Analogy between laser plasma acceleration and GRB

1
Analogy between laser plasma acceleration and GRB


(image credits to CXO/NASA)

• G. Barbiellini(1)
• F. Longo (1), N.Omodei(2), A.Celotti(3), M.Tavani
  (4)
• (1) University and INFN Trieste (2) INFN Pisa
  (3) SISSA Trieste
• (4) INAF Roma Roma2 University

2
Abstract

• The Wake Field Acceleration analogy between
  laboratory and cosmic plasmas may explain some of
  the observed correlations in gamma-ray bursts
  between the collimation of the outflow, the total
  emitted energy, and the energy emitted in
  gamma-rays. The hypothesis that the photons are
  emitted during the acceleration and modulation of
  the leptons in the plasma at 1015 cm from the
  central engine provides a link between spectral
  properties, the total energy, and the collimation
  angle. The energy is constantly transmitted
  mainly within the collimation angle so that the
  burst afterglow properties are linked to the
  prompt emission, since a fraction of the prompt
  energy of the plasma produces the afterglow at
  larger distances. Applying the WFA formulas, the
  luminosity is naturally linked to the local
  particle density, so the historical wind activity
  of the GRB progenitor is related to the
  luminosity behavior of the afterglow.
  Experimental data from GRBs with measured
  redshifts and jet opening angles appear to
  support this hypothesis.

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Outline

• Introduction to GRB phenomenology
• Laboratory Wake Field acceleration
• Experimental results and relevant formulae
• Scaling with particle density n
• Compton Tails GRB environment
• Stochastic Wake Field acceleration
• Surface power and Stochastic Factor
• Applications

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The GRB phenomenon

• GRBs sudden and unpredictable bursts of hard X
  / soft gamma rays with huge intensity, typical
  durations of tens of seconds and coming from
  random directions in the sky
• discovered at the end of the 60s by military
  satellites, first published on an astronomical
  journal (ApJ) in 1973
• during 70s and 80s several experiments onboard
  satellites, but poor improvements in
  understanding these phenomena

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BATSE era

• major contribution came in the 90s from the
  NASA BATSE experiment (25-2000 keV) onboard CGRO
  (1991-2000)
• based on NaI scintillator detectors 8 units
  covering a 4p FOV

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Light curves

• most of the flux detected from 10-20 keV up to
  1-2 MeV
• diverse and unclassifiable light curves. No
  periodicity, highly variability.
• Narrower at higher energy pulse paradigm

HE LE
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Spectral shape

• Non thermal spectra typically described by a
  smoothly broken power-law (Band) ? low-energy
  index, ? high-energy index, E0break energy,
  EpE0 x (2 ?) peak energy of the ?F? spectrum.

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Observables

• Position in the sky isotropic, no association
  with the galactic plane (first hint of a
  cosmological origin)
• Estimated rate 1.8 bursts/day (650/yr)

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Observables

• Duration, or T90 (T95 - T05)
• Two families Short and Long GRBs
• Depends on the background

short
long
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High Energy Emission
GRB940217
2 photons _at_ 3 GeV
Photons _at_ 102 MeV
Photons detected by EGRET during the prompt phase
(100 MeV) Insufficient time resolution to
resolve the pulse shape. Need ltms time resolution
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The Afterglow era
BeppoSax Costa et al. 1997
HST Co. look for Other
Afterglow
J.S. Bloom et al. 1997
Magnitudes of the host Galaxy
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The afterglow phase

• Beppo Sax afterglow afterglow power-law decay
  and power-law spectra
• First evidence of x-ray flashes? (Piro et al.)

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X-Ray Flashes
One of the main discovery by the Swift
mission. Bumps at late times, as energetic as the
prompt emission Not unique Afterglow
decay Correlated with the central engine?
GRB050904
GRB050724
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Delayed/Extended HE emission

• BATSE EGRET joint analysis (Gonzales et al.,
  Nature, 2003)
• 2 separate components
• Independent time evolution (extended HE emission)
• Spectral index of the HE component -1
• Cut-off at higher energies where?
• How common in GRB?

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Present understanding of the afterglow phase

• The afterglow is connected to the prompt emission
• Steep, followed by a shallow decay, sometimes
  re-steepening
• Flares, brakes

-3
( 1 min t hours )
-0.7
105 106 s
- 1.3
-2
102 103 s
104 105 s
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Examples of Swift Afterglows

• Prompt-afterglow connection initial steep decay,
  flattening, flares

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Optical Transient

• Consequent discovery and study of optical, IR,
  radio GRB counterparts (by follow-up of NFI 1
  error box)
• Redshift measurements GRB are at cosmological
  distances!

GRB970228, Van Paradijs et al., Nature, 1997
GRB 970508, Metzger et al., Nature, 1997
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Host Galaxies

• Discovery of GRBs host galaxies
• LONG association with star formation regions
  (massive stars?)
• SHORT association with non SFG (binary mergers?)

Bloom et al., ApJ, 2002
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Redshift distribution

• 70 LONG GRBs with measured redshift (except the
  peculiar GRB980425) lie at cosmological distances
  (z 0.0331 6.3)
• From distance, fluence and spectrum, estimate of
  the radiated energy, which is huge (up to 1054
  erg ) if assuming isotropic emission (Eiso)
• Large dispersion of Eiso

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Jet break time

• Relativistic beaming 1/G. G decreases gt At some
  point the beaming angle should overcamo the Jet
  anglegt different decay slope!
• Jet angles derived from the achromatic break
  time, are of the order of few degrees
• The collimation-corrected radiated energy spans
  the range 1050 1052 erg

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Afterglow light curve presents achromatic break
Evidence that the GRB outflow is collimated
within a jet with a certain opening angle
AG break time
Jet opening angle
GRB 990510 Israel et al. 1999
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Prompt emission spectrum
GRB Peak Energy Where most of power comes out
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Peak energy vs. True energy
cr21.27
Ghirlanda (Ep Etrue0.7)
Amati (EpEiso0.45-0.55)
Epeak(1z)
Ep (1z)
Cosmological use of GRB! Measuring
Ep,tjetgtEtrue Measuring the fluence gtRedshift
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GRB-SN Connection

• Evidence of GRB-SN connection
• Bumps in the AG lightcurve
• Optical spectra

GRB 030329, Hjorth et al., Nature, 2003
GRB 030329, Stanek et al., ApJ, 2003
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Progenitor for LONG GRBs

• The hypernova / collapsar scenario

• energy budget up to gt1054 erg
• long duration
• metal rich (Fe, Ni, Co) WIND circum-burst
  environment
• GRBs occur in star forming regions
• GRBs are associated with SNe
• naturally explained collimated emission

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WakeField Acceleration
(Ta Phuoc et al. 2005)
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Gamma-Ray Bursts in Space
SN explosion
Accretion
GRB
Electromagnetic jets (photons, e e-)
Accretion disk
Explosion of a Massive Star
Collapsing compact object (Rapidly rotating BH
Disk)
Supernova Shell
Wake Field Acceleration!

• An electromagnetic jet (I.e. photons) plays the
  role of the lab laser
• The Supernova Shell is the target plasma (at
  R1015 cm, with n109 cm-3)
• Stochasticity has to be taken into account
  (laser-gtnot coherent radiation)

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WakeField Acceleration
(Ta Phuoc et al. 2005)
Laser Pulse tlaser 3 10-14 s Laser Energy 1
Joule Gas Surface 0.01 mm2 Gas Volume Density
1019 cm3 Power Surface Density ?W 3 1018 W
cm-2
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WakeField Acceleration
(Ta Phuoc et al. 2005)
Electron Spectrum
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WakeField Acceleration
(Ta Phuoc et al. 2005)
Emitted Photon Spectrum
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Bright and Dim GRB

• (Connaughton 2002)

Q cts/peak cts

• BRIGHT GRB
• ? DIM GRB

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The Compton Tail
Barbiellini et al. (2004) MNRAS 350, L5
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The Compton tail

• Prompt luminosity
• Compton Reprocessed luminosity
• Q ratio

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Scaling relations
?p n-1/2
?b n-1/2?1/2
r0 n-1/3 ??1/2
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Scaling relations
V r03 n-1 Qenr03n0
?(1019) 102 ?(109) 2x105 ?(102) 2x108
?n-1/3 Ep 3/4 hcg2 r0/?p2
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Scaling Relations
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Riding Wave
Pictorial View
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Analogy Formulae (I)

• Laser acceleration surface power and GRB surface
  power

Stochastic factor ?(plasma) x 1 s
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Analogy Formulae (II)

• Independent derivation how to induce a
  collective phenomenon from many microscopic
  processes?

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Consequences (I)

• GRB Luminosity depends on environment
• Effective Angle constrain by Jet opening angle
  generates a link between Epeak and Total Energy
  (Amati, Ghirlanda, )

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Consequences (II)

• Large emission in the region with transition
  between low to high density value
• Energy transmitted always in ?jet cone
• Assuming the afterglow produced by the prompt
  emission we could calculate ?2 from total energy

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Consequences (III)

• New formula for evaluating jet opening angle

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Consequences (IV)

• New relation among Epeak and Egamma

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Conclusions

• Electron acceleration in a moderate density
  plasma (109 cm-3) similar to WFA acceleration
  produces many of the GRB properties
• Luminosity is proportional to local density
• This efficient transformation of kinetic energy
  into radiations ends when the surface power
  density crosses the threshold because of dilution
  over increasing surface.