Searching for Gravitational Waves with Millisecond Pulsars:

Searching for Gravitational Waves with

Millisecond Pulsars:

Dan StinebringOberlin College

CWRU – May 21, 2009

George Greenstein(Amherst College)

Discovery of “Millisecond” Pulsars• 1982 – Arecibo Observatory – Don Backer,

Sri Kulkarni, ...• Spun-up by accretion in a binary system• 108 – 1010 years old (compared to 106 – 107)• Timing precision < 1 ms is possible in many

cases (as opposed to ≈ 1 ms)

Millisecond Pulsar Spin-up

B0329+54

The Vela pulsar

The first millisecond pulsar (1982, Backer & Kulkarni)

Arecibo Observatory – the world’s largest radio telescope

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Sky Distribution of Millisecond PulsarsP < 20 ms and not in globular clusters

R. N. Manchester (ATNF)

space

What is a gravitational wave?

• A 2-D analogy

motion in thisdimension ismeaningless

2 free masses

The masses trackeach other with lasers

Ron Hellings (Montana SU)

The gravitational wave is a wave of curvature

each slice is a section ofan arc of constant radius

Ron Hellings (Montana SU)

the free masses remain fixed at their coordinate points

As a gravitational wave passes through the space...

while the distance between them

Ron Hellings (Montana SU)

increases due to the extra space in the curvature wave.

The laser signal has to cover more distance and is delayed

Ron Hellings (Montana SU)

Why are gravitational waves called “a strain in space”?

points that are close have little space injected

between them

points that arefurther away have morespace injected between them

h Δ≡

ll

Ron Hellings (Montana SU)

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[Markus Pössel, AEI

http://www.einstein-online.info/en/spotlights/gw_waves/index.html

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[Markus Pössel, AEI

http://www.einstein-online.info/en/spotlights/gw_waves/index.html

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[Markus Pössel, AEI

http://www.einstein-online.info/en/spotlights/gw_waves/index.html

Detecting Gravitational Waves with Pulsars• Observe the arrival times of pulsars with sub-microsecond precision.• Correct for known effects (spin-down, position, proper motion, ...) through a multi-parameter Model Fit.•Look at the residuals (Observed - Model) for evidence of correlated timing noise between pulsars in different parts of the sky.

Timing residuals for PSR B1855+09

Arecibo data

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Earth

Gravitational Wave passing over EarthOpposite sign in orthogonal directions - Quadrupole

R. N. Manchester

Black slideCorrelation Expected between Pulsars in Different Directions

F. Jenet (UTB)

Fact of Life #1

• The gravitational effect is due only to what happens at the two ends of the path:

h(tthen, xpsr) – h(tnow, xEarth)

Fact of Life #2• Fitting for unknown pulsar parameters

removes power from the data: (P, dP/dt, position, angular motion, binary orbit, ...)

Blandford, Narayan,and Romani 1984

Anne Archibald, McGill UniversityZaven Arzoumanian, Goddard Space Flight CenterDon Backer, University of California, BerkeleyPaul Demorest, National Radio Astronomy ObservatoryRob Ferdman, CNRS, FrancePaulo Freire, NAICMarjorie Gonzalez, University of British ColumbiaRick Jenet, University of Texas, Brownsville, CGWAVictoria Kaspi, McGill UniversityVlad Kondratiev, West Virginia University

Joseph Lazio, Naval Research LaboratoriesAndrea Lommen, Franklin and Marshall CollegeDuncan Lorimer, West Virginia UniversityRyan Lynch, University of VirginiaMaura McLaughlin, West Virginia UniversityDavid Nice, Bryn Mawr CollegeScott Ransom, National Radio Astronomy ObservatoryRyan Shannon, Cornell UniversityIngrid Stairs, University of British ColumbiaDan Stinebring, Oberlin College

The Gravitational Wave Spectrum Spectrum

R. N. Manchester (ATNF)

Figure by Paul Demorest (see arXiv:0902.2968)

Figure by Paul Demorest (see arXiv:0902.2968)

Summary• Pulsars are ideal for detecting the low

frequency (nHz) end of the gravitational wave spectrum.

• This technique is complementary to the LIGO and LISA efforts.

• Arecibo is critical to detecting gravitational waves in the next decade.

• What is needed: more pulsars, more telescope time, reduction in systematics.

Dan StinebringOberlin Collegedan.stinebring@oberlin.edu

Bertotti, Carr, & Rees (1983)

(1)

Only get a non-oscillatory termwhen wuL << 1

Bertotti, Carr, & Rees (1983)

Compact object inspiral

Bertotti, Carr, & Rees (1983)

Quadrupole Gravitational Waves

a ring of free test masses

h+

less space

Ron Hellings (Montana SU)

mor

e sp

ace

Lorimer&Kramer (LK) Fig. 4.2 Sketch showing inhomogeneities in the ISM that result in observed scattering and scintillation effects.

1133+16 dyn & sec

logarithmicgrayscale

lineargrayscale

1133+16 dyn & sec

€

ν

€

t

€

fν

€

ft

logarithmicgrayscale

lineargrayscale

dynamic (or primary) spectrum

secondary spectrum

Cumulative Delay - Arclets

Hemberger & Stinebring 2008, ApJ, 674, L37

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Pulsars are different from VIRGO, etc.

• The only h (t, x) that matters is h (temission, xpulsar) and h (tarrival, xEarth).

• We don’t track the electromagnetic phase, but we do track the pulsar rotational phase (in the best cases to 100 ns resolution).

• Pulsars are located all over the sky. This is a GOOD thing because each pair is a separate detector.

LIGO: Laser Interferometer Gravitational-wave Observatory

• US NSF project• Two sites: Washington State and Louisiana• Two 4-km vacuum arms, forming a laser interferometer • Sensitive to GW signals in the 10 – 500 Hz range• Initial phase now commissioning, Advanced LIGO ~ 2011

Most probable astrophysical source: merger of double neutron-star binary systems

R. N. Manchester (ATNF)

LISA: Laser Interferometer Space Antenna• ESA – NASA project• Orbits Sun, 20o behind the Earth• Three spacecraft in triangle, 5 million km each side• Sensitive to GW signals in the range 10-4 – 10-1 Hz• Planned launch ~2015

Most probable astrophysical sources: Compact stellar binary systems in our Galaxy and merger of binary black holes in cores of galaxies

R. N. Manchester (ATNF)

Detection of Gravitational Waves

• Prediction of general relativity and other theories of gravity • Generated by acceleration of massive object(s)

(K. Thorne, T. Carnahan, LISA Gallery)

• Astrophysical sources: Inflation era Cosmic strings Galaxy formation Binary black holes in galaxies Neutron-star formation in supernovae Coalescing neutron-star binaries Compact X-ray binaries

(NASA GSFC)

R. N. Manchester (ATNF)

What we can measure ...

€

y(t) = I (t)∗h(t)ISM impulse response function

€

h(t)

€

Rh (τ ) = h(t) h(t − τ ) dt∫the autocorrelation of the impulse response

At the moment, we use the centroid of

€

Rh (τ )

Comparison of Dyn/Sec spectra

Cumulative Delay - No Arclets

1133+16 dyn & sec

D. Hemberger

B1737+13 tau_ss + errors (36 epochs)

D. Hemberger

Detecting Gravitational Waves with Pulsars• Observed pulse periods affected by presence of gravitational waves in Galaxy (psr at time of emission; Earth at time of reception)• For stochastic GW background, effects at pulsar and Earth are uncorrelated• Use an array of pulsars to search for the GW background that is correlated because of its effect on the Earth (at time of reception)• Best limits are obtained for GW frequencies ~ 1/T where T is length of data span

Timing residuals for PSR B1855+09

R. N. Manchester (ATNF)

Want to achieve < 1 us residuals for 10 pulsarsfor 5 years

Name DM RMS Residual (us)J0437-4715 2.65 0.12J1744-1134 3.14 0.65J2124-3358 4.62 2.00J1024-0719 6.49 1.20J2145-0750 9.00 1.44J1730-2304 9.61 1.82J1022+1001 10.25 1.11J1909-3744 10.39 0.22J1857+0943 13.31 2.09J1713+0747 15.99 0.19J0711-6830 18.41 1.56J2129-5721 31.85 0.91J1603-7202 38.05 1.34J0613-0200 38.78 0.83J1600-3053 52.19 0.35J1732-5049 56.84 2.40J1045-4509 58.15 1.44J1643-1224 62.41 2.10J1939+2134 71.04 0.17J1824-2452 119.86 0.88

R. N. Manchester Sept 2006

Timing Behavior vs. Dispersion Measure

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00DM (pc cm^-3)

Timing RMS (microseconds)

data: R. N. Manchester

What we measure ...

€

y(t) = I (t)∗h(t)ISM impulse response function

ISM

€

Rh (τ ) = h(t) h(t − τ ) dt∫the autocorrelation of the impulse response

At the moment, we use the centroid of

€

Rh (τ )

€

h(t)

A new result ...

• 6 months of ~ weekly Arecibo observations of a moderate DM pulsar (B1737+13)

• 4 x 50 MHz bands near 21 cm• Investigate time variability of ScintArc

structure and its effect on pulsar timing

B1737+13 secondary spectrum

movie

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D. Hemberger

1133+16 dyn & sec

D. Hemberger

Timing Residuals (Observed – Model) for PSR B1855+09

“Deflection of Pulsar Signal Reveals Compact Structures inthe Galaxy, ” A. S. Hill et al. 2005, 619, L17

The substructure persists

and MOVES!

Hill, A.S., Stinebring, D.R., et al.

2005, ApJ,619, L171 This is the angular velocity of the pulsar across the sky!

Brisken dyn + secondary

1.2

Walter Brisken (NRAO) et al.“Small Ionized and NeutralStructures,” Socorro, NM, 2006 May 23

How Does this Work?

Coherent radiation scatters off electron inhomogeneities

~ 1 kpc

~ 10 mas

Multi-path interference causesa random diffraction pattern

Relative transverse velocities produce a dynamic spectrum

time

Scattering in a thin screen plusa simple core/halo model canexplain the basics ofscintillation arcs

Time variability of scintillation arcswill allow probing of the ISM on AU size scales

Kolmogorov vs. Gaussian PSFHow to produce a “core/halo” psf?

A Gaussian psf will NOT work: No halo.

Kolmogorov vs. Gaussian PSFKolmogorov turbulence DOES work

It produces a psf with broad wings

conjugate time axisConjugate time axis (heuristic)

d

D

€

θ =dD

y

€

y = λd ⎛ ⎝ ⎜

⎞ ⎠ ⎟D

€

ft = 1Pt

= Vxθ x

λ€

=λθ

€

Pt = yV

= λVθ

V

incident plane wave (λ)

conjugate freq axisConjugate frequency axis (heuristic)

€

fν = 1Pν

= πDθ 2

c

D€

Dθ 2

2

€

θ

€

Pν = δν = cπDθ 2

incident plane wave (λ)

€

δt = Dθ 2

2c

€

2π δt δν =1

€

δν

where do the parabolas come from ?”

Where do the parabolas come from?

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fν = πDθ 2

c

€

ft = Vθλ

€

fν = ± πDλ2

cV 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ft

2

€

ft

€

fν

parabola eqn on data plotB2021+25

€

fν

€

ft€

fν ∝ ft2

€

fν

€

ft Walker et al. 2004

1d “image” on the sky

where do the arclets come from ?”

Where do the “arclets” (inverted parabolas) come from?

Some ObservationalHighlights ...

The Earth Orbits the Sun !!

Effective Velocity

Cordes and Rickett 1998, ApJ, 507, 846

€

s ≡Dpsr−screen

Dtotal

€

η=λ2D s (1− s)

2cVeff2

1929+10 velocity plot

Multiple Arcs —>

Multiple “Screens”

“Screen” Locations

fν = η ft2

€

η=λ2D s (1− s)

2cVeff2

PSR 1133+16

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η=D λ2 s(1− s)

2cVeff2

€

Veff = (1− s)Dμ psr + sVobs − Vscreen

proper motion (2d)

s=0 s=1

fν = η ft2

Summary• Pulsars are ideal probes of the ionized ISM • New phenomena to explore and learn to

interpret• Pulsars may detect gravitational waves

before the expensive detectors!• Larger more sensitive telescopes will

provide breakthroughs! LOFAR, SKA ... Thanks to: Sterrewacht Leiden & NWO

Scintillation Arcs Underlie Other Scintillation Patterns

Tilted 0355a

Roger Foster, GB 140 ft

Tilted 0355b

Roger Foster, GB 140 ft

Tilted 0919a

Tilted 0919b

The Gravitational Wave Spectrum

R. N. Manchester (ATNF)

Sky Distribution of Millisecond PulsarsP < 20 ms and not in globular clusters

R. N. Manchester (ATNF)

Black slide

[Markus Pössel, AEI

http://www.einstein-online.info/en/spotlights/gw_waves/index.html

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[Markus Pössel, AEI

http://www.einstein-online.info/en/spotlights/gw_waves/index.html

Discovery of “Millisecond” pulsars in 1982 changed everythingBlack slide

Timing residuals for PSR B1855+09

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