Detecting gravitational-waves byobserving pulsars, nature's mostaccurate natural clocks.

Rutger van Haasteren(Jet Propulsion Lab)
Credit: David ChampionOutline
1. Gravitational-wave detector principles
2. Pulsars and pulsar timing
3. Examples of pulsar timing
4. Gravitational-waves sources
5. Pulsar timing arrays
6. Outlook and detection prospects

What is a GW?

Gravitational wave: ripple inGravity wave: refer to one ofin the curvature of spacetime Tokyo's local surfers
that propagates outward fromthe source as a wave.

Effect and detectability of GWs

Effect of GWs is an oscillating
Speed of light is constant.
Riemann curvature tensor,
possible in two polarisations.
Measure time, not distance.
→ Measure propagation length!

Effect and detectability of GWsabCredit: Advanced Technology Center, NAOJ

Emit light, and reflect backNow it is truly a 'timing
experiment'

LASER has precise frequency→ equivalent to clock
Interferometry for detection

Need precise frequency/clock

Could say that KAGRA uses
a LASER as an accurate
frequency standard

What about pulsar's spin
frequency?
Period of PSR B1937+21:
T = 0.00155780644887275 s

Strain sensitivity per frequency
Energy density function of wavelength
Electromagnetic waves:
Gravitational waves:Ω∝∣E∣2+∣B∣2Ω∝∣ḣ∣2=f 2 h (f )2
Atomic nucleus
is ~1e-15m
With 3km arm, reachsensitivity down todistance variations of~1e-21m??
(zepto-meter)

Yardley et al. (2010)

Pulsars

Discovery: LGM1

Pulsar discovery in 1967: LGM1(= PSR B1919+21)'Knocking sound'Discovery: LGM1

Pulsar discovery in 1967: LGM1(= PSR B1919+21)'Knocking sound'Explanation: neutron starBaade & Zwicky in 1934: "With all reserve we advance theview that a supernova represents the transition of an ordinary
star into a new form of star, the neutron star, which would be
the end point of stellar evolution. Such a star may possess avery small radius and an extremely high density."

Crab Nebula. Remnant of 1054 AD supernova,
seen by Chinese astronomers ('guest star').

Pulse profile of the Crab.

Associated supernova: the Crab
Baade & Zwicky in 1934: "With all reserve we advance theview that a supernova represents the transition of an ordinarystar into a new form of star, the neutron star, which would be
the end point of stellar evolution. Such a star may possess avery small radius and an extremely high density."

Crab Nebula. Remnant of 1054 AD supernova,
seen by Chinese astronomers ('guest star').

Pulse profile of the Crab.

Pulsars

Star dies → core pressure goneStar collapses → compact object
Neutron star for heavy stars

Conserved from star:- Angular momentum- Magnetic field→ Dynamo!

Period of 1.5 ms???
Don Backer et al. (1982), found a pulsar with a spin frequencyof 716 Hz (P = 1.5 ms). This was the first millisecond pulsar.
Can this still be a rotating neutron star?

Arecibo Observatory

Pulse profile of B1937

Period of 1.5 ms???
Don Backer et al. (1982), found a pulsar with a spin frequencyof 716 Hz (P = 1.5 ms). This was the first millisecond pulsar.
Can this still be a rotating neutron star?

Arecibo Observatory

Radius less than 16km. At equator,
spin velocity > 70,000 km/s(= 24% speed of light)

Pulse profile of B1937

P-Pdot diagram
Most stable 'clocks'
are in the bottom
left
Note: almost allbinaries there

Millisecond pulsars

Credit: NASA animations

Pulsar Timing

Parkes Radio TelescopeDispersion

1Δt∝ 2f

Ingrid Stairs (2001)

Pulse profiles

Ingrid Stairs (2001)

Timing residuals

Some typical numbers
Pulse period:●
Pulse width:●
Timing accuracy:●
Pulsar distance:●

5 ms
0.5 ms (~10% of period)
100 nsseveral kpc (3 * 10^19 m)→ sensitivity to distance variations of 30 m ( < 1 part in 10^18)

Can account for every not-observed rotation!

Timing residuals

Wrong proper motion

'Standard' procedure
Observe really often: get coherent solution●Obtain longer time baseline: tune parameters●
Extend the timing model as much as possible●Keep fitting until it looks ok●

Not automated“Pulsar timing is an art”
– G.H. Hobbs

The timing model: spindown

The timing model: declination

Red spin noise / timing noise

Gravitational wave?

Timing noise?

Examples of pulsar timing

Pulsar timing basically uses pulsars as 'tools'. We
do not fully understand pulsar emission, but they
are very useful!
Let's look at some applications of pulsar timing...

The Hulse-Taylor binary
Hulse and Taylor found a binary pulsar in1973. Nobel prize 1993.

Post-keplerian parameters
The PK parameters
are constructed suchthat only the twomasses are unknown.
Thus: only twounknown parameters!

Post-keplerian parameters
The PK parameters
are constructed suchthat only the twomasses are unknown.
Thus: only twounknown parameters!

Weisberg et al. (2003)

Double pulsar
Discovered in the Parkes multibeam survey(Burgay et al. 2003). Incredibly lucky: edge-onsystem. Eclipses probe pulsar magnetosphereDouble pulsar GR tests

w: precession of periastrong: time dilation gravitational redshift
r: Shapiro time delay (range)
S: Shapiro time delay (shape)
Pb: sec. change of the orbital period
R: mass ratio

Kramer et al. (2006)

Double pulsar magnetosphere

Breton et al. (2006)

Geodetic precession

Breton et al. (science)

Only available for the double pulsar.

Constraining dipolar GWs

Freire et al. (2012): dipolar GW emission in pulsar-white dwarf systems are predictions of most alternate
scalar-tensor theories of gravity, and tensor-vector-scalar (TeVeS) theories (relativistic MOND).

Pulsar Timing GWs: SMBHBs
1917. Karl Schwarzschild finds an analyticalsolution for the Einstein field equations,predicting black holes

1962. Quasars discoveredat billions of light years bySchmidt.

1969. Lynden-Bellargues thatsupermassive blackholes should exist
at the centers of many
galaxies.

1964. Zeldovich & Novikov
and Salpeter argue that
Quasars are powered by theaccretion of gas onto
supermassive black holes

1996+. Hubble Telescope observations,analyzed using Martin Schwarzschild’s method,establish that supermassive black holes exist
in the large majority of galaxies with acentral bulge.

Observations: ESO's 8.2 m Very Large Telescope (VLT)

Evolution of galaxies and their
massive black holes

Question: how do black holes evolve?

Galaxy formation
Universe becomes matter-dominatedat z=10000. Gravitational instability
becomes effective.
Small halos collapse first,
small galaxies form firstMarta Volonteri (2003)

Smaller galaxies merge to form large
spirals and ellipticals.
White & Rees 78

Supermassive BH binaries
Begelman, Blandford, &Rees 1982:2pc

10 kpcdynamicalfriction

1pc

0.01pcscattering

wishfulthinkinggas

non-sphericalpotential

mergergravitational
waves

anotherblack hole“last-parsec problem”, considered mostly solved nowFrequency bands GW detectors

Lommen (2012)

Types of waveforms of interest

Inspiral – merger – ringdown
Inspiral: continuous wave
Merger: unresolvable.
Ringdown: unresolvable... but:
The memory effect ispermanent!
Marc Favata (2010)

At low frequencies: backgroundPhinney 01
Jaffe & Backer 03
Wyithe & Loeb 03
Sesana et al. 07, 09

General Relativity predicts:

Pulsars and GW detection

Credit: David Champion
Pulsars are nearly-perfect Einstein clocks. Very precise frequency standard. Can beused just like LASER in interferometers: phase-change due to propagation in GWs isobservable.

Example: 3C66B

3C66B was a proposed
supermassive binary
black hole system. The
emitted GWs shouldhave been seen in
B1855+09. System wasruled out
Jenet et al. (2004)
Data from Kaspi, Taylor, Ryba (1994)
of pulsar PSR B1855+09

Earth term / Pulsar terma b1p
̂̂pδ ν =e A ( Ω̂)Credit:DavidChampionh(t)−h(t)()
abeeppν̂ p̂
2 1+ Ω⋅Earth-term

Pulsar-termAntenna pattern response
a,b: +,x polarisationc,d: vector x,y modes
e: scalar mode
Most efforts focus on theusual +,x polarisations.

a b1p
̂
̂p
δ ν =e A ( Ω̂)Credit:DavidChampionh(t)−h(t)()
abeeppν̂ p̂
2 1+ Ω⋅Earth-term

Pulsar-term

The Pulsar Timing Arrays
Parkes Pulsar Timing Array: Parkes radio telescope (64m). Oldest
fully organised PTA effort. Best timing residuals to date. SouthernHemisphereEuropean Pulsar Timing Array: Effelsberg (100m),
Westerbork synthesis (14x25m), Nancay (94m),
Lovell (76m), Sardinia (64m). Most dishes.

NANOGrav: GreenBank (100m),Arecibo (300m). Biggest dishes.

Typical signals in PTAs

Typical signals in PTAs

Stochastic isotropic signals are correlated between pulsars according to the overlap
reduction function (Hellings & Downs curve). Due to quadrupolar nature of GWs.

Need many, many pulsars!!!

Stochastic GWB mock data

Searching for the H&D curve

Jenet et al. (2005), Demorest et al. (2012), Lentati et al. (2013), Chamberlain (in prep.)(An)Isotropy: millennium simulation

Sesana et al. (2008), Ravi et al. (2012): Theory and simulations suggest there is a
non-zero probability that individual sources have SNR above the background.

Anisotropy: compare with SDSS

Pablo Rosado (AEI, preliminary): use SDSS to find candidates, predict statistics/GW
hotspots. Test statistic based on Millennium simulation.

GW searches in PTA data
Challenges in the analysis (compared to interferometers):●Irregularly sampled data with large gaps
●Unknown noise statistics●Very low frequency signal (and noise)●Various systematics that have to be mitigated (timing model, dispersion
measure variations)
Our approach: Bayesian analysis (marginalisation, sampling, priors, …)
Likelihood a multivariate Gaussian:P(⃗x∣⃗a )=exp [−(x −f (⃗a ))C−1 (x−f (⃗a ))/2]

Practical difficulties... but we are getting there!

√(2 π) det CnContinuous wave searches

Babak, Petiteau et al. (2012): Parameter space of searches for continuouswaves (single BH binaries) is quite large. Idea: use clever searches likegenetic algorithm. Question: how many sources do we need?

Published upper limits: EPTA

Spectrum: h c (f )= Af −αPublished upper limits: EPTA

Spectrum: h c (f )= Af −α

A < 6e-15

Published upper limits:NANOGrav

Demorest et al. (2012)h c (f )= Af−α

A < 7e-15

Current upper limit: EPTA

van Haasteren (in prep.) & Lentati (in prep.): A < 3e-15

Prospects for detection

Sesana (2013)

Prospects for detection

Siemens et al. (in prep.)Scaling laws

Siemens et al. (in prep.)Other applications

Other applicationsHobbs et al. (2012)
Pulsars can beused to construct atimescale,independent fromatomic clocks

Other uses include: studying the solar system ephemeris (planetmasses), cosmic strings, interstellar navigation, ...

Conclusions
Pulsars can be used as sensitive instruments●Lots of fundamental science done
●Ideal for testing gravitational theories●Observing GWs in the near future with pulsar
timing arrays (PTAs)●Unknown: red spin noise millisecond pulsars●Unknown: GW background amplitude●Plenty of other uses for PTAs
●