Looking for the possible gluon condensation signature in sub-TeV gamma-ray spectra: from active galactic nuclei to gamma ray bursts
Wei Zhu, Zechun Zheng, Peng Liu, Lihong Wan, Jianhong Ruan, Fan Wang
aa r X i v : . [ a s t r o - ph . H E ] S e p Looking for the possible gluon condensation signaturein sub-TeV gamma-ray spectra: from active galacticnuclei to gamma ray bursts
Wei Zhu a , Zechun Zheng a , Peng Liu a , Lihong Wan a ,Jianhong Ruan a and Fan Wang b a Department of Physics, East China Normal University, Shanghai 200241, China b Department of Physics, Nanjing University, Nanjing,210093, China
Abstract
The gluon condensation in the proton as a dynamical model is used to treat aseries of unsolved puzzles in sub-TeV gamma ray spectra, they include the brokenpower-law of blazar’s radiation, the hardening confusion of 1ES 1426+428, Mkn501, and the recently recorded sub-TeV gamma spectra of GRB 180720B and GRB190114C. We find that the above anomalous phenomena in gamma ray energy spec-tra can be understood with the simple broken power law based on a QCD gluoncondensation effect. keywords :cosmic ray theory, gamma ray theory, very high energy cosmic rays
Gluons are Boson. A QCD analysis shows that the gluon distribution in the proton mayevolute to a chaos solution at high energy limit, which arouses the strong shadowingand antishadowing effects and squeezes the gluons into a narrow space near a criticalmomentum [1-3]. This is the gluon condensation (GC).The GC would lead to intriguing signatures in proton collisions, provided the GC-threshold E GCp − p enters the observable energy region. However, we have not directly ob-served the GC-effect at the Large Hadron Collider (LHC). Therefore, we turn to theastrophysical and cosmological observations. The energy of the protons accelerated inuniverse may exceed E GCp − p and causes the GC-effect in the collisions.In a previous work [4] we have used the GC model to explain the sharp broken powerlaw of the γ -ray spectra in supernova remnant (SNR) Tycho. In this work we will exploremore GC-examples in the γ -ray spectra of active galactic nuclei (AGN). AGN representsa large population of extragalactic objects characterized with extremely luminous electro-magnetic radiation produced in very compact volumes. AGNs with relativistic directionaljets (so-called blazars) are very effective TeV γ -sources. Therefore, blazars may providean ideal laboratory for studying the GC effect since they have extreme physical conditions.AGNs have relatively large redshift. TeV radiation from these sources is affected byintergalactic absorption. Comparing the observed AGN spectrum with their intrinsic1source) spectrum, one can obtains an important information about the extragalacticbackground light (EBL) at the infrared energy band. Extracting the EBL structure fromintrinsic and observed spectra, or alternatively, using a reasonable EBL model to excavatethe emission mechanism in AGN are the hot subjects in astronomy.Very high energy (VHE) γ -ray spectra have the following features. (i) The spectralenergy distribution (SED) is peaked at GeV-TeV band; (ii) Radiations have strong power,thus, γ -rays can reach the earth trough the EBL absorption. (iii) The intrinsic spectrapresent a sharp broken power-law after deducting the EBL corrections from the observedspectra in a series AGN sources , which does not have any existing radiation theory toexplain. (iv) Some of them have an extra hard tail at the TeV range, it even raises doubtsabout the Lorentz covariance. (v) Many AGN examples present the above phenomenonsand it might imply a new general dynamics, which have never been recognized before.A topic related to VHE gamma ray radiation is gamma ray burst (GRB). GRBsare extremely violent, serendipitous sources of electromagnetic radiation in the Universe.Recently, sub-TeV gamma-rays were detected from GRB by MAGIC 190114C [5] andGRB 180720B by HESS telescopes [6], respectively. This discovery caused great interest.For this sake, we will discuss it using a same GC-framework in a special section 5. We findthat the SED of both these two events have a series of characteristics of the GC-signature.We also show that the VHE gamma spectra in GRB and AGN relate to a same GC-effectbut in two different cosmic environments.Organization of the article is as follows. We will briefly review the hadronic mechanismfor γ -ray spectra in section 2, i.e., p + p → π and π → γ , and show how the GC-processworks in the hadronic mechanism. After a straightforward, but general derivation, wenaturally give a sharp broken power-law in γ -ray spectra. Then a simplified calculationmethod for the EBL is given in section 3. We chose ten examples of γ -ray spectra ofblazars to indicate the GC-effect in section 4. More complex hardening VHE gamma-rayspectra are explained by using the same GC-model in section 5. We discuss VHE spectraof GRB 180720B and GRB 190114C in section 6. A summary is presented in last section. γ -ray spectra The SED of blazars is assumed to be dominated by the emission from a relativistic jetpointing close to our line of sight. The characteristic SED of blazars shows two broad non-thermal well defined continuum peaks. The first hump located between the infrared (IR)and X-ray bands, whereas the second hump exhibits a maximum at the γ − energy band.The origin of low energy peak is attributed to the synchrotron emission of relativisticelectrons in the magnetic field of the jet. The productions of VHE γ − rays have differentexplanations. In leptonic model high energy electrons scatter on low energy photonsthrough inverse Compton (IC) scattering e + γ low energy → e low energy + γ V HE and formTeV- γ . Normally, these low energy photons are produced in the environment of starsdue to thermal emission or due to synchrotron emission by the high energy electrons inthe ambient magnetic fields (the SSC model) [e.g. 7-9]. According to hadronic model,VHE γ − ray emissions are dominated by neutral pion decay into photons in the following2ascade processes: p + nuclus → p ′ + π + others and following π → γ [e.g. 10-12].Using hadronic mechanism the γ -flux Φ γ can be described asΦ γ ( E γ ) = C p ( A ) − p ( A ) (cid:18) E γ E (cid:19) − β γ Z E maxπ E minπ dE π × E p ( A ) − p ( A ) E GCp ( A ) − p ( A ) − β p N π ( E p ( A ) − p ( A ) , E π ) dω π − γ ( E π , E γ ) dE γ , (2 . β γ and β p denote the propagating loss of gamma rays inside the source andthe acceleration process of protons respectively; C p ( A ) − p ( A ) incorporates the kinematicfactor with the flux dimension and the percentage of π → γ .The spectrum of gamma-rays from π decay in the center of mass system will havethe maximum at E γ = m π c /
2, independent of the energy distribution of π mesons andconsequently of the parent protons. Usually, the distribution of N π is parameterized byusing the p − p cross-section σ pp , the resulting distribution Φ γ presents a smooth excessnear E γ ∼ GeV . This prediction has been proven by the γ -ray spectra of supernovaremnants (SNRs)[13] (see figure 1). In a broad GeV-TeV region the total cross-section σ pp ∼ mb , while the angle-averaged total cross-section of inverse Compton scattering σ IC ∼ (8 π/ r e ∼ mb , r e ∼ × − cm . Usually, the lepton mechanism has astronger radiation power than the hadronic mechanism.However, the GC-effect produces a different spectral structure in the same hadronicmodel. According to QCD, the number of secondary particles (they are mostly pions)at the high energy p ( A ) − p ( A ) collisions relates to how much gluons participate intothe multi-interactions. Pions will rapidly grow from E GCπ since a lot of condensed gluonsenter the interaction range. One can image that the number of pion in this case reachesits maximum value, i.e., all available kinetic energy of the collision at the center-of-masssystem is almost used to create pions (see figure 2). Using general relativistic invariantand energy conservation, we straightforwardly obtain the solution N π in p ( A ) − p ( A )collisions using GeV -unit [4, 14].ln N π = 0 . E p − p + a, ln N π = ln E π + b, (2 . where E π ∈ [ E GCπ , E maxπ ] . The parameters are a ≡ . m p ) − ln m π + ln K, (2 . b ≡ ln(2 m p ) − m π + ln K, (2 . K is inelasticity. Equation (2.2) gives the relations among N π , E p ( A ) − p ( A ) and E GCπ byone-to-one, it leads to the following GC-characteristic spectrum.Substituting them into Equation (2.1), we have E γ Φ GCγ ( E γ )3 C p ( A ) − p ( A ) E γ E GCπ ! − β γ Z E GC,maxπ E GCπ or E γ dE π × E p ( A ) − p ( A ) E GCp ( A ) − p ( A ) − β p N π ( E p ( A ) − p ( A ) , E π ) 2 β π E π = C β p − e b ( E GCπ ) (cid:16) E γ E GCπ (cid:17) − β γ +2 if E γ ≤ E GCπ C β p − e b ( E GCπ ) (cid:16) E γ E GCπ (cid:17) − β γ − β p +3 if E γ > E GCπ , (2 . E GCπ (or E γ ) if E γ ≤ E GCπ (or if E γ > E GCπ ).Equation (2.5) is a typical broken power-law, it is formed by the GC-effect in the piondistribution N π rather than the decay mechanism π → γ . This solution is differentfrom all other well known radiation spectra. We regard it as the GC-character (see figure2). Note that comparing with the hadronic model without the GC effect, the total crosssection σ pp has increased by several orders of magnitude.The value of β γ in Equation (2.5) may take the value of 0 ∼
2, where zero meansthat the energy loss of γ -ray is almost negligible when it travel inside the source. Theterm E − β p p − p is from the contributions of the integrated initial proton flux R dE p − p J p , where J p ∼ E − Γ p p − p . Usually the index Γ p ∼
2. On the other hand, Equation (2.5) requests that β p > .
5. Therefore, β p ∼ ± . E GCπ is nuclear number A -dependent: E GCπ ( p − p ) > E GCπ ( A − A )since the nonlinear corrections enhance with increasing A . A rough estimation finds thatthe values of E GCπ may distribute in a range 0 . T eV ∼ T eV for the collisions betweenheavy nuclei and p − p collision [e.g. 15]. Generally, we will meet different values of E GCπ fordifferent γ -ray sources, the result relates to the dominate component of the hadron beam.While we lack a reliable theoretical prediction about them. We expect more informationfrom the AGN observations, which may help us to establish a rule about E GCπ ∼ A .The above discussion is focused on a single GC-source. The observed spectra in skysurvey may origin from several GC-sources in AGN source. We will discuss them in section5. The EBL is the cosmic background photon field, which is mainly produced by stars andinterstellar medium in galaxies throughout the cosmic history. The EBL could be directlymeasured with different instruments. However, the foreground zodiacal light and galacticlight may introduce large uncertainties in such measurements and make it difficult toisolate the EBL contribution from the observed multi-TeV flux from distant blazars. Inthis sense, the determination of the intrinsic γ -ray spectra helps to find a correct EBLmodel.We list the EBL formula, which modify the propagation of VHE γ -rays travelingthrough intergalactic space from the sources. In process γ V HE + γ EBL → e − + e + , theobserved γ -ray flux on Earth is related to the intrinsic flux of the source as refs. [16, 17].4 obγ ( E γ ) = Φ inγ ( E γ ) × e − τ . (3 . τ reads τ = Z R Z λ max λ min σ γγ ( E γ , λ ) λF λ ( λ, r ) dλdr, (3 . λF λ ( λ, r ) describes the spectral and spatial distribution of the target photon fieldin sky.Because of the narrowness of the cross section σ γγ , Equation (3.2) can be simplifiedas τ ≃ A λ ∗ F λ ∗ nW/m sr ! (cid:18) E γ T eV (cid:19) (cid:18) zz (cid:19) , (3 . λ ∗ = 1 . E γ / T eV ) µm and the Hubble constant has been included into the co-efficient A . Usually, A is regarded as a constant. However, we find that such a roughestimation cannot extract the correct intrinsic flux. As an improvement, we take A as afunction of E γ . In next section we will use the data of PKS 2155-304 blazar ( z = 0 . A ∼ E γ (see figure 4). Assuming this relation is fixed for thesources with not too larger value z <
1, one can get a reasonable relation between Φ inγ and τ .Usually the distributions of the EBL at near infrared have different categories. Wetake a distribution λ ∗ F λ ∗ (see figure 3), which is proposed by [18] and it is roughly thelow bound of the EBL by the estimation based on the deep-galaxy-surveys data. We callit as the lower EBL model. We use equation (2.5) and the lower EBL model in figure 3 to extract Ψ inγ from theobserved data. Note that a small modification in Φ obγ at E γ ≫ . T eV may arise alarge deformation in Φ inγ since the amplification of the factor exp ( − τ ) in equation (3.1).Therefore, the actual approach is using a suitable distribution Φ GCγ in equation (2.5) tofit the observed data (the dashed curves) in figure 5. Note that equation (2.5) has onlyfour free parameters, which are much smaller than other radiation models.Figure 5 shows the SEDs of ten blazars in the GC-model (see solid lines). They allpresent the sharp broken power-law. The relating parameters are listed in table 1, whereΓ ≡ β γ and Γ ≡ β γ + 2 β p −
1. One can see that although the EBL may change the indexof the spectrum at E γ > E GCπ , Φ inγ always shows a sharp broken power-law. The differentEBL may deform Φ inγ , however, Korochkin, Neronov and Semikoz [21] found that theintrinsic spectra are still sharply broken after the corrections of the various EBL models.Therefore, we suppose that the GC is the dynamics of the broken power-law.The GC-effect not only exists in blazars, but also appears in non-blazar AGNs. PKS0625+354 has not a clear evidence for optical blazar characteristics [27], however itsintrinsic γ -ray spectrum in figure 5 still presents a broken power-law.5lazars are known for their variability on a wide range of timescales. Most studies ofTeV gamma-ray blazars focus on short timescales. The observations of the blazar 1ES1215+303 from 2008-2017 are investigated by a combining Fermi-LAT and VERITAScollaborations [28]. The results show that the parameters of the observed spectra changein a narrow range, and a sharp broken power-law is still kept.The intrinsic γ -ray spectra will have different forms if different EBL models are usedfor an observed spectrum. PKS 2155-304 and 1ES 1218+304 are located at redshifts z = 0 .
116 and 0 . As well known that the index of a cosmic ray spectrum at the asymptotic range de-creases with increasing energy. While some of TeV-blazars present an opposite trend intheir intrinsic spectra, i.e., the spectra have hard tails. To understand this interestingphenomenon, the photon to axion-like particle (ALP) conversion, and even the Lorentzinvariance violation are proposed. We point out that the multi-GC sources can uniformlyexplain these hard tails. We give a few of hardening examples in figure 8 and table 2.1ES 1426+428 is a TeV γ -ray source that has been noticed earlier. The TeV γ -raysfrom this source arrive the earth after the EBL absorption. However, the measuredspectrum looks significantly different compared to the other blazar spectra since it hasa bump at E γ ∼ T eV [36]. We use the double GC-sources to explain 1ES 1426+428spectrum. The parameters β IIγ = 0 is much smaller than that β Iγ = 0 .
96 and E GCIIπ =10
T eV ≫ E GCIπ = 0 . T eV . This result can be understood that the first GC-sourceproduced in the heavy nuclear collisions deep in the star, while the second GC-sourceproduced by the light nuclear collisions at the surface of this star.TeV blazar Markarian (Mkn) 501 is a striking star. Although its spectrum can be de-scribed, at least qualitatively, by the leptonic and normal hadronic models, it is difficultto explain a pile-up at the end of the absorption-corrected spectrum. For this sake, severalextreme hypotheses have been proposed to overcome this so called ”IR-background-TeVgamma ray crisis”. We try to answer this question. We consider that the leptonic mech-anism dominates the spectrum of Mkn 501 at 0 . T eV − T eV , and it can be describedby a curvilinear form ∼ . × − E − . γ exp ( − E γ / T eV ). However, a GC-effect par-ticipated in the process at E γ > T eV . The result is shown in figure 8, where we assume6emporarily the parameters β p ≃ E GCπ ≃ T eV because we lack the data at higherenergy.
GRBs occur suddenly and unpredictably with a rate of approximately one burst per day.The durations of the GRBs are very short ranging from fractions of a second up to 100seconds. The GRBs appear to be uniformly distributed over the whole sky. The shortburst duration it is very difficult to identify a GRB event with a known object.The generally accepted the sub-TeV emission mechanism of the GRB is the SSC mech-anism synchrotron, where a synchrotron-emitting source must produce high energy radi-ation through up-scattering of synchrotron photons by the same electrons [37-39]. Thus,sub-TeV radiation is expected from GRBs afterglows at early stage. However, severalattempts to detect very high energy (VHE) ( > GeV ) gamma-rays from GRBs wereunsuccessful, resulting only in upper limits. Just recently, VHE photons were detected inGRB 180720B and GRB 190114C.The connection between the VHE emission by IC and the low energy afterglows insynchrotron radiation does not seem inevitable, since most of the GRB events have notthe VHE spectra’s record. we do not exclude the possibility existing a new radiationmechanism in GRB. We try to use the GC-model to understand the VHE spectra fromthese two GRBs.Considering a proton- (or nuclei-) beam after being accelerated to an extremely highenergy in a AGN and traveling in interstellar space. If it randomly collides with high-density matter (meteorite, small star even mini black hole), electromagnetic radiationwill be generated in the short time of collision, which includes VHE gamma-rays if thecollision energy beyond the GC-threshold. These are called as the short-duration burstsUsing equation (3.1) we extract Φ inγ for GRB 190114C (solid curve in figure 9). Ac-cording to equation (2.5) we have the parameters β γ = 0, β p = 2 .
025 and E GCπ = 0 . T eV ,where we consider that the energy loss of gamma-rays inside small target is negligible (i.e., β γ ∼ E γ < . T eV . Weuse the result in ref. [40] to place the upper limits on its SED (see horizontal bars withdownwards arrows), where the instrument resolution and a special program are consid-ered. The result of the GC-model is acceptable.A similar VHE spectrum of RGB 180720B is given in figure 10. Note that the values β p for RGB 180720B and GRB 190114C are obviously larger than the upper limit β p ∼ . β p in the GRB-eventsincludes the corrections due to the energy loss of the proton beam in the interstellarjourney, therefore, β p has a larger value. Note that MAGIC used a higher EBL model toget a hard spectrum Φ inγ ∼ E − . γ for GRB 190114C [5], which corresponds to β p = 1 . E − Γ − a log( E γ /E cut ) γ with a cut factor.7he suddenly increasing p ( A ) − p ( A ) cross section leads to a big excess of γ numberat the GC-threshold E GCπ . This greatly improves the radiative efficiency in the conversionfrom kinetic energy of the accelerated protons to the radiation energy. Besides, this isexactly what the GRB-event needs.If the VHE gamma-ray spectra of both AGN (blazar) and GRB are dominated by theGC-effect, they have a similar broken power-law. However, acceleration and collisions ofthe protons in the blazar occur in a same AGN-source, the observed spectra can maintaina long time, although its intensity changes over time. On the other hand, GRB may be aproduct of extremely fast protons hitting matter during interstellar travel. The recordedGRB spectra are random in a very short formation time. These are well known but haveno satisfactory explanation yet.
We find that the GC is one of possible VHE gamma ray sources, which presents a typicalbroken power law and caused the hardening spectrum. The GC occurs at the deepest levelof matter, it may relate to several seemingly unrelated cosmological phenomena. Usingthe GC-model we present the following features, which are mentioned in introduction. (i)The GC-threshold E GCπ distributes in a broad region from
GeV to T eV energies, whichcoincides with the peak range of γ − ray distribution; (ii) The cross section σ pp rises linearlywith energy rather than increases logarithmically because the GC-effect contributes allavailable kinetic energies to create pions. The channel pp → π → γ with the GC-effecthas a high conversion efficiency from kinetic energy to γ -rays; (iii) The broken power-lawis a natural result of the GC-effect in VHE γ -ray spectra; (iv) Some of blazars spectrahave an extra hard tail at the TeV range, which can be explained by the contributionsof second GC-source; (v) We present a new dynamic in AGNs, although it has neverbeen recognized before, but it can be reasoned in QCD; (vi) In particularly, we exposethe GC-effect in the VHE gamma energy spectra of GRBs. A series of characteristics ofthe spectra predicted by the GC model are consistent with the observed results of GRB180720B and GRB 190114C. Thus, the GC-effect opens a new window to understand theanomalous phenomena in cosmic ray energy spectra. Acknowledgments:
This work is supported by the National Natural Science of China(No.11851303).
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Figure 4: Coefficient A in equation (3.3).14 -3 -2 -1 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)PKS 2155-304 -3 -2 -1 -13 -12 -11 -10 E (cid:215) F g ( T e V c m - s - ) E(TeV)
PKS 1424+240 -4 -3 -2 -1 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)
PKS 0625+354 -3 -2 -1 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)PKS 1510-089 -3 -2 -1 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)1ES 1011+496 -3 -2 -1 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)1ES 1959+650 -3 -2 -1 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)1ES 1215+303 -3 -2 -1 -13 -12 -11 -10 E (cid:215) F g ( T e V c m - s - ) E(TeV)1ES 1218+304 -3 -2 -1 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)
H 2356-309 -4 -3 -2 -1 -13 -12 -11 -10 E (cid:215) F g ( T e V c m - s - ) E(TeV)
PG 1553+113
Figure 5: SEDs of some TeV blazars. Circles denote measurements; the intrinsic spectraof the GC-model are shown in black lines, red dashed curves are the observable spectraabsorbed with the lower EBL model in figure 3.15 .1 1 10110100 (um) l F l ( n W m - s r - ) Figure 6: A SED of the EBL (red dashed curve). Black solid curve is the lower EBLmodel in figure 3 16 -3 -2 -1 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)
Figure 7: SED of 1ES 0229+200, which assumes that the break of the spectrum at 0.3TeV comes entirely from a stronger absorption of the EBL in Figure 7.17 -3 -2 -1 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV) -3 -2 -1 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV) -3 -2 -1 -14 -13 -12 -11 -10 E (cid:215) F g ( T e V c m - s - ) E(TeV) -3 -2 -1 -15 -14 -13 -12 -11 E (cid:215) F g ( T e V c m - s - ) E(TeV)PKS 2005-489 -2 -1 -14 -13 -12 -11 -10 -9 H 1426+428 E (cid:215) F g ( T e V c m - s - ) E(TeV) -13 -12 -11 -10 -9 E (cid:215) F g ( T e V c m - s - ) E(TeV)Mkn 501
Figure 8: Similar to figure 5 but two GC-sources are used, where green and blue linescorrespond to I- and II-sources, while black curve indicates the sum of them. Red dashedcurves are the observable spectra absorbed with the lower EBL model in figure 3.18 -3 -2 -1 -13 -12 -11 -10 -9 -8 E(TeV) E (cid:215) F g ( T e V c m - s - ) GRB190114C
Figure 9: SED of GRB 190114C measured with MAGIC (circles with statistical uncer-tainties)[41] together with best fits for the lower EBL model (dashed curve) and the corre-sponding intrinsic SEDs (solid curve). The parameters β γ = 0 , β p = 2 . , E GCπ = 0 . T eV in Φ inγ . Horizontal bars with downwards arrows is upper limits derived by [40].19 -3 -2 -1 -13 -12 -11 -10 E(TeV) E (cid:215) F g ( T e V c m - s - ) GRB180720B
Figure 10: SED of GRB 180720B measured with HESS (circles with statistical uncertain-ties) [42] together with best fits for the lower EBL model (dashed curve) and the corre-sponding intrinsic SEDs (solid curve). The parameters β γ = 0 , β p = 1 . , E GCπ = 0 . T eV in Φ inγinγ