reconstructing gravity with peculiar velocties
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Reconstructing Gravity with Peculiar VelocitiesRussell Johnston
University of the Western CapeSouth Africa
~collaborators~David Bacon (ICG, Portsmouth)Luis Teodoro (NASA, AMES)Bob Nichol (ICG, Portsmouth)Mike Warren (Los Alamos)Catherine Cress (CHPC, Cape Town)
~in association with~
gravity mapspeculiar velocities weak lensing
( + �)
ds
2 = �(1� 2 )dt2 + a
2(t)(1 + 2�)dx2
Newtonian potentials
�
temporal perturbations
spatial perturbations
THE CONCEPTWe are interested in extending velocity maps to higher redshifts,
concentrating on test.( � �)
vpec
= czobs
�H0d
inferred distance
measured from e.g. Tully-Fisher or Fundamental Plane
typical error on d ~ 20%
THE CONCEPT
Creating an observed velocity field
vpec
= czobs
�H0d
propagate errors on inferred distance into the peculiar
velocities.
�d = 0.3
low-z “high”-z
regularising the reconstruction
Pr(Vhyp|Vdata) / Pr(Vdata|Vhyp) Pr(Vhyp|�v,Pk)
Velocity field derived from a redshift galaxy survey
distribution.
The prior
gravitational potential
@ galz = i gal(k)kz
a new velocity field
�v
gal(k) =3⌦mH2
0�z(k)
2a(t)(k2 + �k2z)
Create a velocity field derived from the galaxy distribution:
The prior �v
The field@ z The fieldcompared to V truez
�v =
NpixX
i=1
(V̂ rec � @ z)2
��v
regularisation parameter
The prior Uses a theoretical velocity power spectrum to regularise V̂ rec
Pk
Pk =ktotX
i=1
[P̂v(k)rec � Pv(k)th]2
[�vP (k)]
2
regularisation parameter
Putting it altogether
Pr(Vhyp|Vdata) / Pr(Vdata|Vhyp) Pr(Vhyp|�v,Pk)
The reconstructed field can be V or
The data could be PV+WL and jointly reconstruct
� &
Pr( hyp|Vdata) / Pr(Vdata| hyp) Pr( hyp|� , P k )
�v =
NpixX
i=1
(V̂ rec � @ z)2
��v
final reconstruction.
Vtrue
@
Embed artificial mass in the field
@ Propagate through to field
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