Introductory Lecture on Astrophysics Part II: non-thermal phenomena - - PowerPoint PPT Presentation

Introductory Lecture on Astrophysics Part II: non-thermal phenomena

Pasquale D. Serpico

• In Lecture I, I argued that modern astrophysicists do not study only

“visible light” to infer properties of celestial bodies. They use also “invisible” photon bands, but are more and more interested in particles different from photons, too.

• This field of “High Energy Astrophysics” has witnessed a very rapid

growth over the last decades, stimulated by the possibilites opened by the space age, but also “contamination” with particle physics technology and techniques

• Nonetheless, some of the key questions at its core, remain only

partially answered despite a century of investigation! I’ll try to introduce you the main pillars of the current paradigm on these topics.

Recap Recap & & Intro Intro

Most of these topics will be covered more in detail in other Lectures, in particular by Johannes Blumer and Abelardo Moralejo, of which hopefully this represent a “natural” introduction

Non-thermal messengers Non-thermal messengers

Cosmic Rays Cosmic Rays: A : A century-old Problem century-old Problem I I II II III III IV IV

direct observation indirect observation (EAS)

• A

A long-standing issue is long-standing issue is the the origin

• rigin of the
• f the

non-thermal particle spectra non-thermal particle spectra of

• f “

“cosmic cosmic rays rays” ” hitting hitting the the Earth from outer Earth from outer space space

• main problem

main problem: : charged particles charged particles are are deflected while propagating deflected while propagating in the in the magnetized magnetized ISM: ISM: they they do do not not track back track back to their sources to their sources! ! How to identify them How to identify them? ? Possible ways to attack the problem:

• Compare what observed at the Earth

with theoretical models accounting for production and propagation of CRs.

• Try to identify the source processes

via the photons (& ν’s) emitted by the CR E-losses in/near the sources

How How do do cosmic rays cosmic rays propagate? propagate?

Charged particles deflected Charged particles deflected in a in a B-field B-field. . Their Their “ “Larmor Radius Larmor Radius” ” is is B B ⊗ ⊗ r rL

L

CRs CRs probe probe thus thus “ “small-scale inhomogeneities small-scale inhomogeneities” ” in the in the field field, , changing changing direction direction by what appear by what appear “ “random kicks random kicks” ”, , similar to brownian motion similar to brownian motion Even for protons Even for protons, , this distance is comparable to distance between neighboring stars this distance is comparable to distance between neighboring stars up up to ~PeV to ~PeV and and smaller than Galactic Sizes smaller than Galactic Sizes up up to EeV to EeV. . Macroscopically Macroscopically, , this is described as this is described as “ “diffusion diffusion” ” Fick Fick’ ’s law s law For homogeneous For homogeneous medium medium properties properties, the , the flux flux can can only change

• nly change due

due to gradients to gradients Continuity Equation Continuity Equation

Diffusion coefficient Diffusion coefficient

In a diffusive In a diffusive motion motion, in a time , in a time t t a a particle moves by particle moves by a a rms distance rms distance: : what CRs what CRs show show does not reflect necessarily present picture given by does not reflect necessarily present picture given by “ “light light” ” β=1, 3/2, 5/3... β=1, 3/2, 5/3... respectively for Bohm respectively for Bohm, , Kraichnan Kraichnan, , Kolmogorov turbulence spectra Kolmogorov turbulence spectra The functional form for D depends on the structure of magnetic field The functional form for D depends on the structure of magnetic field inhomogeneities inhomogeneities, in turn , in turn depending depending also on the flux of also on the flux of CRs CRs themselves (non- themselves (non- linear, non linear, non perturbative perturbative problem!) For example in quasi-linear theory one finds problem!) For example in quasi-linear theory one finds In general, D is parameterized as D~K E In general, D is parameterized as D~K Eδ

δ; free-parameters are fitted from data

; free-parameters are fitted from data The CR propagation problem is further complicated by other processes changing The CR propagation problem is further complicated by other processes changing Energy, nuclear species ( Energy, nuclear species (spallation/decay spallation/decay), ), “ “winds winds” ” in the Galaxy in the Galaxy… …

Diffusion-loss equation Diffusion-loss equation: : from sources to observables from sources to observables

• t = Q +
• (Dsp
• )

p (p

• ) +

+ p p2Dmom (p2) p

• (V
• ) +

p p 3 (

• V
• )
• +

frag

• decay

Fragmentation and decay terms Fragmentation and decay terms (negligible/vanishing for protons) (negligible/vanishing for protons) Convection velocity Convection velocity Diffusive reacceleration Diffusive reacceleration Adiabatic flow term Adiabatic flow term Energy loss Energy loss Source term (time, space, momentum Source term (time, space, momentum dep dep.) .) Includes Includes dec dec. ./frag /frag. for heavier nuclei . for heavier nuclei Diffusion Diffusion

 Arrival directions ~isotropic!

 Energy Spectrum ~featurless!  Chemical Composition

• Production Site
• Production Mechanism
• Propagation

Learning about sources Learning about sources via via ‘ ‘neutral neutral’ ’ E-loss particles E-loss particles

The alternative strategy is to look at “potential sources” and try to learn something from visibile, straight propagating channels, at present photons from radio to γ (in principle also ν and GW) We shall then study of HE particle lose energy, and show some examples

• f how their “waste particles” allow one to make diagnostics

Why do we expect them to “trace” what happens to non-thermal particles? That’s because Cosmic Rays unavoidably undergo energy-loss while being confined, accelerated, and while escaping the sources.

Make an educated guess about Make an educated guess about the the origin

• rigin of
• f CRs

CRs… …

Most Galactic sources are Most Galactic sources are SNRs SNRs & PSR/PWN, most extragalactic ones AGN & PSR/PWN, most extragalactic ones AGN

Electron Electron losses losses in in matter matter

• Interactions with matter are mostly relevant as E-losses at “low energy”, MeV-GeV
• Up to hundreds of MeV, the dominant loss is by Coulomb scattering with electrons

& ions and atomic ionization, using the ISM as target. These effects have little dependence on energy and are not very useful for diagnostics!

• On the other hand, deceleration of e when deflected in

the field of a nucleus provides energetic γ as “loss channel”. Although this Bremsstrahlung process is the dominant E- loss only at GeV energies (at least in the Galaxy) it provides a useful diagnostic tool even at lower energies

Bremsstrahlung Bremsstrahlung at work at work

X-ray emission from Clusters of Galaxies dominated X-ray emission from Clusters of Galaxies dominated by by Bremsstrahlung Bremsstrahlung from from hot hot gas filling space between galaxies, not by Galaxies themselves! gas filling space between galaxies, not by Galaxies themselves! The virial theorem implies ~keV temperatures for these huge bound objects! Measuring X-ray emission allows one to:

• track hot gas (main baryonic component of clusters)
• infer mass of the cluster (if virial theorem can be applied)

e e losses losses in in radiation fields radiation fields: Inverse : Inverse Compton Compton Scattering Scattering

It is the process by which a HE It is the process by which a HE e

e transfers energy & momentum

transfers energy & momentum to a low energy to a low energy “ “target target” ” photon in the environment photon in the environment photon gains energy lower energy photon electron loses some energy high energy electron Final γ energy can be understood as “double frame change”:

• In the HE e frame, γ of energy ε seen

having ε ε’ ’~ ~ γ γ ε ε.

• In this frame, if little recoil is involved,

the scattering leaves ε ε’ ’ unchanged unchanged (not momentum direction, of course!)

• Back in the the Lab frame this means

ε ε’’ ’’~ ~ γ γ ε ε’ ’ ~ ~ γ γ2

2

ε ε

Emax = (h ν)max ≈ 4 γ2 h ν0 ν / ν0

arbitrary unit

log10I(ν)

arbitrary unit

νmax / ν0

e e losses losses in in B-fields B-fields: : Synchrotron radiation Synchrotron radiation

Charge in a B-field moves along an Charge in a B-field moves along an “ “helix helix” ”, , an accelerated charge does radiate an accelerated charge does radiate For relativistic e,

• the cyclotron frequency slows down by a factor Γ
• the radiation is beamed in a cone of size 1/Γ
• a time-dilation effect exists btw e & observer frame

As a result, and when performing the frame transformation, it can be shown that a beamed, continuum spectrum arises, with a peak at doedds

Where does Where does the final the final spectrum spectrum come come from from? ?

the shape of the overall spectrum actually comes from the sum of each the shape of the overall spectrum actually comes from the sum of each electron electron’ ’s contribution. s contribution. Individual electrons spiraling around the magnetic Individual electrons spiraling around the magnetic field lines emit a spectrum that peaks at one particular frequency, field lines emit a spectrum that peaks at one particular frequency, ν

νc

c

log10 ν / νc log10F

ν νc

c

Above the critical frequency νc the spectrum drops exponentially

log10F Log10 ν/ νc

Sum of individual contributions summing the individual contributions of summing the individual contributions of many electrons with a ~power-law many electrons with a ~power-law spectrum gives the resulting quasi spectrum gives the resulting quasi power-law spectrum for SR photons power-law spectrum for SR photons

B-field B-field & & ν ν dependence dependence of the SR

• f the SR spectrum

spectrum

To a first approximation, we can associate To a first approximation, we can associate an emission at frequency an emission at frequency vc vc to the loss to the loss

• f energy of
• f energy of

a electron of energy E. For a a electron of energy E. For a population of electrons N(E), we expect population of electrons N(E), we expect Note that Note that p=2 p=2 corresponds corresponds to to an index 0.5 in an index 0.5 in SR SR Given that Given that ν νsyn

syn∝

∝ B, one derives B, one derives Plugging in the Plugging in the E-loss relation, E-loss relation, The E- The E-ν ν relation implies relation implies for a typical for a typical power law, power law,

Synchrotron Synchrotron & IC & IC losses losses

Thomson scattering cross section Thomson scattering cross section: Note the dependence

• n the mass, which explains why it is mostly relevant for

electrons

Actually, from a QFT field of view, one can see this process as a collision of a particle with a real photon (IC) or virtual one The relative power in the two channels from the same region thus measures the relative density of energy in “light” wrt. B-field → Important diagnostic tool. Both SR & IC E-loss rates have similar expressions

Let Let’ ’s s look at one look at one famous example famous example: : Crab Crab (PW) (PW)Nebula Nebula

This object is probably the “cornerstone” of High Energy Astrophysics (and one of the most observed/admired…in its field) distance ~2 kpc, age =956 yr

Inverse Compton Synchrotron

High B field (~160 µG)

Aharonian et al. 2004 ~ 80% SSC ~ 20% IC FIR,mm, CMB

Multiwavelength spectra Multiwavelength spectra: : Crab Nebula Crab Nebula

This This

• bject seems to be well explained in a framework where the spinning NS
• bject seems to be well explained in a framework where the spinning NS

injects leptons, which produce SR on the B-field & mostly the same SR photons injects leptons, which produce SR on the B-field & mostly the same SR photons are are upscattered upscattered to produce the second peak ( to produce the second peak (Synchrotron Self-Compton Model Synchrotron Self-Compton Model) ) In SSC, comparing the two peaks In SSC, comparing the two peaks allows one to deduce the B-field intensity. allows one to deduce the B-field intensity. GeV GeV TeV TeV MeV MeV keV keV Radio Radio E E2

2 dN/dE

dN/dE [Energy [Energy Emitted ] Emitted ]

Hadronic losses Hadronic losses: in : in matter matter -

• Protons

Protons

Protons usually lose negligible fraction of energy in the ISM (apart when hitting dense objects as molecular clouds) Still, π−production (via σpp~30 mb) is of crucial importance for diagnostics of diffuse π−signals (remote population of CRs) γ’ & ν’s as diagnostics of hadronic accelerators and/or of propagation Direct link with the parent population energy distribution

The Intermediate The Intermediate Latitude Spectrum from Latitude Spectrum from Fermi Fermi

Fermi-LAT Collaboration, Phys.Rev.Lett.103, 251101 (2009) Additional information e.g. from radio consistent with ISM e spectra similar to local ones

Hadronic losses Hadronic losses: in : in matter matter - Nuclei

• Nuclei

Mostly relevant if matter is dense enough (e.g. inside galaxies). For nuclei, spallation is very important.

predicted γ−ray spectrum from nuclear de-excitation of spallated species accelerated due to accretion on the GC-BH. A 5 deg. region around the GC is considered.

V.A. Dogiel et al. arXiv:0909.2110 The main consequences are:

• changed composition of CR wrt injection
• Possible (challenging) observation of γ−lines

Hadronic losses Hadronic losses in in radiation fields radiation fields

• In rarefied media with relatively large

radiation content, meson (mostly π) photoproduction dominates Under similar conditions, nuclei predominantly undergo photodissociation (less useful for diagnostics)

• This requires very energetic population of

protons or of background photons, or both It is believed to be a promising channel for extragalactic γ and ν sources, for example

Hadronic losses Hadronic losses in in extragalactic extragalactic space space

Application Application: For propagation of UHECRs

• ver extragalactic distances, most important

losses are over radiation, CMB in particular Source of “Cosmogenic Neutrinos” Source of “Cosmogenic Photons” Since Eγ~10-3 eV=10-9 MeV, threshold is

• nly at a scale of~1011 GeV=1020 eV!!!

But important source of attenuation… allowed at lower energies

UHECRs UHECRs “ “Horizon Horizon” ”

Above ~5x1019 eV, photo-pion production on CMB kinematically

• allowed. The attenuation length

drops drastically! (Greisen-Zatsepin-Kuz’min ‘66)

p+ γCMB →Δ →π+N

Cosmogenic neutrinos Above ~1018 eV, pair-production

• n CMB kinematically allowed &

dominates energy loss, reaching a maximum at 1019 eV

p+γCMB →p+e+e-

Nuclei suffer by pair-production as well,while GZK-like feature (at Z-dependent energy) is induced by photo-dissociation

“ “Gamma Gamma Horizon Horizon” ”

Also for photons, the onset of high-energy processes makes The universe opaque above a certain energy. The most important is pair production, which has a threshold

• TeV scale photons can be used

to study the EBL!

• Virtually no γ’s can reach us from

remote extragalactic space above ~100 TeV: Beyond, ν’s are the only carriers of directional information ~TeV scale for optical, PeV for CMB photons The absorption length is readily calculated as

 Neutral, keep direction (differently from CR)  No absorption on EBL (differently from γ)  HEν guaranteed; ν are CR secondaries, like (UHECR & HEγ observed)

 “Little” problem  Trace back source hadronic accelerators

 Resolve leptonic vs. hadronic dispute for TeV γ-rays  determine UHECR chemical composition (different primaries have very different cosmogenic ν yields) σ(TeV)~ pb σ(PeV) < nb σ(EeV) ~ 10nb

Neutrinos Neutrinos: : powerful tool for powerful tool for high high energy astrophysics energy astrophysics

50 m

1500 m 2500 m

300 m

IceCube Collaboration

Solutions Solutions

 huge volumes

 sparse instrumentation  natural media 1 km 1 km3: : Gigaton Gigaton scale scale! ! SuperKamiokande, Japan

Size dictated Size dictated in in order to get

• rder to get a few

a few events events per per yr if yr if ν ν spectra comparable to spectra comparable to γ γ spectra spectra measured in measured in Gal. &

• Gal. & Extragalactic Sources

Extragalactic Sources

Acceleration Acceleration of

• f particles

particles

How to How to accelerate accelerate particles particles (in (in astrophysics astrophysics)? )?

Energetics Energetics: : we must take energy somewhere! For example:

Kinetic Energy Kinetic Energy (translational in SNRs, rotational in pulsars) Gravitational Energy Gravitational Energy (accretion disks) Magnetic Magnetic (solar flares) We need to satisfy several requirements:

Mechanism for Energy Transfer: Mechanism for Energy Transfer: in general, we need to envisage

how to transfer energy from macroscopic objects into the (microscopic) acceleration of particles. Ultimately it must be electromagnetic…

Confinement: Confinement: need to check that the particle stays in the accelerator

for the time needed to accelerate it.

Lack of (significant) E-losses: Lack of (significant) E-losses: accelerating particles is useless for

explaining CR if they lose Energy too quickly… We have several candidates to supply the needed energy. The trickiest problem is the second one, first addressed by Fermi… “On the Origin of the Cosmic Radiation”,

• E. Fermi, Physics Review 75, 1169, (1949)

Think of Think of any any physical process requiring a time physical process requiring a time τ τ per cycle (with per cycle (with escape probability escape probability P Pesc

esc) repeating randomly for a time

) repeating randomly for a time T T leading leading to a fixed fractional energy gain to a fixed fractional energy gain ξ ξ

Basics Basics of

• f stochastic acceleration

stochastic acceleration

Note: Note: The resulting (cumulative) spectrum is The resulting (cumulative) spectrum is [sum geometric series with x=1-P]

Fermi Fermi mechanism mechanism (of (of second order second order) )

I.

• I. The acceleration is 2

The acceleration is 2nd

nd order in the

• rder in the

(slow) cloud velocity: inefficient (slow) cloud velocity: inefficient II.

• II. spectral index not universal

spectral index not universal (why an unbroken power-law seen?) (why an unbroken power-law seen?) III.

• III. Spectral index value typically far from

Spectral index value typically far from

• bserved ~1
• bserved ~1

Initial proposal: Initial proposal: the acceleration happens by scattering off “magnetic inhomogeneity” clouds in the ISM, which act as magnetic mirrors. E’<E E

Three main problems: Three main problems:

Vc E’>E E

Detour Detour: (Ideal) : (Ideal) Fluid dynamics Fluid dynamics

Conservation of mass Conservation of momentum Stress (or Reynolds) Tensor Conservation of Energy (includes energy change due to adiabatic transformation) But these equations have a lot of qualitatively different solutions, often fascinating due to their non-linear nature A trivial solution is for example given by a static medium, homogeneous, with a given density and pressure

Sound Sound waves waves

You are probably familiar with the “sound waves” emerging from the linearized Eqs. Perturb the “Trivial” bck. solution Linearize eqs. obeyed by small perturbations Lead to the wave equation (e.g. for δρ) Sound speed Sound speed2

2

γ γ=5/3 for =5/3 for mon

• mon. gas

. gas This solution only holds while the amplitude is small. The full non-linear evolution (unless some damping kicks in) typically leads to discontinuities discontinuities

Shocks Shocks

“Discontinuities” are abrupt changes in macroscopic variables, achieved within microscopic distances! Far from being exotic, there arise quite naturally! Mach number

The condition for entropy increase requires M>1: shocks can only form in supersonic motion. In shocks, there is a large pressure jump; also, the Kinetic Energy (partially) heats the gas

Relativistic generalization is straightforward inviscindfkbfgndnfgnh

The dynamical eqs. in this type of solutions express “conservations” across the shock, i.e. links between physical quantities “at the two sides”. For an ideal fluid Similarly, the limit conditions for pressure and temperature jump are

Plenty Plenty of

• f shocks

shocks in nature in nature… …

Even on Earth! Even on Earth! The main difference is that shock in space are The main difference is that shock in space are collisionless collisionless, i.e. the microscopic , i.e. the microscopic physics is not the collision between atoms or ions, rather the scattering over physics is not the collision between atoms or ions, rather the scattering over magnetic magnetic inhomogeneities inhomogeneities over scales as small as the

• ver scales as small as the gyroradius

gyroradius of the particles.

• f the particles.

Exercise: Exercise: Estimate the collisional length for typical Earth conditions & atomic cross-sections & for space conditions and Thomson cross-sections. Then compare with Larmor radius

Adding B-fields Adding B-fields: : Magnetohydrodynamics Magnetohydrodynamics

In presence of B-fields, fluid dynamics equation generalized to MHD. For example Since now there’s also a “magnetic stress”, more kinds of waves are supported. sound waves generalize to two types of “magnetosonic” waves, sustained by a combination of mechanical and magnetic pressure. Beyond linear analysis, it is perhaps useful to think about these excitations as “quasi-particles” which can interact among themselves and with charged particles Also, a new kind of transversal wave propagating along the B-field direction can be supported, independently from mechanical pressure (Alfven waves) Alfven velocity

What What are are shocks useful for shocks useful for? 1st ? 1st order

• rder Fermi

Fermi mechanism mechanism

Vsh E’>E E

I.

• I. The acceleration is now 1

The acceleration is now 1nd

nd order in

• rder in

the the large shock velocity: efficient! large shock velocity: efficient! II.

• II. spectral index is universal for strong

spectral index is universal for strong (M>>1) shocks in ordinary matter (M>>1) shocks in ordinary matter III.

• III. Spectral index value close to what

Spectral index value close to what inferred~1 inferred~1

Now Now a a “ “preferred preferred” ” direction exists direction exists… … Efficiency can Efficiency can be be higher!!! higher!!!

Change Change of

• f Frames

Frames… …& & acceleration with B-fields acceleration with B-fields(?!) (?!)

Think of a ball bouncing on moving racket: There’s no gain of energy… in the frame of the racket! In the lab frame, the energy of the ball does increase (of course, we are neglecting back-reaction of the much larger racket, which actually loses a bit of E) When the “mirror” is magnetic, in the Lab there is a moving B-field, i.e. in the frame of the “shock” there is an electric field which accelerates the particle

• v

v+2V +V v’=-v-V v’’=+v+V Beware of some counterintuitive features of Beware of some counterintuitive features of “ “change of frame acceleration change of frame acceleration” ” Lab Lab “ “shock shock” ”

Sites Sites of

• f astrophysical

astrophysical acceleration acceleration

The Supernova The Supernova Remnant Paradigm for CRs Remnant Paradigm for CRs

  Energetics Energetics The SNR shock carries about 1051 erg of Kinetic Energy. If only ~10% of it gets converted into CR acceleration, the known rate of ~3 SN per century in the Milky way can supply the needed luminosity: L LCR

CR ≈

≈ 0.1 0.1E Ekin,SNR

kin,SNRR

RSN

SN

  Mechanism Mechanism SNR have a shock whose conditions lead naturally to a ~quasi universal power-law ~E-γ with γ=2+ε. The spectrum ~E-2.7 observed at the Earth is explained (consistently with S/P) with the E-dependent modifcation due to diffusive propagation in the Galaxy   Gamma-Spectra Gamma-Spectra Seem to be produced hadronically at the source, at least in some cases SNR known SNR known leptonic leptonic CR accelerators (radio, X-ray, CR accelerators (radio, X-ray, γ γ-rays

• rays…

…). Also ). Also Hadronic Hadronic? ? Probably Yes Probably Yes There are several good reasons:

Early results from Early results from Fermi (I) Fermi (I)

• S. Funk @
• S. Funk @

Fermi Fermi Symposium Symposium 2009 2009

Very preliminary, but Very preliminary, but

• all points are above

all points are above leptonic leptonic acceleration models acceleration models

• a couple of them by

a couple of them by “ “>3 >3 σ σ” ”

• points fluctuate (within 1-2

points fluctuate (within 1-2 σ σ) around the non-linear ) around the non-linear hadr

• hadr. model prediction

. model prediction… …

Early results from Early results from Fermi and Agile (II) Fermi and Agile (II)

W44

• S. Funk e Y. Uchiyama,

arXiv:1001.1419 ApJL in press

Cas A

• A. Abdo et al.

Science (Express) January 7, 2010

IC 443

• M. Tavani et al.

arXiv:1001.5150

Supernova Supernova Remnants Remnants -

• free expansion

free expansion

When a SN explodes, the ejecta move initially “almost freely”, expanding with ~constant velocity This free-expansion phase where R(t) R(t)~v ~vej

ej

t t ends when the ISM mass swept up is comparable with the mass of the ejecta. Typical Size at the End of Free Expansion Typical Time to reach it This is a “short” phase, virtually over for all known SRNs but SN1987A

Supernova Supernova Remnants Remnants -

• Sedov phase

Sedov phase

As long as significant radiative processes do not kick in, the evolution can be described as self-similar expansion, with the overall energy conserved, just shared between kinetic bulk motion and internal energy. SNR with ~103 yr should be severl pc and radiate strongly in X-rays (keV range) β>10-3 can be mantained for thousands of years: remember acceleration efficiency?

Clearly visible the thermal brems. Continuum + atomic X-ray lines.

Tycho Tycho SNR (1572) SNR (1572) as seen as seen in in X-rays X-rays

Death Death & & Rebirth Rebirth

At later times (t~10 At later times (t~105

5 yr) E-losses kick in & ultimately the SNR merges into the ISM

yr) E-losses kick in & ultimately the SNR merges into the ISM The SNR shocks The SNR shocks are believed to are believed to play an active role in triggering play an active role in triggering instabilities that lead to Star instabilities that lead to Star

• formation. Also, they have an
• formation. Also, they have an

important feedback on the important feedback on the “ “baryonic baryonic” ” component of Galaxies component of Galaxies

NGC 3582

The The confinement condition confinement condition: : Hillas Hillas Plot Plot

The system must be able to contain the particle: its Larmor Radius must be smaller than the size of the accelerator: s>rL SNRs are unable to account for particles of the highest energy

• bserved other objects (&

mechanisms?) are needed! What What else else is is out

• ut there

there? ? We We’ ’ll consider two further ll consider two further class of class of candidates candidates

Pulsar Pulsar “ “Magnetospheres Magnetospheres” ”

• Pulsars are not living “in vacuo”: an e at the

surface of the NS, the rotating B-field induces a E-field which is huge wrt gravity force!

• Stripped charges form a plasma configuration

which is comoving with the NS: this is the “magnetosphere”. It extends up to a distance RL~c/Ω (known as light cylinder).

• Field lines within RL are closed & charges
• f different sign populate different regions

(charge separation regime)

Acceleration Acceleration of

• f Particles

Particles in the in the Magnetosphere Magnetosphere

• Regions exist connecting the NS surface to

Regions exist connecting the NS surface to ∞ ∞, along which one has a potential , along which one has a potential drop of the order drop of the order

• Acceleration of particles happens in the

Acceleration of particles happens in the “ “gaps gaps” ”, regions without saturated , regions without saturated plasma plasma configuration, like regions joining null-charge surfaces (no efficient configuration, like regions joining null-charge surfaces (no efficient “ “refilling refilling” ” can can take place) to take place) to ∞ ∞

Acceleration of Acceleration of e e to E> to E>TeV TeV can take can take place! (unclear if or how many place! (unclear if or how many protons/nuclei protons/nuclei can be stripped) can be stripped)

Cascade development Cascade development

e (1-10 TeV) CR CR < 50 GeV < 50 GeV SYN ICS

e±

X(surface) X(surface) ICS SYN

e± e± e± e± e±

e(.05-500 GeV)

γ+B →e±

But interactions in the magnetosphere are important! But interactions in the magnetosphere are important! Losses and Losses and particle production take place and particle production take place and eletromagnetic eletromagnetic cascades develop. cascades develop.

High-E spectra shaped by conditions @ different locations via: High-E spectra shaped by conditions @ different locations via:

• Synchrotron & curvature radiation

Synchrotron & curvature radiation

• Inverse Compton

Inverse Compton

• pair production in the intense B-field

pair production in the intense B-field

• pair production on

pair production on γ γ backgrounds backgrounds

• triplet pair production

triplet pair production

• …

…

Qualitatively, these processes are Qualitatively, these processes are ultimately responsible for the radio ultimately responsible for the radio and HE observations of Pulsars and HE observations of Pulsars… …

How to distinguish among acceleration models How to distinguish among acceleration models? ?

• 6
• 3

3 6 Log Energy (MeV) CR kT ICS SR

• Different models exist depending on location & geometry of “gaps”
• Constrained via γ-ray spectra (possibly high-energy cutoff!), phase-profile,

multi-wavelength (radio to γ) constraints. “Fermi” region!

For example, interactions with B dominate in the PC model → → superexponential cutoff at relatively low energies (few GeV). γ−γ prevail in outer magnetosphere (d~RL) → → milder (exponential) cutoff & at higher E.

In general, pulsar spectra [observed by Fermi in γ-rays] are consistent with simple exponential cutoffs, indicative of absence of magnetic pair attenuation.

• L. Guillemot, Fermi Symposium,

2 November 2009

Gaensler & Slane astro-ph/061081 X-ray Chandra image of ”composite” SNR G21.5-0.9 (here, no reverse shock of ejecta deceleration moving inward, yet)

But there But there’ ’s s more more than than the the ‘ ‘initial initial’ ’ injection injection! !

• Forward SNR shock in the ISM (which is heated)

Forward SNR shock in the ISM (which is heated)

• Reverse shock propagates inwards, decelerating the SNR

Reverse shock propagates inwards, decelerating the SNR ejecta ejecta

• The relativistic wind (fields plus pairs) launched by the pulsar & called

The relativistic wind (fields plus pairs) launched by the pulsar & called nebula nebula forms forms a a “ “termination shock termination shock” ” when hitting the slower when hitting the slower ejecta ejecta & becoming non-relativistic & becoming non-relativistic

Several environments can be present around Several environments can be present around the Magnetosphere of a NS the Magnetosphere of a NS

What What do do we know about we know about HE HE particles particles in PWN? in PWN?

That X-ray and radio data show evidence for acceleration at the That X-ray and radio data show evidence for acceleration at the “ “termination shock termination shock” ” where the relativistic wind of pairs reaches the where the relativistic wind of pairs reaches the “ “slow slow” ” matter matter ejecta

• ejecta. Hard spectra

. Hard spectra are present up to 0.1-1 are present up to 0.1-1 TeV TeV, storing a large fraction of SD energy. , storing a large fraction of SD energy.

Slane et al. 0802.0206

Log Log10

10N(

N(γ γ) ) Log Log10

10

γ γ E E-1

• 1-E
• E-1.6
• 1.6

E E-2.

• 2.ε

ε

5-6 5-6 Theoretical problems Theoretical problems: :

Required Required E ~ E ~ large fraction large fraction of

• f what injected by spin-down

what injected by spin-down, , but unclear how most but unclear how most

• f the
• f the energy initially

energy initially in in Poynting Flux is converted Poynting Flux is converted in in relativistic particles relativistic particles. . What is What is the the origin

• rigin of
• f such

such hard hard spectra spectra? ?

Slane ‘08

Some Some misconception about misconception about “ “Fermi Fermi spectra spectra” ”

But PWN have a relativistic, oblique ( But PWN have a relativistic, oblique (⊥ ⊥?) shock in a medium filled with pairs! ?) shock in a medium filled with pairs! Diffusion across B line difficult ⇒ no DSA, i.e. no “standard” or generic model DSA paradigm: non-relativistic, strong, parallel shocks in ordinary, DSA paradigm: non-relativistic, strong, parallel shocks in ordinary, ion-e ion-e-

• medium

medium predicts E-2.ε spectrum (although non-trivial to reach Emax~PeV…) Possible ideas put forward:

• Magnetic field reconnection

Magnetic field reconnection Converting B-field energy into particles.

• Resonant Cyclotron Acceleration

Resonant Cyclotron Acceleration Requires a crucial role from ions.

• …

…

~Large efficiencies & hard spectra are hard to predict robustly, not necessarily “unreasonable” : Hard to predict ≠Hard to obtain in Nature!

Both Both hard hard spectra spectra and high and high efficiency possible efficiency possible! !

• 3-component plasma of e‐, e+, p

(very different in mass!)

• Rich in pairs
• Energy dominated by p-component

Particle-in-cell simulation find hard spectra (1<index<2), high efficiency (1-30%), preferential acceleration of e+ (the higher ρ and η, the better). E.g., 30% efficiency for η~5.25

• Acceleration happens via resonant absorption of magnetosonic waves by

pairs, whose frequencies are harmonics of the proton cyclotron frequency.

• Preferential e+ acceleration due to helicity matching with dominant proton

generated wave spectrum

• f

Hoshino & Arons, Physics of Fluids B, 3 (1991) 818 Amato and Arons, ApJ 653 (2006) 325

A particle falling from infinite to a distance R from a body of mass M acquires an energy

Accretion Accretion: : Energy source for Energy source for the the violent universe violent universe

If all this energy is dissipated in a detectable If all this energy is dissipated in a detectable form form, the luminosity due to accretion is If we take for R the surface of a compact object, one gets: Note: Note: It is extremely efficient! Thermonuclear fusion converts in Energy “only”~0.1-1% of burned mass! Question: Question: Can we increase m arbitrarily? The more compact the object, the higher the efficiency.

. .

A too large luminosity will stop further accretion, A too large luminosity will stop further accretion, just because of the just because of the “ “radiation pressure radiation pressure” ”. This can be calculated by asking . This can be calculated by asking

Eddington limit Eddington limit

Higher masses can Higher masses can sustain higher sustain higher luminosities! luminosities!

Largest accretion e.m. luminosity in spherical symmetry spherical symmetry. In systems in spherical accretion, this limit is very hardly reached: it turns out that most of the energy remains in the form of kinetic energy, not converted into internal energy. The exception is in presence of shocks. But high-L requires also high masses, and no analogue of a “bounce back” shock as on NS exist at the BH surface (it’s not a rigid surface!) Actually, efficient accretion phenomena are rarely spherically symmetric Actually, efficient accretion phenomena are rarely spherically symmetric

Disk Disk Accretion Accretion

• In general, a blob of gas does not fall on M radially, since the system must

conserve angular momentum!

• Gravity is a central force and cannot “remove” angular momentum, L
• In relatively short timescales, the gas will settle into a disk, which is the

minimum energy configuration for fixed angular momentum

• Then, accretion can only proceed at the rate at which L can “flow away” from

inner to outer regions. How? It must be a non-gravitational phenomenon! L is thought to be transported outwards via “magnetorotational instability”

The inner element is forced to slow down → reduces its angular momentum, moves to a lower orbit. The outer element instead speeds up → increases angular momentum moves to a higher orbit. The spring tension increases as the two fluid elements grow further apart → runaway process. Consider 2 fluid elements joined by a magnetic field line, acting as a spring. The inner one tends to move faster stretching the line → magnetic tension develops

Sketch of MRI Sketch of MRI

z

R

Bo B m1 m2

Does acceleration occur Does acceleration occur in in accretion disks accretion disks? ?

Details are beyond the introductory level of these lectures. Yet, note that, at least in inner parts velocities of gas clouds are well above velocity of sound. Equating the luminosity of a disk, assumed thermal, of typical size Rs (most luminous zone) to LE On the other hand, orbital velocities are relativistic, of the order of Hence supersonic shocks (required for acceleration) naturally occur!

Accretion disk are usually Accretion disk are usually bright in bright in UV to X-ray bands UV to X-ray bands

Disk-Jet connection: Disk-Jet connection: Blandford-Znajek process Blandford-Znajek process

Possible Possible mechanism by which E can be extracted from a rotating BH into e.m. jets mechanism by which E can be extracted from a rotating BH into e.m. jets Electric currents flow along the field lines into the poles of the BH, over the Electric currents flow along the field lines into the poles of the BH, over the 'surface' of the event horizon, and out of the horizon near the equator. At a 'surface' of the event horizon, and out of the horizon near the equator. At a distance from the BH, the current dumps its energy into the plasma, which is distance from the BH, the current dumps its energy into the plasma, which is blown away from the BH as jets from the poles. blown away from the BH as jets from the poles. M87 rotating Black Hole rotating Black Hole → voltage generator voltage generator B-field lines in the accreting plasma B-field lines in the accreting plasma → wires wires the plasma the plasma → load. load. ” ”Electrical Circuit Electrical Circuit” ” analog analog

From Hess From Hess’ ’ Nobel Nobel Lecture Lecture, 1936 , 1936

On what can we now place our hopes of solving the many riddles which still exist as to the origin and composition of cosmic rays? […]The tracing of the occurrence of these "showers" in the depths of the earth, in mines and through the immersion of recording apparatus in water to some hundreds of meters depth will yield very important results. […]In order to make further progress […] it will be necessary to apply all our resources and apparatus simultaneously and side-by-side

[…] It is likely that further research into "showers" and "bursts" of the

cosmic rays may possibly lead to the discovery of still more elementary particles, neutrinos and negative protons, of which the existence has been postulated by some theoretical physicists in recent years.