding the MJDs of the detected pulses at the best-fitting period P0 = 157 d, which is displayed in Fig. 4. Using the detected period and a duty cycle of 56 |${{\ \rm per\ cent}}$| we extrapolated the activity period over the span of four years of observations including all published detections of FRB 121102 to date (see Table 3 for details of all detections) and the results are presented in Fig. 2. One can see that the activity period aligns very nicely with the until now excluded detections by the MeerKAT telescope (Caleb et al., in preparation), the FAST telescope (Di et al. 2019) and the Deep Space Network (Pearlman et al. 2019). Hence, all the evidence presented here suggests that this is the most likely activity period of FRB 121102.
ID . | MJD . | Reference . |
---|---|---|
0 | 56233.282837007995 | Spitler et al. (2016) |
1 | 57159.737600835 | Spitler et al. (2016) |
2 | 57159.744223619 | Spitler et al. (2016) |
3 | 57175.693143232005 | Spitler et al. (2016) |
4 | 57175.699727825995 | Spitler et al. (2016) |
5 | 57175.742576706 | Spitler et al. (2016) |
6 | 57175.742839344006 | Spitler et al. (2016) |
7 | 57175.743510388 | Spitler et al. (2016) |
8 | 57175.745665832 | Spitler et al. (2016) |
9 | 57175.747624851 | Spitler et al. (2016) |
10 | 57175.748287265 | Spitler et al. (2016) |
ID . | MJD . | Reference . |
---|---|---|
0 | 56233.282837007995 | Spitler et al. (2016) |
1 | 57159.737600835 | Spitler et al. (2016) |
2 | 57159.744223619 | Spitler et al. (2016) |
3 | 57175.693143232005 | Spitler et al. (2016) |
4 | 57175.699727825995 | Spitler et al. (2016) |
5 | 57175.742576706 | Spitler et al. (2016) |
6 | 57175.742839344006 | Spitler et al. (2016) |
7 | 57175.743510388 | Spitler et al. (2016) |
8 | 57175.745665832 | Spitler et al. (2016) |
9 | 57175.747624851 | Spitler et al. (2016) |
10 | 57175.748287265 | Spitler et al. (2016) |
ID . | MJD . | Reference . |
---|---|---|
0 | 56233.282837007995 | Spitler et al. (2016) |
1 | 57159.737600835 | Spitler et al. (2016) |
2 | 57159.744223619 | Spitler et al. (2016) |
3 | 57175.693143232005 | Spitler et al. (2016) |
4 | 57175.699727825995 | Spitler et al. (2016) |
5 | 57175.742576706 | Spitler et al. (2016) |
6 | 57175.742839344006 | Spitler et al. (2016) |
7 | 57175.743510388 | Spitler et al. (2016) |
8 | 57175.745665832 | Spitler et al. (2016) |
9 | 57175.747624851 | Spitler et al. (2016) |
10 | 57175.748287265 | Spitler et al. (2016) |
ID . | MJD . | Reference . |
---|---|---|
0 | 56233.282837007995 | Spitler et al. (2016) |
1 | 57159.737600835 | Spitler et al. (2016) |
2 | 57159.744223619 | Spitler et al. (2016) |
3 | 57175.693143232005 | Spitler et al. (2016) |
4 | 57175.699727825995 | Spitler et al. (2016) |
5 | 57175.742576706 | Spitler et al. (2016) |
6 | 57175.742839344006 | Spitler et al. (2016) |
7 | 57175.743510388 | Spitler et al. (2016) |
8 | 57175.745665832 | Spitler et al. (2016) |
9 | 57175.747624851 | Spitler et al. (2016) |
10 | 57175.748287265 | Spitler et al. (2016) |
4 DISCUSSION
4.1 Periodic activity?
Here, we discuss the significance of the detected periodicity in FRB 121102. Due to the sparse and uneven observing coverage of the whole time-span considered (Fig. 2), we cannot reasonably assume that the pulse detection dates are uniformly distributed in phase under the null hypothesis (i.e. the source exhibits no periodic activity pattern) for a period P0 = 157 d. To estimate that distribution, an exhaustive list of the start and end dates of all attempted observations would be required, but is not available since typically, only detected pulse MJDs are published in the literature. The statistical significance of our detected periodicity thus cannot be rigorously estimated with the data currently available, and should be treated circumspectly as it may result from a chance alignment between the time ranges where no observations have been made. We acknowledge that bootstrapping the available detections is a possible option (Efron & Tibshirani 1993). In this method, one can re-sample the arrival times of the bursts from a uniform distribution and run a periodicity search on the obtained arrival times. By running multiple realizations of the same, one can obtain a probability of detecting the period by chance. Though bootstrapping can give some sort of a significance for the detected peak, the main caveat of this method is the assumption that all the observations conducted in a given time period are randomly distributed over the entire time period. This is not true with follow-ups of repeating sources as telescopes tend to observe these sources with denser cadence when there is a previously known detection. We also note that if the periodic activity in FRB 121102 is in any way similar to FRB180916.J0158+65, one would expect the source to not emit in every single active phase. This can also result in reduction in the significance of detection of periodicity.
Our best-fitting parameters suggest that the next two activity periods should occur in the MJD ranges 59002−59089 (2020 June 2 to 2020 August 28) and 59158–59246 (2020 November 5 to 2021 February 1). We particularly encourage further observations during the predicted quiescence period in-between, as they could falsify our periodicity claim. A confirmation will require extending the baseline of observations, preferably with a regular cadence. How to optimally space observations to search for, or confirm periodicity of a repeating source is a question that deserves further examination. In essence, a large number of cycles need to be sampled before any proper statistical analysis on the significance of detection can be performed.
If the detected period is astrophysical in origin, it has implications on the possible progenitors of repeating FRBs. The CHIME/FRB Collaboration (2020) have invoked orbital motion to cause such periodicities. If we consider now also orbital motion to be the cause of the observed periodicity in FRB 121102, the large range in the observed periods (16–160 d) can constrain the possible binary systems. High-mass X-ray binaries are systems with a neutron star in an orbit with a massive O/B star. HMXBs in our Galaxy and the Small Magellanic Cloud have a large range of orbital periods, ranging from few tens to hundreds of days (see Liu, van Paradijs & van den Heuvel 2006, for more details). Ioka & Zhang (2020) propose a model where the magnetized neutron star is combed by the highly energetic wind of the secondary star. Massive stars in HMXB systems tend to possess energetic winds for this scenario to be feasible. On the other hand, binaries where the donor star fills the Roche lobe of the system have much shorter periods (<10 d) and are unlikely to be possible progenitors. Other progenitor models invoke precessing neutron stars or young flaring magnetars (Levin et al. 2020; Zanazzi & Lai 2020). The authors of these studies expect the time-scale of precession to be of the order of weeks though larger precession periods (a few months) would be harder to explain as the internal magnetic field would have to be lower by at least a factor of 3 compared to the expected internal fields in young magnetars and will have implications on the observed burst energies from these sources (Levin et al. 2020). To draw any inferences about the origin of this repeating class of FRBs, regular monitoring of such sources is imperative along with more discoveries of periodic FRBs and a systematic approach to following up known repeaters with existing instruments can achieve this goal.
4.2 Follow-up strategies
For the follow-up campaign, we assume that each observing session is one hour long. Then, we assess the significance of the true periodicity that is obtained from the simulated detections. In order to achieve this, we generated a folded profile from the obtained sequence of detections and ran a goodness-of-fit test on it for a null hypothesis that the folded profile is uniform across the entire period. We use the reduced χ2 as the test statistic to evaluate the deviation of the resulting profile from the null hypothesis. We note that there is an underlying assumption here that all events within a phase bin of the folded profile follow Gaussian statistics which may not necessarily be true (see The CHIME/FRB Collaboration 2020, for more details). We use a reduced χ2 of 7.0 as a threshold for the detection of a period at a 5-σ level of significance after taking into account the number of trial periods searched in a putative FFA search. Since time on a telescope for such follow-up observations is limited, we ran this analysis for different amounts of allocated time on any given radio telescope. Figs 5 and 6 show the reduced χ2 as a function of separation of observations for 50 and 100 h of observing time. The results of the simulation clearly show that for a burst rate of 0.5 h−1 and FRB 121102 like sources, one would need more than 100 h of observing time to detect a significant period in the range of 10–150 d. On the other hand, CHIME will be able to detect repeaters with higher burst rates within 50 h of on source time while other single dish telescopes will need at least 100 h to detect high burst rate sources. Also, it shows that in order to obtain an accurate and significant detection of periodicity, one needs to have a fairly dense cadence of observations. While CHIME has the advantage of daily cadence, targeted follow-up campaigns will need a cadence ranging from 0.5 to 3 d in order to have the best chance to detect a period regardless of the burst rate.
5 CONCLUSIONS
We have carried out a long-term radio monitoring campaign of FRB 121102 with the Lovell Telescope. Using these pulses and other detections from the literature, we performed a periodicity search and detected a tentative period of 157 d in the periodogram with a duty cycle of 56 |${{\ \rm per\ cent}}$|. We extrapolated the computed period to the most recent activity and show that the detections lie within the activity phase predicted by the period. We do note that the uneven observing strategy prevents us from determining a robust significance of the detection of the said period. To avoid these issues in the future, we performed simulations of periodic FRBs to show that non-transit telescopes need at least 100 h of follow-up time to determine periodicities in these sources. This shows that single dish telescopes and interferometers will be able to follow-up repeating FRBs in reasonable amount of telescope time to detect periodicities. Our study also shows the importance of reporting non-detections for any repeating FRB follow-up campaigns as they are crucial for computing the robustness of any detected periodicity. If the periodicity in FRB 121102 is genuine, it suggests that there is a large range in the periodicities of repeating FRBs and more periodic FRBs need to be discovered to infer the nature of their progenitors.
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ACKNOWLEDGEMENTS
We would like to thank our anonymous reviewer whose remarks vastly improved the manuscript. KMR, BWS, VM, and MC acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694745). DA and DRL acknowledge support from the National Science Foundation awards AAG-1616042, OIA-1458952, and PHY-1430284. RPB acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 715051; Spiders). The authors would like to thank Andrew Lyne for help with the Lovell Telescope observations during this campaign.