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

the Hubble Diagram

Shuang-Nan Zhang

Collaborators: Nan Liang, Wei-Ke Xiao, Yuan Liu,

Tsinghua Center for Astrophysics , Tsinghua University

Paper accepted by ApJ

arxiv: 0802.4262v4 [astro-ph]

July 10July 10thth, 2008, 2008 Cosmic Reionization, KIAA, PKUCosmic Reionization, KIAA, PKU

Gamma Ray Bursts• Discovered in 1967 by Los Alamos Several per

day

• Last from ms to ~ 100 seconds

• Brightest gamma ray phenomenon

• Isotropic on sky (BATSE/CGRO)

• No repetitions

seconds

BATSE

Vela 4a

Isotropy: first sign of cosmological origin

Bimodality of GRB duration

Hardness ratio distribution

Light curves

GRB spectra (Schaefer et al. 1992, ApJ)

Epeak: peak energy

~several hundred keV

Gamma Ray Burst Breakthrough!

• BeppoSAX combination of wide field and narrow field instruments give 6-hr response to gamma ray burst – observations in 1997 revealed a fading X-ray afterglow– 20 mag optical afterglow identified from X-ray position– Afterglow decays as powerlaw with time

6 hours 48 hours

X-ray Images from BeppoSax

HST Image

X-ray Afterglow

Afterglow detection

HST Afterglow Detection

Broadband spectrum

The fireball model

Do you notice a small mistake on this picture?

Jet vs spherical geometry: light curve break

Opening angle and light curve break

Evidence for jet

GRB Luminosity Relations as “standard candles”

• GRB luminosity/energy relations are connections between measurable properties of the γ-ray emission with the luminosity or energy.

• Several GRB luminosity relations as distance indicators have been proposed, for those long and soft GRBs.

• Many authors have made use of these GRB luminosity indicators 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)

Physical Explanations for the Eγ-Epeak relation

Synchrotron radiation + beaming correction (Dai, Liang & Xu 2004; Dai & Lu 2002; Zhang & Meszaros 2002)

Ring-shape jet + viewing angle effect (Levinson & Eichler 2005)

Comptonization of the thermal radiation flux that is advected from the base of an outflow (Rees & Meszaros 2006)

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 cosmological model 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.

The Cosmic Distance Ladder

Extra-galactic

Cepheids

H-z GRBCosmology

L-z SN IaStandard Candle

GalacticCepheids

M-z SN IaCosmology

M-z GRBStandard

Candle

zage

1.7 6.3

3.5 113.5 billion yrs

1998: Discovery of Dark Energy

1929: Discovery of cosmic expansion

• The distances of SN Ia obtained directly from observations are completely cosmological model independent.

• SNe Ia → GRBs :If the luminosity distance 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

• 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 object 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 for 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 previous 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.

We predicted that many GRBs should be produced at z > 10

Brighter GRBs produces harder photons, and are thus detectable from higher redshift

(Amati, 2006, MNRAS; 2002, A&A; Yonetoku et al., 2004, ApJ, 609, 935; Sakamoto et al., 2004, ApJ, 602, 875)

The Amati relation for Long/Soft GRBs

2isopeakE

GRB as probe of cosmic reionization

SN Iarange

Current GRB range

Future GRB range