1. in an active galaxy an ultrarelativistic proton escapes from one of the jets, and collides headon with a photon of the accretion disc radiation which can be approximated by black body radiation with a temperature 10\" K. Assume the photon has energy equal to the mean energy at biackbodr photons '5 = 2.7m [k is Boltzmann's constant and T is the temperature]. The proton has only just enough energy to produce a neutral pion in the collision. ll] Find the threshold proton energy {in Get!) for this to take place Hint: We did similar calculations in the lectures and tutorials. This is very similar, so if you are calculating to more than a page, you may have made a mistake, or missed a simplification. [10] my: 1.67 x lo-zikg m\": 2.4 x 10-13kg Em: 2.7kT whersleo\" K_-_= 3.726 x lD'uJ c: 3 x mm 5-1 Before collision there is a proton (projectile) with total energy Epjc and momentum P: P!\"2 {proton moving in the positive intdirection]. And there is a photon with the total energy EFm and momentum 132 Pm}? [negative as the photon is travelling in the opposite direction to the proton). Hence, the 4momentum is defined by, E E J _Lh 2 c c \" 0 0 . 0 I I 0 , I I e+e 2 c c E2 2 ZPEZ PprPph NowusingtheLorentzlnvariant P'P: ?_P , :21 0 0 I 2 2 .2 IE +13 .- - . Z P i ' Z P Fir2N1 ': ppr_ Lipid: (negative sign due to Minkowski Metric} i=1 i=1 c E 2 i, (lamest-sews +E ) . . fMl.pir+2pprpph+pihi i, iPi'Z-Pizi' 2 i=1 :21