Redshifts of the Long Gamma-Ray Bursts
Baltic Astronomy, vol.12, XXX–XXX, 2003.
THE REDSHIFT OF LONG GRBS’
Z. Bagoly1 and I. Csabai2 and A. Mészáros3 and P. Mészáros4
and I. Horváth5 and L. G. Balázs6 and R. Vavrek7
1 Lab. for Information Technology, Eötvös University, H-1117 Budapest,
Pázmány P. s. 1./A, Hungary
2 Dept. of Physics for Complex Systems, Eötvös University, H-1117 Bu-
dapest, Pázmány P. s. 1./A, Hungary
3 Astronomical Institute of the Charles University, V Holešovičkách 2,
CZ-180 00 Prague 8, Czech Republic
4 Dept. of Astronomy & Astrophysics, Pennsylvania State University,
525 Davey Lab., University Park, PA 16802, USA
5 Dept. of Physics, Bolyai Military University, H-1456 Budapest, POB
12, Hungary
6 Konkoly Observatory, H-1505 Budapest, POB 67, Hungary
7 Max-Planck-Institut für Astronomie, D-69117 Heidelberg, 17 Königstuhl,
Germany
Received October 20, 2003
Abstract. The low energy spectra of some gamma-ray bursts’ show ex-
cess components beside the power-law dependence. The consequences of
such a feature allows to estimate the gamma photometric redshift of the
long gamma-ray bursts in the BATSE Catalog. There is good correla-
tion between the measured optical and the estimated gamma photometric
redshifts. The estimated redshift values for the long bright gamma-ray
bursts are up to z = 4, while for the the faint long bursts - which should
be up to z = 20 - the redshifts cannot be determined unambiguously with
this method. The redshift distribution of all the gamma-ray bursts with
known optical redshift agrees quite well with the BATSE based gamma
photometric redshift distribution.
Key words: Cosmology - Gamma-ray burst
1. INTRODUCTION
In this article we present a new method called gamma photometric
redshift (GPZ) estimation of the estimation of the redshifts for the
http://arxiv.org/abs/0704.0864v1
2 Z.Bagoly et. al
long GRBs. We utilize the fact that broadband fluxes change sys-
tematically, as characteristic spectral features redshift into, or out of
the observational bands. The situation is in some sense similar to
the optical observations of galaxies, where for galaxies and quasars
the photometric redshift estimation (Csabai et. al (2000), Budavári
et. al (2001)) achieved a great success in estimating redshifts from
photometry only.
We construct our template spectrum that will be used in the GPZ
process in the following manner: let the spectrum be a sum of the
Band’s function and of a low energy soft excess power-law function,
observed in several cases (Preece et. al (2000)). The low energy
cross-over is at Ecr = 90 keV, Eo = 500 keV, and the spectral indices
are α = 3.2, β = 0.5 and γ = 3.0.
Let us introduce the peak flux ratio (PFR hereafter) in the fol-
lowing way:
PFR =
l34 − l12
l34 + l12
where lij is the BATSE DISCSC flux in energy channel Ei < E < Ej ,
here E1 = 25 keV, E2 = E3 = 55 keV, E4 = 100 keV.
0 2 4 6 8 10 12 14
α=3.2    β=0.5    Ecr=90 keV    
Fig. 1. The theoretical PFR curves
calculated from the template spec-
trum using the average detector re-
sponse matrix.
The spectra are changing
quite rapidly with time; the typ-
ical timescale for the time vari-
ation is ≃ (0.5 − 2.5) s (Ryde &
Svensson (1999, 2000)). There-
fore, we will consider the spectra
in the 320ms time interval cen-
tered around the peak-flux. If
we redshift the template spec-
trum and use the detector re-
sponse matrix of the given burst,
we can get for any redshift the
observed flux and the PFR value.
On Fig. 1. we plot the the-
oretical PFR curves calculated
from the above defined template
spectrum using the average detector response matrices for the 8 bursts
that have both BATSE data and measured redshifts (Klose (2000))
In the used range of z (i.e. for z<
4) the relation between z and PFR
is invertible, hence we can use it to estimate the gamma photometric
The Redshift of Long GRBs’ 3
redshift (GPZ) from a measured PFR. For the 7 considered GRBs
(leaving out GRB associated with the supernova and GRB having
upper redshift limit only) the estimation error between the real z
and the GPZ is ∆z =≈ 0.33.
2. ESTIMATION OF THE REDSHIFTS
Here restrict ourselves to long and not very faint GRBs with
T90 > 10 s and F256 < 0.65 photon/(cm
2s) to avoid the problems with
the instrumental threshold (Pendleton et. al (1997), Hakkila et. al,
(2000)). Introducing an another cut at F256 > 2.00 photon/(cm
2s) we
can investigate roughly the brighter half of this sample.
As the soft-excess range redshifts out from the BATSE DISCSC
energy channels around z ≈ 4, the theoretical curves converge to a
constant value. For higher z it starts to decrease. This means that
the method is ambiguous: for the given value of PFR one may have
two redshifts - below and above z ≈ 4. Because for the bright GRBs
the values above z ≈ 4 are practically excluded, for them the method
is usable. Using only the 25 − 55 keV and 55 − 100 keV BATSE
energy channels, this method can be used to estimate GPZ only in
the redshift range z <
0  1  2  3  4  5
Gamma Photometric Redshift
F256>0.65 ph/cm
F256>2.0 ph/cm
Fig. 1. The distribution of the GPR
estimators of the long GRBs having
DISCSC data.
Let us assume for a moment
that all observed long bursts, we
have selected above, have z <
4. Then we can simply calculate
the zGPZ redshift for any GRB,
which has PFR from the DISCSC
data. Fig. 2. shows the distribu-
tion of the estimated derived red-
shifts under the assumption that all
GRBs are below z ≈ 4. The dis-
tribution has a clear peak value
around PFR ≈ 0.2, which corre-
sponds to z ≈ (1.5− 2.0).
Although there is a problem
with the degeneracy (e.g. two possible redshift values) we think that
the great majority of values of z obtained for the bright half are
correct. This opinion may be supported by the following arguments:
the obtained distribution of GRBs in z for the bright half is very
similar to the obtained distribution of Schmidt (2001) and Schaefer
4 Z.Bagoly et. al
et. al (2001). An another problem for z as it moves into z>
4 regime for
the bright GRB is the extremely high GRB luminosities, ≃ 1053ergs/s
(Mészáros & Mészáros, 1996).
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
17 bursts with known redshift
GPZ{ F256>0.65 ph/cm2/s
Fig. 3. The redshift distribution of
the 17 GRBs’ with known z and the
distributions from the GPZ estima-
tors.
As an additional statistical
test we compared the redshift
distribution of the 17 GRB with
observed redshift with our re-
constructed GRB z distributions
(limited to the z < 4 range). For
the F256 > 0.65 photon/(cm
group the KS test suggests a 38%
probability, i.e. the observed
N(< z) probability distribution
agrees quite well with the GPZ
reconstructed function.
ACKNOWLEDGMENTS
The useful remarks with Drs. T.
Budavári, S. Klose, D. Reichart,
A.S. Szalay are kindly acknowl-
edged. This research was supported in part through OTKA grants
T024027 (L.G.B.), F029461 (I.H.) and T034549, Czech Research
Grant J13/98: 113200004 (A.M.), NASA grant NAG5-9192 (P.M.).
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