W.-T. Ni

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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
• weitou_at_gmail.com

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Outline

• 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

• 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 observationsBernard F.
SchutzNature 323, 310-311 (25 September 1986)

• 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
  ultracompact, twoneutronstar binary system
  just before the stars coalesce are very likely to
  be detected by the kilometresized
  interferometric gravitational wave antennas now
  being designed14.
• 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
gravitational-wave 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 Classificationhttp//astrod.wikispace
s.com/file/view/GW-classification.pdf (Modern
Physics Letters A 25 2010 pp. 922-935
arXiv1003.3899v1 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.

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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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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 10-2-10-3 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

• 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.

Earth
Sun
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Weak-Light Phase Locking

• 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

• 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) n1, ab, ba abba baab
• (ii) n2, a2b2, b2a2 abab, baba
  ab2a, ba2b
• (iii) n3, 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

• quasar SDSS J153636.221 044127.0 separated in
  velocity by 3,500 km/s.
• A binary system of two black holes, having masses
  of 107.3 and 108.9 solar masses
• Separated by 0.1 parsec with an orbital period of
  100 years.

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NANOGrav Science OpportunityExploring 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 ?-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

• 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

• 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

• Space interferometers (LISA,28 ASTROD,29,30
  ASTROD-GW,12,14 Super-ASTROD,31 DECIGO,32 and Big
  Bang Observer33,34) for gravitational-wave
  detection hold the most promise with
  signal-to-noise ratio.
• LISA28 (Laser Interferometer Space Antenna) is
  aimed at detection of low-frequency (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 10-2-10-3 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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Space GW detectors as dark energy probes

• 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

• 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(?) / ?(?),
  
  
  
• where p is the pressure and ? 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) (1z) ?0?z (H0)-1 ?m(1z')3
  ?DE(1z')3(1w)-(1/2) dz',
• where w is assumed to be constant.

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Summary

• 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!