Intergalactic γ -ray propagation: basic ideas, processes, and constraints
T.A. Dzhatdoev, E.V. Khalikov, E.I. Podlesnyi, A.V. Telegina
aa r X i v : . [ a s t r o - ph . H E ] O c t Intergalactic γ -ray propagation:basic ideas, processes, and constraints Timur Dzhatdoev , , Emil Khalikov , Egor Podlesnyi , and Anastasia Telegina Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia Institute for Cosmic Ray Research, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Japan Faculty of Physics, Moscow State University, Moscow, 119991 RussiaE-mail: [email protected], [email protected], [email protected],[email protected]
Abstract.
We review extragalactic γ -ray propagation models with emphasis on theelectromagnetic (EM) cascade process in the magnetized expanding Universe. We considercascades initiated by primary protons of ultra-high energy accelerated by blazars and show thatthe observable spectrum is similar to the universal spectrum of a purely EM cascade. We alsopresent a detailed calculation of the observable angular distribution for the case of EM cascadesdeveloping from relatively nearby ( <
20 Mpc) sources. Finally, we calculate the point-like sourcedifferential sensitivity of a novel liquid Argon time projection chamber γ -ray telescope and showthat its sensitivity is several times better than the Fermi LAT sensitivity in the 100 MeV – 100GeV energy range.
1. Introduction
Observable γ -ray spectral, angular, and temporal distributions for extragalactic sources may besignificantly transformed during intergalactic propagation. The most basic elementary processesinvolved are:1) electron-positron pair production (PP) γγ → e + e − on extragalactic background light (EBL)[1, 2] and cosmic microwave background (CMB) photons [3] for γ -rays;2) inverse Compton (IC) scattering eγ → e ′ γ ′ for electrons and positrons that occurs mainlyon the CMB (see [4] and references therein);3) Bethe-Heitler pair production (BHPP) and pion photoproduction (PIP) for protons andnuclei . For ultrahigh energy (UHE, E > / (1+ z ) EeV, z is redshift) BHPP is usually dominatedby interactions on the CMB. For 1 / (1 + z ) EeV < E < / (1 + z ) EeV PIP is subdominant; athigher energies it is the main proton energy loss process, occuring mainly on the CMB (see [5]and references therein);4) adiabatic losses (AL).For especially high values of center-of-mass energy, additional processes also set in, such asmuon pair production γγ → µ + µ − [6] and double pair production γγ → e + e − e + e − [7] for hereafter simply “electrons” below we do not consider primary nuclei, thus the photodissociation process is not relevant -rays. Additionally, there is a quest for New Physics processes, such as γ -axion-like particle(ALP) mixing [8]–[11] or Lorentz invariance violation (LIV) [13]–[15].Models involving production and propagation of γ -rays in the intergalactic volume may beclassified as belonging to one of the following three types [16, 17]:1) the absorption-only model, which accounts for only the PP and AL processes;2) cascade models, which also include the IC process, and BHPP and PIP for primary protons;3) exotic models.Following the lines of argument presented in [17], in this paper we concentrate on the cascademodels. To recall, the physics behind the absorption-only model is already very well-known.Many exotic models are already ruled out [18] [19], and there is growing evidence against someother options such as γ -ALP mixing [20, 21]. On the other hand, all existing possible deviationsfrom the absorption-only model, such as [22, 23] (see also [24, 25]), could be qualitativelyaccomodated in the framework of the cascade models [26]. A caveat is that these anomaliesare still not very well established [27, 28] (see also [29]).The present paper is organised as follows. In section 2 we consider two specific cases whereintergalactic electromagnetic (EM) cascades are important, namely: secondary γ -rays from 1)ultra-high energy cosmic rays emitted by blazars (subsection 2.1) and 2) relatively nearby sourcessuch as galaxy clusters with the source-observer distance less than 20 Mpc (subsection 2.2). Anumber of other case studies could be found in [26, 16, 30]. In section 3 we discuss a newexperimental technique called on to measure the extragalactic magnetic field (EGMF), namely,the liquid argon time projection chamber (TPC) approach. Finally, we conclude in section 4.All figures presented below were produced with the ROOT software [31].
2. Specific cases γ -rays from EM cascades initiated by primary protons accelerated in blazars may contribute tothe observable emission (see e.g. [32, 33]). These protons may be strongly deflected on large scalestructure (LSS) filament magnetic fields; below we show that this effect impacts the observable γ -ray spectrum (see also [26]). A simplified scheme of the corresponding geometry is shownin figure 1. A source ( S ) emits UHE protons that first propagate through a void (underdenseregion of space) with the diameter L V and then are deflected on a filament (denoted by twindashed lines). The proton deflection angle is denoted as δ , θ obs is the angle between the directionfrom the source to the observer ( O ) and the direction of an incoming observable γ -ray. L isthe distance between the source and the observer, L int = L V + L f is the characteristic protoninteraction length.Let’s extrapolate the observable γ -ray path until we have a triangle with a right angle. Theshortest side of that triangle can be represented by the following equation: d = sin( θ obs ) · ( L − L V ) = sin( π − α ) · L f (1)At the same time δ + α = π − θ obs → π − α = δ + θ obs (2)Assuming that θ obs ≪ π and δ ≪ π we obtain the following: θ obs · ( L − L V ) ≈ ( δ + θ obs ) · L f (3) θ obs · ( L − L f − L V ) ≈ δ · L f (4)And finally θ obs ≈ δ · L f L − L f − L V = δ L int − L V L − L int . (5) igure 1. A scheme of geometry for the hadronic cascade model (not to scale).Now let’s estimate θ obs assuming L = 750 Mpc and L V = 50 Mpc. Let’s assume L int to beone of the following set of values: 100 ,
200 and 500 Mpc. The proton deflection angle δ may beestimated as follows [34]: δ ≈ ◦ BnG EeVE/Z √ L B l c M pc , (6)where B is the magnetic field strength, E and Z are the energy and charge of the primaryparticles (protons in our case), L B is the thickness of the filament and l c is the coherence lengthof that magnetic field. For B = 1 nG, E = 40 EeV, L B = 1 Mpc, l c = 1 Mpc, we get δ = 1 ◦ and θ obs = 0 . ◦ , . ◦ , . ◦ for the three values of L int . The typical extension of an imagingatmospheric Cherenkov telescope (IACT) point spread function (PSF) is about 0.1 ◦ , thus a partof observable γ -ray flux in our case will not fit into the point-like image of the source. In a morerealistic case of lower proton energies, lesser values of L V , and many filaments on the line ofsight, this leads to the conclusion that most of observable γ -rays produced farther than 100 Mpcfrom the source would not contribute to the observable spectrum of the source. This, in turn,leads to an effective cutoff at the highest observable energies, as pointed out in [26]. In effect,the observable spectrum is almost the same as in the framework of the electromagnetic cascademodel in the universal regime [35]. Another interesting, rarely discussed case is that of relatively nearby sources (
L <
20 Mpc).Here we consider an example of the Virgo cluster located at L =16.8 Mpc from the Earth. Veryrecently, [36] considered this source in context of very heavy dark matter searches. In particular,the authors of [36] estimated the secondary electron deflection angle (see their equation (3.7)).We note that this equation was obtained following e.g. [37]. The latter work assumed blazars assources of primary γ -rays. Blazars typically have z > ∼
10 TeV or less), making the Thomson approximation used by [37]fully applicable in this case. For nearby sources, however, such electrons may have the energywell in excess of 10 TeV, where the Thomson approximation is not valid. Figure 2 shows theelectron mean free path (black curve), as well as the characteristic electron energy loss length L E − e = c · E/ ( dE/dt ) (blue curve). These quantities were computed using the approximation of[38]. For comparison, red line denotes L E − e in the Thomson approximation. We note that forlectron energy in excess of 50 TeV the Thomson approximation fails and thus a new calculationof observable spectral and angular distributions is required.Using the publicly-available code of [39] and assuming the EGMF strength 1 nG on coherencelength 1 Mpc, we have performed a detailed calculation of the observable angular distribution.Such EGMF parameters were promtped by the fact that we do not expect a large void withlow magnetic field strength in the local Universe. We also assumed the EBL model of [40]which is consistent with current constraints such as [41]. Figure 3 shows the observable angulardistribution for three ranges of primary energy: 20–36 TeV (black histogram), 97–158 TeV (redhistogram), and 1–3 PeV (blue histogram). In the first case the primary γ -ray mean free path L γ > L ; the second case corresponds to the one-generation regime, and the last case — to theuniversal regime (see [26] for detailed discussion of the latter two regimes). We note that thetypical total electron deflection angle is well in excess of π ; therefore, EM cascades develop analmost isotropic cloud around the source — the so-called pair halo (PH) [42]. Figure 2.
Characteristic lengths for electronin the intergalactic medium at z =0 vs. energy. Figure 3.
Observable angular distributionsfor various primary energy ranges.
3. Point-like source differential sensitivity of liquid Argon TPC γ -ray telescope The main uncertainty of extragalactic γ -ray propagation models is the unknown strength B andstructure of the EGMF (for a review, see [43, 44]). Possible values of B in voids range from 1nG to 0.01 fG. Additionally, the EGMF may be highly inhomogeneous (see, e.g. [45]).In [30] we argue that the most robust method to measure weak ( B <
10 fG) EGMF in voids isto detect magnetically broadened cascade (MBC) emission from blazars. If
B < γ -ray instruments. Therefore, a new experimental technique with better angular resolution isrequired in order to measure weak EGMF. In [30] we propose, for the first time, to utilize anovel technique of liquid argon time projection chamber (TPC) [46] to constrain the EGMFparameters. Here we provide an estimate of point-like source differential sensitivity vs. energyfor such a detector following [46].We assume a 2.0 m × × corresponding to 5.7 radiationlengths and optical depth τ =3.3 for 100 MeV γ -rays. Currently we are working to develop anenergy reconstruction technique utilizing such a detector of medium thickness.Figure 4 shows sensitivity for this γ -ray instrument assuming 1.7 years of continiousobservation of a source (thick red curve) or 10 years of continious observation (blue thick curve)or 5 σ detection of the source. Additionally, a minimum of 10 signal events are required; wealso require that the number of signal events exceeds the number of background events. Othersensitivity curves were taken from [47] (see also [48]) and denote the differential sensitivity ofFermi LAT and atmospheric Cherenkov telescopes (ACT) [49, 50] (see Figure 5 (left) of [16]for the meaning of these curves). We conclude that the proposed new γ -ray instrument has thesensitivity several times greater than the Fermi LAT one in the wide energy range 100 MeV–100 GeV and could provide a natural low-energy extension for IACT such as the CTA array[49, 50] or LHAASO [51]. Figure 4.
Differential sensitivity for point-like sources for liquid argon TPC and other γ -rayinstruments.
4. Conclusions
In this work we continued our review of extragalactic γ -ray propagation phenomenologyconcentrating on intergalactic EM cascades. We have shown that the typical observable spectrumin the framework of the intergalactic hadronic cascade model practically coincides with theuniversal spectrum of the electromagnetic cascade model. This is due to deflection of primaryprotons in LSS filaments, causing the broadening of the observable angular distribution. Wenote that this effect is relevant even for isotropic sources. We also considered EM cascades fromrelatively nearby ( L <
20 Mpc) sources such as galaxy clusters and calculated the observableangular distribution in this case. Finally, we have estimated the point-like source differentialsensitivity for a novel liquid Argon TPC γ -ray telescope, finding out that it has the sensitivityseveral times better than Fermi LAT in the 100 MeV – 100 GeV energy range. Acknowledgements
This work is supported by the Russian Science Foundation (RSF) (project No 18-72-00083). eferences [1] Nikishov A I 1962
Sov. Phys. JETP Phys. Rev.
Phys. Rev. Lett. Phys. Rev. D Phys. Rev. D Preprint arXiv:0711.4969[7] Brown R W et al. 1973
Phys. Rev. D Phys. Rev. D JCAP Phys. Rev. Lett.
Journal of Instrumentation P11019[12] Coleman S and Glashow S 1999
Phys. Rev. D ApJ
L21[14] Tavecchio F and Bonnoli G 2016
A&A
A25[15] Abdalla H and Boettcher M 2018
ApJ
Proc. of the Moriond-2017 Very High Energy Phenomena in the Universe conf.
La Thuile[17] Dzhatdoev T, Khalikov E and Kircheva A 2017 in
Proc. of Science, the 35th Int. Cosmic Ray Conf. 2017(ICRC-2017)
866 Busan[18] Aharonian F A et al. 2000
ApJ
L39[19] Rubtsov G, Satunin P and Sibiryakov S 2017
JCAP
Phys. Rev. Lett.
Preprint arXiv:1805.04388[22] Horns D and Meyer M 2012
JCAP
Preprint arXiv:1810.03443[24] Furniss A et al. 2015
MNRAS
Phys. Rev. Lett.
A&A
A59[27] Biteau J and Williams D 2015
ApJ
ApJ
L34[29] Fermi-LAT Collaboration and Biteau J 2018
ApJ Supplement Series
Preprint arXiv: 1808.06758[31] Brun R and Rademakers F 1997
Nucl. Instrum. Methods Phys. Res. Sec. A
JETP ApJ
Phys. Rev. D
D93
Phys. Rev. D JCAP
Phys. Rev. D ApJ
MNRAS
MNRAS
MNRAS
ApJ
L5[43] Durrer R and Neronov A 2013
A&A Rev. , 62[44] Han J L 2017 Annual Review of Astronomy and Astrophysics MNRAS
Nucl. Instrum. Methods Phys. Res. Sec. A
225 [Erratum: Bernard D 2013
Nucl. Instrum.Methods Phys. Res. Sec. A
Astropart. Phys. Astropart. Phys. Experimental Astronomy Astropart. Phys. Astropart. Phys.54