• Inverse Compton Effect for CMB photonsagainst electrons in the hot gas of clusters

• Cluster optical depth: τ=nσl where l = a few Mpc = 1025 cm, n < 10-3 cm-3 , σ = 6.65x10-25 cm2

• So τ=nσl = 0.01 : there is a 1% likelihoodthat a CMB photon crossing the cluster isscattered by an electron

• Eelectron >> Ephoton, so the electron transferspart of his energy to the photon. To first order, the energy gain of the photon is

• The resulting CMB temperature anisotropy is

cluster

01.0500

52 =≈=

ΔkeV

keVcm

kT

e

e

νν

41001.001.0 −=×≈Δ

≈Δ

νντ

TT Sunyaev R., Zeldovich Y.B., 1972,

Comm. Astrophys. Space Phys., 4, 173

Birkinshaw M., 1999, Physics Reports, 310, 97-195

CMB photonsSunyaevSunyaev--ZeldovichZeldovich EffectEffect

Bri

ghtn

ess All photons increase their

energy. The result is a distortion of the spectrum of

the CMB in the direction of rich clusters

A decrement at lowfrequencies( <217GHz )

An increment at high frequencies( > 217GHz )

frequency

SunyaevSunyaev--ZeldovichZeldovich EffectEffect

Atmospheric transmission, pwv=0.5mm

ISD Δ emission, 18K6 kJy/sr @ 150 GHz

Thermal SZ

Non-Thermal SZ

Kinematic SZ

Thermal SZ

• Photometric observations of the SZ can besignificantly biased, when there are

• less spectral channels than free parameters.• Components, LOS through a rich cluster:

ThSZ

KSZ

CMB

ISD

NThSZ pmin , Amp

Td , τd ….(β)

• Photometric observations of the SZ can besignificantly biased, when there are

• less spectral channels than free parameters.• Components, LOS through a rich cluster:

ThSZ

KSZ

CMB

ISD

NThSZ pmin , Amp

Td , τd ….(β)

At least, 8 independentparameters !

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

0001.0=ntτ

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

0=ntτ

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

Fitting also ΔTCMB : bias removed, butlarger errors

The solution: spectroscopicmeasurements of the SZ

• Requirements:

– Wide spectral coverage(in principle 100 to 1000 GHz)

– Modest spectral resolution (λ/Δλ = 100 to 1000)– Differential input, high rejection of common mode

signal (CMB is common mode and is 2750000 μK, cluster signal is differential and can be as low as 10 μK).

– Imaging instrument– Wide field of view to image the whole cluster and

have a clean reference area to compare

Comparison among Spectrometers solutions

OK: but constraint on mirrors planarity and movement

OKOKTechnology readiness

SmallSmallLarge: but relaxes detectors sensitivity and mirrors temperature

Background / noise

NONOYESDifferential measurement capability

FixedFixedVariableSpectral resolution

YESNO: linear array per pixel

YESImaging capability

NOYESYESSimultaneous measurements

NO: 3 F-P needed

NO: 4 D-G neededYESSpectral coverage

Fabry-Perot

GratingFTSITEM

DFTS

• The differential fourier transform spectrometer(DFTS) is the best option.

• We decided to produce a prototype to be used(warm) on the OLIMPO balloon-borne telescopeto proof the concept and get preliminary science.

• Scientific targets:– SZ– High redshift galaxies (C+)– Galactic survey (study of CO, also as a contaminant)– Spectral-Spatial anisotropies– ….

• Supponiamo quindi di avere due sorgenti S1 e S’1 , descritte dai vettori di Jones

• Il beam 3, dopo il polarizzatore d’ingresso (asse principale verticale), sarà

⎟⎟⎠

⎞⎜⎜⎝

⎛=

y

x

AA

S1 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

y

x

BB

S '1

⎟⎟⎠

⎞⎜⎜⎝

⎛=+=

y

xrt B

ASPSPS '

113 )0()0(

• Il beam 4 riflesso dal beamsplitter e il beam 4’trasmesso dal beamsplittersaranno:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−

==yx

yx

y

xr BA

BABA

SPS21

1111

21)4/( 34 π

⎟⎟⎠

⎞⎜⎜⎝

⎛++

=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛==

yx

yx

y

xt BA

BABA

SPS21

1111

21)4/( 3

'4 π

• Siccome gli specchi a tetto sono rappresentati da matrici identità, avremo anche

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

==yx

yx

BABA

SS21

46

⎟⎟⎠

⎞⎜⎜⎝

⎛

++

=⎟⎟⎠

⎞⎜⎜⎝

⎛++

== δ

δ

iyx

iyx

yx

yx

eBAeBA

BABA

DDSS)()(

21

21'

4'6

• Il primo è trasmesso dal beamsplitter, il secondo èriflesso, quindi

'66

'668 11

1121

1111

21)4/3()4/( SSSPSPS rt ⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

+⎟⎟⎠

⎞⎜⎜⎝

⎛=+= ππ

• Da cui

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−−−++

=)1()1(

)1()1(21

8 δδ

δδ

iy

ix

iy

ix

eBeAeBeA

S

⎟⎟⎠

⎞⎜⎜⎝

⎛ −++==

0)1()1(

21)0( 89

δδ iy

ix

teBeA

SPS

• Considerando ora il beamsplitterdi uscita, ricaviamo i beam che arrivano sui due rivelatori:

'66

'668 11

1121

1111

21)4/3()4/( SSSPSPS rt ⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

+⎟⎟⎠

⎞⎜⎜⎝

⎛=+= ππ

⎟⎟⎠

⎞⎜⎜⎝

⎛++−

==)1()1(

021)0( 8

'9 δδ i

yi

xr eBeA

SPS

• Possiamo ora calcolare l’intensità su ciascuno dei rivelatori in uscita:

δδδ cos22

)]cos1()cos1([21 2222

229

yxyxyx

BABABAI

−+

+=−++=

δδδ cos22

)]cos1()cos1([21 2222

22'9

yxyxyx

BABABAI

−−

+=++−=

→+= **yyxx EEEEI

• The OLIMPO experiment is a mm-wave balloon-borne telescope, optimized for high-frequency measurements of the Sunyaev-Zeldovich effect. The instrument uses four bolometer arrays, for simultaneous observations at 150, 210, 350, 480 GHz, coupled to a 2.6 m diameter Cassegrain telescope, achieving a resolution of 4,3,2,2 arcmin FWHM respectively.

• OLIMPO is a polar long-duration flight launched from Svalbard islands. The current observation plan includes deep integrations on a selected sample of 40 clusters, plus a wide blind survey of an empty sky area.

• We have recently upgraded the instrument adding spectroscopic capabilities within the 4 bands above, and discuss here the scientific potential of this innovative configuration.

• In fig. 1 we show the OLIMPO balloonpayload (Masi et al.2008), with solarpanels, ground shieldand sun shieldremoved.

• Note the tiltable 2.6m primary mirror and the lightweigth secondary.

• Pointing is obtainedrotating the payloadaround an azimuthpivot and changing the elevation of the innerframe, including the telescope, the FTS and the detector’s cryostat

• The total mass of the payload is 1.5 tons.

The Payload

Elevationmotor

Azimuth pivot

Cryostat withcold optics and detector arrays

Readoutelectronics

window

LHe 60 L

LN 60L

Reimagingoptics

dichroics

arrays

FTS

Low frequency arrays (TES)• Buffer: Si3N4• Thermistor: Ti (60nm) + Au(10/20 nm)• Absorber/heater: spiderweb Ti (10 nm) + Au (5 nm), fillingfactor 5%• NET150GHz=145 µK√s• NET220GHz=275 µK√s• Univ. Of Cardiff (Mauskopf)

Bol. νeff [GHz] ΔνFWHM [GHz] Res. [‘]19 148.4 21.5 4.219 215.4 20.6 2.923 347.7 33.1 1.823 482.9 54.2 1.8

High frequency arrays• NbxSi1-x (x=0.085)• SiN 3x3 mm2• Palladium absorber• NET340GHz=430 µK√s• NET450GHz=4300 µK√s• Inst. Neel Grenoble (Camus)

Filters Stacks (Ade, Tucker, Cardiff)

The spectroscopic instrument• SZ studies can benefit significantly from spectroscopic

measurements, which are required to break degeneraciesbetween the parameters describing cluster and foregroundemissions along the line of sight (see below).

• In 2008 we have studied for ASI a spectroscopic SZ space-mission (SAGACE, see de Bernardis et al. 2010).

• As a pathfinder, we are building a plug-in Differential FTS forOLIMPO.

• The DFTS configuration offers– an imaging spectrometer with very high throughput,– wide spectral coverage, – medium to high spectral resolution, – rejection of common-mode signals, like instrument emission and most

of the ground pickup.• The main problem is the high radiative background on the

bolometers, which is solved splitting the observed frequencyrange in several bands with independent detector arrays. In the case of OLIMPO, this was already implemented in the 4-bands photometer.

The instrument is based on a double Martin PupplettInterferometer configuration toavoid the loss of half of the signal.

A wedge mirror splits the skyimage in two halves IA and IB, used as input signals for bothinputs of the two FTS’s.

Olimpo Telescope

Olimpo Cryostat

⎟⎟⎠

⎞⎜⎜⎝

⎛ +=

0)2/sin()2/cos( δδ yxFTSII AiB

E

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=)2/sin()2/cos(

0δδ xy

FTSI

AiBE

outgoing fields :

Global design of the optical system

Differential field of view

Optical layout of the doublel Martin-Puplett FTS

Mechanical arrangement of the translation stages

The OLIMPO Martin-PuplettDifferential Fourier TransformSpectrometer

OLIMPOPrimaryMirror

DFTS

Cold optics

Simulated OLIMPO measurement of a cluster l.o.s. withτth=0.005, Te=10 keV, τnonth=0.0001, vpec=500 km/s, Idust=6kJy/sr@150GHzThe data with the error bars are simulatedobservations from a single pixel of the OLIMPO-FTS, for anintegration time of 3 hours. The two linesthrough the data pointsrepresent the input theory (thin) and the best fit for the plotteddata realization (thick). The other thin linesrepresent thermal plus non-thermal SZE, and dust emission.

this shift is due to the peculiar velocity of the cluster

The high-frequencyexcess is due to a modest amount of dust

dust

thermal+ non-thermal

Parameters Determination• In the presence of peculiar velocities, non-thermal populations

(from AGNs in the cluster), and foreground dust, there are simplytoo many free parameters to be determined with the observationof a few frequency bands, like in ground-based measurements.

• We have carried out detailed simulations of OLIMPO observations in the spectroscopic configuration with an extended200-300 GHz band.

• The spectroscopic configuration has superior performance in converging to the correct estimate of thermal optical depth and dust parameters, while the photometric configuration, in the absence of priors, tends to converge to biased estimates of the parameters. See de Bernardis et al. A&A 583, A86 (2012).

• No priorsτth =(63+27)10-4

T = (9.0+4.1) keVτnon-th=(14+9)10-5

ΔTCMB=(24+43)μKΔIdust150=(5.7+1.6)kJy/sr

Input parametersτth =50x10-4

T = 10 keVτnon-th=1x10-4

ΔTCMB=22μKΔIdust150=6 kJy/sr

OLIMPOFTS 3h integ.one detector

• Prior T=(10+3) keVτth =(49+6)10-4

T = (9.6+0.5)keVτnon-th=(11+9)10-5

ΔTCMB=(22+43)μKΔIdust150=(5.8+0.9)kJy/sr

Observation Program

• In a circumpolar summer long duration flight (>200h) we plan toobserve 40 selected clusters and to perform a blind deep integrationon a clean sky region

• We have optimized the observation plan distributing the integration time among the different targets according to theirbrightness and diurnal elevation.

Mission Profile

• We will use a long-durationcircumpolar flight launched fromSvalbard Islands (June 2014).

• We have tested these flights in collaboration with ASI, and demonstrared the feasibility of launching heavy payloads fromthe Longyearbyen airport, performing 2-3 weeks flightsaround the north pole during the Arctic summer.

SORA LAUNCH:July 1st 2009 (1.5 ton)

asm

cmD

μλθ 6103103

1 115 =×≅

×== −

ascGMr

rGMc μ222

2 ≅=→=

• Antenna diameter: 10 m• Range of wavelengths: 0.01 – 20 mm• Bolometric sensitivity(λ0.3mm, 1h integration): 5x10-9 Jy• Interferometry sensitivity(λ0.5mm, 300s integration, 16GHz bw) : 10-4 Jy• Interferometer beam: 10-9 arcsec

MillimetronLonger baseline (L2) Shorter wavelength 1

3 hours of observations of a rich cluster with a DFTS on MillimetronAbsolutely outstanding.

3h integration on the same LOS through a richcluster

t

UniversoPrimordiale

UniversoStrutturato

Gravita’

vs. Espansio

ne

510−≈Δρρ

510≈Δρρ

Radiazione Cosmica di Fondo a 3K• L’ universo si e’ raffreddato espandendosi. • C’e’ stata un’epoca nel passato in cui l’ universo era talmente

caldo da essere ionizzato. • Questa fase e’ detta di “Primeval Fireball” e dura per i primi

400000 anni dal Big Bang.• In questa fase lo spessore ottico per scattering Thomson era

estremamente alto, ed i fotoni percorrevano un “randomwalk” da elettrone ad elettrone.

• Quando l’ universo si e’ raffreddato abbastanza da permettere la ricombinazione degli elettroni e protoni in atomi di idrogeno, la sezione d’ urto e’ diminuita drasticamente, e l’ universo e’ diventato trasparente.

LSS• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perche’ l’ universo impiega tempo a diventare trasparente.

zLSS

ΔzLSS

H neutro (trasparente)

H ionizzato (opaco)

LSS (semitrasparente)

LSS• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perche’ l’ universo impiega tempo a diventare trasparente.

zLSS

ΔzLSS

H neutro

H ionizzato

LSS

Random walk

Ultimo scattering

Propagazione libera

LSS• Lo spessore della superficie di ultimo scattering si

puo’ calcolare vedendo quanto e’ profonda la transizione da spessore ottico basso a spessore ottico maggiore di 1.

• In formule

• Dove x(z) e’ la frazione di idrogeno ionizzata.• La soluzione richiede l’ integrazione dell’

equazione di Saha per la frazione ionizzata.• Il risultato e’ un grafico del tipo (vedi corso

astrofisica) :

)()1()(

1)1()())(()(

3

02

)(

0

zxznzn

zzHcdzzndznz

oe

z

oTe

z

Te

+=

Ω++== ∫∫ σστ

l

ll

2000 4000 6000 8000 100000.0

0.2

0.4

0.6

0.8

1.0

X

X

T(K))1()( zTzT o +=

0 1000

τ(z)

z0

1

0.5

zLSS

2

1.5

• Lo spessore ottico, che dipende dalla densità e dal numero di elettroni liberi ha un andamento del tipo :

0 1000

τ(z)

z0

1

0.5

zLSS

2

1.5

)()()( ze ezn

dzzdN τ−∝

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

• Ma se vogliamo sapere quanti fotoni provengono da un certo redshift, dobbiamo calcolare dN/dz :

0 1000z0

1

0.5

zLSS

2

1.5

)()()( ze ezn

dzzdN τ−∝

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

• Ma se vogliamo sapere quanti fotoni provengono da un certo redshift, dobbiamo calcolare dN/dz :

0 1000z0

1

0.5

zLSS

ΔzLSS

2

1.5

)()()( ze ezn

dzzdN τ−∝

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

0 1000z0

1

0.5

zLSS

ΔzLSS

2

1.5

)()()( ze ezn

dzzdN τ−∝

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

Oggi si conosce (WMAP)zLSS con grande precisione:zLSS=1089+1ΔzLSS=185+2 (FWHM)Bennet et al. 2003

• Le fluttuazioni di densita’ sulla superficie di ultimo scattering producono anisotropia CMB, in piu’ modi.

1) DIRETTAMENTE:• Una sovradensita’ fa perdere energia ai fotoni che provengono da

essa, perche’ devono risalire la buca di potenziale. Per effetto del redshift gravitazionale si ha

• La sovradensita’ causa anche una dilatazione del tempo, per cui noi osserviamo un’ epoca piu’ primordiale (e quindi piu’ calda) laddove ci sono sovradensita’. La dilatazione del tempo e’

• Ma, durante la fase radiativa,

• Quindi in totale

2cTT Φ

==δ

νδνδ

2ctt Φ

=δδ

23/2

32

32/1;

ctt

aa

TTaTta Φ

−=−=−=→∝∝δδδδ

231

cTT Φ

=δδ Effetto Sachs-Wolfe (1967)

• Le fluttuazioni di densita’ sulla superficie di ultimo scattering producono anisotropia CMB in piu’ modi.

2) INDIRETTAMENTE:• Una sovradensita’ attira la materia circostante, e genera quindi un campo di

velocita’ peculiare. I fotoni che subiscono la loro ultima diffusione in zone in movimento con velocita’ peculiare v subiscono un effetto Doppler, quindi

3) ADIABATICAMENTE:• Il mezzo primordiale e’ un plasma di fotoni e materia. • Si dicono perturbazioni adiabatiche quelle in cui le densita’ di radiazione e di

materia fluttuano insieme in modo da mantenere l’ entropia del mezzo costante.• l’ entropia del mezzo e’

• Il numero di particelle di materia e’• Il numero di fotoni e’

• Quindi perturbazioni adiabatiche implica

• La teoria inflazionaria prevede che le fluttuazioni siano di tipo adiabatico.

cTT v

==νδνδ

γγ nnS mm /=

mmn ρ∝4/33

γγγ ρ∝∝ Tn

→−=−==γ

γ

γ

γ

γ

γ

ρδρ

ρδρδδδ

430

m

m

m

m

m

m

nn

nn

SS

m

m

m

m

TT

TT

ρδρδδ

ρδρ

ρδρ

γ

γ

314

43

43

=→==→

Anisotropia CMB• Quindi in totale

• Sperimentalmente si vede che, a parte l’ anisotropia di dipolo, dovuta al moto della Terra (10-3), l’ anisotropia intrinseca ΔT/T e’ molto piccola (dell’ ordine di 10-4-10-5).

• Quindi l’ universo primordiale era estremamente omogeneo. Le strutture presenti oggi nell’ universo si sono formate grazie all’ azione della gravita’, che ha fatto crescere le piccole perturbazioni di densita’ presenti alla ricombinazione, attirando la materia circostante.

Fluttuazioni adiabatiche

Effetto SW Dffusione da elettroni in moto

ccTT

m

m v31

31

2 +ΔΦ

+Δ

=Δ

ρρ

CMB anisotropy observables

• The angular power spectrum cl of the anisotropy definesthe contribution tothe rms from the different multipoles:

( ) ( )

∑

∑

+=Δ

=

=Δ

ll

ll

lll

l cT

ac

YaT

m

m

mm

)12(41

,,

2

2

,

π

ϕθϕθ∑ +=Δl

lll cwTmeas

)12(412

π

2)1( σ+−= lll ew LP

• A real experiment will notbe sensitive to all the multipoles of the CMB.

• The window function wldefines the sensitivity of the instrument to differentmultipoles.

• The detected signal will be:

• For example, if the angularresolution is a gaussianbeam with s.d. σ, the corresponding window function is

• Qualitativamente ci aspettiamo il seguente spettro di potenza delle anisotropie CMB:

Am

piez

za d

elle

flut

tuaz

ioni

Log[Multipolo] (inverso della scala angolare)

Sachs-Wolfe

Oscillazioni acustiche

Dampingtail

)gradi(200

θθπ

≈≈l

2

13

lll c)1( +

200=l

0 200 400 600 800 1000 1200 14000

1000

2000

3000

4000

5000

6000

l(l+1

)cl/2

π (μ

K2 )

multipole l

( ) ( )

∑

∑

+=Δ

=

=Δ

ll

ll

lll

l cT

ac

YaT

m

m

mm

)12(41

,,

2

2

,

π

ϕθϕθ

An instrumentwith finite angularresolution is not sensitive to the smallest scales(highest multipoles). For a gaussian beam with s.d. σ:

Expected power spectrum:

0 200 400 600 800 1000 1200 14000.0

0.2

0.4

0.6

0.8

1.0 20' FWHM 10' FWHM 5' FWHM

7o FWHM

wl

multipole

2)1( σ+−= lll ew LP

cl

)( ij ps

GHzj

857,545,353,217,143,100,70,44,30=

jik

jikij nBaps ,,)( +=∑

COhighflowfka ik ,,, =

PLANCK 2013

PLANCK 2013

PLANCK 2013

7 peaksultra-small errorsBeautiful consistencewith theory

esercizio

• costruire mappe dei diversi multipoli• Usare le routines di healpix:• Vedi

http://healpix.jpl.nasa.gov/

PLANCK 2013