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Searching for Gravitational
Waves from Spinning
Neutron Stars
(and other objects)
Keith Riles
University of Michigan
LIGO Scientific Collaboration
U-M HEP / Astro Seminar
April 19, 2010
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What are Gravitational Waves?
• Gravitational Waves = “Ripples in space-time”
• Perturbation propagation similar to light (obeys same wave equation!)
– Propagation speed = c
– Two transverse polarizations - quadrupolar:
+ and x
Example:
Ring of test masses
responding to wave
propagating along z
Amplitude parameterized by (tiny)
dimensionless strain h: DL ~ h(t) x L
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Why look for Gravitational Radiation?
• Because it’s there! (presumably)
• Test General Relativity:
– Quadrupolar radiation? Travels at speed of light?
– Unique probe of strong-field gravity
• Gain different view of Universe:
– Sources cannot be obscured by dust / stellar envelopes
– Detectable sources some of the most interesting,
least understood in the Universe
– Opens up entirely new non-electromagnetic spectrum
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What might the sky look like?
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What makes Gravitational Waves?
• Radiation generated by quadrupolar mass movements:
(with Imn = quadrupole tensor, r = source distance)
• Example: Pair of 1.4 Msolar neutron stars in circular orbit of radius
20 km (imminent coalescence) at orbital frequency 400 Hz gives
800 Hz radiation of amplitude:
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Strong Indirect Evidence:
Binary Orbit Decay
Neutron Binary System – Hulse & Taylor
PSR 1913 + 16 -- Timing of pulsars
Emission of gravitational waves
17 / sec


~ 8 hr
Neutron Binary System
• separated by 106 miles
• m1 = 1.44m; m2 = 1.39m; e = 0.617
Prediction from general relativity
• spiral in by 3 mm/orbit
• rate of change orbital period
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What makes Gravitational Waves?
• Compact binary inspiral:
“chirps”
– NS-NS waveforms are well described
– Recent progress on BH-BH waveforms
• Supernovae / SGRs / ??? :
“bursts”
• Spinning neutron stars in our galaxy:
“periodic”
– burst signals in coincidence with signals
in electromagnetic radiation / neutrinos
– all-sky untriggered searches too
– search for observed neutron stars
– all-sky search (computing challenge)
• Cosmological Signals
“stochastic background”
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Gravitational Wave Detection
• Suspended Interferometers
– Suspended mirrors in “free-fall”
– Michelson IFO is
“natural” GW detector
– Broad-band response
(~10 Hz to few kHz)
– Waveform information
(e.g., chirp reconstruction)
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The Global Interferometer Network
The three (two) LIGO, Virgo and GEO interferometers are part of a Global Network.
Multiple signal detections will increase detection confidence and provide better precision
on source locations and wave polarizations
V1
L1
H1 (H2)
LIGO
G1
GEO
T1
Virgo
TAMA
New proposal: Put one
of the Advanced LIGO
detectors in Australia!
(“LIGO South”)
AIGO (proposed)
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Major Interferometers world-wide
LIGO
Livingston, Louisiana &
Hanford, Washington
VIRGO
Near Pisa, Italy
GEO
Near Hannover, Germany
TAMA
Tokyo, Japan
2 x 4000-m
(1 x 2000-m)
Completed 2-year data
run at design sensitivity –
“Enhanced” detector now
running
1 x 3000-m
Has taken ~10 months
coincident data with LIGO
– Down for its own
enhancement until July
1 x 600-m
Took data during L-V
downtime -- undergoing
upgrade
1 x 300-m
Used for R&D aimed at
future underground
detector
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Data Runs
Have completed a series of Engineering Runs (LIGO E1–E14, Virgo WSR 1-13) and
Science Runs (LIGO S1--S5, Virgo VSR1-2) interspersed with commissioning
S1 run:
17 days (Aug / Sept 2002) – Rough but good practice
S2 run:
59 days (Feb—April 2003) – Many good results
S3 run:
70 days (Oct 2003 – Jan 2004) -- Ragged
S4 run:
30 days (Feb—March 2005) – Another good run
S5 run: (VSR1 for Virgo)
23 months (Nov 2005 – Sept 2007) – At design sensitivity – focus of today’s results
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LIGO S1  S5 Sensitivities
Strain
spectral
noise density
hrms = 3 10-22
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Virgo Sensitivities
Black measurements – VSR1 – 2007
Red measurements – May 2009
Design 
Much better sensitivity than
LIGO below ~40 Hz
 Binary black holes
 “Young” pulsars, e.g., Vela
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Searching for Gravity Waves
Short-Lived
Known
waveform
Long-Lived
Binary Inspirals
Continuous waves
(NS-NS, NS-BH, BH-BH)
Spinning black-hole /
high-mass inspirals
SGR ringdowns
Bursts
Unknown
waveform
(Spinning NS)
(Supernovae, “mergers”)
Young pulsars
(glitchy)
Stochastic background
(Cosmological, astrophysical)
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Search for binary systems
John Rowe, CSIRO
Use calculated templates for inspiral phase (“chirp”) with optimal filtering.
Search for systems with different masses:
– Binary neutron stars (~1-3 solar masses):
~15 sec templates, 1400 Hz end freq
– Binary black holes (< ~30 solar masses):
shorter templates, lower end freq
– Primordial black holes (<1 solar mass):
longer templates, higher end freq
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Searching for binaries
John Rowe, CSIRO
• Use two or more detectors: search for double or triple coincident “triggers”
• Can infer masses and “effective” distance.
• Estimate inverse false alarm probability of resulting candidates: detection?
Triple
Double
Double
Blue – Coincident
Gray – Time lag
S5 Year 1 Search for “Low-Mass” Inspirals
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Searching for binaries
• No evidence of excess
• Use detection efficiency and surveyed galaxies
 Set upper limit vs stellar mass
Phys. Rev. D 79 (2009) 122001
BH-BH
John Rowe, CSIRO
L10 = 1010 × blue solar luminosity
Milky Way = 1.7 L10
NS-BH
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Searching for bursts GRB 070201
• Short, hard gamma-ray burst
– A leading model for short GRBs:
binary merger involving a
neutron star
• Position (from IPN) consistent with
being in M31 (Andromeda)
• LIGO H1 and H2 were operating
• Result from (several) LIGO searches:
No plausible GW signal found;
therefore very unlikely to be
from a binary merger in M31
Ap. J. 681 (2008) 1419
IPN 3-sigma error region from Mazets
et al., ApJ 680, 545
 Likely was SGR giant flare in M31
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Searching for bursts (untriggered)
Search for double or triple coincident triggers (three algorithms)
 Check waveform consistency among interferometers – apply vetoes
 Set a threshold for detection for low false alarm probability
 Evaluate efficiency for variety of simple waveforms

Parameterize strength in terms of “root sum square of h” : hRSS
Sampling of efficiency curves:
 hRSS 
2

  (| h (t ) |2  | h (t ) |2 )dt

hRSS
S5 Year 1 Search for Untriggered Bursts
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Searching for bursts (untriggered)
Detected triggers and
expected background for
one algorithm (Coherent
WaveBurst – wavelet-based)
for triple-coincident triggers
with fcentral > 200 Hz
No candidates found above threshold
in any of the searches
 Set upper limits on rate vs hRSS
Threshold
Coherent network amplitude
Phys Rev D 80 (2009) 102001
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Searching for a
stochastic background
NASA, WMAP
• A primordial isotropic GW stochastic background is predicted by most
cosmological theories.
• Given an energy density spectrum Wgw(f), there is a strain power spectrum:
• The signal can be searched from cross-correlations in different pairs of
detectors: L1-H1 and H1-H2.
• The farther the detectors, the lower the frequencies that can be searched.
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Searching for a
stochastic background
NASA, WMAP
S5 H1-L1 Bayesian 90% UL:
Ω90% = 6.9 × 10-6 (41-170 Hz)
Nature 460
(2009) 990
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Bayesian PDF
Model
Chandra image
Searching for continuous waves
Crab Pulsar
Use coherent, 9-month, time-domain matched filter
Strain amplitude h0
Upper limits on GW strain amplitude h0
Single-template, uniform prior: 3.4 × 10–25
Single-template, restricted prior: 2.7 × 10–25
Multi-template, uniform prior: 1.7 × 10–24
Multi-template, restricted prior: 1.3 × 10–24
Implies that GW
emission accounts
for ≤ 4% of total
spin-down power
Ap. J. Lett 683 (2008) 24
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Searching for continuous waves
Same matched-filter algorithm applied to 116
known pulsars over 23 months of S5
Lowest upper limit on
strain:
h0 < 2.3 × 10-26
Lowest upper limit on
ellipticity:
ε < 7 × 10-8
Updated Crab limit at 2%
of total energy loss
Ap. J. 713 (2010) 671
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Searching for continuous waves
Not all known sources have measured timing
Compact central object in
the Cassiopeia A supernova
remnant
Birth observed in 1681 –
One of the youngest
neutron stars known
Star is observed in X-rays,
but no pulsations observed
Requires a broad band
search over accessible
band
Cassiopeia A
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Searching for continuous waves
Because of the young age,
search must allow for 2nd
derivative in spin in search
Indirect limits on GW
strain can be set, based on
known age and distance,
assuming high initial spin
and GW-driven spindown
Previous indirect upper limit
Preliminary upper
limits from
coherent search
over 12 days of
LIGO S5 data
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Searching for continuous waves
What about neutron stars we don’t already know about?
Radio / X-ray astronomers have found ~2000 pulsars /
neutron stars in the galaxy
Expect ~109 neutron stars produced during age of the
galaxy
Nearly all invisible
(B field too low, rotation speed too low, not beaming
toward Earth)
How many might be visible to LIGO?
Hard to estimate accurately, given severe selection effects
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Searching for continuous waves
Our local neighborhood (within ~500 pc) should contain
104-105 neutron stars
Need only one for discovery
(high spin, not quite axisymmeric, low B)
Should look in all directions over broad band and over
spindown range consistent with distance
 All-sky broadband search
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Searching for continuous waves
Serious technical difficulty: Doppler frequency shifts
– Frequency modulation from earth’s rotation (v/c ~ 10-6)
– Frequency modulation from earth’s orbital motion (v/c ~ 10-4)
Related complication:
– Spin-down of source
How hard is it to do a brute-force coherent search?
Pretty hard…
Sources are weak – coherent search needs O(1 year) integration
 Intrinsic frequency resolution ~ 0.03 µHz
 1 kHz source occupies ~2 × 10-4 × 1 kHz / 0.03 µHz ~ 7 × 106 bins
 Single FFT won’t do – Must demodulate Doppler effects
 Problem: Every point on the sky requires unique set of demodulations
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Searching for continuous waves
What defines separation between two “points” in the sky?
Distinct frequency bins
 Need Δθ × vorb/c × 1 kHz < 0.03 µHz
 Δθ ~ 0.3 µrad
 Need to search ~ 1014 points on the sky
Also need to search over at least one spindown derivative
 Need to keep cumulative phase error over 1 year < 0.5 radian
 For maximum spindown of 10-9 Hz/s, need ~106 spindown steps
Searching a 1-Hz band at 1 kHz requires ~1014 × 107 × 106 ~ 1027 templates,
 Not enough computers in our part of the string landscape to do this
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Searching for continuous waves
Additional, related complications:
– Daily amplitude modulation of antenna pattern
 Need to sample O(5-10) possible polarizations
– Orbital motion of sources in binary systems
 Need to search orbital period, modulation depth for circular orbit
 Additional parameters for elliptical orbits
Bottom line:
Must trade off intrinsic sensitivity for computability
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Searching for continuous waves
Frequency bin
Frequency
Several approaches tried or in development:
• Summed powers from many short (30-minute) FFTs with sky-dependent
corrections for Doppler frequency shifts  “Semi-coherent “
(StackSlide, Hough transform, PowerFlux)
Time
Time
• Push up close to longest coherence time allowed by computing resources
(~1 day) and look for coincidences among outliers in different data
stretches (Einstein@Home)
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Searching for continuous waves
Linearly polarized
Circularly polarized
All-sky search
for unknown
isolated neutron
stars
Semi-coherent,
stacks of 30-minute,
demodulated power
spectra
(“PowerFlux”)
Phys. Rev. Lett. 102 (2009) 111102
Developed at Michigan
(V. Dergachev thesis)
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Searching for continuous waves
All-sky search
for unknown
isolated neutron
stars
Coincidence
among multiple
30-hour coherent
searches
(Einstein@Home)
Phys Rev D 80 (2009) 042003
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http://www.einsteinathome.org/
•
•
•
•
•
•
•
GEO-600 Hannover
LIGO Hanford
LIGO Livingston
Current search point
Current search
coordinates
Known pulsars
Known supernovae
remnants
Improved
(hierarchical)
algorithm
now running
Your
computer
can help
too!
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Searching for continuous waves
Under development or testing:
• Cross correlation among interferometer pairs (robust against model
dependence) – under development
• Power summing in Einstein@Home (in pilot run)
• “Loose coherence” – allowing for smooth phase drift across FFTs
Semi-coherent
Coherent
Loosely coherent
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Searching for continuous waves
Going after pulsars in binaries is even harder
Increases parameter space even more
Necessary to make additional sensitivity tradeoffs
But search is motivated by relatively large fraction of
millisecond pulsars in binaries (~half) and increased
chance of non-axisymmetry driven by accretion
Michigan graduate student Evan Goetz has developed
a new algorithm called TwoSpect based on Fourier
spectra of time series of Fourier spectra
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Searching for continuous waves
Simulation of an absurdly strong signal
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Searching for continuous waves
Simulation of a signal detectable with
95% confidence
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Searching for continuous waves
Noise level
Corresponding detection statistic
Work in progress – Stay tuned…
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Other S5/VSR1 Searches (released)
Search for Gravitational Wave Bursts from Soft Gamma Repeaters
Phys Rev Lett 101 (2008) 211102
Search for High Frequency Gravitational Wave Bursts in the First Calendar Year of LIGO's
Fifth Science Run
Phys Rev D 80 (2009) 102001
Stacked Search for Gravitational Waves from the 2006 SGR 1900+14 Storm
Astroph J 701 (2009) L68
Search for Gravitational Waves from Low Mass Compact Binary Coalescence in 186 Days of
LIGO's fifth Science Run
Phys Rev D 80 (2009) 047101
Search for gravitational-wave bursts associated with gamma-ray bursts using data from LIGO
Science Run 5 and Virgo Science Run
To appear in Astroph J (arXiv:0908:3824)
Search for gravitational-wave inspiral signals associated with short Gamma-Ray Bursts during
LIGO's fifth and Virgo's first science run
To appear in Astroph J (arXiv:1001:0165)
All-sky search for gravitational-wave bursts in the first joint LIGO-GEO-Virgo
To appear in Phys Rev D (arXiv:1002:1036)
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Other S5 (S6) Searches Underway (planned)
Inspirals:
High-mass, spinning black holes
Black hole ringdowns
Bursts:
Electromagnetic followups of GW triggers
Continuous wave:
Full-S5 all-sky searches (semi-coherent, Einstein@Home)
Directed searches (Calvera, globular clusters, galactic center, SN1987A)
“Transient CW” sources
Stochastic:
Directed (anisotropic)
H1-H2
High-frequency (37 kHz – LIGO arm free spectral range)
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Looking Ahead
Both LIGO and Virgo underwent significant upgrades since first joint
science run (S5/VSR1):
Initial LIGO  “Enhanced LIGO”
Initial Virgo  “Virgo +” (2nd stage underway now)
LIGO schedule: S6 data run July 2009 – September 2010
Begin Advanced LIGO installation October 2010
Virgo schedule: VSR2 data run July 2009 – December 2009
Virgo+ install/commission January-July 2010
VSR3 data run August 2010 – Summer 2011
Begin Advanced Virgo installation Summer 2011
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Looking Ahead
Comparing present S6
sensitivity to S5 sensitivity
Factor of 2 improvement above 300 Hz
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Looking Ahead
Where does Virgo sensitivity stand?
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Advanced LIGO
Sampling of source
strengths vis a vis Initial
LIGO and Advanced LIGO
Lower hrms and wider
bandwidth both important
“Signal recycling” offers
potential for tuning shape
of noise curve to improve
sensitivity in target band
(e.g., known pulsar cluster)
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Advanced LIGO
Increased laser power:
10 W  180 W
Improved shot noise (high freq)
Higher-Q test mass:
Fused silica with better optical coatings
Lower internal thermal noise in bandwidth
Increased test mass:
10 kg  40 kg
Compensates increased radiation pressure noise
48
Advanced LIGO
Detector Improvements:
New suspensions:
Single  Quadruple pendulum
Lower suspensions thermal noise
in bandwidth
Improved seismic isolation:
Passive  Active
Lowers seismic “wall” to ~10 Hz
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Advanced LIGO
Neutron Star Binaries:
Horizon > 300 Mpc
Most likely rate ~ 40/year !
The science from the first 3 hours of Advanced LIGO should be
comparable to 1 year of initial LIGO
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Summary
Bottom line:
No GW signal detected yet 
But
• Not all S5 / VSR1 searches completed
• Ongoing S6 / VSR2 searches should be more sensitive
• VSR3 searches may be much more sensitive (or not)
• Advanced LIGO / Virgo will bring major sensitivity improvements
with orders of magnitude increase in expected event rates
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Extra
Slides
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LIGO Observatories
Hanford
Observation of nearly simultaneous signals
3000 km apart rules out terrestrial artifacts
Livingston
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Virgo
Have begun collaborating with Virgo colleagues (Italy/France)
Took data in coincidence for last ~4 months of latest science run
Data exchange and joint analysis underway
Will coordinate closely on detector upgrades and future data taking
3-km Michelson
Interferometer just
outside Pisa, Italy
54
GEO600
Work closely with the GEO600 Experiment (Germany / UK / Spain)
• Arrange coincidence data runs when commissioning schedules permit
• GEO members are full members of the LIGO Scientific Collaboration
• Data exchange and strong collaboration in analysis now routine
• Major partners in proposed Advanced LIGO upgrade
600-meter Michelson Interferometer
just outside Hannover, Germany
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LIGO Detector Facilities
•Stainless-steel tubes
(1.24 m diameter, ~10-8 torr)
•Gate valves for optics isolation
•Protected by concrete enclosure
Vacuum System
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LASER
•
•
LIGO Detector Facilities
Infrared (1064 nm, 10-W) Nd-YAG laser from Lightwave (now commercial product!)
Elaborate intensity & frequency stabilization system, including feedback from main
interferometer
Optics
•
•
•
Fused silica (high-Q, low-absorption, 1 nm surface rms, 25-cm diameter)
Suspended by single steel wire
Actuation of alignment / position via magnets & coils
57
LIGO Detector Facilities
Seismic Isolation
•
•
Multi-stage (mass & springs) optical table support gives 106 suppression
Pendulum suspension gives additional 1 / f 2 suppression above ~1 Hz
102
100
10-2
10-6
10-4
Horizontal
10-6
10-8
Vertical
10-10
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LIGO Interferometer Optical
Scheme
Michelson interferometer
With Fabry-Perot arm cavities
end test mass
•Recycling mirror matches losses,
enhances effective power by ~ 50x
4 km Fabry-Perot cavity
recycling
mirror
150 W
LASER/MC
20000 W
6W
(~0.5W)
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What Limits the Sensitivity
of the Interferometers?
•
Seismic noise & vibration limit at
low frequencies
•
Atomic vibrations (Thermal Noise)
inside components limit at mid
frequencies
•
Quantum nature of light (Shot
Noise) limits at high frequencies
•
Myriad details of the lasers,
electronics, etc., can make
problems above these levels
Best design sensitivity:
~ 3 x 10-23 Hz-1/2 @ 150 Hz
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“Locking” the Interferometer
Sensing gravitational waves requires sustained resonance in the Fabry-Perot arms and in the
recycling cavity
 Need to maintain half-integer # of laser wavelengths between mirrors
 Feedback control servo uses error signals from imposed RF sidebands
 Four primary coupled degrees of freedom to control
 Highly non-linear system with 5-6 orders of magnitude in light intensity
Also need to control mirror rotation (“pitch” & “yaw”)
 Ten more DOF’s (but less coupled)
And need to stabilize laser (intensity & frequency), keep the beam pointed, damp out
seismic noise, correct for tides, etc.,…
61