A Cosmology Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram

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A Cosmology Independent Calibration of Gamma-Ray
Burst Luminosity Relations and the Hubble
Diagram
arxiv 0802.4262v4 astro-ph
Paper accepted by ApJ
Nan Liang Collaborators Wei-Ke Xiao, Yuan Liu,
Shuang-Nan Zhang Tsinghua Center for
Astrophysics , Tsinghua University
Jun. 26th, 2008 Nanjing GRB conference
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GRB Luminosity Relations as standard candles

• GRB luminosity relations are connections between
  measurable properties of the ?-ray emission with
  the luminosity or energy.
• Recent years, several power law GRB relations
  have been proposed in many works.
• Many authors have made use of GRB relations as
  standard candles at very high redshift for
  cosmology research.

see e.g. Ghirlanda, Ghisellini, Firmani (2006),
Schaefer (2007) for reviews
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Five GRB Relations (Schaefer 2007, 69 GRBs)
lag - L relation (Norris, Marani, Bonnell 2000)
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Cosmology research
Some attempts related to the use of GRBs for
cosmology

• Schaefer 2003
• Takahashi et al. 2003
• Dai, Liang, Xu 2004
• Ghirlanda et al. 2004, 2005, 2006
• Ghirlanda, Ghisellini, Firmani 2006
• Firmani et al. 2005, 2006, 2007
• Liang Zhang 2005, 2006
• Xu, Dai, Liang 2005
• Wang Dai 2006 Wang, Dai, Zhu, 2007
• Schaefer 2007
• Qi, Wang, Lu, 2008

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The most important point related to GRB
cosmology ? The dependence of the
cosmological model to the
calibration of GRB relations.

• SN Ia cosmology cosmological model-independent
• ---- The Phillips relation can be calibrated
  with adequate sample at low-z.
• GRB cosmology cosmological model-dependent
• ---- Difficult to calibrate the relations
  using a low-z sample.
• ---- Calibration of GRB relations obtained
  by assuming
• a particular cosmological model.

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The circularity problem

• In order to investigate cosmology, the relations
  of standard candles should be calibrated in a
  cosmology-independent way.
• ? Otherwise the circularity problem can not be
  avoided easily.
• Many previous works treated this problem by means
  of statistical methods.
• ---- A simultaneous fit of the parameters in the
  calibration curves and the cosmology should be
  carried out.
• ---- Because a particular cosmology is required
  in doing the joint fitting, the problem can not
  be avoided completely.

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A new method to calibrate GRB relations

• Cepheids ? SNe Ia (SN cosmology )
• The distances of nearby SNe Ia used to
  calibrate the Phillips relation can be obtained
  by measuring Cepheid variables in the same
  galaxies.
• The distances of SN Ia obtained directly from
  observations are completely cosmological model
  independent.
• SNe Ia ? GRBs If the luminosity distances
  of GRBs can be obtained directly from the SN Ia
  data, we can calibrate the GRB relations in a
  cosmological model independent way.

Cosmic distance ladder
Cepheids ? SNe Ia ? GRBs
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Calibration of GRB relations cosmology
independent

• All types of sources at the same redshift should
  have the same luminosity distance for any certain
  cosmology.
• So many SN Ia samples ? the luminosity
  distance for any objects at any redshift (in SN
  Ia redshift range) can be obtained by
  interpolating from the Hubble diagram of SNe Ia.
• ? If regarding SNe Ia as the first order
  standard candles, we can obtain the luminosity
  distance of GRBs (in SN Ia redshift range) and
  calibrate the relations in a completely cosmology
  independent way.

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We calibrate seven GRB relations with the sample
at zlt1.4
(Amati et al. 2002)
(Liang Zhang 2005)
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Calibration results
Table 1. Calibration results for the 7 GRB
relations with the sample at zlt1.4.
? Results obtained by using the two interpolation
methods are almost identical. ? Results obtained
by assuming the two cosmological models (with the
same sample) differ only slightly from those
obtained by using interpolation methods.
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Fig. 1. The Hubble Diagram of 192 SNe Ia and 69
GRBs
Hubble Diagram of SNe Ia and GRBs
Concordance model
z1.4
? GRB high-z data , obtained from the
calibrated GRB standard candles (weighted
average over 5 relations used in Schaefer 2007)
These data are used to fit cosmological
parameters at high-z.
SN1997ff (z 1.755)
? GRB low-z data, interpolated from SN Ia data,
(thus also cosmology independent). These data are
used to calibrate the GRB standard candles.
? SNe Ia data (Davis et al. 2007), directly from
observations, cosmology independent. These data
used to interpolate the distance moduli of GRB
low-z data,
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Cosmological results from GRBs (for ?CDM model)
Fig. 2. OM -O? joint confidence contours from
42 GRBs (zgt1.4)
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Fig. 3. Confidence region in (OM w0 ) plane
Dark Energy model with a constant EoS (w0)
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Summary and Discussion

• With the basic assumption that objects at the
  same redshift should have the same luminosity
  distance, the distance modulus of a GRB can be
  obtained by interpolating from the Hubble diagram
  of SNe Ia at z lt1.4.
• We construct the GRB Hubble diagram and constrain
  cosmological parameters from 42 GRBs at 1.4ltzlt6.6
• ?OM 0.250.04-0.05 (for the flat ?CDM model)
• ? w0 -1.050.27-0.40 (for DE model with a
  constant EoS)
• Which are consistent with the concordance model
• (w0 -1, OM 0.27, O? 0.73)

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• Our method avoids the circularity problem
  completely, compared to cosmology-dependent
  calibration methods.
• Further examinations to the possible evolution
  effects and selection bias, as well as some
  unknown biases of SN Ia luminosity relations
  should be required for considering GRBs as
  standard candles to cosmological use.