Particle Acceleration Particle Acceleration in Compact Objectsin Compact Objects

Demosthenes KazanasDemosthenes Kazanas

NASANASA

Goddard Space Flight CenterGoddard Space Flight Center

There is plenty of evidence for the There is plenty of evidence for the presence of particle presence of particle acceleration in compact objects:acceleration in compact objects:

i.i. High (and low) energy emission High (and low) energy emission from pulsars.from pulsars.

ii.ii. High (and low) energy emission High (and low) energy emission from plerionic SN remnants.from plerionic SN remnants.

iii.iii. Emission from 10Emission from 1099 – 10 – 102727 Hz in Hz in Active Galactic Nuclei.Active Galactic Nuclei.

OutlineOutline

Direct particle acceleration by Direct particle acceleration by electric fields (in EM gaps).electric fields (in EM gaps).

Bulk acceleration of particles in MHD Bulk acceleration of particles in MHD flows.flows.

Stochastic Acceleration (shocks, Stochastic Acceleration (shocks, turbulence).turbulence).

Dynamic Effects of accelerated Dynamic Effects of accelerated particles (effects on accretion disks, particles (effects on accretion disks, outflows). outflows).

The Seven Highest-Confidence The Seven Highest-Confidence Gamma-ray PulsarsGamma-ray Pulsars

Power peaked in Power peaked in -rays-rays No pulsed emission No pulsed emission

above 20 GeVabove 20 GeV Increase in hardness Increase in hardness

with agewith age

High-energy turnoverHigh-energy turnoverIncrease in hardness Increase in hardness with agewith age

Thermal component Thermal component appears in older appears in older pulsarspulsars

Broad-band spectra

Must distinguish between Must distinguish between acceleration of individual acceleration of individual particles and acceleration in bulk.particles and acceleration in bulk.

These two are generally distinct These two are generally distinct processes, however, there are processes, however, there are cases in which they are intimately cases in which they are intimately related.related.

The most obvious evidence of the The most obvious evidence of the presence of acceleration of presence of acceleration of particles is that of pulsars.particles is that of pulsars.

Rotating Magnetic Rotating Magnetic FieldField

Formation of an Formation of an outflowoutflow

The rotation of the highly conducting The rotation of the highly conducting neutron star crust generates enormous neutron star crust generates enormous potential differences over the surfacepotential differences over the surface

above the surface => very above the surface => very large outward-acting unbalanced large outward-acting unbalanced electric stresseselectric stresses

A charged magnetosphere is A charged magnetosphere is spontaneouslyspontaneously built up in order to built up in order to short-out the parallel component of the short-out the parallel component of the electric field (Goldreich-Julian 1969):electric field (Goldreich-Julian 1969):

BE ||

GJ

The density of charge carriers can be easily estimated:

This density co-rotates with the pulsar out to the light cylinder. Beyond that the magnetic stresses cannot confine the plasma and mustopen-up, i.e. the dipole is not a validmagnetospheric solution

444 ec

B

eR

B

e

En LC

LC

LCGJ

The flux of the open field lines at thelight cylinder defines the polar cap of thepulsar, as the region of the last open field line

22* LCLCpc RBRB

2/1

**

LCpc R

RRR

The pulsar slow down can then The pulsar slow down can then be worked out in a simple way. be worked out in a simple way. It does not require the pulsar It does not require the pulsar to be misaligned; the same to be misaligned; the same slow down works out for a slow down works out for a purely aligned magnetosphere.purely aligned magnetosphere.

246*

*

2

*

2/3

*

2*

22

BRVIW

BRc

RB

c

RRB

c

vRV

RBcnRI

pcpc

GJpc

Surface Fields and Surface Fields and CurrentsCurrents

The presence of a sufficiently dense plasmaThe presence of a sufficiently dense plasmacancels all parallel cancels all parallel EE. Discrepancy between. Discrepancy betweenthe actual charge density from that of the actual charge density from that of GJGJleads to gaps (leads to gaps (Polar Cap; Outer Gap modelsPolar Cap; Outer Gap models). ). Particles can be accelerated at gaps and lead Particles can be accelerated at gaps and lead

to to the creation of photons. The resulting spectra the creation of photons. The resulting spectra depend on the ensuing interactions (A. depend on the ensuing interactions (A.

Harding)Harding)The EM potentials available are of order of The EM potentials available are of order of 10101818 ( (PP/ms) /ms) BB1515 eV.eV. As such they As such theycould produce galactic cosmic rays up to thecould produce galactic cosmic rays up to theenergy of ankle (Arons 02). energy of ankle (Arons 02).

The problem of pulsar magnetosphericThe problem of pulsar magnetospheric

emission, as is the case with all problems emission, as is the case with all problems

that involve magnetic fields (which cannotthat involve magnetic fields (which cannot

be shorted out) is a global one. One has to be shorted out) is a global one. One has to

solve for the currents and the resultingsolve for the currents and the resulting

magnetic fields over all space before we magnetic fields over all space before we cancan

decide the dynamics and radiation decide the dynamics and radiation emissionemission

from a pulsar. from a pulsar.

The magnetosphere is The magnetosphere is determined by the determined by the

balance between the current and balance between the current and electro-electro-

static forces in the static forces in the magnetosphere. Thesemagnetosphere. These

are given by the “Pulsar are given by the “Pulsar Equation”Equation”

AARx

xzxxx

x LC

22

2

2

22 2

1)1(

The parameters involved The parameters involved areare Poloidal Poloidal

electric electric current:current:

Magnetic flux:Magnetic flux: Force-free:Force-free: Space charge Space charge

density:density:21

2

4 x

AAB

cz

e

RBAA )(

01 EBJ ec

Contopoulos, Kazanas & Fendt 1999; Gruzinov Contopoulos, Kazanas & Fendt 1999; Gruzinov 20052005

The solution is smooth, contains a The solution is smooth, contains a returnreturnCurrent, it contains a zero charge line Current, it contains a zero charge line and and it provides the it provides the wind asymptotic wind asymptotic structurestructure..

Emission is expected at places where Emission is expected at places where MHD is violated (polar cap, zero MHD is violated (polar cap, zero charge line, return current boundary, charge line, return current boundary, but not the Light Cylinder).but not the Light Cylinder).

Pulsar Winds/The Pulsar Winds/The -Problem

For the geometry of the magnetic lines beyondthe Light Cylinder (split monopole) for whichBp= 1/R2, B= 1/ R , = 1/R2.Therefore their ratio, ~106 near the LC

should be independent of the radius R .However, the spectra of the Crab nebula However, the spectra of the Crab nebula

need aneed avalue value ~3 10-3 to fit the observed spectrum

andfor Vela one needs ~1.

The asymptotic (split) monopole The asymptotic (split) monopole geometrygeometry

of CKF allows a crack at this problem:of CKF allows a crack at this problem:

The energy conservation equation The energy conservation equation along a fieldalong a field

line has the form:line has the form:

While the flux freezing condition readsWhile the flux freezing condition reads

*1

c

v

R

R

LC

p

p

LC B

B

c

v

R

R

c

v

Under force-free conditions

the energy equation reads

Leading eventually to:

(Contopoulos & DK 2002)

pLC

BR

RB

*

2

11

c

v

R

R p

LC

LCLC R

R

R

R

2/1

2

22*

Under conditions of a Under conditions of a monopole geometrymonopole geometry the Lorentz the Lorentz

factor of the flow factor of the flow increases linearly with distanceincreases linearly with distance. This . This

happens as long as the effects of inertia are negligible. happens as long as the effects of inertia are negligible.

Beyond this point the field geometry should deviate Beyond this point the field geometry should deviate

From monopolar and possibly part of it From monopolar and possibly part of it collimate collimate and and

part form an part form an equatorial windequatorial wind. The wind terminates at a . The wind terminates at a

shock which is responsible for the nebular emission.shock which is responsible for the nebular emission.

(The extent of monopole geometry is debatable. It may(The extent of monopole geometry is debatable. It may

extend only up to the fast magnetosonic point; then theextend only up to the fast magnetosonic point; then the

maximum maximum will be only ~ will be only ~

Plerion ComponentsPlerion Components

Vexp

TORUS

SHOCK

JET

rs

rN

Vlahakis & Konigl 2001Vlahakis & Konigl 2001

Linearly increase Linearly increase in Lorentz factor in Lorentz factor is a property of is a property of general MHD general MHD flows of flows of geometries geometries different from different from monopolar monopolar (Vlahakis&Konigl (Vlahakis&Konigl 2001)2001)

The MHD outflow acceleration and the The MHD outflow acceleration and the --Problem are related issues. They demand the Problem are related issues. They demand the simultaneous solution of the conservation simultaneous solution of the conservation equations along with the transverse force equations along with the transverse force balanc.e balanc.e First axisymmetric First axisymmetric

wind wind

solutions by Blandford solutions by Blandford

& Payne; extended to & Payne; extended to

Relativistic case by Li,Relativistic case by Li,

Chieuh, Begelman (92)Chieuh, Begelman (92)

and Contopoulos (94).and Contopoulos (94).

Solutions known only Solutions known only for for

self-similar geometry.self-similar geometry.

Flow acceleration Flow acceleration depends on assumptionsdepends on assumptionsused. LCB find logarithmicused. LCB find logarithmicacceleration with height.acceleration with height.Contopoulos (94) finds final Contopoulos (94) finds final velocity similar to that at velocity similar to that at the accretion disk at the the accretion disk at the base of the flow (Vlahakis base of the flow (Vlahakis & Konigl 04 for a more & Konigl 04 for a more recent study).recent study).

The relativistic outflows produce shocks, The relativistic outflows produce shocks, which accelerate particles and lead to which accelerate particles and lead to radiation emission. Blazarradiation emission. Blazaremission is thought to be derived this way.emission is thought to be derived this way.

The apparently thin The apparently thin

photon spectra photon spectra indicateindicate

emission from large emission from large

distances and distances and suggests suggests

association with jet association with jet

flows (Mastichiadis & flows (Mastichiadis &

Kirk 1997).Kirk 1997).

Particle accelerationParticle acceleration (in shocks, (in shocks, converging flows, turbulence) is converging flows, turbulence) is the result of an interplay the result of an interplay between particle energy gains in between particle energy gains in scattering and particle scattering and particle transport. The exponentially transport. The exponentially small probability of undergoing small probability of undergoing NN interactions with the plasma interactions with the plasma before escape, coupled with before escape, coupled with exponentially increasing energy exponentially increasing energy with the number of scatterings with the number of scatterings lead to power law distributions.lead to power law distributions.

The geometry of particle transport across a plane The geometry of particle transport across a plane shock. The upstream velocity is shock. The upstream velocity is uu11 and the and the downstream downstream uu22=u=u. The particle velocity is . The particle velocity is v. v. The The shaded region shows the fraction of particles that shaded region shows the fraction of particles that make it upstream and have a chance to accelerate.make it upstream and have a chance to accelerate.

Generic description of the acceleration Generic description of the acceleration process. Application to plane parallel process. Application to plane parallel shocks (r is the compres- sion ratio, shocks (r is the compres- sion ratio, PP(p) (p) is the integral spectrum).is the integral spectrum).

Probability of N returns: P (N) / e¡ N®

Energy of particleafter N returns: p(N)=p0 / eN¯

N =1¯

Lnµ

pp0

¶; Ln[P (p)]= ¡

®¯

Lnµ

pp0

¶; P (p) =

µpp0

¶ ¡ ®=̄

For aplaneparellel shock (J ones& Ellison 1991)

®¯

=3u2

u1 ¡ u2; P (p) =

µpp0

¶ ¡ 3u2=(u1¡ u2)

=µ

pp0

¶ ¡ 3=(r¡ 1)

Effects of acceleration on Effects of acceleration on dynamicsdynamics

The presence of relativistic particlesThe presence of relativistic particles can affect the dynamics of the flow:can affect the dynamics of the flow:

Relativistic particles reduce the fluidRelativistic particles reduce the fluidadiabatic index and increase the adiabatic index and increase the

shockshockcompression ratio compression ratio rr. This hardens . This hardens

the the spectra; most kinetic energy is spectra; most kinetic energy is converted to relativistic particles converted to relativistic particles

that that dominate the pressure. dominate the pressure.

Particle (relativistic) escape from the Particle (relativistic) escape from the system also increases the system also increases the

compressioncompressionratio of the shock with similar effect.ratio of the shock with similar effect.

(Ellison et al 2000)(Ellison et al 2000)

In the vicinity of a compact object, the strong In the vicinity of a compact object, the strong gravitational gravitational

fieldfield could separate the relativistic and the non-relativistic could separate the relativistic and the non-relativistic

populations, provided that cooling does not ; this can cause populations, provided that cooling does not ; this can cause

outflows similar to those inferred in compact objects (DK &outflows similar to those inferred in compact objects (DK &

Ellison 86); Subramanian et al (99), provided that the Ellison 86); Subramanian et al (99), provided that the

accelerated particles do not lose energy on time scales accelerated particles do not lose energy on time scales shortershorter

than free-fall.than free-fall.

Separation can also take place through the production of Separation can also take place through the production of

neutral particles (neutrons) that can increase the power of neutral particles (neutrons) that can increase the power of

relativistic outflows (Contopoulos & DK 94).relativistic outflows (Contopoulos & DK 94).

Plasma production outside an Acc. Disk from Plasma production outside an Acc. Disk from n -> p n -> p ee. For a large black hole, most neutron produced . For a large black hole, most neutron produced protons are relativistic while for a small one most protons are relativistic while for a small one most are non-relativistic. The critical value is M~10are non-relativistic. The critical value is M~1088 M_o M_o

The Radio Jets of GRS The Radio Jets of GRS 1915+1051915+105

The Radio Jets of GRS 1915+105The Radio Jets of GRS 1915+105

The Radio Jets of GRS The Radio Jets of GRS 1915+1051915+105

Acceleration in Accretion Acceleration in Accretion Disks canDisks can

result from particle-wave result from particle-wave interactionsinteractions

(e.g. Dermer, Miller, Li ’96). (e.g. Dermer, Miller, Li ’96). Acceler.Acceler.

Time scales are quite short Time scales are quite short and shouldand should

Produce accelerated Produce accelerated populations.populations.

Accretion Disks could Accretion Disks could accelerate accelerate

particles by their shearing particles by their shearing motionmotion

(Subramanian et al. ’99). (Subramanian et al. ’99). This leads This leads

to 2to 2ndnd order acceleration. order acceleration.

Slope and Maximum EnergiesSlope and Maximum Energies

The slope of accelerated The slope of accelerated population depends on population depends on the interplay between the interplay between energy gain per energy gain per interaction and escape interaction and escape probability (e.g. the probability (e.g. the Comptonization Comptonization parameter parameter kT/mckT/mc22). ). For shocks this is 3/(r-1) For shocks this is 3/(r-1) (integral slope).(integral slope).

The acceleration rate is The acceleration rate is hap-pening on the gyro-hap-pening on the gyro-period at the given field period at the given field ~ E(eV)/B(G)~ E(eV)/B(G)

Maximum energy is given Maximum energy is given by the balance between by the balance between accele-ration and losses accele-ration and losses or escape from the or escape from the system. For electrons this system. For electrons this energy is ~TeV (blazars), energy is ~TeV (blazars), while for protons it gets while for protons it gets close to 10close to 102020 eV. eV.

Eventually, the Eventually, the max.energy is roughly ~R max.energy is roughly ~R (v/c) B, where R is the (v/c) B, where R is the size of the system, v the size of the system, v the velocity and B the velocity and B the magnetic field.magnetic field.

Conclusions - QuestionsConclusions - Questions Particle Acceleration is a ubiquitous process in compact Particle Acceleration is a ubiquitous process in compact

objects (spectra, superluminal motions).objects (spectra, superluminal motions). Particles can get accelerated in EM gaps (deviations from Particles can get accelerated in EM gaps (deviations from

MHD conditions). Energy/particle ~ Potential drop across MHD conditions). Energy/particle ~ Potential drop across gap.gap.

MHD acceleration in rotating magnetospheres. Conversion of MHD acceleration in rotating magnetospheres. Conversion of magnetic to kinetic energy of high efficiency (depends on magnetic to kinetic energy of high efficiency (depends on current distribution). Lorentz factors of ~10 – 10current distribution). Lorentz factors of ~10 – 1066 possible. possible.

Particle acceleration possible in turbulent, shocked plasmas. Particle acceleration possible in turbulent, shocked plasmas. Conversion of KE to relativistic particles with high efficiency. Conversion of KE to relativistic particles with high efficiency. Max. energy depends on particulars of system.Max. energy depends on particulars of system.

Why don’t we see prominent non-thermal emission in the Why don’t we see prominent non-thermal emission in the spectra of accreting binary sources? Why are most AGN radio spectra of accreting binary sources? Why are most AGN radio quiet?quiet?

Does acceleration take place in the Acc. Disks of AGN, GBHC? Does acceleration take place in the Acc. Disks of AGN, GBHC? If yes, do the accelerated particles play any role in the If yes, do the accelerated particles play any role in the dynamics of these disks? Are observational tests to dynamics of these disks? Are observational tests to distinguish between these possibilities? distinguish between these possibilities?

The geometry of particle transport across a shock. The geometry of particle transport across a shock. The upstream velocity is The upstream velocity is uu11 and the downstream and the downstream uu22=u=u. The particle velocity is . The particle velocity is v. v. The shaded region The shaded region shows the fraction of particles that make it shows the fraction of particles that make it upstream and have a chance to accelerate.upstream and have a chance to accelerate.

tion (BP81, Eq. 18) for thephoton occupation number n(r;º

vb ¢r n +13r ¢(

c·

r n) +13(r ¢vb) º

@n@º

= ¡ ~j (r;º);

;º) (PB81) is given in terms of n(r;º)

F (r;º) = ¡1

3· (r)r n ¡

13vbº

@n@º

;