Cosmology & Source Counts - unimi.itcosmo.fisica.unimi.it/assets/RadioAstro/2018-2019/Radio... · 2019-05-27 · dVdM dM where is the survey area, dV=dzd is the cosmological volume

Cosmology & Source Counts

D.Maino

Physics Dept., University of Milano

Radio Astronomy II

D.Maino — Cosmology & Source Counts 1/35

Setting the stage

Background radiation provides unique information not only ondiffuse emission but also on sources beyond detectionlimit

Dispate incredible angular resolution → approaching anastrophysical limitation of the angular resolution close to thephysical size of sources

Only information of the energy output of astrophysicalprocessess powering such sources (especially those fainter)comes from their background intensity and fluctuations


Source Counts

We can compute two quantities

Integral Counts N(S): number of sources per unit area(sqdeg or sr) with flux > SDifferential Counts dN/dS : number of sources per unit area(sqdeg or sr) with flux between S and S + dS


Source Counts

Differential counts are given:

dN

dS=

∫ zh

zl

dzdV

dz

dL(S ; z)

dSΨ[L(S , z), z ]

where Ψ[L(S , z); z ] is the epoch-dependent luminosityfunction and dV /dz is the volume element per unit solid angle

dV

dz=

c

H0

d2L

(1 + z)6(1 + Ωz)1/2

and dL is the luminosity distance

dL =2c

H0Ω2

Ωz + (Ω− 2)

[−1 + (1 + Ωz)1/2

]


Source Counts

The flux S is related to the rest-frame luminosity L in thesame frequency interval ∆ν

S∆ν =L∆νK (L, z)

4πd2L

where K (L, z) is the K-correction

K-correction is related to

K (L, z) = (1 + z)L[ν(1 + z)]

L(ν)


Source Counts

If S is monotonically decreasing with z the integration isbetween:

zh = min[zmax , z(S , Lmax)]

andzl = z(S , Lmin)

where zmax is the maximum redshift at which a source beginsto shine and z(S , L) is the redshift of a source with luminosityL having a source S

Strong L evolution may overhelm the effect of increasingdistance and also for non-evolving sources if emission is risingwith frequency → large K-correction


Source Counts and Cosmology

Both integral and differential source counts depends onadopted cosmology through dV /dz and dL

Assuming a flat-space (euclidian)

N(S) ∝ S−3/2 dN/dS ∝ S−5/2

If evolution dominates counts it is not possible to measuregeometry


Measured Source Counts

One of the largest and complete is the NRAO VLA sky surveyat 1.4GHz covering the north emisphere being flux limitedS >∼ 2.3mJy with a total of 2× 106 sources



Only a small fraction (∼1%) of sources in flux limited surveyare local (i.e. within 100Mpc)

Identification of such sources with optical Hubble types andextracting their distances would give the local luminosityfunction i.e. the density of galaxies as a function of their L



Evolution: counts not consistent with no-evolutionPeak around S ≈ 500mJy → source evolve on cosmologicaltime i.e. their comoving space density vary and was larger inthe pastThis was used as an argument against steady statecosmology



Most of the sources are not “local” sources

Distance sources will be Doppler dimmed and counts shoulddecline monotonically → star-forming galaxies start dominatethe counts (FIR-Radio correlation)

“Cosmological” evolution since 〈z〉 = 0.8


What about un-resolved sources?

There are sources that cannot be detected either for angularresolution issue and/or due to their faint flux

However the population of such sources contribute to abackground of un-resolved sources

We can find this as a CIB: Cosmic Infrared Backgroundand has been detected by Planck


Un-resolved source background

This is of course better “resolved” in the IR but also visible inthe sub-mm and µm

Expected to trace the Large Scale Structure

Clustering properties of dusty galaxies

Correlation between dusty galaxies and DM


Cosmic Sources Background

We can evaluate the contribution of undetected sources by

I =

∫ Sd

0

dN

dSS dS =

=1

4π

c

H0

∫ Lmax

Lmin

L d logL

∫ zmax

z(Sd ,L)dz n(L, z)

K (L, z)

(1 + z)6(1 + Ωz)1/2

Contribution to shot-noise (background is not continuos butcomposed of several individual sources) that is

∝∫ Scut

0S2 dS

dNdS


Cosmic Sources Background

Shot-noise increases toward sub-mm and µwave

Difficult to measure → requires cleaning procedues (CMBdominates the sky)


Sunyaev-Zeldovich effect

Where? Visible in cluster of galaxies (Abell 1689)

A cluster of galaxies is a cluster of galaxies

Galaxies:Ngal ' 10− 1000, Mgal ' 0.02Mcl

Gas: H,He, Tgas ∼ 107−8K = 1− 10keV, Mgas ' 0.1Mcl

DM: Rcl ' 1Mpc and Mcl ' 1014−15M

Lot of hot gas (visible in X-ray): what if a “cold” photoninteracts with and hot e−?


Sunyaev-Zeldovich effect: Compton Scattering

A γ with wavelenght λ and energy hν deflected off an e− atrest with angle θ shows wavelenght gains and loss of energy

λs − λ = λC (1− cosθ) =h

mec(1− cosθ)

and

hνS =hν

1 + λC (ν/c)(1− cosθ)


Sunyaev-Zeldovich effect: Inverse Compton

A γ with wavelenght λ and energy hν deflected off an hot e−

shows wavelenght reduction and gain of energy

Computation done by moving from the observed (S) referenceframe to the electron at rest (S’) frame, computing normalCompton scattering and then back into S

In the transformation process there are two additional factors√(1 + β)/(1− β) and final energy gain is

hνS =

(1 + β

1− β

)hν

1 + 2λC (ν/c)√

(1 + β)/(1− β)

where we assumed head-on collision (i.e. maximum energytransfer)


IC of CMB photons and ICM

Consider low-energy photons, those of CMB at T = 2.725K∼ 10−4eV passing through the isothermal sphere of the ICMwith T ∼ 10keV and Maxwell velocity distribution

SZ is the distortion of the CMB spectrum due to IC

Fractional ν change for a 5keV plasma for a single collisionaverage on all possible θ and Maxwellian v

〈∆νν〉 ≈ 4kTe

mec2≈ 0.04

Scattering probability is the optical depth τ

τ ≈ 2Rcl〈ne〉σT ≈ 2Mpc·(200×10−3cm−3)6.65×10−29m2 ≈ 0.01

Total fractional energy gain

τ × 〈∆νν〉 ≈ 4× 10−4


Spectral Signature of SZ

Decrements in RJ: ∆I (ν) = −2yI (ν)Compton y parameter:

y ≡ σTkBmec2

∫Tene dl

Integrated effect

Y =

∫y dA ∝ neT dV ∝ Ethermal


Compton y parameter

It is the product of the optical depth (neσTdl) and thefractional energy change per single scatter

y ≡ σTkBmec2

∫Tene dl

Typical values ' 10−4

Note that y depends linearly on ne while X-ray brightnessscales as n2

e → SZ can be observed at larger radius than X-ray

Considering the pressure of an ideal gas p = nkBT → y isproportional to the integrated pressure along theline-of-sight


Radial dependence of SZE

Consider a 3D gas β-model for the cluster

ρgas(r) ∝ 1[1 +

(rrc

)2]3β/2

The projects SZE temperature change

∆TSZ (θ) =∆T0(

1 + θ2

θ2c

)3/2β−1/2

where θc is some suitable measure of the cluster radius


The integrated Y parameter

The integrated Y parameter is the integral of y on the solidangle covered by the cluster

YSZE =

∫Ωy dΩ =

2π∆T

T0f (ν,Te)

∫ R500/DA

0θ

(1 +

θ2

θc

2)(1−3β)/2

dθ

where integration goes out to the projected cluster radiusθ500 = R500/DA(z)

Y is proportional to the total thermal energy of the plasmawhich is expected to be related to the cluster mass M →M ∝ Y 3/5

Y is extremely difficul measure


The integrated Y parameter


SZ redshift dependence

SZ is practically independent of z

It is a “shadow” emission of the CMB and it does not sufferthe usual (1 + z)−4 expected by usual sources

This is indeed almost exactely compensated by the increase ofthe CMB temperature with z and by the scaling T ∝ (1 + z)

For Y there is a mild dependence on z in the apparentangular size of the cluster which is ∼ constant up to z ' 0.8


Planck view of SZ

1227 clusters and candidates: 683 known, 178 new confirmedand 366 candidates

Large sky fraction (different from usual X-ray observation) andne dependence of SZ (linear instead of quadratic for X-ray)

z ∈ [0, 1] and M ∈ [1, 20]× 1014M


SZ and Cosmology


SZ and Cosmology

From SZ get information on number of observed clusters of agiven M at a given redshift z

Tricky since possible selection biases

In principle

dN

dz= ∆Ω

dV

dzdΩ

∫ ∞Mlim

dN

dVdMdM

where ∆Ω is the survey area, dV /dzdΩ is the cosmologicalvolume

Mlim is the most problematic: how relate mass with actualminimum detected SZ signal

dN/dvdM is the mass function related to cosmology


SZ and cosmology

Mass can be derived from Y thanks to the expected relation

[E (z)]−2/3 DA(z)Y500

10−4Mpc2= Y?

[h

0.7

]−2+α [(1− b)M500

6× 106M

]αwhere logY? = −0.19, α = 1.79 from a subset of Planckclusters


SZ and cosmology

Not that simple! Real astrophysics hidden into the (1− b)term: parametrizes how well X-ray mass estimation are closeto the true mass

Usually it is assumed (1− b) = 0.8 i.e. small bias. But alsob ∈ [0.7, 1.0] is acceptable

Two mass-related parameters can be constrained with SZ(and X-ray) measurements of clusters: Ωm and σ8

In a global fit: use of external data sets and priors e.g. BBN,BAO and HST


SZ and cosmology


SZ, cosmology and CMB

Other estimate of both Ωm and σ8 can be obtained fromprimary CMB anisotropies. But ...



Is this a problem of Planck SZ clusters?



Planck SZ clusters are in agreement with other SZ estimatesof cosmo parameters

Tension with σ8 from primary CMB

Mass calibration i.e. MX is different from true mass → bMassive neutrinos could influence clustering history and clustermassBaryons in the mass function dN/dVdM → small effectSZ selection function → completness of the sample



Planck SZ clusters are in agreement with other SZ estimatesof cosmo parameters

Tension with σ8 from primary CMB

Mass calibration i.e. MX is different from true mass → bMassive neutrinos could influence clustering history and clustermassBaryons in the mass function dN/dVdM → small effectSZ selection function → completness of the sample


Documents

Cosmology & Source Counts - unimi.itcosmo.fisica.unimi.it/assets/RadioAstro/2018-2019/Radio... · 2019-05-27 · dVdM dM where is the survey area, dV=dzd is the cosmological volume