Transcript Document

Determining the dark energy equation of
state from gravitational-wave (GW)
observations of binary inspirals
W.-T. Ni
Department of Physics
National Tsing Hua University, and
Shanghai United Center for Astrophysics
Shanghai Normal University
[email protected]
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Outline
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Introduction
Binaries
Classification of GWs and methods of detection
(Modern Physics Letters A25, 922, 2010;
ArXiv 1003.3899)
Ground and Space GW detectors
Dark energy equation of state
Outlook
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Introduction
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No confirmed experimental evidence for dark matter except
gravity deficiency (no confirmed positive results for ground
and space experiments)
No confirmed evidence for deviation from general relativity
with cosmological constants
Supernovae as distance standards has problems
No direct detection of GW (Only inspirals from GW radiation
for binary pulsars [Hulse-Taylor Nobel prize 1992])
However, we do expect to detect GW on earth in 2015-2020
And GW from supermassive binaries in space after 2020 and
experimental determining the dark energy equation
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Determining the Hubble constant from
gravitational wave observations
Bernard F. Schutz
Nature 323, 310-311 (25 September 1986)
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Rort here how gravitational wave observations can be used to
determine the Hubble constant, H0.
The nearly monochromatic gravitational waves emitted by the
decaying orbit of an ultra–compact, two–neutron–star binary
system just before the stars coalesce are very likely to be
detected by the kilometre–sized interferometric gravitational
wave antennas now being designed1–4.
The signal is easily identified and contains enough information
to determine the absolute distance to the binary, independently
of any assumptions about the masses of the stars.
Ten events out to 100 Mpc may suffice to measure the Hubble
constant to 3% accuracy.
Now SPACE interferometers for Dark Energy
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Nearby sources and
Cosmological sources
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LIGO instrumental sensitivity for science runs S1
(2002) to S5 (present) in units of gravitationalwave strain per Hz1/2 as a function of frequency
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In addition to adLIGO and adVirgo,
LCGT construction started this year
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Complete GW Classification
http://astrod.wikispaces.com/file/view/GW-classification.pdf
(Modern Physics Letters A 25 [2010] pp. 922-935;
arXiv:1003.3899v1 [astro-ph.CO])
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Here performed a more careful analysis
by explicitly using the potential Planck CMB data as
prior information for these other parameters.
Find that ET will be able to constrain w0 and wa with
accuracies w0 = 0.096 and wa = 0.296, respectively.
These results are compared with projected accuracies
for the JDEM Baryon Acoustic Oscillations (BAO)
project and the SNAP Type Ia supernovae (SNIa)
observations.
Tsing
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More massive binaries, lower frequency
detectors: Sensitivities of Ground and
Space Interferometers in one diagram
AI
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Massive Black Hole Systems:
Massive BH Mergers &
Extreme Mass Ratio Mergers (EMRIs)
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0.1mHz-1 Hz
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~10Hz-kHz
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LISA
LISA consists of a fleet of 3 spacecraft 20º behind earth in solar
orbit keeping a triangular configuration of nearly equal sides (5 × 106 km).
Mapping the space-time outside super-massive black holes by measuring the
capture of compact objects set the LISA requirement sensitivity between 102-10-3 Hz. To measure the properties of massive black hole binaries also
requires good sensitivity down at least to 10-4 Hz. (2020)
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ASTROD-GW Mission Orbit
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Considering the requirement for
optimizing GW detection while
keeping the armlength, mission
orbit design uses nearly equal
arms.
3 S/C are near Sun-Earth
Lagrange points L3、L4、L5，
forming a nearly equilateral
triangle with armlength 260
million km（1.732 AU）.
3 S/C ranging interferometrically
to each other.
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S/C 1 (L4)
(L3)
S/C 2
Sun
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Earth
60
球地
L1 L2
60
S/C 3 (L5)
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Weak-Light Phase Locking
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To 2pW A.-C. Liao, W.-T. Ni and J.-T. Shy, On
the study of weak-light phase-locking for
laser astrodynamical missions, Publications of
the Yunnan Observatory 2002, 88-100
(2002); IJMPD 2002.
To 40 fW G. J. Dick, M., D. Strekalov, K.
Birnbaum, and N. Yu, IPN Progress Report
42-175 (2008).
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Time-delay interferometry for
ASTROD-GW
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Using Planetary Ephemeris to numerically calculate the various
solutions of Dhurandhar, Vinet and Rajesh Nayak for time-delay
interferometry of ASTROD-GW to estimate the residual laser
noise and compare. (G. Wang and W.-T. Ni)
Second generation solution (Dhrandhar, Vinet and Nayak):
(i) n=1, [ab, ba] = abba – baab
(ii) n=2, [a2b2, b2a2]; [abab, baba]; [ab2a, ba2b]
(iii) n=3, [a3b3, b3a3], [a2bab2, b2aba2], [a2b2ab, b2a2ba],
[a2b3a, b2a3b], [aba2b2, bab2a2], [ababab, bababa],
[abab2a, baba2b], [ab2a2b, ba2b2a], [ab2aba, ba2bab],
[ab3a2, ba3b2], lexicographic (binary) order
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Numerical Results
(Wang & Ni)
a-b
[a, b]
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Numerical
Results
(Wang & Ni)
[ab, ba]
[abba, baab]
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Massive Black Hole Systems:
Massive BH Mergers &
Extreme Mass Ratio Mergers (EMRIs)
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A candidate sub-parsec supermassive
binary blackhole system (Nature 2009)
Todd A. Boroson & Tod R. Lauer
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quasar SDSS
J153636.221 044127.0
separated in velocity
by 3,500 km/s.
A binary system of two
black holes, having
masses of 10^7.3 and
10^8.9 solar masses
Separated by 0.1
parsec with an orbital
period of 100 years.
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NANOGrav: Science Opportunity
Exploring the Very-Low-Frequency GW Spectrum
(The North American Nanohertz Observatory for GWs)
What is the nature of space and time? local spacetime metric is
perturbed by the cumulative effect of gravitational waves (GWs)
emitted by numerous massive black hole (MBH) binaries. the
energy density of GWs?
 How did structure form in the Universe? whether MBHs formed
through accretion and/or merger events.
 What is the structure of individual MBH binary systems?
 What contribution do cosmic strings make to the GW background ?
 What currently unknown sources of GW exist in the Universe?
(Every time a new piece of the electromagnetic spectrum has been
opened up to observations (e.g. radio, X-rays, and γ-rays), new
and entirely unexpected classes of objects have been discovered.)
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NANOGrav and PTA expectations
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BH Coevolution with galaxies
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S. Sesana, A. Vecchio and C. N. Colacino, Mon.
Not. R. Astron. Soc. 390, 192-209 (2008).
S. Sesana, A. Vecchio and M. Volonteri, Mon.
Not. R. Astron. Soc. 394, 2255-2265 (2009).
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Demorest et al white paper
Summary
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Given sufficient resources, we expect to detect GWs
through the IPTA within the next five years.
We also expect to gain new astrophysical insight on
the detected sources and, for the first time,
characterize the universe in this completely new
regime.
The international effort is well on its way to
achieving its goals. With sustained effort, and
sufficient resources, this work is poised to offer a
new window into the Universe by 2020.
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probing the black hole co-evolution
with galaxies
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ASTROD-GW has the best sensitivity in the 100
nHz – 1 mHz band and fills the gap
ASTROD-GW
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Space GW Detectors
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Space interferometers (LISA,28 ASTROD,29,30 ASTROD-GW,12,14 SuperASTROD,31 DECIGO,32 and Big Bang Observer33,34) for gravitationalwave detection hold the most promise with signal-to-noise ratio.
LISA28 (Laser Interferometer Space Antenna) is aimed at detection of lowfrequency (10-4 to 1 Hz) gravitational waves with a strain sensitivity of 4 ×
10-21/(Hz) 1/2 at 1 mHz.
There are abundant sources for LISA, ASTROD and ASTROD-GW:
galactic binaries (neutron stars, white dwarfs, etc.). Extra-galactic targets
include supermassive black hole binaries, supermassive black hole
formation, and cosmic background gravitational waves.
A date of LISA launch is hoped for 2020. More discussions will be
presented in the next section.
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LISA
LISA consists of a fleet of 3 spacecraft 20º behind earth in solar
orbit keeping a triangular configuration of nearly equal sides (5 × 106 km).
Mapping the space-time outside super-massive black holes by measuring the
capture of compact objects set the LISA requirement sensitivity between 102-10-3 Hz. To measure the properties of massive black hole binaries also
requires good sensitivity down at least to 10-4 Hz. (2020)
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Dark Energy
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Space GW detectors as dark
energy probes
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Luminosity distance determination to 1
% or better
Measurement of redshift by association
From this, obtain luminosity distance vs
redshift relation, and therefore
equation of state of dark energy
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Space GW detectors and Dark energy
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In the solar system, the equation of motion of a celestial body or a
spacecraft is given by the astrodynamical equation
a = aN + a1PN + a2PN + aGal-Cosm + aGW + anon-grav
In the case of scalar field models, the issue becomes what is the value
of w() in the scalar field equation of state:
w() = p() / ρ(),
where p is the pressure and ρ the density.
For cosmological constant, w = -1.
From cosmological observations, our universe is close to being flat. In
a flat Friedman Lemaître-Robertson-Walker (FLRW) universe, the
luminosity distance is given by
dL(z) = (1+z) ∫0→z (H0)-1 [Ωm(1+z′)3 + ΩDE(1+z′)3(1+w)]-(1/2) dz′,
where w is assumed to be constant.
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Summary
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Binaries as distance indicators
Detection, LCGT, adLIGO, adVirgo: 2017 PTAs:
about 2020
ET sensitivities
Space detectors for Gravitational Waves
BHs coevolution with galaxies & PTAs
Dark energy equation via binary GW observations
Bright future with a lot of works
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Thank you!
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