Observations of particle acceleration in the blast waves of GRB - - PowerPoint PPT Presentation

Observations of particle acceleration in the blast waves

• f GRB afterglows

with Phil Evans, Alexander van der Horst, Rhaana Starling, Mat Page

Peter A. Curran

Laboratoire AIM, Irfu /Service d'Astrophysique CEA Saclay, France

GRB afterglows

(Piran 2003)

External shocks: X-ray, optical, radio

Electrons are accelerated by shock… emit synchrotron radiation

GRB Synchrotron spectra

(Sari et al. 1998)

Optical X-ray Electrons are accelerated by shock… emit synchrotron radiation (Slow cooling, adiabatic expansion) Cooling break freq.

Electron energy distribution

N(E) ∝ E-p

Fermi acceleration of electrons

Number of electrons with Energy, E Energy, E

Electrons are accelerated by shock… to a certain distribution (value of p dependent on the underlying plasma physics)

p – electron energy distribution index

Fermi acceleration of electrons

Single, discrete value of p? Or a distribution? What distribution? How does measured value compare to theory/ simulations? Universal value or variation between sources*?

* GRB (p~2-3), Cosmic Rays (p≈2.5-2.7), X-ray binaries (p≈2.6, σ≈0.4), AGN (p~3)

X-ray spectra ➝ p(βX,NH) ⇒ multiple options ⇒ synchrotron cooling frequency above/below

Derivation of p

Compare predictions of p to light curves (optical & X-ray: small sample) to decide which value of p is correct

Distribution of p

BeppoSAX & Swift (16 GRBs)

(Starling et al. 2008; Curran et al. 2009)

Not consistent with single, discrete value

Cooling frequency: (free parameter) > X-ray < X-ray

0.5

Transform p to β

Probability distributions

(data from Evans et al. 2009)

X-ray spectral index, βX

Swift X-ray Telescope (XRT) (~300 bursts)

i) Assume underlying p distribution ii) Find most-likely parameters iii) Test hypothesis (via Monte Carlo)

Monte Carlo hypothesis test

~105 synthetic data sets

Distribution of spectral index, βX

Swift XRT (~300 bursts)

(Curran et al. 2010)

Single discrete value of p?

synthetic data

Distribution of spectral index, βX

Swift XRT (~300 bursts) Not consistent with single, discrete value

(Curran et al. 2010)

synthetic data

Distribution of spectral index, βX

Swift XRT (~300 bursts)

(Curran et al. 2010)

Gaussian distribution of p? (p=2.39, σ=0.6)

synthetic data

Distribution of spectral index, βX

Swift XRT (~300 bursts) Consistent with a Gaussian distribution p=2.39, σ=0.6

(Curran et al. 2010)

X-ray spectra ➝ p(βX,NH) ⇒ multiple options X-ray light curves ➝ p(indices, density structure, accretion) & accuracy of fit, model dependent ⇒ multiple options

Distribution of p via temporal indices

(Evans et al. in preparation, using model of Van Eerten & Wijers 2009)

Distribution of p via temporal indices

Preliminary (~180 bursts)

p≈2.36, σ≈0.36

Totally independent method, with different data!

Fermi acceleration of electrons

Electron energy distribution

Number of electrons with Energy, E Energy, E

Q: Single value of p? Distribution of p? What distribution? A: Gaussian distribution at p=2.39 and standard deviation, σ=0.6

N(E) ∝ E-p

Q: Single value of p? Distribution of p? What distribution? A: Gaussian distribution at p=2.39 and standard deviation, σ=0.6

Only 1 spectral peak?

Only 1 spectral peak?

Swift XRT (~300 bursts)

?

(Curran et al. submitted)

~94%: cooling frequency below

>94% with cooling frequency < X-ray ≤6% with cooling frequency > X-ray

3σ limit

Fraction of GRBs with νc < X-ray Number of trials

Only 1 spectral peak?

94% 6%

Other explanations?

 Bimodal distribution of p, with mode of p drawn from correlated with position of cooling break? Highly convoluted!  Wide distribution blurs out double peaks? Requires distribution far wider than observed  Not 2 βX(p) relationships?

Synchrotron spectra?

Smoothly broken curves ⇒ continuous range of relationships

(Granot & Sari 2002)

Breaks evolve in time ⇒ spectral & temporal changes (inconsistent with observations)

Other explanations?

 Bimodal distribution of p, with mode of p drawn from correlated with position of cooling break? Highly convoluted!  Wide distribution blurs out double peaks? Requires distribution far wider than observed  Not 2 βX(p) relationships? Inconsistent with observations

No, majority of GRBs have cooling frequency below the X-rays

• supported by preliminary Evans results

Conclusions

 Fermi acceleration can be ‘observed’ in GRBs, and parameters constrained via statistical methods  Allows for comparison with other sources, as well as theory/simulations  not consistent with a single, discrete value of p  consistent with Gaussian of p≈2.4, σ≈0.6*  94% of GRBs have cooling frequency below the X-rays

* Compared to Cosmic Rays (p≈2.5-2.7), X-ray binaries (p≈2.6, σ≈0.4), AGN (p~3)