Gamma-Ray Bursts and Gravitational Waves Shiho Kobayashi (Penn State)
Gamma-Ray Bursts (GRBs) sudden, intense flashes of 0.1- 1MeV γ rays arriving from random directions in the sky. luminosity Time[sec]
Rate ≈ 1 event/day (GRO)
Short Bursts Long Bursts events >2sec Hardness Duration [sec]
Discovery of counterparts of (long) GRBs in longer wave lengths “afterglow” Confirm (1) Cosmological model ≈ z 1 Emission and absorption lines in optical afterglow 51 54 Isotropic gamma-ray energy 10 − 10 ergs (2) Relativistic Fireball model
Internal Shocks External Shocks Faster and slower shells Outflow and ambient matter GRB afterglow ? Relativistic Outflow 10 14 Lorentz factor > 100 ≈ R cm 16 − 18 R ≈ 10 cm
We know HOW GRBs are produced. ---- relativistic shocks and synchrotron process What produces the relativistic flow? Catastrophic events involving Neutron Star or a Stellar-mass Black Hole? γ Bulk of energy radiated into ray band Energy budget comparable to kinetic energy in Supernovae Variability in GRBs: msec time scale
The engine must active much longer than its variablity timescale! BH - massive Accretion Disk System Massive stellar collapse Collapsar, Hypernova, failed SN: iron core collapses to BH Compact mergers NS-NS } Short Bursts? NS-BH White dwarf - BH Helium star - BH
X O R GW GRB afterglow 6 14 16 ≈ 10 cm ≈ 10 cm > 10 cm Bloom
In-spiral merger Ring-down Merger begins when orbital evolution BH is initially deformed. As binary losses energy by GW is so rapid that adiabatic evolution is Energy associated with the masses gradually spiral in toward not a good approximation. deformation is radiated each other. Masses violently merger to form a BH. as GWs ~ 1 G dE ≈ ≈ h c ≡ f h ( f ) N h 3 π d 10 c df & 2 = N f / f S.K & Meszaros, astro-ph/0210211
Massive stellar collapse leading to a GRB requires a high core rotation rate, which may be easier to achieve if the star is in a binary system, although this is not necessary. Anyway, In-spiral signal terminates at a frequency well below seismic cutoff. Fryer, Woosley & Hartmann 99
Numerical calculations of GW radiation from collapsars have been done in the Newtonian approximation in 2D ( e.g. Fryer et al 1999; MacFadyen & Woosley 1999 ), relativistic in 2D (Dimmelmeier et al. 2002). They suggest that GW emission from collapsars may be much less important than from compact binaries, even though these numerical estimates are not conclusive as a number of effects ( GR, secular evolution, non-axisymmetry) are neglected. High rotation rate is required to form centrifugally supported disk around BH to power GRB jet. The same high rotation rate could lead to a bar or fragmentation type instability in the collapsing core or/and in the massive disk. (Nakamura & Fukugita 1989; Fryer et al 2002; van Putten 2002; Davies et al 2002) Infalling matter perturbs BH’s geometry.
GRBs and GWBs GRBs and Afterglows can give the occurrence times and the directions. Binaries, bars, fragmentations and QNMs ( ) emit GWs more strongly = m = l 2 along the polar axis, along which GRB jets are also launched. Then, GRB souces are stonger than the average. (Kochanek & Piran 1993; S.K & Meszaros in prep) 2 ∝ + θ ∝ θ h ( 1 cos ), h 2 cos + ×
t Internal shocks 13 14 R = 10 − 10 cm Gamma-rays R 2 γ ≈ − R / 2 c msec sec ringdown Relativistic Jet γ Lorentz factor > 100 merger inspiral World line GW of observer
msec-sec EM waves ???Waveform??? GWs BH formation The correlated output of two GW detectors evaluated in the moment just prior to GRB (on) will differ from that evaluated at other time (off). (Finn et al. 1999)
Output of two detectors (identical locations and arm orientations) s ( t ) = n ( t ) + h ( t ), s ( t ) = n ( t ) + h ( t ) 1 1 1 2 2 2 ( , ) = 0 n n 1 2 Cross-correlation 2 h ( f ) 0 0 ∞ c ′ ′ ′ = = − ≈ X ( s , s ) dt d t s ( t ) s ( t ) Q ( t t ) df ∫ ∫ ∫ on 1 2 1 2 2 2 − − − ∞ T T f S ( f ) Averaged over source population − 2 ∝ Q ( f ) S ( f ) Filter function ~ 2 if we knew Q ( f ) = h ( f ) / S ( f ) h ( t ) T ∞ df 2 2 σ = ≈ ( n , n ) ∫ off 1 2 2 − ∞ 4 S ( f ) 2 σ ∝ X / h / T on off c
if h << n By collecting many sample, we can get some information on association between GRBs and GWs. X on > 2 . 58 (99% significance) σ / N off on 4 ∝ N T / h on c
We should select nearby GRBs. Typical GRB at 3000Mpc GRO : almost full sky coverage but large error box HETE, Swift: smaller coverage accurate positioning allow the follow up by optical-telescope
When we analyze the nearest events n ne in a year 1 / 3 d ∝ n Typical distance (uniform distribution) ne The number of events needed − 4 4 / 3 N ∝ h ∝ n to detect the association on c ne The number of years it takes 1 / 3 to collect sample ∝ n ne
Contamination to estimate on by undetected GRBs X off Possibly we do not see a large fraction of GRBs − − 2 − 1 Sky coverage by gamma-ray detectors 10 10 − − 3 − 1 Beaming of GRB jets 10 10 If the reduction factor is 10 − 4 r = − 1 δ t r 3 n ne < 10 − 4 3 sec 10
Bloom
Light curves of afterglow 3 / 8 − 1 / 8 1 / 8 t E n j iso ISM θ ≈ 0 . 05 j − 53 3 1 day 10 erg 0 . 1 cm Distribution of Opening Angles 4 . 54 f ( θ ∝ ) θ true 1 / 500 We can observe Sample : 10+5 GRBs (Frail et al. 2001)
2 ≈ × θ E E γ iso 50 ≈ × 5 10 erg
Fast X-ray Transients (FXTs) BATSE(>20keV) SAX-WFC(2-26keV) GRB FXT??? Kippen et al. 2001
Binary , QNM(l=m=2), bar... 2 h ∝ ( 1 + cos θ ), h ∝ 2 cos θ + × The amplitude and polarization of GWs depend on the viewing angle from the polar axis! θ GRB Luminosity also depends on the polar angle!!!
Correlation 4 GW Linear Polarization degree ∝ θ P − 2 ∝ θ L GRB luminosity LIGO observatories are co-aligned, no information about P (S.K. & Meszaros in prep)
Distance to GRB sources might be determined by GW observation! “Dark GRBs” 26 well localized GRBs Kulkarni et al. 2000
Detection of counterparts of GRBs in GWs will revolutionize GRB field. GRBs and Afterglows provide occurrence time and sky position. Cross-correlation technique can be used to get some information of association between GRBs and GWBs.
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