T90histogram.eps

Acta Polytechnica Vol. 52 No. 1/2012

On the Relation Between GRB Classes and X-ray Flashes

Z. Bagoly, P. Veres, I. Horváth, A. Mészáros, L. G. Balázs

Abstract

Gamma-ray bursts are usually classified into either short-duration or long-duration bursts. Going beyond the short-long
classification scheme, it has been shown on statistical grounds that a third, intermediate population is needed in this
classification scheme. We are looking for physical properties which discriminate the intermediate duration bursts from
the other two classes. As the intermediate group is the softest, we argue that we have related them with X-ray flashes
among the GRBs. We give a new, probabilistic definition for this class of events.

Keywords: gamma rays, bursts, observations.

1 Introduction

To discern the physical properties of GRBs as a
whole, we need to understand the number of physi-
cally different underlying classes of the phenomenon.
With the launch of the Swift satellite [1], a new per-
spective has opened up in the study of gamma-ray
bursts and their afterglows. The intermediate GRB
population in the studies [2–5] so far has always been
the softest among the groups, meaning that inter-
mediate GRBs emit the bulk of their energy in the
low-energy gamma-rays.

Here we report on a significant difference in the
peak-flux distribution between the intermediate and
the short populations, and between the intermediate
and long populations. We identify a third popula-
tion using a multi-component model and we show
that this group has a significant overlap with X-
ray flashes. The First Swift BAT Catalog [6] was
augmented with bursts up to August 7, 2009. After
excluding the outliers and bursts without measured
parameters, our sample has a total of 408 GRBs. To
obtain the spectral parameters we fitted the spec-
tra integrated for the duration of the burst with a
power law model and a power law model with an
exponential cutoff. The most widely used duration
measure is T90, which is defined as the period be-
tween the 5 % and 95 % of the incoming counts.
To find the fluences (SEmin,Emax) we integrated the
model spectrum in the usual Swift energy bands with
15 − 25 − 50 − 100 − 150 keV as their boundaries. We
define the hardness ratio (Hij , where i and j mark
the two energy intervals) as the ratio of the fluences
in different channels for a given burst.

2 Classification

There are many indications that the phenomenon
which we observe as gamma-ray bursts has more than

one underlying population. The goal is to identify
classes which are physically different. By using T90
and H32 we include a basic temporal and spectral
characteristic of the bursts. We carry out three types
of classifications: model-based multivariate classifi-
cation, k-means clustering and hierarchical cluster-
ing. We use the algorithms implemented in the R
software1.

Studies show that for example the distribu-
tion of the logarithm of the duration can be ade-
quately described by a superposition of three Gaus-
sians [2]. Here we find the model parameters us-
ing the Expectation-Maximization (EM) maximum
likelihood method. We use the Bayesian Informa-
tion Criterion (BIC), introduced by [7, 8], to find the
most probable model (including the number of com-
ponents) and the parameters of this model. For k
components (bivariate Gaussians) the number of free
parameters is 6k − 1, since the sum of the weights
is 1.

We have applied this classification scheme on our
sample, and found that the model with three com-
ponents gives the best fit for the data in the BIC
sense, where the shape of the bivariate Gaussians is
the same (σlog

10
T90,i = σlog10 T90,j and σlog10 H32,i =

σlog
10

H32,j for i, j = {short, long, intermediate}) for
each group, only their weights are different with no
correlation, the best model has a value of BIC =
−262.14. The clustering method of this model shows
that a three bivariate component model is the most
preferred. Two components models have the best
BIC ∼ −276 and for models with four components
the best BIC ∼ −274, both are clearly below the
maximum. The best-fit model has 10 free parame-
ters and has three bivariate Gaussian components.
We assign class memberships probabilities using the
ratio of the fitted bivariate models at the burst lo-
cation on the duration-hardness plane. The model
has the following three components with equal stan-

1http://cran.r-project.org

Acta Polytechnica Vol. 52 No. 1/2012

Table 1: Bivariate model parameters for the best-fitted (EEI) model. The standard deviations in the direction of the
coordinate axes and the correlation coefficients are constrained by the model

Groups pl lg T90C lg H32C σlgT90 σlgH32 r Nl

short 0.08 −0.331 0.247 0.509 0.090 0 31

interm. 0.12 1.136 −0.116 0.509 0.090 0 46

long 0.80 1.699 0.114 0.509 0.090 0 331

dard deviations in both directions and with no cor-
relation (r = 0) (see also Table 1):

1. The first component is the known short class of
GRBs (shortest duration and hardest spectra).
The average duration is 0.47 s and the average
hardness ratio is 1.77. It has 31 members, and
the weight of this model component is 0.08.

2. The second, most numerous model component is
the long class, also identified in many previous
studies. It has an average duration of 50.0 s and
an average hardness of 1.30. It has 331 mem-
bers and the weight of the model component is
0.80.

3. The third and softest class is intermediate in
duration. It has overlapping regions with pre-
vious definitions of the intermediate class [4].
The average duration is 13.7 s, and the average
hardness of this class is 0.77. It has 46 mem-
bers and the weight of the model component is
0.12.

-2 -1 0 1 2 3
log

10
T

-0.4

-0.2

0.0

0.2

0.4

0.6

lo
g

1
0
H

3
2

XRF

Fig. 1: GRBpopulations on the duration-hardness plane.
Triangles mark the long class, squares mark the short
class and circles mark the intermediate class. Filled sym-
bols mark bursts with measured redshifts. One and two
sigma ellipses are superimposed on the figure to illustrate
the model components found as described in the text.
The dashed line indicates the definition of X-ray flashes
(XRFs) given by [9]

All components have the same standard deviation
in both directions. This means the shape of the Gaus-
sian is the same for the three groups (though obvi-
ously their weight is different). Models with non-zero
correlation coefficients between the two variables are
not favored in the BIC sense, contrary to the models
with r = 0.

Using both model-based and non-parametric k-
means and hierarchical clustering methods we have
experimented by using T50 instead of T90, by us-

ing different hardness ratios (e.g., H42 =
S100−150
S25−50

H432 =
S100−150

S25−50 + S50−100
etc.). The classification re-

mained essentially the same.

3 Discussion

Our analysis on the Swift GRBs supports the earlier
results that there are three distinct groups of bursts.
Again, besides the long and the short population, the
intermediate duration class appears to be the softest.

The intermediate bursts’ peak-flux are systemat-
ically lower than the long ones, while their redshift
range is either lower or similar. We thus conclude
that the intermediate class is intrinsically dimmer. If
the intermediate population is part of the long pop-
ulation, the lower peak-flux requires a physical ex-
planation. The observational properties show that
intermediate bursts are the softest among the three
groups, meaning that their emission is concentrated
to low-energy bands.

As the intermediate population is the softest, it
is worth searching for a link with the similar and
softer phenomenon compared to classical gamma-
ray bursts, the X-ray flashes (XRFs) (for a review,
see [11]). [9] gives a working definition for X-ray
flashes (XRF) and X-ray rich GRBs (XRR) for Swift
using the fluence ratio. The S23 fluence ratio is the
reciprocal of the hardness (H32 = (S23)

−1). Cur-
rent understanding of XRFs indicate that they are
related to long bursts and they form a continuous
distribution in the peak energy (Epeak) of the νFν
spectrum [9].

According to the fuzzy classification model we
do not get a definite membership for a given burst,
rather a probability that a burst belongs to a group.
To identify the intermediate population (and tenta-
tively the X-ray flashes), we use the indicator func-
tion:

IInterm.(log10 T90, log10 H32) = (1)

Pinterm. × P (log10 T90, log10 H32|”Interm.”)
∑

l∈{short,interm.,long}

Pl × P (log10 T90, log10 H32|l)

Acta Polytechnica Vol. 52 No. 1/2012

The values of the parameters in this equation
should be taken from Table 1. The joint distribu-
tion function of the fitted model can be seen in gray
in Figure 2 and the probability contours of the third
population are drawn in black with probability level
contours shown.

Fig. 2: Contour plot of the Swift’s duration-hardness dis-
tributionbased on theEEImodelwith three components.
Points show individual bursts. The dashed line shows the
region belonging to the XRF population, and the indica-
tor function of the intermediate group is shown by solid
lines. One can observe the strong coincidence between
the XRFs and the intermediate group

[9] define XRFs as events with hardness ratio
H32 < 0.76. The limit is found using a pseudo-burst
with spectral parameters: α = −1, β = −2.5 and
Epeak = 100 keV for a Band spectrum [10]. Based
on this definition we identify 24 bursts from our 408
burst sample. The average of these bursts’ probabili-
ties, (i.e. the XRF belongs to the intermediate group)
is 95 %. This high value allows us to conclude that
all XRFs belong to the intermediate group defined
by the EEI model with high probability. We propose
that the members of the third component are proba-
bly X-ray flashes. Therefore, using the model based
classification method we can give a probabilistic def-
inition for the X-ray flashes based on the duration-
hardness distribution. This definition defines 22 ad-
ditional bursts that belong to the intermediate pop-
ulation and hence to the XRFs.

All the X-ray flashes are in the region where the
third component has the highest probability, but not
all third component bursts can be unambiguously
classified as X-ray flashes according to the [9] cri-
terion. In other words the third component in the
EEI model contains all the X-ray flashes and some
additional, very soft bursts.

The mechanism behind the X-ray flashes is still
not clear. There are various scenarios that could pro-
duce these phenomena (e.g. dirty fireballs, inefficient
internal shocks, structured jets with off-axis viewing
angle, etc., for a review of the models see [12]). A

more precise experimental definition of XRFs can re-
sult in more stringent constraints on the models.

Acknowledgement

This work was supported by OTKA grant K077795,
by OTKA/NKTH A08-77719 and A08-77815 grants
(Z.B.), by GAČR grant No. P209/10/0734 (A.M.),
by the Research Program MSM0021620860 of the
Ministry of Education of the Czech Republic (A.M.)
and by a Bolyai Scholarship (I.H.). We thank Pe-
ter Mészáros, Gábor Tusnády, Ĺidia Rejtő and Jakub
Řı́pa for valuable comments.

References

[1] Gehrels, N., et. al: ApJ, 611, 1 005–1 020.

[2] Horváth, I., et. al: A & A, 447, 23–30.

[3] Huja, D., Mészáros, A., Řı́pa, J.: A & A, 504,
67.

[4] Horváth, I., et. al: A & A, 713, 552.

[5] Řı́pa, J., et. al: A & A, 498, 399.

[6] Sakamoto, T., et. al: ApJ Suppl., 175, 179–190.

[7] Schwarz, G.: Annals of Statistics, 6, 2, 461–464.

[8] Liddle, A. R.: MNRAS, 377, L74–L78.

[9] Sakamoto, T., et. al: ApJ, 679, 570–586.

[10] Band, D., et. al: ApJ, 413, 281–292.

[11] Hullinger, D.: Early afterglow evolution of x-ray
flashes observed by Swift, PhD thesis, University
of Maryland, College Park, 2006.

[12] Zhang, B.: Chinese Journal of Astronomy and
Astrophysics, 7, 1–50.

Z. Bagoly
Department of Physics of Complex Systems
Eötvös University
1518 Budapest, Pf. 32, Hungary
Department of Physics
Bolyai Military University
1581 Budapest, POB 15, Hungary

P. Veres
Department of Physics of Complex Systems
Eötvös University
1518 Budapest, Pf. 32, Hungary
Department of Physics
Bolyai Military University
1581 Budapest, POB 15, Hungary
Konkoly Observatory
1505 Budapest, POB 67, Hungary

Acta Polytechnica Vol. 52 No. 1/2012

I. Horváth
Department of Physics
Bolyai Military University
1581 Budapest, POB 15, Hungary

L. G. Balázs
Konkoly Observatory
1505 Budapest, POB 67, Hungary

A. Mészáros
Astronomical Institute
Faculty of Mathematics and Physics
Charles University
V Holešovičkách 2, 180 00 Prague 8, Czech Republic