Gamma-Ray Bursts and Gravitational Waves Shiho Kobayashi (Penn - - PowerPoint PPT Presentation

Gamma-Ray Bursts and Gravitational Waves

Shiho Kobayashi (Penn State)

Gamma-Ray Bursts (GRBs) sudden, intense flashes of 0.1- 1MeV rays arriving from random directions in the sky.

γ

Time[sec]

luminosity

(GRO) event/day 1 Rate ≈

[sec]

Hardness

Duration

events

Long Bursts Short Bursts

>2sec

Discovery of counterparts of (long) GRBs in longer wave lengths “afterglow”

(2) Relativistic Fireball model

1 ≈ z

(1) Cosmological model

Emission and absorption lines in optical afterglow

Confirm

Isotropic gamma-ray energy ergs

54 51

10 10 −

External Shocks Internal Shocks

GRB afterglow

cm 1014 ≈ R cm 10

18 16−

≈ R

?

Relativistic Outflow Lorentz factor > 100 Outflow and ambient matter Faster and slower shells

What produces the relativistic flow?

Catastrophic events involving Neutron Star or a Stellar-mass Black Hole?

Energy budget comparable to kinetic energy in Supernovae Bulk of energy radiated into ray band Variability in GRBs: msec time scale

γ

We know HOW GRBs are produced.

• --- relativistic shocks and synchrotron process

The engine must active much longer than its variablity timescale!

BH - massive Accretion Disk System

Massive stellar collapse Compact mergers

Collapsar, Hypernova, failed SN: iron core collapses to BH

}Short Bursts?

NS-NS NS-BH White dwarf - BH Helium star - BH

X O R

cm

14

10 ≈

GRB

cm

16

10 >

afterglow

GW

cm

6

10 ≈

Bloom

In-spiral

As binary losses energy by GW the masses gradually spiral in toward each other.

merger

Merger begins when orbital evolution is so rapid that adiabatic evolution is not a good approximation. Masses violently merger to form a BH.

Ring-down

BH is initially deformed. Energy associated with deformation is radiated as GWs

S.K & Meszaros, astro-ph/0210211

f f N df dE c G d h N f h f hc & / 10 1 ) ( ~

2 3

= ≈ ≈ ≡ π

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

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.

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

• f effects ( GR, secular evolution, non-axisymmetry) are neglected.

GRBs and GWBs GRBs and Afterglows can give the occurrence times and the directions.

2 = = m l

Binaries, bars, fragmentations and QNMs ( ) emit GWs more strongly along the polar axis, along which GRB jets are also launched. Then, GRB souces are stonger than the average.

θ θ cos 2 ), cos 1 (

2

∝ + ∝

× +

h h

(Kochanek & Piran 1993; S.K & Meszaros in prep)

inspiral merger ringdown

t R

GW

World line

• f observer

sec msec 2 /

2

− ≈ γ c R

Relativistic Jet

Lorentz factor > 100

γ

Internal shocks

Gamma-rays

cm R

14 13

10 10 − =

EM waves GWs msec-sec

???Waveform??? 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) ) ( ) ( ) ( ), ( ) ( ) (

2 2 2 1 1 1

t h t n t s t h t n t s + = + =

∫ ∫ ∫

∞ ∞ − − −

≈ ′ − ′ ′ = = ) ( ) ( ) ( ) ( ) ( ) , (

2 2 2 2 1 2 1

f S f f h df t t Q t s t s t d dt s s X

c T T

• n

Cross-correlation

Averaged over source population

Filter function

) ( ) (

2

f S f Q

−

∝

if we knew

) ( / ) ( ~ ) (

2

f S f h f Q =

) (t h

∫

∞ ∞ −

≈ = ) ( 4 ) , (

2 2 2 1 2

f S df T n n

• ff

σ ) , (

2 1

= n n

T h X

c

• ff
• n

/ /

2

∝ σ

n h <<

By collecting many sample, we can get some information

• n association between GRBs and GWs.

if

58 . 2 / >

• n
• ff
• n

N X σ

(99% significance) 4

/

c

• n

h T N ∝

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 in a year

ne

n

Typical distance

3 / 1 ne

n d ∝

The number of events needed to detect the association

3 / 4 4 ne c

• n

n h N ∝ ∝

−

The number of years it takes to collect sample

3 / 1 ne

n ∝

(uniform distribution)

Contamination to estimate on by undetected GRBs

• ff

X

Possibly we do not see a large fraction of GRBs

Sky coverage by gamma-ray detectors

1 2

10 10

− − −

Beaming of GRB jets

1 3

10 10

− − −

If the reduction factor is

4

10− = r

            <

− − 4 1 3

10 sec 3 10 r t nne δ

Bloom

Light curves of afterglow

Distribution of Opening Angles

8 / 1 3 8 / 1 53 8 / 3

1 . 10 1 05 .                       ≈ θ

− −

cm n erg E day t

ISM iso j j

54 . 4

) ( θ θ ∝

true

f (Frail et al. 2001)

500 / 1

We can observe Sample : 10+5 GRBs

erg E E

iso 50 2

10 5 × ≈ θ × ≈

γ

Kippen et al. 2001

Fast X-ray Transients (FXTs)

BATSE(>20keV) SAX-WFC(2-26keV)

GRB

FXT???

θ θ cos 2 ), cos 1 (

2

∝ + ∝

× +

h h

Binary , QNM(l=m=2), bar... The amplitude and polarization of GWs depend on the viewing angle from the polar axis!

θ

GRB Luminosity also depends on the polar angle!!!

GW Linear Polarization degree

4

P θ ∝

GRB luminosity

2 −

∝θ L

Correlation

(S.K. & Meszaros in prep)

LIGO observatories are co-aligned, no information about P

Kulkarni et al. 2000

Distance to GRB sources might be determined by GW observation!

“Dark GRBs”

26 well localized GRBs

Detection of counterparts of GRBs in GWs will revolutionize GRB field. GRBs and Afterglows provide

• ccurrence time and sky position.

Cross-correlation technique can be used to get some information

• f association between GRBs and GWBs.