Benvenuti al Mera-TeV!

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1 Benvenuti al Mera-TeV! Ottobre 2011 Sala POE di OAB a Merate

3 Lorenzo Sironi

4 FATE DOMANDE! Le domande sono gradite, anche prima della fine dei contributi. L'incontro è volutamente informale, e lo spirito è orientato alla comprensione delle tematiche ed alla interazione tra i partecipanti.

5 SOCIAL EVENT w Visita alle Cupole Zeiss e Ruths: Mercoledì 5, ore 18.15

6 SOCIAL DINNER Taverna dei Cacciatori Imbersago Ore Mercoledì Partenza da Osservatorio ore 19.45

7 Pranzi e Pause Caffè Pranzi: alle nel parco, di fronte alla Cupola Ruths Coffe Breaks: nella Biblioteca, piano seminterrato edificio principale.

8 Buon Mera-TeV!!

9 Beaming

10 Radio-loud AGNs Gamma Ray Bursts ~ 0.1 M o yr-1 G~20 ~ 10-5 M o in a few sec G~300

11 Text book special relativity Lorentz transformations: v along x x = G (x vt) y = y z = z t = G (t v x/c 2 ) x = G (x + vt ) y = y z = z t = G (t + v x /c 2 ) for Dt t = 0 Dx x = Dx / x /G Contraction for Dx = 0 Dt t = G Dt time dilation To remember: mesons created at a height of ~15 km can reach the earth, even if their lifetime is a few microsec ct life =hundreds of meters.

12 Can we see contracted spheres? v=0 G=1 v v=0.866c G=2 Einstein: Yes!

13 v v=0 G=1 James Terrel 1959 NO! Roger Penrose 1959 v=0.866c G=2

14 Relativity with photons From rulers and clocks to photographs and frequencies Or: from elementary particles to extended objects

15 The moving square b=0.5 Your camera, very far away

16 The moving square t=l /c l tot = l (b+1/ +1/G) max:2 1/2 l (diag) min: l (for b=0) vt=bl l /G

17 l cosa = bl cosa = b cos(p-p/2-a) = sina a = 1/G l p/2-a

18 a ) p/2-a

19 p/2-a

20 Time Dt e = emission time in lab frame Dt e = emission time in comov. frame Dt e = Dt e G CD = cdt e cdt e bcos cosq Dt A = Dt e (1-bcos cosq) Dt A = Dt e G(1-bcosq)

21 Relativistic Doppler factor d Dt A = Dt e G(1-bcosq) n= n / G(1-bcosq) d = 1 G(1-bcosq) You change frame Standard relativity Doppler effect You remain in lab frame

22 Relativistic Doppler factor d d = 1 G(1-bcosq) = { 2G for q=0 o G for q=1/ =1/G 1/G for q=90 o At small angles, Doppler wins over Spec. Relat.

24 Nucleo

25 Ds app Dt A = v app = v Dt sinq e Dt (1-bcos e cosq) There is no G. Correct? b app = b sinq 1-bcosq app =0 q=0 o b app cosq=b; sinq=1/ =1/G b app =bg q=90 o b app =b

26 Aberration of light

27 Aberration of light sinq = sinq / /d dw = dw / /d 2

28 Aberration of light sinq = sinq / /d v dw = dw / /d 2 K K

29 Observed vs intrinsic Intensity I(n) n 3 I (n ) ) = n 3 = invariant invariant I( I(n) = d 3 I (n ) ) I(n) = erg = cm 2 s Hz sterad E da dt dn dw

30 Observed vs intrinsic Intensity I(n) n 3 I (n ) ) = n 3 = invariant invariant I( I(n) = d 3 I (n ) ) I(n) = erg = cm 2 s Hz sterad E da dt dn dw

31 Observed vs intrinsic Intensity I(n) n 3 I (n ) ) = n 3 = invariant invariant I( I(n) = d 3 I (n ) ) I(n) = erg = cm 2 s Hz sterad E d da dw /d 2 = d 3 I (n ) ) I = d 4 I F = d 4 F d blueshift d time d 2 aberration

32 v=0 L=100 W

33 v=0.995c G=10 L=0.6mW L=16MW L=10mW

34 v=0.995c G=10.? blazars radiogalaxies

35 v=0.995c G=10 blazars! blazars radiogalaxies

36 v counterjet (invisible) jet v

37 Radiation processes

38 Radiation processes Line emission and radiative transitions in atoms and molecules Breemstrahlung/Blackbody Curvature radiation Cherenkov Annihilation Unruh radiation Hawking radiation Synchrotron Inverse Compton

39 V=0 E

40 V (g=2) Contracted sphere E E-field lines at time 9.00 point to where the charge is at 9.00 Charge at time 9.00

41 dp = e 2 a 2 sin 2 Q dw 4p c 3 V Stop at 8:00

42 dp = e 2 a 2 sin 2 Q dw 4p c 3 P = 2 e 2 a 2 3 c 3

43 Synchrotron

44 Synchrotron Ingredients: Magnetic field and relativistic charges Responsible: Lorentz force Curiously, the Lorentz force doesn t work. q F L = d dt (gmv) = e c v x B

45 Total losses P e = P e P=E/t and E and t Lorentz transform in the same way Please, P e is not P received!!

46 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 )

47 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 ) P = P e e = 2e2 3c 3 g 2 a 2 a = g 2 a a = 0 sinq a = e v B sin g mc

48 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 ) P = P e e = 2e2 3c 3 P S (q) = 2e4 3m 2 c 3 g 2 a 2 B 2 g 2 b 2 sin 2 q a = g 2 a a = 0 sinq a = e v B sin g mc

49 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 ) P = P e e = 2e2 3c 3 g 2 a 2 a = g 2 a P S (q) = 2e4 3m 2 c 3 B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q a = 0 sinq a = e v B sin g mc

50 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 ) P = P e e = 2e2 3c 3 g 2 a 2 a = g 2 a P S (q) = 2e4 3m 2 c 3 B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q a = 0 sinq a = e v B sin g mc = S 4 s cu T B g2 b 2 3 If pitch angles are isotropic

51 Total losses P = P e e = 2e 2 3c 3 a 2 = 2e2 3c 3 (a 2 + a 2 ) P = P e e = 2e2 3c 3 g 2 a 2 a = g 2 a P S (q) = 2e4 3m 2 c 3 B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q a = 0 sinq a = e v B sin g mc = S 4 s cu T B g2 b 2 3 If pitch angles are isotropic

52 Log P S g 2 ~ E 2 Why g 2?? Log E P S (q) = 2s U T B g2 b 2 sin 2 q What happens when q 0? Sure, but what happens to the received power if you are in the beam of the particles?

53 Synchrotron Spectrum Characteristic frequency r L = v2 a = g mc 2 b sinq eb n B e B = a = 2p gmc e v B sinq g mc n = 1/T T = 2p r /v L This is not the characteristic frequency

54 v<<c v ~ c

55 D ta =?

56 n S = 1 Dt A = g 2 eb 2pmc Compare with n B. n S = n B g3 b

57 The real stuff x=

58 The real stuff x=

59 Max synchro frequency Guilbert Fabian Rees 1983 q t syn = T 6p gm e c 2 s T B 2 g 2 g max ~ 1 B 1/2 = 2p g m e c eb shock hn S,max 2 S,max ~ B g max = m e c 2 /a F (+ beaming) = 70 MeV.

60 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions Log g Log n e(n) ) dn = 1 4p N(g) P dg S

61 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions dg dn Log g Log n e(n) ~ 1 4p Kg-p B 2 g 2 dg dn Emission is peaked! g n n S = g 2 eb 2pmc

62 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions e(n) ~ Log g Log n 1 4p K B(1+p)/2 n (1-p)/2

63 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions e(n) ~ Log g Log n 1 4p K Ba +1 n - a a= p-1 2

64 Log F(n) So, what? e(n) ~ F(n) ~ 1 4p K Ba +1 n - a 4pVol e(n) ~ qs 2 R K B a +1 n - a 4pd 2 K B a +1 If you know q s and R Log n Two unknowns, one equation we need another one

65 Synchrotron self-absorption If you can emit you can also absorb Synchrotron is no exception With Maxwellians it would be easy (Kirchhoff law) to get the absorption coefficient But with power laws? Help: electrons able to emit n are also the ones that can absorb n

66 Log N( N(g) g) A useful trick g -p Many Maxwellians with kt=gmc 2 Log g I(n) = 2 kt n 2 /c 2 = 2 gmc 2 n 2 /c 2 n 5/2 B 1/2 ~ There is no K! n = g 2 eb g ~ (n/ n/b) 2pmc B) 1/2

67 From data to physical parameters n t belongs to thick and thin part. Then in principle one observation is enough get B insert B and get K

68 Inverse Compton

69 Inverse Compton Scattering is one the basic interactions between matter and radiation. At low photon frequencies it is a classical process (i.e. e.m.. waves) At low frequencies the cross section is called the Thomson cross section, and it is a peanut. At high energies the electron recoils, and the cross section is the Klein-Nishina one.

70 Thomson scattering n 1 n 0 q = scattering angle hv << m 0 e c2 tennis ball against a wall The wall doesn t move The ball bounces back with the same speed (if it is elastic) n 1 = n 0

71 Thomson cross section ds T dw = r (1+cos2 q) a peanut s 8p T = r r 0 = e 2 m e c 2

72 Why a peanut?

73 Why a peanut?

74 Why a peanut? B E

75 Why a peanut? Remember: dp e 2 a 2 dw = 4p c 3 sin 2 Q

77 2 1 ds T dw = r (1+cos2 q)

78 Direct Compton x 0 q x = hn m e c 2 x 1 x 1 = x 0 1+x (1-cos 0 cosq) Klein-Nishina cross section

79 Klein-Nishina cross section

80 Klein-Nishina cross section ~ E -1

81 Inverse Compton: typical frequencies Thomson regime x x x 1 =x x 1 Rest frame K Lab frame K

82 Min and max frequencies =180 o 1 =0o x 1 =4g2 x =0 o 1 =180o x 1 =x/4g2

83 Total loss rate Everything in the lab frame n(e) = density of seed photons of energy e=hn v rel v rel rel = relative velocity between photon and electron rel = c-vcos = c(1-bcos ) s T

84 Total loss rate s T There are many e 1, because there are many 1.. We must average the term 1-bcos 1, getting

85 { Total loss rate There are many e 1, because there are many 1.. We must average the term 1-bcos 1, getting U rad

86 { Total loss rate U rad If seed are isotropic, average over, and take out the power of the incoming radiation, to get the net electron losses: = c 4 s T cu rad g 2 b 2 3 = S 4 s T cu B g 2 b 2 3 Compare with synchrotron losses:

87 Inverse Compton spectrum The typical frequency is: n = g 2 n 0 Going to the rest frame of the e- we see gn 0 There the scattered radiation is isotropized Going back to lab we add another g-factor.

88 The real stuff down upscattering

89 The real stuff down upscattering 75%

90 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions Log g Log n e(n) ) dn = 1 4p N(g) P dg C

91 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions dg dn Log g Log n e(n) ~ 1 4p Kg-p U rad g 2 dg dn Emission is peaked! g n 4 n = g 2 n 0 3

92 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions e(n) ~ Log g 1 4p KU Log n KU rad n(2 (2-p)/2 n -1/2

93 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions e(n) ~ Log g Log n 1 4p KU rad n- a a= p-1 2

94 Synchrotron Self Compton: SSC Due to synchro, then proportional to: proportional to: t c Ba +1 n - a e c (n) ~ t 2 c Ba +1 n -a c Electrons work twice

96 End

100

101

102

103 The moving bar

104 b=0

105 b app ~ 30

106 Gravity bends space

107 Max synchro frequency Guilbert Fabian Rees 1983 There is max frequency of synchro radiation produced by shock-accelerated electrons. Even if we have relativistic shocks, so that Dg/g can be ~1 for each passage through the shock, there is a max energy attainable which corresponds to a g e for which t syn [propto 1/(g e B 2 )] is comparable to the gyroperiod (propto g /B). e This gives a max g e scaling as 1/B1/2 1/2, so that n S becomes independent of B and which corresponds to a wavelength e 2 /m e c 2 =classical electron radius: i.e. a photon of energy hn S,max = m = m e c 2 /a F = 70 MeV.

108

109 F L = d dt (gmv) = e c v x B g~constant, at least for one gyroradius a = 0 P S (q) = 2e4 3m 2 c 3 sinq g mc a = e v B sin B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q q=pitch angle r 0 =e2 /m e c 2 2 s = 8pr T 0 /3 = S 4 s cu T B g2 b 2 3 If pitch angles are isotropic

110 F L = d dt (gmv) = e c v x B g~constant, at least for one gyroradius a = 0 P S (q) = 2e4 3m 2 c 3 sinq g mc a = e v B sin B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q q=pitch angle r 0 =e2 /m e c 2 2 s = 8pr T 0 /3 = S 4 s cu T B g2 b 2 3 If pitch angles are isotropic

111 F L = d dt (gmv) = e c v x B sinq g mc a = e v B sin P S (q) = 2e4 3m 2 c 3 B 2 g 2 b 2 sin 2 q P S (q) = 2s cu T B g2 b 2 sin 2 q r 0 =e2 /m e c 2 2 s = 8pr T 0 /3 = S 4 s cu T B g2 b 2 3 If pitch angles are isotropic

112 Log N(g) Log e(n) Emission from many particles N(g) = Kg -p The queen of relativistic distributions e(n) ~ Log g 1 4p K B Log n K B2 n (2-p)/2 n -1/2 B (2-p)/2 B 1/2

113 Core

Special relativity and light RL 4.1, 4.9, 5.4, (6.7)

Special relativity and light RL 4.1, 4.9, 5.4, (6.7) First: Bremsstrahlung recap Braking radiation, free-free emission Important in hot plasma (e.g. coronae) Most relevant: thermal Bremsstrahlung What