ISW

Tópicos

PUC 2008

Fondo de Radiación Cósmica

Fin de la época dominada por radiación

– Ocurre cuando r deja de dominar,

• zeq≈3000,

• Teq ≈8190 oK=0.7 eV

• teq ≈6.1x104 años

– Universo Euclideano dominado por materia NR

Época de Plasma

– Inicio : 6.1x104 años (equilibrio rad-mat)– Fin : 2.1x105 años (combianción H)– Hay fotones, protones, neutrinos

desacoplados y elementos livianos– Dominio materia NR y partículas cargadas,

iones Plasma• T0.3 eV• zH1300• t2.1x105 años

Época Atómica

– Inicio : 2.1x105 años (combinación de H)– Fin : 2.7x105 años (desacoplo de fotones)– Hay fotones, átomos neutros, neutrinos

desacoplados y pocos e- y protonesFotones se desacoplan Fotones se desacoplan Fondo de radiación Cósmica Fondo de radiación Cósmica

Interacción dominante: eInteracción dominante: e- - + + + e + e--

– Tdes0.27 eV = 3100 oK– zdes1150– tdes2.7x105 años

Fotones no volverán a interactuar con la materia

Superficie de Último Esparcimiento

Radiación que se observa viene de esta superficie; sin embargo, esta superficie tiene un espesor

Zue 1089z 195

zProfundidad ópticaFunción de visibildad = Probabilidad que un fotón sufra un escátering

CMB Distortions

• Global Black Body Radiation

• Directional Anisotropies

€

T

T=

Δρ b

3ρ b

−Δφ

3−

r n ⋅

r v

z9z198

z=0z

Global DistortionsC

om

pto

niz

atio

n

Directional - Primary

€

T

T∝−

Δφ

3≈10−5

( )

Δθ > Δθ H

€

T

T∝

Δρ b

3ρ b

≈ 3 ×10−5( )

Δθue < Δθ < Δθ H

€

T

T∝−

r n ⋅

r v ≈10−3,10−5

( )

Δθue < Δθ < Δθ H

€

l =π

Δθ

Directional - Secondary

Sunyaev-Zel’dovich (SZ) clusters

e-

e-

e-

e-

e-

e-

e-

e-

e-

Coma Cluster Telectron = 108 K

Optical: Redshift and Mass

mm-Wave: SZ –Compton Scattering

X-ray Flux: Mass

ZS Effect

Directional - Tertiary

Extragalactic Radio Sources•Radio Galaxies•QSOs

Galactic Radio Sources•Dust and Gas in MW

Must map these sources and subtract them from the CMB signal

Sachs-Wolfe Effect

CMB Photons travelling to an observer encounter metric perturbations which induce a frequency change.

Metric perturbations are associated to gravitational potentials, , which are associated to density fluctuations,

f

iLast scattering surface

Density fluctuation,

f

i

f

=f-i

€

⇒T

T=

1

3

Δφ

c 2

Integrated SW

€

T

T=

1

3

Δφ

c 2+ 2

dφ

dτdτ

ls

0

∫

i zf

=f- i

Flat universe, in linear regime =cte.

€

Let's consider, ΔT

T≈ Δφ

φ = −GM

R⇒ Δφ ≈

GΔM

R

δ ≡ρ − ρ

ρ =

Δρ

ρ =

ΔM

M and ρ =

M4

3πR3

⇒ Δφ ≈GδM

R

In an Einstein - deSitter universe, in linear theory regime

δ = aδ0 or δ

R=

δ0

R0

⇒ Δφ ≈ GMδ

R

⎛

⎝ ⎜

⎞

⎠ ⎟= GM

δ0

R0

⎛

⎝ ⎜

⎞

⎠ ⎟≡ cte.

=cte NO ISW

≠cteAt z1.2 the universe becomes dark energy dominated and the expansion is accelerated.≠cte anymorePhotons get redshifted with respect to the original CMB photonsGenerates a large scale anisotropy in the CMB

ISW

ISW

Early: Transition from to m is not instantaneous. During teq to trec the scale factor does not change linearly varies

Late: starts at the transition from m to DE

The ISW

i f

€

Induced anisotropy,

ΔTr n ( ) = −2 dz

dφr n ,z( )

dz∫

z=1089 z=0

Order of Magnitude and Scale

€

T

T≈

Δφ

c 2

Δφ =GM

c 2

δ

R

⎛

⎝ ⎜

⎞

⎠ ⎟

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪

ΔT

T= Gρ m

4

3π

R

c

⎛

⎝ ⎜

⎞

⎠ ⎟2

δ

In terms of Ωm =ρ m

ρ c

ΔT

T=

Ωm

2

H0R

c

⎛

⎝ ⎜

⎞

⎠ ⎟2

δ ∝Ωm

2

R

3000Mpc

⎛

⎝ ⎜

⎞

⎠ ⎟

2

δ

If R = 8Mpc and δ ≈1

⇒ΔT

T≈10−5σ 8 and scales Δθ > Δθ H

How to detect the ISW

• Given the CMB temperature resolution achieved with modern microwave explorers such as WMAP (existing) and PLANCK (future), it is possible to cross correlate the local (z<1.2) matter structure with the observed CMB structure.

• The cross correlation amplitude depends on the acceleration modulus which in turn depends on the dark energy (DE) density.

Cross-Correlation CMB-LSS

€

Define,

δgˆ n ( ) ≡

Ng − N gN g

; for galaxies

ΔT ˆ n ( ) ≡T − T0

T0

; for CMB temperatue

The expectation value of density fluctuations is the cross-correlation function

€

ωTg θ( ) = ΔT ˆ n 1( ) δGˆ n 2( ) , where θ = ˆ n 2 − ˆ n 1

From a pixel map

€

ωTg θ( ) =

ΔT ˆ n i( )δgˆ n j( )W i W j

i, j

∑

W i W j

i, j

∑

where W is the window function and the sum

extends to all pairs i, j separated by θ and θ +Δθ

Cross Correlation CMB-LSS

The ISW dominates the X-Corr. signal at angular scales 1 deg.

(at smaller scale the signal is dominated by the SZ effect)

Given fields A and B Legendre polynomial order l

The window function of the anisotropy field, Generated by the ISW effect

The window function of the galaxy field

The error on each multipole

The Survey

Therefore, to unambiguously measure the signal, we propose a large, deep survey of galaxies.

• Detect the ISW signal with S/N > 3• Telescope: VST (2.6mt) at Paranal• Area: 5000 deg2 • Band: r band, r 23.8• # of nights: 64 nights, 16 per year

– 4 years, start 2009B ¿? 2013A

• Exposure time = 240 sec.

Area LayoutLAYOUT

Now we show that a survey with the following characteristics, – 5000 deg2 ,

– in one band, down to r = 23.8,

– on 0.5 degrees scales and

– no redshift information

provides the large scale data (i.e. galaxy map) to clearly measure the ISW signal.

Optimum average zS/N vs <z>

CDM: m=0.3, =0.7, k=0, H0=70, w=-1

The ISW effect is driven by the accelerated expansionExtremely distant galaxies are not affected by the accelerated expansion, so will not produce anisotropies in the CMB.

Limiting Magnitude

mlim=23.8

Redshift Distribution, N(z)

dn

dzz( ) ∝ φ(M )dM

dVdzMhigh

Mlow

∫M high =−25

M low =mlim −25 −5 log(r(z))mlim =23.

S/N()

Predicted S/N()

Why 1 deg scale?Maximize S/NMinimize primary & secondary CMB anisotropies

SZ important at scales smaller

Optimize OmegaCam scale size.

Why redshifts are not necessary

Cumulative S/N(z) in redshits slices of z=0.1. Slightly higher than the S/N with no slices

Why multi-band is not necessary

We only need to detect galaxies Need one deep band

To get photometric redshifts we need at least 4 bandsReduce the area by 4.S/N reduces by more than 2

The VST

• A 2.6 m telescope • Wide Field Imaging• 16k x 16k CCD mosaic

camera (Omegacam) with a 15 micron pixel, equivalent to 1 square deg. (0.21 arcsec/pixel scale)

• 32 thinned CCD 2x4k (26x26 cm2)

ISW@VST + ATLASWe have designed a plan to produce results earlier than any competing survey. The survey area will be the same as the approved ESO public survey VST ATLAS. Arrangements have been carried out so that we provide the deep r band observations and the VST ATLAS provide a deep 120 seconds g band survey. Having deep g and r bands in hand, a number of other programs are possible. In addition, negotiations are in progress to add IR J and H bands with VISTA. The finished product, in 2013, will be a deep (2 magnitudes deeper tha SDSS)

Value Added Projects

1. Weak Lensing in the ACT Strip

2. The Number Density of LSB and VLSBs

3. Local Census of Dwarf Galaxies

4. Dwarf Galaxies in the Local Group

5. … (welcome ideas)

Summary

• We propose a southern 5000 deg2 deep survey of galaxies in the r band to detect the Integrated Sachs-Wolfe Effect with a signal to noise ratio 40% higher than any other survey so far (e.g. SDSS DR4)

• The aim is to determine the equation of state of the universe by cross-correlating this galaxy map with high resolution CMB anisotropy maps from existing WMAP and future Planck observations.

• To cover the desired field, 64 nights in 4 years (rAB . 23.8, 16 dark-grey 1.0 arcsec seeing nights per year) are required with VST

• To maximize the output and open this survey to further science goals (ACT clusters, SZ effect, Red sequence galaxy clusters, LSBs, UCDs, Dwarf Galaxies, lenses) we will observe the same area as the approved VST ATLAS survey, which will provide de deep g band observations.