Mouyuan Sun S upervisor : Wei-min Gu Collaborator: Tong Liu Xiamen University 2011/8/24

1. Mouyuan Sun Supervisor: Wei-min Gu Collaborator: Tong Liu Xiamen University 2011/8/24 Gravitational wave from GRB-Accretion system

2. Outlines • 1. Jet Precession machanism • 2. Gravitational wave from a precessing system. • 3. Our Results • 4. Summary

3. Jet Precession in GRBs • Light curves that show fast rise exponentially decay behavior are hard explained by Internal shock model and maybe indicate the precessing Jet in GRBs (Romero et al. 1999, Zwart et al. 1999). • Romero et al. 2006 suggested a spin-induced precess model. • Liu et al. 2010 proposed another model to account for jet precession in GRBs. Pecession rate w=2J/r^3 Critical radius determined by Jd=Jbh (mass, viscosity, spin, mdot)

4. Precession Period and Accretion rate Liu et al. 2010

5. GW vs EM • Gravitational wave astronomy's advantages: a. Gamma ray photons come from jet, thus quiet far away from central engine, while GWs are closer. b. GRBs are strongly beamed, while GWs are not. c. Not affected by ISM d. Last but not least, system may show the same behavior in EM but not in GW Here, we consider Gravitational wave associate with jet precession phenomenon and hope GW can reveal the physical mechanism that make jet precess.

6. GW from a precession system • Zimmermann & Szedenits 1979 consider gravitational waves from rotating and precessing rigid bodies and applied their formula to a free-precessing NS. • Romero et al. 2010 estimated GW from their disk precessing model based on Zimmermann & Szedenits 1979 and concluded that GW produced by their disk precessing model can detect by advanced LIGO. But something is wrong in their calculation since the disk precessing motion is not free!!! • We avoid their mistakes and calculate gravitational wave from Liu et al. 2010 model. We developed the formula to estimate GW from Torque-induced precessing system.

7. GWs from a Torque-induced system BH spin & disk rotational axis Conserved angular momentum direction Inertial Moments transformation: From I=diag{I1,I2,I3} in body frame to To observer frame Thus time dependent

8. GW from a Torque-induced system • 1. Mass distribution in radial and vertical direction: radial distribution: solve accretion disk equations. Vertical distribution: assume polytropic relation • 2. Transformation between body frame and lab frame Known spin, alpha, mass and mdot Disk mass distribution Inertial moment In body frame Transformation To lab frame GW And BH inertial Moments

9. GW Detectors 1. LIGO and Advanced LIGO: 10 ~ 1000Hz, 2. LISA (ESA & NASA): 0.1 ~ 100mHz, 3. DECIGO (Japan): 0.1 ~ 10Hz, 4. BBO (NASA): 0.1 ~ 10Hz. The frequency of gravitaional wave we consider here is: 0.1~10 HZ DECIGO detector

10. GW as a function of BH spin

11. Detectable distance (1)(The DECIGO and BBO sensitivity adopted from Yagi & Seto 2011)

12. Detectable Distance (2)

13. Detectable Distance (3)

14. Summary • 1. The detectable distance reaches the Local Group (~1 Mpc) for a BH mass ~5M and spin ~0.95 (if such a GRB just happened in Milky way or nearby galaxy, we can get information on mass distribution in GRBs' accretion disk from the detected GW by future DECIGO or BBO); • 2. The detectable event rate is very small (assume local true GRBs rate is~ 250Gpc^-3 yr^-1 (Frail et al. 2001), the detectable rate is 10^-7 yr^-1). But if the detector sensitivity is ~10-50 times higher, we can detect GW events ~1 yr^-1. • 3. It's hard to say if GW signal can make a distinguish between Liu et al. 2010's jet precession model and that of Romero et al. 2006 since we argue that their calculation isn't correct.

15. Thank you very much!