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

the Hubble Diagram

Nan Liang

Collaborators: Wei-Ke Xiao, Yuan Liu, Shuang-Nan Zhang

Tsinghua Center for Astrophysics , Tsinghua UniversityTsinghua Center for Astrophysics , Tsinghua University

Paper accepted by ApJ

arxiv: 0802.4262v4 [astro-ph]

Jun. 26Jun. 26thth, 2008, 2008 Nanjing GRB conferenceNanjing GRB conference

GRB Luminosity Relations as “standard candles”

• GRB luminosity relations are connections between measurable properties of the γ-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

Five GRB Relations (Schaefer 2007, 69 GRBs)

lag - L relation(Norris, Marani, & Bonnell 2000)

Variability - L relation (Fenimore & Ramirez-Ruiz 2000)

Epeak- L relation (Schaefer 2003; Yonetoku et al. 2004) τRT - L relation (Schaefer, 2007)

E γ -Epeak relation (Ghirlanda, Ghisellini & Lazzati 2004)

Cosmology research

• 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;• …

Some attempts related to the use of GRBs for cosmology:

• 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.

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

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.

• 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.

A new method to calibrate GRB relations

Cosmic distance ladder: Cepheids → SNe Ia → GRBs

• 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.

Calibration of GRB relations: cosmology independent

1(1) : log ( (1 ) / 0.1

(2) : log ( (1 ) / 0.02

(3) : log ( (1 ) / 300

(4) : log ( (1 ) / 300

(5)

lag lag

p p

p p

R

L L a b z s

V L L a b V z

L E L a b E z keV

E E E a b E z keV

1: log ( (1 ) / 0.1

---- the five GRB luminosity relations used in Schaefer (2007)

T RTL L a b z s

1

2

(6) : log ( (1 ) / 300

(7) : log ( (1 ) / 300

( /(1 ) /1

iso p iso p

iso p b iso p

b

E E E a b E z keV

E E t E a b E z keV

b t z day

We calibrate seven GRB relations with the sample at z<1.4

(Amati et al. 2002)

(Liang & Zhang 2005)

→ 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.

Calibration results

Table 1. Calibration results for the 7 GRB relations with the sample at z<1.4.

Fig. 1. The Hubble Diagram of 192 SNe Ia and 69 GRBs

→ 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”,

→ GRB low-z “data”, interpolated from SN Ia data, (thus also cosmology independent). These data are used to calibrate the GRB “standard” candles.

→ 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.

Concordance modelz=1.4

Hubble Diagram of SNe Ia and GRBs

SN1997ff (z = 1.755)

Cosmological results from GRBs (for ΛCDM model)

Fig. 2. ΩM -ΩΛ joint confidence contours from 42 GRBs (z>1.4)

Fig. 3. Confidence region in (ΩM –w0 ) plane

Dark Energy model with a constant EoS (w0)

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 <1.4.

• We construct the GRB Hubble diagram and constrain cosmological parameters from 42 GRBs at 1.4<z<6.6

→ΩM = 0.25+0.04−0.05 (for the flat ΛCDM model)

→ w0 = −1.05+0.27−0.40 (for DE model with a constant EoS)

Which are consistent with the concordance model

(w0 = −1, ΩM = 0.27, ΩΛ = 0.73)

• 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.