1. Tight Liso-Ep-Γ0 Relation of Long Gamma-Ray Bursts
Enwei Liang
Guangxi University, China
Good afternoon, every body. Thanks to the organizers to give me a talk. I am going to talk a tight correlation among the isotropic gamma-ray luminosity, the peak energy of the spectrum, and the initial Lorentz factor of long gamma-ray bursts.
IAUS 324: New Frontiers in BH Astrophys.
, Ljubljana Selovenia

2. General Picture of Gamma-Ray Bursts
GRBs and their afterglows are produced from extremely relativistic jets
powered by the central engine.
V ≥ c
It is well known that gamma-ray bursts and their afterglows are from a relativistic jet powered by the GRB central engine from the death of massive stars or mergers of two compact stars. The initial Lorentz factor of the GRB outflow is usually believed to be more than one hundred and even one thousand. 2

3. Estimating the Initial Γ0 of GRB jets
With the fireball deceleration time(e.g.,Sari & Piran 1999)
With the "compactness" argument: (e.g.,Lithwick & Sari 2001)
With the photosphere radiation: (e.g. Zou )
Liang
Tang
The initial Lorentz factor is critical to revealing the GRB physics. It usually can be estimated with the fireball deceleration time scale observed in the early afterglow lightcurves. In the thin shell scenario, the standard afterglow model predicts a clear onset peak and the peak time is the deceleration time of the fireball when it propagates into the circum medium. You can see here that the Initial Lorentz factor is sensitive to the peak time and weakly depends on the jet kinetic energy and medium density. Another way to estimate the initial Lorentz factor is using the high energy cutoff energy observed in the gamma-ray burst spectrum based on the compactness argument. In addition, we can also estimate the initial Lorentz factor with the detection of thermal emission. In this analysis we use the fireball deceleration time to estimate Gamma_0.
Peng

4. Optical and X-ray afterglow Cartoon Lightcurves
Currently, we have a large sample of afterglow lightcurves. Swift X-ray telescope has collected a large sample of X-ray afterglow data. The X-ray afterglow lightcurves usually covers from tens to several thousands of second after the gamma-ray burst trigger. The early X-ray lightcurves are dominated by the flares and a steep tail emission of the prompt gamma-rays. So, no clear afterglow onset peak was detected in the X-ray band. In the optical band, we collect the optical afterglow lightcurves of 146 GRBs. These lightcurves are well-sampled. We find one-third of the lightcurves show a clear onset bump as predicted by the fireball model.
X-ray Emission components
Optical Emission components
Zhang et al. 2006, ApJ; Li, Liang et al. 2012, ApJ

5. Relation between afterglow onset and prompt gamma-rays
Optical afterglow onset is detected for 1/3 of GRBs
Onset peak luminosity is correlated with prompt gamma-ray luminosity.
Onset peak luminosity is correlated with prompt gamma-ray luminosity.
Liang et al. 2010, ApJ

6. Eiso (or Liso)-Γ0 Relation
A tight correlation between the Eiso and the Lorentz factor of GRB fireball
We estimate the Lorentz factors of these GRBs and find that they are correlated with the Isotropic gamma-ray energy and luminosity.
Liang et al. 2010，2013, ApJ; LV et al. 2012, ApJL

7. Eiso (or Liso)-Ep Relation
These relations was found with GRBs detected with BeppoSAX and also confirmed with Swift/BAT and Fermi/GBM GRBs.
It is well also well known that the GRB spectrum can be fitted with a smoothly broken power-law. The peak energy of the nu f_nu spectrum are correlated with isotropic gamma-ray energy and luminosity.
Amati et al. 2012, IJMPD
Yonetoku et al. 2004, ApJ
Lu et al. 2012, ApJ

8. Eiso (or Liso)-Ep vs. Eiso (or Liso)-Γ0 Relation
Amati et al. 2012, IJMPD
Liang et al. 2010, ApJ
We compare here the Ep- isotropic luminosity relation with the relation between Gamma_0 and isotropic gamma-ray energy. One can observe that the two correlations have large intrinsic scatters. Whether or not the Large intrinsic dispersions are due to missing of the other parameter? Is there a tighter correlation among the three parameters?
Is the large intrinsic dispersion of pair correlations due to missing of the third part?
Relation among the three parameters?

9. A tight Liso-Ep,z-Γ0 relation
We make regression analysis for deriving a correlation among these parameters. A much tighter correlation is found. For extending the range of this relation, we also include low-luminosity GRB in our sample. The Lorentz factor of this GRB is derived from radio data and its value is 2.3.
GRB : Γ0 ~ 2.3
（Soderberg ）
Liang , ApJ 9

10. A tight Liso-Ep,z-Γ0 relation
Double check with GRBs whose Γ0 are derived from the spectral cutoff energy observed with Fermi/LAT.
We also double check the correlation with GRBs whose Γ0 are derived from the spectral cutoff energy observed with Fermi/LAT.
GRB : Γ0 ~ 2.3
（Soderberg ）
Liang , ApJ 10

11. Liso-Ep,z-Γ0 as a new GRB cosmology ruler?
Ejet-Ep relation (Ghirlanda )
Eiso-Ep-tjet relation (Liang & Zhang 2005)
The tight correlation motivate to consider for taking it as a new GRB cosmology ruler. In 2004 an d2005, we have used the some empirical relation of GRBs as cosmology rulers for measuring the cosmological parameters.
Dai, Liang, & Xu 2004, ApJL； Liang & Zhang 2005, ApJ

12. ？ Liso-Ep,z-Γ0 as a new GRB cosmology ruler? Advantages:
A tighter relation than previous ones.
Issues:
Needing to be confirmed with LL-GRBs (moderate relativistic jets?)
Needing to geometric correction to Liso
Identifying the cosmic evolution of jet luminosity. ？
The tight correlation motivate to consider for taking it as a new GRB cosmology ruler. In 2004 an d2005, we have used the some empirical relation of GRBs as cosmology rulers for measuring the cosmological parameters.
Liang ; Xin

13. 3. Our On-Going Observational Project
GRB trigger Follow-up
Flux magnitude
GRBs
Hu+ 2014
Optical Tels
R=13 Mini-GWAC
Singer+2012
R=16 GWAC
R=19 60/80cm
R=21
iPTF
-400s s s 5m 1h 1d

14. Our Current Optical Monitoring Project
trigger
Identification and early photometry
Spectrum、redshift
30s
Late photometry
hours
GWAC/GRB alert 60/80cm Telescope2m telescope

15. Examples of Our Monitoring Results
Mini-GWAC upper limit : M=13.2
GRB A
B, V, R, I observations with our 60/ 80 cm telescopes in Xinglong Observatory.
Liang , in prep.

16. GRB
Xin , ApJ, submitted

17. Zhong , ApJ, in press

18. Huang , ApJ, in press

19. Xin a, ApJ

21. Summary
Thanks!
Measuring the jet initial Lorentz factors of GRBs with the fireball deceleration time observed in the optical band range from ~100 to 1000.
The Lorentz factors are correlated with Liso (or Eiso), and a tighter correlation is found by adding Ep.
The Liso-Ep,z-Γ0 may be a promising GRB cosmology ruler, but issues are still there.
Our new observational project is going on for pushing the cosmology use of this relation . 21