high-energy astrophysicsgarret/teaching/hea-2016-lec9.pdf · high-energy astrophysics: synopsis 1)...
TRANSCRIPT
M.Phys.&M.Math.Phys.
High-EnergyAstrophysics
Garret Cotter
High-EnergyAstrophysicsMT2016Lecture9
High-Energy Astrophysics: Synopsis
1) Supernovablastwaves;shocks.
2) Accelerationofparticlestoultra-relativisticenergies.
3) Synchrotronemission;totalpowerandspectrum
4) Synchrotronself-absorption,populationageing,radiogalaxies.
5) Accretiondiscs:structuresandluminosities.
6) Accretiondiscs:spectra,evidenceforblackholes.
7) Relativisticjets;relativisticprojectioneffects;Dopplerboosting.
8) CosmicevolutionofAGN;high-energybackgroundradiationandcosmic
accretionhistoryofblackholes.
9) Bremsstrahlung;inverse-Comptonscattering;clustersofgalaxies;Sunyaev-
Zel’dovich effect.
10) Cosmicraysandvery-high-energygammarays;Cherenkovtelescopes.
Today’s lecture
• Inverse-Compton scattering.
• Hot plasma in galaxy clusters and thermal bremsstrahlung.
• Inverse-Compton scattering in radiosources and galaxyclusters.
Thomson, Compton and Inverse-Compton scattering
Inverse-Compton scattering is a mechanism which is seen in bothhighly-relativistic and “merely” very hot plasma, and today we shallsee examples of this in both AGN and in clusters of galaxies.
First however we will remind ourselves of the low-energy limit forelectron/photon scattering, namely Thomson scattering. Here theelectron has little or no kinetic energy and the incident radiation hasvery little power; we simply treat the interaction as the oscillation ofthe electron in response to an incident electromagnetic wave.
Thomson scattering
Incident EM wave
Electron oscillates sinusoidally: dipole emission uniformly in all azimuthal angles
The scattered light is polarized with its E vector parallel to theacceleration of the electron. Recall from classicalelectromagnetism that we can define the Thomson cross-sectionhere, such that the power radiated is
P = �T
curad
where c is the speed of light and urad
is the energy density of theincoming radiation field.
We see Thomson-scattered light in many astrophysical situations,typically where optical or ultraviolet light is scattered by relatively“cold” electrons (e.g. in the ⇠ 10
4 K phase of the interstellarmedium). Scattered, polarized, light from young stellar outflowsand in AGN allows us an indirect view of the central regions.
Compton scattering
When the momentum of the incident photons becomes significant,we have to treat the scattering process as a relativisticparticle-particle collision. This was originally experimentallydemonstrated by Compton’s measurement that the wavelength ofX-rays increases when they are scattered against electrons.
α
θIncident photon energy E1
Outgoing photon energy E2
Outgoing electron energy mc^2γ
The solution to this is Compton’s famous result
E1
E2
= 1+
E1
mc2(1 � cos ↵)
However in high-energy astrophysical situations we find the inverse
of this process often occurs. With relativistic, or extremely hotthermal electrons, scattering against radio-wavelength photons, thephotons are scattered up to high energy at the expense of theelectron energy.
To calculate the rate at which electrons lose energy toinverse-Compton scattering we shall use the same trick as we usedfor synchrotron emission: transform into the instantaneous restframe of the electron and use the fact that the total power emitted isLorentz invariant.
Inverse-Compton: calculation
For radio-wavelength photons, the photon energy in the electronrest frame will always be << mec2, even for electrons with Lorentzfactors of many thousands. So we know that the power emitted inthe electron rest frame is given by
P 0= �
T
cu0rad
and our task is to determine the energy density of the radiation fieldin the electron rest frame, u0
rad
.
In the rest frame of the electron, the incident energy density fromsome observed angle ✓ is boosted by two relativistic Dopplerfactors; one because the photon energy is increased, and onebecause the photon arrival rate is increased. So we have
u0rad
(✓) = urad
[�(1 + �cos ✓)]2
Now we must average over all incident angles
u0rad
=
4
3
urad
(�2 �1
4
)
P = P 0=
4
3
�T
curad
(�2 �1
4
)
Inverse-Compton calculation cont’d.
There is a subtlety here which is easy to miss among the algebra.The power P we have calculated is the rate at which the electron“emits” scattered energy in high-energy photons. But we mustremember that the incident photons carry a power �
T
curad
. So thenet rate at which the electron energy decreases is
dE
dtIC
=
4
3
�T
curad
(�2 �1
4
) � �T
curad
=
4
3
�T
curad
(�2 � 1)
=
4
3
�T
curad
�2�2
And we have our final result. Note that it has just the same form asthe relation for energy lost by synchrotron electrons:
dE
dtsynch
=
4
3
�T
cumag
�2�2
Synchrotron self-Compton
Synchrotron electrons can inverse-Compton scatter low-energy photons up toX-rays and �-rays. The sources of the photons can be
• The synchrotron radio photons themselves.
• Optical/UV light from the AGN nucleus.
• Cosmic Microwave Background photons.
Self-Compton against the CMB is observationally important because we know
urad
, and so we can infer the Lorentz factors of the synchrotron electrons from
the observed power in up-scattered X-rays.
Inverse-Compton X-rays from hotspots in Cygnus A
Synchrotron & Compton component models I
14 William J. Potter and Garret Cotter
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-6 10-4 10-2 100 102 104 106 108 1010 1012
νFν(
erg
s-1 c
m-2
)
eV
SynchrotronInverse-compton
Accretion discPKS0227
Figure 6. This figure shows the results of fitting the model to the SED of PKS0227 using a transition region within the dusty torus. The model fits theobservations well across all wavelengths including radio observations. We find the model fit requires a high jet power, high Lorentz factor jet observed at asmall angle to the jet axis. We find that the inverse-Compton peak is due to scattering of Doppler-boosted dusty torus photons at high energies and CMBphotons at low energies.
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-6 10-4 10-2 100 102 104 106 108 1010 1012
νFν(
erg
s-1 c
m-2
)
eV
SynchrotronAccretion disc
Total ICSSC
EC (CMB)EC (Accretion disc)
EC (BLR)EC (Starlight)
EC (Dusty Torus)EC (NLR)PKS0227
(a) The fit to PKS0227 showing the different contributions to the inverse-Compton emission.
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-6 10-4 10-2 100 102 104 106 108 1010 1012
νFν(
erg
s-1 c
m-2
)
eV
Total<105Rs
105Rs<x<106Rs106Rs<x<107Rs
x>107RsPKS0227
(b) The fit to PKS0227 showing the emission from different distancesalong the jet
Figure 7. This figure shows the different inverse-Compton components in Figure a and the jet emission from different distances in Figure b, using a transitionregion within the dusty torus (Fit 2). Figure a shows that the inverse-Compton emission is produced by scattering dusty torus photons at high energies whilstthe x-ray emission is due to scattering CMB photons. Figure b shows that the optically thin synchrotron emission is dominated by the transition region, withthe radio emission coming from larger distances as we expect. The high energy inverse-Compton emission originates close to the transition region within thetorus whilst the x-ray emission due to scattering CMB photons comes from further along the jet.
We find that the inferred black hole mass of a transition regionwithin the BLR is relatively low and the high peak frequency of thecorresponding accretion disc radiation makes fitting the spectrumdifficult. In this fit we use a separate black hole mass for the ac-cretion disc M
acc
and jet geometry M . For the value of Macc
we
use 2 ⇥ 10
9
M� found by Ghisellini et al. (2009) from fitting anaccretion disc to the spectrum.
c� 2011 RAS, MNRAS 000, 1–19
Synchrotron & Compton component models II
New constraints on the structure and dynamics of black hole jets 9
RT
RT
RT Jet Power
Max. bulk Lorentz factor RT1/4
RT/xT Jet Power
xT
FSRQs:
10-3/0.1pc 5x1036W (~5x10-4LEDD)
0.1/10pc
2/200pc 1040W (~1LEDD)
BL Lacs:
5x1038W (~0.05LEDD)
BL Lacs - Small radius transition region with large magnetic field strength leading to high peak synchrotron frequency. Gamma rays dominated by SSC emitted within transition region.
xT
FSRQs - Large radius transition region with small magnetic field strength leading to low peak synchrotron frequency. Gamma rays dominated by scattering CMB photons at large distances.
Figure 5. A summary of our main results. The reader may find it useful to refer to the jet schematic in Fig. 1 to understand the jet geometry and basicassumptions of our model.
ing lifetimes for these high energy electrons decreases rapidly andso it is difficult to replenish this high energy population and main-tain Compton-dominance via SSC (unless the electron spectrum,N
e
(E
e
) / E
�↵
e
, has a very low spectral index, i.e. ↵ < 1, so thatthe majority of the energy in the electron population is concentratedin the highest energy electrons).
In FSRQs we find that the radius of the brightest synchrotronemitting region, constrained by fitting the synchrotron break, is toolarge, and the magnetic field strength too small, for substantial SSCemission to occur. This is because SSC emission requires a largeenergy density of synchrotron seed photons to Compton up-scatterand the power emitted by synchrotron radiation is proportional thethe square of the magnetic field strength. For FSRQs we find theradius of the transition region to be between 0.1pc-2pc and thecorresponding distance to be ⇡ 10pc-200pc. At these large dis-tances which are well outside of the BLR (R
BLR
< 1pc, e.g. Kaspiet al. 2005) and outside the dusty torus (R
DT
< 10pc, e.g. Elitzur2006 and Nenkova et al. 2008), we find the high energy emissionis well fitted by scattering CMB photons. Since inverse-Comptonscattering of external photon sources is generally required to fit tomost low-peak frequency, Compton-dominant FSRQ spectra, it isno surprise that most previous studies have required the brightestemitting region to occur within the BLR or dusty torus, since thesewere the only external photon sources which were modelled (e.g.Błazejowski et al. (2000), Ghisellini & Tavecchio (2008), Sikoraet al. (2009), Tavecchio et al. (2011) and Joshi et al. (2014)). How-ever, crucially, these works neglected to model the radio observa-tions. We find that by simultaneously modelling both the radio andhigh energy emission we are able to constrain the brightest regionin FSRQs, to occur at much larger distances than the BLR or dustytorus.
3.5 Limitations of a time-independent model
In this and our preceding papers we have developed the first rela-tivistic fluid jet model which calculates the emission from all sec-
tions of the jet. We decided to initially study a time-independentmodel in order to understand the average properties of the jet fluidflow before adding time-dependent perturbations. Whilst this hasthe benefit of allowing us to understand correlations between thelong-term average jet properties it does not allow us to investigatethe dramatic short-term variability of blazars. Bearing in mind thevery short timescales for gamma-ray flares (e.g. Albert et al. 2007,Aharonian et al. 2007 and Abdo et al. 2010) and the range in flaringbehaviour, we expect that whilst the long-term steady gamma-rayemission seems to be well fitted by scattering CMB photons at largedistances, it seems very unlikely that flares at such large distancescould be responsible for the very short timescale gamma-ray vari-ability observed due to the long radiative cooling and light-crossingtimescales. We therefore expect that short timescale flaring eventsare likely to occur at much shorter distances along the jet, probablywithin the parabolic accelerating region. We shall investigate vari-ability and flaring by adding time-dependent perturbations to thesteady fluid flow in the near future.
4 CONCLUSION
In this work we have used one of the most realistic jet emissionmodels to date to fit with unprecedented accuracy to the spectra ofthe entire sample of Fermi blazars with simultaneous multiwave-length observations and redshifts from Abdo et al. (2010). Fromthis we have been able to place constraints on the basic structureand dynamics of blazar jets. Our main results are as follows:
• We find a linear correlation between the radius of the brightestsynchrotron emission region and the jet power, which we constrainvia the optically thick to thin synchrotron break. In most FSRQsthis radius (>0.1pc) is large enough to place this region, containingthe most intense particle acceleration, well beyond the broad lineregion and dusty torus.• We find a correlation between the final radius of the accelerat-
c� 2011 RAS, MNRAS 000, 1–11
X-ray emission from clusters of galaxies: thermalbremsstrahlung
X-ray emission from clusters of galaxies: thermalbremsstrahlung
The notion that the space between galaxies in a cluster must befilled with some material which gravitates but does not emit light (atleast, in the optical) was first proposed by Zwicky in the 1930’s. Hisobservations showed that the orbital speeds of galaxies in nearbyclusters were too great for the systems to be bound by the stellarmass of the galaxies alone.
We now know that there is typically a factor of ten times as muchmass in intra-cluster plasma as there is mass in stars, and thatthere is a factor of ten times as much mass again in some form ofmatter which gravitates but interacts via the electro-weak forcenegligibly, if at all.
Fritz Zwicky
Spherical bastards!
Whatever way you look at
them, they’re bastards!
X-ray emission from clusters of galaxies: thermalbremsstrahlung
The plasma particles in a galaxy cluster will not have neat circularorbits, but if their random thermal motions are sufficiently energetic,the plasma will not collapse in the cluster’s gravitational potentialwell.
We can estimate this temperature via the virial theorem:
kB
T ⇠GMmH
R
Here M and R are the total mass and characteristic size of thecluster. For the most massive galaxies clusters known, with total
masses on the order of 1015M�, the plasma reachestemperatures of several keV (1 keV ⌘ 1.16 ⇥ 10
7 K).
Here we are dealing with a thermal distribution of energies in theplasma: even the electrons, at rest mass 511 keV, are only barelyrelativistic at these temperatures. However because the plasmadensity is so low, we don’t get a black-body spectrum. The emittedradiation is in the form of thermal bremsstrahlung.
Bremsstrahlung: calculation
Impact parameter b
Electron speed v vt = 2b
Electron is accelerated in a region of length
Stationary ion, charge Q
An individual electron being accelerated will emit a very short pulseof radiation.
Bremsstrahlung: calculation cont’d.
Acceleration of the electron is given by:
a =
Qe
4⇡me✏0
b2
Power from an accelerated electron (Larmor):
P =
e2a2
6⇡✏0
c3=
Q2e4
96⇡3m2
e ✏30
b4c3
Time taken is t = 2b/v so the total energy radiated by a singleacceleration event is
E ⇡Q2c�
T
8⇡2✏0
b3v
Bremsstrahlung: calculation cont’d.
To get the spectral shape we use the same trick as for synchrotronemission: take the Fourier transform. The FT of a sharp pulse ofduration t is broad in frequency space, with a cutoff at ⌫
max
⇡ 1/t.So we divide by 1/t to estimate the energy per unit frequency
E⌫d⌫ ⇡Q2c�
T
4⇡2✏0
b2v2d⌫
Recall this is for a single electron. Next we integrate over theelectron impact parameters.
Bremsstrahlung: calculation cont’d.
Number of collisions per unit time at impact parameter b per ion:
Ndb = nev2⇡bdb
Number of collisions per unit time at b for all ions:
N 0db = neniv2⇡bdb
So we get the total emissivity (power per unit volume per unitfrequency) via:
j⌫d⌫ ⇠Z b
max
bmin
Q2cneni�T
4⇡✏0
bvdbd⌫
j⌫d⌫ ⇠Q2cneni�
T
4⇡✏0
vln
bmax
bmin
!
d⌫
Bremsstrahlung: calculation cont’d.
Next estimate the impact parameters. We have an upper limit infrequency of ⌫
max
so
bmax
⇠v
2⌫
And the closest impact parameter is governed by the quantum limit
mvbmin
⇠ h
So we get to
j⌫d⌫ ⇡Q2cneni�
T
4⇡✏0
vln
mv2
2 h⌫
!
d⌫
Since we are dealing with a thermal distribution of particle energies,we can approximate 1
2
mv2 ⇠ kB
T . Notice immediately that thismeans photon energies above k
B
T become exponentially unlikely.
So we have shown the significant properties of the thermalbremsstrahlung spectrum:
• Emissivity is proportional to the square of the plasma density.
• Emissivity varies as v�1 and hence as T�1/2.
• The spectrum has a sharp cutoff above photon energies⇠ k
B
T
• From observation of bremsstrahlung we can measure ne andTe.
Inverse-Compton in cluster plasma: Sunyaev-Zel’dovich effect
A cluster of galaxies sitting in deep space will be illuminated(almost) isotropically by the CMBR. However, as the CMBRphotons pass through the cluster, some fraction of them will beinverse-Compton scattered by the cluster plasma. In effect, theCMBR will be heated by the cluster. The rate of change of photonoccupancy is given by the Kompaneets equation:
n =
✓�T
neh
mec
◆1
!2
@
@!
⇢!4
n(n +1)+
kT
h
@n
@!
��
Yakov Borisovich Zel’dovich
Happily this simplifies greatly if Tgas
� TCMB
and we observe inthe Rayleigh-Jeans region. Here, the fractional change inbrightness of the CMBR travelling through a column of plasma willbe:
�I⌫
I⌫= �2
Zne�
T
kB
T
mec2dl
Note that we don’t get a higher temperature CMBR spectrum as aresult of this process; rather, the black-body spectrum is shifted tothe right, as the photon numbers are conserved, but the meanphoton energy is slightly increased (and the energy distribution isbroadened by the scattering). For typical massive clusters, theenergy change is of order 10�4.
Frequency
Brig
htne
ss
So in the Rayleigh-Jeans region we see a small dip in brightnesstowards the cluster. Knowing ne and Te from an X-ray observation,we can calculate the line-of-sight depth of the cluster.
There is another very profound consequence: whatever thedistance to the cluster, the fractional change in the CMBRspectrum is the same. A cluster at z = 0.01 gives the sameSunyaev-Zel’dovich effect as one at z = 1 or more!
