Photo credit: NASA/CXC/SAO

LIGO-G040276-00-Z

Results from LIGO’s second science run: a search for continuous gravitational waves Michael LandryLIGO Hanford ObservatoryCalifornia Institute of Technology

on behalf of the LIGO Scientific Collaborationhttp://www.ligo.org

CAP CongressJune 16, 2004Winnipeg, Canada

Photo credit: NASA/CXC/SAO

Landry - CAP Congress, 16 June 2004 2LIGO-G040276-00-Z

Talk overview

• Laser Interferometer Gravitational Wave Observatory (LIGO) overview» The what and how of gravitational radiation

• Search for continuous waves (CW)» Source model

» Time-domain Analysis method– Limit our search (for the analysis presented here, only)to gravitational

waves from a triaxial neutron star emitted at twice its rotational frequency, 2*frot

– Signal would be frequency modulated by relative motion of detector and source, plus amplitude modulated by the motion of the antenna pattern of the detector

» Validation by hardware injection of fake pulsars

» Results


• Gravitational Waves = “Ripples in space-time”

• Perturbation propagation similar to light (obeys same wave equation!)» Propagation speed = c

» Two transverse polarizations - quadrupolar: + and x

What are Gravitational Waves?

Example:

Ring of test masses

responding to wave

propagating along z

Amplitude parameterized by (tiny) dimensionless strain h: L ~ h(t) x L


• Compact binary inspiral: “chirps”» NS-NS waveforms are well described» BH-BH need better waveforms

• Supernovae / GRBs: “bursts” » burst signals in coincidence with signals in

electromagnetic radiation / neutrinos» all-sky untriggered searches too

• Cosmological Signal: “stochastic background”

• Pulsars in our galaxy: “periodic”» search for observed neutron stars (this talk)

» all-sky search (computing challenge)

What makes Gravitational Waves?


Gravitational Wave Detection

• Suspended Interferometers

» Suspended mirrors in “free-fall”

» Michelson IFO is

“natural” GW detector

» Broad-band response

(~50 Hz to few kHz)

» Waveform information

(e.g., chirp reconstruction)


LIGO Observatories

Livingston (L1=4km)

Hanford (H1=4km, H2=2km)Observation of nearly simultaneous signals 3000 km apart rules out terrestrial artifacts


Strain noise comparison: science runs

Initial LIGO Design

S1 (L1)1st Science Runend Sept. 2002

17 daysS2 (L1)2nd Science Runend Apr. 2003

59 days

S3 (H1)3rd Science Runend Jan. 2004

70 days

With GEO:Phys Rev D 69, 082004 (2004)


S2 expectations

• Coloured spectra: average amplitude detectable in time T (1% false alarm, 10% false dismissal rates):

0 11.4 ( ) /hh S f T• Solid black lines: LIGO and

GEO science requirement, for T=1 year

• Circles: upper limits on gravitational waves from known EM pulsars, obtained from measured spindown (if spindown is entirely attributable to GW emission)

• Only known, isolated targets shown here

LIGO

GEO


CW source model

• F+ and Fx : strain antenna patterns of the detector to plus and cross polarization, bounded between -1 and 1

• Here, signal parameters are:» h0 – amplitude of the gravitational wave signal

» – polarization angle of signal» – inclination angle of source with respect to line of sight

» 0 – initial phase of pulsar; (t=0), and (t)= t0

2

0 0

1 cost F t; h cos ( ) F t; h cos sin ( )

2h t t

so that the expected demodulated signal is then:

00 cosh;tF2

cos1h;tF4

1;ty 0k

20kk

ii eie a

The expected signal has the form:

Heterodyne, i.e. multiply by: ( )i te

Here, a = a(h0, , , 0), a vector of the signal parameters.

PRD 58 063001 (1998)


Compute likelihoods

Analysis summary

k2

k k

1p B a

B ynn

k

Heterodyne, lowpass,

average, calibrate: Bk

Model: yk

Compute pdf for h0

Compute upper limit “h95”

aBpap B|ap kk

Raw Data

uniform priorson h0(>0), cos

h95

1

PDF

0strain


Injection of fake pulsars during S2

Parameters of P1:P1: Constant Intrinsic FrequencySky position: 0.3766960246 latitude (radians)

5.1471621319 longitude (radians)Signal parameters are defined at SSB GPS time733967667.026112310 which corresponds to a wavefront passing:LHO at GPS time 733967713.000000000LLO at GPS time 733967713.007730720In the SSB the signal is defined byf = 1279.123456789012 Hzfdot = 0phi = 0psi = 0iota = /2h0 = 2.0 x 10-21

Two simulated pulsars, P1 and P2, were injected in the LIGO

interferometers for a period of ~ 12 hours during S2


Preliminary

upper limits for 28 known pulsars

h0 UL range Pulsar

10-23-10-22 J1939+2134, B1951+32, J1913+1011, B0531+21

10-24-10-23

B0021-72C, B0021-72D, B0021-72F, B0021-72G, B0021-72L, B0021-72M, B0021-72N, J0711-6830, B1820-30A, J1730-2304, J1721-2457, J1629-6902, J1910-5959E, J2124-3358, J1910-5959C, J0030+0451, J1024-0719,

J1910-5959D, J2322+2057, B1516+02A, J1748-2446C, J1910-5959B, J1744-1134, B1821-24

Blue: pulsar timing checked by Michael Kramer, Jodrell Bank

Purple: pulsar timing from ATNF catalogue


Equatorial Ellipticity

• Results on h0 can be interpreted as upper limit on equatorial ellipticity

• Ellipticity scales with the difference in radii along x and y axes

xx yy

zz

I I

I

40

2 24 gw zz

c r h

G f I

• Distance r to pulsar is known, Izz is assumed to be typical, 1045 g cm2


Preliminary ellipticitylimits for 28 known pulsars

UL range Pulsar

10-2-10-1 B1951+32, J1913+1011, B0531+21

10-3-10-2 -

10-4-10-3 B1821-24, B0021-72D, J1910-5959D, B1516+02A, J1748-2446C, J1910-5959B

10-5-10-4

J1939+2134, B0021-72C, B0021-72F, B0021-72L, B0021-72G, B0021-72M, B0021-72N, B1820-30A, J0711-6830, J1730-2304,

J1721-2457, J1629-6902, J1910-5959E, J1910-5959C, J2322+2057

10-6-10-5 J1024-0719, J2124-3358, J0030+0451, J1744-1134

Blue: timing checked by Jodrell Bank

Purple: ATNF catalogue


Summary and future outlook

• LIGO» Good progress towards design sensitivity

» Initial results from first two data runs

• S2 analyses» Time-domain analysis of 28 known pulsars complete

» Broadband frequency-domain all-sky search underway

» ScoX-1 LMXB frequency-domain search near completion

» Incoherent searches reaching maturity, preliminary S2 results produced

• S3 run» Time-domain analysis on more pulsars, including binaries

» Improved sensitivity LIGO/GEO run

» Oct 31 03 – Jan 9 04

» Approaching spindown limit for Crab pulsar


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


Strong Indirect Evidence: Orbital Decay

Neutron Binary System – Hulse & Taylor

PSR 1913 + 16 -- Timing of pulsars

17 / sec

Neutron Binary System• separated by 106 miles• m1 = 1.4m; m2 = 1.36m; = 0.617

Prediction from general relativity• spiral in by 3 mm/orbit• rate of change orbital period

~ 8 hr

Emission of gravitational waves


What Limits the Sensitivityof 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


CW sources

• Nearly-monochromatic continuous sources of gravitational waves include neutron stars with:

» spin precession at ~frot

» excited oscillatory modes such as the r-mode at 4/3 * frot

» non-axisymmetric distortion of crystalline structure, at 2frot

• Limit our search to gravitational waves from a triaxial neutron star emitted at twice its rotational frequency (for the analysis presented here, only)

• Signal would be frequency modulated by relative motion of detector and source, plus amplitude modulated by the motion of the antenna pattern of the detector


Source model

• F+ and Fx : strain antenna patterns of the detector to plus and cross polarization, bounded between -1 and 1

• Here, signal parameters are:» h0 – amplitude of the gravitational wave signal

» – polarization angle of signal» – inclination angle of source with respect to line of sight

» 0 – initial phase of pulsar; (t=0), and (t)= t0

2

0 0

1 cost F t; h cos ( ) F t; h cos sin ( )

2h t t

so that the expected demodulated signal is then:

00 cosh;tF2

cos1h;tF4

1;ty 0k

20kk

ii eie a

The expected signal has the form:

Heterodyne, i.e. multiply by: ( )i te

Here, a = a(h0, , , 0), a vector of the signal parameters.

PRD 58 063001 (1998)


Compute likelihoods

Analysis summary

k2

k k

1p B a

B ynn

k

Heterodyne, lowpass,

average, calibrate: Bk

Model: yk

Compute pdf for h0

Compute upper limit “h95”

aBpap B|ap kk

Raw Data

uniform priorson h0(>0), cos

h95

1

PDF

0strain

Photo credit: NASA/CXC/SAO

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