Searching for Gravitational
Waves with
Millisecond Pulsars:
Dan Stinebring
Oberlin 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
8
10
6
7
• 10 – 10 years old (compared to 10 – 10 )
• 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
Black slide
Sky Distribution of Millisecond Pulsars
P < 20 ms and not in globular clusters
R. N. Manchester (ATNF)
What is a gravitational wave?
• A 2-D analogy
space
motion in this
dimension is
meaningless
2 free masses
The masses track
each other with lasers
Ron Hellings (Montana SU)
The gravitational wave is a wave of curvature
each slice is a section of
an arc of constant radius
Ron Hellings (Montana SU)
As a gravitational wave passes through the space...
the free masses remain fixed at their coordinate points
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
l
h
l
points that are
further away have more
space injected between them
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
Black slide
[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.
Arecibo data
Timing residuals for PSR B1855+09
Gravitational Wave passing over Earth
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Opposite sign in orthogonal directions - Quadrupole
Earth
R. N. Manchester
Correlation Expected between Pulsars in Different Directions
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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 University
Zaven Arzoumanian, Goddard Space Flight Center
Don Backer, University of California, Berkeley
Paul Demorest, National Radio Astronomy Observatory
Rob Ferdman, CNRS, France
Paulo Freire, NAIC
Marjorie Gonzalez, University of British Columbia
Rick Jenet, University of Texas, Brownsville, CGWA
Victoria Kaspi, McGill University
Vlad Kondratiev, West Virginia University
Joseph Lazio, Naval Research Laboratories
Andrea Lommen, Franklin and Marshall College
Duncan Lorimer, West Virginia University
Ryan Lynch, University of Virginia
Maura McLaughlin, West Virginia University
David Nice, Bryn Mawr College
Scott Ransom, National Radio Astronomy Observatory
Ryan Shannon, Cornell University
Ingrid Stairs, University of British Columbia
Dan 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)
Dan Stinebring
Oberlin College
dan.stinebring@oberlin.edu
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.
(1)
Bertotti, Carr, & Rees (1983)
Bertotti, Carr, & Rees (1983)
Compact object inspiral
Bertotti, Carr, & Rees (1983)
Quadrupole Gravitational Waves
a ring of free
test masses
more space
h
less space
Ron Hellings (Montana SU)
+
Lorimer&Kramer (LK) Fig. 4.2 Sketch showing inhomogeneities in
the ISM that result in observed scattering and scintillation effects.
1133+16 dyn & sec
linear
grayscale
logarithmic
grayscale
dynamic (or primary) spectrum

1133+16 dyn & sec
linear
grayscale
t


f
secondary spectrum
logarithmic
grayscale

ft
Cumulative Delay - Arclets
Hemberger & Stinebring 2008, ApJ, 674, L37
Black slide
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 neutronstar binary systems
R. N. Manchester (ATNF)
LISA: Laser Interferometer Space Antenna
• ESA – NASA project
o
• Orbits Sun, 20 behind the Earth
• Three spacecraft in triangle, 5 million km each side
-4
-1
• Sensitive to GW signals in the range 10 – 10 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
(NASA GSFC)
• Generated by acceleration of massive object(s)
• 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
R. N. Manchester (ATNF)
(K. Thorne, T. Carnahan, LISA Gallery)
h(t)
y(t)  I(t) h(t)

ISM impulse response function
What we can measure ...
Rh ( ) 
h(t)
h(t


)
dt

the autocorrelation of the impulse response
At the moment, we use the centroid of
Rh ( )
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
Want to achieve < 1 us residuals for 10 pulsars
for 5 years
Timing residuals for PSR B1855+09
R. N. Manchester (ATNF)
Name
J0437-4715
J1744-1134
J2124-3358
J1024-0719
J2145-0750
J1730-2304
J1022+1001
J1909-3744
J1857+0943
J1713+0747
J0711-6830
J2129-5721
J1603-7202
J0613-0200
J1600-3053
J1732-5049
J1045-4509
J1643-1224
J1939+2134
J1824-2452
DM
2.65
3.14
4.62
6.49
9.00
9.61
10.25
10.39
13.31
15.99
18.41
31.85
38.05
38.78
52.19
56.84
58.15
62.41
71.04
119.86
RMS Residual (us)
0.12
0.65
2.00
1.20
1.44
1.82
1.11
0.22
2.09
0.19
1.56
0.91
1.34
0.83
0.35
2.40
1.44
2.10
0.17
0.88
R. N. Manchester Sept 2006
Timing RMS (microseconds)
3.00
Timing Behavior vs. Dispersion Measure
2.50
2.00
1.50
1.00
0.50
0.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
DM (pc cm^-3)
data: R. N. Manchester
140.00
h(t)
ISM
y(t)  I(t)
 h(t)
ISM impulse response function
What we measure ...
Rh ( ) 
h(t)
h(t


)
dt

the autocorrelation of the impulse response
At the moment, we use the centroid of
Rh ( )
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
1133+16 dyn & sec
D. Hemberger
1133+16 dyn & sec
D. Hemberger
Timing Residuals (Observed – Model) for PSR B1855+09
“Deflection of Pulsar Signal Reveals Compact Structures in
the 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!
Walter Brisken (NRAO) et al.
“Small Ionized and Neutral
Structures,” Socorro, NM, 2006 May 23
Brisken dyn + secondary
1.2
How Does this Work?
Coherent radiation scatters off
electron inhomogeneities
~ 10 mas
~ 1 kpc
Multi-path interference causes
a random diffraction pattern
Relative transverse velocities
produce a dynamic spectrum
time
Scattering in a thin screen plus
a simple core/halo model can
explain the basics of
scintillation arcs
Time variability of scintillation arcs
will allow probing of the ISM on
AU size scales
Kolmogorov vs. Gaussian PSF
How to produce a “core/halo” psf?
A Gaussian psf will NOT work: No halo.
Kolmogorov vs. Gaussian PSF
Kolmogorov turbulence DOES work
It produces a psf with broad wings
Conjugate time axis (heuristic)
conjugate time axis
D
incident plane wave ()
d
 

y   D 
d 


y 
Pt  
V
V


y
1 Vx x
ft  
Pt

V
Conjugate frequency axis (heuristic)
incident plane wave ()

conjugate freq axis
D
2
2


D
D
t 
2c
2

2 t  1
c
P   
2
D


1 D
f  
P
c
2
where do the parabolas come
2
V from ?” D
ft 
f 
Where do the parabolas come from?

c
D  2
f     2  ft
cV


f
2
ft


parabola eqn on data plot
B2021+25
f  ft
f

2
ft
Where do the “arclets” (inverted parabolas)
come from?
where do the arclets come from
?”
1d “image” on the sky
f
ft
Walker et al. 2004
Some Observational
Highlights ...
The Earth Orbits
the Sun !!
Effective Velocity
Cordes and Rickett 1998, ApJ, 507, 846

s
 D s (1 s)
2

2
eff
2cV
Dpsrscreen
Dtotal
1929+10 velocity plot
Multiple Arcs —>
Multiple “Screens”
“Screen” Locations
f = 
2
ft


 D s (1 s)
2
2
eff
2cV
PSR 1133+16
D  s(1 s)

2
2cVeff
2
s=0
s=1
Veff  (1 s)Dm psr  sVobs  Vscreen
proper motion (2d)
f = 
2
ft
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 Pulsars
P < 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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