gravitational field by sathyaprakash .pdf

Gravitational

Astronomy

The New FrontierB.S. Sathyaprakash

Gravitational Physics Group, School of Physics and Astronomy

Gravitational Waves - The New Frontierp2

Gravitational Physics Users of ARCCA

Leonid Grishchuk

Stephen Fairhurst

Patrick Sutton

B Sathyaprakash

Bernard Schutz

Deepak Baskaran

James Clark

Alex Dietz

Gareth Jones

Craig Robinson

Van Den Broeck

Wen Zhao

David McKechan

Devanka Pathak

Ian Harry

Edmund Schluessel

Jack Yu


Newtons law of Gravity

The force of gravity

between two masses m

and M separated by a

distance r is

F(t) = G m M / r(t)2

Newtons law of gravity

transmits force

instantaneously - if the

mass M changes its

position, it is felt by body

m instantaneously


Newtons law of Gravity

When Earth reaches the

point A let us remove the

Sun from its position

At that very instant Earth

would no more feel the

force of Sun

Newtons law of inertia

states Earth would take

the path tangent to the

orbit at A

However, Sun will be

seen by Earthlings for

about 5 minutes as the

Earth zips across

A

..


Einsteins Special Theory of Relativity

The speed of light is the

same for all

Woman on the ground

measures the same speed

for the light from the torch

held by the girl speeding on

a rocket

One famous consequence

of this is E = mc2

Another consequence is

the twin-paradox

The one we are interested

is nothing can travel

faster than light


Newtons Gravity Vs Relativity

At the turn of the last century Einstein faced the

contradiction between Newtons theory of gravity and his

new special theory of relativity

According to Newton, Gravity acts instantaneously

Relativity, a very successful theory supported by

Maxwells theory of light, does not allow any signal to

propagate faster than light

Either abandon special relativity or find a new theory of

gravity


Einsteins Gravity

According to Einstein,

gravity is not a force but a

warping of space & time

Space is said to be warped

if familiar laws of

geometry in flat space do

not hold

Time is warped if clocks at

different points in space

dont run at the same rate

Someone living close to a

black hole would age more

slowly relative to their

twin sister on Earth


Einsteins Gravity

Earth Moves around sun

not because of there is

a force of gravity

Earth moves in

straightest possible

paths in the curved

geometry of space

caused by the Sun

Gravitational force,

just as all other forces,

is transmitted at a

finite speed


Einsteins Gravity

Again, when the Earth reaches

point A let us remove the Sun

from its position

According to Einstein Earth

would continue to move in its

orbit around the Sun for about

5 minutes after the Sun has

been removed

It takes a path that is tangent

to orbit at B

Gravity travels at a finite

speed: implies wavelike

phenomenon must be

associated with gravity

A

..

B


Einsteins Gravity & Gravitational Waves


What are Gravitational Waves?

A natural consequence of

Einsteins gravity and special

theory of relativity

Ripples on space-time curvature

travelling at the speed of light

Anything that accelerates

produces gravitational waves

A falling cannon ball, an

astronomical binary system, an

exploding star

We know gravitational waves exist

Decaying orbit of the double

binary pulsar for which Hulse and

Taylor were awarded the Nobel

Prize in 1992


Tidal gravitational forces

Gravitational effect of

a distant source can

only be felt through

its tidal forces

Gravitational waves

are traveling, time-

dependent tidal

forces.

Tidal forces scale with

size, typically produce

elliptical

deformations.


Gravitational Waves & Tidal Forces

Cross polarizationPlus polarization


Evidence for gravitational waves

In 1974 Hulse and Taylor observed

the first binary pulsar

Two neutron stars

Orbital period ~ 7.5 Hrs

Stars whirling around at a thousandth

the speed of light

Einsteins gravity says the binary

should emit gravitational

radiation

Causes the two stars to spiral in

towards each other

Observed decrease in period - about

10 s per year - is exactly as predicted by Einsteins theory

Eventually the two stars will coalesce, but that will take another 100 million years


A world network of

Interferometric Gravitational

Wave Detectors


Gravitational Wave Detectors

About 1 billion US $ investment worldwide

STFC has invested about US $ 50


American LIGO at HanfordAmerican LIGO at LivingstoneBritish-German GEO

French Italian VIRGO near PISALaser Interferometer Space Antenna


The LIGO Scientific Collaboration

Comprises ~ 30 institutions and > 400 people


Recent Results from GW Searches

The largest mountain on the

Crab pulsar (or radius 10 km) is

no more than 10 cm

Primordial gravitational waves

did not limit primordial

synthesis of heavy elements

(helium, deuterium, etc.)

A recent (Feb 1, 2007) gamma-

ray burst that occurred in

Andromeda was a new

phenomena that needs further

explanation


Gravitational waves: A New Window

Was Einstein right?

Is the nature of gravitational radiation as predicted by Einstein

or is it something different?

Are black holes hairless?

Are there naked singularities?

How did the black holes at galactic nuclei form?

The centre of our galaxy has a million solar-mass black hole?

How and when did it form? Galactic cannibalism via slow

accretion of smaller black holes, gas and other stars?

Fundamental questions about our existence

What were the physical conditions at the big bang?

What is the nature of quantum gravity, origin of space and

time?

How many spatial dimensions are there, only 3?


Most of the Universe is Dark


Astronomical Sources

Compact binary mergersBinary neutron stars

Binary black holes

Black hole-neutron star binaries

Gravitational wave burstsBlack hole collisions

Supernovae

gamma-ray bursts

Continuous waves Rapidly spinning neutron stars or other objects

Stochastic backgroundPrimordial background

Astrophysical background


Slide by: P Shellard


Why are GW searches challenging?

All sky sensitivity

Any one detector is sensitive to

a significant portion of the sky

Large data rates

Tens of terabytes per year from

a worldwide detector network

Wide band sensitivity

Different types of signals all

present in the same data set

Beam Pattern Functions of an American and a European Detector


Computational Cost of our Searches

Current searches are limited by computational resources

Can only search for non-spinning black hole binaries

A month of search takes 60,000 CPU hours

Bigger computers afford better searches

Future SearchesSearch for black holes with spins

Would require at least 10-100 times more computational cost

ARCCA Cluster Can Help Detect Gravitational Waves


Targeting the biggest discovery of

our times through ARCCAHere are some signals from colliding black holes as predicted by Einsteins theory

Black hole spins modulate the waveform

We use matched filtering to search for signals buried in noise

Pattern matching algorithm

But matched filters, i.e. templates used in the search, depend on many parameters

A search in 17-dimensional space involving the masses, spins of the stars, position on the sky, etc.

About 100 million shapes must be searched for in each piece of data

A

m

p

l

i

t

u

d

e

Time

Increasin

g Spin


What do we need?

Compute cycles: a lot of themOur algorithms are embarrassingly parallel

Literally no communication between different compute nodes

Data Access:Each detector produces about 30 TBytes of data per year and will run for 2 to 3 years at a time

About 10% of this should be available for compute nodes

Multiple nodes (100s of them) might access data at any one time

Centralized data archives are a bottleneck and a nightmare in our game


A typical pipeline: Searching for colliding

black holes


All sky search for spinning neutron stars


Gravitational Astronomy

(Very) Early Universe

GW observations with

ARCCA

Stellar interiorsCosmology

Quantum theory

Astrophysics

Fundamental physics Extreme Gravity

gravitational field by sathyaprakash .pdf

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