The ultra-high energy cosmic rays image of Virgo A

Transcription

1 The ultra-high energy csmic rays image f Virg A Radmír Šmída Karlsruhe Institute f Technlgy, Germany radmir.smida@kit.edu Ralph Engel Karlsruhe Institute f Technlgy, Germany Arrival directins f ultra-high energy csmic rays frm the directin f ten brightest radi surces lying within 5 Mpc frm ur Galaxy were studied by using recent mdels f the largescale Galactic magnetic field. A detailed study, where als small-scale turbulent magnetic field cmpnent was implemented, is presented fr the radigalaxy Virg A. This radigalaxy is lcated far frm the Galactic plane which leads t a unique image f this UHECR surce candidate, if the flux is cmpsed frm a mixture f intermediate mass nuclei. We present a methd suitable fr identifying csmic rays arriving frm this clse-by radigalaxy. PS(ICRC215)47 The 34th Internatinal Csmic Ray Cnference, July- 6 August, 215 The Hague, The Netherlands Speaker. c Cpyright wned by the authr(s) under the terms f the Creative Cmmns Attributin-NnCmmercial-ShareAlike Licence.

2 The UHECRs image f Virg A Radmír Šmída 1. Intrductin The search f a pint surce f ultra-high energy csmic rays (UHECRs), defined as csmic rays with energy abve 5 EeV in this paper, lacks an answer mre than half-century after their discvery [1, 2]. The primary particles are charged nuclei accelerated in astrnmical bjects. Mrever, the distance t such surces must be within 1 Mpc fr UHECRs because f energylss prcesses n varius phtn backgrunds [3, 4]. Categries f astrnmical bjects pwerful enugh t accelerate nuclei up t the highest measured energy [5] have been classified in the past [6]. Fr the search f the site f the UHECR rigin an identificatin f a lcal pint surce is f the primary cncern, because the flux frm such surce lcated within a few tens f Mpc wn t be significantly attenuated fr mst f nuclei [7, 8]. Mrever, extragalactic magnetic fields might be rather unifrm ver such distance. The mst interesting psitin f the surce in the sky is at high Galactic latitude, because the large-scale Galactic magnetic field (GMF) between the surce and the Earth has the least cmplex structure in this directin. Any nuclei f an electric charge Z will be deflected during their prpagatin thrugh the GMF. Under an assumptin that all particles frm the same surce travel thrugh the same magnetic field the angular deflectin will scale linearly with the electric charge. It is therefre useful t study the angular deflectin as a functin f the magnetic rigidity R(V) = E(eV)/Z instead f energy E(eV). We will assume that UHECRs arrive t the Galaxy in a parallel beam frm an extragalactic pint surce and infrmatin abut the surce psitin is nt lst during the prpagatin in the extragalactic space. Under such assumptins we can study an effect f the large-scale GMF and als small-scale turbulent magnetic fields n the surce image at the Earth. 2. Simulatins Pint surce candidates and the GMF mdel must be selected befre perfrming a simulatin. Fr the frmer the full-sky the catalgue f radigalaxies f the lcal universe [1] was selected. This catalgue was prepared fr any study f UHECRs and prvides infrmatin required fr ur analysis. Ten brightest radigalaxies within the distance D = 5 Mpc have been selected frm this catalgue and their list is prvided in Tab. 1. The clsest bject frm ur selectin is Cen A at the distance 3.6 Mpc fllwed by Virg A and Frnax A. These ten celestial bjects are nt unifrmly distributed acrss the sky, because they fllw the lcal mass distributin. Fr example the sky psitins f radigalaxies NGC 59 and Cen A are separated by nly 1 and in the case f Virg A and NGC 4261 nly 7. All simulated particles were randmly generated in a flat circular area having its centre 5 kpc frm the Galactic centre. The psitin f the centre was at the sky psitin f a radigalaxy. The area was always perpendicular t the directin cnnecting the Galactic centre and the radigalaxy. The radius f this area was 2 kpc and 1 kpc fr ur simulatins withut and with the turbulent magnetic field, respectively. The radius f a detectr at the psitin f the Earth was 1 pc. The maximum time t track particle was ne millin years and the minimum time step was 1 years. The CRT uses adaptive Runge-Kutta integratin methds t determine the trajectry f a charged particle thrugh PS(ICRC215)47 2

3 The UHECRs image f Virg A Radmír Šmída Name α δ l b D Frnax A Virg A NGC Cen A NGC NGC IC NGC NGC NGC Table 1: Ten brightest radigalaxies within D < 5 Mpc [1]. Clumns: name f radigalaxy, right ascensin, declinatin, galactic lngitude and latitude, distance in Mpc. a magnetic field accrding t the relativistic Lrentz frce. Detailed descriptin f the CRT cde can be fund in [9] and in the manual. 3. Regular GMF The Jansn&Farrar (JF12) GMF mdel [11] was primarily used, but als ther mdels were studied [12, 13]. We will present nly results btained fr the JF12 mdel in this paper. A parallel beam f particles pinted twards the Earth was generated in a circular area f 2 kpc diameter at the Galactcentric distance 5 kpc. The studied magnetic rigidity was between 1 and 15 EV and the spectral index was 1. In a unifrm magnetic field the angular deflectin is inversely prprtinal t the magnetic rigidity θ = K/R. Results f ur simulatins abve EV were used t btain the cnstant K. Then all results were cmpared with the inverse linear fit, see fr example Fig. 1 fr Virg A. Our results are summarised in Tab. 2, where the numerical cnstant K and the rigidity where simulated arrival directin differs mre than 3 frm the fit are prvided. The uncertainty f values in Tab. 2 is ±5 EV fr the cnstant K and ±1 EV fr R 3. Tw values f R 3 are prvided fr NGC 2663, because f tw different trajectries hitting the Earth at the same rigidity. The same happens fr NGC 4696 and NGC 59, but nly belw EV. (Let us ntice, that tw pssible trajectries at the same rigidity have been fund even fr Virg A and ther GMF mdel, namely Sun et al. [12].) Results btained fr the JF12 mdel, see Tab. 2, shw that the angular deflectin is 2 4 at R = 1 EV fr all studied radigalaxies. The simulated data are described by the inverse linear fit belw 1 EV nly fr radigalaxies lying far frm the Galactic plane, i.e. b > 5. All ther radigalaxies have R 3 1 EV, i.e. the energy f 7 and 14 EeV fr nitrgen and silicn nuclei, respectively. Interestingly, the lwest value f R 3 has the strngest lcal radigalaxy Frnax A. Hwever, by checking the sky map ne can recgnise that even if the angular deflectin scales with R the PS(ICRC215)47 3

4 The UHECRs image f Virg A Radmír Šmída Angular deflectin frm Virg A [deg] Rigidity [EV] inverse linear fit simulated (JF212) Figure 1: Red crsses shw the angular deflectin frm Virg A as functin f the rigidity, black slid line shws the inverse linear fit and dashed lines the ±3 ffset frm the fit. Ntice missing successful hits between 2.5 and 5.4 EV, i.e. when particles crss the Galactic plane. Radigalaxy K ( EV) R 3 (EV) Frnax A Virg A 6 7 NGC Cen A NGC NGC IC NGC NGC , 25 NGC Table 2: Results fr the JF12 mdel f the regular GMF. Parameters f the linear fit described in the text are prvided. PS(ICRC215)47 directin abruptly turns at R 1 EV, see Fig. 2. It is reasnable t study a lcatin f a pint-surce nly at rigidities, where the infrmatin is nt cmpletely lst r vastly reduced by the prpagatin. We can identify this rigidity with R 3. In the case f Virg A the simulated results abve 7 EV agree within 3 with values btained frm the inverse linear fit as can be seen in Fig. 1 and Tab. 2. An increase f discrepancy between calculated and simulated values belw R 3 is caused by mre cmplex structure f the GMF in the vicinity f the Galactic plane. Due t this plane nne arrival f simulated particles between 2.5 and 5.4 EV was registered at the Earth and arrival directins f particles at rigidities belw 2.5 EV are highly scattered, see Fig. 3. 4

5 The UHECRs image f Virg A Radmír Šmída 6 Virg A (1, 15] EV 1 EV (6, 1) EV (3, 6] EV l= Frnax A Figure 2: Arrival directins f csmic rays frm Virg A and Frnax A, indicated by big red squares. The Galactic crdinates are used and the Galactic centre is in the centre f this map. Blue (black) clur is used Virg A (Frnax A). Fr clarity nly events abve 3 EV are shwn (1, 15] EeV 1 EeV (6, 1) EeV (3, 6] EeV (2, 3] EeV (1.5, 2] EeV (1, 1.5] EeV Figure 3: Arrival directins f csmic rays frm Virg A between 1 and 15 EV. Red line cnnects sky psitins f a radigalaxy and 1 EV event and its length is Turbulent magnetic field Frm ten studied lcal radigalaxies the arrival deflectin fllws a single arc and the deflectin can be described by the inverse linear fit belw R = 1 EV nly fr tw f them, Virg A and NGC Fr further investigatin f the UHECR image we have selected the radigalaxy Virg A. The small-scale randm magnetic fields have t be included t the large-scale regular GMF t btain mre realistic descriptin f arrival directins. We used fur realisatins f randm magnetic field characterised by a Klmgrv spectrum and generated in CRT. Fur fields f spheres with sizes and field magnitude drawn frm Gaussian distributins and each a randmly riented field vectr were generated. Each randm magnetic field realisatin is described by eight parameters: number f divisins within the KRF bx in each space crdinate axis (NX, NY, NZ), length f each side f the KRF bx (LX, LY, LZ), the minimum and maximum wavelengths (LMI and LMX). Values used in ur simulatins are in Tab. 3. As fr the regular GMF study a parallel beam f particles was generated in a circle centred at the sky psitin f Virg A at the galactcentric distance f 5 kpc. The differences frm the previus case were as fllws: the diameter was 1 kpc, the rigidity was 5 15 EV and the l=18 PS(ICRC215)47 5

6 The UHECRs image f Virg A Radmír Šmída Realisatin NX, NY, NZ LX, LY, LZ (kpc) LMI, LMX (pc) KRF1 256, 256, , 5.12, , 1 KRF2 256, 256, , 5.12, , 1 KRF3 256, 256, , 5.12, , 512 KRF4 256, 256, , 2.56, , 1 Table 3: Eight parameters describing fur magnetic field realisatins. Tw realisatins (KRF1 and KRF2) have the same parameters, but different seed number was used fr them. spectral index was 3. The lwer limit f the rigidity was set at 5 EV t avid trajectries crssing the Galactic plane. Simulatins were stpped when at least 9 hits were reached. The least difference between a KRF realisatin and the regular JF12 field was fr KRF4, which had the smallest side length amng used KRF realisatins. Otherwise, all KRF realisatins shw similar features: small ffset at the highest rigidities, departure mre than ±3 frm the inverse linear fit between 1 and 2 EV and large scattering f angular deflectins between 5 and 8 EV. All these effects culd be expected and they indicate an increasing imprtance f the turbulent cmpnent f the GMF n the prpagatin at rigidities belw 1 EV. Our results fr Virg A can be cmpared with similar study made fr Cen A [14], which lies clse t the Galactic plane (b = 19.4 ). 5. Triangular area Arrival directins fr fur different realisatins f the randm magnetic field are shwn in Fig. 4. Our simulatins shw that arrival directins f the majrity f events frm a triangular rather area in all fur cases. Similar bservatin has been presented in [15]. This can be understd by lking in tw types f deflectin experienced by UHECRs. First, a rigidity-dependent ffset frm the surce psitin can be expected due t deflectins in large-scale magnetic fields. Secnd, a scattering f the arrival directins caused by turbulent magnetic fields with the amplitude inversely depending n the rigidity is expected fr UHECRs frm the same surce. The cmbinatin f these tw effects then leads t a triangular rather than circular image in the sky. We suggest t cnstruct the triangular area frm sky psitins f a surce candidate and ne event. These tw psitins frm an axis f the triangular area. The event shuld lie at angular distance θ(1,s) frm the surce candidate larger than an angular reslutin f a csmic-ray bservatin and an angular deflectin expected in the GMF. frm the studied surce candidate. We will call such event the leading event. The triangular area is then defined by the axis, the maximum angular distance ψ frm the surce candidate 1 and tw half-pening angles α 1 and α 2 alng the axis, see Fig. 5. In Fig. 4 we shw the triangular area fr fur KRF realisatins. The same parameters were used fr the triangular area in all fur cases t allw a cmparisn f arrival directins between ur PS(ICRC215)47 1 The value f ψ must be less than 9 t avid shrinking f the spherical area at larger angular distances. 6

7 The UHECRs image f Virg A Radmír Šmída 6 (1, 15] EeV 6 (1, 15] EeV 1 EeV 1 EeV (6, 1) EeV (6, 1) EeV (5, 6] EeV (5, 6] EeV l=18 l= (a) JF12 + KRF1 (b) JF12 + KRF (c) JF12 + KRF3 (1, 15] EeV 1 EeV (6, 1) EeV (5, 6] EeV l= (d) JF12 + KRF4 Figure 4: Arrival directins fr a cmbinatin f the JF12 large-scale regular GMF field and fur randm field realisatins. The triangular area is als shwn ψ θ (1, S) α 1 Leading event Axis Surce (1, 15] EeV 1 EeV (6, 1) EeV (5, 6] EeV l=18 PS(ICRC215)47 α 2 Figure 5: Sketch f the triangular area described by angles ψ, α 1 and α 2. The pint surce and leading event are separated by the angular distance θ(1,s). simulatins. The parameters are as fllws: the leading event is 1 EV event frm the simulatin fr the JF mdel with nly regular magnetic field, ψ = 7, α 1 = α 2 = Cnclusins Angular deflectins in the GMF fr the 1 brightest radigalaxies lcated within the distance f 5 Mpc were studied. Frm them Virg A was investigated mre extensively and even an effect 7

8 The UHECRs image f Virg A Radmír Šmída f varius turbulent magnetic fields was included. We have shwn that the expected UHECR image f Virg A has an asymmetric shape fr the magnetic rigidity abve 5 EV. If the UHECR flux is a mixture f nuclei (i.e. prtns and heavy nuclei) the image takes a triangular rather than circular shape. This unique feature is due t high galactic latitude f Virg A and can be used fr an identificatin f Virg A as the UHECR pint surce. Our analysis is based n the JF12 mdel and even if it is the mst elabrated mdel f the GMF, it des nt prvide cmplete picture f magnetic fields neither in the interstellar space nr in the Galactic hal. Any discrepancy between this GMF mdel and real envirnment may affect the arrival directins, particularly at lw rigidities. Nevertheless, ur results can be adpted t any GMF mdel and csmic-ray data. 7. Acknwledgement It is a pleasure t acknwledge discussins with ur clleagues f the Pierre Auger Cllabratin. References [1] J. Linsley et al., Phys. Rev. Lett. 6 (1961) 485 [2] J. Linsley, Phys. Rev. Lett. 1 (1963) 146 [3] K. Greisen, Phys. Rev. Lett. 16 (1966) 748 [4] G.T. Zatsepin, V.A. Kuzmin, JETPL 4 (1966) 78 [5] D.J. Bird et al., Astrphys. J. 441 (1995) 144 [6] A.M. Hillas, Annu. Rev. Astr. Astrphys. 22 (1984) 425 [7] K. Ktera & A. Olint, Annu. Rev. Astr. Astrphys. 49 (211) 119 [8] D. Allard, Astrpart. Phys (212) 33 [9] M.S. Sutherland et al., Astrpart. Phys. 34 (21) 198 [1] S. van Velzen et al., Astrn. & Astrphys. 544 (212) A18 [11] R. Janssn & G.R. Farrar, Astrphys. J. 757 (212) 14 [12] X.H. Sun et al., Astrn. & Astrphys. 477 (28) 573 [13] M.S. Pshirkv et al., Astrphys. J. 738 (211) 192 [14] A. Keivani et al., Astrpart. Phys. 61 (214) 47 [15] G. Giacinti & D.V. Semikz, Phys. Rev. D 83 (211) 82 PS(ICRC215)47 8