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LIGO-G040443-00-W
Gregory Mendell LIGO Hanford Observatory
Gravitational Waves From Neutron & Strange Quark Stars
http://www.ligo.caltech.eduSupported by the National Science Foundation
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The Neutron Star Idea•Chandrasekhar 1931: white dwarf stars will collapse if M > 1.4 solar masses. Then what?
•Chadwick 1932: discovers the neutron.
•Landau 1932: suggests stars have neutron cores.
•Oppenheimer & Volkoff 1939: work out NS models.
•Baade & Zwicky 1934: suggest SN form NS.
http://www.aao.gov.au/images/captions/aat050.html
Anglo-Australian Observatory, photograph by David Malin.
SN 1987A
(http://www.jb.man.ac.uk/
~pulsar/tutorial/tut/tut.html; Jodrell Bank
Tutorial)
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Discovery of Pulsars• Bell notes “scruff” on chart in 1967.
• Close up reveals the first pulsar (pulsating radio source) with P = 1.337 s.
• Rises & sets with the stars: source is extraterrestrial.
• LGM?
• More pulsars discovered indicating pulsars are natural phenomena.
• Hewish, wins 1974 Nobel Prize.
www.jb.man.ac.uk/~pulsar/tutorial/tut/node3.html#SECTION00012000000000000000 A. G. Lyne and F. G. Smith. Pulsar Astronomy. Cambridge University Press, 1990.
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Pulsars = Neutron Stars•From the Sung-shih (Chinese Astronomical Treatise): "On the 1st year of the Chi-ho reign period, 5th month, chi-chou (day) [1054 AD], a guest star appeared…south-east of Tian-kuan [Aldebaran].(http://super.colorado.edu/~astr1020/sung.html)
•Pacini 1967: neutron stars power the crab nebula
• Gold 1968: pulsars are rotating neutron stars.
•orbital motion
•oscillation
•rotation
http://antwrp.gsfc.nasa.gov/apod/ap991122.html
Crab Nebula: FORS Team, 8.2-meter VLT, ESO
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Pulsars Seen and Heard
Play Me
(Vela Pulsar)
(Crab Pulsar)
http://www.noao.edu/image_gallery/html/im0565.html
Crab Pulsar: N.A.Sharp/NOAO/AURA/NSF
http://www.jb.man.ac.u
k/~pulsar/Education/Sounds/
sounds.html
Jodrell Bank Observatory,
Dept. of Physics & Astronomy,
The University of Manchester
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Why Neutron Stars?
Masses ~ 1.4 Solar Masses
• Fastest pulsar spins 642 times per seconds; R < 74 km• Thermal observations and theory suggest R ~ 5-15 km
S. E. Thorsett and D. Chanrabarty, astro-ph/9803260
www.physik.uni-muenchen.de/sektion/suessmann/astro/cool/
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The back of the envelope please…
Mass neutron 1.67 × 10-24 g------------------------ = --------------------Volume neutron 4/3 (10-13 cm) 3
= 4.0 × 1014 g/cm 3 (billion tons/teaspoon)
1.4 Solar Masses 1.4(1.99 × 1033 g)------------------------ = --------------------10 km Sphere 4/3(106 cm) 3
Average density = 6.7 × 1014 g/cm 3
… but parts of you are as dense as a neutron star.
Don’t take this the wrong way…
p + e n +e (inverse beta and beta decay)p + e = n (beta equilibrium)np = ne (charge neutrality)
Seen: SN 1987A! Nuclear density: 95% n, 5% p & e
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Cosmic lighthouses with terra-gauss magnetic fields !
D. Page http://www.astroscu.unam.mx/neutrones/home.html
http://online.itp.ucsb.edu/online/neustars00rmode/kaspi/oh/05.html; Vicky Kaspi McGill University, Montreal Canada
More on PulsarsKnown: 1000+
Unknown: up to 100,000 in the
Milkyway.
Respun to 642 Hz!In theory up to 2 kHz. http://astrosun2.astro.cornell.edu/academics/courses/
astro201/pulsar_graph.htm
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What else is seen?
http://www.astroscu.unam.mx/neutrones/home.html
http://antwrp.gsfc.nasa.gov/apod/
ap980527.html
Robert Mallozzi (UAH, MSFC)
http://www.jb.man.ac.uk/~pulsar/tutorial/tut/tut.html
HMXBs
LMXBs
Magnetars
Pulsar Glitches
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Now it gets interesting…
D. Page http://www.astroscu.unam.mx/n
eutrones/home.html
•Fermi Temp = 1012 K
•NS born at 1011 K, cools below 109 K within a year; BCS superfluids form.
•Cools to 106 K over 107 K yrs.
•NS are compact “cold” degenerate objects; GR & QM required to understand.
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…and strange…
http://chandra.harvard.edu/resources/illustrations/neutronstars_4.html
NASA/CXC/SAO
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… and hyper-
stranger still!
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Strange Stars in the News
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Recent Papers
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Some Of The Big Questions?• What is the NS/SQS max. mass; min radius? (1.4-3.5 M? R = ?)
• How fast can NS/SQS spin (up to 2 kHz?) and what controls their spin cycles?
•What are the final states of matter before collapse to BH, i.e., what’s inside these stars, really?
• Are quark nuggets hitting the Earth? (Ice-9 Scenerios?)
J. M. Lattimer & M. Prakash, astro-ph/0405262
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Laser Interferometer Gravitational-wave Observatories
Figures: K. S. Thorne gr-qc/9704042; D. Sigg LIGO-P980007-00-D
LIGO is a lab looking for direct detection of GW’s.
LIGO is an observatory, “listening” for GW’s cosmic spacetime vibrations.
Gravitational-wave Strain: LLh /
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Continuous Periodic Gravitational-Wave Sources
Wobbling star
“Mountain” on star
Accreting star
Oscillating star
A. Vecchio on behalf of the LIGO Scientific Collaboration : GR17 – 22nd July, 2004
I
II 21
Triaxial Ellipsoid:Ellipticity
LMXB:e.g., Sco X-1:balance GW torque with accretion torque.
Free PrecessionWobble Angle
Mode with Saturation Amplitude A
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• Triaxial ellipsoid: h ~ (G/c4) MR24frot 2/r ~ 10–26 (for ellipticity ~
10–6, frot = 200 Hz, M = 1.4 M, R = 106 cm, r = 1 kpc = 3 1021 cm)
• Precession: h ~ (G/c4) sin (2) MR2frot2/r ~ 10-27 (for ellipticity ~
10-6 ; wobble angle = /4, etc…)
• LMXB Sco-X1: h ~ 10-26 (balance GW torque with accretion torque)
• R-modes: h ~ (G/c4) MA2R2 (16/9) frot
2/r ~ 10–26 ( for saturation amplitude A ~ 10–3, etc…)
• Pulsar Glitch h ~ (G/c4) MA2R2frot
2/r ~ 10 –32 ( for glitch amplitude A ~ 10–6, etc…)
.22149
.2
24
)(10~;)(~
~;)/)(/(/
asymGWasym fMRerghMVQ
MRQrQcGLLh
Approximate forms of the Quadrupole Formula
The back of the envelope please…
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LSC Period/CW Search GroupSearch Techniques
• ~ 30+ members of the LIGO Science Collaboration.
• Has developed Coherent & Incoherent Search Methods
• Known, Targeted,and All Sky Searches are underway.
4/17
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7
2/12326
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Hz
Sh
T
s
Hz
Sh
TShSNR
dtthhcoh
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Figure: P. Brady ITP seminar summer 2000
Sensitivity Curves
The r-mode saturation amplitude was thought to be much larger in 2000
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Coherent Power vs. Tobs
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Incoherent Power vs. Tobs
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Phase Modulation
0
10 )ˆ
)((
)!1(s
ss
nc
trt
s
f
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Frequency Modulation
• The frequency is modulated by the intrinsic frequency evolution of the source and by the doppler shifts due to the Earth’s motion
• The Doppler shifts are important for observation times
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ss
nc
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105.50
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HzT
Schutz & Papa gr-qc/9905018; Williams and Schutz gr-qc/9912029; Berukoff and Papa LAL Documentation
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Figure: D. Sigg LIGO-P980007-00-D
]2cos2sincos2sin2cos)cos1(5.0[
]2sin2sincos2cos2cos)cos1(5.0[)(
);()();()(ˆ)(ˆˆ)(ˆ)(
2
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h
hth
tFthtFthyMMhyxMMhxth tTTtTT
Amplitude Modulation
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Maximum Likelihood
0,0,0cos
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Likelihood of getting data x for model h for Gaussian Noise:
Chi-squared
Minimize Chi-squared = Maximize the Likelihood
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Coherent Match Filtering
1
0
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Jaranowski, Krolak, & Schutz gr-qc/9804014; Schutz & Papa gr-qc/9905018; Williams and Schutz gr-qc/9912029; Berukoff and Papa
LAL Documentation
222
*2222 24
FFFF
XXeFFXFXF
MF
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The StackSlide Search• An incoherent search method that stacks
and slides power to search for periodic sources. (P. Brady & T. Creighton Phys. Rev. D61 (2000) 082001; gr-qc/9812014.)
• The periodic search is computationally bound. A hierarchical approach that combines coherent & incoherent methods is needed to optimize sensitivity.
• Sources like LXMBs with short coherence times (~ 2 weeks) require incoherent methods.
• Mendell and Landry are developing the StackSlide Search for the CW group. (The group also uses Hough Transforms and Power Flux, for incoherent searches.)
Bins with frequency domain data, e.g., from SFTs or F-statistic.
A. Stack the power.
B. Slide to correct for spindown/doppler shifts.
C. Sum and search for significant peaks.
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Validation: Fake Pulsar vs Fake Instrument Line
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Sky Distribution of PowerFake Pulsar and Fake Noise:
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Sky Distribution of PowerFake Instrument Line and Noise
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Sky Distribution of PowerFake Noise Only:
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Find peaks above threshold
Slide Stacks and SUM
Veto peak based on width
Select template
Veto on Coincidence
Veto Instrument Lines
Veto SNR does not grow as T
Yes
SFTs are generated only once
Input a band from SFTs
Raw Data
Compute PSDs from SFTs
Normalize PSDs
Template placement
Output event
StackSlide Pipeline
Normalize SFTs
Compute F-statistic for each point in the course grid
Template placement
Parameter space metric placement
Uniform placement
No
Set UL from LE
Detection candidate
MonteCarlo
LineRemoval
VetoSFTs
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Statistics
dzedzzP
rdrdzyxrz
rdredrrP
ryrx
dxdyeedxdyyxP
yxniyxn
nFFTNormalizedn
z
r
yx
2/
222
2/
2/2/
222
2
1)(
2
1
)(
sincos2
1
2
1),(
~
)(~
2
22
Gaussian Noise
Rayleigh Dist.
2 variable, with 2 degrees freedom
2 Distribution
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Statistics: False Alarm Rate; False Dismissal Rate and UL from LE
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-- GEO-- L 2km-- H 4km-- L 4km
<h 0
>
S1 sensitivities
PSR J1939+2134P = 0.00155781 sfGW = 1283.86 Hz
dP/dt = -1.0511 10-19 s/sD = 3.6 kpc
obs
h0 T
)f(S4.11h
Result: S1 Coherent Search
• ho<1.4x10-22 constrains ellipticity < 2.7 x 10-4 (M=1.4 Msun, r=10 km, R=3.6 kpc)
B Allen and G Woan on behalf of the LIGO Scientific Collaboration : Amaldi 9 July, 2003.