Statistical Analysis of GRBs with Known Redshifts

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Statistical Analysis of GRBs with Known Redshifts

• G. Beskin, G. Greco, D. Badjin, S. Karpov,
• C. Bartolini, A. Guarnieri

Many faces of
GRB phenomena -optics vs high energy
SAO Workshop, October 12-16, 2009
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From 970228 to 090929B

• 787 GRBs localized within a few hours to days to
  less than 1 degree .

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GRBs with Spectroscopy redshifts

• Redshift distribution

N total Mean Minimum
Maximum 193 1,96 0,0085
8,26
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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

Optical Parameters

• Optical Peak Flux
• First Observation after ?-ray emission

• Isotropic Luminosity

kopt(z) is the cosmological correction that
takes into account the transformation of the R
passband in the proper GRB frame.
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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

Optical Parameters
by numerically integrating the afterglow in the
interval from the earliest observation to the
latest one

• Optical Fluence

• Optical Energy
• R Band

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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

Optical Parameters
determined as the time since the afterglow
detection during which 90 of the optical
fluence was received

• Optical Duration

The delay of the optical peak relative to the
time of burst detection in ?-ray

• Optical Peak

Proper frame quantities are also calculated
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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

Optical Parameters
the flux decay with time in the dependence F t??
at the initial observed afterglow phase.

• Power-Law Index

In our sample there are 11 well-detected optical
peaks that are not coincident with the work of
the ?-ray activity phase.

• Luminosity
• Optical Peak

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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

Optical Parameters
We consider the extrapolated optical luminosity
Le immediately after the corresponding duration
of the prompt - ray emission in the rest frame of
the source. The extrapolation is performed using
the slope calculated at early stage. We
extrapolate the total energy Eto and total time
duration Ttot of the optical afterglow.

• Extrapolated
• Luminosity

• Total Optical Energy

• Total Optical Duration

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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

?-ray Parameters

• Peak ?-ray Flux

Observed Peak Flux

• Peak ?-ray Luminosity

k?(z) is the k correction. FE is the spectral
flux density, e1 and e2 are the lower and upper
boundaries of the energy range in which F? was
obtained, E1 and E2 are the boundaries the energy
range of interest in the proper burst frame..
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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

?-ray Parameters
determined from published observations by
reducing them to the energy range 15-150 keV.

• ?-ray Fluence

• Isotropic ?-ray Energy

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Our Sample 87 long GRBs

• with confirmed redshift
• well-sampled light curves observed in R-band

?-ray Parameters

• Prompt ?-ray emission duration
• observed

we used the universally accepted
parameter that is published in the results of
?-ray observations.

• Prompt ?-ray emission duration
• intrinsic

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Pair Correlation Intrinsic Frame
Pearson correlation coefficients for the observed
GRB parameters.
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Pair Correlation Observed Frame
Pearson correlation coefficients for the observed
GRB parameters.
The observed quantities show a weaker
correlation, which is indicative of the actual
physical relationships between the
characteristics of afterglows in their proper
reference frame.
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Universal Optical Light CurveEopt versus Lopt
Lopt
versus TpeaK
r 0.76
r 0.79
The observed correlations suggest a universal
underlying structure for optical afterglow
emissions
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Universal ?-ray Light CurveEiso versus Liso

r 0.98
The observed correlations suggest a universal
underlying structure for the ?-ray emissions
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Luminosity Optical Peak
Late time peaks are excluded (i.e GRB 970508).
r 0.9 (SL 6.5 x 10 -8)
The detected correlation is confirmed in new 5
optical peak light curves.
Many faces of GRB phenomena -optics vs
high energy SAO
Workshop, October 12-16, 2009
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Discussion Conclusion
Our statistical analysis has tried to answer the
following questions

• Is there evidence of cosmological evolution on
  ?-ray burst features?
• Is there evidence of cosmological evolution on
  optical afterglow?
• Despite the morphological differences between the
  high-energy emission and their afterglows, can we
  assume a universal underlying structure for both
  emissions ?
• The intrinsic properties of prompt ?-ray emission
  show some degree of correlation with their
  afterglows or the afterglow 'forget' the initial
  physical conditions ?

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Discussion Conclusion

• We have demonstrated, for a sample of 87 GRB with
  confirmed spectroscopic redshift, that the
  properties of the ?-ray emission are not affected
  by any cosmological evolution.
• On the other hand the first stage of the
  afterglow evolution has a dependence on redshift
  and is even clearer if we consider the peaks that
  arise when the prompt ?-ray emission has been
  completely extinguished.
• There are correlations between the luminosity,
  the total energy and the duration of the ?-ray
  and optical emission separately, which can arise
  from universal features of the observed light
  curves.
• The intrinsic properties of prompt ?-ray emission
  show no degree of correlation with their
  afterglows.

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Our References

• Connections between parameters of GRB afterglows,
  Beskin, G. M. Bartolini, C. Cosentino, G.
  Guarnieri, A. Lodi, S. Piccioni, A. GAMMA-RAY
  BURSTS 5th Huntsville Symposium. AIP Conference
  Proceedings, Volume 526, pp. 355-359 (2000)
• GRB Optical Afterglows Correlation between Pair
  of Parameters, C. Bartolini,  G. Beskin,  G.
  Cosentino,  A. Guarnieri, A. Piccioni, A.
  Pozanenko,  Gamma-Ray Bursts in the Afterglow
  Era Proceedings of the International Workshop
  Held in Rome, Italy, 17-20 October 2000, ESO
  ASTROPHYSICS SYMPOSIA. ISBN 3-540-42771-6. Edited
  by E. Costa, F. Frontera, and J. Hjorth.
  Springer-Verlag, 2001, p. 151
• GRBs with optical afterglow and known redshift A
  statistical study, Il Nuovo Cimento B, vol. 121,
  Issue 12, p.1487-1488 G. Greco, D. Bad'in, G.
  Beskin, C. Bartolini, S. Karpov, A. Guarnieri, A.
  Piccioni, A. Biryukov, 2006.
• Statistical Analysis of GRBs with Known Redshifts
  AIP Conference Proceedings, Volume 1065, pp.
  75-78 G. Greco, G. Beskin, D. Bad'in, S. Karpov,
  C. Bartolini, A. Guarnieri, 2008.
• Investigation of gamma-ray bursts with known
  redshifts Statistical analysis of parameter ,
  Astronomy Letters 351, 7-24 D. Bad'in, G. Beskin
  G. Greco, 2009