**Extending the cosmic ladder to z~7 and beyond: using SNIa to** calibrate GRB standard candels Speaker:Shuang-Nan Zhang Collaborators: Nan Liang, Pu-Xun Wu Tsinghua Center for Astrophysics , Tsinghua University New Directions of Cosmology Mar, 18th, 2009, KITPC/ITP - CAS

**GRB luminosity relations** • Gamma-Ray Bursts (GRBs) are the most intense explosions observed so far. → GRBs are likely to occur in high redshift range (z~7). • 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

**Eγ -Epeak relation** (Ghirlanda, Ghisellini & Lazzati 2004) Epeak- L relation (Schaefer 2003; Yonetoku et al. 2004) Variability - L relation (Fenimore & Ramirez-Ruiz 2000) τRT - L relation (Schaefer, 2007) FiveGRB luminosity relations(Schaefer 2007, 69 GRBs) lag - L relation (Norris, Marani, & Bonnell 2000)

**Calibration of GRB relations** • SN Ia cosmology: ---- adequate sample at low-z which can be used to calibrate the Phillips relation essentially independent of any cosmology. • GRB cosmology : ---- difficult to calibrate the relations using a low-z sample. ---- Calibration of GRB relations so far have been derived by assuming a particular cosmology (e.g. ΛCDM model).

**The circularity problem** • In order to investigate cosmology, the relations of standard candles should be calibrated in a cosmological model independent way. ----Otherwise the circularity problem can not be avoided easily. • In principle, the circularity problem can be avoided in two ways (Ghirlanda et al. 2006): (i) A solid physical interpretation of these relations which would fix their slope independently from cosmology. (ii) The calibration of these relations by several low redshift GRBs.

**Statistical approaches** Many previous works treated the circularity problem by means of statistical approaches. →simultaneous fitting (Schaefer 2003) the parameters in the calibration curves and the cosmology should be carried out at the same time. → Bayesian method (Firmani et al. 2005) → Markov Chain Monte Carlo global fitting (Li et al. 2008, Wang 2008)

**Cosmic distance ladder** • It is obvious that the sources at the same redshift should have the same luminosity distance for any certain cosmology. • Distance of SN Ia obtained directly from observations are completely cosmological model independent. • SN Ia cosmology: the distance of nearby SN Ia used to calibrate the Phillips relation can be obtained by measuring Cepheids in the same galaxy. Thus Cepheids has been regard as the first order standard candle to calibrate SNe Ia as the secondly order standard candle. • If distance modulus of GRBs can be obtained direct from the SN Ia data, we can calibrate the relations of GRBs in a cosmology independent way. Cepheids → SN Ia SN Ia → GRBs

**Using SN Ia calibrate GRB relations** • There are so many SN Ia samples that we can obtain the distance modulus at any redshift in the redshift range of SN Ia directly from the Hubble diagram of SN Ia. →InterpolationMethod (Liang et al, 2008, ApJ) → Iterative Method (Liang & Zhang, 2008, AIPC) • If regarding the SN Ia as the first order standard candle, we can obtain the distance modulus of GRBs in the redshift range of SN Ia andcalibrate the relations of GRBs in a completely cosmology independent way. • By utilizing the relations to the GRB data at high redshift, we can use the standard Hubble diagram method to constrain the cosmological parameters.

**Low-z GRB** Standard Candle High-z GRB Cosmology 1929: Discovery of cosmic expansion Distinguish cosmological models ？ Nearby SN Ia Standard Candle Low-z SN Ia Cosmology z SN: 1.7 GRB: ~7 Cosmic distance ladder: Cepheids→SNe Ia → GRBs Extra-galactic Cepheids Galactic Cepheids 1998: Discovery of Dark Energy

**GRB Luminosity Relations Calibration** We calibrate seven GRB relations with the sample at z<1.4 (Liang et al, 2008, ApJ) (Amati et al. 2002) (Liang & Zhang 2005)

**Calibration results** Table 1.Calibration results for the 7 GRB relations with the sample at z<1.4. → Results obtained by using the two interpolation methods are almost identical. → Results obtained by assuming the two cosmological models (with the samesample) differ only slightlyfrom those obtained by using interpolation methods.

**Hubble Diagram of SNe Ia and GRBs** Fig. 1. The Hubble Diagram of SNe Ia and GRBs z=1.4 Concordance model → 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”,

**Cosmological results from GRBs (for ΛCDM model)** Fig. 2.ΩM -ΩΛ joint confidence contours from42 GRBs (z>1.4)

**Dark Energy model with a constant EoS (w0)** Fig. 3. Confidence region in (ΩM –w0 ) plane

**About double-use of SN Ia data** • After using SN Ia data to calibrate GRB relations, some of the SN Ia events are no-longer independent of GRB relations (Yun Wang 2008) • Problematic for combining SN Ia data with GRB data • A possible solution to this problem • Simply throw away those SN Ia events used for calibrating GRB relations

**Combined GRBs with SNe Ia, WMAP5, BAO** (Liang, Wu & Zhang, 2009) New SN Ia data • 307 SCP Union data (Kowalski et al. 2008) • 397 CfA SN Ia data (Hicken et al. 2009) CfA3 sample is added to Union data 69 GRB Data • Using 40 SN Ia points from 397 CfA SN Ia data to interpolate 27 GRB distance modulus (z<1.4) → 42 GRB data (1.4<z<=6.6) Independent distance modulus data: 357 SNe Ia + 42 GRBs

**CMB and BAO Data** → The shift parameter R of CMB (WMAP5) → The distance parameter A of baryon acoustic oscillation (SDSS+ WMAP5)

**GRB + SN Ia + CMB + BAO** 357 SN Ia + 42 GRB CMB (WMAP5) BAO(SDSS+WMAP5)

**(i) ΛCDM model: ΩM0 -ΩΛ joint confidence** ΩM0 = 0.288+0.028−0.026 , ΩΛ = 0.721+0.024−0.023 flat universe ΩM0 = 0.278+0.017−0.015

**(ii) wCDM model: ΩM0 - w joint confidence** ΩM0 = 0.275+0.025−0.023 , w = -0.94+0.08−0.08

**(iii)Parameterized w(z) model:** w0 = -0.95+0.19−0.20 , w a = 0.66+0.32−0.58

**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. • Thus we construct the GRB Hubble diagram and constrain cosmological parameters for 42 GRBs at 1.4<z<6.6. • Finally, we fit the cosmological parameters by combining the SN Ia and GRB data with the new WMAP 5-year data and BAO data.

**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. • Our method avoids the circularity problem completely, compared to previous cosmology-dependent calibration methods.