Cosmological Parameters from 6dF and 2MRS

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Cosmological Parameters from 6dF and 2MRS

Anaïs Rassat (University
College London)
6dF workshop, AAO/Sydney, 26-27 April 2005
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Cosmological Parameters

• From 2MRS Anaïs Rassat, Ofer Lahav
• From 6dFv Alexandra Abate, Sarah Bridle
• Cosmology Group,
• University College, London, UK.

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6dF and 2MRS

• 6dF survey of southern hemisphere
• Spectroscopic Redshift Survey (150K galaxies)
• 2MRS Whole Sky Survey (Huchra et al.)
• Southern Sky 6dFRS
• Northern Sky FLWO, Arizona, USA
• Low Latitutes CTIO, Chile
• Median redshift z0.02
• Flux limited survey, Kslt11.25
• Current data 25K galaxies (nearly complete)

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6dF Velocity Survey (6dFv)

• 6dF survey of southern hemisphere
• Velocity Survey (15K galaxies)
• Distances determined by diameter/velocity
  dispersion ? Peculiar Velocities

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The two structure formation parameters

• Wm matter density of the universe
• dark baryonic matter
• in units of the critical density
• s8 clumpiness of the universe
• rms fluctuation in 8 Mpc spheres
• present day

Velocities and clustering probe these parameters
as they trace the underlying mass
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Why do we need Wm and s8 ?
Bridle, Lahav, Ostriker Steinhardt (2003)
Science
Need more measurements to improve precision
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UCL Cosmology

• 2MRS Anais Rassat Ofer Lahav
• 6dF Alexandra Abate Sarah Bridle

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2MRS data
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2MRS data
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Redshift Space vs. Real Space
z

• ?obs/?emit-1

Vpec v.r is the component along the line of
sight of the peculiar velocity
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Redshift Space vs. Real Space

• Observed Redshift is not only due to Hubble flow
  it is also due to the Peculiar Velocity along
  the line of sight.
• Peculiar Velocities are due to large-scale
  streaming motions or local velocities within
  clusters
• These are not always negligible in the local
  universe unfortunately they are not always easy
  to measure especially at large scales.

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Spherical Harmonics

• The Spherical Harmonics

are defined for m0 by
where m -l, -l1, ..., 0, , l-1, l
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Spherical Harmonics
Any function can be expanded as a function of the
Ylms, as
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Spherical Harmonics
The coefficients of expansion for the density
field can be obtained by
Spherical Harmonics and Likelihood formalism
developed and applied to IRAS data by Fisher,
Scharf and Lahav (1994) (Similar method in
Heavens and Taylor (1995) ).
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Spherical Harmonics Theory
How is the harmonic decomposition in redshift
space related to that in real space? Assume the
density fluctuations
If the perturbations induced by peculiar motions
are small, then can expand redshift quantities to
first order
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Spherical Harmonics Theory
So that one can write
Sum of Real-Space and Redshift-Space
contributions to the harmonics.
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Spherical Harmonics Theory
Where
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Spherical Harmonics Theory
Predicted harmonics Theoretical Harmonics
Poisson Shot Noise component
Calculate the mean weighted harmonic power
spectrum
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Spherical Harmonics Real and Redshift Space
Dashed line is alm_s Solid line is alm_r
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Spherical Harmonics Real and Redshift Space
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Spherical Harmonics Data
Decompose the density field in redshift space,
using
Calculate the mean weighted harmonic power
spectrum
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Spherical Harmonics Data

• The method of Sphercial Harmonics can only be
  used on Whole-Sky data. In our analysis, we
  must mask the region of the Zone of Avoidance and
  fill it in order to obtain a whole-sky map.
• This masking can be done in several ways
• The ZoA is filled with a random distribution of
  galaxies, with the same density as the mean
  density for the rest of the sky
• The distribution of galaxies in the ZoA is
  interpolated from the neighbouring distribution

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Spherical Harmonics Data vs. Theory
Next steps Test different methods of including
the masked region Use Selection Function
obtained from 2MRS, Pirin Erdogdu et al. in
Preparation. Compare results using different
Power Spectra Simulate universes with different
cosmological parameters and apply the same method
to them. This will permit us to quantify how
accurate our measurements of ß, s8, Om are.
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s8 from 6dFv Alexandra Abate, Sarah Bridle
Galaxies simulated, and each assigned a velocity.
Via likelihood analysis a constraint on s8 was
obtained.
Error bar on s8 to be determined.
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s8 from 6dFv Alexandra Abate, Sarah Bridle

• Previous work on velocities
• Freudling et al 1999 calculated velocity
  correlations, similar to our present work
• 1300 velocities from SFI catalogue
• Found s81.69 0.25
• 6df expects to get 15000 velocities
• Back of the envelope calculation
• error we expect (1300/15000)½ Freudlings
  error
• s8 0.07

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How? Velocities correlation function ?12

• Basic definition
• where S1 and S2 are peculiar velocities
• Full version derived from
• Continuity equation
• Linear theory
• Giving velocities in terms of densities
• Power spectrum definition
• Only can measure radial velocity component

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Full correlation function

• Final form
• It can be split up into its parallel and
  perpendicular parts

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Physical meaning of ?- and ?-

• ?- tells you how correlated galaxy velocities are
  in the line of sight direction (shown in red)
• ?- tells you how correlated galaxy velocities are
  perpendicular to the line of sight direction
  (shown in blue)

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Current work

• Aim to constrain s8
• Use ?12 and Maximum Likelihood technique

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Maximum Likelihood technique

• Bayes Theorem
• P(dM) is the likelihood function, this is used
  to constrain s8

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Likelihood function

• Form used
• To constrain s8, plot likelihood function against
  range of s8 values
• Peak corresponds to s8
• Width of peak corresponds to error on s8

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Progress so far.

• Simulating galaxies
• Attaching a velocity to each via ?12, assuming
  concordance with a fixed s8.
• Calculating likelihood for each ?12 for a range
  of s8
• Plot likelihood to find 1 s constraint on s8
• To be repeated with actual data when released

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6dF and 2MRS Summary

• Constraining Cosmological Parameters
• 2MRS Spherical Harmonic Analysis
• 6dFv Velocity Correlations