Gravitational wave astrophysics

Denis Martynov,Massachusetts Institute of Technology

Baikal School on High Energy Physics and Astrophysics July 11, 2016

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Overview

Different ways to observe the universe Plane wave solution to Einstein equations Gravitational waves detectors Signal processing in LIGO Astrophysical sources

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Different ways to observe

• Electromagnetic waves

• Particles

• Gravitational waves

Electromagnetic waves

Radiation Wavelength,m Sources Detectors

Gamma rays 10-12 pulsars, quasars, collision of compact objects Swift, Integral

X-rays 10-10 supernovae, binary stars, black holes NuSTAR, Chandra

Ultraviolet 10-8 young and old stars Astrosat, IRIS

Visible 10-6 stars, galaxies, planets Hubble, Kepler

Infrared 10-5 cool stars, nebular, redshifted galaxies JWST, SST

Microwave 10-2 CMB, compact sources COBE, WMAP

Radio 103 masers, gravitational lenses, early Universe VLBI, Spectr-R

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Particles

Particles Energy,eV Sources Detectors

Cosmic rays 109-1021 supernovae, active galactic nuclei Fermi, Veritas

Neutrinos 1011-1021 core of the stars, starburst galaxies IceCube, Baikal

Axion 10–6-100 possible component of cold dark matter CAST, Casper

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CLEO Conference, June 6, 2016LIGO-G1600884-v2

Gravity as a geometrical propertyMetric g defines distance between all points of the spacetime

Once metric is known, geodesic (‘free-fall’) equations read

ds

2 =X

uv

guv(x, t)dxudx

vx

u

x

v

ds

d

2x

u

d⌧

2+ �u

k,vdx

k

d⌧

dx

v

d⌧

= 0, where

�uk,v =

1

2g

um

✓@gmk

@x

v+

@gmv

@x

k� @gkv

@x

m

◆

are Christoffel symbols.

Einstein equationsconnect spacetime metric with mass-energy distribution

Rik = �8⇡G

c4(Tik � 1

2gikT

mm)

is the Ricci tensor;is the energy-momentum tensor.

Rik(gik)

Tik

Rik = (@�l

jk

@x

l� @�l

il

@x

k+ �l

ik�mlm � �m

il �lkm)

Ricci tensor is a function of the metric tensor

Plane wave solutionIn the weak field regime the space-time is almost flat

The largest contribution to gravitational wave radiation comes from the quadruple moment I

huv(t) =2G

rc4Iuv(t�

r

c)

guv = diag(1,�1,�1,�1) + huv, huv ⌧ 1

Einstein equations can be simplified to ⇤huv = 0

hij =

0

BB@

0 0 0 0

0 �h+ h⇥ 0

0 h⇥ h+ 0

0 0 0 0

1

CCA cos(!t� kz)

Gravitational waves

Time

Metric g defines distance between all points of the spacetimeds

2 =X

uv

guv(x, t)dxudx

v

Distance between particles fluctuates together with strain

�L = h+L

10

In this particular example in the figure h=1/5LIGO target sensitivity is h ~ 3e-24

Michelson interferometer (LIGO design)

measures differential length of two arms using the detector at the antisymmetric port

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Network of antennas

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LIGO Livingston

LIGO Hanford

Virgo, Italy

Kagra, Japan

Network of antennas

13

4 km

100 kW

1064 nm

Laser

22W800W

85mW

25mW

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Optical configuration

h =�L

L

10Hz < f < 10 kHz

Advanced LIGO Timeline

Year Occasion

2004 Advanced LIGO approved

2008 Start of Advanced LIGO construction

2011-2014 Advanced LIGO installation and testing

2013-2015 Commissioning of Advanced LIGO

2015-2016 First science run of Advanced LIGO

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Some of the Fundamental Questions That Gravitational Waves Can Address

Fundamental Physics» Is General Relativity the correct theory of gravity?» How does matter behave under extreme conditions?» Are black holes truly bald?

Astrophysics, Astronomy, Cosmology» Do compact binary mergers cause GRBs?» What is the supernova mechanism in core-collapse of massive stars?» How many low mass black holes are there in the universe?» Do intermediate mass black holes exist?» How bumpy are neutron stars?» Is there a primordial gravitational-wave residue?» Can we observe populations of weak gravitational wave sources?» Can binary inspirals be used as “standard sirens” to measure the local Hubble

parameter?

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Signal processing in LIGO

We need to separate signal from noise:

1. power spectrum density 2. coherence tools 3. waveform matching

Gravitational wave signal

0 0.02 0.04 0.06 0.08 0.1Time, sec

-3

-2

-1

0

1

2

3

Ampl

itude

noise+signalsignal * 10

101 102 103

Frequency, Hz

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Ampl

itude

spe

crum

den

sity

, 1 /

Hz1/

2 noise+signal

In the time domain

Units:

h(t) = hgw(t) + hn(t)

[h(t)] = 1

Gravitational wave signalIn the frequency domain

Units:

0 0.02 0.04 0.06 0.08 0.1Time, sec

-3

-2

-1

0

1

2

3

Ampl

itude

noise+signalsignal * 10

101 102 103

Frequency, Hz

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Ampl

itude

spe

crum

den

sity

, 1 /

Hz1/

2 noise+signal

S(!) =

Z +1

�1< h(t)h(t+ ⌧) > e�i!⌧d⌧

h(!1�!2) =1

⇡

Z !2

!1

S(!)d!

[h(!)] =1pHz

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Past, current and goal LIGO sensitivities

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Excess power in the signal

Monitor signal in different frequency bands over time

But! Need to be careful and separate GW signal from internal instrument transients.

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Coherence between the two instruments

Two interferometers measure gravitational waves and noise. GW signal is the same while noise is independent.

C(!) =S12S⇤

12

S11S22

where is the cross-power spectrum.S12(!)

S12(!) =

Z +1

�1< h1(t)h2(t+ ⌧) > e�i!⌧d⌧

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Waveform matching

In the case we know what to expect:

where is the expected gravitational wave signal, and is the measured signal.

SNR ⇠Z T

0h(t)htl(t)dt

htl(t)h(t)

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Harvesting astrophysical sources

We expect signals from

1. Binary compact objects (waveforms are known) • black hole - black hole • neutron star - black hole • neutron star - neutron star

2. Bursts • supernovae • gamma ray bursts

3. Stochastic background

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Compact objects in LIGO: neutron stars and black holes

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Neutron stars• Gravitational field at the surface of the neutron star

is 2*1011 times higher than on Earth

• Gravitational field acts as a gravitational lens and normally invisible parts of the neutron star become visible

• The inside temperature of a newly formed neutron star is 1011-1012K

• Equation of state of neutron stars is still unknown, radius is ~10 km

Neutron Star Formation

Image credit: NASA

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Merger of compact objects

• Waveforms are computed using the general theory of relativity

• It is possible to distinguish masses and spins of neutron stars and black holes

• Limits on the speed of gravitational waves can be set

• Sky localization allows us to produce population estimates

Merger of compact objects

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GW150914 (BH-BH merger)

4 x 10-18 m

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GW150914 (BH-BH merger)

CLEO Conference, June 6, 2016LIGO-G1600884-v2

36 M◉

29 M◉

Simulation Slowed Down ~ 100X

CLEO Conference, June 6, 2016LIGO-G1600884-v2

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GW150914 parameters

Radiated Energy: M◉ Peak Luminosity: erg/s3−0.5+0.5 3.6−0.4

+0.5 × 1056

Hanford

Livingston

Abbott, et al. ,LIGO Scientific Collaboration and Virgo Collaboration, “Observation of Gravitational Waves from a Binary Black Hole Merger” Phys. Rev. Lett. 116, 061102 (2016)

Waveform is entirely consistent with General Relativity!

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GW151226 (BH-BH merger)

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GW151226 (BH-BH merger)

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Population statistics

SNR ⇠ 1

R�

SNR ⇠ 1

R�⇥ exp(�R/R0)

Propagation laws considered in the literature

E. Calabrese et al. Testing Gravity with Gravitational Wave Source Counts. arXiv:1602.03883

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Neutron star equation of state

Many models are listed in the literature LIGO can measured GW from the coalescence at

2-5kHz Prove of connection between BNS and GRB Where do metals come from?

Supernovae Binary neutron star mergers

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Neutron star equation of state

500 700 1000 3000 500010�25

10�24

10�23

10�22

Frequency [Hz]

p S(f)

and

2p f|h(

f)|[

Hz�

1/2 ] Source Distance: 100 MpcaLIGO

VoyagerCryo Lungo

1.35 � 1.35 M� EOS 2H1.35 � 1.35 M� EOS HB

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Physics of supernovae

GW burst from SN can help to understand explosion Signal is expected to be broadband (100Hz - 3kHz) New facilities are required for frequent detections

Burst signals• Fast catastrophic processes in the

Universe

• Supernovae are potential sources of gravitational waves

Supernovae models give different results in

gravitational wave signal

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Physics of supernovae

Stochastic background

• Early universe

• Many unresolved inspirals

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Summary of discussed topics

Generation of gravitational waves Signal processing in LIGO Astrophysical sources in the LIGO band

https://www.lsc-group.phys.uwm.edu/ppcomm/Papers.html

Source RangeBH-BH (30 Ms) 1Gpc

NS-NS 80MpcCore Colapse SN 10kpc-1Mpc

CLEO Conference, June 6, 2016LIGO-G1600884-v2

GW150914 in popular culture

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From The Guardian

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LIGO Scientific Collaboration

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Continuous waves

Billion NS in our galaxy Strongest emitters are rapidly rotating NS (~1kHz) Theoretical ellipticity upper limit is 2e-5

Continuous waves• Sources have a fairly constant

and well-defined frequency

• Examples are rotating neutron stars with a non-zero ellipticity

Phase locked lasers (LISA design)

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Measure timing pulsars (Nanograv design)

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Tests of alternative theories

Alternative gravity theories suggest extra dimensions, finite mass of graviton and etc

We can use EM from short GRB to set constrains on graviton mass and speed

Even counts and events

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Alternative theories

10-1 100 101 102m2 (M-)

1016

1017

1018

1019

Bou

ndson

c=(c!

v g)

10-1 100 101 102m2 (M-)

10-23

10-22

10-21

Bou

ndson

mg

(eV

)

aLIGOVoyagerCryo Lungo

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Continuous waves

Frequency (Hz)

Freq

uenc

y de

rivat

ive (H

z/s)

5 10 20 100 300 1000 3000

1e−1

31e−1

11e−0

91e−0

7 ε=1e−4 ε=1e−5 ε=1e−6

ε=1e−7

ε=1e−8

ε=1e−9

1 kpc

10 kpc

100 kpc

1 Mpc