On the problems of detecting Fast Radio Bursts with the LPA LPI

We present a verification of fast radio bursts (FRBs) previously published by V.A. Fedorova and A.E. Rodin. These FRBs were found in the monitoring data with the Large Phased Array (LPA) radio telescope using a search algorithm based on data convolution with a scattered pulse pattern. The same 6-channel data (channel width 415 kHz) were used for verification, in which FRBs were found with dispersion measures of 247, 570, and 1767 pc/cm³. An additional verification of the published FRBs was also carried out in 32‑channel data (channel width 78 kHz). We can not confirm any of the published FRBs on the signal-to-noise ratios claimed in the original paper. The main errors are caused by incorrect determination of the baseline and incorrect estimation of noise standard deviations.

Keywords: fast radio bursts; nature of radio bursts

Copyright comment ISSN 1063-7729, Astronomy Reports, 2023, Vol. 67, No. 2, pp. 163–171. © Pleiades Publishing, Ltd., 2023. Russian Text © The Author(s), 2023, published in Astronomicheskii Zhurnal, 2023, Vol. 100, No. 2, pp. 186–195.

In 2007, a paper was published that discussed the detection of a dispersed pulse in archival data obtained in observations with the 64-m Parkes radio telescope at a frequency of 1.4 GHz. It was the first fast radio burst (FRB) found [[1]]. It was a short pulse less than 5 ms long, similar to that of an ordinary pulsar. The observed dispersion measure (DM) for this pulse was 375 pc/cm3. Based on the direction in which the burst was determined and the observed DM, one could assume its extragalactic origin. The distance to the burst source was estimated as 600 Mpc. The distance estimate and the observed flux density of 30 Jy at a frequency of 1.4 GHz showed that the luminosity of the burst is orders of magnitude higher than the luminosity of ordinary pulsar pulses. This value of the luminosity estimate indicates that the emission mechanism is different from that of ordinary pulsar pulses.

There are 118 sources in the FRB catalog[1] [[2]], the last FRB was cataloged in January 2020. Considering the work of the Canadian radio telescope CHIME[2] [[3]], to date, the number of detected FRBs is more than six hundred. According to the FRB and CHIME catalogs, bursts were observed at frequencies from 0.1 to 1.4 GHz, and at dispersion measures from 103.5 to 3038 pc/cm3.

There are many different hypotheses attempting to explain the nature of FRBs: the merger of a pair of neutron stars (NSs) [[4]], the merger of a pair of white dwarfs (WDs) [[5]], the merger of an NS and a black hole (BH) [[6]], the merger of charged BHs [[7]], the collapse of NS into BH [[8]], the presence of a planet orbiting a radio pulsar [[9]], giant pulses of young pulsars [[10]], giant bursts/flares of magnetars [[11]], quantum string collisions [[13]] and others. The observed properties of FRBs and some of the hypotheses about their origin can also be found in reviews [[14]]. Such a wide variety of hypotheses about the nature of FRBs indicates that the nature of radio bursts is not clear, and the available observations are still not sufficient to select an unambiguous hypothesis about the origin of FRBs.

All currently detected FRBs can be divided into two groups—repeating and non-repeating. It is believed that the nature of non-repeating FRBs is associated with some kind of cataclysmic events, while repeating FRBs can be, for example, a manifestation of magnetar activity.

Since the bulk of the found FRBs are non-repeating events, observers always face the question of the reliability of a "one-time" detection. It would seem that by choosing events with a high signal-to-noise ratio (S/N), one can get rid of unreliable detections. However, in [[16]], it was shown how a conventional microwave oven can massively generate "new FRBs" having different DMs. Trying to avoid such cases, the authors of the original methods very carefully develop the method of processing observations as applied to observations with specific telescopes.

According to the FRB catalog, the median DM value of detected bursts falls within the range of 500–600 pc/cm3. At frequencies above one gigahertz, where the first bursts were detected, the scattering () of the pulse in the interstellar medium slightly broadens the pulse compared to that at low frequencies. The pulse broadening due to scattering leads to a decrease in the observed peak flux density (a decrease in the S/N). Thus, at frequencies of 100–150 MHz, the scattering is so strong that there are practically no detections of pulsars with DM pc/cm3. Pulsars are objects with periodic emission and, unlike FRBs, it is possible to accumulate a signal for them, increasing the observed S/N. The absence of detections of pulsars with large DM in the meter wavelength range, despite signal accumulation, indicates lower chances of finding single pulses at large DM in low-frequency observations compared to high-frequency observations. Despite the low chances, attempts to detect FRBs in the meter wave range have been made. For example, in [[17]], a directed search was carried out at a frequency of 145 MHz with the LOFAR radio telescope. In [[18]], the search was carried out at a frequency of 182 MHz with the MWA telescope. The result of the work carried out was the upper estimates for the expected number of FRBs in the sky, but no real FRBs were found.

In 2019, a paper by Fedorova and Rodin [[19]] was published, according to which the Large Phased Array (LPA) radio telescope of the Lebedev Physical Institute (LPI) of the Russian Academy of Sciences, which is the main instrument of the Pushchino Radio Astronomy Observatory (PRAO), at a frequency of 111 MHz, three bursts were found with dispersion measures of 247, 570, and 1767 pc/cm3. The presentation of this work in the PRAO seminar was accompanied a large number of criticisms regarding the processing of observations and the reliability of the results obtained. In the present paper, we verified the discovered sources using the same data that were used by the authors and repeating the proposed search technique.

The search for pulsed radiation was carried out in the data obtained with the LPA LPI radio telescope. LPA LPI is a meridian-type radio telescope with a filled aperture, which is a flat equidistant array of 16 384 wave dipoles. The size of the beam size is approximately , the time of passage of the source through the meridian is 3.5 min/ ( is the declination) at half power. The central observation frequency is 110.3 MHz, the reception bandwidth is 2.5 MHz. Daily and round-the-clock monitoring in 96 beams of the telescope began in August 2014, but partial monitoring (not for all beams and not for all dates) has been carried out since 2012.

Data is synchronously recorded in two modes: six channels with a channel width of 415 kHz and a sampling time of one point ms; 32 channels at 78 kHz channel width and sampling time 12.5 ms. To search for FRBs, the authors of [[19]] used data with a low frequency-time resolution.

The search for new FRBs in [[19]] was carried out according to the following scheme:

—the baseline (the background of the Galaxy) was subtracted from the original hourly data file, representing the initial data, which, according to [[19]], were smoothed by the median filter. The median filter is not described in the paper, and we used the usual definition. An array is taken from a data file. The points are arranged in ascending or descending order. The output value after running the median filter is the point in the middle position. A shift is made in the original array by a length equal to the length of the array in which the median value was searched, and the procedure is repeated. As a result, we have a set of points that can be connected by segments. It is assumed that each se-gment describes the baseline for the length of the segment;

—for the search, a twenty-minute interval was taken, the coordinate of the center of which in right ascension was (the coordinate of the repeating FRB 121102);

—the DM was enumerated with a step of 50 pc/cm3 in the range of pc/cm3, and after adding the frequency channels with the assumed DM, convolution was made with the pattern. The pattern is a model pulse broadened in the receiver band according to the test DM = 360 pc/cm3 and convoluted with an exponential function (thin screen assumption) with a scattering scale s, assuming ; and

—upon detection of an FRB candidate, convolution was performed with pulses corresponding to different DMs, and it was considered that the DM was determined correctly when the resulting S/N is maximum. Here and below, we defined the S/N as the ratio of the value of the maximum to be checked in the array of points on the expected dispersion measure of the FRB candidate to the root-mean-square deviations of the noise in this array per pc/cm3. The transfer function for taking into account scattering for the pattern was calculated using the formula:

Graph

where is the pulse broadening due to scattering according to the model [[20]] for the tested DM.

The data taken in the interval from July 2012 to May 2018 were processed for two directions in the sky. For each direction, 355 hours of recording were accumulated over 6 years. We partially reproduce Table 1 from [[19]] with data on the found FRBs. Two columns with expected FRB redshifts and pulse energies have been removed from the original table. The left columns of the table sequentially present: the dates of FRB detection, coordinates, their DM and S/N estimates, the estimate of the peak momentum flux density (), and the estimate of the characteristic scattering time () according to the observations by the authors of [[19]]. The adjacent column gives our estimate of the expected scattering () for putative DM FRB candidates calculated using the empirical model of Kuzmin et al. [[20]]. In this model, pulsars with pc/cm3 were considered, and it was found that . The authors of [[19]] assumed that at higher values of DM, the slope of the dependence of the scattering magnitude on DM does not change. Note that for pulsars the dependence can be even steeper (see [[21]]), but for extragalactic sources the formal application of scattering from [[20]] can be justified [[23]]. In columns 9 and 10, we present the intra-channel broadening of the pulse, i.e., its dispersion smoothing, in frequency channels for 6 () and 32 () channel observations, at the DM value indicated in column 4 and determined by the formula:

2

Graph

where is the time delay of the signal due to passing through the medium in milliseconds, and are the midpoints of the frequency channels expressed in MHz.

Table 1. Checked events

Below, we consider the processing of the event on June 6, 2017, in which an FRB candidate was found, which has the smallest dispersion measure (DM = 247 pc/cm3), and, consequently, the minimum scattering on the line of sight and intrachannel pulse broadening. The coordinates of the FRBs found by the authors of the original paper [[19]] are given in right ascension with an accuracy of one time minute, so the expected location can be minute from the event coordinate. Visual search was carried out by us on the entire data interval, that is, minutes from the event coordinate. After compensating the gain in the frequency channels according to the calibration signal (see details in [[24]]), the recording was shifted in individual channels, considering DM, then the channels were combined and the subsequent cross-correlation with the pattern , the value of which is given in Table 1.

Figures 1a–1c show the stages of processing. Fig. 1a shows raw data, the center corresponds to the coordinate 5h32m. According to [[19]], the baseline is the original data smoothed by the median. The median step is not given in the original paper. When choosing the median step, we were guided by the considerations that if the median step is chosen to be less than the pulse scattering time, then the pulse in the processed record can be strongly smoothed out or completely destroyed. If the median step is chosen many times larger than the scattering time, then after subtracting the baseline, poorly subtracted discrete sources and details of the background of the Galaxy may remain in the remaining record. So, according to Table 1, the expected scattering of an FRB having DM = 1767 pc/cm3 is almost half a minute, and the LPA half-power beam size is min. Selecting a median step of 3 min (six times greater than ) will result in discrete sources being visible in the recording. It is obvious that the median step must be chosen depending on the expected amount of scattering. When searching for FRB, the scattering is a priori unknown, the magnitude of which depends on DM. Therefore, it is necessary to enumerate all possible values of the median step corresponding to different scatterings. In the present work, candidates are tested for which their DM is known and there is an estimate of the amount of scattering. For the median step, we chose twice the size of the estimate according to the model of Kuz'min et al. [[20]]. For the tested FRB with DM = 247 pc/cm3, the median step was chosen to be 1.2 s (12 points). In all figures, the horizontal axis shows time, and the vertical axis shows the flux density in conventional units. The blue and green lines in the figures show the levels of and . Vertical segments show height values in conventional units. The arrow indicates the expected location of the source from Table 1.

Graph: Fig. 1. Panel (a) presents 20-minute raw data record on June 6, 2017 without DM compensation (black color). The background signal being subtracted is shown in red. At the beginning of the record, the peak of the source 4С+41.14 is visible with a flux density of 16.1 Jy at a frequency of 102.5 MHz according to the catalog http://astro.prao.ru/db/; (b) data after baseline subtraction before (red) and after (black) compensation with DM = 247 pc/cm3; and (c) data after passing the convolution procedure with the scattering function according to Kuz'min et al. [[20]] in 6-channel data.

Figure 1b presents the data of Fig. 1a after baseline subtraction before (red) and after (black) DM compensation. Separate peak signals are visible, the maxima of which are higher before, and not after, dispersion compensation. That is, these peak signals are ordinary impulse noise having DM = 0 pc/cm3. Fig. 1c shows the data after convolution. It can be seen that some of the impulse signals after dispersion compensation and frequency channel addition have levels higher than , but less than (blue (lower) and green (upper) lines in the figure). However, verification shows that all these signals are associated with impulse noise, the height of which is DM = 0 pc/cm3 higher than their height after the channels are combined, considering DM = 247 pc/cm3. The remaining peak signals visible after convolution with the scattered signal are less than .

We also ran parallel processing on 32-channel data. The final patterns after convolution for 6- and 32‑channel data do not match. If there are real sources in the records, the sensitivity in data with high frequency/time resolution should almost always be higher than in data with low frequency/time resolution. In data with a channel width of 415 kHz (6-channel data), the broadening within the frequency channel due to the dispersion lag for the case under study is about 5.4 times greater than in 32-channel data (channel width of 78 kHz), and, therefore, the S/N in 32‑channel data can grow up to times. In other words, if the original signal was narrow, and its scattering was less than the dispersion spread in the frequency channel, then the narrower the channel, the greater the gain in sensitivity for 32-channel data, all other things being equal. If the scattered pulse width was greater than the dispersion smearing in the channel, then there will be no gain in sensitivity, but with the same averaging of the data over time, the pulse profiles should repeat each other. However, a comparison of the processing of 6- and 32-channel data shows that no increase in S/N, and in general any pronounced signal at levels of S/N > 4, is not visible in the records. The signals for 6- and 32-channel data do not repeat each other, and we can say that in the co-nsidered case we are talking about a purely noise process.

When checking the event on October 18, 2015, where the authors detect a signal with DM = 570 pc/cm3, a problem arose related to the right ascension coordinates of the event used by the authors of [[19]]. In this paper, 20 minutes of recording with the center at were studied, and therefore the extreme points of the record should have coordinates and . At the same time, the authors indicated the coordinate of the found event . It is possible that this is a typo, it is possible that the region was explored slightly longer than the 20 minutes indicated in the paper. We checked both the region and the region around . Figures 2a–2f show the event on October 18, 2015, where we able to detect a signal as close as possible to the signal received by the authors. It is located at coordinates close to . The baseline was subtracted by straight line segments, the length of which (5.6 s, 56 points) was determined by twice the expected scattering time (see Table 1).

Graph: Fig. 2. Panel (a) presents approximately eight minutes of raw data in black on October 18, 2015 centered on . The baseline being subtracted is shown in red; (b) signal after baseline subtraction and compensation DM = 570 pc/cm3; and (c) signal after convolution with scattered pulse and summation of all frequency channels. The arrow points to the detected signal, which coincides with the signal from [[19]]; panels (d) and (e) show signals after processing of 6- and 32-channel data, most similar to the signal from [[19]], a fragment of which is shown in Fig. 2e.

Figures 2d–2f are similar in terms of the location of the maxima and the general shape. The left side shows 6-channel data, the middle one shows 32-channel data, and the right side shows a fragment of the original figure with the supposed FRB detection in [[19]]. However, Fig. 2c (see arrow) also shows that the S/N of these peaks is much smaller than 4, which indicates the absence of significant signals.

For the event on September 20, 2016 (Fig. 3) with DM = 1767 pc/cm3, the pulse in the channel should spread up to 33 s due to scattering. Subtracting the data smoothed by the median with a step of 1 min leads to the appearance of trends in the record (Fig. 3a). Figure 3b shows a record after convolution with a scattered signal. We failed to find a signal similar to the signal given in [[19]].

Graph: Fig. 3. Panel (a) shows the results of baseline subtraction before (red) and after (black) accounting for smearing in the band with DM = 1767 pc/cm3 of the FRB candidate on September 20, 2016; panel (b) shows signal after convolution with a scattered pulse.

Thus, our estimates give S/N < 4 for all events from [[19]]. We think that this indicates the absence of real detection.

In the previous section, we considered the main, in our opinion, signature of the discovery for a new FRB—this is its S/N. The S/N level at which the probability of a false detection becomes negligible depends on the number of cases considered. In radio astronomy, the criterion S/N = 6–7 is adopted, when the probability of false detection becomes negligible. An important condition in determining the S/N is the correct subtraction of the average level (baseline). It was shown that at the coordinates corresponding to the detected FRBs, there are no signals with a S/N level > 4, which contradicts the declared S/N values from 6.1 to 9.2 [[19]]. The signal levels found by us clearly indicate the low reliability of the detection of new FRBs.

We do not consider in our paper all the comments made at the PRAO seminars, but we note some of them.

—The dispersion delay lines in the figures are smooth, and there is a feeling of a large number of used frequency channels. What is it connected with?

—In the given convolutions of the original signal with a scattered profile, the baseline (average signal level) is not indicated, which does not allow visually assessing the significance of the event. For example, for a candidate with DM = 247 pc/cm3 (see [[19]], Fig. 8), there is a minimum of the same scale in front of the maximum, which falls at count 80, that falls at count 50. There is a feeling that the conducted noise convolution with scattered model signal simply redistributed the energy of the noise track, and gave a minimum and maximum with the same energy.

—When searching for dispersed pulses for each direction under study, many iterations are made on different DMs, and random noise arrays are obtained with each enumeration. These enumerations were made for observations made daily over an interval of six years. How many iterations during the search were actually made, and what is the probability of a statistically significant detection of a false (noise) signal on different signal to noise ratios?

—Why, for all FRB candidates, the given scattering estimates are much less than those expected from the empirical relationship of the scattering value from DM according to [[20]], which was taken by the authors as a basis for scattering estimates? Why does the duration (half-width) of pulses for the found sources not correspond to empirical models of pulse scattering in the interstellar medium?

—Why in high frequency-time-resolution data (32‑channels), which are recorded in parallel with data of low frequency-time-resolution (6-channels), the S/N of the found sources is lower with the same time averaging? The question was raised by the fact that in 32-channel data the intrachannel dispersion smoothing is five times smaller, which should lead to larger values of the observed burst S/N, at least for a source with DM = 247 pc/cm3.

—It seems strange that two events with DM = 247 and 1767 pc/cm3 completely coincided in coordinates.

—According to [[19]], FRB 121102 (DM = 570 pc/cm3) could be detected in the side lobe of the LPA LPI. The maximum of the first side lobe is approximately 4% of the energy in the main lobe. Therefore, if this pulse were observed in the main lobe, its signal-to-noise ratio would be S/N 150. As of 2021, more than 1600 pulses have been recorded for FRB 121102 [[25]]. What is the probability that a pulse was detected in the side lobe, where an insignificant part of the total pulse energy is observed, and that no pulse was detected in the main lobe for six years? The alternative explanation of the authors suggests the possible detection of some other FRB. In this case, it is surprising that its DM matches with great accuracy the DM of the known repetitive FRB.

As it turned out at the seminars, the figures called dynamic spectra in [[19]] are not them in the generally accepted sense. The convolution of the initial data with the scattering pattern acts as the flux density in the frequency channel. To obtain a "beautiful" picture, the authors used digital filters not described in the paper, which smoothed the image, giving a false impression of a large number of observed frequency channels and continuity of the dispersion delay line. Most likely, these are non-linear filters. While obtaining a very similar profile in 6-channel data for a pulse with DM = 570 pc/cm3, we did not able to obtain a similar picture of the dynamic spectrum.

Let's give an answer to one of the questions asked at the seminars, namely, to the question about the probability of a false signal detection. Fortunately, there is enough data in [[19]] to provide an answer. We assume that the noise is distributed according to the normal law. The number of iterations in the search for a transient for each beam of the LPA LPI can be determined as 355 hours 3600 (seconds per hour) 10 (counts per second) 60 (enumerated DM) = 766.8 millions of independent and verifiable events in which the authors tried to find dispersed pulses. Even at a level above 4, 48 571 false events will be detected, at a level above 5—439 events, and at a level above 6—1 event. We have given estimates of the probability of false detection of an impulsive signal for ideal white noise. Considering the noise recorded at the LPA LPI both in the frequency and time domains, and having, among other things, explicit dispersion signal delays [[26]], the obtained estimates of the number of expected false events should be taken as lower estimates. According to the previous paragraph, the scores are S/N < 4 for all tested events. Therefore, we believe that all three "found" events are false detections.

One of the unpleasant points that appeared when trying to repeat the technique [[19]] with the LPA LPI data was the choice of the median step used to obtain smoothed data and subsequent subtraction of the baseline. In [[19]], nothing is said about the median step for background subtraction, as well as about the method for determining the S/N. We wrote above that we used twice the value of the scattering on the tested measure of dispersion. However, observations [[20]–[22]] show that the scattering can be an order of magnitude larger than that in the model [[20]]. In this case, the median step should also change accordingly. If it is not changed (not increased), we can lose a pulse. Thus, when searching for an FRB with DM = 1767 pc/cm3, the median step can be up to 33 s × 5.5 min. Median step in 5.5 min almost equal to the time it takes the source to pass through the antenna pattern. Therefore, with such a chosen median step, discrete sources will not be subtracted and will remain in the record. This means that when searching for FRB candidates in the LPA radio telescope data, it is necessary to restrict ourselves to such dispersion measures, the median step of which is such that discrete sources disappear after subtracting the baseline.

For the candidate with DM = 247 pc/cm3, we repeated the processing with a median step of 12 s (120 points), which is 20 times the expected scattering time. FRB not found. For the candidate with DM = 570 pc/cm3, no reprocessing with a median step corresponding to the larger expected scattering time was performed, because the resulting picture (see Fig. 2) almost completely coincided with the picture from [[19]]. The candidate with DM = 1767 pc/cm3 was not reprocessed for the reasons given in the previous paragraph.

Critical remarks on the reliability of detection of new FRBs, without consideration of the processing technique, were made to two papers by Fedorova and Rodin in [[28]], where a repeating FRB 20180916B was detected at low frequencies.

In 2021, paper [[29]] was published, where the S/Ns of the cases we considered were changed. In particular, for the case with DM = 570 pc/cm3, instead of S/N = 6.2, the new value is S/N = 5.9. However, as shown above, for this case, S/N < 4. No attempts have been made to correct the search technique. The S/N for almost half of the 60 "new FRBs" is less than 6, and for five candidates it is less than 4. Breaks are observed in some of the presented dynamic spectra. Of course, there may be real FRBs among the 60 published cases. It is necessary to carry out a complete audit of all candidates. This is beyond the scope of this paper, which is devoted only to testing the search technique and the first three candidates discovered.

When searching for dispersed pulses, usually the evidence for the discovery of a new source is an estimate of S/N = 6–7 or more. The S/N is defined as the amplitude of the peak signal divided by the standard deviation of the noise. The standard deviation of noise, other things being equal, is the smaller, the better the baseline is subtracted. The baseline is a set of line segments. The length of these segments is determined by the amount of pulse scattering in the interstellar and intergalactic medium. If the dispersion measure is large, then the length of the segments used to subtract the background can be comparable to the duration of the passage of a discrete source through the radiation pattern of the LPA LPI transit radio telescope. Thus, the search for FRBs at large DMs with the LPA LPI radio telescope is automatically limited. After detecting signals with S/N > 6–7, it is necessary to check the source by indirect signatures. It should be detected in one or two LPA beams. The dynamic spectrum should show a pronounced dispersion delay line.

When checking the FRB candidates found in [[19]], no signals with S/N > 4 were found, which indicates that all these detections are false. It is possible that the authors, in order to estimate the standard deviations, took a short segment of the processed record, on which they see something similar to a pulse, and calculated the standard deviations on a small part of the record outside the impulse. The processed record with a large number of significant points shows that the standard deviations of the noise are much larger, and the determined S/N value is much smaller.

Unfortunately, the methodology of the authors of [[19]] regarding the choice of the step for the median filter and the choice of points for estimating the standard deviations is written so ambiguously that we had to be guided by common sense when trying to repeat the processing technique. We managed to "discover" only one of the three "FRBs" presented in the work. Judging by the noise track in Fig. 2c and the value of S/N = 1, equal to the distance between the lines drawn at S/N = 4 and 5, for this "FRB" S/N < 2.

In this paper, the question on the fundamental possibility or impossibility of detecting FRBs with the LPA LPI remained unanswered. Here are some considerations that speak in favor of possible FRB detections. The main factor hindering the detection of FRBs is the scattering of pulses in the interstellar medium. It is known that the scattering for any chosen DM, according to observations in the meter wavelength range, can vary by more than an order of magnitude, both up and down from the average value [[20]]. The average values extracted from Fig. 2 of this paper show that the scattering , 30, and 200 ms at dispersion measures DM = 50, 100, and 200 pc/cm3, but can be less than 1, 10, and 100 ms at the same dispersion measures. According to the FRB catalog [[2]], after excluding the "Pushchino" FRBs, the widths of the found pulses are in the range from 0.08 to 34 ms, and the median value is 1.9 ms. Recall that the sampling time in the monitoring survey conducted the LPA LPI is 12.5 ms. In the same catalog, 11 FRBs (approximately 10% of the list of all FRBs in the catalog) have an observed DM < 200 pc/cm3, and the minimum is 103.5 pc/cm3. The CHIME radio telescope found an FRB with DM = 81.82 pc/cm3 [[30]], which is not yet included in the FRB catalog. Thus, FRBs have already been found, the pulse widths and dispersion measures of which indicate the possibility of their detection in observations with the LPA LPI, if, of course, the sensitivity of the instrument is sufficient.

In the study on the search for rotating transients, carried out in the PRAO [[31]], Table 1 shows the se-nsitivity of the LPA when searching for single pulses in comparison with the sensitivity of other large instruments with which FRBs have already been detected. The threshold sensitivity was recalculated to a frequency of 111 MHz assuming a spectral index (). According to this table, the threshold sensitivities in the search for pulsed signals with S/N = 7 for telescopes with a mirror diameter of 64, 100, and 300 m (Parks, Effelsberg, Arecibo) and LPA antennas are 4, 0.55, 0.5, and 2.1 Jy, respectively. The sensitivity of 2.1 Jy in the search for pulsed radiation with the LPA has been confirmed by practical detections of new RRATs and pulses from known pulsars [[31]]. The weakest detected pulses have a flux density of approximately 2 Jy. Pulses have been detected from 115 known pulsars and 46 new RRATs. Thus, the confirmed sensitivity of the LPA in the search for FRBs is at a level comparable to the sensitivity levels of some of the best radio telescopes in the world. Finally, the detection of a repeating FRB 20180916B in the frequency range of 110–190 MHz with the LOFAR radio telescope [[32]] once again indicates that the detection of FRBs with DM < 200–300 pc/cm3 with the LPA LPI is a matter of time and competent processing of observations.

The authors express their gratitude to the staff of the observatory V.M. Malofeev, T.V. Smirnova, and V.A. Potapov for preliminary reading of the paper and a number of comments that allowed to improve the text, as well as L.B. Potapova for help in the design of the figures.

This work was supported by the Russian Scientific Foundation[3] (project no. 22-12-00236).

Translated by E. Seifina