Le Fond Gravitationnel Stochastique

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Le Fond Gravitationnel Stochastique

• Tania Regimbau
• ARTEMIS - OCA

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The GW Stochastic Background
10-43s gravitons decoupled (T 1019 GeV)

• Two contributions
• cosmological signature of the early Universe
• inflation, cosmic strings, phase transitions
• astrophysical superposition of all the sources
  since the beginning of the stellar activity
• Compact binairies, supernovae, BH ring down,
  supermassive BH

• characterized by the energy density parameter

300000 yrs photons decoupled (T 0.2 eV)
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Observational Constraints
Maggiore, 2000
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Cosmological Predictions
Maggiore, 2000
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Future Sensitivities
Figure courtesy of Don Backer
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Astrophysical Stochastic Background

• Superposition of all the sources since the
  beginning of the stellar activity
• periodic (compact binaries, pulsars)
• bursts (supernovae, oscillation modes, collapse,
  BH ringdown )
• Astrophysical backgrounds spectrum are determined
  by
• - The cosmological model (H0, Wm , Wn)
• The source rate
• The individual energy spectral density

Regimbau de Freitas Pacheco, 2001-2005
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Astrophysical Stochastic Background

• periodic sources
• Continuous stochastic background when the number
  of sources per resolution frequency interval is
  gtgt1.
• bursts
• the nature of the stochastic backgroud is
  determined by the ratio between the mean duration
  of a single event and the mean time interval
  between successive events
• tev gtgt Dt continuous
• tev Dt pop-corn
• tevltlt Dt shot noise

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Detection Regimes (ex, DNSs)
The duty cycle characterizes the nature of the
background. lttgt 1000 s, which corresponds to
96 of the energy released, in the frequency
range 10-1500 Hz

• D gt1 continuous (zgt0.23, 96)
• The time interval between successive events is
  short compared to the duration of a single event.
• D lt1 shot noise (zlt0.027)
• The time interval between successive events is
  long compared to the duration of a single event
• D 1 popcorn (0.027ltzlt0.23)
• The time interval between successive events is of
  the same order as the duration of a single event

Regimbau de Freitas Pacheco, 2005, ApJ, 642, 455
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Population Synthesis
Last thousands seconds before the last stable
orbit 96 of the energy released, in the range
10-1500 Hz

• redshift of formation of massive binaries
  (Coward et al. 2002)

• redshift of formation of NS/NS

x N106 (uncertainty on Wgw lt0.1)

• coalescence time

• redshift of coalescence

• observed fluence

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Probability Event Horizon
Coward et al., astro-ph/0510203
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Galactic Confusion Foreground
Between 0.2-3 mHz LISA is expected to be limited
by the galactic foreground, essentially the WD
binary contribution, rather than by the
instrumental noise.
Hils, Bender Webbink, 1990, ApJ, 360, 75,
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Galactic CWDBs (HBW 90)

• 3 107 sources
• intrinsic parameters
• - masses m1, m2
• - orbital period Porb(t)
• extrinsic parameters
• - Inclination angle i, polarisationy, initial
  phase j0
• - position (d, l, d)
• signal
• with

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Galactic CWDBs (HBW 90)

• masses
• - initial mass of the first progenitor m10 from
  Scalo IMF
• WD masses (m1 and m2) calculated from m10
• age from uniform distribution
• orbital period
• initial period from uniform distribution of log
  Po
• between log Po,minlog Pomax, calculated from
  m10
• final period Pc calculated from m10
• actual period
• position in the Galaxy (d, l, b), converted into
  ecliptic coordinate (d,a,d)

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Galactic CWDBs (HBW 90)
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Detection with Ground Based Interferometers

• Because the stochastic background cannot be
  distinguished from the instrumental noise
  background, the optimal detection strategy is to
  correlate the outputs of two (or more)
  detectors.
• hypothesis
• isotropic, gaussian, stationnary (cosmological
  origin)
• signal and noise, detector noises uncorrelated
• Cross correlation statistic
• combine the signal outputs using an optimal
  filter to optimize the signal to noise ratio
• the signal is given by the mean m ltYgt and the
  noise by the variance s lt(Y m)2gt
• Upper limit
• the 90 confidence level upper limit is given by

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Detection with LISA
The three Michelson interferometers share common
spacecrafts, therefore the instumental noise is
not removed by cross correlating the signal
outputs. The idea is to use the Sagnac
configuration, almost insensitive to the GW
signal, to estimate the instrumental noise
background and substract it to the standard
configuration.
Symmetrized Sagnac f-3 monitor noise
Michelson f-2 Seach signal
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LISA Mock Data Challenge

• Small group
• Nelemans (Nijmegen), Regimbau (OCA), Romano
  (Cardiff), Ungarelli (Italy),
• Whelan (AEI)
• But lot of work
• Simulation of the galactic foregrounds
• Simulation of the Cosmological background
• Detection methods
• ..

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• Thank you!