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### Delensing Gravitational Wave Standard Sirens

### Delensing Gravitational Wave Standard Sirens

Dr Martin Hendry

Astronomy and Astrophysics Group, Institute for Gravitational Research

Dept of Physics and Astronomy, University of Glasgow

Dr Martin Hendry

Astronomy and Astrophysics Group, Institute for Gravitational Research

Dept of Physics and Astronomy, University of Glasgow

With thanks to:

David Bacon, Chaz Shapiro, Ben Hoyle

ICG, Portsmouth

See astro-ph/0907.3635; MNRAS in press

Gravity in Einstein’s Universe

“The greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition and mathematical skill.” Max Born

Spacetime curvature

Matter

(and energy)

Nottingham, March 2010

Gravity in Einstein’s Universe

Spacetime tells matter how to move, and matter tells spacetime how to curve

Gravitational Waves

- Produced by violent acceleration of mass in:
- neutron star binary coalescences
- black hole formation and interactions
- cosmic string vibrations in the early universe (?)

- and in less violent events:
- pulsars
- binary stars

Gravitational waves

- ‘ripples in the curvature of spacetime’
- that carry information about changing gravitational fields – or fluctuating strains in space of amplitude h where:

“Indirect” detection from orbital decay of binary pulsar: Hulse & Taylor

Evidence for gravitational waves

PSR 1913+16

Gravitational Waves: possible sources

- Pulsed
Compact Binary Coalescences:

NS/NS; NS/BH; BH/BH

Stellar Collapse (asymmetric) to NS or BH

- Continuous Wave
Pulsars

Low mass X-ray binaries (e.g. SCO X1)

Modes and Instabilities of Neutron Stars

- Stochastic
Inflation

Cosmic Strings

Science goals of the gravitational wave field

Fundamental physics and GR

• What are the properties of gravitational waves?

• Is general relativity the correct theory of gravity?

• Is GR still valid under strong-gravity conditions?

• Are Nature’s black holes the black holes of GR?

• How does matter behave under extremes of

density and pressure?

Cosmology

• What is the history of the accelerating

expansion of the Universe?

• Were there phase transitions in the early

Universe?

Science goals of the gravitational wave field

Astronomy and astrophysics

• How abundant are stellar-mass black holes?

• What is the central engine that powers GRBs?

• Do intermediate mass black holes exist?

• Where and when do massive black holes form

and how are they connected to galaxy formation?

• What happens when a massive star collapses?

• Do spinning neutron stars emit gravitational waves?

• What is the distribution of white dwarf and

neutron star binaries in the galaxy?

• How massive can a neutron star be?

• What makes a pulsar glitch?

• What causes intense flashes of X- and gamma-

ray radiation in magnetars?

• What is the star formation history of the Universe?

How can we detect them?

- Gravitational wave amplitude h ~

L

Sensing the induced excitations of a large bar is one way to measure this

Field originated with J. Weber looking for the effect of strains in space on aluminium bars at room temperature

Claim of coincident events between detectors at Argonne Lab and Maryland – subsequently shown to be false

L + DL

VESF School on Gravitational Waves, Cascina May 25th - 29th 2009

How can we detect them?

L + DL

Jim Hough and

Ron Drever, March 1978

31 yrs on - Interferometric ground-based detectors

(BRIGHT)

+

laser

+

DESTRUCTIVE

(DARK)

Nottingham, March 2010

It’s all done with mirrors

Michelson Interferometer

path 1

path 2

Detecting gravitational waves

GW produces quadrupolar distortion of a ring of test particles

Expect movements of

less than 10-18 m over 4km

Dimensionless strain

Nottingham, March 2010

Ground based Detector Network – audio frequency rangeLIGO Hanford

TAMA, CLIO

300 m100 m

600 m

4 km2 km

LIGO Livingston

LIGO Livingston

3 km

VIRGO

4 km

P. Shawhan, LIGO-G0900080-v1

State of the Universe: March 2010

Some key questions for cosmology:

- What is driving the cosmic
- acceleration?
- Why is 96% of the Universe
- ‘strange’ matter and energy?
- Is dark energy = Λ ?
- How, and when, did galaxies
- evolve?
- Big bang + inflation + gravity = LSS?

State of the Universe: May 2010

WMAP5

BAO: 2dFGRS+SDSS

SNIa: ‘union’ sample

HSTKP

From Kowalski et al (2008)

State of the Universe: March 2010

Some key questions for cosmology:

- What is driving the cosmic
- acceleration?
- Why is 96% of the Universe
- ‘strange’ matter and energy?
- Is dark energy = Λ ?
- How, and when, did galaxies
- evolve?
- Big bang + inflation + gravity = LSS?

What rôle could gravitational waves play in answering these questions?

Gravitational Wave Sources as Cosmological Probes

Much recent interest in Following original idea in Schutz (1986);

‘Standard Sirens’ see also Cutler & Flanagan (1994)

‘Chirping’ waveform

Chirp mass

amplitude

Measure

time

Gravitational Wave Sources as Cosmological Probes

Much recent interest in ‘Standard Sirens’:

e.g. SMBHs at cosmological distances, for which DL can in principle be determined to exquisite accuracy.

Inspiral waveform strongly dependent on SMBH masses.

Since amplitude falls off

linearly with (luminosity) distance, measured strain determines the distance of the source to high precision.

Long tail due to parameter degeneracies

Holz and Hughes 2005

Gravitational Wave Sources as Cosmological Probes

What could we do with standard sirens?

- Completely independent, gravitational, calibration of
- the distance scale and the Hubble parameter
- Useful adjunct to existing constraints from CMBR, BAO,
- subject to completely different systematic errors.
- High precision probe of
- Extension of beyond the reach of SNIe and BAO.

Are these goals realistic?...

Gravitational Wave Sources as Cosmological Probes

Currently three major issues:

- Identification of E-M counterpart
- Impact of weak lensing
- Predicting merger event rates

Determining source directions

Directions via 2 methods: AM & FM

- FM: Frequency modulation due to orbital doppler shifts
- Analogous to pulsar timing
- gives best resolution for f > 1 mHz

- AM: Amplitude modulation due to change in orientation of array with respect to source over the LISA orbit
- AM gives best resolution for f < 1 mHz
LISA will have sub-degree resolution for strong, SMBH sources

See e.g. Cutler (98), Hughes (02), Cornish &

Rubbo (03), Vecchio (04), Lang & Hughes (06)

- AM gives best resolution for f < 1 mHz

Gravitational Wave Sources as Cosmological Probes

Identifying an E-M counterpart:

- GWs are redshifted, just like E-M radiation.
- Hence we determine (very precisely)
- If our goal is to probe e.g. how varies with
- we can assume and break the
- degeneracy. (See e.g. Hughes 02, Sesana et al. 07, 08)

- If we want to use sirens to measure ,
- we must observe the E-M counterpart.
- For this we need an accurate sky position!

Gravitational Wave Sources as Cosmological Probes

Lang & Hughes (2006) include spin-induced precession of the SMBHs

(See Vecchio 2004).

This significantly improves estimation of sky position and .

Gravitational Wave Sources as Cosmological Probes

Lang & Hughes (2006) include spin-induced precession of the SMBHs

(See Vecchio 2004).

This significantly improves estimation of sky position and .

Gravitational Wave Sources as Cosmological Probes

Lang & Hughes (2008) extend analysis to consider pre-merger evolution

Sky position error ellipses shown at

28, 21, 14, 7, 4, 2,

1 and 0 days before the merger.

Largest effect seen during final day – spin effects less important earlier.

Similar analysis in Kocsis et al (2007)

Gravitational Wave Sources as Cosmological Probes

So what exactly can we do with sirens?....

Adapted from Holz & Hughes (2005)

Gravitational Wave Sources as Cosmological Probes

So what exactly can we do with sirens?....

Adapted from Holz & Hughes (2005)

Gravitational Wave Sources as Cosmological Probes

GW sources will be (de-)magnified by weak lensing due to LSS.

Same effect as for SN

[ See e.g. Misner, Thorne &

Wheeler; Varvella et al (2004),

Takahashi (2006) ].

However, WL has much

greater impact for sirens,

because of their much

smaller intrinsic scatter.

Weak lensing may also limit identification of E-M counterpart

Correcting for weak lensing?...

Weak lensing by intervening large-scale structure distorts images of background galaxies

Distortion matrix:

Shear

Convergence

Following Refregier 2003

Correcting for weak lensing?...

- Observed siren brightness
- increased by magnification
- What can we expect?
- Can measure from shear
- maps derived from simulations
- Typically at
- which means ~5% error in
- Could we correct individual
- sirens by mapping on small
- angular scales?

Correcting for weak lensing?...

- Dalal et al (2003) concluded
- cosmic shear maps too noisy
- on sub-arcminute scales.

Unlensed

Lensed

Correcting for weak lensing?...

- Dalal et al (2003) concluded
- cosmic shear maps too noisy
- on sub-arcminute scales.
- Following Bacon (2008):
- → 3.8% at
- Templating? Jönsson et al (2006)
- Find galaxies near to line of sight to siren.
- ‘Pin’ on realistic DM halos. → 2.5%
- But what about ‘dark’ halos?...Systematics?...

Unlensed

Lensed

Correcting for weak lensing?...

Correcting for weak lensing?...

- Shapiro et al (2009): Shear varies from place to place.
- Gradient of shear → arcing, or flexion
- see e.g. Bacon (2005)
- Can measure flexion from galaxy survey, giving better estimate of
- matter density on small angular scales. → 1.8% at
- → 1.4% at

Correcting for weak lensing?...

- Shapiro et al (2009): Shear varies from place to place.
- Gradient of shear → arcing, or flexion
- Can measure flexion from galaxy survey, giving better estimate of
- matter density on small angular scales. → 1.8% at
- → 1.4% at

Major ‘multimessenger’ challenge

Correcting for weak lensing?...

- Can measure flexion from galaxy survey, giving better estimate of
- matter density on small angular scales. → 1.8% at
- → 1.4% at

No correction

EUCLID

Shear map only, ELT

Shear + flexion, ELT + Space

Shear + flexion, ELT

EELT

Major ‘multimessenger’ challenge

What could be done from the ground?

Dalal et al. (2006):

Short-duration GRBS, due to

NS-NS mergers, will also be observed by ALIGO network.

First optical observation of a NS-NS merger?

GRB 080503 (Perley et al 2008)

What could be done from the ground?

Dalal et al. (2006):

Short-duration GRBS, due to

NS-NS mergers, will also be observed by ALIGO network.

Beaming of GRBs (blue curves), aligned with GW emission, could boost GW SNR.

All-sky monitoring of GRBs + 1 year operation of ALIGO network

H0 to ~2% ?

What could be done from the ground?

- Nissanke et al. (2009):
- Very thorough treatment.
- Considers impact of:
- siren true distance;
- no. of detectors in network;
- Identifies strong degeneracy
- between distance and inclination.
- Need E-M observations /
- beaming assumption to break this?
- to 10 – 30% at 600 Mpc (NS-NS); 1400 Mpc (NS-BH).
- Competitive with traditional ‘distance ladder’; probe of peculiar velocities?

Looking ahead to the Einstein Telescope…

Third Generation Network — Incorporating Low Frequency Detectors

- Third-generation underground facilities are aimed at having excellent sensitivity from ~1 Hz to ~104 Hz.
- This will greatly expand the new frontier of gravitational wave astrophysics.

Recently begun:

Three year-long European design study, with EU funding, underway for a 3rd-generation gravitational wave facility, the Einstein Telescope (ET).

Goal: 100 times better sensitivity than first generation instruments.

Looking ahead to the Einstein Telescope…

Third Generation Network — Incorporating Low Frequency Detectors

- Third-generation underground facilities are aimed at having excellent sensitivity from ~1 Hz to ~104 Hz.
- This will greatly expand the new frontier of gravitational wave astrophysics.

Recently begun:

Three year-long European design study, with EU funding, underway for a 3rd-generation gravitational wave facility, the Einstein Telescope (ET).

Goal: 100 times better sensitivity than first generation instruments.

Looking ahead to the Einstein Telescope…

Sathyaprakash et al. (2009):

~106 NS-NS mergers observed by

ET. Assume that E-M counterparts

observed for ~1000 GRBs, 0 < z < 2.

De-lensed

Weak lensing

Fit , ,

Competitive with ‘traditional’ methods

…And even further ahead to BBO…

BBO schematic

Cutler and Holz (2009):

~3 x 105 sirens observed, with unique E-M counterparts, for 0 < z < 5.

Extremely good angular resolution, even at z = 5!

Robust E-M identification of host galaxy, for determining redshift

…And even further ahead to BBO…

Cutler and Holz (2009):

~3 x 105 sirens observed, with unique E-M counterparts, for 0 < z < 5.

Simulated Hubble diagram, including effects of lensing

…And even further ahead to BBO…

Hubble constant to ~0.1%

w0 to ~1%, wa to ~10%

…And even further ahead to BBO…

Hubble constant to ~0.1%

w0 to ~1%, wa to ~10%

All of this lies far ahead, but the key is to work on development of the science case now

Opening a new window on the Universe

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