HIGH ENERGY ASTROPHYSICS (HEA)- a (theoretical) introduction

PD Frank Rieger

MPIK & ITA Univ. Heidelberg

1 Introduction

1.1 HEA Energy Range

• Electromagnetic spectrum: Photon energies from X- up to Gamma-ray ener-

gies. Charged particle energies up to ∼ 1020 eV (Cosmic Ray Spectrum)

• X-rays: 0.1-100 keV, HE γ-rays ≥ 100 MeV, VHE γ-rays ≥ 100 GeV

• Note: 1 eV [SI]= 1.6× 10−12 erg [cgs]; 1 eV = hν = h (2.4× 1014 Hz)

• ”Non-thermal Universe” regime: ε kT ∼ 2 × 105(T/109K) eV (thermal

black body, Planck), particle distributions not Maxwellian, but e.g. power-

laws (no characteristic scale)...

Figure 1: Electromagnetic spectrum designating the range of High Energy Astrophysics.

2

1.2 Definition

High Energy Astrophysics = ”Astrophysics of high energy processes and their

application in astrophysical and cosmological contexts.’’ (M. Longair).

3

Figure 2: Example: Electromagnetic radiation (photon energy distribution) seen from an Active Galaxy(3C279, z = 0.54) as a function of frequency [Credits: ASDC].

4

Figure 3: Example: Energy flux of charged particles (cosmic rays; most of which are protons) striking theatmosphere of the Earth as a function of energy up to 1021 GeV [Credits: Hillas 2006].

5

1.3 Syllabus

1. Introduction, Energy bands, Astrophysical Sources

2. Magnetic Fields in Astrophysics (Maxwell Eq., Particle Dynamics, Drifts)

3. Radiation & Radiative Transfer (Basics, Transfer equation, black body)

4. Radiation from moving charges, Larmor’s formula, relativistic invariants

5. Synchrotron & Curvature Radiation

6. Compton scattering

7. Comptonization

8. Hadronic Processes

9. Photo-photo pair production

10. Fermi acceleration/stochastic & kinetic equation

11. Shock formation, Jump conditions, diffusive shock acceleration

12. Direct Electric Field Acceleration

13. Reconnection

6

1.4 Literature

• M. Bartelmann: Theoretical Astrophysics: An Introduction (Wiley 2012)

• A.R. Choudhuri: The Physics of Fluids and Plasmas (Cambridge UP 2008)

• T.J.-L. Courvoisier: High Energy Astrophysics (Springer 2013)

• M.S. Longair: High Energy Astrophysics (Cambridge UP 2011)

• G.R. Rybicki & A.P. Lightman: Radiative Processes in Astrophysics (Wiley

and Sons 1985)

7

2 History

Challenge: Gamma-rays, X-rays and UV with λ ≤ 300 nm (ν >∼ 1015 Hz) are

absorbed by ozone (O3) in upper atmosphere. Most of infrared radiation also

absorbed by H2O and CO2. Need space instrumentations or indirect techniques.

Figure 4: Atmospheric Transmittance of Electromagnetic Radiation [Credits: NASA/IPAC].

8

Direct space (X-rays and HE gamma-rays, since 70s) and indirect ground

explorations (VHE gamma-rays; since 90s).

Figure 5: History chart of selected X-ray mission activities during the last decades [Credits: NASA].

9

Figure 6: An artist’s illustration of the Chandra X-ray Observatory [0.1-10 keV], operating in space since 1999.The spacecraft carries a high resolution mirror assembly (HRMA), two focal plane imaging detectors (a highresolution camera [HRC] and an advanced CCD imaging spectrometer (ACIS), and two sets of transmissiongratings (LETG, HTEG) for high-resolution X-ray spectroscopy [Credits: NASA].

10

Figure 7: An artist’s illustration of the Fermi Gamma-Ray Space Telescope [100 MeV - 300 GeV] for thedirect detection of high energy gamma-rays, operating in space since 2008 and weighting about ∼ 4500 kg.The picture to the right illustrates the LAT detection technique [Credits: NASA].

11

Figure 8: Top: Working principle of imaging atmospheric Cherenkov telescopes (IACTs) for the detectionof VHE gamma-rays based on the registration of the Cherenkov light from gamma-ray-initiated air showers.Bottom: The H.E.S.S. (I+II) array in the Khoma Highlands of Namibia, exemplifying the modern IACTdesign [Credits: H.E.S.S. Collaboration].

12

3 Astrophysical Sources

• Pulsars

• Pulsar Wind Nebulae

• Supernova remnants

• Active Galactic Nuclei

• Gamma-Ray Bursts

• ....

13

4 PULSARS

4.1 Phenomenology

• Pulsar = rotating, strongly magnetized (BN ∼ 1010−15G at surface, upper

value for magnetars) neutron star, that emits coherent beams of (radio) ra-

diation along its magnetic poles.

• Neutron star results from gravitational collapse of a massive star during a su-

pernova (SN) event. Magnetic field is expected to be dipolar close to the star.

• To account for the observed pulses, rotation axis and magnetic axis (direction

of beamed emission) must be misaligned.

• Typical mass 1.4− 3.2M (Chandrasekhar limit), radius of RN ' 10 km.

• Rotation/pulse periods P = 2π/Ω between 1 ms - 9 sec: Crab=33.5 ms=0.033

sec (950 yr old); Vela=89 ms; Geminga=237 ms (nearest to us).

14

15

4.2 Basic Physics

• Lower limit for pulsar period: Centrifugal force smaller than gravita-

tional force, i.e. mv2/R = mΩ2R = m4π2R/P 2<GMm/R2, implies:

P 2 > 4π2R3/GM (1)

In terms of mean density ρ = M/(4πR3/3) one has P > (3π/Gρ)1/2 or

ρ > 3πGP 2 . For Crab this gives ρ > 1011 g/cm3.

Can also constrain radius assuming neutron star mass ∼ 1.4M, yielding

R < 170 km.

• Origin of magnetic field: Magnetic flux conservation (∫~B ·~n da=const.)

during collapse implies

BN = B0 · (R0/RN)2

(Example: - sun: size R0 ' 7 × 1010 cm; average m.f. B0 ∼ 1 G, so

BN ∼ B0 × 1010 G).

16

• Rotational energy: Pulsar is living off its rotational kinetic energy (the

”spin-down luminosity”)

Erot =1

2IΩ2 =

2π2I

P 2, (2)

I = 25MR2 the moment of inertia (uniform-density sphere) with M ' 1.4M

and R ' 10 km. For the Crab: I ' 1045 g cm2.

Decrease in rotational energy

dErot

dt= −4π2IP

P 3. (3)

For the Crab: P = 10−12.4, so dErot/dt ∼ 4× 1038 erg/s

17

• Magnetic dipole radiation= electromagnetic radiation of a varying mag-

netic moment.

Remember: magnetic dipole of current loop of current I and radius R is

~m = πcR

2I~ez (cgs) [note: B ∼ πI/(Rc), Biot-Savart]; if current varies with

time, dipole will radiate elm wave).

Magnetic dipole radiation in pulsar comes from time-dependence of mag-

netic moment of star.

Compare: Larmor’s formula (total power radiated by a non-relativistic point

charge as it accelerates):

Prad =2

3

e2a2

c3

(cgs!) with a = v the acceleration.

For a rotating electric dipole a = r sin(α) where α inclination to rotation

axis (vanishes for α = 0). With p⊥ := er sin(α) = perpendicular component

of electric dipole moment:

Prad =2

3

p2⊥c3

18

In analogy, magnetic dipole moment magnitude of uniformly mag-

netized sphere of radius R is

m0 = BR3

If magnetic field is not aligned with rotation axis, magnetic field will change

with time and therefore energy will be radiated

Prad =2

3

m2⊥c3

, (4)

(α misalignment angle). For rotating dipole, m = m0 exp(−iΩt), so that

m = Ω2m and

Prad =2

3

(Ω2m⊥)2

c3=

2

3c3(BR3 sinα)2

(2π

P

)4

(5)

with P=pulsar period. Typically at frequency ν ∼ 1/P < 1 kHz, so cannot

be observed. Power radiated away is responsible for spin-down/slow down of

pulsar rotation (P > 0)!

• Crab pulsar: Prad = −dErot/dt ∼ 4 × 1038 erg/s at ν = 30 Hz. This is

absorbed and powers the Crab Nebula.

19

• Electrodynamics: A spinning magnetic dipole acts like a unipolar induc-

tor. On closed field lines within light cylinder radius

rL :=c

Ω, (6)

(for, e.g., the Crab rL ' 108 cm ∼ 102RN) plasma co-rotates with star, and

charges re-arrange themselves (provided there are enough) until electrostatic

field is created as to cancel magnetic force (Lorentz force = e[ ~E+~v× ~B/c] = 0)

~E = −1

c~v × ~B = −(~Ω× ~r)/c× ~B (7)

(Similarly: ~E ′ = 0 in co-rotating frame/good electrical conductor, then ex-

pressing with lab.frame quantities: ~E ′ = ~E + ~v/c × ~B = 0 [trafo for non-

relativistic motion]).

Electric field needs to be supported by charge density (Poisson: ∇· ~E = 4πρ);

required Goldreich-Julian number (!) density [particles/cm3]:

nGJ = ρGJ/e = ΩB cosα/(2πec) = 0.07 B cosα/P . (8)

On open field lines, particles can escape (forming a pulsar wind); plasma

crossing light cylinder can no longer co-rotate with star (field line bending).

Electrons are accelerated to high energies in gap regions, emitting curvature

radiation, triggering pair cascades.

20

5 PULSAR WIND NEBULAE (PWNe)

5.1 Phenomenology

• PWN = the bubble of shocked relativistic particles produced when pulsar

wind interacts with its environment.

• Crab Nebula (associated with SN explosion in 1054 A.D.) located 2 kpc from

Earth, extension = 3.4 pc > 1010× light cylinder.

21

Figure 9: Crab Nebula - composite image: Chandra X-ray [blue], HST optical [red and yellow], Spitzerinfrared [purple]. X-ray image is smaller than others as extremely energetic electrons emitting X-rays radiateaway their energy more quickly than lower-energy electrons emitting in optical and infrared [Credits: NASA].

22

5.2 Basic Physics

• Pulsar wind is efficiently confined by surrounding supernova remnant. The

edge of the remnant is expanding at a few 1000 km/s.

• Un-shocked wind is much faster. Wind expands until its ram pressure is

balanced by surrounding nebula. Formation of a hydrodynamical pulsar

wind termination shock (TS) inside nebula, which slows down the wind and

leads to randomization of particles.

• TS location given when pressure balance between relativistic wind (with total

magnetic and particle pressure) and non-relativisitc nebula is reached. For

the Crab Nebula at approximately 0.1 pc from the pulsar.

23

• Rough estimate (Rees & Gunn 74): Balance ram pressure of wind with en-

ergy reservoir in nebula accumulated steadily over its lifetime (ignoring, e.g.

adiabatic and radiative losses, anisotropy etc):

EtTS/(4πR3TS) = Etage/(4πR3

PWN)

with tage = RPWN/vPWN age of nebula and tTS = RTS/c light travel time to

TS, E spin-down luminosity. This yields

RTS ∼ RPWN

(VPWN

c

)1/2

. (9)

• The outward velocity (for r > RTS) of the relativistic gas accumulated in the

nebula decreases smoothly from ∼ c/√

3 at RTS to vPWN at RPWN, varying

roughly at r−2.

24

6 SUPERNOVA REMNANTS (SNRs)

6.1 Phenomenology

• Supernova (SN) explosions (ESN ∼ 1051 erg/s) drive cold and dense SN

ejecta with highly supersonic speed into ambient medium creating a shock

wave.

• SNR=the expanding cloud of hot gas generated by a SN explosion. SNRs

are usually observed as non-thermal radio (synchrotron) sources.

• Typical numbers: Mej ∼ (1.4 − 10)M, thus (for Ek,ej ' ESN) initial

vej = (2Ek,ej/Mej)1/2 ' 104(ESN/1051erg/s)1/2(M/Mej)

1/2 km/s ISM

sound speed ∼ (1 − 10) km/s (speed at which pressure disturbances travel

in medium).

25

Figure 10: Stills from a 3D supernova animation showing the SN explosion and remnant formation [Credits:NASA, ESA, Hubble Collaboration].

26

Figure 11: Kepler SNR (SN in 1604, distance 3− 6 kpc) - composite image: Chandra X-ray (blue and green),HST optical (yellow), and Spitzer infrared (red), showing a cloud of gas and dust (size ∼ 4 pc) expandingat ∼ 2000 km/s. The optical image reveals gas heated up to ∼ 104 K at the position where the SN shockwave hits the densest regions of the surrounding gas. The infrared image highlights microscopic dust particlesswept up and heated by the SN shock wave. The X-ray data show regions with multimillion degree gas, orextremely high energy particles. The higher-energy X-rays (blue) come primarily from the regions directlybehind the shock front. Lower-energy X-rays (green) mark the location of the hot remains of the explodedstar [Credits: NASA].

27

6.2 Physics/SNR dynamics

• Free expansion phase (lasting a few 102 yr): Surrounding ISM has no

influence on shock dynamics. Ejection velocity and shock radius scale as

vej = (2Ek,ej/Mej)1/2 and RS(t) = vejt , (10)

respectively. Ejecta initially expand almost freely and rapidly cool adiabati-

cally to very low temperatures.

• Subsequently ambient medium is accelerated, compressed and heated. It

pushes back into the ejecta, creating a reverse shock, heating and slowing

down the ejecta. Happens when Mej = 43πR

3SWρ0, i.e., at ”sweep-up

radius”

RSW = (3Mej/4πρ0)1/3 , (11)

with ρ0 ∼ n0mp initial density of ISM. ”Sweep-up time” tSW = RSW/vej,

end of the free expansion phase.

28

Supernova Remnant Cartoon

Shocked ISMUnshocked Ejecta

Forward Shockinto Interstellar or

Circumstellar Medium

ContactDiscontinuity

Reverse Shockinto Ejecta

Shocked ISM

Forward shock moves supersonically into interstellar/circumstellar mediumReverse shock propagates into ejecta, starting from outside

ShockedEjecta

29

• Sedov-Taylor-Phase=thermal pressure-driven (adiabatic) expansion (about

104 yr) becomes relevant (cf. Bartelmann 3.5.5.): Sweep-up material M =43πR

3ρ0 is accelerated from rest to velocity v ∼ R/t. An amount of kinetic

energy Ekin = 12Mv2 ∼ 2

3πρ0R5/t2 must thus be put into the sweep-up ma-

terial by the explosion ESN (energy conservation; radiation losses are negligi-

ble during this phase, so thermal+kinetic energy=explosion energy; amount

thermal = amount kinetic). This implies

RS(t) '(

3ESN

4πρ0

)1/5

t2/5 (12)

and shock velocity

vS(t) = dR/dt ' 2

5

(3ESN

4πρ0

)1/5

t−3/5 (13)

Temperature decreases with time as kT ∼ mpv2s ∝ t−6/5.

• At some point, T < Trecomb ∼ 106 K (∼ 1 keV), gas recombines rapidly and

cooling function increases steeply (cooling arises mainly due to deposition of

energy by electron collisions with C,N,O grains and by subsequent radiation

in the infrared, cf. Kahn 1976 approximation). Radiative SNR phase starts....

30

7 ACTIVE GALAXIES

7.1 Phenomenology

• Galaxy that shows peculiar spectral features not related to ordinary stellar

processes (bright, variable core region, outshining light of all stars by up to

a factor 103; non-thermal continuum emission).

• Only a few percent of all galaxies are active.

• Nuclear region (AGN=Active Galactic Nuclei) harbors central engine con-

sisting of supermassive black hole (∼ 106− 1010M), accretion disk and two

collimated relativistic outflow/jet (in radio-loud objects).

31

Figure 12: Image of the nearest (d ∼ 3.7 Mpc) radio-loud AGN Centaurus A (Cen A), exhibiting collimatedlarge-scale jet (∼ 4 kpc) emerging from the central region.

32

Figure 13: Sketch of the central engine in the nuclear region of a radio-loud active galaxy. Radio-quiet AGNare thought to show no collimated jets (either, because they did not get started, or because they are disruptedquickly).

33

7.2 Basic Physics

• Eddington luminosity: For matter to be able to fall onto black hole,

outward directed radiation pressure force ≤ gravitational force.

For each electron, there is a proton electromagnetically coupled. Gravita-

tional force per electron-proton pair: Fg ' GMBHmp/r2.

Outward energy flux at some distance r is F = L/4πr2, where L is luminos-

ity (erg/s) of source. Momentum carried by photon=energy/c, so outward

momentum flux or pressure Prad = F/c = L/4πr2c.

Outward radiation force on a single electron given by multiplication with

cross-section for interaction (Thomson scattering of photons by free elec-

trons), Frad = σTL/(4πr2c).

Requirement Frad ≤ Fg, i.e., σTL/(4πr2c) ≤ GMBHmp/r2 implies

LEdd ≤4πGcmp

σTMBH ' 1.26× 1046(MBH/108M) erg/s (14)

34

• Powering AGN: Conversion of mass to energy at some efficiency η: E :=

ηMc2. Thus, rate at which energy can be emitted from a source is

L = dE/dt = ηMc2

where M = mass accretion rate (gram/sec).

The rate at which potential energy (U = GMBHM/r) of infalling matter

(mass M) can be converted to radiation is L = dU/dt ' GMBHM/r, hence

η ∝MBH/r. Typically η ∼ 0.1.

Eddington accretion rate:

MEdd =LEddηc2∼ 2.2 (MBH/108M)M/yr . (15)

35

8 GAMMA-RAY BURSTS (GRBs)

8.1 Phenomenology

• GRB = short burst of gamma-rays, ranging from 10−3 − 103 sec

• observations by BATSE on CGRO (1991-2000), identified as GRB yymmdd

• huge variety of bursts

Figure 14: BATSE light curves of GRBs

36

• classification: short bursts ≤ 2 sec, long bursts ≥ 2 sec.

• Long GRBs are on average spectrally softer (Fermi/GBM)

Figure 15: GRB Durations from the BATSE 4B (1991-1996) Catalog (energy range ∼ 25 keV to ∼ 2 MeV).T90 = time over which a burst emits from 5% of its total measured counts to 95%.

37

• Cosmological origin: (1) isotropic distribution on sky, (2) measurement of

afterglow of GRB970228 in optical, absorption lines z = 0.695.

• implies huge burst luminosities (isotropic-equivalent) Lγ>∼ 1050 erg/sec

+90

-90

-180+180

2704 BATSE Gamma-Ray Bursts

10-7 10-6 10-5 10-4

Fluence, 50-300 keV (ergs cm-2)

Figure 16: Skymap: Location of 2704 GRBs recorded by BATSE over its 9 year of mission. Color-code givesfluence = energy flux of the burst integrated over the total duration of event. Long duration, bright burstsappear in red, and short duration, weak bursts appear in purple. Grey for bursts with incomplete data.

38

8.2 Physics

• Pair production (γγ → e+e−) - optical depth: Naively

τ ' σγγ nT r ∼ σTLγ

4πrcεγ∼ 1012 1 (16)

with nT ' Lγ4πr2cεγ

and r = c∆t, t = 10−3 sec, εγ = 1 MeV

⇒ should not expect to detect gamma-rays !?

⇒ Relativistic Motion!

• Photosphere = innermost region from which photons can be observed (last

scattering)

• Physical scenarios (progenitors):

long bursts = collapsar (superluminous supernova)

short bursts = binary merger (e.g. neutron star/NS – neutron star/NS):

First direct measurement of a (short) GRB engine: GRB 170817A – nearby (d ∼ 40 Mpc) binary NS merger;

detected in grav. waves (LIGO-Virgo), seen ∼ 2 sec later in γ-rays by Fermi/GBM (10 keV-1 MeV).

39

Figure 17: GRB progenitors & illustration of the internal /external shock scenario (credit NASA).

40