Coincidences between gravitational waves (with LIGO) and gamma-ray bursts (with HETE-2)

Should we look for coincidences between the two? Of course! (Why not?) We could see GRB's which are “off-axis”. But what exactly are we getting ourselves into...?

Katherine Rawlins and Nat Butler, MIT

GWDAW-9, December 2004

Outline

1) How many coincidences do we expect?

A Toy Monte-Carlo simulation throws events on the sky, using one model of long-duration GRB's

2) How might the answer to 1) be wrong?

Alternative models, or the lack thereof, could change what we expect

A little GRB backstory

GRB's are generally divided into two categories:

A little GRB backstory

GRB's are generally divided into two categories:

Long-duration:

-- distances observed

-- relationships known between spectrum and energy

-- detailed jet models

-- some believed to be associated with SNe

A little GRB backstory

GRB's are generally divided into two categories:

Short-duration:

-- no distances or afterglows measured yet

-- limited spectral information

-- sources completely unknown (possibly binary mergers?)

A Toy Monte Carlo for GRB's

Simulate a population of GRB's, with distributions of:

Sky position

Distance

Orientation angle

Polarization angle (for GW's)

... and a model of:

gamma-ray emission properties

GW emission properties

cosmology and SFR

local event rate

Distances

Simulate events as though they were uniform in comoving distance Dc (and compute luminosity distance and z)

Give each event a weight according to changing star formation rate as a function of z

If Dc < 3 Mpc, draw from a list of known nearby galaxies

If Dc < Milky Way, draw from a Galactic mass distribution:

Sky position (RA,dec)

Creates objects only within HETE field of view (~1.5 sr); can specify S2, S3, full-year, or all-sky.

GW emission

Two simple models: binary-like and supernova-like

In plane of propagation:

“binary-like”

h+(t) = 1/2(1+cos2q) h0(t)

hx(t) = cosq h0(t)

q

Source:

h0(t) = sine-Gaussians

At the detector:

h(t) = F+(a,d,y,t)h+(t) + Fx(a,d,y,t)hx(t)

plane of propagation is rotated relative to detector by angle y

“supernova-like”

h+(t) = sin2q h0(t)

hx(t) = 0

Gamma-ray emission

Two simple uniform-jet models: “Gaussian”, and “q-2”, candidates for long-duration GRB's:

energy = f(q) =

q

jet axis

line of sight

a q-2

Gauss(q,t)

{

More assumptions

polarization angle: randomized

orientation angle: randomized

For gamma-rays, GRB's are a standard candle of 1051 ergs

For gravitational-waves, GRB's are a standard candle of hrss = 10-20 at 1kpc

GW's produced are sine-Gaussian waveforms, with f=250 Hz and t=10ms

Local rate of GRB's = local rate of SNe Ib/Ic / 100

Importance sampling is used to enhance interesting regions of small angle and small distance

Effects: binary-like or supernova-like

binary-like supernova-like

gamma-rays

gamma-rays

grav. waves

grav. waves

Effects: binary-like or supernova-like

Differences are minimal for all loud GW events, but if you apply a gamma-ray cut, the supernova-like events (whose GW point away from the jet axis) become rarer.

hrss

All events

Seen in gamma-rays

Predictions: different jet models

gamma-rays

Predictions: which season?

S2 observed closer to the Galactic Center

S3 observed some of Andromeda

g-

rays

hrss

tails of distributions

Predictions: event rates

Total events during S2 above HETE SNR=4:

(optimal hrss at 1 kpc = 10-20)

detector sens. binary-like SN-like 1e-20 in 1Mpc

10-26: 6.8 x 10-2 4.9 x 10-5

10-25: 1.5 x 10-4 1.4 x 10-7

10-24: 1.9 x 10-7 7.3 x 10-10

10-23: 7.3 x 10-10 6.8 x 10-10 6.8 x 10-2

10-22: 7.3 x 10-10 3.6 x 10-10 1.5 x 10-4

10-21: 2.3 x 10-10 2.2 x 10-11 1.9 x 10-7

Limitations

No absorption of gamma-rays

Hanford-only antenna pattern used

Science run LIGO ontime assumed to be 100%

Detector efficiency ->1 at a fixed hrss

GRB's are standard candles in GW's

GRB's are standard candles in GR's

Only “standard long-duration cosmological” bursts are modeled

Where to go from here?

Are inspirals/short GRB's a better hope?

More favorable emission pattern

Better range in LIGO

Swift is expected to see many short GRB's

“Third category” of GRB's?

Some bursts are underluminous in gamma-rays, have different spectral properties (i.e. GRB031203)

The bursts that look funny are the close-by ones

Both these things are difficult to model

To-do list

Expand GRB models; make some educated guesses and take a crack at short-duration and under-luminous

Repeat for SWIFT satellite

“Collect” triggers from both instruments, for S2, S3, (S4?) and compare

The End!

Inputs: GRB time

For S2, use actual satellite on-times

For S3 and others, hypothesize on-times based on orbital period

Inputs: Distance

Simulate events as though they were uniform in comoving distance Dc

From Dc, compute redshift z and luminosity distance DL

Give each event a weight according to changing star formation rate as a function of z

Importance-sample, to emphasize nearby (more insteresting) events

Nearby distances: the Galaxy

If an event is generated in the Milky Way, it is pulled from a Galactic mass distribution:

Input: Orientation angle

theta is the angle between the GRB jet axis (or angular momentum axis) and the line of sight

Generate events uniformly in cos(theta). But because small-angles are most interesting, importance-sample to smoothen the distribution there.

Long vs. short-range simulations

Need long-range simulations to know about low-SNR events, but short-range simulations are sufficient for loud-GW events.

Katherine Rawlins

2004-08-12T08:46:55

Katherine Rawlins