Daisuke Yonetoku, Toshio Murakami, Yoshiki Kodama (Kanazawa Univ.) Ryo Tsutsui, Takashi Nakamura (Kyoto Univ.)

This is the first work about the dark energy measurement in the redshift range of 1.8 < z < 5.6 with Gamma-Ray Bursts.We recognize the existence of the non-zero WL – The Dark Energy - based on the Type Ia Supernovae observations. However we have little knowledge about its characteristics. So first of all, we hope to know the time dependence of the cosmological parameters.

Tully-Fisher

Type Ia SNe

HR Diagram

Cephied

parallax

Gamma-Ray Bursts

There are several distance indicators to determine the cosmological luminosity distance dL(z), such as “parallax”, “the HR diagram”, “the Tully-Fisher relation” and also “Type Ia Supernovae”. One luminosity indicator should be calibrated with the closer one, and extend toward more remote range. This system is known as “the cosmic distance ladder”.

NEARBY (z=0)

THE MOSTDISTANT SNe Ia(z=1.8, dL=14Gpc )

NEIGHBORGALAXIES(z=0.01, dL=43Mpc ) CMB (z=1089)

THE MOSTDISTANT GRB(z=6.7 , dL=67Gpc )

Z=1.788

Just

aft

er t

he

Big

Ban

g

The energy spectrum of the GRB prompt emission can be described as smoothly connected broken power-law function (Band et al. 1993).

We found a strong correlation between the peak energy (Ep) and the peak luminosity in the past work (Yonetoku et al. 2004). In those days, we simply assume the concordance cosmology of Wm = 0.27 and WL = 0.73, so we need to calibrate the function withthe luminosity distance measured by the Type Ia SNe observation.

νFν spectrum

∝ Eα

∝ Eβ

Peak Energy (Ep)

Photon Energy (MeV)

nFn

flu

x (e

rg/c

m2/s

)fl

ux

(ph

oto

n/c

m2/s

/MeV

)

Yonetoku et al. 2004

Peak Energy – Ep (1+z) (keV)

Pea

k L

um

ino

sity

(1 s

eco

nd

) (10

52er

g/s

)

We used 33 GRBs with the redshift of z < 1.8. The Ep value can be obtained by the spectral analyses. The luminosity is estimated with the luminosity distance measured from Type Ia SNewhich is purely observational value. Therefore we succeeded in calibrating the Ep-Lrelationwithout any assumption of theoretical cosmological models.

Pea

k L

um

ino

sity

(1 s

eco

nd

) (10

52er

g/s

)

Peak Energy – Ep (1+z) (keV)

L = 5.93×1047 [Ep (1+z)]1.85

Corr. Coef. = 0.9476

Chance Prob. = 6×10－17

The calibrated Ep-L relation

Kodama & Yonetoku et al. 2008

NEW Luminosity IndicatorWhen we obtain 3 parameters “Ep”, ”Flux” and “redshift”from gamma-ray observation,we enable to measure dL

beyond z > 2.

Lu

min

osi

ty D

ista

nce

(cm

)10

26

1027

102

810

29 ■GRB data (z < 1.8)

■GRB data (1.8 < z < 5.6)＋Type Ia SNe

Redshift

New!GRBs

CalibratedGRBs

0.01 0.1 1 10

Measure the universe Using the calibrated relation, we scale the dL at z > 2.The most important point is this result is based on the true observation, and free from theoretical model

Hubble Diagram at z > 2

Then, we adopt the theoreticalcosmological model for the (z,dL)data set, especially GRBs (z > 1.8) and calculate confidence contour on the (Wm, WL) plane.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Matter Wm

Dar

k E

ner

gy W

L

Dar

k E

ner

gy W

L

Matter Wm

Knop et al. 2003

This Result: 30 GRBs (1.8 < z < 5.6) SNe Cosmology Project

Kodama & Yonetoku et al. 2008

The most likely value: Wm = 0.25 , WL = 1.25 +0.27

-0.14+0.10-1.25

For the flat cosmological prior: Wm = 0.37 , WL = 0.63 +0.14-0.11

+0.11-0.14

The result is consistent with the concordance cosmology, and the time variation of the dark energy is small – like a cosmological constant.

arXiv: 0802.3428

Kodama, Yonetoku + (2008)

MNRAS Letters, 391, 1, L1-L4