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 [email protected]
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
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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
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Rh (τ )
Comparison of Dyn/Sec spectra
Cumulative Delay - No Arclets
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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
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 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
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ft = 1Pt
= Vxθ x
λ€
=λθ
€
Pt = yV
= λVθ
V
incident plane wave (λ)
conjugate freq axisConjugate frequency axis (heuristic)
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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
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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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