Novel pre-burst stage of gamma-ray bursts from machine learning
aa r X i v : . [ a s t r o - ph . H E ] O c t N OVEL PR E - BURST STAGE OF GAMMA - RAY BUR STS FROMMAC HINE LEAR NING
A P
REPRINT
Yingtian Chen
School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijing 100871, China
Bo-Qiang Ma ∗ School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijing 100871, ChinaCollaborative Innovation Center of Quantum MatterBeijing, ChinaCenter for High Energy PhysicsPeking UniversityBeijing 100871, ChinaCenter for History and Philosophy of SciencePeking UniversityBeijing 100871, ChinaOctober 18, 2019 A BSTRACT
Gamma-ray bursts (GRBs), as extremely energetic explosions in the universe, are widely believedto consist of two stages: the prompt phase and the subsequent afterglow. Recent studies indicatethat some high-energy photons are emitted earlier at source than the prompt phase. Due to the lightspeed variation, these high-energy photons travel slowly than the low-energy photons, so that theyare observed after the prompt low-energy photons at the detector. Based on the data from the FermiGamma-ray Space Telescope (FGST), we analyse the photon distribution before the prompt emissionin detail and propose the existence of a hitherto unknown pre-burst stage of GRBs by adoptinga classification method of machine learning. Analysis on the photons automatically selected bymachine learning also produce a light speed variation at E LV = 3 . × GeV . K eywords Gamma-ray bursts · pre-burst stage · light speed variation · machine learning Gamma-ray bursts (GRBs) were first discovered by the Vela satellites in 1967 [1]. The random occurrence ofGRBs and the limitation of positioning capability of the earlier facilities limited the progress of studying these lu-minous explosions. The situation has changed dramatically since the launch of the Fermi Gamma-ray Space Tele-scope (FGST) [2, 3], with the detection of over 1600 GRBs including 25 bright ones with known redshifts [4, 5].FGST has two instruments, the Gamma-ray Burst Monitor (GBM) [2], which is sensitive to X-rays and gamma pho-tons with observed energies between and
40 MeV , and the Large Area Telescope (LAT) [3], which detectshigher-energy photons from
20 MeV to more than
300 GeV . The combination of LAT and GBM gives a wide energyrange of GRB photon detection. GBM is triggered when it detects a sudden gamma-ray enhancement, which is usually ∗ Corresponding author at: School of Physics, Peking University, Beijing 100871, China. Email address: [email protected]
PREPRINT - O
CTOBER
18, 2019Table 1: 25 GRBs analysed in this workGRB z a t (s) b GRB z a t (s) b a . The redshift data can be found in Ref. [14]. b . The time zeros (observed times of the first main peak) are from Ref. [10]. regarded as the precursor of a GRB. Previous studies focused on the events observed after the trigger time, that is, theprompt phase and the subsequent afterglow (in this paper, we combine them as the “main-burst” stage). The promptphase lasts commonly several tens of seconds with the release of a large content of total energy ( ergs ). Followingthe prompt phase is the afterglow, which lasts from few weeks to a year, offering a method to measure the redshifts ofGRBs and their extragalactic origin.Recent studies [6, 7, 8, 9, 11, 10, 12] on the light speed variation from GRBs suggested that some high-energy photons,though observed after the onset of the prompt phase, are emitted before the main-burst at source. We simply call theseearlier emission as the “pre-burst” stage of GRBs. In this work, we statistically analyse the data from FGST of 25bright GRBs with measured redshifts [13, 14] by adopting a classification method of machine learning. The machinelearning method automatically provides 4 main classifications to suggest the existence of the pre-burst stage of GRBsin all cases. Analysis on the photons automatically classified by machine learning also produce a light speed variationat E LV = 3 . × GeV . It is suggested in References [8, 9, 10, 12] that the first main peak of the GBM light curve can be regarded as thecharacteristic time for the low energy photons of the prompt phase (see Table 1). We set the first main peak time t peak as time zero t = 0 in our analysis.Considering the redshift effect of cosmic scale, we can convert the observed time ( t obs ) and energy ( E obs ) of eachphoton event to the re-scaled time τ and the intrinsic energy E in ) as τ = t obs / (1 + z ) ,E in = (1 + z ) E obs , (1)where z is the redshift of each GRB (see Table 1). Unlike previous studies, we also focus on the photons observedbefore time zero (in fact we should focus on photons emitted at source before time zero. But it is impossible to clearlyidentify these photons without considering the time difference caused by the light speed variation at present. Thisproblem will be discussed later after the consideration of the light speed variation).According to the default values of the LAT website [13], we select photons from all 25 GRBs with known redshifts (seeTable 1) within an time window of −
100 s < τ <
100 s , an energy interval of
100 MeV < E in <
300 GeV and asearch radius range of θ < ◦ .Since photons with energy greater than the threshold of 1 GeV is widely regarded as high energy photons [15, 16],we adopt the threshold of 1 GeV to identify high energy photons. Considering different distributions between higher-energy and lower-energy photons, we divide all photons into two groups according to their energy ranges: photonswith E in < are assigned to Group 1 and photons with E in > are assigned to Group 2.2 PREPRINT - O
CTOBER
18, 2019
Group 2Angular Separation ( (cid:176))Group 1 P h o t o n D e n s i t y ( S r - ) Figure 1: The density-angle relation of GRB photon events with energies E in < (Group 1) and E in > (Group 2). The horizontal coordinates are the angular separation of the photons to the centers. -100 -50 0 50 100012345024681012 t (s) P h o t o n s p e r S e c o nd ( s - ) Group 2Group 1
Figure 2: The photon density-time relation of GRB photon events. Since the scale of the blue curve on the left of eachfigure is quite different from the scale of the red curve on the right, we adopt different vertical ordinates.It is certain that the spatial distribution of photons is not random in the time interval of τ > . We note that suchnon-randomness also exists in the time interval of τ < : photons of each GRB are distributed more densely near acertain center. We use the average coordinate of photons as the center of each GRB. This method is reasonable whenthe search radius is not big ( θ < ◦ ).By plotting the relation between the photon density and the angular separation (see Figure 1), we can demonstrate suchnon-randomness concretely. It can be seen that the photon density decreases rapidly with the increase of the angularseparation, especially for the higher-energy Group 2.The time distribution of photons is also not random in the time interval of τ < . This relation can be directly shownby plotting the light curve (see Figure 2). It can be seen that as time approaches time zero from both the positive andnegative axes, the photon density increases gradually.Figures 1 and 2 show that even before the main-burst, the photon distribution still has certain convergence.Such conver-gence is consistent for both low and high energy photons from Groups 1 and 2 respectively. It is reasonable to conclude3 PREPRINT - O
CTOBER
18, 2019
Group 2Angular Separation ( (cid:176))Group 1 P h o t o n D e n s i t y ( S r - ) Figure 3: The photon density-angle relation of GRB photon events within the time interval of τ < −
20 s .that some photons observed before the main-burst still belong to the GRB rather than the background. Although theabove discussion does not consider the time difference caused by the light speed variation, the aforementioned factimplies that there might be a pre-burst stage before the main-burst stage at source.The above discussion seems imprecise since the rising edge of the main-burst stage is also included in the time intervalof τ < . Such concern can be dispelled when we do the same analysis with the time interval of τ < −
20 s and obtainsimilar results (see Figure 3). It can be seen that the aforementioned convergence still exists.We can not rule out the possibility that the photon detection efficiency of Fermi detectors may have angle dependenceso that the observed angle dependence of the photon events presented in Figs. 1 and 2 is due the artificial consequenceof the Fermi data but not due to the realistic physical mechanism. Therefore the results of our Figs. 1 and 2 canonly serve as a hint to suggest the possibility for the existence of the pre-burst stage, and we need to perform moresophisticated study with detailed analysis on the photon events about the pre-burst stage of GRBs.
Amelino-Camelia et al. [18] first suggested that the data from GRBs could be used to test the quantum gravity effect.Many studies (see, e.g., References [20, 21, 22, 23, 24, 15, 16, 17, 6, 7, 8, 9, 11, 10, 12, 19, 25, 26]) applied this methodto search for the light speed variation caused by the Lorentz violation (LV) effect or the cosmic matter effect. Someof these studies [6, 7, 9, 8, 10] suggest that some high-energy photons observed after time zero t are emitted before t at source due to the light speed variation. Such effect is especially important for higher-energy (about 10-300 GeV)photons.We suppose that the pre-burst and main-burst photons can be distinguished via their geometric features on a certaincoordinate system. Since the light speed variation is a primary cause of the difficulty to distinguish photons fromtwo stages, the coordinate system should be able to demonstrate such speed variation effect. Luckily, some previousworks [6, 7, 8, 9, 11, 10] proposed a coordinate system which meets our needs well, and detailed descriptions are givenin the following.The light speed variation might be caused by the Lorentz violation effect or by the cosmic medium effect. When theenergy of a photon is much lower than the Planck scale E Pl , its speed variation can be written in a general form of theleading term of Taylor series [20, 21, 22, 23, 24, 15, 16, 17, 6, 7, 8, 9, 11, 10, 12] v ( E ) = c (cid:20) − s n n + 12 (cid:18) EE LV ,n (cid:19) n (cid:21) , (2)where s represents whether the photon speed is faster ( s = − ) or slower ( s = 1 ) comparing to the light speed constant c for E → and E LV represents a LV scale to be determined by data for the light speed variation. where s n representswhether the photon speed is faster ( s n = − ) or slower ( s n = 1 ) comparing to the light speed constant c for E → and E LV ,n represents a LV scale to be determined by data for the light speed variation, with n = 1 corresponding to4 PREPRINT - O
CTOBER
18, 2019the simplest linear correction v ( E ) = c (cid:18) − s EE LV (cid:19) . (3)Equation (2) shows that the speed of a photon depends on its energy. So the photons simultaneously emitted at sourcecan be observed at different times. The time difference ∆ t LV caused by the speed variation is [20, 27] ∆ t LV = (1 + z ) κE LV , (4)where κ = s E obs − E peak H (1 + z ) Z z ζ p Ω m (1 + ζ ) + Ω Λ dζ, (5)in which H = 67 . ± . − Mpc − is the Hubble expansion constant; [Ω m , Ω Λ ] = [0 . +0 . − . , . +0 . − . ] arethe cosmological constants [28] of pressureless matter density of the universe and dark energy density of the universe. E peak (the energy of the first main peak photons, detected by GBM) can be omitted because it is negligible comparingto E obs (detected by LAT). Since the redshifts of observed GRBs are of the same scale, κ is roughly proportional tothe observed energy E obs of each photon.Taking into account of the intrinsic emitting time t in of the photon at the source, we obtain the observed time since t = 0 as t obs = ∆ t LV + t in (1 + z ) , (6)from which we get τ = t obs z = ∆ t LV z + t in = κE LV + t in . (7)Thus we arrive at a simple relation τ = κE LV + t in . (8)Equation (8) permits us to construct a coordinate system whose horizontal axis is κ and the vertical axis is τ . Thiscoordinate axis system demonstrates the speed variation effect because all simultaneously emitted photons will beplotted on a straight line, whose slope is /E LV and the intercept is t in , regardless of the energies and redshifts ofthese photons. In previous studies on high energy photons [17, 6, 7, 8, 9, 11, 10, 12], a regularity has been found thatseveral high energy GRB events fall on a straight line in the κ - τ plot to indicate a light speed variation. Such studiesalso suggest a scenario that these high energy photons are emitted earlier than low energy photons at source. Thepurpose of the present paper is to re-check the κ - τ plot of high energy photons from a machine learning analysis.Since the speed variation effect is more significant for high-energy photons, we only take the higher-energy Group 2into consideration, and the τ - κ plot is shown in Figure 4. The boundary of the pre-burst and main-burst stages can beroughly seen by naked eyes. To concretely illustrate such boundary, we apply a primary method of machine learningto produce classifications. Such machine learning method resembles the K -means method [29] with remarkableapplication in recent works (see, e.g., Reference [30]).The K -means classification method, first proposed by Macqueen, is a process to classify a population of elementsinto K clusters via their geometric features. If Σ = { Σ , Σ , · · · , S K } is a classification of point set V , that is, anyelement of V belongs to and only belongs to an Σ i ∈ S . The purpose of the K -means method is to find an optimalclassification Σ minimizing the error function w (Σ) = K X i =1 " X z ∈ Σ i d ( z, u i ) , (9)where z is elements of set V . In Macqueen’s work [29], u i is the average coordinate of subset Σ i , and d ( z, u i ) is theEuclidean distance function. Function w (Σ) represents the divergence degree of classification Σ .Finding the global optimal classification Σ is computationally difficult. However, the K -means method provides anefficient way to produce a local optimal classification iteratively. The K -means method first begins with K randompoints { u , u , · · · , u K } , then calculates d ( z, u i ) of each z ∈ V , and places z to the nearest subset Σ i accordingto the distance d ( z, u i ) . The next step is to set the average coordinate of each Σ i as the new point u i . Repeat theabove process until the change of { u ni } is negligible. It is obvious that the K -means method gives a local optimalclassification Σ because an arbitrary change of Σ will increase the error function w (Σ) unless Σ is unstable.We develop a new method similar to the K -means method in our work. The modifications are shown below.5 PREPRINT - O
CTOBER
18, 2019 t ( s ) k (10 s(cid:215)GeV) Figure 4: The τ - κ plot of Group 2. Each blue circle represents a photon with intrinsic energy E in > . Thereare 979 photons in total.1. The dimension N is set as N = 2 because our coordinate axis system is -dimensional.2. Since the simplest case of the K-means method is K=2, we set K=2 to illustrate the efficiency and enlighten-ment of the analysis.3. Instead of calculating the average coordinate of subset Σ i in each iteration as u i , we compute the linear fittingline τ = k i κ + b i as u i of Σ i , and { u , u , · · · , u K } are K random lines.4. We use the Euclidean distance function between a point z ( κ, τ ) and the line u i as d ( z, u i ) : d ( z, u i ) = | k i κ − τ + b i | p k i + 1 . (10)One of the modifications is to change the K initial points into K initial lines, where K = 2 in our work. Since wecalculate K fitting lines in each step instead of K mean values, we rename the new method as the K -lines method.As an ideal situation, one may expect the K -lines method might be able to find a global optimal classification regardlessof the initially given lines, however, in general situation there is still limitation of this machine learning method. Fromthis sense, the K -lines method is still not able to give the global optimal classification and is initial-value dependent.Thus, we fix one initial line as the τ -axis, and perform a continuous scan over the parameter space of another initialline to illustrate such initial-value dependence. (see Figure 5). It can be seen that even a large range of initial valuesmay result in a same classification, and the 4 main classification results are represented by A, B, C, D respectively.It is reasonable to expect the obtained classifications in several options can provide a relatively complete view of theproblem under study.The largest block in Figure 5 represents classification A, which provides a good referential classification of the pre-burst and main-burst stages (see Figure 6). The two fitting lines of classification A read τ = α κ + β ,τ = α κ − β , (11)where [ α , β ] = [5 . ± . , . ± . , [ α , β ] = [7 . ± . , − . ± . (12)and the boundary line of classification A reads τ = α b κ − β b , (13)where [ α b , β b ] = [6 . ± . , − ± , (14)which is found by machine learning automatically. Considering the uncertainties of the energies of LAT pho-tons [13], we produce the uncertainties of coefficients in the above equations (here we us the containment half6 PREPRINT - O
CTOBER
18, 2019Figure 5: The phase diagram of results caused by different initial values. Blocks A, B, C, D represent 4 main resultscaused by different initial values of the slope and the intercept of the second line.width as the uncertainty). It can be seen that some high-energy (high- κ ) photon events observed after time zero areclassified by machine learning into the pre-burst stage. This result is interesting because it indicates that GRBs canemit considerably high-energy photon events which are belong to the pre-burst stage at source, and these high-energyphoton events are detected after time zero due to the light speed variation effect.Classification B is another classification also found by machine learning automatically. This result deserves noticebecause it divides all photons into three clusters (see Figure 6). The coefficients of the two fitting lines of classificationB read [ α , β ] = [3 . ± . , . ± . , [ α , β ] = [1 . ± . , . ± . (15)and the coefficients of the boundary lines of classification B read [ α b , , β b , ] = [2 . ± . , . ± . , [ α b , , β b , ] = [ − . ± . , − ± (16)which are also produced by machine learning automatically. By definition, the boundary lines of a classification resultare the two angular bisectors of the two fitting lines, and the two angular bisectors are perpendicular to each other. Inclassification B, the two boundary lines separate all photons into three clusters, though the upper-cluster and lower-cluster of classification B are indeed fitted with the same fitting line. (The two boundary lines of classification B inFigure 6 do not look perpendicular because the axis is stretched). However, the separation of the upper-cluster andlower-cluster implies that the geometric features of the middle-cluster are quite unique: the middle-cluster is likely the“prompt phase”, since it contains a large number of high-energy photons; the lower-cluster is the “pre-burst” stage;and the upper-cluster is the “afterglow”.Classification C is like a rough version of classification B (see Figure 7). It roughly combine the pre-burst stage (thelower-cluster) and the prompt phase (the middle-cluster) together.The coefficients of the two fitting lines of classifica-tion C read [ α , β ] = [ − . ± . , . ± . , [ α , β ] = [1 . ± . , − . ± . (17)and the coefficients of the boundary line of classification C read [ α b , β b ] = [ − . ± . , ± , (18)Classification D is very close to classification C (see Figure 7). The coefficients of the two fitting lines of classificationD read [ α , β ] = [1 . ± . , − . ± . , [ α , β ] = [ − . ± . , . ± . (19)and the coefficients of the boundary line of classification D read [ α b , β b ] = [ − . ± . , ± , (20)In fact, by plotting the κ density curve of all photons in Group 2, this boundary line (to be precise, the intercept τ = 22 . of the boundary line) locates in a local minimum point of this curve (see Figure 8).7 PREPRINT - O
CTOBER
18, 2019
Main-burstPre-burst
Classification A t ( s ) k (10 s(cid:215)GeV) Middle-clusterLower-clusterUpper-cluster
Classification B t ( s ) k (10 s(cid:215)GeV) Figure 6: Classifications A and B. The boundary lines of each classification are colored in blue. In classification A,some high-energy photons of the pre-burst stage (like the two marked photons from GRB 160509A and 090902B) areobserved after time zero t while they are emitted before t at source. The uncertainty of the boundary lines areshown as gray regions. Lower-cluster
Classification C t ( s ) k (10 s(cid:215)GeV) Upper-cluster
Lower-cluster
Classification D t ( s ) k (10 s(cid:215)GeV) Upper-cluster
Figure 7: Classifications C and D. In classification D, two high-energy photon events of GRB 090902B and 160509Aare separated from the lower-cluster. The uncertainty of the boundary lines are shown as gray regions. -100 -50 0 50 1000.00.51.01.52.02.5 T o t a l k p e r S e c o nd ( G e V ) t (s) t=22.19 s Figure 8: The κ density curve versus τ fo classification D. The curve roughly represents the time distribution of theenergy density, and the intercept of the boundary line of classification D ( τ = 22 .
19 s ) locates in a local minimumpoint. 8
PREPRINT - O
CTOBER
18, 2019
DN/DE in (cid:181)E in-2.1 DN/DE in (cid:181)E in-2.4 DN/DE in (cid:181)E in-1.7 log E in (log GeV)
DN/DE in (cid:181)E in-2.1 Middle-clusterPre-burstMain-burstAll photons l o g ( D N / D E i n ) ( l o g G e V - ) Figure 9: The plots of intrinsic energy distributions. In logarithmic coordinate systems, the power-law functions areshown in grey lines.
We analyse the classification results based on above referential classifications. The energy distributions of the pre/main-burst stages, the middle-cluster, and all photons are present in Figure 9. It can be seen that the energy spectrum of thepre-burst stage is more flat than the main-burst stage, which indicates that the pre-burst stage has a larger proportionof higher-energy photons in comparison to that of the main-burst stage.We then follow Reference [10] by adopting a general method with a complete scan over the E LV space to find the lightspeed variation effect with the maximization of the S ( E LV ) -function, which is defined as S ( E LV ) = 1 N − ρ N − ρ X i =1 ln (cid:18) ρt i + ρ − t i (cid:19) , (21)where E LV is the LV scale (mentioned in Equation (2)); t i is the intrinsic emitting time (mentioned in Equation (8))of the i -th photon in the data set (sorted in ascending order); N is the size of the data set; ρ is a pre-set parameter (therecommended value of ρ in Reference [10] is ρ = 5 , with ρ = 1 to also examined to give similar results). Dueto the light speed variation effect, a light curve with peak at source will be flattened when observed. By adoptingthe aforementioned method, we can identify the undetermined E LV of the light speed variation as the location ofthe maximized S ( E LV ) -function. The S ( E LV ) -function can be traced back to the concept of “information entropy”based on the expectation that a trial of a true E LV can produce a maximal value of the S ( E LV ) -function. It can beseen that a pair of simultaneously emitted photons is able to create a large contribution to the S ( E LV ) -function, if E LV corresponds to the correct LV scale. As a result, the location of the peak in the S ( E LV ) plot represents theundetermined E LV of the light speed variation.Without loss of generality, we apply such method only on photons within the energy interval of E in >
20 GeV (thesephotons belong to set 3 in Reference [10]), and provide the σ -regions by the Monte-Carlo method, and the randomiza-tion process of the Monte-Carlo method is as follows. 9 PREPRINT - O
CTOBER
18, 2019
5s 3s 1s
Original plot (E in >20 GeV) I m f o r m a t i o n E n t r o p y S log E LV (log GeV) E LV =3.55 10 GeV
5s 3s 1s
Pre-burst stage (E in >20 GeV) I m f o r m a t i o n E n t r o p y S log E LV (log GeV) E LV =3.55 10 GeV
5s 3s 1s
Middle-cluster (E in >20 GeV) I m f o r m a t i o n E n t r o p y S log E LV (log GeV) E LV =3.55 10 GeV
Figure 10: The S ( E LV ) plots of 3 situations. (a) is the original plot of the unclassified situation; (b) is the plot of thepre-burst stage in classification A; (c) is the plot of the middle-cluster in classification B.1. The size of each random data set is the same as each actual data set.2. The τ values are randomly permutated and then used as those of the random data sets.3. The intrinsic energies of each random data set are produced to satisfy the power-law functions mentionedearlier in Figure 9, and have the same range with the actual data set.As shown in Figure 10, the S ( E LV ) plots of the pre-burst stage and the middle-cluster have sharper peaks in compar-ison to the original plot, and the plot of the pre-burst stage even exceeds the σ -region at E LV = 3 . × GeV .This result also fits well with References [9, 8, 10].The middle-cluster of classification B roughly represents the prompt phase. Since this cluster has many high-energyphotons, we can find a peak of the S ( E LV ) plot even if the energy threshold is considerably low (see Figure 11).We also provide the S ( E LV ) plots of the lower-clusters of classifications C and D (see Figure 12). It can be seen thatthe plot of classification C has a peak, which is compatible with those from classifications A and B.Classification D also has a peak in the S ( E LV ) plot but the peak is flat. However, such flatness is not in conflict withthe speed variation. In fact, a flat distribution of light curve at source cannot produce a sharp peak for the observed S ( E LV ) plot. Previous works (see References [6, 7, 9, 8, 10]) suggested that some photons of GRBs may be emitted before themain-burst stage at source. In this work, we propose the pre-burst stage of GRBs by a first glimpse of the FGST data.Considering the light speed variation effect, we adopt a primary method of machine learning to analyse the high-energyphoton events of 25 bright GRBs with known redshifts. The machine learning method automatically provides 4 main10
PREPRINT - O
CTOBER
18, 2019
5s 3s 1s I m f o r m a t i o n E n t r o p y S log E LV (log GeV) E LV =3.55 10 GeV
Figure 11: The S ( E LV ) plot of the middle-cluster of classification B. The energy interval is set as E in > , andthe peak is also located at E LV = 3 . × GeV .
5s 3s 1s
Classification C (E in >20 GeV) I m f o r m a t i o n E n t r o p y S log E LV (log GeV)
5s 3s 1s
Classification D (E in >20 GeV) I m f o r m a t i o n E n t r o p y S log E LV (log GeV)
Figure 12: The S ( E LV ) plots of the lower-clusters of classifications C and D.classifications, which propose the existence of the pre-burst stage of GRBs in all cases. Classification A indicatesthat some high-energy photons observed after the onset of the prompt low energy photons are emitted in the pre-burststage before the prompt phase at source. Classification B suggests a special middle-cluster which includes most ofthe high-energy photon events. We then adopt a general method to extract the light speed variation from the pre-burststage of classification A and the middle-cluster of classification B, and get consistent result of a light speed variation at E LV = 3 . × GeV . Such speed variation conversely confirms the existence of the hitherto unknown pre-burststage of GRBs with earlier emission of both higher-energy and low energy photons at source. The novel pre-burststage of GRBs can also provides novel insights about the dynamics of GRBs. We thus conclude that the machinelearning method provides a powerful tool to analyse the GRB data with fruitful results.
References [1] R. W. Klebesadel, I. B. Strong and R. A. Olson, Observations of Gamma-Ray Bursts of Cosmic Origin. Astrophys.J. (1973) L85.[2] C. Meegan, G. Lichti, P. N. Bhat et al. , The Fermi Gamma-Ray Busrt Monitor. Astrophys. J. (2009) 791.[3] W. G. Atwood, A. A. Abdo, M. Ackermann et al. , The Large Area Telescope on the Fermi Gamma-ray SpaceTelescope mission. Astrophys. J. (2009) 1071.[4] M. Ackermann, M. Ajello and K. Asano [Fermi-LAT Collaboration], The First Fermi LAT Gamma-Ray BurstCatalog. Astrophys. J. Suppl. (2013) 11. 11
PREPRINT - O
CTOBER
18, 2019[5] E. Bissaldi, F. Longo and N. Omodei [Fermi-LAT Collaboration], Gamma-Ray Burst observations with Fermi.PoS ICRC 2015 (2016) 796.[6] L. Shao, Z. Xiao and B.-Q. Ma, Lorentz violation from cosmological objects with very high energy photon emis-sions. Astropart. Phys. (2010) 312.[7] S. Zhang and B.-Q. Ma, Lorentz violation from gamma-ray bursts. Astropart. Phys. (2015) 108.[8] H. Xu and B.-Q. Ma, Light speed variation from gamma-ray bursts. Astropart. Phys. (2016) 72.[9] H. Xu and B.-Q. Ma, Light speed variation from gamma ray burst GRB 160509A. Phys. Lett. B (2016) 602.[10] H. Xu and B.-Q. Ma, Regularity of high energy photon events from gamma ray bursts. JCAP (2018) 050.[11] G. Amelino-Camelia, G. D’Amico, G. Rosati and N. Loret, In-vacuo-dispersion features for GRB neutrinos andphotons. Nat. Astron. (2017) 0139.[12] Y. Liu and B.-Q. Ma, Light speed variation from gamma ray bursts: criteria for low energy photons. Eur. Phys. J.C (2018) 825.[13] Specific data can be downloaded from http://fermi.gsfc.nasa.gov/ssc/data/access/ or http://fermi.gsfc.nasa.gov/ssc/observations/types/grbs/\lat_grbs/table.php or https://fermi.gsfc.nasa.gov/cgi-bin/ssc/LAT/\LATDataQuery.cgi or https://fermi.gsfc.nasa.gov/ssc/data/analysis/LAT_caveats.html [14] Information about GRB redshifts can be found in GCN Circular Archive http://gcn.gsfc.nasa.gov/gcn3_archive.html or .[15] A. A. Abdo, M. Ackermann, M. Arimoto, K. Asano, W. B. Atwood et al. [Fermi LAT and Fermi GBM Col-laborations], Fermi observations of high-energy gamma-ray emission from GRB 080916C. Science (2009)1688.[16] A. A. Abdo, M. Ackermann, M. Ajello, K. Asano, W. B. Atwood et al. , A limit on the variation of the speed oflight arising from quantum gravity effects. Nature (2009) 331.[17] Z. Xiao and B.-Q. Ma, Constraints on Lorentz invariance violation from gamma-ray burst GRB090510. Phys.Rev. D (2009) 116005.[18] G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos and S. Sarkar, Tests of quantum gravity fromobservations of gamma-ray bursts. Nature (1998) 763.[19] J. R. Ellis, K. Farakos, N. E. Mavromatos, V. A. Mitsou and D. V. Nanopoulos, Quantum-Spacetime Phenomenol-ogy. Astrophys. J. (2000) 139.[20] J. Ellis, N. E. Mavromatos and A. S. Sakharov, Quantum-gravity analysis of gamma-ray bursts using wavelets.Astron. Astrophys. (2003) 409.[21] J. Ellis, N. E. Mavromatos, D. Nanopoulos, A. S. Sakharov and E. K. G. Sarkisyan, Robust limits on Lorentzviolation from gamma-ray bursts. Astron. Astrophys. (2006) 402.[22] M. Rodriguez Martinez, T. Piran and Y. Oren, GRB 051221A and tests of Lorentz symmetry. JCAP (2006)017.[23] R. Lamon, N. Produit and F. Steiner, Study of Lorentz violation in INTEGRAL gamma-ray bursts. Gen. Relativ.Gravit. (2008) 1731.[24] J. D. Scargle, J. P. Norris and J. T. Bonnell, An algorithm for detecting quantum gravity photon dispersion ingamma-ray bursts: DisCan. Astrophys. J. (2008) 972.[25] Z. Chang, Y. Jiang and H. Lin, A unified constraint on the Lorentz invariance violation from both short and longGRBs. Astropart. Phys. (2012) 47.[26] J. Ellis, R. Konoplich, N. E. Mavromatos, A. S. Sakharov and E. K. Sarkisyan-Grinbaum, Robust Constraint onLorentz Violation Using Fermi-LAT Gamma-Ray Burst Data. Phys. Rev. D (2018) 083009.[27] U. Jacob and T. Piran, Lorentz-violation-induced arrival delays of cosmological particles. JCAP (2008) 031.[28] K. A. Olive et al. [Particle Data Group], Review of particle physics. Chin. Phys. C , 090001 (2014).[29] J. Macqueen, Some Methods for Classification and Analysis of MultiVariate Observations. Proc. of BerkeleySymposium on Mathematical Statistics and Probability (1965) 281.[30] Y. M. Marzouk and A. F. Ghoniem, K-means clustering for optimal partitioning and dynamic load balancing ofparallel hierarchical N-body simulations. Journal of Computational Physics207