Tests of Curvature Effects in the Temporal and Spectral Properties of

GRB Pulses

Ashwin Shenoy1

In collaboration with Eda Sonbas2, Charles Dermer3,

Kalvir Dhuga1, Leonard Maximon1, William Parke1 and Glen MacLachlan1

1. Physics Department, The George Washington University

2. NASA Goddard Space Flight Center

3. Naval Research Laboratories, Space Sciences Division

An Outline of this presentation

Motivation. A relativistic colliding shell model. Some previous work. Selection of GRBs. A test of curvature. Results and Summary. Proposed future work.

Motivation

Curvature dominated models with different cooling mechanisms such as synchrotron emission

f Єpk(t) ~ Єpkλ

Tests of this form will allow us to distinguish between, or validate/constrain such models.

These relations could lead to an estimate of the bulk lorentz factor of the jet.

Predictions of the Model (Dermer 2004.)

Thin shells

Spherically symmetric and emit homogenously.

The spectrum follows a broken power law.

Curvature effects dominate at later times and f Єpk(t) ~ Єpk3

Some Previous Work

Soderberg and Fenimore (2001).

- Intensity vs. time, analogous to f Єpk(t) ~ Єpk3 - (a+b)

- 2 GRBs, with a negative result. Borgonovo and Ryde (2001).

- BATSE GRBs: f Єpk(t) ~ Єpkλ with 0.6 ≤ λ ≤ 3.

- Pulse properties within a GRB are similar.

Light curve selection and extraction GRBs with high fluxes and count

rates. (GBM circulars, Nava et al. 2009).

Choice of 3/4 brightest NaI detectors from GBM quicklook products.

In this case: Detectors 0,6,7 and 9.

- Background-subtracted light curves. - 200 μs binning. - Energy range: ~ 8 keV - 1MeV.

Light curves were re-binned until pulse structures were visible.

GRBs with distinct peaks were selected and analyzed.

Acknowledgement: Narayan Bhat.

GRB 081224887

Single peak GRB with T90 ~ 50 secs

Pulse has a FRED profile

The Peak is at ~2.6 secs. FWHM for this pulse is

about 10 secs.

Temporal fit of the Pulse-Decay

Decay portion of the pulse is fit by C*(t-t

p)α

We chose the square-root of the count rates as their errors.

Pulse fit parameters of selected GRBs

GRB Name

α α error Best fit range (secs)

Chi2 Range for Spectral analysis

081224887 -0.45 0.012 5.0 - 14.0 1.23 4 – 10 (1-second)

110625881

-0.93 0.034 11.5 - 13.5 1.63 11 – 13.5 (0.5-second)

081009140 -5.66 0.133 42.0 - 49.0 1.23 Poor Spectral fit

Light Curve Segments for Spectral fits

3 - 4 brightest detectors were chosen.

Pre- and post- burst regions were selected for background subtraction.

Light curves were background-subtracted with a polynomial fit.

Divided into 1 second segments (4.0 – 9.0 seconds)

Spectral Fitting

For each time segment the spectrum was fit with a Band function.

The Epeak

was determined

The flux in the Epeak

region was extracted.

Results for Band function fits for GRB 081224887

TimeSegment (secs)

Epeak

(keV) α β Flux10-7 ergs/cm2. s

4 -5 207.0 +/- 24.6 -0.44 +/- 0 .09 -1.90 +/- 0.12 2.98 +/- 0.17

5 - 6 183.3 +/- 27.2 -0.49 +/- 0.12 -1.89 +/- 0.13 2.60 +/- 0.16

6 - 7 178.9 +/- 26.7 -0.53 +/- 0.13 -2.09 +/- 0.22 2.00 +/- 0.15

7 - 8 154.3 +/- 42.4 -0.63 +/- 0.20 -1.75 +/- 0.12 2.47 +/- 0.17

8 -9 159.1 +/- 44.2 -0.69 +/- 0.21 -1.98 +/- 0.27 1.88 +/- 0.18

Єpk3

Summary

We have selected bright GRBs with FRED like pulse shapes. We analyzed the decay portion of these pulses by extracting

spectral parameters via a band function fit for time slices of the pulse and extracted the E

peak and the fluxes under the E

peak

region. We looked for curvature effects in GRB prompt emission

data via the relation

- f Єpk(t) ~ Єpk3

We tested this relation for a few candidate GRBs and we found encouraging results.

Proposed Future Work Identify other candidate GRBs including short GRBs for GBM

Extend the analysis to BATSE and Swift GRBs.

Test other relations such as (Kumar and Paneitescu, 2000)

- α ~ 2 - β

- Fv (t) ~ v

β (t-tpk)α

Move from a relatively simple kinematic model to a more sophisticated phenomenological model

http://iopscience.iop.org/0004-637X/614/1/284/pdf/60132.web.pdf

Test the rise profiles of GRB pulses.

The Talk Ends Here

Following are extra/discarded slides

The colliding shell model

We looked at the light curves of ~70 bright GRBs. On close inspection, only the following 3 GRBs had distinct single peak-pulse profiles without secondary overlapping peaks. We fit the temporal profile of these peaks with a simple power law. As is customary, we chose the square root of the counts as the error for each count. The table below provides the parameters of the fit.

GRB Name α % error Reduced Chi^2 Best fit range for α (in secs) βGRB 090718762 4.59 +/- 0.382 8.34 1.45 23.5 - 26.5 GRB 081224887 0.45 +/- 0.012 2.68 1.23 5.0 - 14.0 ~ 1.30GRB 081009140 5.66 +/- 0.133 2.36 1.23 42.0 - 49.0 GRB 110625881 0.81 +/- 1.63 11.5 13.5

As the table shows, only one GRB (GRB 081224887) satisfies the equation

α ~ 2 - β eqn.1

We then tested the following 2 equations for this GRB.

f ~ Єpk3

eqn.2, And

Fν ~ ν-β (t-tpk)-α eqn.3.

This is a single peak GRB with the peak at ~2.6 secs. The following 2 figures show the light curve and the zoomed in profile of the pulse respectively. We fit the decaying portion of the pulse with a power law of the form C*(t-tpk)-α

To obtain the νFν corresponding to this peak photon energy, E_peak, we chose an energy range, E_peak ± 20 keV and determined the νFν values in this range. Following are the slides detailing the spectral fitting procedure corresponding to one time-segment (3- 5 s).

To obtain the νFν corresponding to this peak photon energy, E_peak, we chose an energy range, E_peak ± 20 keV and determined the νFν values in this range. Following are the slides detailing the spectral fitting procedure corresponding to one time-segment (3- 5 s).

The figure shows the time-segment extraction and the background fit to the light curve.

These steps applied for N7 and N9 detectors as well.

The unfolded spectrum (convoluted with the detector response) corresponding to the light segment.

Spectral Fitting

Rmfit supplies several test statistics. We used C-Stat which is -2log(likelihood) and performed a spectral fit for each of the 3 detectors using both the Band function and a simple power law.

The fluence and other parameters are extracted in the range E_peak +/- 20 keV.

To confirm our results obtained using RMFITS, the same fit was performed with XSPEC. The results were found to be compatible for these two methods.

f(t) vs. Єpk -β (t-tpk)-α correlation for each

time segment.

To test this relation the spectral analysis was performed on a time resolved spectrum (64 ms resolution). It was found that the spectral index for an energy range E_peak +/- 20 keV obtained by a power law fit was not very different from that for the entire spectral range. We therefore decided to fix the value of ν to νpk. This allowed us to obtain an νF(ν = vpk, t) flux and a β(t) for every 64 ms bin over the 2 second length of the segment. Once we included errorbars in our plots, we found that the flux (F) errors became large beyond 9 secs suggesting that the 64ms resolution was too fine beyond this range to allow for sufficient photon counts.Also, the y errorbars were obtained by treating the parameters α , β and vpk as independent parameters. This leads to an overestimate of the error given that α and β are correlated and so are vpk  and β. We will address these issues in our next run.

Following are the plots for the 3 relevant time segments.

νFν vs ν-β+1 (t-tp)-α for 3-5 second

νFν

ν-β+1 (t-tp)-α

vFν vs ν-β+1 (t-tp)-α for 5-7 seconds

ν-β+1 (t-tp)-α

νFν

vFν vs ν-β+1( t-tp)-α for 7-9 second

ν-β+1 (t-tp)-α

νFν

• We noted a hard to soft evolution of the E_peak across several time segments. We think it worthwhile to determine the spectral lags for this GRB to try and connect the lag to the curvature effect.

• We will also search for new single peak GBM GRBs and will apply these tests according to your suggestions and comments.

• In place of a simple power law for the spectral fit, we will attempt to fit the spectrum with a broken powerlaw or log-parabola.

• We will also use a time resolution for the spectral analysis that reduces the flux errors and  use Monte-carlo simulations to improve our error estimates of derived quantities while accounting for correlations between the free parameters.

Proposed Future Work