Cosmological parameters from peculiar velocities

Alexandra Abate (LAL, Orsay)with Sarah Bridle (UCL), Pirin Erdogdu (UCL, AUK),

Martin Hendry (Glasgow), Ofer Lahav (UCL), Luis Teodoro (NASA Ames), Michael Warren (LANL)

2/25

Outline

Why care about peculiar velocities? Galaxy peculiar velocity constraints:

The SFI++ survey Analysis Method Results

SN1a peculiar velocity constraints: Importance of low z SN1a Perturbed luminosity distance Results

Conclusions & Future data sets 6dF Status

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Cosmological Velocity Field

The motion at a point in space due to the gravitational attraction of surrounding masses; distinct from the expansion

Usually measured using tracers e.g.: galaxies; SN1a; galaxy clusters

Radial motion of a galaxy (vp) is therefore: cz=H0d+vp

Better than the galaxy density field because: the velocities are directly related to the underlying gravitational potential field

Worse that the galaxy density field because: really hard to measure accurately!

Hubble expansion (H0d)

Additional motion relative to Hubble

expansion peculiar velocity

€

v = -i a(t)˙ a (t)k

k2∂(k)

dD

da

In linear theory the velocity field is directly

related to the density field, and the growth of structure: dD/da

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Why is this interesting?

Don’t need to worry (as much) about galaxy biasing Only way to measure redshift zero clustering

WMAP5 CDM: 8=0.80+/-0.03, CDM+: 8=0.67+/-0.08

Very sensitive to the derivative of the growth function Use growth of structure to detect departures from CDM

They are a “useful” systematic of BAO and SN1a measurements You will have to care!

Recent large-scale bulk flow measurements seem to disagree with CDM ….

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Recent large scale flow results

Watkins, Feldman & Hudson (2009) Use all galaxy PV catalogues Data suggest the bulk flow within a

Gaussian window of 50Mpc/h is 407+/-81km/s (not rms)

Probability of this flow in WMAP5 normalised CDM universe is of order 1%

Similar result in Lavaux et al. (2008) using 2MASS

Kashlinsky et al. (2008) Use kSZ effect measured from

CMB+X-ray data

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8

mh2

2

3

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Challenges

Large errors Galaxy peculiar velocities use FP or

Dn- scaling relations: 15-22% distance error

SN1a use peak brightness-width relation: 5-10% distance error

~(kSZ may have errors of just 100km/s)

Malmquist bias If error is >8% distance then non-

uniform sampling due to the inhomogeneous density distribution induces spurious flows if not corrected

Nonlinearities

Fundamental Plane:

log re

cz=H0d+vp

-measure z, d

-get vp

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Galaxy peculiar velocity constraintswork from:AA & Erdogdu P. 2009 (Applied to SFI++ data) AA, Bridle S., Teodoro L., Warren M., Hendry M. 2008 (Method)

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Spiral Field I Band: SFI++ Survey

5000 spiral galaxies (Masters et al. 2006) with rotation widths measured from: HI line widths (60%) H (40%)

Peculiar velocity sample (Springob et al. 2007, 2009) Corrected for Malmquist bias using

2MASS 4053 galaxies with median z=0.019 Distance errors ~22% of the

distance Sample covers most of the sky

above the Galactic plane

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Blue: cz<1000km/s

Cyan: 1000<cz<3000km/s

Green: 3000<cz<5000km/s

Yellow: 5000<cz<7000km/s

Red: 7000<cz<9000km/s

Magenta: cz>9000km/s

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Smoothing method

Need to smooth over radial velocity field: Average out nonlinear scales Apply some data compression

We choose to smooth with a grid Simple window function

Doesn’t preferentially pick out high density peaks (c.f. FOF)

Fast computation

For full details see AA et al. (2008) arXiv:0802.1935

€

vsm = v i

εsm =ε i

n

€

W 2(k) =8

L3

sin(ki L 2)

ki3

i= x,y,z

∏ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

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Velocity correlation function

From the linear relation between velocity and density field

Can show that:

where:

€

Ψ|| =H0Ωm

γ( )

2

2π 2

j0' (kr)

krP(k)W 2(k)dk∫

€

Ψ⊥ =H0Ωm

γ( )

2

2π 2j0

'' (kr)P(k)W2(k) dk∫

€

ξ ij = v i ⋅ ˆ r i( ) v j ⋅ ˆ r j( ) = sinθ i sinθ jΨ|| + cosθ i cosθ jΨ⊥

€

Ψ||

€

Ψ⊥

€

v(k) = -i a(t)˙ a (t)k

k2∂(k)

dD

da

€

cosθX = ˆ r X ⋅ ˆ r

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Likelihood analysis

Likelihood function

Smoothing method was rigorously tested in AA et al. (2008)

Double check smoothing method for SFI++: Vary 8 only Blue points: SFI++ data Green points: simulation of SFI+

+ data (8=0.9) Optimum L=25Mpc/h

€

L(Θ) =1

2π( )N

det ξ ij (Θ)[ ]exp -

1

2v iξ ij

−1(Θ)v j

i, j

N

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

average velocity in grid cell

velocity correlation function of grid cells

model parameters

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Parameter constraints

Marginalised constraints S S Consistent with CDM to 1-

Contours Solid contours: our constraints grey-scale contours: 100 deg2

weak lensing survey

Comparison to other PV estimates Gordon, Land & Slosar (2007)

using 124 SN1a Watkins, Feldman & Hudson

(2009) 2- limit

€

8 = 0.91−0.18+0.22

€

m = 0.13−0.04+0.10

€

8 = 0.79 ± 0.22

€

8 ≈1.7 ± 0.59

8

m

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Growth Index In linear theory, the velocity

field is directly related to the growth of structure

At low redshift

LCDM =0.55; DGP =0.69 Marginalised constraint

=0.55±0.14

Consistent with other constraints Rapetti et al. (2008) Nesseris & Perivolaropoulos

(2008)

€

=0.51−0.15+0.16

€

=0.67−0.17+0.20

m

€

ξ ij ∝ f 2(Ωm ) ≈ Ωm2γ

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SN1a peculiar velocity constraintswork from:AA & Lahav O. 2008

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Importance of low z (<0.1) SN1a

Provide well measured sample to calibrate Phillips relation

Anchor the Hubble diagram Independent of interesting

cosmological parameters, so break degeneracy between

M-log10(H0) and w, Ωm, etc

These supernovae are also sensitive to local flows

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m

w

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Perturbed luminosity distance

The velocity field has the effect of perturbing the luminosity distance:

where:

The covariance of ∂dL/dL:

where is the peculiar velocity correlation function:

€

∂dL

dL

=vr

c1−

(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟

€

∂dL

dL

=dL

obs(z) − d L (z)

d L (z)

€

d L (z)

Hui & Greene 2006

denotes the calculation of the luminosity distance at the observed redshift through the equation for dL in an homogeneous universe€

CLL =vrivrj

c 21−

(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟i

1−(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟j

€

vrivrj = ξ ij = cosθ i cosθ jΨ|| + sinθ i sinθ jΨ⊥

€

Ψ||,⊥(r) = D|(zi)D|(z j )

P(k)

2π 2B||,⊥(kr)dk∫

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Perturbed luminosity distance

The velocity field has the effect of perturbing the luminosity distance:

where:

The covariance of ∂dL/dL:

where is the peculiar velocity correlation function:

€

∂dL

dL

=vr

c1−

(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟

€

∂dL

dL

=dL

obs(z) − d L (z)

d L (z)

€

d L (z)

Hui & Greene 2006

denotes the calculation of the luminosity distance at the observed redshift through the equation for dL in an homogeneous universe€

CLL =vrivrj

c 21−

(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟i

1−(1+ z)2

H(z)d L (z)

⎛

⎝ ⎜

⎞

⎠ ⎟j

€

vrivrj = ξ ij = cosθ i cosθ jΨ|| + sinθ i sinθ jΨ⊥

€

Ψ||,⊥(r) = D|(zi)D|(z j )

P(k)

2π 2B||,⊥(kr)dk∫

geometry

Power spectrum

growth of structure

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Results

Jha, Riess and Kirshner 2007+ Davis et al. 2007 data set 271 SN1a with 0.0023<z<1.76

Calculate likelihood as a function of the 3 “faces” of Ωm

Are they all consistent? €

mdyn

€

mgeom

€

mgeom

€

mdyn

€

mps

€

mps

€

mA

€

mB

D(z) is often parameterised as f=Ωm(z)

For CDM: =~0.55For DGP gravity =~0.6For this data set =0.72+/-0.21 For a future survey with 1000 SN1a ∂~0.04 is possible

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Conclusions

Galaxy and SN1a peculiar velocities can provide a low redshift anchor for measuring the evolution of the growth of structure.

Their sensitivity to the derivative of the growth function mean they are a useful tool for detecting departures from LCDM.

Our constraints are consistent with many other constraints found in the literature, and with LCDM. However the constraints come from a mix of scales, and are dominated by the smaller scales. Any departure from LCDM on larger scales (> 100Mpc/h) will not be well tested by this data set.

Because peculiar velocities will be subject to different systematic effects to other probes such as cluster-counts, weak lensing or redshift distortions, they are an important complementary probe of cosmology.

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Future velocity field studies

6dFGS galaxy velocity data release Expect around 10,000 velocities out to z~0.055 Soon! See next slide ….

SN1a Larger future data sets from SNFactory, SkyMapper, GAIA

Kinematic Sunyaev-Zeldovich effect Compton scattering of CMB photons by hot electrons in galaxy cluster gas Can measure temperature shift of CMB photons -> line of sight momentum of the

cluster

Redshift distortions Flattening of large scale structures in redshift space is caused by

peculiar velocities A systematic error when measuring BAO (with spec-z) BUT can be modelled and contains cosmological information!

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Status: 6dF velocity sample

The following information was kindly given by Chris Springob (AAO): The survey is completed, all data reduction is done, and velocity dispersions

measured. Final redshift catalogue is published (Jones et al. 2009 MNRAS 399, 683). Photometric parameters have been derived from 2MASS images. Measurement errors and correlations have been derived on both photometric

parameters and velocity dispersions. Next step is to fit the fundamental plane via a maximum likelihood fit to a 3D

Gaussian, as was used for EFAR. Issues still to solve: how to weight the galaxies to account for the selection

effects, and what criteria to use to eliminate outliers. May have a best fit FP as early as next week. Then they will either move onto peculiar velocities, or first do a more

systematic study of how the FP depends on environment, stellar populations, etc.

Alex Merson at Durham is working on producing a 6dF group catalogue. Currently there is just a preliminary version, but the final version will be ready soon.

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A redshift histogram in the CMB frame of the SFI++ TF sample (blue) and the 6dFGS FP sample (red).

6dFGS will give us many more galaxies with cz > 10,000 km/s.

Currently about 10,000 galaxies but morphological classification check still to be done to remove late type galaxy contamination

Credit: C. Springob

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A preliminary fit to the sample

Red is galaxies in large groups; green in medium sized groups; and blue is singletons

There is no evidence for variation with

environment.

Credit: C. Springob