Implications of Correlated
GRB Pulse Properties
Jon Hakkila
Presented at Los Alamos
August 29, 2011
2nd GTAC
Collaborators: Rob Preece, Tom Loredo, Carlo
Graziani, Tim Giblin, Robert Wolpert, Alex Greene.
General Prompt GRB Properties
Light Curves
Spectra

25-50 keV, 50-100 keV,
100-300 keV, 300 keV-1 MeV
Synchrotron shock model (e.g.
Rees & Meszaros, ApJL, 1994,
430, 94) or jitter radiation
(Medvedev 2000, ApJ 540, 704.
Epk

GRB Classes
Short
Long
Hypernova Central Engine Model of
Long GRBs
Intermediate?
The Intermediate class - statistically
identified in BATSE and Swift data,
although not unambiguously associated
with a separate source population.
Merging Compact Objects Central
Engine Model of Short GRBs
Many GRB bulk properties (e.g. lag, Epeak, variability) correlate
with luminosity. How can the intrinsic effects leading to these
correlations be separated from other effects (e.g. class differences
and selection biases)?
• GRB complexity results from overlapping pulses.
• Long and Short GRBs appear to be inherently different.
• Relativistic cosmology alters GRB observed properties:
 Inverse square law: distant GRBs appear fainter than similar nearby ones
 Time dilation: distant GRBs have longer durations and temporal
structures than similar nearby ones.
 Energy shift: distant GRBs have their fluxes shifted to lower observed
energies than similar nearby ones.
GRB pulse properties can help disentangle GRB complexity, via
• Inherent time asymmetry (longer decay than rise rates),
• Hard-to-soft spectral evolution, and
• Longer pulse durations at lower energies.
Observable Pulse Properties - obtained
using semi-automated 4-parameter pulse
model (Norris et al. 2005 ApJ, 627, 324;
Hakkila et al. 2008 ApJ 677, L81):
• Pulse peak flux (p256) - peak flux of
summed multichannel data (black)
measured on 256 ms timescale.
• Pulse duration - time span when flux
is e-3 of pulse peak flux.
• Pulse peak lag- time span between
channel 3 peak (100-300 keV; green)
and channel 1 peak (25-50 keV; red).
• Fluence - time-integrated flux.
• Hardness - ratio of channel 3 fluence
to channel 1 fluence.
• Asymmetry - pulse shape measure; 0
is symmetric and 1 is asymmetric.
Black - summed 4-channel emission
Green - high energy channel emission
Red - low energy channel emission
300 keV - 1 MeV
Pulse-fitting example: GRB
950325a (BATSE 3480)
100 keV - 300 keV
25 keV - 1 MeV
3
50 keV - 100 keV
12
lag
Pulse 1
Pulse 2
Pulse 3
0.01 s ± 0.01
0.11s ± 0.05
0.85 s ± 0.15
25 keV - 50 keV
duration
1.00 s ± 0.08
3.06 s ± 0.10
9.45 s ± 0.52
peak fl ux
(256 ms)
19.47 c/s ± 0.21
6.35 c/s ± 0.14
1.35 c/s ± 0.03
Pulse-fitting example: GRB
910930 (BATSE 0840)
1
300 keV - 1 MeV
100 keV - 300 keV
2 3 4
25 keV - 1 MeV
Pulse 1
Pulse 2
Pulse 3
Pulse 4
lag
0.00 s ± 0.
0.02 s ± 0.
0.00 s ± 0.
0.06 s ± 0.
duration
4.84 s ± 12.54
1.97 s ± 0.47
2.22 s ± 6.29
1.6 s ± 0.35
peak fl ux
(256 ms)
1.260 c/s ± 927.
0.818 c/s ± 0.05
0.492 c/s ± 12.15
0.647 c/s ± 0.1
50 keV - 100 keV
25 keV - 50 keV
Pulse-fitting example: GRB
930123 (BATSE 2600)
100 keV - 300 keV
1
2
50 keV - 100 keV
25 keV - 1 MeV
Pulse 1
Pulse 2
lag
6.71 s ± 0.31
0.70s ± 0.30
duration
45.8 s ± 4.6
6.4 s ± 0.3
peak fl ux
(256 ms)
0.39 c/s ± 0.01
0.80 c/s ± 0.02
25 keV - 50 keV
1
2
original burst CCF;
short lag
25 keV - 1 MeV
GRB 930123 (BATSE 2600)
CCF of reconstructed
pulse 1: long lag
What does GRB lag measure
(as obtained from the CCF)?
The CCF lag is dominated by large
amplitude, short pulses with short lags.
Longer-lag pulses and pulse overlap can
smear out this behavior.
CCF of reconstructed
pulse 2: short lag
CCF of reconstructed
pulses 1+2: short lag
Pulse Property Correlations
(1390 pulses in 646 BATSE
GRBs)
The GRB lag vs. luminosity relation (Norris,
Marani, & Bonnell 2000, ApJ 534, 248) is actually a
pulse lag vs. pulse luminosity relation (Hakkila et
al. 2008, ApJ 677, L81). Pulse duration also
correlates with pulse lag, so pulse duration also
indicates luminosity.
2.5
2.0
log(pulse duration)
1.5
1.0
0.5
0.0
-0.5
Peak luminosity (L) vs. duration (w) and
lag (l0) for BATSE GRBs: Pulse relations
replace bulk prompt emission relations.
-1.0
-1.5
-2.0
-5
-4
-3
-2
-1
log(pulse peak lag)
0
1
2
Supportive Pulse Observations from
HETE-2 and Swift
Pulse lag and pulse duration vs.
pulse luminosity relations are found
in HETE-2 (Arimoto et al. 2010, PASJ,
62, 487) and Swift (Chincarini et al.
(MNRAS, 2010, 406, 2113).
X-ray flares share many -ray pulse
characteristics. However, flare
energetics decrease and pulse
durations increase with time after the
trigger, indicating that less energy is
present as flares develop (Margutti et
al. 2010, MNRAS, 406, 2149).
More Pulse Property Correlations
2.5
5
2
4.5
1.5
4
1
0.5
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-0.5
-1
log(pulse fluence)
log(pulse peak flux)
1338 pulses in 610 BATSE GRBs: (Hakkila and Preece, 2011 ApJ (in
press))
3.5
3
2.5
2
1.5
1
-1.5
0.5
-2
0
-2.5
-2
-1.5
-1
log(pulse duration)
-0.5
0
0.5
1
1.5
2
2.5
0.9
1
log(pulse duration)
2.5
1.5
2.0
log(pulse duration)
log(pulse hardness)
1.0
0.5
0.0
-0.5
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.0
-1.5
-1.5
-2.0
-2.0
-2
-1.5
-1
-0.5
0
0.5
1
log(pulse duration)
1.5
2
2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
pulse asymmetry
0.7
0.8
Long (upper) and Short (lower) GRB Pulse Correlations
Uncorrelated
probability
Duration
Lag
p256
Hardness
Asymm etry
Fluence
Lag
<0.01%
<0.01%
---
p256
---
<0.01%
<0.01%
<0.01%
54%
---
Hardness
---
---
<0.01%
6.8%
<0.01%
25%
<0.01%
<0.01%
---
Asymm etry
---
---
---
<0.01%
76%
<0.01%
22%
0.03%
54%
<0.01%
93%
---
<0.01%
11%
<0.01%
50%
<0.01%
<0.01%
3.1%
<0.01%
<0.01%
43%
GRB pulse property correlations: short duration pulses have shorter lags, are brighter,
are harder, and are more time symmetric than long duration pulses (Hakkila and Preece,
ApJ 2011 (in press)).
GRB classification using pulse properties
The pulses in single-pulsed Long GRBs are
demonstrably longer than those in singlepulsed Short GRBs (Hakkila et al., 2010
BAAS).
However, double- and triple-pulsed GRBs
have less distinctive pulse differences
(Adams et al., 2010 BAAS).
Single Pulsed Events Classified by EM Algorithm
1-3 Pulsed Events
2
2
1.5
1.5
log (pulse duration)
1
log (pulse duration)
1
0.5
Single pulsed long
events
Single pulsed short
events
Double pulsed long
events
Double pulsed short
events
Triple pulsed long
events
Triple pulsed short
events
0
-0.5
Single pulsed long
events
0
0.5
-1
-0.5
-1.5
Single pulsed short
events
-4
-3
-2
-1
0
1
log (pulse lag)
-1
1-3 Pulsed Events
-1.5
-4
-3
-2
-1
0
1
4.5
log (pulse lag)
4
3.5
log (pulse fluence)
-> The pulse distribution can help determine
whether a GRB belongs to the Long or Short
burst class, even though individual pulses are
likely formed by a progenitor-independent
process.
Single pulsed long
events
Single pulsed short
events
Double pulsed long
events
Double pulsed short
events
Triple pulsed long
events
Triple pulsed short
events
3
2.5
2
1.5
1
-1.5
-1
-0.5
0
0.5
log (pulse peak flux)
1
1.5
2
Correlated pulse properties are measured in the
observer’s frame, indicating that effects of
relativistic cosmology, including the inverse-square
law, are of only secondary importance to intrinsic
effects.
2.5
log(pulse peak flux)
2
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-0.5
-1
-1.5
-2
-2.5
log(pulse duration)
Peak luminosity (L) vs. duration (w)for
BATSE GRBs.
Relates to the GRB pulse
luminosity function!!!
2
2.5
BATSE 0111; z ≈ 0.9
BATSE 0332; z ≈ 0.9
BATSE 0563; z ≈ 0.8
BATSE 1406; z ≈ 0.8
Some low-z BATSE bursts
Correlated pulse
properties can be used
to estimate Long GRB
redshifts (Hakkila,
Fragile, & Giblin, 2009,
AIP Conf. 1133, 479) .
BATSE 0214; z ≈ 4.3
BATSE 0594; z ≈ 5.4
BATSE 0237; z ≈ 5.3
BATSE 0803; z ≈ 4.6
Some high-z BATSE bursts
Short GRB Pulses
10000
Short Swift GRBs (Norris, Gehrels, and
Scargle 2011, ApJ 735, 23) extend the peak
flux vs. duration relation to ms timescales.
EE
non-EE
log[intensity(c/s)]
1000
> Short and Long burst observable pulse
properties appear to indicate a single
distribution.
100
10
1
1
10
100
1000
log[duration(ms)]
How can peak flux correlations be
reconciled with differing luminosities of
Short and Long GRBs?
> Short and Long GRB pulse peak
luminosities do not differ dramatically when
the number of pulses per burst is taken into
account (data from Ghirlanda et al. 2009,
A&A 496, 585).
Isotropic luminosity per pulse
100.00
10.00
1.00
1
10
100
0.10
Short GRB pulses
Long GRB pulses
0.01
approximate number of pulses
» GRB pulses have similar correlated properties independent of GRB
class (and potentially of progenitor, environment, etc.).
Many GRB prompt emission properties that
correlate with luminosity are actually
properties of convolved pulses:
 The lag vs. peak luminosity relation (Norris et al. 2000, ApJ 534,
248): burst lag is convolved from pulse lags; peak luminosity is most
often based on peak flux of the brightest pulse.
 Variability vs. luminosity (Reichart et al. 2001, ApJ 552, 57):
variability is a convolved measure of pulse duration and number of
pulses; peak luminosity is most often based on peak flux of the
brightest pulse.
 Epeak vs. Eiso (Amati et al. 2002, A&A 390, 81): Epeak is the timeintegrated peak of the combined spectra of all pulses; Eiso is the
summed fluence luminosity of all pulses.
 The internal luminosity function (Hakkila et al. 2007, ApJS, 169,62):
the distribution of luminosity within a burst is a convolution of the
luminosity within each pulse and the number of pulses.
Mean properties of pulses within GRBs
(Hakkila and Preece, ApJ 2011 (in press)).
Correlative properties are bulk measurements
of hard-to-soft (H2S) pulse evolution
 Pulses start nearsimultaneously at all
energies (Hakkila and
Nemiroff 2009, ApJ 705, 372).
 Pulse Epeak values
appear to decay from
the pulse onset (e.g. Peng
et al. 2009, ApJ 698, 417).
Peng et al. (2009, ApJ 698, 417)
Intensity tracking GRB pulses
apparently do not exist
• Detailed study of 27 GRB pulses (14 hard-tosoft, 10 Intensity tracking, 3 ambiguous) pulses
common to BATSE pulse database (Peng et al.
2009, ApJ 698, 417; Peng et al. 2010 NA, 332,
92; Lu et al. 2010 ApJ, 1146, 1154).
• Intensity tracking pulses typically originate in
complex, multi-pulsed GRBs, and most of these
are composed of overlapping pulses. No IT pulses
can be unambiguously fitted by a single pulse
model, while 7 hard-to-soft pulses can.
• There appears to be a single pulse type.
Intensity Tracking pulse:
BATSE trigger 1886
A Conundrum
• Pulse peak intensity indicates the
maximum photon rate detected
from the decaying pulse spectrum.
Yet instrumental spectral response,
initial pulse spectrum, and GRB
redshift all alter the pulse peak
intensity. How does the detector
sample observable pulse properties
so that they always correlate with
what should be a distorted peak
intensity?
• Occam’s Razor: A pulse should be defined by its hard-to-soft spectral evolution
rather than by its intensity evolution. Since pulse intensity increases while the
energy decays, peak intensity and pulse rise are symptoms of hard-to-soft evolution,
rather than the climax.
Energy is injected at the beginning of the pulse, and the pulse we observe is simply
the energy decay resulting from this initial injection. This appears to be true for all
GRB pulses, regardless of class.
Implications of Correlated GRB Pulse Properties:
• Pulse physics appears ubiquitous and is easily replicated across a variety of GRB
environments. Properties of individual pulses within Long and Short GRBs may not be
appropriate classification tools whereas pulse distributions within a GRB may be.
• Theoretical pulse model needs not have many free parameters.
• Standard model: Kinematic energy injection into a medium via relativistic shocks; the
medium cools. Standard spectral model is preferentially a synchrotron spectrum (e.g.
Rees & Meszaros, ApJL, 1994, 430, 94) or a thermal plus power law spectrum (e.g.
Goodman 1986, ApJ 308, L47; Daigne & Mochkovitch 2002, MNRAS 336, 1271).
• Correlative pulse relations are not a direct and simple consequence of the standard
synchrotron shock model, which has no time-dependent component (Boci, Hafizi, &
Mochkovitch 2010, A&A, 519, 76).
• Jitter radiation appears to produce reasonable spectra coupled with short intensity
tracking time histories that do not have correlated pulse properties (e.g. Medvedev,
Pothapragada, & Reynolds 2009, ApJL, 702 L91).
• Curvature in a relativistic outflow can explain some, evolving pulse correlations (e.g.
Qin et al., Phys. Rev. D, 2006), but is model-dependent (rise vs. decay).