CRAFTS for Fast Radio Bursts Extending the dispersion-fluence relation with new FRBs detected by FAST
Chen-Hui Niu, Di Li, Rui Luo, Wei-Yang Wang, Jumei Yao, Bing Zhang, Wei-Wei Zhu, Pei Wang, Haoyang Ye, Yong-Kun Zhang, Jia-rui Niu, Ning-yu Tang, Ran Duan, Marko Krco, Shi Dai, Yi Feng, Chenchen Miao, Zhichen Pan, Lei Qian, Mengyao Xue, Mao Yuan, Youling Yue, Lei Zhang, Xinxin Zhang
DDraft version February 23, 2021
Typeset using L A TEX twocolumn style in AASTeX63
CRAFTS for Fast Radio BurstsExtending the dispersion-fluence relation with new FRBs detected by FAST
Chen-Hui Niu, Di Li,
1, 2, 3
Rui Luo, Wei-Yang Wang,
1, 5
Jumei Yao, Bing Zhang, Wei-Wei Zhu, Pei Wang, Haoyang Ye, Yong-Kun Zhang, Jia-rui Niu, Ning-yu Tang, Ran Duan, Marko Krco, Shi Dai,
4, 8
Yi Feng, Chenchen Miao, Zhichen Pan, Lei Qian, Mengyao Xue, Mao Yuan, Youling Yue, Lei Zhang,
1, 9 andXinxin Zhang National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China University of Chinese Academy of Sciences, Beijing 100049, China NAOC-UKZN Computational Astrophysics Centre, University of KwaZulu-Natal, Durban 4000, South Africa CSIRO Astronomy and Space Science, Australia Telescope National Facility, Epping, NSW 1710, Australia School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871,China Department of Physics and Astronomy, University of Nevada, Las Vegas, Las Vegas, NV 89154, USA School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China Western Sydney University, Locked Bag 1797, Penrith South DC, NSW 1797, Australia School of Physics and Technology, Wuhan University, Wuhan 430072, China (Accepted February 18, 2021)
Submitted to ApJLABSTRACTWe report three new FRBs discovered by the Five-hundred-meter Aperture Spherical radio Telescope(FAST), namely FRB 181017.J0036+11, FRB 181118 and FRB 181130, through the Commensal RadioAstronomy FAST Survey (CRAFTS). Together with FRB 181123 that was reported earlier, all fourFAST-discovered FRBs share the same characteristics of low fluence ( ≤ > − ), consistent with the anti-correlation between DM and fluence of theentire FRB population. FRB 181118 and FRB 181130 exhibit band-limited features. FRB 181130 isprominently scattered ( τ s (cid:39) E diagram, previously out of reach of other surveys. The implied all sky event rate of FRBs is1 . +1 . − . × sky − day − at the 95% confidence interval above 0.0146 Jy ms. We also demonstratehere that the probability density function of CRAFTS FRB detections is sensitive to the assumedintrinsic FRB luminosity function and cosmological evolution, which may be further constrained withmore discoveries. Keywords:
Radio transient sources (2008); Radio astronomy (1338); Astronomical object identification(87); Radio bursts (1339)
Corresponding author: Di [email protected] author: Wei-Wei [email protected] author: Chenhui [email protected] INTRODUCTIONFast radio bursts (FRBs) are bright, millisecond-duration cosmological radio transients (see Cordes &Chatterjee 2019; Petroff et al. 2019; Zhang 2020 forreviews). The origin of FRBs remains a mystery (seePlatts et al. 2019 for a summary of models). Based a r X i v : . [ a s t r o - ph . H E ] F e b Niu et al. on their large dispersion measures (DMs) in excess ofthe expected corresponding Galactic contribution, theircosmological origin was first hypothesized and later con-firmed (Lorimer et al. 2007; Thornton et al. 2013; Bassaet al. 2017; Chatterjee et al. 2017; Marcote et al. 2017;Tendulkar et al. 2017; Ravi et al. 2019; Marcote et al.2020; Macquart et al. 2020).Motivated by the “Lorimer burst” (Lorimer et al.2007) and the confirmation of FRBs being a distinctivetransient population (Thornton et al. 2013), a numberof dedicated FRB surveys and searches have resultedin an increasing pace of discoveries (e.g., Spitler et al.2014; Masui et al. 2015a; Caleb et al. 2017; Farah et al.2018; Ravi et al. 2019; CHIME/FRB Collaboration et al.2019b; Farah et al. 2019), with the anticipation of theupcoming new CHIME sample being a substantial leapforward.The last sentence in the abstract of Thornton et al.(2013)– “Characterization of the source population andidentification of host galaxies offers an opportunity todetermine the baryonic content of the universe.”–turnsout to be both insightful and visionary. There existsan anti-correlation between DM and fluence of FRBs,which is consistent with DM being a proxy of distance(Shannon et al. 2018). The relation has a broad scatter,implying a broad range of intrinsic luminosity and/orenergy functions of FRBs (see also Luo et al. 2018, 2020;Lu et al. 2020a,b; Zhang et al. 2021). The observed sam-ple is obviously limited by the available instruments. Inaddition to event rate and other intrinsic characteris-tics of FRBs, the instrumental gain, RFI, and detectionalgorithms all affect the apparent fluence distribution.Still, high-DM FRBs are most likely luminous and dis-tant, thus crucial for extending the dispersion-fluencerelation. For example, the source with the highest DM ∼ − (Bhandari et al. 2018; Caleb et al. 2018)detected thus far, FRB 160102, can be inferred to havean upper-limit of redshift z ∼ z ∼
10 (Zhang 2018), if they exist there. Based ona novel high-cadence CAL technique, the CommensalRadio Astronomy FAST Survey ( Li et al. 2018) as-pires to cover the FAST sky ( ∼
57% of the full sky)with the 19-beam receiver in drift scan mode and si-multaneously obtain four data streams, namely Galac- https://crafts.bao.ac.cn tic HI, extra-galactic HI, pulsar search, and transients,the last two of which are searched for FRBs. As a driftscan, CRAFTS spends most of its time off the Galac-tic plane(85% of observation time with | b | > ◦ ). In(Zhu et al. 2020) the first FAST discovery–FRB181123–was reported. In this paper, we report three newFRBs. Together, the four discoveries, with high-DMas well as low fluence, occupy a previously empty re-gion (DM E ∈ [1099 . − , . − ] , Fluence ∈ [42 mJy ms ,
200 mJy ms]) in the DM-fluence space.We describe the observation and searching methods inSec.2 and the characteristics of the three new FRBs inSec.3. We discuss the all sky FRB event rate expectedfor CRAFTS, the implications of these High-DM andlow-fluence FRBs in Sec.4. The summary is in Sec.5. OBSERVATIONSThe FAST’s L-band receiver Array of 19-beams(FLAN, Li et al. 2018) covers a frequency band of 1.0-1.5 GHz. CRAFTS employs a novel high-cadence CALinjection technique invented by the survey team, whichproduced a system temperature measurement for eachdetected pulse. In this work, we search for FRBs in thepulsar data stream, with 0.122 MHz frequency resolu-tion at 196.608 µ s sampling interval. The raw data areof 8-bits sampling with full polarization, reaching datarate of ∼
300 GB per hour. The observed data werecompressed to the 1-bit filterbank format and the polar-izations were merged.We established a
HEIMDALL -based pipeline called FAST Miner . FAST Miner distributes the workload tomore than 20 GPU servers. The pipeline records theS/N (Signal-to-Noise ratio), start time, pulse width,DM, beam ID, etc. For each single-pulse candidate, thepipeline produces an overview plot including two profilesand two- dimensional waterfall plots, corresponding tobefore and after the de-dispersion process, respectively.For a total of 1667 hours CRAFTS data taken be-tween June and the end of 2018,
FAST Miner were runwith a DM trial range between 100 to 5000 pc cm − .Candidates detected by less than 4 adjacent beams butwith a S/N > σ were kept for further inspection.Thecandidates were then manually examined, particularlyin terms of the DM sweep in the dynamic spectrum andtheir surrounding RFI background. According to theradiometer equation: S peak = β · T sys · S / N G √ t ∆ ν , (1) http://sourceforge.net/projects/heimdall-astro (Barsdell et al.2012) https://github.com/peterniuzai/FAST FRB.git RAFTS for Fast Radio Bursts β is π/ ν is the bandwidth, the detection threshold of ourCRAFTS FRB search is roughly 0.0146 Jy ms for a 1 mspulse width. FRB DISCOVERIESThree new FRBs were captured on October 17th,November 18th, and November 30th in 2018. Since twoother distinctive FRBs have already been reported to oc-cur on October 17th (CHIME/FRB Collaboration et al.2019a; Farah et al. 2019), we denote the CRAFTS dis-covery as FRB181017.J0036+11 to avoid confusion. Allthe detailed results of the three new FRBs are exhibitedin Table 1. 3.1.
Burst Characteristics
FRB 181017.J0036+11, FRB 181118, and FRB181130 were detected within different FLAN beams. Weused the average gain ( G ∼
15 K/Jy, Jiang et al. 2020)with Zenith angle correction and the average systemtemperature ( T sys ∼
20 K) to estimate the peak fluxes.The 0.042 Jy ms fluence of FRB 181017.J0036+11 is thelowest one-off event ever reported in the FRB Catalog(Petroff et al. 2016).The pulse profiles and waterfall plots of the three newFRBs are presented in Figure 1. FRB 181017.J0036+11swept across the full observing band of 500 MHz,whereas FRB 181118 and FRB 181130 are band-limited.Both FRB 181017.J0036+11 and FRB 181118 show adecrease in the power as the frequency increases, whichis similar to the negative spectra index commonly seenin pulsars, while FRB 181130 behaves in the oppositeway. The available observing bandwidth and SNR is in-sufficient for a direct determination of the FRB spectralindex. 3.2.
Propagation effects
The DM obs for each FRB is estimated through (Hes-sels et al. 2019)DM obs = Max (cid:40)(cid:88) (cid:18) dI(DM , t)dt (cid:19) (cid:41) , (2)where I(DM , t) stands for the burst profile at a givenDM and sampling time t . All three FAST FRBs ex-hibit high DMs (DM obs in Table 1). The highestDM obs in this work is DM obs =1845.2 pc cm − for FRB181017.J0036+11. The Full Width at Half Maximum(FWHM) of the fitted DM is taken as the uncertainty.Considering the high Galactic latitudes of these events,these FRBs are most likely to have cosmological origins,which we analyze in Appendix A. Following Masui et al. (2015b), we were able to ob-tain a scattering timescale 7 . +4 . − . ms for FRB 181130as shown in panel (c) of Figure 1,the details are in Ap-pendix B. No measurable scattering was seen for theother two sources, but the upper limits are given accord-ing to the sharpest decline in signal power with time.No measurable scintillation bandwidth was found for allthree. 3.3. Follow-up Observations
On April 4th and 5th, 2020, we tracked all three newFRBs for one-hour each source with FLAN. We trackedFRB 181123 for a total of 6 hours between Februaryand July of 2020. The data with higher time resolution(98 µ s) with full stokes polarization were recorded. Nomore burst was detected in any of the follow-up obser-vation. IMPLICATIONS AND DISCUSSIONWe look into the implications of FAST discoveries forthe event rate, DM-fluence relation, and the intrinsicluminosity of FRBs.For a Poissonion FRB distribution in an isotropicuniverse and an effective beam area of 0.019 d andtaking the events possibility from Gehrels (1986), fourFRBs in 1667 hours drift scan and 9 hours follow-upobservations corresponds to an all sky event rate as1 . +1 . − . × sky − day − at the 95% confidence levelabove 0.0146 Jy ms (7 σ for a 1 ms duration), which isthe lowest fluence threshold ever considered.Figure 2 shows the updated fluence-DM E relation withthe FAST events added, where DM E represents the DMvalue after deducting the DM contribution from theMilky Way (Cordes & Lazio 2002; Yao et al. 2017). To-gether with FRB 181123 reported in Zhu et al. (2020),the four FAST FRBs clusters to the bottom right ofFigure 2, which are consistent with the extrapolation ofASKAP FRB fluence to higher DM E (Shannon et al.2018). The DM-fluence relation has been extended tothe more distant and low fluence region in the DM-fluence space.Identifying the host galaxies of these FRBs and mea-suring their redshifts will help extend the DM − z relation(also known as the Macquart relation) (Macquart et al.2020; Li et al. 2020) to higher redshifts. Alternatively,a low fluence burst could be due to a low luminosity ofa nearby FRB. In this case, the large DM must be as-sociated with the nearby environment or host galaxy ofthe FRB. Identifying these low-luminosity events wouldbe essential to constrain the low end of FRB luminos-ity function (Luo et al. 2018). Given the short integra-tion realized by drift scan, systematic long integration Niu et al.
Table 1.
Properties of three new FRBs detected in CRAFTSFRB YYMMDD(.J2000) FRB 181017.J0036+11 FRB 181118 FRB 181130
Measured Parameters
Event MJD at 1.5 GHz 58408.665197 58440.877654 58452.542674FAST Beam ID (M01 – M19) M14 M07 M11Right Ascension (J2000) 00 h m s .8 07 h m s .87 00 h m s .85Declination (J2000) 11 ◦ (cid:48) (cid:48)(cid:48) .8 16 ◦ (cid:48) (cid:48)(cid:48) .7 19 ◦ (cid:48) (cid:48)(cid:48) .7Galactic Coordinates ( l, b ) 117 ◦ . , − ◦ . ◦ . , ◦ . ◦ . , − ◦ . − ) 1845.2 ± ± . ± . a b ± .
25 5.3 ± .
72 9 . +5 . − . Scattering effect at 1.25GHz (ms) < . < .
08 7 . +4 . − . Measured S/N 14.3 11.0 30.9Observed peak flux density (mJy) ∼ . ∼ . ∼ . c Inferred Parameters d DM Gal (pc cm − ) e z ) f . +0 . − . , 2 . +0 . − . . +0 . − . , 1 . +0 . − . . +0 . − . , 1 . +0 . − . Max. comoving distance (Gpc) 5.4 4.0 5.1Max. luminosity distance (Gpc) 16.5 8.7 14.8Max. isotropic energy (10 erg) g erg s − ) 0.3 0.05 0.16 a The referenced frequency for smear calculation takes center of the emission frequency band. b Full pulse width at the half maximum from Gaussian fitted profile. Note that the intrinsic width can be much narrower forFRB181017 since we do not save the raw data (Qiu et al. 2020). c Take the gain at the center of the beam. d The parameters for Cosmology model are from Planck Collaboration et al. (2020). e DM Gal denotes the DM contribution from the Galaxy, and is calculated using the NE2001 and the YMW16 model, respec-tively. f Redshifts inferred from the extra-galactic DM calculated using the NE2001 and the YMW16 model, respectively. Thecorresponding deduction and error analysis can be found in Appendix A. g Calculated by assuming a flat spectrum within a width of 1 GHz tentatively, due to a lack of complete spectrum measurementfor FRBs currently. on apparent non-repeaters is necessary to distinguishwhether repeaters have low intrinsic luminosity or thewe just under-sampled the non-repeaters. This pointsto the value of systematic long integration on apparentnon-repeaters to distinguish effects of under-sampling vslower intrinsic luminosity.Following Luo et al. (2018) and Luo et al. (2020), wequantify the DM distribution of FAST detections by as-suming a Schechter luminosity function for all FRBs φ ( L ) d L = φ ∗ (cid:18) LL ∗ (cid:19) α e − LL ∗ d (cid:18) LL ∗ (cid:19) , (3)where α is the power-law index, and L ∗ is the uppercut-off luminosity. The lower cut-off luminosity is de-fined as the intrinsic minimum luminosity of the FRBpopulation, which was denoted as L . We then car-ried out mock observation of the FRBs generated basedon Eq. 3 as well as under an assumption of cosmologi- cal evolution (e.g. following the star-formation history).The specifics are described in detail in Appendix C. Theprobability density function (PDF) of DM expected forthe FAST sample thus simulated is shown in Figure 3.Three points to note from our simulation. First, thePDF of FAST-FRB’s DM is more sensitive to α than L . Second, the non-evolving flatter luminosity func-tion ( α = − .
5) provide the best apparent match to theobservation, although including evolution will also movethe PDF peak to higher DM. Third, for all the modelparameters explored here, FAST will have significant de-tection probability ( > > − ,which is beyond reach for other surveys. SUMMARYIn this paper, we report three new highly dispersedand low-luminosity FRBs discovered by the Commen-sal Radio Astronomy FAST Survey, which is a multi-
RAFTS for Fast Radio Bursts Time (ms) F r e qu e n c y ( M H z ) (a) FRB 181017.J0036+11 Time (ms) F r e qu e n c y ( M H z ) (b) FRB 181118 F r e qu e n c y ( M H z ) Time (ms) (c) FRB 181130
Figure 1.
The center plot of (a) (b) and (c) shows the 2-dimensional dynamic spectrum of the three newly-discovered FRBswhere RFIs are masked. The top panel of each plot is the normalized pulse profile, while the right panel shows the characteristicspectrum within 2 σ range(gray shadow) of each burst. No scattering tail was found in the profiles of either FRB 181017 (a)or FRB 181118 (b) at their intrinsic DM values, so Gaussian fittings are outlined. FRB 181130 exhibits an evident scatteringeffect on a Gaussian-fitted profile. DM E (pc cm -3 ) -4 -3 -2 -1 F l uen c e ( Jy m s ) ParkesASKAPGBTDSA-10AreciboCHIMEMeerKATVLAUTMOSTEffelsbergFAST (Z20)FAST (this work) < e r g < e r g < e r g < e r g < e r g < e r g FASTAreciboGBTParkesCHIME
Figure 2.
A radio fluence-DM E diagram for FRBs, whereDM E represents the DM value after deducting the DM con-tribution from the Milky Way. With the assumption of anisotropic beam and DM host = 0, contours of the energy upperlimits are plotted in slanted lines, with respective numericalvalues of E labeled. The sensitivities of the telescopes aremarked by horizontal lines. Note that the FAST sensitivityis for the CRAFTS mode (1-bit quantization in 2018 data)and will be even lower for other modes. The FRBs detectedby different telescopes are represented by different symbols.In particular, orange pentagram represents the FRB 181123in (Zhu et al. 2020, Z20) and the red pentagrams are FRBsreported in this work. The filled symbols represent knownrepeating FRBs. purpose drift scan survey with the 19-beam system ofFAST. Our main findings are as follows.1) Along with the first discovery–FRB181123–previous reported, four events in a total of ∼ . +1 . − . × DM (pc cm ) P r o b a b ili t y d e n s i t y × = 1.8,log L =40, No evolution= 1.8,log L =38, No evolution= 1.5,log L =38, No evolution= 1.8,log L =40, Star-formation driven Figure 3.
The PDF of the DM distribution of FRBs wouldbe detectable by the FAST telescope. The x-axis is the DMvalue in units of pc cm − , and the y-axis is the probabilitydensity scaled up by a factor of 1000. The four curves rep-resent the DM PDFs of FRBs detectable by the FAST inour four simulation cases: α = − . L = 10 erg s − without cosmological evolution (black solid), α = − . L = 10 erg s − without cosmological evolution (black dot-ted), α = − . L = 10 erg s − without cosmolog-ical evolution (blue dashed-dotted), and α = − . L = 10 erg s − with star-formation history as cosmologi-cal evolution (red dashed).The green shaded rectangle region shows the DM range ofthe four FRBs detected so far in CRAFTS. sky − day − at the 95% confidence interval above0.0146 Jy ms, by far the deepest such estimate.2) All three new FRBs are off the Galactic plan, withGalactic latitudes | b | = 21 . ◦ , 43 . ◦ , and 51 . ◦ , for FRB181118, FRB 181130, and FRB 181017.J0036+11, re- Niu et al. spectively. The estimated Galactic contribution DM MM are all less then 10% of the total DM, suggesting extra-galactic origins.3) The measured DM, 1187.7 ± .
3, 1705.5 ± .
5, and1845.2 ±
1, when with DM MW subtracted, correspond toupper limits of the estimated redshifts of these eventsbetween z = 1 .
17 and z = 2 . α and cosmological evolution.7) These CRAFTS FRBs occupies a previously emptyregion in the DM-fluence space. With more discoveriesand possible localization, they have the potential to ex-tend the DM- z Macquart relation.ACKNOWLEDGMENTSThis work is supported by National Key R&D Pro-gram of China No.2017YFA0402600 and is partiallysupported by the National Natural Science Founda-tion of China Grant No. 11988101,11725313, 12041303,11873067,the Cultivation Project for FAST ScientificPayoff and Research Achievement of CAMS-CAS, theCAS-MPG LEGACY project, the Strategic Priority Re-search Program of the Chinese Academy of SciencesGrant No. XDB23000000 and the National SKA Pro-gram of China No. 2020SKA0120200. C-H. Niu is grate-ful for the funding of the FAST Fellowship.APPENDIX A. REDSHIFT ESTIMATIONWe describe the method to estimate redshifts of the three new FAST-discovered FRBs here. The observed DM isgenerally given by DM obs = DM MW + DM halo + DM IGM + DM
LocHG , sr z , (A1)where DM MW is the DM contribution from the Milky Way galaxy, DM halo denotes the DM contribution associatedwith the Milky Way halo, DM IGM represents the DM contributed by the IGM, and DM
LocHG , sr denotes DM contributedby the source itself and its host galaxy in the source frame, respectively. Here, DM MW can be derived from the Galacticelectron density models (Cordes & Lazio 2002; Yao et al. 2017). The differences between results calculated using thetwo models for these FRBs are several tens pc cm − . The DM contribution associated with the Milky Way halo isassumed as DM halo = 30 ±
15 pc cm − following Dolag et al. (2015). The average DM contributed by the IGM forΛCDM cosmology is (Deng & Zhang 2014)DM IGM = 3 cH Ω b f IGM πGm p (cid:90) z χ ( z )(1 + z ) dz [Ω m (1 + z ) + Ω λ ] , (A2)where the free electron number per baryon in the universe is χ ( z ) ≈ / f IGM ∼ . z , we assume that the DM contribution from the host galaxy DM LocHG , sr is in the range of 0 to 200 pc cm − ,which is consistent with several simulated results (Xu & Han 2015; Luo et al. 2018, 2020) as well as results constrainedfrom the observational data (Li et al. 2020). The inferred redshifts are listed in Table 1. B. THE PULSE WIDTH AND SCATTERING TIMESCALE OF FRB 181130To measure the pulse width and scattering timescale of FRB 181130, we first fold the frequency and normalized thepulse profile using the dynamic spectra in Figure 1. Following Masui et al. (2015b), we then analyze the 78 ms-longdata centered around the pulse peak by using emcee (Foreman-Mackey et al. 2013). In Figure 4, we show the datafitting results for the width σ of the intrinsic Gaussian pulse component, the scattering timescale τ s (centered at1250 MHz) and the pulse arrival time t relative to the starting point of the selected data. RAFTS for Fast Radio Bursts = 4.76 +2.972.54
481 2 s s = 7.64 +4.964.51 .
53 3 .
03 4 . t s . . . t t = 33.09 +1.511.61 Figure 4.
Posterior distributions of σ , τ s (centered at 1250 MHz) and t obtained by using emcee . The dashed lines represent16, 50 and 84 percentiles in the corresponding histograms.C. SIMULATIONS ON FRB DETECTABILITY FOR CRAFTSReferring to the verification section for Bayesian inference in Luo et al. (2018, 2020), we can also use the Monte-Carlo method to simulate FRBs that are detectable by FAST surveys such as CRAFTS. The specific procedures aredescribed as follows:(i) Sample the FRB luminosities L according to the LF parameters measured in Luo et al. (2020).(ii) Sample the host redshifts for two cases: 1) Non-evolved: z merely follows a uniform distribution of FRBs acrossthe universe; 2) Star-formation driven: z follows both galaxy uniform distribution and the star-formation historydescribed in Zhang et al. (2021) . Then calculate the DM values contributed from the intergalactic medium.(iii) Sample the intrinsic FRB pulse widths in the local rest frame of FRBs using the log-normal distribution con-strained in Luo et al. (2020). The current FRB sample is too small to constrain FRB redshiftdistribution models (Lu & Piro 2019; Zhang et al. 2021), so weuse the simplest z -distribution model in our simulations. Niu et al. (iv) Based on the cosmologically evolving DM distributions of host galaxies at redshifts z described by Luo et al.(2018), generate the DM contributions from host galaxies in the local rest frame of FRBs.(v) Generate DM values contributed by the local circumstance of FRB progenitors using the uniform distributionassumed in Luo et al. (2018).(vi) Generate Galactic DM values using the YMW16 model, and then sum the DMs from all of components mentionedabove to obtain the total observed values.(vii) Produce a number of FRB positions randomly falling inside the FAST’s beams, and then calculate the receivedpeak flux density using the simulated luminosities, redshifts and beam responses of the FRB positions withinthe beam size.(viii) Based on the emitted pulse widths, redshifts and DMs of FRBs obtained in the steps above, calculate the observedpulse width considering DM smearing and cosmological time dilution.(ix) Select the FRBs whose peak fluxes are above the threshold of CRAFTS as positive detections.With the simulated data from mock FRBs, we then obtain the PDF of DMs for the CRAFTS’ detectable FRBs,which are shown in Figure 3. REFERENCES Barsdell, B. R., Bailes, M., Barnes, D. G., & Fluke, C. J.2012, MNRAS, 422, 379Bassa, C. G., Tendulkar, S. P., Adams, E. A. K., et al.2017, ApJL, 843, L8Bhandari, S., Keane, E. F., Barr, E. D., et al. 2018,MNRAS, 475, 1427Caleb, M., Flynn, C., Bailes, M., et al. 2017, MNRAS, 468,3746Caleb, M., Keane, E. F., van Straten, W., et al. 2018,MNRAS, 478, 2046Chatterjee, S., Law, C. J., Wharton, R. S., et al. 2017,Nature, 541, 58Qiu, H., Shannon, R. M., Farah, W., et al. 2020, MNRAS,497, 1382. doi:10.1093/mnras/staa1916CHIME/FRB Collaboration, Andersen, B. C., Bandura, K.,et al. 2019a, ApJL, 885, L24CHIME/FRB Collaboration, Amiri, M., Bandura, K., et al.2019b, Nature, 566, 230Cordes, J. M., & Chatterjee, S. 2019, ARA&A, 57, 417Cordes, J. M., & Lazio, T. J. W. 2002, arXiv e-prints, astroDeng, W., & Zhang, B. 2014, ApJL, 783, L35Dolag, K., Gaensler, B. M., Beck, A. M., & Beck, M. C.2015, MNRAS, 451, 4277Farah, W., Flynn, C., Bailes, M., et al. 2018, MNRAS, 478,1209—. 2019, MNRAS, 488, 2989Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman,J. 2013, PASP, 125, 306Hessels, J. W. T., Spitler, L. G., Seymour, A. D., et al.2019, ApJL, 876, L23 Jiang, P., Tang, N.-Y., Hou, L.-G., et al. 2020, Research inAstronomy and Astrophysics, 20, 064Li, D., Dickey, J. M., & Liu, S. 2019, Research inAstronomy and Astrophysics, 19, 016Li, D., & Pan, Z. 2016, Radio Science, 51, 1060Li, D., Wang, P., Qian, L., et al. 2018, IEEE MicrowaveMagazine, 19, 112Li, Z., Gao, H., Wei, J. J., et al. 2020, MNRAS, 496, L28Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic,D. J., & Crawford, F. 2007, Science, 318, 777Lu, W., Kumar, P., & Zhang, B. 2020a, MNRAS, 498, 1397Lu, W., & Piro, A. L. 2019, ApJ, 883, 40Lu, W., Piro, A. L., & Waxman, E. 2020b, MNRAS, 498,1973Luo, R., Lee, K., Lorimer, D. R., & Zhang, B. 2018,MNRAS, 481, 2320Luo, R., Men, Y., Lee, K., et al. 2020, MNRAS, 494, 665Gehrels, N. 1986, ApJ, 303, 336. doi:10.1086/164079Macquart, J. P., Prochaska, J. X., McQuinn, M., et al.2020, Nature, 581, 391Marcote, B., Paragi, Z., Hessels, J. W. T., et al. 2017,ApJL, 834, L8Marcote, B., Nimmo, K., Hessels, J. W. T., et al. 2020,Nature, 577, 190Masui, K., Lin, H.-H., Sievers, J., et al. 2015a, Nature, 528,523—. 2015b, Nature, 528, 523Nan, R., Li, D., Jin, C., et al. 2011, International Journal ofModern Physics D, 20, 989
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